/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# AProVE Commit ID: c69e44bd14796315568835c1ffa2502984884775 mhark 20210624 unpublished


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, 0 ms]
(6) YES


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

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

Q is empty.

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

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

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

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

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

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

The certificate found is represented by the following graph.
The certificate consists of the following enumerated nodes:
222, 223, 224, 225, 226, 227, 228, 229, 230, 231, 232, 233, 234, 235, 236, 237, 238, 239

Node 222 is start node and node 223 is final node.

Those nodes are connected through the following edges:

* 222 to 224 labelled b_1(0)* 223 to 223 labelled #_1(0)* 224 to 225 labelled a_1(0)* 225 to 226 labelled a_1(0)* 226 to 227 labelled b_1(0)* 227 to 228 labelled a_1(0)* 228 to 229 labelled b_1(0)* 229 to 230 labelled a_1(0)* 229 to 232 labelled b_1(1)* 230 to 231 labelled b_1(0)* 231 to 223 labelled a_1(0)* 231 to 232 labelled b_1(1)* 232 to 233 labelled a_1(1)* 233 to 234 labelled a_1(1)* 234 to 235 labelled b_1(1)* 235 to 236 labelled a_1(1)* 236 to 237 labelled b_1(1)* 237 to 238 labelled a_1(1)* 237 to 232 labelled b_1(1)* 238 to 239 labelled b_1(1)* 239 to 223 labelled a_1(1)* 239 to 232 labelled b_1(1)


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(6)
YES