LTS Termination Proof

by T2Cert

Input

Integer Transition System

Proof

1 Invariant Updates

The following invariants are asserted.

0: TRUE
1: 1 − arg1P ≤ 01 − arg1 ≤ 0
2: 1 − arg1P ≤ 01 − arg2P ≤ 01 − arg1 ≤ 01 − arg2 ≤ 0
3: 1 − arg1P ≤ 01 − arg2P ≤ 01 − arg1 ≤ 01 − arg2 ≤ 0
4: 1 − arg4P ≤ 01 − arg4 ≤ 0
5: 1 − arg3P ≤ 01 − arg3 ≤ 0
6: 1 − arg3P ≤ 01 − arg3 ≤ 0
7: 1 − arg1P ≤ 01 − arg1 ≤ 0
8: TRUE

The invariants are proved as follows.

IMPACT Invariant Proof

2 Switch to Cooperation Termination Proof

We consider the following cutpoint-transitions:
1 25 1: x63 + x63 ≤ 0x63x63 ≤ 0x56 + x56 ≤ 0x56x56 ≤ 0x205 + x205 ≤ 0x205x205 ≤ 0x204 + x204 ≤ 0x204x204 ≤ 0x191 + x191 ≤ 0x191x191 ≤ 0x190 + x190 ≤ 0x190x190 ≤ 0x177 + x177 ≤ 0x177x177 ≤ 0x176 + x176 ≤ 0x176x176 ≤ 0x163 + x163 ≤ 0x163x163 ≤ 0x162 + x162 ≤ 0x162x162 ≤ 0x156 + x156 ≤ 0x156x156 ≤ 0x148 + x148 ≤ 0x148x148 ≤ 0x147 + x147 ≤ 0x147x147 ≤ 0x146 + x146 ≤ 0x146x146 ≤ 0x140 + x140 ≤ 0x140x140 ≤ 0x132 + x132 ≤ 0x132x132 ≤ 0x131 + x131 ≤ 0x131x131 ≤ 0x130 + x130 ≤ 0x130x130 ≤ 0x116 + x116 ≤ 0x116x116 ≤ 0x115 + x115 ≤ 0x115x115 ≤ 0x114 + x114 ≤ 0x114x114 ≤ 0x106 + x106 ≤ 0x106x106 ≤ 0x105 + x105 ≤ 0x105x105 ≤ 0arg7P + arg7P ≤ 0arg7Parg7P ≤ 0arg7 + arg7 ≤ 0arg7arg7 ≤ 0arg6P + arg6P ≤ 0arg6Parg6P ≤ 0arg6 + arg6 ≤ 0arg6arg6 ≤ 0arg5P + arg5P ≤ 0arg5Parg5P ≤ 0arg5 + arg5 ≤ 0arg5arg5 ≤ 0arg4P + arg4P ≤ 0arg4Parg4P ≤ 0arg4 + arg4 ≤ 0arg4arg4 ≤ 0arg3P + arg3P ≤ 0arg3Parg3P ≤ 0arg3 + arg3 ≤ 0arg3arg3 ≤ 0arg2P + arg2P ≤ 0arg2Parg2P ≤ 0arg2 + arg2 ≤ 0arg2arg2 ≤ 0arg1P + arg1P ≤ 0arg1Parg1P ≤ 0arg1 + arg1 ≤ 0arg1arg1 ≤ 0
2 32 2: x63 + x63 ≤ 0x63x63 ≤ 0x56 + x56 ≤ 0x56x56 ≤ 0x205 + x205 ≤ 0x205x205 ≤ 0x204 + x204 ≤ 0x204x204 ≤ 0x191 + x191 ≤ 0x191x191 ≤ 0x190 + x190 ≤ 0x190x190 ≤ 0x177 + x177 ≤ 0x177x177 ≤ 0x176 + x176 ≤ 0x176x176 ≤ 0x163 + x163 ≤ 0x163x163 ≤ 0x162 + x162 ≤ 0x162x162 ≤ 0x156 + x156 ≤ 0x156x156 ≤ 0x148 + x148 ≤ 0x148x148 ≤ 0x147 + x147 ≤ 0x147x147 ≤ 0x146 + x146 ≤ 0x146x146 ≤ 0x140 + x140 ≤ 0x140x140 ≤ 0x132 + x132 ≤ 0x132x132 ≤ 0x131 + x131 ≤ 0x131x131 ≤ 0x130 + x130 ≤ 0x130x130 ≤ 0x116 + x116 ≤ 0x116x116 ≤ 0x115 + x115 ≤ 0x115x115 ≤ 0x114 + x114 ≤ 0x114x114 ≤ 0x106 + x106 ≤ 0x106x106 ≤ 0x105 + x105 ≤ 0x105x105 ≤ 0arg7P + arg7P ≤ 0arg7Parg7P ≤ 0arg7 + arg7 ≤ 0arg7arg7 ≤ 0arg6P + arg6P ≤ 0arg6Parg6P ≤ 0arg6 + arg6 ≤ 0arg6arg6 ≤ 0arg5P + arg5P ≤ 0arg5Parg5P ≤ 0arg5 + arg5 ≤ 0arg5arg5 ≤ 0arg4P + arg4P ≤ 0arg4Parg4P ≤ 0arg4 + arg4 ≤ 0arg4arg4 ≤ 0arg3P + arg3P ≤ 0arg3Parg3P ≤ 0arg3 + arg3 ≤ 0arg3arg3 ≤ 0arg2P + arg2P ≤ 0arg2Parg2P ≤ 0arg2 + arg2 ≤ 0arg2arg2 ≤ 0arg1P + arg1P ≤ 0arg1Parg1P ≤ 0arg1 + arg1 ≤ 0arg1arg1 ≤ 0
