2.98/1.56	WORST_CASE(NON_POLY, ?)
2.98/1.56	proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
2.98/1.56	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
2.98/1.56	
2.98/1.56	
2.98/1.56	The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(INF, INF).
2.98/1.56	
2.98/1.56	(0) CpxTRS
2.98/1.56	(1) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms]
2.98/1.56	(2) TRS for Loop Detection
2.98/1.56	(3) InfiniteLowerBoundProof [FINISHED, 0 ms]
2.98/1.56	(4) BOUNDS(INF, INF)
2.98/1.56	
2.98/1.56	
2.98/1.56	----------------------------------------
2.98/1.56	
2.98/1.56	(0)
2.98/1.56	Obligation:
2.98/1.56	The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(INF, INF).
2.98/1.56	
2.98/1.56	
2.98/1.56	The TRS R consists of the following rules:
2.98/1.56	
2.98/1.56	   from(X) -> cons(X, from(s(X)))
2.98/1.56	   length(nil) -> 0
2.98/1.56	   length(cons(X, Y)) -> s(length1(Y))
2.98/1.56	   length1(X) -> length(X)
2.98/1.56	
2.98/1.56	S is empty.
2.98/1.56	Rewrite Strategy: INNERMOST
2.98/1.56	----------------------------------------
2.98/1.56	
2.98/1.56	(1) RelTrsToDecreasingLoopProblemProof (LOWER BOUND(ID))
2.98/1.56	Transformed a relative TRS into a decreasing-loop problem.
2.98/1.56	----------------------------------------
2.98/1.56	
2.98/1.56	(2)
2.98/1.56	Obligation:
2.98/1.56	Analyzing the following TRS for decreasing loops:
2.98/1.56	
2.98/1.56	The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(INF, INF).
2.98/1.56	
2.98/1.56	
2.98/1.56	The TRS R consists of the following rules:
2.98/1.56	
2.98/1.56	   from(X) -> cons(X, from(s(X)))
2.98/1.56	   length(nil) -> 0
2.98/1.56	   length(cons(X, Y)) -> s(length1(Y))
2.98/1.56	   length1(X) -> length(X)
2.98/1.56	
2.98/1.56	S is empty.
2.98/1.56	Rewrite Strategy: INNERMOST
2.98/1.56	----------------------------------------
2.98/1.56	
2.98/1.56	(3) InfiniteLowerBoundProof (FINISHED)
2.98/1.56	The following loop proves infinite runtime complexity:
2.98/1.56	
2.98/1.56	The rewrite sequence
2.98/1.56	
2.98/1.56	from(X) ->^+ cons(X, from(s(X)))
2.98/1.56	
2.98/1.56	gives rise to a decreasing loop by considering the right hand sides subterm at position [1].
2.98/1.56	
2.98/1.56	The pumping substitution is [ ].
2.98/1.56	
2.98/1.56	The result substitution is [X / s(X)].
2.98/1.56	
2.98/1.56	
2.98/1.56	
2.98/1.56	
2.98/1.56	----------------------------------------
2.98/1.56	
2.98/1.56	(4)
2.98/1.56	BOUNDS(INF, INF)
3.20/1.58	EOF