/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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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, 0 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(b(b(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(b(b(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(b(b(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(b(b(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(b(b(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(b(b(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:
3, 300, 301, 302, 303, 304, 305, 306, 307, 308, 309, 310, 311, 312, 313, 314, 315, 316, 317, 318, 319, 320, 321, 322, 323, 324

Node 3 is start node and node 300 is final node.

Those nodes are connected through the following edges:

* 3 to 301 labelled b_1(0)* 300 to 300 labelled #_1(0)* 301 to 302 labelled b_1(0)* 302 to 303 labelled a_1(0)* 303 to 304 labelled b_1(0)* 304 to 305 labelled b_1(0)* 305 to 306 labelled a_1(0)* 306 to 307 labelled b_1(0)* 307 to 308 labelled b_1(0)* 308 to 309 labelled a_1(0)* 308 to 313 labelled b_1(1)* 309 to 310 labelled a_1(0)* 309 to 313 labelled b_1(1)* 310 to 311 labelled a_1(0)* 310 to 313 labelled b_1(1)* 311 to 312 labelled a_1(0)* 311 to 313 labelled b_1(1)* 312 to 300 labelled a_1(0)* 312 to 313 labelled b_1(1)* 313 to 314 labelled b_1(1)* 314 to 315 labelled a_1(1)* 315 to 316 labelled b_1(1)* 316 to 317 labelled b_1(1)* 317 to 318 labelled a_1(1)* 318 to 319 labelled b_1(1)* 319 to 320 labelled b_1(1)* 320 to 321 labelled a_1(1)* 320 to 313 labelled b_1(1)* 321 to 322 labelled a_1(1)* 321 to 313 labelled b_1(1)* 322 to 323 labelled a_1(1)* 322 to 313 labelled b_1(1)* 323 to 324 labelled a_1(1)* 323 to 313 labelled b_1(1)* 324 to 300 labelled a_1(1)* 324 to 313 labelled b_1(1)


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(6)
YES