3.09/1.54	WORST_CASE(?, O(1))
3.19/1.56	proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
3.19/1.56	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
3.19/1.56	
3.19/1.56	
3.19/1.56	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(1, 1).
3.19/1.56	
3.19/1.56	(0) CpxTRS
3.19/1.56	(1) DependencyGraphProof [UPPER BOUND(ID), 0 ms]
3.19/1.56	(2) CpxTRS
3.19/1.56	(3) NarrowingOnBasicTermsTerminatesProof [FINISHED, 0 ms]
3.19/1.56	(4) BOUNDS(1, 1)
3.19/1.56	
3.19/1.56	
3.19/1.56	----------------------------------------
3.19/1.56	
3.19/1.56	(0)
3.19/1.56	Obligation:
3.19/1.56	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(1, 1).
3.19/1.56	
3.19/1.56	
3.19/1.56	The TRS R consists of the following rules:
3.19/1.56	
3.19/1.56	   f(f(x, y, z), u, f(x, y, v)) -> f(x, y, f(z, u, v))
3.19/1.56	   f(x, y, y) -> y
3.19/1.56	   f(x, y, g(y)) -> x
3.19/1.56	   f(x, x, y) -> x
3.19/1.56	   f(g(x), x, y) -> y
3.19/1.56	
3.19/1.56	S is empty.
3.19/1.56	Rewrite Strategy: FULL
3.19/1.56	----------------------------------------
3.19/1.56	
3.19/1.56	(1) DependencyGraphProof (UPPER BOUND(ID))
3.19/1.56	The following rules are not reachable from basic terms in the dependency graph and can be removed:
3.19/1.56	
3.19/1.56	f(f(x, y, z), u, f(x, y, v)) -> f(x, y, f(z, u, v))
3.19/1.56	
3.19/1.56	----------------------------------------
3.19/1.56	
3.19/1.56	(2)
3.19/1.56	Obligation:
3.19/1.56	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(1, 1).
3.19/1.56	
3.19/1.56	
3.19/1.56	The TRS R consists of the following rules:
3.19/1.56	
3.19/1.56	   f(x, y, y) -> y
3.19/1.56	   f(x, y, g(y)) -> x
3.19/1.56	   f(x, x, y) -> x
3.19/1.56	   f(g(x), x, y) -> y
3.19/1.56	
3.19/1.56	S is empty.
3.19/1.56	Rewrite Strategy: FULL
3.19/1.56	----------------------------------------
3.19/1.56	
3.19/1.56	(3) NarrowingOnBasicTermsTerminatesProof (FINISHED)
3.19/1.56	Constant runtime complexity proven by termination of constructor-based narrowing.
3.19/1.56	
3.19/1.56	The maximal most general narrowing sequences give rise to the following rewrite sequences:
3.19/1.56	
3.19/1.56	f(x0, x1, x2) ->^* f(x0, x1, x2)
3.19/1.56	
3.19/1.56	
3.19/1.56	
3.19/1.56	
3.19/1.56	----------------------------------------
3.19/1.56	
3.19/1.56	(4)
3.19/1.56	BOUNDS(1, 1)
3.19/1.60	EOF