Initial Problem

Start: eval_cousot9_start
Program_Vars: Arg_0, Arg_1, Arg_2, Arg_3
Temp_Vars:
Locations: eval_cousot9_bb0_in, eval_cousot9_bb1_in, eval_cousot9_bb2_in, eval_cousot9_bb3_in, eval_cousot9_start, eval_cousot9_stop
Transitions:
1:eval_cousot9_bb0_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_cousot9_bb1_in(Arg_3,Arg_1,Arg_1,Arg_3)
2:eval_cousot9_bb1_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_cousot9_bb2_in(Arg_0,Arg_1,Arg_2,Arg_3):|:0<Arg_2
3:eval_cousot9_bb1_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_cousot9_bb3_in(Arg_0,Arg_1,Arg_2,Arg_3):|:Arg_2<=0
4:eval_cousot9_bb2_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_cousot9_bb1_in(Arg_0-1,Arg_1,Arg_2,Arg_3):|:0<Arg_0 && 0<Arg_0
5:eval_cousot9_bb2_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_cousot9_bb1_in(Arg_1,Arg_1,Arg_2,Arg_3):|:0<Arg_0 && Arg_0<=0
6:eval_cousot9_bb2_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_cousot9_bb1_in(Arg_0-1,Arg_1,Arg_2-1,Arg_3):|:Arg_0<=0 && 0<Arg_0
7:eval_cousot9_bb2_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_cousot9_bb1_in(Arg_1,Arg_1,Arg_2-1,Arg_3):|:Arg_0<=0 && Arg_0<=0
8:eval_cousot9_bb3_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_cousot9_stop(Arg_0,Arg_1,Arg_2,Arg_3)
0:eval_cousot9_start(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_cousot9_bb0_in(Arg_0,Arg_1,Arg_2,Arg_3)

Preprocessing

Cut unsatisfiable transition 5: eval_cousot9_bb2_in->eval_cousot9_bb1_in

Cut unsatisfiable transition 6: eval_cousot9_bb2_in->eval_cousot9_bb1_in

Found invariant Arg_2<=0 && Arg_2<=Arg_1 for location eval_cousot9_stop

Found invariant Arg_2<=Arg_1 for location eval_cousot9_bb1_in

Found invariant Arg_2<=Arg_1 && 1<=Arg_2 && 2<=Arg_1+Arg_2 && 1<=Arg_1 for location eval_cousot9_bb2_in

Found invariant Arg_2<=0 && Arg_2<=Arg_1 for location eval_cousot9_bb3_in

Problem after Preprocessing

Start: eval_cousot9_start
Program_Vars: Arg_0, Arg_1, Arg_2, Arg_3
Temp_Vars:
Locations: eval_cousot9_bb0_in, eval_cousot9_bb1_in, eval_cousot9_bb2_in, eval_cousot9_bb3_in, eval_cousot9_start, eval_cousot9_stop
Transitions:
1:eval_cousot9_bb0_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_cousot9_bb1_in(Arg_3,Arg_1,Arg_1,Arg_3)
2:eval_cousot9_bb1_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_cousot9_bb2_in(Arg_0,Arg_1,Arg_2,Arg_3):|:Arg_2<=Arg_1 && 0<Arg_2
3:eval_cousot9_bb1_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_cousot9_bb3_in(Arg_0,Arg_1,Arg_2,Arg_3):|:Arg_2<=Arg_1 && Arg_2<=0
4:eval_cousot9_bb2_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_cousot9_bb1_in(Arg_0-1,Arg_1,Arg_2,Arg_3):|:Arg_2<=Arg_1 && 1<=Arg_2 && 2<=Arg_1+Arg_2 && 1<=Arg_1 && 0<Arg_0 && 0<Arg_0
7:eval_cousot9_bb2_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_cousot9_bb1_in(Arg_1,Arg_1,Arg_2-1,Arg_3):|:Arg_2<=Arg_1 && 1<=Arg_2 && 2<=Arg_1+Arg_2 && 1<=Arg_1 && Arg_0<=0 && Arg_0<=0
8:eval_cousot9_bb3_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_cousot9_stop(Arg_0,Arg_1,Arg_2,Arg_3):|:Arg_2<=0 && Arg_2<=Arg_1
0:eval_cousot9_start(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_cousot9_bb0_in(Arg_0,Arg_1,Arg_2,Arg_3)

