/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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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, 15 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:
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67

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

Those nodes are connected through the following edges:

* 1 to 3 labelled a_1(0)* 2 to 2 labelled #_1(0)* 3 to 4 labelled b_1(0)* 4 to 5 labelled a_1(0)* 5 to 6 labelled c_1(0)* 6 to 7 labelled b_1(0)* 6 to 41 labelled a_1(1)* 7 to 8 labelled b_1(0)* 7 to 12 labelled a_1(1)* 8 to 9 labelled a_1(0)* 9 to 10 labelled b_1(0)* 10 to 11 labelled a_1(0)* 11 to 2 labelled c_1(0)* 12 to 13 labelled b_1(1)* 13 to 14 labelled a_1(1)* 14 to 15 labelled c_1(1)* 15 to 16 labelled b_1(1)* 15 to 50 labelled a_1(2)* 16 to 17 labelled b_1(1)* 16 to 12 labelled a_1(1)* 17 to 18 labelled a_1(1)* 18 to 19 labelled b_1(1)* 19 to 20 labelled a_1(1)* 20 to 2 labelled c_1(1)* 41 to 42 labelled b_1(1)* 42 to 43 labelled a_1(1)* 43 to 44 labelled c_1(1)* 44 to 45 labelled b_1(1)* 45 to 46 labelled b_1(1)* 45 to 59 labelled a_1(2)* 46 to 47 labelled a_1(1)* 47 to 48 labelled b_1(1)* 48 to 49 labelled a_1(1)* 49 to 12 labelled c_1(1)* 50 to 51 labelled b_1(2)* 51 to 52 labelled a_1(2)* 52 to 53 labelled c_1(2)* 53 to 54 labelled b_1(2)* 54 to 55 labelled b_1(2)* 54 to 59 labelled a_1(2)* 55 to 56 labelled a_1(2)* 56 to 57 labelled b_1(2)* 57 to 58 labelled a_1(2)* 58 to 12 labelled c_1(2)* 59 to 60 labelled b_1(2)* 60 to 61 labelled a_1(2)* 61 to 62 labelled c_1(2)* 62 to 63 labelled b_1(2)* 63 to 64 labelled b_1(2)* 64 to 65 labelled a_1(2)* 65 to 66 labelled b_1(2)* 66 to 67 labelled a_1(2)* 67 to 14 labelled c_1(2)


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(2)
YES