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_bb4_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<0
3:eval_foo_bb1_in(Arg_0,Arg_1) -> eval_foo_bb2_in(Arg_0,Arg_1):|:0<Arg_0
4:eval_foo_bb1_in(Arg_0,Arg_1) -> eval_foo_bb4_in(Arg_0,Arg_1):|:Arg_0<=0 && 0<=Arg_0
6:eval_foo_bb2_in(Arg_0,Arg_1) -> eval_foo_bb1_in(Arg_0,Arg_1):|:Arg_0+5<=0
7:eval_foo_bb2_in(Arg_0,Arg_1) -> eval_foo_bb1_in(Arg_0,Arg_1):|:5<=Arg_0
5:eval_foo_bb2_in(Arg_0,Arg_1) -> eval_foo_bb3_in(Arg_0,Arg_1):|:0<5+Arg_0 && Arg_0<5
8:eval_foo_bb3_in(Arg_0,Arg_1) -> eval_foo_bb1_in(Arg_0,Arg_1):|:Arg_0<0 && 0<1+Arg_0
9:eval_foo_bb3_in(Arg_0,Arg_1) -> eval_foo_bb1_in(Arg_0+1,Arg_1):|:Arg_0<0 && Arg_0+1<=0
10:eval_foo_bb3_in(Arg_0,Arg_1) -> eval_foo_bb1_in(Arg_0-1,Arg_1):|:0<=Arg_0 && 0<Arg_0
11:eval_foo_bb3_in(Arg_0,Arg_1) -> eval_foo_bb1_in(Arg_0,Arg_1):|:0<=Arg_0 && Arg_0<=0
12:eval_foo_bb4_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

Cut unsatisfiable transition 8: eval_foo_bb3_in->eval_foo_bb1_in

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

Found invariant Arg_0<=4 && 0<=4+Arg_0 for location eval_foo_bb3_in

Found invariant Arg_0<=0 && 0<=Arg_0 for location eval_foo_bb4_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_bb4_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<0
3:eval_foo_bb1_in(Arg_0,Arg_1) -> eval_foo_bb2_in(Arg_0,Arg_1):|:0<Arg_0
4:eval_foo_bb1_in(Arg_0,Arg_1) -> eval_foo_bb4_in(Arg_0,Arg_1):|:Arg_0<=0 && 0<=Arg_0
6:eval_foo_bb2_in(Arg_0,Arg_1) -> eval_foo_bb1_in(Arg_0,Arg_1):|:Arg_0+5<=0
7:eval_foo_bb2_in(Arg_0,Arg_1) -> eval_foo_bb1_in(Arg_0,Arg_1):|:5<=Arg_0
5:eval_foo_bb2_in(Arg_0,Arg_1) -> eval_foo_bb3_in(Arg_0,Arg_1):|:0<5+Arg_0 && Arg_0<5
9:eval_foo_bb3_in(Arg_0,Arg_1) -> eval_foo_bb1_in(Arg_0+1,Arg_1):|:Arg_0<=4 && 0<=4+Arg_0 && Arg_0<0 && Arg_0+1<=0
10:eval_foo_bb3_in(Arg_0,Arg_1) -> eval_foo_bb1_in(Arg_0-1,Arg_1):|:Arg_0<=4 && 0<=4+Arg_0 && 0<=Arg_0 && 0<Arg_0
11:eval_foo_bb3_in(Arg_0,Arg_1) -> eval_foo_bb1_in(Arg_0,Arg_1):|:Arg_0<=4 && 0<=4+Arg_0 && 0<=Arg_0 && Arg_0<=0
12:eval_foo_bb4_in(Arg_0,Arg_1) -> eval_foo_stop(Arg_0,Arg_1):|:Arg_0<=0 && 0<=Arg_0
0:eval_foo_start(Arg_0,Arg_1) -> eval_foo_bb0_in(Arg_0,Arg_1)

Analysing control-flow refined program

Cut unsatisfiable transition 176: n_eval_foo_bb1_in___14->eval_foo_bb4_in

Cut unsatisfiable transition 134: n_eval_foo_bb1_in___5->n_eval_foo_bb2_in___4

Cut unsatisfiable transition 178: n_eval_foo_bb1_in___8->eval_foo_bb4_in

Cut unreachable locations [n_eval_foo_bb2_in___4; n_eval_foo_bb3_in___2] from the program graph

