Initial Problem

Start: eval_loops_start
Program_Vars: Arg_0, Arg_1, Arg_2
Temp_Vars:
Locations: eval_loops_0, eval_loops_1, eval_loops_2, eval_loops_bb0_in, eval_loops_bb1_in, eval_loops_bb2_in, eval_loops_bb3_in, eval_loops_bb4_in, eval_loops_bb5_in, eval_loops_bb6_in, eval_loops_start, eval_loops_stop
Transitions:
2:eval_loops_0(Arg_0,Arg_1,Arg_2) -> eval_loops_1(Arg_0,Arg_1,Arg_2)
3:eval_loops_1(Arg_0,Arg_1,Arg_2) -> eval_loops_2(Arg_0,Arg_1,Arg_2)
4:eval_loops_2(Arg_0,Arg_1,Arg_2) -> eval_loops_bb1_in(Arg_0,Arg_0,Arg_2):|:0<=Arg_0
5:eval_loops_2(Arg_0,Arg_1,Arg_2) -> eval_loops_bb6_in(Arg_0,Arg_1,Arg_2):|:Arg_0<0
1:eval_loops_bb0_in(Arg_0,Arg_1,Arg_2) -> eval_loops_0(Arg_0,Arg_1,Arg_2)
6:eval_loops_bb1_in(Arg_0,Arg_1,Arg_2) -> eval_loops_bb2_in(Arg_0,Arg_1,Arg_2):|:0<=Arg_1
7:eval_loops_bb1_in(Arg_0,Arg_1,Arg_2) -> eval_loops_bb6_in(Arg_0,Arg_1,Arg_2):|:Arg_1<0
8:eval_loops_bb2_in(Arg_0,Arg_1,Arg_2) -> eval_loops_bb3_in(Arg_0,Arg_1,1):|:1<Arg_1
9:eval_loops_bb2_in(Arg_0,Arg_1,Arg_2) -> eval_loops_bb5_in(Arg_0,Arg_1,Arg_2):|:Arg_1<=1
10:eval_loops_bb3_in(Arg_0,Arg_1,Arg_2) -> eval_loops_bb4_in(Arg_0,Arg_1,Arg_2):|:Arg_2<Arg_1
11:eval_loops_bb3_in(Arg_0,Arg_1,Arg_2) -> eval_loops_bb5_in(Arg_0,Arg_1,Arg_2):|:Arg_1<=Arg_2
12:eval_loops_bb4_in(Arg_0,Arg_1,Arg_2) -> eval_loops_bb3_in(Arg_0,Arg_1,2*Arg_2)
13:eval_loops_bb5_in(Arg_0,Arg_1,Arg_2) -> eval_loops_bb1_in(Arg_0,Arg_1-1,Arg_2)
14:eval_loops_bb6_in(Arg_0,Arg_1,Arg_2) -> eval_loops_stop(Arg_0,Arg_1,Arg_2)
0:eval_loops_start(Arg_0,Arg_1,Arg_2) -> eval_loops_bb0_in(Arg_0,Arg_1,Arg_2)

Preprocessing

Found invariant Arg_1<=Arg_0 && 0<=Arg_1 && 0<=Arg_0+Arg_1 && 0<=Arg_0 for location eval_loops_bb2_in

Found invariant Arg_1<=Arg_0 && 0<=1+Arg_1 && 0<=1+Arg_0+Arg_1 && 0<=Arg_0 for location eval_loops_bb1_in

Found invariant Arg_1<=Arg_0 && 0<=Arg_1 && 0<=Arg_0+Arg_1 && 0<=Arg_0 for location eval_loops_bb5_in

Found invariant 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 && 2<=Arg_0 for location eval_loops_bb3_in

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 && 2<=Arg_0 for location eval_loops_bb4_in

