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(0,3,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_1,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_2<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_2
6:eval_foo_bb3_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> eval_foo_bb2_in(Arg_0,Arg_1,Arg_2+1,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_2,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_3,Arg_4} that do not contribute to the problem

Found invariant 3<=Arg_1 && 13<=Arg_0+Arg_1 && 10<=Arg_0 for location eval_foo_bb5_in

Found invariant 3<=Arg_1 && 13<=Arg_0+Arg_1 && 10<=Arg_0 for location eval_foo_stop

Found invariant Arg_2<=11 && Arg_2<=8+Arg_1 && Arg_1+Arg_2<=22 && Arg_2<=11+Arg_0 && 3<=Arg_2 && 6<=Arg_1+Arg_2 && Arg_1<=Arg_2 && 3<=Arg_0+Arg_2 && 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_2 && 6<=Arg_1+Arg_2 && Arg_1<=Arg_2 && 3<=Arg_0+Arg_2 && 3<=Arg_1 && 3<=Arg_0+Arg_1 && 0<=Arg_0 for location eval_foo_bb2_in

Found invariant 3<=Arg_1 && 3<=Arg_0+Arg_1 && 0<=Arg_0 for location eval_foo_bb1_in

Found invariant 12<=Arg_2 && 15<=Arg_1+Arg_2 && Arg_1<=Arg_2 && 12<=Arg_0+Arg_2 && 3<=Arg_1 && 3<=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, Arg_2
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,Arg_2) -> eval_foo_bb1_in(0,3,Arg_2)
19:eval_foo_bb1_in(Arg_0,Arg_1,Arg_2) -> eval_foo_bb2_in(Arg_0,Arg_1,Arg_1):|:3<=Arg_1 && 3<=Arg_0+Arg_1 && 0<=Arg_0 && Arg_0<10
20:eval_foo_bb1_in(Arg_0,Arg_1,Arg_2) -> eval_foo_bb5_in(Arg_0,Arg_1,Arg_2):|:3<=Arg_1 && 3<=Arg_0+Arg_1 && 0<=Arg_0 && 10<=Arg_0
21:eval_foo_bb2_in(Arg_0,Arg_1,Arg_2) -> eval_foo_bb3_in(Arg_0,Arg_1,Arg_2):|:3<=Arg_2 && 6<=Arg_1+Arg_2 && Arg_1<=Arg_2 && 3<=Arg_0+Arg_2 && 3<=Arg_1 && 3<=Arg_0+Arg_1 && 0<=Arg_0 && Arg_2<12
22:eval_foo_bb2_in(Arg_0,Arg_1,Arg_2) -> eval_foo_bb4_in(Arg_0,Arg_1,Arg_2):|:3<=Arg_2 && 6<=Arg_1+Arg_2 && Arg_1<=Arg_2 && 3<=Arg_0+Arg_2 && 3<=Arg_1 && 3<=Arg_0+Arg_1 && 0<=Arg_0 && 12<=Arg_2
23:eval_foo_bb3_in(Arg_0,Arg_1,Arg_2) -> eval_foo_bb2_in(Arg_0,Arg_1,Arg_2+1):|:Arg_2<=11 && Arg_2<=8+Arg_1 && Arg_1+Arg_2<=22 && Arg_2<=11+Arg_0 && 3<=Arg_2 && 6<=Arg_1+Arg_2 && Arg_1<=Arg_2 && 3<=Arg_0+Arg_2 && 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,Arg_2) -> eval_foo_bb1_in(Arg_0+1,Arg_2,Arg_2):|:12<=Arg_2 && 15<=Arg_1+Arg_2 && Arg_1<=Arg_2 && 12<=Arg_0+Arg_2 && 3<=Arg_1 && 3<=Arg_0+Arg_1 && 0<=Arg_0
25:eval_foo_bb5_in(Arg_0,Arg_1,Arg_2) -> eval_foo_stop(Arg_0,Arg_1,Arg_2):|:3<=Arg_1 && 13<=Arg_0+Arg_1 && 10<=Arg_0
26:eval_foo_start(Arg_0,Arg_1,Arg_2) -> eval_foo_bb0_in(Arg_0,Arg_1,Arg_2)

MPRF for transition 19:eval_foo_bb1_in(Arg_0,Arg_1,Arg_2) -> eval_foo_bb2_in(Arg_0,Arg_1,Arg_1):|:3<=Arg_1 && 3<=Arg_0+Arg_1 && 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,Arg_2) -> eval_foo_bb3_in(Arg_0,Arg_1,Arg_2):|:3<=Arg_2 && 6<=Arg_1+Arg_2 && Arg_1<=Arg_2 && 3<=Arg_0+Arg_2 && 3<=Arg_1 && 3<=Arg_0+Arg_1 && 0<=Arg_0 && Arg_2<12 of depth 1:

new bound:

15 {O(1)}

MPRF:

eval_foo_bb3_in [11-Arg_2 ]
eval_foo_bb2_in [12-Arg_2 ]
eval_foo_bb4_in [12-Arg_2 ]
eval_foo_bb1_in [12-Arg_1 ]

MPRF for transition 23:eval_foo_bb3_in(Arg_0,Arg_1,Arg_2) -> eval_foo_bb2_in(Arg_0,Arg_1,Arg_2+1):|:Arg_2<=11 && Arg_2<=8+Arg_1 && Arg_1+Arg_2<=22 && Arg_2<=11+Arg_0 && 3<=Arg_2 && 6<=Arg_1+Arg_2 && Arg_1<=Arg_2 && 3<=Arg_0+Arg_2 && Arg_1<=11 && Arg_1<=11+Arg_0 && 3<=Arg_1 && 3<=Arg_0+Arg_1 && 0<=Arg_0 of depth 1:

new bound:

15 {O(1)}

MPRF:

eval_foo_bb3_in [12-Arg_2 ]
eval_foo_bb2_in [12-Arg_2 ]
eval_foo_bb4_in [12-Arg_2 ]
eval_foo_bb1_in [12-Arg_1 ]

knowledge_propagation leads to new time bound 25 {O(1)} for transition 22:eval_foo_bb2_in(Arg_0,Arg_1,Arg_2) -> eval_foo_bb4_in(Arg_0,Arg_1,Arg_2):|:3<=Arg_2 && 6<=Arg_1+Arg_2 && Arg_1<=Arg_2 && 3<=Arg_0+Arg_2 && 3<=Arg_1 && 3<=Arg_0+Arg_1 && 0<=Arg_0 && 12<=Arg_2

knowledge_propagation leads to new time bound 25 {O(1)} for transition 24:eval_foo_bb4_in(Arg_0,Arg_1,Arg_2) -> eval_foo_bb1_in(Arg_0+1,Arg_2,Arg_2):|:12<=Arg_2 && 15<=Arg_1+Arg_2 && Arg_1<=Arg_2 && 12<=Arg_0+Arg_2 && 3<=Arg_1 && 3<=Arg_0+Arg_1 && 0<=Arg_0

All Bounds

Timebounds

Overall timebound:94 {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: 15 {O(1)}
22: eval_foo_bb2_in->eval_foo_bb4_in: 25 {O(1)}
23: eval_foo_bb3_in->eval_foo_bb2_in: 15 {O(1)}
24: eval_foo_bb4_in->eval_foo_bb1_in: 25 {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: 94 {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: 15 {O(1)}
22: eval_foo_bb2_in->eval_foo_bb4_in: 25 {O(1)}
23: eval_foo_bb3_in->eval_foo_bb2_in: 15 {O(1)}
24: eval_foo_bb4_in->eval_foo_bb1_in: 25 {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: 3 {O(1)}
18: eval_foo_bb0_in->eval_foo_bb1_in, Arg_2: Arg_2 {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: 18 {O(1)}
19: eval_foo_bb1_in->eval_foo_bb2_in, Arg_2: 15 {O(1)}
20: eval_foo_bb1_in->eval_foo_bb5_in, Arg_0: 19 {O(1)}
20: eval_foo_bb1_in->eval_foo_bb5_in, Arg_1: 15 {O(1)}
20: eval_foo_bb1_in->eval_foo_bb5_in, Arg_2: 15 {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)}
21: eval_foo_bb2_in->eval_foo_bb3_in, Arg_2: 11 {O(1)}
22: eval_foo_bb2_in->eval_foo_bb4_in, Arg_0: 18 {O(1)}
22: eval_foo_bb2_in->eval_foo_bb4_in, Arg_1: 29 {O(1)}
22: eval_foo_bb2_in->eval_foo_bb4_in, Arg_2: 15 {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: 11 {O(1)}
23: eval_foo_bb3_in->eval_foo_bb2_in, Arg_2: 12 {O(1)}
24: eval_foo_bb4_in->eval_foo_bb1_in, Arg_0: 19 {O(1)}
24: eval_foo_bb4_in->eval_foo_bb1_in, Arg_1: 15 {O(1)}
24: eval_foo_bb4_in->eval_foo_bb1_in, Arg_2: 15 {O(1)}
25: eval_foo_bb5_in->eval_foo_stop, Arg_0: 19 {O(1)}
25: eval_foo_bb5_in->eval_foo_stop, Arg_1: 15 {O(1)}
25: eval_foo_bb5_in->eval_foo_stop, Arg_2: 15 {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)}
26: eval_foo_start->eval_foo_bb0_in, Arg_2: Arg_2 {O(n)}