Initial Problem

Start: n_eval_foo_start
Program_Vars: Arg_0, Arg_1, Arg_2
Temp_Vars:
Locations: n_eval_foo_bb0_in___7, n_eval_foo_bb1_in___5, n_eval_foo_bb1_in___6, n_eval_foo_bb2_in___3, n_eval_foo_bb2_in___4, n_eval_foo_start, n_eval_foo_stop___1, n_eval_foo_stop___2
Transitions:
0:n_eval_foo_bb0_in___7(Arg_0,Arg_1,Arg_2) -> n_eval_foo_bb1_in___6(Arg_0,Arg_1,Arg_1)
1:n_eval_foo_bb1_in___5(Arg_0,Arg_1,Arg_2) -> n_eval_foo_bb1_in___5(Arg_0,Arg_1,Arg_2-1):|:2<Arg_2
2:n_eval_foo_bb1_in___5(Arg_0,Arg_1,Arg_2) -> n_eval_foo_bb2_in___3(Arg_0,Arg_1,Arg_2):|:Arg_2<=2
3:n_eval_foo_bb1_in___6(Arg_0,Arg_1,Arg_2) -> n_eval_foo_bb1_in___5(Arg_0,Arg_1,Arg_2-1):|:Arg_1<=Arg_2 && Arg_2<=Arg_1 && 2<Arg_2
4:n_eval_foo_bb1_in___6(Arg_0,Arg_1,Arg_2) -> n_eval_foo_bb2_in___4(Arg_0,Arg_1,Arg_2):|:Arg_1<=Arg_2 && Arg_2<=Arg_1 && Arg_2<=2
5:n_eval_foo_bb2_in___3(Arg_0,Arg_1,Arg_2) -> n_eval_foo_stop___2(Arg_0,Arg_1,Arg_2):|:Arg_2<=2
6:n_eval_foo_bb2_in___4(Arg_0,Arg_1,Arg_2) -> n_eval_foo_stop___1(Arg_0,Arg_1,Arg_2):|:Arg_1<=2 && Arg_1<=Arg_2 && Arg_2<=Arg_1
7:n_eval_foo_start(Arg_0,Arg_1,Arg_2) -> n_eval_foo_bb0_in___7(Arg_0,Arg_1,Arg_2)

Preprocessing

Eliminate variables {Arg_0} that do not contribute to the problem

Found invariant Arg_2<=2 && Arg_2<=Arg_1 && Arg_1+Arg_2<=4 && Arg_1<=Arg_2 && Arg_1<=2 for location n_eval_foo_bb2_in___4

Found invariant Arg_2<=2 && 1+Arg_2<=Arg_1 && 2<=Arg_2 && 5<=Arg_1+Arg_2 && 3<=Arg_1 for location n_eval_foo_stop___2

Found invariant 1+Arg_2<=Arg_1 && 2<=Arg_2 && 5<=Arg_1+Arg_2 && 3<=Arg_1 for location n_eval_foo_bb1_in___5

Found invariant Arg_2<=2 && Arg_2<=Arg_1 && Arg_1+Arg_2<=4 && Arg_1<=Arg_2 && Arg_1<=2 for location n_eval_foo_stop___1

Found invariant Arg_2<=2 && 1+Arg_2<=Arg_1 && 2<=Arg_2 && 5<=Arg_1+Arg_2 && 3<=Arg_1 for location n_eval_foo_bb2_in___3

Found invariant Arg_2<=Arg_1 && Arg_1<=Arg_2 for location n_eval_foo_bb1_in___6

Problem after Preprocessing

Start: n_eval_foo_start
Program_Vars: Arg_1, Arg_2
Temp_Vars:
Locations: n_eval_foo_bb0_in___7, n_eval_foo_bb1_in___5, n_eval_foo_bb1_in___6, n_eval_foo_bb2_in___3, n_eval_foo_bb2_in___4, n_eval_foo_start, n_eval_foo_stop___1, n_eval_foo_stop___2
Transitions:
16:n_eval_foo_bb0_in___7(Arg_1,Arg_2) -> n_eval_foo_bb1_in___6(Arg_1,Arg_1)
17:n_eval_foo_bb1_in___5(Arg_1,Arg_2) -> n_eval_foo_bb1_in___5(Arg_1,Arg_2-1):|:1+Arg_2<=Arg_1 && 2<=Arg_2 && 5<=Arg_1+Arg_2 && 3<=Arg_1 && 2<Arg_2
18:n_eval_foo_bb1_in___5(Arg_1,Arg_2) -> n_eval_foo_bb2_in___3(Arg_1,Arg_2):|:1+Arg_2<=Arg_1 && 2<=Arg_2 && 5<=Arg_1+Arg_2 && 3<=Arg_1 && Arg_2<=2
19:n_eval_foo_bb1_in___6(Arg_1,Arg_2) -> n_eval_foo_bb1_in___5(Arg_1,Arg_2-1):|:Arg_2<=Arg_1 && Arg_1<=Arg_2 && Arg_1<=Arg_2 && Arg_2<=Arg_1 && 2<Arg_2
20:n_eval_foo_bb1_in___6(Arg_1,Arg_2) -> n_eval_foo_bb2_in___4(Arg_1,Arg_2):|:Arg_2<=Arg_1 && Arg_1<=Arg_2 && Arg_1<=Arg_2 && Arg_2<=Arg_1 && Arg_2<=2
21:n_eval_foo_bb2_in___3(Arg_1,Arg_2) -> n_eval_foo_stop___2(Arg_1,Arg_2):|:Arg_2<=2 && 1+Arg_2<=Arg_1 && 2<=Arg_2 && 5<=Arg_1+Arg_2 && 3<=Arg_1 && Arg_2<=2
22:n_eval_foo_bb2_in___4(Arg_1,Arg_2) -> n_eval_foo_stop___1(Arg_1,Arg_2):|:Arg_2<=2 && Arg_2<=Arg_1 && Arg_1+Arg_2<=4 && Arg_1<=Arg_2 && Arg_1<=2 && Arg_1<=2 && Arg_1<=Arg_2 && Arg_2<=Arg_1
23:n_eval_foo_start(Arg_1,Arg_2) -> n_eval_foo_bb0_in___7(Arg_1,Arg_2)

