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

Cut unsatisfiable transition 5: eval_foo_bb2_in->eval_foo_bb1_in

Found invariant Arg_0<=5 && 0<=5+Arg_0 for location eval_foo_bb2_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):|:0<=5+Arg_0 && Arg_0<=5
3:eval_foo_bb1_in(Arg_0,Arg_1) -> eval_foo_bb3_in(Arg_0,Arg_1):|:Arg_0+5<0
4:eval_foo_bb1_in(Arg_0,Arg_1) -> eval_foo_bb3_in(Arg_0,Arg_1):|:5<Arg_0
6:eval_foo_bb2_in(Arg_0,Arg_1) -> eval_foo_bb1_in(Arg_0-1,Arg_1):|:Arg_0<=5 && 0<=5+Arg_0 && 0<Arg_0 && 1<=Arg_0
7:eval_foo_bb2_in(Arg_0,Arg_1) -> eval_foo_bb1_in(Arg_0+1,Arg_1):|:Arg_0<=5 && 0<=5+Arg_0 && Arg_0<=0 && Arg_0<0
8:eval_foo_bb2_in(Arg_0,Arg_1) -> eval_foo_bb1_in(Arg_0,Arg_1):|:Arg_0<=5 && 0<=5+Arg_0 && Arg_0<=0 && 0<=Arg_0
9: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)

Analysing control-flow refined program

Found invariant 1+Arg_1<=0 && 1+Arg_1<=Arg_0 && 1+Arg_0+Arg_1<=0 && 0<=5+Arg_1 && 0<=9+Arg_0+Arg_1 && Arg_0<=5+Arg_1 && Arg_0<=0 && 0<=4+Arg_0 for location n_eval_foo_bb1_in___7

Found invariant 1+Arg_1<=0 && 1+Arg_1<=Arg_0 && 1+Arg_0+Arg_1<=0 && 0<=5+Arg_1 && 0<=9+Arg_0+Arg_1 && Arg_0<=5+Arg_1 && Arg_0<=0 && 0<=4+Arg_0 for location n_eval_foo_bb2_in___2

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

Found invariant 0<=5+Arg_1 && 0<=5+Arg_0+Arg_1 && Arg_0<=5+Arg_1 && Arg_0<=0 && 0<=Arg_0 for location n_eval_foo_bb1_in___4

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

Found invariant Arg_1<=5 && Arg_1<=5+Arg_0 && Arg_0+Arg_1<=9 && 1<=Arg_1 && 1<=Arg_0+Arg_1 && 1+Arg_0<=Arg_1 && Arg_0<=4 && 0<=Arg_0 for location n_eval_foo_bb2_in___5

Found invariant Arg_1<=0 && Arg_1<=Arg_0 && Arg_0+Arg_1<=0 && 0<=Arg_1 && 0<=Arg_0+Arg_1 && Arg_0<=Arg_1 && Arg_0<=0 && 0<=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<=5 && Arg_1<=5+Arg_0 && Arg_0+Arg_1<=9 && 1<=Arg_1 && 1<=Arg_0+Arg_1 && 1+Arg_0<=Arg_1 && Arg_0<=4 && 0<=Arg_0 for location n_eval_foo_bb1_in___8

Found invariant 0<=5+Arg_1 && 0<=5+Arg_0+Arg_1 && Arg_0<=5+Arg_1 && Arg_0<=0 && 0<=Arg_0 for location n_eval_foo_bb2_in___3

Found invariant Arg_1<=5 && Arg_1<=Arg_0 && Arg_0+Arg_1<=10 && 0<=5+Arg_1 && 0<=10+Arg_0+Arg_1 && Arg_0<=Arg_1 && Arg_0<=5 && 0<=5+Arg_0 for location n_eval_foo_bb2_in___9

Found invariant Arg_1<=0 && Arg_1<=Arg_0 && Arg_0+Arg_1<=0 && 0<=Arg_1 && 0<=Arg_0+Arg_1 && Arg_0<=Arg_1 && Arg_0<=0 && 0<=Arg_0 for location n_eval_foo_bb1_in___6

Cut unsatisfiable transition 87: n_eval_foo_bb2_in___2->n_eval_foo_bb1_in___8

MPRF for transition 82:n_eval_foo_bb1_in___7(Arg_0,Arg_1) -> n_eval_foo_bb2_in___2(Arg_0,Arg_1):|:1+Arg_1<=0 && 1+Arg_1<=Arg_0 && 1+Arg_0+Arg_1<=0 && 0<=5+Arg_1 && 0<=9+Arg_0+Arg_1 && Arg_0<=5+Arg_1 && Arg_0<=0 && 0<=4+Arg_0 && Arg_0<=5 && 0<=5+Arg_0 && 0<=5+Arg_0 && Arg_0<=5 && 0<=5+Arg_0 && Arg_0<=5 of depth 1:

new bound:

5 {O(1)}

MPRF:

n_eval_foo_bb2_in___2 [-Arg_0 ]
n_eval_foo_bb1_in___7 [1-Arg_0 ]

MPRF for transition 86:n_eval_foo_bb2_in___2(Arg_0,Arg_1) -> n_eval_foo_bb1_in___7(Arg_0+1,Arg_1):|:1+Arg_1<=0 && 1+Arg_1<=Arg_0 && 1+Arg_0+Arg_1<=0 && 0<=5+Arg_1 && 0<=9+Arg_0+Arg_1 && Arg_0<=5+Arg_1 && Arg_0<=0 && 0<=4+Arg_0 && Arg_0<=5 && 0<=5+Arg_0 && 0<=5+Arg_0 && Arg_0<0 of depth 1:

new bound:

5 {O(1)}

MPRF:

n_eval_foo_bb2_in___2 [1-Arg_0 ]
n_eval_foo_bb1_in___7 [1-Arg_0 ]

MPRF for transition 83:n_eval_foo_bb1_in___8(Arg_0,Arg_1) -> n_eval_foo_bb2_in___5(Arg_0,Arg_1):|:Arg_1<=5 && Arg_1<=5+Arg_0 && Arg_0+Arg_1<=9 && 1<=Arg_1 && 1<=Arg_0+Arg_1 && 1+Arg_0<=Arg_1 && Arg_0<=4 && 0<=Arg_0 && Arg_0<=5 && 0<=5+Arg_0 && 0<=5+Arg_0 && Arg_0<=5 && 0<=Arg_0 && Arg_0<=4 && 0<=5+Arg_0 && Arg_0<=5 of depth 1:

new bound:

5 {O(1)}

MPRF:

n_eval_foo_bb2_in___5 [Arg_0 ]
n_eval_foo_bb1_in___8 [Arg_0+1 ]

MPRF for transition 90:n_eval_foo_bb2_in___5(Arg_0,Arg_1) -> n_eval_foo_bb1_in___8(Arg_0-1,Arg_1):|:Arg_1<=5 && Arg_1<=5+Arg_0 && Arg_0+Arg_1<=9 && 1<=Arg_1 && 1<=Arg_0+Arg_1 && 1+Arg_0<=Arg_1 && Arg_0<=4 && 0<=Arg_0 && Arg_0<=4 && 0<=Arg_0 && 1<=Arg_0 && Arg_0<=5 of depth 1:

new bound:

5 {O(1)}

MPRF:

n_eval_foo_bb2_in___5 [Arg_0+1 ]
n_eval_foo_bb1_in___8 [Arg_0+1 ]

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_bb1_in->eval_foo_bb3_in: 1 {O(1)}
6: eval_foo_bb2_in->eval_foo_bb1_in: inf {Infinity}
7: eval_foo_bb2_in->eval_foo_bb1_in: inf {Infinity}
8: eval_foo_bb2_in->eval_foo_bb1_in: inf {Infinity}
9: 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_bb1_in->eval_foo_bb3_in: 1 {O(1)}
6: eval_foo_bb2_in->eval_foo_bb1_in: inf {Infinity}
7: eval_foo_bb2_in->eval_foo_bb1_in: inf {Infinity}
8: eval_foo_bb2_in->eval_foo_bb1_in: inf {Infinity}
9: 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: 5 {O(1)}
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 {O(n)}
3: eval_foo_bb1_in->eval_foo_bb3_in, Arg_1: Arg_1 {O(n)}
4: eval_foo_bb1_in->eval_foo_bb3_in, Arg_0: Arg_1 {O(n)}
4: eval_foo_bb1_in->eval_foo_bb3_in, Arg_1: Arg_1 {O(n)}
6: eval_foo_bb2_in->eval_foo_bb1_in, Arg_0: 4 {O(1)}
6: eval_foo_bb2_in->eval_foo_bb1_in, Arg_1: Arg_1 {O(n)}
7: eval_foo_bb2_in->eval_foo_bb1_in, Arg_0: 4 {O(1)}
7: eval_foo_bb2_in->eval_foo_bb1_in, Arg_1: Arg_1 {O(n)}
8: eval_foo_bb2_in->eval_foo_bb1_in, Arg_0: 0 {O(1)}
8: eval_foo_bb2_in->eval_foo_bb1_in, Arg_1: Arg_1 {O(n)}
9: eval_foo_bb3_in->eval_foo_stop, Arg_0: 2*Arg_1 {O(n)}
9: 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)}