Problem after Preprocessing

Start: eval_loops_start
Program_Vars: Arg_0, Arg_1, Arg_2
Temp_Vars:
Locations: eval_loops_0, eval_loops_1, eval_loops_2, eval_loops_bb0_in, eval_loops_bb1_in, eval_loops_bb2_in, eval_loops_bb3_in, eval_loops_bb4_in, eval_loops_bb5_in, eval_loops_bb6_in, eval_loops_start, eval_loops_stop
Transitions:
2:eval_loops_0(Arg_0,Arg_1,Arg_2) -> eval_loops_1(Arg_0,Arg_1,Arg_2)
3:eval_loops_1(Arg_0,Arg_1,Arg_2) -> eval_loops_2(Arg_0,Arg_1,Arg_2)
4:eval_loops_2(Arg_0,Arg_1,Arg_2) -> eval_loops_bb1_in(Arg_0,Arg_0,Arg_2):|:0<=Arg_0
5:eval_loops_2(Arg_0,Arg_1,Arg_2) -> eval_loops_bb6_in(Arg_0,Arg_1,Arg_2):|:Arg_0<0
1:eval_loops_bb0_in(Arg_0,Arg_1,Arg_2) -> eval_loops_0(Arg_0,Arg_1,Arg_2)
6:eval_loops_bb1_in(Arg_0,Arg_1,Arg_2) -> eval_loops_bb2_in(Arg_0,Arg_1,Arg_2):|:Arg_1<=Arg_0 && 0<=1+Arg_1 && 0<=1+Arg_0+Arg_1 && 0<=Arg_0 && 0<=Arg_1
7:eval_loops_bb1_in(Arg_0,Arg_1,Arg_2) -> eval_loops_bb6_in(Arg_0,Arg_1,Arg_2):|:Arg_1<=Arg_0 && 0<=1+Arg_1 && 0<=1+Arg_0+Arg_1 && 0<=Arg_0 && Arg_1<0
8:eval_loops_bb2_in(Arg_0,Arg_1,Arg_2) -> eval_loops_bb3_in(Arg_0,Arg_1,1):|:Arg_1<=Arg_0 && 0<=Arg_1 && 0<=Arg_0+Arg_1 && 0<=Arg_0 && 1<Arg_1
9:eval_loops_bb2_in(Arg_0,Arg_1,Arg_2) -> eval_loops_bb5_in(Arg_0,Arg_1,Arg_2):|:Arg_1<=Arg_0 && 0<=Arg_1 && 0<=Arg_0+Arg_1 && 0<=Arg_0 && Arg_1<=1
10:eval_loops_bb3_in(Arg_0,Arg_1,Arg_2) -> eval_loops_bb4_in(Arg_0,Arg_1,Arg_2):|: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 && 2<=Arg_0 && Arg_2<Arg_1
11:eval_loops_bb3_in(Arg_0,Arg_1,Arg_2) -> eval_loops_bb5_in(Arg_0,Arg_1,Arg_2):|: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 && 2<=Arg_0 && Arg_1<=Arg_2
12:eval_loops_bb4_in(Arg_0,Arg_1,Arg_2) -> eval_loops_bb3_in(Arg_0,Arg_1,2*Arg_2):|: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 && 2<=Arg_0
13:eval_loops_bb5_in(Arg_0,Arg_1,Arg_2) -> eval_loops_bb1_in(Arg_0,Arg_1-1,Arg_2):|:Arg_1<=Arg_0 && 0<=Arg_1 && 0<=Arg_0+Arg_1 && 0<=Arg_0
14:eval_loops_bb6_in(Arg_0,Arg_1,Arg_2) -> eval_loops_stop(Arg_0,Arg_1,Arg_2)
0:eval_loops_start(Arg_0,Arg_1,Arg_2) -> eval_loops_bb0_in(Arg_0,Arg_1,Arg_2)

MPRF for transition 6:eval_loops_bb1_in(Arg_0,Arg_1,Arg_2) -> eval_loops_bb2_in(Arg_0,Arg_1,Arg_2):|:Arg_1<=Arg_0 && 0<=1+Arg_1 && 0<=1+Arg_0+Arg_1 && 0<=Arg_0 && 0<=Arg_1 of depth 1:

new bound:

Arg_0+1 {O(n)}

MPRF:

eval_loops_bb2_in [Arg_1 ]
eval_loops_bb4_in [Arg_1 ]
eval_loops_bb3_in [Arg_1 ]
eval_loops_bb5_in [Arg_1 ]
eval_loops_bb1_in [Arg_1+1 ]

MPRF for transition 8:eval_loops_bb2_in(Arg_0,Arg_1,Arg_2) -> eval_loops_bb3_in(Arg_0,Arg_1,1):|:Arg_1<=Arg_0 && 0<=Arg_1 && 0<=Arg_0+Arg_1 && 0<=Arg_0 && 1<Arg_1 of depth 1:

new bound:

Arg_0+1 {O(n)}

MPRF:

eval_loops_bb2_in [Arg_1+1 ]
eval_loops_bb4_in [Arg_1 ]
eval_loops_bb3_in [Arg_1 ]
eval_loops_bb5_in [Arg_1 ]
eval_loops_bb1_in [Arg_1+1 ]

MPRF for transition 9:eval_loops_bb2_in(Arg_0,Arg_1,Arg_2) -> eval_loops_bb5_in(Arg_0,Arg_1,Arg_2):|:Arg_1<=Arg_0 && 0<=Arg_1 && 0<=Arg_0+Arg_1 && 0<=Arg_0 && Arg_1<=1 of depth 1:

new bound:

Arg_0+1 {O(n)}

MPRF:

eval_loops_bb2_in [Arg_1+1 ]
eval_loops_bb4_in [Arg_1 ]
eval_loops_bb3_in [Arg_1 ]
eval_loops_bb5_in [Arg_1 ]
eval_loops_bb1_in [Arg_1+1 ]

MPRF for transition 11:eval_loops_bb3_in(Arg_0,Arg_1,Arg_2) -> eval_loops_bb5_in(Arg_0,Arg_1,Arg_2):|: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 && 2<=Arg_0 && Arg_1<=Arg_2 of depth 1:

new bound:

2*Arg_0+3 {O(n)}

MPRF:

eval_loops_bb2_in [Arg_0+Arg_1-3 ]
eval_loops_bb4_in [Arg_0+Arg_1-3 ]
eval_loops_bb3_in [Arg_0+Arg_1-3 ]
eval_loops_bb5_in [Arg_0+Arg_1-4 ]
eval_loops_bb1_in [Arg_0+Arg_1-3 ]

MPRF for transition 13:eval_loops_bb5_in(Arg_0,Arg_1,Arg_2) -> eval_loops_bb1_in(Arg_0,Arg_1-1,Arg_2):|:Arg_1<=Arg_0 && 0<=Arg_1 && 0<=Arg_0+Arg_1 && 0<=Arg_0 of depth 1:

new bound:

Arg_0+1 {O(n)}

MPRF:

eval_loops_bb2_in [Arg_1+1 ]
eval_loops_bb4_in [Arg_1+1 ]
eval_loops_bb3_in [Arg_1+1 ]
eval_loops_bb5_in [Arg_1+1 ]
eval_loops_bb1_in [Arg_1+1 ]

MPRF for transition 10:eval_loops_bb3_in(Arg_0,Arg_1,Arg_2) -> eval_loops_bb4_in(Arg_0,Arg_1,Arg_2):|: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 && 2<=Arg_0 && Arg_2<Arg_1 of depth 1:

new bound:

2*Arg_0*Arg_0+4*Arg_0 {O(n^2)}

MPRF:

eval_loops_bb2_in [Arg_0 ]
eval_loops_bb4_in [Arg_0-Arg_2-1 ]
eval_loops_bb3_in [Arg_0-Arg_2 ]
eval_loops_bb5_in [Arg_0 ]
eval_loops_bb1_in [Arg_0 ]

MPRF for transition 12:eval_loops_bb4_in(Arg_0,Arg_1,Arg_2) -> eval_loops_bb3_in(Arg_0,Arg_1,2*Arg_2):|: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 && 2<=Arg_0 of depth 1:

new bound:

4*Arg_0*Arg_0+8*Arg_0 {O(n^2)}

MPRF:

eval_loops_bb2_in [2*Arg_0 ]
eval_loops_bb4_in [2*Arg_0-2*Arg_2-1 ]
eval_loops_bb3_in [2*Arg_0-Arg_2-2 ]
eval_loops_bb5_in [2*Arg_0 ]
eval_loops_bb1_in [2*Arg_0 ]

Analysing control-flow refined program

Cut unsatisfiable transition 7: eval_loops_bb1_in->eval_loops_bb6_in

Cut unsatisfiable transition 138: n_eval_loops_bb1_in___5->eval_loops_bb6_in

Found invariant Arg_1<=0 && 1+Arg_1<=Arg_0 && 0<=Arg_1 && 1<=Arg_0+Arg_1 && 1<=Arg_0 for location n_eval_loops_bb2_in___1

Found invariant 2<=Arg_2 && 4<=Arg_1+Arg_2 && Arg_1<=Arg_2 && 4<=Arg_0+Arg_2 && Arg_1<=Arg_0 && 2<=Arg_1 && 4<=Arg_0+Arg_1 && 2<=Arg_0 for location n_eval_loops_bb5_in___6

Found invariant Arg_1<=Arg_0 && 0<=Arg_1 && 0<=Arg_0+Arg_1 && Arg_0<=Arg_1 && 0<=Arg_0 for location eval_loops_bb1_in

Found invariant Arg_1<=1 && 1+Arg_1<=Arg_0 && 0<=Arg_1 && 1<=Arg_0+Arg_1 && 1<=Arg_0 for location n_eval_loops_bb5_in___3

Found invariant Arg_1<=0 && 1+Arg_1<=Arg_0 && 0<=1+Arg_1 && 0<=1+Arg_0+Arg_1 && 0<=Arg_0 for location n_eval_loops_bb1_in___2

