2.97/1.58	WORST_CASE(NON_POLY, ?)
2.97/1.59	proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
2.97/1.59	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
2.97/1.59	
2.97/1.59	
2.97/1.59	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(INF, INF).
2.97/1.59	
2.97/1.59	(0) CpxTRS
2.97/1.59	(1) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms]
2.97/1.59	(2) TRS for Loop Detection
2.97/1.59	(3) InfiniteLowerBoundProof [FINISHED, 0 ms]
2.97/1.59	(4) BOUNDS(INF, INF)
2.97/1.59	
2.97/1.59	
2.97/1.59	----------------------------------------
2.97/1.59	
2.97/1.59	(0)
2.97/1.59	Obligation:
2.97/1.59	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(INF, INF).
2.97/1.59	
2.97/1.59	
2.97/1.59	The TRS R consists of the following rules:
2.97/1.59	
2.97/1.59	   from(X) -> cons(X, from(s(X)))
2.97/1.59	   head(cons(X, XS)) -> X
2.97/1.59	   2nd(cons(X, XS)) -> head(XS)
2.97/1.59	   take(0, XS) -> nil
2.97/1.59	   take(s(N), cons(X, XS)) -> cons(X, take(N, XS))
2.97/1.59	   sel(0, cons(X, XS)) -> X
2.97/1.59	   sel(s(N), cons(X, XS)) -> sel(N, XS)
2.97/1.59	
2.97/1.59	S is empty.
2.97/1.59	Rewrite Strategy: FULL
2.97/1.59	----------------------------------------
2.97/1.59	
2.97/1.59	(1) RelTrsToDecreasingLoopProblemProof (LOWER BOUND(ID))
2.97/1.59	Transformed a relative TRS into a decreasing-loop problem.
2.97/1.59	----------------------------------------
2.97/1.59	
2.97/1.59	(2)
2.97/1.59	Obligation:
2.97/1.59	Analyzing the following TRS for decreasing loops:
2.97/1.59	
2.97/1.59	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(INF, INF).
2.97/1.59	
2.97/1.59	
2.97/1.59	The TRS R consists of the following rules:
2.97/1.59	
2.97/1.59	   from(X) -> cons(X, from(s(X)))
2.97/1.59	   head(cons(X, XS)) -> X
2.97/1.59	   2nd(cons(X, XS)) -> head(XS)
2.97/1.59	   take(0, XS) -> nil
2.97/1.59	   take(s(N), cons(X, XS)) -> cons(X, take(N, XS))
2.97/1.59	   sel(0, cons(X, XS)) -> X
2.97/1.59	   sel(s(N), cons(X, XS)) -> sel(N, XS)
2.97/1.59	
2.97/1.59	S is empty.
2.97/1.59	Rewrite Strategy: FULL
2.97/1.59	----------------------------------------
2.97/1.59	
2.97/1.59	(3) InfiniteLowerBoundProof (FINISHED)
2.97/1.59	The following loop proves infinite runtime complexity:
2.97/1.59	
2.97/1.59	The rewrite sequence
2.97/1.59	
2.97/1.59	from(X) ->^+ cons(X, from(s(X)))
2.97/1.59	
2.97/1.59	gives rise to a decreasing loop by considering the right hand sides subterm at position [1].
2.97/1.59	
2.97/1.59	The pumping substitution is [ ].
2.97/1.59	
2.97/1.59	The result substitution is [X / s(X)].
2.97/1.59	
2.97/1.59	
2.97/1.59	
2.97/1.59	
2.97/1.59	----------------------------------------
2.97/1.59	
2.97/1.59	(4)
2.97/1.59	BOUNDS(INF, INF)
3.23/1.62	EOF