Initial Problem

Start: eval_foo_start
Program_Vars: Arg_0, Arg_1, Arg_2, Arg_3, Arg_4, Arg_5, Arg_6
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,Arg_5,Arg_6) -> eval_foo_bb1_in(Arg_4,Arg_6,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6)
2:eval_foo_bb1_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6) -> eval_foo_bb2_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6):|:Arg_1<0
3:eval_foo_bb1_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6) -> eval_foo_bb2_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6):|:0<Arg_1
4:eval_foo_bb1_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6) -> eval_foo_bb5_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6):|:Arg_1<=0 && 0<=Arg_1
5:eval_foo_bb2_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6) -> eval_foo_bb1_in(Arg_1,Arg_0,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6):|:Arg_0<=0
6:eval_foo_bb2_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6) -> eval_foo_bb1_in(Arg_1,Arg_0,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6):|:Arg_1<=0
7:eval_foo_bb2_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6) -> eval_foo_bb1_in(Arg_1,Arg_0,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6):|:Arg_0<=Arg_1 && Arg_1<=Arg_0
8:eval_foo_bb2_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6) -> eval_foo_bb3_in(Arg_0,Arg_1,Arg_0,Arg_3,Arg_4,Arg_5,Arg_6):|:0<Arg_0 && 0<Arg_1 && Arg_0<Arg_1
9:eval_foo_bb2_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6) -> eval_foo_bb3_in(Arg_0,Arg_1,Arg_0,Arg_3,Arg_4,Arg_5,Arg_6):|:0<Arg_0 && 0<Arg_1 && Arg_1<Arg_0
11:eval_foo_bb3_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6) -> eval_foo_bb1_in(Arg_1,Arg_2,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6):|:Arg_2<=Arg_1
10:eval_foo_bb3_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6) -> eval_foo_bb4_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6):|:Arg_1<Arg_2
12:eval_foo_bb4_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6) -> eval_foo_bb3_in(Arg_0,Arg_1,Arg_2-Arg_1,Arg_3,Arg_4,Arg_5,Arg_6)
13:eval_foo_bb5_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6) -> eval_foo_stop(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6)
0:eval_foo_start(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6) -> eval_foo_bb0_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6)

