diff --git a/Cargo.toml b/Cargo.toml
index e1be4e2..7a2c53f 100644
--- a/Cargo.toml
+++ b/Cargo.toml
@@ -37,7 +37,7 @@ thiserror = "1.0"
 pasta-msm = { version = "0.1.4" }
 
 [dev-dependencies]
-criterion = "0.3.1"
+criterion = { version = "0.4", features = ["html_reports"] }
 rand = "0.8.4"
 hex = "0.4.3"
 
diff --git a/benches/compressed-snark.rs b/benches/compressed-snark.rs
index 595bb34..4a06b6d 100644
--- a/benches/compressed-snark.rs
+++ b/benches/compressed-snark.rs
@@ -43,46 +43,46 @@ fn bench_compressed_snark(c: &mut Criterion) {
     let mut group = c.benchmark_group(format!("CompressedSNARK-StepCircuitSize-{num_cons}"));
     group.sample_size(num_samples);
 
+    let c_primary = NonTrivialTestCircuit::new(num_cons);
+    let c_secondary = TrivialTestCircuit::default();
+
     // Produce public parameters
-    let pp = PublicParams::<G1, G2, C1, C2>::setup(
-      NonTrivialTestCircuit::new(num_cons),
-      TrivialTestCircuit::default(),
-    );
+    let pp = PublicParams::<G1, G2, C1, C2>::setup(c_primary.clone(), c_secondary.clone());
 
     // Produce prover and verifier keys for CompressedSNARK
     let (pk, vk) = CompressedSNARK::<_, _, _, _, S1, S2>::setup(&pp).unwrap();
 
     // produce a recursive SNARK
     let num_steps = 3;
-    let mut recursive_snark: Option<RecursiveSNARK<G1, G2, C1, C2>> = None;
+    let mut recursive_snark: RecursiveSNARK<G1, G2, C1, C2> = RecursiveSNARK::new(
+      &pp,
+      &c_primary,
+      &c_secondary,
+      vec![<G1 as Group>::Scalar::from(2u64)],
+      vec![<G2 as Group>::Scalar::from(2u64)],
+    );
 
     for i in 0..num_steps {
-      let res = RecursiveSNARK::prove_step(
+      let res = recursive_snark.prove_step(
         &pp,
-        recursive_snark,
-        NonTrivialTestCircuit::new(num_cons),
-        TrivialTestCircuit::default(),
+        &c_primary,
+        &c_secondary,
         vec![<G1 as Group>::Scalar::from(2u64)],
         vec![<G2 as Group>::Scalar::from(2u64)],
       );
       assert!(res.is_ok());
-      let recursive_snark_unwrapped = res.unwrap();
 
       // verify the recursive snark at each step of recursion
-      let res = recursive_snark_unwrapped.verify(
+      let res = recursive_snark.verify(
         &pp,
         i + 1,
-        vec![<G1 as Group>::Scalar::from(2u64)],
-        vec![<G2 as Group>::Scalar::from(2u64)],
+        &vec![<G1 as Group>::Scalar::from(2u64)][..],
+        &vec![<G2 as Group>::Scalar::from(2u64)][..],
       );
       assert!(res.is_ok());
-
-      // set the running variable for the next iteration
-      recursive_snark = Some(recursive_snark_unwrapped);
     }
 
     // Bench time to produce a compressed SNARK
-    let recursive_snark = recursive_snark.unwrap();
     group.bench_function("Prove", |b| {
       b.iter(|| {
         assert!(CompressedSNARK::<_, _, _, _, S1, S2>::prove(
diff --git a/benches/recursive-snark.rs b/benches/recursive-snark.rs
index 3cf520a..aec865d 100644
--- a/benches/recursive-snark.rs
+++ b/benches/recursive-snark.rs
@@ -38,61 +38,60 @@ fn bench_recursive_snark(c: &mut Criterion) {
     let mut group = c.benchmark_group(format!("RecursiveSNARK-StepCircuitSize-{num_cons}"));
     group.sample_size(10);
 
+    let c_primary = NonTrivialTestCircuit::new(num_cons);
+    let c_secondary = TrivialTestCircuit::default();
+
     // Produce public parameters
-    let pp = PublicParams::<G1, G2, C1, C2>::setup(
-      NonTrivialTestCircuit::new(num_cons),
-      TrivialTestCircuit::default(),
-    );
+    let pp = PublicParams::<G1, G2, C1, C2>::setup(c_primary.clone(), c_secondary.clone());
 
     // Bench time to produce a recursive SNARK;
     // we execute a certain number of warm-up steps since executing
     // the first step is cheaper than other steps owing to the presence of
     // a lot of zeros in the satisfying assignment
     let num_warmup_steps = 10;
-    let mut recursive_snark: Option<RecursiveSNARK<G1, G2, C1, C2>> = None;
+    let mut recursive_snark: RecursiveSNARK<G1, G2, C1, C2> = RecursiveSNARK::new(
+      &pp,
+      &c_primary,
+      &c_secondary,
+      vec![<G1 as Group>::Scalar::from(2u64)],
+      vec![<G2 as Group>::Scalar::from(2u64)],
+    );
 
     for i in 0..num_warmup_steps {
-      let res = RecursiveSNARK::prove_step(
+      let res = recursive_snark.prove_step(
         &pp,
-        recursive_snark,
-        NonTrivialTestCircuit::new(num_cons),
-        TrivialTestCircuit::default(),
+        &c_primary,
+        &c_secondary,
         vec![<G1 as Group>::Scalar::from(2u64)],
         vec![<G2 as Group>::Scalar::from(2u64)],
       );
       assert!(res.is_ok());
-      let recursive_snark_unwrapped = res.unwrap();
 
