Initial Problem

Start: eval_foo_start
Program_Vars: Arg_0, Arg_1
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) -> eval_foo_bb1_in(Arg_1,Arg_1)
2:eval_foo_bb1_in(Arg_0,Arg_1) -> eval_foo_bb2_in(Arg_0,Arg_1):|:5<Arg_0
3:eval_foo_bb1_in(Arg_0,Arg_1) -> eval_foo_bb3_in(Arg_0,Arg_1):|:Arg_0<=5
4:eval_foo_bb2_in(Arg_0,Arg_1) -> eval_foo_bb1_in(Arg_0-1,Arg_1):|:Arg_0<10
5:eval_foo_bb2_in(Arg_0,Arg_1) -> eval_foo_bb1_in(Arg_0-1,Arg_1):|:10<Arg_0
6:eval_foo_bb2_in(Arg_0,Arg_1) -> eval_foo_bb1_in(Arg_0,Arg_1):|:Arg_0<=10 && 10<=Arg_0
7:eval_foo_bb3_in(Arg_0,Arg_1) -> eval_foo_stop(Arg_0,Arg_1)
0:eval_foo_start(Arg_0,Arg_1) -> eval_foo_bb0_in(Arg_0,Arg_1)

Preprocessing

Found invariant Arg_0<=Arg_1 && Arg_0<=5 for location eval_foo_stop

Found invariant Arg_0<=Arg_1 && Arg_0<=5 for location eval_foo_bb3_in

Found invariant 6<=Arg_1 && 12<=Arg_0+Arg_1 && Arg_0<=Arg_1 && 6<=Arg_0 for location eval_foo_bb2_in

Found invariant Arg_0<=Arg_1 for location eval_foo_bb1_in

Problem after Preprocessing

Start: eval_foo_start
Program_Vars: Arg_0, Arg_1
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) -> eval_foo_bb1_in(Arg_1,Arg_1)
2:eval_foo_bb1_in(Arg_0,Arg_1) -> eval_foo_bb2_in(Arg_0,Arg_1):|:Arg_0<=Arg_1 && 5<Arg_0
3:eval_foo_bb1_in(Arg_0,Arg_1) -> eval_foo_bb3_in(Arg_0,Arg_1):|:Arg_0<=Arg_1 && Arg_0<=5
4:eval_foo_bb2_in(Arg_0,Arg_1) -> eval_foo_bb1_in(Arg_0-1,Arg_1):|:6<=Arg_1 && 12<=Arg_0+Arg_1 && Arg_0<=Arg_1 && 6<=Arg_0 && Arg_0<10
5:eval_foo_bb2_in(Arg_0,Arg_1) -> eval_foo_bb1_in(Arg_0-1,Arg_1):|:6<=Arg_1 && 12<=Arg_0+Arg_1 && Arg_0<=Arg_1 && 6<=Arg_0 && 10<Arg_0
6:eval_foo_bb2_in(Arg_0,Arg_1) -> eval_foo_bb1_in(Arg_0,Arg_1):|:6<=Arg_1 && 12<=Arg_0+Arg_1 && Arg_0<=Arg_1 && 6<=Arg_0 && Arg_0<=10 && 10<=Arg_0
7:eval_foo_bb3_in(Arg_0,Arg_1) -> eval_foo_stop(Arg_0,Arg_1):|:Arg_0<=Arg_1 && Arg_0<=5
0:eval_foo_start(Arg_0,Arg_1) -> eval_foo_bb0_in(Arg_0,Arg_1)

MPRF for transition 4:eval_foo_bb2_in(Arg_0,Arg_1) -> eval_foo_bb1_in(Arg_0-1,Arg_1):|:6<=Arg_1 && 12<=Arg_0+Arg_1 && Arg_0<=Arg_1 && 6<=Arg_0 && Arg_0<10 of depth 1:

new bound:

Arg_1+5 {O(n)}

MPRF:

eval_foo_bb2_in [Arg_0-5 ]
eval_foo_bb1_in [Arg_0-5 ]

MPRF for transition 5:eval_foo_bb2_in(Arg_0,Arg_1) -> eval_foo_bb1_in(Arg_0-1,Arg_1):|:6<=Arg_1 && 12<=Arg_0+Arg_1 && Arg_0<=Arg_1 && 6<=Arg_0 && 10<Arg_0 of depth 1:

new bound:

Arg_1+5 {O(n)}

MPRF:

eval_foo_bb2_in [Arg_0-5 ]
eval_foo_bb1_in [Arg_0-5 ]

Analysing control-flow refined program

Cut unsatisfiable transition 92: n_eval_foo_bb1_in___4->eval_foo_bb3_in

Cut unsatisfiable transition 94: n_eval_foo_bb1_in___8->eval_foo_bb3_in

Cut unsatisfiable transition 95: n_eval_foo_bb1_in___9->eval_foo_bb3_in

Found invariant 11<=Arg_1 && 21<=Arg_0+Arg_1 && 1+Arg_0<=Arg_1 && 10<=Arg_0 for location n_eval_foo_bb1_in___9

