/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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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, 1 ms]
(6) YES


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

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

The certificate found is represented by the following graph.
The certificate consists of the following enumerated nodes:
3, 5, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32

Node 3 is start node and node 5 is final node.

Those nodes are connected through the following edges:

* 3 to 9 labelled c_1(0)* 5 to 5 labelled #_1(0)* 9 to 10 labelled b_1(0)* 10 to 11 labelled b_1(0)* 11 to 12 labelled a_1(0)* 12 to 13 labelled a_1(0)* 13 to 14 labelled a_1(0)* 14 to 15 labelled c_1(0)* 15 to 16 labelled b_1(0)* 16 to 17 labelled b_1(0)* 17 to 18 labelled a_1(0)* 17 to 21 labelled c_1(1)* 18 to 19 labelled a_1(0)* 18 to 21 labelled c_1(1)* 19 to 20 labelled a_1(0)* 19 to 21 labelled c_1(1)* 20 to 5 labelled a_1(0)* 20 to 21 labelled c_1(1)* 21 to 22 labelled b_1(1)* 22 to 23 labelled b_1(1)* 23 to 24 labelled a_1(1)* 24 to 25 labelled a_1(1)* 25 to 26 labelled a_1(1)* 26 to 27 labelled c_1(1)* 27 to 28 labelled b_1(1)* 28 to 29 labelled b_1(1)* 29 to 30 labelled a_1(1)* 29 to 21 labelled c_1(1)* 30 to 31 labelled a_1(1)* 30 to 21 labelled c_1(1)* 31 to 32 labelled a_1(1)* 31 to 21 labelled c_1(1)* 32 to 5 labelled a_1(1)* 32 to 21 labelled c_1(1)


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(6)
YES