2.90/1.58	YES
2.90/1.59	proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
2.90/1.59	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
2.90/1.59	
2.90/1.59	
2.90/1.59	Termination of the given ETRS could be proven:
2.90/1.59	
2.90/1.59	(0) ETRS
2.90/1.59	(1) EDirectTerminationProof [EQUIVALENT, 0 ms]
2.90/1.59	(2) YES
2.90/1.59	
2.90/1.59	
2.90/1.59	----------------------------------------
2.90/1.59	
2.90/1.59	(0)
2.90/1.59	Obligation:
2.90/1.59	Equational rewrite system:
2.90/1.59	The TRS R consists of the following rules:
2.90/1.59	
2.90/1.59	   eq(x, x) -> true
2.90/1.59	   not(eq(x, y)) -> neq(x, y)
2.90/1.59	   not(neq(x, y)) -> eq(x, y)
2.90/1.59	   not(true) -> false
2.90/1.59	   not(false) -> true
2.90/1.59	   not(not(x)) -> x
2.90/1.59	   not(and(x, y)) -> or(not(x), not(y))
2.90/1.59	   not(or(x, y)) -> and(not(x), not(y))
2.90/1.59	   neq(x, x) -> false
2.90/1.59	   or(and(x, y), z) -> and(or(x, z), or(y, z))
2.90/1.59	   or(x, x) -> x
2.90/1.59	   or(x, true) -> true
2.90/1.59	   or(x, false) -> x
2.90/1.59	   and(x, x) -> x
2.90/1.59	   and(x, true) -> x
2.90/1.59	   and(x, false) -> false
2.90/1.59	   and(x, or(x, y)) -> x
2.90/1.59	
2.90/1.59	The set E consists of the following equations:
2.90/1.59	
2.90/1.59	   eq(x, y) == eq(y, x)
2.90/1.59	   neq(x, y) == neq(y, x)
2.90/1.59	   and(x, y) == and(y, x)
2.90/1.59	   or(x, y) == or(y, x)
2.90/1.59	   and(and(x, y), z) == and(x, and(y, z))
2.90/1.59	   or(or(x, y), z) == or(x, or(y, z))
2.90/1.59	
2.90/1.59	
2.90/1.59	----------------------------------------
2.90/1.59	
2.90/1.59	(1) EDirectTerminationProof (EQUIVALENT)
2.90/1.59	We use [DA_FALKE] with the following order to prove termination.
2.90/1.59	
2.90/1.59	Precedence:
2.90/1.59	not_1 > eq_2 > true
2.90/1.59	not_1 > neq_2 > false
2.90/1.59	not_1 > or_2 > and_2
2.90/1.59	
2.90/1.59	
2.90/1.59	Status:
2.90/1.59	and_2: flat status
2.90/1.59	or_2: flat status
2.90/1.59	eq_2: flat status
2.90/1.59	neq_2: flat status
2.90/1.59	
2.90/1.59	
2.90/1.59	
2.90/1.59	----------------------------------------
2.90/1.59	
2.90/1.59	(2)
2.90/1.59	YES
3.15/1.62	EOF