Initial Problem

Start: n_evalsipmabubblestart
Program_Vars: Arg_0, Arg_1
Temp_Vars:
Locations: n_evalsipmabubblebb1in___11, n_evalsipmabubblebb1in___6, n_evalsipmabubblebb2in___4, n_evalsipmabubblebb2in___9, n_evalsipmabubblebb3in___3, n_evalsipmabubblebb3in___8, n_evalsipmabubblebb4in___13, n_evalsipmabubblebb4in___7, n_evalsipmabubblebb5in___10, n_evalsipmabubblebb5in___5, n_evalsipmabubblebb6in___14, n_evalsipmabubblebb6in___2, n_evalsipmabubbleentryin___15, n_evalsipmabubblereturnin___12, n_evalsipmabubblestart, n_evalsipmabubblestop___1
Transitions:
0:n_evalsipmabubblebb1in___11(Arg_0,Arg_1) -> n_evalsipmabubblebb2in___9(Arg_0,Arg_1):|:1<=Arg_0 && Arg_1<=0 && 0<=Arg_1
1:n_evalsipmabubblebb1in___11(Arg_0,Arg_1) -> n_evalsipmabubblebb3in___8(Arg_0,Arg_1):|:1<=Arg_0 && Arg_1<=0 && 0<=Arg_1
2:n_evalsipmabubblebb1in___6(Arg_0,Arg_1) -> n_evalsipmabubblebb2in___4(Arg_0,Arg_1):|:1+Arg_1<=Arg_0
3:n_evalsipmabubblebb1in___6(Arg_0,Arg_1) -> n_evalsipmabubblebb3in___3(Arg_0,Arg_1):|:1+Arg_1<=Arg_0
4:n_evalsipmabubblebb2in___4(Arg_0,Arg_1) -> n_evalsipmabubblebb3in___3(Arg_0,Arg_1):|:1+Arg_1<=Arg_0
5:n_evalsipmabubblebb2in___9(Arg_0,Arg_1) -> n_evalsipmabubblebb3in___8(Arg_0,Arg_1):|:1<=Arg_0 && Arg_1<=0 && 0<=Arg_1
6:n_evalsipmabubblebb3in___3(Arg_0,Arg_1) -> n_evalsipmabubblebb4in___7(Arg_0,Arg_1+1):|:1+Arg_1<=Arg_0
7:n_evalsipmabubblebb3in___8(Arg_0,Arg_1) -> n_evalsipmabubblebb4in___7(Arg_0,Arg_1+1):|:1<=Arg_0 && Arg_1<=0 && 0<=Arg_1
8:n_evalsipmabubblebb4in___13(Arg_0,Arg_1) -> n_evalsipmabubblebb1in___11(Arg_0,Arg_1):|:Arg_1<=0 && 0<=Arg_1 && 0<=Arg_0 && 1+Arg_1<=Arg_0
9:n_evalsipmabubblebb4in___13(Arg_0,Arg_1) -> n_evalsipmabubblebb5in___10(Arg_0,Arg_1):|:Arg_1<=0 && 0<=Arg_1 && 0<=Arg_0 && Arg_0<=Arg_1
10:n_evalsipmabubblebb4in___7(Arg_0,Arg_1) -> n_evalsipmabubblebb1in___6(Arg_0,Arg_1):|:1+Arg_1<=Arg_0
11:n_evalsipmabubblebb4in___7(Arg_0,Arg_1) -> n_evalsipmabubblebb5in___5(Arg_0,Arg_1):|:Arg_0<=Arg_1
12:n_evalsipmabubblebb5in___10(Arg_0,Arg_1) -> n_evalsipmabubblebb6in___2(Arg_0-1,Arg_1):|:Arg_0<=0 && 0<=Arg_0 && Arg_1<=0 && 0<=Arg_1
13:n_evalsipmabubblebb5in___5(Arg_0,Arg_1) -> n_evalsipmabubblebb6in___14(Arg_0-1,Arg_1):|:Arg_0<=Arg_1
14:n_evalsipmabubblebb6in___14(Arg_0,Arg_1) -> n_evalsipmabubblebb4in___13(Arg_0,0):|:0<=Arg_0
15:n_evalsipmabubblebb6in___14(Arg_0,Arg_1) -> n_evalsipmabubblereturnin___12(Arg_0,Arg_1):|:1+Arg_0<=0
16:n_evalsipmabubblebb6in___2(Arg_0,Arg_1) -> n_evalsipmabubblereturnin___12(Arg_0,Arg_1):|:1+Arg_0<=0 && 1+Arg_0<=0
17:n_evalsipmabubbleentryin___15(Arg_0,Arg_1) -> n_evalsipmabubblebb6in___14(Arg_0,Arg_1)
18:n_evalsipmabubblereturnin___12(Arg_0,Arg_1) -> n_evalsipmabubblestop___1(Arg_0,Arg_1):|:1+Arg_0<=0
19:n_evalsipmabubblestart(Arg_0,Arg_1) -> n_evalsipmabubbleentryin___15(Arg_0,Arg_1)

Preprocessing

Found invariant Arg_1<=0 && 1+Arg_1<=Arg_0 && 0<=Arg_1 && 1<=Arg_0+Arg_1 && 1<=Arg_0 for location n_evalsipmabubblebb2in___9

