2.85/1.57	WORST_CASE(NON_POLY, ?)
2.85/1.58	proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml
2.85/1.58	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
2.85/1.58	
2.85/1.58	
2.85/1.58	The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(INF, INF).
2.85/1.58	
2.85/1.58	(0) CpxTRS
2.85/1.58	(1) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms]
2.85/1.58	(2) TRS for Loop Detection
2.85/1.58	(3) InfiniteLowerBoundProof [FINISHED, 0 ms]
2.85/1.58	(4) BOUNDS(INF, INF)
2.85/1.58	
2.85/1.58	
2.85/1.58	----------------------------------------
2.85/1.58	
2.85/1.58	(0)
2.85/1.58	Obligation:
2.85/1.58	The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(INF, INF).
2.85/1.58	
2.85/1.58	
2.85/1.58	The TRS R consists of the following rules:
2.85/1.58	
2.85/1.58	   2nd(cons(X, cons(Y, Z))) -> Y
2.85/1.58	   from(X) -> cons(X, from(s(X)))
2.85/1.58	
2.85/1.58	S is empty.
2.85/1.58	Rewrite Strategy: INNERMOST
2.85/1.58	----------------------------------------
2.85/1.58	
2.85/1.58	(1) RelTrsToDecreasingLoopProblemProof (LOWER BOUND(ID))
2.85/1.58	Transformed a relative TRS into a decreasing-loop problem.
2.85/1.58	----------------------------------------
2.85/1.58	
2.85/1.58	(2)
2.85/1.58	Obligation:
2.85/1.58	Analyzing the following TRS for decreasing loops:
2.85/1.58	
2.85/1.58	The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(INF, INF).
2.85/1.58	
2.85/1.58	
2.85/1.58	The TRS R consists of the following rules:
2.85/1.58	
2.85/1.58	   2nd(cons(X, cons(Y, Z))) -> Y
2.85/1.58	   from(X) -> cons(X, from(s(X)))
2.85/1.58	
2.85/1.58	S is empty.
2.85/1.58	Rewrite Strategy: INNERMOST
2.85/1.58	----------------------------------------
2.85/1.58	
2.85/1.58	(3) InfiniteLowerBoundProof (FINISHED)
2.85/1.58	The following loop proves infinite runtime complexity:
2.85/1.58	
2.85/1.58	The rewrite sequence
2.85/1.58	
2.85/1.58	from(X) ->^+ cons(X, from(s(X)))
2.85/1.58	
2.85/1.58	gives rise to a decreasing loop by considering the right hand sides subterm at position [1].
2.85/1.58	
2.85/1.58	The pumping substitution is [ ].
2.85/1.58	
2.85/1.58	The result substitution is [X / s(X)].
2.85/1.58	
2.85/1.58	
2.85/1.58	
2.85/1.58	
2.85/1.58	----------------------------------------
2.85/1.58	
2.85/1.58	(4)
2.85/1.58	BOUNDS(INF, INF)
3.17/1.61	EOF