5 39 5: x63 + x63 ≤ 0x63x63 ≤ 0x56 + x56 ≤ 0x56x56 ≤ 0x205 + x205 ≤ 0x205x205 ≤ 0x204 + x204 ≤ 0x204x204 ≤ 0x191 + x191 ≤ 0x191x191 ≤ 0x190 + x190 ≤ 0x190x190 ≤ 0x177 + x177 ≤ 0x177x177 ≤ 0x176 + x176 ≤ 0x176x176 ≤ 0x163 + x163 ≤ 0x163x163 ≤ 0x162 + x162 ≤ 0x162x162 ≤ 0x156 + x156 ≤ 0x156x156 ≤ 0x148 + x148 ≤ 0x148x148 ≤ 0x147 + x147 ≤ 0x147x147 ≤ 0x146 + x146 ≤ 0x146x146 ≤ 0x140 + x140 ≤ 0x140x140 ≤ 0x132 + x132 ≤ 0x132x132 ≤ 0x131 + x131 ≤ 0x131x131 ≤ 0x130 + x130 ≤ 0x130x130 ≤ 0x116 + x116 ≤ 0x116x116 ≤ 0x115 + x115 ≤ 0x115x115 ≤ 0x114 + x114 ≤ 0x114x114 ≤ 0x106 + x106 ≤ 0x106x106 ≤ 0x105 + x105 ≤ 0x105x105 ≤ 0arg7P + arg7P ≤ 0arg7Parg7P ≤ 0arg7 + arg7 ≤ 0arg7arg7 ≤ 0arg6P + arg6P ≤ 0arg6Parg6P ≤ 0arg6 + arg6 ≤ 0arg6arg6 ≤ 0arg5P + arg5P ≤ 0arg5Parg5P ≤ 0arg5 + arg5 ≤ 0arg5arg5 ≤ 0arg4P + arg4P ≤ 0arg4Parg4P ≤ 0arg4 + arg4 ≤ 0arg4arg4 ≤ 0arg3P + arg3P ≤ 0arg3Parg3P ≤ 0arg3 + arg3 ≤ 0arg3arg3 ≤ 0arg2P + arg2P ≤ 0arg2Parg2P ≤ 0arg2 + arg2 ≤ 0arg2arg2 ≤ 0arg1P + arg1P ≤ 0arg1Parg1P ≤ 0arg1 + arg1 ≤ 0arg1arg1 ≤ 0
6 46 6: x63 + x63 ≤ 0x63x63 ≤ 0x56 + x56 ≤ 0x56x56 ≤ 0x205 + x205 ≤ 0x205x205 ≤ 0x204 + x204 ≤ 0x204x204 ≤ 0x191 + x191 ≤ 0x191x191 ≤ 0x190 + x190 ≤ 0x190x190 ≤ 0x177 + x177 ≤ 0x177x177 ≤ 0x176 + x176 ≤ 0x176x176 ≤ 0x163 + x163 ≤ 0x163x163 ≤ 0x162 + x162 ≤ 0x162x162 ≤ 0x156 + x156 ≤ 0x156x156 ≤ 0x148 + x148 ≤ 0x148x148 ≤ 0x147 + x147 ≤ 0x147x147 ≤ 0x146 + x146 ≤ 0x146x146 ≤ 0x140 + x140 ≤ 0x140x140 ≤ 0x132 + x132 ≤ 0x132x132 ≤ 0x131 + x131 ≤ 0x131x131 ≤ 0x130 + x130 ≤ 0x130x130 ≤ 0x116 + x116 ≤ 0x116x116 ≤ 0x115 + x115 ≤ 0x115x115 ≤ 0x114 + x114 ≤ 0x114x114 ≤ 0x106 + x106 ≤ 0x106x106 ≤ 0x105 + x105 ≤ 0x105x105 ≤ 0arg7P + arg7P ≤ 0arg7Parg7P ≤ 0arg7 + arg7 ≤ 0arg7arg7 ≤ 0arg6P + arg6P ≤ 0arg6Parg6P ≤ 0arg6 + arg6 ≤ 0arg6arg6 ≤ 0arg5P + arg5P ≤ 0arg5Parg5P ≤ 0arg5 + arg5 ≤ 0arg5arg5 ≤ 0arg4P + arg4P ≤ 0arg4Parg4P ≤ 0arg4 + arg4 ≤ 0arg4arg4 ≤ 0arg3P + arg3P ≤ 0arg3Parg3P ≤ 0arg3 + arg3 ≤ 0arg3arg3 ≤ 0arg2P + arg2P ≤ 0arg2Parg2P ≤ 0arg2 + arg2 ≤ 0arg2arg2 ≤ 0arg1P + arg1P ≤ 0arg1Parg1P ≤ 0arg1 + arg1 ≤ 0arg1arg1 ≤ 0
7 53 7: x63 + x63 ≤ 0x63x63 ≤ 0x56 + x56 ≤ 0x56x56 ≤ 0x205 + x205 ≤ 0x205x205 ≤ 0x204 + x204 ≤ 0x204x204 ≤ 0x191 + x191 ≤ 0x191x191 ≤ 0x190 + x190 ≤ 0x190x190 ≤ 0x177 + x177 ≤ 0x177x177 ≤ 0x176 + x176 ≤ 0x176x176 ≤ 0x163 + x163 ≤ 0x163x163 ≤ 0x162 + x162 ≤ 0x162x162 ≤ 0x156 + x156 ≤ 0x156x156 ≤ 0x148 + x148 ≤ 0x148x148 ≤ 0x147 + x147 ≤ 0x147x147 ≤ 0x146 + x146 ≤ 0x146x146 ≤ 0x140 + x140 ≤ 0x140x140 ≤ 0x132 + x132 ≤ 0x132x132 ≤ 0x131 + x131 ≤ 0x131x131 ≤ 0x130 + x130 ≤ 0x130x130 ≤ 0x116 + x116 ≤ 0x116x116 ≤ 0x115 + x115 ≤ 0x115x115 ≤ 0x114 + x114 ≤ 0x114x114 ≤ 0x106 + x106 ≤ 0x106x106 ≤ 0x105 + x105 ≤ 0x105x105 ≤ 0arg7P + arg7P ≤ 0arg7Parg7P ≤ 0arg7 + arg7 ≤ 0arg7arg7 ≤ 0arg6P + arg6P ≤ 0arg6Parg6P ≤ 0arg6 + arg6 ≤ 0arg6arg6 ≤ 0arg5P + arg5P ≤ 0arg5Parg5P ≤ 0arg5 + arg5 ≤ 0arg5arg5 ≤ 0arg4P + arg4P ≤ 0arg4Parg4P ≤ 0arg4 + arg4 ≤ 0arg4arg4 ≤ 0arg3P + arg3P ≤ 0arg3Parg3P ≤ 0arg3 + arg3 ≤ 0arg3arg3 ≤ 0arg2P + arg2P ≤ 0arg2Parg2P ≤ 0arg2 + arg2 ≤ 0arg2arg2 ≤ 0arg1P + arg1P ≤ 0arg1Parg1P ≤ 0arg1 + arg1 ≤ 0arg1arg1 ≤ 0
and for every transition t, a duplicate t is considered.

