1089.43/291.53	WORST_CASE(Omega(n^1), ?)
1089.43/291.55	proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml
1089.43/291.55	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
1089.43/291.55	
1089.43/291.55	
1089.43/291.55	The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, INF).
1089.43/291.55	
1089.43/291.55	(0) CpxTRS
1089.43/291.55	(1) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms]
1089.43/291.55	(2) TRS for Loop Detection
1089.43/291.55	(3) DecreasingLoopProof [LOWER BOUND(ID), 0 ms]
1089.43/291.55	(4) BEST
1089.43/291.55	    (5) proven lower bound
1089.43/291.55	        (6) LowerBoundPropagationProof [FINISHED, 0 ms]
1089.43/291.55	        (7) BOUNDS(n^1, INF)
1089.43/291.55	    (8) TRS for Loop Detection
1089.43/291.55	
1089.43/291.55	
1089.43/291.55	----------------------------------------
1089.43/291.55	
1089.43/291.55	(0)
1089.43/291.55	Obligation:
1089.43/291.55	The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, INF).
1089.43/291.55	
1089.43/291.55	
1089.43/291.55	The TRS R consists of the following rules:
1089.43/291.55	
1089.43/291.55	   f(node(s(n), xs)) -> f(addchild(select(xs), node(n, xs)))
1089.43/291.55	   select(cons(ap, xs)) -> ap
1089.43/291.55	   select(cons(ap, xs)) -> select(xs)
1089.43/291.55	   addchild(node(y, ys), node(n, xs)) -> node(y, cons(node(n, xs), ys))
1089.43/291.55	
1089.43/291.55	S is empty.
1089.43/291.55	Rewrite Strategy: INNERMOST
1089.43/291.55	----------------------------------------
1089.43/291.55	
1089.43/291.55	(1) RelTrsToDecreasingLoopProblemProof (LOWER BOUND(ID))
1089.43/291.55	Transformed a relative TRS into a decreasing-loop problem.
1089.43/291.55	----------------------------------------
1089.43/291.55	
1089.43/291.55	(2)
1089.43/291.55	Obligation:
1089.43/291.55	Analyzing the following TRS for decreasing loops:
1089.43/291.55	
1089.43/291.55	The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, INF).
1089.43/291.55	
1089.43/291.55	
1089.43/291.55	The TRS R consists of the following rules:
1089.43/291.55	
1089.43/291.55	   f(node(s(n), xs)) -> f(addchild(select(xs), node(n, xs)))
1089.43/291.55	   select(cons(ap, xs)) -> ap
1089.43/291.55	   select(cons(ap, xs)) -> select(xs)
1089.43/291.55	   addchild(node(y, ys), node(n, xs)) -> node(y, cons(node(n, xs), ys))
1089.43/291.55	
1089.43/291.55	S is empty.
1089.43/291.55	Rewrite Strategy: INNERMOST
1089.43/291.55	----------------------------------------
1089.43/291.55	
1089.43/291.55	(3) DecreasingLoopProof (LOWER BOUND(ID))
1089.43/291.55	The following loop(s) give(s) rise to the lower bound Omega(n^1):
1089.43/291.55	
1089.43/291.55	The rewrite sequence
1089.43/291.55	
1089.43/291.55	select(cons(ap, xs)) ->^+ select(xs)
1089.43/291.55	
1089.43/291.55	gives rise to a decreasing loop by considering the right hand sides subterm at position [].
1089.43/291.55	
1089.43/291.55	The pumping substitution is [xs / cons(ap, xs)].
1089.43/291.55	
1089.43/291.55	The result substitution is [ ].
1089.43/291.55	
1089.43/291.55	
1089.43/291.55	
1089.43/291.55	
1089.43/291.55	----------------------------------------
1089.43/291.55	
1089.43/291.55	(4)
1089.43/291.55	Complex Obligation (BEST)
1089.43/291.55	
1089.43/291.55	----------------------------------------
1089.43/291.55	
1089.43/291.55	(5)
1089.43/291.55	Obligation:
1089.43/291.55	Proved the lower bound n^1 for the following obligation:
1089.43/291.55	
1089.43/291.55	The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, INF).
1089.43/291.55	
1089.43/291.55	
1089.43/291.55	The TRS R consists of the following rules:
1089.43/291.55	
1089.43/291.55	   f(node(s(n), xs)) -> f(addchild(select(xs), node(n, xs)))
1089.43/291.55	   select(cons(ap, xs)) -> ap
1089.43/291.55	   select(cons(ap, xs)) -> select(xs)
1089.43/291.55	   addchild(node(y, ys), node(n, xs)) -> node(y, cons(node(n, xs), ys))
1089.43/291.55	
1089.43/291.55	S is empty.
1089.43/291.55	Rewrite Strategy: INNERMOST
1089.43/291.55	----------------------------------------
1089.43/291.55	
1089.43/291.55	(6) LowerBoundPropagationProof (FINISHED)
1089.43/291.55	Propagated lower bound.
1089.43/291.55	----------------------------------------
1089.43/291.55	
1089.43/291.55	(7)
1089.43/291.55	BOUNDS(n^1, INF)
1089.43/291.55	
1089.43/291.55	----------------------------------------
1089.43/291.55	
1089.43/291.55	(8)
1089.43/291.55	Obligation:
1089.43/291.55	Analyzing the following TRS for decreasing loops:
1089.43/291.55	
1089.43/291.55	The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, INF).
1089.43/291.55	
1089.43/291.55	
1089.43/291.55	The TRS R consists of the following rules:
1089.43/291.55	
1089.43/291.55	   f(node(s(n), xs)) -> f(addchild(select(xs), node(n, xs)))
1089.43/291.55	   select(cons(ap, xs)) -> ap
1089.43/291.55	   select(cons(ap, xs)) -> select(xs)
1089.43/291.55	   addchild(node(y, ys), node(n, xs)) -> node(y, cons(node(n, xs), ys))
1089.43/291.55	
1089.43/291.55	S is empty.
1089.43/291.55	Rewrite Strategy: INNERMOST
1089.66/291.61	EOF