/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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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, 4 ms]
(6) YES


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(0)
Obligation:
Q restricted rewrite system:
The TRS R consists of the following rules:

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

The certificate found is represented by the following graph.
The certificate consists of the following enumerated nodes:
45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108

Node 45 is start node and node 46 is final node.

Those nodes are connected through the following edges:

* 45 to 47 labelled c_1(0)* 46 to 46 labelled #_1(0)* 47 to 48 labelled a_1(0)* 48 to 49 labelled b_1(0)* 49 to 50 labelled a_1(0)* 50 to 51 labelled a_1(0)* 51 to 52 labelled c_1(0)* 52 to 53 labelled a_1(0)* 53 to 54 labelled b_1(0)* 54 to 55 labelled a_1(0)* 54 to 97 labelled c_1(1)* 55 to 56 labelled a_1(0)* 55 to 97 labelled c_1(1)* 56 to 57 labelled a_1(0)* 56 to 97 labelled c_1(1)* 57 to 58 labelled a_1(0)* 57 to 97 labelled c_1(1)* 58 to 46 labelled a_1(0)* 58 to 97 labelled c_1(1)* 97 to 98 labelled a_1(1)* 98 to 99 labelled b_1(1)* 99 to 100 labelled a_1(1)* 100 to 101 labelled a_1(1)* 101 to 102 labelled c_1(1)* 102 to 103 labelled a_1(1)* 103 to 104 labelled b_1(1)* 104 to 105 labelled a_1(1)* 104 to 97 labelled c_1(1)* 105 to 106 labelled a_1(1)* 105 to 97 labelled c_1(1)* 106 to 107 labelled a_1(1)* 106 to 97 labelled c_1(1)* 107 to 108 labelled a_1(1)* 107 to 97 labelled c_1(1)* 108 to 46 labelled a_1(1)* 108 to 97 labelled c_1(1)


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(6)
YES