3.08/1.52	WORST_CASE(?, O(1))
3.08/1.53	proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml
3.08/1.53	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
3.08/1.53	
3.08/1.53	
3.08/1.53	The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(1, 1).
3.08/1.53	
3.08/1.53	(0) CpxTRS
3.08/1.53	(1) NarrowingOnBasicTermsTerminatesProof [FINISHED, 0 ms]
3.08/1.53	(2) BOUNDS(1, 1)
3.08/1.53	
3.08/1.53	
3.08/1.53	----------------------------------------
3.08/1.53	
3.08/1.53	(0)
3.08/1.53	Obligation:
3.08/1.53	The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(1, 1).
3.08/1.53	
3.08/1.53	
3.08/1.53	The TRS R consists of the following rules:
3.08/1.53	
3.08/1.53	   not(x) -> xor(x, true)
3.08/1.53	   implies(x, y) -> xor(and(x, y), xor(x, true))
3.08/1.53	   or(x, y) -> xor(and(x, y), xor(x, y))
3.08/1.53	   =(x, y) -> xor(x, xor(y, true))
3.08/1.53	
3.08/1.53	S is empty.
3.08/1.53	Rewrite Strategy: INNERMOST
3.08/1.53	----------------------------------------
3.08/1.53	
3.08/1.53	(1) NarrowingOnBasicTermsTerminatesProof (FINISHED)
3.08/1.53	Constant runtime complexity proven by termination of constructor-based narrowing.
3.08/1.53	
3.08/1.53	The maximal most general narrowing sequences give rise to the following rewrite sequences:
3.08/1.53	
3.08/1.53	=(x0, x1) ->^* xor(x0, xor(x1, true))
3.08/1.53	
3.08/1.53	not(x0) ->^* xor(x0, true)
3.08/1.53	
3.08/1.53	implies(x0, x1) ->^* xor(and(x0, x1), xor(x0, true))
3.08/1.53	
3.08/1.53	or(x0, x1) ->^* xor(and(x0, x1), xor(x0, x1))
3.08/1.53	
3.08/1.53	
3.08/1.53	
3.08/1.53	
3.08/1.53	----------------------------------------
3.08/1.53	
3.08/1.53	(2)
3.08/1.53	BOUNDS(1, 1)
3.15/1.57	EOF