LTS Termination Proof

Input

Integer Transition System

Initial Location: f218_0_test_LE, f134_0_test_LE, f162_0_test_LE, f176_0_test_LE, __init, f92_0_test_LE, f148_0_test_LE, f190_0_test_LE, f31_0_main_Cmp, f43_0_main_GE, f78_0_test_LE, f120_0_test_LE, f1_0_main_Load, f106_0_test_LE, f64_0_test_LE, f204_0_test_LE

Transitions: (pre-variables and post-variables)

f1_0_main_Load	1	f31_0_main_Cmp:	x1 = _arg1 ∧ x2 = _arg2 ∧ x3 = _arg3 ∧ x1 = _arg1P ∧ x2 = _arg2P ∧ x3 = _arg3P ∧ _arg2 = _arg1P ∧ −1 ≤ _arg2 − 1 ∧ 0 ≤ _arg1 − 1
f31_0_main_Cmp	2	f43_0_main_GE:	x1 = _x ∧ x2 = _x1 ∧ x3 = _x2 ∧ x1 = _x3 ∧ x2 = _x4 ∧ x3 = _x5 ∧ _x = _x5 ∧ _x = _x4 ∧ _x = _x3
f43_0_main_GE	3	f31_0_main_Cmp:	x1 = _x6 ∧ x2 = _x7 ∧ x3 = _x8 ∧ x1 = _x9 ∧ x2 = _x10 ∧ x3 = _x11 ∧ _x6 − 1 = _x9 ∧ _x7 = _x8 ∧ 99 ≤ _x7 − 1 ∧ 0 ≤ _x6 − 1
f43_0_main_GE	4	f43_0_main_GE:	x1 = _x12 ∧ x2 = _x13 ∧ x3 = _x14 ∧ x1 = _x15 ∧ x2 = _x16 ∧ x3 = _x17 ∧ _x13 + 1 = _x17 ∧ _x13 + 1 = _x16 ∧ _x12 = _x15 ∧ _x13 = _x14 ∧ _x13 ≤ 99 ∧ 0 ≤ _x13 − 1
f43_0_main_GE	5	f64_0_test_LE:	x1 = _x18 ∧ x2 = _x19 ∧ x3 = _x20 ∧ x1 = _x21 ∧ x2 = _x22 ∧ x3 = _x23 ∧ _x19 = _x23 ∧ _x19 = _x22 ∧ _x19 = _x21 ∧ _x19 = _x20 ∧ _x19 ≤ 99 ∧ 0 ≤ _x19 − 1
f64_0_test_LE	6	f64_0_test_LE:	x1 = _x24 ∧ x2 = _x25 ∧ x3 = _x26 ∧ x1 = _x27 ∧ x2 = _x28 ∧ x3 = _x29 ∧ _x25 − 1 = _x29 ∧ _x25 − 1 = _x28 ∧ _x24 = _x27 ∧ _x25 = _x26 ∧ 0 ≤ _x25 − 1
f64_0_test_LE	7	f78_0_test_LE:	x1 = _x30 ∧ x2 = _x31 ∧ x3 = _x32 ∧ x1 = _x33 ∧ x2 = _x34 ∧ x3 = _x35 ∧ _x30 = _x35 ∧ _x30 = _x34 ∧ _x30 = _x33 ∧ 0 = _x32 ∧ 0 = _x31
f78_0_test_LE	8	f78_0_test_LE:	x1 = _x36 ∧ x2 = _x37 ∧ x3 = _x38 ∧ x1 = _x39 ∧ x2 = _x40 ∧ x3 = _x41 ∧ _x37 − 1 = _x41 ∧ _x37 − 1 = _x40 ∧ _x36 = _x39 ∧ _x37 = _x38 ∧ 0 ≤ _x37 − 1
f78_0_test_LE	9	f92_0_test_LE:	x1 = _x42 ∧ x2 = _x43 ∧ x3 = _x44 ∧ x1 = _x45 ∧ x2 = _x46 ∧ x3 = _x47 ∧ _x42 = _x47 ∧ _x42 = _x46 ∧ _x42 = _x45 ∧ 0 = _x44 ∧ 0 = _x43
f92_0_test_LE	10	f92_0_test_LE:	x1 = _x48 ∧ x2 = _x49 ∧ x3 = _x50 ∧ x1 = _x51 ∧ x2 = _x52 ∧ x3 = _x53 ∧ _x49 − 1 = _x53 ∧ _x49 − 1 = _x52 ∧ _x48 = _x51 ∧ _x49 = _x50 ∧ 0 ≤ _x49 − 1
f92_0_test_LE	11	f106_0_test_LE:	x1 = _x54 ∧ x2 = _x55 ∧ x3 = _x56 ∧ x1 = _x57 ∧ x2 = _x58 ∧ x3 = _x59 ∧ _x54 = _x59 ∧ _x54 = _x58 ∧ _x54 = _x57 ∧ 0 = _x56 ∧ 0 = _x55
f106_0_test_LE	12	f106_0_test_LE:	x1 = _x60 ∧ x2 = _x61 ∧ x3 = _x62 ∧ x1 = _x63 ∧ x2 = _x64 ∧ x3 = _x65 ∧ _x61 − 1 = _x65 ∧ _x61 − 1 = _x64 ∧ _x60 = _x63 ∧ _x61 = _x62 ∧ 0 ≤ _x61 − 1
f106_0_test_LE	13	f120_0_test_LE:	x1 = _x66 ∧ x2 = _x67 ∧ x3 = _x68 ∧ x1 = _x69 ∧ x2 = _x70 ∧ x3 = _x71 ∧ _x66 = _x71 ∧ _x66 = _x70 ∧ _x66 = _x69 ∧ 0 = _x68 ∧ 0 = _x67
f120_0_test_LE	14	f120_0_test_LE:	x1 = _x72 ∧ x2 = _x73 ∧ x3 = _x74 ∧ x1 = _x75 ∧ x2 = _x76 ∧ x3 = _x77 ∧ _x73 − 1 = _x77 ∧ _x73 − 1 = _x76 ∧ _x72 = _x75 ∧ _x73 = _x74 ∧ 0 ≤ _x73 − 1
