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_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_3,0,Arg_2,Arg_3,Arg_4,Arg_5):|:0<=Arg_3 && 0<Arg_2
2:eval_foo_bb0_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):|:Arg_3<0
3:eval_foo_bb0_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):|:Arg_2<=0
4: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):|:0<Arg_0
5:eval_foo_bb1_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):|:Arg_0<=0
7:eval_foo_bb2_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5) -> eval_foo_bb1_in(Arg_0,0,Arg_2,Arg_3,Arg_4,Arg_5):|:Arg_2<=Arg_1
6:eval_foo_bb2_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5) -> eval_foo_bb3_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5):|:Arg_1<Arg_2
8:eval_foo_bb3_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5) -> eval_foo_bb1_in(Arg_0-1,Arg_1+1,Arg_2,Arg_3,Arg_4,Arg_5)
9:eval_foo_bb4_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_4,Arg_5} that do not contribute to the problem

Found invariant 1<=Arg_3 && 2<=Arg_2+Arg_3 && 1<=Arg_1+Arg_3 && 2<=Arg_0+Arg_3 && Arg_0<=Arg_3 && 1<=Arg_2 && 1<=Arg_1+Arg_2 && 1+Arg_1<=Arg_2 && 2<=Arg_0+Arg_2 && 0<=Arg_1 && 1<=Arg_0+Arg_1 && 1<=Arg_0 for location eval_foo_bb3_in

Found invariant 1<=Arg_3 && 2<=Arg_2+Arg_3 && 1<=Arg_1+Arg_3 && 2<=Arg_0+Arg_3 && Arg_0<=Arg_3 && 1<=Arg_2 && 1<=Arg_1+Arg_2 && Arg_1<=Arg_2 && 2<=Arg_0+Arg_2 && 0<=Arg_1 && 1<=Arg_0+Arg_1 && 1<=Arg_0 for location eval_foo_bb2_in

Found invariant 0<=Arg_3 && 1<=Arg_2+Arg_3 && 0<=Arg_1+Arg_3 && 0<=Arg_0+Arg_3 && Arg_0<=Arg_3 && 1<=Arg_2 && 1<=Arg_1+Arg_2 && Arg_1<=Arg_2 && 1<=Arg_0+Arg_2 && 0<=Arg_1 && 0<=Arg_0+Arg_1 && 0<=Arg_0 for location eval_foo_bb1_in

Problem after Preprocessing

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_start, eval_foo_stop
Transitions:
20:eval_foo_bb0_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_foo_bb1_in(Arg_3,0,Arg_2,Arg_3):|:0<=Arg_3 && 0<Arg_2
21:eval_foo_bb0_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_foo_bb4_in(Arg_0,Arg_1,Arg_2,Arg_3):|:Arg_3<0
22:eval_foo_bb0_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_foo_bb4_in(Arg_0,Arg_1,Arg_2,Arg_3):|:Arg_2<=0
23:eval_foo_bb1_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_foo_bb2_in(Arg_0,Arg_1,Arg_2,Arg_3):|:0<=Arg_3 && 1<=Arg_2+Arg_3 && 0<=Arg_1+Arg_3 && 0<=Arg_0+Arg_3 && Arg_0<=Arg_3 && 1<=Arg_2 && 1<=Arg_1+Arg_2 && Arg_1<=Arg_2 && 1<=Arg_0+Arg_2 && 0<=Arg_1 && 0<=Arg_0+Arg_1 && 0<=Arg_0 && 0<Arg_0
24:eval_foo_bb1_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_foo_bb4_in(Arg_0,Arg_1,Arg_2,Arg_3):|:0<=Arg_3 && 1<=Arg_2+Arg_3 && 0<=Arg_1+Arg_3 && 0<=Arg_0+Arg_3 && Arg_0<=Arg_3 && 1<=Arg_2 && 1<=Arg_1+Arg_2 && Arg_1<=Arg_2 && 1<=Arg_0+Arg_2 && 0<=Arg_1 && 0<=Arg_0+Arg_1 && 0<=Arg_0 && Arg_0<=0
26:eval_foo_bb2_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_foo_bb1_in(Arg_0,0,Arg_2,Arg_3):|:1<=Arg_3 && 2<=Arg_2+Arg_3 && 1<=Arg_1+Arg_3 && 2<=Arg_0+Arg_3 && Arg_0<=Arg_3 && 1<=Arg_2 && 1<=Arg_1+Arg_2 && Arg_1<=Arg_2 && 2<=Arg_0+Arg_2 && 0<=Arg_1 && 1<=Arg_0+Arg_1 && 1<=Arg_0 && Arg_2<=Arg_1
25: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_3 && 2<=Arg_2+Arg_3 && 1<=Arg_1+Arg_3 && 2<=Arg_0+Arg_3 && Arg_0<=Arg_3 && 1<=Arg_2 && 1<=Arg_1+Arg_2 && Arg_1<=Arg_2 && 2<=Arg_0+Arg_2 && 0<=Arg_1 && 1<=Arg_0+Arg_1 && 1<=Arg_0 && Arg_1<Arg_2
27:eval_foo_bb3_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_foo_bb1_in(Arg_0-1,Arg_1+1,Arg_2,Arg_3):|:1<=Arg_3 && 2<=Arg_2+Arg_3 && 1<=Arg_1+Arg_3 && 2<=Arg_0+Arg_3 && Arg_0<=Arg_3 && 1<=Arg_2 && 1<=Arg_1+Arg_2 && 1+Arg_1<=Arg_2 && 2<=Arg_0+Arg_2 && 0<=Arg_1 && 1<=Arg_0+Arg_1 && 1<=Arg_0
28:eval_foo_bb4_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_foo_stop(Arg_0,Arg_1,Arg_2,Arg_3)
29:eval_foo_start(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_foo_bb0_in(Arg_0,Arg_1,Arg_2,Arg_3)

