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_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_6,73,74,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):|:0<=Arg_0
3:eval_foo_bb1_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_3,Arg_4,Arg_5,Arg_6):|:Arg_0<0
4:eval_foo_bb2_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6) -> eval_foo_bb1_in(Arg_0-Arg_1,Arg_2+1,Arg_1+1,Arg_3,Arg_4,Arg_5,Arg_6)
5:eval_foo_bb3_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_4,Arg_5} that do not contribute to the problem

Found invariant Arg_0<=Arg_6 && Arg_2<=1+Arg_1 && 74<=Arg_2 && 147<=Arg_1+Arg_2 && Arg_1<=1+Arg_2 && 75+Arg_0<=Arg_2 && 73<=Arg_1 && 74+Arg_0<=Arg_1 && 1+Arg_0<=0 for location eval_foo_stop

Found invariant Arg_0<=Arg_6 && Arg_2<=1+Arg_1 && 74<=Arg_2 && 147<=Arg_1+Arg_2 && Arg_1<=1+Arg_2 && 75+Arg_0<=Arg_2 && 73<=Arg_1 && 74+Arg_0<=Arg_1 && 1+Arg_0<=0 for location eval_foo_bb3_in

Found invariant 0<=Arg_6 && 74<=Arg_2+Arg_6 && 73<=Arg_1+Arg_6 && 0<=Arg_0+Arg_6 && Arg_0<=Arg_6 && Arg_2<=1+Arg_1 && 74<=Arg_2 && 147<=Arg_1+Arg_2 && Arg_1<=1+Arg_2 && 74<=Arg_0+Arg_2 && 73<=Arg_1 && 73<=Arg_0+Arg_1 && 0<=Arg_0 for location eval_foo_bb2_in

Found invariant Arg_0<=Arg_6 && Arg_2<=1+Arg_1 && 74<=Arg_2 && 147<=Arg_1+Arg_2 && Arg_1<=1+Arg_2 && 73<=Arg_1 for location eval_foo_bb1_in

Problem after Preprocessing

Start: eval_foo_start
Program_Vars: Arg_0, Arg_1, Arg_2, Arg_6
Temp_Vars:
Locations: eval_foo_bb0_in, eval_foo_bb1_in, eval_foo_bb2_in, eval_foo_bb3_in, eval_foo_start, eval_foo_stop
Transitions:
12:eval_foo_bb0_in(Arg_0,Arg_1,Arg_2,Arg_6) -> eval_foo_bb1_in(Arg_6,73,74,Arg_6)
13:eval_foo_bb1_in(Arg_0,Arg_1,Arg_2,Arg_6) -> eval_foo_bb2_in(Arg_0,Arg_1,Arg_2,Arg_6):|:Arg_0<=Arg_6 && Arg_2<=1+Arg_1 && 74<=Arg_2 && 147<=Arg_1+Arg_2 && Arg_1<=1+Arg_2 && 73<=Arg_1 && 0<=Arg_0
14:eval_foo_bb1_in(Arg_0,Arg_1,Arg_2,Arg_6) -> eval_foo_bb3_in(Arg_0,Arg_1,Arg_2,Arg_6):|:Arg_0<=Arg_6 && Arg_2<=1+Arg_1 && 74<=Arg_2 && 147<=Arg_1+Arg_2 && Arg_1<=1+Arg_2 && 73<=Arg_1 && Arg_0<0
15:eval_foo_bb2_in(Arg_0,Arg_1,Arg_2,Arg_6) -> eval_foo_bb1_in(Arg_0-Arg_1,Arg_2+1,Arg_1+1,Arg_6):|:0<=Arg_6 && 74<=Arg_2+Arg_6 && 73<=Arg_1+Arg_6 && 0<=Arg_0+Arg_6 && Arg_0<=Arg_6 && Arg_2<=1+Arg_1 && 74<=Arg_2 && 147<=Arg_1+Arg_2 && Arg_1<=1+Arg_2 && 74<=Arg_0+Arg_2 && 73<=Arg_1 && 73<=Arg_0+Arg_1 && 0<=Arg_0
16:eval_foo_bb3_in(Arg_0,Arg_1,Arg_2,Arg_6) -> eval_foo_stop(Arg_0,Arg_1,Arg_2,Arg_6):|:Arg_0<=Arg_6 && Arg_2<=1+Arg_1 && 74<=Arg_2 && 147<=Arg_1+Arg_2 && Arg_1<=1+Arg_2 && 75+Arg_0<=Arg_2 && 73<=Arg_1 && 74+Arg_0<=Arg_1 && 1+Arg_0<=0
17:eval_foo_start(Arg_0,Arg_1,Arg_2,Arg_6) -> eval_foo_bb0_in(Arg_0,Arg_1,Arg_2,Arg_6)

MPRF for transition 13:eval_foo_bb1_in(Arg_0,Arg_1,Arg_2,Arg_6) -> eval_foo_bb2_in(Arg_0,Arg_1,Arg_2,Arg_6):|:Arg_0<=Arg_6 && Arg_2<=1+Arg_1 && 74<=Arg_2 && 147<=Arg_1+Arg_2 && Arg_1<=1+Arg_2 && 73<=Arg_1 && 0<=Arg_0 of depth 1:

new bound:

