diff --git a/circuitcompiler/Programm.go b/circuitcompiler/Programm.go
index dac2006..7e02960 100644
--- a/circuitcompiler/Programm.go
+++ b/circuitcompiler/Programm.go
@@ -24,6 +24,7 @@ type R1CS struct {
 type Program struct {
 	functions             map[string]*Circuit
 	globalInputs          []string
+	globalOutput          map[string]bool
 	arithmeticEnvironment utils //find a better name
 
 	//key 1: the hash chain indicating from where the variable is called H( H(main(a,b)) , doSomething(x,z) ), where H is a hash function.
@@ -67,6 +68,10 @@ func (p *Program) BuildConstraintTrees() {
 	for _, in := range p.getMainCircuit().Inputs {
 		p.globalInputs = append(p.globalInputs, in)
 	}
+	for key, _ := range p.globalOutput {
+		p.globalInputs = append(p.globalInputs, key)
+	}
+	//TODO do the same with the outputs
 	var wg = sync.WaitGroup{}
 
 	//we build the parse trees concurrently! because we can! go rocks
@@ -193,8 +198,14 @@ func (p *Program) r1CSRecursiveBuild(currentCircuit *Circuit, node *gate, hashTr
 		out := hashTogether(leftHash, rightHash)
 		rootGate.value.V1 = rootGate.value.V1 + string(leftHash[:10])
 		rootGate.value.V2 = rootGate.value.V2 + string(rightHash[:10])
-		rootGate.value.Out = rootGate.value.Out + string(out[:10])
+
+		//note we only check for existence, but not for truth.
+		if _, ex := p.globalOutput[rootGate.value.Out]; !ex {
+			rootGate.value.Out = rootGate.value.Out + string(out[:10])
+		}
+
 		p.computedInContext[string(hashTraceBuildup)][node.value.Out] = rootGate.value.Out
+
 		p.computedFactors[sig] = rootGate.value.Out
 		*orderedmGates = append(*orderedmGates, *rootGate)
 
@@ -449,6 +460,7 @@ func NewProgram() (p *Program) {
 	p = &Program{
 		functions:             map[string]*Circuit{},
 		globalInputs:          []string{"one"},
+		globalOutput:          map[string]bool{"main": true},
 		arithmeticEnvironment: prepareUtils(),
 	}
 	return
@@ -458,7 +470,7 @@ func NewProgram() (p *Program) {
 func (p *Program) GenerateReducedR1CS(mGates []gate) (r1CS R1CS) {
 	// from flat code to R1CS
 
-	offset := len(p.globalInputs)
+	offset := len(p.globalInputs) - len(p.globalOutput)
 	//  one + in1 +in2+... + gate1 + gate2 .. + out
 	size := offset + len(mGates)
 	indexMap := make(map[string]int)
@@ -467,8 +479,11 @@ func (p *Program) GenerateReducedR1CS(mGates []gate) (r1CS R1CS) {
 		indexMap[v] = i
 
 	}
-	for i, v := range mGates {
-		indexMap[v.value.Out] = i + offset
+	for _, v := range mGates {
+		if _, ex := indexMap[v.value.Out]; !ex {
+			indexMap[v.value.Out] = len(indexMap)
+		}
+
 	}
 
 	for _, g := range mGates {
diff --git a/circuitcompiler/Programm_test.go b/circuitcompiler/Programm_test.go
index 1b8960a..412e23f 100644
--- a/circuitcompiler/Programm_test.go
+++ b/circuitcompiler/Programm_test.go
@@ -154,7 +154,7 @@ func TestNewProgramm(t *testing.T) {
 			w := CalculateWitness(inputs, r1cs)
 			fmt.Println("witness")
 			fmt.Println(w)
-			assert.Equal(t, io.result, w[len(w)-1])
+			assert.Equal(t, io.result, w[len(program.globalInputs)-1])
 		}
 
 	}
diff --git a/r1csqap/r1csqap.go b/r1csqap/r1csqap.go
index d5d668f..048f855 100644
--- a/r1csqap/r1csqap.go
+++ b/r1csqap/r1csqap.go
@@ -6,6 +6,8 @@ import (
 	"github.com/arnaucube/go-snark/fields"
 )
 
+var bigZero = big.NewInt(int64(0))
+
 // Transpose transposes the *big.Int matrix
 func Transpose(matrix [][]*big.Int) [][]*big.Int {
 	r := make([][]*big.Int, len(matrix[0]))
@@ -22,7 +24,7 @@ func Transpose(matrix [][]*big.Int) [][]*big.Int {
 
