Initial Problem

Start: n_eval_foo_start
Program_Vars: Arg_0, Arg_1, Arg_2
Temp_Vars:
Locations: n_eval_foo_bb0_in___8, n_eval_foo_bb1_in___3, n_eval_foo_bb1_in___5, n_eval_foo_bb1_in___7, n_eval_foo_bb2_in___4, n_eval_foo_bb2_in___6, n_eval_foo_bb3_in___2, n_eval_foo_start, n_eval_foo_stop___1
Transitions:
0:n_eval_foo_bb0_in___8(Arg_0,Arg_1,Arg_2) -> n_eval_foo_bb1_in___7(0,Arg_1,Arg_2)
1:n_eval_foo_bb1_in___3(Arg_0,Arg_1,Arg_2) -> n_eval_foo_bb2_in___4(Arg_0,Arg_1,Arg_2):|:Arg_0<=10
2:n_eval_foo_bb1_in___3(Arg_0,Arg_1,Arg_2) -> n_eval_foo_bb3_in___2(Arg_0,Arg_1,Arg_2):|:10<Arg_0
3:n_eval_foo_bb1_in___5(Arg_0,Arg_1,Arg_2) -> n_eval_foo_bb2_in___4(Arg_0,Arg_1,Arg_2):|:Arg_0<=10 && Arg_0<=10 && Arg_0<=10
4:n_eval_foo_bb1_in___7(Arg_0,Arg_1,Arg_2) -> n_eval_foo_bb2_in___6(Arg_0,Arg_1,Arg_2):|:Arg_0<=10 && Arg_0<=0 && 0<=Arg_0 && Arg_0<=10 && Arg_0<=10
5:n_eval_foo_bb2_in___4(Arg_0,Arg_1,Arg_2) -> n_eval_foo_bb1_in___3(Arg_0+1,Arg_1,Arg_2):|:Arg_0<=10
6:n_eval_foo_bb2_in___6(Arg_0,Arg_1,Arg_2) -> n_eval_foo_bb1_in___5(Arg_0+1,Arg_1,Arg_2):|:Arg_0<=0 && 0<=Arg_0
7:n_eval_foo_bb3_in___2(Arg_0,Arg_1,Arg_2) -> n_eval_foo_stop___1(Arg_0,Arg_1,Arg_2):|:10<Arg_0
8:n_eval_foo_start(Arg_0,Arg_1,Arg_2) -> n_eval_foo_bb0_in___8(Arg_0,Arg_1,Arg_2)

Preprocessing

Eliminate variables {Arg_1,Arg_2} that do not contribute to the problem

Found invariant Arg_0<=10 && 1<=Arg_0 for location n_eval_foo_bb2_in___4

Found invariant Arg_0<=11 && 11<=Arg_0 for location n_eval_foo_bb3_in___2

Found invariant Arg_0<=0 && 0<=Arg_0 for location n_eval_foo_bb1_in___7

Found invariant Arg_0<=11 && 2<=Arg_0 for location n_eval_foo_bb1_in___3

Found invariant Arg_0<=1 && 1<=Arg_0 for location n_eval_foo_bb1_in___5

Found invariant Arg_0<=11 && 11<=Arg_0 for location n_eval_foo_stop___1

Found invariant Arg_0<=0 && 0<=Arg_0 for location n_eval_foo_bb2_in___6

Problem after Preprocessing

Start: n_eval_foo_start
Program_Vars: Arg_0
Temp_Vars:
Locations: n_eval_foo_bb0_in___8, n_eval_foo_bb1_in___3, n_eval_foo_bb1_in___5, n_eval_foo_bb1_in___7, n_eval_foo_bb2_in___4, n_eval_foo_bb2_in___6, n_eval_foo_bb3_in___2, n_eval_foo_start, n_eval_foo_stop___1
Transitions:
18:n_eval_foo_bb0_in___8(Arg_0) -> n_eval_foo_bb1_in___7(0)
19:n_eval_foo_bb1_in___3(Arg_0) -> n_eval_foo_bb2_in___4(Arg_0):|:Arg_0<=11 && 2<=Arg_0 && Arg_0<=10
20:n_eval_foo_bb1_in___3(Arg_0) -> n_eval_foo_bb3_in___2(Arg_0):|:Arg_0<=11 && 2<=Arg_0 && 10<Arg_0
21:n_eval_foo_bb1_in___5(Arg_0) -> n_eval_foo_bb2_in___4(Arg_0):|:Arg_0<=1 && 1<=Arg_0 && Arg_0<=10 && Arg_0<=10 && Arg_0<=10
22:n_eval_foo_bb1_in___7(Arg_0) -> n_eval_foo_bb2_in___6(Arg_0):|:Arg_0<=0 && 0<=Arg_0 && Arg_0<=10 && Arg_0<=0 && 0<=Arg_0 && Arg_0<=10 && Arg_0<=10
23:n_eval_foo_bb2_in___4(Arg_0) -> n_eval_foo_bb1_in___3(Arg_0+1):|:Arg_0<=10 && 1<=Arg_0 && Arg_0<=10
24:n_eval_foo_bb2_in___6(Arg_0) -> n_eval_foo_bb1_in___5(Arg_0+1):|:Arg_0<=0 && 0<=Arg_0 && Arg_0<=0 && 0<=Arg_0
25:n_eval_foo_bb3_in___2(Arg_0) -> n_eval_foo_stop___1(Arg_0):|:Arg_0<=11 && 11<=Arg_0 && 10<Arg_0
26:n_eval_foo_start(Arg_0) -> n_eval_foo_bb0_in___8(Arg_0)