3 Transition Removal

We remove transitions 0, 2, 10, 12, 14, 16, 17, 18, 21, 24 using the following ranking functions, which are bounded by −29.

8: 0
0: 0
1: 0
2: 0
3: 0
4: 0
5: 0
6: 0
7: 0
8: −9
0: −10
1: −11
1_var_snapshot: −11
1*: −11
2: −14
3: −14
2_var_snapshot: −14
2*: −14
4: −15
5: −16
5_var_snapshot: −16
5*: −16
6: −19
6_var_snapshot: −19
6*: −19
7: −22
7_var_snapshot: −22
7*: −22

4 Location Addition

The following skip-transition is inserted and corresponding redirections w.r.t. the old location are performed.

1* 28 1: x63 + x63 ≤ 0x63x63 ≤ 0x56 + x56 ≤ 0x56x56 ≤ 0x205 + x205 ≤ 0x205x205 ≤ 0x204 + x204 ≤ 0x204x204 ≤ 0x191 + x191 ≤ 0x191x191 ≤ 0x190 + x190 ≤ 0x190x190 ≤ 0x177 + x177 ≤ 0x177x177 ≤ 0x176 + x176 ≤ 0x176x176 ≤ 0x163 + x163 ≤ 0x163x163 ≤ 0x162 + x162 ≤ 0x162x162 ≤ 0x156 + x156 ≤ 0x156x156 ≤ 0x148 + x148 ≤ 0x148x148 ≤ 0x147 + x147 ≤ 0x147x147 ≤ 0x146 + x146 ≤ 0x146x146 ≤ 0x140 + x140 ≤ 0x140x140 ≤ 0x132 + x132 ≤ 0x132x132 ≤ 0x131 + x131 ≤ 0x131x131 ≤ 0x130 + x130 ≤ 0x130x130 ≤ 0x116 + x116 ≤ 0x116x116 ≤ 0x115 + x115 ≤ 0x115x115 ≤ 0x114 + x114 ≤ 0x114x114 ≤ 0x106 + x106 ≤ 0x106x106 ≤ 0x105 + x105 ≤ 0x105x105 ≤ 0arg7P + arg7P ≤ 0arg7Parg7P ≤ 0arg7 + arg7 ≤ 0arg7arg7 ≤ 0arg6P + arg6P ≤ 0arg6Parg6P ≤ 0arg6 + arg6 ≤ 0arg6arg6 ≤ 0arg5P + arg5P ≤ 0arg5Parg5P ≤ 0arg5 + arg5 ≤ 0arg5arg5 ≤ 0arg4P + arg4P ≤ 0arg4Parg4P ≤ 0arg4 + arg4 ≤ 0arg4arg4 ≤ 0arg3P + arg3P ≤ 0arg3Parg3P ≤ 0arg3 + arg3 ≤ 0arg3arg3 ≤ 0arg2P + arg2P ≤ 0arg2Parg2P ≤ 0arg2 + arg2 ≤ 0arg2arg2 ≤ 0arg1P + arg1P ≤ 0arg1Parg1P ≤ 0arg1 + arg1 ≤ 0arg1arg1 ≤ 0

5 Location Addition

The following skip-transition is inserted and corresponding redirections w.r.t. the old location are performed.

