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(Arg_3,Arg_5,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<Arg_4
3: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_4<=Arg_0
4:eval_foo_bb2_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5) -> eval_foo_bb1_in(Arg_0+1,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5):|:Arg_0<Arg_1 && Arg_0<Arg_1
5:eval_foo_bb2_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5) -> eval_foo_bb1_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5):|:Arg_0<Arg_1 && Arg_1<=Arg_0
6:eval_foo_bb2_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5) -> eval_foo_bb1_in(Arg_0+1,Arg_1+1,Arg_2,Arg_3,Arg_4,Arg_5):|:Arg_1<=Arg_0 && Arg_0<Arg_1
7: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_0 && Arg_1<=Arg_0
8: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

Cut unsatisfiable transition 5: eval_foo_bb2_in->eval_foo_bb1_in

Cut unsatisfiable transition 6: eval_foo_bb2_in->eval_foo_bb1_in

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

Found invariant Arg_5<=Arg_1 && Arg_4<=Arg_0 && Arg_3<=Arg_0 for location eval_foo_stop

Found invariant Arg_5<=Arg_1 && Arg_4<=Arg_0 && Arg_3<=Arg_0 for location eval_foo_bb3_in

Found invariant Arg_5<=Arg_1 && 1+Arg_3<=Arg_4 && 1+Arg_0<=Arg_4 && Arg_3<=Arg_0 for location eval_foo_bb2_in

Found invariant Arg_5<=Arg_1 && Arg_3<=Arg_0 for location eval_foo_bb1_in

Problem after Preprocessing

Start: eval_foo_start
Program_Vars: Arg_0, Arg_1, 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:
18:eval_foo_bb0_in(Arg_0,Arg_1,Arg_3,Arg_4,Arg_5) -> eval_foo_bb1_in(Arg_3,Arg_5,Arg_3,Arg_4,Arg_5)
19:eval_foo_bb1_in(Arg_0,Arg_1,Arg_3,Arg_4,Arg_5) -> eval_foo_bb2_in(Arg_0,Arg_1,Arg_3,Arg_4,Arg_5):|:Arg_5<=Arg_1 && Arg_3<=Arg_0 && Arg_0<Arg_4
20:eval_foo_bb1_in(Arg_0,Arg_1,Arg_3,Arg_4,Arg_5) -> eval_foo_bb3_in(Arg_0,Arg_1,Arg_3,Arg_4,Arg_5):|:Arg_5<=Arg_1 && Arg_3<=Arg_0 && Arg_4<=Arg_0
21:eval_foo_bb2_in(Arg_0,Arg_1,Arg_3,Arg_4,Arg_5) -> eval_foo_bb1_in(Arg_0+1,Arg_1,Arg_3,Arg_4,Arg_5):|:Arg_5<=Arg_1 && 1+Arg_3<=Arg_4 && 1+Arg_0<=Arg_4 && Arg_3<=Arg_0 && Arg_0<Arg_1 && Arg_0<Arg_1
22:eval_foo_bb2_in(Arg_0,Arg_1,Arg_3,Arg_4,Arg_5) -> eval_foo_bb1_in(Arg_0,Arg_1+1,Arg_3,Arg_4,Arg_5):|:Arg_5<=Arg_1 && 1+Arg_3<=Arg_4 && 1+Arg_0<=Arg_4 && Arg_3<=Arg_0 && Arg_1<=Arg_0 && Arg_1<=Arg_0
23:eval_foo_bb3_in(Arg_0,Arg_1,Arg_3,Arg_4,Arg_5) -> eval_foo_stop(Arg_0,Arg_1,Arg_3,Arg_4,Arg_5):|:Arg_5<=Arg_1 && Arg_4<=Arg_0 && Arg_3<=Arg_0
24:eval_foo_start(Arg_0,Arg_1,Arg_3,Arg_4,Arg_5) -> eval_foo_bb0_in(Arg_0,Arg_1,Arg_3,Arg_4,Arg_5)

MPRF for transition 21:eval_foo_bb2_in(Arg_0,Arg_1,Arg_3,Arg_4,Arg_5) -> eval_foo_bb1_in(Arg_0+1,Arg_1,Arg_3,Arg_4,Arg_5):|:Arg_5<=Arg_1 && 1+Arg_3<=Arg_4 && 1+Arg_0<=Arg_4 && Arg_3<=Arg_0 && Arg_0<Arg_1 && Arg_0<Arg_1 of depth 1:

new bound:

Arg_3+Arg_4 {O(n)}

MPRF:

eval_foo_bb2_in [Arg_4-Arg_0 ]
eval_foo_bb1_in [Arg_4-Arg_0 ]

MPRF for transition 22:eval_foo_bb2_in(Arg_0,Arg_1,Arg_3,Arg_4,Arg_5) -> eval_foo_bb1_in(Arg_0,Arg_1+1,Arg_3,Arg_4,Arg_5):|:Arg_5<=Arg_1 && 1+Arg_3<=Arg_4 && 1+Arg_0<=Arg_4 && Arg_3<=Arg_0 && Arg_1<=Arg_0 && Arg_1<=Arg_0 of depth 1:

new bound:

Arg_4+Arg_5 {O(n)}

MPRF:

eval_foo_bb2_in [Arg_4-Arg_1 ]
eval_foo_bb1_in [Arg_4-Arg_1 ]

knowledge_propagation leads to new time bound 2*Arg_4+Arg_3+Arg_5+1 {O(n)} for transition 19:eval_foo_bb1_in(Arg_0,Arg_1,Arg_3,Arg_4,Arg_5) -> eval_foo_bb2_in(Arg_0,Arg_1,Arg_3,Arg_4,Arg_5):|:Arg_5<=Arg_1 && Arg_3<=Arg_0 && Arg_0<Arg_4