       // verify the recursive snark at each step of recursion
-      let res = recursive_snark_unwrapped.verify(
+      let res = recursive_snark.verify(
         &pp,
         i + 1,
-        vec![<G1 as Group>::Scalar::from(2u64)],
-        vec![<G2 as Group>::Scalar::from(2u64)],
+        &[<G1 as Group>::Scalar::from(2u64)],
+        &[<G2 as Group>::Scalar::from(2u64)],
       );
       assert!(res.is_ok());
-
-      // set the running variable for the next iteration
-      recursive_snark = Some(recursive_snark_unwrapped);
     }
 
     group.bench_function("Prove", |b| {
       b.iter(|| {
         // produce a recursive SNARK for a step of the recursion
-        assert!(RecursiveSNARK::prove_step(
-          black_box(&pp),
-          black_box(recursive_snark.clone()),
-          black_box(NonTrivialTestCircuit::new(num_cons)),
-          black_box(TrivialTestCircuit::default()),
-          black_box(vec![<G1 as Group>::Scalar::from(2u64)]),
-          black_box(vec![<G2 as Group>::Scalar::from(2u64)]),
-        )
-        .is_ok());
+        assert!(black_box(&mut recursive_snark.clone())
+          .prove_step(
+            black_box(&pp),
+            black_box(&c_primary),
+            black_box(&c_secondary),
+            black_box(vec![<G1 as Group>::Scalar::from(2u64)]),
+            black_box(vec![<G2 as Group>::Scalar::from(2u64)]),
+          )
+          .is_ok());
       })
     });
 
-    let recursive_snark = recursive_snark.unwrap();
-
     // Benchmark the verification time
     group.bench_function("Verify", |b| {
       b.iter(|| {
@@ -100,8 +99,8 @@ fn bench_recursive_snark(c: &mut Criterion) {
           .verify(
             black_box(&pp),
             black_box(num_warmup_steps),
-            black_box(vec![<G1 as Group>::Scalar::from(2u64)]),
-            black_box(vec![<G2 as Group>::Scalar::from(2u64)]),
+            black_box(&vec![<G1 as Group>::Scalar::from(2u64)][..]),
+            black_box(&vec![<G2 as Group>::Scalar::from(2u64)][..]),
           )
           .is_ok());
       });
diff --git a/examples/minroot.rs b/examples/minroot.rs
index 52162a4..3220417 100644
--- a/examples/minroot.rs
+++ b/examples/minroot.rs
@@ -172,7 +172,7 @@ fn main() {
       G2,
       MinRootCircuit<<G1 as Group>::Scalar>,
       TrivialTestCircuit<<G2 as Group>::Scalar>,
-    >::setup(circuit_primary, circuit_secondary.clone());
+    >::setup(circuit_primary.clone(), circuit_secondary.clone());
     println!("PublicParams::setup, took {:?} ", start.elapsed());
 
     println!(
@@ -218,15 +218,20 @@ fn main() {
     type C2 = TrivialTestCircuit<<G2 as Group>::Scalar>;
     // produce a recursive SNARK
     println!("Generating a RecursiveSNARK...");
-    let mut recursive_snark: Option<RecursiveSNARK<G1, G2, C1, C2>> = None;
+    let mut recursive_snark: RecursiveSNARK<G1, G2, C1, C2> = RecursiveSNARK::<G1, G2, C1, C2>::new(
+      &pp,
+      &minroot_circuits[0],
+      &circuit_secondary,
+      z0_primary.clone(),
+      z0_secondary.clone(),
+    );
 
     for (i, circuit_primary) in minroot_circuits.iter().take(num_steps).enumerate() {
       let start = Instant::now();
-      let res = RecursiveSNARK::prove_step(
+      let res = recursive_snark.prove_step(
         &pp,
-        recursive_snark,
-        circuit_primary.clone(),
-        circuit_secondary.clone(),
+        circuit_primary,
+        &circuit_secondary,
         z0_primary.clone(),
         z0_secondary.clone(),
       );
@@ -237,16 +242,12 @@ fn main() {
         res.is_ok(),
         start.elapsed()
       );
-      recursive_snark = Some(res.unwrap());
     }
 
-    assert!(recursive_snark.is_some());
-    let recursive_snark = recursive_snark.unwrap();
-
     // verify the recursive SNARK
     println!("Verifying a RecursiveSNARK...");
     let start = Instant::now();
-    let res = recursive_snark.verify(&pp, num_steps, z0_primary.clone(), z0_secondary.clone());
+    let res = recursive_snark.verify(&pp, num_steps, &z0_primary, &z0_secondary);
     println!(
       "RecursiveSNARK::verify: {:?}, took {:?}",
       res.is_ok(),
diff --git a/src/gadgets/ecc.rs b/src/gadgets/ecc.rs
index 677b6cd..997180d 100644
--- a/src/gadgets/ecc.rs
+++ b/src/gadgets/ecc.rs
@@ -1067,13 +1067,13 @@ mod tests {
   {
     let a = alloc_random_point(cs.namespace(|| "a")).unwrap();
     inputize_allocted_point(&a, cs.namespace(|| "inputize a")).unwrap();
-    let mut b = a.clone();
+    let mut b = &mut a.clone();
     b.y = AllocatedNum::alloc(cs.namespace(|| "allocate negation of a"), || {
       Ok(G::Base::ZERO)
     })
     .unwrap();
-    inputize_allocted_point(&b, cs.namespace(|| "inputize b")).unwrap();
-    let e = a.add(cs.namespace(|| "add a to b"), &b).unwrap();
+    inputize_allocted_point(b, cs.namespace(|| "inputize b")).unwrap();
+    let e = a.add(cs.namespace(|| "add a to b"), b).unwrap();
     e
   }
 