MPRF for transition 23:eval_foo_bb1_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_foo_bb2_in(Arg_0,Arg_1,Arg_2,Arg_3):|:0<=Arg_3 && 1<=Arg_2+Arg_3 && 0<=Arg_1+Arg_3 && 0<=Arg_0+Arg_3 && Arg_0<=Arg_3 && 1<=Arg_2 && 1<=Arg_1+Arg_2 && Arg_1<=Arg_2 && 1<=Arg_0+Arg_2 && 0<=Arg_1 && 0<=Arg_0+Arg_1 && 0<=Arg_0 && 0<Arg_0 of depth 1:

new bound:

2*Arg_3+1 {O(n)}

MPRF:

eval_foo_bb2_in [2*Arg_0+Arg_1 ]
eval_foo_bb3_in [2*Arg_0+Arg_1 ]
eval_foo_bb1_in [2*Arg_0+Arg_1+1 ]

MPRF for transition 25: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_3 && 2<=Arg_2+Arg_3 && 1<=Arg_1+Arg_3 && 2<=Arg_0+Arg_3 && Arg_0<=Arg_3 && 1<=Arg_2 && 1<=Arg_1+Arg_2 && Arg_1<=Arg_2 && 2<=Arg_0+Arg_2 && 0<=Arg_1 && 1<=Arg_0+Arg_1 && 1<=Arg_0 && Arg_1<Arg_2 of depth 1:

new bound:

Arg_3 {O(n)}

MPRF:

eval_foo_bb2_in [Arg_0 ]
eval_foo_bb3_in [Arg_0-1 ]
eval_foo_bb1_in [Arg_0 ]

MPRF for transition 26:eval_foo_bb2_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_foo_bb1_in(Arg_0,0,Arg_2,Arg_3):|:1<=Arg_3 && 2<=Arg_2+Arg_3 && 1<=Arg_1+Arg_3 && 2<=Arg_0+Arg_3 && Arg_0<=Arg_3 && 1<=Arg_2 && 1<=Arg_1+Arg_2 && Arg_1<=Arg_2 && 2<=Arg_0+Arg_2 && 0<=Arg_1 && 1<=Arg_0+Arg_1 && 1<=Arg_0 && Arg_2<=Arg_1 of depth 1:

new bound:

Arg_3 {O(n)}

MPRF:

eval_foo_bb2_in [Arg_0+Arg_1 ]
eval_foo_bb3_in [Arg_0+Arg_1 ]
eval_foo_bb1_in [Arg_0+Arg_1 ]

MPRF for transition 27:eval_foo_bb3_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_foo_bb1_in(Arg_0-1,Arg_1+1,Arg_2,Arg_3):|:1<=Arg_3 && 2<=Arg_2+Arg_3 && 1<=Arg_1+Arg_3 && 2<=Arg_0+Arg_3 && Arg_0<=Arg_3 && 1<=Arg_2 && 1<=Arg_1+Arg_2 && 1+Arg_1<=Arg_2 && 2<=Arg_0+Arg_2 && 0<=Arg_1 && 1<=Arg_0+Arg_1 && 1<=Arg_0 of depth 1:

new bound:

Arg_3 {O(n)}

MPRF:

eval_foo_bb2_in [Arg_0 ]
eval_foo_bb3_in [Arg_0 ]
eval_foo_bb1_in [Arg_0 ]

All Bounds

Timebounds

Overall timebound:5*Arg_3+7 {O(n)}
20: eval_foo_bb0_in->eval_foo_bb1_in: 1 {O(1)}
21: eval_foo_bb0_in->eval_foo_bb4_in: 1 {O(1)}
22: eval_foo_bb0_in->eval_foo_bb4_in: 1 {O(1)}
23: eval_foo_bb1_in->eval_foo_bb2_in: 2*Arg_3+1 {O(n)}
24: eval_foo_bb1_in->eval_foo_bb4_in: 1 {O(1)}
25: eval_foo_bb2_in->eval_foo_bb3_in: Arg_3 {O(n)}
26: eval_foo_bb2_in->eval_foo_bb1_in: Arg_3 {O(n)}
27: eval_foo_bb3_in->eval_foo_bb1_in: Arg_3 {O(n)}
28: eval_foo_bb4_in->eval_foo_stop: 1 {O(1)}
29: eval_foo_start->eval_foo_bb0_in: 1 {O(1)}