f120_0_test_LE	15	f134_0_test_LE:	x1 = _x78 ∧ x2 = _x79 ∧ x3 = _x80 ∧ x1 = _x81 ∧ x2 = _x82 ∧ x3 = _x83 ∧ _x78 = _x83 ∧ _x78 = _x82 ∧ _x78 = _x81 ∧ 0 = _x80 ∧ 0 = _x79
f134_0_test_LE	16	f134_0_test_LE:	x1 = _x84 ∧ x2 = _x85 ∧ x3 = _x86 ∧ x1 = _x87 ∧ x2 = _x88 ∧ x3 = _x89 ∧ _x85 − 1 = _x89 ∧ _x85 − 1 = _x88 ∧ _x84 = _x87 ∧ _x85 = _x86 ∧ 0 ≤ _x85 − 1
f134_0_test_LE	17	f148_0_test_LE:	x1 = _x90 ∧ x2 = _x91 ∧ x3 = _x92 ∧ x1 = _x93 ∧ x2 = _x94 ∧ x3 = _x95 ∧ _x90 = _x95 ∧ _x90 = _x94 ∧ _x90 = _x93 ∧ 0 = _x92 ∧ 0 = _x91
f148_0_test_LE	18	f148_0_test_LE:	x1 = _x96 ∧ x2 = _x97 ∧ x3 = _x98 ∧ x1 = _x99 ∧ x2 = _x100 ∧ x3 = _x101 ∧ _x97 − 1 = _x101 ∧ _x97 − 1 = _x100 ∧ _x96 = _x99 ∧ _x97 = _x98 ∧ 0 ≤ _x97 − 1
f148_0_test_LE	19	f162_0_test_LE:	x1 = _x102 ∧ x2 = _x103 ∧ x3 = _x104 ∧ x1 = _x105 ∧ x2 = _x106 ∧ x3 = _x107 ∧ _x102 = _x107 ∧ _x102 = _x106 ∧ _x102 = _x105 ∧ 0 = _x104 ∧ 0 = _x103
f162_0_test_LE	20	f162_0_test_LE:	x1 = _x108 ∧ x2 = _x109 ∧ x3 = _x110 ∧ x1 = _x111 ∧ x2 = _x112 ∧ x3 = _x113 ∧ _x109 − 1 = _x113 ∧ _x109 − 1 = _x112 ∧ _x108 = _x111 ∧ _x109 = _x110 ∧ 0 ≤ _x109 − 1
f162_0_test_LE	21	f176_0_test_LE:	x1 = _x114 ∧ x2 = _x115 ∧ x3 = _x116 ∧ x1 = _x117 ∧ x2 = _x118 ∧ x3 = _x119 ∧ _x114 = _x119 ∧ _x114 = _x118 ∧ _x114 = _x117 ∧ 0 = _x116 ∧ 0 = _x115
f176_0_test_LE	22	f176_0_test_LE:	x1 = _x120 ∧ x2 = _x121 ∧ x3 = _x122 ∧ x1 = _x123 ∧ x2 = _x124 ∧ x3 = _x125 ∧ _x121 − 1 = _x125 ∧ _x121 − 1 = _x124 ∧ _x120 = _x123 ∧ _x121 = _x122 ∧ 0 ≤ _x121 − 1
f176_0_test_LE	23	f190_0_test_LE:	x1 = _x126 ∧ x2 = _x127 ∧ x3 = _x128 ∧ x1 = _x129 ∧ x2 = _x130 ∧ x3 = _x131 ∧ _x126 = _x131 ∧ _x126 = _x130 ∧ _x126 = _x129 ∧ 0 = _x128 ∧ 0 = _x127
f190_0_test_LE	24	f190_0_test_LE:	x1 = _x132 ∧ x2 = _x133 ∧ x3 = _x134 ∧ x1 = _x135 ∧ x2 = _x136 ∧ x3 = _x137 ∧ _x133 − 1 = _x137 ∧ _x133 − 1 = _x136 ∧ _x132 = _x135 ∧ _x133 = _x134 ∧ 0 ≤ _x133 − 1
f190_0_test_LE	25	f204_0_test_LE:	x1 = _x138 ∧ x2 = _x139 ∧ x3 = _x140 ∧ x1 = _x141 ∧ x2 = _x142 ∧ x3 = _x143 ∧ _x138 = _x143 ∧ _x138 = _x142 ∧ _x138 = _x141 ∧ 0 = _x140 ∧ 0 = _x139
f204_0_test_LE	26	f204_0_test_LE:	x1 = _x144 ∧ x2 = _x145 ∧ x3 = _x146 ∧ x1 = _x147 ∧ x2 = _x148 ∧ x3 = _x149 ∧ _x145 − 1 = _x149 ∧ _x145 − 1 = _x148 ∧ _x144 = _x147 ∧ _x145 = _x146 ∧ 0 ≤ _x145 − 1
f204_0_test_LE	27	f218_0_test_LE:	x1 = _x150 ∧ x2 = _x151 ∧ x3 = _x152 ∧ x1 = _x153 ∧ x2 = _x154 ∧ x3 = _x155 ∧ _x150 = _x153 ∧ 0 = _x152 ∧ 0 = _x151
f218_0_test_LE	28	f218_0_test_LE:	x1 = _x156 ∧ x2 = _x157 ∧ x3 = _x158 ∧ x1 = _x159 ∧ x2 = _x160 ∧ x3 = _x161 ∧ _x156 − 1 = _x159 ∧ 0 ≤ _x156 − 1
__init	29	f1_0_main_Load:	x1 = _x162 ∧ x2 = _x163 ∧ x3 = _x164 ∧ x1 = _x165 ∧ x2 = _x166 ∧ x3 = _x167 ∧ 0 ≤ 0

