3.02/1.54	YES
3.04/1.55	proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml
3.04/1.55	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
3.04/1.55	
3.04/1.55	
3.04/1.55	Termination of the given ETRS could be proven:
3.04/1.55	
3.04/1.55	(0) ETRS
3.04/1.55	(1) EDirectTerminationProof [EQUIVALENT, 0 ms]
3.04/1.55	(2) YES
3.04/1.55	
3.04/1.55	
3.04/1.55	----------------------------------------
3.04/1.55	
3.04/1.55	(0)
3.04/1.55	Obligation:
3.04/1.55	Equational rewrite system:
3.04/1.55	The TRS R consists of the following rules:
3.04/1.55	
3.04/1.55	   plus(x, 0) -> x
3.04/1.55	   plus(x, i(x)) -> 0
3.04/1.55	   i(0) -> 0
3.04/1.55	   i(i(x)) -> x
3.04/1.55	   i(plus(x, y)) -> plus(i(x), i(y))
3.04/1.55	   times(x, 1) -> x
3.04/1.55	   times(x, 0) -> 0
3.04/1.55	   times(x, i(y)) -> i(times(x, y))
3.04/1.55	   times(x, plus(y, z)) -> plus(times(x, y), times(x, z))
3.04/1.55	
3.04/1.55	The set E consists of the following equations:
3.04/1.55	
3.04/1.55	   plus(x, y) == plus(y, x)
3.04/1.55	   times(x, y) == times(y, x)
3.04/1.55	   plus(plus(x, y), z) == plus(x, plus(y, z))
3.04/1.55	   times(times(x, y), z) == times(x, times(y, z))
3.04/1.55	
3.04/1.55	
3.04/1.55	----------------------------------------
3.04/1.55	
3.04/1.55	(1) EDirectTerminationProof (EQUIVALENT)
3.04/1.55	We use [DA_FALKE] with the following order to prove termination.
3.04/1.55	
3.04/1.55	Precedence:
3.04/1.55	times_2 > i_1 > plus_2
3.04/1.55	times_2 > i_1 > 0
3.04/1.55	
3.04/1.55	
3.04/1.55	Status:
3.04/1.55	plus_2: flat status
3.04/1.55	times_2: flat status
3.04/1.55	
3.04/1.55	
3.04/1.55	
3.04/1.55	----------------------------------------
3.04/1.55	
3.04/1.55	(2)
3.04/1.55	YES
3.04/1.57	EOF