LTS Termination Proof

by AProVE

Input

Integer Transition System

Proof

1 Switch to Cooperation Termination Proof

We consider the following cutpoint-transitions:
f4642_0_removeLastOccurrence_EQ f4642_0_removeLastOccurrence_EQ f4642_0_removeLastOccurrence_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 = x25x26 = x26x27 = x27x28 = x28x29 = x29x30 = x30
f554_0_createList_Return f554_0_createList_Return f554_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 = x25x26 = x26x27 = x27x28 = x28x29 = x29x30 = x30
f3355_0_removeLastOccurrence_EQ f3355_0_removeLastOccurrence_EQ f3355_0_removeLastOccurrence_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 = x25x26 = x26x27 = x27x28 = x28x29 = x29x30 = x30
f4538_0_remove_FieldAccess f4538_0_remove_FieldAccess f4538_0_remove_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 = x25x26 = x26x27 = x27x28 = x28x29 = x29x30 = x30
f4490_0_remove_FieldAccess f4490_0_remove_FieldAccess f4490_0_remove_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 = x25x26 = x26x27 = x27x28 = x28x29 = x29x30 = x30
f4536_0_remove_FieldAccess f4536_0_remove_FieldAccess f4536_0_remove_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 = x25x26 = x26x27 = x27x28 = x28x29 = x29x30 = x30
f3958_0_main_CheckCast f3958_0_main_CheckCast f3958_0_main_CheckCast: 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 = x25x26 = x26x27 = x27x28 = x28x29 = x29x30 = x30
f4641_0_removeLastOccurrence_EQ f4641_0_removeLastOccurrence_EQ f4641_0_removeLastOccurrence_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 = x25x26 = x26x27 = x27x28 = x28x29 = x29x30 = x30
f3460_0_equals_Return f3460_0_equals_Return f3460_0_equals_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 = x25x26 = x26x27 = x27x28 = x28x29 = x29x30 = x30
f2700_0_createList_LE f2700_0_createList_LE f2700_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 = x25x26 = x26x27 = x27x28 = x28x29 = x29x30 = x30
__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 = x25x26 = x26x27 = x27x28 = x28x29 = x29x30 = x30
f3867_0_entry_GT f3867_0_entry_GT f3867_0_entry_GT: 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 = x25x26 = x26x27 = x27x28 = x28x29 = x29x30 = x30
f4209_0_removeLastOccurrence_EQ f4209_0_removeLastOccurrence_EQ f4209_0_removeLastOccurrence_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 = x25x26 = x26x27 = x27x28 = x28x29 = x29x30 = x30
f4558_0_remove_FieldAccess f4558_0_remove_FieldAccess f4558_0_remove_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 = x25x26 = x26x27 = x27x28 = x28x29 = x29x30 = x30
f3688_0_remove_FieldAccess f3688_0_remove_FieldAccess f3688_0_remove_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 = x25x26 = x26x27 = x27x28 = x28x29 = x29x30 = x30
f996_0_createList_Load f996_0_createList_Load f996_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 = x25x26 = x26x27 = x27x28 = x28x29 = x29x30 = x30
f4556_0_remove_FieldAccess f4556_0_remove_FieldAccess f4556_0_remove_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 = x25x26 = x26x27 = x27x28 = x28x29 = x29x30 = x30
f4640_0_removeLastOccurrence_EQ f4640_0_removeLastOccurrence_EQ f4640_0_removeLastOccurrence_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 = x25x26 = x26x27 = x27x28 = x28x29 = x29x30 = x30
f4472_0_remove_FieldAccess f4472_0_remove_FieldAccess f4472_0_remove_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 = x25x26 = x26x27 = x27x28 = x28x29 = x29x30 = x30
f3629_0_entry_LE f3629_0_entry_LE f3629_0_entry_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 = x25x26 = x26x27 = x27x28 = x28x29 = x29x30 = x30
f3453_0_equals_Return f3453_0_equals_Return f3453_0_equals_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 = x25x26 = x26x27 = x27x28 = x28x29 = x29x30 = x30
f3808_0_remove_FieldAccess f3808_0_remove_FieldAccess f3808_0_remove_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 = x25x26 = x26x27 = x27x28 = x28x29 = x29x30 = x30
f4279_0_removeLastOccurrence_EQ f4279_0_removeLastOccurrence_EQ f4279_0_removeLastOccurrence_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 = x25x26 = x26x27 = x27x28 = x28x29 = x29x30 = x30
f3709_0_remove_FieldAccess f3709_0_remove_FieldAccess f3709_0_remove_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 = x25x26 = x26x27 = x27x28 = x28x29 = x29x30 = x30
f4278_0_removeLastOccurrence_EQ f4278_0_removeLastOccurrence_EQ f4278_0_removeLastOccurrence_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 = x25x26 = x26x27 = x27x28 = x28x29 = x29x30 = x30
f4210_0_removeLastOccurrence_EQ f4210_0_removeLastOccurrence_EQ f4210_0_removeLastOccurrence_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 = x25x26 = x26x27 = x27x28 = x28x29 = x29x30 = x30
f2820_0_random_ArrayAccess f2820_0_random_ArrayAccess f2820_0_random_ArrayAccess: 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 = x25x26 = x26x27 = x27x28 = x28x29 = x29x30 = x30
f3446_0_equals_Return f3446_0_equals_Return f3446_0_equals_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 = x25x26 = x26x27 = x27x28 = x28x29 = x29x30 = x30
f3798_0_remove_FieldAccess f3798_0_remove_FieldAccess f3798_0_remove_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 = x25x26 = x26x27 = x27x28 = x28x29 = x29x30 = x30
f3689_0_remove_FieldAccess f3689_0_remove_FieldAccess f3689_0_remove_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 = x25x26 = x26x27 = x27x28 = x28x29 = x29x30 = x30
f4643_0_removeLastOccurrence_EQ f4643_0_removeLastOccurrence_EQ f4643_0_removeLastOccurrence_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 = x25x26 = x26x27 = x27x28 = x28x29 = x29x30 = x30
f3356_0_removeLastOccurrence_EQ f3356_0_removeLastOccurrence_EQ f3356_0_removeLastOccurrence_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 = x25x26 = x26x27 = x27x28 = x28x29 = x29x30 = x30
f522_0_createList_Load f522_0_createList_Load f522_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 = x25x26 = x26x27 = x27x28 = x28x29 = x29x30 = x30
f3439_0_equals_Return f3439_0_equals_Return f3439_0_equals_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 = x25x26 = x26x27 = x27x28 = x28x29 = x29x30 = x30
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 = x25x26 = x26x27 = x27x28 = x28x29 = x29x30 = x30
and for every transition t, a duplicate t is considered.

