3.14/1.54	WORST_CASE(?, O(1))
3.14/1.56	proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml
3.14/1.56	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
3.14/1.56	
3.14/1.56	
3.14/1.56	The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(1, 1).
3.14/1.56	
3.14/1.56	(0) CpxTRS
3.14/1.56	(1) NarrowingOnBasicTermsTerminatesProof [FINISHED, 0 ms]
3.14/1.56	(2) BOUNDS(1, 1)
3.14/1.56	
3.14/1.56	
3.14/1.56	----------------------------------------
3.14/1.56	
3.14/1.56	(0)
3.14/1.56	Obligation:
3.14/1.56	The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(1, 1).
3.14/1.56	
3.14/1.56	
3.14/1.56	The TRS R consists of the following rules:
3.14/1.56	
3.14/1.56	   fst(0, Z) -> nil
3.14/1.56	   fst(s, cons(Y)) -> cons(Y)
3.14/1.56	   from(X) -> cons(X)
3.14/1.56	   add(0, X) -> X
3.14/1.56	   add(s, Y) -> s
3.14/1.56	   len(nil) -> 0
3.14/1.56	   len(cons(X)) -> s
3.14/1.56	
3.14/1.56	S is empty.
3.14/1.56	Rewrite Strategy: INNERMOST
3.14/1.56	----------------------------------------
3.14/1.56	
3.14/1.56	(1) NarrowingOnBasicTermsTerminatesProof (FINISHED)
3.14/1.56	Constant runtime complexity proven by termination of constructor-based narrowing.
3.14/1.56	
3.14/1.56	The maximal most general narrowing sequences give rise to the following rewrite sequences:
3.14/1.56	
3.14/1.56	len(cons(x0)) ->^* s
3.14/1.56	
3.14/1.56	len(nil) ->^* 0
3.14/1.56	
3.14/1.56	from(x0) ->^* cons(x0)
3.14/1.56	
3.14/1.56	add(s, x0) ->^* s
3.14/1.56	
3.14/1.56	fst(s, cons(x0)) ->^* cons(x0)
3.14/1.56	
3.14/1.56	fst(0, x0) ->^* nil
3.14/1.56	
3.14/1.56	
3.14/1.56	
3.14/1.56	
3.14/1.56	----------------------------------------
3.14/1.56	
3.14/1.56	(2)
3.14/1.56	BOUNDS(1, 1)
3.29/1.60	EOF