/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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, 0 ms]
(2) YES


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

   c(a(a(b(c(a(x1)))))) -> a(a(b(c(c(a(a(b(c(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:

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

The certificate found is represented by the following graph.
The certificate consists of the following enumerated nodes:
1, 3, 5, 6, 7, 8, 9, 10, 11, 12, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 61, 62, 63, 64, 65, 66, 67, 68

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

Those nodes are connected through the following edges:

* 1 to 5 labelled a_1(0)* 3 to 3 labelled #_1(0)* 5 to 6 labelled a_1(0)* 6 to 7 labelled b_1(0)* 7 to 8 labelled c_1(0)* 7 to 29 labelled a_1(1)* 8 to 9 labelled c_1(0)* 8 to 21 labelled a_1(1)* 9 to 10 labelled a_1(0)* 10 to 11 labelled a_1(0)* 11 to 12 labelled b_1(0)* 12 to 3 labelled c_1(0)* 12 to 21 labelled a_1(1)* 21 to 22 labelled a_1(1)* 22 to 23 labelled b_1(1)* 23 to 24 labelled c_1(1)* 23 to 37 labelled a_1(2)* 24 to 25 labelled c_1(1)* 24 to 21 labelled a_1(1)* 25 to 26 labelled a_1(1)* 26 to 27 labelled a_1(1)* 27 to 28 labelled b_1(1)* 28 to 3 labelled c_1(1)* 28 to 21 labelled a_1(1)* 29 to 30 labelled a_1(1)* 30 to 31 labelled b_1(1)* 31 to 32 labelled c_1(1)* 32 to 33 labelled c_1(1)* 32 to 61 labelled a_1(2)* 33 to 34 labelled a_1(1)* 34 to 35 labelled a_1(1)* 35 to 36 labelled b_1(1)* 36 to 21 labelled c_1(1)* 37 to 38 labelled a_1(2)* 38 to 39 labelled b_1(2)* 39 to 40 labelled c_1(2)* 40 to 41 labelled c_1(2)* 40 to 61 labelled a_1(2)* 41 to 42 labelled a_1(2)* 42 to 43 labelled a_1(2)* 43 to 44 labelled b_1(2)* 44 to 21 labelled c_1(2)* 61 to 62 labelled a_1(2)* 62 to 63 labelled b_1(2)* 63 to 64 labelled c_1(2)* 64 to 65 labelled c_1(2)* 65 to 66 labelled a_1(2)* 66 to 67 labelled a_1(2)* 67 to 68 labelled b_1(2)* 68 to 22 labelled c_1(2)


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(2)
YES