2.92/1.63	WORST_CASE(NON_POLY, ?)
2.92/1.64	proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
2.92/1.64	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
2.92/1.64	
2.92/1.64	
2.92/1.64	The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(INF, INF).
2.92/1.64	
2.92/1.64	(0) CpxTRS
2.92/1.64	(1) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms]
2.92/1.64	(2) TRS for Loop Detection
2.92/1.64	(3) InfiniteLowerBoundProof [FINISHED, 0 ms]
2.92/1.64	(4) BOUNDS(INF, INF)
2.92/1.64	
2.92/1.64	
2.92/1.64	----------------------------------------
2.92/1.64	
2.92/1.64	(0)
2.92/1.64	Obligation:
2.92/1.64	The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(INF, INF).
2.92/1.64	
2.92/1.64	
2.92/1.64	The TRS R consists of the following rules:
2.92/1.64	
2.92/1.64	   from(X) -> cons(X, from(s(X)))
2.92/1.64	   2ndspos(0, Z) -> rnil
2.92/1.64	   2ndspos(s(N), cons(X, cons(Y, Z))) -> rcons(posrecip(Y), 2ndsneg(N, Z))
2.92/1.64	   2ndsneg(0, Z) -> rnil
2.92/1.64	   2ndsneg(s(N), cons(X, cons(Y, Z))) -> rcons(negrecip(Y), 2ndspos(N, Z))
2.92/1.64	   pi(X) -> 2ndspos(X, from(0))
2.92/1.64	   plus(0, Y) -> Y
2.92/1.64	   plus(s(X), Y) -> s(plus(X, Y))
2.92/1.64	   times(0, Y) -> 0
2.92/1.64	   times(s(X), Y) -> plus(Y, times(X, Y))
2.92/1.64	   square(X) -> times(X, X)
2.92/1.64	
2.92/1.64	S is empty.
2.92/1.64	Rewrite Strategy: INNERMOST
2.92/1.64	----------------------------------------
2.92/1.64	
2.92/1.64	(1) RelTrsToDecreasingLoopProblemProof (LOWER BOUND(ID))
2.92/1.64	Transformed a relative TRS into a decreasing-loop problem.
2.92/1.64	----------------------------------------
2.92/1.64	
2.92/1.64	(2)
2.92/1.64	Obligation:
2.92/1.64	Analyzing the following TRS for decreasing loops:
2.92/1.64	
2.92/1.64	The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(INF, INF).
2.92/1.64	
2.92/1.64	
2.92/1.64	The TRS R consists of the following rules:
2.92/1.64	
2.92/1.64	   from(X) -> cons(X, from(s(X)))
2.92/1.64	   2ndspos(0, Z) -> rnil
2.92/1.64	   2ndspos(s(N), cons(X, cons(Y, Z))) -> rcons(posrecip(Y), 2ndsneg(N, Z))
2.92/1.64	   2ndsneg(0, Z) -> rnil
2.92/1.64	   2ndsneg(s(N), cons(X, cons(Y, Z))) -> rcons(negrecip(Y), 2ndspos(N, Z))
2.92/1.64	   pi(X) -> 2ndspos(X, from(0))
2.92/1.64	   plus(0, Y) -> Y
2.92/1.64	   plus(s(X), Y) -> s(plus(X, Y))
2.92/1.64	   times(0, Y) -> 0
2.92/1.64	   times(s(X), Y) -> plus(Y, times(X, Y))
2.92/1.64	   square(X) -> times(X, X)
2.92/1.64	
2.92/1.64	S is empty.
2.92/1.64	Rewrite Strategy: INNERMOST
2.92/1.64	----------------------------------------
2.92/1.64	
2.92/1.64	(3) InfiniteLowerBoundProof (FINISHED)
2.92/1.64	The following loop proves infinite runtime complexity:
2.92/1.64	
2.92/1.64	The rewrite sequence
2.92/1.64	
2.92/1.64	from(X) ->^+ cons(X, from(s(X)))
2.92/1.64	
2.92/1.64	gives rise to a decreasing loop by considering the right hand sides subterm at position [1].
2.92/1.64	
2.92/1.64	The pumping substitution is [ ].
2.92/1.64	
2.92/1.64	The result substitution is [X / s(X)].
2.92/1.64	
2.92/1.64	
2.92/1.64	
2.92/1.64	
2.92/1.64	----------------------------------------
2.92/1.64	
2.92/1.64	(4)
2.92/1.64	BOUNDS(INF, INF)
3.24/1.66	EOF