3.18/1.58	WORST_CASE(NON_POLY, ?)
3.18/1.59	proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml
3.18/1.59	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
3.18/1.59	
3.18/1.59	
3.18/1.59	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(INF, INF).
3.18/1.59	
3.18/1.59	(0) CpxTRS
3.18/1.59	(1) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms]
3.18/1.59	(2) TRS for Loop Detection
3.18/1.59	(3) InfiniteLowerBoundProof [FINISHED, 0 ms]
3.18/1.59	(4) BOUNDS(INF, INF)
3.18/1.59	
3.18/1.59	
3.18/1.59	----------------------------------------
3.18/1.59	
3.18/1.59	(0)
3.18/1.59	Obligation:
3.18/1.59	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(INF, INF).
3.18/1.59	
3.18/1.59	
3.18/1.59	The TRS R consists of the following rules:
3.18/1.59	
3.18/1.59	   p(0) -> 0
3.18/1.59	   p(s(X)) -> X
3.18/1.59	   leq(0, Y) -> true
3.18/1.59	   leq(s(X), 0) -> false
3.18/1.59	   leq(s(X), s(Y)) -> leq(X, Y)
3.18/1.59	   if(true, X, Y) -> activate(X)
3.18/1.59	   if(false, X, Y) -> activate(Y)
3.18/1.59	   diff(X, Y) -> if(leq(X, Y), n__0, n__s(diff(p(X), Y)))
3.18/1.59	   0 -> n__0
3.18/1.59	   s(X) -> n__s(X)
3.18/1.59	   activate(n__0) -> 0
3.18/1.59	   activate(n__s(X)) -> s(X)
3.18/1.59	   activate(X) -> X
3.18/1.59	
3.18/1.59	S is empty.
3.18/1.59	Rewrite Strategy: FULL
3.18/1.59	----------------------------------------
3.18/1.59	
3.18/1.59	(1) RelTrsToDecreasingLoopProblemProof (LOWER BOUND(ID))
3.18/1.59	Transformed a relative TRS into a decreasing-loop problem.
3.18/1.59	----------------------------------------
3.18/1.59	
3.18/1.59	(2)
3.18/1.59	Obligation:
3.18/1.59	Analyzing the following TRS for decreasing loops:
3.18/1.59	
3.18/1.59	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(INF, INF).
3.18/1.59	
3.18/1.59	
3.18/1.59	The TRS R consists of the following rules:
3.18/1.59	
3.18/1.59	   p(0) -> 0
3.18/1.59	   p(s(X)) -> X
3.18/1.59	   leq(0, Y) -> true
3.18/1.59	   leq(s(X), 0) -> false
3.18/1.59	   leq(s(X), s(Y)) -> leq(X, Y)
3.18/1.59	   if(true, X, Y) -> activate(X)
3.18/1.59	   if(false, X, Y) -> activate(Y)
3.18/1.59	   diff(X, Y) -> if(leq(X, Y), n__0, n__s(diff(p(X), Y)))
3.18/1.59	   0 -> n__0
3.18/1.59	   s(X) -> n__s(X)
3.18/1.59	   activate(n__0) -> 0
3.18/1.59	   activate(n__s(X)) -> s(X)
3.18/1.59	   activate(X) -> X
3.18/1.59	
3.18/1.59	S is empty.
3.18/1.59	Rewrite Strategy: FULL
3.18/1.59	----------------------------------------
3.18/1.59	
3.18/1.59	(3) InfiniteLowerBoundProof (FINISHED)
3.18/1.59	The following loop proves infinite runtime complexity:
3.18/1.59	
3.18/1.59	The rewrite sequence
3.18/1.59	
3.18/1.59	diff(X, Y) ->^+ if(leq(X, Y), n__0, n__s(diff(p(X), Y)))
3.18/1.59	
3.18/1.59	gives rise to a decreasing loop by considering the right hand sides subterm at position [2,0].
3.18/1.59	
3.18/1.59	The pumping substitution is [ ].
3.18/1.59	
3.18/1.59	The result substitution is [X / p(X)].
3.18/1.59	
3.18/1.59	
3.18/1.59	
3.18/1.59	
3.18/1.59	----------------------------------------
3.18/1.59	
3.18/1.59	(4)
3.18/1.59	BOUNDS(INF, INF)
3.18/1.62	EOF