/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# AProVE Commit ID: c69e44bd14796315568835c1ffa2502984884775 mhark 20210624 unpublished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) QTRS Reverse [EQUIVALENT, 0 ms]
(2) QTRS
(3) Strip Symbols Proof [SOUND, 0 ms]
(4) QTRS
(5) RFCMatchBoundsTRSProof [EQUIVALENT, 0 ms]
(6) 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(a(x1))))))) -> a(b(a(a(b(b(a(a(b(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(b(a(a(b(b(a(x1))))))) -> b(a(a(b(b(a(a(b(a(x1)))))))))

Q is empty.

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

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

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

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

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(4)
Obligation:
Q restricted rewrite system:
The TRS R consists of the following rules:

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

Q is empty.

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

The certificate found is represented by the following graph.
The certificate consists of the following enumerated nodes:
3, 4, 16, 17, 18, 19, 20, 21, 22, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 75, 76, 77, 78, 79, 80, 81

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

Those nodes are connected through the following edges:

* 3 to 16 labelled b_1(0)* 4 to 4 labelled #_1(0)* 16 to 17 labelled a_1(0)* 17 to 18 labelled a_1(0)* 18 to 19 labelled b_1(0)* 19 to 20 labelled b_1(0)* 20 to 21 labelled a_1(0)* 20 to 60 labelled b_1(1)* 21 to 22 labelled a_1(0)* 21 to 53 labelled b_1(1)* 22 to 4 labelled b_1(0)* 53 to 54 labelled a_1(1)* 54 to 55 labelled a_1(1)* 55 to 56 labelled b_1(1)* 56 to 57 labelled b_1(1)* 57 to 58 labelled a_1(1)* 57 to 75 labelled b_1(2)* 58 to 59 labelled a_1(1)* 58 to 53 labelled b_1(1)* 59 to 4 labelled b_1(1)* 60 to 61 labelled a_1(1)* 61 to 62 labelled a_1(1)* 62 to 63 labelled b_1(1)* 63 to 64 labelled b_1(1)* 64 to 65 labelled a_1(1)* 64 to 75 labelled b_1(2)* 65 to 66 labelled a_1(1)* 65 to 53 labelled b_1(1)* 66 to 57 labelled b_1(1)* 75 to 76 labelled a_1(2)* 76 to 77 labelled a_1(2)* 77 to 78 labelled b_1(2)* 78 to 79 labelled b_1(2)* 79 to 80 labelled a_1(2)* 79 to 75 labelled b_1(2)* 80 to 81 labelled a_1(2)* 80 to 53 labelled b_1(1)* 81 to 57 labelled b_1(2)


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(6)
YES