3.18/1.60	WORST_CASE(NON_POLY, ?)
3.18/1.60	proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
3.18/1.60	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
3.18/1.60	
3.18/1.60	
3.18/1.60	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(INF, INF).
3.18/1.60	
3.18/1.60	(0) CpxTRS
3.18/1.60	(1) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms]
3.18/1.60	(2) TRS for Loop Detection
3.18/1.60	(3) InfiniteLowerBoundProof [FINISHED, 0 ms]
3.18/1.60	(4) BOUNDS(INF, INF)
3.18/1.60	
3.18/1.60	
3.18/1.60	----------------------------------------
3.18/1.60	
3.18/1.60	(0)
3.18/1.60	Obligation:
3.18/1.60	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(INF, INF).
3.18/1.60	
3.18/1.60	
3.18/1.60	The TRS R consists of the following rules:
3.18/1.60	
3.18/1.60	   from(X) -> cons(X, from(s(X)))
3.18/1.60	   sel(0, cons(X, XS)) -> X
3.18/1.60	   sel(s(N), cons(X, XS)) -> sel(N, XS)
3.18/1.60	   minus(X, 0) -> 0
3.18/1.60	   minus(s(X), s(Y)) -> minus(X, Y)
3.18/1.60	   quot(0, s(Y)) -> 0
3.18/1.60	   quot(s(X), s(Y)) -> s(quot(minus(X, Y), s(Y)))
3.18/1.60	   zWquot(XS, nil) -> nil
3.18/1.60	   zWquot(nil, XS) -> nil
3.18/1.60	   zWquot(cons(X, XS), cons(Y, YS)) -> cons(quot(X, Y), zWquot(XS, YS))
3.18/1.60	
3.18/1.60	S is empty.
3.18/1.60	Rewrite Strategy: FULL
3.18/1.60	----------------------------------------
3.18/1.60	
3.18/1.60	(1) RelTrsToDecreasingLoopProblemProof (LOWER BOUND(ID))
3.18/1.60	Transformed a relative TRS into a decreasing-loop problem.
3.18/1.60	----------------------------------------
3.18/1.60	
3.18/1.60	(2)
3.18/1.60	Obligation:
3.18/1.60	Analyzing the following TRS for decreasing loops:
3.18/1.60	
3.18/1.60	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(INF, INF).
3.18/1.60	
3.18/1.60	
3.18/1.60	The TRS R consists of the following rules:
3.18/1.60	
3.18/1.60	   from(X) -> cons(X, from(s(X)))
3.18/1.60	   sel(0, cons(X, XS)) -> X
3.18/1.60	   sel(s(N), cons(X, XS)) -> sel(N, XS)
3.18/1.60	   minus(X, 0) -> 0
3.18/1.60	   minus(s(X), s(Y)) -> minus(X, Y)
3.18/1.60	   quot(0, s(Y)) -> 0
3.18/1.60	   quot(s(X), s(Y)) -> s(quot(minus(X, Y), s(Y)))
3.18/1.60	   zWquot(XS, nil) -> nil
3.18/1.60	   zWquot(nil, XS) -> nil
3.18/1.60	   zWquot(cons(X, XS), cons(Y, YS)) -> cons(quot(X, Y), zWquot(XS, YS))
3.18/1.60	
3.18/1.60	S is empty.
3.18/1.60	Rewrite Strategy: FULL
3.18/1.60	----------------------------------------
3.18/1.60	
3.18/1.60	(3) InfiniteLowerBoundProof (FINISHED)
3.18/1.60	The following loop proves infinite runtime complexity:
3.18/1.60	
3.18/1.60	The rewrite sequence
3.18/1.60	
3.18/1.60	from(X) ->^+ cons(X, from(s(X)))
3.18/1.60	
3.18/1.60	gives rise to a decreasing loop by considering the right hand sides subterm at position [1].
3.18/1.60	
3.18/1.60	The pumping substitution is [ ].
3.18/1.60	
3.18/1.60	The result substitution is [X / s(X)].
3.18/1.60	
3.18/1.60	
3.18/1.60	
3.18/1.60	
3.18/1.60	----------------------------------------
3.18/1.60	
3.18/1.60	(4)
3.18/1.60	BOUNDS(INF, INF)
3.18/1.62	EOF