3.07/1.58	WORST_CASE(NON_POLY, ?)
3.07/1.59	proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
3.07/1.59	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
3.07/1.59	
3.07/1.59	
3.07/1.59	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(INF, INF).
3.07/1.59	
3.07/1.59	(0) CpxTRS
3.07/1.59	(1) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms]
3.07/1.59	(2) TRS for Loop Detection
3.07/1.59	(3) InfiniteLowerBoundProof [FINISHED, 0 ms]
3.07/1.59	(4) BOUNDS(INF, INF)
3.07/1.59	
3.07/1.59	
3.07/1.59	----------------------------------------
3.07/1.59	
3.07/1.59	(0)
3.07/1.59	Obligation:
3.07/1.59	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(INF, INF).
3.07/1.59	
3.07/1.59	
3.07/1.59	The TRS R consists of the following rules:
3.07/1.59	
3.07/1.59	   nats -> adx(zeros)
3.07/1.59	   zeros -> cons(0, zeros)
3.07/1.59	   incr(cons(X, Y)) -> cons(s(X), incr(Y))
3.07/1.59	   adx(cons(X, Y)) -> incr(cons(X, adx(Y)))
3.07/1.59	   hd(cons(X, Y)) -> X
3.07/1.59	   tl(cons(X, Y)) -> Y
3.07/1.59	
3.07/1.59	S is empty.
3.07/1.59	Rewrite Strategy: FULL
3.07/1.59	----------------------------------------
3.07/1.59	
3.07/1.59	(1) RelTrsToDecreasingLoopProblemProof (LOWER BOUND(ID))
3.07/1.59	Transformed a relative TRS into a decreasing-loop problem.
3.07/1.59	----------------------------------------
3.07/1.59	
3.07/1.59	(2)
3.07/1.59	Obligation:
3.07/1.59	Analyzing the following TRS for decreasing loops:
3.07/1.59	
3.07/1.59	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(INF, INF).
3.07/1.59	
3.07/1.59	
3.07/1.59	The TRS R consists of the following rules:
3.07/1.59	
3.07/1.59	   nats -> adx(zeros)
3.07/1.59	   zeros -> cons(0, zeros)
3.07/1.59	   incr(cons(X, Y)) -> cons(s(X), incr(Y))
3.07/1.59	   adx(cons(X, Y)) -> incr(cons(X, adx(Y)))
3.07/1.59	   hd(cons(X, Y)) -> X
3.07/1.59	   tl(cons(X, Y)) -> Y
3.07/1.59	
3.07/1.59	S is empty.
3.07/1.59	Rewrite Strategy: FULL
3.07/1.59	----------------------------------------
3.07/1.59	
3.07/1.59	(3) InfiniteLowerBoundProof (FINISHED)
3.07/1.59	The following loop proves infinite runtime complexity:
3.07/1.59	
3.07/1.59	The rewrite sequence
3.07/1.59	
3.07/1.59	zeros ->^+ cons(0, zeros)
3.07/1.59	
3.07/1.59	gives rise to a decreasing loop by considering the right hand sides subterm at position [1].
3.07/1.59	
3.07/1.59	The pumping substitution is [ ].
3.07/1.59	
3.07/1.59	The result substitution is [ ].
3.07/1.59	
3.07/1.59	
3.07/1.59	
3.07/1.59	
3.07/1.59	----------------------------------------
3.07/1.59	
3.07/1.59	(4)
3.07/1.59	BOUNDS(INF, INF)
3.21/1.63	EOF