Initial Problem

Start: eval_ax_start
Program_Vars: Arg_0, Arg_1, Arg_2, Arg_3, Arg_4
Temp_Vars:
Locations: eval_ax_bb0_in, eval_ax_bb1_in, eval_ax_bb2_in, eval_ax_bb3_in, eval_ax_bb4_in, eval_ax_bb5_in, eval_ax_start, eval_ax_stop
Transitions:
1:eval_ax_bb0_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> eval_ax_bb1_in(0,Arg_1,Arg_2,Arg_3,Arg_4)
2:eval_ax_bb1_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> eval_ax_bb2_in(Arg_0,0,Arg_2,Arg_3,Arg_4)
3:eval_ax_bb2_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> eval_ax_bb3_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4):|:Arg_1+1<Arg_4
4:eval_ax_bb2_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> eval_ax_bb4_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4):|:Arg_4<=1+Arg_1
5:eval_ax_bb3_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> eval_ax_bb2_in(Arg_0,Arg_1+1,Arg_2,Arg_3,Arg_4)
6:eval_ax_bb4_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> eval_ax_bb1_in(Arg_0+1,Arg_1,Arg_2,Arg_3,Arg_4):|:Arg_4<=1+Arg_1 && Arg_0+2<Arg_4
7:eval_ax_bb4_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> eval_ax_bb5_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4):|:Arg_1+1<Arg_4
8:eval_ax_bb4_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> eval_ax_bb5_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4):|:Arg_4<=2+Arg_0
9:eval_ax_bb5_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> eval_ax_stop(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4)
0:eval_ax_start(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> eval_ax_bb0_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4)

Preprocessing

Cut unsatisfiable transition 7: eval_ax_bb4_in->eval_ax_bb5_in

Eliminate variables {Arg_2,Arg_3} that do not contribute to the problem

Found invariant 0<=Arg_1 && 0<=Arg_0+Arg_1 && 0<=Arg_0 for location eval_ax_bb2_in

Found invariant 2<=Arg_4 && 2<=Arg_1+Arg_4 && 2+Arg_1<=Arg_4 && 2<=Arg_0+Arg_4 && 0<=Arg_1 && 0<=Arg_0+Arg_1 && 0<=Arg_0 for location eval_ax_bb3_in

Found invariant Arg_4<=1+Arg_1 && Arg_4<=2+Arg_0 && 0<=Arg_1 && 0<=Arg_0+Arg_1 && 0<=Arg_0 for location eval_ax_stop

Found invariant Arg_4<=1+Arg_1 && 0<=Arg_1 && 0<=Arg_0+Arg_1 && 0<=Arg_0 for location eval_ax_bb4_in

Found invariant Arg_4<=1+Arg_1 && Arg_4<=2+Arg_0 && 0<=Arg_1 && 0<=Arg_0+Arg_1 && 0<=Arg_0 for location eval_ax_bb5_in

