Initial Problem

Start: eval_foo_start
Program_Vars: Arg_0, Arg_1, Arg_2, Arg_3, Arg_4
Temp_Vars: nondef.0
Locations: eval_foo_0, eval_foo_1, eval_foo_bb0_in, eval_foo_bb1_in, eval_foo_bb2_in, eval_foo_bb3_in, eval_foo_start, eval_foo_stop
Transitions:
7:eval_foo_0(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> eval_foo_1(Arg_0,nondef.0,Arg_2,Arg_3,Arg_4)
8:eval_foo_1(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):|:Arg_1<0
9:eval_foo_1(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):|:0<Arg_1
10:eval_foo_1(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):|:Arg_1<=0 && 0<=Arg_1
1:eval_foo_bb0_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> eval_foo_bb1_in(1,Arg_1,Arg_2,Arg_3,Arg_4):|:0<Arg_3
2:eval_foo_bb0_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_3<=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):|:Arg_0<=Arg_3
4:eval_foo_bb1_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_3<Arg_0
5:eval_foo_bb2_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> eval_foo_0(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4)
11:eval_foo_bb3_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_2,Arg_4} that do not contribute to the problem

Found invariant 1<=Arg_3 && 2<=Arg_0+Arg_3 && Arg_0<=Arg_3 && 1<=Arg_0 for location eval_foo_0

Found invariant 1<=Arg_3 && 2<=Arg_0+Arg_3 && Arg_0<=Arg_3 && 1<=Arg_0 for location eval_foo_bb2_in

Found invariant 1<=Arg_3 && 2<=Arg_0+Arg_3 && Arg_0<=Arg_3 && 1<=Arg_0 for location eval_foo_1

Found invariant 1<=Arg_3 && 2<=Arg_0+Arg_3 && Arg_0<=1+Arg_3 && 1<=Arg_0 for location eval_foo_bb1_in

Problem after Preprocessing

Start: eval_foo_start
Program_Vars: Arg_0, Arg_1, Arg_3
Temp_Vars: nondef.0
Locations: eval_foo_0, eval_foo_1, eval_foo_bb0_in, eval_foo_bb1_in, eval_foo_bb2_in, eval_foo_bb3_in, eval_foo_start, eval_foo_stop
Transitions:
24:eval_foo_0(Arg_0,Arg_1,Arg_3) -> eval_foo_1(Arg_0,nondef.0,Arg_3):|:1<=Arg_3 && 2<=Arg_0+Arg_3 && Arg_0<=Arg_3 && 1<=Arg_0
25:eval_foo_1(Arg_0,Arg_1,Arg_3) -> eval_foo_bb1_in(Arg_0+1,Arg_1,Arg_3):|:1<=Arg_3 && 2<=Arg_0+Arg_3 && Arg_0<=Arg_3 && 1<=Arg_0 && Arg_1<0
26:eval_foo_1(Arg_0,Arg_1,Arg_3) -> eval_foo_bb1_in(Arg_0+1,Arg_1,Arg_3):|:1<=Arg_3 && 2<=Arg_0+Arg_3 && Arg_0<=Arg_3 && 1<=Arg_0 && 0<Arg_1
27:eval_foo_1(Arg_0,Arg_1,Arg_3) -> eval_foo_bb1_in(Arg_0+1,Arg_1,Arg_3):|:1<=Arg_3 && 2<=Arg_0+Arg_3 && Arg_0<=Arg_3 && 1<=Arg_0 && Arg_1<=0 && 0<=Arg_1
28:eval_foo_bb0_in(Arg_0,Arg_1,Arg_3) -> eval_foo_bb1_in(1,Arg_1,Arg_3):|:0<Arg_3
29:eval_foo_bb0_in(Arg_0,Arg_1,Arg_3) -> eval_foo_bb3_in(Arg_0,Arg_1,Arg_3):|:Arg_3<=0
30:eval_foo_bb1_in(Arg_0,Arg_1,Arg_3) -> eval_foo_bb2_in(Arg_0,Arg_1,Arg_3):|:1<=Arg_3 && 2<=Arg_0+Arg_3 && Arg_0<=1+Arg_3 && 1<=Arg_0 && Arg_0<=Arg_3
31:eval_foo_bb1_in(Arg_0,Arg_1,Arg_3) -> eval_foo_bb3_in(Arg_0,Arg_1,Arg_3):|:1<=Arg_3 && 2<=Arg_0+Arg_3 && Arg_0<=1+Arg_3 && 1<=Arg_0 && Arg_3<Arg_0
32:eval_foo_bb2_in(Arg_0,Arg_1,Arg_3) -> eval_foo_0(Arg_0,Arg_1,Arg_3):|:1<=Arg_3 && 2<=Arg_0+Arg_3 && Arg_0<=Arg_3 && 1<=Arg_0
33:eval_foo_bb3_in(Arg_0,Arg_1,Arg_3) -> eval_foo_stop(Arg_0,Arg_1,Arg_3)
34:eval_foo_start(Arg_0,Arg_1,Arg_3) -> eval_foo_bb0_in(Arg_0,Arg_1,Arg_3)

