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):|:0<=Arg_0 && 0<=Arg_1
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<0
4: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_1<0
5:eval_foo_bb2_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> eval_foo_bb1_in(Arg_1-1,Arg_0-1,Arg_2,Arg_3,Arg_4)
6: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 0<=Arg_1 && 0<=Arg_0+Arg_1 && 0<=Arg_0 for location eval_foo_bb2_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:
14:eval_foo_bb0_in(Arg_0,Arg_1,Arg_3,Arg_4) -> eval_foo_bb1_in(Arg_3,Arg_4,Arg_3,Arg_4)
15:eval_foo_bb1_in(Arg_0,Arg_1,Arg_3,Arg_4) -> eval_foo_bb2_in(Arg_0,Arg_1,Arg_3,Arg_4):|:0<=Arg_0 && 0<=Arg_1
16: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_0<0
17: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_1<0
18:eval_foo_bb2_in(Arg_0,Arg_1,Arg_3,Arg_4) -> eval_foo_bb1_in(Arg_1-1,Arg_0-1,Arg_3,Arg_4):|:0<=Arg_1 && 0<=Arg_0+Arg_1 && 0<=Arg_0
19:eval_foo_bb3_in(Arg_0,Arg_1,Arg_3,Arg_4) -> eval_foo_stop(Arg_0,Arg_1,Arg_3,Arg_4)
20: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 15:eval_foo_bb1_in(Arg_0,Arg_1,Arg_3,Arg_4) -> eval_foo_bb2_in(Arg_0,Arg_1,Arg_3,Arg_4):|:0<=Arg_0 && 0<=Arg_1 of depth 1:

new bound:

Arg_3+Arg_4+1 {O(n)}

MPRF:

eval_foo_bb2_in [Arg_0+Arg_1-1 ]
eval_foo_bb1_in [Arg_0+Arg_1+1 ]

MPRF for transition 18:eval_foo_bb2_in(Arg_0,Arg_1,Arg_3,Arg_4) -> eval_foo_bb1_in(Arg_1-1,Arg_0-1,Arg_3,Arg_4):|:0<=Arg_1 && 0<=Arg_0+Arg_1 && 0<=Arg_0 of depth 1:

new bound:

Arg_3+Arg_4+1 {O(n)}

MPRF:

eval_foo_bb2_in [Arg_0+Arg_1+1 ]
eval_foo_bb1_in [Arg_0+Arg_1+1 ]

All Bounds

Timebounds

Overall timebound:2*Arg_3+2*Arg_4+7 {O(n)}
14: eval_foo_bb0_in->eval_foo_bb1_in: 1 {O(1)}
15: eval_foo_bb1_in->eval_foo_bb2_in: Arg_3+Arg_4+1 {O(n)}
16: eval_foo_bb1_in->eval_foo_bb3_in: 1 {O(1)}
17: eval_foo_bb1_in->eval_foo_bb3_in: 1 {O(1)}
18: eval_foo_bb2_in->eval_foo_bb1_in: Arg_3+Arg_4+1 {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_3+2*Arg_4+7 {O(n)}
14: eval_foo_bb0_in->eval_foo_bb1_in: 1 {O(1)}
15: eval_foo_bb1_in->eval_foo_bb2_in: Arg_3+Arg_4+1 {O(n)}
16: eval_foo_bb1_in->eval_foo_bb3_in: 1 {O(1)}
17: eval_foo_bb1_in->eval_foo_bb3_in: 1 {O(1)}
18: eval_foo_bb2_in->eval_foo_bb1_in: Arg_3+Arg_4+1 {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_3 {O(n)}
14: eval_foo_bb0_in->eval_foo_bb1_in, Arg_1: Arg_4 {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_4: Arg_4 {O(n)}
15: eval_foo_bb1_in->eval_foo_bb2_in, Arg_0: Arg_3+Arg_4+1 {O(n)}
15: eval_foo_bb1_in->eval_foo_bb2_in, Arg_1: Arg_3+Arg_4+1 {O(n)}
15: eval_foo_bb1_in->eval_foo_bb2_in, Arg_3: Arg_3 {O(n)}
15: eval_foo_bb1_in->eval_foo_bb2_in, Arg_4: Arg_4 {O(n)}
16: eval_foo_bb1_in->eval_foo_bb3_in, Arg_0: 2*Arg_3+Arg_4+1 {O(n)}
16: eval_foo_bb1_in->eval_foo_bb3_in, Arg_1: 2*Arg_4+Arg_3+1 {O(n)}
16: eval_foo_bb1_in->eval_foo_bb3_in, Arg_3: 2*Arg_3 {O(n)}
16: eval_foo_bb1_in->eval_foo_bb3_in, Arg_4: 2*Arg_4 {O(n)}
17: eval_foo_bb1_in->eval_foo_bb3_in, Arg_0: 2*Arg_3+Arg_4+1 {O(n)}
17: eval_foo_bb1_in->eval_foo_bb3_in, Arg_1: 2*Arg_4+Arg_3+1 {O(n)}
17: eval_foo_bb1_in->eval_foo_bb3_in, Arg_3: 2*Arg_3 {O(n)}
17: eval_foo_bb1_in->eval_foo_bb3_in, Arg_4: 2*Arg_4 {O(n)}
18: eval_foo_bb2_in->eval_foo_bb1_in, Arg_0: Arg_3+Arg_4+1 {O(n)}
18: eval_foo_bb2_in->eval_foo_bb1_in, Arg_1: Arg_3+Arg_4+1 {O(n)}
18: eval_foo_bb2_in->eval_foo_bb1_in, Arg_3: Arg_3 {O(n)}
18: eval_foo_bb2_in->eval_foo_bb1_in, Arg_4: Arg_4 {O(n)}
19: eval_foo_bb3_in->eval_foo_stop, Arg_0: 2*Arg_4+4*Arg_3+2 {O(n)}
19: eval_foo_bb3_in->eval_foo_stop, Arg_1: 2*Arg_3+4*Arg_4+2 {O(n)}
19: eval_foo_bb3_in->eval_foo_stop, Arg_3: 4*Arg_3 {O(n)}
19: eval_foo_bb3_in->eval_foo_stop, Arg_4: 4*Arg_4 {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_3: Arg_3 {O(n)}
20: eval_foo_start->eval_foo_bb0_in, Arg_4: Arg_4 {O(n)}