3.06/1.50	WORST_CASE(NON_POLY, ?)
3.06/1.51	proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
3.06/1.51	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
3.06/1.51	
3.06/1.51	
3.06/1.51	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(INF, INF).
3.06/1.51	
3.06/1.51	(0) CpxTRS
3.06/1.51	(1) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms]
3.06/1.51	(2) TRS for Loop Detection
3.06/1.51	(3) InfiniteLowerBoundProof [FINISHED, 0 ms]
3.06/1.51	(4) BOUNDS(INF, INF)
3.06/1.51	
3.06/1.51	
3.06/1.51	----------------------------------------
3.06/1.51	
3.06/1.51	(0)
3.06/1.51	Obligation:
3.06/1.51	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(INF, INF).
3.06/1.51	
3.06/1.51	
3.06/1.51	The TRS R consists of the following rules:
3.06/1.51	
3.06/1.51	   nats -> cons(0, n__incr(nats))
3.06/1.51	   pairs -> cons(0, n__incr(odds))
3.06/1.51	   odds -> incr(pairs)
3.06/1.51	   incr(cons(X, XS)) -> cons(s(X), n__incr(activate(XS)))
3.06/1.51	   head(cons(X, XS)) -> X
3.06/1.51	   tail(cons(X, XS)) -> activate(XS)
3.06/1.51	   incr(X) -> n__incr(X)
3.06/1.51	   activate(n__incr(X)) -> incr(X)
3.06/1.51	   activate(X) -> X
3.06/1.51	
3.06/1.51	S is empty.
3.06/1.51	Rewrite Strategy: FULL
3.06/1.51	----------------------------------------
3.06/1.51	
3.06/1.51	(1) RelTrsToDecreasingLoopProblemProof (LOWER BOUND(ID))
3.06/1.51	Transformed a relative TRS into a decreasing-loop problem.
3.06/1.51	----------------------------------------
3.06/1.51	
3.06/1.51	(2)
3.06/1.51	Obligation:
3.06/1.51	Analyzing the following TRS for decreasing loops:
3.06/1.51	
3.06/1.51	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(INF, INF).
3.06/1.51	
3.06/1.51	
3.06/1.51	The TRS R consists of the following rules:
3.06/1.51	
3.06/1.51	   nats -> cons(0, n__incr(nats))
3.06/1.51	   pairs -> cons(0, n__incr(odds))
3.06/1.51	   odds -> incr(pairs)
3.06/1.51	   incr(cons(X, XS)) -> cons(s(X), n__incr(activate(XS)))
3.06/1.51	   head(cons(X, XS)) -> X
3.06/1.51	   tail(cons(X, XS)) -> activate(XS)
3.06/1.51	   incr(X) -> n__incr(X)
3.06/1.51	   activate(n__incr(X)) -> incr(X)
3.06/1.51	   activate(X) -> X
3.06/1.51	
3.06/1.51	S is empty.
3.06/1.51	Rewrite Strategy: FULL
3.06/1.51	----------------------------------------
3.06/1.51	
3.06/1.51	(3) InfiniteLowerBoundProof (FINISHED)
3.06/1.51	The following loop proves infinite runtime complexity:
3.06/1.51	
3.06/1.51	The rewrite sequence
3.06/1.51	
3.06/1.51	nats ->^+ cons(0, n__incr(nats))
3.06/1.51	
3.06/1.51	gives rise to a decreasing loop by considering the right hand sides subterm at position [1,0].
3.06/1.51	
3.06/1.51	The pumping substitution is [ ].
3.06/1.51	
3.06/1.51	The result substitution is [ ].
3.06/1.51	
3.06/1.51	
3.06/1.51	
3.06/1.51	
3.06/1.51	----------------------------------------
3.06/1.51	
3.06/1.51	(4)
3.06/1.51	BOUNDS(INF, INF)
3.06/1.54	EOF