/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# AProVE Commit ID: c69e44bd14796315568835c1ffa2502984884775 mhark 20210624 unpublished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(a(b(b(a(b(x1)))))) -> a(b(b(a(a(b(b(a(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:

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

Q is empty.

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

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

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

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

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

   b(a(b(b(a(x))))) -> a(b(b(a(a(b(b(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 2. This implies Q-termination of R.
The following rules were used to construct the certificate:

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

The certificate found is represented by the following graph.
The certificate consists of the following enumerated nodes:
47, 48, 268, 269, 270, 271, 272, 273, 274, 275, 276, 277, 278, 279, 280, 281, 282, 283, 284, 285, 286, 287, 288, 289, 290, 291

Node 47 is start node and node 48 is final node.

Those nodes are connected through the following edges:

* 47 to 268 labelled a_1(0)* 48 to 48 labelled #_1(0)* 268 to 269 labelled b_1(0)* 269 to 270 labelled b_1(0)* 270 to 271 labelled a_1(0)* 271 to 272 labelled a_1(0)* 272 to 273 labelled b_1(0)* 272 to 280 labelled a_1(1)* 273 to 48 labelled b_1(0)* 273 to 274 labelled a_1(1)* 274 to 275 labelled b_1(1)* 275 to 276 labelled b_1(1)* 276 to 277 labelled a_1(1)* 277 to 278 labelled a_1(1)* 278 to 279 labelled b_1(1)* 278 to 286 labelled a_1(2)* 279 to 48 labelled b_1(1)* 279 to 274 labelled a_1(1)* 280 to 281 labelled b_1(1)* 281 to 282 labelled b_1(1)* 282 to 283 labelled a_1(1)* 283 to 284 labelled a_1(1)* 284 to 285 labelled b_1(1)* 284 to 286 labelled a_1(2)* 285 to 277 labelled b_1(1)* 285 to 274 labelled a_1(1)* 286 to 287 labelled b_1(2)* 287 to 288 labelled b_1(2)* 288 to 289 labelled a_1(2)* 289 to 290 labelled a_1(2)* 290 to 291 labelled b_1(2)* 290 to 286 labelled a_1(2)* 291 to 277 labelled b_1(2)* 291 to 274 labelled a_1(1)


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(6)
YES