Initial Problem

Start: eval_foo_start
Program_Vars: Arg_0, Arg_1, Arg_2, Arg_3, Arg_4
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) -> eval_foo_bb1_in(Arg_3,Arg_4,Arg_2,Arg_3,Arg_4)
2: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_1
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_1<Arg_0
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_0<=Arg_1 && Arg_1<=Arg_0
5:eval_foo_bb2_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> eval_foo_bb1_in(Arg_0,Arg_1+1,Arg_2,Arg_3,Arg_4):|:Arg_1<Arg_0 && Arg_1<Arg_0
6:eval_foo_bb2_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> eval_foo_bb1_in(Arg_0+1,Arg_1+1,Arg_2,Arg_3,Arg_4):|:Arg_1<Arg_0 && Arg_0<=Arg_1
7:eval_foo_bb2_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> eval_foo_bb1_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4):|:Arg_0<=Arg_1 && Arg_1<Arg_0
8:eval_foo_bb2_in(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_0<=Arg_1 && Arg_0<=Arg_1
9: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

Cut unsatisfiable transition 6: eval_foo_bb2_in->eval_foo_bb1_in

Cut unsatisfiable transition 7: eval_foo_bb2_in->eval_foo_bb1_in

Eliminate variables {Arg_2} that do not contribute to the problem

Found invariant Arg_4<=Arg_1 && Arg_4<=Arg_0 && Arg_3<=Arg_1 && Arg_3<=Arg_0 && Arg_1<=Arg_0 && Arg_0<=Arg_1 for location eval_foo_stop

Found invariant Arg_4<=Arg_1 && Arg_4<=Arg_0 && Arg_3<=Arg_1 && Arg_3<=Arg_0 && Arg_1<=Arg_0 && Arg_0<=Arg_1 for location eval_foo_bb3_in

Found invariant Arg_4<=Arg_1 && Arg_3<=Arg_0 for location eval_foo_bb2_in

Found invariant Arg_4<=Arg_1 && Arg_3<=Arg_0 for location eval_foo_bb1_in

Problem after Preprocessing

Start: eval_foo_start
Program_Vars: Arg_0, Arg_1, Arg_3, Arg_4
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:
23:eval_foo_bb0_in(Arg_0,Arg_1,Arg_3,Arg_4) -> eval_foo_bb1_in(Arg_3,Arg_4,Arg_3,Arg_4)
24:eval_foo_bb1_in(Arg_0,Arg_1,Arg_3,Arg_4) -> eval_foo_bb2_in(Arg_0,Arg_1,Arg_3,Arg_4):|:Arg_4<=Arg_1 && Arg_3<=Arg_0 && Arg_0<Arg_1
25:eval_foo_bb1_in(Arg_0,Arg_1,Arg_3,Arg_4) -> eval_foo_bb2_in(Arg_0,Arg_1,Arg_3,Arg_4):|:Arg_4<=Arg_1 && Arg_3<=Arg_0 && Arg_1<Arg_0
26:eval_foo_bb1_in(Arg_0,Arg_1,Arg_3,Arg_4) -> eval_foo_bb3_in(Arg_0,Arg_1,Arg_3,Arg_4):|:Arg_4<=Arg_1 && Arg_3<=Arg_0 && Arg_0<=Arg_1 && Arg_1<=Arg_0
27:eval_foo_bb2_in(Arg_0,Arg_1,Arg_3,Arg_4) -> eval_foo_bb1_in(Arg_0,Arg_1+1,Arg_3,Arg_4):|:Arg_4<=Arg_1 && Arg_3<=Arg_0 && Arg_1<Arg_0 && Arg_1<Arg_0
28:eval_foo_bb2_in(Arg_0,Arg_1,Arg_3,Arg_4) -> eval_foo_bb1_in(Arg_0+1,Arg_1,Arg_3,Arg_4):|:Arg_4<=Arg_1 && Arg_3<=Arg_0 && Arg_0<=Arg_1 && Arg_0<=Arg_1
29:eval_foo_bb3_in(Arg_0,Arg_1,Arg_3,Arg_4) -> eval_foo_stop(Arg_0,Arg_1,Arg_3,Arg_4):|:Arg_4<=Arg_1 && Arg_4<=Arg_0 && Arg_3<=Arg_1 && Arg_3<=Arg_0 && Arg_1<=Arg_0 && Arg_0<=Arg_1
30:eval_foo_start(Arg_0,Arg_1,Arg_3,Arg_4) -> eval_foo_bb0_in(Arg_0,Arg_1,Arg_3,Arg_4)

