/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty


Termination w.r.t. Q of the given QTRS could be proven:

(0) QTRS
(1) Strip Symbols Proof [SOUND, 0 ms]
(2) QTRS
(3) RFCMatchBoundsTRSProof [EQUIVALENT, 0 ms]
(4) YES


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(0)
Obligation:
Q restricted rewrite system:
The TRS R consists of the following rules:

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

Q is empty.

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

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

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

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

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(2)
Obligation:
Q restricted rewrite system:
The TRS R consists of the following rules:

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

Q is empty.

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(3) 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:

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

The certificate found is represented by the following graph.
The certificate consists of the following enumerated nodes:
25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114

Node 25 is start node and node 26 is final node.

Those nodes are connected through the following edges:

* 25 to 27 labelled a_1(0)* 26 to 26 labelled #_1(0)* 27 to 28 labelled b_1(0)* 28 to 29 labelled a_1(0)* 29 to 30 labelled b_1(0)* 30 to 31 labelled a_1(0)* 31 to 32 labelled a_1(0)* 32 to 33 labelled b_1(0)* 32 to 105 labelled a_1(1)* 33 to 34 labelled a_1(0)* 34 to 35 labelled a_1(0)* 35 to 36 labelled b_1(0)* 35 to 105 labelled a_1(1)* 36 to 26 labelled a_1(0)* 105 to 106 labelled b_1(1)* 106 to 107 labelled a_1(1)* 107 to 108 labelled b_1(1)* 108 to 109 labelled a_1(1)* 109 to 110 labelled a_1(1)* 110 to 111 labelled b_1(1)* 110 to 105 labelled a_1(1)* 111 to 112 labelled a_1(1)* 112 to 113 labelled a_1(1)* 113 to 114 labelled b_1(1)* 113 to 105 labelled a_1(1)* 114 to 26 labelled a_1(1)


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(4)
YES