/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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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, 0 ms]
(2) YES


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

   c(b(a(X))) -> a(a(b(b(c(c(X))))))
   a(X) -> e
   b(X) -> e
   c(X) -> e

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(b(a(X))) -> a(a(b(b(c(c(X))))))
   a(X) -> e
   b(X) -> e
   c(X) -> e

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

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), e(1)* 1 to 2 labelled e(0)* 2 to 2 labelled #_1(0)* 3 to 4 labelled a_1(0), e(1)* 4 to 5 labelled b_1(0), e(1)* 5 to 6 labelled b_1(0), e(1)* 6 to 7 labelled c_1(0), e(1)* 7 to 2 labelled c_1(0), e(1)* 7 to 8 labelled a_1(1), e(2)* 8 to 9 labelled a_1(1), e(2)* 9 to 10 labelled b_1(1), e(2)* 10 to 11 labelled b_1(1), e(2)* 11 to 12 labelled c_1(1), e(2)* 12 to 2 labelled c_1(1), e(2)* 12 to 8 labelled a_1(1), e(2)


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(2)
YES