/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# AProVE Commit ID: c69e44bd14796315568835c1ffa2502984884775 mhark 20210624 unpublished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, 0 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(b(a(a(a(b(x1)))))))))) -> a(b(a(b(a(a(a(b(a(b(a(a(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(b(a(a(a(b(x1)))))))))) -> a(b(a(b(a(a(a(b(a(b(a(a(b(x1)))))))))))))

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

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

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

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

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

The certificate found is represented by the following graph.
The certificate consists of the following enumerated nodes:
3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84

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

Those nodes are connected through the following edges:

* 3 to 5 labelled a_1(0)* 4 to 4 labelled #_1(0)* 5 to 6 labelled b_1(0)* 6 to 7 labelled a_1(0)* 7 to 8 labelled b_1(0)* 8 to 9 labelled a_1(0)* 9 to 10 labelled a_1(0)* 10 to 11 labelled a_1(0)* 11 to 12 labelled b_1(0)* 11 to 27 labelled a_1(1)* 12 to 13 labelled a_1(0)* 13 to 14 labelled b_1(0)* 13 to 16 labelled a_1(1)* 14 to 15 labelled a_1(0)* 15 to 4 labelled a_1(0)* 16 to 17 labelled b_1(1)* 17 to 18 labelled a_1(1)* 18 to 19 labelled b_1(1)* 19 to 20 labelled a_1(1)* 20 to 21 labelled a_1(1)* 21 to 22 labelled a_1(1)* 22 to 23 labelled b_1(1)* 22 to 74 labelled a_1(2)* 23 to 24 labelled a_1(1)* 24 to 25 labelled b_1(1)* 24 to 16 labelled a_1(1)* 25 to 26 labelled a_1(1)* 26 to 4 labelled a_1(1)* 27 to 28 labelled b_1(1)* 28 to 29 labelled a_1(1)* 29 to 30 labelled b_1(1)* 30 to 31 labelled a_1(1)* 31 to 32 labelled a_1(1)* 32 to 33 labelled a_1(1)* 33 to 34 labelled b_1(1)* 33 to 74 labelled a_1(2)* 34 to 35 labelled a_1(1)* 35 to 36 labelled b_1(1)* 35 to 16 labelled a_1(1)* 36 to 37 labelled a_1(1)* 37 to 22 labelled a_1(1)* 74 to 75 labelled b_1(2)* 75 to 76 labelled a_1(2)* 76 to 77 labelled b_1(2)* 77 to 78 labelled a_1(2)* 78 to 79 labelled a_1(2)* 79 to 80 labelled a_1(2)* 80 to 81 labelled b_1(2)* 80 to 74 labelled a_1(2)* 81 to 82 labelled a_1(2)* 82 to 83 labelled b_1(2)* 82 to 16 labelled a_1(1)* 83 to 84 labelled a_1(2)* 84 to 22 labelled a_1(2)


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(4)
YES