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):|:Arg_2<0
2: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_2
3: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_2<=0 && 0<=Arg_2
4: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 && 0<Arg_3
5: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
6: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_3<=0
7:eval_foo_bb2_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_foo_bb1_in(Arg_0-Arg_3,Arg_1,Arg_2,Arg_3)
8: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 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:
18:eval_foo_bb0_in(Arg_0,Arg_2,Arg_3) -> eval_foo_bb1_in(Arg_2,Arg_2,Arg_3):|:Arg_2<0
19:eval_foo_bb0_in(Arg_0,Arg_2,Arg_3) -> eval_foo_bb1_in(Arg_2,Arg_2,Arg_3):|:0<Arg_2
20:eval_foo_bb0_in(Arg_0,Arg_2,Arg_3) -> eval_foo_bb3_in(Arg_0,Arg_2,Arg_3):|:Arg_2<=0 && 0<=Arg_2
21:eval_foo_bb1_in(Arg_0,Arg_2,Arg_3) -> eval_foo_bb2_in(Arg_0,Arg_2,Arg_3):|:Arg_0<=Arg_2 && 0<Arg_0 && 0<Arg_3
22:eval_foo_bb1_in(Arg_0,Arg_2,Arg_3) -> eval_foo_bb3_in(Arg_0,Arg_2,Arg_3):|:Arg_0<=Arg_2 && Arg_0<=0
23:eval_foo_bb1_in(Arg_0,Arg_2,Arg_3) -> eval_foo_bb3_in(Arg_0,Arg_2,Arg_3):|:Arg_0<=Arg_2 && Arg_3<=0
24:eval_foo_bb2_in(Arg_0,Arg_2,Arg_3) -> eval_foo_bb1_in(Arg_0-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
25:eval_foo_bb3_in(Arg_0,Arg_2,Arg_3) -> eval_foo_stop(Arg_0,Arg_2,Arg_3)
26:eval_foo_start(Arg_0,Arg_2,Arg_3) -> eval_foo_bb0_in(Arg_0,Arg_2,Arg_3)

MPRF for transition 21:eval_foo_bb1_in(Arg_0,Arg_2,Arg_3) -> eval_foo_bb2_in(Arg_0,Arg_2,Arg_3):|:Arg_0<=Arg_2 && 0<Arg_0 && 0<Arg_3 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 24:eval_foo_bb2_in(Arg_0,Arg_2,Arg_3) -> eval_foo_bb1_in(Arg_0-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 of depth 1:

new bound:

Arg_2+Arg_3+1 {O(n)}

MPRF:

eval_foo_bb2_in [Arg_0 ]
eval_foo_bb1_in [Arg_0+Arg_3-1 ]

All Bounds

Timebounds

Overall timebound:2*Arg_2+Arg_3+8 {O(n)}
18: eval_foo_bb0_in->eval_foo_bb1_in: 1 {O(1)}
19: eval_foo_bb0_in->eval_foo_bb1_in: 1 {O(1)}
20: eval_foo_bb0_in->eval_foo_bb3_in: 1 {O(1)}
21: eval_foo_bb1_in->eval_foo_bb2_in: Arg_2 {O(n)}
22: eval_foo_bb1_in->eval_foo_bb3_in: 1 {O(1)}
23: eval_foo_bb1_in->eval_foo_bb3_in: 1 {O(1)}
24: eval_foo_bb2_in->eval_foo_bb1_in: Arg_2+Arg_3+1 {O(n)}
25: eval_foo_bb3_in->eval_foo_stop: 1 {O(1)}
26: eval_foo_start->eval_foo_bb0_in: 1 {O(1)}

Costbounds

Overall costbound: 2*Arg_2+Arg_3+8 {O(n)}
18: eval_foo_bb0_in->eval_foo_bb1_in: 1 {O(1)}
19: eval_foo_bb0_in->eval_foo_bb1_in: 1 {O(1)}
20: eval_foo_bb0_in->eval_foo_bb3_in: 1 {O(1)}
21: eval_foo_bb1_in->eval_foo_bb2_in: Arg_2 {O(n)}
22: eval_foo_bb1_in->eval_foo_bb3_in: 1 {O(1)}
23: eval_foo_bb1_in->eval_foo_bb3_in: 1 {O(1)}
24: eval_foo_bb2_in->eval_foo_bb1_in: Arg_2+Arg_3+1 {O(n)}
25: eval_foo_bb3_in->eval_foo_stop: 1 {O(1)}
26: eval_foo_start->eval_foo_bb0_in: 1 {O(1)}

Sizebounds

18: eval_foo_bb0_in->eval_foo_bb1_in, Arg_0: Arg_2 {O(n)}
18: eval_foo_bb0_in->eval_foo_bb1_in, Arg_2: Arg_2 {O(n)}
18: eval_foo_bb0_in->eval_foo_bb1_in, Arg_3: Arg_3 {O(n)}
19: eval_foo_bb0_in->eval_foo_bb1_in, Arg_0: Arg_2 {O(n)}
19: eval_foo_bb0_in->eval_foo_bb1_in, Arg_2: Arg_2 {O(n)}
19: eval_foo_bb0_in->eval_foo_bb1_in, Arg_3: Arg_3 {O(n)}
20: eval_foo_bb0_in->eval_foo_bb3_in, Arg_0: Arg_0 {O(n)}
20: eval_foo_bb0_in->eval_foo_bb3_in, Arg_2: 0 {O(1)}
20: eval_foo_bb0_in->eval_foo_bb3_in, Arg_3: Arg_3 {O(n)}
21: eval_foo_bb1_in->eval_foo_bb2_in, Arg_0: Arg_2+Arg_3 {O(n)}
21: eval_foo_bb1_in->eval_foo_bb2_in, Arg_2: Arg_2 {O(n)}
21: eval_foo_bb1_in->eval_foo_bb2_in, Arg_3: Arg_3 {O(n)}
22: eval_foo_bb1_in->eval_foo_bb3_in, Arg_0: 2*Arg_2+Arg_3 {O(n)}
22: eval_foo_bb1_in->eval_foo_bb3_in, Arg_2: 2*Arg_2 {O(n)}
22: eval_foo_bb1_in->eval_foo_bb3_in, Arg_3: 2*Arg_3 {O(n)}
23: eval_foo_bb1_in->eval_foo_bb3_in, Arg_0: 2*Arg_2 {O(n)}
23: eval_foo_bb1_in->eval_foo_bb3_in, Arg_2: 2*Arg_2 {O(n)}
23: eval_foo_bb1_in->eval_foo_bb3_in, Arg_3: 2*Arg_3 {O(n)}
24: eval_foo_bb2_in->eval_foo_bb1_in, Arg_0: Arg_2+Arg_3 {O(n)}
24: eval_foo_bb2_in->eval_foo_bb1_in, Arg_2: Arg_2 {O(n)}
24: eval_foo_bb2_in->eval_foo_bb1_in, Arg_3: Arg_3 {O(n)}
25: eval_foo_bb3_in->eval_foo_stop, Arg_0: 4*Arg_2+Arg_0+Arg_3 {O(n)}
25: eval_foo_bb3_in->eval_foo_stop, Arg_2: 4*Arg_2 {O(n)}
25: eval_foo_bb3_in->eval_foo_stop, Arg_3: 5*Arg_3 {O(n)}
26: eval_foo_start->eval_foo_bb0_in, Arg_0: Arg_0 {O(n)}
26: eval_foo_start->eval_foo_bb0_in, Arg_2: Arg_2 {O(n)}
26: eval_foo_start->eval_foo_bb0_in, Arg_3: Arg_3 {O(n)}