Preprocessing

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

Found invariant Arg_1<=0 && 0<=Arg_1 for location eval_foo_bb5_in

Found invariant Arg_1<=0 && 0<=Arg_1 for location eval_foo_stop

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

Found invariant Arg_2<=Arg_0 && 2<=Arg_2 && 3<=Arg_1+Arg_2 && 1+Arg_1<=Arg_2 && 4<=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, Arg_4, Arg_6
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:
29:eval_foo_bb0_in(Arg_0,Arg_1,Arg_2,Arg_4,Arg_6) -> eval_foo_bb1_in(Arg_4,Arg_6,Arg_2,Arg_4,Arg_6)
30:eval_foo_bb1_in(Arg_0,Arg_1,Arg_2,Arg_4,Arg_6) -> eval_foo_bb2_in(Arg_0,Arg_1,Arg_2,Arg_4,Arg_6):|:Arg_1<0
31:eval_foo_bb1_in(Arg_0,Arg_1,Arg_2,Arg_4,Arg_6) -> eval_foo_bb2_in(Arg_0,Arg_1,Arg_2,Arg_4,Arg_6):|:0<Arg_1
32:eval_foo_bb1_in(Arg_0,Arg_1,Arg_2,Arg_4,Arg_6) -> eval_foo_bb5_in(Arg_0,Arg_1,Arg_2,Arg_4,Arg_6):|:Arg_1<=0 && 0<=Arg_1
33:eval_foo_bb2_in(Arg_0,Arg_1,Arg_2,Arg_4,Arg_6) -> eval_foo_bb1_in(Arg_1,Arg_0,Arg_2,Arg_4,Arg_6):|:Arg_0<=0
34:eval_foo_bb2_in(Arg_0,Arg_1,Arg_2,Arg_4,Arg_6) -> eval_foo_bb1_in(Arg_1,Arg_0,Arg_2,Arg_4,Arg_6):|:Arg_1<=0
35:eval_foo_bb2_in(Arg_0,Arg_1,Arg_2,Arg_4,Arg_6) -> eval_foo_bb1_in(Arg_1,Arg_0,Arg_2,Arg_4,Arg_6):|:Arg_0<=Arg_1 && Arg_1<=Arg_0
36:eval_foo_bb2_in(Arg_0,Arg_1,Arg_2,Arg_4,Arg_6) -> eval_foo_bb3_in(Arg_0,Arg_1,Arg_0,Arg_4,Arg_6):|:0<Arg_0 && 0<Arg_1 && Arg_0<Arg_1
37:eval_foo_bb2_in(Arg_0,Arg_1,Arg_2,Arg_4,Arg_6) -> eval_foo_bb3_in(Arg_0,Arg_1,Arg_0,Arg_4,Arg_6):|:0<Arg_0 && 0<Arg_1 && Arg_1<Arg_0
39:eval_foo_bb3_in(Arg_0,Arg_1,Arg_2,Arg_4,Arg_6) -> eval_foo_bb1_in(Arg_1,Arg_2,Arg_2,Arg_4,Arg_6):|:Arg_2<=Arg_0 && 2<=Arg_1+Arg_2 && 2<=Arg_0+Arg_2 && 1<=Arg_1 && 3<=Arg_0+Arg_1 && 1<=Arg_0 && Arg_2<=Arg_1
38:eval_foo_bb3_in(Arg_0,Arg_1,Arg_2,Arg_4,Arg_6) -> eval_foo_bb4_in(Arg_0,Arg_1,Arg_2,Arg_4,Arg_6):|:Arg_2<=Arg_0 && 2<=Arg_1+Arg_2 && 2<=Arg_0+Arg_2 && 1<=Arg_1 && 3<=Arg_0+Arg_1 && 1<=Arg_0 && Arg_1<Arg_2
40:eval_foo_bb4_in(Arg_0,Arg_1,Arg_2,Arg_4,Arg_6) -> eval_foo_bb3_in(Arg_0,Arg_1,Arg_2-Arg_1,Arg_4,Arg_6):|:Arg_2<=Arg_0 && 2<=Arg_2 && 3<=Arg_1+Arg_2 && 1+Arg_1<=Arg_2 && 4<=Arg_0+Arg_2 && 1+Arg_1<=Arg_0 && 1<=Arg_1 && 3<=Arg_0+Arg_1 && 2<=Arg_0
41:eval_foo_bb5_in(Arg_0,Arg_1,Arg_2,Arg_4,Arg_6) -> eval_foo_stop(Arg_0,Arg_1,Arg_2,Arg_4,Arg_6):|:Arg_1<=0 && 0<=Arg_1
42:eval_foo_start(Arg_0,Arg_1,Arg_2,Arg_4,Arg_6) -> eval_foo_bb0_in(Arg_0,Arg_1,Arg_2,Arg_4,Arg_6)

MPRF for transition 38:eval_foo_bb3_in(Arg_0,Arg_1,Arg_2,Arg_4,Arg_6) -> eval_foo_bb4_in(Arg_0,Arg_1,Arg_2,Arg_4,Arg_6):|:Arg_2<=Arg_0 && 2<=Arg_1+Arg_2 && 2<=Arg_0+Arg_2 && 1<=Arg_1 && 3<=Arg_0+Arg_1 && 1<=Arg_0 && Arg_1<Arg_2 of depth 1:

new bound:

Arg_4+Arg_6+1 {O(n)}

MPRF:

eval_foo_bb2_in [Arg_0+Arg_1-1 ]
eval_foo_bb1_in [Arg_0+Arg_1-1 ]
eval_foo_bb4_in [Arg_1+Arg_2-2 ]
eval_foo_bb3_in [Arg_1+Arg_2-1 ]

MPRF for transition 40:eval_foo_bb4_in(Arg_0,Arg_1,Arg_2,Arg_4,Arg_6) -> eval_foo_bb3_in(Arg_0,Arg_1,Arg_2-Arg_1,Arg_4,Arg_6):|:Arg_2<=Arg_0 && 2<=Arg_2 && 3<=Arg_1+Arg_2 && 1+Arg_1<=Arg_2 && 4<=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_4+Arg_6+2 {O(n)}

