2.99/1.55	WORST_CASE(?, O(1))
2.99/1.56	proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
2.99/1.56	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
2.99/1.56	
2.99/1.56	
2.99/1.56	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(1, 1).
2.99/1.56	
2.99/1.56	(0) CpxTRS
2.99/1.56	(1) NarrowingOnBasicTermsTerminatesProof [FINISHED, 0 ms]
2.99/1.56	(2) BOUNDS(1, 1)
2.99/1.56	
2.99/1.56	
2.99/1.56	----------------------------------------
2.99/1.56	
2.99/1.56	(0)
2.99/1.56	Obligation:
2.99/1.56	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(1, 1).
2.99/1.56	
2.99/1.56	
2.99/1.56	The TRS R consists of the following rules:
2.99/1.56	
2.99/1.56	   d(x) -> e(u(x))
2.99/1.56	   d(u(x)) -> c(x)
2.99/1.56	   c(u(x)) -> b(x)
2.99/1.56	   v(e(x)) -> x
2.99/1.56	   b(u(x)) -> a(e(x))
2.99/1.56	
2.99/1.56	S is empty.
2.99/1.56	Rewrite Strategy: FULL
2.99/1.56	----------------------------------------
2.99/1.56	
2.99/1.56	(1) NarrowingOnBasicTermsTerminatesProof (FINISHED)
2.99/1.56	Constant runtime complexity proven by termination of constructor-based narrowing.
2.99/1.56	
2.99/1.56	The maximal most general narrowing sequences give rise to the following rewrite sequences:
2.99/1.56	
2.99/1.56	v(x0) ->^* v(x0)
2.99/1.56	
2.99/1.56	d(u(u(u(x0)))) ->^* a(e(x0))
2.99/1.56	
2.99/1.56	d(x0) ->^* e(u(x0))
2.99/1.56	
2.99/1.56	c(u(u(x0))) ->^* a(e(x0))
2.99/1.56	
2.99/1.56	b(u(x0)) ->^* a(e(x0))
2.99/1.56	
2.99/1.56	
2.99/1.56	
2.99/1.56	
2.99/1.56	----------------------------------------
2.99/1.56	
2.99/1.56	(2)
2.99/1.56	BOUNDS(1, 1)
2.99/1.60	EOF