3.01/1.55	YES
3.01/1.56	proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml
3.01/1.56	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
3.01/1.56	
3.01/1.56	
3.01/1.56	Termination of the given ETRS could be proven:
3.01/1.56	
3.01/1.56	(0) ETRS
3.01/1.56	(1) EDirectTerminationProof [EQUIVALENT, 0 ms]
3.01/1.56	(2) YES
3.01/1.56	
3.01/1.56	
3.01/1.56	----------------------------------------
3.01/1.56	
3.01/1.56	(0)
3.01/1.56	Obligation:
3.01/1.56	Equational rewrite system:
3.01/1.56	The TRS R consists of the following rules:
3.01/1.56	
3.01/1.56	   f(g(f(h(x), x)), x) -> f(h(x), f(x, x))
3.01/1.56	   f(h(x), g(x)) -> f(g(h(x)), x)
3.01/1.56	   f(g(h(x)), f(x, f(x, y))) -> f(g(f(h(x), y)), x)
3.01/1.56	   f(g(g(x)), x) -> f(g(x), g(x))
3.01/1.56	
3.01/1.56	The set E consists of the following equations:
3.01/1.56	
3.01/1.56	   f(x, y) == f(y, x)
3.01/1.56	   f(f(x, y), z) == f(x, f(y, z))
3.01/1.56	
3.01/1.56	
3.01/1.56	----------------------------------------
3.01/1.56	
3.01/1.56	(1) EDirectTerminationProof (EQUIVALENT)
3.01/1.56	We use [DA_FALKE] with the following order to prove termination.
3.01/1.56	
3.01/1.56	Precedence:
3.01/1.56	h_1 > f_2 > g_1
3.01/1.56	
3.01/1.56	
3.01/1.56	Status:
3.01/1.56	f_2: flat status
3.01/1.56	
3.01/1.56	
3.01/1.56	
3.01/1.56	----------------------------------------
3.01/1.56	
3.01/1.56	(2)
3.01/1.56	YES
3.29/1.59	EOF