3.14/1.64	YES
3.14/1.64	proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml
3.14/1.64	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
3.14/1.64	
3.14/1.64	
3.14/1.64	Termination of the given ETRS could be proven:
3.14/1.64	
3.14/1.64	(0) ETRS
3.14/1.64	(1) EDirectTerminationProof [EQUIVALENT, 0 ms]
3.14/1.64	(2) YES
3.14/1.64	
3.14/1.64	
3.14/1.64	----------------------------------------
3.14/1.64	
3.14/1.64	(0)
3.14/1.64	Obligation:
3.14/1.64	Equational rewrite system:
3.14/1.64	The TRS R consists of the following rules:
3.14/1.64	
3.14/1.64	   if(true, x, y) -> x
3.14/1.64	   if(false, x, y) -> y
3.14/1.64	   eq(0, 0) -> true
3.14/1.64	   eq(0, s(x)) -> false
3.14/1.64	   eq(s(x), s(y)) -> eq(x, y)
3.14/1.64	   union(empty, x) -> x
3.14/1.64	   inter(empty, x) -> empty
3.14/1.64	   inter(union(y, z), x) -> union(inter(x, y), inter(x, z))
3.14/1.64	   inter(singl(x), singl(y)) -> if(eq(x, y), singl(x), empty)
3.14/1.64	
3.14/1.64	The set E consists of the following equations:
3.14/1.64	
3.14/1.64	   eq(x, y) == eq(y, x)
3.14/1.64	   inter(x, y) == inter(y, x)
3.14/1.64	   union(x, y) == union(y, x)
3.14/1.64	   inter(inter(x, y), z) == inter(x, inter(y, z))
3.14/1.64	   union(union(x, y), z) == union(x, union(y, z))
3.14/1.64	
3.14/1.64	
3.14/1.64	----------------------------------------
3.14/1.64	
3.14/1.64	(1) EDirectTerminationProof (EQUIVALENT)
3.14/1.64	We use [DA_FALKE] with the following order to prove termination.
3.14/1.64	
3.14/1.64	Precedence:
3.14/1.64	s_1 > false
3.14/1.64	inter_2 > if_3
3.14/1.64	inter_2 > eq_2 > true
3.14/1.64	inter_2 > union_2
3.14/1.64	singl_1 > empty
3.14/1.64	
3.14/1.64	
3.14/1.64	Status:
3.14/1.64	inter_2: flat status
3.14/1.64	union_2: flat status
3.14/1.64	eq_2: flat status
3.14/1.64	
3.14/1.64	
3.14/1.64	
3.14/1.64	----------------------------------------
3.14/1.64	
3.14/1.64	(2)
3.14/1.64	YES
3.14/1.68	EOF