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_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) -> eval_foo_bb1_in(Arg_2,Arg_1,Arg_2,Arg_3)
2:eval_foo_bb1_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_foo_bb2_in(Arg_0,10,Arg_2,Arg_3):|:Arg_0<=10
3:eval_foo_bb1_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_foo_bb5_in(Arg_0,Arg_1,Arg_2,Arg_3):|:10<Arg_0
4:eval_foo_bb2_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_foo_bb3_in(Arg_0,Arg_1,Arg_2,Arg_3):|:1<Arg_1
5:eval_foo_bb2_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_foo_bb4_in(Arg_0,Arg_1,Arg_2,Arg_3):|:Arg_1<=1
6:eval_foo_bb3_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_foo_bb2_in(Arg_0,Arg_1-1,Arg_2,Arg_3)
7:eval_foo_bb4_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_foo_bb1_in(Arg_0+1,Arg_1,Arg_2,Arg_3)
8:eval_foo_bb5_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_3} that do not contribute to the problem

Found invariant Arg_2<=Arg_0 && 11<=Arg_0 for location eval_foo_bb5_in

Found invariant Arg_2<=Arg_0 && 11<=Arg_0 for location eval_foo_stop

Found invariant Arg_2<=10 && Arg_2<=8+Arg_1 && Arg_1+Arg_2<=20 && Arg_2<=Arg_0 && Arg_0+Arg_2<=20 && Arg_1<=10 && Arg_0+Arg_1<=20 && 2<=Arg_1 && Arg_0<=8+Arg_1 && Arg_0<=10 for location eval_foo_bb3_in

Found invariant Arg_2<=10 && Arg_1+Arg_2<=20 && Arg_2<=Arg_0 && Arg_0+Arg_2<=20 && Arg_1<=10 && Arg_0+Arg_1<=20 && Arg_0<=10 for location eval_foo_bb2_in

Found invariant Arg_2<=Arg_0 for location eval_foo_bb1_in

Found invariant Arg_2<=10 && Arg_1+Arg_2<=11 && Arg_2<=Arg_0 && Arg_0+Arg_2<=20 && Arg_1<=1 && Arg_0+Arg_1<=11 && Arg_0<=10 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(Arg_2,Arg_1,Arg_2)
19:eval_foo_bb1_in(Arg_0,Arg_1,Arg_2) -> eval_foo_bb2_in(Arg_0,10,Arg_2):|:Arg_2<=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):|:Arg_2<=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):|:Arg_2<=10 && Arg_1+Arg_2<=20 && Arg_2<=Arg_0 && Arg_0+Arg_2<=20 && Arg_1<=10 && Arg_0+Arg_1<=20 && Arg_0<=10 && 1<Arg_1
22:eval_foo_bb2_in(Arg_0,Arg_1,Arg_2) -> eval_foo_bb4_in(Arg_0,Arg_1,Arg_2):|:Arg_2<=10 && Arg_1+Arg_2<=20 && Arg_2<=Arg_0 && Arg_0+Arg_2<=20 && Arg_1<=10 && Arg_0+Arg_1<=20 && Arg_0<=10 && Arg_1<=1
23:eval_foo_bb3_in(Arg_0,Arg_1,Arg_2) -> eval_foo_bb2_in(Arg_0,Arg_1-1,Arg_2):|:Arg_2<=10 && Arg_2<=8+Arg_1 && Arg_1+Arg_2<=20 && Arg_2<=Arg_0 && Arg_0+Arg_2<=20 && Arg_1<=10 && Arg_0+Arg_1<=20 && 2<=Arg_1 && Arg_0<=8+Arg_1 && Arg_0<=10
24:eval_foo_bb4_in(Arg_0,Arg_1,Arg_2) -> eval_foo_bb1_in(Arg_0+1,Arg_1,Arg_2):|:Arg_2<=10 && Arg_1+Arg_2<=11 && Arg_2<=Arg_0 && Arg_0+Arg_2<=20 && Arg_1<=1 && Arg_0+Arg_1<=11 && Arg_0<=10
25:eval_foo_bb5_in(Arg_0,Arg_1,Arg_2) -> eval_foo_stop(Arg_0,Arg_1,Arg_2):|:Arg_2<=Arg_0 && 11<=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_0,10,Arg_2):|:Arg_2<=Arg_0 && Arg_0<=10 of depth 1:

new bound:

