2.88/1.52	YES
3.07/1.52	proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml
3.07/1.52	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
3.07/1.52	
3.07/1.52	
3.07/1.52	Termination of the given ETRS could be proven:
3.07/1.52	
3.07/1.52	(0) ETRS
3.07/1.52	(1) EDirectTerminationProof [EQUIVALENT, 0 ms]
3.07/1.52	(2) YES
3.07/1.52	
3.07/1.52	
3.07/1.52	----------------------------------------
3.07/1.52	
3.07/1.52	(0)
3.07/1.52	Obligation:
3.07/1.52	Equational rewrite system:
3.07/1.52	The TRS R consists of the following rules:
3.07/1.52	
3.07/1.52	   plus(x, 0) -> x
3.07/1.52	   plus(x, s(y)) -> s(plus(x, y))
3.07/1.52	   times(x, 0) -> 0
3.07/1.52	   times(x, s(y)) -> plus(x, times(x, y))
3.07/1.52	   power(x, 0) -> s(0)
3.07/1.52	   power(x, s(y)) -> times(x, power(x, y))
3.07/1.52	
3.07/1.52	The set E consists of the following equations:
3.07/1.52	
3.07/1.52	   plus(x, y) == plus(y, x)
3.07/1.52	   times(x, y) == times(y, x)
3.07/1.52	   plus(plus(x, y), z) == plus(x, plus(y, z))
3.07/1.52	   times(times(x, y), z) == times(x, times(y, z))
3.07/1.52	
3.07/1.52	
3.07/1.52	----------------------------------------
3.07/1.52	
3.07/1.52	(1) EDirectTerminationProof (EQUIVALENT)
3.07/1.52	We use [DA_FALKE] with the following order to prove termination.
3.07/1.52	
3.07/1.52	Precedence:
3.07/1.52	power_2 > times_2 > plus_2 > s_1
3.07/1.52	
3.07/1.52	
3.07/1.52	Status:
3.07/1.52	plus_2: flat status
3.07/1.52	times_2: flat status
3.07/1.52	
3.07/1.52	
3.07/1.52	
3.07/1.52	----------------------------------------
3.07/1.52	
3.07/1.52	(2)
3.07/1.52	YES
3.10/1.56	EOF