2.83/1.73	WORST_CASE(?, O(1))
3.06/1.74	proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
3.06/1.74	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
3.06/1.74	
3.06/1.74	
3.06/1.74	The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(1, 1).
3.06/1.74	
3.06/1.74	(0) CpxTRS
3.06/1.74	(1) NarrowingOnBasicTermsTerminatesProof [FINISHED, 0 ms]
3.06/1.74	(2) BOUNDS(1, 1)
3.06/1.74	
3.06/1.74	
3.06/1.74	----------------------------------------
3.06/1.74	
3.06/1.74	(0)
3.06/1.74	Obligation:
3.06/1.74	The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(1, 1).
3.06/1.74	
3.06/1.74	
3.06/1.74	The TRS R consists of the following rules:
3.06/1.74	
3.06/1.74	   p(f(f(x))) -> q(f(g(x)))
3.06/1.74	   p(g(g(x))) -> q(g(f(x)))
3.06/1.74	   q(f(f(x))) -> p(f(g(x)))
3.06/1.74	   q(g(g(x))) -> p(g(f(x)))
3.06/1.74	
3.06/1.74	S is empty.
3.06/1.74	Rewrite Strategy: INNERMOST
3.06/1.74	----------------------------------------
3.06/1.74	
3.06/1.74	(1) NarrowingOnBasicTermsTerminatesProof (FINISHED)
3.06/1.74	Constant runtime complexity proven by termination of constructor-based narrowing.
3.06/1.74	
3.06/1.74	The maximal most general narrowing sequences give rise to the following rewrite sequences:
3.06/1.74	
3.06/1.74	q(g(g(x0))) ->^* p(g(f(x0)))
3.06/1.74	
3.06/1.74	q(f(f(x0))) ->^* p(f(g(x0)))
3.06/1.74	
3.06/1.74	p(g(g(x0))) ->^* q(g(f(x0)))
3.06/1.74	
3.06/1.74	p(f(f(x0))) ->^* q(f(g(x0)))
3.06/1.74	
3.06/1.74	
3.06/1.74	
3.06/1.74	
3.06/1.74	----------------------------------------
3.06/1.74	
3.06/1.74	(2)
3.06/1.74	BOUNDS(1, 1)
3.08/1.78	EOF