3.16/1.53	WORST_CASE(?, O(1))
3.16/1.53	proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
3.16/1.53	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
3.16/1.53	
3.16/1.53	
3.16/1.53	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(1, 1).
3.16/1.53	
3.16/1.53	(0) CpxTRS
3.16/1.53	(1) DependencyGraphProof [UPPER BOUND(ID), 0 ms]
3.16/1.53	(2) CpxTRS
3.16/1.53	(3) NarrowingOnBasicTermsTerminatesProof [FINISHED, 0 ms]
3.16/1.53	(4) BOUNDS(1, 1)
3.16/1.53	
3.16/1.53	
3.16/1.53	----------------------------------------
3.16/1.53	
3.16/1.53	(0)
3.16/1.53	Obligation:
3.16/1.53	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(1, 1).
3.16/1.53	
3.16/1.53	
3.16/1.53	The TRS R consists of the following rules:
3.16/1.53	
3.16/1.53	   f(s(a), s(b), x) -> f(x, x, x)
3.16/1.53	   g(f(s(x), s(y), z)) -> g(f(x, y, z))
3.16/1.53	   cons(x, y) -> x
3.16/1.53	   cons(x, y) -> y
3.16/1.53	
3.16/1.53	S is empty.
3.16/1.53	Rewrite Strategy: FULL
3.16/1.53	----------------------------------------
3.16/1.53	
3.16/1.53	(1) DependencyGraphProof (UPPER BOUND(ID))
3.16/1.53	The following rules are not reachable from basic terms in the dependency graph and can be removed:
3.16/1.53	
3.16/1.53	g(f(s(x), s(y), z)) -> g(f(x, y, z))
3.16/1.53	
3.16/1.53	----------------------------------------
3.16/1.53	
3.16/1.53	(2)
3.16/1.53	Obligation:
3.16/1.53	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(1, 1).
3.16/1.53	
3.16/1.53	
3.16/1.53	The TRS R consists of the following rules:
3.16/1.53	
3.16/1.53	   f(s(a), s(b), x) -> f(x, x, x)
3.16/1.53	   cons(x, y) -> x
3.16/1.53	   cons(x, y) -> y
3.16/1.53	
3.16/1.53	S is empty.
3.16/1.53	Rewrite Strategy: FULL
3.16/1.53	----------------------------------------
3.16/1.53	
3.16/1.53	(3) NarrowingOnBasicTermsTerminatesProof (FINISHED)
3.16/1.53	Constant runtime complexity proven by termination of constructor-based narrowing.
3.16/1.53	
3.16/1.53	The maximal most general narrowing sequences give rise to the following rewrite sequences:
3.16/1.53	
3.16/1.53	cons(x0, x1) ->^* cons(x0, x1)
3.16/1.53	
3.16/1.53	f(s(a), s(b), x0) ->^* f(x0, x0, x0)
3.16/1.53	
3.16/1.53	
3.16/1.53	
3.16/1.53	
3.16/1.53	----------------------------------------
3.16/1.53	
3.16/1.53	(4)
3.16/1.53	BOUNDS(1, 1)
3.16/1.56	EOF