1 26 1_var_snapshot: x63 + x63 ≤ 0x63x63 ≤ 0x56 + x56 ≤ 0x56x56 ≤ 0x205 + x205 ≤ 0x205x205 ≤ 0x204 + x204 ≤ 0x204x204 ≤ 0x191 + x191 ≤ 0x191x191 ≤ 0x190 + x190 ≤ 0x190x190 ≤ 0x177 + x177 ≤ 0x177x177 ≤ 0x176 + x176 ≤ 0x176x176 ≤ 0x163 + x163 ≤ 0x163x163 ≤ 0x162 + x162 ≤ 0x162x162 ≤ 0x156 + x156 ≤ 0x156x156 ≤ 0x148 + x148 ≤ 0x148x148 ≤ 0x147 + x147 ≤ 0x147x147 ≤ 0x146 + x146 ≤ 0x146x146 ≤ 0x140 + x140 ≤ 0x140x140 ≤ 0x132 + x132 ≤ 0x132x132 ≤ 0x131 + x131 ≤ 0x131x131 ≤ 0x130 + x130 ≤ 0x130x130 ≤ 0x116 + x116 ≤ 0x116x116 ≤ 0x115 + x115 ≤ 0x115x115 ≤ 0x114 + x114 ≤ 0x114x114 ≤ 0x106 + x106 ≤ 0x106x106 ≤ 0x105 + x105 ≤ 0x105x105 ≤ 0arg7P + arg7P ≤ 0arg7Parg7P ≤ 0arg7 + arg7 ≤ 0arg7arg7 ≤ 0arg6P + arg6P ≤ 0arg6Parg6P ≤ 0arg6 + arg6 ≤ 0arg6arg6 ≤ 0arg5P + arg5P ≤ 0arg5Parg5P ≤ 0arg5 + arg5 ≤ 0arg5arg5 ≤ 0arg4P + arg4P ≤ 0arg4Parg4P ≤ 0arg4 + arg4 ≤ 0arg4arg4 ≤ 0arg3P + arg3P ≤ 0arg3Parg3P ≤ 0arg3 + arg3 ≤ 0arg3arg3 ≤ 0arg2P + arg2P ≤ 0arg2Parg2P ≤ 0arg2 + arg2 ≤ 0arg2arg2 ≤ 0arg1P + arg1P ≤ 0arg1Parg1P ≤ 0arg1 + arg1 ≤ 0arg1arg1 ≤ 0

6 Location Addition

The following skip-transition is inserted and corresponding redirections w.r.t. the old location are performed.

2* 35 2: x63 + x63 ≤ 0x63x63 ≤ 0x56 + x56 ≤ 0x56x56 ≤ 0x205 + x205 ≤ 0x205x205 ≤ 0x204 + x204 ≤ 0x204x204 ≤ 0x191 + x191 ≤ 0x191x191 ≤ 0x190 + x190 ≤ 0x190x190 ≤ 0x177 + x177 ≤ 0x177x177 ≤ 0x176 + x176 ≤ 0x176x176 ≤ 0x163 + x163 ≤ 0x163x163 ≤ 0x162 + x162 ≤ 0x162x162 ≤ 0x156 + x156 ≤ 0x156x156 ≤ 0x148 + x148 ≤ 0x148x148 ≤ 0x147 + x147 ≤ 0x147x147 ≤ 0x146 + x146 ≤ 0x146x146 ≤ 0x140 + x140 ≤ 0x140x140 ≤ 0x132 + x132 ≤ 0x132x132 ≤ 0x131 + x131 ≤ 0x131x131 ≤ 0x130 + x130 ≤ 0x130x130 ≤ 0x116 + x116 ≤ 0x116x116 ≤ 0x115 + x115 ≤ 0x115x115 ≤ 0x114 + x114 ≤ 0x114x114 ≤ 0x106 + x106 ≤ 0x106x106 ≤ 0x105 + x105 ≤ 0x105x105 ≤ 0arg7P + arg7P ≤ 0arg7Parg7P ≤ 0arg7 + arg7 ≤ 0arg7arg7 ≤ 0arg6P + arg6P ≤ 0arg6Parg6P ≤ 0arg6 + arg6 ≤ 0arg6arg6 ≤ 0arg5P + arg5P ≤ 0arg5Parg5P ≤ 0arg5 + arg5 ≤ 0arg5arg5 ≤ 0arg4P + arg4P ≤ 0arg4Parg4P ≤ 0arg4 + arg4 ≤ 0arg4arg4 ≤ 0arg3P + arg3P ≤ 0arg3Parg3P ≤ 0arg3 + arg3 ≤ 0arg3arg3 ≤ 0arg2P + arg2P ≤ 0arg2Parg2P ≤ 0arg2 + arg2 ≤ 0arg2arg2 ≤ 0arg1P + arg1P ≤ 0arg1Parg1P ≤ 0arg1 + arg1 ≤ 0arg1arg1 ≤ 0

7 Location Addition

The following skip-transition is inserted and corresponding redirections w.r.t. the old location are performed.