MPRF for transition 17:n_eval_foo_bb1_in___5(Arg_1,Arg_2) -> n_eval_foo_bb1_in___5(Arg_1,Arg_2-1):|:1+Arg_2<=Arg_1 && 2<=Arg_2 && 5<=Arg_1+Arg_2 && 3<=Arg_1 && 2<Arg_2 of depth 1:

new bound:

Arg_1 {O(n)}

MPRF:

n_eval_foo_bb1_in___5 [Arg_2 ]

All Bounds

Timebounds

Overall timebound:Arg_1+7 {O(n)}
16: n_eval_foo_bb0_in___7->n_eval_foo_bb1_in___6: 1 {O(1)}
17: n_eval_foo_bb1_in___5->n_eval_foo_bb1_in___5: Arg_1 {O(n)}
18: n_eval_foo_bb1_in___5->n_eval_foo_bb2_in___3: 1 {O(1)}
19: n_eval_foo_bb1_in___6->n_eval_foo_bb1_in___5: 1 {O(1)}
20: n_eval_foo_bb1_in___6->n_eval_foo_bb2_in___4: 1 {O(1)}
21: n_eval_foo_bb2_in___3->n_eval_foo_stop___2: 1 {O(1)}
22: n_eval_foo_bb2_in___4->n_eval_foo_stop___1: 1 {O(1)}
23: n_eval_foo_start->n_eval_foo_bb0_in___7: 1 {O(1)}

Costbounds

Overall costbound: Arg_1+7 {O(n)}
16: n_eval_foo_bb0_in___7->n_eval_foo_bb1_in___6: 1 {O(1)}
17: n_eval_foo_bb1_in___5->n_eval_foo_bb1_in___5: Arg_1 {O(n)}
18: n_eval_foo_bb1_in___5->n_eval_foo_bb2_in___3: 1 {O(1)}
19: n_eval_foo_bb1_in___6->n_eval_foo_bb1_in___5: 1 {O(1)}
20: n_eval_foo_bb1_in___6->n_eval_foo_bb2_in___4: 1 {O(1)}
21: n_eval_foo_bb2_in___3->n_eval_foo_stop___2: 1 {O(1)}
22: n_eval_foo_bb2_in___4->n_eval_foo_stop___1: 1 {O(1)}
23: n_eval_foo_start->n_eval_foo_bb0_in___7: 1 {O(1)}

Sizebounds

16: n_eval_foo_bb0_in___7->n_eval_foo_bb1_in___6, Arg_1: Arg_1 {O(n)}
16: n_eval_foo_bb0_in___7->n_eval_foo_bb1_in___6, Arg_2: Arg_1 {O(n)}
17: n_eval_foo_bb1_in___5->n_eval_foo_bb1_in___5, Arg_1: Arg_1 {O(n)}
17: n_eval_foo_bb1_in___5->n_eval_foo_bb1_in___5, Arg_2: Arg_1 {O(n)}
18: n_eval_foo_bb1_in___5->n_eval_foo_bb2_in___3, Arg_1: 2*Arg_1 {O(n)}
18: n_eval_foo_bb1_in___5->n_eval_foo_bb2_in___3, Arg_2: 2 {O(1)}
19: n_eval_foo_bb1_in___6->n_eval_foo_bb1_in___5, Arg_1: Arg_1 {O(n)}
19: n_eval_foo_bb1_in___6->n_eval_foo_bb1_in___5, Arg_2: Arg_1 {O(n)}
20: n_eval_foo_bb1_in___6->n_eval_foo_bb2_in___4, Arg_1: Arg_1 {O(n)}
20: n_eval_foo_bb1_in___6->n_eval_foo_bb2_in___4, Arg_2: Arg_1 {O(n)}
21: n_eval_foo_bb2_in___3->n_eval_foo_stop___2, Arg_1: 2*Arg_1 {O(n)}
21: n_eval_foo_bb2_in___3->n_eval_foo_stop___2, Arg_2: 2 {O(1)}
22: n_eval_foo_bb2_in___4->n_eval_foo_stop___1, Arg_1: Arg_1 {O(n)}
22: n_eval_foo_bb2_in___4->n_eval_foo_stop___1, Arg_2: Arg_1 {O(n)}
23: n_eval_foo_start->n_eval_foo_bb0_in___7, Arg_1: Arg_1 {O(n)}
23: n_eval_foo_start->n_eval_foo_bb0_in___7, Arg_2: Arg_2 {O(n)}