Initial Problem

Start: eval_foo_start
Program_Vars: Arg_0, Arg_1, 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:
1:eval_foo_bb0_in(Arg_0,Arg_1,Arg_2) -> eval_foo_bb1_in(0,Arg_1,Arg_2)
2:eval_foo_bb1_in(Arg_0,Arg_1,Arg_2) -> eval_foo_bb2_in(Arg_0,Arg_1,Arg_2):|:Arg_0<20
3:eval_foo_bb1_in(Arg_0,Arg_1,Arg_2) -> eval_foo_bb3_in(Arg_0,Arg_1,Arg_2):|:20<=Arg_0
4:eval_foo_bb2_in(Arg_0,Arg_1,Arg_2) -> eval_foo_bb1_in(Arg_0+1,Arg_1,Arg_2):|:Arg_0<=9
5:eval_foo_bb2_in(Arg_0,Arg_1,Arg_2) -> eval_foo_bb1_in(Arg_0+1,Arg_1,Arg_2):|:9<Arg_0
6:eval_foo_bb3_in(Arg_0,Arg_1,Arg_2) -> eval_foo_stop(Arg_0,Arg_1,Arg_2)
0:eval_foo_start(Arg_0,Arg_1,Arg_2) -> eval_foo_bb0_in(Arg_0,Arg_1,Arg_2)

Preprocessing

Eliminate variables {Arg_1,Arg_2} that do not contribute to the problem

Found invariant 20<=Arg_0 for location eval_foo_stop

Found invariant 20<=Arg_0 for location eval_foo_bb3_in

Found invariant Arg_0<=19 && 0<=Arg_0 for location eval_foo_bb2_in

Found invariant 0<=Arg_0 for location eval_foo_bb1_in

Problem after Preprocessing

Start: eval_foo_start
Program_Vars: Arg_0
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) -> eval_foo_bb1_in(0)
15:eval_foo_bb1_in(Arg_0) -> eval_foo_bb2_in(Arg_0):|:0<=Arg_0 && Arg_0<20
16:eval_foo_bb1_in(Arg_0) -> eval_foo_bb3_in(Arg_0):|:0<=Arg_0 && 20<=Arg_0
17:eval_foo_bb2_in(Arg_0) -> eval_foo_bb1_in(Arg_0+1):|:Arg_0<=19 && 0<=Arg_0 && Arg_0<=9
18:eval_foo_bb2_in(Arg_0) -> eval_foo_bb1_in(Arg_0+1):|:Arg_0<=19 && 0<=Arg_0 && 9<Arg_0
19:eval_foo_bb3_in(Arg_0) -> eval_foo_stop(Arg_0):|:20<=Arg_0
20:eval_foo_start(Arg_0) -> eval_foo_bb0_in(Arg_0)

MPRF for transition 15:eval_foo_bb1_in(Arg_0) -> eval_foo_bb2_in(Arg_0):|:0<=Arg_0 && Arg_0<20 of depth 1:

new bound:

20 {O(1)}

MPRF:

eval_foo_bb2_in [19-Arg_0 ]
eval_foo_bb1_in [20-Arg_0 ]

MPRF for transition 17:eval_foo_bb2_in(Arg_0) -> eval_foo_bb1_in(Arg_0+1):|:Arg_0<=19 && 0<=Arg_0 && Arg_0<=9 of depth 1:

new bound:

20 {O(1)}

MPRF:

eval_foo_bb2_in [20-Arg_0 ]
eval_foo_bb1_in [20-Arg_0 ]

MPRF for transition 18:eval_foo_bb2_in(Arg_0) -> eval_foo_bb1_in(Arg_0+1):|:Arg_0<=19 && 0<=Arg_0 && 9<Arg_0 of depth 1:

new bound:

20 {O(1)}

MPRF:

eval_foo_bb2_in [20-Arg_0 ]
eval_foo_bb1_in [20-Arg_0 ]

All Bounds

Timebounds

Overall timebound:64 {O(1)}
14: eval_foo_bb0_in->eval_foo_bb1_in: 1 {O(1)}
15: eval_foo_bb1_in->eval_foo_bb2_in: 20 {O(1)}
16: eval_foo_bb1_in->eval_foo_bb3_in: 1 {O(1)}
17: eval_foo_bb2_in->eval_foo_bb1_in: 20 {O(1)}
18: eval_foo_bb2_in->eval_foo_bb1_in: 20 {O(1)}
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: 64 {O(1)}
14: eval_foo_bb0_in->eval_foo_bb1_in: 1 {O(1)}
15: eval_foo_bb1_in->eval_foo_bb2_in: 20 {O(1)}
16: eval_foo_bb1_in->eval_foo_bb3_in: 1 {O(1)}
17: eval_foo_bb2_in->eval_foo_bb1_in: 20 {O(1)}
18: eval_foo_bb2_in->eval_foo_bb1_in: 20 {O(1)}
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: 0 {O(1)}
15: eval_foo_bb1_in->eval_foo_bb2_in, Arg_0: 19 {O(1)}
16: eval_foo_bb1_in->eval_foo_bb3_in, Arg_0: 20 {O(1)}
17: eval_foo_bb2_in->eval_foo_bb1_in, Arg_0: 10 {O(1)}
18: eval_foo_bb2_in->eval_foo_bb1_in, Arg_0: 20 {O(1)}
19: eval_foo_bb3_in->eval_foo_stop, Arg_0: 20 {O(1)}
20: eval_foo_start->eval_foo_bb0_in, Arg_0: Arg_0 {O(n)}