/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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, 9 ms]
(2) YES


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

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

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

The certificate found is represented by the following graph.
The certificate consists of the following enumerated nodes:
1, 3, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112

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

Those nodes are connected through the following edges:

* 1 to 17 labelled a_1(0)* 3 to 3 labelled #_1(0)* 17 to 18 labelled b_1(0)* 18 to 19 labelled a_1(0)* 19 to 20 labelled b_1(0)* 20 to 21 labelled b_1(0)* 21 to 22 labelled a_1(0)* 22 to 23 labelled b_1(0)* 23 to 24 labelled b_1(0)* 24 to 25 labelled c_1(0)* 24 to 89 labelled a_1(1)* 25 to 26 labelled a_1(0)* 26 to 27 labelled b_1(0)* 27 to 28 labelled c_1(0)* 27 to 77 labelled a_1(1)* 28 to 3 labelled a_1(0)* 77 to 78 labelled b_1(1)* 78 to 79 labelled a_1(1)* 79 to 80 labelled b_1(1)* 80 to 81 labelled b_1(1)* 81 to 82 labelled a_1(1)* 82 to 83 labelled b_1(1)* 83 to 84 labelled b_1(1)* 84 to 85 labelled c_1(1)* 84 to 101 labelled a_1(2)* 85 to 86 labelled a_1(1)* 86 to 87 labelled b_1(1)* 87 to 88 labelled c_1(1)* 87 to 77 labelled a_1(1)* 88 to 3 labelled a_1(1)* 89 to 90 labelled b_1(1)* 90 to 91 labelled a_1(1)* 91 to 92 labelled b_1(1)* 92 to 93 labelled b_1(1)* 93 to 94 labelled a_1(1)* 94 to 95 labelled b_1(1)* 95 to 96 labelled b_1(1)* 96 to 97 labelled c_1(1)* 97 to 98 labelled a_1(1)* 98 to 99 labelled b_1(1)* 99 to 100 labelled c_1(1)* 100 to 78 labelled a_1(1)* 101 to 102 labelled b_1(2)* 102 to 103 labelled a_1(2)* 103 to 104 labelled b_1(2)* 104 to 105 labelled b_1(2)* 105 to 106 labelled a_1(2)* 106 to 107 labelled b_1(2)* 107 to 108 labelled b_1(2)* 108 to 109 labelled c_1(2)* 109 to 110 labelled a_1(2)* 110 to 111 labelled b_1(2)* 111 to 112 labelled c_1(2)* 112 to 78 labelled a_1(2)


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(2)
YES