Initial Problem

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

Preprocessing

Eliminate variables {Arg_1} that do not contribute to the problem

Found invariant 1<=Arg_3 && 2<=Arg_2+Arg_3 && 2<=Arg_0+Arg_3 && 1<=Arg_2 && 2<=Arg_0+Arg_2 && Arg_0<=Arg_2 && 1<=Arg_0 for location eval_foo_bb2_in

Found invariant 1<=Arg_3 && Arg_0<=Arg_2 for location eval_foo_bb1_in

Problem after Preprocessing

Start: eval_foo_start
Program_Vars: Arg_0, Arg_2, Arg_3
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_2,Arg_3) -> eval_foo_bb1_in(Arg_2,Arg_2,Arg_3):|:0<Arg_3
17:eval_foo_bb0_in(Arg_0,Arg_2,Arg_3) -> eval_foo_bb3_in(Arg_0,Arg_2,Arg_3):|:Arg_3<=0
18:eval_foo_bb1_in(Arg_0,Arg_2,Arg_3) -> eval_foo_bb2_in(Arg_0,Arg_2,Arg_3):|:1<=Arg_3 && Arg_0<=Arg_2 && 0<Arg_0
19:eval_foo_bb1_in(Arg_0,Arg_2,Arg_3) -> eval_foo_bb3_in(Arg_0,Arg_2,Arg_3):|:1<=Arg_3 && Arg_0<=Arg_2 && Arg_0<=0
20:eval_foo_bb2_in(Arg_0,Arg_2,Arg_3) -> eval_foo_bb1_in(Arg_3,Arg_2,Arg_3):|:1<=Arg_3 && 2<=Arg_2+Arg_3 && 2<=Arg_0+Arg_3 && 1<=Arg_2 && 2<=Arg_0+Arg_2 && Arg_0<=Arg_2 && 1<=Arg_0 && Arg_3<Arg_0
21:eval_foo_bb2_in(Arg_0,Arg_2,Arg_3) -> eval_foo_bb1_in(Arg_0-1,Arg_2,Arg_3):|:1<=Arg_3 && 2<=Arg_2+Arg_3 && 2<=Arg_0+Arg_3 && 1<=Arg_2 && 2<=Arg_0+Arg_2 && Arg_0<=Arg_2 && 1<=Arg_0 && Arg_0<=Arg_3
22:eval_foo_bb3_in(Arg_0,Arg_2,Arg_3) -> eval_foo_stop(Arg_0,Arg_2,Arg_3)
23:eval_foo_start(Arg_0,Arg_2,Arg_3) -> eval_foo_bb0_in(Arg_0,Arg_2,Arg_3)

MPRF for transition 18:eval_foo_bb1_in(Arg_0,Arg_2,Arg_3) -> eval_foo_bb2_in(Arg_0,Arg_2,Arg_3):|:1<=Arg_3 && Arg_0<=Arg_2 && 0<Arg_0 of depth 1:

new bound:

Arg_2 {O(n)}

MPRF:

eval_foo_bb2_in [Arg_0-1 ]
eval_foo_bb1_in [Arg_0 ]

MPRF for transition 20:eval_foo_bb2_in(Arg_0,Arg_2,Arg_3) -> eval_foo_bb1_in(Arg_3,Arg_2,Arg_3):|:1<=Arg_3 && 2<=Arg_2+Arg_3 && 2<=Arg_0+Arg_3 && 1<=Arg_2 && 2<=Arg_0+Arg_2 && Arg_0<=Arg_2 && 1<=Arg_0 && Arg_3<Arg_0 of depth 1:

new bound:

Arg_2 {O(n)}

MPRF:

eval_foo_bb2_in [Arg_0 ]
eval_foo_bb1_in [Arg_0 ]

MPRF for transition 21:eval_foo_bb2_in(Arg_0,Arg_2,Arg_3) -> eval_foo_bb1_in(Arg_0-1,Arg_2,Arg_3):|:1<=Arg_3 && 2<=Arg_2+Arg_3 && 2<=Arg_0+Arg_3 && 1<=Arg_2 && 2<=Arg_0+Arg_2 && Arg_0<=Arg_2 && 1<=Arg_0 && Arg_0<=Arg_3 of depth 1:

new bound:

Arg_2 {O(n)}

MPRF:

eval_foo_bb2_in [Arg_0 ]
eval_foo_bb1_in [Arg_0 ]

All Bounds

Timebounds

Overall timebound:3*Arg_2+5 {O(n)}
16: eval_foo_bb0_in->eval_foo_bb1_in: 1 {O(1)}
17: eval_foo_bb0_in->eval_foo_bb3_in: 1 {O(1)}
18: eval_foo_bb1_in->eval_foo_bb2_in: Arg_2 {O(n)}
19: eval_foo_bb1_in->eval_foo_bb3_in: 1 {O(1)}
20: eval_foo_bb2_in->eval_foo_bb1_in: Arg_2 {O(n)}
21: eval_foo_bb2_in->eval_foo_bb1_in: Arg_2 {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: 3*Arg_2+5 {O(n)}
16: eval_foo_bb0_in->eval_foo_bb1_in: 1 {O(1)}
17: eval_foo_bb0_in->eval_foo_bb3_in: 1 {O(1)}
18: eval_foo_bb1_in->eval_foo_bb2_in: Arg_2 {O(n)}
19: eval_foo_bb1_in->eval_foo_bb3_in: 1 {O(1)}
20: eval_foo_bb2_in->eval_foo_bb1_in: Arg_2 {O(n)}
21: eval_foo_bb2_in->eval_foo_bb1_in: Arg_2 {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: Arg_2 {O(n)}
16: eval_foo_bb0_in->eval_foo_bb1_in, Arg_2: Arg_2 {O(n)}
16: eval_foo_bb0_in->eval_foo_bb1_in, Arg_3: Arg_3 {O(n)}
17: eval_foo_bb0_in->eval_foo_bb3_in, Arg_0: Arg_0 {O(n)}
17: eval_foo_bb0_in->eval_foo_bb3_in, Arg_2: Arg_2 {O(n)}
17: eval_foo_bb0_in->eval_foo_bb3_in, Arg_3: Arg_3 {O(n)}
18: eval_foo_bb1_in->eval_foo_bb2_in, Arg_0: Arg_2 {O(n)}
18: eval_foo_bb1_in->eval_foo_bb2_in, Arg_2: Arg_2 {O(n)}
18: eval_foo_bb1_in->eval_foo_bb2_in, Arg_3: Arg_3 {O(n)}
19: eval_foo_bb1_in->eval_foo_bb3_in, Arg_0: 2*Arg_2 {O(n)}
19: eval_foo_bb1_in->eval_foo_bb3_in, Arg_2: 2*Arg_2 {O(n)}
19: eval_foo_bb1_in->eval_foo_bb3_in, Arg_3: 2*Arg_3 {O(n)}
20: eval_foo_bb2_in->eval_foo_bb1_in, Arg_0: Arg_2 {O(n)}
20: eval_foo_bb2_in->eval_foo_bb1_in, Arg_2: Arg_2 {O(n)}
20: eval_foo_bb2_in->eval_foo_bb1_in, Arg_3: Arg_3 {O(n)}
21: eval_foo_bb2_in->eval_foo_bb1_in, Arg_0: Arg_2 {O(n)}
21: eval_foo_bb2_in->eval_foo_bb1_in, Arg_2: Arg_2 {O(n)}
21: eval_foo_bb2_in->eval_foo_bb1_in, Arg_3: Arg_3 {O(n)}
22: eval_foo_bb3_in->eval_foo_stop, Arg_0: 2*Arg_2+Arg_0 {O(n)}
22: eval_foo_bb3_in->eval_foo_stop, Arg_2: 3*Arg_2 {O(n)}
22: eval_foo_bb3_in->eval_foo_stop, Arg_3: 3*Arg_3 {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_2: Arg_2 {O(n)}
23: eval_foo_start->eval_foo_bb0_in, Arg_3: Arg_3 {O(n)}