2.91/1.59	YES
2.91/1.60	proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml
2.91/1.60	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
2.91/1.60	
2.91/1.60	
2.91/1.60	Termination of the given ETRS could be proven:
2.91/1.60	
2.91/1.60	(0) ETRS
2.91/1.60	(1) EDirectTerminationProof [EQUIVALENT, 0 ms]
2.91/1.60	(2) YES
2.91/1.60	
2.91/1.60	
2.91/1.60	----------------------------------------
2.91/1.60	
2.91/1.60	(0)
2.91/1.60	Obligation:
2.91/1.60	Equational rewrite system:
2.91/1.60	The TRS R consists of the following rules:
2.91/1.60	
2.91/1.60	   plus(x, 0) -> x
2.91/1.60	   plus(s(x), y) -> s(plus(x, y))
2.91/1.60	   times(x, 0) -> 0
2.91/1.60	   times(s(x), y) -> plus(times(x, y), y)
2.91/1.60	   times(x, plus(y, z)) -> plus(times(x, y), times(x, z))
2.91/1.60	
2.91/1.60	The set E consists of the following equations:
2.91/1.60	
2.91/1.60	   plus(x, y) == plus(y, x)
2.91/1.60	   times(x, y) == times(y, x)
2.91/1.60	   plus(plus(x, y), z) == plus(x, plus(y, z))
2.91/1.60	   times(times(x, y), z) == times(x, times(y, z))
2.91/1.60	
2.91/1.60	
2.91/1.60	----------------------------------------
2.91/1.60	
2.91/1.60	(1) EDirectTerminationProof (EQUIVALENT)
2.91/1.60	We use [DA_FALKE] with the following order to prove termination.
2.91/1.60	
2.91/1.60	Precedence:
2.91/1.60	times_2 > plus_2 > s_1
2.91/1.60	
2.91/1.60	
2.91/1.60	Status:
2.91/1.60	plus_2: flat status
2.91/1.60	times_2: flat status
2.91/1.60	
2.91/1.60	
2.91/1.60	
2.91/1.60	----------------------------------------
2.91/1.60	
2.91/1.60	(2)
2.91/1.60	YES
2.91/1.63	EOF