2.96/1.49	WORST_CASE(?, O(1))
3.08/1.52	proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
3.08/1.52	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
3.08/1.52	
3.08/1.52	
3.08/1.52	The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(1, 1).
3.08/1.52	
3.08/1.52	(0) CpxTRS
3.08/1.52	(1) NarrowingOnBasicTermsTerminatesProof [FINISHED, 0 ms]
3.08/1.52	(2) BOUNDS(1, 1)
3.08/1.52	
3.08/1.52	
3.08/1.52	----------------------------------------
3.08/1.52	
3.08/1.52	(0)
3.08/1.52	Obligation:
3.08/1.52	The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(1, 1).
3.08/1.52	
3.08/1.52	
3.08/1.52	The TRS R consists of the following rules:
3.08/1.52	
3.08/1.52	   2nd(cons1(X, cons(Y, Z))) -> Y
3.08/1.52	   2nd(cons(X, X1)) -> 2nd(cons1(X, activate(X1)))
3.08/1.52	   from(X) -> cons(X, n__from(s(X)))
3.08/1.52	   from(X) -> n__from(X)
3.08/1.52	   activate(n__from(X)) -> from(X)
3.08/1.52	   activate(X) -> X
3.08/1.52	
3.08/1.52	S is empty.
3.08/1.52	Rewrite Strategy: INNERMOST
3.08/1.52	----------------------------------------
3.08/1.52	
3.08/1.52	(1) NarrowingOnBasicTermsTerminatesProof (FINISHED)
3.08/1.52	Constant runtime complexity proven by termination of constructor-based narrowing.
3.08/1.52	
3.08/1.52	The maximal most general narrowing sequences give rise to the following rewrite sequences:
3.08/1.52	
3.08/1.52	activate(n__from(x0)) ->^* n__from(x0)
3.08/1.52	
3.08/1.52	activate(n__from(x0)) ->^* cons(x0, n__from(s(x0)))
3.08/1.52	
3.08/1.52	from(x0) ->^* n__from(x0)
3.08/1.52	
3.08/1.52	from(x0) ->^* cons(x0, n__from(s(x0)))
3.08/1.52	
3.08/1.52	2nd(cons(x0, x1)) ->^* 2nd(cons1(x0, x1))
3.08/1.52	
3.08/1.52	2nd(cons(x0, n__from(x1))) ->^* 2nd(cons1(x0, n__from(x1)))
3.08/1.52	
3.08/1.52	2nd(cons(x0, n__from(x1))) ->^* 2nd(cons1(x0, cons(x1, n__from(s(x1)))))
3.08/1.52	
3.08/1.52	
3.08/1.52	
3.08/1.52	
3.08/1.52	----------------------------------------
3.08/1.52	
3.08/1.52	(2)
3.08/1.52	BOUNDS(1, 1)
3.17/1.57	EOF