/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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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(a(a(x1)))))) -> a(a(a(a(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(a(a(a(b(a(x1)))))) -> b(a(b(a(a(b(a(b(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(b(a(x1)))))) -> b(a(b(a(a(b(a(b(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(b(x))))) -> b(a(b(a(a(b(a(b(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(b(x))))) -> b(a(b(a(a(b(a(b(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(b(x))))) -> b(a(b(a(a(b(a(b(a(a(a(a(x))))))))))))

The certificate found is represented by the following graph.
The certificate consists of the following enumerated nodes:
55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78

Node 55 is start node and node 56 is final node.

Those nodes are connected through the following edges:

* 55 to 57 labelled b_1(0)* 56 to 56 labelled #_1(0)* 57 to 58 labelled a_1(0)* 58 to 59 labelled b_1(0)* 59 to 60 labelled a_1(0)* 60 to 61 labelled a_1(0)* 61 to 62 labelled b_1(0)* 62 to 63 labelled a_1(0)* 63 to 64 labelled b_1(0)* 64 to 65 labelled a_1(0)* 64 to 68 labelled b_1(1)* 65 to 66 labelled a_1(0)* 65 to 68 labelled b_1(1)* 66 to 67 labelled a_1(0)* 66 to 68 labelled b_1(1)* 67 to 56 labelled a_1(0)* 67 to 68 labelled b_1(1)* 68 to 69 labelled a_1(1)* 69 to 70 labelled b_1(1)* 70 to 71 labelled a_1(1)* 71 to 72 labelled a_1(1)* 72 to 73 labelled b_1(1)* 73 to 74 labelled a_1(1)* 74 to 75 labelled b_1(1)* 75 to 76 labelled a_1(1)* 75 to 68 labelled b_1(1)* 76 to 77 labelled a_1(1)* 76 to 68 labelled b_1(1)* 77 to 78 labelled a_1(1)* 77 to 68 labelled b_1(1)* 78 to 56 labelled a_1(1)* 78 to 68 labelled b_1(1)


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(6)
YES