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_bb6_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(Arg_2,Arg_1,Arg_2,Arg_3,Arg_4):|:0<=Arg_2
2:eval_foo_bb0_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> eval_foo_bb6_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4):|:Arg_2<0
3:eval_foo_bb1_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> eval_foo_bb2_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4):|:0<=Arg_0
4:eval_foo_bb1_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> eval_foo_bb6_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4):|:Arg_0<0
5:eval_foo_bb2_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> eval_foo_bb3_in(Arg_0,1,Arg_2,Arg_3,Arg_4):|:1<Arg_0
6:eval_foo_bb2_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):|:Arg_0<=1
7:eval_foo_bb3_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):|:Arg_1<Arg_0
8:eval_foo_bb3_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):|:Arg_0<=Arg_1
9:eval_foo_bb4_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> eval_foo_bb3_in(Arg_0,2*Arg_1,Arg_2,Arg_3,Arg_4)
10:eval_foo_bb5_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)
11:eval_foo_bb6_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 0<=Arg_2 && 0<=Arg_0+Arg_2 && Arg_0<=Arg_2 && 0<=Arg_0 for location eval_foo_bb5_in

Found invariant 2<=Arg_2 && 3<=Arg_1+Arg_2 && 4<=Arg_0+Arg_2 && Arg_0<=Arg_2 && 1<=Arg_1 && 3<=Arg_0+Arg_1 && 2<=Arg_0 for location eval_foo_bb3_in

Found invariant 0<=Arg_2 && 0<=Arg_0+Arg_2 && Arg_0<=Arg_2 && 0<=Arg_0 for location eval_foo_bb2_in

Found invariant 0<=Arg_2 && 0<=1+Arg_0+Arg_2 && Arg_0<=Arg_2 && 0<=1+Arg_0 for location eval_foo_bb1_in

Found invariant 2<=Arg_2 && 3<=Arg_1+Arg_2 && 1+Arg_1<=Arg_2 && 4<=Arg_0+Arg_2 && Arg_0<=Arg_2 && 1+Arg_1<=Arg_0 && 1<=Arg_1 && 3<=Arg_0+Arg_1 && 2<=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_bb6_in, eval_foo_start, eval_foo_stop
Transitions:
24:eval_foo_bb0_in(Arg_0,Arg_1,Arg_2) -> eval_foo_bb1_in(Arg_2,Arg_1,Arg_2):|:0<=Arg_2
25:eval_foo_bb0_in(Arg_0,Arg_1,Arg_2) -> eval_foo_bb6_in(Arg_0,Arg_1,Arg_2):|:Arg_2<0
26:eval_foo_bb1_in(Arg_0,Arg_1,Arg_2) -> eval_foo_bb2_in(Arg_0,Arg_1,Arg_2):|:0<=Arg_2 && 0<=1+Arg_0+Arg_2 && Arg_0<=Arg_2 && 0<=1+Arg_0 && 0<=Arg_0
27:eval_foo_bb1_in(Arg_0,Arg_1,Arg_2) -> eval_foo_bb6_in(Arg_0,Arg_1,Arg_2):|:0<=Arg_2 && 0<=1+Arg_0+Arg_2 && Arg_0<=Arg_2 && 0<=1+Arg_0 && Arg_0<0
28:eval_foo_bb2_in(Arg_0,Arg_1,Arg_2) -> eval_foo_bb3_in(Arg_0,1,Arg_2):|:0<=Arg_2 && 0<=Arg_0+Arg_2 && Arg_0<=Arg_2 && 0<=Arg_0 && 1<Arg_0
29:eval_foo_bb2_in(Arg_0,Arg_1,Arg_2) -> eval_foo_bb5_in(Arg_0,Arg_1,Arg_2):|:0<=Arg_2 && 0<=Arg_0+Arg_2 && Arg_0<=Arg_2 && 0<=Arg_0 && Arg_0<=1
30:eval_foo_bb3_in(Arg_0,Arg_1,Arg_2) -> eval_foo_bb4_in(Arg_0,Arg_1,Arg_2):|:2<=Arg_2 && 3<=Arg_1+Arg_2 && 4<=Arg_0+Arg_2 && Arg_0<=Arg_2 && 1<=Arg_1 && 3<=Arg_0+Arg_1 && 2<=Arg_0 && Arg_1<Arg_0
31:eval_foo_bb3_in(Arg_0,Arg_1,Arg_2) -> eval_foo_bb5_in(Arg_0,Arg_1,Arg_2):|:2<=Arg_2 && 3<=Arg_1+Arg_2 && 4<=Arg_0+Arg_2 && Arg_0<=Arg_2 && 1<=Arg_1 && 3<=Arg_0+Arg_1 && 2<=Arg_0 && Arg_0<=Arg_1
32:eval_foo_bb4_in(Arg_0,Arg_1,Arg_2) -> eval_foo_bb3_in(Arg_0,2*Arg_1,Arg_2):|:2<=Arg_2 && 3<=Arg_1+Arg_2 && 1+Arg_1<=Arg_2 && 4<=Arg_0+Arg_2 && Arg_0<=Arg_2 && 1+Arg_1<=Arg_0 && 1<=Arg_1 && 3<=Arg_0+Arg_1 && 2<=Arg_0
33:eval_foo_bb5_in(Arg_0,Arg_1,Arg_2) -> eval_foo_bb1_in(Arg_0-1,Arg_1,Arg_2):|:0<=Arg_2 && 0<=Arg_0+Arg_2 && Arg_0<=Arg_2 && 0<=Arg_0
34:eval_foo_bb6_in(Arg_0,Arg_1,Arg_2) -> eval_foo_stop(Arg_0,Arg_1,Arg_2)
35:eval_foo_start(Arg_0,Arg_1,Arg_2) -> eval_foo_bb0_in(Arg_0,Arg_1,Arg_2)

