2.90/1.60	YES
2.90/1.61	proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
2.90/1.61	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
2.90/1.61	
2.90/1.61	
2.90/1.61	Termination of the given ETRS could be proven:
2.90/1.61	
2.90/1.61	(0) ETRS
2.90/1.61	(1) EDirectTerminationProof [EQUIVALENT, 0 ms]
2.90/1.61	(2) YES
2.90/1.61	
2.90/1.61	
2.90/1.61	----------------------------------------
2.90/1.61	
2.90/1.61	(0)
2.90/1.61	Obligation:
2.90/1.61	Equational rewrite system:
2.90/1.61	The TRS R consists of the following rules:
2.90/1.61	
2.90/1.61	   times(x, 0) -> 0
2.90/1.61	   times(x, s(y)) -> plus(times(x, y), x)
2.90/1.61	   plus(x, 0) -> x
2.90/1.61	   plus(0, x) -> x
2.90/1.61	   plus(x, s(y)) -> s(plus(x, y))
2.90/1.61	   plus(s(x), y) -> s(plus(x, y))
2.90/1.61	
2.90/1.61	The set E consists of the following equations:
2.90/1.61	
2.90/1.61	   plus(x, y) == plus(y, x)
2.90/1.61	   times(x, y) == times(y, x)
2.90/1.61	   plus(plus(x, y), z) == plus(x, plus(y, z))
2.90/1.61	   times(times(x, y), z) == times(x, times(y, z))
2.90/1.61	
2.90/1.61	
2.90/1.61	----------------------------------------
2.90/1.61	
2.90/1.61	(1) EDirectTerminationProof (EQUIVALENT)
2.90/1.61	We use [DA_FALKE] with the following order to prove termination.
2.90/1.61	
2.90/1.61	Precedence:
2.90/1.61	times_2 > plus_2 > s_1
2.90/1.61	
2.90/1.61	
2.90/1.61	Status:
2.90/1.61	plus_2: flat status
2.90/1.61	times_2: flat status
2.90/1.61	
2.90/1.61	
2.90/1.61	
2.90/1.61	----------------------------------------
2.90/1.61	
2.90/1.61	(2)
2.90/1.61	YES
3.18/1.64	EOF