Initial Problem

Start: eval_foo_start
Program_Vars: Arg_0, Arg_1, Arg_2, Arg_3, Arg_4, Arg_5
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_bb6_in, eval_foo_start, eval_foo_stop
Transitions:
1:eval_foo_bb0_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5) -> eval_foo_bb1_in(Arg_4,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5)
2:eval_foo_bb1_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5) -> eval_foo_bb2_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5):|:1<Arg_0
3:eval_foo_bb1_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5) -> eval_foo_bb6_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5):|:Arg_0<=1
4:eval_foo_bb2_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5) -> eval_foo_bb3_in(Arg_0,Arg_0-2,Arg_2,Arg_3,Arg_4,Arg_5)
5:eval_foo_bb3_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5) -> eval_foo_bb4_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5):|:1<Arg_1
6:eval_foo_bb3_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5) -> eval_foo_bb5_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5):|:Arg_1<=1
7:eval_foo_bb4_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5) -> eval_foo_bb3_in(Arg_0,Arg_1-2,Arg_2,Arg_3,Arg_4,Arg_5)
8:eval_foo_bb5_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5) -> eval_foo_bb1_in(Arg_1+1,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5)
9:eval_foo_bb6_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5) -> eval_foo_stop(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5)
0:eval_foo_start(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5) -> eval_foo_bb0_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5)

Preprocessing

Eliminate variables {Arg_2,Arg_3,Arg_5} that do not contribute to the problem

Found invariant 2<=Arg_4 && 2<=Arg_1+Arg_4 && 2+Arg_1<=Arg_4 && 4<=Arg_0+Arg_4 && Arg_0<=Arg_4 && Arg_1<=1 && 2+Arg_1<=Arg_0 && 0<=Arg_1 && 2<=Arg_0+Arg_1 && 2<=Arg_0 for location eval_foo_bb5_in

Found invariant Arg_0<=Arg_4 && Arg_0<=1 for location eval_foo_stop

Found invariant 2<=Arg_4 && 2<=Arg_1+Arg_4 && 2+Arg_1<=Arg_4 && 4<=Arg_0+Arg_4 && Arg_0<=Arg_4 && 2+Arg_1<=Arg_0 && 0<=Arg_1 && 2<=Arg_0+Arg_1 && 2<=Arg_0 for location eval_foo_bb3_in

Found invariant 2<=Arg_4 && 4<=Arg_0+Arg_4 && Arg_0<=Arg_4 && 2<=Arg_0 for location eval_foo_bb2_in

Found invariant Arg_0<=Arg_4 for location eval_foo_bb1_in

Found invariant Arg_0<=Arg_4 && Arg_0<=1 for location eval_foo_bb6_in

Found invariant 4<=Arg_4 && 6<=Arg_1+Arg_4 && 2+Arg_1<=Arg_4 && 8<=Arg_0+Arg_4 && Arg_0<=Arg_4 && 2+Arg_1<=Arg_0 && 2<=Arg_1 && 6<=Arg_0+Arg_1 && 4<=Arg_0 for location eval_foo_bb4_in

