# LTS Termination Proof

by AProVE

## Input

Integer Transition System
• Transitions: (pre-variables and post-variables)  f309_0_createList_Load 1 f510_0_createList_Load: x1 = _arg1 ∧ x2 = _arg2 ∧ x3 = _arg3 ∧ x4 = _arg4 ∧ x5 = _arg5 ∧ x6 = _arg6 ∧ x7 = _arg7 ∧ x8 = _arg8 ∧ x9 = _arg9 ∧ x10 = _arg10 ∧ x11 = _arg11 ∧ x12 = _arg12 ∧ x13 = _arg13 ∧ x14 = _arg14 ∧ x15 = _arg15 ∧ x16 = _arg16 ∧ x17 = _arg17 ∧ x18 = _arg18 ∧ x19 = _arg19 ∧ x20 = _arg20 ∧ x1 = _arg1P ∧ x2 = _arg2P ∧ x3 = _arg3P ∧ x4 = _arg4P ∧ x5 = _arg5P ∧ x6 = _arg6P ∧ x7 = _arg7P ∧ x8 = _arg8P ∧ x9 = _arg9P ∧ x10 = _arg10P ∧ x11 = _arg11P ∧ x12 = _arg12P ∧ x13 = _arg13P ∧ x14 = _arg14P ∧ x15 = _arg15P ∧ x16 = _arg16P ∧ x17 = _arg17P ∧ x18 = _arg18P ∧ x19 = _arg19P ∧ x20 = _arg20P ∧ _arg7 = _arg19P ∧ _arg6 = _arg18P ∧ _arg5 = _arg17P ∧ _arg4 = _arg15P ∧ _arg4 = _arg14P ∧ _arg3 = _arg13P ∧ 0 = _arg9P ∧ 0 = _arg8P ∧ 0 = _arg7P ∧ _arg3 = _arg5P ∧ 0 = _arg4P ∧ 0 = _arg3P ∧ _arg1 = _arg1P ∧ _arg6 + 5 ≤ _arg2 ∧ _arg7 + 3 ≤ _arg2 ∧ 9 ≤ _arg2P − 1 ∧ 9 ≤ _arg2 − 1 ∧ _arg2P ≤ _arg2 f1_0_main_Load 2 f309_0_createList_Load: x1 = _x ∧ x2 = _x1 ∧ x3 = _x2 ∧ x4 = _x3 ∧ x5 = _x4 ∧ x6 = _x5 ∧ x7 = _x6 ∧ x8 = _x7 ∧ x9 = _x8 ∧ x10 = _x9 ∧ x11 = _x10 ∧ x12 = _x11 ∧ x13 = _x12 ∧ x14 = _x13 ∧ x15 = _x14 ∧ x16 = _x15 ∧ x17 = _x16 ∧ x18 = _x17 ∧ x19 = _x18 ∧ x20 = _x19 ∧ x1 = _x20 ∧ x2 = _x21 ∧ x3 = _x22 ∧ x4 = _x23 ∧ x5 = _x24 ∧ x6 = _x25 ∧ x7 = _x26 ∧ x8 = _x27 ∧ x9 = _x28 ∧ x10 = _x29 ∧ x11 = _x30 ∧ x12 = _x31 ∧ x13 = _x32 ∧ x14 = _x33 ∧ x15 = _x34 ∧ x16 = _x35 ∧ x17 = _x36 ∧ x18 = _x37 ∧ x19 = _x38 ∧ x20 = _x39 ∧ 0 = _x26 ∧ 0 = _x25 ∧ 1 = _x24 ∧ 7 ≤ _x21 − 1 ∧ 0 ≤ _x − 1 ∧ _x21 − 7 ≤ _x ∧ 0 ≤ _x1 − 1 ∧ −1 ≤ _x20 − 1 f510_0_createList_Load 3 f673_0_createList_LE: x1 = _x40 ∧ x2 = _x42 ∧ x3 = _x43 ∧ x4 = _x44 ∧ x5 = _x45 ∧ x6 = _x46 ∧ x7 = _x47 ∧ x8 = _x48 ∧ x9 = _x49 ∧ x10 = _x50 ∧ x11 = _x51 ∧ x12 = _x52 ∧ x13 = _x53 ∧ x14 = _x54 ∧ x15 = _x55 ∧ x16 = _x56 ∧ x17 = _x57 ∧ x18 = _x58 ∧ x19 = _x59 ∧ x20 = _x60 ∧ x1 = _x61 ∧ x2 = _x62 ∧ x3 = _x63 ∧ x4 = _x64 ∧ x5 = _x65 ∧ x6 = _x66 ∧ x7 = _x67 ∧ x8 = _x68 ∧ x9 = _x69 ∧ x10 = _x70 ∧ x11 = _x71 ∧ x12 = _x72 ∧ x13 = _x73 ∧ x14 = _x74 ∧ x15 = _x75 ∧ x16 = _x77 ∧ x17 = _x78 ∧ x18 = _x79 ∧ x19 = _x80 ∧ x20 = _x81 ∧ _x59 = _x81 ∧ _x58 = _x80 ∧ _x57 = _x77 ∧ _x55 = _x75 ∧ _x54 = _x74 ∧ _x53 = _x73 ∧ _x52 = _x72 ∧ _x49 = _x71 ∧ _x48 = _x70 ∧ _x47 = _x69 ∧ _x46 = _x68 ∧ _x43 = _x67 ∧ _x50 = _x66 ∧ _x51 = _x65 ∧ _x45 = _x64 ∧ _x44 = _x63 ∧ _x40 = _x62 ∧ _x58 + 5 ≤ _x42 ∧ _x59 + 3 ≤ _x42 ∧ 11 ≤ _x61 − 1 ∧ 11 ≤ _x42 − 1 f673_0_createList_LE 4 f673_0_createList_LE: x1 = _x82 ∧ x2 = _x83 ∧ x3 = _x84 ∧ x4 = _x85 ∧ x5 = _x86 ∧ x6 = _x87 ∧ x7 = _x88 ∧ x8 = _x89 ∧ x9 = _x90 ∧ x10 = _x91 ∧ x11 = _x92 ∧ x12 = _x93 ∧ x13 = _x94 ∧ x14 = _x95 ∧ x15 = _x96 ∧ x16 = _x97 ∧ x17 = _x98 ∧ x18 = _x99 ∧ x19 = _x100 ∧ x20 = _x101 ∧ x1 = _x102 ∧ x2 = _x103 ∧ x3 = _x104 ∧ x4 = _x105 ∧ x5 = _x106 ∧ x6 = _x107 ∧ x7 = _x108 ∧ x8 = _x109 ∧ x9 = _x110 ∧ x10 = _x111 ∧ x11 = _x112 ∧ x12 = _x113 ∧ x13 = _x114 ∧ x14 = _x115 ∧ x15 = _x116 ∧ x16 = _x117 ∧ x17 = _x118 ∧ x18 = _x119 ∧ x19 = _x120 ∧ x20 = _x121 ∧ 0 ≤ _x83 − 1 ∧ −1 ≤ _x122 − 1 ∧ 0 ≤ _x97 − 1 ∧ _x97 ≤ _x122 − 1 ∧ 0 ≤ _x85 − 1 ∧ 0 ≤ _x84 − 1 ∧ 0 ≤ _x88 − 1 ∧ 0 ≤ _x87 − 1 ∧ 0 ≤ _x86 − 1 ∧ 0 ≤ _x96 − 1 ∧ −1 ≤ _x123 − 1 ∧ 0 ≤ _x90 − 1 ∧ 0 ≤ _x93 − 1 ∧ 0 ≤ _x91 − 1 ∧ 0 ≤ _x95 − 1 ∧ 0 ≤ _x94 − 1 ∧ 0 ≤ _x92 − 1 ∧ 0 ≤ _x89 − 1 ∧ −1 ≤ _x101 − 1 ∧ −1 ≤ _x100 − 1 ∧ 11 ≤ _x82 − 1 ∧ 11 ≤ _x102 − 1 ∧ _x98 + 11 ≤ _x82 ∧ _x99 + 9 ≤ _x82 ∧ _x101 + 3 ≤ _x82 ∧ _x100 + 5 ≤ _x82 ∧ _x83 − 1 = _x103 ∧ _x84 = _x104 ∧ _x85 = _x105 ∧ _x97 + 1 = _x117 ∧ _x100 + 1 = _x120 ∧ _x101 + 1 = _x121 __init 5 f1_0_main_Load: x1 = _x124 ∧ x2 = _x125 ∧ x3 = _x126 ∧ x4 = _x127 ∧ x5 = _x128 ∧ x6 = _x129 ∧ x7 = _x130 ∧ x8 = _x131 ∧ x9 = _x132 ∧ x10 = _x133 ∧ x11 = _x134 ∧ x12 = _x135 ∧ x13 = _x136 ∧ x14 = _x137 ∧ x15 = _x138 ∧ x16 = _x139 ∧ x17 = _x140 ∧ x18 = _x141 ∧ x19 = _x142 ∧ x20 = _x143 ∧ x1 = _x144 ∧ x2 = _x145 ∧ x3 = _x146 ∧ x4 = _x147 ∧ x5 = _x148 ∧ x6 = _x149 ∧ x7 = _x150 ∧ x8 = _x151 ∧ x9 = _x152 ∧ x10 = _x153 ∧ x11 = _x154 ∧ x12 = _x155 ∧ x13 = _x156 ∧ x14 = _x157 ∧ x15 = _x158 ∧ x16 = _x159 ∧ x17 = _x160 ∧ x18 = _x161 ∧ x19 = _x162 ∧ x20 = _x163 ∧ 0 ≤ 0