MPRF for transition 26:eval_foo_bb1_in(Arg_0,Arg_1,Arg_2) -> eval_foo_bb2_in(Arg_0,Arg_1,Arg_2):|:0<=Arg_2 && 0<=1+Arg_0+Arg_2 && Arg_0<=Arg_2 && 0<=1+Arg_0 && 0<=Arg_0 of depth 1:

new bound:

Arg_2+1 {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+1 ]

MPRF for transition 28:eval_foo_bb2_in(Arg_0,Arg_1,Arg_2) -> eval_foo_bb3_in(Arg_0,1,Arg_2):|:0<=Arg_2 && 0<=Arg_0+Arg_2 && Arg_0<=Arg_2 && 0<=Arg_0 && 1<Arg_0 of depth 1:

new bound:

Arg_2+1 {O(n)}

MPRF:

eval_foo_bb2_in [Arg_0+1 ]
eval_foo_bb4_in [Arg_0 ]
eval_foo_bb3_in [Arg_0 ]
eval_foo_bb5_in [Arg_0 ]
eval_foo_bb1_in [Arg_0+1 ]

MPRF for transition 29:eval_foo_bb2_in(Arg_0,Arg_1,Arg_2) -> eval_foo_bb5_in(Arg_0,Arg_1,Arg_2):|:0<=Arg_2 && 0<=Arg_0+Arg_2 && Arg_0<=Arg_2 && 0<=Arg_0 && Arg_0<=1 of depth 1:

new bound:

Arg_2+1 {O(n)}

MPRF:

eval_foo_bb2_in [Arg_0+1 ]
eval_foo_bb4_in [Arg_0 ]
eval_foo_bb3_in [Arg_0 ]
eval_foo_bb5_in [Arg_0 ]
eval_foo_bb1_in [Arg_0+1 ]

MPRF for transition 31:eval_foo_bb3_in(Arg_0,Arg_1,Arg_2) -> eval_foo_bb5_in(Arg_0,Arg_1,Arg_2):|:2<=Arg_2 && 3<=Arg_1+Arg_2 && 4<=Arg_0+Arg_2 && Arg_0<=Arg_2 && 1<=Arg_1 && 3<=Arg_0+Arg_1 && 2<=Arg_0 && Arg_0<=Arg_1 of depth 1:

new bound:

Arg_2+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 33:eval_foo_bb5_in(Arg_0,Arg_1,Arg_2) -> eval_foo_bb1_in(Arg_0-1,Arg_1,Arg_2):|:0<=Arg_2 && 0<=Arg_0+Arg_2 && Arg_0<=Arg_2 && 0<=Arg_0 of depth 1:

new bound:

Arg_2+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+1 ]
eval_foo_bb1_in [Arg_0+1 ]

