/export/starexec/sandbox2/solver/bin/starexec_run_standard /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files


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YES
proof of /export/starexec/sandbox2/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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, 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(a(a(a(a(a(x1))))))))) -> a(a(a(a(a(a(a(a(b(a(b(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(a(a(a(a(a(a(b(a(x1))))))))) -> b(a(b(a(b(a(a(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(a(a(b(a(x1))))))))) -> b(a(b(a(b(a(a(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(a(a(b(x)))))))) -> b(a(b(a(b(a(a(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(a(a(b(x)))))))) -> b(a(b(a(b(a(a(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(a(a(b(x)))))))) -> b(a(b(a(b(a(a(a(a(a(a(a(x))))))))))))

The certificate found is represented by the following graph.
The certificate consists of the following enumerated nodes:
247, 248, 249, 250, 251, 252, 253, 254, 255, 256, 257, 258, 259, 260, 261, 262, 263, 264, 265, 266, 267, 268, 269, 270

Node 247 is start node and node 248 is final node.

Those nodes are connected through the following edges:

* 247 to 249 labelled b_1(0)* 248 to 248 labelled #_1(0)* 249 to 250 labelled a_1(0)* 250 to 251 labelled b_1(0)* 251 to 252 labelled a_1(0)* 252 to 253 labelled b_1(0)* 253 to 254 labelled a_1(0)* 253 to 260 labelled b_1(1)* 254 to 255 labelled a_1(0)* 254 to 260 labelled b_1(1)* 255 to 256 labelled a_1(0)* 255 to 260 labelled b_1(1)* 256 to 257 labelled a_1(0)* 256 to 260 labelled b_1(1)* 257 to 258 labelled a_1(0)* 257 to 260 labelled b_1(1)* 258 to 259 labelled a_1(0)* 258 to 260 labelled b_1(1)* 259 to 248 labelled a_1(0)* 259 to 260 labelled b_1(1)* 260 to 261 labelled a_1(1)* 261 to 262 labelled b_1(1)* 262 to 263 labelled a_1(1)* 263 to 264 labelled b_1(1)* 264 to 265 labelled a_1(1)* 264 to 260 labelled b_1(1)* 265 to 266 labelled a_1(1)* 265 to 260 labelled b_1(1)* 266 to 267 labelled a_1(1)* 266 to 260 labelled b_1(1)* 267 to 268 labelled a_1(1)* 267 to 260 labelled b_1(1)* 268 to 269 labelled a_1(1)* 268 to 260 labelled b_1(1)* 269 to 270 labelled a_1(1)* 269 to 260 labelled b_1(1)* 270 to 248 labelled a_1(1)* 270 to 260 labelled b_1(1)


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(6)
YES