Found invariant 5+Arg_1<=0 && Arg_1<=Arg_0 && 10+Arg_0+Arg_1<=0 && Arg_0<=Arg_1 && 5+Arg_0<=0 for location n_eval_foo_bb1_in___14

Found invariant 2+Arg_1<=0 && 1+Arg_1<=Arg_0 && 3+Arg_0+Arg_1<=0 && 0<=4+Arg_1 && 0<=7+Arg_0+Arg_1 && Arg_0<=3+Arg_1 && 1+Arg_0<=0 && 0<=3+Arg_0 for location n_eval_foo_bb3_in___9

Found invariant 1+Arg_1<=0 && Arg_1<=Arg_0 && 2+Arg_0+Arg_1<=0 && Arg_0<=Arg_1 && 1+Arg_0<=0 for location n_eval_foo_bb2_in___16

Found invariant Arg_1<=4 && Arg_1<=3+Arg_0 && Arg_0+Arg_1<=7 && 2<=Arg_1 && 3<=Arg_0+Arg_1 && 1+Arg_0<=Arg_1 && Arg_0<=3 && 1<=Arg_0 for location n_eval_foo_bb3_in___1

Found invariant Arg_1<=4 && Arg_1<=4+Arg_0 && Arg_0+Arg_1<=4 && Arg_0<=0 && 0<=Arg_0 for location eval_foo_stop

Found invariant 1+Arg_1<=0 && 1+Arg_1<=Arg_0 && 1+Arg_0+Arg_1<=0 && 0<=4+Arg_1 && 0<=7+Arg_0+Arg_1 && Arg_0<=4+Arg_1 && Arg_0<=0 && 0<=3+Arg_0 for location n_eval_foo_bb1_in___11

Found invariant 2+Arg_1<=0 && 1+Arg_1<=Arg_0 && 3+Arg_0+Arg_1<=0 && 0<=4+Arg_1 && 0<=7+Arg_0+Arg_1 && Arg_0<=3+Arg_1 && 1+Arg_0<=0 && 0<=3+Arg_0 for location n_eval_foo_bb2_in___10

Found invariant Arg_1<=4 && Arg_1<=4+Arg_0 && Arg_0+Arg_1<=7 && 1<=Arg_1 && 1<=Arg_0+Arg_1 && 1+Arg_0<=Arg_1 && Arg_0<=3 && 0<=Arg_0 for location n_eval_foo_bb1_in___5

Found invariant 5+Arg_1<=0 && Arg_1<=Arg_0 && 10+Arg_0+Arg_1<=0 && Arg_0<=Arg_1 && 5+Arg_0<=0 for location n_eval_foo_bb2_in___12

Found invariant Arg_1<=4 && Arg_1<=Arg_0 && Arg_0+Arg_1<=8 && 1<=Arg_1 && 2<=Arg_0+Arg_1 && Arg_0<=Arg_1 && Arg_0<=4 && 1<=Arg_0 for location n_eval_foo_bb3_in___7

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

Found invariant Arg_1<=Arg_0 && 5<=Arg_1 && 10<=Arg_0+Arg_1 && Arg_0<=Arg_1 && 5<=Arg_0 for location n_eval_foo_bb1_in___8

Found invariant Arg_1<=4 && Arg_1<=3+Arg_0 && Arg_0+Arg_1<=7 && 2<=Arg_1 && 3<=Arg_0+Arg_1 && 1+Arg_0<=Arg_1 && Arg_0<=3 && 1<=Arg_0 for location n_eval_foo_bb2_in___3

Found invariant Arg_1<=Arg_0 && 5<=Arg_1 && 10<=Arg_0+Arg_1 && Arg_0<=Arg_1 && 5<=Arg_0 for location n_eval_foo_bb2_in___6

Found invariant 1+Arg_1<=0 && Arg_1<=Arg_0 && 2+Arg_0+Arg_1<=0 && 0<=4+Arg_1 && 0<=8+Arg_0+Arg_1 && Arg_0<=Arg_1 && 1+Arg_0<=0 && 0<=4+Arg_0 for location n_eval_foo_bb3_in___13

Found invariant Arg_1<=Arg_0 && 1<=Arg_1 && 2<=Arg_0+Arg_1 && Arg_0<=Arg_1 && 1<=Arg_0 for location n_eval_foo_bb2_in___15

Found invariant Arg_1<=4 && Arg_1<=4+Arg_0 && Arg_0+Arg_1<=4 && 0<=4+Arg_1 && 0<=4+Arg_0+Arg_1 && Arg_0<=4+Arg_1 && Arg_0<=0 && 0<=Arg_0 for location eval_foo_bb4_in

