/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# AProVE Commit ID: c69e44bd14796315568835c1ffa2502984884775 mhark 20210624 unpublished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) 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(b(a(b(a(a(a(b(x1))))))))) -> a(a(b(a(a(a(b(a(b(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(b(a(b(a(a(a(b(x1))))))))) -> a(a(b(a(a(a(b(a(b(a(b(a(b(x1)))))))))))))

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

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

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

   b(a(b(a(b(a(a(a(x)))))))) -> a(a(b(a(a(a(b(a(b(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(b(a(b(a(a(a(x)))))))) -> a(a(b(a(a(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:
41, 42, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150

Node 41 is start node and node 42 is final node.

Those nodes are connected through the following edges:

* 41 to 129 labelled a_1(0)* 42 to 42 labelled #_1(0)* 129 to 130 labelled a_1(0)* 130 to 131 labelled b_1(0)* 131 to 132 labelled a_1(0)* 132 to 133 labelled a_1(0)* 133 to 134 labelled a_1(0)* 134 to 135 labelled b_1(0)* 134 to 140 labelled a_1(1)* 135 to 136 labelled a_1(0)* 136 to 137 labelled b_1(0)* 136 to 140 labelled a_1(1)* 137 to 138 labelled a_1(0)* 138 to 139 labelled b_1(0)* 138 to 140 labelled a_1(1)* 139 to 42 labelled a_1(0)* 140 to 141 labelled a_1(1)* 141 to 142 labelled b_1(1)* 142 to 143 labelled a_1(1)* 143 to 144 labelled a_1(1)* 144 to 145 labelled a_1(1)* 145 to 146 labelled b_1(1)* 145 to 140 labelled a_1(1)* 146 to 147 labelled a_1(1)* 147 to 148 labelled b_1(1)* 147 to 140 labelled a_1(1)* 148 to 149 labelled a_1(1)* 149 to 150 labelled b_1(1)* 149 to 140 labelled a_1(1)* 150 to 42 labelled a_1(1)


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(4)
YES