diff --git a/src/lib.rs b/src/lib.rs
index 930ae1f..57b0c18 100644
--- a/src/lib.rs
+++ b/src/lib.rs
@@ -192,197 +192,207 @@ where
   C1: StepCircuit<G1::Scalar>,
   C2: StepCircuit<G2::Scalar>,
 {
+  /// Create new instance of recursive SNARK
+  pub fn new(
+    pp: &PublicParams<G1, G2, C1, C2>,
+    c_primary: &C1,
+    c_secondary: &C2,
+    z0_primary: Vec<G1::Scalar>,
+    z0_secondary: Vec<G2::Scalar>,
+  ) -> Self {
+    // Expected outputs of the two circuits
+    let zi_primary = c_primary.output(&z0_primary);
+    let zi_secondary = c_secondary.output(&z0_secondary);
+
+    // base case for the primary
+    let mut cs_primary: SatisfyingAssignment<G1> = SatisfyingAssignment::new();
+    let inputs_primary: NovaAugmentedCircuitInputs<G2> = NovaAugmentedCircuitInputs::new(
+      scalar_as_base::<G1>(pp.digest),
+      G1::Scalar::ZERO,
+      z0_primary,
+      None,
+      None,
+      None,
+      None,
+    );
+
+    let circuit_primary: NovaAugmentedCircuit<G2, C1> = NovaAugmentedCircuit::new(
+      pp.augmented_circuit_params_primary.clone(),
+      Some(inputs_primary),
+      c_primary.clone(),
+      pp.ro_consts_circuit_primary.clone(),
+    );
+    let _ = circuit_primary.synthesize(&mut cs_primary);
+    let (u_primary, w_primary) = cs_primary
+      .r1cs_instance_and_witness(&pp.r1cs_shape_primary, &pp.ck_primary)
+      .map_err(|_e| NovaError::UnSat)
+      .expect("Nova error unsat");
+
+    // base case for the secondary
+    let mut cs_secondary: SatisfyingAssignment<G2> = SatisfyingAssignment::new();
+    let inputs_secondary: NovaAugmentedCircuitInputs<G1> = NovaAugmentedCircuitInputs::new(
+      pp.digest,
+      G2::Scalar::ZERO,
+      z0_secondary,
+      None,
+      None,
+      Some(u_primary.clone()),
+      None,
+    );
+    let circuit_secondary: NovaAugmentedCircuit<G1, C2> = NovaAugmentedCircuit::new(
+      pp.augmented_circuit_params_secondary.clone(),
+      Some(inputs_secondary),
+      c_secondary.clone(),
+      pp.ro_consts_circuit_secondary.clone(),
+    );
+    let _ = circuit_secondary.synthesize(&mut cs_secondary);
+    let (u_secondary, w_secondary) = cs_secondary
+      .r1cs_instance_and_witness(&pp.r1cs_shape_secondary, &pp.ck_secondary)
+      .map_err(|_e| NovaError::UnSat)
+      .expect("Nova error unsat");
+
+    // IVC proof for the primary circuit
+    let l_w_primary = w_primary;
+    let l_u_primary = u_primary;
+    let r_W_primary = RelaxedR1CSWitness::from_r1cs_witness(&pp.r1cs_shape_primary, &l_w_primary);
+    let r_U_primary =
+      RelaxedR1CSInstance::from_r1cs_instance(&pp.ck_primary, &pp.r1cs_shape_primary, &l_u_primary);
+
+    // IVC proof of the secondary circuit
+    let l_w_secondary = w_secondary;
+    let l_u_secondary = u_secondary;
+    let r_W_secondary = RelaxedR1CSWitness::<G2>::default(&pp.r1cs_shape_secondary);
+    let r_U_secondary =
+      RelaxedR1CSInstance::<G2>::default(&pp.ck_secondary, &pp.r1cs_shape_secondary);
+
+    if zi_primary.len() != pp.F_arity_primary || zi_secondary.len() != pp.F_arity_secondary {
+      panic!("Invalid step length");
+    }
+
+    Self {
+      r_W_primary,
+      r_U_primary,
+      r_W_secondary,
+      r_U_secondary,
+      l_w_secondary,
+      l_u_secondary,
+      i: 0,
+      zi_primary,
+      zi_secondary,
+      _p_c1: Default::default(),
+      _p_c2: Default::default(),
+    }
+  }
+
   /// Create a new `RecursiveSNARK` (or updates the provided `RecursiveSNARK`)
   /// by executing a step of the incremental computation
   pub fn prove_step(
+    &mut self,
     pp: &PublicParams<G1, G2, C1, C2>,
-    recursive_snark: Option<Self>,
-    c_primary: C1,
-    c_secondary: C2,
+    c_primary: &C1,
+    c_secondary: &C2,
     z0_primary: Vec<G1::Scalar>,
     z0_secondary: Vec<G2::Scalar>,
-  ) -> Result<Self, NovaError> {
+  ) -> Result<(), NovaError> {
     if z0_primary.len() != pp.F_arity_primary || z0_secondary.len() != pp.F_arity_secondary {
       return Err(NovaError::InvalidInitialInputLength);
     }
 
