3.17/1.49	WORST_CASE(?, O(1))
3.17/1.49	proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
3.17/1.49	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
3.17/1.49	
3.17/1.49	
3.17/1.49	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(1, 1).
3.17/1.49	
3.17/1.49	(0) CpxTRS
3.17/1.49	(1) NarrowingOnBasicTermsTerminatesProof [FINISHED, 0 ms]
3.17/1.49	(2) BOUNDS(1, 1)
3.17/1.49	
3.17/1.49	
3.17/1.49	----------------------------------------
3.17/1.49	
3.17/1.49	(0)
3.17/1.49	Obligation:
3.17/1.49	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(1, 1).
3.17/1.49	
3.17/1.49	
3.17/1.49	The TRS R consists of the following rules:
3.17/1.49	
3.17/1.49	   f(s(X), X) -> f(X, a(X))
3.17/1.49	   f(X, c(X)) -> f(s(X), X)
3.17/1.49	   f(X, X) -> c(X)
3.17/1.49	
3.17/1.49	S is empty.
3.17/1.49	Rewrite Strategy: FULL
3.17/1.49	----------------------------------------
3.17/1.49	
3.17/1.49	(1) NarrowingOnBasicTermsTerminatesProof (FINISHED)
3.17/1.49	Constant runtime complexity proven by termination of constructor-based narrowing.
3.17/1.49	
3.17/1.49	The maximal most general narrowing sequences give rise to the following rewrite sequences:
3.17/1.49	
3.17/1.49	f(x0, x0) ->^* c(x0)
3.17/1.49	
3.17/1.49	f(x0, c(x0)) ->^* f(x0, a(x0))
3.17/1.49	
3.17/1.49	f(s(x0), x0) ->^* f(x0, a(x0))
3.17/1.49	
3.17/1.49	
3.17/1.49	
3.17/1.49	
3.17/1.49	----------------------------------------
3.17/1.49	
3.17/1.49	(2)
3.17/1.49	BOUNDS(1, 1)
3.17/1.52	EOF