/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# AProVE Commit ID: c69e44bd14796315568835c1ffa2502984884775 mhark 20210624 unpublished


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, 2 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(a(a(b(b(a(a(b(x1))))))))))) -> a(a(b(b(a(a(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(a(a(b(b(a(a(b(x1))))))))))) -> a(a(b(b(a(a(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(a(a(b(b(a(a(x)))))))))) -> a(a(b(b(a(a(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(a(a(b(b(a(a(x)))))))))) -> a(a(b(b(a(a(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(a(a(b(b(a(a(x)))))))))) -> a(a(b(b(a(a(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:
3, 4, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82

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

Those nodes are connected through the following edges:

* 3 to 47 labelled a_1(0)* 4 to 4 labelled #_1(0)* 47 to 48 labelled a_1(0)* 48 to 49 labelled b_1(0)* 49 to 50 labelled b_1(0)* 50 to 51 labelled a_1(0)* 51 to 52 labelled a_1(0)* 52 to 53 labelled b_1(0)* 52 to 71 labelled a_1(1)* 53 to 54 labelled a_1(0)* 54 to 55 labelled a_1(0)* 55 to 56 labelled b_1(0)* 55 to 71 labelled a_1(1)* 56 to 57 labelled a_1(0)* 57 to 58 labelled a_1(0)* 58 to 4 labelled b_1(0)* 58 to 71 labelled a_1(1)* 71 to 72 labelled a_1(1)* 72 to 73 labelled b_1(1)* 73 to 74 labelled b_1(1)* 74 to 75 labelled a_1(1)* 75 to 76 labelled a_1(1)* 76 to 77 labelled b_1(1)* 76 to 71 labelled a_1(1)* 77 to 78 labelled a_1(1)* 78 to 79 labelled a_1(1)* 79 to 80 labelled b_1(1)* 79 to 71 labelled a_1(1)* 80 to 81 labelled a_1(1)* 81 to 82 labelled a_1(1)* 82 to 4 labelled b_1(1)* 82 to 71 labelled a_1(1)


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(4)
YES