2 33 2_var_snapshot: x63 + x63 ≤ 0x63x63 ≤ 0x56 + x56 ≤ 0x56x56 ≤ 0x205 + x205 ≤ 0x205x205 ≤ 0x204 + x204 ≤ 0x204x204 ≤ 0x191 + x191 ≤ 0x191x191 ≤ 0x190 + x190 ≤ 0x190x190 ≤ 0x177 + x177 ≤ 0x177x177 ≤ 0x176 + x176 ≤ 0x176x176 ≤ 0x163 + x163 ≤ 0x163x163 ≤ 0x162 + x162 ≤ 0x162x162 ≤ 0x156 + x156 ≤ 0x156x156 ≤ 0x148 + x148 ≤ 0x148x148 ≤ 0x147 + x147 ≤ 0x147x147 ≤ 0x146 + x146 ≤ 0x146x146 ≤ 0x140 + x140 ≤ 0x140x140 ≤ 0x132 + x132 ≤ 0x132x132 ≤ 0x131 + x131 ≤ 0x131x131 ≤ 0x130 + x130 ≤ 0x130x130 ≤ 0x116 + x116 ≤ 0x116x116 ≤ 0x115 + x115 ≤ 0x115x115 ≤ 0x114 + x114 ≤ 0x114x114 ≤ 0x106 + x106 ≤ 0x106x106 ≤ 0x105 + x105 ≤ 0x105x105 ≤ 0arg7P + arg7P ≤ 0arg7Parg7P ≤ 0arg7 + arg7 ≤ 0arg7arg7 ≤ 0arg6P + arg6P ≤ 0arg6Parg6P ≤ 0arg6 + arg6 ≤ 0arg6arg6 ≤ 0arg5P + arg5P ≤ 0arg5Parg5P ≤ 0arg5 + arg5 ≤ 0arg5arg5 ≤ 0arg4P + arg4P ≤ 0arg4Parg4P ≤ 0arg4 + arg4 ≤ 0arg4arg4 ≤ 0arg3P + arg3P ≤ 0arg3Parg3P ≤ 0arg3 + arg3 ≤ 0arg3arg3 ≤ 0arg2P + arg2P ≤ 0arg2Parg2P ≤ 0arg2 + arg2 ≤ 0arg2arg2 ≤ 0arg1P + arg1P ≤ 0arg1Parg1P ≤ 0arg1 + arg1 ≤ 0arg1arg1 ≤ 0

8 Location Addition

The following skip-transition is inserted and corresponding redirections w.r.t. the old location are performed.

5* 42 5: x63 + x63 ≤ 0x63x63 ≤ 0x56 + x56 ≤ 0x56x56 ≤ 0x205 + x205 ≤ 0x205x205 ≤ 0x204 + x204 ≤ 0x204x204 ≤ 0x191 + x191 ≤ 0x191x191 ≤ 0x190 + x190 ≤ 0x190x190 ≤ 0x177 + x177 ≤ 0x177x177 ≤ 0x176 + x176 ≤ 0x176x176 ≤ 0x163 + x163 ≤ 0x163x163 ≤ 0x162 + x162 ≤ 0x162x162 ≤ 0x156 + x156 ≤ 0x156x156 ≤ 0x148 + x148 ≤ 0x148x148 ≤ 0x147 + x147 ≤ 0x147x147 ≤ 0x146 + x146 ≤ 0x146x146 ≤ 0x140 + x140 ≤ 0x140x140 ≤ 0x132 + x132 ≤ 0x132x132 ≤ 0x131 + x131 ≤ 0x131x131 ≤ 0x130 + x130 ≤ 0x130x130 ≤ 0x116 + x116 ≤ 0x116x116 ≤ 0x115 + x115 ≤ 0x115x115 ≤ 0x114 + x114 ≤ 0x114x114 ≤ 0x106 + x106 ≤ 0x106x106 ≤ 0x105 + x105 ≤ 0x105x105 ≤ 0arg7P + arg7P ≤ 0arg7Parg7P ≤ 0arg7 + arg7 ≤ 0arg7arg7 ≤ 0arg6P + arg6P ≤ 0arg6Parg6P ≤ 0arg6 + arg6 ≤ 0arg6arg6 ≤ 0arg5P + arg5P ≤ 0arg5Parg5P ≤ 0arg5 + arg5 ≤ 0arg5arg5 ≤ 0arg4P + arg4P ≤ 0arg4Parg4P ≤ 0arg4 + arg4 ≤ 0arg4arg4 ≤ 0arg3P + arg3P ≤ 0arg3Parg3P ≤ 0arg3 + arg3 ≤ 0arg3arg3 ≤ 0arg2P + arg2P ≤ 0arg2Parg2P ≤ 0arg2 + arg2 ≤ 0arg2arg2 ≤ 0arg1P + arg1P ≤ 0arg1Parg1P ≤ 0arg1 + arg1 ≤ 0arg1arg1 ≤ 0

9 Location Addition

The following skip-transition is inserted and corresponding redirections w.r.t. the old location are performed.