Costbounds

Overall costbound: 5*Arg_3+7 {O(n)}
20: eval_foo_bb0_in->eval_foo_bb1_in: 1 {O(1)}
21: eval_foo_bb0_in->eval_foo_bb4_in: 1 {O(1)}
22: eval_foo_bb0_in->eval_foo_bb4_in: 1 {O(1)}
23: eval_foo_bb1_in->eval_foo_bb2_in: 2*Arg_3+1 {O(n)}
24: eval_foo_bb1_in->eval_foo_bb4_in: 1 {O(1)}
25: eval_foo_bb2_in->eval_foo_bb3_in: Arg_3 {O(n)}
26: eval_foo_bb2_in->eval_foo_bb1_in: Arg_3 {O(n)}
27: eval_foo_bb3_in->eval_foo_bb1_in: Arg_3 {O(n)}
28: eval_foo_bb4_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_3 {O(n)}
20: eval_foo_bb0_in->eval_foo_bb1_in, Arg_1: 0 {O(1)}
20: eval_foo_bb0_in->eval_foo_bb1_in, Arg_2: Arg_2 {O(n)}
20: eval_foo_bb0_in->eval_foo_bb1_in, Arg_3: Arg_3 {O(n)}
21: eval_foo_bb0_in->eval_foo_bb4_in, Arg_0: Arg_0 {O(n)}
21: eval_foo_bb0_in->eval_foo_bb4_in, Arg_1: Arg_1 {O(n)}
21: eval_foo_bb0_in->eval_foo_bb4_in, Arg_2: Arg_2 {O(n)}
21: eval_foo_bb0_in->eval_foo_bb4_in, Arg_3: Arg_3 {O(n)}
22: eval_foo_bb0_in->eval_foo_bb4_in, Arg_0: Arg_0 {O(n)}
22: eval_foo_bb0_in->eval_foo_bb4_in, Arg_1: Arg_1 {O(n)}
22: eval_foo_bb0_in->eval_foo_bb4_in, Arg_2: Arg_2 {O(n)}
22: eval_foo_bb0_in->eval_foo_bb4_in, Arg_3: Arg_3 {O(n)}
23: eval_foo_bb1_in->eval_foo_bb2_in, Arg_0: Arg_3 {O(n)}
23: eval_foo_bb1_in->eval_foo_bb2_in, Arg_1: Arg_3 {O(n)}
23: eval_foo_bb1_in->eval_foo_bb2_in, Arg_2: Arg_2 {O(n)}
23: eval_foo_bb1_in->eval_foo_bb2_in, Arg_3: Arg_3 {O(n)}
24: eval_foo_bb1_in->eval_foo_bb4_in, Arg_0: 0 {O(1)}
24: eval_foo_bb1_in->eval_foo_bb4_in, Arg_1: Arg_3 {O(n)}
24: eval_foo_bb1_in->eval_foo_bb4_in, Arg_2: 2*Arg_2 {O(n)}
24: eval_foo_bb1_in->eval_foo_bb4_in, Arg_3: 2*Arg_3 {O(n)}
25: eval_foo_bb2_in->eval_foo_bb3_in, Arg_0: Arg_3 {O(n)}
25: eval_foo_bb2_in->eval_foo_bb3_in, Arg_1: Arg_3 {O(n)}
25: eval_foo_bb2_in->eval_foo_bb3_in, Arg_2: Arg_2 {O(n)}
25: eval_foo_bb2_in->eval_foo_bb3_in, Arg_3: Arg_3 {O(n)}
26: eval_foo_bb2_in->eval_foo_bb1_in, Arg_0: Arg_3 {O(n)}
26: eval_foo_bb2_in->eval_foo_bb1_in, Arg_1: 0 {O(1)}
26: eval_foo_bb2_in->eval_foo_bb1_in, Arg_2: Arg_2 {O(n)}
26: eval_foo_bb2_in->eval_foo_bb1_in, Arg_3: Arg_3 {O(n)}
27: eval_foo_bb3_in->eval_foo_bb1_in, Arg_0: Arg_3 {O(n)}
27: eval_foo_bb3_in->eval_foo_bb1_in, Arg_1: Arg_3 {O(n)}
27: eval_foo_bb3_in->eval_foo_bb1_in, Arg_2: Arg_2 {O(n)}
27: eval_foo_bb3_in->eval_foo_bb1_in, Arg_3: Arg_3 {O(n)}
28: eval_foo_bb4_in->eval_foo_stop, Arg_0: 2*Arg_0 {O(n)}
28: eval_foo_bb4_in->eval_foo_stop, Arg_1: 2*Arg_1+Arg_3 {O(n)}
28: eval_foo_bb4_in->eval_foo_stop, Arg_2: 4*Arg_2 {O(n)}
28: eval_foo_bb4_in->eval_foo_stop, Arg_3: 4*Arg_3 {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_2: Arg_2 {O(n)}
29: eval_foo_start->eval_foo_bb0_in, Arg_3: Arg_3 {O(n)}