MPRF for transition 133:n_eval_foo_bb1_in___5(Arg_0,Arg_1) -> n_eval_foo_bb2_in___3(Arg_0,Arg_1):|:Arg_1<=4 && Arg_1<=4+Arg_0 && Arg_0+Arg_1<=7 && 1<=Arg_1 && 1<=Arg_0+Arg_1 && 1+Arg_0<=Arg_1 && Arg_0<=3 && 0<=Arg_0 && 0<5+Arg_0 && 0<=4+Arg_0 && Arg_0<5 && Arg_0<=4 && 0<Arg_0 of depth 1:

new bound:

4 {O(1)}

MPRF:

n_eval_foo_bb2_in___3 [Arg_0 ]
n_eval_foo_bb3_in___1 [Arg_0 ]
n_eval_foo_bb1_in___5 [Arg_0+1 ]

MPRF for transition 142:n_eval_foo_bb2_in___3(Arg_0,Arg_1) -> n_eval_foo_bb3_in___1(Arg_0,Arg_1):|:Arg_1<=4 && Arg_1<=3+Arg_0 && Arg_0+Arg_1<=7 && 2<=Arg_1 && 3<=Arg_0+Arg_1 && 1+Arg_0<=Arg_1 && Arg_0<=3 && 1<=Arg_0 && Arg_0<=4 && 0<Arg_0 && 0<5+Arg_0 && Arg_0<5 of depth 1:

new bound:

3 {O(1)}

MPRF:

n_eval_foo_bb2_in___3 [Arg_0 ]
n_eval_foo_bb3_in___1 [Arg_0-1 ]
n_eval_foo_bb1_in___5 [Arg_0 ]

MPRF for transition 145:n_eval_foo_bb3_in___1(Arg_0,Arg_1) -> n_eval_foo_bb1_in___5(Arg_0-1,Arg_1):|:Arg_1<=4 && Arg_1<=3+Arg_0 && Arg_0+Arg_1<=7 && 2<=Arg_1 && 3<=Arg_0+Arg_1 && 1+Arg_0<=Arg_1 && Arg_0<=3 && 1<=Arg_0 && Arg_0<=4 && 0<Arg_0 && 0<Arg_0 && Arg_0<=4 of depth 1:

new bound:

3 {O(1)}

MPRF:

n_eval_foo_bb2_in___3 [Arg_0 ]
n_eval_foo_bb3_in___1 [Arg_0 ]
n_eval_foo_bb1_in___5 [Arg_0 ]

MPRF for transition 129:n_eval_foo_bb1_in___11(Arg_0,Arg_1) -> n_eval_foo_bb2_in___10(Arg_0,Arg_1):|:1+Arg_1<=0 && 1+Arg_1<=Arg_0 && 1+Arg_0+Arg_1<=0 && 0<=4+Arg_1 && 0<=7+Arg_0+Arg_1 && Arg_0<=4+Arg_1 && Arg_0<=0 && 0<=3+Arg_0 && 0<5+Arg_0 && 0<=4+Arg_0 && Arg_0<5 && Arg_0<=4 && 0<=3+Arg_0 && Arg_0<=0 && Arg_0<0 of depth 1:

new bound:

4 {O(1)}

MPRF:

n_eval_foo_bb2_in___10 [-Arg_0 ]
n_eval_foo_bb3_in___9 [-Arg_0 ]
n_eval_foo_bb1_in___11 [1-Arg_0 ]

MPRF for transition 136:n_eval_foo_bb2_in___10(Arg_0,Arg_1) -> n_eval_foo_bb3_in___9(Arg_0,Arg_1):|:2+Arg_1<=0 && 1+Arg_1<=Arg_0 && 3+Arg_0+Arg_1<=0 && 0<=4+Arg_1 && 0<=7+Arg_0+Arg_1 && Arg_0<=3+Arg_1 && 1+Arg_0<=0 && 0<=3+Arg_0 && Arg_0<0 && 0<=3+Arg_0 && 0<5+Arg_0 && Arg_0<5 of depth 1:

new bound:

3 {O(1)}

MPRF:

n_eval_foo_bb2_in___10 [-Arg_0 ]
n_eval_foo_bb3_in___9 [-Arg_0-1 ]
n_eval_foo_bb1_in___11 [-Arg_0 ]