## Proof

### 1 Switch to Cooperation Termination Proof

We consider the following cutpoint-transitions:
 f673_0_createList_LE f673_0_createList_LE f673_0_createList_LE: x1 = x1 ∧ x2 = x2 ∧ x3 = x3 ∧ x4 = x4 ∧ x5 = x5 ∧ x6 = x6 ∧ x7 = x7 ∧ x8 = x8 ∧ x9 = x9 ∧ x10 = x10 ∧ x11 = x11 ∧ x12 = x12 ∧ x13 = x13 ∧ x14 = x14 ∧ x15 = x15 ∧ x16 = x16 ∧ x17 = x17 ∧ x18 = x18 ∧ x19 = x19 ∧ x20 = x20 f309_0_createList_Load f309_0_createList_Load f309_0_createList_Load: x1 = x1 ∧ x2 = x2 ∧ x3 = x3 ∧ x4 = x4 ∧ x5 = x5 ∧ x6 = x6 ∧ x7 = x7 ∧ x8 = x8 ∧ x9 = x9 ∧ x10 = x10 ∧ x11 = x11 ∧ x12 = x12 ∧ x13 = x13 ∧ x14 = x14 ∧ x15 = x15 ∧ x16 = x16 ∧ x17 = x17 ∧ x18 = x18 ∧ x19 = x19 ∧ x20 = x20 f510_0_createList_Load f510_0_createList_Load f510_0_createList_Load: x1 = x1 ∧ x2 = x2 ∧ x3 = x3 ∧ x4 = x4 ∧ x5 = x5 ∧ x6 = x6 ∧ x7 = x7 ∧ x8 = x8 ∧ x9 = x9 ∧ x10 = x10 ∧ x11 = x11 ∧ x12 = x12 ∧ x13 = x13 ∧ x14 = x14 ∧ x15 = x15 ∧ x16 = x16 ∧ x17 = x17 ∧ x18 = x18 ∧ x19 = x19 ∧ x20 = x20 f1_0_main_Load f1_0_main_Load f1_0_main_Load: x1 = x1 ∧ x2 = x2 ∧ x3 = x3 ∧ x4 = x4 ∧ x5 = x5 ∧ x6 = x6 ∧ x7 = x7 ∧ x8 = x8 ∧ x9 = x9 ∧ x10 = x10 ∧ x11 = x11 ∧ x12 = x12 ∧ x13 = x13 ∧ x14 = x14 ∧ x15 = x15 ∧ x16 = x16 ∧ x17 = x17 ∧ x18 = x18 ∧ x19 = x19 ∧ x20 = x20 __init __init __init: x1 = x1 ∧ x2 = x2 ∧ x3 = x3 ∧ x4 = x4 ∧ x5 = x5 ∧ x6 = x6 ∧ x7 = x7 ∧ x8 = x8 ∧ x9 = x9 ∧ x10 = x10 ∧ x11 = x11 ∧ x12 = x12 ∧ x13 = x13 ∧ x14 = x14 ∧ x15 = x15 ∧ x16 = x16 ∧ x17 = x17 ∧ x18 = x18 ∧ x19 = x19 ∧ x20 = x20
and for every transition t, a duplicate t is considered.

### 2 SCC Decomposition

We consider subproblems for each of the 1 SCC(s) of the program graph.

### 2.1 SCC Subproblem 1/1

Here we consider the SCC { f673_0_createList_LE }.

### 2.1.1 Transition Removal

We remove transition 4 using the following ranking functions, which are bounded by 0.

 f673_0_createList_LE: x2

### 2.1.2 Trivial Cooperation Program

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

## Tool configuration

AProVE

• version: AProVE Commit ID: unknown
• strategy: Statistics for single proof: 100.00 % (4 real / 0 unknown / 0 assumptions / 4 total proof steps)