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(1,Arg_4,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_0<0
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):|:0<Arg_0
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_0<=0 && 0<=Arg_0
5:eval_foo_bb2_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5) -> eval_foo_bb1_in(0,Arg_1+1,Arg_2,Arg_3,Arg_4,Arg_5):|:Arg_5<=Arg_1
6:eval_foo_bb2_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5) -> eval_foo_bb1_in(Arg_0,Arg_1+1,Arg_2,Arg_3,Arg_4,Arg_5):|:Arg_1<Arg_5
7: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} that do not contribute to the problem

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

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

Found invariant Arg_4<=Arg_1 && Arg_0<=1 && 1<=Arg_0 for location eval_foo_bb2_in

Found invariant Arg_4<=Arg_1 && Arg_0<=1 && 0<=Arg_0 for location eval_foo_bb1_in

Cut unsatisfiable transition 17: eval_foo_bb1_in->eval_foo_bb2_in

Problem after Preprocessing

Start: eval_foo_start
Program_Vars: Arg_0, Arg_1, 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:
16:eval_foo_bb0_in(Arg_0,Arg_1,Arg_4,Arg_5) -> eval_foo_bb1_in(1,Arg_4,Arg_4,Arg_5)
18:eval_foo_bb1_in(Arg_0,Arg_1,Arg_4,Arg_5) -> eval_foo_bb2_in(Arg_0,Arg_1,Arg_4,Arg_5):|:Arg_4<=Arg_1 && Arg_0<=1 && 0<=Arg_0 && 0<Arg_0
19:eval_foo_bb1_in(Arg_0,Arg_1,Arg_4,Arg_5) -> eval_foo_bb3_in(Arg_0,Arg_1,Arg_4,Arg_5):|:Arg_4<=Arg_1 && Arg_0<=1 && 0<=Arg_0 && Arg_0<=0 && 0<=Arg_0
20:eval_foo_bb2_in(Arg_0,Arg_1,Arg_4,Arg_5) -> eval_foo_bb1_in(0,Arg_1+1,Arg_4,Arg_5):|:Arg_4<=Arg_1 && Arg_0<=1 && 1<=Arg_0 && Arg_5<=Arg_1
21:eval_foo_bb2_in(Arg_0,Arg_1,Arg_4,Arg_5) -> eval_foo_bb1_in(Arg_0,Arg_1+1,Arg_4,Arg_5):|:Arg_4<=Arg_1 && Arg_0<=1 && 1<=Arg_0 && Arg_1<Arg_5
22:eval_foo_bb3_in(Arg_0,Arg_1,Arg_4,Arg_5) -> eval_foo_stop(Arg_0,Arg_1,Arg_4,Arg_5):|:Arg_4<=Arg_1 && Arg_0<=0 && 0<=Arg_0
23:eval_foo_start(Arg_0,Arg_1,Arg_4,Arg_5) -> eval_foo_bb0_in(Arg_0,Arg_1,Arg_4,Arg_5)

MPRF for transition 20:eval_foo_bb2_in(Arg_0,Arg_1,Arg_4,Arg_5) -> eval_foo_bb1_in(0,Arg_1+1,Arg_4,Arg_5):|:Arg_4<=Arg_1 && Arg_0<=1 && 1<=Arg_0 && Arg_5<=Arg_1 of depth 1:

new bound:

1 {O(1)}

MPRF:

eval_foo_bb2_in [1 ]
eval_foo_bb1_in [Arg_0 ]

MPRF for transition 21:eval_foo_bb2_in(Arg_0,Arg_1,Arg_4,Arg_5) -> eval_foo_bb1_in(Arg_0,Arg_1+1,Arg_4,Arg_5):|:Arg_4<=Arg_1 && Arg_0<=1 && 1<=Arg_0 && Arg_1<Arg_5 of depth 1:

new bound:

Arg_4+Arg_5 {O(n)}

MPRF:

eval_foo_bb2_in [Arg_5-Arg_1 ]
eval_foo_bb1_in [Arg_5-Arg_1 ]

knowledge_propagation leads to new time bound Arg_4+Arg_5+1 {O(n)} for transition 18:eval_foo_bb1_in(Arg_0,Arg_1,Arg_4,Arg_5) -> eval_foo_bb2_in(Arg_0,Arg_1,Arg_4,Arg_5):|:Arg_4<=Arg_1 && Arg_0<=1 && 0<=Arg_0 && 0<Arg_0

