2.85/1.61	YES
3.18/1.62	proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml
3.18/1.62	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
3.18/1.62	
3.18/1.62	
3.18/1.62	Termination of the given ETRS could be proven:
3.18/1.62	
3.18/1.62	(0) ETRS
3.18/1.62	(1) EDirectTerminationProof [EQUIVALENT, 0 ms]
3.18/1.62	(2) YES
3.18/1.62	
3.18/1.62	
3.18/1.62	----------------------------------------
3.18/1.62	
3.18/1.62	(0)
3.18/1.62	Obligation:
3.18/1.62	Equational rewrite system:
3.18/1.62	The TRS R consists of the following rules:
3.18/1.62	
3.18/1.62	   xor(F, x) -> x
3.18/1.62	   xor(neg(x), x) -> F
3.18/1.62	   and(T, x) -> x
3.18/1.62	   and(F, x) -> F
3.18/1.62	   and(x, x) -> x
3.18/1.62	   and(xor(x, y), z) -> xor(and(x, z), and(y, z))
3.18/1.62	   xor(x, x) -> F
3.18/1.62	   impl(x, y) -> xor(and(x, y), xor(T, x))
3.18/1.62	   or(x, y) -> xor(and(x, y), xor(x, y))
3.18/1.62	   equiv(x, y) -> xor(xor(T, y), x)
3.18/1.62	   neg(x) -> xor(T, x)
3.18/1.62	
3.18/1.62	The set E consists of the following equations:
3.18/1.62	
3.18/1.62	   and(x, y) == and(y, x)
3.18/1.62	   or(x, y) == or(y, x)
3.18/1.62	   xor(x, y) == xor(y, x)
3.18/1.62	   and(and(x, y), z) == and(x, and(y, z))
3.18/1.62	   or(or(x, y), z) == or(x, or(y, z))
3.18/1.62	   xor(xor(x, y), z) == xor(x, xor(y, z))
3.18/1.62	
3.18/1.62	
3.18/1.62	----------------------------------------
3.18/1.62	
3.18/1.62	(1) EDirectTerminationProof (EQUIVALENT)
3.18/1.62	We use [DA_FALKE] with the following order to prove termination.
3.18/1.62	
3.18/1.62	Precedence:
3.18/1.62	neg_1 > xor_2 > F
3.18/1.62	neg_1 > T
3.18/1.62	impl_2 > and_2 > xor_2 > F
3.18/1.62	impl_2 > T
3.18/1.62	or_2 > and_2 > xor_2 > F
3.18/1.62	equiv_2 > xor_2 > F
3.18/1.62	equiv_2 > T
3.18/1.62	
3.18/1.62	
3.18/1.62	Status:
3.18/1.62	and_2: flat status
3.18/1.62	or_2: flat status
3.18/1.62	xor_2: flat status
3.18/1.62	
3.18/1.62	
3.18/1.62	
3.18/1.62	----------------------------------------
3.18/1.62	
3.18/1.62	(2)
3.18/1.62	YES
3.18/1.67	EOF