Initial Problem

Start: eval_foo_start
Program_Vars: Arg_0, Arg_1, Arg_2, Arg_3, Arg_4, Arg_5
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,Arg_3,Arg_4,Arg_5) -> eval_foo_bb1_in(0,1,Arg_2,Arg_3,Arg_4,Arg_5)
2:eval_foo_bb1_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5) -> eval_foo_bb2_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5):|:Arg_1<Arg_4
3:eval_foo_bb1_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5) -> eval_foo_bb2_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5):|:Arg_4<Arg_1
4:eval_foo_bb1_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5) -> eval_foo_bb3_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5):|:Arg_1<=Arg_4 && Arg_4<=Arg_1
5:eval_foo_bb2_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5) -> eval_foo_bb1_in(Arg_1,Arg_1+Arg_0,Arg_2,Arg_3,Arg_4,Arg_5)
6:eval_foo_bb3_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5) -> eval_foo_stop(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5)
0:eval_foo_start(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5) -> eval_foo_bb0_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5)

Preprocessing

Eliminate variables {Arg_2,Arg_3,Arg_5} that do not contribute to the problem

Found invariant Arg_4<=Arg_1 && 1<=Arg_4 && 2<=Arg_1+Arg_4 && Arg_1<=Arg_4 && 1<=Arg_0+Arg_4 && Arg_0<=Arg_4 && 1<=Arg_1 && 1<=Arg_0+Arg_1 && Arg_0<=Arg_1 && 0<=Arg_0 for location eval_foo_stop

Found invariant Arg_4<=Arg_1 && 1<=Arg_4 && 2<=Arg_1+Arg_4 && Arg_1<=Arg_4 && 1<=Arg_0+Arg_4 && Arg_0<=Arg_4 && 1<=Arg_1 && 1<=Arg_0+Arg_1 && Arg_0<=Arg_1 && 0<=Arg_0 for location eval_foo_bb3_in

Found invariant 1<=Arg_1 && 1<=Arg_0+Arg_1 && Arg_0<=Arg_1 && 0<=Arg_0 for location eval_foo_bb2_in

Found invariant 1<=Arg_1 && 1<=Arg_0+Arg_1 && Arg_0<=Arg_1 && 0<=Arg_0 for location eval_foo_bb1_in

Problem after Preprocessing

Start: eval_foo_start
Program_Vars: Arg_0, Arg_1, Arg_4
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,Arg_4) -> eval_foo_bb1_in(0,1,Arg_4)
15:eval_foo_bb1_in(Arg_0,Arg_1,Arg_4) -> eval_foo_bb2_in(Arg_0,Arg_1,Arg_4):|:1<=Arg_1 && 1<=Arg_0+Arg_1 && Arg_0<=Arg_1 && 0<=Arg_0 && Arg_1<Arg_4
16:eval_foo_bb1_in(Arg_0,Arg_1,Arg_4) -> eval_foo_bb2_in(Arg_0,Arg_1,Arg_4):|:1<=Arg_1 && 1<=Arg_0+Arg_1 && Arg_0<=Arg_1 && 0<=Arg_0 && Arg_4<Arg_1
17:eval_foo_bb1_in(Arg_0,Arg_1,Arg_4) -> eval_foo_bb3_in(Arg_0,Arg_1,Arg_4):|:1<=Arg_1 && 1<=Arg_0+Arg_1 && Arg_0<=Arg_1 && 0<=Arg_0 && Arg_1<=Arg_4 && Arg_4<=Arg_1
18:eval_foo_bb2_in(Arg_0,Arg_1,Arg_4) -> eval_foo_bb1_in(Arg_1,Arg_1+Arg_0,Arg_4):|:1<=Arg_1 && 1<=Arg_0+Arg_1 && Arg_0<=Arg_1 && 0<=Arg_0
19:eval_foo_bb3_in(Arg_0,Arg_1,Arg_4) -> eval_foo_stop(Arg_0,Arg_1,Arg_4):|:Arg_4<=Arg_1 && 1<=Arg_4 && 2<=Arg_1+Arg_4 && Arg_1<=Arg_4 && 1<=Arg_0+Arg_4 && Arg_0<=Arg_4 && 1<=Arg_1 && 1<=Arg_0+Arg_1 && Arg_0<=Arg_1 && 0<=Arg_0
20:eval_foo_start(Arg_0,Arg_1,Arg_4) -> eval_foo_bb0_in(Arg_0,Arg_1,Arg_4)

MPRF for transition 15:eval_foo_bb1_in(Arg_0,Arg_1,Arg_4) -> eval_foo_bb2_in(Arg_0,Arg_1,Arg_4):|:1<=Arg_1 && 1<=Arg_0+Arg_1 && Arg_0<=Arg_1 && 0<=Arg_0 && Arg_1<Arg_4 of depth 1:

new bound:

2*Arg_4+2 {O(n)}

MPRF:

eval_foo_bb2_in [2*Arg_4-Arg_0-Arg_1-2 ]
eval_foo_bb1_in [2*Arg_4-Arg_0-Arg_1-1 ]

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: 2*Arg_4+2 {O(n)}
16: eval_foo_bb1_in->eval_foo_bb2_in: inf {Infinity}
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: 2*Arg_4+2 {O(n)}
16: eval_foo_bb1_in->eval_foo_bb2_in: inf {Infinity}
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: 0 {O(1)}
14: eval_foo_bb0_in->eval_foo_bb1_in, Arg_1: 1 {O(1)}
14: eval_foo_bb0_in->eval_foo_bb1_in, Arg_4: Arg_4 {O(n)}
15: eval_foo_bb1_in->eval_foo_bb2_in, Arg_4: 2*Arg_4 {O(n)}
16: eval_foo_bb1_in->eval_foo_bb2_in, Arg_4: 2*Arg_4 {O(n)}
17: eval_foo_bb1_in->eval_foo_bb3_in, Arg_4: 3*Arg_4 {O(n)}
18: eval_foo_bb2_in->eval_foo_bb1_in, Arg_4: 2*Arg_4 {O(n)}
19: eval_foo_bb3_in->eval_foo_stop, Arg_4: 3*Arg_4 {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)}
20: eval_foo_start->eval_foo_bb0_in, Arg_4: Arg_4 {O(n)}