3.10/1.57	WORST_CASE(?, O(1))
3.10/1.59	proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
3.10/1.59	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
3.10/1.59	
3.10/1.59	
3.10/1.59	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(1, 1).
3.10/1.59	
3.10/1.59	(0) CpxTRS
3.10/1.59	(1) NarrowingOnBasicTermsTerminatesProof [FINISHED, 0 ms]
3.10/1.59	(2) BOUNDS(1, 1)
3.10/1.59	
3.10/1.59	
3.10/1.59	----------------------------------------
3.10/1.59	
3.10/1.59	(0)
3.10/1.59	Obligation:
3.10/1.59	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(1, 1).
3.10/1.59	
3.10/1.59	
3.10/1.59	The TRS R consists of the following rules:
3.10/1.59	
3.10/1.59	   f(0) -> cons(0)
3.10/1.59	   f(s(0)) -> f(p(s(0)))
3.10/1.59	   p(s(X)) -> X
3.10/1.59	
3.10/1.59	S is empty.
3.10/1.59	Rewrite Strategy: FULL
3.10/1.59	----------------------------------------
3.10/1.59	
3.10/1.59	(1) NarrowingOnBasicTermsTerminatesProof (FINISHED)
3.10/1.59	Constant runtime complexity proven by termination of constructor-based narrowing.
3.10/1.59	
3.10/1.59	The maximal most general narrowing sequences give rise to the following rewrite sequences:
3.10/1.59	
3.10/1.59	f(s(0)) ->^* cons(0)
3.10/1.59	
3.10/1.59	f(0) ->^* cons(0)
3.10/1.59	
3.10/1.59	p(x0) ->^* p(x0)
3.10/1.59	
3.10/1.59	
3.10/1.59	
3.10/1.59	
3.10/1.59	----------------------------------------
3.10/1.59	
3.10/1.59	(2)
3.10/1.59	BOUNDS(1, 1)
3.39/2.17	EOF