Found invariant Arg_1<=0 && 1+Arg_1<=Arg_0 && 0<=Arg_1 && 1<=Arg_0+Arg_1 && 1<=Arg_0 for location n_evalsipmabubblebb1in___11

Found invariant Arg_1<=Arg_0 && 1<=Arg_1 && 2<=Arg_0+Arg_1 && Arg_0<=Arg_1 && 1<=Arg_0 for location n_evalsipmabubblebb5in___5

Found invariant Arg_1<=0 && 1+Arg_1<=Arg_0 && 0<=Arg_1 && 1<=Arg_0+Arg_1 && 1<=Arg_0 for location n_evalsipmabubblebb3in___8

Found invariant Arg_1<=Arg_0 && 1<=Arg_1 && 2<=Arg_0+Arg_1 && 1<=Arg_0 for location n_evalsipmabubblebb4in___7

Found invariant Arg_1<=0 && Arg_1<=1+Arg_0 && 1+Arg_0+Arg_1<=0 && 0<=Arg_1 && 0<=1+Arg_0+Arg_1 && 1+Arg_0<=Arg_1 && 1+Arg_0<=0 && 0<=1+Arg_0 for location n_evalsipmabubblebb6in___2

Found invariant 1+Arg_1<=Arg_0 && 1<=Arg_1 && 3<=Arg_0+Arg_1 && 2<=Arg_0 for location n_evalsipmabubblebb3in___3

Found invariant Arg_1<=0 && Arg_1<=Arg_0 && 0<=Arg_1 && 0<=Arg_0+Arg_1 && 0<=Arg_0 for location n_evalsipmabubblebb4in___13

Found invariant 1+Arg_0<=0 for location n_evalsipmabubblestop___1

Found invariant 1+Arg_0<=0 for location n_evalsipmabubblereturnin___12

Found invariant 1+Arg_1<=Arg_0 && 1<=Arg_1 && 3<=Arg_0+Arg_1 && 2<=Arg_0 for location n_evalsipmabubblebb1in___6

Found invariant 1+Arg_1<=Arg_0 && 1<=Arg_1 && 3<=Arg_0+Arg_1 && 2<=Arg_0 for location n_evalsipmabubblebb2in___4

Found invariant Arg_1<=0 && Arg_1<=Arg_0 && Arg_0+Arg_1<=0 && 0<=Arg_1 && 0<=Arg_0+Arg_1 && Arg_0<=Arg_1 && Arg_0<=0 && 0<=Arg_0 for location n_evalsipmabubblebb5in___10