MPRF:

eval_foo_bb2_in [Arg_0+Arg_1-2 ]
eval_foo_bb1_in [Arg_0+Arg_1-2 ]
eval_foo_bb4_in [Arg_2-1 ]
eval_foo_bb3_in [Arg_1+Arg_2-2 ]

All Bounds

Timebounds

Overall timebound:inf {Infinity}
29: eval_foo_bb0_in->eval_foo_bb1_in: 1 {O(1)}
30: eval_foo_bb1_in->eval_foo_bb2_in: inf {Infinity}
31: eval_foo_bb1_in->eval_foo_bb2_in: inf {Infinity}
32: eval_foo_bb1_in->eval_foo_bb5_in: 1 {O(1)}
33: eval_foo_bb2_in->eval_foo_bb1_in: inf {Infinity}
34: eval_foo_bb2_in->eval_foo_bb1_in: inf {Infinity}
35: eval_foo_bb2_in->eval_foo_bb1_in: inf {Infinity}
36: eval_foo_bb2_in->eval_foo_bb3_in: inf {Infinity}
37: eval_foo_bb2_in->eval_foo_bb3_in: inf {Infinity}
38: eval_foo_bb3_in->eval_foo_bb4_in: Arg_4+Arg_6+1 {O(n)}
39: eval_foo_bb3_in->eval_foo_bb1_in: inf {Infinity}
40: eval_foo_bb4_in->eval_foo_bb3_in: Arg_4+Arg_6+2 {O(n)}
41: eval_foo_bb5_in->eval_foo_stop: 1 {O(1)}
42: eval_foo_start->eval_foo_bb0_in: 1 {O(1)}

Costbounds

Overall costbound: inf {Infinity}
29: eval_foo_bb0_in->eval_foo_bb1_in: 1 {O(1)}
30: eval_foo_bb1_in->eval_foo_bb2_in: inf {Infinity}
31: eval_foo_bb1_in->eval_foo_bb2_in: inf {Infinity}
32: eval_foo_bb1_in->eval_foo_bb5_in: 1 {O(1)}
33: eval_foo_bb2_in->eval_foo_bb1_in: inf {Infinity}
34: eval_foo_bb2_in->eval_foo_bb1_in: inf {Infinity}
35: eval_foo_bb2_in->eval_foo_bb1_in: inf {Infinity}
36: eval_foo_bb2_in->eval_foo_bb3_in: inf {Infinity}
37: eval_foo_bb2_in->eval_foo_bb3_in: inf {Infinity}
38: eval_foo_bb3_in->eval_foo_bb4_in: Arg_4+Arg_6+1 {O(n)}
39: eval_foo_bb3_in->eval_foo_bb1_in: inf {Infinity}
40: eval_foo_bb4_in->eval_foo_bb3_in: Arg_4+Arg_6+2 {O(n)}
41: eval_foo_bb5_in->eval_foo_stop: 1 {O(1)}
42: eval_foo_start->eval_foo_bb0_in: 1 {O(1)}

