3.11/1.56	WORST_CASE(?, O(1))
3.11/1.59	proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
3.11/1.59	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
3.11/1.59	
3.11/1.59	
3.11/1.59	The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(1, 1).
3.11/1.59	
3.11/1.59	(0) CpxTRS
3.11/1.59	(1) NarrowingOnBasicTermsTerminatesProof [FINISHED, 0 ms]
3.11/1.59	(2) BOUNDS(1, 1)
3.11/1.59	
3.11/1.59	
3.11/1.59	----------------------------------------
3.11/1.59	
3.11/1.59	(0)
3.11/1.59	Obligation:
3.11/1.59	The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(1, 1).
3.11/1.59	
3.11/1.59	
3.11/1.59	The TRS R consists of the following rules:
3.11/1.59	
3.11/1.59	   f(g(i(a, b, b'), c), d) -> if(e, f(.(b, c), d'), f(.(b', c), d'))
3.11/1.59	   f(g(h(a, b), c), d) -> if(e, f(.(b, g(h(a, b), c)), d), f(c, d'))
3.11/1.59	
3.11/1.59	S is empty.
3.11/1.59	Rewrite Strategy: INNERMOST
3.11/1.59	----------------------------------------
3.11/1.59	
3.11/1.59	(1) NarrowingOnBasicTermsTerminatesProof (FINISHED)
3.11/1.59	Constant runtime complexity proven by termination of constructor-based narrowing.
3.11/1.59	
3.11/1.59	The maximal most general narrowing sequences give rise to the following rewrite sequences:
3.11/1.59	
3.11/1.59	f(g(h(a, b), c), d) ->^* if(e, f(.(b, g(h(a, b), c)), d), f(c, d'))
3.11/1.59	
3.11/1.59	f(g(i(a, b, b'), c), d) ->^* if(e, f(.(b, c), d'), f(.(b', c), d'))
3.11/1.59	
3.11/1.59	
3.11/1.59	
3.11/1.59	
3.11/1.59	----------------------------------------
3.11/1.59	
3.11/1.59	(2)
3.11/1.59	BOUNDS(1, 1)
3.43/1.69	EOF