/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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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(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(b(a(a(b(a(x1)))))))) -> b(a(a(b(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(a(b(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(a(b(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(a(b(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(a(b(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:
7, 8, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69

Node 7 is start node and node 8 is final node.

Those nodes are connected through the following edges:

* 7 to 22 labelled b_1(0)* 8 to 8 labelled #_1(0)* 22 to 23 labelled a_1(0)* 23 to 24 labelled a_1(0)* 24 to 25 labelled b_1(0)* 25 to 26 labelled a_1(0)* 26 to 27 labelled b_1(0)* 27 to 28 labelled a_1(0)* 28 to 29 labelled b_1(0)* 29 to 30 labelled a_1(0)* 29 to 58 labelled b_1(1)* 30 to 31 labelled b_1(0)* 31 to 32 labelled a_1(0)* 31 to 58 labelled b_1(1)* 32 to 33 labelled b_1(0)* 33 to 8 labelled a_1(0)* 33 to 58 labelled b_1(1)* 58 to 59 labelled a_1(1)* 59 to 60 labelled a_1(1)* 60 to 61 labelled b_1(1)* 61 to 62 labelled a_1(1)* 62 to 63 labelled b_1(1)* 63 to 64 labelled a_1(1)* 64 to 65 labelled b_1(1)* 65 to 66 labelled a_1(1)* 65 to 58 labelled b_1(1)* 66 to 67 labelled b_1(1)* 67 to 68 labelled a_1(1)* 67 to 58 labelled b_1(1)* 68 to 69 labelled b_1(1)* 69 to 8 labelled a_1(1)* 69 to 58 labelled b_1(1)


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(6)
YES