2.89/1.51	WORST_CASE(?, O(1))
2.89/1.51	proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
2.89/1.51	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
2.89/1.51	
2.89/1.51	
2.89/1.51	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(1, 1).
2.89/1.51	
2.89/1.51	(0) CpxTRS
2.89/1.51	(1) DependencyGraphProof [UPPER BOUND(ID), 0 ms]
2.89/1.51	(2) CpxTRS
2.89/1.51	(3) NarrowingOnBasicTermsTerminatesProof [FINISHED, 0 ms]
2.89/1.51	(4) BOUNDS(1, 1)
2.89/1.51	
2.89/1.51	
2.89/1.51	----------------------------------------
2.89/1.51	
2.89/1.51	(0)
2.89/1.51	Obligation:
2.89/1.51	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(1, 1).
2.89/1.51	
2.89/1.51	
2.89/1.51	The TRS R consists of the following rules:
2.89/1.51	
2.89/1.51	   f(f(x)) -> f(c(f(x)))
2.89/1.51	   f(f(x)) -> f(d(f(x)))
2.89/1.51	   g(c(x)) -> x
2.89/1.51	   g(d(x)) -> x
2.89/1.51	   g(c(0)) -> g(d(1))
2.89/1.51	   g(c(1)) -> g(d(0))
2.89/1.51	
2.89/1.51	S is empty.
2.89/1.51	Rewrite Strategy: FULL
2.89/1.51	----------------------------------------
2.89/1.51	
2.89/1.51	(1) DependencyGraphProof (UPPER BOUND(ID))
2.89/1.51	The following rules are not reachable from basic terms in the dependency graph and can be removed:
2.89/1.51	
2.89/1.51	f(f(x)) -> f(c(f(x)))
2.89/1.51	f(f(x)) -> f(d(f(x)))
2.89/1.51	
2.89/1.51	----------------------------------------
2.89/1.51	
2.89/1.51	(2)
2.89/1.51	Obligation:
2.89/1.52	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(1, 1).
2.89/1.52	
2.89/1.52	
2.89/1.52	The TRS R consists of the following rules:
2.89/1.52	
2.89/1.52	   g(c(x)) -> x
2.89/1.52	   g(d(x)) -> x
2.89/1.52	   g(c(0)) -> g(d(1))
2.89/1.52	   g(c(1)) -> g(d(0))
2.89/1.52	
2.89/1.52	S is empty.
2.89/1.52	Rewrite Strategy: FULL
2.89/1.52	----------------------------------------
2.89/1.52	
2.89/1.52	(3) NarrowingOnBasicTermsTerminatesProof (FINISHED)
2.89/1.52	Constant runtime complexity proven by termination of constructor-based narrowing.
2.89/1.52	
2.89/1.52	The maximal most general narrowing sequences give rise to the following rewrite sequences:
2.89/1.52	
2.89/1.52	g(c(1)) ->^* 0
2.89/1.52	
2.89/1.52	g(c(0)) ->^* 1
2.89/1.52	
2.89/1.52	
2.89/1.52	
2.89/1.52	
2.89/1.52	----------------------------------------
2.89/1.52	
2.89/1.52	(4)
2.89/1.52	BOUNDS(1, 1)
2.89/1.55	EOF