/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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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(a(a(b(a(b(a(x1)))))))) -> a(a(b(a(b(a(b(a(b(a(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(b(a(b(a(a(b(a(x1)))))))) -> b(a(b(a(a(b(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(b(a(a(b(a(x1)))))))) -> b(a(b(a(a(b(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(b(a(a(b(x))))))) -> b(a(b(a(a(b(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(b(a(a(b(x))))))) -> b(a(b(a(a(b(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(b(a(a(b(x))))))) -> b(a(b(a(a(b(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:
210, 211, 212, 213, 214, 215, 216, 217, 218, 219, 220, 221, 222, 223, 224, 225, 226, 227, 228, 229, 230, 231, 232, 233, 234, 235

Node 210 is start node and node 211 is final node.

Those nodes are connected through the following edges:

* 210 to 212 labelled b_1(0)* 211 to 211 labelled #_1(0)* 212 to 213 labelled a_1(0)* 213 to 214 labelled b_1(0)* 214 to 215 labelled a_1(0)* 215 to 216 labelled a_1(0)* 216 to 217 labelled b_1(0)* 217 to 218 labelled a_1(0)* 218 to 219 labelled b_1(0)* 219 to 220 labelled a_1(0)* 219 to 224 labelled b_1(1)* 220 to 221 labelled b_1(0)* 221 to 222 labelled a_1(0)* 221 to 224 labelled b_1(1)* 222 to 223 labelled b_1(0)* 223 to 211 labelled a_1(0)* 223 to 224 labelled b_1(1)* 224 to 225 labelled a_1(1)* 225 to 226 labelled b_1(1)* 226 to 227 labelled a_1(1)* 227 to 228 labelled a_1(1)* 228 to 229 labelled b_1(1)* 229 to 230 labelled a_1(1)* 230 to 231 labelled b_1(1)* 231 to 232 labelled a_1(1)* 231 to 224 labelled b_1(1)* 232 to 233 labelled b_1(1)* 233 to 234 labelled a_1(1)* 233 to 224 labelled b_1(1)* 234 to 235 labelled b_1(1)* 235 to 211 labelled a_1(1)* 235 to 224 labelled b_1(1)


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(6)
YES