2 SCC Decomposition

We consider subproblems for each of the 9 SCC(s) of the program graph.

2.1 SCC Subproblem 1/9

Here we consider the SCC { f3867_0_entry_GT }.

2.1.1 Transition Removal

We remove transitions 53, 54, 55, 56, 57 using the following ranking functions, which are bounded by 0.

f3867_0_entry_GT: x4 + x5

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 2/9

Here we consider the SCC { f3629_0_entry_LE }.

2.2.1 Transition Removal

We remove transitions 30, 31, 32, 33, 34 using the following ranking functions, which are bounded by 0.

f3629_0_entry_LE: x5 + x4

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 3/9

Here we consider the SCC { f4642_0_removeLastOccurrence_EQ, f4643_0_removeLastOccurrence_EQ, f4279_0_removeLastOccurrence_EQ }.

2.3.1 Transition Removal

We remove transitions 87, 88, 94, 93, 96 using the following ranking functions, which are bounded by 0.

f4279_0_removeLastOccurrence_EQ: −2 + x7 + x9
f4642_0_removeLastOccurrence_EQ: −2 + x7 + x9
f4643_0_removeLastOccurrence_EQ: −1 − x4 + x5 + x7

2.3.2 Transition Removal

We remove transition 95 using the following ranking functions, which are bounded by 0.

f4642_0_removeLastOccurrence_EQ: −2 + 0⋅x4 + x7 + x9
f4279_0_removeLastOccurrence_EQ: −2 + x7 + x9
f4643_0_removeLastOccurrence_EQ: −2 + 0⋅x4 + x5 + x7

2.3.3 Transition Removal

We remove transitions 99, 100 using the following ranking functions, which are bounded by 0.

f4642_0_removeLastOccurrence_EQ: 0⋅x4
f4279_0_removeLastOccurrence_EQ: −1
f4643_0_removeLastOccurrence_EQ: 0⋅x4

2.3.4 Trivial Cooperation Program

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

2.4 SCC Subproblem 4/9

Here we consider the SCC { f4640_0_removeLastOccurrence_EQ, f4641_0_removeLastOccurrence_EQ, f4278_0_removeLastOccurrence_EQ }.

