2.89/1.52	YES
2.89/1.53	proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
2.89/1.53	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
2.89/1.53	
2.89/1.53	
2.89/1.53	Termination of the given ETRS could be proven:
2.89/1.53	
2.89/1.53	(0) ETRS
2.89/1.53	(1) EDirectTerminationProof [EQUIVALENT, 0 ms]
2.89/1.53	(2) YES
2.89/1.53	
2.89/1.53	
2.89/1.53	----------------------------------------
2.89/1.53	
2.89/1.53	(0)
2.89/1.53	Obligation:
2.89/1.53	Equational rewrite system:
2.89/1.53	The TRS R consists of the following rules:
2.89/1.53	
2.89/1.53	   plus(x, 0) -> x
2.89/1.53	   plus(x, s(y)) -> s(plus(x, y))
2.89/1.53	   plus(x, plus(s(y), z)) -> plus(s(plus(x, y)), z)
2.89/1.53	   times(x, 0) -> 0
2.89/1.53	   times(x, times(0, z)) -> times(0, z)
2.89/1.53	   times(x, s(y)) -> plus(times(x, y), x)
2.89/1.53	   times(x, times(s(y), z)) -> times(plus(times(x, y), x), z)
2.89/1.53	
2.89/1.53	The set E consists of the following equations:
2.89/1.53	
2.89/1.53	   plus(x, y) == plus(y, x)
2.89/1.53	   times(x, y) == times(y, x)
2.89/1.53	   plus(plus(x, y), z) == plus(x, plus(y, z))
2.89/1.53	   times(times(x, y), z) == times(x, times(y, z))
2.89/1.53	
2.89/1.53	
2.89/1.53	----------------------------------------
2.89/1.53	
2.89/1.53	(1) EDirectTerminationProof (EQUIVALENT)
2.89/1.53	We use [DA_FALKE] with the following order to prove termination.
2.89/1.53	
2.89/1.53	Precedence:
2.89/1.53	times_2 > plus_2 > s_1
2.89/1.53	
2.89/1.53	
2.89/1.53	Status:
2.89/1.53	plus_2: flat status
2.89/1.53	times_2: flat status
2.89/1.53	
2.89/1.53	
2.89/1.53	
2.89/1.53	----------------------------------------
2.89/1.53	
2.89/1.53	(2)
2.89/1.53	YES
3.04/1.56	EOF