LTS Termination Proof

by AProVE

Input

Integer Transition System

Proof

1 Switch to Cooperation Termination Proof

We consider the following cutpoint-transitions:
f2837_0__init__GE f2837_0__init__GE f2837_0__init__GE: x1 = x1x2 = x2x3 = x3x4 = x4x5 = x5x6 = x6x7 = x7x8 = x8x9 = x9x10 = x10x11 = x11x12 = x12x13 = x13x14 = x14x15 = x15x16 = x16x17 = x17x18 = x18x19 = x19x20 = x20x21 = x21x22 = x22x23 = x23x24 = x24x25 = x25
f3367_0_hasPrevious_EQ f3367_0_hasPrevious_EQ f3367_0_hasPrevious_EQ: x1 = x1x2 = x2x3 = x3x4 = x4x5 = x5x6 = x6x7 = x7x8 = x8x9 = x9x10 = x10x11 = x11x12 = x12x13 = x13x14 = x14x15 = x15x16 = x16x17 = x17x18 = x18x19 = x19x20 = x20x21 = x21x22 = x22x23 = x23x24 = x24x25 = x25
f3422_0_previous_FieldAccess f3422_0_previous_FieldAccess f3422_0_previous_FieldAccess: x1 = x1x2 = x2x3 = x3x4 = x4x5 = x5x6 = x6x7 = x7x8 = x8x9 = x9x10 = x10x11 = x11x12 = x12x13 = x13x14 = x14x15 = x15x16 = x16x17 = x17x18 = x18x19 = x19x20 = x20x21 = x21x22 = x22x23 = x23x24 = x24x25 = x25
f381_0_createList_Load f381_0_createList_Load f381_0_createList_Load: x1 = x1x2 = x2x3 = x3x4 = x4x5 = x5x6 = x6x7 = x7x8 = x8x9 = x9x10 = x10x11 = x11x12 = x12x13 = x13x14 = x14x15 = x15x16 = x16x17 = x17x18 = x18x19 = x19x20 = x20x21 = x21x22 = x22x23 = x23x24 = x24x25 = x25
f664_0_createList_Load f664_0_createList_Load f664_0_createList_Load: x1 = x1x2 = x2x3 = x3x4 = x4x5 = x5x6 = x6x7 = x7x8 = x8x9 = x9x10 = x10x11 = x11x12 = x12x13 = x13x14 = x14x15 = x15x16 = x16x17 = x17x18 = x18x19 = x19x20 = x20x21 = x21x22 = x22x23 = x23x24 = x24x25 = x25
f399_0_createList_Return f399_0_createList_Return f399_0_createList_Return: x1 = x1x2 = x2x3 = x3x4 = x4x5 = x5x6 = x6x7 = x7x8 = x8x9 = x9x10 = x10x11 = x11x12 = x12x13 = x13x14 = x14x15 = x15x16 = x16x17 = x17x18 = x18x19 = x19x20 = x20x21 = x21x22 = x22x23 = x23x24 = x24x25 = x25
f2241_0__init__GE f2241_0__init__GE f2241_0__init__GE: x1 = x1x2 = x2x3 = x3x4 = x4x5 = x5x6 = x6x7 = x7x8 = x8x9 = x9x10 = x10x11 = x11x12 = x12x13 = x13x14 = x14x15 = x15x16 = x16x17 = x17x18 = x18x19 = x19x20 = x20x21 = x21x22 = x22x23 = x23x24 = x24x25 = x25
__init __init __init: x1 = x1x2 = x2x3 = x3x4 = x4x5 = x5x6 = x6x7 = x7x8 = x8x9 = x9x10 = x10x11 = x11x12 = x12x13 = x13x14 = x14x15 = x15x16 = x16x17 = x17x18 = x18x19 = x19x20 = x20x21 = x21x22 = x22x23 = x23x24 = x24x25 = x25
f2885_0__init__GE f2885_0__init__GE f2885_0__init__GE: x1 = x1x2 = x2x3 = x3x4 = x4x5 = x5x6 = x6x7 = x7x8 = x8x9 = x9x10 = x10x11 = x11x12 = x12x13 = x13x14 = x14x15 = x15x16 = x16x17 = x17x18 = x18x19 = x19x20 = x20x21 = x21x22 = x22x23 = x23x24 = x24x25 = x25
f1981_0_createList_LE f1981_0_createList_LE f1981_0_createList_LE: x1 = x1x2 = x2x3 = x3x4 = x4x5 = x5x6 = x6x7 = x7x8 = x8x9 = x9x10 = x10x11 = x11x12 = x12x13 = x13x14 = x14x15 = x15x16 = x16x17 = x17x18 = x18x19 = x19x20 = x20x21 = x21x22 = x22x23 = x23x24 = x24x25 = x25
f2886_0__init__GE f2886_0__init__GE f2886_0__init__GE: x1 = x1x2 = x2x3 = x3x4 = x4x5 = x5x6 = x6x7 = x7x8 = x8x9 = x9x10 = x10x11 = x11x12 = x12x13 = x13x14 = x14x15 = x15x16 = x16x17 = x17x18 = x18x19 = x19x20 = x20x21 = x21x22 = x22x23 = x23x24 = x24x25 = x25
f2838_0__init__GE f2838_0__init__GE f2838_0__init__GE: x1 = x1x2 = x2x3 = x3x4 = x4x5 = x5x6 = x6x7 = x7x8 = x8x9 = x9x10 = x10x11 = x11x12 = x12x13 = x13x14 = x14x15 = x15x16 = x16x17 = x17x18 = x18x19 = x19x20 = x20x21 = x21x22 = x22x23 = x23x24 = x24x25 = x25
f1_0_main_Load f1_0_main_Load f1_0_main_Load: x1 = x1x2 = x2x3 = x3x4 = x4x5 = x5x6 = x6x7 = x7x8 = x8x9 = x9x10 = x10x11 = x11x12 = x12x13 = x13x14 = x14x15 = x15x16 = x16x17 = x17x18 = x18x19 = x19x20 = x20x21 = x21x22 = x22x23 = x23x24 = x24x25 = x25
and for every transition t, a duplicate t is considered.