Found invariant 1+Arg_2<=Arg_1 && 1+Arg_2<=Arg_0 && 2<=Arg_2 && 5<=Arg_1+Arg_2 && 5<=Arg_0+Arg_2 && Arg_1<=Arg_0 && 3<=Arg_1 && 6<=Arg_0+Arg_1 && 3<=Arg_0 for location n_eval_loops_bb4_in___7

Found invariant Arg_1<=1 && Arg_1<=Arg_0 && Arg_0+Arg_1<=2 && 0<=Arg_1 && 0<=Arg_0+Arg_1 && Arg_0<=Arg_1 && Arg_0<=1 && 0<=Arg_0 for location n_eval_loops_bb5_in___10

Found invariant Arg_2<=1 && 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 && 2<=Arg_0 for location n_eval_loops_bb4_in___9

Found invariant 2<=Arg_2 && 3<=Arg_1+Arg_2 && 1+Arg_1<=Arg_2 && 4<=Arg_0+Arg_2 && 1+Arg_1<=Arg_0 && 1<=Arg_1 && 3<=Arg_0+Arg_1 && 2<=Arg_0 for location n_eval_loops_bb1_in___5

Found invariant Arg_1<=Arg_0 && 0<=Arg_1 && 0<=Arg_0+Arg_1 && Arg_0<=Arg_1 && 0<=Arg_0 for location n_eval_loops_bb2_in___12

Found invariant 2<=Arg_2 && 4<=Arg_1+Arg_2 && 4<=Arg_0+Arg_2 && Arg_1<=Arg_0 && 2<=Arg_1 && 4<=Arg_0+Arg_1 && 2<=Arg_0 for location n_eval_loops_bb3_in___8

Found invariant Arg_2<=1 && 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 && 2<=Arg_0 for location n_eval_loops_bb3_in___11

Found invariant 2<=Arg_2 && 3<=Arg_1+Arg_2 && 1+Arg_1<=Arg_2 && 4<=Arg_0+Arg_2 && 1+Arg_1<=Arg_0 && 1<=Arg_1 && 3<=Arg_0+Arg_1 && 2<=Arg_0 for location n_eval_loops_bb2_in___4

MPRF for transition 111:n_eval_loops_bb1_in___5(Arg_0,Arg_1,Arg_2) -> n_eval_loops_bb2_in___4(Arg_0,Arg_1,Arg_2):|:2<=Arg_2 && 3<=Arg_1+Arg_2 && 1+Arg_1<=Arg_2 && 4<=Arg_0+Arg_2 && 1+Arg_1<=Arg_0 && 1<=Arg_1 && 3<=Arg_0+Arg_1 && 2<=Arg_0 && Arg_1<=Arg_0 && 0<=Arg_1 && 0<=Arg_1 && Arg_1<=Arg_0 && 0<=1+Arg_1 && 1+Arg_1<=Arg_0 && Arg_1<=Arg_0 && 0<=Arg_1 of depth 1:

new bound:

Arg_0 {O(n)}

MPRF:

n_eval_loops_bb2_in___4 [Arg_1 ]
n_eval_loops_bb3_in___11 [Arg_1 ]
n_eval_loops_bb4_in___7 [Arg_1 ]
n_eval_loops_bb4_in___9 [Arg_1 ]
n_eval_loops_bb3_in___8 [Arg_1 ]
n_eval_loops_bb5_in___6 [Arg_1 ]
n_eval_loops_bb1_in___5 [Arg_1+1 ]

MPRF for transition 115:n_eval_loops_bb2_in___4(Arg_0,Arg_1,Arg_2) -> n_eval_loops_bb3_in___11(Arg_0,Arg_1,1):|:2<=Arg_2 && 3<=Arg_1+Arg_2 && 1+Arg_1<=Arg_2 && 4<=Arg_0+Arg_2 && 1+Arg_1<=Arg_0 && 1<=Arg_1 && 3<=Arg_0+Arg_1 && 2<=Arg_0 && 1+Arg_1<=Arg_0 && 0<=Arg_1 && Arg_1<=Arg_0 && 1<Arg_1 of depth 1:

new bound:

Arg_0 {O(n)}

MPRF:

n_eval_loops_bb2_in___4 [Arg_1+1 ]
n_eval_loops_bb3_in___11 [Arg_1 ]
n_eval_loops_bb4_in___7 [Arg_1 ]
n_eval_loops_bb4_in___9 [Arg_1 ]
n_eval_loops_bb3_in___8 [Arg_1 ]
n_eval_loops_bb5_in___6 [Arg_1 ]
n_eval_loops_bb1_in___5 [Arg_1+1 ]

