3.29/1.72	WORST_CASE(NON_POLY, ?)
3.29/1.72	proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
3.29/1.72	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
3.29/1.72	
3.29/1.72	
3.29/1.72	The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(INF, INF).
3.29/1.72	
3.29/1.72	(0) CpxTRS
3.29/1.72	(1) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms]
3.29/1.72	(2) TRS for Loop Detection
3.29/1.72	(3) InfiniteLowerBoundProof [FINISHED, 0 ms]
3.29/1.72	(4) BOUNDS(INF, INF)
3.29/1.72	
3.29/1.72	
3.29/1.72	----------------------------------------
3.29/1.72	
3.29/1.72	(0)
3.29/1.72	Obligation:
3.29/1.72	The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(INF, INF).
3.29/1.72	
3.29/1.72	
3.29/1.72	The TRS R consists of the following rules:
3.29/1.72	
3.29/1.72	   is_empty(nil) -> true
3.29/1.72	   is_empty(cons(x, l)) -> false
3.29/1.72	   hd(cons(x, l)) -> x
3.29/1.72	   tl(cons(x, l)) -> cons(x, l)
3.29/1.72	   append(l1, l2) -> ifappend(l1, l2, is_empty(l1))
3.29/1.72	   ifappend(l1, l2, true) -> l2
3.29/1.72	   ifappend(l1, l2, false) -> cons(hd(l1), append(tl(l1), l2))
3.29/1.72	
3.29/1.72	S is empty.
3.29/1.72	Rewrite Strategy: INNERMOST
3.29/1.72	----------------------------------------
3.29/1.72	
3.29/1.72	(1) RelTrsToDecreasingLoopProblemProof (LOWER BOUND(ID))
3.29/1.72	Transformed a relative TRS into a decreasing-loop problem.
3.29/1.72	----------------------------------------
3.29/1.72	
3.29/1.72	(2)
3.29/1.72	Obligation:
3.29/1.72	Analyzing the following TRS for decreasing loops:
3.29/1.72	
3.29/1.72	The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(INF, INF).
3.29/1.72	
3.29/1.72	
3.29/1.72	The TRS R consists of the following rules:
3.29/1.72	
3.29/1.72	   is_empty(nil) -> true
3.29/1.72	   is_empty(cons(x, l)) -> false
3.29/1.72	   hd(cons(x, l)) -> x
3.29/1.72	   tl(cons(x, l)) -> cons(x, l)
3.29/1.72	   append(l1, l2) -> ifappend(l1, l2, is_empty(l1))
3.29/1.72	   ifappend(l1, l2, true) -> l2
3.29/1.72	   ifappend(l1, l2, false) -> cons(hd(l1), append(tl(l1), l2))
3.29/1.72	
3.29/1.72	S is empty.
3.29/1.72	Rewrite Strategy: INNERMOST
3.29/1.72	----------------------------------------
3.29/1.72	
3.29/1.72	(3) InfiniteLowerBoundProof (FINISHED)
3.29/1.72	The following loop proves infinite runtime complexity:
3.29/1.72	
3.29/1.72	The rewrite sequence
3.29/1.72	
3.29/1.72	ifappend(cons(x1_0, l2_0), l2, false) ->^+ cons(hd(cons(x1_0, l2_0)), ifappend(cons(x1_0, l2_0), l2, false))
3.29/1.72	
3.29/1.72	gives rise to a decreasing loop by considering the right hand sides subterm at position [1].
3.29/1.72	
3.29/1.72	The pumping substitution is [ ].
3.29/1.72	
3.29/1.72	The result substitution is [ ].
3.29/1.72	
3.29/1.72	
3.29/1.72	
3.29/1.72	
3.29/1.72	----------------------------------------
3.29/1.72	
3.29/1.72	(4)
3.29/1.72	BOUNDS(INF, INF)
3.29/1.76	EOF