/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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, 3 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(b(b(c(a(x1)))))))))) -> a(a(b(b(c(a(b(b(c(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(c(b(b(a(a(c(b(b(a(x1)))))))))) -> c(b(b(a(a(c(b(b(a(c(b(b(a(a(x1))))))))))))))

Q is empty.

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

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

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

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

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

   a(c(b(b(a(a(c(b(b(x))))))))) -> c(b(b(a(a(c(b(b(a(c(b(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(c(b(b(a(a(c(b(b(x))))))))) -> c(b(b(a(a(c(b(b(a(c(b(b(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, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83

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 b_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 b_1(0)* 53 to 54 labelled b_1(0)* 54 to 55 labelled a_1(0)* 54 to 72 labelled c_1(1)* 55 to 56 labelled c_1(0)* 56 to 57 labelled b_1(0)* 57 to 58 labelled b_1(0)* 58 to 46 labelled a_1(0)* 58 to 72 labelled c_1(1)* 72 to 73 labelled b_1(1)* 73 to 74 labelled b_1(1)* 74 to 75 labelled a_1(1)* 75 to 76 labelled a_1(1)* 76 to 77 labelled c_1(1)* 77 to 78 labelled b_1(1)* 78 to 79 labelled b_1(1)* 79 to 80 labelled a_1(1)* 79 to 72 labelled c_1(1)* 80 to 81 labelled c_1(1)* 81 to 82 labelled b_1(1)* 82 to 83 labelled b_1(1)* 83 to 46 labelled a_1(1)* 83 to 72 labelled c_1(1)


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(6)
YES