/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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) Strip Symbols Proof [SOUND, 0 ms]
(2) QTRS
(3) RFCMatchBoundsTRSProof [EQUIVALENT, 6 ms]
(4) YES


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

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

Q is empty.

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

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

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

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

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

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

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

The certificate found is represented by the following graph.
The certificate consists of the following enumerated nodes:
4, 6, 7, 8, 9, 10, 11, 24, 25, 26, 27, 28

Node 4 is start node and node 6 is final node.

Those nodes are connected through the following edges:

* 4 to 7 labelled a_1(0)* 6 to 6 labelled #_1(0)* 7 to 8 labelled b_1(0)* 8 to 9 labelled a_1(0)* 9 to 10 labelled b_1(0)* 10 to 11 labelled b_1(0)* 10 to 24 labelled a_1(1)* 11 to 6 labelled a_1(0)* 24 to 25 labelled b_1(1)* 25 to 26 labelled a_1(1)* 26 to 27 labelled b_1(1)* 27 to 28 labelled b_1(1)* 27 to 24 labelled a_1(1)* 28 to 6 labelled a_1(1)


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(4)
YES