2*Arg_6+149 {O(n)}

MPRF:

eval_foo_bb2_in [2*Arg_0+Arg_2-Arg_1-146 ]
eval_foo_bb1_in [2*Arg_0+Arg_2+2-Arg_1 ]

MPRF for transition 15:eval_foo_bb2_in(Arg_0,Arg_1,Arg_2,Arg_6) -> eval_foo_bb1_in(Arg_0-Arg_1,Arg_2+1,Arg_1+1,Arg_6):|:0<=Arg_6 && 74<=Arg_2+Arg_6 && 73<=Arg_1+Arg_6 && 0<=Arg_0+Arg_6 && Arg_0<=Arg_6 && Arg_2<=1+Arg_1 && 74<=Arg_2 && 147<=Arg_1+Arg_2 && Arg_1<=1+Arg_2 && 74<=Arg_0+Arg_2 && 73<=Arg_1 && 73<=Arg_0+Arg_1 && 0<=Arg_0 of depth 1:

new bound:

2*Arg_6+1 {O(n)}

MPRF:

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

All Bounds

Timebounds

Overall timebound:4*Arg_6+154 {O(n)}
12: eval_foo_bb0_in->eval_foo_bb1_in: 1 {O(1)}
13: eval_foo_bb1_in->eval_foo_bb2_in: 2*Arg_6+149 {O(n)}
14: eval_foo_bb1_in->eval_foo_bb3_in: 1 {O(1)}
15: eval_foo_bb2_in->eval_foo_bb1_in: 2*Arg_6+1 {O(n)}
16: eval_foo_bb3_in->eval_foo_stop: 1 {O(1)}
17: eval_foo_start->eval_foo_bb0_in: 1 {O(1)}

Costbounds

Overall costbound: 4*Arg_6+154 {O(n)}
12: eval_foo_bb0_in->eval_foo_bb1_in: 1 {O(1)}
13: eval_foo_bb1_in->eval_foo_bb2_in: 2*Arg_6+149 {O(n)}
14: eval_foo_bb1_in->eval_foo_bb3_in: 1 {O(1)}
15: eval_foo_bb2_in->eval_foo_bb1_in: 2*Arg_6+1 {O(n)}
16: eval_foo_bb3_in->eval_foo_stop: 1 {O(1)}
17: eval_foo_start->eval_foo_bb0_in: 1 {O(1)}

Sizebounds

12: eval_foo_bb0_in->eval_foo_bb1_in, Arg_0: Arg_6 {O(n)}
12: eval_foo_bb0_in->eval_foo_bb1_in, Arg_1: 73 {O(1)}
12: eval_foo_bb0_in->eval_foo_bb1_in, Arg_2: 74 {O(1)}
12: eval_foo_bb0_in->eval_foo_bb1_in, Arg_6: Arg_6 {O(n)}
13: eval_foo_bb1_in->eval_foo_bb2_in, Arg_0: 5*Arg_6+75 {O(n)}
13: eval_foo_bb1_in->eval_foo_bb2_in, Arg_1: 4*Arg_6+75 {O(n)}
13: eval_foo_bb1_in->eval_foo_bb2_in, Arg_2: 4*Arg_6+150 {O(n)}
13: eval_foo_bb1_in->eval_foo_bb2_in, Arg_6: Arg_6 {O(n)}
14: eval_foo_bb1_in->eval_foo_bb3_in, Arg_0: 6*Arg_6+75 {O(n)}
14: eval_foo_bb1_in->eval_foo_bb3_in, Arg_1: 4*Arg_6+148 {O(n)}
14: eval_foo_bb1_in->eval_foo_bb3_in, Arg_2: 4*Arg_6+150 {O(n)}
14: eval_foo_bb1_in->eval_foo_bb3_in, Arg_6: 2*Arg_6 {O(n)}
15: eval_foo_bb2_in->eval_foo_bb1_in, Arg_0: 5*Arg_6+75 {O(n)}
15: eval_foo_bb2_in->eval_foo_bb1_in, Arg_1: 4*Arg_6+75 {O(n)}
15: eval_foo_bb2_in->eval_foo_bb1_in, Arg_2: 4*Arg_6+76 {O(n)}
15: eval_foo_bb2_in->eval_foo_bb1_in, Arg_6: Arg_6 {O(n)}
16: eval_foo_bb3_in->eval_foo_stop, Arg_0: 6*Arg_6+75 {O(n)}
16: eval_foo_bb3_in->eval_foo_stop, Arg_1: 4*Arg_6+148 {O(n)}
16: eval_foo_bb3_in->eval_foo_stop, Arg_2: 4*Arg_6+150 {O(n)}
16: eval_foo_bb3_in->eval_foo_stop, Arg_6: 2*Arg_6 {O(n)}
17: eval_foo_start->eval_foo_bb0_in, Arg_0: Arg_0 {O(n)}
17: eval_foo_start->eval_foo_bb0_in, Arg_1: Arg_1 {O(n)}
17: eval_foo_start->eval_foo_bb0_in, Arg_2: Arg_2 {O(n)}
17: eval_foo_start->eval_foo_bb0_in, Arg_6: Arg_6 {O(n)}