/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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, 5 ms]
(6) YES


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

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

The certificate found is represented by the following graph.
The certificate consists of the following enumerated nodes:
5, 6, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89

Node 5 is start node and node 6 is final node.

Those nodes are connected through the following edges:

* 5 to 32 labelled b_1(0)* 6 to 6 labelled #_1(0)* 32 to 33 labelled c_1(0)* 33 to 34 labelled b_1(0)* 34 to 35 labelled a_1(0)* 35 to 36 labelled a_1(0)* 36 to 37 labelled b_1(0)* 37 to 38 labelled c_1(0)* 38 to 39 labelled b_1(0)* 39 to 40 labelled a_1(0)* 39 to 79 labelled b_1(1)* 40 to 41 labelled a_1(0)* 40 to 79 labelled b_1(1)* 41 to 42 labelled a_1(0)* 41 to 79 labelled b_1(1)* 42 to 6 labelled a_1(0)* 42 to 79 labelled b_1(1)* 79 to 80 labelled c_1(1)* 80 to 81 labelled b_1(1)* 81 to 82 labelled a_1(1)* 82 to 83 labelled a_1(1)* 83 to 84 labelled b_1(1)* 84 to 85 labelled c_1(1)* 85 to 86 labelled b_1(1)* 86 to 87 labelled a_1(1)* 86 to 79 labelled b_1(1)* 87 to 88 labelled a_1(1)* 87 to 79 labelled b_1(1)* 88 to 89 labelled a_1(1)* 88 to 79 labelled b_1(1)* 89 to 6 labelled a_1(1)* 89 to 79 labelled b_1(1)


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(6)
YES