MPRF for transition 149:n_eval_foo_bb3_in___9(Arg_0,Arg_1) -> n_eval_foo_bb1_in___11(Arg_0+1,Arg_1):|:2+Arg_1<=0 && 1+Arg_1<=Arg_0 && 3+Arg_0+Arg_1<=0 && 0<=4+Arg_1 && 0<=7+Arg_0+Arg_1 && Arg_0<=3+Arg_1 && 1+Arg_0<=0 && 0<=3+Arg_0 && Arg_0<0 && 0<=3+Arg_0 && 1+Arg_0<=0 && 0<=4+Arg_0 of depth 1:

new bound:

3 {O(1)}

MPRF:

n_eval_foo_bb2_in___10 [-Arg_0 ]
n_eval_foo_bb3_in___9 [-Arg_0 ]
n_eval_foo_bb1_in___11 [-Arg_0 ]

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_bb2_in: inf {Infinity}
4: eval_foo_bb1_in->eval_foo_bb4_in: 1 {O(1)}
5: eval_foo_bb2_in->eval_foo_bb3_in: inf {Infinity}
6: eval_foo_bb2_in->eval_foo_bb1_in: inf {Infinity}
7: eval_foo_bb2_in->eval_foo_bb1_in: inf {Infinity}
9: eval_foo_bb3_in->eval_foo_bb1_in: inf {Infinity}
10: eval_foo_bb3_in->eval_foo_bb1_in: inf {Infinity}
11: eval_foo_bb3_in->eval_foo_bb1_in: inf {Infinity}
12: eval_foo_bb4_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_bb2_in: inf {Infinity}
4: eval_foo_bb1_in->eval_foo_bb4_in: 1 {O(1)}
5: eval_foo_bb2_in->eval_foo_bb3_in: inf {Infinity}
6: eval_foo_bb2_in->eval_foo_bb1_in: inf {Infinity}
7: eval_foo_bb2_in->eval_foo_bb1_in: inf {Infinity}
9: eval_foo_bb3_in->eval_foo_bb1_in: inf {Infinity}
10: eval_foo_bb3_in->eval_foo_bb1_in: inf {Infinity}
11: eval_foo_bb3_in->eval_foo_bb1_in: inf {Infinity}
12: eval_foo_bb4_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+3 {O(n)}
2: eval_foo_bb1_in->eval_foo_bb2_in, Arg_1: 2*Arg_1 {O(n)}
3: eval_foo_bb1_in->eval_foo_bb2_in, Arg_0: Arg_1+3 {O(n)}
3: eval_foo_bb1_in->eval_foo_bb2_in, Arg_1: 2*Arg_1 {O(n)}
4: eval_foo_bb1_in->eval_foo_bb4_in, Arg_0: 0 {O(1)}
4: eval_foo_bb1_in->eval_foo_bb4_in, Arg_1: 7*Arg_1 {O(n)}
5: eval_foo_bb2_in->eval_foo_bb3_in, Arg_0: 4 {O(1)}
5: eval_foo_bb2_in->eval_foo_bb3_in, Arg_1: 2*Arg_1 {O(n)}
6: eval_foo_bb2_in->eval_foo_bb1_in, Arg_0: Arg_1+3 {O(n)}
6: eval_foo_bb2_in->eval_foo_bb1_in, Arg_1: 2*Arg_1 {O(n)}
7: eval_foo_bb2_in->eval_foo_bb1_in, Arg_0: Arg_1+3 {O(n)}
7: eval_foo_bb2_in->eval_foo_bb1_in, Arg_1: 2*Arg_1 {O(n)}
9: eval_foo_bb3_in->eval_foo_bb1_in, Arg_0: 3 {O(1)}
9: eval_foo_bb3_in->eval_foo_bb1_in, Arg_1: 2*Arg_1 {O(n)}
10: eval_foo_bb3_in->eval_foo_bb1_in, Arg_0: 3 {O(1)}
10: eval_foo_bb3_in->eval_foo_bb1_in, Arg_1: 2*Arg_1 {O(n)}
11: eval_foo_bb3_in->eval_foo_bb1_in, Arg_0: 0 {O(1)}
11: eval_foo_bb3_in->eval_foo_bb1_in, Arg_1: 2*Arg_1 {O(n)}
12: eval_foo_bb4_in->eval_foo_stop, Arg_0: 0 {O(1)}
12: eval_foo_bb4_in->eval_foo_stop, Arg_1: 7*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)}