5 40 5_var_snapshot: x63 + x63 ≤ 0x63x63 ≤ 0x56 + x56 ≤ 0x56x56 ≤ 0x205 + x205 ≤ 0x205x205 ≤ 0x204 + x204 ≤ 0x204x204 ≤ 0x191 + x191 ≤ 0x191x191 ≤ 0x190 + x190 ≤ 0x190x190 ≤ 0x177 + x177 ≤ 0x177x177 ≤ 0x176 + x176 ≤ 0x176x176 ≤ 0x163 + x163 ≤ 0x163x163 ≤ 0x162 + x162 ≤ 0x162x162 ≤ 0x156 + x156 ≤ 0x156x156 ≤ 0x148 + x148 ≤ 0x148x148 ≤ 0x147 + x147 ≤ 0x147x147 ≤ 0x146 + x146 ≤ 0x146x146 ≤ 0x140 + x140 ≤ 0x140x140 ≤ 0x132 + x132 ≤ 0x132x132 ≤ 0x131 + x131 ≤ 0x131x131 ≤ 0x130 + x130 ≤ 0x130x130 ≤ 0x116 + x116 ≤ 0x116x116 ≤ 0x115 + x115 ≤ 0x115x115 ≤ 0x114 + x114 ≤ 0x114x114 ≤ 0x106 + x106 ≤ 0x106x106 ≤ 0x105 + x105 ≤ 0x105x105 ≤ 0arg7P + arg7P ≤ 0arg7Parg7P ≤ 0arg7 + arg7 ≤ 0arg7arg7 ≤ 0arg6P + arg6P ≤ 0arg6Parg6P ≤ 0arg6 + arg6 ≤ 0arg6arg6 ≤ 0arg5P + arg5P ≤ 0arg5Parg5P ≤ 0arg5 + arg5 ≤ 0arg5arg5 ≤ 0arg4P + arg4P ≤ 0arg4Parg4P ≤ 0arg4 + arg4 ≤ 0arg4arg4 ≤ 0arg3P + arg3P ≤ 0arg3Parg3P ≤ 0arg3 + arg3 ≤ 0arg3arg3 ≤ 0arg2P + arg2P ≤ 0arg2Parg2P ≤ 0arg2 + arg2 ≤ 0arg2arg2 ≤ 0arg1P + arg1P ≤ 0arg1Parg1P ≤ 0arg1 + arg1 ≤ 0arg1arg1 ≤ 0

10 Location Addition

The following skip-transition is inserted and corresponding redirections w.r.t. the old location are performed.

6* 49 6: x63 + x63 ≤ 0x63x63 ≤ 0x56 + x56 ≤ 0x56x56 ≤ 0x205 + x205 ≤ 0x205x205 ≤ 0x204 + x204 ≤ 0x204x204 ≤ 0x191 + x191 ≤ 0x191x191 ≤ 0x190 + x190 ≤ 0x190x190 ≤ 0x177 + x177 ≤ 0x177x177 ≤ 0x176 + x176 ≤ 0x176x176 ≤ 0x163 + x163 ≤ 0x163x163 ≤ 0x162 + x162 ≤ 0x162x162 ≤ 0x156 + x156 ≤ 0x156x156 ≤ 0x148 + x148 ≤ 0x148x148 ≤ 0x147 + x147 ≤ 0x147x147 ≤ 0x146 + x146 ≤ 0x146x146 ≤ 0x140 + x140 ≤ 0x140x140 ≤ 0x132 + x132 ≤ 0x132x132 ≤ 0x131 + x131 ≤ 0x131x131 ≤ 0x130 + x130 ≤ 0x130x130 ≤ 0x116 + x116 ≤ 0x116x116 ≤ 0x115 + x115 ≤ 0x115x115 ≤ 0x114 + x114 ≤ 0x114x114 ≤ 0x106 + x106 ≤ 0x106x106 ≤ 0x105 + x105 ≤ 0x105x105 ≤ 0arg7P + arg7P ≤ 0arg7Parg7P ≤ 0arg7 + arg7 ≤ 0arg7arg7 ≤ 0arg6P + arg6P ≤ 0arg6Parg6P ≤ 0arg6 + arg6 ≤ 0arg6arg6 ≤ 0arg5P + arg5P ≤ 0arg5Parg5P ≤ 0arg5 + arg5 ≤ 0arg5arg5 ≤ 0arg4P + arg4P ≤ 0arg4Parg4P ≤ 0arg4 + arg4 ≤ 0arg4arg4 ≤ 0arg3P + arg3P ≤ 0arg3Parg3P ≤ 0arg3 + arg3 ≤ 0arg3arg3 ≤ 0arg2P + arg2P ≤ 0arg2Parg2P ≤ 0arg2 + arg2 ≤ 0arg2arg2 ≤ 0arg1P + arg1P ≤ 0arg1Parg1P ≤ 0arg1 + arg1 ≤ 0arg1arg1 ≤ 0

11 Location Addition

The following skip-transition is inserted and corresponding redirections w.r.t. the old location are performed.

6 47 6_var_snapshot: x63 + x63 ≤ 0x63x63 ≤ 0x56 + x56 ≤ 0x56x56 ≤ 0x205 + x205 ≤ 0x205x205 ≤ 0x204 + x204 ≤ 0x204x204 ≤ 0x191 + x191 ≤ 0x191x191 ≤ 0x190 + x190 ≤ 0x190x190 ≤ 0x177 + x177 ≤ 0x177x177 ≤ 0x176 + x176 ≤ 0x176x176 ≤ 0x163 + x163 ≤ 0x163x163 ≤ 0x162 + x162 ≤ 0x162x162 ≤ 0x156 + x156 ≤ 0x156x156 ≤ 0x148 + x148 ≤ 0x148x148 ≤ 0x147 + x147 ≤ 0x147x147 ≤ 0x146 + x146 ≤ 0x146x146 ≤ 0x140 + x140 ≤ 0x140x140 ≤ 0x132 + x132 ≤ 0x132x132 ≤ 0x131 + x131 ≤ 0x131x131 ≤ 0x130 + x130 ≤ 0x130x130 ≤ 0x116 + x116 ≤ 0x116x116 ≤ 0x115 + x115 ≤ 0x115x115 ≤ 0x114 + x114 ≤ 0x114x114 ≤ 0x106 + x106 ≤ 0x106x106 ≤ 0x105 + x105 ≤ 0x105x105 ≤ 0arg7P + arg7P ≤ 0arg7Parg7P ≤ 0arg7 + arg7 ≤ 0arg7arg7 ≤ 0arg6P + arg6P ≤ 0arg6Parg6P ≤ 0arg6 + arg6 ≤ 0arg6arg6 ≤ 0arg5P + arg5P ≤ 0arg5Parg5P ≤ 0arg5 + arg5 ≤ 0arg5arg5 ≤ 0arg4P + arg4P ≤ 0arg4Parg4P ≤ 0arg4 + arg4 ≤ 0arg4arg4 ≤ 0arg3P + arg3P ≤ 0arg3Parg3P ≤ 0arg3 + arg3 ≤ 0arg3arg3 ≤ 0arg2P + arg2P ≤ 0arg2Parg2P ≤ 0arg2 + arg2 ≤ 0arg2arg2 ≤ 0arg1P + arg1P ≤ 0arg1Parg1P ≤ 0arg1 + arg1 ≤ 0arg1arg1 ≤ 0

