3.10/2.35	WORST_CASE(NON_POLY, ?)
3.10/2.35	proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
3.10/2.35	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
3.10/2.35	
3.10/2.35	
3.10/2.35	The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(INF, INF).
3.10/2.35	
3.10/2.35	(0) CpxTRS
3.10/2.35	(1) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms]
3.10/2.35	(2) TRS for Loop Detection
3.10/2.35	(3) InfiniteLowerBoundProof [FINISHED, 0 ms]
3.10/2.35	(4) BOUNDS(INF, INF)
3.10/2.35	
3.10/2.35	
3.10/2.35	----------------------------------------
3.10/2.35	
3.10/2.35	(0)
3.10/2.35	Obligation:
3.10/2.35	The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(INF, INF).
3.10/2.35	
3.10/2.35	
3.10/2.35	The TRS R consists of the following rules:
3.10/2.35	
3.10/2.35	   eq -> true
3.10/2.35	   eq -> eq
3.10/2.35	   eq -> false
3.10/2.35	   inf(X) -> cons
3.10/2.35	   take(0, X) -> nil
3.10/2.35	   take(s, cons) -> cons
3.10/2.35	   length(nil) -> 0
3.10/2.35	   length(cons) -> s
3.10/2.35	
3.10/2.35	S is empty.
3.10/2.35	Rewrite Strategy: INNERMOST
3.10/2.35	----------------------------------------
3.10/2.35	
3.10/2.35	(1) RelTrsToDecreasingLoopProblemProof (LOWER BOUND(ID))
3.10/2.35	Transformed a relative TRS into a decreasing-loop problem.
3.10/2.35	----------------------------------------
3.10/2.35	
3.10/2.35	(2)
3.10/2.35	Obligation:
3.10/2.35	Analyzing the following TRS for decreasing loops:
3.10/2.35	
3.10/2.35	The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(INF, INF).
3.10/2.35	
3.10/2.35	
3.10/2.35	The TRS R consists of the following rules:
3.10/2.35	
3.10/2.35	   eq -> true
3.10/2.35	   eq -> eq
3.10/2.35	   eq -> false
3.10/2.35	   inf(X) -> cons
3.10/2.35	   take(0, X) -> nil
3.10/2.35	   take(s, cons) -> cons
3.10/2.35	   length(nil) -> 0
3.10/2.35	   length(cons) -> s
3.10/2.35	
3.10/2.35	S is empty.
3.10/2.35	Rewrite Strategy: INNERMOST
3.10/2.35	----------------------------------------
3.10/2.35	
3.10/2.35	(3) InfiniteLowerBoundProof (FINISHED)
3.10/2.35	The following loop proves infinite runtime complexity:
3.10/2.35	
3.10/2.35	The rewrite sequence
3.10/2.35	
3.10/2.35	eq ->^+ eq
3.10/2.35	
3.10/2.35	gives rise to a decreasing loop by considering the right hand sides subterm at position [].
3.10/2.35	
3.10/2.35	The pumping substitution is [ ].
3.10/2.35	
3.10/2.35	The result substitution is [ ].
3.10/2.35	
3.10/2.35	
3.10/2.35	
3.10/2.35	
3.10/2.35	----------------------------------------
3.10/2.35	
3.10/2.35	(4)
3.10/2.35	BOUNDS(INF, INF)
3.10/2.38	EOF