Initial Problem

Start: eval_foo_start
Program_Vars: Arg_0, Arg_1, Arg_2, Arg_3
Temp_Vars:
Locations: eval_foo_bb0_in, eval_foo_bb1_in, eval_foo_bb2_in, eval_foo_bb3_in, eval_foo_start, eval_foo_stop
Transitions:
1:eval_foo_bb0_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_foo_bb1_in(Arg_2,Arg_3,Arg_2,Arg_3)
2:eval_foo_bb1_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_foo_bb2_in(Arg_0,Arg_1,Arg_2,Arg_3):|:Arg_1<Arg_0
3:eval_foo_bb1_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_foo_bb3_in(Arg_0,Arg_1,Arg_2,Arg_3):|:Arg_0<=Arg_1
4:eval_foo_bb2_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_foo_bb1_in(Arg_1-Arg_0,Arg_1+1,Arg_2,Arg_3)
5:eval_foo_bb3_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_foo_stop(Arg_0,Arg_1,Arg_2,Arg_3)
0:eval_foo_start(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_foo_bb0_in(Arg_0,Arg_1,Arg_2,Arg_3)

Preprocessing

Found invariant Arg_3<=Arg_1 && Arg_0<=Arg_1 for location eval_foo_stop

Found invariant Arg_3<=Arg_1 && Arg_0<=Arg_1 for location eval_foo_bb3_in

Found invariant Arg_3<=Arg_1 && 1+Arg_3<=Arg_0 && 1+Arg_1<=Arg_0 for location eval_foo_bb2_in

Found invariant Arg_3<=Arg_1 for location eval_foo_bb1_in

Problem after Preprocessing

Start: eval_foo_start
Program_Vars: Arg_0, Arg_1, Arg_2, Arg_3
Temp_Vars:
Locations: eval_foo_bb0_in, eval_foo_bb1_in, eval_foo_bb2_in, eval_foo_bb3_in, eval_foo_start, eval_foo_stop
Transitions:
1:eval_foo_bb0_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_foo_bb1_in(Arg_2,Arg_3,Arg_2,Arg_3)
2:eval_foo_bb1_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_foo_bb2_in(Arg_0,Arg_1,Arg_2,Arg_3):|:Arg_3<=Arg_1 && Arg_1<Arg_0
3:eval_foo_bb1_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_foo_bb3_in(Arg_0,Arg_1,Arg_2,Arg_3):|:Arg_3<=Arg_1 && Arg_0<=Arg_1
4:eval_foo_bb2_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_foo_bb1_in(Arg_1-Arg_0,Arg_1+1,Arg_2,Arg_3):|:Arg_3<=Arg_1 && 1+Arg_3<=Arg_0 && 1+Arg_1<=Arg_0
5:eval_foo_bb3_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_foo_stop(Arg_0,Arg_1,Arg_2,Arg_3):|:Arg_3<=Arg_1 && Arg_0<=Arg_1
0:eval_foo_start(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_foo_bb0_in(Arg_0,Arg_1,Arg_2,Arg_3)

Analysing control-flow refined program

Found invariant Arg_3<=Arg_1 && Arg_0<=Arg_1 for location eval_foo_stop

Found invariant Arg_3<=Arg_1 && Arg_0<=Arg_1 for location eval_foo_bb3_in

Found invariant 1+Arg_3<=Arg_2 && 1+Arg_3<=Arg_1 for location n_eval_foo_bb1_in___2

Found invariant 3+Arg_3<=0 && 1+Arg_3<=Arg_2 && 1+Arg_3<=Arg_1 && 5+Arg_1+Arg_3<=0 && 2+Arg_3<=Arg_0 && 4+Arg_0+Arg_3<=0 && 2+Arg_1<=0 && 1+Arg_1<=Arg_0 && 3+Arg_0+Arg_1<=0 && 1+Arg_0<=0 for location n_eval_foo_bb2_in___1

Found invariant Arg_3<=Arg_1 && Arg_1<=Arg_3 && Arg_2<=Arg_0 && Arg_0<=Arg_2 for location eval_foo_bb1_in

Found invariant 1+Arg_3<=Arg_2 && Arg_3<=Arg_1 && 1+Arg_3<=Arg_0 && Arg_1<=Arg_3 && Arg_2<=Arg_0 && 1+Arg_1<=Arg_2 && Arg_0<=Arg_2 && 1+Arg_1<=Arg_0 for location n_eval_foo_bb2_in___3