MPRF for transition 7:eval_cousot9_bb2_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_cousot9_bb1_in(Arg_1,Arg_1,Arg_2-1,Arg_3):|:Arg_2<=Arg_1 && 1<=Arg_2 && 2<=Arg_1+Arg_2 && 1<=Arg_1 && Arg_0<=0 && Arg_0<=0 of depth 1:

new bound:

Arg_1 {O(n)}

MPRF:

eval_cousot9_bb2_in [Arg_2 ]
eval_cousot9_bb1_in [Arg_2 ]

MPRF for transition 4:eval_cousot9_bb2_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_cousot9_bb1_in(Arg_0-1,Arg_1,Arg_2,Arg_3):|:Arg_2<=Arg_1 && 1<=Arg_2 && 2<=Arg_1+Arg_2 && 1<=Arg_1 && 0<Arg_0 && 0<Arg_0 of depth 1:

new bound:

Arg_1*Arg_1+Arg_1+Arg_3+1 {O(n^2)}

MPRF:

eval_cousot9_bb2_in [Arg_0+1 ]
eval_cousot9_bb1_in [Arg_0+1 ]

knowledge_propagation leads to new time bound Arg_1*Arg_1+2*Arg_1+Arg_3+2 {O(n^2)} for transition 2:eval_cousot9_bb1_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_cousot9_bb2_in(Arg_0,Arg_1,Arg_2,Arg_3):|:Arg_2<=Arg_1 && 0<Arg_2

Analysing control-flow refined program

Cut unsatisfiable transition 71: n_eval_cousot9_bb1_in___2->eval_cousot9_bb3_in

Cut unsatisfiable transition 73: n_eval_cousot9_bb1_in___6->eval_cousot9_bb3_in

Found invariant Arg_3<=Arg_0 && Arg_0<=Arg_3 && Arg_2<=Arg_1 && 1<=Arg_2 && 2<=Arg_1+Arg_2 && Arg_1<=Arg_2 && 1<=Arg_1 for location n_eval_cousot9_bb2_in___7

Found invariant Arg_2<=Arg_1 && 1<=Arg_2 && 2<=Arg_1+Arg_2 && 1<=Arg_0+Arg_2 && 1<=Arg_1 && 1<=Arg_0+Arg_1 && 0<=Arg_0 for location n_eval_cousot9_bb1_in___6

Found invariant Arg_2<=0 && Arg_2<=Arg_1 for location eval_cousot9_stop

Found invariant Arg_2<=Arg_1 && 1<=Arg_2 && 2<=Arg_1+Arg_2 && 1<=Arg_0+Arg_2 && 1<=Arg_1 && 1<=Arg_0+Arg_1 && 0<=Arg_0 for location n_eval_cousot9_bb2_in___4

Found invariant Arg_3<=Arg_0 && Arg_0<=Arg_3 && Arg_2<=Arg_1 && Arg_1<=Arg_2 for location eval_cousot9_bb1_in

Found invariant 1+Arg_2<=Arg_1 && Arg_2<=Arg_0 && 1<=Arg_2 && 3<=Arg_1+Arg_2 && 2<=Arg_0+Arg_2 && Arg_1<=1+Arg_0 && 2<=Arg_1 && 3<=Arg_0+Arg_1 && 1+Arg_0<=Arg_1 && 1<=Arg_0 for location n_eval_cousot9_bb1_in___2

Found invariant 1+Arg_2<=Arg_1 && 1+Arg_2<=Arg_0 && 1<=Arg_2 && 3<=Arg_1+Arg_2 && 3<=Arg_0+Arg_2 && Arg_1<=Arg_0 && 2<=Arg_1 && 4<=Arg_0+Arg_1 && Arg_0<=Arg_1 && 2<=Arg_0 for location n_eval_cousot9_bb2_in___3

