3.23/1.55	WORST_CASE(?, O(1))
3.23/1.56	proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml
3.23/1.56	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
3.23/1.56	
3.23/1.56	
3.23/1.56	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(1, 1).
3.23/1.56	
3.23/1.56	(0) CpxTRS
3.23/1.56	(1) NarrowingOnBasicTermsTerminatesProof [FINISHED, 0 ms]
3.23/1.56	(2) BOUNDS(1, 1)
3.23/1.56	
3.23/1.56	
3.23/1.56	----------------------------------------
3.23/1.56	
3.23/1.56	(0)
3.23/1.56	Obligation:
3.23/1.56	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(1, 1).
3.23/1.56	
3.23/1.56	
3.23/1.56	The TRS R consists of the following rules:
3.23/1.56	
3.23/1.56	   c(c(b(c(x)))) -> b(a(0, c(x)))
3.23/1.56	   c(c(x)) -> b(c(b(c(x))))
3.23/1.56	   a(0, x) -> c(c(x))
3.23/1.56	
3.23/1.56	S is empty.
3.23/1.56	Rewrite Strategy: FULL
3.23/1.56	----------------------------------------
3.23/1.56	
3.23/1.56	(1) NarrowingOnBasicTermsTerminatesProof (FINISHED)
3.23/1.56	Constant runtime complexity proven by termination of constructor-based narrowing.
3.23/1.56	
3.23/1.56	The maximal most general narrowing sequences give rise to the following rewrite sequences:
3.23/1.56	
3.23/1.56	c(x0) ->^* c(x0)
3.23/1.56	
3.23/1.56	a(0, x0) ->^* b(c(b(c(x0))))
3.23/1.56	
3.23/1.56	
3.23/1.56	
3.23/1.56	
3.23/1.56	----------------------------------------
3.23/1.56	
3.23/1.56	(2)
3.23/1.56	BOUNDS(1, 1)
3.23/1.59	EOF