3.26/1.73	WORST_CASE(?, O(1))
3.26/1.74	proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml
3.26/1.74	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
3.26/1.74	
3.26/1.74	
3.26/1.74	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(1, 1).
3.26/1.74	
3.26/1.74	(0) CpxTRS
3.26/1.74	(1) NestedDefinedSymbolProof [UPPER BOUND(ID), 0 ms]
3.26/1.74	(2) CpxTRS
3.26/1.74	(3) NarrowingOnBasicTermsTerminatesProof [FINISHED, 0 ms]
3.26/1.74	(4) BOUNDS(1, 1)
3.26/1.74	
3.26/1.74	
3.26/1.74	----------------------------------------
3.26/1.74	
3.26/1.74	(0)
3.26/1.74	Obligation:
3.26/1.74	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(1, 1).
3.26/1.74	
3.26/1.74	
3.26/1.74	The TRS R consists of the following rules:
3.26/1.74	
3.26/1.74	   f(c(a, z, x)) -> b(a, z)
3.26/1.74	   b(x, b(z, y)) -> f(b(f(f(z)), c(x, z, y)))
3.26/1.74	   b(y, z) -> z
3.26/1.74	
3.26/1.74	S is empty.
3.26/1.74	Rewrite Strategy: FULL
3.26/1.74	----------------------------------------
3.26/1.74	
3.26/1.74	(1) NestedDefinedSymbolProof (UPPER BOUND(ID))
3.26/1.74	The TRS does not nest defined symbols.
3.26/1.74	Hence, the left-hand sides of the following rules are not basic-reachable and can be removed:
3.26/1.74	b(x, b(z, y)) -> f(b(f(f(z)), c(x, z, y)))
3.26/1.74	
3.26/1.74	----------------------------------------
3.26/1.74	
3.26/1.74	(2)
3.26/1.74	Obligation:
3.26/1.74	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(1, 1).
3.26/1.74	
3.26/1.74	
3.26/1.74	The TRS R consists of the following rules:
3.26/1.74	
3.26/1.74	   f(c(a, z, x)) -> b(a, z)
3.26/1.74	   b(y, z) -> z
3.26/1.74	
3.26/1.74	S is empty.
3.26/1.74	Rewrite Strategy: FULL
3.26/1.74	----------------------------------------
3.26/1.74	
3.26/1.74	(3) NarrowingOnBasicTermsTerminatesProof (FINISHED)
3.26/1.74	Constant runtime complexity proven by termination of constructor-based narrowing.
3.26/1.74	
3.26/1.74	The maximal most general narrowing sequences give rise to the following rewrite sequences:
3.26/1.74	
3.26/1.74	f(c(a, x0, x1)) ->^* b(a, x0)
3.26/1.74	
3.26/1.74	b(x0, x1) ->^* b(x0, x1)
3.26/1.74	
3.26/1.74	
3.26/1.74	
3.26/1.74	
3.26/1.74	----------------------------------------
3.26/1.74	
3.26/1.74	(4)
3.26/1.74	BOUNDS(1, 1)
3.47/1.77	EOF