Sizebounds

29: eval_foo_bb0_in->eval_foo_bb1_in, Arg_0: Arg_4 {O(n)}
29: eval_foo_bb0_in->eval_foo_bb1_in, Arg_1: Arg_6 {O(n)}
29: eval_foo_bb0_in->eval_foo_bb1_in, Arg_2: Arg_2 {O(n)}
29: eval_foo_bb0_in->eval_foo_bb1_in, Arg_4: Arg_4 {O(n)}
29: eval_foo_bb0_in->eval_foo_bb1_in, Arg_6: Arg_6 {O(n)}
30: eval_foo_bb1_in->eval_foo_bb2_in, Arg_0: 2*Arg_4+2*Arg_6 {O(n)}
30: eval_foo_bb1_in->eval_foo_bb2_in, Arg_1: 2*Arg_4+2*Arg_6 {O(n)}
30: eval_foo_bb1_in->eval_foo_bb2_in, Arg_2: 2*Arg_2+8*Arg_4+8*Arg_6 {O(n)}
30: eval_foo_bb1_in->eval_foo_bb2_in, Arg_4: 2*Arg_4 {O(n)}
30: eval_foo_bb1_in->eval_foo_bb2_in, Arg_6: 2*Arg_6 {O(n)}
31: eval_foo_bb1_in->eval_foo_bb2_in, Arg_0: 2*Arg_4+2*Arg_6 {O(n)}
31: eval_foo_bb1_in->eval_foo_bb2_in, Arg_1: 2*Arg_4+2*Arg_6 {O(n)}
31: eval_foo_bb1_in->eval_foo_bb2_in, Arg_2: 2*Arg_2+8*Arg_4+8*Arg_6 {O(n)}
31: eval_foo_bb1_in->eval_foo_bb2_in, Arg_4: 2*Arg_4 {O(n)}
31: eval_foo_bb1_in->eval_foo_bb2_in, Arg_6: 2*Arg_6 {O(n)}
32: eval_foo_bb1_in->eval_foo_bb5_in, Arg_0: 8*Arg_6+9*Arg_4 {O(n)}
32: eval_foo_bb1_in->eval_foo_bb5_in, Arg_1: 0 {O(1)}
32: eval_foo_bb1_in->eval_foo_bb5_in, Arg_2: 28*Arg_4+28*Arg_6+7*Arg_2 {O(n)}
32: eval_foo_bb1_in->eval_foo_bb5_in, Arg_4: 9*Arg_4 {O(n)}
32: eval_foo_bb1_in->eval_foo_bb5_in, Arg_6: 9*Arg_6 {O(n)}
33: eval_foo_bb2_in->eval_foo_bb1_in, Arg_0: 2*Arg_4+2*Arg_6 {O(n)}
33: eval_foo_bb2_in->eval_foo_bb1_in, Arg_1: 2*Arg_4+2*Arg_6 {O(n)}
33: eval_foo_bb2_in->eval_foo_bb1_in, Arg_2: 2*Arg_2+8*Arg_4+8*Arg_6 {O(n)}
33: eval_foo_bb2_in->eval_foo_bb1_in, Arg_4: 2*Arg_4 {O(n)}
33: eval_foo_bb2_in->eval_foo_bb1_in, Arg_6: 2*Arg_6 {O(n)}
34: eval_foo_bb2_in->eval_foo_bb1_in, Arg_0: 2*Arg_4+2*Arg_6 {O(n)}
34: eval_foo_bb2_in->eval_foo_bb1_in, Arg_1: 2*Arg_4+2*Arg_6 {O(n)}
34: eval_foo_bb2_in->eval_foo_bb1_in, Arg_2: 2*Arg_2+8*Arg_4+8*Arg_6 {O(n)}
34: eval_foo_bb2_in->eval_foo_bb1_in, Arg_4: 2*Arg_4 {O(n)}
34: eval_foo_bb2_in->eval_foo_bb1_in, Arg_6: 2*Arg_6 {O(n)}
35: eval_foo_bb2_in->eval_foo_bb1_in, Arg_0: 2*Arg_4+2*Arg_6 {O(n)}
35: eval_foo_bb2_in->eval_foo_bb1_in, Arg_1: 2*Arg_4+2*Arg_6 {O(n)}
35: eval_foo_bb2_in->eval_foo_bb1_in, Arg_2: 2*Arg_2+8*Arg_4+8*Arg_6 {O(n)}
35: eval_foo_bb2_in->eval_foo_bb1_in, Arg_4: 2*Arg_4 {O(n)}