Problem after Preprocessing

Start: eval_foo_start
Program_Vars: Arg_0, Arg_1, 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_bb6_in, eval_foo_start, eval_foo_stop
Transitions:
20:eval_foo_bb0_in(Arg_0,Arg_1,Arg_4) -> eval_foo_bb1_in(Arg_4,Arg_1,Arg_4)
21:eval_foo_bb1_in(Arg_0,Arg_1,Arg_4) -> eval_foo_bb2_in(Arg_0,Arg_1,Arg_4):|:Arg_0<=Arg_4 && 1<Arg_0
22:eval_foo_bb1_in(Arg_0,Arg_1,Arg_4) -> eval_foo_bb6_in(Arg_0,Arg_1,Arg_4):|:Arg_0<=Arg_4 && Arg_0<=1
23:eval_foo_bb2_in(Arg_0,Arg_1,Arg_4) -> eval_foo_bb3_in(Arg_0,Arg_0-2,Arg_4):|:2<=Arg_4 && 4<=Arg_0+Arg_4 && Arg_0<=Arg_4 && 2<=Arg_0
24:eval_foo_bb3_in(Arg_0,Arg_1,Arg_4) -> eval_foo_bb4_in(Arg_0,Arg_1,Arg_4):|:2<=Arg_4 && 2<=Arg_1+Arg_4 && 2+Arg_1<=Arg_4 && 4<=Arg_0+Arg_4 && Arg_0<=Arg_4 && 2+Arg_1<=Arg_0 && 0<=Arg_1 && 2<=Arg_0+Arg_1 && 2<=Arg_0 && 1<Arg_1
25:eval_foo_bb3_in(Arg_0,Arg_1,Arg_4) -> eval_foo_bb5_in(Arg_0,Arg_1,Arg_4):|:2<=Arg_4 && 2<=Arg_1+Arg_4 && 2+Arg_1<=Arg_4 && 4<=Arg_0+Arg_4 && Arg_0<=Arg_4 && 2+Arg_1<=Arg_0 && 0<=Arg_1 && 2<=Arg_0+Arg_1 && 2<=Arg_0 && Arg_1<=1
26:eval_foo_bb4_in(Arg_0,Arg_1,Arg_4) -> eval_foo_bb3_in(Arg_0,Arg_1-2,Arg_4):|:4<=Arg_4 && 6<=Arg_1+Arg_4 && 2+Arg_1<=Arg_4 && 8<=Arg_0+Arg_4 && Arg_0<=Arg_4 && 2+Arg_1<=Arg_0 && 2<=Arg_1 && 6<=Arg_0+Arg_1 && 4<=Arg_0
27:eval_foo_bb5_in(Arg_0,Arg_1,Arg_4) -> eval_foo_bb1_in(Arg_1+1,Arg_1,Arg_4):|:2<=Arg_4 && 2<=Arg_1+Arg_4 && 2+Arg_1<=Arg_4 && 4<=Arg_0+Arg_4 && Arg_0<=Arg_4 && Arg_1<=1 && 2+Arg_1<=Arg_0 && 0<=Arg_1 && 2<=Arg_0+Arg_1 && 2<=Arg_0
28:eval_foo_bb6_in(Arg_0,Arg_1,Arg_4) -> eval_foo_stop(Arg_0,Arg_1,Arg_4):|:Arg_0<=Arg_4 && Arg_0<=1
29:eval_foo_start(Arg_0,Arg_1,Arg_4) -> eval_foo_bb0_in(Arg_0,Arg_1,Arg_4)

MPRF for transition 21:eval_foo_bb1_in(Arg_0,Arg_1,Arg_4) -> eval_foo_bb2_in(Arg_0,Arg_1,Arg_4):|:Arg_0<=Arg_4 && 1<Arg_0 of depth 1:

new bound:

Arg_4+1 {O(n)}

MPRF:

eval_foo_bb2_in [Arg_0-2 ]
eval_foo_bb4_in [Arg_1 ]
eval_foo_bb3_in [Arg_1 ]
eval_foo_bb5_in [Arg_1 ]
eval_foo_bb1_in [Arg_0-1 ]

MPRF for transition 23:eval_foo_bb2_in(Arg_0,Arg_1,Arg_4) -> eval_foo_bb3_in(Arg_0,Arg_0-2,Arg_4):|:2<=Arg_4 && 4<=Arg_0+Arg_4 && Arg_0<=Arg_4 && 2<=Arg_0 of depth 1:

new bound:

Arg_4+1 {O(n)}

MPRF:

eval_foo_bb2_in [Arg_0-1 ]
eval_foo_bb4_in [Arg_0-2 ]
eval_foo_bb3_in [Arg_0-2 ]
eval_foo_bb5_in [Arg_1 ]
eval_foo_bb1_in [Arg_0-1 ]

MPRF for transition 24:eval_foo_bb3_in(Arg_0,Arg_1,Arg_4) -> eval_foo_bb4_in(Arg_0,Arg_1,Arg_4):|:2<=Arg_4 && 2<=Arg_1+Arg_4 && 2+Arg_1<=Arg_4 && 4<=Arg_0+Arg_4 && Arg_0<=Arg_4 && 2+Arg_1<=Arg_0 && 0<=Arg_1 && 2<=Arg_0+Arg_1 && 2<=Arg_0 && 1<Arg_1 of depth 1:

new bound:

Arg_4 {O(n)}

MPRF:

eval_foo_bb2_in [Arg_0 ]
eval_foo_bb4_in [Arg_1 ]
eval_foo_bb3_in [Arg_1+2 ]
eval_foo_bb5_in [Arg_1+2 ]
eval_foo_bb1_in [Arg_0 ]

MPRF for transition 25:eval_foo_bb3_in(Arg_0,Arg_1,Arg_4) -> eval_foo_bb5_in(Arg_0,Arg_1,Arg_4):|:2<=Arg_4 && 2<=Arg_1+Arg_4 && 2+Arg_1<=Arg_4 && 4<=Arg_0+Arg_4 && Arg_0<=Arg_4 && 2+Arg_1<=Arg_0 && 0<=Arg_1 && 2<=Arg_0+Arg_1 && 2<=Arg_0 && Arg_1<=1 of depth 1:

new bound:

Arg_4+1 {O(n)}

MPRF:

eval_foo_bb2_in [Arg_0-1 ]
eval_foo_bb4_in [Arg_0-1 ]
eval_foo_bb3_in [Arg_0-1 ]
eval_foo_bb5_in [Arg_0-2 ]
eval_foo_bb1_in [Arg_0-1 ]

MPRF for transition 26:eval_foo_bb4_in(Arg_0,Arg_1,Arg_4) -> eval_foo_bb3_in(Arg_0,Arg_1-2,Arg_4):|:4<=Arg_4 && 6<=Arg_1+Arg_4 && 2+Arg_1<=Arg_4 && 8<=Arg_0+Arg_4 && Arg_0<=Arg_4 && 2+Arg_1<=Arg_0 && 2<=Arg_1 && 6<=Arg_0+Arg_1 && 4<=Arg_0 of depth 1:

new bound:

Arg_4+3 {O(n)}

MPRF:

eval_foo_bb2_in [Arg_0-3 ]
eval_foo_bb4_in [Arg_1-1 ]
eval_foo_bb3_in [Arg_1-1 ]
eval_foo_bb5_in [-1 ]
eval_foo_bb1_in [Arg_0-3 ]

MPRF for transition 27:eval_foo_bb5_in(Arg_0,Arg_1,Arg_4) -> eval_foo_bb1_in(Arg_1+1,Arg_1,Arg_4):|:2<=Arg_4 && 2<=Arg_1+Arg_4 && 2+Arg_1<=Arg_4 && 4<=Arg_0+Arg_4 && Arg_0<=Arg_4 && Arg_1<=1 && 2+Arg_1<=Arg_0 && 0<=Arg_1 && 2<=Arg_0+Arg_1 && 2<=Arg_0 of depth 1:

new bound:

Arg_4 {O(n)}

MPRF:

eval_foo_bb2_in [Arg_0 ]
eval_foo_bb4_in [Arg_0 ]
eval_foo_bb3_in [Arg_0 ]
eval_foo_bb5_in [Arg_0 ]
eval_foo_bb1_in [Arg_0 ]

All Bounds

Timebounds

Overall timebound:6*Arg_4+10 {O(n)}
20: eval_foo_bb0_in->eval_foo_bb1_in: 1 {O(1)}
21: eval_foo_bb1_in->eval_foo_bb2_in: Arg_4+1 {O(n)}
22: eval_foo_bb1_in->eval_foo_bb6_in: 1 {O(1)}
23: eval_foo_bb2_in->eval_foo_bb3_in: Arg_4+1 {O(n)}
24: eval_foo_bb3_in->eval_foo_bb4_in: Arg_4 {O(n)}
25: eval_foo_bb3_in->eval_foo_bb5_in: Arg_4+1 {O(n)}
26: eval_foo_bb4_in->eval_foo_bb3_in: Arg_4+3 {O(n)}
27: eval_foo_bb5_in->eval_foo_bb1_in: Arg_4 {O(n)}
28: eval_foo_bb6_in->eval_foo_stop: 1 {O(1)}
29: eval_foo_start->eval_foo_bb0_in: 1 {O(1)}

