Initial Problem

Start: n_evalexministart
Program_Vars: Arg_0, Arg_1, Arg_2
Temp_Vars:
Locations: n_evalexminibb1in___6, n_evalexminibbin___5, n_evalexminientryin___7, n_evalexminireturnin___3, n_evalexminireturnin___4, n_evalexministart, n_evalexministop___1, n_evalexministop___2
Transitions:
0:n_evalexminibb1in___6(Arg_0,Arg_1,Arg_2) -> n_evalexminibbin___5(Arg_0,Arg_1,Arg_2):|:Arg_2<=Arg_0 && Arg_1<=100
1:n_evalexminibb1in___6(Arg_0,Arg_1,Arg_2) -> n_evalexminireturnin___3(Arg_0,Arg_1,Arg_2):|:1+Arg_0<=Arg_2
2:n_evalexminibb1in___6(Arg_0,Arg_1,Arg_2) -> n_evalexminireturnin___4(Arg_0,Arg_1,Arg_2):|:101<=Arg_1
3:n_evalexminibbin___5(Arg_0,Arg_1,Arg_2) -> n_evalexminibb1in___6(Arg_0-1,Arg_2,Arg_1+1):|:Arg_1<=100 && Arg_2<=Arg_0
4:n_evalexminientryin___7(Arg_0,Arg_1,Arg_2) -> n_evalexminibb1in___6(Arg_1,Arg_0,Arg_2)
5:n_evalexminireturnin___3(Arg_0,Arg_1,Arg_2) -> n_evalexministop___1(Arg_0,Arg_1,Arg_2):|:1+Arg_0<=Arg_2
6:n_evalexminireturnin___4(Arg_0,Arg_1,Arg_2) -> n_evalexministop___2(Arg_0,Arg_1,Arg_2):|:101<=Arg_1
7:n_evalexministart(Arg_0,Arg_1,Arg_2) -> n_evalexminientryin___7(Arg_0,Arg_1,Arg_2)

Preprocessing

Found invariant 1+Arg_0<=Arg_2 for location n_evalexministop___1

Found invariant 101<=Arg_1 for location n_evalexminireturnin___4

Found invariant Arg_2<=Arg_0 && Arg_1<=100 for location n_evalexminibbin___5

Found invariant 101<=Arg_1 for location n_evalexministop___2

Found invariant 1+Arg_0<=Arg_2 for location n_evalexminireturnin___3

Problem after Preprocessing

Start: n_evalexministart
Program_Vars: Arg_0, Arg_1, Arg_2
Temp_Vars:
Locations: n_evalexminibb1in___6, n_evalexminibbin___5, n_evalexminientryin___7, n_evalexminireturnin___3, n_evalexminireturnin___4, n_evalexministart, n_evalexministop___1, n_evalexministop___2
Transitions:
0:n_evalexminibb1in___6(Arg_0,Arg_1,Arg_2) -> n_evalexminibbin___5(Arg_0,Arg_1,Arg_2):|:Arg_2<=Arg_0 && Arg_1<=100
1:n_evalexminibb1in___6(Arg_0,Arg_1,Arg_2) -> n_evalexminireturnin___3(Arg_0,Arg_1,Arg_2):|:1+Arg_0<=Arg_2
2:n_evalexminibb1in___6(Arg_0,Arg_1,Arg_2) -> n_evalexminireturnin___4(Arg_0,Arg_1,Arg_2):|:101<=Arg_1
3:n_evalexminibbin___5(Arg_0,Arg_1,Arg_2) -> n_evalexminibb1in___6(Arg_0-1,Arg_2,Arg_1+1):|:Arg_2<=Arg_0 && Arg_1<=100 && Arg_1<=100 && Arg_2<=Arg_0
4:n_evalexminientryin___7(Arg_0,Arg_1,Arg_2) -> n_evalexminibb1in___6(Arg_1,Arg_0,Arg_2)
5:n_evalexminireturnin___3(Arg_0,Arg_1,Arg_2) -> n_evalexministop___1(Arg_0,Arg_1,Arg_2):|:1+Arg_0<=Arg_2 && 1+Arg_0<=Arg_2
6:n_evalexminireturnin___4(Arg_0,Arg_1,Arg_2) -> n_evalexministop___2(Arg_0,Arg_1,Arg_2):|:101<=Arg_1 && 101<=Arg_1
7:n_evalexministart(Arg_0,Arg_1,Arg_2) -> n_evalexminientryin___7(Arg_0,Arg_1,Arg_2)

MPRF for transition 0:n_evalexminibb1in___6(Arg_0,Arg_1,Arg_2) -> n_evalexminibbin___5(Arg_0,Arg_1,Arg_2):|:Arg_2<=Arg_0 && Arg_1<=100 of depth 1:

new bound:

Arg_0+Arg_1+Arg_2+101 {O(n)}

MPRF:

n_evalexminibbin___5 [Arg_0+99-Arg_1-Arg_2 ]
n_evalexminibb1in___6 [Arg_0+101-Arg_1-Arg_2 ]

MPRF for transition 3:n_evalexminibbin___5(Arg_0,Arg_1,Arg_2) -> n_evalexminibb1in___6(Arg_0-1,Arg_2,Arg_1+1):|:Arg_2<=Arg_0 && Arg_1<=100 && Arg_1<=100 && Arg_2<=Arg_0 of depth 1:

new bound:

Arg_0+Arg_1+Arg_2+101 {O(n)}

MPRF:

n_evalexminibbin___5 [Arg_0+101-Arg_1-Arg_2 ]
n_evalexminibb1in___6 [Arg_0+101-Arg_1-Arg_2 ]

