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_5,Arg_3,Arg_4,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<=100 && Arg_2<=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):|:100<Arg_1
4: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<Arg_2
5:eval_foo_bb2_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6) -> eval_foo_bb1_in(Arg_0-1,Arg_2,Arg_1+1,Arg_3,Arg_4,Arg_5,Arg_6)
6: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_6} that do not contribute to the problem

Found invariant Arg_0<=Arg_5 for location eval_foo_stop

Found invariant Arg_0<=Arg_5 for location eval_foo_bb3_in

Found invariant Arg_2<=Arg_5 && Arg_0<=Arg_5 && Arg_2<=Arg_0 && Arg_1<=100 for location eval_foo_bb2_in

Found invariant Arg_0<=Arg_5 for location eval_foo_bb1_in

Problem after Preprocessing

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_start, eval_foo_stop
Transitions:
14:eval_foo_bb0_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5) -> eval_foo_bb1_in(Arg_5,Arg_3,Arg_4,Arg_3,Arg_4,Arg_5)
15: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):|:Arg_0<=Arg_5 && Arg_1<=100 && Arg_2<=Arg_0
16:eval_foo_bb1_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_0<=Arg_5 && 100<Arg_1
17:eval_foo_bb1_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_0<=Arg_5 && Arg_0<Arg_2
18:eval_foo_bb2_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5) -> eval_foo_bb1_in(Arg_0-1,Arg_2,Arg_1+1,Arg_3,Arg_4,Arg_5):|:Arg_2<=Arg_5 && Arg_0<=Arg_5 && Arg_2<=Arg_0 && Arg_1<=100
19:eval_foo_bb3_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):|:Arg_0<=Arg_5
20: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)

MPRF for transition 15: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):|:Arg_0<=Arg_5 && Arg_1<=100 && Arg_2<=Arg_0 of depth 1:

new bound:

Arg_3+Arg_4+Arg_5+101 {O(n)}

MPRF:

eval_foo_bb2_in [Arg_0+99-Arg_1-Arg_2 ]
eval_foo_bb1_in [Arg_0+101-Arg_1-Arg_2 ]

MPRF for transition 18:eval_foo_bb2_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5) -> eval_foo_bb1_in(Arg_0-1,Arg_2,Arg_1+1,Arg_3,Arg_4,Arg_5):|:Arg_2<=Arg_5 && Arg_0<=Arg_5 && Arg_2<=Arg_0 && Arg_1<=100 of depth 1:

new bound:

Arg_3+Arg_4+Arg_5+101 {O(n)}

MPRF:

eval_foo_bb2_in [Arg_0+101-Arg_1-Arg_2 ]
eval_foo_bb1_in [Arg_0+101-Arg_1-Arg_2 ]

All Bounds

Timebounds

Overall timebound:2*Arg_3+2*Arg_4+2*Arg_5+207 {O(n)}
14: eval_foo_bb0_in->eval_foo_bb1_in: 1 {O(1)}
15: eval_foo_bb1_in->eval_foo_bb2_in: Arg_3+Arg_4+Arg_5+101 {O(n)}
16: eval_foo_bb1_in->eval_foo_bb3_in: 1 {O(1)}
17: eval_foo_bb1_in->eval_foo_bb3_in: 1 {O(1)}
18: eval_foo_bb2_in->eval_foo_bb1_in: Arg_3+Arg_4+Arg_5+101 {O(n)}
19: eval_foo_bb3_in->eval_foo_stop: 1 {O(1)}
20: eval_foo_start->eval_foo_bb0_in: 1 {O(1)}

Costbounds

Overall costbound: 2*Arg_3+2*Arg_4+2*Arg_5+207 {O(n)}
14: eval_foo_bb0_in->eval_foo_bb1_in: 1 {O(1)}
15: eval_foo_bb1_in->eval_foo_bb2_in: Arg_3+Arg_4+Arg_5+101 {O(n)}
16: eval_foo_bb1_in->eval_foo_bb3_in: 1 {O(1)}
17: eval_foo_bb1_in->eval_foo_bb3_in: 1 {O(1)}
18: eval_foo_bb2_in->eval_foo_bb1_in: Arg_3+Arg_4+Arg_5+101 {O(n)}
19: eval_foo_bb3_in->eval_foo_stop: 1 {O(1)}
20: eval_foo_start->eval_foo_bb0_in: 1 {O(1)}

