0.00/0.15	YES
0.00/0.15	
0.00/0.15	Problem 1: 
0.00/0.15	
0.00/0.15	(VAR x)
0.00/0.15	(THEORY 
0.00/0.15	(AC times))
0.00/0.15	(RULES
0.00/0.15	fac(0) -> s(0)
0.00/0.15	fac(s(x)) -> times(s(x),fac(p(s(x))))
0.00/0.15	p(s(x)) -> x
0.00/0.15	)
0.00/0.15	
0.00/0.15	Problem 1: 
0.00/0.15	
0.00/0.15	Dependency Pairs Processor:
0.00/0.15	-> FAxioms:
0.00/0.15	 TIMES(times(x1,x2),x3) = TIMES(x1,times(x2,x3))
0.00/0.15	 TIMES(x1,x2) = TIMES(x2,x1)
0.00/0.15	-> Pairs:
0.00/0.15	 FAC(s(x)) -> FAC(p(s(x)))
0.00/0.15	 FAC(s(x)) -> P(s(x))
0.00/0.15	-> EAxioms:
0.00/0.15	 times(times(x1,x2),x3) = times(x1,times(x2,x3))
0.00/0.15	 times(x1,x2) = times(x2,x1)
0.00/0.15	-> Rules:
0.00/0.15	 fac(0) -> s(0)
0.00/0.15	 fac(s(x)) -> times(s(x),fac(p(s(x))))
0.00/0.15	 p(s(x)) -> x
0.00/0.15	-> SRules:
0.00/0.15	 TIMES(times(x1,x2),x3) -> TIMES(x1,x2)
0.00/0.15	 TIMES(x1,times(x2,x3)) -> TIMES(x2,x3)
0.00/0.15	
0.00/0.15	Problem 1: 
0.00/0.15	
0.00/0.15	SCC Processor:
0.00/0.15	-> FAxioms:
0.00/0.15	 TIMES(times(x1,x2),x3) = TIMES(x1,times(x2,x3))
0.00/0.15	 TIMES(x1,x2) = TIMES(x2,x1)
0.00/0.15	-> Pairs:
0.00/0.15	 FAC(s(x)) -> FAC(p(s(x)))
0.00/0.15	 FAC(s(x)) -> P(s(x))
0.00/0.15	-> EAxioms:
0.00/0.15	 times(times(x1,x2),x3) = times(x1,times(x2,x3))
0.00/0.15	 times(x1,x2) = times(x2,x1)
0.00/0.15	-> Rules:
0.00/0.15	 fac(0) -> s(0)
0.00/0.15	 fac(s(x)) -> times(s(x),fac(p(s(x))))
0.00/0.15	 p(s(x)) -> x
0.00/0.15	-> SRules:
0.00/0.15	 TIMES(times(x1,x2),x3) -> TIMES(x1,x2)
0.00/0.15	 TIMES(x1,times(x2,x3)) -> TIMES(x2,x3)
0.00/0.15	->Strongly Connected Components:
0.00/0.15	->->Cycle:
0.00/0.15	->->-> Pairs:
0.00/0.15	 FAC(s(x)) -> FAC(p(s(x)))
0.00/0.15	-> FAxioms:
0.00/0.15	 times(times(x1,x2),x3) -> times(x1,times(x2,x3))
0.00/0.15	 times(x1,x2) -> times(x2,x1)
0.00/0.15	-> EAxioms:
0.00/0.15	 times(times(x1,x2),x3) = times(x1,times(x2,x3))
0.00/0.15	 times(x1,x2) = times(x2,x1)
0.00/0.15	->->-> Rules:
0.00/0.15	 fac(0) -> s(0)
0.00/0.15	 fac(s(x)) -> times(s(x),fac(p(s(x))))
0.00/0.15	 p(s(x)) -> x
0.00/0.15	-> SRules:
0.00/0.15	 Empty
0.00/0.15	
0.00/0.15	Problem 1: 
0.00/0.15	
0.00/0.15	Reduction Pairs Processor:
0.00/0.15	-> FAxioms:
0.00/0.15	 Empty
0.00/0.15	-> Pairs:
0.00/0.15	 FAC(s(x)) -> FAC(p(s(x)))
0.00/0.15	-> EAxioms:
0.00/0.15	 times(times(x1,x2),x3) = times(x1,times(x2,x3))
0.00/0.15	 times(x1,x2) = times(x2,x1)
0.00/0.15	-> Usable Equations:
0.00/0.15	 Empty
0.00/0.15	-> Rules:
0.00/0.15	 fac(0) -> s(0)
0.00/0.15	 fac(s(x)) -> times(s(x),fac(p(s(x))))
0.00/0.15	 p(s(x)) -> x
0.00/0.15	-> Usable Rules:
0.00/0.15	 p(s(x)) -> x
0.00/0.15	-> SRules:
0.00/0.15	 Empty
0.00/0.15	->Interpretation type:
0.00/0.15	 Linear
0.00/0.15	->Coefficients:
0.00/0.15	 All rationals
0.00/0.15	->Dimension:
0.00/0.15	 1
0.00/0.15	->Bound:
0.00/0.15	 3
0.00/0.15	->Interpretation:
0.00/0.15	 
0.00/0.15	[fac](X) = 0
0.00/0.15	[p](X) = 1/2.X
0.00/0.15	[0] = 0
0.00/0.15	[s](X) = 2.X + 3
0.00/0.15	[times](X1,X2) = 0
0.00/0.15	[FAC](X) = 3/2.X
0.00/0.15	[P](X) = 0
0.00/0.15	[TIMES](X1,X2) = 0
0.00/0.15	
0.00/0.15	Problem 1: 
0.00/0.15	
0.00/0.15	SCC Processor:
0.00/0.15	-> FAxioms:
0.00/0.15	 Empty
0.00/0.15	-> Pairs:
0.00/0.15	 Empty
0.00/0.15	-> EAxioms:
0.00/0.15	 times(times(x1,x2),x3) = times(x1,times(x2,x3))
0.00/0.15	 times(x1,x2) = times(x2,x1)
0.00/0.15	-> Rules:
0.00/0.15	 fac(0) -> s(0)
0.00/0.15	 fac(s(x)) -> times(s(x),fac(p(s(x))))
0.00/0.15	 p(s(x)) -> x
0.00/0.15	-> SRules:
0.00/0.15	 Empty
0.00/0.15	->Strongly Connected Components:
0.00/0.15	 There is no strongly connected component
0.00/0.15	
0.00/0.15	The problem is finite.
0.00/0.15	EOF