3.34/1.62	WORST_CASE(?, O(1))
3.34/1.63	proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
3.34/1.63	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
3.34/1.63	
3.34/1.63	
3.34/1.63	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(1, 1).
3.34/1.63	
3.34/1.63	(0) CpxTRS
3.34/1.63	(1) NarrowingOnBasicTermsTerminatesProof [FINISHED, 16 ms]
3.34/1.63	(2) BOUNDS(1, 1)
3.34/1.63	
3.34/1.63	
3.34/1.63	----------------------------------------
3.34/1.63	
3.34/1.63	(0)
3.34/1.63	Obligation:
3.34/1.63	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(1, 1).
3.34/1.63	
3.34/1.63	
3.34/1.63	The TRS R consists of the following rules:
3.34/1.63	
3.34/1.63	   c(c(c(y))) -> c(c(a(y, 0)))
3.34/1.63	   c(a(a(0, x), y)) -> a(c(c(c(0))), y)
3.34/1.63	   c(y) -> y
3.34/1.63	
3.34/1.63	S is empty.
3.34/1.63	Rewrite Strategy: FULL
3.34/1.63	----------------------------------------
3.34/1.63	
3.34/1.63	(1) NarrowingOnBasicTermsTerminatesProof (FINISHED)
3.34/1.63	Constant runtime complexity proven by termination of constructor-based narrowing.
3.34/1.63	
3.34/1.63	The maximal most general narrowing sequences give rise to the following rewrite sequences:
3.34/1.63	
3.34/1.63	c(a(a(0, x0), x1)) ->^* a(0, x1)
3.34/1.63	
3.34/1.63	c(a(a(0, x0), x1)) ->^* a(a(0, 0), x1)
3.34/1.63	
3.34/1.63	
3.34/1.63	
3.34/1.63	
3.34/1.63	----------------------------------------
3.34/1.63	
3.34/1.63	(2)
3.34/1.63	BOUNDS(1, 1)
3.66/1.68	EOF