/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty


Termination w.r.t. Q of the given QTRS could be proven:

(0) QTRS
(1) RFCMatchBoundsTRSProof [EQUIVALENT, 0 ms]
(2) YES


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

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

The certificate found is represented by the following graph.
The certificate consists of the following enumerated nodes:
1, 2, 7, 8, 9, 10, 11, 12, 13, 14, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84

Node 1 is start node and node 2 is final node.

Those nodes are connected through the following edges:

* 1 to 7 labelled a_1(0)* 2 to 2 labelled #_1(0)* 7 to 8 labelled b_1(0)* 8 to 9 labelled a_1(0)* 8 to 38 labelled a_1(1)* 9 to 10 labelled a_1(0)* 10 to 11 labelled b_1(0)* 11 to 12 labelled a_1(0)* 11 to 46 labelled a_1(1)* 12 to 13 labelled a_1(0)* 12 to 30 labelled a_1(1)* 13 to 14 labelled a_1(0)* 14 to 2 labelled b_1(0)* 30 to 31 labelled b_1(1)* 31 to 32 labelled a_1(1)* 31 to 69 labelled a_1(2)* 32 to 33 labelled a_1(1)* 33 to 34 labelled b_1(1)* 34 to 35 labelled a_1(1)* 34 to 77 labelled a_1(2)* 35 to 36 labelled a_1(1)* 35 to 30 labelled a_1(1)* 36 to 37 labelled a_1(1)* 37 to 2 labelled b_1(1)* 38 to 39 labelled b_1(1)* 39 to 40 labelled a_1(1)* 40 to 41 labelled a_1(1)* 41 to 42 labelled b_1(1)* 42 to 43 labelled a_1(1)* 43 to 44 labelled a_1(1)* 44 to 45 labelled a_1(1)* 45 to 32 labelled b_1(1)* 45 to 69 labelled b_1(1)* 46 to 47 labelled b_1(1)* 47 to 48 labelled a_1(1)* 47 to 69 labelled a_1(2)* 48 to 49 labelled a_1(1)* 49 to 50 labelled b_1(1)* 50 to 51 labelled a_1(1)* 50 to 77 labelled a_1(2)* 51 to 52 labelled a_1(1)* 51 to 30 labelled a_1(1)* 52 to 53 labelled a_1(1)* 53 to 35 labelled b_1(1)* 53 to 77 labelled b_1(1)* 69 to 70 labelled b_1(2)* 70 to 71 labelled a_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 a_1(2)* 75 to 76 labelled a_1(2)* 76 to 32 labelled b_1(2)* 76 to 69 labelled b_1(2)* 77 to 78 labelled b_1(2)* 78 to 79 labelled a_1(2)* 78 to 69 labelled a_1(2)* 79 to 80 labelled a_1(2)* 80 to 81 labelled b_1(2)* 81 to 82 labelled a_1(2)* 81 to 77 labelled a_1(2)* 82 to 83 labelled a_1(2)* 82 to 30 labelled a_1(1)* 83 to 84 labelled a_1(2)* 84 to 35 labelled b_1(2)* 84 to 77 labelled b_1(2)


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(2)
YES