3.20/1.60	WORST_CASE(?, O(1))
3.20/1.61	proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
3.20/1.61	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
3.20/1.61	
3.20/1.61	
3.20/1.61	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(1, 1).
3.20/1.61	
3.20/1.61	(0) CpxTRS
3.20/1.61	(1) NarrowingOnBasicTermsTerminatesProof [FINISHED, 0 ms]
3.20/1.61	(2) BOUNDS(1, 1)
3.20/1.61	
3.20/1.61	
3.20/1.61	----------------------------------------
3.20/1.61	
3.20/1.61	(0)
3.20/1.61	Obligation:
3.20/1.61	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(1, 1).
3.20/1.61	
3.20/1.61	
3.20/1.61	The TRS R consists of the following rules:
3.20/1.61	
3.20/1.61	   f(g(i(a, b, b'), c), d) -> if(e, f(.(b, c), d'), f(.(b', c), d'))
3.20/1.61	   f(g(h(a, b), c), d) -> if(e, f(.(b, g(h(a, b), c)), d), f(c, d'))
3.20/1.61	
3.20/1.61	S is empty.
3.20/1.61	Rewrite Strategy: FULL
3.20/1.61	----------------------------------------
3.20/1.61	
3.20/1.61	(1) NarrowingOnBasicTermsTerminatesProof (FINISHED)
3.20/1.61	Constant runtime complexity proven by termination of constructor-based narrowing.
3.20/1.61	
3.20/1.61	The maximal most general narrowing sequences give rise to the following rewrite sequences:
3.20/1.61	
3.20/1.61	f(g(h(a, b), c), d) ->^* if(e, f(.(b, g(h(a, b), c)), d), f(c, d'))
3.20/1.61	
3.20/1.61	f(g(i(a, b, b'), c), d) ->^* if(e, f(.(b, c), d'), f(.(b', c), d'))
3.20/1.61	
3.20/1.61	
3.20/1.61	
3.20/1.61	
3.20/1.61	----------------------------------------
3.20/1.61	
3.20/1.61	(2)
3.20/1.61	BOUNDS(1, 1)
3.32/1.65	EOF