Costbounds

Overall costbound: 6*Arg_4+10 {O(n)}
20: eval_foo_bb0_in->eval_foo_bb1_in: 1 {O(1)}
21: eval_foo_bb1_in->eval_foo_bb2_in: Arg_4+1 {O(n)}
22: eval_foo_bb1_in->eval_foo_bb6_in: 1 {O(1)}
23: eval_foo_bb2_in->eval_foo_bb3_in: Arg_4+1 {O(n)}
24: eval_foo_bb3_in->eval_foo_bb4_in: Arg_4 {O(n)}
25: eval_foo_bb3_in->eval_foo_bb5_in: Arg_4+1 {O(n)}
26: eval_foo_bb4_in->eval_foo_bb3_in: Arg_4+3 {O(n)}
27: eval_foo_bb5_in->eval_foo_bb1_in: Arg_4 {O(n)}
28: eval_foo_bb6_in->eval_foo_stop: 1 {O(1)}
29: eval_foo_start->eval_foo_bb0_in: 1 {O(1)}

Sizebounds

20: eval_foo_bb0_in->eval_foo_bb1_in, Arg_0: Arg_4 {O(n)}
20: eval_foo_bb0_in->eval_foo_bb1_in, Arg_1: Arg_1 {O(n)}
20: eval_foo_bb0_in->eval_foo_bb1_in, Arg_4: Arg_4 {O(n)}
21: eval_foo_bb1_in->eval_foo_bb2_in, Arg_0: Arg_4+2 {O(n)}
21: eval_foo_bb1_in->eval_foo_bb2_in, Arg_1: Arg_1+1 {O(n)}
21: eval_foo_bb1_in->eval_foo_bb2_in, Arg_4: Arg_4 {O(n)}
22: eval_foo_bb1_in->eval_foo_bb6_in, Arg_0: Arg_4+2 {O(n)}
22: eval_foo_bb1_in->eval_foo_bb6_in, Arg_1: Arg_1+1 {O(n)}
22: eval_foo_bb1_in->eval_foo_bb6_in, Arg_4: 2*Arg_4 {O(n)}
23: eval_foo_bb2_in->eval_foo_bb3_in, Arg_0: Arg_4+2 {O(n)}
23: eval_foo_bb2_in->eval_foo_bb3_in, Arg_1: Arg_4+2 {O(n)}
23: eval_foo_bb2_in->eval_foo_bb3_in, Arg_4: Arg_4 {O(n)}
24: eval_foo_bb3_in->eval_foo_bb4_in, Arg_0: Arg_4+2 {O(n)}
24: eval_foo_bb3_in->eval_foo_bb4_in, Arg_1: Arg_4+2 {O(n)}
24: eval_foo_bb3_in->eval_foo_bb4_in, Arg_4: Arg_4 {O(n)}
25: eval_foo_bb3_in->eval_foo_bb5_in, Arg_0: 2*Arg_4+4 {O(n)}
25: eval_foo_bb3_in->eval_foo_bb5_in, Arg_1: 1 {O(1)}
25: eval_foo_bb3_in->eval_foo_bb5_in, Arg_4: Arg_4 {O(n)}
26: eval_foo_bb4_in->eval_foo_bb3_in, Arg_0: Arg_4+2 {O(n)}
26: eval_foo_bb4_in->eval_foo_bb3_in, Arg_1: Arg_4+2 {O(n)}
26: eval_foo_bb4_in->eval_foo_bb3_in, Arg_4: Arg_4 {O(n)}
27: eval_foo_bb5_in->eval_foo_bb1_in, Arg_0: 2 {O(1)}
27: eval_foo_bb5_in->eval_foo_bb1_in, Arg_1: 1 {O(1)}
27: eval_foo_bb5_in->eval_foo_bb1_in, Arg_4: Arg_4 {O(n)}
28: eval_foo_bb6_in->eval_foo_stop, Arg_0: Arg_4+2 {O(n)}
28: eval_foo_bb6_in->eval_foo_stop, Arg_1: Arg_1+1 {O(n)}
28: eval_foo_bb6_in->eval_foo_stop, Arg_4: 2*Arg_4 {O(n)}
29: eval_foo_start->eval_foo_bb0_in, Arg_0: Arg_0 {O(n)}
29: eval_foo_start->eval_foo_bb0_in, Arg_1: Arg_1 {O(n)}
29: eval_foo_start->eval_foo_bb0_in, Arg_4: Arg_4 {O(n)}