/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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) Strip Symbols Proof [SOUND, 0 ms]
(2) QTRS
(3) RFCMatchBoundsTRSProof [EQUIVALENT, 3 ms]
(4) YES


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

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

Q is empty.

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

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

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

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

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(2)
Obligation:
Q restricted rewrite system:
The TRS R consists of the following rules:

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

Q is empty.

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(3) 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:

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

The certificate found is represented by the following graph.
The certificate consists of the following enumerated nodes:
2, 4, 27, 28, 29, 30, 31, 32, 33, 34, 35, 46, 47, 48, 49, 50, 51, 52, 53, 54

Node 2 is start node and node 4 is final node.

Those nodes are connected through the following edges:

* 2 to 27 labelled a_1(0)* 4 to 4 labelled #_1(0)* 27 to 28 labelled a_1(0)* 28 to 29 labelled b_1(0)* 29 to 30 labelled b_1(0)* 30 to 31 labelled a_1(0)* 31 to 32 labelled a_1(0)* 32 to 33 labelled b_1(0)* 32 to 46 labelled a_1(1)* 33 to 34 labelled a_1(0)* 34 to 35 labelled a_1(0)* 35 to 4 labelled b_1(0)* 35 to 46 labelled a_1(1)* 46 to 47 labelled a_1(1)* 47 to 48 labelled b_1(1)* 48 to 49 labelled b_1(1)* 49 to 50 labelled a_1(1)* 50 to 51 labelled a_1(1)* 51 to 52 labelled b_1(1)* 51 to 46 labelled a_1(1)* 52 to 53 labelled a_1(1)* 53 to 54 labelled a_1(1)* 54 to 4 labelled b_1(1)* 54 to 46 labelled a_1(1)


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(4)
YES