Arg_2+11 {O(n)}

MPRF:

eval_foo_bb3_in [10-Arg_0 ]
eval_foo_bb2_in [10-Arg_0 ]
eval_foo_bb4_in [10-Arg_0 ]
eval_foo_bb1_in [11-Arg_0 ]

MPRF for transition 22:eval_foo_bb2_in(Arg_0,Arg_1,Arg_2) -> eval_foo_bb4_in(Arg_0,Arg_1,Arg_2):|:Arg_2<=10 && Arg_1+Arg_2<=20 && Arg_2<=Arg_0 && Arg_0+Arg_2<=20 && Arg_1<=10 && Arg_0+Arg_1<=20 && Arg_0<=10 && Arg_1<=1 of depth 1:

new bound:

Arg_2+11 {O(n)}

MPRF:

eval_foo_bb3_in [11-Arg_0 ]
eval_foo_bb2_in [11-Arg_0 ]
eval_foo_bb4_in [10-Arg_0 ]
eval_foo_bb1_in [11-Arg_0 ]

MPRF for transition 24:eval_foo_bb4_in(Arg_0,Arg_1,Arg_2) -> eval_foo_bb1_in(Arg_0+1,Arg_1,Arg_2):|:Arg_2<=10 && Arg_1+Arg_2<=11 && Arg_2<=Arg_0 && Arg_0+Arg_2<=20 && Arg_1<=1 && Arg_0+Arg_1<=11 && Arg_0<=10 of depth 1:

new bound:

Arg_2+11 {O(n)}

MPRF:

eval_foo_bb3_in [11-Arg_0 ]
eval_foo_bb2_in [11-Arg_0 ]
eval_foo_bb4_in [11-Arg_0 ]
eval_foo_bb1_in [11-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):|:Arg_2<=10 && Arg_1+Arg_2<=20 && Arg_2<=Arg_0 && Arg_0+Arg_2<=20 && Arg_1<=10 && Arg_0+Arg_1<=20 && Arg_0<=10 && 1<Arg_1 of depth 1:

new bound:

9*Arg_2+108 {O(n)}

MPRF:

eval_foo_bb1_in [9 ]
eval_foo_bb4_in [Arg_1-1 ]
eval_foo_bb3_in [Arg_1-2 ]
eval_foo_bb2_in [Arg_1-1 ]

MPRF for transition 23:eval_foo_bb3_in(Arg_0,Arg_1,Arg_2) -> eval_foo_bb2_in(Arg_0,Arg_1-1,Arg_2):|:Arg_2<=10 && Arg_2<=8+Arg_1 && Arg_1+Arg_2<=20 && Arg_2<=Arg_0 && Arg_0+Arg_2<=20 && Arg_1<=10 && Arg_0+Arg_1<=20 && 2<=Arg_1 && Arg_0<=8+Arg_1 && Arg_0<=10 of depth 1:

new bound:

9*Arg_2+108 {O(n)}

MPRF:

eval_foo_bb1_in [9 ]
eval_foo_bb4_in [Arg_1-1 ]
eval_foo_bb3_in [Arg_1-1 ]
eval_foo_bb2_in [Arg_1-1 ]

