3.16/1.55	WORST_CASE(NON_POLY, ?)
3.16/1.55	proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
3.16/1.55	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
3.16/1.55	
3.16/1.55	
3.16/1.55	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(INF, INF).
3.16/1.55	
3.16/1.55	(0) CpxTRS
3.16/1.55	(1) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms]
3.16/1.55	(2) TRS for Loop Detection
3.16/1.55	(3) InfiniteLowerBoundProof [FINISHED, 0 ms]
3.16/1.55	(4) BOUNDS(INF, INF)
3.16/1.55	
3.16/1.55	
3.16/1.55	----------------------------------------
3.16/1.55	
3.16/1.55	(0)
3.16/1.55	Obligation:
3.16/1.55	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(INF, INF).
3.16/1.55	
3.16/1.55	
3.16/1.55	The TRS R consists of the following rules:
3.16/1.55	
3.16/1.55	   f(g(a)) -> f(s(g(b)))
3.16/1.55	   f(f(x)) -> b
3.16/1.55	   g(x) -> f(g(x))
3.16/1.55	
3.16/1.55	S is empty.
3.16/1.55	Rewrite Strategy: FULL
3.16/1.55	----------------------------------------
3.16/1.55	
3.16/1.55	(1) RelTrsToDecreasingLoopProblemProof (LOWER BOUND(ID))
3.16/1.55	Transformed a relative TRS into a decreasing-loop problem.
3.16/1.55	----------------------------------------
3.16/1.55	
3.16/1.55	(2)
3.16/1.55	Obligation:
3.16/1.55	Analyzing the following TRS for decreasing loops:
3.16/1.55	
3.16/1.55	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(INF, INF).
3.16/1.55	
3.16/1.55	
3.16/1.55	The TRS R consists of the following rules:
3.16/1.55	
3.16/1.55	   f(g(a)) -> f(s(g(b)))
3.16/1.55	   f(f(x)) -> b
3.16/1.55	   g(x) -> f(g(x))
3.16/1.55	
3.16/1.55	S is empty.
3.16/1.55	Rewrite Strategy: FULL
3.16/1.55	----------------------------------------
3.16/1.55	
3.16/1.55	(3) InfiniteLowerBoundProof (FINISHED)
3.16/1.55	The following loop proves infinite runtime complexity:
3.16/1.55	
3.16/1.55	The rewrite sequence
3.16/1.55	
3.16/1.55	g(x) ->^+ f(g(x))
3.16/1.55	
3.16/1.55	gives rise to a decreasing loop by considering the right hand sides subterm at position [0].
3.16/1.55	
3.16/1.55	The pumping substitution is [ ].
3.16/1.55	
3.16/1.55	The result substitution is [ ].
3.16/1.55	
3.16/1.55	
3.16/1.55	
3.16/1.55	
3.16/1.55	----------------------------------------
3.16/1.55	
3.16/1.55	(4)
3.16/1.55	BOUNDS(INF, INF)
3.16/1.59	EOF