Problem after Preprocessing

Start: n_evalsipmabubblestart
Program_Vars: Arg_0, Arg_1
Temp_Vars:
Locations: n_evalsipmabubblebb1in___11, n_evalsipmabubblebb1in___6, n_evalsipmabubblebb2in___4, n_evalsipmabubblebb2in___9, n_evalsipmabubblebb3in___3, n_evalsipmabubblebb3in___8, n_evalsipmabubblebb4in___13, n_evalsipmabubblebb4in___7, n_evalsipmabubblebb5in___10, n_evalsipmabubblebb5in___5, n_evalsipmabubblebb6in___14, n_evalsipmabubblebb6in___2, n_evalsipmabubbleentryin___15, n_evalsipmabubblereturnin___12, n_evalsipmabubblestart, n_evalsipmabubblestop___1
Transitions:
0:n_evalsipmabubblebb1in___11(Arg_0,Arg_1) -> n_evalsipmabubblebb2in___9(Arg_0,Arg_1):|:Arg_1<=0 && 1+Arg_1<=Arg_0 && 0<=Arg_1 && 1<=Arg_0+Arg_1 && 1<=Arg_0 && 1<=Arg_0 && Arg_1<=0 && 0<=Arg_1
1:n_evalsipmabubblebb1in___11(Arg_0,Arg_1) -> n_evalsipmabubblebb3in___8(Arg_0,Arg_1):|:Arg_1<=0 && 1+Arg_1<=Arg_0 && 0<=Arg_1 && 1<=Arg_0+Arg_1 && 1<=Arg_0 && 1<=Arg_0 && Arg_1<=0 && 0<=Arg_1
2:n_evalsipmabubblebb1in___6(Arg_0,Arg_1) -> n_evalsipmabubblebb2in___4(Arg_0,Arg_1):|:1+Arg_1<=Arg_0 && 1<=Arg_1 && 3<=Arg_0+Arg_1 && 2<=Arg_0 && 1+Arg_1<=Arg_0
3:n_evalsipmabubblebb1in___6(Arg_0,Arg_1) -> n_evalsipmabubblebb3in___3(Arg_0,Arg_1):|:1+Arg_1<=Arg_0 && 1<=Arg_1 && 3<=Arg_0+Arg_1 && 2<=Arg_0 && 1+Arg_1<=Arg_0
4:n_evalsipmabubblebb2in___4(Arg_0,Arg_1) -> n_evalsipmabubblebb3in___3(Arg_0,Arg_1):|:1+Arg_1<=Arg_0 && 1<=Arg_1 && 3<=Arg_0+Arg_1 && 2<=Arg_0 && 1+Arg_1<=Arg_0
5:n_evalsipmabubblebb2in___9(Arg_0,Arg_1) -> n_evalsipmabubblebb3in___8(Arg_0,Arg_1):|:Arg_1<=0 && 1+Arg_1<=Arg_0 && 0<=Arg_1 && 1<=Arg_0+Arg_1 && 1<=Arg_0 && 1<=Arg_0 && Arg_1<=0 && 0<=Arg_1
6:n_evalsipmabubblebb3in___3(Arg_0,Arg_1) -> n_evalsipmabubblebb4in___7(Arg_0,Arg_1+1):|:1+Arg_1<=Arg_0 && 1<=Arg_1 && 3<=Arg_0+Arg_1 && 2<=Arg_0 && 1+Arg_1<=Arg_0
7:n_evalsipmabubblebb3in___8(Arg_0,Arg_1) -> n_evalsipmabubblebb4in___7(Arg_0,Arg_1+1):|:Arg_1<=0 && 1+Arg_1<=Arg_0 && 0<=Arg_1 && 1<=Arg_0+Arg_1 && 1<=Arg_0 && 1<=Arg_0 && Arg_1<=0 && 0<=Arg_1
8:n_evalsipmabubblebb4in___13(Arg_0,Arg_1) -> n_evalsipmabubblebb1in___11(Arg_0,Arg_1):|:Arg_1<=0 && Arg_1<=Arg_0 && 0<=Arg_1 && 0<=Arg_0+Arg_1 && 0<=Arg_0 && Arg_1<=0 && 0<=Arg_1 && 0<=Arg_0 && 1+Arg_1<=Arg_0
9:n_evalsipmabubblebb4in___13(Arg_0,Arg_1) -> n_evalsipmabubblebb5in___10(Arg_0,Arg_1):|:Arg_1<=0 && Arg_1<=Arg_0 && 0<=Arg_1 && 0<=Arg_0+Arg_1 && 0<=Arg_0 && Arg_1<=0 && 0<=Arg_1 && 0<=Arg_0 && Arg_0<=Arg_1
10:n_evalsipmabubblebb4in___7(Arg_0,Arg_1) -> n_evalsipmabubblebb1in___6(Arg_0,Arg_1):|:Arg_1<=Arg_0 && 1<=Arg_1 && 2<=Arg_0+Arg_1 && 1<=Arg_0 && 1+Arg_1<=Arg_0
11:n_evalsipmabubblebb4in___7(Arg_0,Arg_1) -> n_evalsipmabubblebb5in___5(Arg_0,Arg_1):|:Arg_1<=Arg_0 && 1<=Arg_1 && 2<=Arg_0+Arg_1 && 1<=Arg_0 && Arg_0<=Arg_1
12:n_evalsipmabubblebb5in___10(Arg_0,Arg_1) -> n_evalsipmabubblebb6in___2(Arg_0-1,Arg_1):|:Arg_1<=0 && Arg_1<=Arg_0 && Arg_0+Arg_1<=0 && 0<=Arg_1 && 0<=Arg_0+Arg_1 && Arg_0<=Arg_1 && Arg_0<=0 && 0<=Arg_0 && Arg_0<=0 && 0<=Arg_0 && Arg_1<=0 && 0<=Arg_1
13:n_evalsipmabubblebb5in___5(Arg_0,Arg_1) -> n_evalsipmabubblebb6in___14(Arg_0-1,Arg_1):|:Arg_1<=Arg_0 && 1<=Arg_1 && 2<=Arg_0+Arg_1 && Arg_0<=Arg_1 && 1<=Arg_0 && Arg_0<=Arg_1
14:n_evalsipmabubblebb6in___14(Arg_0,Arg_1) -> n_evalsipmabubblebb4in___13(Arg_0,0):|:0<=Arg_0
15:n_evalsipmabubblebb6in___14(Arg_0,Arg_1) -> n_evalsipmabubblereturnin___12(Arg_0,Arg_1):|:1+Arg_0<=0
16:n_evalsipmabubblebb6in___2(Arg_0,Arg_1) -> n_evalsipmabubblereturnin___12(Arg_0,Arg_1):|:Arg_1<=0 && Arg_1<=1+Arg_0 && 1+Arg_0+Arg_1<=0 && 0<=Arg_1 && 0<=1+Arg_0+Arg_1 && 1+Arg_0<=Arg_1 && 1+Arg_0<=0 && 0<=1+Arg_0 && 1+Arg_0<=0 && 1+Arg_0<=0
17:n_evalsipmabubbleentryin___15(Arg_0,Arg_1) -> n_evalsipmabubblebb6in___14(Arg_0,Arg_1)
18:n_evalsipmabubblereturnin___12(Arg_0,Arg_1) -> n_evalsipmabubblestop___1(Arg_0,Arg_1):|:1+Arg_0<=0 && 1+Arg_0<=0
19:n_evalsipmabubblestart(Arg_0,Arg_1) -> n_evalsipmabubbleentryin___15(Arg_0,Arg_1)

MPRF for transition 0:n_evalsipmabubblebb1in___11(Arg_0,Arg_1) -> n_evalsipmabubblebb2in___9(Arg_0,Arg_1):|:Arg_1<=0 && 1+Arg_1<=Arg_0 && 0<=Arg_1 && 1<=Arg_0+Arg_1 && 1<=Arg_0 && 1<=Arg_0 && Arg_1<=0 && 0<=Arg_1 of depth 1:

new bound:

Arg_0+1 {O(n)}

MPRF:

n_evalsipmabubblebb2in___4 [Arg_0 ]
n_evalsipmabubblebb2in___9 [Arg_0 ]
n_evalsipmabubblebb3in___3 [Arg_0 ]
n_evalsipmabubblebb3in___8 [Arg_0 ]
n_evalsipmabubblebb1in___11 [Arg_0+1 ]
n_evalsipmabubblebb1in___6 [Arg_0 ]
n_evalsipmabubblebb4in___7 [Arg_0 ]
n_evalsipmabubblebb5in___5 [Arg_1 ]
n_evalsipmabubblebb6in___14 [Arg_0+1 ]
n_evalsipmabubblebb4in___13 [Arg_0+1 ]

MPRF for transition 1:n_evalsipmabubblebb1in___11(Arg_0,Arg_1) -> n_evalsipmabubblebb3in___8(Arg_0,Arg_1):|:Arg_1<=0 && 1+Arg_1<=Arg_0 && 0<=Arg_1 && 1<=Arg_0+Arg_1 && 1<=Arg_0 && 1<=Arg_0 && Arg_1<=0 && 0<=Arg_1 of depth 1:

new bound:

Arg_0 {O(n)}

MPRF:

n_evalsipmabubblebb2in___4 [Arg_0-1 ]
n_evalsipmabubblebb2in___9 [Arg_0 ]
n_evalsipmabubblebb3in___3 [Arg_0-1 ]
n_evalsipmabubblebb3in___8 [Arg_0-1 ]
n_evalsipmabubblebb1in___11 [Arg_0 ]
n_evalsipmabubblebb1in___6 [Arg_0-1 ]
n_evalsipmabubblebb4in___7 [Arg_0-1 ]
n_evalsipmabubblebb5in___5 [Arg_1-1 ]
n_evalsipmabubblebb6in___14 [Arg_0 ]
n_evalsipmabubblebb4in___13 [Arg_0 ]

MPRF for transition 5:n_evalsipmabubblebb2in___9(Arg_0,Arg_1) -> n_evalsipmabubblebb3in___8(Arg_0,Arg_1):|:Arg_1<=0 && 1+Arg_1<=Arg_0 && 0<=Arg_1 && 1<=Arg_0+Arg_1 && 1<=Arg_0 && 1<=Arg_0 && Arg_1<=0 && 0<=Arg_1 of depth 1:

new bound:

Arg_0+1 {O(n)}

MPRF:

n_evalsipmabubblebb2in___4 [Arg_0 ]
n_evalsipmabubblebb2in___9 [Arg_0+1 ]
n_evalsipmabubblebb3in___3 [Arg_0 ]
n_evalsipmabubblebb3in___8 [Arg_0 ]
n_evalsipmabubblebb1in___11 [Arg_0+1 ]
n_evalsipmabubblebb1in___6 [Arg_0 ]
n_evalsipmabubblebb4in___7 [Arg_0 ]
n_evalsipmabubblebb5in___5 [Arg_0 ]
n_evalsipmabubblebb6in___14 [Arg_0+1 ]
n_evalsipmabubblebb4in___13 [Arg_0+1 ]

MPRF for transition 7:n_evalsipmabubblebb3in___8(Arg_0,Arg_1) -> n_evalsipmabubblebb4in___7(Arg_0,Arg_1+1):|:Arg_1<=0 && 1+Arg_1<=Arg_0 && 0<=Arg_1 && 1<=Arg_0+Arg_1 && 1<=Arg_0 && 1<=Arg_0 && Arg_1<=0 && 0<=Arg_1 of depth 1:

new bound:

Arg_0+1 {O(n)}

MPRF:

n_evalsipmabubblebb2in___4 [Arg_0 ]
n_evalsipmabubblebb2in___9 [Arg_0+1 ]
n_evalsipmabubblebb3in___3 [Arg_0 ]
n_evalsipmabubblebb3in___8 [Arg_0+1 ]
n_evalsipmabubblebb1in___11 [Arg_0+1 ]
n_evalsipmabubblebb1in___6 [Arg_0 ]
n_evalsipmabubblebb4in___7 [Arg_0 ]
n_evalsipmabubblebb5in___5 [Arg_0 ]
n_evalsipmabubblebb6in___14 [Arg_0+1 ]
n_evalsipmabubblebb4in___13 [Arg_0+1 ]

MPRF for transition 8:n_evalsipmabubblebb4in___13(Arg_0,Arg_1) -> n_evalsipmabubblebb1in___11(Arg_0,Arg_1):|:Arg_1<=0 && Arg_1<=Arg_0 && 0<=Arg_1 && 0<=Arg_0+Arg_1 && 0<=Arg_0 && Arg_1<=0 && 0<=Arg_1 && 0<=Arg_0 && 1+Arg_1<=Arg_0 of depth 1:

new bound:

Arg_0+1 {O(n)}

MPRF:

n_evalsipmabubblebb2in___4 [Arg_0 ]
n_evalsipmabubblebb2in___9 [Arg_0 ]
n_evalsipmabubblebb3in___3 [Arg_0 ]
n_evalsipmabubblebb3in___8 [Arg_0 ]
n_evalsipmabubblebb1in___11 [Arg_0 ]
n_evalsipmabubblebb1in___6 [Arg_0 ]
n_evalsipmabubblebb4in___7 [Arg_0 ]
n_evalsipmabubblebb5in___5 [Arg_1 ]
n_evalsipmabubblebb6in___14 [Arg_0+1 ]
n_evalsipmabubblebb4in___13 [Arg_0+1 ]

MPRF for transition 11:n_evalsipmabubblebb4in___7(Arg_0,Arg_1) -> n_evalsipmabubblebb5in___5(Arg_0,Arg_1):|:Arg_1<=Arg_0 && 1<=Arg_1 && 2<=Arg_0+Arg_1 && 1<=Arg_0 && Arg_0<=Arg_1 of depth 1:

new bound:

Arg_0+2 {O(n)}

MPRF:

n_evalsipmabubblebb2in___4 [Arg_0+2 ]
n_evalsipmabubblebb2in___9 [Arg_0+2 ]
n_evalsipmabubblebb3in___3 [Arg_0+2 ]
n_evalsipmabubblebb3in___8 [Arg_0+2 ]
n_evalsipmabubblebb1in___11 [Arg_0+2 ]
n_evalsipmabubblebb1in___6 [Arg_0+2 ]
n_evalsipmabubblebb4in___7 [Arg_0+2 ]
n_evalsipmabubblebb5in___5 [Arg_0+1 ]
n_evalsipmabubblebb6in___14 [Arg_0+2 ]
n_evalsipmabubblebb4in___13 [Arg_0+2 ]

MPRF for transition 13:n_evalsipmabubblebb5in___5(Arg_0,Arg_1) -> n_evalsipmabubblebb6in___14(Arg_0-1,Arg_1):|:Arg_1<=Arg_0 && 1<=Arg_1 && 2<=Arg_0+Arg_1 && Arg_0<=Arg_1 && 1<=Arg_0 && Arg_0<=Arg_1 of depth 1:

new bound:

Arg_0 {O(n)}

MPRF:

n_evalsipmabubblebb2in___4 [Arg_0 ]
n_evalsipmabubblebb2in___9 [Arg_0 ]
n_evalsipmabubblebb3in___3 [Arg_0 ]
n_evalsipmabubblebb3in___8 [Arg_0 ]
n_evalsipmabubblebb1in___11 [Arg_0 ]
n_evalsipmabubblebb1in___6 [Arg_0 ]
n_evalsipmabubblebb4in___7 [Arg_0 ]
n_evalsipmabubblebb5in___5 [Arg_0 ]
n_evalsipmabubblebb6in___14 [Arg_0 ]
n_evalsipmabubblebb4in___13 [Arg_0 ]

MPRF for transition 14:n_evalsipmabubblebb6in___14(Arg_0,Arg_1) -> n_evalsipmabubblebb4in___13(Arg_0,0):|:0<=Arg_0 of depth 1:

new bound:

Arg_0+1 {O(n)}

MPRF:

n_evalsipmabubblebb2in___4 [Arg_0 ]
n_evalsipmabubblebb2in___9 [Arg_0 ]
n_evalsipmabubblebb3in___3 [Arg_0 ]
n_evalsipmabubblebb3in___8 [Arg_0 ]
n_evalsipmabubblebb1in___11 [Arg_0 ]
n_evalsipmabubblebb1in___6 [Arg_0 ]
n_evalsipmabubblebb4in___7 [Arg_0 ]
n_evalsipmabubblebb5in___5 [Arg_1 ]
n_evalsipmabubblebb6in___14 [Arg_0+1 ]
n_evalsipmabubblebb4in___13 [Arg_0 ]

MPRF for transition 2:n_evalsipmabubblebb1in___6(Arg_0,Arg_1) -> n_evalsipmabubblebb2in___4(Arg_0,Arg_1):|:1+Arg_1<=Arg_0 && 1<=Arg_1 && 3<=Arg_0+Arg_1 && 2<=Arg_0 && 1+Arg_1<=Arg_0 of depth 1:

new bound:

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

MPRF:

n_evalsipmabubblebb2in___4 [Arg_0-Arg_1 ]
n_evalsipmabubblebb2in___9 [Arg_0 ]
n_evalsipmabubblebb3in___3 [Arg_0-Arg_1 ]
n_evalsipmabubblebb3in___8 [Arg_0 ]
n_evalsipmabubblebb4in___13 [Arg_0 ]
n_evalsipmabubblebb1in___11 [Arg_0 ]
n_evalsipmabubblebb1in___6 [Arg_0+1-Arg_1 ]
n_evalsipmabubblebb4in___7 [Arg_0+1-Arg_1 ]
n_evalsipmabubblebb5in___5 [Arg_0+1-Arg_1 ]
n_evalsipmabubblebb6in___14 [1 ]

MPRF for transition 3:n_evalsipmabubblebb1in___6(Arg_0,Arg_1) -> n_evalsipmabubblebb3in___3(Arg_0,Arg_1):|:1+Arg_1<=Arg_0 && 1<=Arg_1 && 3<=Arg_0+Arg_1 && 2<=Arg_0 && 1+Arg_1<=Arg_0 of depth 1:

new bound:

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

MPRF:

n_evalsipmabubblebb2in___4 [2*Arg_0-Arg_1 ]
n_evalsipmabubblebb2in___9 [2*Arg_0 ]
n_evalsipmabubblebb3in___3 [2*Arg_0-Arg_1-1 ]
n_evalsipmabubblebb3in___8 [2*Arg_0 ]
n_evalsipmabubblebb4in___13 [2*Arg_0 ]
n_evalsipmabubblebb1in___11 [2*Arg_0 ]
n_evalsipmabubblebb1in___6 [2*Arg_0-Arg_1 ]
n_evalsipmabubblebb4in___7 [2*Arg_0-Arg_1 ]
n_evalsipmabubblebb5in___5 [2*Arg_0-Arg_1 ]
n_evalsipmabubblebb6in___14 [Arg_0+1 ]

MPRF for transition 4:n_evalsipmabubblebb2in___4(Arg_0,Arg_1) -> n_evalsipmabubblebb3in___3(Arg_0,Arg_1):|:1+Arg_1<=Arg_0 && 1<=Arg_1 && 3<=Arg_0+Arg_1 && 2<=Arg_0 && 1+Arg_1<=Arg_0 of depth 1:

new bound:

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

MPRF:

n_evalsipmabubblebb2in___4 [2*Arg_0-Arg_1 ]
n_evalsipmabubblebb2in___9 [2*Arg_0 ]
n_evalsipmabubblebb3in___3 [2*Arg_0-Arg_1-1 ]
n_evalsipmabubblebb3in___8 [2*Arg_0 ]
n_evalsipmabubblebb4in___13 [2*Arg_0 ]
n_evalsipmabubblebb1in___11 [2*Arg_0 ]
n_evalsipmabubblebb1in___6 [2*Arg_0-Arg_1 ]
n_evalsipmabubblebb4in___7 [2*Arg_0-Arg_1 ]
n_evalsipmabubblebb5in___5 [2*Arg_0-Arg_1 ]
n_evalsipmabubblebb6in___14 [Arg_0+1 ]

MPRF for transition 6:n_evalsipmabubblebb3in___3(Arg_0,Arg_1) -> n_evalsipmabubblebb4in___7(Arg_0,Arg_1+1):|:1+Arg_1<=Arg_0 && 1<=Arg_1 && 3<=Arg_0+Arg_1 && 2<=Arg_0 && 1+Arg_1<=Arg_0 of depth 1:

new bound:

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

MPRF:

n_evalsipmabubblebb2in___4 [4*Arg_0-Arg_1-2 ]
n_evalsipmabubblebb2in___9 [4*Arg_0 ]
n_evalsipmabubblebb3in___3 [4*Arg_0-Arg_1-2 ]
n_evalsipmabubblebb3in___8 [4*Arg_0 ]
n_evalsipmabubblebb4in___13 [4*Arg_0 ]
n_evalsipmabubblebb1in___11 [4*Arg_0 ]
n_evalsipmabubblebb1in___6 [4*Arg_0-Arg_1-2 ]
n_evalsipmabubblebb4in___7 [4*Arg_0-Arg_1-2 ]
n_evalsipmabubblebb5in___5 [3*Arg_0-2 ]
n_evalsipmabubblebb6in___14 [3*Arg_0+1 ]

MPRF for transition 10:n_evalsipmabubblebb4in___7(Arg_0,Arg_1) -> n_evalsipmabubblebb1in___6(Arg_0,Arg_1):|:Arg_1<=Arg_0 && 1<=Arg_1 && 2<=Arg_0+Arg_1 && 1<=Arg_0 && 1+Arg_1<=Arg_0 of depth 1:

new bound:

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

MPRF:

n_evalsipmabubblebb2in___4 [Arg_0-Arg_1 ]
n_evalsipmabubblebb2in___9 [Arg_0 ]
n_evalsipmabubblebb3in___3 [Arg_0-Arg_1 ]
n_evalsipmabubblebb3in___8 [Arg_0 ]
n_evalsipmabubblebb4in___13 [Arg_0 ]
n_evalsipmabubblebb1in___11 [Arg_0 ]
n_evalsipmabubblebb1in___6 [Arg_0-Arg_1 ]
n_evalsipmabubblebb4in___7 [Arg_0+1-Arg_1 ]
n_evalsipmabubblebb5in___5 [Arg_0+1-Arg_1 ]
n_evalsipmabubblebb6in___14 [1 ]