MPRF for transition 30:eval_foo_bb3_in(Arg_0,Arg_1,Arg_2) -> eval_foo_bb4_in(Arg_0,Arg_1,Arg_2):|:2<=Arg_2 && 3<=Arg_1+Arg_2 && 4<=Arg_0+Arg_2 && Arg_0<=Arg_2 && 1<=Arg_1 && 3<=Arg_0+Arg_1 && 2<=Arg_0 && Arg_1<Arg_0 of depth 1:

new bound:

Arg_2*Arg_2+2*Arg_2 {O(n^2)}

MPRF:

eval_foo_bb2_in [Arg_2 ]
eval_foo_bb4_in [Arg_2-2*Arg_1 ]
eval_foo_bb3_in [Arg_2-Arg_1 ]
eval_foo_bb5_in [Arg_2 ]
eval_foo_bb1_in [Arg_2 ]

MPRF for transition 32:eval_foo_bb4_in(Arg_0,Arg_1,Arg_2) -> eval_foo_bb3_in(Arg_0,2*Arg_1,Arg_2):|:2<=Arg_2 && 3<=Arg_1+Arg_2 && 1+Arg_1<=Arg_2 && 4<=Arg_0+Arg_2 && Arg_0<=Arg_2 && 1+Arg_1<=Arg_0 && 1<=Arg_1 && 3<=Arg_0+Arg_1 && 2<=Arg_0 of depth 1:

new bound:

Arg_2*Arg_2+2*Arg_2 {O(n^2)}

MPRF:

eval_foo_bb2_in [Arg_2 ]
eval_foo_bb4_in [Arg_0-Arg_1 ]
eval_foo_bb3_in [Arg_0-Arg_1 ]
eval_foo_bb5_in [Arg_2 ]
eval_foo_bb1_in [Arg_2 ]

All Bounds

Timebounds

Overall timebound:2*Arg_2*Arg_2+9*Arg_2+10 {O(n^2)}
24: eval_foo_bb0_in->eval_foo_bb1_in: 1 {O(1)}
25: eval_foo_bb0_in->eval_foo_bb6_in: 1 {O(1)}
26: eval_foo_bb1_in->eval_foo_bb2_in: Arg_2+1 {O(n)}
27: eval_foo_bb1_in->eval_foo_bb6_in: 1 {O(1)}
28: eval_foo_bb2_in->eval_foo_bb3_in: Arg_2+1 {O(n)}
29: eval_foo_bb2_in->eval_foo_bb5_in: Arg_2+1 {O(n)}
30: eval_foo_bb3_in->eval_foo_bb4_in: Arg_2*Arg_2+2*Arg_2 {O(n^2)}
31: eval_foo_bb3_in->eval_foo_bb5_in: Arg_2+1 {O(n)}
32: eval_foo_bb4_in->eval_foo_bb3_in: Arg_2*Arg_2+2*Arg_2 {O(n^2)}
33: eval_foo_bb5_in->eval_foo_bb1_in: Arg_2+1 {O(n)}
34: eval_foo_bb6_in->eval_foo_stop: 1 {O(1)}
35: eval_foo_start->eval_foo_bb0_in: 1 {O(1)}

Costbounds

Overall costbound: 2*Arg_2*Arg_2+9*Arg_2+10 {O(n^2)}
24: eval_foo_bb0_in->eval_foo_bb1_in: 1 {O(1)}
25: eval_foo_bb0_in->eval_foo_bb6_in: 1 {O(1)}
26: eval_foo_bb1_in->eval_foo_bb2_in: Arg_2+1 {O(n)}
27: eval_foo_bb1_in->eval_foo_bb6_in: 1 {O(1)}
28: eval_foo_bb2_in->eval_foo_bb3_in: Arg_2+1 {O(n)}
29: eval_foo_bb2_in->eval_foo_bb5_in: Arg_2+1 {O(n)}
30: eval_foo_bb3_in->eval_foo_bb4_in: Arg_2*Arg_2+2*Arg_2 {O(n^2)}
31: eval_foo_bb3_in->eval_foo_bb5_in: Arg_2+1 {O(n)}
32: eval_foo_bb4_in->eval_foo_bb3_in: Arg_2*Arg_2+2*Arg_2 {O(n^2)}
33: eval_foo_bb5_in->eval_foo_bb1_in: Arg_2+1 {O(n)}
34: eval_foo_bb6_in->eval_foo_stop: 1 {O(1)}
35: eval_foo_start->eval_foo_bb0_in: 1 {O(1)}

