/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# AProVE Commit ID: c69e44bd14796315568835c1ffa2502984884775 mhark 20210624 unpublished


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(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(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(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(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(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(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:
7, 8, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 183, 184, 185, 186, 187, 188, 189, 190, 191, 192, 194

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

Those nodes are connected through the following edges:

* 7 to 21 labelled b_1(0)* 8 to 8 labelled #_1(0)* 21 to 22 labelled a_1(0)* 22 to 23 labelled b_1(0)* 23 to 24 labelled a_1(0)* 24 to 25 labelled a_1(0)* 25 to 26 labelled b_1(0)* 26 to 27 labelled a_1(0)* 27 to 28 labelled b_1(0)* 28 to 29 labelled a_1(0)* 28 to 183 labelled b_1(1)* 29 to 30 labelled a_1(0)* 29 to 183 labelled b_1(1)* 30 to 31 labelled a_1(0)* 30 to 183 labelled b_1(1)* 31 to 8 labelled a_1(0)* 31 to 183 labelled b_1(1)* 183 to 184 labelled a_1(1)* 184 to 185 labelled b_1(1)* 185 to 186 labelled a_1(1)* 186 to 187 labelled a_1(1)* 187 to 188 labelled b_1(1)* 188 to 189 labelled a_1(1)* 189 to 190 labelled b_1(1)* 190 to 191 labelled a_1(1)* 190 to 183 labelled b_1(1)* 191 to 192 labelled a_1(1)* 191 to 183 labelled b_1(1)* 192 to 194 labelled a_1(1)* 192 to 183 labelled b_1(1)* 194 to 8 labelled a_1(1)* 194 to 183 labelled b_1(1)


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(6)
YES