All Bounds

Timebounds

Overall timebound:10*Arg_0*Arg_0+18*Arg_0+14 {O(n^2)}
0: n_evalsipmabubblebb1in___11->n_evalsipmabubblebb2in___9: Arg_0+1 {O(n)}
1: n_evalsipmabubblebb1in___11->n_evalsipmabubblebb3in___8: Arg_0 {O(n)}
2: n_evalsipmabubblebb1in___6->n_evalsipmabubblebb2in___4: Arg_0*Arg_0+Arg_0 {O(n^2)}
3: n_evalsipmabubblebb1in___6->n_evalsipmabubblebb3in___3: 2*Arg_0*Arg_0+2*Arg_0 {O(n^2)}
4: n_evalsipmabubblebb2in___4->n_evalsipmabubblebb3in___3: 2*Arg_0*Arg_0+2*Arg_0 {O(n^2)}
5: n_evalsipmabubblebb2in___9->n_evalsipmabubblebb3in___8: Arg_0+1 {O(n)}
6: n_evalsipmabubblebb3in___3->n_evalsipmabubblebb4in___7: 4*Arg_0*Arg_0+4*Arg_0 {O(n^2)}
7: n_evalsipmabubblebb3in___8->n_evalsipmabubblebb4in___7: Arg_0+1 {O(n)}
8: n_evalsipmabubblebb4in___13->n_evalsipmabubblebb1in___11: Arg_0+1 {O(n)}
9: n_evalsipmabubblebb4in___13->n_evalsipmabubblebb5in___10: 1 {O(1)}
10: n_evalsipmabubblebb4in___7->n_evalsipmabubblebb1in___6: Arg_0*Arg_0+Arg_0 {O(n^2)}
11: n_evalsipmabubblebb4in___7->n_evalsipmabubblebb5in___5: Arg_0+2 {O(n)}
12: n_evalsipmabubblebb5in___10->n_evalsipmabubblebb6in___2: 1 {O(1)}
13: n_evalsipmabubblebb5in___5->n_evalsipmabubblebb6in___14: Arg_0 {O(n)}
14: n_evalsipmabubblebb6in___14->n_evalsipmabubblebb4in___13: Arg_0+1 {O(n)}
15: n_evalsipmabubblebb6in___14->n_evalsipmabubblereturnin___12: 1 {O(1)}
16: n_evalsipmabubblebb6in___2->n_evalsipmabubblereturnin___12: 1 {O(1)}
17: n_evalsipmabubbleentryin___15->n_evalsipmabubblebb6in___14: 1 {O(1)}
18: n_evalsipmabubblereturnin___12->n_evalsipmabubblestop___1: 1 {O(1)}
19: n_evalsipmabubblestart->n_evalsipmabubbleentryin___15: 1 {O(1)}

Costbounds

Overall costbound: 10*Arg_0*Arg_0+18*Arg_0+14 {O(n^2)}
0: n_evalsipmabubblebb1in___11->n_evalsipmabubblebb2in___9: Arg_0+1 {O(n)}
1: n_evalsipmabubblebb1in___11->n_evalsipmabubblebb3in___8: Arg_0 {O(n)}
2: n_evalsipmabubblebb1in___6->n_evalsipmabubblebb2in___4: Arg_0*Arg_0+Arg_0 {O(n^2)}
3: n_evalsipmabubblebb1in___6->n_evalsipmabubblebb3in___3: 2*Arg_0*Arg_0+2*Arg_0 {O(n^2)}
4: n_evalsipmabubblebb2in___4->n_evalsipmabubblebb3in___3: 2*Arg_0*Arg_0+2*Arg_0 {O(n^2)}
5: n_evalsipmabubblebb2in___9->n_evalsipmabubblebb3in___8: Arg_0+1 {O(n)}
6: n_evalsipmabubblebb3in___3->n_evalsipmabubblebb4in___7: 4*Arg_0*Arg_0+4*Arg_0 {O(n^2)}
7: n_evalsipmabubblebb3in___8->n_evalsipmabubblebb4in___7: Arg_0+1 {O(n)}
8: n_evalsipmabubblebb4in___13->n_evalsipmabubblebb1in___11: Arg_0+1 {O(n)}
9: n_evalsipmabubblebb4in___13->n_evalsipmabubblebb5in___10: 1 {O(1)}
10: n_evalsipmabubblebb4in___7->n_evalsipmabubblebb1in___6: Arg_0*Arg_0+Arg_0 {O(n^2)}
11: n_evalsipmabubblebb4in___7->n_evalsipmabubblebb5in___5: Arg_0+2 {O(n)}
12: n_evalsipmabubblebb5in___10->n_evalsipmabubblebb6in___2: 1 {O(1)}
13: n_evalsipmabubblebb5in___5->n_evalsipmabubblebb6in___14: Arg_0 {O(n)}
14: n_evalsipmabubblebb6in___14->n_evalsipmabubblebb4in___13: Arg_0+1 {O(n)}
15: n_evalsipmabubblebb6in___14->n_evalsipmabubblereturnin___12: 1 {O(1)}
16: n_evalsipmabubblebb6in___2->n_evalsipmabubblereturnin___12: 1 {O(1)}
17: n_evalsipmabubbleentryin___15->n_evalsipmabubblebb6in___14: 1 {O(1)}
18: n_evalsipmabubblereturnin___12->n_evalsipmabubblestop___1: 1 {O(1)}
19: n_evalsipmabubblestart->n_evalsipmabubbleentryin___15: 1 {O(1)}