Sizebounds

24: eval_foo_bb0_in->eval_foo_bb1_in, Arg_0: Arg_2 {O(n)}
24: eval_foo_bb0_in->eval_foo_bb1_in, Arg_1: Arg_1 {O(n)}
24: eval_foo_bb0_in->eval_foo_bb1_in, Arg_2: Arg_2 {O(n)}
25: eval_foo_bb0_in->eval_foo_bb6_in, Arg_0: Arg_0 {O(n)}
25: eval_foo_bb0_in->eval_foo_bb6_in, Arg_1: Arg_1 {O(n)}
25: eval_foo_bb0_in->eval_foo_bb6_in, Arg_2: Arg_2 {O(n)}
26: eval_foo_bb1_in->eval_foo_bb2_in, Arg_0: Arg_2+2 {O(n)}
26: eval_foo_bb1_in->eval_foo_bb2_in, Arg_1: 2^(Arg_2*Arg_2+2*Arg_2)+Arg_1 {O(EXP)}
26: eval_foo_bb1_in->eval_foo_bb2_in, Arg_2: Arg_2 {O(n)}
27: eval_foo_bb1_in->eval_foo_bb6_in, Arg_0: 1 {O(1)}
27: eval_foo_bb1_in->eval_foo_bb6_in, Arg_1: 2^(Arg_2*Arg_2+2*Arg_2)+Arg_1 {O(EXP)}
27: eval_foo_bb1_in->eval_foo_bb6_in, Arg_2: Arg_2 {O(n)}
28: eval_foo_bb2_in->eval_foo_bb3_in, Arg_0: Arg_2+2 {O(n)}
28: eval_foo_bb2_in->eval_foo_bb3_in, Arg_1: 1 {O(1)}
28: eval_foo_bb2_in->eval_foo_bb3_in, Arg_2: Arg_2 {O(n)}
29: eval_foo_bb2_in->eval_foo_bb5_in, Arg_0: 1 {O(1)}
29: eval_foo_bb2_in->eval_foo_bb5_in, Arg_1: 2^(Arg_2*Arg_2+2*Arg_2)+Arg_1 {O(EXP)}
29: eval_foo_bb2_in->eval_foo_bb5_in, Arg_2: Arg_2 {O(n)}
30: eval_foo_bb3_in->eval_foo_bb4_in, Arg_0: Arg_2+2 {O(n)}
30: eval_foo_bb3_in->eval_foo_bb4_in, Arg_1: 2^(Arg_2*Arg_2+2*Arg_2) {O(EXP)}
30: eval_foo_bb3_in->eval_foo_bb4_in, Arg_2: Arg_2 {O(n)}
31: eval_foo_bb3_in->eval_foo_bb5_in, Arg_0: Arg_2+2 {O(n)}
31: eval_foo_bb3_in->eval_foo_bb5_in, Arg_1: 2^(Arg_2*Arg_2+2*Arg_2) {O(EXP)}
31: eval_foo_bb3_in->eval_foo_bb5_in, Arg_2: Arg_2 {O(n)}
32: eval_foo_bb4_in->eval_foo_bb3_in, Arg_0: Arg_2+2 {O(n)}
32: eval_foo_bb4_in->eval_foo_bb3_in, Arg_1: 2^(Arg_2*Arg_2+2*Arg_2) {O(EXP)}
32: eval_foo_bb4_in->eval_foo_bb3_in, Arg_2: Arg_2 {O(n)}
33: eval_foo_bb5_in->eval_foo_bb1_in, Arg_0: Arg_2+2 {O(n)}
33: eval_foo_bb5_in->eval_foo_bb1_in, Arg_1: 2^(Arg_2*Arg_2+2*Arg_2)+Arg_1 {O(EXP)}
33: eval_foo_bb5_in->eval_foo_bb1_in, Arg_2: Arg_2 {O(n)}
34: eval_foo_bb6_in->eval_foo_stop, Arg_0: Arg_0+1 {O(n)}
34: eval_foo_bb6_in->eval_foo_stop, Arg_1: 2^(Arg_2*Arg_2+2*Arg_2)+2*Arg_1 {O(EXP)}
34: eval_foo_bb6_in->eval_foo_stop, Arg_2: 2*Arg_2 {O(n)}
35: eval_foo_start->eval_foo_bb0_in, Arg_0: Arg_0 {O(n)}
35: eval_foo_start->eval_foo_bb0_in, Arg_1: Arg_1 {O(n)}
35: eval_foo_start->eval_foo_bb0_in, Arg_2: Arg_2 {O(n)}