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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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

   xor(F, x) -> x
   xor(neg(x), x) -> F
   and(T, x) -> x
   and(F, x) -> F
   and(x, x) -> x
   and(xor(x, y), z) -> xor(and(x, z), and(y, z))
   xor(x, x) -> F
   impl(x, y) -> xor(and(x, y), xor(T, x))
   or(x, y) -> xor(and(x, y), xor(x, y))
   equiv(x, y) -> xor(xor(T, y), x)
   neg(x) -> xor(T, x)

The set E consists of the following equations:

   and(x, y) == and(y, x)
   or(x, y) == or(y, x)
   xor(x, y) == xor(y, x)
   and(and(x, y), z) == and(x, and(y, z))
   or(or(x, y), z) == or(x, or(y, z))
   xor(xor(x, y), z) == xor(x, xor(y, z))


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

Precedence:
neg_1 > xor_2 > F
neg_1 > T
impl_2 > and_2 > xor_2 > F
impl_2 > T
or_2 > and_2 > xor_2 > F
equiv_2 > xor_2 > F
equiv_2 > T


Status:
and_2: flat status
or_2: flat status
xor_2: flat status



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(2)
YES