/export/starexec/sandbox/solver/bin/starexec_run_standard /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files


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YES
proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty


Termination w.r.t. Q of the given QTRS could be proven:

(0) QTRS
(1) QTRS Reverse [EQUIVALENT, 0 ms]
(2) QTRS
(3) Strip Symbols Proof [SOUND, 0 ms]
(4) QTRS
(5) RFCMatchBoundsTRSProof [EQUIVALENT, 7 ms]
(6) YES


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(0)
Obligation:
Q restricted rewrite system:
The TRS R consists of the following rules:

   a(b(b(a(a(a(a(a(x1)))))))) -> a(a(a(a(a(a(b(b(a(a(a(a(b(b(x1))))))))))))))

Q is empty.

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(1) QTRS Reverse (EQUIVALENT)
We applied the QTRS Reverse Processor [REVERSE].
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(2)
Obligation:
Q restricted rewrite system:
The TRS R consists of the following rules:

   a(a(a(a(a(b(b(a(x1)))))))) -> b(b(a(a(a(a(b(b(a(a(a(a(a(a(x1))))))))))))))

Q is empty.

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(3) Strip Symbols Proof (SOUND)
We were given the following TRS:

   a(a(a(a(a(b(b(a(x1)))))))) -> b(b(a(a(a(a(b(b(a(a(a(a(a(a(x1))))))))))))))

By stripping symbols from the only rule of the system, we obtained the following TRS [ENDRULLIS]: 

   a(a(a(a(a(b(b(x))))))) -> b(b(a(a(a(a(b(b(a(a(a(a(a(x)))))))))))))

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(4)
Obligation:
Q restricted rewrite system:
The TRS R consists of the following rules:

   a(a(a(a(a(b(b(x))))))) -> b(b(a(a(a(a(b(b(a(a(a(a(a(x)))))))))))))

Q is empty.

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(5) RFCMatchBoundsTRSProof (EQUIVALENT)
Termination of the TRS R could be shown with a Match Bound [MATCHBOUNDS1,MATCHBOUNDS2] of 1. This implies Q-termination of R.
The following rules were used to construct the certificate:

   a(a(a(a(a(b(b(x))))))) -> b(b(a(a(a(a(b(b(a(a(a(a(a(x)))))))))))))

The certificate found is represented by the following graph.
The certificate consists of the following enumerated nodes:
147, 148, 149, 150, 151, 152, 153, 154, 155, 156, 157, 158, 159, 160, 161, 162, 163, 164, 165, 166, 167, 168, 169, 170, 171, 172

Node 147 is start node and node 148 is final node.

Those nodes are connected through the following edges:

* 147 to 149 labelled b_1(0)* 148 to 148 labelled #_1(0)* 149 to 150 labelled b_1(0)* 150 to 151 labelled a_1(0)* 151 to 152 labelled a_1(0)* 152 to 153 labelled a_1(0)* 153 to 154 labelled a_1(0)* 154 to 155 labelled b_1(0)* 155 to 156 labelled b_1(0)* 156 to 157 labelled a_1(0)* 156 to 161 labelled b_1(1)* 157 to 158 labelled a_1(0)* 157 to 161 labelled b_1(1)* 158 to 159 labelled a_1(0)* 158 to 161 labelled b_1(1)* 159 to 160 labelled a_1(0)* 159 to 161 labelled b_1(1)* 160 to 148 labelled a_1(0)* 160 to 161 labelled b_1(1)* 161 to 162 labelled b_1(1)* 162 to 163 labelled a_1(1)* 163 to 164 labelled a_1(1)* 164 to 165 labelled a_1(1)* 165 to 166 labelled a_1(1)* 166 to 167 labelled b_1(1)* 167 to 168 labelled b_1(1)* 168 to 169 labelled a_1(1)* 168 to 161 labelled b_1(1)* 169 to 170 labelled a_1(1)* 169 to 161 labelled b_1(1)* 170 to 171 labelled a_1(1)* 170 to 161 labelled b_1(1)* 171 to 172 labelled a_1(1)* 171 to 161 labelled b_1(1)* 172 to 148 labelled a_1(1)* 172 to 161 labelled b_1(1)


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(6)
YES