12 Location Addition

The following skip-transition is inserted and corresponding redirections w.r.t. the old location are performed.

7* 56 7: x63 + x63 ≤ 0x63x63 ≤ 0x56 + x56 ≤ 0x56x56 ≤ 0x205 + x205 ≤ 0x205x205 ≤ 0x204 + x204 ≤ 0x204x204 ≤ 0x191 + x191 ≤ 0x191x191 ≤ 0x190 + x190 ≤ 0x190x190 ≤ 0x177 + x177 ≤ 0x177x177 ≤ 0x176 + x176 ≤ 0x176x176 ≤ 0x163 + x163 ≤ 0x163x163 ≤ 0x162 + x162 ≤ 0x162x162 ≤ 0x156 + x156 ≤ 0x156x156 ≤ 0x148 + x148 ≤ 0x148x148 ≤ 0x147 + x147 ≤ 0x147x147 ≤ 0x146 + x146 ≤ 0x146x146 ≤ 0x140 + x140 ≤ 0x140x140 ≤ 0x132 + x132 ≤ 0x132x132 ≤ 0x131 + x131 ≤ 0x131x131 ≤ 0x130 + x130 ≤ 0x130x130 ≤ 0x116 + x116 ≤ 0x116x116 ≤ 0x115 + x115 ≤ 0x115x115 ≤ 0x114 + x114 ≤ 0x114x114 ≤ 0x106 + x106 ≤ 0x106x106 ≤ 0x105 + x105 ≤ 0x105x105 ≤ 0arg7P + arg7P ≤ 0arg7Parg7P ≤ 0arg7 + arg7 ≤ 0arg7arg7 ≤ 0arg6P + arg6P ≤ 0arg6Parg6P ≤ 0arg6 + arg6 ≤ 0arg6arg6 ≤ 0arg5P + arg5P ≤ 0arg5Parg5P ≤ 0arg5 + arg5 ≤ 0arg5arg5 ≤ 0arg4P + arg4P ≤ 0arg4Parg4P ≤ 0arg4 + arg4 ≤ 0arg4arg4 ≤ 0arg3P + arg3P ≤ 0arg3Parg3P ≤ 0arg3 + arg3 ≤ 0arg3arg3 ≤ 0arg2P + arg2P ≤ 0arg2Parg2P ≤ 0arg2 + arg2 ≤ 0arg2arg2 ≤ 0arg1P + arg1P ≤ 0arg1Parg1P ≤ 0arg1 + arg1 ≤ 0arg1arg1 ≤ 0

13 Location Addition

The following skip-transition is inserted and corresponding redirections w.r.t. the old location are performed.

7 54 7_var_snapshot: x63 + x63 ≤ 0x63x63 ≤ 0x56 + x56 ≤ 0x56x56 ≤ 0x205 + x205 ≤ 0x205x205 ≤ 0x204 + x204 ≤ 0x204x204 ≤ 0x191 + x191 ≤ 0x191x191 ≤ 0x190 + x190 ≤ 0x190x190 ≤ 0x177 + x177 ≤ 0x177x177 ≤ 0x176 + x176 ≤ 0x176x176 ≤ 0x163 + x163 ≤ 0x163x163 ≤ 0x162 + x162 ≤ 0x162x162 ≤ 0x156 + x156 ≤ 0x156x156 ≤ 0x148 + x148 ≤ 0x148x148 ≤ 0x147 + x147 ≤ 0x147x147 ≤ 0x146 + x146 ≤ 0x146x146 ≤ 0x140 + x140 ≤ 0x140x140 ≤ 0x132 + x132 ≤ 0x132x132 ≤ 0x131 + x131 ≤ 0x131x131 ≤ 0x130 + x130 ≤ 0x130x130 ≤ 0x116 + x116 ≤ 0x116x116 ≤ 0x115 + x115 ≤ 0x115x115 ≤ 0x114 + x114 ≤ 0x114x114 ≤ 0x106 + x106 ≤ 0x106x106 ≤ 0x105 + x105 ≤ 0x105x105 ≤ 0arg7P + arg7P ≤ 0arg7Parg7P ≤ 0arg7 + arg7 ≤ 0arg7arg7 ≤ 0arg6P + arg6P ≤ 0arg6Parg6P ≤ 0arg6 + arg6 ≤ 0arg6arg6 ≤ 0arg5P + arg5P ≤ 0arg5Parg5P ≤ 0arg5 + arg5 ≤ 0arg5arg5 ≤ 0arg4P + arg4P ≤ 0arg4Parg4P ≤ 0arg4 + arg4 ≤ 0arg4arg4 ≤ 0arg3P + arg3P ≤ 0arg3Parg3P ≤ 0arg3 + arg3 ≤ 0arg3arg3 ≤ 0arg2P + arg2P ≤ 0arg2Parg2P ≤ 0arg2 + arg2 ≤ 0arg2arg2 ≤ 0arg1P + arg1P ≤ 0arg1Parg1P ≤ 0arg1 + arg1 ≤ 0arg1arg1 ≤ 0

14 SCC Decomposition

We consider subproblems for each of the 5 SCC(s) of the program graph.