MPRF for transition 117:n_eval_loops_bb3_in___11(Arg_0,Arg_1,Arg_2) -> n_eval_loops_bb4_in___9(Arg_0,Arg_1,Arg_2):|:Arg_2<=1 && 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 && 2<=Arg_0 && Arg_2<Arg_1 && 1<=Arg_2 && Arg_1<=Arg_0 && Arg_1<=Arg_0 && 2<=Arg_1 && Arg_2<Arg_1 && 1<=Arg_2 of depth 1:

new bound:

2*Arg_0+1 {O(n)}

MPRF:

n_eval_loops_bb2_in___4 [Arg_0+Arg_1+1 ]
n_eval_loops_bb3_in___11 [Arg_0+Arg_1+1 ]
n_eval_loops_bb4_in___7 [Arg_0+Arg_1 ]
n_eval_loops_bb4_in___9 [Arg_0+Arg_1 ]
n_eval_loops_bb3_in___8 [Arg_0+Arg_1 ]
n_eval_loops_bb5_in___6 [Arg_0+Arg_1 ]
n_eval_loops_bb1_in___5 [Arg_0+Arg_1+1 ]

MPRF for transition 119:n_eval_loops_bb3_in___8(Arg_0,Arg_1,Arg_2) -> n_eval_loops_bb5_in___6(Arg_0,Arg_1,Arg_2):|:2<=Arg_2 && 4<=Arg_1+Arg_2 && 4<=Arg_0+Arg_2 && Arg_1<=Arg_0 && 2<=Arg_1 && 4<=Arg_0+Arg_1 && 2<=Arg_0 && 2<=Arg_1 && 1<=Arg_2 && Arg_1<=Arg_0 && 2<=Arg_2 && 2+Arg_2<=2*Arg_1 && Arg_1<=Arg_0 && 2<=Arg_1 && Arg_1<=Arg_0 && Arg_1<=Arg_2 of depth 1:

new bound:

Arg_0+1 {O(n)}

MPRF:

n_eval_loops_bb2_in___4 [Arg_1-1 ]
n_eval_loops_bb3_in___11 [Arg_1-Arg_2 ]
n_eval_loops_bb4_in___7 [Arg_1-1 ]
n_eval_loops_bb4_in___9 [Arg_1+1-2*Arg_2 ]
n_eval_loops_bb3_in___8 [Arg_1-1 ]
n_eval_loops_bb5_in___6 [Arg_1-2 ]
n_eval_loops_bb1_in___5 [Arg_1-1 ]

MPRF for transition 121:n_eval_loops_bb4_in___9(Arg_0,Arg_1,Arg_2) -> n_eval_loops_bb3_in___8(Arg_0,Arg_1,2*Arg_2):|:Arg_2<=1 && 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 && 2<=Arg_0 && 2<=Arg_1 && Arg_2<Arg_1 && 1<=Arg_2 && Arg_1<=Arg_0 && Arg_1<=Arg_0 && 1+Arg_2<=Arg_1 && 1<=Arg_2 of depth 1:

new bound:

Arg_0+3 {O(n)}

MPRF:

n_eval_loops_bb2_in___4 [Arg_1-1 ]
n_eval_loops_bb3_in___11 [Arg_1+Arg_2-2 ]
n_eval_loops_bb4_in___7 [Arg_1-2 ]
n_eval_loops_bb4_in___9 [Arg_1-1 ]
n_eval_loops_bb3_in___8 [Arg_1-2 ]
n_eval_loops_bb5_in___6 [Arg_1-2 ]
n_eval_loops_bb1_in___5 [Arg_1-1 ]

MPRF for transition 124:n_eval_loops_bb5_in___6(Arg_0,Arg_1,Arg_2) -> n_eval_loops_bb1_in___5(Arg_0,Arg_1-1,Arg_2):|:2<=Arg_2 && 4<=Arg_1+Arg_2 && Arg_1<=Arg_2 && 4<=Arg_0+Arg_2 && Arg_1<=Arg_0 && 2<=Arg_1 && 4<=Arg_0+Arg_1 && 2<=Arg_0 && Arg_1<=Arg_0 && 2+Arg_2<=2*Arg_1 && Arg_1<=Arg_2 && Arg_1<=Arg_0 && 0<=Arg_1 of depth 1:

new bound:

Arg_0 {O(n)}

MPRF:

n_eval_loops_bb2_in___4 [Arg_1 ]
n_eval_loops_bb3_in___11 [Arg_1 ]
n_eval_loops_bb4_in___7 [Arg_1 ]
n_eval_loops_bb4_in___9 [Arg_1 ]
n_eval_loops_bb3_in___8 [Arg_1 ]
n_eval_loops_bb5_in___6 [Arg_1 ]
n_eval_loops_bb1_in___5 [Arg_1 ]

