Initial Problem

Start: eval_foo_start
Program_Vars: Arg_0, Arg_1, Arg_2, Arg_3, Arg_4, Arg_5, Arg_6, Arg_7, Arg_8
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,Arg_6,Arg_7,Arg_8) -> eval_foo_bb1_in(Arg_7,Arg_8,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6,Arg_7,Arg_8)
2:eval_foo_bb1_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6,Arg_7,Arg_8) -> eval_foo_bb2_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6,Arg_7,Arg_8):|:Arg_0<Arg_2
3:eval_foo_bb1_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6,Arg_7,Arg_8) -> eval_foo_bb2_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6,Arg_7,Arg_8):|:Arg_1<Arg_3
4:eval_foo_bb1_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6,Arg_7,Arg_8) -> eval_foo_bb3_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6,Arg_7,Arg_8):|:Arg_2<=Arg_0 && Arg_3<=Arg_1
5:eval_foo_bb2_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6,Arg_7,Arg_8) -> eval_foo_bb1_in(Arg_0+1,Arg_1+1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6,Arg_7,Arg_8)
6:eval_foo_bb3_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6,Arg_7,Arg_8) -> eval_foo_stop(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6,Arg_7,Arg_8)
0:eval_foo_start(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6,Arg_7,Arg_8) -> eval_foo_bb0_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6,Arg_7,Arg_8)

Preprocessing

Eliminate variables {Arg_4,Arg_5,Arg_6} that do not contribute to the problem

Found invariant Arg_8<=Arg_1 && Arg_7<=Arg_0 && Arg_3<=Arg_1 && Arg_2<=Arg_0 for location eval_foo_stop

Found invariant Arg_8<=Arg_1 && Arg_7<=Arg_0 && Arg_3<=Arg_1 && Arg_2<=Arg_0 for location eval_foo_bb3_in

Found invariant Arg_8<=Arg_1 && Arg_7<=Arg_0 for location eval_foo_bb2_in

Found invariant Arg_8<=Arg_1 && Arg_7<=Arg_0 for location eval_foo_bb1_in

Problem after Preprocessing

Start: eval_foo_start
Program_Vars: Arg_0, Arg_1, Arg_2, Arg_3, Arg_7, Arg_8
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_2,Arg_3,Arg_7,Arg_8) -> eval_foo_bb1_in(Arg_7,Arg_8,Arg_2,Arg_3,Arg_7,Arg_8)
15:eval_foo_bb1_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_7,Arg_8) -> eval_foo_bb2_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_7,Arg_8):|:Arg_8<=Arg_1 && Arg_7<=Arg_0 && Arg_0<Arg_2
16:eval_foo_bb1_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_7,Arg_8) -> eval_foo_bb2_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_7,Arg_8):|:Arg_8<=Arg_1 && Arg_7<=Arg_0 && Arg_1<Arg_3
17:eval_foo_bb1_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_7,Arg_8) -> eval_foo_bb3_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_7,Arg_8):|:Arg_8<=Arg_1 && Arg_7<=Arg_0 && Arg_2<=Arg_0 && Arg_3<=Arg_1
18:eval_foo_bb2_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_7,Arg_8) -> eval_foo_bb1_in(Arg_0+1,Arg_1+1,Arg_2,Arg_3,Arg_7,Arg_8):|:Arg_8<=Arg_1 && Arg_7<=Arg_0
19:eval_foo_bb3_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_7,Arg_8) -> eval_foo_stop(Arg_0,Arg_1,Arg_2,Arg_3,Arg_7,Arg_8):|:Arg_8<=Arg_1 && Arg_7<=Arg_0 && Arg_3<=Arg_1 && Arg_2<=Arg_0
20:eval_foo_start(Arg_0,Arg_1,Arg_2,Arg_3,Arg_7,Arg_8) -> eval_foo_bb0_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_7,Arg_8)

MPRF for transition 15:eval_foo_bb1_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_7,Arg_8) -> eval_foo_bb2_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_7,Arg_8):|:Arg_8<=Arg_1 && Arg_7<=Arg_0 && Arg_0<Arg_2 of depth 1:

new bound:

Arg_2+Arg_7 {O(n)}

MPRF:

eval_foo_bb2_in [Arg_2-Arg_0-1 ]
eval_foo_bb1_in [Arg_2-Arg_0 ]

MPRF for transition 16:eval_foo_bb1_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_7,Arg_8) -> eval_foo_bb2_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_7,Arg_8):|:Arg_8<=Arg_1 && Arg_7<=Arg_0 && Arg_1<Arg_3 of depth 1:

new bound:

Arg_3+Arg_8 {O(n)}

MPRF:

eval_foo_bb2_in [Arg_3-Arg_1-1 ]
eval_foo_bb1_in [Arg_3-Arg_1 ]

knowledge_propagation leads to new time bound Arg_2+Arg_3+Arg_7+Arg_8 {O(n)} for transition 18:eval_foo_bb2_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_7,Arg_8) -> eval_foo_bb1_in(Arg_0+1,Arg_1+1,Arg_2,Arg_3,Arg_7,Arg_8):|:Arg_8<=Arg_1 && Arg_7<=Arg_0