35: eval_foo_bb2_in->eval_foo_bb1_in, Arg_6: 2*Arg_6 {O(n)}
36: eval_foo_bb2_in->eval_foo_bb3_in, Arg_0: 2*Arg_4+2*Arg_6 {O(n)}
36: eval_foo_bb2_in->eval_foo_bb3_in, Arg_1: 2*Arg_4+2*Arg_6 {O(n)}
36: eval_foo_bb2_in->eval_foo_bb3_in, Arg_2: 2*Arg_4+2*Arg_6 {O(n)}
36: eval_foo_bb2_in->eval_foo_bb3_in, Arg_4: 2*Arg_4 {O(n)}
36: eval_foo_bb2_in->eval_foo_bb3_in, Arg_6: 2*Arg_6 {O(n)}
37: eval_foo_bb2_in->eval_foo_bb3_in, Arg_0: 2*Arg_4+2*Arg_6 {O(n)}
37: eval_foo_bb2_in->eval_foo_bb3_in, Arg_1: 2*Arg_4+2*Arg_6 {O(n)}
37: eval_foo_bb2_in->eval_foo_bb3_in, Arg_2: 2*Arg_4+2*Arg_6 {O(n)}
37: eval_foo_bb2_in->eval_foo_bb3_in, Arg_4: 2*Arg_4 {O(n)}
37: eval_foo_bb2_in->eval_foo_bb3_in, Arg_6: 2*Arg_6 {O(n)}
38: eval_foo_bb3_in->eval_foo_bb4_in, Arg_0: 2*Arg_4+2*Arg_6 {O(n)}
38: eval_foo_bb3_in->eval_foo_bb4_in, Arg_1: 2*Arg_4+2*Arg_6 {O(n)}
38: eval_foo_bb3_in->eval_foo_bb4_in, Arg_2: 2*Arg_4+2*Arg_6 {O(n)}
38: eval_foo_bb3_in->eval_foo_bb4_in, Arg_4: 2*Arg_4 {O(n)}
38: eval_foo_bb3_in->eval_foo_bb4_in, Arg_6: 2*Arg_6 {O(n)}
39: eval_foo_bb3_in->eval_foo_bb1_in, Arg_0: 2*Arg_4+2*Arg_6 {O(n)}
39: eval_foo_bb3_in->eval_foo_bb1_in, Arg_1: 2*Arg_4+2*Arg_6 {O(n)}
39: eval_foo_bb3_in->eval_foo_bb1_in, Arg_2: 4*Arg_4+4*Arg_6 {O(n)}
39: eval_foo_bb3_in->eval_foo_bb1_in, Arg_4: 2*Arg_4 {O(n)}
39: eval_foo_bb3_in->eval_foo_bb1_in, Arg_6: 2*Arg_6 {O(n)}
40: eval_foo_bb4_in->eval_foo_bb3_in, Arg_0: 2*Arg_4+2*Arg_6 {O(n)}
40: eval_foo_bb4_in->eval_foo_bb3_in, Arg_1: 2*Arg_4+2*Arg_6 {O(n)}
40: eval_foo_bb4_in->eval_foo_bb3_in, Arg_2: 2*Arg_4+2*Arg_6 {O(n)}
40: eval_foo_bb4_in->eval_foo_bb3_in, Arg_4: 2*Arg_4 {O(n)}
40: eval_foo_bb4_in->eval_foo_bb3_in, Arg_6: 2*Arg_6 {O(n)}
41: eval_foo_bb5_in->eval_foo_stop, Arg_0: 8*Arg_6+9*Arg_4 {O(n)}
41: eval_foo_bb5_in->eval_foo_stop, Arg_1: 0 {O(1)}
41: eval_foo_bb5_in->eval_foo_stop, Arg_2: 28*Arg_4+28*Arg_6+7*Arg_2 {O(n)}
41: eval_foo_bb5_in->eval_foo_stop, Arg_4: 9*Arg_4 {O(n)}
41: eval_foo_bb5_in->eval_foo_stop, Arg_6: 9*Arg_6 {O(n)}
42: eval_foo_start->eval_foo_bb0_in, Arg_0: Arg_0 {O(n)}
42: eval_foo_start->eval_foo_bb0_in, Arg_1: Arg_1 {O(n)}
42: eval_foo_start->eval_foo_bb0_in, Arg_2: Arg_2 {O(n)}
42: eval_foo_start->eval_foo_bb0_in, Arg_4: Arg_4 {O(n)}
42: eval_foo_start->eval_foo_bb0_in, Arg_6: Arg_6 {O(n)}