All Bounds

Timebounds

Overall timebound:21*Arg_2+253 {O(n)}
18: eval_foo_bb0_in->eval_foo_bb1_in: 1 {O(1)}
19: eval_foo_bb1_in->eval_foo_bb2_in: Arg_2+11 {O(n)}
20: eval_foo_bb1_in->eval_foo_bb5_in: 1 {O(1)}
21: eval_foo_bb2_in->eval_foo_bb3_in: 9*Arg_2+108 {O(n)}
22: eval_foo_bb2_in->eval_foo_bb4_in: Arg_2+11 {O(n)}
23: eval_foo_bb3_in->eval_foo_bb2_in: 9*Arg_2+108 {O(n)}
24: eval_foo_bb4_in->eval_foo_bb1_in: Arg_2+11 {O(n)}
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: 21*Arg_2+253 {O(n)}
18: eval_foo_bb0_in->eval_foo_bb1_in: 1 {O(1)}
19: eval_foo_bb1_in->eval_foo_bb2_in: Arg_2+11 {O(n)}
20: eval_foo_bb1_in->eval_foo_bb5_in: 1 {O(1)}
21: eval_foo_bb2_in->eval_foo_bb3_in: 9*Arg_2+108 {O(n)}
22: eval_foo_bb2_in->eval_foo_bb4_in: Arg_2+11 {O(n)}
23: eval_foo_bb3_in->eval_foo_bb2_in: 9*Arg_2+108 {O(n)}
24: eval_foo_bb4_in->eval_foo_bb1_in: Arg_2+11 {O(n)}
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: Arg_2 {O(n)}
18: eval_foo_bb0_in->eval_foo_bb1_in, Arg_1: Arg_1 {O(n)}
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: 2*Arg_2+11 {O(n)}
19: eval_foo_bb1_in->eval_foo_bb2_in, Arg_1: 10 {O(1)}
19: eval_foo_bb1_in->eval_foo_bb2_in, Arg_2: Arg_2 {O(n)}
20: eval_foo_bb1_in->eval_foo_bb5_in, Arg_0: 3*Arg_2+11 {O(n)}
20: eval_foo_bb1_in->eval_foo_bb5_in, Arg_1: Arg_1+9 {O(n)}
20: eval_foo_bb1_in->eval_foo_bb5_in, Arg_2: 2*Arg_2 {O(n)}
21: eval_foo_bb2_in->eval_foo_bb3_in, Arg_0: 2*Arg_2+11 {O(n)}
21: eval_foo_bb2_in->eval_foo_bb3_in, Arg_1: 10 {O(1)}
21: eval_foo_bb2_in->eval_foo_bb3_in, Arg_2: Arg_2 {O(n)}
22: eval_foo_bb2_in->eval_foo_bb4_in, Arg_0: 2*Arg_2+11 {O(n)}
22: eval_foo_bb2_in->eval_foo_bb4_in, Arg_1: 9 {O(1)}
22: eval_foo_bb2_in->eval_foo_bb4_in, Arg_2: Arg_2 {O(n)}
23: eval_foo_bb3_in->eval_foo_bb2_in, Arg_0: 2*Arg_2+11 {O(n)}
23: eval_foo_bb3_in->eval_foo_bb2_in, Arg_1: 9 {O(1)}
23: eval_foo_bb3_in->eval_foo_bb2_in, Arg_2: Arg_2 {O(n)}
24: eval_foo_bb4_in->eval_foo_bb1_in, Arg_0: 2*Arg_2+11 {O(n)}
24: eval_foo_bb4_in->eval_foo_bb1_in, Arg_1: 9 {O(1)}
24: eval_foo_bb4_in->eval_foo_bb1_in, Arg_2: Arg_2 {O(n)}
25: eval_foo_bb5_in->eval_foo_stop, Arg_0: 3*Arg_2+11 {O(n)}
25: eval_foo_bb5_in->eval_foo_stop, Arg_1: Arg_1+9 {O(n)}
25: eval_foo_bb5_in->eval_foo_stop, Arg_2: 2*Arg_2 {O(n)}
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)}