/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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, 4 ms]
(4) YES


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

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

Q is empty.

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

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

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

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

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

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

The certificate found is represented by the following graph.
The certificate consists of the following enumerated nodes:
2, 8, 9, 12, 14, 16, 18, 20, 22, 25, 43, 44, 45, 46, 47, 48, 49, 50

Node 2 is start node and node 8 is final node.

Those nodes are connected through the following edges:

* 2 to 9 labelled a_1(0)* 8 to 8 labelled #_1(0)* 9 to 12 labelled b_1(0)* 12 to 14 labelled a_1(0)* 14 to 16 labelled a_1(0)* 16 to 18 labelled b_1(0)* 18 to 20 labelled b_1(0)* 18 to 43 labelled a_1(1)* 20 to 22 labelled a_1(0)* 22 to 25 labelled b_1(0)* 25 to 8 labelled b_1(0)* 25 to 43 labelled a_1(1)* 43 to 44 labelled b_1(1)* 44 to 45 labelled a_1(1)* 45 to 46 labelled a_1(1)* 46 to 47 labelled b_1(1)* 47 to 48 labelled b_1(1)* 47 to 43 labelled a_1(1)* 48 to 49 labelled a_1(1)* 49 to 50 labelled b_1(1)* 50 to 8 labelled b_1(1)* 50 to 43 labelled a_1(1)


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(4)
YES