Found invariant 0<=Arg_0 for location eval_ax_bb1_in

Problem after Preprocessing

Start: eval_ax_start
Program_Vars: Arg_0, Arg_1, Arg_4
Temp_Vars:
Locations: eval_ax_bb0_in, eval_ax_bb1_in, eval_ax_bb2_in, eval_ax_bb3_in, eval_ax_bb4_in, eval_ax_bb5_in, eval_ax_start, eval_ax_stop
Transitions:
20:eval_ax_bb0_in(Arg_0,Arg_1,Arg_4) -> eval_ax_bb1_in(0,Arg_1,Arg_4)
21:eval_ax_bb1_in(Arg_0,Arg_1,Arg_4) -> eval_ax_bb2_in(Arg_0,0,Arg_4):|:0<=Arg_0
22:eval_ax_bb2_in(Arg_0,Arg_1,Arg_4) -> eval_ax_bb3_in(Arg_0,Arg_1,Arg_4):|:0<=Arg_1 && 0<=Arg_0+Arg_1 && 0<=Arg_0 && Arg_1+1<Arg_4
23:eval_ax_bb2_in(Arg_0,Arg_1,Arg_4) -> eval_ax_bb4_in(Arg_0,Arg_1,Arg_4):|:0<=Arg_1 && 0<=Arg_0+Arg_1 && 0<=Arg_0 && Arg_4<=1+Arg_1
24:eval_ax_bb3_in(Arg_0,Arg_1,Arg_4) -> eval_ax_bb2_in(Arg_0,Arg_1+1,Arg_4):|:2<=Arg_4 && 2<=Arg_1+Arg_4 && 2+Arg_1<=Arg_4 && 2<=Arg_0+Arg_4 && 0<=Arg_1 && 0<=Arg_0+Arg_1 && 0<=Arg_0
25:eval_ax_bb4_in(Arg_0,Arg_1,Arg_4) -> eval_ax_bb1_in(Arg_0+1,Arg_1,Arg_4):|:Arg_4<=1+Arg_1 && 0<=Arg_1 && 0<=Arg_0+Arg_1 && 0<=Arg_0 && Arg_4<=1+Arg_1 && Arg_0+2<Arg_4
26:eval_ax_bb4_in(Arg_0,Arg_1,Arg_4) -> eval_ax_bb5_in(Arg_0,Arg_1,Arg_4):|:Arg_4<=1+Arg_1 && 0<=Arg_1 && 0<=Arg_0+Arg_1 && 0<=Arg_0 && Arg_4<=2+Arg_0
27:eval_ax_bb5_in(Arg_0,Arg_1,Arg_4) -> eval_ax_stop(Arg_0,Arg_1,Arg_4):|:Arg_4<=1+Arg_1 && Arg_4<=2+Arg_0 && 0<=Arg_1 && 0<=Arg_0+Arg_1 && 0<=Arg_0
28:eval_ax_start(Arg_0,Arg_1,Arg_4) -> eval_ax_bb0_in(Arg_0,Arg_1,Arg_4)

MPRF for transition 25:eval_ax_bb4_in(Arg_0,Arg_1,Arg_4) -> eval_ax_bb1_in(Arg_0+1,Arg_1,Arg_4):|:Arg_4<=1+Arg_1 && 0<=Arg_1 && 0<=Arg_0+Arg_1 && 0<=Arg_0 && Arg_4<=1+Arg_1 && Arg_0+2<Arg_4 of depth 1:

new bound:

Arg_4+2 {O(n)}

MPRF:

eval_ax_bb3_in [Arg_4-Arg_0-2 ]
eval_ax_bb2_in [Arg_4-Arg_0-2 ]
eval_ax_bb4_in [Arg_4-Arg_0-2 ]
eval_ax_bb1_in [Arg_4-Arg_0-2 ]

knowledge_propagation leads to new time bound Arg_4+3 {O(n)} for transition 21:eval_ax_bb1_in(Arg_0,Arg_1,Arg_4) -> eval_ax_bb2_in(Arg_0,0,Arg_4):|:0<=Arg_0

MPRF for transition 22:eval_ax_bb2_in(Arg_0,Arg_1,Arg_4) -> eval_ax_bb3_in(Arg_0,Arg_1,Arg_4):|:0<=Arg_1 && 0<=Arg_0+Arg_1 && 0<=Arg_0 && Arg_1+1<Arg_4 of depth 1:

new bound:

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

MPRF:

eval_ax_bb1_in [Arg_4 ]
eval_ax_bb4_in [Arg_4-Arg_1-1 ]
eval_ax_bb3_in [Arg_4-Arg_1-2 ]
eval_ax_bb2_in [Arg_4-Arg_1-1 ]

MPRF for transition 23:eval_ax_bb2_in(Arg_0,Arg_1,Arg_4) -> eval_ax_bb4_in(Arg_0,Arg_1,Arg_4):|:0<=Arg_1 && 0<=Arg_0+Arg_1 && 0<=Arg_0 && Arg_4<=1+Arg_1 of depth 1:

new bound:

Arg_4+3 {O(n)}

MPRF:

eval_ax_bb1_in [1 ]
eval_ax_bb4_in [-Arg_0 ]
eval_ax_bb3_in [1 ]
eval_ax_bb2_in [1 ]