2.4.1 Transition Removal

We remove transitions 85, 86, 90, 89, 92 using the following ranking functions, which are bounded by 0.

f4278_0_removeLastOccurrence_EQ: −2 + x7 + x9
f4640_0_removeLastOccurrence_EQ: −2 + x7 + x9
f4641_0_removeLastOccurrence_EQ: −1 − x4 + x5 + x7

2.4.2 Transition Removal

We remove transition 91 using the following ranking functions, which are bounded by 0.

f4640_0_removeLastOccurrence_EQ: −2 + 0⋅x4 + x7 + x9
f4278_0_removeLastOccurrence_EQ: −2 + x7 + x9
f4641_0_removeLastOccurrence_EQ: −2 + 0⋅x4 + x5 + x7

2.4.3 Transition Removal

We remove transitions 97, 98 using the following ranking functions, which are bounded by 0.

f4640_0_removeLastOccurrence_EQ: 0⋅x4
f4278_0_removeLastOccurrence_EQ: −1
f4641_0_removeLastOccurrence_EQ: 0⋅x4

2.4.4 Trivial Cooperation Program

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

2.5 SCC Subproblem 5/9

Here we consider the SCC { f4210_0_removeLastOccurrence_EQ }.

2.5.1 Transition Removal

We remove transitions 64, 65 using the following ranking functions, which are bounded by 0.

f4210_0_removeLastOccurrence_EQ: x5

2.5.2 Trivial Cooperation Program

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

2.6 SCC Subproblem 6/9

Here we consider the SCC { f4209_0_removeLastOccurrence_EQ }.

2.6.1 Transition Removal

We remove transitions 62, 63 using the following ranking functions, which are bounded by 0.

f4209_0_removeLastOccurrence_EQ: x5

2.6.2 Trivial Cooperation Program

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

2.7 SCC Subproblem 7/9

Here we consider the SCC { f3356_0_removeLastOccurrence_EQ, f3460_0_equals_Return, f3453_0_equals_Return }.

2.7.1 Transition Removal

We remove transitions 14, 15, 17, 16, 79, 80 using the following ranking functions, which are bounded by 0.

f3356_0_removeLastOccurrence_EQ: −3 + x6 + x8
f3453_0_equals_Return: −3 + x7 + x9
f3460_0_equals_Return: −3 + x5 + x7

2.7.2 Transition Removal

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

f3453_0_equals_Return: 0
f3356_0_removeLastOccurrence_EQ: −1
f3460_0_equals_Return: 0

2.7.3 Trivial Cooperation Program

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

2.8 SCC Subproblem 8/9

Here we consider the SCC { f3446_0_equals_Return, f3355_0_removeLastOccurrence_EQ, f3439_0_equals_Return }.

2.8.1 Transition Removal

We remove transitions 10, 11, 12, 77, 78 using the following ranking functions, which are bounded by 0.

f3355_0_removeLastOccurrence_EQ: 2⋅x6 + 2⋅x8 − 1
f3439_0_equals_Return: 2⋅x9 + 2⋅x7
f3446_0_equals_Return: 2⋅x5 + 2⋅x7

2.8.2 Transition Removal

We remove transitions 22, 23, 13 using the following ranking functions, which are bounded by −8.

f3439_0_equals_Return: x2 − 8
f3355_0_removeLastOccurrence_EQ: −8
f3446_0_equals_Return: −16⋅x4

2.8.3 Trivial Cooperation Program

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

2.9 SCC Subproblem 9/9

Here we consider the SCC { f2700_0_createList_LE }.

2.9.1 Transition Removal

We remove transitions 107, 108 using the following ranking functions, which are bounded by 0.

f2700_0_createList_LE: x2

2.9.2 Trivial Cooperation Program

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

Tool configuration

AProVE