/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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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:

   a__g(X) -> a__h(X)
   a__c -> d
   a__h(d) -> a__g(c)
   mark(g(X)) -> a__g(X)
   mark(h(X)) -> a__h(X)
   mark(c) -> a__c
   mark(d) -> d
   a__g(X) -> g(X)
   a__h(X) -> h(X)
   a__c -> c

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 4. This implies Q-termination of R.
The following rules were used to construct the certificate:

   a__g(X) -> a__h(X)
   a__c -> d
   a__h(d) -> a__g(c)
   mark(g(X)) -> a__g(X)
   mark(h(X)) -> a__h(X)
   mark(c) -> a__c
   mark(d) -> d
   a__g(X) -> g(X)
   a__h(X) -> h(X)
   a__c -> c

The certificate found is represented by the following graph.
The certificate consists of the following enumerated nodes:
1, 2, 3, 4

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

Those nodes are connected through the following edges:

* 1 to 2 labelled a__h_1(0), d(0), a__g_1(0), a__c(0), g_1(0), h_1(0), c(0), h_1(1), a__h_1(1), g_1(1), d(1), c(1), h_1(2)* 1 to 3 labelled a__g_1(0), a__h_1(1), g_1(1), h_1(2)* 1 to 1 labelled a__g_1(1), a__h_1(2), g_1(2), h_1(3)* 1 to 4 labelled a__g_1(2), a__h_1(3), g_1(3), h_1(4)* 2 to 2 labelled #_1(0)* 3 to 2 labelled c(0)* 4 to 2 labelled c(2)


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(2)
YES