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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty


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

(0) QTRS
(1) RFCMatchBoundsTRSProof [EQUIVALENT, 22 ms]
(2) 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(x1)))))) -> a(b(a(b(a(b(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 3. This implies Q-termination of R.
The following rules were used to construct the certificate:

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

The certificate found is represented by the following graph.
The certificate consists of the following enumerated nodes:
1, 2, 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, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58

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

Those nodes are connected through the following edges:

* 1 to 5 labelled a_1(0)* 2 to 2 labelled #_1(0)* 5 to 6 labelled b_1(0)* 5 to 23 labelled a_1(1)* 6 to 7 labelled a_1(0)* 7 to 8 labelled b_1(0)* 7 to 17 labelled a_1(1)* 8 to 9 labelled a_1(0)* 9 to 10 labelled b_1(0)* 9 to 11 labelled a_1(1)* 10 to 2 labelled a_1(0)* 11 to 12 labelled b_1(1)* 11 to 47 labelled a_1(2)* 12 to 13 labelled a_1(1)* 13 to 14 labelled b_1(1)* 13 to 29 labelled a_1(2)* 14 to 15 labelled a_1(1)* 15 to 16 labelled b_1(1)* 15 to 11 labelled a_1(1)* 16 to 2 labelled a_1(1)* 17 to 18 labelled b_1(1)* 17 to 47 labelled a_1(2)* 18 to 19 labelled a_1(1)* 19 to 20 labelled b_1(1)* 19 to 29 labelled a_1(2)* 20 to 21 labelled a_1(1)* 21 to 22 labelled b_1(1)* 21 to 11 labelled a_1(1)* 22 to 14 labelled a_1(1)* 23 to 24 labelled b_1(1)* 24 to 25 labelled a_1(1)* 25 to 26 labelled b_1(1)* 26 to 27 labelled a_1(1)* 27 to 28 labelled b_1(1)* 28 to 20 labelled a_1(1)* 29 to 30 labelled b_1(2)* 29 to 53 labelled a_1(3)* 30 to 31 labelled a_1(2)* 31 to 32 labelled b_1(2)* 31 to 29 labelled a_1(2)* 32 to 33 labelled a_1(2)* 33 to 34 labelled b_1(2)* 33 to 11 labelled a_1(1)* 34 to 14 labelled a_1(2)* 47 to 48 labelled b_1(2)* 48 to 49 labelled a_1(2)* 49 to 50 labelled b_1(2)* 50 to 51 labelled a_1(2)* 51 to 52 labelled b_1(2)* 52 to 32 labelled a_1(2)* 53 to 54 labelled b_1(3)* 54 to 55 labelled a_1(3)* 55 to 56 labelled b_1(3)* 56 to 57 labelled a_1(3)* 57 to 58 labelled b_1(3)* 58 to 32 labelled a_1(3)


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(2)
YES