/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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty


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

(0) QTRS
(1) RFCMatchBoundsTRSProof [EQUIVALENT, 11 ms]
(2) YES


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

   a(b(a(a(x1)))) -> c(b(a(b(a(x1)))))
   a(c(b(x1))) -> a(a(b(c(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 2. This implies Q-termination of R.
The following rules were used to construct the certificate:

   a(b(a(a(x1)))) -> c(b(a(b(a(x1)))))
   a(c(b(x1))) -> a(a(b(c(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, 23, 24, 25, 26, 27, 28, 29, 30, 31, 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 c_1(0)* 1 to 9 labelled a_1(0)* 2 to 2 labelled #_1(0)* 5 to 6 labelled b_1(0)* 6 to 7 labelled a_1(0)* 6 to 23 labelled c_1(1)* 7 to 8 labelled b_1(0)* 8 to 2 labelled a_1(0)* 8 to 23 labelled c_1(1)* 8 to 27 labelled a_1(1)* 9 to 10 labelled a_1(0)* 10 to 11 labelled b_1(0)* 11 to 12 labelled c_1(0)* 12 to 13 labelled b_1(0)* 13 to 2 labelled a_1(0)* 13 to 23 labelled c_1(1)* 13 to 27 labelled a_1(1)* 23 to 24 labelled b_1(1)* 24 to 25 labelled a_1(1)* 24 to 23 labelled c_1(1)* 24 to 55 labelled c_1(2)* 25 to 26 labelled b_1(1)* 26 to 2 labelled a_1(1)* 26 to 23 labelled c_1(1)* 26 to 27 labelled a_1(1)* 26 to 28 labelled a_1(1)* 27 to 28 labelled a_1(1)* 28 to 29 labelled b_1(1)* 29 to 30 labelled c_1(1)* 30 to 31 labelled b_1(1)* 31 to 2 labelled a_1(1)* 31 to 23 labelled c_1(1)* 31 to 27 labelled a_1(1)* 55 to 56 labelled b_1(2)* 56 to 57 labelled a_1(2)* 57 to 58 labelled b_1(2)* 58 to 28 labelled a_1(2)


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(2)
YES