/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# AProVE Commit ID: c69e44bd14796315568835c1ffa2502984884775 mhark 20210624 unpublished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, 4 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:
3, 4, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151, 152, 153, 154, 155, 156

Node 3 is start node and node 4 is final node.

Those nodes are connected through the following edges:

* 3 to 137 labelled a_1(0)* 4 to 4 labelled #_1(0)* 137 to 138 labelled b_1(0)* 138 to 139 labelled a_1(0)* 139 to 140 labelled b_1(0)* 140 to 141 labelled a_1(0)* 141 to 142 labelled a_1(0)* 142 to 143 labelled b_1(0)* 142 to 147 labelled a_1(1)* 143 to 144 labelled a_1(0)* 144 to 145 labelled a_1(0)* 145 to 146 labelled b_1(0)* 145 to 147 labelled a_1(1)* 146 to 4 labelled a_1(0)* 147 to 148 labelled b_1(1)* 148 to 149 labelled a_1(1)* 149 to 150 labelled b_1(1)* 150 to 151 labelled a_1(1)* 151 to 152 labelled a_1(1)* 152 to 153 labelled b_1(1)* 152 to 147 labelled a_1(1)* 153 to 154 labelled a_1(1)* 154 to 155 labelled a_1(1)* 155 to 156 labelled b_1(1)* 155 to 147 labelled a_1(1)* 156 to 4 labelled a_1(1)


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(4)
YES