MPRF for transition 118:n_eval_loops_bb3_in___8(Arg_0,Arg_1,Arg_2) -> n_eval_loops_bb4_in___7(Arg_0,Arg_1,Arg_2):|:2<=Arg_2 && 4<=Arg_1+Arg_2 && 4<=Arg_0+Arg_2 && Arg_1<=Arg_0 && 2<=Arg_1 && 4<=Arg_0+Arg_1 && 2<=Arg_0 && 2<=Arg_1 && 1<=Arg_2 && Arg_1<=Arg_0 && 2<=Arg_2 && 2+Arg_2<=2*Arg_1 && Arg_1<=Arg_0 && Arg_1<=Arg_0 && 2<=Arg_1 && Arg_2<Arg_1 && 1<=Arg_2 of depth 1:

new bound:

Arg_0*Arg_0+Arg_0 {O(n^2)}

MPRF:

n_eval_loops_bb1_in___5 [Arg_1 ]
n_eval_loops_bb2_in___4 [Arg_1 ]
n_eval_loops_bb3_in___11 [Arg_1 ]
n_eval_loops_bb5_in___6 [Arg_1-Arg_2 ]
n_eval_loops_bb4_in___7 [Arg_1-2*Arg_2 ]
n_eval_loops_bb4_in___9 [Arg_1-2*Arg_2 ]
n_eval_loops_bb3_in___8 [Arg_1-Arg_2 ]

MPRF for transition 120:n_eval_loops_bb4_in___7(Arg_0,Arg_1,Arg_2) -> n_eval_loops_bb3_in___8(Arg_0,Arg_1,2*Arg_2):|:1+Arg_2<=Arg_1 && 1+Arg_2<=Arg_0 && 2<=Arg_2 && 5<=Arg_1+Arg_2 && 5<=Arg_0+Arg_2 && Arg_1<=Arg_0 && 3<=Arg_1 && 6<=Arg_0+Arg_1 && 3<=Arg_0 && Arg_1<=Arg_0 && Arg_2<Arg_1 && 2<=Arg_2 && Arg_1<=Arg_0 && 1+Arg_2<=Arg_1 && 1<=Arg_2 of depth 1:

new bound:

Arg_0*Arg_0+Arg_0 {O(n^2)}

MPRF:

n_eval_loops_bb1_in___5 [Arg_0 ]
n_eval_loops_bb2_in___4 [Arg_0 ]
n_eval_loops_bb3_in___11 [Arg_0 ]
n_eval_loops_bb5_in___6 [Arg_0-Arg_2 ]
n_eval_loops_bb4_in___7 [Arg_0-Arg_2 ]
n_eval_loops_bb4_in___9 [Arg_0-2*Arg_2 ]
n_eval_loops_bb3_in___8 [Arg_0-Arg_2 ]

MPRF for transition 110:n_eval_loops_bb1_in___2(Arg_0,Arg_1,Arg_2) -> n_eval_loops_bb2_in___1(Arg_0,Arg_1,Arg_2):|:Arg_1<=0 && 1+Arg_1<=Arg_0 && 0<=1+Arg_1 && 0<=1+Arg_0+Arg_1 && 0<=Arg_0 && Arg_1<=Arg_0 && Arg_1<=1 && 0<=1+Arg_1 && 1+Arg_1<=Arg_0 && Arg_1<=Arg_0 && 0<=Arg_1 of depth 1:

new bound:

3 {O(1)}

MPRF:

n_eval_loops_bb2_in___1 [0 ]
n_eval_loops_bb5_in___3 [Arg_1 ]
n_eval_loops_bb1_in___2 [Arg_1+1 ]

MPRF for transition 112:n_eval_loops_bb2_in___1(Arg_0,Arg_1,Arg_2) -> n_eval_loops_bb5_in___3(Arg_0,Arg_1,Arg_2):|:Arg_1<=0 && 1+Arg_1<=Arg_0 && 0<=Arg_1 && 1<=Arg_0+Arg_1 && 1<=Arg_0 && Arg_1<=1 && 0<=Arg_1 && 1+Arg_1<=Arg_0 && Arg_1<=Arg_0 && 0<=Arg_1 && Arg_1<=1 of depth 1:

new bound:

3 {O(1)}

MPRF:

n_eval_loops_bb2_in___1 [1 ]
n_eval_loops_bb5_in___3 [Arg_1 ]
n_eval_loops_bb1_in___2 [Arg_1+1 ]