MPRF for transition 24:eval_foo_bb1_in(Arg_0,Arg_1,Arg_3,Arg_4) -> eval_foo_bb2_in(Arg_0,Arg_1,Arg_3,Arg_4):|:Arg_4<=Arg_1 && Arg_3<=Arg_0 && Arg_0<Arg_1 of depth 1:

new bound:

Arg_3+Arg_4 {O(n)}

MPRF:

eval_foo_bb2_in [Arg_1-Arg_0-1 ]
eval_foo_bb1_in [Arg_1-Arg_0 ]

MPRF for transition 28:eval_foo_bb2_in(Arg_0,Arg_1,Arg_3,Arg_4) -> eval_foo_bb1_in(Arg_0+1,Arg_1,Arg_3,Arg_4):|:Arg_4<=Arg_1 && Arg_3<=Arg_0 && Arg_0<=Arg_1 && Arg_0<=Arg_1 of depth 1:

new bound:

Arg_3+Arg_4+1 {O(n)}

MPRF:

eval_foo_bb2_in [Arg_1+1-Arg_0 ]
eval_foo_bb1_in [Arg_1+1-Arg_0 ]

MPRF for transition 25:eval_foo_bb1_in(Arg_0,Arg_1,Arg_3,Arg_4) -> eval_foo_bb2_in(Arg_0,Arg_1,Arg_3,Arg_4):|:Arg_4<=Arg_1 && Arg_3<=Arg_0 && Arg_1<Arg_0 of depth 1:

new bound:

2*Arg_3*Arg_3+2*Arg_4*Arg_4+4*Arg_3*Arg_4+6*Arg_3+6*Arg_4+5 {O(n^2)}

MPRF:

eval_foo_bb2_in [Arg_0+1-Arg_1 ]
eval_foo_bb1_in [Arg_0+2-Arg_1 ]

MPRF for transition 27:eval_foo_bb2_in(Arg_0,Arg_1,Arg_3,Arg_4) -> eval_foo_bb1_in(Arg_0,Arg_1+1,Arg_3,Arg_4):|:Arg_4<=Arg_1 && Arg_3<=Arg_0 && Arg_1<Arg_0 && Arg_1<Arg_0 of depth 1:

new bound:

2*Arg_3*Arg_3+2*Arg_4*Arg_4+4*Arg_3*Arg_4+5*Arg_3+5*Arg_4+3 {O(n^2)}

MPRF:

eval_foo_bb2_in [Arg_0+1-Arg_1 ]
eval_foo_bb1_in [Arg_0+1-Arg_1 ]

All Bounds

Timebounds

Overall timebound:4*Arg_3*Arg_3+4*Arg_4*Arg_4+8*Arg_3*Arg_4+13*Arg_3+13*Arg_4+13 {O(n^2)}
23: eval_foo_bb0_in->eval_foo_bb1_in: 1 {O(1)}
24: eval_foo_bb1_in->eval_foo_bb2_in: Arg_3+Arg_4 {O(n)}
25: eval_foo_bb1_in->eval_foo_bb2_in: 2*Arg_3*Arg_3+2*Arg_4*Arg_4+4*Arg_3*Arg_4+6*Arg_3+6*Arg_4+5 {O(n^2)}
26: eval_foo_bb1_in->eval_foo_bb3_in: 1 {O(1)}
27: eval_foo_bb2_in->eval_foo_bb1_in: 2*Arg_3*Arg_3+2*Arg_4*Arg_4+4*Arg_3*Arg_4+5*Arg_3+5*Arg_4+3 {O(n^2)}
28: eval_foo_bb2_in->eval_foo_bb1_in: Arg_3+Arg_4+1 {O(n)}
29: eval_foo_bb3_in->eval_foo_stop: 1 {O(1)}
30: eval_foo_start->eval_foo_bb0_in: 1 {O(1)}

Costbounds

Overall costbound: 4*Arg_3*Arg_3+4*Arg_4*Arg_4+8*Arg_3*Arg_4+13*Arg_3+13*Arg_4+13 {O(n^2)}
23: eval_foo_bb0_in->eval_foo_bb1_in: 1 {O(1)}
24: eval_foo_bb1_in->eval_foo_bb2_in: Arg_3+Arg_4 {O(n)}
25: eval_foo_bb1_in->eval_foo_bb2_in: 2*Arg_3*Arg_3+2*Arg_4*Arg_4+4*Arg_3*Arg_4+6*Arg_3+6*Arg_4+5 {O(n^2)}
26: eval_foo_bb1_in->eval_foo_bb3_in: 1 {O(1)}
27: eval_foo_bb2_in->eval_foo_bb1_in: 2*Arg_3*Arg_3+2*Arg_4*Arg_4+4*Arg_3*Arg_4+5*Arg_3+5*Arg_4+3 {O(n^2)}
28: eval_foo_bb2_in->eval_foo_bb1_in: Arg_3+Arg_4+1 {O(n)}
29: eval_foo_bb3_in->eval_foo_stop: 1 {O(1)}
30: eval_foo_start->eval_foo_bb0_in: 1 {O(1)}

