2.94/1.65	WORST_CASE(NON_POLY, ?)
2.94/1.65	proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
2.94/1.65	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
2.94/1.65	
2.94/1.65	
2.94/1.65	The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(INF, INF).
2.94/1.65	
2.94/1.65	(0) CpxTRS
2.94/1.65	(1) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms]
2.94/1.65	(2) TRS for Loop Detection
2.94/1.65	(3) InfiniteLowerBoundProof [FINISHED, 0 ms]
2.94/1.65	(4) BOUNDS(INF, INF)
2.94/1.65	
2.94/1.65	
2.94/1.65	----------------------------------------
2.94/1.65	
2.94/1.65	(0)
2.94/1.65	Obligation:
2.94/1.65	The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(INF, INF).
2.94/1.65	
2.94/1.65	
2.94/1.65	The TRS R consists of the following rules:
2.94/1.65	
2.94/1.65	   fst(0, Z) -> nil
2.94/1.65	   fst(s(X), cons(Y, Z)) -> cons(Y, fst(X, Z))
2.94/1.65	   from(X) -> cons(X, from(s(X)))
2.94/1.65	   add(0, X) -> X
2.94/1.65	   add(s(X), Y) -> s(add(X, Y))
2.94/1.65	   len(nil) -> 0
2.94/1.65	   len(cons(X, Z)) -> s(len(Z))
2.94/1.65	
2.94/1.65	S is empty.
2.94/1.65	Rewrite Strategy: INNERMOST
2.94/1.65	----------------------------------------
2.94/1.65	
2.94/1.65	(1) RelTrsToDecreasingLoopProblemProof (LOWER BOUND(ID))
2.94/1.65	Transformed a relative TRS into a decreasing-loop problem.
2.94/1.65	----------------------------------------
2.94/1.65	
2.94/1.65	(2)
2.94/1.65	Obligation:
2.94/1.65	Analyzing the following TRS for decreasing loops:
2.94/1.65	
2.94/1.65	The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(INF, INF).
2.94/1.65	
2.94/1.65	
2.94/1.65	The TRS R consists of the following rules:
2.94/1.65	
2.94/1.65	   fst(0, Z) -> nil
2.94/1.65	   fst(s(X), cons(Y, Z)) -> cons(Y, fst(X, Z))
2.94/1.65	   from(X) -> cons(X, from(s(X)))
2.94/1.65	   add(0, X) -> X
2.94/1.65	   add(s(X), Y) -> s(add(X, Y))
2.94/1.65	   len(nil) -> 0
2.94/1.65	   len(cons(X, Z)) -> s(len(Z))
2.94/1.65	
2.94/1.65	S is empty.
2.94/1.65	Rewrite Strategy: INNERMOST
2.94/1.65	----------------------------------------
2.94/1.65	
2.94/1.65	(3) InfiniteLowerBoundProof (FINISHED)
2.94/1.65	The following loop proves infinite runtime complexity:
2.94/1.65	
2.94/1.65	The rewrite sequence
2.94/1.65	
2.94/1.65	from(X) ->^+ cons(X, from(s(X)))
2.94/1.65	
2.94/1.65	gives rise to a decreasing loop by considering the right hand sides subterm at position [1].
2.94/1.65	
2.94/1.65	The pumping substitution is [ ].
2.94/1.65	
2.94/1.65	The result substitution is [X / s(X)].
2.94/1.65	
2.94/1.65	
2.94/1.65	
2.94/1.65	
2.94/1.65	----------------------------------------
2.94/1.65	
2.94/1.65	(4)
2.94/1.65	BOUNDS(INF, INF)
3.10/1.69	EOF