MPRF for transition 19:n_eval_foo_bb1_in___3(Arg_0) -> n_eval_foo_bb2_in___4(Arg_0):|:Arg_0<=11 && 2<=Arg_0 && Arg_0<=10 of depth 1:

new bound:

11 {O(1)}

MPRF:

n_eval_foo_bb2_in___4 [10-Arg_0 ]
n_eval_foo_bb1_in___3 [11-Arg_0 ]

MPRF for transition 23:n_eval_foo_bb2_in___4(Arg_0) -> n_eval_foo_bb1_in___3(Arg_0+1):|:Arg_0<=10 && 1<=Arg_0 && Arg_0<=10 of depth 1:

new bound:

12 {O(1)}

MPRF:

n_eval_foo_bb2_in___4 [11-Arg_0 ]
n_eval_foo_bb1_in___3 [11-Arg_0 ]

All Bounds

Timebounds

Overall timebound:30 {O(1)}
18: n_eval_foo_bb0_in___8->n_eval_foo_bb1_in___7: 1 {O(1)}
19: n_eval_foo_bb1_in___3->n_eval_foo_bb2_in___4: 11 {O(1)}
20: n_eval_foo_bb1_in___3->n_eval_foo_bb3_in___2: 1 {O(1)}
21: n_eval_foo_bb1_in___5->n_eval_foo_bb2_in___4: 1 {O(1)}
22: n_eval_foo_bb1_in___7->n_eval_foo_bb2_in___6: 1 {O(1)}
23: n_eval_foo_bb2_in___4->n_eval_foo_bb1_in___3: 12 {O(1)}
24: n_eval_foo_bb2_in___6->n_eval_foo_bb1_in___5: 1 {O(1)}
25: n_eval_foo_bb3_in___2->n_eval_foo_stop___1: 1 {O(1)}
26: n_eval_foo_start->n_eval_foo_bb0_in___8: 1 {O(1)}

Costbounds

Overall costbound: 30 {O(1)}
18: n_eval_foo_bb0_in___8->n_eval_foo_bb1_in___7: 1 {O(1)}
19: n_eval_foo_bb1_in___3->n_eval_foo_bb2_in___4: 11 {O(1)}
20: n_eval_foo_bb1_in___3->n_eval_foo_bb3_in___2: 1 {O(1)}
21: n_eval_foo_bb1_in___5->n_eval_foo_bb2_in___4: 1 {O(1)}
22: n_eval_foo_bb1_in___7->n_eval_foo_bb2_in___6: 1 {O(1)}
23: n_eval_foo_bb2_in___4->n_eval_foo_bb1_in___3: 12 {O(1)}
24: n_eval_foo_bb2_in___6->n_eval_foo_bb1_in___5: 1 {O(1)}
25: n_eval_foo_bb3_in___2->n_eval_foo_stop___1: 1 {O(1)}
26: n_eval_foo_start->n_eval_foo_bb0_in___8: 1 {O(1)}

Sizebounds

18: n_eval_foo_bb0_in___8->n_eval_foo_bb1_in___7, Arg_0: 0 {O(1)}
19: n_eval_foo_bb1_in___3->n_eval_foo_bb2_in___4, Arg_0: 10 {O(1)}
20: n_eval_foo_bb1_in___3->n_eval_foo_bb3_in___2, Arg_0: 11 {O(1)}
21: n_eval_foo_bb1_in___5->n_eval_foo_bb2_in___4, Arg_0: 1 {O(1)}
22: n_eval_foo_bb1_in___7->n_eval_foo_bb2_in___6, Arg_0: 0 {O(1)}
23: n_eval_foo_bb2_in___4->n_eval_foo_bb1_in___3, Arg_0: 11 {O(1)}
24: n_eval_foo_bb2_in___6->n_eval_foo_bb1_in___5, Arg_0: 1 {O(1)}
25: n_eval_foo_bb3_in___2->n_eval_foo_stop___1, Arg_0: 11 {O(1)}
26: n_eval_foo_start->n_eval_foo_bb0_in___8, Arg_0: Arg_0 {O(n)}