Sizebounds

0: n_evalsipmabubblebb1in___11->n_evalsipmabubblebb2in___9, Arg_0: Arg_0 {O(n)}
0: n_evalsipmabubblebb1in___11->n_evalsipmabubblebb2in___9, Arg_1: 0 {O(1)}
1: n_evalsipmabubblebb1in___11->n_evalsipmabubblebb3in___8, Arg_0: Arg_0 {O(n)}
1: n_evalsipmabubblebb1in___11->n_evalsipmabubblebb3in___8, Arg_1: 0 {O(1)}
2: n_evalsipmabubblebb1in___6->n_evalsipmabubblebb2in___4, Arg_0: Arg_0 {O(n)}
2: n_evalsipmabubblebb1in___6->n_evalsipmabubblebb2in___4, Arg_1: 4*Arg_0*Arg_0+4*Arg_0+1 {O(n^2)}
3: n_evalsipmabubblebb1in___6->n_evalsipmabubblebb3in___3, Arg_0: Arg_0 {O(n)}
3: n_evalsipmabubblebb1in___6->n_evalsipmabubblebb3in___3, Arg_1: 4*Arg_0*Arg_0+4*Arg_0+1 {O(n^2)}
4: n_evalsipmabubblebb2in___4->n_evalsipmabubblebb3in___3, Arg_0: Arg_0 {O(n)}
4: n_evalsipmabubblebb2in___4->n_evalsipmabubblebb3in___3, Arg_1: 4*Arg_0*Arg_0+4*Arg_0+1 {O(n^2)}
5: n_evalsipmabubblebb2in___9->n_evalsipmabubblebb3in___8, Arg_0: Arg_0 {O(n)}
5: n_evalsipmabubblebb2in___9->n_evalsipmabubblebb3in___8, Arg_1: 0 {O(1)}
6: n_evalsipmabubblebb3in___3->n_evalsipmabubblebb4in___7, Arg_0: Arg_0 {O(n)}
6: n_evalsipmabubblebb3in___3->n_evalsipmabubblebb4in___7, Arg_1: 4*Arg_0*Arg_0+4*Arg_0+1 {O(n^2)}
7: n_evalsipmabubblebb3in___8->n_evalsipmabubblebb4in___7, Arg_0: Arg_0 {O(n)}
7: n_evalsipmabubblebb3in___8->n_evalsipmabubblebb4in___7, Arg_1: 1 {O(1)}
8: n_evalsipmabubblebb4in___13->n_evalsipmabubblebb1in___11, Arg_0: Arg_0 {O(n)}
8: n_evalsipmabubblebb4in___13->n_evalsipmabubblebb1in___11, Arg_1: 0 {O(1)}
9: n_evalsipmabubblebb4in___13->n_evalsipmabubblebb5in___10, Arg_0: 0 {O(1)}
9: n_evalsipmabubblebb4in___13->n_evalsipmabubblebb5in___10, Arg_1: 0 {O(1)}
10: n_evalsipmabubblebb4in___7->n_evalsipmabubblebb1in___6, Arg_0: Arg_0 {O(n)}
10: n_evalsipmabubblebb4in___7->n_evalsipmabubblebb1in___6, Arg_1: 4*Arg_0*Arg_0+4*Arg_0+1 {O(n^2)}
11: n_evalsipmabubblebb4in___7->n_evalsipmabubblebb5in___5, Arg_0: Arg_0 {O(n)}
11: n_evalsipmabubblebb4in___7->n_evalsipmabubblebb5in___5, Arg_1: 4*Arg_0*Arg_0+4*Arg_0+2 {O(n^2)}
12: n_evalsipmabubblebb5in___10->n_evalsipmabubblebb6in___2, Arg_0: 1 {O(1)}
12: n_evalsipmabubblebb5in___10->n_evalsipmabubblebb6in___2, Arg_1: 0 {O(1)}
13: n_evalsipmabubblebb5in___5->n_evalsipmabubblebb6in___14, Arg_0: Arg_0 {O(n)}
13: n_evalsipmabubblebb5in___5->n_evalsipmabubblebb6in___14, Arg_1: 4*Arg_0*Arg_0+4*Arg_0+2 {O(n^2)}
14: n_evalsipmabubblebb6in___14->n_evalsipmabubblebb4in___13, Arg_0: Arg_0 {O(n)}
14: n_evalsipmabubblebb6in___14->n_evalsipmabubblebb4in___13, Arg_1: 0 {O(1)}
15: n_evalsipmabubblebb6in___14->n_evalsipmabubblereturnin___12, Arg_0: Arg_0 {O(n)}
15: n_evalsipmabubblebb6in___14->n_evalsipmabubblereturnin___12, Arg_1: Arg_1 {O(n)}
16: n_evalsipmabubblebb6in___2->n_evalsipmabubblereturnin___12, Arg_0: 1 {O(1)}
16: n_evalsipmabubblebb6in___2->n_evalsipmabubblereturnin___12, Arg_1: 0 {O(1)}
17: n_evalsipmabubbleentryin___15->n_evalsipmabubblebb6in___14, Arg_0: Arg_0 {O(n)}
17: n_evalsipmabubbleentryin___15->n_evalsipmabubblebb6in___14, Arg_1: Arg_1 {O(n)}
18: n_evalsipmabubblereturnin___12->n_evalsipmabubblestop___1, Arg_0: Arg_0+1 {O(n)}
18: n_evalsipmabubblereturnin___12->n_evalsipmabubblestop___1, Arg_1: Arg_1 {O(n)}
19: n_evalsipmabubblestart->n_evalsipmabubbleentryin___15, Arg_0: Arg_0 {O(n)}
19: n_evalsipmabubblestart->n_evalsipmabubbleentryin___15, Arg_1: Arg_1 {O(n)}