Proof

1 Switch to Cooperation Termination Proof

We consider the following cutpoint-transitions:

f218_0_test_LE	f218_0_test_LE	f218_0_test_LE:	x1 = x1 ∧ x2 = x2 ∧ x3 = x3
f134_0_test_LE	f134_0_test_LE	f134_0_test_LE:	x1 = x1 ∧ x2 = x2 ∧ x3 = x3
f162_0_test_LE	f162_0_test_LE	f162_0_test_LE:	x1 = x1 ∧ x2 = x2 ∧ x3 = x3
f176_0_test_LE	f176_0_test_LE	f176_0_test_LE:	x1 = x1 ∧ x2 = x2 ∧ x3 = x3
__init	__init	__init:	x1 = x1 ∧ x2 = x2 ∧ x3 = x3
f92_0_test_LE	f92_0_test_LE	f92_0_test_LE:	x1 = x1 ∧ x2 = x2 ∧ x3 = x3
f148_0_test_LE	f148_0_test_LE	f148_0_test_LE:	x1 = x1 ∧ x2 = x2 ∧ x3 = x3
f190_0_test_LE	f190_0_test_LE	f190_0_test_LE:	x1 = x1 ∧ x2 = x2 ∧ x3 = x3
f31_0_main_Cmp	f31_0_main_Cmp	f31_0_main_Cmp:	x1 = x1 ∧ x2 = x2 ∧ x3 = x3
f43_0_main_GE	f43_0_main_GE	f43_0_main_GE:	x1 = x1 ∧ x2 = x2 ∧ x3 = x3
f78_0_test_LE	f78_0_test_LE	f78_0_test_LE:	x1 = x1 ∧ x2 = x2 ∧ x3 = x3
f120_0_test_LE	f120_0_test_LE	f120_0_test_LE:	x1 = x1 ∧ x2 = x2 ∧ x3 = x3
f1_0_main_Load	f1_0_main_Load	f1_0_main_Load:	x1 = x1 ∧ x2 = x2 ∧ x3 = x3
f106_0_test_LE	f106_0_test_LE	f106_0_test_LE:	x1 = x1 ∧ x2 = x2 ∧ x3 = x3
f64_0_test_LE	f64_0_test_LE	f64_0_test_LE:	x1 = x1 ∧ x2 = x2 ∧ x3 = x3
f204_0_test_LE	f204_0_test_LE	f204_0_test_LE:	x1 = x1 ∧ x2 = x2 ∧ x3 = x3

