2.99/1.55	WORST_CASE(NON_POLY, ?)
2.99/1.56	proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml
2.99/1.56	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
2.99/1.56	
2.99/1.56	
2.99/1.56	The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(INF, INF).
2.99/1.56	
2.99/1.56	(0) CpxTRS
2.99/1.56	(1) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms]
2.99/1.56	(2) TRS for Loop Detection
2.99/1.56	(3) InfiniteLowerBoundProof [FINISHED, 0 ms]
2.99/1.56	(4) BOUNDS(INF, INF)
2.99/1.56	
2.99/1.56	
2.99/1.56	----------------------------------------
2.99/1.56	
2.99/1.56	(0)
2.99/1.56	Obligation:
2.99/1.56	The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(INF, INF).
2.99/1.56	
2.99/1.56	
2.99/1.56	The TRS R consists of the following rules:
2.99/1.56	
2.99/1.56	   nats -> cons(0, n__incr(nats))
2.99/1.56	   pairs -> cons(0, n__incr(odds))
2.99/1.56	   odds -> incr(pairs)
2.99/1.56	   incr(cons(X, XS)) -> cons(s(X), n__incr(activate(XS)))
2.99/1.56	   head(cons(X, XS)) -> X
2.99/1.56	   tail(cons(X, XS)) -> activate(XS)
2.99/1.56	   incr(X) -> n__incr(X)
2.99/1.56	   activate(n__incr(X)) -> incr(X)
2.99/1.56	   activate(X) -> X
2.99/1.56	
2.99/1.56	S is empty.
2.99/1.56	Rewrite Strategy: INNERMOST
2.99/1.56	----------------------------------------
2.99/1.56	
2.99/1.56	(1) RelTrsToDecreasingLoopProblemProof (LOWER BOUND(ID))
2.99/1.56	Transformed a relative TRS into a decreasing-loop problem.
2.99/1.56	----------------------------------------
2.99/1.56	
2.99/1.56	(2)
2.99/1.56	Obligation:
2.99/1.56	Analyzing the following TRS for decreasing loops:
2.99/1.56	
2.99/1.56	The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(INF, INF).
2.99/1.56	
2.99/1.56	
2.99/1.56	The TRS R consists of the following rules:
2.99/1.56	
2.99/1.56	   nats -> cons(0, n__incr(nats))
2.99/1.56	   pairs -> cons(0, n__incr(odds))
2.99/1.56	   odds -> incr(pairs)
2.99/1.56	   incr(cons(X, XS)) -> cons(s(X), n__incr(activate(XS)))
2.99/1.56	   head(cons(X, XS)) -> X
2.99/1.56	   tail(cons(X, XS)) -> activate(XS)
2.99/1.56	   incr(X) -> n__incr(X)
2.99/1.56	   activate(n__incr(X)) -> incr(X)
2.99/1.56	   activate(X) -> X
2.99/1.56	
2.99/1.56	S is empty.
2.99/1.56	Rewrite Strategy: INNERMOST
2.99/1.56	----------------------------------------
2.99/1.56	
2.99/1.56	(3) InfiniteLowerBoundProof (FINISHED)
2.99/1.56	The following loop proves infinite runtime complexity:
2.99/1.56	
2.99/1.56	The rewrite sequence
2.99/1.56	
2.99/1.56	nats ->^+ cons(0, n__incr(nats))
2.99/1.56	
2.99/1.56	gives rise to a decreasing loop by considering the right hand sides subterm at position [1,0].
2.99/1.56	
2.99/1.56	The pumping substitution is [ ].
2.99/1.56	
2.99/1.56	The result substitution is [ ].
2.99/1.56	
2.99/1.56	
2.99/1.56	
2.99/1.56	
2.99/1.56	----------------------------------------
2.99/1.56	
2.99/1.56	(4)
2.99/1.56	BOUNDS(INF, INF)
2.99/1.60	EOF