/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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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(b(a(a(b(a(a(b(a(x1))))))))))) -> a(a(b(a(a(b(a(a(b(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(b(a(a(b(a(a(b(a(b(a(x1))))))))))) -> b(a(b(a(b(a(a(b(a(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(a(b(a(b(a(x1))))))))))) -> b(a(b(a(b(a(a(b(a(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(a(a(b(a(b(x)))))))))) -> b(a(b(a(b(a(a(b(a(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(a(a(b(a(b(x)))))))))) -> b(a(b(a(b(a(a(b(a(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(a(a(b(a(b(x)))))))))) -> b(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:
142, 143, 144, 145, 146, 147, 148, 149, 150, 151, 159, 160, 161, 179, 180, 181, 182, 183, 184, 185, 186, 187, 188, 189

Node 142 is start node and node 143 is final node.

Those nodes are connected through the following edges:

* 142 to 144 labelled b_1(0)* 143 to 143 labelled #_1(0)* 144 to 145 labelled a_1(0)* 145 to 146 labelled b_1(0)* 146 to 147 labelled a_1(0)* 146 to 179 labelled b_1(1)* 147 to 148 labelled b_1(0)* 148 to 149 labelled a_1(0)* 149 to 150 labelled a_1(0)* 149 to 179 labelled b_1(1)* 150 to 151 labelled b_1(0)* 151 to 159 labelled a_1(0)* 159 to 160 labelled a_1(0)* 159 to 179 labelled b_1(1)* 160 to 161 labelled b_1(0)* 161 to 143 labelled a_1(0)* 161 to 179 labelled b_1(1)* 179 to 180 labelled a_1(1)* 180 to 181 labelled b_1(1)* 181 to 182 labelled a_1(1)* 181 to 179 labelled b_1(1)* 182 to 183 labelled b_1(1)* 183 to 184 labelled a_1(1)* 184 to 185 labelled a_1(1)* 184 to 179 labelled b_1(1)* 185 to 186 labelled b_1(1)* 186 to 187 labelled a_1(1)* 187 to 188 labelled a_1(1)* 187 to 179 labelled b_1(1)* 188 to 189 labelled b_1(1)* 189 to 143 labelled a_1(1)* 189 to 179 labelled b_1(1)


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(6)
YES