/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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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) QTRS Reverse [EQUIVALENT, 0 ms]
(2) QTRS
(3) RFCMatchBoundsTRSProof [EQUIVALENT, 0 ms]
(4) YES


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

   f(g(X)) -> g(f(f(X)))
   f(h(X)) -> h(g(X))

Q is empty.

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(1) QTRS Reverse (EQUIVALENT)
We applied the QTRS Reverse Processor [REVERSE].
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(2)
Obligation:
Q restricted rewrite system:
The TRS R consists of the following rules:

   g(f(X)) -> f(f(g(X)))
   h(f(X)) -> g(h(X))

Q is empty.

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(3) RFCMatchBoundsTRSProof (EQUIVALENT)
Termination of the TRS R could be shown with a Match Bound [MATCHBOUNDS1,MATCHBOUNDS2] of 1. This implies Q-termination of R.
The following rules were used to construct the certificate:

   g(f(X)) -> f(f(g(X)))
   h(f(X)) -> g(h(X))

The certificate found is represented by the following graph.
The certificate consists of the following enumerated nodes:
39, 40, 41, 42, 43, 44, 45, 46

Node 39 is start node and node 40 is final node.

Those nodes are connected through the following edges:

* 39 to 41 labelled f_1(0)* 39 to 43 labelled g_1(0)* 40 to 40 labelled #_1(0)* 41 to 42 labelled f_1(0)* 42 to 40 labelled g_1(0)* 42 to 44 labelled f_1(1)* 43 to 40 labelled h_1(0)* 43 to 46 labelled g_1(1)* 44 to 45 labelled f_1(1)* 45 to 40 labelled g_1(1)* 45 to 44 labelled f_1(1)* 46 to 40 labelled h_1(1)* 46 to 46 labelled g_1(1)


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(4)
YES