All Bounds

Timebounds

Overall timebound:2*Arg_2+2*Arg_3+2*Arg_7+2*Arg_8+4 {O(n)}
14: eval_foo_bb0_in->eval_foo_bb1_in: 1 {O(1)}
15: eval_foo_bb1_in->eval_foo_bb2_in: Arg_2+Arg_7 {O(n)}
16: eval_foo_bb1_in->eval_foo_bb2_in: Arg_3+Arg_8 {O(n)}
17: eval_foo_bb1_in->eval_foo_bb3_in: 1 {O(1)}
18: eval_foo_bb2_in->eval_foo_bb1_in: Arg_2+Arg_3+Arg_7+Arg_8 {O(n)}
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: 2*Arg_2+2*Arg_3+2*Arg_7+2*Arg_8+4 {O(n)}
14: eval_foo_bb0_in->eval_foo_bb1_in: 1 {O(1)}
15: eval_foo_bb1_in->eval_foo_bb2_in: Arg_2+Arg_7 {O(n)}
16: eval_foo_bb1_in->eval_foo_bb2_in: Arg_3+Arg_8 {O(n)}
17: eval_foo_bb1_in->eval_foo_bb3_in: 1 {O(1)}
18: eval_foo_bb2_in->eval_foo_bb1_in: Arg_2+Arg_3+Arg_7+Arg_8 {O(n)}
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_7 {O(n)}
14: eval_foo_bb0_in->eval_foo_bb1_in, Arg_1: Arg_8 {O(n)}
14: eval_foo_bb0_in->eval_foo_bb1_in, Arg_2: Arg_2 {O(n)}
14: eval_foo_bb0_in->eval_foo_bb1_in, Arg_3: Arg_3 {O(n)}
14: eval_foo_bb0_in->eval_foo_bb1_in, Arg_7: Arg_7 {O(n)}
14: eval_foo_bb0_in->eval_foo_bb1_in, Arg_8: Arg_8 {O(n)}
15: eval_foo_bb1_in->eval_foo_bb2_in, Arg_0: 3*Arg_7+Arg_2+Arg_3+Arg_8 {O(n)}
15: eval_foo_bb1_in->eval_foo_bb2_in, Arg_1: 3*Arg_8+Arg_2+Arg_3+Arg_7 {O(n)}
15: eval_foo_bb1_in->eval_foo_bb2_in, Arg_2: 2*Arg_2 {O(n)}
15: eval_foo_bb1_in->eval_foo_bb2_in, Arg_3: 2*Arg_3 {O(n)}
15: eval_foo_bb1_in->eval_foo_bb2_in, Arg_7: 2*Arg_7 {O(n)}
15: eval_foo_bb1_in->eval_foo_bb2_in, Arg_8: 2*Arg_8 {O(n)}
16: eval_foo_bb1_in->eval_foo_bb2_in, Arg_0: 3*Arg_7+Arg_2+Arg_3+Arg_8 {O(n)}
16: eval_foo_bb1_in->eval_foo_bb2_in, Arg_1: 3*Arg_8+Arg_2+Arg_3+Arg_7 {O(n)}
16: eval_foo_bb1_in->eval_foo_bb2_in, Arg_2: 2*Arg_2 {O(n)}
16: eval_foo_bb1_in->eval_foo_bb2_in, Arg_3: 2*Arg_3 {O(n)}
16: eval_foo_bb1_in->eval_foo_bb2_in, Arg_7: 2*Arg_7 {O(n)}
16: eval_foo_bb1_in->eval_foo_bb2_in, Arg_8: 2*Arg_8 {O(n)}
17: eval_foo_bb1_in->eval_foo_bb3_in, Arg_0: 4*Arg_7+Arg_2+Arg_3+Arg_8 {O(n)}
17: eval_foo_bb1_in->eval_foo_bb3_in, Arg_1: 4*Arg_8+Arg_2+Arg_3+Arg_7 {O(n)}
17: eval_foo_bb1_in->eval_foo_bb3_in, Arg_2: 3*Arg_2 {O(n)}
17: eval_foo_bb1_in->eval_foo_bb3_in, Arg_3: 3*Arg_3 {O(n)}
17: eval_foo_bb1_in->eval_foo_bb3_in, Arg_7: 3*Arg_7 {O(n)}
17: eval_foo_bb1_in->eval_foo_bb3_in, Arg_8: 3*Arg_8 {O(n)}
18: eval_foo_bb2_in->eval_foo_bb1_in, Arg_0: 3*Arg_7+Arg_2+Arg_3+Arg_8 {O(n)}
18: eval_foo_bb2_in->eval_foo_bb1_in, Arg_1: 3*Arg_8+Arg_2+Arg_3+Arg_7 {O(n)}
18: eval_foo_bb2_in->eval_foo_bb1_in, Arg_2: 2*Arg_2 {O(n)}
18: eval_foo_bb2_in->eval_foo_bb1_in, Arg_3: 2*Arg_3 {O(n)}
18: eval_foo_bb2_in->eval_foo_bb1_in, Arg_7: 2*Arg_7 {O(n)}
18: eval_foo_bb2_in->eval_foo_bb1_in, Arg_8: 2*Arg_8 {O(n)}
19: eval_foo_bb3_in->eval_foo_stop, Arg_0: 4*Arg_7+Arg_2+Arg_3+Arg_8 {O(n)}
19: eval_foo_bb3_in->eval_foo_stop, Arg_1: 4*Arg_8+Arg_2+Arg_3+Arg_7 {O(n)}
19: eval_foo_bb3_in->eval_foo_stop, Arg_2: 3*Arg_2 {O(n)}
19: eval_foo_bb3_in->eval_foo_stop, Arg_3: 3*Arg_3 {O(n)}
19: eval_foo_bb3_in->eval_foo_stop, Arg_7: 3*Arg_7 {O(n)}
19: eval_foo_bb3_in->eval_foo_stop, Arg_8: 3*Arg_8 {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_2: Arg_2 {O(n)}
20: eval_foo_start->eval_foo_bb0_in, Arg_3: Arg_3 {O(n)}
20: eval_foo_start->eval_foo_bb0_in, Arg_7: Arg_7 {O(n)}
20: eval_foo_start->eval_foo_bb0_in, Arg_8: Arg_8 {O(n)}