3.34/1.62	YES
3.34/1.63	proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
3.34/1.63	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
3.34/1.63	
3.34/1.63	
3.34/1.63	Termination of the given ETRS could be proven:
3.34/1.63	
3.34/1.63	(0) ETRS
3.34/1.63	(1) EDirectTerminationProof [EQUIVALENT, 96 ms]
3.34/1.63	(2) YES
3.34/1.63	
3.34/1.63	
3.34/1.63	----------------------------------------
3.34/1.63	
3.34/1.63	(0)
3.34/1.63	Obligation:
3.34/1.63	Equational rewrite system:
3.34/1.63	The TRS R consists of the following rules:
3.34/1.63	
3.34/1.63	   plus(f(x), g(x)) -> plus(g(x), plus(g(x), g(x)))
3.34/1.63	   f(x) -> plus(g(x), a)
3.34/1.63	
3.34/1.63	The set E consists of the following equations:
3.34/1.63	
3.34/1.63	   plus(x, y) == plus(y, x)
3.34/1.63	   plus(plus(x, y), z) == plus(x, plus(y, z))
3.34/1.63	
3.34/1.63	
3.34/1.63	----------------------------------------
3.34/1.63	
3.34/1.63	(1) EDirectTerminationProof (EQUIVALENT)
3.34/1.63	We use [DA_FALKE] with the following order to prove termination.
3.34/1.63	
3.34/1.63	Precedence:
3.34/1.63	f_1 > plus_2
3.34/1.63	f_1 > g_1
3.34/1.63	f_1 > a
3.34/1.63	
3.34/1.63	
3.34/1.63	Status:
3.34/1.63	plus_2: flat status
3.34/1.63	
3.34/1.63	
3.34/1.63	
3.34/1.63	----------------------------------------
3.34/1.63	
3.34/1.63	(2)
3.34/1.63	YES
3.52/1.67	EOF