YES
proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty


Termination w.r.t. Q of the given QTRS could be proven:

(0) QTRS
(1) QTRSRRRProof [EQUIVALENT, 42 ms]
(2) QTRS
(3) RisEmptyProof [EQUIVALENT, 0 ms]
(4) YES


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

   __(__(X, Y), Z) -> __(X, __(Y, Z))
   __(X, nil) -> X
   __(nil, X) -> X
   U11(tt) -> U12(tt)
   U12(tt) -> tt
   isNePal(__(I, __(P, I))) -> U11(tt)
   activate(X) -> X

Q is empty.

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(1) QTRSRRRProof (EQUIVALENT)
Used ordering:
Knuth-Bendix order [KBO] with precedence:U12_1 > activate_1 > isNePal_1 > nil > ___2 > tt > U11_1

and weight map:

   nil=1
   tt=4
   U11_1=1
   U12_1=0
   isNePal_1=2
   activate_1=1
   ___2=0

The variable weight is 1With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly:

   __(__(X, Y), Z) -> __(X, __(Y, Z))
   __(X, nil) -> X
   __(nil, X) -> X
   U11(tt) -> U12(tt)
   U12(tt) -> tt
   isNePal(__(I, __(P, I))) -> U11(tt)
   activate(X) -> X




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(2)
Obligation:
Q restricted rewrite system:
R is empty.
Q is empty.

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(3) RisEmptyProof (EQUIVALENT)
The TRS R is empty. Hence, termination is trivially proven.
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(4)
YES