-    match recursive_snark {
-      None => {
-        // base case for the primary
-        let mut cs_primary: SatisfyingAssignment<G1> = SatisfyingAssignment::new();
-        let inputs_primary: NovaAugmentedCircuitInputs<G2> = NovaAugmentedCircuitInputs::new(
-          scalar_as_base::<G1>(pp.digest),
-          G1::Scalar::ZERO,
-          z0_primary.clone(),
-          None,
-          None,
-          None,
-          None,
-        );
+    // Frist step was already done in the constructor
+    if self.i == 0 {
+      self.i = 1;
+      return Ok(());
+    }
 
-        let circuit_primary: NovaAugmentedCircuit<G2, C1> = NovaAugmentedCircuit::new(
-          pp.augmented_circuit_params_primary.clone(),
-          Some(inputs_primary),
-          c_primary.clone(),
-          pp.ro_consts_circuit_primary.clone(),
-        );
-        let _ = circuit_primary.synthesize(&mut cs_primary);
-        let (u_primary, w_primary) = cs_primary
-          .r1cs_instance_and_witness(&pp.r1cs_shape_primary, &pp.ck_primary)
-          .map_err(|_e| NovaError::UnSat)?;
-
-        // base case for the secondary
-        let mut cs_secondary: SatisfyingAssignment<G2> = SatisfyingAssignment::new();
-        let inputs_secondary: NovaAugmentedCircuitInputs<G1> = NovaAugmentedCircuitInputs::new(
-          pp.digest,
-          G2::Scalar::ZERO,
-          z0_secondary.clone(),
-          None,
-          None,
-          Some(u_primary.clone()),
-          None,
-        );
-        let circuit_secondary: NovaAugmentedCircuit<G1, C2> = NovaAugmentedCircuit::new(
-          pp.augmented_circuit_params_secondary.clone(),
-          Some(inputs_secondary),
-          c_secondary.clone(),
-          pp.ro_consts_circuit_secondary.clone(),
-        );
-        let _ = circuit_secondary.synthesize(&mut cs_secondary);
-        let (u_secondary, w_secondary) = cs_secondary
-          .r1cs_instance_and_witness(&pp.r1cs_shape_secondary, &pp.ck_secondary)
-          .map_err(|_e| NovaError::UnSat)?;
-
-        // IVC proof for the primary circuit
-        let l_w_primary = w_primary;
-        let l_u_primary = u_primary;
-        let r_W_primary =
-          RelaxedR1CSWitness::from_r1cs_witness(&pp.r1cs_shape_primary, &l_w_primary);
-        let r_U_primary = RelaxedR1CSInstance::from_r1cs_instance(
-          &pp.ck_primary,
-          &pp.r1cs_shape_primary,
-          &l_u_primary,
-        );
+    // fold the secondary circuit's instance
+    let (nifs_secondary, (r_U_secondary, r_W_secondary)) = NIFS::prove(
+      &pp.ck_secondary,
+      &pp.ro_consts_secondary,
+      &scalar_as_base::<G1>(pp.digest),
+      &pp.r1cs_shape_secondary,
+      &self.r_U_secondary,
+      &self.r_W_secondary,
+      &self.l_u_secondary,
+      &self.l_w_secondary,
+    )
+    .expect("Unable to fold secondary");
+
+    let mut cs_primary: SatisfyingAssignment<G1> = SatisfyingAssignment::new();
+    let inputs_primary: NovaAugmentedCircuitInputs<G2> = NovaAugmentedCircuitInputs::new(
+      scalar_as_base::<G1>(pp.digest),
+      G1::Scalar::from(self.i as u64),
+      z0_primary,
+      Some(self.zi_primary.clone()),
+      Some(self.r_U_secondary.clone()),
+      Some(self.l_u_secondary.clone()),
+      Some(Commitment::<G2>::decompress(&nifs_secondary.comm_T)?),
+    );
 
-        // IVC proof of the secondary circuit
-        let l_w_secondary = w_secondary;
-        let l_u_secondary = u_secondary;
-        let r_W_secondary = RelaxedR1CSWitness::<G2>::default(&pp.r1cs_shape_secondary);
-        let r_U_secondary =
-          RelaxedR1CSInstance::<G2>::default(&pp.ck_secondary, &pp.r1cs_shape_secondary);
+    let circuit_primary: NovaAugmentedCircuit<G2, C1> = NovaAugmentedCircuit::new(
+      pp.augmented_circuit_params_primary.clone(),
+      Some(inputs_primary),
+      c_primary.clone(),
+      pp.ro_consts_circuit_primary.clone(),
+    );
+    let _ = circuit_primary.synthesize(&mut cs_primary);
+
+    let (l_u_primary, l_w_primary) = cs_primary
+      .r1cs_instance_and_witness(&pp.r1cs_shape_primary, &pp.ck_primary)
+      .map_err(|_e| NovaError::UnSat)
+      .expect("Nova error unsat");
+
+    // fold the primary circuit's instance
+    let (nifs_primary, (r_U_primary, r_W_primary)) = NIFS::prove(
+      &pp.ck_primary,
+      &pp.ro_consts_primary,
+      &pp.digest,
+      &pp.r1cs_shape_primary,
+      &self.r_U_primary,
+      &self.r_W_primary,
+      &l_u_primary,
+      &l_w_primary,
+    )
+    .expect("Unable to fold primary");
+
+    let mut cs_secondary: SatisfyingAssignment<G2> = SatisfyingAssignment::new();
+    let inputs_secondary: NovaAugmentedCircuitInputs<G1> = NovaAugmentedCircuitInputs::new(
+      pp.digest,
+      G2::Scalar::from(self.i as u64),
+      z0_secondary,
+      Some(self.zi_secondary.clone()),
+      Some(self.r_U_primary.clone()),
+      Some(l_u_primary),
+      Some(Commitment::<G1>::decompress(&nifs_primary.comm_T)?),
+    );
 
