3.22/1.52	WORST_CASE(NON_POLY, ?)
3.22/1.53	proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
3.22/1.53	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
3.22/1.53	
3.22/1.53	
3.22/1.53	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(INF, INF).
3.22/1.53	
3.22/1.53	(0) CpxTRS
3.22/1.53	(1) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms]
3.22/1.53	(2) TRS for Loop Detection
3.22/1.53	(3) InfiniteLowerBoundProof [FINISHED, 0 ms]
3.22/1.53	(4) BOUNDS(INF, INF)
3.22/1.53	
3.22/1.53	
3.22/1.53	----------------------------------------
3.22/1.53	
3.22/1.53	(0)
3.22/1.53	Obligation:
3.22/1.53	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(INF, INF).
3.22/1.53	
3.22/1.53	
3.22/1.53	The TRS R consists of the following rules:
3.22/1.53	
3.22/1.53	   c -> f(g(c))
3.22/1.53	   f(g(X)) -> g(X)
3.22/1.53	
3.22/1.53	S is empty.
3.22/1.53	Rewrite Strategy: FULL
3.22/1.53	----------------------------------------
3.22/1.53	
3.22/1.53	(1) RelTrsToDecreasingLoopProblemProof (LOWER BOUND(ID))
3.22/1.53	Transformed a relative TRS into a decreasing-loop problem.
3.22/1.53	----------------------------------------
3.22/1.53	
3.22/1.53	(2)
3.22/1.53	Obligation:
3.22/1.53	Analyzing the following TRS for decreasing loops:
3.22/1.53	
3.22/1.53	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(INF, INF).
3.22/1.53	
3.22/1.53	
3.22/1.53	The TRS R consists of the following rules:
3.22/1.53	
3.22/1.53	   c -> f(g(c))
3.22/1.53	   f(g(X)) -> g(X)
3.22/1.53	
3.22/1.53	S is empty.
3.22/1.53	Rewrite Strategy: FULL
3.22/1.53	----------------------------------------
3.22/1.53	
3.22/1.53	(3) InfiniteLowerBoundProof (FINISHED)
3.22/1.53	The following loop proves infinite runtime complexity:
3.22/1.53	
3.22/1.53	The rewrite sequence
3.22/1.53	
3.22/1.53	c ->^+ f(g(c))
3.22/1.53	
3.22/1.53	gives rise to a decreasing loop by considering the right hand sides subterm at position [0,0].
3.22/1.53	
3.22/1.53	The pumping substitution is [ ].
3.22/1.53	
3.22/1.53	The result substitution is [ ].
3.22/1.53	
3.22/1.53	
3.22/1.53	
3.22/1.53	
3.22/1.53	----------------------------------------
3.22/1.53	
3.22/1.53	(4)
3.22/1.53	BOUNDS(INF, INF)
3.30/1.55	EOF