3.05/1.49	YES
3.05/1.50	proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
3.05/1.50	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
3.05/1.50	
3.05/1.50	
3.05/1.50	Termination of the given ETRS could be proven:
3.05/1.50	
3.05/1.50	(0) ETRS
3.05/1.50	(1) EDirectTerminationProof [EQUIVALENT, 0 ms]
3.05/1.50	(2) YES
3.05/1.50	
3.05/1.50	
3.05/1.50	----------------------------------------
3.05/1.50	
3.05/1.50	(0)
3.05/1.50	Obligation:
3.05/1.50	Equational rewrite system:
3.05/1.50	The TRS R consists of the following rules:
3.05/1.50	
3.05/1.50	   plus(x, 0) -> x
3.05/1.50	   plus(x, s(y)) -> s(plus(x, y))
3.05/1.50	
3.05/1.50	The set E consists of the following equations:
3.05/1.50	
3.05/1.50	   plus(x, y) == plus(y, x)
3.05/1.50	   plus(plus(x, y), z) == plus(x, plus(y, z))
3.05/1.50	
3.05/1.50	
3.05/1.50	----------------------------------------
3.05/1.50	
3.05/1.50	(1) EDirectTerminationProof (EQUIVALENT)
3.05/1.50	We use [DA_FALKE] with the following order to prove termination.
3.05/1.50	
3.05/1.50	Precedence:
3.05/1.50	plus_2 > s_1
3.05/1.50	
3.05/1.50	
3.05/1.50	Status:
3.05/1.50	plus_2: flat status
3.05/1.50	
3.05/1.50	
3.05/1.50	
3.05/1.50	----------------------------------------
3.05/1.50	
3.05/1.50	(2)
3.05/1.50	YES
3.05/1.54	EOF