MPRF for transition 24:eval_ax_bb3_in(Arg_0,Arg_1,Arg_4) -> eval_ax_bb2_in(Arg_0,Arg_1+1,Arg_4):|:2<=Arg_4 && 2<=Arg_1+Arg_4 && 2+Arg_1<=Arg_4 && 2<=Arg_0+Arg_4 && 0<=Arg_1 && 0<=Arg_0+Arg_1 && 0<=Arg_0 of depth 1:

new bound:

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

MPRF:

eval_ax_bb1_in [Arg_4 ]
eval_ax_bb4_in [Arg_4-Arg_1-1 ]
eval_ax_bb3_in [Arg_4-Arg_1-1 ]
eval_ax_bb2_in [Arg_4-Arg_1-1 ]

Analysing control-flow refined program

Found invariant Arg_1<=0 && Arg_1<=Arg_0 && 0<=Arg_1 && 0<=Arg_0+Arg_1 && 0<=Arg_0 for location eval_ax_bb2_in

Found invariant 2<=Arg_4 && 2<=Arg_1+Arg_4 && 2+Arg_1<=Arg_4 && 2<=Arg_0+Arg_4 && Arg_1<=0 && Arg_1<=Arg_0 && 0<=Arg_1 && 0<=Arg_0+Arg_1 && 0<=Arg_0 for location n_eval_ax_bb3_in___3

Found invariant 3<=Arg_4 && 4<=Arg_1+Arg_4 && 2+Arg_1<=Arg_4 && 3<=Arg_0+Arg_4 && 1<=Arg_1 && 1<=Arg_0+Arg_1 && 0<=Arg_0 for location n_eval_ax_bb3_in___1

Found invariant Arg_4<=1+Arg_1 && Arg_4<=2+Arg_0 && 0<=Arg_1 && 0<=Arg_0+Arg_1 && 0<=Arg_0 for location eval_ax_stop

Found invariant 2<=Arg_4 && 3<=Arg_1+Arg_4 && 1+Arg_1<=Arg_4 && 2<=Arg_0+Arg_4 && 1<=Arg_1 && 1<=Arg_0+Arg_1 && 0<=Arg_0 for location n_eval_ax_bb2_in___2

Found invariant Arg_4<=1+Arg_1 && 0<=Arg_1 && 0<=Arg_0+Arg_1 && 0<=Arg_0 for location eval_ax_bb4_in

Found invariant Arg_4<=1+Arg_1 && Arg_4<=2+Arg_0 && 0<=Arg_1 && 0<=Arg_0+Arg_1 && 0<=Arg_0 for location eval_ax_bb5_in

Found invariant 0<=Arg_0 for location eval_ax_bb1_in

knowledge_propagation leads to new time bound Arg_4+3 {O(n)} for transition 60:eval_ax_bb2_in(Arg_0,Arg_1,Arg_4) -> n_eval_ax_bb3_in___3(Arg_0,Arg_1,Arg_4):|:Arg_1<=0 && Arg_1<=Arg_0 && 0<=Arg_1 && 0<=Arg_0+Arg_1 && 0<=Arg_0 && 0<=Arg_1 && 0<=Arg_0 && Arg_1<=0 && 0<=Arg_1 && 0<=Arg_0 && 0<=Arg_0 && 0<=Arg_1 && 1+Arg_1<Arg_4

knowledge_propagation leads to new time bound Arg_4+3 {O(n)} for transition 62:n_eval_ax_bb3_in___3(Arg_0,Arg_1,Arg_4) -> n_eval_ax_bb2_in___2(Arg_0,Arg_1+1,Arg_4):|:2<=Arg_4 && 2<=Arg_1+Arg_4 && 2+Arg_1<=Arg_4 && 2<=Arg_0+Arg_4 && Arg_1<=0 && Arg_1<=Arg_0 && 0<=Arg_1 && 0<=Arg_0+Arg_1 && 0<=Arg_0 && 1<Arg_4 && 0<=Arg_0 && Arg_1<=0 && 0<=Arg_1 && 0<=Arg_1 && 0<=Arg_0 && 2+Arg_1<=Arg_4

