Initial Problem

Start: eval_foo_start
Program_Vars: Arg_0, Arg_1, Arg_2
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,Arg_2) -> eval_foo_bb1_in(Arg_1,Arg_1,Arg_2)
2:eval_foo_bb1_in(Arg_0,Arg_1,Arg_2) -> eval_foo_bb2_in(Arg_0,Arg_1,Arg_2):|:Arg_0<0
3:eval_foo_bb1_in(Arg_0,Arg_1,Arg_2) -> eval_foo_bb2_in(Arg_0,Arg_1,Arg_2):|:0<Arg_0
4:eval_foo_bb1_in(Arg_0,Arg_1,Arg_2) -> eval_foo_bb3_in(Arg_0,Arg_1,Arg_2):|:Arg_0<=0 && 0<=Arg_0
5:eval_foo_bb2_in(Arg_0,Arg_1,Arg_2) -> eval_foo_bb1_in(Arg_0-1,Arg_1,Arg_2)
6:eval_foo_bb3_in(Arg_0,Arg_1,Arg_2) -> eval_foo_stop(Arg_0,Arg_1,Arg_2)
0:eval_foo_start(Arg_0,Arg_1,Arg_2) -> eval_foo_bb0_in(Arg_0,Arg_1,Arg_2)

Preprocessing

Eliminate variables {Arg_2} that do not contribute to the problem

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

Found invariant 0<=Arg_1 && 0<=Arg_0+Arg_1 && Arg_0<=Arg_1 && Arg_0<=0 && 0<=Arg_0 for location eval_foo_bb3_in

Found invariant Arg_0<=Arg_1 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:
14:eval_foo_bb0_in(Arg_0,Arg_1) -> eval_foo_bb1_in(Arg_1,Arg_1)
15:eval_foo_bb1_in(Arg_0,Arg_1) -> eval_foo_bb2_in(Arg_0,Arg_1):|:Arg_0<=Arg_1 && Arg_0<0
16:eval_foo_bb1_in(Arg_0,Arg_1) -> eval_foo_bb2_in(Arg_0,Arg_1):|:Arg_0<=Arg_1 && 0<Arg_0
17:eval_foo_bb1_in(Arg_0,Arg_1) -> eval_foo_bb3_in(Arg_0,Arg_1):|:Arg_0<=Arg_1 && Arg_0<=0 && 0<=Arg_0
18:eval_foo_bb2_in(Arg_0,Arg_1) -> eval_foo_bb1_in(Arg_0-1,Arg_1):|:Arg_0<=Arg_1
19:eval_foo_bb3_in(Arg_0,Arg_1) -> eval_foo_stop(Arg_0,Arg_1):|:0<=Arg_1 && 0<=Arg_0+Arg_1 && Arg_0<=Arg_1 && Arg_0<=0 && 0<=Arg_0
20:eval_foo_start(Arg_0,Arg_1) -> eval_foo_bb0_in(Arg_0,Arg_1)

MPRF for transition 16:eval_foo_bb1_in(Arg_0,Arg_1) -> eval_foo_bb2_in(Arg_0,Arg_1):|:Arg_0<=Arg_1 && 0<Arg_0 of depth 1:

new bound:

Arg_1 {O(n)}

MPRF:

eval_foo_bb2_in [Arg_0-1 ]
eval_foo_bb1_in [Arg_0 ]

Analysing control-flow refined program

Cut unsatisfiable transition 52: n_eval_foo_bb1_in___3->n_eval_foo_bb2_in___2

Cut unsatisfiable transition 68: n_eval_foo_bb1_in___5->eval_foo_bb3_in

Cut unreachable locations [n_eval_foo_bb2_in___2] from the program graph

Found invariant 1+Arg_1<=0 && 3+Arg_0+Arg_1<=0 && 1+Arg_0<=Arg_1 && 2+Arg_0<=0 for location n_eval_foo_bb2_in___4

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___7

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

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___3

Found invariant 0<=Arg_1 && 0<=Arg_0+Arg_1 && Arg_0<=Arg_1 && Arg_0<=0 && 0<=Arg_0 for location eval_foo_bb3_in

