3.16/1.65	WORST_CASE(NON_POLY, ?)
3.16/1.66	proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
3.16/1.66	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
3.16/1.66	
3.16/1.66	
3.16/1.66	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(INF, INF).
3.16/1.66	
3.16/1.66	(0) CpxTRS
3.16/1.66	(1) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms]
3.16/1.66	(2) TRS for Loop Detection
3.16/1.66	(3) InfiniteLowerBoundProof [FINISHED, 0 ms]
3.16/1.66	(4) BOUNDS(INF, INF)
3.16/1.66	
3.16/1.66	
3.16/1.66	----------------------------------------
3.16/1.66	
3.16/1.66	(0)
3.16/1.66	Obligation:
3.16/1.66	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(INF, INF).
3.16/1.66	
3.16/1.66	
3.16/1.66	The TRS R consists of the following rules:
3.16/1.66	
3.16/1.66	   f(X) -> g(n__h(f(X)))
3.16/1.66	   h(X) -> n__h(X)
3.16/1.66	   activate(n__h(X)) -> h(X)
3.16/1.66	   activate(X) -> X
3.16/1.66	
3.16/1.66	S is empty.
3.16/1.66	Rewrite Strategy: FULL
3.16/1.66	----------------------------------------
3.16/1.66	
3.16/1.66	(1) RelTrsToDecreasingLoopProblemProof (LOWER BOUND(ID))
3.16/1.66	Transformed a relative TRS into a decreasing-loop problem.
3.16/1.66	----------------------------------------
3.16/1.66	
3.16/1.66	(2)
3.16/1.66	Obligation:
3.16/1.66	Analyzing the following TRS for decreasing loops:
3.16/1.66	
3.16/1.66	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(INF, INF).
3.16/1.66	
3.16/1.66	
3.16/1.66	The TRS R consists of the following rules:
3.16/1.66	
3.16/1.66	   f(X) -> g(n__h(f(X)))
3.16/1.66	   h(X) -> n__h(X)
3.16/1.66	   activate(n__h(X)) -> h(X)
3.16/1.66	   activate(X) -> X
3.16/1.66	
3.16/1.66	S is empty.
3.16/1.66	Rewrite Strategy: FULL
3.16/1.66	----------------------------------------
3.16/1.66	
3.16/1.66	(3) InfiniteLowerBoundProof (FINISHED)
3.16/1.66	The following loop proves infinite runtime complexity:
3.16/1.66	
3.16/1.66	The rewrite sequence
3.16/1.66	
3.16/1.66	f(X) ->^+ g(n__h(f(X)))
3.16/1.66	
3.16/1.66	gives rise to a decreasing loop by considering the right hand sides subterm at position [0,0].
3.16/1.66	
3.16/1.66	The pumping substitution is [ ].
3.16/1.66	
3.16/1.66	The result substitution is [ ].
3.16/1.66	
3.16/1.66	
3.16/1.66	
3.16/1.66	
3.16/1.66	----------------------------------------
3.16/1.66	
3.16/1.66	(4)
3.16/1.66	BOUNDS(INF, INF)
3.31/1.70	EOF