Sizebounds

14: eval_foo_bb0_in->eval_foo_bb1_in, Arg_0: Arg_5 {O(n)}
14: eval_foo_bb0_in->eval_foo_bb1_in, Arg_1: Arg_3 {O(n)}
14: eval_foo_bb0_in->eval_foo_bb1_in, Arg_2: Arg_4 {O(n)}
14: eval_foo_bb0_in->eval_foo_bb1_in, Arg_3: Arg_3 {O(n)}
14: eval_foo_bb0_in->eval_foo_bb1_in, Arg_4: Arg_4 {O(n)}
14: eval_foo_bb0_in->eval_foo_bb1_in, Arg_5: Arg_5 {O(n)}
15: eval_foo_bb1_in->eval_foo_bb2_in, Arg_0: 2*Arg_5+Arg_3+Arg_4+101 {O(n)}
15: eval_foo_bb1_in->eval_foo_bb2_in, Arg_1: 2*Arg_3+2*Arg_4+Arg_5+101 {O(n)}
15: eval_foo_bb1_in->eval_foo_bb2_in, Arg_2: 2*Arg_3+2*Arg_4+Arg_5+101 {O(n)}
15: eval_foo_bb1_in->eval_foo_bb2_in, Arg_3: Arg_3 {O(n)}
15: eval_foo_bb1_in->eval_foo_bb2_in, Arg_4: Arg_4 {O(n)}
15: eval_foo_bb1_in->eval_foo_bb2_in, Arg_5: Arg_5 {O(n)}
16: eval_foo_bb1_in->eval_foo_bb3_in, Arg_0: 3*Arg_5+Arg_3+Arg_4+101 {O(n)}
16: eval_foo_bb1_in->eval_foo_bb3_in, Arg_1: 2*Arg_4+3*Arg_3+Arg_5+101 {O(n)}
16: eval_foo_bb1_in->eval_foo_bb3_in, Arg_2: 2*Arg_3+3*Arg_4+Arg_5+101 {O(n)}
16: eval_foo_bb1_in->eval_foo_bb3_in, Arg_3: 2*Arg_3 {O(n)}
16: eval_foo_bb1_in->eval_foo_bb3_in, Arg_4: 2*Arg_4 {O(n)}
16: eval_foo_bb1_in->eval_foo_bb3_in, Arg_5: 2*Arg_5 {O(n)}
17: eval_foo_bb1_in->eval_foo_bb3_in, Arg_0: 3*Arg_5+Arg_3+Arg_4+101 {O(n)}
17: eval_foo_bb1_in->eval_foo_bb3_in, Arg_1: 2*Arg_4+3*Arg_3+Arg_5+101 {O(n)}
17: eval_foo_bb1_in->eval_foo_bb3_in, Arg_2: 2*Arg_3+3*Arg_4+Arg_5+101 {O(n)}
17: eval_foo_bb1_in->eval_foo_bb3_in, Arg_3: 2*Arg_3 {O(n)}
17: eval_foo_bb1_in->eval_foo_bb3_in, Arg_4: 2*Arg_4 {O(n)}
17: eval_foo_bb1_in->eval_foo_bb3_in, Arg_5: 2*Arg_5 {O(n)}
18: eval_foo_bb2_in->eval_foo_bb1_in, Arg_0: 2*Arg_5+Arg_3+Arg_4+101 {O(n)}
18: eval_foo_bb2_in->eval_foo_bb1_in, Arg_1: 2*Arg_3+2*Arg_4+Arg_5+101 {O(n)}
18: eval_foo_bb2_in->eval_foo_bb1_in, Arg_2: 2*Arg_3+2*Arg_4+Arg_5+101 {O(n)}
18: eval_foo_bb2_in->eval_foo_bb1_in, Arg_3: Arg_3 {O(n)}
18: eval_foo_bb2_in->eval_foo_bb1_in, Arg_4: Arg_4 {O(n)}
18: eval_foo_bb2_in->eval_foo_bb1_in, Arg_5: Arg_5 {O(n)}
19: eval_foo_bb3_in->eval_foo_stop, Arg_0: 2*Arg_3+2*Arg_4+6*Arg_5+202 {O(n)}
19: eval_foo_bb3_in->eval_foo_stop, Arg_1: 2*Arg_5+4*Arg_4+6*Arg_3+202 {O(n)}
19: eval_foo_bb3_in->eval_foo_stop, Arg_2: 2*Arg_5+4*Arg_3+6*Arg_4+202 {O(n)}
19: eval_foo_bb3_in->eval_foo_stop, Arg_3: 4*Arg_3 {O(n)}
19: eval_foo_bb3_in->eval_foo_stop, Arg_4: 4*Arg_4 {O(n)}
19: eval_foo_bb3_in->eval_foo_stop, Arg_5: 4*Arg_5 {O(n)}
20: eval_foo_start->eval_foo_bb0_in, Arg_0: Arg_0 {O(n)}
20: eval_foo_start->eval_foo_bb0_in, Arg_1: Arg_1 {O(n)}
20: eval_foo_start->eval_foo_bb0_in, Arg_2: Arg_2 {O(n)}
20: eval_foo_start->eval_foo_bb0_in, Arg_3: Arg_3 {O(n)}
20: eval_foo_start->eval_foo_bb0_in, Arg_4: Arg_4 {O(n)}
20: eval_foo_start->eval_foo_bb0_in, Arg_5: Arg_5 {O(n)}