3.05/1.56	WORST_CASE(?, O(1))
3.23/1.58	proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
3.23/1.58	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
3.23/1.58	
3.23/1.58	
3.23/1.58	The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(1, 1).
3.23/1.58	
3.23/1.58	(0) CpxTRS
3.23/1.58	(1) NarrowingOnBasicTermsTerminatesProof [FINISHED, 0 ms]
3.23/1.58	(2) BOUNDS(1, 1)
3.23/1.58	
3.23/1.58	
3.23/1.58	----------------------------------------
3.23/1.58	
3.23/1.58	(0)
3.23/1.58	Obligation:
3.23/1.58	The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(1, 1).
3.23/1.58	
3.23/1.58	
3.23/1.58	The TRS R consists of the following rules:
3.23/1.58	
3.23/1.58	   d(x) -> e(u(x))
3.23/1.58	   d(u(x)) -> c(x)
3.23/1.58	   c(u(x)) -> b(x)
3.23/1.58	   v(e(x)) -> x
3.23/1.58	   b(u(x)) -> a(e(x))
3.23/1.58	
3.23/1.58	S is empty.
3.23/1.58	Rewrite Strategy: INNERMOST
3.23/1.58	----------------------------------------
3.23/1.58	
3.23/1.58	(1) NarrowingOnBasicTermsTerminatesProof (FINISHED)
3.23/1.58	Constant runtime complexity proven by termination of constructor-based narrowing.
3.23/1.58	
3.23/1.58	The maximal most general narrowing sequences give rise to the following rewrite sequences:
3.23/1.58	
3.23/1.58	v(x0) ->^* v(x0)
3.23/1.58	
3.23/1.58	d(u(u(u(x0)))) ->^* a(e(x0))
3.23/1.58	
3.23/1.58	d(x0) ->^* e(u(x0))
3.23/1.58	
3.23/1.58	c(u(u(x0))) ->^* a(e(x0))
3.23/1.58	
3.23/1.58	b(u(x0)) ->^* a(e(x0))
3.23/1.58	
3.23/1.58	
3.23/1.58	
3.23/1.58	
3.23/1.58	----------------------------------------
3.23/1.58	
3.23/1.58	(2)
3.23/1.58	BOUNDS(1, 1)
3.23/1.61	EOF