1.58/1.68	WORST_CASE(NON_POLY, ?)
1.58/1.69	proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
1.58/1.69	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
1.58/1.69	
1.58/1.69	
1.58/1.69	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(INF, INF).
1.58/1.69	
1.58/1.69	(0) CpxTRS
1.58/1.69	(1) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms]
1.58/1.69	(2) TRS for Loop Detection
1.58/1.69	(3) InfiniteLowerBoundProof [FINISHED, 0 ms]
1.58/1.69	(4) BOUNDS(INF, INF)
1.58/1.69	
1.58/1.69	
1.58/1.69	----------------------------------------
1.58/1.69	
1.58/1.69	(0)
1.58/1.69	Obligation:
1.58/1.69	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(INF, INF).
1.58/1.69	
1.58/1.69	
1.58/1.69	The TRS R consists of the following rules:
1.58/1.69	
1.58/1.69	   eq -> true
1.58/1.69	   eq -> eq
1.58/1.69	   eq -> false
1.58/1.69	   inf(X) -> cons
1.58/1.69	   take(0, X) -> nil
1.58/1.69	   take(s, cons) -> cons
1.58/1.69	   length(nil) -> 0
1.58/1.69	   length(cons) -> s
1.58/1.69	
1.58/1.69	S is empty.
1.58/1.69	Rewrite Strategy: FULL
1.58/1.69	----------------------------------------
1.58/1.69	
1.58/1.69	(1) RelTrsToDecreasingLoopProblemProof (LOWER BOUND(ID))
1.58/1.69	Transformed a relative TRS into a decreasing-loop problem.
1.58/1.69	----------------------------------------
1.58/1.69	
1.58/1.69	(2)
1.58/1.69	Obligation:
1.58/1.69	Analyzing the following TRS for decreasing loops:
1.58/1.69	
1.58/1.69	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(INF, INF).
1.58/1.69	
1.58/1.69	
1.58/1.69	The TRS R consists of the following rules:
1.58/1.69	
1.58/1.69	   eq -> true
1.58/1.69	   eq -> eq
1.58/1.69	   eq -> false
1.58/1.69	   inf(X) -> cons
1.58/1.69	   take(0, X) -> nil
1.58/1.69	   take(s, cons) -> cons
1.58/1.69	   length(nil) -> 0
1.58/1.69	   length(cons) -> s
1.58/1.69	
1.58/1.69	S is empty.
1.58/1.69	Rewrite Strategy: FULL
1.58/1.69	----------------------------------------
1.58/1.69	
1.58/1.69	(3) InfiniteLowerBoundProof (FINISHED)
1.58/1.69	The following loop proves infinite runtime complexity:
1.58/1.69	
1.58/1.69	The rewrite sequence
1.58/1.69	
1.58/1.69	eq ->^+ eq
1.58/1.69	
1.58/1.69	gives rise to a decreasing loop by considering the right hand sides subterm at position [].
1.58/1.69	
1.58/1.69	The pumping substitution is [ ].
1.58/1.69	
1.58/1.69	The result substitution is [ ].
1.58/1.69	
1.58/1.69	
1.58/1.69	
1.58/1.69	
1.58/1.69	----------------------------------------
1.58/1.69	
1.58/1.69	(4)
1.58/1.69	BOUNDS(INF, INF)
3.37/1.72	EOF