Sizebounds

23: eval_foo_bb0_in->eval_foo_bb1_in, Arg_0: Arg_3 {O(n)}
23: eval_foo_bb0_in->eval_foo_bb1_in, Arg_1: Arg_4 {O(n)}
23: eval_foo_bb0_in->eval_foo_bb1_in, Arg_3: Arg_3 {O(n)}
23: eval_foo_bb0_in->eval_foo_bb1_in, Arg_4: Arg_4 {O(n)}
24: eval_foo_bb1_in->eval_foo_bb2_in, Arg_0: 2*Arg_3+Arg_4+1 {O(n)}
24: eval_foo_bb1_in->eval_foo_bb2_in, Arg_1: Arg_4 {O(n)}
24: eval_foo_bb1_in->eval_foo_bb2_in, Arg_3: Arg_3 {O(n)}
24: eval_foo_bb1_in->eval_foo_bb2_in, Arg_4: Arg_4 {O(n)}
25: eval_foo_bb1_in->eval_foo_bb2_in, Arg_0: 3*Arg_3+Arg_4+1 {O(n)}
25: eval_foo_bb1_in->eval_foo_bb2_in, Arg_1: 2*Arg_3*Arg_3+2*Arg_4*Arg_4+4*Arg_3*Arg_4+5*Arg_3+7*Arg_4+3 {O(n^2)}
25: eval_foo_bb1_in->eval_foo_bb2_in, Arg_3: 2*Arg_3 {O(n)}
25: eval_foo_bb1_in->eval_foo_bb2_in, Arg_4: 2*Arg_4 {O(n)}
26: eval_foo_bb1_in->eval_foo_bb3_in, Arg_0: 2*Arg_4+6*Arg_3+2 {O(n)}
26: eval_foo_bb1_in->eval_foo_bb3_in, Arg_1: 2*Arg_3*Arg_3+2*Arg_4*Arg_4+4*Arg_3*Arg_4+5*Arg_3+9*Arg_4+3 {O(n^2)}
26: eval_foo_bb1_in->eval_foo_bb3_in, Arg_3: 4*Arg_3 {O(n)}
26: eval_foo_bb1_in->eval_foo_bb3_in, Arg_4: 4*Arg_4 {O(n)}
27: eval_foo_bb2_in->eval_foo_bb1_in, Arg_0: 3*Arg_3+Arg_4+1 {O(n)}
27: eval_foo_bb2_in->eval_foo_bb1_in, Arg_1: 2*Arg_3*Arg_3+2*Arg_4*Arg_4+4*Arg_3*Arg_4+5*Arg_3+7*Arg_4+3 {O(n^2)}
27: eval_foo_bb2_in->eval_foo_bb1_in, Arg_3: 2*Arg_3 {O(n)}
27: eval_foo_bb2_in->eval_foo_bb1_in, Arg_4: 2*Arg_4 {O(n)}
28: eval_foo_bb2_in->eval_foo_bb1_in, Arg_0: 2*Arg_3+Arg_4+1 {O(n)}
28: eval_foo_bb2_in->eval_foo_bb1_in, Arg_1: Arg_4 {O(n)}
28: eval_foo_bb2_in->eval_foo_bb1_in, Arg_3: Arg_3 {O(n)}
28: eval_foo_bb2_in->eval_foo_bb1_in, Arg_4: Arg_4 {O(n)}
29: eval_foo_bb3_in->eval_foo_stop, Arg_0: 2*Arg_4+6*Arg_3+2 {O(n)}
29: eval_foo_bb3_in->eval_foo_stop, Arg_1: 2*Arg_3*Arg_3+2*Arg_4*Arg_4+4*Arg_3*Arg_4+5*Arg_3+9*Arg_4+3 {O(n^2)}
29: eval_foo_bb3_in->eval_foo_stop, Arg_3: 4*Arg_3 {O(n)}
29: eval_foo_bb3_in->eval_foo_stop, Arg_4: 4*Arg_4 {O(n)}
30: eval_foo_start->eval_foo_bb0_in, Arg_0: Arg_0 {O(n)}
30: eval_foo_start->eval_foo_bb0_in, Arg_1: Arg_1 {O(n)}
30: eval_foo_start->eval_foo_bb0_in, Arg_3: Arg_3 {O(n)}
30: eval_foo_start->eval_foo_bb0_in, Arg_4: Arg_4 {O(n)}