Initial Problem

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

Preprocessing

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

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

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

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

Found invariant Arg_4<=Arg_1 && Arg_0<=Arg_3 for location eval_foo_bb1_in

Problem after Preprocessing

Start: eval_foo_start
Program_Vars: Arg_0, Arg_1, Arg_3, 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:
12:eval_foo_bb0_in(Arg_0,Arg_1,Arg_3,Arg_4) -> eval_foo_bb1_in(Arg_3,Arg_4,Arg_3,Arg_4)
13:eval_foo_bb1_in(Arg_0,Arg_1,Arg_3,Arg_4) -> eval_foo_bb2_in(Arg_0,Arg_1,Arg_3,Arg_4):|:Arg_4<=Arg_1 && Arg_0<=Arg_3 && Arg_1<Arg_0
14:eval_foo_bb1_in(Arg_0,Arg_1,Arg_3,Arg_4) -> eval_foo_bb3_in(Arg_0,Arg_1,Arg_3,Arg_4):|:Arg_4<=Arg_1 && Arg_0<=Arg_3 && Arg_0<=Arg_1
15:eval_foo_bb2_in(Arg_0,Arg_1,Arg_3,Arg_4) -> eval_foo_bb1_in(Arg_0-1,Arg_1+1,Arg_3,Arg_4):|:1+Arg_4<=Arg_3 && Arg_4<=Arg_1 && 1+Arg_4<=Arg_0 && 1+Arg_1<=Arg_3 && Arg_0<=Arg_3 && 1+Arg_1<=Arg_0
16:eval_foo_bb3_in(Arg_0,Arg_1,Arg_3,Arg_4) -> eval_foo_stop(Arg_0,Arg_1,Arg_3,Arg_4):|:Arg_4<=Arg_1 && Arg_0<=Arg_3 && Arg_0<=Arg_1
17:eval_foo_start(Arg_0,Arg_1,Arg_3,Arg_4) -> eval_foo_bb0_in(Arg_0,Arg_1,Arg_3,Arg_4)

MPRF for transition 13:eval_foo_bb1_in(Arg_0,Arg_1,Arg_3,Arg_4) -> eval_foo_bb2_in(Arg_0,Arg_1,Arg_3,Arg_4):|:Arg_4<=Arg_1 && Arg_0<=Arg_3 && Arg_1<Arg_0 of depth 1:

new bound:

Arg_3+Arg_4 {O(n)}

MPRF:

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

MPRF for transition 15:eval_foo_bb2_in(Arg_0,Arg_1,Arg_3,Arg_4) -> eval_foo_bb1_in(Arg_0-1,Arg_1+1,Arg_3,Arg_4):|:1+Arg_4<=Arg_3 && Arg_4<=Arg_1 && 1+Arg_4<=Arg_0 && 1+Arg_1<=Arg_3 && Arg_0<=Arg_3 && 1+Arg_1<=Arg_0 of depth 1:

new bound:

Arg_3+Arg_4 {O(n)}

MPRF:

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

All Bounds

Timebounds

Overall timebound:2*Arg_3+2*Arg_4+4 {O(n)}
12: eval_foo_bb0_in->eval_foo_bb1_in: 1 {O(1)}
13: eval_foo_bb1_in->eval_foo_bb2_in: Arg_3+Arg_4 {O(n)}
14: eval_foo_bb1_in->eval_foo_bb3_in: 1 {O(1)}
15: eval_foo_bb2_in->eval_foo_bb1_in: Arg_3+Arg_4 {O(n)}
16: eval_foo_bb3_in->eval_foo_stop: 1 {O(1)}
17: eval_foo_start->eval_foo_bb0_in: 1 {O(1)}

Costbounds

Overall costbound: 2*Arg_3+2*Arg_4+4 {O(n)}
12: eval_foo_bb0_in->eval_foo_bb1_in: 1 {O(1)}
13: eval_foo_bb1_in->eval_foo_bb2_in: Arg_3+Arg_4 {O(n)}
14: eval_foo_bb1_in->eval_foo_bb3_in: 1 {O(1)}
15: eval_foo_bb2_in->eval_foo_bb1_in: Arg_3+Arg_4 {O(n)}
16: eval_foo_bb3_in->eval_foo_stop: 1 {O(1)}
17: eval_foo_start->eval_foo_bb0_in: 1 {O(1)}

Sizebounds

12: eval_foo_bb0_in->eval_foo_bb1_in, Arg_0: Arg_3 {O(n)}
12: eval_foo_bb0_in->eval_foo_bb1_in, Arg_1: Arg_4 {O(n)}
12: eval_foo_bb0_in->eval_foo_bb1_in, Arg_3: Arg_3 {O(n)}
12: eval_foo_bb0_in->eval_foo_bb1_in, Arg_4: Arg_4 {O(n)}
13: eval_foo_bb1_in->eval_foo_bb2_in, Arg_0: 2*Arg_3+Arg_4 {O(n)}
13: eval_foo_bb1_in->eval_foo_bb2_in, Arg_1: 2*Arg_4+Arg_3 {O(n)}
13: eval_foo_bb1_in->eval_foo_bb2_in, Arg_3: Arg_3 {O(n)}
13: eval_foo_bb1_in->eval_foo_bb2_in, Arg_4: Arg_4 {O(n)}
14: eval_foo_bb1_in->eval_foo_bb3_in, Arg_0: 3*Arg_3+Arg_4 {O(n)}
14: eval_foo_bb1_in->eval_foo_bb3_in, Arg_1: 3*Arg_4+Arg_3 {O(n)}
14: eval_foo_bb1_in->eval_foo_bb3_in, Arg_3: 2*Arg_3 {O(n)}
14: eval_foo_bb1_in->eval_foo_bb3_in, Arg_4: 2*Arg_4 {O(n)}
15: eval_foo_bb2_in->eval_foo_bb1_in, Arg_0: 2*Arg_3+Arg_4 {O(n)}
15: eval_foo_bb2_in->eval_foo_bb1_in, Arg_1: 2*Arg_4+Arg_3 {O(n)}
15: eval_foo_bb2_in->eval_foo_bb1_in, Arg_3: Arg_3 {O(n)}
15: eval_foo_bb2_in->eval_foo_bb1_in, Arg_4: Arg_4 {O(n)}
16: eval_foo_bb3_in->eval_foo_stop, Arg_0: 3*Arg_3+Arg_4 {O(n)}
16: eval_foo_bb3_in->eval_foo_stop, Arg_1: 3*Arg_4+Arg_3 {O(n)}
16: eval_foo_bb3_in->eval_foo_stop, Arg_3: 2*Arg_3 {O(n)}
16: eval_foo_bb3_in->eval_foo_stop, Arg_4: 2*Arg_4 {O(n)}
17: eval_foo_start->eval_foo_bb0_in, Arg_0: Arg_0 {O(n)}
17: eval_foo_start->eval_foo_bb0_in, Arg_1: Arg_1 {O(n)}
17: eval_foo_start->eval_foo_bb0_in, Arg_3: Arg_3 {O(n)}
17: eval_foo_start->eval_foo_bb0_in, Arg_4: Arg_4 {O(n)}