2.94/1.53	WORST_CASE(?, O(1))
2.94/1.53	proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml
2.94/1.53	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
2.94/1.53	
2.94/1.53	
2.94/1.53	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(1, 1).
2.94/1.53	
2.94/1.53	(0) CpxTRS
2.94/1.53	(1) NarrowingOnBasicTermsTerminatesProof [FINISHED, 0 ms]
2.94/1.53	(2) BOUNDS(1, 1)
2.94/1.53	
2.94/1.53	
2.94/1.53	----------------------------------------
2.94/1.53	
2.94/1.53	(0)
2.94/1.53	Obligation:
2.94/1.53	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(1, 1).
2.94/1.53	
2.94/1.53	
2.94/1.53	The TRS R consists of the following rules:
2.94/1.53	
2.94/1.53	   g(X) -> u(h(X), h(X), X)
2.94/1.53	   u(d, c(Y), X) -> k(Y)
2.94/1.53	   h(d) -> c(a)
2.94/1.53	   h(d) -> c(b)
2.94/1.53	   f(k(a), k(b), X) -> f(X, X, X)
2.94/1.53	
2.94/1.53	S is empty.
2.94/1.53	Rewrite Strategy: FULL
2.94/1.53	----------------------------------------
2.94/1.53	
2.94/1.53	(1) NarrowingOnBasicTermsTerminatesProof (FINISHED)
2.94/1.53	Constant runtime complexity proven by termination of constructor-based narrowing.
2.94/1.53	
2.94/1.53	The maximal most general narrowing sequences give rise to the following rewrite sequences:
2.94/1.53	
2.94/1.53	u(d, c(x0), x1) ->^* k(x0)
2.94/1.53	
2.94/1.53	g(d) ->^* u(c(b), c(b), d)
2.94/1.53	
2.94/1.53	g(d) ->^* u(c(a), c(b), d)
2.94/1.53	
2.94/1.53	g(d) ->^* u(c(b), c(a), d)
2.94/1.53	
2.94/1.53	g(d) ->^* u(c(a), c(a), d)
2.94/1.53	
2.94/1.53	h(d) ->^* c(b)
2.94/1.53	
2.94/1.53	h(d) ->^* c(a)
2.94/1.53	
2.94/1.53	f(k(a), k(b), x0) ->^* f(x0, x0, x0)
2.94/1.53	
2.94/1.53	
2.94/1.53	
2.94/1.53	
2.94/1.53	----------------------------------------
2.94/1.53	
2.94/1.53	(2)
2.94/1.53	BOUNDS(1, 1)
3.01/1.56	EOF