3.79/1.84	NO
3.79/1.85	proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
3.79/1.85	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
3.79/1.85	
3.79/1.85	
3.79/1.85	Termination of the given RelTRS could be disproven:
3.79/1.85	
3.79/1.85	(0) RelTRS
3.79/1.85	(1) RelTRSLoopFinderProof [COMPLETE, 72 ms]
3.79/1.85	(2) NO
3.79/1.85	
3.79/1.85	
3.79/1.85	----------------------------------------
3.79/1.85	
3.79/1.85	(0)
3.79/1.85	Obligation:
3.79/1.85	Relative term rewrite system:
3.79/1.85	The relative TRS consists of the following R rules:
3.79/1.85	
3.79/1.85	   top(U(x, y)) -> top(check(D(x, y)))
3.79/1.85	   D(x, B) -> U(x, B)
3.79/1.85	   F(x, U(O(y), z)) -> U(x, F(y, z))
3.79/1.85	   F(x, U(N(y), z)) -> U(x, F(y, z))
3.79/1.85	   D(O(x), F(y, z)) -> F(x, D(y, z))
3.79/1.85	   D(N(x), F(y, z)) -> F(x, D(y, z))
3.79/1.85	   F(x, U(E, y)) -> U(x, F(E, y))
3.79/1.85	   D(E, F(x, y)) -> F(E, D(x, y))
3.79/1.85	
3.79/1.85	The relative TRS consists of the following S rules:
3.79/1.85	
3.79/1.85	   E -> N(E)
3.79/1.85	   check(O(x)) -> O(x)
3.79/1.85	   check(U(x, y)) -> U(check(x), y)
3.79/1.85	   check(U(x, y)) -> U(x, check(y))
3.79/1.85	   check(D(x, y)) -> D(check(x), y)
3.79/1.85	   check(D(x, y)) -> D(x, check(y))
3.79/1.85	   check(F(x, y)) -> F(check(x), y)
3.79/1.85	   check(F(x, y)) -> F(x, check(y))
3.79/1.85	   check(O(x)) -> O(check(x))
3.79/1.85	   check(N(x)) -> N(check(x))
3.79/1.85	
3.79/1.85	
3.79/1.85	----------------------------------------
3.79/1.85	
3.79/1.85	(1) RelTRSLoopFinderProof (COMPLETE)
3.79/1.85	The following loop was found:
3.79/1.85	
3.79/1.85	---------- Loop: ----------
3.79/1.85	
3.79/1.85	top(check(D(x, B))) -> top(D(check(x), B)) with rule check(D(x', y)) -> D(check(x'), y) at position [0] and matcher [x' / x, y / B]
3.79/1.85	
3.79/1.85	top(D(check(x), B)) -> top(U(check(x), B)) with rule D(x', B) -> U(x', B) at position [0] and matcher [x' / check(x)]
3.79/1.85	
3.79/1.85	top(U(check(x), B)) -> top(check(D(check(x), B))) with rule top(U(x', y)) -> top(check(D(x', y))) at position [] and matcher [x' / check(x), y / B]
3.79/1.85	
3.79/1.85	Now an instance of the first term with Matcher [x / check(x)] occurs in the last term at position [].
3.79/1.85	
3.79/1.85	Context: []
3.79/1.85	
3.79/1.85	Therefore, the relative TRS problem does not terminate.
3.79/1.85	----------------------------------------
3.79/1.85	
3.79/1.85	(2)
3.79/1.85	NO
3.79/1.88	EOF