Initial Problem

Start: n_evalfstart
Program_Vars: Arg_0, Arg_1
Temp_Vars:
Locations: n_evalfbb1in___4, n_evalfbbin___3, n_evalfentryin___5, n_evalfreturnin___2, n_evalfstart, n_evalfstop___1
Transitions:
0:n_evalfbb1in___4(Arg_0,Arg_1) -> n_evalfbbin___3(Arg_0,Arg_1):|:Arg_1<=Arg_0
1:n_evalfbb1in___4(Arg_0,Arg_1) -> n_evalfreturnin___2(Arg_0,Arg_1):|:1+Arg_0<=Arg_1
2:n_evalfbbin___3(Arg_0,Arg_1) -> n_evalfbb1in___4(Arg_0,Arg_1+1):|:Arg_1<=Arg_0
3:n_evalfentryin___5(Arg_0,Arg_1) -> n_evalfbb1in___4(Arg_1,Arg_0)
4:n_evalfreturnin___2(Arg_0,Arg_1) -> n_evalfstop___1(Arg_0,Arg_1):|:1+Arg_0<=Arg_1
5:n_evalfstart(Arg_0,Arg_1) -> n_evalfentryin___5(Arg_0,Arg_1)

Preprocessing

Found invariant 1+Arg_0<=Arg_1 for location n_evalfreturnin___2

Found invariant 1+Arg_0<=Arg_1 for location n_evalfstop___1

Found invariant Arg_1<=Arg_0 for location n_evalfbbin___3

Problem after Preprocessing

Start: n_evalfstart
Program_Vars: Arg_0, Arg_1
Temp_Vars:
Locations: n_evalfbb1in___4, n_evalfbbin___3, n_evalfentryin___5, n_evalfreturnin___2, n_evalfstart, n_evalfstop___1
Transitions:
0:n_evalfbb1in___4(Arg_0,Arg_1) -> n_evalfbbin___3(Arg_0,Arg_1):|:Arg_1<=Arg_0
1:n_evalfbb1in___4(Arg_0,Arg_1) -> n_evalfreturnin___2(Arg_0,Arg_1):|:1+Arg_0<=Arg_1
2:n_evalfbbin___3(Arg_0,Arg_1) -> n_evalfbb1in___4(Arg_0,Arg_1+1):|:Arg_1<=Arg_0 && Arg_1<=Arg_0
3:n_evalfentryin___5(Arg_0,Arg_1) -> n_evalfbb1in___4(Arg_1,Arg_0)
4:n_evalfreturnin___2(Arg_0,Arg_1) -> n_evalfstop___1(Arg_0,Arg_1):|:1+Arg_0<=Arg_1 && 1+Arg_0<=Arg_1
5:n_evalfstart(Arg_0,Arg_1) -> n_evalfentryin___5(Arg_0,Arg_1)

MPRF for transition 0:n_evalfbb1in___4(Arg_0,Arg_1) -> n_evalfbbin___3(Arg_0,Arg_1):|:Arg_1<=Arg_0 of depth 1:

new bound:

Arg_0+Arg_1+1 {O(n)}

MPRF:

n_evalfbbin___3 [Arg_0-Arg_1 ]
n_evalfbb1in___4 [Arg_0+1-Arg_1 ]

MPRF for transition 2:n_evalfbbin___3(Arg_0,Arg_1) -> n_evalfbb1in___4(Arg_0,Arg_1+1):|:Arg_1<=Arg_0 && Arg_1<=Arg_0 of depth 1:

new bound:

Arg_0+Arg_1+1 {O(n)}

MPRF:

n_evalfbbin___3 [Arg_0+1-Arg_1 ]
n_evalfbb1in___4 [Arg_0+1-Arg_1 ]

All Bounds

Timebounds

Overall timebound:2*Arg_0+2*Arg_1+6 {O(n)}
0: n_evalfbb1in___4->n_evalfbbin___3: Arg_0+Arg_1+1 {O(n)}
1: n_evalfbb1in___4->n_evalfreturnin___2: 1 {O(1)}
2: n_evalfbbin___3->n_evalfbb1in___4: Arg_0+Arg_1+1 {O(n)}
3: n_evalfentryin___5->n_evalfbb1in___4: 1 {O(1)}
4: n_evalfreturnin___2->n_evalfstop___1: 1 {O(1)}
5: n_evalfstart->n_evalfentryin___5: 1 {O(1)}

Costbounds

Overall costbound: 2*Arg_0+2*Arg_1+6 {O(n)}
0: n_evalfbb1in___4->n_evalfbbin___3: Arg_0+Arg_1+1 {O(n)}
1: n_evalfbb1in___4->n_evalfreturnin___2: 1 {O(1)}
2: n_evalfbbin___3->n_evalfbb1in___4: Arg_0+Arg_1+1 {O(n)}
3: n_evalfentryin___5->n_evalfbb1in___4: 1 {O(1)}
4: n_evalfreturnin___2->n_evalfstop___1: 1 {O(1)}
5: n_evalfstart->n_evalfentryin___5: 1 {O(1)}

Sizebounds

0: n_evalfbb1in___4->n_evalfbbin___3, Arg_0: Arg_1 {O(n)}
0: n_evalfbb1in___4->n_evalfbbin___3, Arg_1: 2*Arg_0+Arg_1+1 {O(n)}
1: n_evalfbb1in___4->n_evalfreturnin___2, Arg_0: 2*Arg_1 {O(n)}
1: n_evalfbb1in___4->n_evalfreturnin___2, Arg_1: 3*Arg_0+Arg_1+1 {O(n)}
2: n_evalfbbin___3->n_evalfbb1in___4, Arg_0: Arg_1 {O(n)}
2: n_evalfbbin___3->n_evalfbb1in___4, Arg_1: 2*Arg_0+Arg_1+1 {O(n)}
3: n_evalfentryin___5->n_evalfbb1in___4, Arg_0: Arg_1 {O(n)}
3: n_evalfentryin___5->n_evalfbb1in___4, Arg_1: Arg_0 {O(n)}
4: n_evalfreturnin___2->n_evalfstop___1, Arg_0: 2*Arg_1 {O(n)}
4: n_evalfreturnin___2->n_evalfstop___1, Arg_1: 3*Arg_0+Arg_1+1 {O(n)}
5: n_evalfstart->n_evalfentryin___5, Arg_0: Arg_0 {O(n)}
5: n_evalfstart->n_evalfentryin___5, Arg_1: Arg_1 {O(n)}