All Bounds

Timebounds

Overall timebound:2*Arg_3+2*Arg_5+4*Arg_4+5 {O(n)}
18: eval_foo_bb0_in->eval_foo_bb1_in: 1 {O(1)}
19: eval_foo_bb1_in->eval_foo_bb2_in: 2*Arg_4+Arg_3+Arg_5+1 {O(n)}
20: eval_foo_bb1_in->eval_foo_bb3_in: 1 {O(1)}
21: eval_foo_bb2_in->eval_foo_bb1_in: Arg_3+Arg_4 {O(n)}
22: eval_foo_bb2_in->eval_foo_bb1_in: Arg_4+Arg_5 {O(n)}
23: eval_foo_bb3_in->eval_foo_stop: 1 {O(1)}
24: eval_foo_start->eval_foo_bb0_in: 1 {O(1)}

Costbounds

Overall costbound: 2*Arg_3+2*Arg_5+4*Arg_4+5 {O(n)}
18: eval_foo_bb0_in->eval_foo_bb1_in: 1 {O(1)}
19: eval_foo_bb1_in->eval_foo_bb2_in: 2*Arg_4+Arg_3+Arg_5+1 {O(n)}
20: eval_foo_bb1_in->eval_foo_bb3_in: 1 {O(1)}
21: eval_foo_bb2_in->eval_foo_bb1_in: Arg_3+Arg_4 {O(n)}
22: eval_foo_bb2_in->eval_foo_bb1_in: Arg_4+Arg_5 {O(n)}
23: eval_foo_bb3_in->eval_foo_stop: 1 {O(1)}
24: eval_foo_start->eval_foo_bb0_in: 1 {O(1)}

Sizebounds

18: eval_foo_bb0_in->eval_foo_bb1_in, Arg_0: Arg_3 {O(n)}
18: eval_foo_bb0_in->eval_foo_bb1_in, Arg_1: Arg_5 {O(n)}
18: eval_foo_bb0_in->eval_foo_bb1_in, Arg_3: Arg_3 {O(n)}
18: eval_foo_bb0_in->eval_foo_bb1_in, Arg_4: Arg_4 {O(n)}
18: eval_foo_bb0_in->eval_foo_bb1_in, Arg_5: Arg_5 {O(n)}
19: eval_foo_bb1_in->eval_foo_bb2_in, Arg_0: 2*Arg_3+Arg_4 {O(n)}
19: eval_foo_bb1_in->eval_foo_bb2_in, Arg_1: 2*Arg_5+Arg_4 {O(n)}
19: eval_foo_bb1_in->eval_foo_bb2_in, Arg_3: Arg_3 {O(n)}
19: eval_foo_bb1_in->eval_foo_bb2_in, Arg_4: Arg_4 {O(n)}
19: eval_foo_bb1_in->eval_foo_bb2_in, Arg_5: Arg_5 {O(n)}
20: eval_foo_bb1_in->eval_foo_bb3_in, Arg_0: 3*Arg_3+Arg_4 {O(n)}
20: eval_foo_bb1_in->eval_foo_bb3_in, Arg_1: 3*Arg_5+Arg_4 {O(n)}
20: eval_foo_bb1_in->eval_foo_bb3_in, Arg_3: 2*Arg_3 {O(n)}
20: eval_foo_bb1_in->eval_foo_bb3_in, Arg_4: 2*Arg_4 {O(n)}
20: eval_foo_bb1_in->eval_foo_bb3_in, Arg_5: 2*Arg_5 {O(n)}
21: eval_foo_bb2_in->eval_foo_bb1_in, Arg_0: 2*Arg_3+Arg_4 {O(n)}
21: eval_foo_bb2_in->eval_foo_bb1_in, Arg_1: 2*Arg_5+Arg_4 {O(n)}
21: eval_foo_bb2_in->eval_foo_bb1_in, Arg_3: Arg_3 {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_bb2_in->eval_foo_bb1_in, Arg_0: 2*Arg_3+Arg_4 {O(n)}
22: eval_foo_bb2_in->eval_foo_bb1_in, Arg_1: 2*Arg_5+Arg_4 {O(n)}
22: eval_foo_bb2_in->eval_foo_bb1_in, Arg_3: Arg_3 {O(n)}
22: eval_foo_bb2_in->eval_foo_bb1_in, Arg_4: Arg_4 {O(n)}
22: eval_foo_bb2_in->eval_foo_bb1_in, Arg_5: Arg_5 {O(n)}
23: eval_foo_bb3_in->eval_foo_stop, Arg_0: 3*Arg_3+Arg_4 {O(n)}
23: eval_foo_bb3_in->eval_foo_stop, Arg_1: 3*Arg_5+Arg_4 {O(n)}
23: eval_foo_bb3_in->eval_foo_stop, Arg_3: 2*Arg_3 {O(n)}
23: eval_foo_bb3_in->eval_foo_stop, Arg_4: 2*Arg_4 {O(n)}
23: eval_foo_bb3_in->eval_foo_stop, Arg_5: 2*Arg_5 {O(n)}
24: eval_foo_start->eval_foo_bb0_in, Arg_0: Arg_0 {O(n)}
24: eval_foo_start->eval_foo_bb0_in, Arg_1: Arg_1 {O(n)}
24: eval_foo_start->eval_foo_bb0_in, Arg_3: Arg_3 {O(n)}
24: eval_foo_start->eval_foo_bb0_in, Arg_4: Arg_4 {O(n)}
24: eval_foo_start->eval_foo_bb0_in, Arg_5: Arg_5 {O(n)}