/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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) QTRS Reverse [EQUIVALENT, 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:

   b(a(b(a(a(x1))))) -> a(a(b(b(a(b(a(b(a(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(b(a(b(x1))))) -> a(b(a(b(a(b(b(a(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 2. This implies Q-termination of R.
The following rules were used to construct the certificate:

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

The certificate found is represented by the following graph.
The certificate consists of the following enumerated nodes:
5, 6, 22, 23, 24, 25, 26, 27, 28, 29, 46, 47, 48, 49, 50, 51, 52, 53, 70, 71, 72, 73, 74, 75, 76, 77

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

Those nodes are connected through the following edges:

* 5 to 22 labelled a_1(0)* 6 to 6 labelled #_1(0)* 22 to 23 labelled b_1(0)* 23 to 24 labelled a_1(0)* 24 to 25 labelled b_1(0)* 25 to 26 labelled a_1(0)* 26 to 27 labelled b_1(0)* 27 to 28 labelled b_1(0)* 28 to 29 labelled a_1(0)* 28 to 46 labelled a_1(1)* 29 to 6 labelled a_1(0)* 29 to 46 labelled a_1(1)* 46 to 47 labelled b_1(1)* 47 to 48 labelled a_1(1)* 48 to 49 labelled b_1(1)* 49 to 50 labelled a_1(1)* 50 to 51 labelled b_1(1)* 51 to 52 labelled b_1(1)* 52 to 53 labelled a_1(1)* 52 to 46 labelled a_1(1)* 52 to 70 labelled a_1(2)* 53 to 6 labelled a_1(1)* 53 to 46 labelled a_1(1)* 53 to 49 labelled a_1(1)* 70 to 71 labelled b_1(2)* 71 to 72 labelled a_1(2)* 72 to 73 labelled b_1(2)* 73 to 74 labelled a_1(2)* 74 to 75 labelled b_1(2)* 75 to 76 labelled b_1(2)* 76 to 77 labelled a_1(2)* 77 to 49 labelled a_1(2)


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(4)
YES