3.14/1.54	WORST_CASE(NON_POLY, ?)
3.14/1.54	proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml
3.14/1.54	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
3.14/1.54	
3.14/1.54	
3.14/1.54	The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(INF, INF).
3.14/1.54	
3.14/1.54	(0) CpxTRS
3.14/1.54	(1) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms]
3.14/1.54	(2) TRS for Loop Detection
3.14/1.54	(3) InfiniteLowerBoundProof [FINISHED, 0 ms]
3.14/1.54	(4) BOUNDS(INF, INF)
3.14/1.54	
3.14/1.54	
3.14/1.54	----------------------------------------
3.14/1.54	
3.14/1.54	(0)
3.14/1.54	Obligation:
3.14/1.54	The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(INF, INF).
3.14/1.54	
3.14/1.54	
3.14/1.54	The TRS R consists of the following rules:
3.14/1.54	
3.14/1.54	   app(nil, YS) -> YS
3.14/1.54	   app(cons(X, XS), YS) -> cons(X, app(XS, YS))
3.14/1.54	   from(X) -> cons(X, from(s(X)))
3.14/1.54	   zWadr(nil, YS) -> nil
3.14/1.54	   zWadr(XS, nil) -> nil
3.14/1.54	   zWadr(cons(X, XS), cons(Y, YS)) -> cons(app(Y, cons(X, nil)), zWadr(XS, YS))
3.14/1.54	   prefix(L) -> cons(nil, zWadr(L, prefix(L)))
3.14/1.54	
3.14/1.54	S is empty.
3.14/1.54	Rewrite Strategy: INNERMOST
3.14/1.54	----------------------------------------
3.14/1.54	
3.14/1.54	(1) RelTrsToDecreasingLoopProblemProof (LOWER BOUND(ID))
3.14/1.54	Transformed a relative TRS into a decreasing-loop problem.
3.14/1.54	----------------------------------------
3.14/1.54	
3.14/1.54	(2)
3.14/1.54	Obligation:
3.14/1.54	Analyzing the following TRS for decreasing loops:
3.14/1.54	
3.14/1.54	The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(INF, INF).
3.14/1.54	
3.14/1.54	
3.14/1.54	The TRS R consists of the following rules:
3.14/1.54	
3.14/1.54	   app(nil, YS) -> YS
3.14/1.54	   app(cons(X, XS), YS) -> cons(X, app(XS, YS))
3.14/1.54	   from(X) -> cons(X, from(s(X)))
3.14/1.54	   zWadr(nil, YS) -> nil
3.14/1.54	   zWadr(XS, nil) -> nil
3.14/1.54	   zWadr(cons(X, XS), cons(Y, YS)) -> cons(app(Y, cons(X, nil)), zWadr(XS, YS))
3.14/1.54	   prefix(L) -> cons(nil, zWadr(L, prefix(L)))
3.14/1.54	
3.14/1.54	S is empty.
3.14/1.54	Rewrite Strategy: INNERMOST
3.14/1.54	----------------------------------------
3.14/1.54	
3.14/1.54	(3) InfiniteLowerBoundProof (FINISHED)
3.14/1.54	The following loop proves infinite runtime complexity:
3.14/1.54	
3.14/1.54	The rewrite sequence
3.14/1.54	
3.14/1.54	from(X) ->^+ cons(X, from(s(X)))
3.14/1.54	
3.14/1.54	gives rise to a decreasing loop by considering the right hand sides subterm at position [1].
3.14/1.54	
3.14/1.54	The pumping substitution is [ ].
3.14/1.54	
3.14/1.54	The result substitution is [X / s(X)].
3.14/1.54	
3.14/1.54	
3.14/1.54	
3.14/1.54	
3.14/1.54	----------------------------------------
3.14/1.54	
3.14/1.54	(4)
3.14/1.54	BOUNDS(INF, INF)
3.14/1.57	EOF