 // ArrayOfBigZeros creates a *big.Int array with n elements to zero
 func ArrayOfBigZeros(num int) []*big.Int {
-	bigZero := big.NewInt(int64(0))
+
 	var r = make([]*big.Int, num, num)
 	for i := 0; i < num; i++ {
 		r[i] = bigZero
@@ -155,7 +157,11 @@ func (pf PolynomialField) LagrangeInterpolation(v []*big.Int) []*big.Int {
 	// https://en.wikipedia.org/wiki/Lagrange_polynomial
 	var r []*big.Int
 	for i := 0; i < len(v); i++ {
-		r = pf.Add(r, pf.NewPolZeroAt(i+1, len(v), v[i]))
+		//NOTE this comparison gives a huge performance boost
+		if v[i].Cmp(bigZero) != 0 {
+			r = pf.Add(r, pf.NewPolZeroAt(i+1, len(v), v[i]))
+		}
+
 		//r = pf.Mul(v[i], pf.NewPolZeroAt(i+1, len(v), v[i]))
 	}
 	//
diff --git a/snark.go b/snark.go
index 0f3f71d..135dc70 100644
--- a/snark.go
+++ b/snark.go
@@ -2,7 +2,6 @@ package snark
 
 import (
 	"fmt"
-	"github.com/arnaucube/go-snark/circuitcompiler"
 	"math/big"
 	"os"
 
@@ -91,7 +90,7 @@ func prepareUtils() utils {
 }
 
 // GenerateTrustedSetup generates the Trusted Setup from a compiled Circuit. The Setup.Toxic sub data structure must be destroyed
-func GenerateTrustedSetup(witnessLength int, alphas, betas, gammas [][]*big.Int) (Setup, error) {
+func GenerateTrustedSetup(inputs int, alphas, betas, gammas [][]*big.Int) (Setup, error) {
 	var setup Setup
 	var err error
 
@@ -174,13 +173,13 @@ func GenerateTrustedSetup(witnessLength int, alphas, betas, gammas [][]*big.Int)
 	setup.Vk.G2Kg = Utils.Bn.G2.MulScalar(Utils.Bn.G2.G, setup.Toxic.Kgamma)
 
 	// for i := 0; i < circuit.NVars; i++ {
-	for i := 0; i < witnessLength; i++ {
+	for i := 0; i < len(alphas); i++ {
 		at := Utils.PF.Eval(alphas[i], setup.Toxic.T)
 		// rhoAat := Utils.Bn.Fq1.Mul(setup.Toxic.RhoA, at)
 		rhoAat := Utils.FqR.Mul(setup.Toxic.RhoA, at)
 		a := Utils.Bn.G1.MulScalar(Utils.Bn.G1.G, rhoAat)
 		setup.Pk.A = append(setup.Pk.A, a)
-		if i <= 4 {
+		if i < inputs {
 			setup.Vk.IC = append(setup.Vk.IC, a)
 		}
 
@@ -322,7 +321,7 @@ func VerifyProof(setup Setup, proof Proof, publicSignals []*big.Int, debug bool)
 	// Vkx, to then calculate Vkx+piA
 	vkxpia := setup.Vk.IC[0]
 	for i := 0; i < len(publicSignals); i++ {
-		vkxpia = Utils.Bn.G1.Add(vkxpia, Utils.Bn.G1.MulScalar(setup.Vk.IC[i+1], publicSignals[i]))
+		vkxpia = Utils.Bn.G1.Add(vkxpia, Utils.Bn.G1.MulScalar(setup.Vk.IC[i], publicSignals[i]))
 	}
 
