NO
proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml
# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty


Termination of the given RelTRS could be disproven:

(0) RelTRS
(1) RelTRSLoopFinderProof [COMPLETE, 91 ms]
(2) NO


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(0)
Obligation:
Relative term rewrite system:
The relative TRS consists of the following R rules:

   top(U(x, y)) -> top(check(D(x, y)))
   D(x, B) -> U(x, B)
   F(x, U(O(y), z)) -> U(x, F(y, z))
   F(x, U(N(y), z)) -> U(x, F(y, z))
   D(O(x), F(y, z)) -> F(x, D(y, z))
   D(N(x), F(y, z)) -> F(x, D(y, z))
   F(x, U(E, y)) -> U(x, F(E, y))
   D(E, F(x, y)) -> F(E, D(x, y))

The relative TRS consists of the following S rules:

   E -> N(E)
   check(O(x)) -> O(x)
   check(U(x, y)) -> U(check(x), y)
   check(U(x, y)) -> U(x, check(y))
   check(D(x, y)) -> D(check(x), y)
   check(D(x, y)) -> D(x, check(y))
   check(F(x, y)) -> F(check(x), y)
   check(F(x, y)) -> F(x, check(y))
   check(O(x)) -> O(check(x))
   check(N(x)) -> N(check(x))


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(1) RelTRSLoopFinderProof (COMPLETE)
The following loop was found:

---------- Loop: ----------

top(check(D(x, B))) -> top(D(check(x), B)) with rule check(D(x', y)) -> D(check(x'), y) at position [0] and matcher [x' / x, y / B]

top(D(check(x), B)) -> top(U(check(x), B)) with rule D(x', B) -> U(x', B) at position [0] and matcher [x' / check(x)]

top(U(check(x), B)) -> top(check(D(check(x), B))) with rule top(U(x', y)) -> top(check(D(x', y))) at position [] and matcher [x' / check(x), y / B]

Now an instance of the first term with Matcher [x / check(x)] occurs in the last term at position [].

Context: []

Therefore, the relative TRS problem does not terminate.
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(2)
NO