All Bounds

Timebounds

Overall timebound:2*Arg_4+2*Arg_5+6 {O(n)}
16: eval_foo_bb0_in->eval_foo_bb1_in: 1 {O(1)}
18: eval_foo_bb1_in->eval_foo_bb2_in: Arg_4+Arg_5+1 {O(n)}
19: eval_foo_bb1_in->eval_foo_bb3_in: 1 {O(1)}
20: eval_foo_bb2_in->eval_foo_bb1_in: 1 {O(1)}
21: eval_foo_bb2_in->eval_foo_bb1_in: Arg_4+Arg_5 {O(n)}
22: eval_foo_bb3_in->eval_foo_stop: 1 {O(1)}
23: eval_foo_start->eval_foo_bb0_in: 1 {O(1)}

Costbounds

Overall costbound: 2*Arg_4+2*Arg_5+6 {O(n)}
16: eval_foo_bb0_in->eval_foo_bb1_in: 1 {O(1)}
18: eval_foo_bb1_in->eval_foo_bb2_in: Arg_4+Arg_5+1 {O(n)}
19: eval_foo_bb1_in->eval_foo_bb3_in: 1 {O(1)}
20: eval_foo_bb2_in->eval_foo_bb1_in: 1 {O(1)}
21: eval_foo_bb2_in->eval_foo_bb1_in: Arg_4+Arg_5 {O(n)}
22: eval_foo_bb3_in->eval_foo_stop: 1 {O(1)}
23: eval_foo_start->eval_foo_bb0_in: 1 {O(1)}

Sizebounds

16: eval_foo_bb0_in->eval_foo_bb1_in, Arg_0: 1 {O(1)}
16: eval_foo_bb0_in->eval_foo_bb1_in, Arg_1: Arg_4 {O(n)}
16: eval_foo_bb0_in->eval_foo_bb1_in, Arg_4: Arg_4 {O(n)}
16: eval_foo_bb0_in->eval_foo_bb1_in, Arg_5: Arg_5 {O(n)}
18: eval_foo_bb1_in->eval_foo_bb2_in, Arg_0: 1 {O(1)}
18: eval_foo_bb1_in->eval_foo_bb2_in, Arg_1: 2*Arg_4+Arg_5 {O(n)}
18: eval_foo_bb1_in->eval_foo_bb2_in, Arg_4: Arg_4 {O(n)}
18: eval_foo_bb1_in->eval_foo_bb2_in, Arg_5: Arg_5 {O(n)}
19: eval_foo_bb1_in->eval_foo_bb3_in, Arg_0: 0 {O(1)}
19: eval_foo_bb1_in->eval_foo_bb3_in, Arg_1: 2*Arg_4+Arg_5+1 {O(n)}
19: eval_foo_bb1_in->eval_foo_bb3_in, Arg_4: Arg_4 {O(n)}
19: eval_foo_bb1_in->eval_foo_bb3_in, Arg_5: Arg_5 {O(n)}
20: eval_foo_bb2_in->eval_foo_bb1_in, Arg_0: 0 {O(1)}
20: eval_foo_bb2_in->eval_foo_bb1_in, Arg_1: 2*Arg_4+Arg_5+1 {O(n)}
20: eval_foo_bb2_in->eval_foo_bb1_in, Arg_4: Arg_4 {O(n)}
20: eval_foo_bb2_in->eval_foo_bb1_in, Arg_5: Arg_5 {O(n)}
21: eval_foo_bb2_in->eval_foo_bb1_in, Arg_0: 1 {O(1)}
21: eval_foo_bb2_in->eval_foo_bb1_in, Arg_1: 2*Arg_4+Arg_5 {O(n)}
21: eval_foo_bb2_in->eval_foo_bb1_in, Arg_4: Arg_4 {O(n)}
21: eval_foo_bb2_in->eval_foo_bb1_in, Arg_5: Arg_5 {O(n)}
22: eval_foo_bb3_in->eval_foo_stop, Arg_0: 0 {O(1)}
22: eval_foo_bb3_in->eval_foo_stop, Arg_1: 2*Arg_4+Arg_5+1 {O(n)}
22: eval_foo_bb3_in->eval_foo_stop, Arg_4: Arg_4 {O(n)}
22: eval_foo_bb3_in->eval_foo_stop, Arg_5: Arg_5 {O(n)}
23: eval_foo_start->eval_foo_bb0_in, Arg_0: Arg_0 {O(n)}
23: eval_foo_start->eval_foo_bb0_in, Arg_1: Arg_1 {O(n)}
23: eval_foo_start->eval_foo_bb0_in, Arg_4: Arg_4 {O(n)}
23: eval_foo_start->eval_foo_bb0_in, Arg_5: Arg_5 {O(n)}