-        // Outputs of the two circuits thus far
-        let zi_primary = c_primary.output(&z0_primary);
-        let zi_secondary = c_secondary.output(&z0_secondary);
+    let circuit_secondary: NovaAugmentedCircuit<G1, C2> = NovaAugmentedCircuit::new(
+      pp.augmented_circuit_params_secondary.clone(),
+      Some(inputs_secondary),
+      c_secondary.clone(),
+      pp.ro_consts_circuit_secondary.clone(),
+    );
+    let _ = circuit_secondary.synthesize(&mut cs_secondary);
 
-        if zi_primary.len() != pp.F_arity_primary || zi_secondary.len() != pp.F_arity_secondary {
-          return Err(NovaError::InvalidStepOutputLength);
-        }
+    let (l_u_secondary, l_w_secondary) = cs_secondary
+      .r1cs_instance_and_witness(&pp.r1cs_shape_secondary, &pp.ck_secondary)
+      .map_err(|_e| NovaError::UnSat)?;
 
-        Ok(Self {
-          r_W_primary,
-          r_U_primary,
-          r_W_secondary,
-          r_U_secondary,
-          l_w_secondary,
-          l_u_secondary,
-          i: 1_usize,
-          zi_primary,
-          zi_secondary,
-          _p_c1: Default::default(),
-          _p_c2: Default::default(),
-        })
-      }
-      Some(r_snark) => {
-        // fold the secondary circuit's instance
-        let (nifs_secondary, (r_U_secondary, r_W_secondary)) = NIFS::prove(
-          &pp.ck_secondary,
-          &pp.ro_consts_secondary,
-          &scalar_as_base::<G1>(pp.digest),
-          &pp.r1cs_shape_secondary,
-          &r_snark.r_U_secondary,
-          &r_snark.r_W_secondary,
-          &r_snark.l_u_secondary,
-          &r_snark.l_w_secondary,
-        )?;
-
-        let mut cs_primary: SatisfyingAssignment<G1> = SatisfyingAssignment::new();
-        let inputs_primary: NovaAugmentedCircuitInputs<G2> = NovaAugmentedCircuitInputs::new(
-          scalar_as_base::<G1>(pp.digest),
-          G1::Scalar::from(r_snark.i as u64),
-          z0_primary,
-          Some(r_snark.zi_primary.clone()),
-          Some(r_snark.r_U_secondary.clone()),
-          Some(r_snark.l_u_secondary.clone()),
-          Some(Commitment::<G2>::decompress(&nifs_secondary.comm_T)?),
-        );
+    // update the running instances and witnesses
+    self.zi_primary = c_primary.output(&self.zi_primary);
+    self.zi_secondary = c_secondary.output(&self.zi_secondary);
 
-        let circuit_primary: NovaAugmentedCircuit<G2, C1> = NovaAugmentedCircuit::new(
-          pp.augmented_circuit_params_primary.clone(),
-          Some(inputs_primary),
-          c_primary.clone(),
-          pp.ro_consts_circuit_primary.clone(),
-        );
-        let _ = circuit_primary.synthesize(&mut cs_primary);
+    self.l_u_secondary = l_u_secondary;
+    self.l_w_secondary = l_w_secondary;
 
-        let (l_u_primary, l_w_primary) = cs_primary
-          .r1cs_instance_and_witness(&pp.r1cs_shape_primary, &pp.ck_primary)
-          .map_err(|_e| NovaError::UnSat)?;
+    self.r_U_primary = r_U_primary;
+    self.r_W_primary = r_W_primary;
 
-        // fold the primary circuit's instance
-        let (nifs_primary, (r_U_primary, r_W_primary)) = NIFS::prove(
-          &pp.ck_primary,
-          &pp.ro_consts_primary,
-          &pp.digest,
-          &pp.r1cs_shape_primary,
-          &r_snark.r_U_primary,
-          &r_snark.r_W_primary,
-          &l_u_primary,
-          &l_w_primary,
-        )?;
-
-        let mut cs_secondary: SatisfyingAssignment<G2> = SatisfyingAssignment::new();
-        let inputs_secondary: NovaAugmentedCircuitInputs<G1> = NovaAugmentedCircuitInputs::new(
-          pp.digest,
-          G2::Scalar::from(r_snark.i as u64),
-          z0_secondary,
-          Some(r_snark.zi_secondary.clone()),
-          Some(r_snark.r_U_primary.clone()),
-          Some(l_u_primary),
-          Some(Commitment::<G1>::decompress(&nifs_primary.comm_T)?),
-        );
+    self.i += 1;
 