Found invariant 1+Arg_1<=0 && 3+Arg_0+Arg_1<=0 && 1+Arg_0<=Arg_1 && 2+Arg_0<=0 for location n_eval_foo_bb1_in___5

Found invariant 2<=Arg_1 && 3<=Arg_0+Arg_1 && 1+Arg_0<=Arg_1 && 1<=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<=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 51:n_eval_foo_bb1_in___3(Arg_0,Arg_1) -> n_eval_foo_bb2_in___1(Arg_0,Arg_1):|:1<=Arg_1 && 1<=Arg_0+Arg_1 && 1+Arg_0<=Arg_1 && 0<=Arg_0 && Arg_0<=Arg_1 && 1+Arg_0<=Arg_1 && 0<Arg_0 && Arg_0<=Arg_1 of depth 1:

new bound:

Arg_1+1 {O(n)}

MPRF:

n_eval_foo_bb2_in___1 [Arg_0 ]
n_eval_foo_bb1_in___3 [Arg_0+1 ]

MPRF for transition 56:n_eval_foo_bb2_in___1(Arg_0,Arg_1) -> n_eval_foo_bb1_in___3(Arg_0-1,Arg_1):|:2<=Arg_1 && 3<=Arg_0+Arg_1 && 1+Arg_0<=Arg_1 && 1<=Arg_0 && 1+Arg_0<=Arg_1 && 0<Arg_0 && Arg_0<=Arg_1 of depth 1:

new bound:

Arg_1 {O(n)}

MPRF:

n_eval_foo_bb2_in___1 [Arg_0 ]
n_eval_foo_bb1_in___3 [Arg_0 ]

CFR did not improve the program. Rolling back

All Bounds

Timebounds

Overall timebound:inf {Infinity}
14: eval_foo_bb0_in->eval_foo_bb1_in: 1 {O(1)}
15: eval_foo_bb1_in->eval_foo_bb2_in: inf {Infinity}
16: eval_foo_bb1_in->eval_foo_bb2_in: Arg_1 {O(n)}
17: eval_foo_bb1_in->eval_foo_bb3_in: 1 {O(1)}
18: eval_foo_bb2_in->eval_foo_bb1_in: inf {Infinity}
19: eval_foo_bb3_in->eval_foo_stop: 1 {O(1)}
20: eval_foo_start->eval_foo_bb0_in: 1 {O(1)}

Costbounds

Overall costbound: inf {Infinity}
14: eval_foo_bb0_in->eval_foo_bb1_in: 1 {O(1)}
15: eval_foo_bb1_in->eval_foo_bb2_in: inf {Infinity}
16: eval_foo_bb1_in->eval_foo_bb2_in: Arg_1 {O(n)}
17: eval_foo_bb1_in->eval_foo_bb3_in: 1 {O(1)}
18: eval_foo_bb2_in->eval_foo_bb1_in: inf {Infinity}
19: eval_foo_bb3_in->eval_foo_stop: 1 {O(1)}
20: eval_foo_start->eval_foo_bb0_in: 1 {O(1)}

Sizebounds

14: eval_foo_bb0_in->eval_foo_bb1_in, Arg_0: Arg_1 {O(n)}
14: eval_foo_bb0_in->eval_foo_bb1_in, Arg_1: Arg_1 {O(n)}
15: eval_foo_bb1_in->eval_foo_bb2_in, Arg_1: 2*Arg_1 {O(n)}
16: eval_foo_bb1_in->eval_foo_bb2_in, Arg_1: 2*Arg_1 {O(n)}
17: eval_foo_bb1_in->eval_foo_bb3_in, Arg_0: 0 {O(1)}
17: eval_foo_bb1_in->eval_foo_bb3_in, Arg_1: 3*Arg_1 {O(n)}
18: eval_foo_bb2_in->eval_foo_bb1_in, Arg_1: 2*Arg_1 {O(n)}
19: eval_foo_bb3_in->eval_foo_stop, Arg_0: 0 {O(1)}
19: eval_foo_bb3_in->eval_foo_stop, Arg_1: 3*Arg_1 {O(n)}
20: eval_foo_start->eval_foo_bb0_in, Arg_0: Arg_0 {O(n)}
20: eval_foo_start->eval_foo_bb0_in, Arg_1: Arg_1 {O(n)}