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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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

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

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

The certificate found is represented by the following graph.
The certificate consists of the following enumerated nodes:
2, 4, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85

Node 2 is start node and node 4 is final node.

Those nodes are connected through the following edges:

* 2 to 23 labelled a_1(0)* 4 to 4 labelled #_1(0)* 23 to 24 labelled b_1(0)* 24 to 25 labelled a_1(0)* 25 to 26 labelled c_1(0)* 26 to 27 labelled b_1(0)* 26 to 59 labelled a_1(1)* 27 to 28 labelled b_1(0)* 27 to 32 labelled a_1(1)* 28 to 29 labelled a_1(0)* 29 to 30 labelled b_1(0)* 30 to 31 labelled a_1(0)* 31 to 4 labelled c_1(0)* 32 to 33 labelled b_1(1)* 33 to 34 labelled a_1(1)* 34 to 35 labelled c_1(1)* 35 to 36 labelled b_1(1)* 35 to 68 labelled a_1(2)* 36 to 37 labelled b_1(1)* 36 to 32 labelled a_1(1)* 37 to 38 labelled a_1(1)* 38 to 39 labelled b_1(1)* 39 to 40 labelled a_1(1)* 40 to 4 labelled c_1(1)* 59 to 60 labelled b_1(1)* 60 to 61 labelled a_1(1)* 61 to 62 labelled c_1(1)* 62 to 63 labelled b_1(1)* 63 to 64 labelled b_1(1)* 63 to 77 labelled a_1(2)* 64 to 65 labelled a_1(1)* 65 to 66 labelled b_1(1)* 66 to 67 labelled a_1(1)* 67 to 32 labelled c_1(1)* 68 to 69 labelled b_1(2)* 69 to 70 labelled a_1(2)* 70 to 71 labelled c_1(2)* 71 to 72 labelled b_1(2)* 72 to 73 labelled b_1(2)* 72 to 77 labelled a_1(2)* 73 to 74 labelled a_1(2)* 74 to 75 labelled b_1(2)* 75 to 76 labelled a_1(2)* 76 to 32 labelled c_1(2)* 77 to 78 labelled b_1(2)* 78 to 79 labelled a_1(2)* 79 to 80 labelled c_1(2)* 80 to 81 labelled b_1(2)* 81 to 82 labelled b_1(2)* 82 to 83 labelled a_1(2)* 83 to 84 labelled b_1(2)* 84 to 85 labelled a_1(2)* 85 to 34 labelled c_1(2)


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(2)
YES