-        let circuit_secondary: NovaAugmentedCircuit<G1, C2> = NovaAugmentedCircuit::new(
-          pp.augmented_circuit_params_secondary.clone(),
-          Some(inputs_secondary),
-          c_secondary.clone(),
-          pp.ro_consts_circuit_secondary.clone(),
-        );
-        let _ = circuit_secondary.synthesize(&mut cs_secondary);
-
-        let (l_u_secondary, l_w_secondary) = cs_secondary
-          .r1cs_instance_and_witness(&pp.r1cs_shape_secondary, &pp.ck_secondary)
-          .map_err(|_e| NovaError::UnSat)?;
-
-        // update the running instances and witnesses
-        let zi_primary = c_primary.output(&r_snark.zi_primary);
-        let zi_secondary = c_secondary.output(&r_snark.zi_secondary);
-
-        Ok(Self {
-          r_W_primary,
-          r_U_primary,
-          r_W_secondary,
-          r_U_secondary,
-          l_w_secondary,
-          l_u_secondary,
-          i: r_snark.i + 1,
-          zi_primary,
-          zi_secondary,
-          _p_c1: Default::default(),
-          _p_c2: Default::default(),
-        })
-      }
-    }
+    self.r_U_secondary = r_U_secondary;
+    self.r_W_secondary = r_W_secondary;
+
+    Ok(())
   }
 
   /// Verify the correctness of the `RecursiveSNARK`
@@ -390,8 +400,8 @@ where
     &self,
     pp: &PublicParams<G1, G2, C1, C2>,
     num_steps: usize,
-    z0_primary: Vec<G1::Scalar>,
-    z0_secondary: Vec<G2::Scalar>,
+    z0_primary: &[G1::Scalar],
+    z0_secondary: &[G2::Scalar],
   ) -> Result<(Vec<G1::Scalar>, Vec<G2::Scalar>), NovaError> {
     // number of steps cannot be zero
     if num_steps == 0 {
@@ -419,7 +429,7 @@ where
       );
       hasher.absorb(pp.digest);
       hasher.absorb(G1::Scalar::from(num_steps as u64));
-      for e in &z0_primary {
+      for e in z0_primary {
         hasher.absorb(*e);
       }
       for e in &self.zi_primary {
@@ -433,7 +443,7 @@ where
       );
       hasher2.absorb(scalar_as_base::<G1>(pp.digest));
       hasher2.absorb(G2::Scalar::from(num_steps as u64));
-      for e in &z0_secondary {
+      for e in z0_secondary {
         hasher2.absorb(*e);
       }
       for e in &self.zi_secondary {
@@ -906,23 +916,30 @@ mod tests {
     let num_steps = 1;
 
     // produce a recursive SNARK
-    let res = RecursiveSNARK::prove_step(
+    let mut recursive_snark = RecursiveSNARK::new(
       &pp,
-      None,
-      test_circuit1,
-      test_circuit2,
+      &test_circuit1,
+      &test_circuit2,
+      vec![<G1 as Group>::Scalar::ZERO],
+      vec![<G2 as Group>::Scalar::ZERO],
+    );
+
+    let res = recursive_snark.prove_step(
+      &pp,
+      &test_circuit1,
+      &test_circuit2,
       vec![<G1 as Group>::Scalar::ZERO],
       vec![<G2 as Group>::Scalar::ZERO],
     );
+
     assert!(res.is_ok());
-    let recursive_snark = res.unwrap();
 
     // verify the recursive SNARK
     let res = recursive_snark.verify(
       &pp,
       num_steps,
-      vec![<G1 as Group>::Scalar::ZERO],
-      vec![<G2 as Group>::Scalar::ZERO],
+      &vec![<G1 as Group>::Scalar::ZERO][..],
+      &vec![<G2 as Group>::Scalar::ZERO][..],
     );
     assert!(res.is_ok());
   }
@@ -953,49 +970,45 @@ mod tests {
     let num_steps = 3;
 
     // produce a recursive SNARK
-    let mut recursive_snark: Option<
-      RecursiveSNARK<
-        G1,
-        G2,
-        TrivialTestCircuit<<G1 as Group>::Scalar>,
-        CubicCircuit<<G2 as Group>::Scalar>,
-      >,
-    > = None;
+    let mut recursive_snark = RecursiveSNARK::<
+      G1,
+      G2,
+      TrivialTestCircuit<<G1 as Group>::Scalar>,
+      CubicCircuit<<G2 as Group>::Scalar>,
+    >::new(
+      &pp,
+      &circuit_primary,
+      &circuit_secondary,
+      vec![<G1 as Group>::Scalar::ONE],
+      vec![<G2 as Group>::Scalar::ZERO],
+    );
 
     for i in 0..num_steps {
-      let res = RecursiveSNARK::prove_step(
+      let res = recursive_snark.prove_step(
         &pp,
-        recursive_snark,
-        circuit_primary.clone(),
-        circuit_secondary.clone(),
+        &circuit_primary,
+        &circuit_secondary,
         vec![<G1 as Group>::Scalar::ONE],
         vec![<G2 as Group>::Scalar::ZERO],
       );
       assert!(res.is_ok());
-      let recursive_snark_unwrapped = res.unwrap();
 