All Bounds

Timebounds

Overall timebound:2*Arg_0+2*Arg_1+2*Arg_2+208 {O(n)}
0: n_evalexminibb1in___6->n_evalexminibbin___5: Arg_0+Arg_1+Arg_2+101 {O(n)}
1: n_evalexminibb1in___6->n_evalexminireturnin___3: 1 {O(1)}
2: n_evalexminibb1in___6->n_evalexminireturnin___4: 1 {O(1)}
3: n_evalexminibbin___5->n_evalexminibb1in___6: Arg_0+Arg_1+Arg_2+101 {O(n)}
4: n_evalexminientryin___7->n_evalexminibb1in___6: 1 {O(1)}
5: n_evalexminireturnin___3->n_evalexministop___1: 1 {O(1)}
6: n_evalexminireturnin___4->n_evalexministop___2: 1 {O(1)}
7: n_evalexministart->n_evalexminientryin___7: 1 {O(1)}

Costbounds

Overall costbound: 2*Arg_0+2*Arg_1+2*Arg_2+208 {O(n)}
0: n_evalexminibb1in___6->n_evalexminibbin___5: Arg_0+Arg_1+Arg_2+101 {O(n)}
1: n_evalexminibb1in___6->n_evalexminireturnin___3: 1 {O(1)}
2: n_evalexminibb1in___6->n_evalexminireturnin___4: 1 {O(1)}
3: n_evalexminibbin___5->n_evalexminibb1in___6: Arg_0+Arg_1+Arg_2+101 {O(n)}
4: n_evalexminientryin___7->n_evalexminibb1in___6: 1 {O(1)}
5: n_evalexminireturnin___3->n_evalexministop___1: 1 {O(1)}
6: n_evalexminireturnin___4->n_evalexministop___2: 1 {O(1)}
7: n_evalexministart->n_evalexminientryin___7: 1 {O(1)}

Sizebounds

0: n_evalexminibb1in___6->n_evalexminibbin___5, Arg_0: 2*Arg_1+Arg_0+Arg_2+101 {O(n)}
0: n_evalexminibb1in___6->n_evalexminibbin___5, Arg_1: 2*Arg_0+2*Arg_2+Arg_1+101 {O(n)}
0: n_evalexminibb1in___6->n_evalexminibbin___5, Arg_2: 2*Arg_0+2*Arg_2+Arg_1+101 {O(n)}
1: n_evalexminibb1in___6->n_evalexminireturnin___3, Arg_0: 3*Arg_1+Arg_0+Arg_2+101 {O(n)}
1: n_evalexminibb1in___6->n_evalexminireturnin___3, Arg_1: 2*Arg_2+3*Arg_0+Arg_1+101 {O(n)}
1: n_evalexminibb1in___6->n_evalexminireturnin___3, Arg_2: 2*Arg_0+3*Arg_2+Arg_1+101 {O(n)}
2: n_evalexminibb1in___6->n_evalexminireturnin___4, Arg_0: 3*Arg_1+Arg_0+Arg_2+101 {O(n)}
2: n_evalexminibb1in___6->n_evalexminireturnin___4, Arg_1: 2*Arg_2+3*Arg_0+Arg_1+101 {O(n)}
2: n_evalexminibb1in___6->n_evalexminireturnin___4, Arg_2: 2*Arg_0+3*Arg_2+Arg_1+101 {O(n)}
3: n_evalexminibbin___5->n_evalexminibb1in___6, Arg_0: 2*Arg_1+Arg_0+Arg_2+101 {O(n)}
3: n_evalexminibbin___5->n_evalexminibb1in___6, Arg_1: 2*Arg_0+2*Arg_2+Arg_1+101 {O(n)}
3: n_evalexminibbin___5->n_evalexminibb1in___6, Arg_2: 2*Arg_0+2*Arg_2+Arg_1+101 {O(n)}
4: n_evalexminientryin___7->n_evalexminibb1in___6, Arg_0: Arg_1 {O(n)}
4: n_evalexminientryin___7->n_evalexminibb1in___6, Arg_1: Arg_0 {O(n)}
4: n_evalexminientryin___7->n_evalexminibb1in___6, Arg_2: Arg_2 {O(n)}
5: n_evalexminireturnin___3->n_evalexministop___1, Arg_0: 3*Arg_1+Arg_0+Arg_2+101 {O(n)}
5: n_evalexminireturnin___3->n_evalexministop___1, Arg_1: 2*Arg_2+3*Arg_0+Arg_1+101 {O(n)}
5: n_evalexminireturnin___3->n_evalexministop___1, Arg_2: 2*Arg_0+3*Arg_2+Arg_1+101 {O(n)}
6: n_evalexminireturnin___4->n_evalexministop___2, Arg_0: 3*Arg_1+Arg_0+Arg_2+101 {O(n)}
6: n_evalexminireturnin___4->n_evalexministop___2, Arg_1: 2*Arg_2+3*Arg_0+Arg_1+101 {O(n)}
6: n_evalexminireturnin___4->n_evalexministop___2, Arg_2: 2*Arg_0+3*Arg_2+Arg_1+101 {O(n)}
7: n_evalexministart->n_evalexminientryin___7, Arg_0: Arg_0 {O(n)}
7: n_evalexministart->n_evalexminientryin___7, Arg_1: Arg_1 {O(n)}
7: n_evalexministart->n_evalexminientryin___7, Arg_2: Arg_2 {O(n)}