3.20/1.55	WORST_CASE(?, O(1))
3.20/1.59	proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml
3.20/1.59	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
3.20/1.59	
3.20/1.59	
3.20/1.59	The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(1, 1).
3.20/1.59	
3.20/1.59	(0) CpxTRS
3.20/1.59	(1) NarrowingOnBasicTermsTerminatesProof [FINISHED, 0 ms]
3.20/1.59	(2) BOUNDS(1, 1)
3.20/1.59	
3.20/1.59	
3.20/1.59	----------------------------------------
3.20/1.59	
3.20/1.59	(0)
3.20/1.59	Obligation:
3.20/1.59	The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(1, 1).
3.20/1.59	
3.20/1.59	
3.20/1.59	The TRS R consists of the following rules:
3.20/1.59	
3.20/1.59	   g(X) -> u(h(X), h(X), X)
3.20/1.59	   u(d, c(Y), X) -> k(Y)
3.20/1.59	   h(d) -> c(a)
3.20/1.59	   h(d) -> c(b)
3.20/1.59	   f(k(a), k(b), X) -> f(X, X, X)
3.20/1.59	
3.20/1.59	S is empty.
3.20/1.59	Rewrite Strategy: INNERMOST
3.20/1.59	----------------------------------------
3.20/1.59	
3.20/1.59	(1) NarrowingOnBasicTermsTerminatesProof (FINISHED)
3.20/1.59	Constant runtime complexity proven by termination of constructor-based narrowing.
3.20/1.59	
3.20/1.59	The maximal most general narrowing sequences give rise to the following rewrite sequences:
3.20/1.59	
3.20/1.59	u(d, c(x0), x1) ->^* k(x0)
3.20/1.59	
3.20/1.59	g(d) ->^* u(c(b), c(b), d)
3.20/1.59	
3.20/1.59	g(d) ->^* u(c(a), c(b), d)
3.20/1.59	
3.20/1.59	g(d) ->^* u(c(b), c(a), d)
3.20/1.59	
3.20/1.59	g(d) ->^* u(c(a), c(a), d)
3.20/1.59	
3.20/1.59	g(d) ->^* u(c(b), c(b), d)
3.20/1.59	
3.20/1.59	g(d) ->^* u(c(b), c(a), d)
3.20/1.59	
3.20/1.59	g(d) ->^* u(c(a), c(b), d)
3.20/1.59	
3.20/1.59	g(d) ->^* u(c(a), c(a), d)
3.20/1.59	
3.20/1.59	h(d) ->^* c(b)
3.20/1.59	
3.20/1.59	h(d) ->^* c(a)
3.20/1.59	
3.20/1.59	f(k(a), k(b), x0) ->^* f(x0, x0, x0)
3.20/1.59	
3.20/1.59	
3.20/1.59	
3.20/1.59	
3.20/1.59	----------------------------------------
3.20/1.59	
3.20/1.59	(2)
3.20/1.59	BOUNDS(1, 1)
3.57/1.64	EOF