2.76/1.36	NO
2.97/1.37	proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml
2.97/1.37	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
2.97/1.37	
2.97/1.37	
2.97/1.37	Outermost Termination of the given OTRS could be disproven:
2.97/1.37	
2.97/1.37	(0) OTRS
2.97/1.37	(1) OutermostNonTerminationProof [COMPLETE, 0 ms]
2.97/1.37	(2) NO
2.97/1.37	
2.97/1.37	
2.97/1.37	----------------------------------------
2.97/1.37	
2.97/1.37	(0)
2.97/1.37	Obligation:
2.97/1.37	Term rewrite system R:
2.97/1.37	The TRS R consists of the following rules:
2.97/1.37	
2.97/1.37	   dbl(0) -> 0
2.97/1.37	   dbl(s(X)) -> s(s(dbl(X)))
2.97/1.37	   dbls(nil) -> nil
2.97/1.37	   dbls(cons(X, Y)) -> cons(dbl(X), dbls(Y))
2.97/1.37	   sel(0, cons(X, Y)) -> X
2.97/1.37	   sel(s(X), cons(Y, Z)) -> sel(X, Z)
2.97/1.37	   indx(nil, X) -> nil
2.97/1.37	   indx(cons(X, Y), Z) -> cons(sel(X, Z), indx(Y, Z))
2.97/1.37	   from(X) -> cons(X, from(s(X)))
2.97/1.37	   dbl1(0) -> 01
2.97/1.37	   dbl1(s(X)) -> s1(s1(dbl1(X)))
2.97/1.37	   sel1(0, cons(X, Y)) -> X
2.97/1.37	   sel1(s(X), cons(Y, Z)) -> sel1(X, Z)
2.97/1.37	   quote(0) -> 01
2.97/1.37	   quote(s(X)) -> s1(quote(X))
2.97/1.37	   quote(dbl(X)) -> dbl1(X)
2.97/1.37	   quote(sel(X, Y)) -> sel1(X, Y)
2.97/1.37	
2.97/1.37	
2.97/1.37	
2.97/1.37	Outermost Strategy.
2.97/1.37	
2.97/1.37	----------------------------------------
2.97/1.37	
2.97/1.37	(1) OutermostNonTerminationProof (COMPLETE)
2.97/1.37	Term rewrite system R:
2.97/1.37	The TRS R consists of the following rules:
2.97/1.37	
2.97/1.37	   dbl(0) -> 0
2.97/1.37	   dbl(s(X)) -> s(s(dbl(X)))
2.97/1.37	   dbls(nil) -> nil
2.97/1.37	   dbls(cons(X, Y)) -> cons(dbl(X), dbls(Y))
2.97/1.37	   sel(0, cons(X, Y)) -> X
2.97/1.37	   sel(s(X), cons(Y, Z)) -> sel(X, Z)
2.97/1.37	   indx(nil, X) -> nil
2.97/1.37	   indx(cons(X, Y), Z) -> cons(sel(X, Z), indx(Y, Z))
2.97/1.37	   from(X) -> cons(X, from(s(X)))
2.97/1.37	   dbl1(0) -> 01
2.97/1.37	   dbl1(s(X)) -> s1(s1(dbl1(X)))
2.97/1.37	   sel1(0, cons(X, Y)) -> X
2.97/1.37	   sel1(s(X), cons(Y, Z)) -> sel1(X, Z)
2.97/1.37	   quote(0) -> 01
2.97/1.37	   quote(s(X)) -> s1(quote(X))
2.97/1.37	   quote(dbl(X)) -> dbl1(X)
2.97/1.37	   quote(sel(X, Y)) -> sel1(X, Y)
2.97/1.37	
2.97/1.37	
2.97/1.37	
2.97/1.37	Outermost Strategy.
2.97/1.37	
2.97/1.37	---------- Loop: ----------
2.97/1.37	
2.97/1.37	from(X) -> cons(X, from(s(X))) with rule from(X') -> cons(X', from(s(X'))) at position [] and matcher [X' / X]
2.97/1.37	
2.97/1.37	Now an instance of the first term with Matcher [X / s(X)] occurs in the last term at position [1].
2.97/1.37	
2.97/1.37	Context: cons(X, [])
2.97/1.37	
2.97/1.37	We used [THIEMANN_LOOPS_UNDER_STRATEGIES] to show that this Loop is an Outermost-Loop.
2.97/1.37	----------------------------------------
2.97/1.37	
2.97/1.37	(2)
2.97/1.37	NO
2.97/1.40	EOF