2.48/1.31	NO
2.48/1.32	proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml
2.48/1.32	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
2.48/1.32	
2.48/1.32	
2.48/1.32	Outermost Termination of the given OTRS could be disproven:
2.48/1.32	
2.48/1.32	(0) OTRS
2.48/1.32	(1) OutermostNonTerminationProof [COMPLETE, 0 ms]
2.48/1.32	(2) NO
2.48/1.32	
2.48/1.32	
2.48/1.32	----------------------------------------
2.48/1.32	
2.48/1.32	(0)
2.48/1.32	Obligation:
2.48/1.32	Term rewrite system R:
2.48/1.32	The TRS R consists of the following rules:
2.48/1.32	
2.48/1.32	   sel(s(X), cons(Y, Z)) -> sel(X, Z)
2.48/1.32	   sel(0, cons(X, Z)) -> X
2.48/1.32	   first(0, Z) -> nil
2.48/1.32	   first(s(X), cons(Y, Z)) -> cons(Y, first(X, Z))
2.48/1.32	   from(X) -> cons(X, from(s(X)))
2.48/1.32	   sel1(s(X), cons(Y, Z)) -> sel1(X, Z)
2.48/1.32	   sel1(0, cons(X, Z)) -> quote(X)
2.48/1.32	   first1(0, Z) -> nil1
2.48/1.32	   first1(s(X), cons(Y, Z)) -> cons1(quote(Y), first1(X, Z))
2.48/1.32	   quote(0) -> 01
2.48/1.32	   quote1(cons(X, Z)) -> cons1(quote(X), quote1(Z))
2.48/1.32	   quote1(nil) -> nil1
2.48/1.32	   quote(s(X)) -> s1(quote(X))
2.48/1.32	   quote(sel(X, Z)) -> sel1(X, Z)
2.48/1.32	   quote1(first(X, Z)) -> first1(X, Z)
2.48/1.32	   unquote(01) -> 0
2.48/1.32	   unquote(s1(X)) -> s(unquote(X))
2.48/1.32	   unquote1(nil1) -> nil
2.48/1.32	   unquote1(cons1(X, Z)) -> fcons(unquote(X), unquote1(Z))
2.48/1.32	   fcons(X, Z) -> cons(X, Z)
2.48/1.32	
2.48/1.32	
2.48/1.32	
2.48/1.32	Outermost Strategy.
2.48/1.32	
2.48/1.32	----------------------------------------
2.48/1.32	
2.48/1.32	(1) OutermostNonTerminationProof (COMPLETE)
2.48/1.32	Term rewrite system R:
2.48/1.32	The TRS R consists of the following rules:
2.48/1.32	
2.48/1.32	   sel(s(X), cons(Y, Z)) -> sel(X, Z)
2.48/1.32	   sel(0, cons(X, Z)) -> X
2.48/1.32	   first(0, Z) -> nil
2.48/1.32	   first(s(X), cons(Y, Z)) -> cons(Y, first(X, Z))
2.48/1.32	   from(X) -> cons(X, from(s(X)))
2.48/1.32	   sel1(s(X), cons(Y, Z)) -> sel1(X, Z)
2.48/1.32	   sel1(0, cons(X, Z)) -> quote(X)
2.48/1.32	   first1(0, Z) -> nil1
2.48/1.32	   first1(s(X), cons(Y, Z)) -> cons1(quote(Y), first1(X, Z))
2.48/1.32	   quote(0) -> 01
2.48/1.32	   quote1(cons(X, Z)) -> cons1(quote(X), quote1(Z))
2.48/1.32	   quote1(nil) -> nil1
2.48/1.32	   quote(s(X)) -> s1(quote(X))
2.48/1.32	   quote(sel(X, Z)) -> sel1(X, Z)
2.48/1.32	   quote1(first(X, Z)) -> first1(X, Z)
2.48/1.32	   unquote(01) -> 0
2.48/1.32	   unquote(s1(X)) -> s(unquote(X))
2.48/1.32	   unquote1(nil1) -> nil
2.48/1.32	   unquote1(cons1(X, Z)) -> fcons(unquote(X), unquote1(Z))
2.48/1.32	   fcons(X, Z) -> cons(X, Z)
2.48/1.32	
2.48/1.32	
2.48/1.32	
2.48/1.32	Outermost Strategy.
2.48/1.32	
2.48/1.32	---------- Loop: ----------
2.48/1.32	
2.48/1.32	from(X) -> cons(X, from(s(X))) with rule from(X') -> cons(X', from(s(X'))) at position [] and matcher [X' / X]
2.48/1.32	
2.48/1.32	Now an instance of the first term with Matcher [X / s(X)] occurs in the last term at position [1].
2.48/1.32	
2.48/1.32	Context: cons(X, [])
2.48/1.32	
2.48/1.32	We used [THIEMANN_LOOPS_UNDER_STRATEGIES] to show that this Loop is an Outermost-Loop.
2.48/1.32	----------------------------------------
2.48/1.32	
2.48/1.32	(2)
2.48/1.32	NO
2.48/1.33	EOF