MPRF for transition 24:eval_foo_0(Arg_0,Arg_1,Arg_3) -> eval_foo_1(Arg_0,nondef.0,Arg_3):|:1<=Arg_3 && 2<=Arg_0+Arg_3 && Arg_0<=Arg_3 && 1<=Arg_0 of depth 1:

new bound:

2*Arg_3+1 {O(n)}

MPRF:

eval_foo_1 [2*Arg_3-Arg_0-1 ]
eval_foo_bb1_in [2*Arg_3-Arg_0 ]
eval_foo_bb2_in [2*Arg_3-Arg_0 ]
eval_foo_0 [2*Arg_3-Arg_0 ]

MPRF for transition 25:eval_foo_1(Arg_0,Arg_1,Arg_3) -> eval_foo_bb1_in(Arg_0+1,Arg_1,Arg_3):|:1<=Arg_3 && 2<=Arg_0+Arg_3 && Arg_0<=Arg_3 && 1<=Arg_0 && Arg_1<0 of depth 1:

new bound:

Arg_3+2 {O(n)}

MPRF:

eval_foo_1 [Arg_3+1-Arg_0 ]
eval_foo_bb1_in [Arg_3+1-Arg_0 ]
eval_foo_bb2_in [Arg_3+1-Arg_0 ]
eval_foo_0 [Arg_3+1-Arg_0 ]

MPRF for transition 26:eval_foo_1(Arg_0,Arg_1,Arg_3) -> eval_foo_bb1_in(Arg_0+1,Arg_1,Arg_3):|:1<=Arg_3 && 2<=Arg_0+Arg_3 && Arg_0<=Arg_3 && 1<=Arg_0 && 0<Arg_1 of depth 1:

new bound:

Arg_3+2 {O(n)}

MPRF:

eval_foo_1 [Arg_3+1-Arg_0 ]
eval_foo_bb1_in [Arg_3+1-Arg_0 ]
eval_foo_bb2_in [Arg_3+1-Arg_0 ]
eval_foo_0 [Arg_3+1-Arg_0 ]

MPRF for transition 27:eval_foo_1(Arg_0,Arg_1,Arg_3) -> eval_foo_bb1_in(Arg_0+1,Arg_1,Arg_3):|:1<=Arg_3 && 2<=Arg_0+Arg_3 && Arg_0<=Arg_3 && 1<=Arg_0 && Arg_1<=0 && 0<=Arg_1 of depth 1:

new bound:

Arg_3+2 {O(n)}

MPRF:

eval_foo_1 [Arg_3+1-Arg_0 ]
eval_foo_bb1_in [Arg_3+1-Arg_0 ]
eval_foo_bb2_in [Arg_3+1-Arg_0 ]
eval_foo_0 [Arg_3+1-Arg_0 ]

MPRF for transition 30:eval_foo_bb1_in(Arg_0,Arg_1,Arg_3) -> eval_foo_bb2_in(Arg_0,Arg_1,Arg_3):|:1<=Arg_3 && 2<=Arg_0+Arg_3 && Arg_0<=1+Arg_3 && 1<=Arg_0 && Arg_0<=Arg_3 of depth 1:

new bound:

Arg_3+2 {O(n)}

MPRF:

eval_foo_1 [Arg_3-Arg_0 ]
eval_foo_bb1_in [Arg_3+1-Arg_0 ]
eval_foo_bb2_in [Arg_3-Arg_0 ]
eval_foo_0 [Arg_3-Arg_0 ]

MPRF for transition 32:eval_foo_bb2_in(Arg_0,Arg_1,Arg_3) -> eval_foo_0(Arg_0,Arg_1,Arg_3):|:1<=Arg_3 && 2<=Arg_0+Arg_3 && Arg_0<=Arg_3 && 1<=Arg_0 of depth 1:

new bound:

Arg_3+2 {O(n)}

MPRF:

eval_foo_1 [Arg_3-Arg_0 ]
eval_foo_bb1_in [Arg_3+1-Arg_0 ]
eval_foo_bb2_in [Arg_3+1-Arg_0 ]
eval_foo_0 [Arg_3-Arg_0 ]