14.1 SCC Subproblem 1/5

Here we consider the SCC { 7, 7_var_snapshot, 7* }.

14.1.1 Transition Removal

We remove transitions 22, 23 using the following ranking functions, which are bounded by 2.

7: 1 − 2⋅arg4arg5 + 3⋅arg7
7_var_snapshot: −2⋅arg4arg5 + 3⋅arg7
7*: 2 − 2⋅arg4arg5 + 3⋅arg7

14.1.2 Transition Removal

We remove transitions 54, 56 using the following ranking functions, which are bounded by −2.

7: −1
7_var_snapshot: −2
7*: 0

14.1.3 Splitting Cut-Point Transitions

We consider 1 subproblems corresponding to sets of cut-point transitions as follows.

14.1.3.1 Cut-Point Subproblem 1/1

Here we consider cut-point transition 53.

14.1.3.1.1 Splitting Cut-Point Transitions

There remain no cut-point transition to consider. Hence the cooperation termination is trivial.

14.2 SCC Subproblem 2/5

Here we consider the SCC { 6, 6_var_snapshot, 6* }.

14.2.1 Transition Removal

We remove transition 20 using the following ranking functions, which are bounded by −1.

6: 1 − 3⋅arg4 + 3⋅arg5
6_var_snapshot: −3⋅arg4 + 3⋅arg5
6*: 2 − 3⋅arg4 + 3⋅arg5

14.2.2 Transition Removal

We remove transitions 47, 49 using the following ranking functions, which are bounded by −1.

6: 0
6_var_snapshot: −1
6*: arg3P

14.2.3 Splitting Cut-Point Transitions

We consider 1 subproblems corresponding to sets of cut-point transitions as follows.

14.2.3.1 Cut-Point Subproblem 1/1

Here we consider cut-point transition 46.

14.2.3.1.1 Splitting Cut-Point Transitions

There remain no cut-point transition to consider. Hence the cooperation termination is trivial.

14.3 SCC Subproblem 3/5

Here we consider the SCC { 5, 5_var_snapshot, 5* }.

14.3.1 Transition Removal

We remove transition 19 using the following ranking functions, which are bounded by −1.

5: 1 − 2⋅arg4arg5 + 3⋅arg6
5_var_snapshot: −2⋅arg4arg5 + 3⋅arg6
5*: 2 − 2⋅arg4arg5 + 3⋅arg6

14.3.2 Transition Removal

We remove transitions 40, 42 using the following ranking functions, which are bounded by −2.

5: −1
5_var_snapshot: −2⋅arg3
5*: 0

14.3.3 Splitting Cut-Point Transitions

We consider 1 subproblems corresponding to sets of cut-point transitions as follows.

14.3.3.1 Cut-Point Subproblem 1/1

Here we consider cut-point transition 39.

14.3.3.1.1 Splitting Cut-Point Transitions

There remain no cut-point transition to consider. Hence the cooperation termination is trivial.

14.4 SCC Subproblem 4/5

Here we consider the SCC { 2, 3, 2_var_snapshot, 2* }.

14.4.1 Transition Removal

We remove transitions 3, 4, 5, 6, 7, 8, 9, 11, 13, 15 using the following ranking functions, which are bounded by 2.

2: 1 − 5⋅arg3 + 5⋅arg4
3: −2 − 5⋅arg3 + 5⋅arg4
2_var_snapshot: −5⋅arg3 + 5⋅arg4
2*: 2 − 5⋅arg3 + 5⋅arg4

14.4.2 Transition Removal

We remove transitions 33, 35 using the following ranking functions, which are bounded by −1.

2: 0
3: 0
2_var_snapshot: −1
2*: 1

14.4.3 Splitting Cut-Point Transitions

We consider 1 subproblems corresponding to sets of cut-point transitions as follows.

14.4.3.1 Cut-Point Subproblem 1/1

Here we consider cut-point transition 32.

14.4.3.1.1 Splitting Cut-Point Transitions

There remain no cut-point transition to consider. Hence the cooperation termination is trivial.

14.5 SCC Subproblem 5/5

Here we consider the SCC { 1, 1_var_snapshot, 1* }.

14.5.1 Transition Removal

We remove transition 1 using the following ranking functions, which are bounded by 2.

1: 1 − 3⋅arg2 + 3⋅arg3
1_var_snapshot: −3⋅arg2 + 3⋅arg3
1*: 2 − 3⋅arg2 + 3⋅arg3

14.5.2 Transition Removal

We remove transitions 26, 28 using the following ranking functions, which are bounded by −1.

1: 0
1_var_snapshot: arg1
1*: arg1

14.5.3 Splitting Cut-Point Transitions

We consider 1 subproblems corresponding to sets of cut-point transitions as follows.

14.5.3.1 Cut-Point Subproblem 1/1

Here we consider cut-point transition 25.

14.5.3.1.1 Splitting Cut-Point Transitions

There remain no cut-point transition to consider. Hence the cooperation termination is trivial.

Tool configuration

T2Cert