3.03/1.61	WORST_CASE(?, O(1))
3.03/1.61	proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
3.03/1.61	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
3.03/1.61	
3.03/1.61	
3.03/1.61	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(1, 1).
3.03/1.61	
3.03/1.61	(0) CpxTRS
3.03/1.61	(1) DependencyGraphProof [UPPER BOUND(ID), 0 ms]
3.03/1.61	(2) CpxTRS
3.03/1.61	(3) NarrowingOnBasicTermsTerminatesProof [FINISHED, 0 ms]
3.03/1.61	(4) BOUNDS(1, 1)
3.03/1.61	
3.03/1.61	
3.03/1.61	----------------------------------------
3.03/1.61	
3.03/1.61	(0)
3.03/1.61	Obligation:
3.03/1.61	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(1, 1).
3.03/1.61	
3.03/1.61	
3.03/1.61	The TRS R consists of the following rules:
3.03/1.61	
3.03/1.61	   f(c(c(a, y, a), b(x, z), a)) -> b(y, f(c(f(a), z, z)))
3.03/1.61	   f(b(b(x, f(y)), z)) -> c(z, x, f(b(b(f(a), y), y)))
3.03/1.61	   c(b(a, a), b(y, z), x) -> b(a, b(z, z))
3.03/1.61	
3.03/1.61	S is empty.
3.03/1.61	Rewrite Strategy: FULL
3.03/1.61	----------------------------------------
3.03/1.61	
3.03/1.61	(1) DependencyGraphProof (UPPER BOUND(ID))
3.03/1.61	The following rules are not reachable from basic terms in the dependency graph and can be removed:
3.03/1.61	
3.03/1.61	f(c(c(a, y, a), b(x, z), a)) -> b(y, f(c(f(a), z, z)))
3.03/1.61	f(b(b(x, f(y)), z)) -> c(z, x, f(b(b(f(a), y), y)))
3.03/1.61	
3.03/1.61	----------------------------------------
3.03/1.61	
3.03/1.61	(2)
3.03/1.61	Obligation:
3.03/1.61	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(1, 1).
3.03/1.61	
3.03/1.61	
3.03/1.61	The TRS R consists of the following rules:
3.03/1.61	
3.03/1.61	   c(b(a, a), b(y, z), x) -> b(a, b(z, z))
3.03/1.61	
3.03/1.61	S is empty.
3.03/1.61	Rewrite Strategy: FULL
3.03/1.61	----------------------------------------
3.03/1.61	
3.03/1.61	(3) NarrowingOnBasicTermsTerminatesProof (FINISHED)
3.03/1.61	Constant runtime complexity proven by termination of constructor-based narrowing.
3.03/1.61	
3.03/1.61	The maximal most general narrowing sequences give rise to the following rewrite sequences:
3.03/1.61	
3.03/1.61	c(b(a, a), b(x0, x1), x2) ->^* b(a, b(x1, x1))
3.03/1.61	
3.03/1.61	
3.03/1.61	
3.03/1.61	
3.03/1.61	----------------------------------------
3.03/1.61	
3.03/1.61	(4)
3.03/1.61	BOUNDS(1, 1)
3.33/1.65	EOF