3.08/1.53	WORST_CASE(NON_POLY, ?)
3.08/1.54	proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
3.08/1.54	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
3.08/1.54	
3.08/1.54	
3.08/1.54	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(INF, INF).
3.08/1.54	
3.08/1.54	(0) CpxTRS
3.08/1.54	(1) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms]
3.08/1.54	(2) TRS for Loop Detection
3.08/1.54	(3) InfiniteLowerBoundProof [FINISHED, 0 ms]
3.08/1.54	(4) BOUNDS(INF, INF)
3.08/1.54	
3.08/1.54	
3.08/1.54	----------------------------------------
3.08/1.54	
3.08/1.54	(0)
3.08/1.54	Obligation:
3.08/1.54	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(INF, INF).
3.08/1.54	
3.08/1.54	
3.08/1.54	The TRS R consists of the following rules:
3.08/1.54	
3.08/1.54	   incr(nil) -> nil
3.08/1.54	   incr(cons(X, L)) -> cons(s(X), incr(L))
3.08/1.54	   adx(nil) -> nil
3.08/1.54	   adx(cons(X, L)) -> incr(cons(X, adx(L)))
3.08/1.54	   nats -> adx(zeros)
3.08/1.54	   zeros -> cons(0, zeros)
3.08/1.54	   head(cons(X, L)) -> X
3.08/1.54	   tail(cons(X, L)) -> L
3.08/1.54	
3.08/1.54	S is empty.
3.08/1.54	Rewrite Strategy: FULL
3.08/1.54	----------------------------------------
3.08/1.54	
3.08/1.54	(1) RelTrsToDecreasingLoopProblemProof (LOWER BOUND(ID))
3.08/1.54	Transformed a relative TRS into a decreasing-loop problem.
3.08/1.54	----------------------------------------
3.08/1.54	
3.08/1.54	(2)
3.08/1.54	Obligation:
3.08/1.54	Analyzing the following TRS for decreasing loops:
3.08/1.54	
3.08/1.54	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(INF, INF).
3.08/1.54	
3.08/1.54	
3.08/1.54	The TRS R consists of the following rules:
3.08/1.54	
3.08/1.54	   incr(nil) -> nil
3.08/1.54	   incr(cons(X, L)) -> cons(s(X), incr(L))
3.08/1.54	   adx(nil) -> nil
3.08/1.54	   adx(cons(X, L)) -> incr(cons(X, adx(L)))
3.08/1.54	   nats -> adx(zeros)
3.08/1.54	   zeros -> cons(0, zeros)
3.08/1.54	   head(cons(X, L)) -> X
3.08/1.54	   tail(cons(X, L)) -> L
3.08/1.54	
3.08/1.54	S is empty.
3.08/1.54	Rewrite Strategy: FULL
3.08/1.54	----------------------------------------
3.08/1.54	
3.08/1.54	(3) InfiniteLowerBoundProof (FINISHED)
3.08/1.54	The following loop proves infinite runtime complexity:
3.08/1.54	
3.08/1.54	The rewrite sequence
3.08/1.54	
3.08/1.54	zeros ->^+ cons(0, zeros)
3.08/1.54	
3.08/1.54	gives rise to a decreasing loop by considering the right hand sides subterm at position [1].
3.08/1.54	
3.08/1.54	The pumping substitution is [ ].
3.08/1.54	
3.08/1.54	The result substitution is [ ].
3.08/1.54	
3.08/1.54	
3.08/1.54	
3.08/1.54	
3.08/1.54	----------------------------------------
3.08/1.54	
3.08/1.54	(4)
3.08/1.54	BOUNDS(INF, INF)
3.20/1.57	EOF