3.02/1.54	YES
3.02/1.54	proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
3.02/1.54	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
3.02/1.54	
3.02/1.54	
3.02/1.54	Termination of the given ETRS could be proven:
3.02/1.54	
3.02/1.54	(0) ETRS
3.02/1.54	(1) EDirectTerminationProof [EQUIVALENT, 0 ms]
3.02/1.54	(2) YES
3.02/1.54	
3.02/1.54	
3.02/1.54	----------------------------------------
3.02/1.54	
3.02/1.54	(0)
3.02/1.54	Obligation:
3.02/1.54	Equational rewrite system:
3.02/1.54	The TRS R consists of the following rules:
3.02/1.54	
3.02/1.54	   plus(x, 0) -> x
3.02/1.54	   plus(x, s(y)) -> s(plus(x, y))
3.02/1.54	   times(x, 0) -> 0
3.02/1.54	   times(x, s(y)) -> plus(times(x, y), x)
3.02/1.54	   times(x, plus(y, z)) -> plus(times(x, y), times(x, z))
3.02/1.54	
3.02/1.54	The set E consists of the following equations:
3.02/1.54	
3.02/1.54	   plus(x, y) == plus(y, x)
3.02/1.54	   times(x, y) == times(y, x)
3.02/1.54	   plus(plus(x, y), z) == plus(x, plus(y, z))
3.02/1.54	   times(times(x, y), z) == times(x, times(y, z))
3.02/1.54	
3.02/1.54	
3.02/1.54	----------------------------------------
3.02/1.54	
3.02/1.54	(1) EDirectTerminationProof (EQUIVALENT)
3.02/1.54	We use [DA_FALKE] with the following order to prove termination.
3.02/1.54	
3.02/1.54	Precedence:
3.02/1.54	times_2 > plus_2 > s_1
3.02/1.54	
3.02/1.54	
3.02/1.54	Status:
3.02/1.54	plus_2: flat status
3.02/1.54	times_2: flat status
3.02/1.54	
3.02/1.54	
3.02/1.54	
3.02/1.54	----------------------------------------
3.02/1.54	
3.02/1.54	(2)
3.02/1.54	YES
3.02/1.57	EOF