3.08/1.51	WORST_CASE(NON_POLY, ?)
3.08/1.52	proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
3.08/1.52	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
3.08/1.52	
3.08/1.52	
3.08/1.52	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(INF, INF).
3.08/1.52	
3.08/1.52	(0) CpxTRS
3.08/1.52	(1) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms]
3.08/1.52	(2) TRS for Loop Detection
3.08/1.52	(3) InfiniteLowerBoundProof [FINISHED, 0 ms]
3.08/1.52	(4) BOUNDS(INF, INF)
3.08/1.52	
3.08/1.52	
3.08/1.52	----------------------------------------
3.08/1.52	
3.08/1.52	(0)
3.08/1.52	Obligation:
3.08/1.52	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(INF, INF).
3.08/1.52	
3.08/1.52	
3.08/1.52	The TRS R consists of the following rules:
3.08/1.52	
3.08/1.52	   from(X) -> cons(X, from(s(X)))
3.08/1.52	   2ndspos(0, Z) -> rnil
3.08/1.52	   2ndspos(s(N), cons(X, cons(Y, Z))) -> rcons(posrecip(Y), 2ndsneg(N, Z))
3.08/1.52	   2ndsneg(0, Z) -> rnil
3.08/1.52	   2ndsneg(s(N), cons(X, cons(Y, Z))) -> rcons(negrecip(Y), 2ndspos(N, Z))
3.08/1.52	   pi(X) -> 2ndspos(X, from(0))
3.08/1.52	   plus(0, Y) -> Y
3.08/1.52	   plus(s(X), Y) -> s(plus(X, Y))
3.08/1.52	   times(0, Y) -> 0
3.08/1.52	   times(s(X), Y) -> plus(Y, times(X, Y))
3.08/1.52	   square(X) -> times(X, X)
3.08/1.52	
3.08/1.52	S is empty.
3.08/1.52	Rewrite Strategy: FULL
3.08/1.52	----------------------------------------
3.08/1.52	
3.08/1.52	(1) RelTrsToDecreasingLoopProblemProof (LOWER BOUND(ID))
3.08/1.52	Transformed a relative TRS into a decreasing-loop problem.
3.08/1.52	----------------------------------------
3.08/1.52	
3.08/1.52	(2)
3.08/1.52	Obligation:
3.08/1.52	Analyzing the following TRS for decreasing loops:
3.08/1.52	
3.08/1.52	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(INF, INF).
3.08/1.52	
3.08/1.52	
3.08/1.52	The TRS R consists of the following rules:
3.08/1.52	
3.08/1.52	   from(X) -> cons(X, from(s(X)))
3.08/1.52	   2ndspos(0, Z) -> rnil
3.08/1.52	   2ndspos(s(N), cons(X, cons(Y, Z))) -> rcons(posrecip(Y), 2ndsneg(N, Z))
3.08/1.52	   2ndsneg(0, Z) -> rnil
3.08/1.52	   2ndsneg(s(N), cons(X, cons(Y, Z))) -> rcons(negrecip(Y), 2ndspos(N, Z))
3.08/1.52	   pi(X) -> 2ndspos(X, from(0))
3.08/1.52	   plus(0, Y) -> Y
3.08/1.52	   plus(s(X), Y) -> s(plus(X, Y))
3.08/1.52	   times(0, Y) -> 0
3.08/1.52	   times(s(X), Y) -> plus(Y, times(X, Y))
3.08/1.52	   square(X) -> times(X, X)
3.08/1.52	
3.08/1.52	S is empty.
3.08/1.52	Rewrite Strategy: FULL
3.08/1.52	----------------------------------------
3.08/1.52	
3.08/1.52	(3) InfiniteLowerBoundProof (FINISHED)
3.08/1.52	The following loop proves infinite runtime complexity:
3.08/1.52	
3.08/1.52	The rewrite sequence
3.08/1.52	
3.08/1.52	from(X) ->^+ cons(X, from(s(X)))
3.08/1.52	
3.08/1.52	gives rise to a decreasing loop by considering the right hand sides subterm at position [1].
3.08/1.52	
3.08/1.52	The pumping substitution is [ ].
3.08/1.52	
3.08/1.52	The result substitution is [X / s(X)].
3.08/1.52	
3.08/1.52	
3.08/1.52	
3.08/1.52	
3.08/1.52	----------------------------------------
3.08/1.52	
3.08/1.52	(4)
3.08/1.52	BOUNDS(INF, INF)
3.08/1.56	EOF