/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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, 0 ms]
(4) YES


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

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

Q is empty.

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

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

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

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

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

   b(b(a(a(b(x1))))) -> a(b(b(a(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 0. This implies Q-termination of R.
The following rules were used to construct the certificate:

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

The certificate found is represented by the following graph.
The certificate consists of the following enumerated nodes:
3, 4, 11, 12, 13, 14, 15

Node 3 is start node and node 4 is final node.

Those nodes are connected through the following edges:

* 3 to 11 labelled a_1(0)* 4 to 4 labelled #_1(0)* 11 to 12 labelled b_1(0)* 12 to 13 labelled b_1(0)* 13 to 14 labelled a_1(0)* 14 to 15 labelled b_1(0)* 15 to 4 labelled a_1(0)


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(4)
YES