Found invariant Arg_1<=9 && Arg_1<=3+Arg_0 && Arg_0+Arg_1<=17 && 7<=Arg_1 && 13<=Arg_0+Arg_1 && 1+Arg_0<=Arg_1 && Arg_0<=8 && 6<=Arg_0 for location n_eval_foo_bb2_in___7

Found invariant 11<=Arg_1 && 21<=Arg_0+Arg_1 && 1+Arg_0<=Arg_1 && Arg_0<=10 && 10<=Arg_0 for location n_eval_foo_bb2_in___2

Found invariant Arg_1<=9 && Arg_1<=4+Arg_0 && Arg_0+Arg_1<=14 && Arg_0<=Arg_1 && Arg_0<=5 for location eval_foo_stop

Found invariant 11<=Arg_1 && 21<=Arg_0+Arg_1 && 1+Arg_0<=Arg_1 && Arg_0<=10 && 10<=Arg_0 for location n_eval_foo_bb1_in___4

Found invariant Arg_1<=9 && Arg_1<=4+Arg_0 && Arg_0+Arg_1<=14 && Arg_0<=Arg_1 && Arg_0<=5 for location eval_foo_bb3_in

Found invariant Arg_1<=9 && Arg_1<=4+Arg_0 && Arg_0+Arg_1<=17 && 6<=Arg_1 && 11<=Arg_0+Arg_1 && 1+Arg_0<=Arg_1 && Arg_0<=8 && 5<=Arg_0 for location n_eval_foo_bb1_in___10

Found invariant Arg_1<=Arg_0 && 6<=Arg_1 && 12<=Arg_0+Arg_1 && Arg_0<=Arg_1 && 6<=Arg_0 for location n_eval_foo_bb2_in___11

Found invariant 1<=0 for location n_eval_foo_bb1_in___5

Found invariant Arg_1<=10 && Arg_1<=Arg_0 && Arg_0+Arg_1<=20 && 10<=Arg_1 && 20<=Arg_0+Arg_1 && Arg_0<=Arg_1 && Arg_0<=10 && 10<=Arg_0 for location n_eval_foo_bb2_in___1

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

Found invariant Arg_1<=10 && Arg_1<=Arg_0 && Arg_0+Arg_1<=20 && 10<=Arg_1 && 20<=Arg_0+Arg_1 && Arg_0<=Arg_1 && Arg_0<=10 && 10<=Arg_0 for location n_eval_foo_bb1_in___8

Found invariant 1<=0 for location n_eval_foo_bb2_in___3

Found invariant 11<=Arg_1 && 21<=Arg_0+Arg_1 && 1+Arg_0<=Arg_1 && 10<=Arg_0 for location n_eval_foo_bb2_in___6

Cut unsatisfiable transition 68: n_eval_foo_bb1_in___5->n_eval_foo_bb2_in___3

Cut unsatisfiable transition 93: n_eval_foo_bb1_in___5->eval_foo_bb3_in

Cut unsatisfiable transition 76: n_eval_foo_bb2_in___3->n_eval_foo_bb1_in___5

Cut unsatisfiable transition 78: n_eval_foo_bb2_in___6->n_eval_foo_bb1_in___5

Cut unreachable locations [n_eval_foo_bb1_in___5; n_eval_foo_bb2_in___3] from the program graph

MPRF for transition 65:n_eval_foo_bb1_in___10(Arg_0,Arg_1) -> n_eval_foo_bb2_in___7(Arg_0,Arg_1):|:Arg_1<=9 && Arg_1<=4+Arg_0 && Arg_0+Arg_1<=17 && 6<=Arg_1 && 11<=Arg_0+Arg_1 && 1+Arg_0<=Arg_1 && Arg_0<=8 && 5<=Arg_0 && Arg_0<10 && Arg_0<=Arg_1 && 5<Arg_0 && Arg_0<=Arg_1 of depth 1:

new bound:

12 {O(1)}

MPRF:

n_eval_foo_bb2_in___7 [Arg_0-5 ]
n_eval_foo_bb1_in___10 [Arg_0-4 ]

MPRF for transition 80:n_eval_foo_bb2_in___7(Arg_0,Arg_1) -> n_eval_foo_bb1_in___10(Arg_0-1,Arg_1):|:Arg_1<=9 && Arg_1<=3+Arg_0 && Arg_0+Arg_1<=17 && 7<=Arg_1 && 13<=Arg_0+Arg_1 && 1+Arg_0<=Arg_1 && Arg_0<=8 && 6<=Arg_0 && Arg_0<10 && 5<Arg_0 && Arg_0<=Arg_1 && 6<=Arg_0 && Arg_0<=Arg_1 && Arg_0<10 of depth 1:

new bound:

13 {O(1)}

MPRF:

n_eval_foo_bb2_in___7 [Arg_0-5 ]
n_eval_foo_bb1_in___10 [Arg_0-5 ]

MPRF for transition 70:n_eval_foo_bb1_in___9(Arg_0,Arg_1) -> n_eval_foo_bb2_in___6(Arg_0,Arg_1):|:11<=Arg_1 && 21<=Arg_0+Arg_1 && 1+Arg_0<=Arg_1 && 10<=Arg_0 && 5<Arg_0 && Arg_0<=Arg_1 && 6<=Arg_0 && 10<=Arg_1 && 6<=Arg_0 && Arg_0<=Arg_1 && 5<Arg_0 && Arg_0<=Arg_1 of depth 1:

new bound:

Arg_1+5 {O(n)}

MPRF:

n_eval_foo_bb2_in___6 [Arg_0-6 ]
n_eval_foo_bb1_in___9 [Arg_0-5 ]

MPRF for transition 79:n_eval_foo_bb2_in___6(Arg_0,Arg_1) -> n_eval_foo_bb1_in___9(Arg_0-1,Arg_1):|:11<=Arg_1 && 21<=Arg_0+Arg_1 && 1+Arg_0<=Arg_1 && 10<=Arg_0 && Arg_0<=Arg_1 && 6<=Arg_0 && 10<=Arg_1 && 10<Arg_0 && Arg_0<=Arg_1 of depth 1:

new bound:

Arg_1+10 {O(n)}

MPRF:

n_eval_foo_bb2_in___6 [Arg_0-10 ]
n_eval_foo_bb1_in___9 [Arg_0-10 ]

CFR did not improve the program. Rolling back

All Bounds

Timebounds

Overall timebound:inf {Infinity}
1: eval_foo_bb0_in->eval_foo_bb1_in: 1 {O(1)}
2: eval_foo_bb1_in->eval_foo_bb2_in: inf {Infinity}
3: eval_foo_bb1_in->eval_foo_bb3_in: 1 {O(1)}
4: eval_foo_bb2_in->eval_foo_bb1_in: Arg_1+5 {O(n)}
5: eval_foo_bb2_in->eval_foo_bb1_in: Arg_1+5 {O(n)}
6: eval_foo_bb2_in->eval_foo_bb1_in: inf {Infinity}
7: eval_foo_bb3_in->eval_foo_stop: 1 {O(1)}
0: eval_foo_start->eval_foo_bb0_in: 1 {O(1)}

Costbounds

Overall costbound: inf {Infinity}
1: eval_foo_bb0_in->eval_foo_bb1_in: 1 {O(1)}
2: eval_foo_bb1_in->eval_foo_bb2_in: inf {Infinity}
3: eval_foo_bb1_in->eval_foo_bb3_in: 1 {O(1)}
4: eval_foo_bb2_in->eval_foo_bb1_in: Arg_1+5 {O(n)}
5: eval_foo_bb2_in->eval_foo_bb1_in: Arg_1+5 {O(n)}
6: eval_foo_bb2_in->eval_foo_bb1_in: inf {Infinity}
7: eval_foo_bb3_in->eval_foo_stop: 1 {O(1)}
0: eval_foo_start->eval_foo_bb0_in: 1 {O(1)}

Sizebounds

1: eval_foo_bb0_in->eval_foo_bb1_in, Arg_0: Arg_1 {O(n)}
1: eval_foo_bb0_in->eval_foo_bb1_in, Arg_1: Arg_1 {O(n)}
2: eval_foo_bb1_in->eval_foo_bb2_in, Arg_0: Arg_1+18 {O(n)}
2: eval_foo_bb1_in->eval_foo_bb2_in, Arg_1: Arg_1 {O(n)}
3: eval_foo_bb1_in->eval_foo_bb3_in, Arg_0: Arg_1+8 {O(n)}
3: eval_foo_bb1_in->eval_foo_bb3_in, Arg_1: 2*Arg_1 {O(n)}
4: eval_foo_bb2_in->eval_foo_bb1_in, Arg_0: 8 {O(1)}
4: eval_foo_bb2_in->eval_foo_bb1_in, Arg_1: Arg_1 {O(n)}
5: eval_foo_bb2_in->eval_foo_bb1_in, Arg_0: Arg_1+18 {O(n)}
5: eval_foo_bb2_in->eval_foo_bb1_in, Arg_1: Arg_1 {O(n)}
6: eval_foo_bb2_in->eval_foo_bb1_in, Arg_0: 10 {O(1)}
6: eval_foo_bb2_in->eval_foo_bb1_in, Arg_1: Arg_1 {O(n)}
7: eval_foo_bb3_in->eval_foo_stop, Arg_0: Arg_1+8 {O(n)}
7: eval_foo_bb3_in->eval_foo_stop, Arg_1: 2*Arg_1 {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)}