Found invariant 1+Arg_2<=Arg_1 && Arg_2<=Arg_0 && 1<=Arg_2 && 3<=Arg_1+Arg_2 && 2<=Arg_0+Arg_2 && Arg_1<=1+Arg_0 && 2<=Arg_1 && 3<=Arg_0+Arg_1 && 1+Arg_0<=Arg_1 && 1<=Arg_0 for location n_eval_cousot9_bb2_in___1

Found invariant Arg_2<=0 && Arg_2<=Arg_1 for location eval_cousot9_bb3_in

Found invariant 1+Arg_2<=Arg_1 && 1+Arg_2<=Arg_0 && 0<=Arg_2 && 1<=Arg_1+Arg_2 && 1<=Arg_0+Arg_2 && Arg_1<=Arg_0 && 1<=Arg_1 && 2<=Arg_0+Arg_1 && Arg_0<=Arg_1 && 1<=Arg_0 for location n_eval_cousot9_bb1_in___5

MPRF for transition 54:n_eval_cousot9_bb1_in___2(Arg_0,Arg_1,Arg_2,Arg_3) -> n_eval_cousot9_bb2_in___1(Arg_0,Arg_1,Arg_2,Arg_3):|:1+Arg_2<=Arg_1 && Arg_2<=Arg_0 && 1<=Arg_2 && 3<=Arg_1+Arg_2 && 2<=Arg_0+Arg_2 && Arg_1<=1+Arg_0 && 2<=Arg_1 && 3<=Arg_0+Arg_1 && 1+Arg_0<=Arg_1 && 1<=Arg_0 && Arg_2<=Arg_1 && 0<Arg_2 && 1<=Arg_2 && 0<Arg_0 && 1<=Arg_2 && Arg_2<=Arg_1 && 0<=Arg_0 && 1<=Arg_2 && Arg_2<=Arg_1 && Arg_2<=Arg_1 && 0<Arg_2 of depth 1:

new bound:

4*Arg_1+1 {O(n)}

MPRF:

n_eval_cousot9_bb2_in___1 [Arg_1+Arg_2-1 ]
n_eval_cousot9_bb2_in___3 [Arg_1+Arg_2 ]
n_eval_cousot9_bb1_in___2 [Arg_1+Arg_2 ]
n_eval_cousot9_bb1_in___5 [Arg_1+Arg_2 ]
n_eval_cousot9_bb2_in___4 [Arg_1+Arg_2-1 ]
n_eval_cousot9_bb1_in___6 [Arg_1+Arg_2-1 ]

MPRF for transition 55:n_eval_cousot9_bb1_in___5(Arg_0,Arg_1,Arg_2,Arg_3) -> n_eval_cousot9_bb2_in___3(Arg_0,Arg_1,Arg_2,Arg_3):|:1+Arg_2<=Arg_1 && 1+Arg_2<=Arg_0 && 0<=Arg_2 && 1<=Arg_1+Arg_2 && 1<=Arg_0+Arg_2 && Arg_1<=Arg_0 && 1<=Arg_1 && 2<=Arg_0+Arg_1 && Arg_0<=Arg_1 && 1<=Arg_0 && Arg_2<=Arg_1 && 0<Arg_0 && Arg_0<=Arg_1 && Arg_1<=Arg_0 && 0<=Arg_2 && 1+Arg_2<=Arg_0 && Arg_2<=Arg_1 && 0<Arg_2 of depth 1:

new bound:

2*Arg_1+1 {O(n)}

MPRF:

n_eval_cousot9_bb2_in___1 [Arg_2 ]
n_eval_cousot9_bb2_in___3 [Arg_2 ]
n_eval_cousot9_bb1_in___2 [Arg_2 ]
n_eval_cousot9_bb1_in___5 [Arg_2+1 ]
n_eval_cousot9_bb2_in___4 [Arg_2 ]
n_eval_cousot9_bb1_in___6 [Arg_2 ]