MPRF for transition 123:n_eval_loops_bb5_in___3(Arg_0,Arg_1,Arg_2) -> n_eval_loops_bb1_in___2(Arg_0,Arg_1-1,Arg_2):|:Arg_1<=1 && 1+Arg_1<=Arg_0 && 0<=Arg_1 && 1<=Arg_0+Arg_1 && 1<=Arg_0 && Arg_1<=1 && 0<=Arg_1 && 1+Arg_1<=Arg_0 && Arg_1<=Arg_0 && 0<=Arg_1 of depth 1:

new bound:

4 {O(1)}

MPRF:

n_eval_loops_bb2_in___1 [1 ]
n_eval_loops_bb5_in___3 [Arg_1+1 ]
n_eval_loops_bb1_in___2 [Arg_1+1 ]

CFR did not improve the program. Rolling back

All Bounds

Timebounds

Overall timebound:6*Arg_0*Arg_0+18*Arg_0+15 {O(n^2)}
2: eval_loops_0->eval_loops_1: 1 {O(1)}
3: eval_loops_1->eval_loops_2: 1 {O(1)}
4: eval_loops_2->eval_loops_bb1_in: 1 {O(1)}
5: eval_loops_2->eval_loops_bb6_in: 1 {O(1)}
1: eval_loops_bb0_in->eval_loops_0: 1 {O(1)}
6: eval_loops_bb1_in->eval_loops_bb2_in: Arg_0+1 {O(n)}
7: eval_loops_bb1_in->eval_loops_bb6_in: 1 {O(1)}
8: eval_loops_bb2_in->eval_loops_bb3_in: Arg_0+1 {O(n)}
9: eval_loops_bb2_in->eval_loops_bb5_in: Arg_0+1 {O(n)}
10: eval_loops_bb3_in->eval_loops_bb4_in: 2*Arg_0*Arg_0+4*Arg_0 {O(n^2)}
11: eval_loops_bb3_in->eval_loops_bb5_in: 2*Arg_0+3 {O(n)}
12: eval_loops_bb4_in->eval_loops_bb3_in: 4*Arg_0*Arg_0+8*Arg_0 {O(n^2)}
13: eval_loops_bb5_in->eval_loops_bb1_in: Arg_0+1 {O(n)}
14: eval_loops_bb6_in->eval_loops_stop: 1 {O(1)}
0: eval_loops_start->eval_loops_bb0_in: 1 {O(1)}

Costbounds

Overall costbound: 6*Arg_0*Arg_0+18*Arg_0+15 {O(n^2)}
2: eval_loops_0->eval_loops_1: 1 {O(1)}
3: eval_loops_1->eval_loops_2: 1 {O(1)}
4: eval_loops_2->eval_loops_bb1_in: 1 {O(1)}
5: eval_loops_2->eval_loops_bb6_in: 1 {O(1)}
1: eval_loops_bb0_in->eval_loops_0: 1 {O(1)}
6: eval_loops_bb1_in->eval_loops_bb2_in: Arg_0+1 {O(n)}
7: eval_loops_bb1_in->eval_loops_bb6_in: 1 {O(1)}
8: eval_loops_bb2_in->eval_loops_bb3_in: Arg_0+1 {O(n)}
9: eval_loops_bb2_in->eval_loops_bb5_in: Arg_0+1 {O(n)}
10: eval_loops_bb3_in->eval_loops_bb4_in: 2*Arg_0*Arg_0+4*Arg_0 {O(n^2)}
11: eval_loops_bb3_in->eval_loops_bb5_in: 2*Arg_0+3 {O(n)}
12: eval_loops_bb4_in->eval_loops_bb3_in: 4*Arg_0*Arg_0+8*Arg_0 {O(n^2)}
13: eval_loops_bb5_in->eval_loops_bb1_in: Arg_0+1 {O(n)}
14: eval_loops_bb6_in->eval_loops_stop: 1 {O(1)}
0: eval_loops_start->eval_loops_bb0_in: 1 {O(1)}

