YES
proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml
# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty


Termination of the given ETRS could be proven:

(0) ETRS
(1) EDirectTerminationProof [EQUIVALENT, 0 ms]
(2) YES


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

   eq(x, x) -> true
   not(eq(x, y)) -> neq(x, y)
   not(neq(x, y)) -> eq(x, y)
   not(true) -> false
   not(false) -> true
   not(not(x)) -> x
   not(and(x, y)) -> or(not(x), not(y))
   not(or(x, y)) -> and(not(x), not(y))
   neq(x, x) -> false
   or(and(x, y), z) -> and(or(x, z), or(y, z))
   or(x, x) -> x
   or(x, true) -> true
   or(x, false) -> x
   and(x, x) -> x
   and(x, true) -> x
   and(x, false) -> false
   and(x, or(x, y)) -> x

The set E consists of the following equations:

   eq(x, y) == eq(y, x)
   neq(x, y) == neq(y, x)
   and(x, y) == and(y, x)
   or(x, y) == or(y, x)
   and(and(x, y), z) == and(x, and(y, z))
   or(or(x, y), z) == or(x, or(y, z))


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(1) EDirectTerminationProof (EQUIVALENT)
We use [DA_FALKE] with the following order to prove termination.

Precedence:
not_1 > eq_2 > true
not_1 > neq_2 > false
not_1 > or_2 > and_2


Status:
and_2: flat status
or_2: flat status
eq_2: flat status
neq_2: flat status



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(2)
YES