MPRF for transition 58:n_eval_cousot9_bb2_in___1(Arg_0,Arg_1,Arg_2,Arg_3) -> n_eval_cousot9_bb1_in___6(Arg_0-1,Arg_1,Arg_2,Arg_3):|:1+Arg_2<=Arg_1 && Arg_2<=Arg_0 && 1<=Arg_2 && 3<=Arg_1+Arg_2 && 2<=Arg_0+Arg_2 && Arg_1<=1+Arg_0 && 2<=Arg_1 && 3<=Arg_0+Arg_1 && 1+Arg_0<=Arg_1 && 1<=Arg_0 && Arg_2<=Arg_1 && 1<=Arg_2 && 0<Arg_0 && 0<Arg_0 && Arg_2<=Arg_1 && 1<=Arg_2 of depth 1:

new bound:

2*Arg_1+1 {O(n)}

MPRF:

n_eval_cousot9_bb2_in___1 [Arg_2 ]
n_eval_cousot9_bb2_in___3 [Arg_2 ]
n_eval_cousot9_bb1_in___2 [Arg_2 ]
n_eval_cousot9_bb1_in___5 [Arg_2 ]
n_eval_cousot9_bb2_in___4 [Arg_2-1 ]
n_eval_cousot9_bb1_in___6 [Arg_2-1 ]

MPRF for transition 59:n_eval_cousot9_bb2_in___3(Arg_0,Arg_1,Arg_2,Arg_3) -> n_eval_cousot9_bb1_in___2(Arg_0-1,Arg_1,Arg_2,Arg_3):|:1+Arg_2<=Arg_1 && 1+Arg_2<=Arg_0 && 1<=Arg_2 && 3<=Arg_1+Arg_2 && 3<=Arg_0+Arg_2 && Arg_1<=Arg_0 && 2<=Arg_1 && 4<=Arg_0+Arg_1 && Arg_0<=Arg_1 && 2<=Arg_0 && 1+Arg_2<=Arg_0 && 0<Arg_2 && Arg_0<=Arg_1 && Arg_1<=Arg_0 && 0<Arg_0 && Arg_2<=Arg_1 && 1<=Arg_2 of depth 1:

new bound:

2*Arg_1+1 {O(n)}

MPRF:

n_eval_cousot9_bb2_in___1 [Arg_2-1 ]
n_eval_cousot9_bb2_in___3 [Arg_2 ]
n_eval_cousot9_bb1_in___2 [Arg_2-1 ]
n_eval_cousot9_bb1_in___5 [Arg_2 ]
n_eval_cousot9_bb2_in___4 [Arg_2-1 ]
n_eval_cousot9_bb1_in___6 [Arg_2-1 ]

MPRF for transition 60:n_eval_cousot9_bb2_in___4(Arg_0,Arg_1,Arg_2,Arg_3) -> n_eval_cousot9_bb1_in___5(Arg_1,Arg_1,Arg_2-1,Arg_3):|:Arg_2<=Arg_1 && 1<=Arg_2 && 2<=Arg_1+Arg_2 && 1<=Arg_0+Arg_2 && 1<=Arg_1 && 1<=Arg_0+Arg_1 && 0<=Arg_0 && Arg_2<=Arg_1 && 1<=Arg_2 && Arg_2<=Arg_1 && 1<=Arg_2 && Arg_0<=0 of depth 1:

new bound:

2*Arg_1 {O(n)}

MPRF:

n_eval_cousot9_bb2_in___1 [Arg_2 ]
n_eval_cousot9_bb2_in___3 [Arg_2 ]
n_eval_cousot9_bb1_in___2 [Arg_2 ]
n_eval_cousot9_bb1_in___5 [Arg_2 ]
n_eval_cousot9_bb2_in___4 [Arg_2 ]
n_eval_cousot9_bb1_in___6 [Arg_2 ]

