3.12/1.56	WORST_CASE(NON_POLY, ?)
3.12/1.57	proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml
3.12/1.57	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
3.12/1.57	
3.12/1.57	
3.12/1.57	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(INF, INF).
3.12/1.57	
3.12/1.57	(0) CpxTRS
3.12/1.57	(1) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms]
3.12/1.57	(2) TRS for Loop Detection
3.12/1.57	(3) InfiniteLowerBoundProof [FINISHED, 0 ms]
3.12/1.57	(4) BOUNDS(INF, INF)
3.12/1.57	
3.12/1.57	
3.12/1.57	----------------------------------------
3.12/1.57	
3.12/1.57	(0)
3.12/1.57	Obligation:
3.12/1.57	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(INF, INF).
3.12/1.57	
3.12/1.57	
3.12/1.57	The TRS R consists of the following rules:
3.12/1.57	
3.12/1.57	   from(X) -> cons(X, from(s(X)))
3.12/1.57	   sel(0, cons(X, Y)) -> X
3.12/1.57	   sel(s(X), cons(Y, Z)) -> sel(X, Z)
3.12/1.57	
3.12/1.57	S is empty.
3.12/1.57	Rewrite Strategy: FULL
3.12/1.57	----------------------------------------
3.12/1.57	
3.12/1.57	(1) RelTrsToDecreasingLoopProblemProof (LOWER BOUND(ID))
3.12/1.57	Transformed a relative TRS into a decreasing-loop problem.
3.12/1.57	----------------------------------------
3.12/1.57	
3.12/1.57	(2)
3.12/1.57	Obligation:
3.12/1.57	Analyzing the following TRS for decreasing loops:
3.12/1.57	
3.12/1.57	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(INF, INF).
3.12/1.57	
3.12/1.57	
3.12/1.57	The TRS R consists of the following rules:
3.12/1.57	
3.12/1.57	   from(X) -> cons(X, from(s(X)))
3.12/1.57	   sel(0, cons(X, Y)) -> X
3.12/1.57	   sel(s(X), cons(Y, Z)) -> sel(X, Z)
3.12/1.57	
3.12/1.57	S is empty.
3.12/1.57	Rewrite Strategy: FULL
3.12/1.57	----------------------------------------
3.12/1.57	
3.12/1.57	(3) InfiniteLowerBoundProof (FINISHED)
3.12/1.57	The following loop proves infinite runtime complexity:
3.12/1.57	
3.12/1.57	The rewrite sequence
3.12/1.57	
3.12/1.57	from(X) ->^+ cons(X, from(s(X)))
3.12/1.57	
3.12/1.57	gives rise to a decreasing loop by considering the right hand sides subterm at position [1].
3.12/1.57	
3.12/1.57	The pumping substitution is [ ].
3.12/1.57	
3.12/1.57	The result substitution is [X / s(X)].
3.12/1.57	
3.12/1.57	
3.12/1.57	
3.12/1.57	
3.12/1.57	----------------------------------------
3.12/1.57	
3.12/1.57	(4)
3.12/1.57	BOUNDS(INF, INF)
3.12/1.60	EOF