3.31/1.53	WORST_CASE(?, O(1))
3.31/1.54	proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml
3.31/1.54	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
3.31/1.54	
3.31/1.54	
3.31/1.54	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(1, 1).
3.31/1.54	
3.31/1.54	(0) CpxTRS
3.31/1.54	(1) NarrowingOnBasicTermsTerminatesProof [FINISHED, 0 ms]
3.31/1.54	(2) BOUNDS(1, 1)
3.31/1.54	
3.31/1.54	
3.31/1.54	----------------------------------------
3.31/1.54	
3.31/1.54	(0)
3.31/1.54	Obligation:
3.31/1.54	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(1, 1).
3.31/1.54	
3.31/1.54	
3.31/1.54	The TRS R consists of the following rules:
3.31/1.54	
3.31/1.54	   2nd(cons1(X, cons(Y, Z))) -> Y
3.31/1.54	   2nd(cons(X, X1)) -> 2nd(cons1(X, activate(X1)))
3.31/1.54	   from(X) -> cons(X, n__from(s(X)))
3.31/1.54	   from(X) -> n__from(X)
3.31/1.54	   activate(n__from(X)) -> from(X)
3.31/1.54	   activate(X) -> X
3.31/1.54	
3.31/1.54	S is empty.
3.31/1.54	Rewrite Strategy: FULL
3.31/1.54	----------------------------------------
3.31/1.54	
3.31/1.54	(1) NarrowingOnBasicTermsTerminatesProof (FINISHED)
3.31/1.54	Constant runtime complexity proven by termination of constructor-based narrowing.
3.31/1.54	
3.31/1.54	The maximal most general narrowing sequences give rise to the following rewrite sequences:
3.31/1.54	
3.31/1.54	activate(n__from(x0)) ->^* n__from(x0)
3.31/1.54	
3.31/1.54	activate(n__from(x0)) ->^* cons(x0, n__from(s(x0)))
3.31/1.54	
3.31/1.54	from(x0) ->^* n__from(x0)
3.31/1.54	
3.31/1.54	from(x0) ->^* cons(x0, n__from(s(x0)))
3.31/1.54	
3.31/1.54	2nd(cons(x0, x1)) ->^* 2nd(cons1(x0, x1))
3.31/1.54	
3.31/1.54	2nd(cons(x0, n__from(x1))) ->^* 2nd(cons1(x0, n__from(x1)))
3.31/1.54	
3.31/1.54	2nd(cons(x0, n__from(x1))) ->^* 2nd(cons1(x0, cons(x1, n__from(s(x1)))))
3.31/1.54	
3.31/1.54	
3.31/1.54	
3.31/1.54	
3.31/1.54	----------------------------------------
3.31/1.54	
3.31/1.54	(2)
3.31/1.54	BOUNDS(1, 1)
3.40/1.57	EOF