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:
2:eval_foo_bb0_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_foo_bb1_in(2,Arg_1,Arg_2,Arg_3):|:0<=Arg_2
1: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
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):|:Arg_0<Arg_2
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_2<=Arg_0
5:eval_foo_bb2_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_foo_bb1_in(Arg_0^2,Arg_1,Arg_2,Arg_3)
6: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,Arg_3} that do not contribute to the problem

Found invariant 3<=Arg_2 && 5<=Arg_0+Arg_2 && 1+Arg_0<=Arg_2 && 2<=Arg_0 for location eval_foo_bb2_in

Found invariant 0<=Arg_2 && 2<=Arg_0+Arg_2 && 2<=Arg_0 for location eval_foo_bb1_in

Problem after Preprocessing

Start: eval_foo_start
Program_Vars: Arg_0, Arg_2
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:
15:eval_foo_bb0_in(Arg_0,Arg_2) -> eval_foo_bb1_in(2,Arg_2):|:0<=Arg_2
14:eval_foo_bb0_in(Arg_0,Arg_2) -> eval_foo_bb3_in(Arg_0,Arg_2):|:Arg_2<0
16:eval_foo_bb1_in(Arg_0,Arg_2) -> eval_foo_bb2_in(Arg_0,Arg_2):|:0<=Arg_2 && 2<=Arg_0+Arg_2 && 2<=Arg_0 && Arg_0<Arg_2
17:eval_foo_bb1_in(Arg_0,Arg_2) -> eval_foo_bb3_in(Arg_0,Arg_2):|:0<=Arg_2 && 2<=Arg_0+Arg_2 && 2<=Arg_0 && Arg_2<=Arg_0
18:eval_foo_bb2_in(Arg_0,Arg_2) -> eval_foo_bb1_in(Arg_0^2,Arg_2):|:3<=Arg_2 && 5<=Arg_0+Arg_2 && 1+Arg_0<=Arg_2 && 2<=Arg_0
19:eval_foo_bb3_in(Arg_0,Arg_2) -> eval_foo_stop(Arg_0,Arg_2)
20:eval_foo_start(Arg_0,Arg_2) -> eval_foo_bb0_in(Arg_0,Arg_2)

MPRF for transition 16:eval_foo_bb1_in(Arg_0,Arg_2) -> eval_foo_bb2_in(Arg_0,Arg_2):|:0<=Arg_2 && 2<=Arg_0+Arg_2 && 2<=Arg_0 && Arg_0<Arg_2 of depth 1:

new bound:

Arg_2+2 {O(n)}

MPRF:

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

MPRF for transition 18:eval_foo_bb2_in(Arg_0,Arg_2) -> eval_foo_bb1_in(Temp_Int_66,Arg_2):|:3<=Arg_2 && 5<=Arg_0+Arg_2 && 1+Arg_0<=Arg_2 && 2<=Arg_0 && Arg_0<Temp_Int_66 && 4<=Temp_Int_66 of depth 1:

new bound:

Arg_2+2 {O(n)}

MPRF:

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

All Bounds

Timebounds

Overall timebound:2*Arg_2+9 {O(n)}
14: eval_foo_bb0_in->eval_foo_bb3_in: 1 {O(1)}
15: eval_foo_bb0_in->eval_foo_bb1_in: 1 {O(1)}
16: eval_foo_bb1_in->eval_foo_bb2_in: Arg_2+2 {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+2 {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+9 {O(n)}
14: eval_foo_bb0_in->eval_foo_bb3_in: 1 {O(1)}
15: eval_foo_bb0_in->eval_foo_bb1_in: 1 {O(1)}
16: eval_foo_bb1_in->eval_foo_bb2_in: Arg_2+2 {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+2 {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_bb3_in, Arg_0: Arg_0 {O(n)}
14: eval_foo_bb0_in->eval_foo_bb3_in, Arg_2: Arg_2 {O(n)}
15: eval_foo_bb0_in->eval_foo_bb1_in, Arg_0: 2 {O(1)}
15: eval_foo_bb0_in->eval_foo_bb1_in, Arg_2: Arg_2 {O(n)}
16: eval_foo_bb1_in->eval_foo_bb2_in, Arg_2: Arg_2 {O(n)}
17: eval_foo_bb1_in->eval_foo_bb3_in, Arg_2: 2*Arg_2 {O(n)}
18: eval_foo_bb2_in->eval_foo_bb1_in, Arg_2: Arg_2 {O(n)}
19: eval_foo_bb3_in->eval_foo_stop, Arg_2: 3*Arg_2 {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_2: Arg_2 {O(n)}