MPRF for transition 56:n_eval_cousot9_bb1_in___6(Arg_0,Arg_1,Arg_2,Arg_3) -> n_eval_cousot9_bb2_in___4(Arg_0,Arg_1,Arg_2,Arg_3):|:Arg_2<=Arg_1 && 1<=Arg_2 && 2<=Arg_1+Arg_2 && 1<=Arg_0+Arg_2 && 1<=Arg_1 && 1<=Arg_0+Arg_1 && 0<=Arg_0 && Arg_2<=Arg_1 && 0<Arg_2 && 1<=Arg_2 && 1<=Arg_2 && Arg_2<=Arg_1 && Arg_2<=Arg_1 && 0<Arg_2 of depth 1:

new bound:

12*Arg_1*Arg_1+3*Arg_1+Arg_3+1 {O(n^2)}

MPRF:

n_eval_cousot9_bb1_in___5 [2*Arg_0-Arg_1 ]
n_eval_cousot9_bb2_in___1 [Arg_0 ]
n_eval_cousot9_bb2_in___3 [2*Arg_0-Arg_1 ]
n_eval_cousot9_bb1_in___2 [Arg_0 ]
n_eval_cousot9_bb2_in___4 [Arg_0 ]
n_eval_cousot9_bb1_in___6 [Arg_0+1 ]

MPRF for transition 61:n_eval_cousot9_bb2_in___4(Arg_0,Arg_1,Arg_2,Arg_3) -> n_eval_cousot9_bb1_in___6(Arg_0-1,Arg_1,Arg_2,Arg_3):|:Arg_2<=Arg_1 && 1<=Arg_2 && 2<=Arg_1+Arg_2 && 1<=Arg_0+Arg_2 && 1<=Arg_1 && 1<=Arg_0+Arg_1 && 0<=Arg_0 && Arg_2<=Arg_1 && 1<=Arg_2 && 0<Arg_0 && Arg_2<=Arg_1 && 1<=Arg_2 of depth 1:

new bound:

4*Arg_1*Arg_1+Arg_1+Arg_3+1 {O(n^2)}

MPRF:

n_eval_cousot9_bb1_in___5 [Arg_0 ]
n_eval_cousot9_bb2_in___1 [Arg_0 ]
n_eval_cousot9_bb2_in___3 [Arg_1 ]
n_eval_cousot9_bb1_in___2 [Arg_0 ]
n_eval_cousot9_bb2_in___4 [Arg_0+1 ]
n_eval_cousot9_bb1_in___6 [Arg_0+1 ]

CFR did not improve the program. Rolling back

All Bounds

Timebounds

Overall timebound:2*Arg_1*Arg_1+2*Arg_3+4*Arg_1+7 {O(n^2)}
1: eval_cousot9_bb0_in->eval_cousot9_bb1_in: 1 {O(1)}
2: eval_cousot9_bb1_in->eval_cousot9_bb2_in: Arg_1*Arg_1+2*Arg_1+Arg_3+2 {O(n^2)}
3: eval_cousot9_bb1_in->eval_cousot9_bb3_in: 1 {O(1)}
4: eval_cousot9_bb2_in->eval_cousot9_bb1_in: Arg_1*Arg_1+Arg_1+Arg_3+1 {O(n^2)}
7: eval_cousot9_bb2_in->eval_cousot9_bb1_in: Arg_1 {O(n)}
8: eval_cousot9_bb3_in->eval_cousot9_stop: 1 {O(1)}
0: eval_cousot9_start->eval_cousot9_bb0_in: 1 {O(1)}

