/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# AProVE Commit ID: c69e44bd14796315568835c1ffa2502984884775 mhark 20210624 unpublished


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, 22 ms]
(4) YES


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

   f(f(X)) -> c(n__f(g(n__f(X))))
   c(X) -> d(activate(X))
   h(X) -> c(n__d(X))
   f(X) -> n__f(X)
   d(X) -> n__d(X)
   activate(n__f(X)) -> f(X)
   activate(n__d(X)) -> d(X)
   activate(X) -> 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:

   f(f(X)) -> n__f(g(n__f(c(X))))
   c(X) -> activate(d(X))
   h(X) -> n__d(c(X))
   f(X) -> n__f(X)
   d(X) -> n__d(X)
   n__f(activate(X)) -> f(X)
   n__d(activate(X)) -> d(X)
   activate(X) -> 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 5. This implies Q-termination of R.
The following rules were used to construct the certificate:

   f(f(X)) -> n__f(g(n__f(c(X))))
   c(X) -> activate(d(X))
   h(X) -> n__d(c(X))
   f(X) -> n__f(X)
   d(X) -> n__d(X)
   n__f(activate(X)) -> f(X)
   n__d(activate(X)) -> d(X)
   activate(X) -> X

The certificate found is represented by the following graph.
The certificate consists of the following enumerated nodes:
27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38

Node 27 is start node and node 28 is final node.

Those nodes are connected through the following edges:

* 27 to 29 labelled n__f_1(0)* 27 to 32 labelled activate_1(0)* 27 to 31 labelled n__d_1(0)* 27 to 28 labelled n__f_1(0), n__d_1(0), f_1(0), d_1(0), g_1(0), c_1(0), activate_1(0), h_1(0), n__f_1(1), n__d_1(1), d_1(1), f_1(1), g_1(1), c_1(1), activate_1(1), h_1(1), n__d_1(2), n__f_1(2), c_1(2), d_1(2), n__d_1(3), d_1(3), n__d_1(4), d_1(4), n__d_1(5)* 27 to 33 labelled activate_1(1), d_1(1), n__d_1(2)* 27 to 34 labelled n__f_1(1)* 27 to 37 labelled activate_1(2), f_1(1), d_1(1), activate_1(1), f_1(2), d_1(2), d_1(3), f_1(3), n__f_1(2), n__d_1(2), n__f_1(3), n__d_1(3), n__d_1(4), n__f_1(4), n__d_1(1), d_1(4), n__d_1(5)* 27 to 38 labelled activate_1(3), f_1(1), d_1(1), activate_1(1), f_1(2), d_1(2), activate_1(2), d_1(3), f_1(3), d_1(4), n__f_1(2), n__d_1(2), n__f_1(3), n__d_1(3), n__d_1(4), n__f_1(4), n__d_1(5), n__d_1(1)* 28 to 28 labelled #_1(0), c_1(1), c_1(2), d_1(3), n__d_1(4), n__d_1(3), d_1(4), n__d_1(5), d_1(1), d_1(2), n__d_1(2)* 28 to 37 labelled activate_1(2), d_1(3), n__d_1(4), n__d_1(3), d_1(4), n__d_1(5)* 28 to 38 labelled activate_1(3), d_1(4), d_1(3), n__d_1(5), n__d_1(4), n__d_1(3)* 29 to 30 labelled g_1(0)* 30 to 31 labelled n__f_1(0)* 30 to 33 labelled f_1(1), n__f_1(2)* 31 to 28 labelled c_1(0), d_1(2), n__d_1(3), n__d_1(2), d_1(1)* 31 to 33 labelled activate_1(1)* 31 to 37 labelled d_1(3), d_1(2), n__d_1(4), n__d_1(3), n__d_1(2)* 31 to 38 labelled d_1(4), d_1(3), n__d_1(5), n__d_1(4), d_1(2), n__d_1(3), n__d_1(2)* 32 to 28 labelled d_1(0), n__d_1(1), d_1(1), n__d_1(2)* 32 to 37 labelled d_1(2), n__d_1(3), d_1(3), n__d_1(4)* 32 to 38 labelled d_1(2), d_1(3), n__d_1(3), n__d_1(4)* 33 to 28 labelled d_1(1), n__d_1(2)* 33 to 37 labelled d_1(3), n__d_1(4)* 33 to 38 labelled d_1(3), n__d_1(4)* 34 to 35 labelled g_1(1)* 35 to 36 labelled n__f_1(1)* 35 to 37 labelled f_1(2), n__f_1(3)* 36 to 28 labelled c_1(1), d_1(3), n__d_1(4), n__d_1(3), d_1(1), d_1(2), n__d_1(2)* 36 to 37 labelled activate_1(2), d_1(3), n__d_1(4), n__d_1(3)* 36 to 38 labelled d_1(4), d_1(3), n__d_1(5), n__d_1(4), n__d_1(3)* 37 to 28 labelled d_1(2), n__d_1(3), d_1(1), n__d_1(2)* 37 to 37 labelled d_1(3), n__d_1(4)* 37 to 38 labelled d_1(4), n__d_1(5), d_1(3), n__d_1(4)* 38 to 28 labelled d_1(3), n__d_1(4), d_1(1), n__d_1(2)* 38 to 37 labelled d_1(3), n__d_1(4)* 38 to 38 labelled d_1(4), n__d_1(5), d_1(3), n__d_1(4)


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(4)
YES