3.27/1.55	WORST_CASE(?, O(1))
3.27/1.56	proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
3.27/1.56	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
3.27/1.56	
3.27/1.56	
3.27/1.56	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(1, 1).
3.27/1.56	
3.27/1.56	(0) CpxTRS
3.27/1.56	(1) DependencyGraphProof [UPPER BOUND(ID), 0 ms]
3.27/1.56	(2) CpxTRS
3.27/1.56	(3) NarrowingOnBasicTermsTerminatesProof [FINISHED, 0 ms]
3.27/1.56	(4) BOUNDS(1, 1)
3.27/1.56	
3.27/1.56	
3.27/1.56	----------------------------------------
3.27/1.56	
3.27/1.56	(0)
3.27/1.56	Obligation:
3.27/1.56	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(1, 1).
3.27/1.56	
3.27/1.56	
3.27/1.56	The TRS R consists of the following rules:
3.27/1.56	
3.27/1.56	   2nd(cons(X, n__cons(Y, Z))) -> activate(Y)
3.27/1.56	   from(X) -> cons(X, n__from(s(X)))
3.27/1.56	   cons(X1, X2) -> n__cons(X1, X2)
3.27/1.56	   from(X) -> n__from(X)
3.27/1.56	   activate(n__cons(X1, X2)) -> cons(X1, X2)
3.27/1.56	   activate(n__from(X)) -> from(X)
3.27/1.56	   activate(X) -> X
3.27/1.56	
3.27/1.56	S is empty.
3.27/1.56	Rewrite Strategy: FULL
3.27/1.56	----------------------------------------
3.27/1.56	
3.27/1.56	(1) DependencyGraphProof (UPPER BOUND(ID))
3.27/1.56	The following rules are not reachable from basic terms in the dependency graph and can be removed:
3.27/1.56	
3.27/1.56	2nd(cons(X, n__cons(Y, Z))) -> activate(Y)
3.27/1.56	
3.27/1.56	----------------------------------------
3.27/1.56	
3.27/1.56	(2)
3.27/1.56	Obligation:
3.27/1.56	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(1, 1).
3.27/1.56	
3.27/1.56	
3.27/1.56	The TRS R consists of the following rules:
3.27/1.56	
3.27/1.56	   from(X) -> cons(X, n__from(s(X)))
3.27/1.56	   cons(X1, X2) -> n__cons(X1, X2)
3.27/1.56	   from(X) -> n__from(X)
3.27/1.56	   activate(n__cons(X1, X2)) -> cons(X1, X2)
3.27/1.56	   activate(n__from(X)) -> from(X)
3.27/1.56	   activate(X) -> X
3.27/1.56	
3.27/1.56	S is empty.
3.27/1.56	Rewrite Strategy: FULL
3.27/1.56	----------------------------------------
3.27/1.56	
3.27/1.56	(3) NarrowingOnBasicTermsTerminatesProof (FINISHED)
3.27/1.56	Constant runtime complexity proven by termination of constructor-based narrowing.
3.27/1.56	
3.27/1.56	The maximal most general narrowing sequences give rise to the following rewrite sequences:
3.27/1.56	
3.27/1.56	activate(n__from(x0)) ->^* n__from(x0)
3.27/1.56	
3.27/1.56	activate(n__from(x0)) ->^* n__cons(x0, n__from(s(x0)))
3.27/1.56	
3.27/1.56	activate(n__cons(x0, x1)) ->^* n__cons(x0, x1)
3.27/1.56	
3.27/1.56	from(x0) ->^* n__from(x0)
3.27/1.56	
3.27/1.56	from(x0) ->^* n__cons(x0, n__from(s(x0)))
3.27/1.56	
3.27/1.56	cons(x0, x1) ->^* n__cons(x0, x1)
3.27/1.56	
3.27/1.56	
3.27/1.56	
3.27/1.56	
3.27/1.56	----------------------------------------
3.27/1.56	
3.27/1.56	(4)
3.27/1.56	BOUNDS(1, 1)
3.35/1.59	EOF