and for every transition t, a duplicate t is considered.

2 SCC Decomposition

We consider subproblems for each of the 13 SCC(s) of the program graph.

2.1 SCC Subproblem 1/13

Here we consider the SCC { f31_0_main_Cmp, f43_0_main_GE }.

2.1.1 Transition Removal

We remove transition 3 using the following ranking functions, which are bounded by 0.

f31_0_main_Cmp:	−1 + x1
f43_0_main_GE:	−1 + x1

2.1.2 Transition Removal

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

f31_0_main_Cmp:	99 − x1
f43_0_main_GE:	99 − x2

2.1.3 Transition Removal

We remove transition 2 using the following ranking functions, which are bounded by 0.

f31_0_main_Cmp:	0
f43_0_main_GE:	−1

2.1.4 Trivial Cooperation Program

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

2.2 SCC Subproblem 2/13

Here we consider the SCC { f64_0_test_LE }.

2.2.1 Transition Removal

We remove transition 6 using the following ranking functions, which are bounded by 0.

f64_0_test_LE:

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 3/13

Here we consider the SCC { f78_0_test_LE }.

2.3.1 Transition Removal

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

f78_0_test_LE:

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 4/13

Here we consider the SCC { f92_0_test_LE }.

2.4.1 Transition Removal

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

f92_0_test_LE:

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 5/13

Here we consider the SCC { f106_0_test_LE }.

2.5.1 Transition Removal

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

f106_0_test_LE:

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 6/13

Here we consider the SCC { f120_0_test_LE }.

2.6.1 Transition Removal

We remove transition 14 using the following ranking functions, which are bounded by 0.

f120_0_test_LE:

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 7/13

Here we consider the SCC { f134_0_test_LE }.

2.7.1 Transition Removal

We remove transition 16 using the following ranking functions, which are bounded by 0.

f134_0_test_LE:

2.7.2 Trivial Cooperation Program

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

2.8 SCC Subproblem 8/13

Here we consider the SCC { f148_0_test_LE }.

2.8.1 Transition Removal

We remove transition 18 using the following ranking functions, which are bounded by 0.

f148_0_test_LE:

2.8.2 Trivial Cooperation Program

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

2.9 SCC Subproblem 9/13

Here we consider the SCC { f162_0_test_LE }.

2.9.1 Transition Removal

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

f162_0_test_LE:

2.9.2 Trivial Cooperation Program

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

2.10 SCC Subproblem 10/13

Here we consider the SCC { f176_0_test_LE }.

2.10.1 Transition Removal

We remove transition 22 using the following ranking functions, which are bounded by 0.

f176_0_test_LE:

2.10.2 Trivial Cooperation Program

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

2.11 SCC Subproblem 11/13

Here we consider the SCC { f190_0_test_LE }.

2.11.1 Transition Removal

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

f190_0_test_LE:

2.11.2 Trivial Cooperation Program

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

2.12 SCC Subproblem 12/13

Here we consider the SCC { f204_0_test_LE }.

2.12.1 Transition Removal

We remove transition 26 using the following ranking functions, which are bounded by 0.

f204_0_test_LE:

2.12.2 Trivial Cooperation Program

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

2.13 SCC Subproblem 13/13

Here we consider the SCC { f218_0_test_LE }.

2.13.1 Transition Removal

We remove transition 28 using the following ranking functions, which are bounded by 0.

f218_0_test_LE:

2.13.2 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 % (32 real / 0 unknown / 0 assumptions / 32 total proof steps)