3.18/1.55	YES
3.18/1.56	proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
3.18/1.56	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
3.18/1.56	
3.18/1.56	
3.18/1.56	Termination of the given ETRS could be proven:
3.18/1.56	
3.18/1.56	(0) ETRS
3.18/1.56	(1) EDirectTerminationProof [EQUIVALENT, 0 ms]
3.18/1.56	(2) YES
3.18/1.56	
3.18/1.56	
3.18/1.56	----------------------------------------
3.18/1.56	
3.18/1.56	(0)
3.18/1.56	Obligation:
3.18/1.56	Equational rewrite system:
3.18/1.56	The TRS R consists of the following rules:
3.18/1.56	
3.18/1.56	   f(plus(a, a)) -> plus(f(a), f(a))
3.18/1.56	   plus(a, f(f(a))) -> plus(f(a), f(a))
3.18/1.56	
3.18/1.56	The set E consists of the following equations:
3.18/1.56	
3.18/1.56	   plus(x, y) == plus(y, x)
3.18/1.56	   plus(plus(x, y), z) == plus(x, plus(y, z))
3.18/1.56	
3.18/1.56	
3.18/1.56	----------------------------------------
3.18/1.56	
3.18/1.56	(1) EDirectTerminationProof (EQUIVALENT)
3.18/1.56	We use [DA_FALKE] with the following order to prove termination.
3.18/1.56	
3.18/1.56	Precedence:
3.18/1.56	f_1 > plus_2
3.18/1.56	
3.18/1.56	
3.18/1.56	Status:
3.18/1.56	plus_2: flat status
3.18/1.56	
3.18/1.56	
3.18/1.56	
3.18/1.56	----------------------------------------
3.18/1.56	
3.18/1.56	(2)
3.18/1.56	YES
3.33/1.57	EOF