MPRF for transition 59:n_eval_ax_bb2_in___2(Arg_0,Arg_1,Arg_4) -> n_eval_ax_bb3_in___1(Arg_0,Arg_1,Arg_4):|:2<=Arg_4 && 3<=Arg_1+Arg_4 && 1+Arg_1<=Arg_4 && 2<=Arg_0+Arg_4 && 1<=Arg_1 && 1<=Arg_0+Arg_1 && 0<=Arg_0 && 0<=Arg_1 && 0<=Arg_0 && 0<=Arg_0 && 1<=Arg_1 && 1+Arg_1<=Arg_4 && 0<=Arg_0 && 0<=Arg_1 && 1+Arg_1<Arg_4 of depth 1:

new bound:

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

MPRF:

eval_ax_bb2_in [0 ]
n_eval_ax_bb3_in___3 [0 ]
eval_ax_bb1_in [0 ]
eval_ax_bb4_in [0 ]
n_eval_ax_bb3_in___1 [Arg_4-Arg_1-1 ]
n_eval_ax_bb2_in___2 [Arg_4-Arg_1 ]

MPRF for transition 67:n_eval_ax_bb2_in___2(Arg_0,Arg_1,Arg_4) -> eval_ax_bb4_in(Arg_0,Arg_1,Arg_4):|:2<=Arg_4 && 3<=Arg_1+Arg_4 && 1+Arg_1<=Arg_4 && 2<=Arg_0+Arg_4 && 1<=Arg_1 && 1<=Arg_0+Arg_1 && 0<=Arg_0 && 0<=Arg_1 && 0<=Arg_0+Arg_1 && 0<=Arg_0 && Arg_4<=1+Arg_1 of depth 1:

new bound:

2*Arg_4*Arg_4+9*Arg_4+11 {O(n^2)}

MPRF:

eval_ax_bb2_in [2 ]
n_eval_ax_bb3_in___3 [2 ]
eval_ax_bb1_in [2 ]
eval_ax_bb4_in [2*Arg_4-4 ]
n_eval_ax_bb3_in___1 [2*Arg_4-3 ]
n_eval_ax_bb2_in___2 [2*Arg_4-3 ]

MPRF for transition 61:n_eval_ax_bb3_in___1(Arg_0,Arg_1,Arg_4) -> n_eval_ax_bb2_in___2(Arg_0,Arg_1+1,Arg_4):|:3<=Arg_4 && 4<=Arg_1+Arg_4 && 2+Arg_1<=Arg_4 && 3<=Arg_0+Arg_4 && 1<=Arg_1 && 1<=Arg_0+Arg_1 && 0<=Arg_0 && 1+Arg_1<Arg_4 && 1<=Arg_1 && 0<=Arg_0 && 0<=Arg_1 && 0<=Arg_0 && 2+Arg_1<=Arg_4 of depth 1:

new bound:

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

MPRF:

eval_ax_bb2_in [0 ]
n_eval_ax_bb3_in___3 [0 ]
eval_ax_bb1_in [0 ]
eval_ax_bb4_in [0 ]
n_eval_ax_bb3_in___1 [Arg_4-Arg_1-1 ]
n_eval_ax_bb2_in___2 [Arg_4-Arg_1-1 ]

CFR did not improve the program. Rolling back

All Bounds

Timebounds

Overall timebound:2*Arg_4*Arg_4+9*Arg_4+12 {O(n^2)}
20: eval_ax_bb0_in->eval_ax_bb1_in: 1 {O(1)}
21: eval_ax_bb1_in->eval_ax_bb2_in: Arg_4+3 {O(n)}
22: eval_ax_bb2_in->eval_ax_bb3_in: Arg_4*Arg_4+3*Arg_4 {O(n^2)}
23: eval_ax_bb2_in->eval_ax_bb4_in: Arg_4+3 {O(n)}
24: eval_ax_bb3_in->eval_ax_bb2_in: Arg_4*Arg_4+3*Arg_4 {O(n^2)}
25: eval_ax_bb4_in->eval_ax_bb1_in: Arg_4+2 {O(n)}
26: eval_ax_bb4_in->eval_ax_bb5_in: 1 {O(1)}
27: eval_ax_bb5_in->eval_ax_stop: 1 {O(1)}
28: eval_ax_start->eval_ax_bb0_in: 1 {O(1)}