MPRF for transition 37:n_eval_foo_bb1_in___2(Arg_0,Arg_1,Arg_2,Arg_3) -> n_eval_foo_bb2_in___1(Arg_0,Arg_1,Arg_2,Arg_3):|:1+Arg_3<=Arg_2 && 1+Arg_3<=Arg_1 && Arg_3<=Arg_1 && 1+Arg_3<=Arg_1 && 1+Arg_0<=0 && Arg_1<Arg_0 && Arg_3<=Arg_1 of depth 1:

new bound:

Arg_3+2 {O(n)}

MPRF:

n_eval_foo_bb2_in___1 [-Arg_1-2 ]
n_eval_foo_bb1_in___2 [-Arg_1-1 ]

MPRF for transition 39:n_eval_foo_bb2_in___1(Arg_0,Arg_1,Arg_2,Arg_3) -> n_eval_foo_bb1_in___2(Arg_1-Arg_0,Arg_1+1,Arg_2,Arg_3):|:3+Arg_3<=0 && 1+Arg_3<=Arg_2 && 1+Arg_3<=Arg_1 && 5+Arg_1+Arg_3<=0 && 2+Arg_3<=Arg_0 && 4+Arg_0+Arg_3<=0 && 2+Arg_1<=0 && 1+Arg_1<=Arg_0 && 3+Arg_0+Arg_1<=0 && 1+Arg_0<=0 && 1+Arg_0<=0 && Arg_1<Arg_0 && 1+Arg_3<=Arg_1 && 1+Arg_1<=Arg_0 && Arg_3<=Arg_1 of depth 1:

new bound:

Arg_3+2 {O(n)}

MPRF:

n_eval_foo_bb2_in___1 [-Arg_1-1 ]
n_eval_foo_bb1_in___2 [-Arg_1-1 ]

CFR: Improvement to new bound with the following program:

new bound:

2*Arg_3+4 {O(n)}

cfr-program:

Start: eval_foo_start
Program_Vars: Arg_0, Arg_1, Arg_2, Arg_3
Temp_Vars:
Locations: eval_foo_bb0_in, eval_foo_bb1_in, eval_foo_bb3_in, eval_foo_start, eval_foo_stop, n_eval_foo_bb1_in___2, n_eval_foo_bb2_in___1, n_eval_foo_bb2_in___3
Transitions:
1:eval_foo_bb0_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_foo_bb1_in(Arg_2,Arg_3,Arg_2,Arg_3)
3:eval_foo_bb1_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_foo_bb3_in(Arg_0,Arg_1,Arg_2,Arg_3):|:Arg_3<=Arg_1 && Arg_1<=Arg_3 && Arg_2<=Arg_0 && Arg_0<=Arg_2 && Arg_3<=Arg_1 && Arg_0<=Arg_1
38:eval_foo_bb1_in(Arg_0,Arg_1,Arg_2,Arg_3) -> n_eval_foo_bb2_in___3(Arg_0,Arg_1,Arg_2,Arg_3):|:Arg_3<=Arg_1 && Arg_1<=Arg_3 && Arg_2<=Arg_0 && Arg_0<=Arg_2 && Arg_3<=Arg_1 && Arg_1<=Arg_3 && Arg_3<=Arg_1 && Arg_0<=Arg_2 && Arg_2<=Arg_0 && Arg_1<Arg_0 && Arg_3<=Arg_1
5:eval_foo_bb3_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_foo_stop(Arg_0,Arg_1,Arg_2,Arg_3):|:Arg_3<=Arg_1 && Arg_0<=Arg_1 && Arg_3<=Arg_1 && Arg_0<=Arg_1
0:eval_foo_start(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_foo_bb0_in(Arg_0,Arg_1,Arg_2,Arg_3)
45:n_eval_foo_bb1_in___2(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_foo_bb3_in(Arg_0,Arg_1,Arg_2,Arg_3):|:1+Arg_3<=Arg_2 && 1+Arg_3<=Arg_1 && Arg_3<=Arg_1 && Arg_0<=Arg_1
37:n_eval_foo_bb1_in___2(Arg_0,Arg_1,Arg_2,Arg_3) -> n_eval_foo_bb2_in___1(Arg_0,Arg_1,Arg_2,Arg_3):|:1+Arg_3<=Arg_2 && 1+Arg_3<=Arg_1 && Arg_3<=Arg_1 && 1+Arg_3<=Arg_1 && 1+Arg_0<=0 && Arg_1<Arg_0 && Arg_3<=Arg_1
39:n_eval_foo_bb2_in___1(Arg_0,Arg_1,Arg_2,Arg_3) -> n_eval_foo_bb1_in___2(Arg_1-Arg_0,Arg_1+1,Arg_2,Arg_3):|:3+Arg_3<=0 && 1+Arg_3<=Arg_2 && 1+Arg_3<=Arg_1 && 5+Arg_1+Arg_3<=0 && 2+Arg_3<=Arg_0 && 4+Arg_0+Arg_3<=0 && 2+Arg_1<=0 && 1+Arg_1<=Arg_0 && 3+Arg_0+Arg_1<=0 && 1+Arg_0<=0 && 1+Arg_0<=0 && Arg_1<Arg_0 && 1+Arg_3<=Arg_1 && 1+Arg_1<=Arg_0 && Arg_3<=Arg_1
40:n_eval_foo_bb2_in___3(Arg_0,Arg_1,Arg_2,Arg_3) -> n_eval_foo_bb1_in___2(Arg_1-Arg_0,Arg_1+1,Arg_2,Arg_3):|:1+Arg_3<=Arg_2 && Arg_3<=Arg_1 && 1+Arg_3<=Arg_0 && Arg_1<=Arg_3 && Arg_2<=Arg_0 && 1+Arg_1<=Arg_2 && Arg_0<=Arg_2 && 1+Arg_1<=Arg_0 && Arg_1<Arg_0 && Arg_1<=Arg_3 && Arg_3<=Arg_1 && Arg_0<=Arg_2 && Arg_2<=Arg_0 && 1+Arg_1<=Arg_0 && Arg_3<=Arg_1