       // verify the recursive snark at each step of recursion
-      let res = recursive_snark_unwrapped.verify(
+      let res = recursive_snark.verify(
         &pp,
         i + 1,
-        vec![<G1 as Group>::Scalar::ONE],
-        vec![<G2 as Group>::Scalar::ZERO],
+        &vec![<G1 as Group>::Scalar::ONE][..],
+        &vec![<G2 as Group>::Scalar::ZERO][..],
       );
       assert!(res.is_ok());
-
-      // set the running variable for the next iteration
-      recursive_snark = Some(recursive_snark_unwrapped);
     }
 
-    assert!(recursive_snark.is_some());
-    let recursive_snark = recursive_snark.unwrap();
-
     // verify the recursive SNARK
     let res = recursive_snark.verify(
       &pp,
       num_steps,
-      vec![<G1 as Group>::Scalar::ONE],
-      vec![<G2 as Group>::Scalar::ZERO],
+      &vec![<G1 as Group>::Scalar::ONE][..],
+      &vec![<G2 as Group>::Scalar::ZERO][..],
     );
     assert!(res.is_ok());
 
@@ -1043,37 +1056,36 @@ mod tests {
     let num_steps = 3;
 
     // produce a recursive SNARK
-    let mut recursive_snark: Option<
-      RecursiveSNARK<
-        G1,
-        G2,
-        TrivialTestCircuit<<G1 as Group>::Scalar>,
-        CubicCircuit<<G2 as Group>::Scalar>,
-      >,
-    > = None;
+    let mut recursive_snark = RecursiveSNARK::<
+      G1,
+      G2,
+      TrivialTestCircuit<<G1 as Group>::Scalar>,
+      CubicCircuit<<G2 as Group>::Scalar>,
+    >::new(
+      &pp,
+      &circuit_primary,
+      &circuit_secondary,
+      vec![<G1 as Group>::Scalar::ONE],
+      vec![<G2 as Group>::Scalar::ZERO],
+    );
 
     for _i in 0..num_steps {
-      let res = RecursiveSNARK::prove_step(
+      let res = recursive_snark.prove_step(
         &pp,
-        recursive_snark,
-        circuit_primary.clone(),
-        circuit_secondary.clone(),
+        &circuit_primary,
+        &circuit_secondary,
         vec![<G1 as Group>::Scalar::ONE],
         vec![<G2 as Group>::Scalar::ZERO],
       );
       assert!(res.is_ok());
-      recursive_snark = Some(res.unwrap());
     }
 
-    assert!(recursive_snark.is_some());
-    let recursive_snark = recursive_snark.unwrap();
-
     // verify the recursive SNARK
     let res = recursive_snark.verify(
       &pp,
       num_steps,
-      vec![<G1 as Group>::Scalar::ONE],
-      vec![<G2 as Group>::Scalar::ZERO],
+      &vec![<G1 as Group>::Scalar::ONE][..],
+      &vec![<G2 as Group>::Scalar::ZERO][..],
     );
     assert!(res.is_ok());
 
@@ -1138,37 +1150,36 @@ mod tests {
     let num_steps = 3;
 
     // produce a recursive SNARK
-    let mut recursive_snark: Option<
-      RecursiveSNARK<
-        G1,
-        G2,
-        TrivialTestCircuit<<G1 as Group>::Scalar>,
-        CubicCircuit<<G2 as Group>::Scalar>,
-      >,
-    > = None;
+    let mut recursive_snark = RecursiveSNARK::<
+      G1,
+      G2,
+      TrivialTestCircuit<<G1 as Group>::Scalar>,
+      CubicCircuit<<G2 as Group>::Scalar>,
+    >::new(
+      &pp,
+      &circuit_primary,
+      &circuit_secondary,
+      vec![<G1 as Group>::Scalar::ONE],
+      vec![<G2 as Group>::Scalar::ZERO],
+    );
 
     for _i in 0..num_steps {
-      let res = RecursiveSNARK::prove_step(
+      let res = recursive_snark.prove_step(
         &pp,
-        recursive_snark,
-        circuit_primary.clone(),
-        circuit_secondary.clone(),
+        &circuit_primary,
+        &circuit_secondary,
         vec![<G1 as Group>::Scalar::ONE],
         vec![<G2 as Group>::Scalar::ZERO],
       );
       assert!(res.is_ok());
-      recursive_snark = Some(res.unwrap());
     }
 
-    assert!(recursive_snark.is_some());
-    let recursive_snark = recursive_snark.unwrap();
-
     // verify the recursive SNARK
     let res = recursive_snark.verify(
       &pp,
       num_steps,
-      vec![<G1 as Group>::Scalar::ONE],
-      vec![<G2 as Group>::Scalar::ZERO],
+      &vec![<G1 as Group>::Scalar::ONE][..],
+      &vec![<G2 as Group>::Scalar::ZERO][..],
     );
     assert!(res.is_ok());
 
@@ -1237,14 +1248,9 @@ mod tests {
         let rng = &mut rand::rngs::OsRng;
         let mut seed = F::random(rng);
         for _i in 0..num_steps + 1 {
-          let mut power = seed;
-          power = power.square();
-          power = power.square();
-          power *= seed;
+          seed *= seed.clone().square().square();
 
-          powers.push(Self { y: power });
-
-          seed = power;
+          powers.push(Self { y: seed });
         }
 
