/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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(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(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(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(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(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(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:
61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121

Node 61 is start node and node 62 is final node.

Those nodes are connected through the following edges:

* 61 to 63 labelled b_1(0)* 62 to 62 labelled #_1(0)* 63 to 64 labelled a_1(0)* 64 to 65 labelled a_1(0)* 65 to 66 labelled b_1(0)* 66 to 67 labelled a_1(0)* 67 to 68 labelled b_1(0)* 68 to 69 labelled a_1(0)* 69 to 70 labelled b_1(0)* 70 to 71 labelled a_1(0)* 71 to 72 labelled b_1(0)* 72 to 73 labelled a_1(0)* 72 to 110 labelled b_1(1)* 73 to 74 labelled b_1(0)* 74 to 62 labelled a_1(0)* 74 to 110 labelled b_1(1)* 110 to 111 labelled a_1(1)* 111 to 112 labelled a_1(1)* 112 to 113 labelled b_1(1)* 113 to 114 labelled a_1(1)* 114 to 115 labelled b_1(1)* 115 to 116 labelled a_1(1)* 116 to 117 labelled b_1(1)* 117 to 118 labelled a_1(1)* 118 to 119 labelled b_1(1)* 119 to 120 labelled a_1(1)* 119 to 110 labelled b_1(1)* 120 to 121 labelled b_1(1)* 121 to 62 labelled a_1(1)* 121 to 110 labelled b_1(1)


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(6)
YES