All Bounds

Timebounds

Overall timebound:7*Arg_3+16 {O(n)}
24: eval_foo_0->eval_foo_1: 2*Arg_3+1 {O(n)}
25: eval_foo_1->eval_foo_bb1_in: Arg_3+2 {O(n)}
26: eval_foo_1->eval_foo_bb1_in: Arg_3+2 {O(n)}
27: eval_foo_1->eval_foo_bb1_in: Arg_3+2 {O(n)}
28: eval_foo_bb0_in->eval_foo_bb1_in: 1 {O(1)}
29: eval_foo_bb0_in->eval_foo_bb3_in: 1 {O(1)}
30: eval_foo_bb1_in->eval_foo_bb2_in: Arg_3+2 {O(n)}
31: eval_foo_bb1_in->eval_foo_bb3_in: 1 {O(1)}
32: eval_foo_bb2_in->eval_foo_0: Arg_3+2 {O(n)}
33: eval_foo_bb3_in->eval_foo_stop: 1 {O(1)}
34: eval_foo_start->eval_foo_bb0_in: 1 {O(1)}

Costbounds

Overall costbound: 7*Arg_3+16 {O(n)}
24: eval_foo_0->eval_foo_1: 2*Arg_3+1 {O(n)}
25: eval_foo_1->eval_foo_bb1_in: Arg_3+2 {O(n)}
26: eval_foo_1->eval_foo_bb1_in: Arg_3+2 {O(n)}
27: eval_foo_1->eval_foo_bb1_in: Arg_3+2 {O(n)}
28: eval_foo_bb0_in->eval_foo_bb1_in: 1 {O(1)}
29: eval_foo_bb0_in->eval_foo_bb3_in: 1 {O(1)}
30: eval_foo_bb1_in->eval_foo_bb2_in: Arg_3+2 {O(n)}
31: eval_foo_bb1_in->eval_foo_bb3_in: 1 {O(1)}
32: eval_foo_bb2_in->eval_foo_0: Arg_3+2 {O(n)}
33: eval_foo_bb3_in->eval_foo_stop: 1 {O(1)}
34: eval_foo_start->eval_foo_bb0_in: 1 {O(1)}

Sizebounds

24: eval_foo_0->eval_foo_1, Arg_0: 3*Arg_3+7 {O(n)}
24: eval_foo_0->eval_foo_1, Arg_3: Arg_3 {O(n)}
25: eval_foo_1->eval_foo_bb1_in, Arg_0: 3*Arg_3+7 {O(n)}
25: eval_foo_1->eval_foo_bb1_in, Arg_3: Arg_3 {O(n)}
26: eval_foo_1->eval_foo_bb1_in, Arg_0: 3*Arg_3+7 {O(n)}
26: eval_foo_1->eval_foo_bb1_in, Arg_3: Arg_3 {O(n)}
27: eval_foo_1->eval_foo_bb1_in, Arg_0: 3*Arg_3+7 {O(n)}
27: eval_foo_1->eval_foo_bb1_in, Arg_1: 0 {O(1)}
27: eval_foo_1->eval_foo_bb1_in, Arg_3: Arg_3 {O(n)}
28: eval_foo_bb0_in->eval_foo_bb1_in, Arg_0: 1 {O(1)}
28: eval_foo_bb0_in->eval_foo_bb1_in, Arg_1: Arg_1 {O(n)}
28: eval_foo_bb0_in->eval_foo_bb1_in, Arg_3: Arg_3 {O(n)}
29: eval_foo_bb0_in->eval_foo_bb3_in, Arg_0: Arg_0 {O(n)}
29: eval_foo_bb0_in->eval_foo_bb3_in, Arg_1: Arg_1 {O(n)}
29: eval_foo_bb0_in->eval_foo_bb3_in, Arg_3: Arg_3 {O(n)}
30: eval_foo_bb1_in->eval_foo_bb2_in, Arg_0: 3*Arg_3+7 {O(n)}
30: eval_foo_bb1_in->eval_foo_bb2_in, Arg_3: Arg_3 {O(n)}
31: eval_foo_bb1_in->eval_foo_bb3_in, Arg_0: 9*Arg_3+21 {O(n)}
31: eval_foo_bb1_in->eval_foo_bb3_in, Arg_3: 3*Arg_3 {O(n)}
32: eval_foo_bb2_in->eval_foo_0, Arg_0: 3*Arg_3+7 {O(n)}
32: eval_foo_bb2_in->eval_foo_0, Arg_3: Arg_3 {O(n)}
33: eval_foo_bb3_in->eval_foo_stop, Arg_0: 9*Arg_3+Arg_0+21 {O(n)}
33: eval_foo_bb3_in->eval_foo_stop, Arg_3: 4*Arg_3 {O(n)}
34: eval_foo_start->eval_foo_bb0_in, Arg_0: Arg_0 {O(n)}
34: eval_foo_start->eval_foo_bb0_in, Arg_1: Arg_1 {O(n)}
34: eval_foo_start->eval_foo_bb0_in, Arg_3: Arg_3 {O(n)}