/export/starexec/sandbox2/solver/bin/starexec_run_standard /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files


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YES
proof of /export/starexec/sandbox2/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# AProVE Commit ID: c69e44bd14796315568835c1ffa2502984884775 mhark 20210624 unpublished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) RFCMatchBoundsTRSProof [EQUIVALENT, 8 ms]
(2) YES


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

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

Q is empty.

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

The certificate found is represented by the following graph.
The certificate consists of the following enumerated nodes:
1, 3, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74

Node 1 is start node and node 3 is final node.

Those nodes are connected through the following edges:

* 1 to 40 labelled b_1(0)* 3 to 3 labelled #_1(0)* 40 to 41 labelled b_1(0)* 41 to 42 labelled b_1(0)* 42 to 43 labelled b_1(0)* 43 to 44 labelled a_1(0)* 43 to 54 labelled b_1(1)* 44 to 45 labelled a_1(0)* 44 to 47 labelled b_1(1)* 45 to 46 labelled a_1(0)* 45 to 47 labelled b_1(1)* 46 to 3 labelled a_1(0)* 46 to 47 labelled b_1(1)* 47 to 48 labelled b_1(1)* 48 to 49 labelled b_1(1)* 49 to 50 labelled b_1(1)* 50 to 51 labelled a_1(1)* 50 to 61 labelled b_1(2)* 51 to 52 labelled a_1(1)* 51 to 47 labelled b_1(1)* 52 to 53 labelled a_1(1)* 52 to 47 labelled b_1(1)* 53 to 3 labelled a_1(1)* 53 to 47 labelled b_1(1)* 54 to 55 labelled b_1(1)* 55 to 56 labelled b_1(1)* 56 to 57 labelled b_1(1)* 57 to 58 labelled a_1(1)* 58 to 59 labelled a_1(1)* 58 to 68 labelled b_1(2)* 59 to 60 labelled a_1(1)* 60 to 49 labelled a_1(1)* 61 to 62 labelled b_1(2)* 62 to 63 labelled b_1(2)* 63 to 64 labelled b_1(2)* 64 to 65 labelled a_1(2)* 65 to 66 labelled a_1(2)* 65 to 68 labelled b_1(2)* 66 to 67 labelled a_1(2)* 67 to 49 labelled a_1(2)* 68 to 69 labelled b_1(2)* 69 to 70 labelled b_1(2)* 70 to 71 labelled b_1(2)* 71 to 72 labelled a_1(2)* 72 to 73 labelled a_1(2)* 73 to 74 labelled a_1(2)* 74 to 62 labelled a_1(2)


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(2)
YES