All Bounds

Timebounds

Overall timebound:2*Arg_3+11 {O(n)}
1: eval_foo_bb0_in->eval_foo_bb1_in: 1 {O(1)}
3: eval_foo_bb1_in->eval_foo_bb3_in: 1 {O(1)}
38: eval_foo_bb1_in->n_eval_foo_bb2_in___3: 1 {O(1)}
5: eval_foo_bb3_in->eval_foo_stop: 1 {O(1)}
0: eval_foo_start->eval_foo_bb0_in: 1 {O(1)}
37: n_eval_foo_bb1_in___2->n_eval_foo_bb2_in___1: Arg_3+2 {O(n)}
45: n_eval_foo_bb1_in___2->eval_foo_bb3_in: 1 {O(1)}
39: n_eval_foo_bb2_in___1->n_eval_foo_bb1_in___2: Arg_3+2 {O(n)}
40: n_eval_foo_bb2_in___3->n_eval_foo_bb1_in___2: 1 {O(1)}

Costbounds

Overall costbound: 2*Arg_3+11 {O(n)}
1: eval_foo_bb0_in->eval_foo_bb1_in: 1 {O(1)}
3: eval_foo_bb1_in->eval_foo_bb3_in: 1 {O(1)}
38: eval_foo_bb1_in->n_eval_foo_bb2_in___3: 1 {O(1)}
5: eval_foo_bb3_in->eval_foo_stop: 1 {O(1)}
0: eval_foo_start->eval_foo_bb0_in: 1 {O(1)}
37: n_eval_foo_bb1_in___2->n_eval_foo_bb2_in___1: Arg_3+2 {O(n)}
45: n_eval_foo_bb1_in___2->eval_foo_bb3_in: 1 {O(1)}
39: n_eval_foo_bb2_in___1->n_eval_foo_bb1_in___2: Arg_3+2 {O(n)}
40: n_eval_foo_bb2_in___3->n_eval_foo_bb1_in___2: 1 {O(1)}

