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_start
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_bb1_in(Arg_0,Arg_1):|:0<Arg_0 && Arg_0<1
3:eval_foo_bb1_in(Arg_0,Arg_1) -> eval_foo_bb1_in(Arg_0-1,Arg_1):|:0<Arg_0 && 1<=Arg_0
4:eval_foo_bb1_in(Arg_0,Arg_1) -> eval_foo_bb1_in(Arg_0+1,Arg_1):|:Arg_0<=0 && Arg_0<0
5:eval_foo_bb1_in(Arg_0,Arg_1) -> eval_foo_bb1_in(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)

Preprocessing

Cut unsatisfiable transition 2: eval_foo_bb1_in->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_start
Transitions:
1:eval_foo_bb0_in(Arg_0,Arg_1) -> eval_foo_bb1_in(Arg_1,Arg_1)
3:eval_foo_bb1_in(Arg_0,Arg_1) -> eval_foo_bb1_in(Arg_0-1,Arg_1):|:0<Arg_0 && 1<=Arg_0
4:eval_foo_bb1_in(Arg_0,Arg_1) -> eval_foo_bb1_in(Arg_0+1,Arg_1):|:Arg_0<=0 && Arg_0<0
5:eval_foo_bb1_in(Arg_0,Arg_1) -> eval_foo_bb1_in(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)

MPRF for transition 3:eval_foo_bb1_in(Arg_0,Arg_1) -> eval_foo_bb1_in(Arg_0-1,Arg_1):|:0<Arg_0 && 1<=Arg_0 of depth 1:

new bound:

Arg_1 {O(n)}

MPRF:

eval_foo_bb1_in [Arg_0 ]

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

new bound:

Arg_1+1 {O(n)}

MPRF:

eval_foo_bb1_in [1-Arg_0 ]

Analysing control-flow refined program

Cut unsatisfiable transition 74: n_eval_foo_bb1_in___3->n_eval_foo_bb1_in___4

Found invariant Arg_0<=0 && 0<=Arg_0 for location n_eval_foo_bb1_in___1

Found invariant 1+Arg_1<=0 && 1+Arg_1<=Arg_0 && 1+Arg_0+Arg_1<=0 && Arg_0<=0 for location n_eval_foo_bb1_in___3

Found invariant 1<=Arg_1 && 1<=Arg_0+Arg_1 && 1+Arg_0<=Arg_1 && 0<=Arg_0 for location n_eval_foo_bb1_in___4

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___2

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

MPRF for transition 73:n_eval_foo_bb1_in___3(Arg_0,Arg_1) -> n_eval_foo_bb1_in___3(Arg_0+1,Arg_1):|:1+Arg_1<=0 && 1+Arg_1<=Arg_0 && 1+Arg_0+Arg_1<=0 && Arg_0<=0 && Arg_0<0 of depth 1:

new bound:

Arg_1+1 {O(n)}

MPRF:

n_eval_foo_bb1_in___3 [1-Arg_0 ]

MPRF for transition 76:n_eval_foo_bb1_in___4(Arg_0,Arg_1) -> n_eval_foo_bb1_in___4(Arg_0-1,Arg_1):|:1<=Arg_1 && 1<=Arg_0+Arg_1 && 1+Arg_0<=Arg_1 && 0<=Arg_0 && 0<=Arg_0 && 1<=Arg_0 of depth 1:

new bound:

Arg_1+1 {O(n)}

MPRF:

n_eval_foo_bb1_in___4 [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)}
3: eval_foo_bb1_in->eval_foo_bb1_in: Arg_1 {O(n)}
4: eval_foo_bb1_in->eval_foo_bb1_in: Arg_1+1 {O(n)}
5: eval_foo_bb1_in->eval_foo_bb1_in: inf {Infinity}
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)}
3: eval_foo_bb1_in->eval_foo_bb1_in: Arg_1 {O(n)}
4: eval_foo_bb1_in->eval_foo_bb1_in: Arg_1+1 {O(n)}
5: eval_foo_bb1_in->eval_foo_bb1_in: inf {Infinity}
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)}
3: eval_foo_bb1_in->eval_foo_bb1_in, Arg_0: Arg_1 {O(n)}
3: eval_foo_bb1_in->eval_foo_bb1_in, Arg_1: Arg_1 {O(n)}
4: eval_foo_bb1_in->eval_foo_bb1_in, Arg_0: Arg_1 {O(n)}
4: eval_foo_bb1_in->eval_foo_bb1_in, Arg_1: Arg_1 {O(n)}
5: eval_foo_bb1_in->eval_foo_bb1_in, Arg_0: 0 {O(1)}
5: eval_foo_bb1_in->eval_foo_bb1_in, Arg_1: 3*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)}