Costbounds

Overall costbound: 2*Arg_1*Arg_1+2*Arg_3+4*Arg_1+7 {O(n^2)}
1: eval_cousot9_bb0_in->eval_cousot9_bb1_in: 1 {O(1)}
2: eval_cousot9_bb1_in->eval_cousot9_bb2_in: Arg_1*Arg_1+2*Arg_1+Arg_3+2 {O(n^2)}
3: eval_cousot9_bb1_in->eval_cousot9_bb3_in: 1 {O(1)}
4: eval_cousot9_bb2_in->eval_cousot9_bb1_in: Arg_1*Arg_1+Arg_1+Arg_3+1 {O(n^2)}
7: eval_cousot9_bb2_in->eval_cousot9_bb1_in: Arg_1 {O(n)}
8: eval_cousot9_bb3_in->eval_cousot9_stop: 1 {O(1)}
0: eval_cousot9_start->eval_cousot9_bb0_in: 1 {O(1)}

Sizebounds

1: eval_cousot9_bb0_in->eval_cousot9_bb1_in, Arg_0: Arg_3 {O(n)}
1: eval_cousot9_bb0_in->eval_cousot9_bb1_in, Arg_1: Arg_1 {O(n)}
1: eval_cousot9_bb0_in->eval_cousot9_bb1_in, Arg_2: Arg_1 {O(n)}
1: eval_cousot9_bb0_in->eval_cousot9_bb1_in, Arg_3: Arg_3 {O(n)}
2: eval_cousot9_bb1_in->eval_cousot9_bb2_in, Arg_0: Arg_1+Arg_3 {O(n)}
2: eval_cousot9_bb1_in->eval_cousot9_bb2_in, Arg_1: Arg_1 {O(n)}
2: eval_cousot9_bb1_in->eval_cousot9_bb2_in, Arg_2: Arg_1 {O(n)}
2: eval_cousot9_bb1_in->eval_cousot9_bb2_in, Arg_3: Arg_3 {O(n)}
3: eval_cousot9_bb1_in->eval_cousot9_bb3_in, Arg_0: Arg_1+Arg_3 {O(n)}
3: eval_cousot9_bb1_in->eval_cousot9_bb3_in, Arg_1: 2*Arg_1 {O(n)}
3: eval_cousot9_bb1_in->eval_cousot9_bb3_in, Arg_2: 2*Arg_1 {O(n)}
3: eval_cousot9_bb1_in->eval_cousot9_bb3_in, Arg_3: 2*Arg_3 {O(n)}
4: eval_cousot9_bb2_in->eval_cousot9_bb1_in, Arg_0: Arg_1+Arg_3 {O(n)}
4: eval_cousot9_bb2_in->eval_cousot9_bb1_in, Arg_1: Arg_1 {O(n)}
4: eval_cousot9_bb2_in->eval_cousot9_bb1_in, Arg_2: Arg_1 {O(n)}
4: eval_cousot9_bb2_in->eval_cousot9_bb1_in, Arg_3: Arg_3 {O(n)}
7: eval_cousot9_bb2_in->eval_cousot9_bb1_in, Arg_0: Arg_1 {O(n)}
7: eval_cousot9_bb2_in->eval_cousot9_bb1_in, Arg_1: Arg_1 {O(n)}
7: eval_cousot9_bb2_in->eval_cousot9_bb1_in, Arg_2: Arg_1 {O(n)}
7: eval_cousot9_bb2_in->eval_cousot9_bb1_in, Arg_3: Arg_3 {O(n)}
8: eval_cousot9_bb3_in->eval_cousot9_stop, Arg_0: Arg_1+Arg_3 {O(n)}
8: eval_cousot9_bb3_in->eval_cousot9_stop, Arg_1: 2*Arg_1 {O(n)}
8: eval_cousot9_bb3_in->eval_cousot9_stop, Arg_2: 2*Arg_1 {O(n)}
8: eval_cousot9_bb3_in->eval_cousot9_stop, Arg_3: 2*Arg_3 {O(n)}
0: eval_cousot9_start->eval_cousot9_bb0_in, Arg_0: Arg_0 {O(n)}
0: eval_cousot9_start->eval_cousot9_bb0_in, Arg_1: Arg_1 {O(n)}
0: eval_cousot9_start->eval_cousot9_bb0_in, Arg_2: Arg_2 {O(n)}
0: eval_cousot9_start->eval_cousot9_bb0_in, Arg_3: Arg_3 {O(n)}