3.98/1.83	YES
3.98/1.84	proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
3.98/1.84	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
3.98/1.84	
3.98/1.84	
3.98/1.84	Termination of the given ETRS could be proven:
3.98/1.84	
3.98/1.84	(0) ETRS
3.98/1.84	(1) EDirectTerminationProof [EQUIVALENT, 200 ms]
3.98/1.84	(2) YES
3.98/1.84	
3.98/1.84	
3.98/1.84	----------------------------------------
3.98/1.84	
3.98/1.84	(0)
3.98/1.84	Obligation:
3.98/1.84	Equational rewrite system:
3.98/1.84	The TRS R consists of the following rules:
3.98/1.84	
3.98/1.84	   ac1(a, ac2(b, c)) -> ac1(b, f(ac2(a, c)))
3.98/1.84	   ac2(a, ac1(b, c)) -> ac2(b, f(ac1(a, c)))
3.98/1.84	
3.98/1.84	The set E consists of the following equations:
3.98/1.84	
3.98/1.84	   ac1(x, y) == ac1(y, x)
3.98/1.84	   ac2(x, y) == ac2(y, x)
3.98/1.84	   ac1(ac1(x, y), z) == ac1(x, ac1(y, z))
3.98/1.84	   ac2(ac2(x, y), z) == ac2(x, ac2(y, z))
3.98/1.84	
3.98/1.84	
3.98/1.84	----------------------------------------
3.98/1.84	
3.98/1.84	(1) EDirectTerminationProof (EQUIVALENT)
3.98/1.84	We use [DA_FALKE] with the following order to prove termination.
3.98/1.84	
3.98/1.84	Precedence:
3.98/1.84	ac1_2 > b > a > c
3.98/1.84	ac1_2 > f_1
3.98/1.84	ac2_2 > f_1
3.98/1.84	
3.98/1.84	
3.98/1.84	Status:
3.98/1.84	ac1_2: flat status
3.98/1.84	ac2_2: flat status
3.98/1.84	
3.98/1.84	
3.98/1.84	
3.98/1.84	----------------------------------------
3.98/1.84	
3.98/1.84	(2)
3.98/1.84	YES
3.98/1.87	EOF