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_bb4_in, eval_foo_bb5_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(0,Arg_1,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_0,3,Arg_2,Arg_3,Arg_4):|:Arg_0<10
3:eval_foo_bb1_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> eval_foo_bb5_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4):|:10<=Arg_0
4:eval_foo_bb2_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<12
5:eval_foo_bb2_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> eval_foo_bb4_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4):|:12<=Arg_1
6:eval_foo_bb3_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> eval_foo_bb2_in(Arg_0,Arg_1+1,Arg_2,Arg_3,Arg_4)
7:eval_foo_bb4_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> eval_foo_bb1_in(Arg_0+1,Arg_1,Arg_2,Arg_3,Arg_4)
8:eval_foo_bb5_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,Arg_3,Arg_4} that do not contribute to the problem

Found invariant 10<=Arg_0 for location eval_foo_bb5_in

Found invariant 10<=Arg_0 for location eval_foo_stop

Found invariant Arg_1<=11 && Arg_1<=11+Arg_0 && 3<=Arg_1 && 3<=Arg_0+Arg_1 && 0<=Arg_0 for location eval_foo_bb3_in

Found invariant 3<=Arg_1 && 3<=Arg_0+Arg_1 && 0<=Arg_0 for location eval_foo_bb2_in

Found invariant 0<=Arg_0 for location eval_foo_bb1_in

Found invariant 12<=Arg_1 && 12<=Arg_0+Arg_1 && 0<=Arg_0 for location eval_foo_bb4_in

Problem after Preprocessing

Start: eval_foo_start
Program_Vars: Arg_0, Arg_1
Temp_Vars:
Locations: eval_foo_bb0_in, eval_foo_bb1_in, eval_foo_bb2_in, eval_foo_bb3_in, eval_foo_bb4_in, eval_foo_bb5_in, eval_foo_start, eval_foo_stop
Transitions:
18:eval_foo_bb0_in(Arg_0,Arg_1) -> eval_foo_bb1_in(0,Arg_1)
19:eval_foo_bb1_in(Arg_0,Arg_1) -> eval_foo_bb2_in(Arg_0,3):|:0<=Arg_0 && Arg_0<10
20:eval_foo_bb1_in(Arg_0,Arg_1) -> eval_foo_bb5_in(Arg_0,Arg_1):|:0<=Arg_0 && 10<=Arg_0
21:eval_foo_bb2_in(Arg_0,Arg_1) -> eval_foo_bb3_in(Arg_0,Arg_1):|:3<=Arg_1 && 3<=Arg_0+Arg_1 && 0<=Arg_0 && Arg_1<12
22:eval_foo_bb2_in(Arg_0,Arg_1) -> eval_foo_bb4_in(Arg_0,Arg_1):|:3<=Arg_1 && 3<=Arg_0+Arg_1 && 0<=Arg_0 && 12<=Arg_1
23:eval_foo_bb3_in(Arg_0,Arg_1) -> eval_foo_bb2_in(Arg_0,Arg_1+1):|:Arg_1<=11 && Arg_1<=11+Arg_0 && 3<=Arg_1 && 3<=Arg_0+Arg_1 && 0<=Arg_0
24:eval_foo_bb4_in(Arg_0,Arg_1) -> eval_foo_bb1_in(Arg_0+1,Arg_1):|:12<=Arg_1 && 12<=Arg_0+Arg_1 && 0<=Arg_0
25:eval_foo_bb5_in(Arg_0,Arg_1) -> eval_foo_stop(Arg_0,Arg_1):|:10<=Arg_0
26:eval_foo_start(Arg_0,Arg_1) -> eval_foo_bb0_in(Arg_0,Arg_1)

MPRF for transition 19:eval_foo_bb1_in(Arg_0,Arg_1) -> eval_foo_bb2_in(Arg_0,3):|:0<=Arg_0 && Arg_0<10 of depth 1:

new bound:

10 {O(1)}

MPRF:

eval_foo_bb3_in [9-Arg_0 ]
eval_foo_bb2_in [9-Arg_0 ]
eval_foo_bb4_in [9-Arg_0 ]
eval_foo_bb1_in [10-Arg_0 ]

MPRF for transition 21:eval_foo_bb2_in(Arg_0,Arg_1) -> eval_foo_bb3_in(Arg_0,Arg_1):|:3<=Arg_1 && 3<=Arg_0+Arg_1 && 0<=Arg_0 && Arg_1<12 of depth 1:

new bound:

150 {O(1)}

MPRF:

eval_foo_bb3_in [11-Arg_1 ]
eval_foo_bb2_in [12-Arg_1 ]
eval_foo_bb4_in [-Arg_1 ]
eval_foo_bb1_in [-Arg_1 ]

MPRF for transition 22:eval_foo_bb2_in(Arg_0,Arg_1) -> eval_foo_bb4_in(Arg_0,Arg_1):|:3<=Arg_1 && 3<=Arg_0+Arg_1 && 0<=Arg_0 && 12<=Arg_1 of depth 1:

new bound:

10 {O(1)}

MPRF:

eval_foo_bb3_in [1 ]
eval_foo_bb2_in [1 ]
eval_foo_bb4_in [0 ]
eval_foo_bb1_in [0 ]

MPRF for transition 23:eval_foo_bb3_in(Arg_0,Arg_1) -> eval_foo_bb2_in(Arg_0,Arg_1+1):|:Arg_1<=11 && Arg_1<=11+Arg_0 && 3<=Arg_1 && 3<=Arg_0+Arg_1 && 0<=Arg_0 of depth 1:

new bound:

150 {O(1)}

MPRF:

eval_foo_bb3_in [12-Arg_1 ]
eval_foo_bb2_in [12-Arg_1 ]
eval_foo_bb4_in [-Arg_1 ]
eval_foo_bb1_in [-Arg_1 ]

MPRF for transition 24:eval_foo_bb4_in(Arg_0,Arg_1) -> eval_foo_bb1_in(Arg_0+1,Arg_1):|:12<=Arg_1 && 12<=Arg_0+Arg_1 && 0<=Arg_0 of depth 1:

new bound:

10 {O(1)}

MPRF:

eval_foo_bb3_in [1 ]
eval_foo_bb2_in [1 ]
eval_foo_bb4_in [1 ]
eval_foo_bb1_in [2-2*Arg_0 ]

All Bounds

Timebounds

Overall timebound:334 {O(1)}
18: eval_foo_bb0_in->eval_foo_bb1_in: 1 {O(1)}
19: eval_foo_bb1_in->eval_foo_bb2_in: 10 {O(1)}
20: eval_foo_bb1_in->eval_foo_bb5_in: 1 {O(1)}
21: eval_foo_bb2_in->eval_foo_bb3_in: 150 {O(1)}
22: eval_foo_bb2_in->eval_foo_bb4_in: 10 {O(1)}
23: eval_foo_bb3_in->eval_foo_bb2_in: 150 {O(1)}
24: eval_foo_bb4_in->eval_foo_bb1_in: 10 {O(1)}
25: eval_foo_bb5_in->eval_foo_stop: 1 {O(1)}
26: eval_foo_start->eval_foo_bb0_in: 1 {O(1)}

Costbounds

Overall costbound: 334 {O(1)}
18: eval_foo_bb0_in->eval_foo_bb1_in: 1 {O(1)}
19: eval_foo_bb1_in->eval_foo_bb2_in: 10 {O(1)}
20: eval_foo_bb1_in->eval_foo_bb5_in: 1 {O(1)}
21: eval_foo_bb2_in->eval_foo_bb3_in: 150 {O(1)}
22: eval_foo_bb2_in->eval_foo_bb4_in: 10 {O(1)}
23: eval_foo_bb3_in->eval_foo_bb2_in: 150 {O(1)}
24: eval_foo_bb4_in->eval_foo_bb1_in: 10 {O(1)}
25: eval_foo_bb5_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: 0 {O(1)}
18: eval_foo_bb0_in->eval_foo_bb1_in, Arg_1: Arg_1 {O(n)}
19: eval_foo_bb1_in->eval_foo_bb2_in, Arg_0: 9 {O(1)}
19: eval_foo_bb1_in->eval_foo_bb2_in, Arg_1: 3 {O(1)}
20: eval_foo_bb1_in->eval_foo_bb5_in, Arg_0: 10 {O(1)}
20: eval_foo_bb1_in->eval_foo_bb5_in, Arg_1: 12 {O(1)}
21: eval_foo_bb2_in->eval_foo_bb3_in, Arg_0: 9 {O(1)}
21: eval_foo_bb2_in->eval_foo_bb3_in, Arg_1: 11 {O(1)}
22: eval_foo_bb2_in->eval_foo_bb4_in, Arg_0: 9 {O(1)}
22: eval_foo_bb2_in->eval_foo_bb4_in, Arg_1: 12 {O(1)}
23: eval_foo_bb3_in->eval_foo_bb2_in, Arg_0: 9 {O(1)}
23: eval_foo_bb3_in->eval_foo_bb2_in, Arg_1: 12 {O(1)}
24: eval_foo_bb4_in->eval_foo_bb1_in, Arg_0: 10 {O(1)}
24: eval_foo_bb4_in->eval_foo_bb1_in, Arg_1: 12 {O(1)}
25: eval_foo_bb5_in->eval_foo_stop, Arg_0: 10 {O(1)}
25: eval_foo_bb5_in->eval_foo_stop, Arg_1: 12 {O(1)}
26: eval_foo_start->eval_foo_bb0_in, Arg_0: Arg_0 {O(n)}
26: eval_foo_start->eval_foo_bb0_in, Arg_1: Arg_1 {O(n)}