         // reverse the powers to get roots
@@ -1289,12 +1295,7 @@ mod tests {
       fn output(&self, z: &[F]) -> Vec<F> {
         // sanity check
         let x = z[0];
-        let y_pow_5 = {
-          let y = self.y;
-          let y_sq = y.square();
-          let y_quad = y_sq.square();
-          y_quad * self.y
-        };
+        let y_pow_5 = self.y * self.y.clone().square().square();
         assert_eq!(x, y_pow_5);
 
         // return non-deterministic advice
@@ -1324,33 +1325,37 @@ mod tests {
     let z0_secondary = vec![<G2 as Group>::Scalar::ZERO];
 
     // produce a recursive SNARK
-    let mut recursive_snark: Option<
-      RecursiveSNARK<
-        G1,
-        G2,
-        FifthRootCheckingCircuit<<G1 as Group>::Scalar>,
-        TrivialTestCircuit<<G2 as Group>::Scalar>,
-      >,
-    > = None;
+    let mut recursive_snark: RecursiveSNARK<
+      G1,
+      G2,
+      FifthRootCheckingCircuit<<G1 as Group>::Scalar>,
+      TrivialTestCircuit<<G2 as Group>::Scalar>,
+    > = RecursiveSNARK::<
+      G1,
+      G2,
+      FifthRootCheckingCircuit<<G1 as Group>::Scalar>,
+      TrivialTestCircuit<<G2 as Group>::Scalar>,
+    >::new(
+      &pp,
+      &roots[0],
+      &circuit_secondary,
+      z0_primary.clone(),
+      z0_secondary.clone(),
+    );
 
     for circuit_primary in roots.iter().take(num_steps) {
-      let res = RecursiveSNARK::prove_step(
+      let res = recursive_snark.prove_step(
         &pp,
-        recursive_snark,
-        circuit_primary.clone(),
-        circuit_secondary.clone(),
+        circuit_primary,
+        &circuit_secondary.clone(),
         z0_primary.clone(),
         z0_secondary.clone(),
       );
       assert!(res.is_ok());
-      recursive_snark = Some(res.unwrap());
     }
 
-    assert!(recursive_snark.is_some());
-    let recursive_snark = recursive_snark.unwrap();
-
     // verify the recursive SNARK
-    let res = recursive_snark.verify(&pp, num_steps, z0_primary.clone(), z0_secondary.clone());
+    let res = recursive_snark.verify(&pp, num_steps, &z0_primary, &z0_secondary);
     assert!(res.is_ok());
 
     // produce the prover and verifier keys for compressed snark
@@ -1379,34 +1384,50 @@ mod tests {
     G1: Group<Base = <G2 as Group>::Scalar>,
     G2: Group<Base = <G1 as Group>::Scalar>,
   {
+    let test_circuit1 = TrivialTestCircuit::<<G1 as Group>::Scalar>::default();
+    let test_circuit2 = CubicCircuit::<<G2 as Group>::Scalar>::default();
+
     // produce public parameters
     let pp = PublicParams::<
       G1,
       G2,
       TrivialTestCircuit<<G1 as Group>::Scalar>,
       CubicCircuit<<G2 as Group>::Scalar>,
-    >::setup(TrivialTestCircuit::default(), CubicCircuit::default());
+    >::setup(test_circuit1.clone(), test_circuit2.clone());
 
     let num_steps = 1;
 
     // produce a recursive SNARK
-    let res = RecursiveSNARK::prove_step(
+    let mut recursive_snark = RecursiveSNARK::<
+      G1,
+      G2,
+      TrivialTestCircuit<<G1 as Group>::Scalar>,
+      CubicCircuit<<G2 as Group>::Scalar>,
+    >::new(
       &pp,
-      None,
-      TrivialTestCircuit::default(),
-      CubicCircuit::default(),
+      &test_circuit1,
+      &test_circuit2,
       vec![<G1 as Group>::Scalar::ONE],
       vec![<G2 as Group>::Scalar::ZERO],
     );
+
+    // produce a recursive SNARK
+    let res = recursive_snark.prove_step(
+      &pp,
+      &test_circuit1,
+      &test_circuit2,
+      vec![<G1 as Group>::Scalar::ONE],
+      vec![<G2 as Group>::Scalar::ZERO],
+    );
+
     assert!(res.is_ok());
-    let recursive_snark = res.unwrap();
 
     // verify the recursive SNARK
     let res = recursive_snark.verify(
       &pp,
       num_steps,
-      vec![<G1 as Group>::Scalar::ONE],
-      vec![<G2 as Group>::Scalar::ZERO],
+      &vec![<G1 as Group>::Scalar::ONE][..],
+      &vec![<G2 as Group>::Scalar::ZERO][..],
     );
     assert!(res.is_ok());
 
diff --git a/src/provider/pedersen.rs b/src/provider/pedersen.rs
index b5a45e1..bad1247 100644
--- a/src/provider/pedersen.rs
+++ b/src/provider/pedersen.rs
@@ -69,7 +69,7 @@ impl<G: Group> Default for Commitment<G> {
 impl<G: Group> TranscriptReprTrait<G> for Commitment<G> {
   fn to_transcript_bytes(&self) -> Vec<u8> {
     let (x, y, is_infinity) = self.comm.to_coordinates();
-    let is_infinity_byte = if is_infinity { 0u8 } else { 1u8 };
+    let is_infinity_byte = (!is_infinity).into();
     [
       x.to_transcript_bytes(),
       y.to_transcript_bytes(),