Costbounds

Overall costbound: 2*Arg_4*Arg_4+9*Arg_4+12 {O(n^2)}
20: eval_ax_bb0_in->eval_ax_bb1_in: 1 {O(1)}
21: eval_ax_bb1_in->eval_ax_bb2_in: Arg_4+3 {O(n)}
22: eval_ax_bb2_in->eval_ax_bb3_in: Arg_4*Arg_4+3*Arg_4 {O(n^2)}
23: eval_ax_bb2_in->eval_ax_bb4_in: Arg_4+3 {O(n)}
24: eval_ax_bb3_in->eval_ax_bb2_in: Arg_4*Arg_4+3*Arg_4 {O(n^2)}
25: eval_ax_bb4_in->eval_ax_bb1_in: Arg_4+2 {O(n)}
26: eval_ax_bb4_in->eval_ax_bb5_in: 1 {O(1)}
27: eval_ax_bb5_in->eval_ax_stop: 1 {O(1)}
28: eval_ax_start->eval_ax_bb0_in: 1 {O(1)}

Sizebounds

20: eval_ax_bb0_in->eval_ax_bb1_in, Arg_0: 0 {O(1)}
20: eval_ax_bb0_in->eval_ax_bb1_in, Arg_1: Arg_1 {O(n)}
20: eval_ax_bb0_in->eval_ax_bb1_in, Arg_4: Arg_4 {O(n)}
21: eval_ax_bb1_in->eval_ax_bb2_in, Arg_0: Arg_4+2 {O(n)}
21: eval_ax_bb1_in->eval_ax_bb2_in, Arg_1: 0 {O(1)}
21: eval_ax_bb1_in->eval_ax_bb2_in, Arg_4: Arg_4 {O(n)}
22: eval_ax_bb2_in->eval_ax_bb3_in, Arg_0: Arg_4+2 {O(n)}
22: eval_ax_bb2_in->eval_ax_bb3_in, Arg_1: Arg_4*Arg_4+3*Arg_4 {O(n^2)}
22: eval_ax_bb2_in->eval_ax_bb3_in, Arg_4: Arg_4 {O(n)}
23: eval_ax_bb2_in->eval_ax_bb4_in, Arg_0: Arg_4+2 {O(n)}
23: eval_ax_bb2_in->eval_ax_bb4_in, Arg_1: Arg_4*Arg_4+3*Arg_4 {O(n^2)}
23: eval_ax_bb2_in->eval_ax_bb4_in, Arg_4: Arg_4 {O(n)}
24: eval_ax_bb3_in->eval_ax_bb2_in, Arg_0: Arg_4+2 {O(n)}
24: eval_ax_bb3_in->eval_ax_bb2_in, Arg_1: Arg_4*Arg_4+3*Arg_4 {O(n^2)}
24: eval_ax_bb3_in->eval_ax_bb2_in, Arg_4: Arg_4 {O(n)}
25: eval_ax_bb4_in->eval_ax_bb1_in, Arg_0: Arg_4+2 {O(n)}
25: eval_ax_bb4_in->eval_ax_bb1_in, Arg_1: Arg_4*Arg_4+3*Arg_4 {O(n^2)}
25: eval_ax_bb4_in->eval_ax_bb1_in, Arg_4: Arg_4 {O(n)}
26: eval_ax_bb4_in->eval_ax_bb5_in, Arg_0: Arg_4+2 {O(n)}
26: eval_ax_bb4_in->eval_ax_bb5_in, Arg_1: Arg_4*Arg_4+3*Arg_4 {O(n^2)}
26: eval_ax_bb4_in->eval_ax_bb5_in, Arg_4: Arg_4 {O(n)}
27: eval_ax_bb5_in->eval_ax_stop, Arg_0: Arg_4+2 {O(n)}
27: eval_ax_bb5_in->eval_ax_stop, Arg_1: Arg_4*Arg_4+3*Arg_4 {O(n^2)}
27: eval_ax_bb5_in->eval_ax_stop, Arg_4: Arg_4 {O(n)}
28: eval_ax_start->eval_ax_bb0_in, Arg_0: Arg_0 {O(n)}
28: eval_ax_start->eval_ax_bb0_in, Arg_1: Arg_1 {O(n)}
28: eval_ax_start->eval_ax_bb0_in, Arg_4: Arg_4 {O(n)}