3.07/1.64	WORST_CASE(?, O(1))
3.07/1.65	proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml
3.07/1.65	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
3.07/1.65	
3.07/1.65	
3.07/1.65	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(1, 1).
3.07/1.65	
3.07/1.65	(0) CpxTRS
3.07/1.65	(1) NestedDefinedSymbolProof [UPPER BOUND(ID), 0 ms]
3.07/1.65	(2) CpxTRS
3.07/1.65	(3) NarrowingOnBasicTermsTerminatesProof [FINISHED, 0 ms]
3.07/1.65	(4) BOUNDS(1, 1)
3.07/1.65	
3.07/1.65	
3.07/1.65	----------------------------------------
3.07/1.65	
3.07/1.65	(0)
3.07/1.65	Obligation:
3.07/1.65	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(1, 1).
3.07/1.65	
3.07/1.65	
3.07/1.65	The TRS R consists of the following rules:
3.07/1.65	
3.07/1.65	   b(x, y) -> c(a(c(y), a(0, x)))
3.07/1.65	   a(y, x) -> y
3.07/1.65	   a(y, c(b(a(0, x), 0))) -> b(a(c(b(0, y)), x), 0)
3.07/1.65	
3.07/1.65	S is empty.
3.07/1.65	Rewrite Strategy: FULL
3.07/1.65	----------------------------------------
3.07/1.65	
3.07/1.65	(1) NestedDefinedSymbolProof (UPPER BOUND(ID))
3.07/1.65	The following defined symbols can occur below the 1th argument of a: a
3.07/1.65	
3.07/1.65	Hence, the left-hand sides of the following rules are not basic-reachable and can be removed:
3.07/1.65	a(y, c(b(a(0, x), 0))) -> b(a(c(b(0, y)), x), 0)
3.07/1.65	
3.07/1.65	----------------------------------------
3.07/1.65	
3.07/1.65	(2)
3.07/1.65	Obligation:
3.07/1.65	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(1, 1).
3.07/1.65	
3.07/1.65	
3.07/1.65	The TRS R consists of the following rules:
3.07/1.65	
3.07/1.65	   b(x, y) -> c(a(c(y), a(0, x)))
3.07/1.65	   a(y, x) -> y
3.07/1.65	
3.07/1.65	S is empty.
3.07/1.65	Rewrite Strategy: FULL
3.07/1.65	----------------------------------------
3.07/1.65	
3.07/1.65	(3) NarrowingOnBasicTermsTerminatesProof (FINISHED)
3.07/1.65	Constant runtime complexity proven by termination of constructor-based narrowing.
3.07/1.65	
3.07/1.65	The maximal most general narrowing sequences give rise to the following rewrite sequences:
3.07/1.65	
3.07/1.65	b(x0, x1) ->^* c(c(x1))
3.07/1.65	
3.07/1.65	a(x0, x1) ->^* a(x0, x1)
3.07/1.65	
3.07/1.65	
3.07/1.65	
3.07/1.65	
3.07/1.65	----------------------------------------
3.07/1.65	
3.07/1.65	(4)
3.07/1.65	BOUNDS(1, 1)
3.07/1.68	EOF