 	// e(Vkx+piA, piB) == e(piH, Vkz) * e(piC, g2)
@@ -355,31 +354,3 @@ func VerifyProof(setup Setup, proof Proof, publicSignals []*big.Int, debug bool)
 
 	return true
 }
-
-//TODO this is just a workaround to place the output after the input signals. Will be removed once the handling of private variables is already considered in the lexer
-func moveOutputToBegining(r1cs circuitcompiler.R1CS) (r circuitcompiler.R1CS) {
-	return r1cs
-	// activating this part, causes a huge messup I want to deal with a bit later
-	tmpA, tmpB, tmpC := [][]*big.Int{}, [][]*big.Int{}, [][]*big.Int{}
-
-	tmpA = append(tmpA, r1cs.A[len(r1cs.A)-1])
-	tmpA = append(tmpA, r1cs.A[:len(r1cs.A)-1]...)
-
-	tmpB = append(tmpB, r1cs.B[len(r1cs.B)-1])
-	tmpB = append(tmpB, r1cs.B[:len(r1cs.B)-1]...)
-
-	tmpC = append(tmpC, r1cs.C[len(r1cs.C)-1])
-	tmpC = append(tmpC, r1cs.C[:len(r1cs.C)-1]...)
-
-	return circuitcompiler.R1CS{A: tmpA, B: tmpB, C: tmpC}
-}
-
-//TODO this is just a workaround to place the output after the input signals. Will be removed once the handling of private variables is already considered in the lexer
-func moveWitnessOutputAfterInputs(numberOfInputs int, witness []*big.Int) (w []*big.Int) {
-	return witness
-	// activating this part, causes a huge messup I want to deal with a bit later
-	wtmp := append(witness[:numberOfInputs], witness[len(witness)-1])
-	wtmp = append(wtmp, witness[numberOfInputs:len(witness)-2]...)
-
-	return wtmp
-}
diff --git a/snark_test.go b/snark_test.go
index 5cb969c..6653899 100644
--- a/snark_test.go
+++ b/snark_test.go
@@ -143,7 +143,7 @@ func TestGenerateAndVerifyProof(t *testing.T) {
 
 		fmt.Println("generating R1CS")
 		//NOTE MOVE DOES NOTHING CURRENTLY
-		r1cs := moveOutputToBegining(program.GenerateReducedR1CS(gates))
+		r1cs := program.GenerateReducedR1CS(gates)
 		//[[0 1 0 0 0 0 0 0 0 0] [0 0 0 1 0 0 0 0 0 0] [0 0 0 0 0 1 0 0 0 0] [0 0 0 0 0 0 0 0 1 0] [0 0 0 0 0 0 0 1 0 0]]
 		//[[0 0 1 0 0 0 0 0 0 0] [0 0 0 0 1 0 0 0 0 0] [0 0 0 0 0 0 1 0 0 0] [0 0 0 0 0 1 0 0 0 0] [0 0 0 0 0 0 0 0 5 0]]
 		//[[0 0 0 0 0 1 0 0 0 0] [0 0 0 0 0 0 1 0 0 0] [0 0 0 0 0 0 0 1 0 0] [0 0 0 0 0 0 0 1 0 0] [0 0 0 0 0 0 0 0 0 1]]
@@ -163,7 +163,7 @@ func TestGenerateAndVerifyProof(t *testing.T) {
 
 		before := time.Now()
 		//calculate trusted setup
-		setup, err := GenerateTrustedSetup(len(alphas[0]), alphas, betas, gammas)
+		setup, err := GenerateTrustedSetup(program.GlobalInputCount(), alphas, betas, gammas)
 		fmt.Println("Generate CRS time elapsed:", time.Since(before))
 		assert.Nil(t, err)
 		fmt.Println("\nt:", setup.Toxic.T)
@@ -175,11 +175,8 @@ func TestGenerateAndVerifyProof(t *testing.T) {
 			fmt.Println(inputs)
 			w := circuitcompiler.CalculateWitness(inputs, r1cs)
 			fmt.Println("\nwitness", w)
-			//NOTE MOVE DOES NOTHING
-			w = moveWitnessOutputAfterInputs(program.GlobalInputCount(), w)
-			fmt.Println("\nwitness Reordered ", w)
 
-			assert.Equal(t, io.result, w[len(w)-1])
+			assert.Equal(t, io.result, w[program.GlobalInputCount()-1])
 
 			ax, bx, cx, px := Utils.PF.CombinePolynomials(w, alphas, betas, gammas)
 			fmt.Println("ax length", len(ax))
@@ -219,7 +216,7 @@ func TestGenerateAndVerifyProof(t *testing.T) {
 			assert.Nil(t, err)
 
 			before = time.Now()
-			assert.True(t, VerifyProof(setup, proof, append(w[1:program.GlobalInputCount()], w[len(w)-1]), true))
+			assert.True(t, VerifyProof(setup, proof, w[:program.GlobalInputCount()], true))
 			fmt.Println("verify proof time elapsed:", time.Since(before))
 
 		}