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):|:0<Arg_1
2:eval_foo_bb0_in(Arg_0,Arg_1) -> eval_foo_bb3_in(Arg_0,Arg_1):|:Arg_1<=0
3:eval_foo_bb1_in(Arg_0,Arg_1) -> eval_foo_bb2_in(Arg_0,Arg_1):|:Arg_0<0
4:eval_foo_bb1_in(Arg_0,Arg_1) -> eval_foo_bb2_in(Arg_0,Arg_1):|:0<Arg_0
5:eval_foo_bb1_in(Arg_0,Arg_1) -> eval_foo_bb3_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_0-2,Arg_1)
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 1<=Arg_1 && Arg_0<=Arg_1 for location eval_foo_bb2_in

Found invariant 1<=Arg_1 && 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):|:0<Arg_1
2:eval_foo_bb0_in(Arg_0,Arg_1) -> eval_foo_bb3_in(Arg_0,Arg_1):|:Arg_1<=0
3:eval_foo_bb1_in(Arg_0,Arg_1) -> eval_foo_bb2_in(Arg_0,Arg_1):|:1<=Arg_1 && Arg_0<=Arg_1 && Arg_0<0
4:eval_foo_bb1_in(Arg_0,Arg_1) -> eval_foo_bb2_in(Arg_0,Arg_1):|:1<=Arg_1 && Arg_0<=Arg_1 && 0<Arg_0
5:eval_foo_bb1_in(Arg_0,Arg_1) -> eval_foo_bb3_in(Arg_0,Arg_1):|:1<=Arg_1 && Arg_0<=Arg_1 && Arg_0<=0 && 0<=Arg_0
6:eval_foo_bb2_in(Arg_0,Arg_1) -> eval_foo_bb1_in(Arg_0-2,Arg_1):|:1<=Arg_1 && Arg_0<=Arg_1
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)

MPRF for transition 4:eval_foo_bb1_in(Arg_0,Arg_1) -> eval_foo_bb2_in(Arg_0,Arg_1):|:1<=Arg_1 && Arg_0<=Arg_1 && 0<Arg_0 of depth 1:

new bound:

Arg_1 {O(n)}

MPRF:

eval_foo_bb2_in [Arg_0-2 ]
eval_foo_bb1_in [Arg_0 ]

Analysing control-flow refined program

Cut unsatisfiable transition 5: eval_foo_bb1_in->eval_foo_bb3_in

Cut unsatisfiable transition 71: n_eval_foo_bb1_in___2->eval_foo_bb3_in

Found invariant 1<=Arg_1 && 0<=Arg_0+Arg_1 && 2+Arg_0<=Arg_1 && 1+Arg_0<=0 && 0<=1+Arg_0 for location n_eval_foo_bb2_in___4

Found invariant 1<=Arg_1 && 0<=Arg_0+Arg_1 && 2+Arg_0<=Arg_1 && 0<=1+Arg_0 for location n_eval_foo_bb1_in___5

Found invariant 1<=Arg_1 && 4+Arg_0<=Arg_1 && 3+Arg_0<=0 for location n_eval_foo_bb1_in___2

Found invariant 1<=Arg_1 && 4+Arg_0<=Arg_1 && 3+Arg_0<=0 for location n_eval_foo_bb2_in___1

Found invariant Arg_1<=Arg_0 && 1<=Arg_1 && 2<=Arg_0+Arg_1 && Arg_0<=Arg_1 && 1<=Arg_0 for location eval_foo_bb1_in

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

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___6

MPRF for transition 58:n_eval_foo_bb1_in___5(Arg_0,Arg_1) -> n_eval_foo_bb2_in___3(Arg_0,Arg_1):|:1<=Arg_1 && 0<=Arg_0+Arg_1 && 2+Arg_0<=Arg_1 && 0<=1+Arg_0 && 1<=Arg_1 && Arg_0<=Arg_1 && 1<=Arg_1 && 2+Arg_0<=Arg_1 && 0<Arg_0 && 1<=Arg_1 && Arg_0<=Arg_1 of depth 1:

new bound:

Arg_1+2 {O(n)}

MPRF:

n_eval_foo_bb2_in___3 [Arg_0 ]
n_eval_foo_bb1_in___5 [Arg_0+2 ]

MPRF for transition 62:n_eval_foo_bb2_in___3(Arg_0,Arg_1) -> n_eval_foo_bb1_in___5(Arg_0-2,Arg_1):|:3<=Arg_1 && 4<=Arg_0+Arg_1 && 2+Arg_0<=Arg_1 && 1<=Arg_0 && 2+Arg_0<=Arg_1 && 0<Arg_0 && 1<=Arg_1 && Arg_0<=Arg_1 of depth 1:

new bound:

Arg_1 {O(n)}

MPRF:

n_eval_foo_bb2_in___3 [Arg_0 ]
n_eval_foo_bb1_in___5 [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_bb0_in->eval_foo_bb3_in: 1 {O(1)}
3: eval_foo_bb1_in->eval_foo_bb2_in: inf {Infinity}
4: eval_foo_bb1_in->eval_foo_bb2_in: Arg_1 {O(n)}
5: 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_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_bb0_in->eval_foo_bb3_in: 1 {O(1)}
3: eval_foo_bb1_in->eval_foo_bb2_in: inf {Infinity}
4: eval_foo_bb1_in->eval_foo_bb2_in: Arg_1 {O(n)}
5: 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_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_bb0_in->eval_foo_bb3_in, Arg_0: Arg_0 {O(n)}
2: eval_foo_bb0_in->eval_foo_bb3_in, Arg_1: Arg_1 {O(n)}
3: eval_foo_bb1_in->eval_foo_bb2_in, Arg_1: Arg_1 {O(n)}
4: eval_foo_bb1_in->eval_foo_bb2_in, Arg_1: Arg_1 {O(n)}
5: eval_foo_bb1_in->eval_foo_bb3_in, Arg_0: 0 {O(1)}
5: eval_foo_bb1_in->eval_foo_bb3_in, Arg_1: Arg_1 {O(n)}
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_0 {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)}