/export/starexec/sandbox2/solver/bin/starexec_run_standard /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files


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YES
proof of /export/starexec/sandbox2/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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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(c(b(a(b(a(c(b(a(x1))))))))) -> a(b(a(c(b(a(c(b(a(b(a(c(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(c(a(b(a(b(c(a(x1))))))))) -> c(a(b(a(b(c(a(b(c(a(b(a(x1))))))))))))

Q is empty.

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(3) Strip Symbols Proof (SOUND)
We were given the following TRS:

   a(b(c(a(b(a(b(c(a(x1))))))))) -> c(a(b(a(b(c(a(b(c(a(b(a(x1))))))))))))

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

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

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(4)
Obligation:
Q restricted rewrite system:
The TRS R consists of the following rules:

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

The certificate found is represented by the following graph.
The certificate consists of the following enumerated nodes:
4, 8, 73, 74, 75, 77, 78, 80, 82, 84, 86, 88, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102

Node 4 is start node and node 8 is final node.

Those nodes are connected through the following edges:

* 4 to 73 labelled c_1(0)* 8 to 8 labelled #_1(0)* 73 to 74 labelled a_1(0)* 74 to 75 labelled b_1(0)* 75 to 77 labelled a_1(0)* 77 to 78 labelled b_1(0)* 78 to 80 labelled c_1(0)* 80 to 82 labelled a_1(0)* 80 to 93 labelled c_1(1)* 82 to 84 labelled b_1(0)* 84 to 86 labelled c_1(0)* 86 to 88 labelled a_1(0)* 86 to 93 labelled c_1(1)* 88 to 8 labelled b_1(0)* 93 to 94 labelled a_1(1)* 94 to 95 labelled b_1(1)* 95 to 96 labelled a_1(1)* 96 to 97 labelled b_1(1)* 97 to 98 labelled c_1(1)* 98 to 99 labelled a_1(1)* 98 to 93 labelled c_1(1)* 99 to 100 labelled b_1(1)* 100 to 101 labelled c_1(1)* 101 to 102 labelled a_1(1)* 101 to 93 labelled c_1(1)* 102 to 8 labelled b_1(1)


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(6)
YES