3.32/1.58	WORST_CASE(NON_POLY, ?)
3.32/1.58	proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
3.32/1.58	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
3.32/1.58	
3.32/1.58	
3.32/1.58	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(INF, INF).
3.32/1.58	
3.32/1.58	(0) CpxTRS
3.32/1.58	(1) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms]
3.32/1.58	(2) TRS for Loop Detection
3.32/1.58	(3) InfiniteLowerBoundProof [FINISHED, 56 ms]
3.32/1.58	(4) BOUNDS(INF, INF)
3.32/1.58	
3.32/1.58	
3.32/1.58	----------------------------------------
3.32/1.58	
3.32/1.58	(0)
3.32/1.58	Obligation:
3.32/1.58	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(INF, INF).
3.32/1.58	
3.32/1.58	
3.32/1.58	The TRS R consists of the following rules:
3.32/1.58	
3.32/1.58	   f(n__a, X, X) -> f(activate(X), b, n__b)
3.32/1.58	   b -> a
3.32/1.58	   a -> n__a
3.32/1.58	   b -> n__b
3.32/1.58	   activate(n__a) -> a
3.32/1.58	   activate(n__b) -> b
3.32/1.58	   activate(X) -> X
3.32/1.58	
3.32/1.58	S is empty.
3.32/1.58	Rewrite Strategy: FULL
3.32/1.58	----------------------------------------
3.32/1.58	
3.32/1.58	(1) RelTrsToDecreasingLoopProblemProof (LOWER BOUND(ID))
3.32/1.58	Transformed a relative TRS into a decreasing-loop problem.
3.32/1.58	----------------------------------------
3.32/1.58	
3.32/1.58	(2)
3.32/1.58	Obligation:
3.32/1.58	Analyzing the following TRS for decreasing loops:
3.32/1.59	
3.32/1.59	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(INF, INF).
3.32/1.59	
3.32/1.59	
3.32/1.59	The TRS R consists of the following rules:
3.32/1.59	
3.32/1.59	   f(n__a, X, X) -> f(activate(X), b, n__b)
3.32/1.59	   b -> a
3.32/1.59	   a -> n__a
3.32/1.59	   b -> n__b
3.32/1.59	   activate(n__a) -> a
3.32/1.59	   activate(n__b) -> b
3.32/1.59	   activate(X) -> X
3.32/1.59	
3.32/1.59	S is empty.
3.32/1.59	Rewrite Strategy: FULL
3.32/1.59	----------------------------------------
3.32/1.59	
3.32/1.59	(3) InfiniteLowerBoundProof (FINISHED)
3.32/1.59	The following loop proves infinite runtime complexity:
3.32/1.59	
3.32/1.59	The rewrite sequence
3.32/1.59	
3.32/1.59	f(n__a, n__b, n__b) ->^+ f(n__a, n__b, n__b)
3.32/1.59	
3.32/1.59	gives rise to a decreasing loop by considering the right hand sides subterm at position [].
3.32/1.59	
3.32/1.59	The pumping substitution is [ ].
3.32/1.59	
3.32/1.59	The result substitution is [ ].
3.32/1.59	
3.32/1.59	
3.32/1.59	
3.32/1.59	
3.32/1.59	----------------------------------------
3.32/1.59	
3.32/1.59	(4)
3.32/1.59	BOUNDS(INF, INF)
3.45/1.61	EOF