Sizebounds

2: eval_loops_0->eval_loops_1, Arg_0: Arg_0 {O(n)}
2: eval_loops_0->eval_loops_1, Arg_1: Arg_1 {O(n)}
2: eval_loops_0->eval_loops_1, Arg_2: Arg_2 {O(n)}
3: eval_loops_1->eval_loops_2, Arg_0: Arg_0 {O(n)}
3: eval_loops_1->eval_loops_2, Arg_1: Arg_1 {O(n)}
3: eval_loops_1->eval_loops_2, Arg_2: Arg_2 {O(n)}
4: eval_loops_2->eval_loops_bb1_in, Arg_0: Arg_0 {O(n)}
4: eval_loops_2->eval_loops_bb1_in, Arg_1: Arg_0 {O(n)}
4: eval_loops_2->eval_loops_bb1_in, Arg_2: Arg_2 {O(n)}
5: eval_loops_2->eval_loops_bb6_in, Arg_0: Arg_0 {O(n)}
5: eval_loops_2->eval_loops_bb6_in, Arg_1: Arg_1 {O(n)}
5: eval_loops_2->eval_loops_bb6_in, Arg_2: Arg_2 {O(n)}
1: eval_loops_bb0_in->eval_loops_0, Arg_0: Arg_0 {O(n)}
1: eval_loops_bb0_in->eval_loops_0, Arg_1: Arg_1 {O(n)}
1: eval_loops_bb0_in->eval_loops_0, Arg_2: Arg_2 {O(n)}
6: eval_loops_bb1_in->eval_loops_bb2_in, Arg_0: Arg_0 {O(n)}
6: eval_loops_bb1_in->eval_loops_bb2_in, Arg_1: Arg_0+2 {O(n)}
6: eval_loops_bb1_in->eval_loops_bb2_in, Arg_2: 2^(4*Arg_0*Arg_0+8*Arg_0)+Arg_2 {O(EXP)}
7: eval_loops_bb1_in->eval_loops_bb6_in, Arg_0: Arg_0 {O(n)}
7: eval_loops_bb1_in->eval_loops_bb6_in, Arg_1: 1 {O(1)}
7: eval_loops_bb1_in->eval_loops_bb6_in, Arg_2: 2^(4*Arg_0*Arg_0+8*Arg_0)+Arg_2 {O(EXP)}
8: eval_loops_bb2_in->eval_loops_bb3_in, Arg_0: Arg_0 {O(n)}
8: eval_loops_bb2_in->eval_loops_bb3_in, Arg_1: Arg_0+2 {O(n)}
8: eval_loops_bb2_in->eval_loops_bb3_in, Arg_2: 1 {O(1)}
9: eval_loops_bb2_in->eval_loops_bb5_in, Arg_0: Arg_0 {O(n)}
9: eval_loops_bb2_in->eval_loops_bb5_in, Arg_1: 1 {O(1)}
9: eval_loops_bb2_in->eval_loops_bb5_in, Arg_2: 2^(4*Arg_0*Arg_0+8*Arg_0)+Arg_2 {O(EXP)}
10: eval_loops_bb3_in->eval_loops_bb4_in, Arg_0: Arg_0 {O(n)}
10: eval_loops_bb3_in->eval_loops_bb4_in, Arg_1: Arg_0+2 {O(n)}
10: eval_loops_bb3_in->eval_loops_bb4_in, Arg_2: 2^(4*Arg_0*Arg_0+8*Arg_0) {O(EXP)}
11: eval_loops_bb3_in->eval_loops_bb5_in, Arg_0: Arg_0 {O(n)}
11: eval_loops_bb3_in->eval_loops_bb5_in, Arg_1: Arg_0+2 {O(n)}
11: eval_loops_bb3_in->eval_loops_bb5_in, Arg_2: 2^(4*Arg_0*Arg_0+8*Arg_0) {O(EXP)}
12: eval_loops_bb4_in->eval_loops_bb3_in, Arg_0: Arg_0 {O(n)}
12: eval_loops_bb4_in->eval_loops_bb3_in, Arg_1: Arg_0+2 {O(n)}
12: eval_loops_bb4_in->eval_loops_bb3_in, Arg_2: 2^(4*Arg_0*Arg_0+8*Arg_0) {O(EXP)}
13: eval_loops_bb5_in->eval_loops_bb1_in, Arg_0: Arg_0 {O(n)}
13: eval_loops_bb5_in->eval_loops_bb1_in, Arg_1: Arg_0+2 {O(n)}
13: eval_loops_bb5_in->eval_loops_bb1_in, Arg_2: 2^(4*Arg_0*Arg_0+8*Arg_0)+Arg_2 {O(EXP)}
14: eval_loops_bb6_in->eval_loops_stop, Arg_0: 2*Arg_0 {O(n)}
14: eval_loops_bb6_in->eval_loops_stop, Arg_1: Arg_1+1 {O(n)}
14: eval_loops_bb6_in->eval_loops_stop, Arg_2: 2^(4*Arg_0*Arg_0+8*Arg_0)+2*Arg_2 {O(EXP)}
0: eval_loops_start->eval_loops_bb0_in, Arg_0: Arg_0 {O(n)}
0: eval_loops_start->eval_loops_bb0_in, Arg_1: Arg_1 {O(n)}
0: eval_loops_start->eval_loops_bb0_in, Arg_2: Arg_2 {O(n)}