Sizebounds

1: eval_foo_bb0_in->eval_foo_bb1_in, Arg_0: Arg_2 {O(n)}
1: eval_foo_bb0_in->eval_foo_bb1_in, Arg_1: Arg_3 {O(n)}
1: eval_foo_bb0_in->eval_foo_bb1_in, Arg_2: Arg_2 {O(n)}
1: eval_foo_bb0_in->eval_foo_bb1_in, Arg_3: Arg_3 {O(n)}
3: eval_foo_bb1_in->eval_foo_bb3_in, Arg_0: Arg_2 {O(n)}
3: eval_foo_bb1_in->eval_foo_bb3_in, Arg_1: Arg_3 {O(n)}
3: eval_foo_bb1_in->eval_foo_bb3_in, Arg_2: Arg_2 {O(n)}
3: eval_foo_bb1_in->eval_foo_bb3_in, Arg_3: Arg_3 {O(n)}
38: eval_foo_bb1_in->n_eval_foo_bb2_in___3, Arg_0: Arg_2 {O(n)}
38: eval_foo_bb1_in->n_eval_foo_bb2_in___3, Arg_1: Arg_3 {O(n)}
38: eval_foo_bb1_in->n_eval_foo_bb2_in___3, Arg_2: Arg_2 {O(n)}
38: eval_foo_bb1_in->n_eval_foo_bb2_in___3, Arg_3: Arg_3 {O(n)}
5: eval_foo_bb3_in->eval_foo_stop, Arg_0: 2*Arg_2+2*Arg_3+1 {O(n)}
5: eval_foo_bb3_in->eval_foo_stop, Arg_1: 3*Arg_3+2 {O(n)}
5: eval_foo_bb3_in->eval_foo_stop, Arg_2: 3*Arg_2 {O(n)}
5: eval_foo_bb3_in->eval_foo_stop, Arg_3: 3*Arg_3 {O(n)}
0: eval_foo_start->eval_foo_bb0_in, Arg_0: Arg_0 {O(n)}
0: eval_foo_start->eval_foo_bb0_in, Arg_1: Arg_1 {O(n)}
0: eval_foo_start->eval_foo_bb0_in, Arg_2: Arg_2 {O(n)}
0: eval_foo_start->eval_foo_bb0_in, Arg_3: Arg_3 {O(n)}
37: n_eval_foo_bb1_in___2->n_eval_foo_bb2_in___1, Arg_0: 2*Arg_3+Arg_2+1 {O(n)}
37: n_eval_foo_bb1_in___2->n_eval_foo_bb2_in___1, Arg_1: Arg_3+1 {O(n)}
37: n_eval_foo_bb1_in___2->n_eval_foo_bb2_in___1, Arg_2: Arg_2 {O(n)}
37: n_eval_foo_bb1_in___2->n_eval_foo_bb2_in___1, Arg_3: Arg_3 {O(n)}
45: n_eval_foo_bb1_in___2->eval_foo_bb3_in, Arg_0: 2*Arg_3+Arg_2+1 {O(n)}
45: n_eval_foo_bb1_in___2->eval_foo_bb3_in, Arg_1: 2*Arg_3+2 {O(n)}
45: n_eval_foo_bb1_in___2->eval_foo_bb3_in, Arg_2: 2*Arg_2 {O(n)}
45: n_eval_foo_bb1_in___2->eval_foo_bb3_in, Arg_3: 2*Arg_3 {O(n)}
39: n_eval_foo_bb2_in___1->n_eval_foo_bb1_in___2, Arg_0: Arg_3+1 {O(n)}
39: n_eval_foo_bb2_in___1->n_eval_foo_bb1_in___2, Arg_1: Arg_3+1 {O(n)}
39: n_eval_foo_bb2_in___1->n_eval_foo_bb1_in___2, Arg_2: Arg_2 {O(n)}
39: n_eval_foo_bb2_in___1->n_eval_foo_bb1_in___2, Arg_3: Arg_3 {O(n)}
40: n_eval_foo_bb2_in___3->n_eval_foo_bb1_in___2, Arg_0: Arg_2+Arg_3 {O(n)}
40: n_eval_foo_bb2_in___3->n_eval_foo_bb1_in___2, Arg_1: Arg_3+1 {O(n)}
40: n_eval_foo_bb2_in___3->n_eval_foo_bb1_in___2, Arg_2: Arg_2 {O(n)}
40: n_eval_foo_bb2_in___3->n_eval_foo_bb1_in___2, Arg_3: Arg_3 {O(n)}