2 SCC Decomposition

We consider subproblems for each of the 6 SCC(s) of the program graph.

2.1 SCC Subproblem 1/6

Here we consider the SCC { f2886_0__init__GE }.

2.1.1 Transition Removal

We remove transitions 12, 13 using the following ranking functions, which are bounded by 0.

f2886_0__init__GE: x9 + x8

2.1.2 Trivial Cooperation Program

There are no more "sharp" transitions in the cooperation program. Hence the cooperation termination is proved.

2.2 SCC Subproblem 2/6

Here we consider the SCC { f2885_0__init__GE }.

2.2.1 Transition Removal

We remove transitions 10, 11 using the following ranking functions, which are bounded by 0.

f2885_0__init__GE: x11 + x9

2.2.2 Trivial Cooperation Program

There are no more "sharp" transitions in the cooperation program. Hence the cooperation termination is proved.

2.3 SCC Subproblem 3/6

Here we consider the SCC { f2838_0__init__GE }.

2.3.1 Transition Removal

We remove transition 9 using the following ranking functions, which are bounded by 0.

f2838_0__init__GE: x4 + x1

2.3.2 Trivial Cooperation Program

There are no more "sharp" transitions in the cooperation program. Hence the cooperation termination is proved.

2.4 SCC Subproblem 4/6

Here we consider the SCC { f2837_0__init__GE }.

2.4.1 Transition Removal

We remove transition 8 using the following ranking functions, which are bounded by 0.

f2837_0__init__GE: x6 + x4

2.4.2 Trivial Cooperation Program

There are no more "sharp" transitions in the cooperation program. Hence the cooperation termination is proved.

2.5 SCC Subproblem 5/6

Here we consider the SCC { f3367_0_hasPrevious_EQ, f3422_0_previous_FieldAccess }.

2.5.1 Transition Removal

We remove transitions 19, 20 using the following ranking functions, which are bounded by 0.

f3367_0_hasPrevious_EQ: 3⋅x5
f3422_0_previous_FieldAccess: 3⋅x6 + 1

2.5.2 Transition Removal

We remove transition 21 using the following ranking functions, which are bounded by 0.

f3422_0_previous_FieldAccess: 0
f3367_0_hasPrevious_EQ: −1 + 0⋅x2 + 0⋅x3

2.5.3 Trivial Cooperation Program

There are no more "sharp" transitions in the cooperation program. Hence the cooperation termination is proved.

2.6 SCC Subproblem 6/6

Here we consider the SCC { f1981_0_createList_LE }.

2.6.1 Transition Removal

We remove transitions 24, 25 using the following ranking functions, which are bounded by 0.

f1981_0_createList_LE: x2

2.6.2 Trivial Cooperation Program

There are no more "sharp" transitions in the cooperation program. Hence the cooperation termination is proved.

Tool configuration

AProVE