1.71/2.28	YES
1.71/2.28	
1.71/2.28	Problem 1: 
1.71/2.28	
1.71/2.28	(VAR x y z)
1.71/2.28	(THEORY 
1.71/2.28	(AC times plus))
1.71/2.28	(RULES
1.71/2.28	times(plus(x,y),z) -> plus(times(x,z),times(y,z))
1.71/2.28	times(z,plus(x,f(y))) -> times(g(z,y),plus(x,a))
1.71/2.28	)
1.71/2.28	
1.71/2.28	Problem 1: 
1.71/2.28	
1.71/2.28	Dependency Pairs Processor:
1.71/2.28	-> FAxioms:
1.71/2.28	 TIMES(times(x3,x4),x5) = TIMES(x3,times(x4,x5))
1.71/2.28	 TIMES(x3,x4) = TIMES(x4,x3)
1.71/2.28	 PLUS(plus(x3,x4),x5) = PLUS(x3,plus(x4,x5))
1.71/2.28	 PLUS(x3,x4) = PLUS(x4,x3)
1.71/2.28	-> Pairs:
1.71/2.28	 TIMES(times(plus(x,y),z),x3) -> TIMES(plus(times(x,z),times(y,z)),x3)
1.71/2.28	 TIMES(times(plus(x,y),z),x3) -> TIMES(x,z)
1.71/2.28	 TIMES(times(plus(x,y),z),x3) -> TIMES(y,z)
1.71/2.28	 TIMES(times(z,plus(x,f(y))),x3) -> TIMES(times(g(z,y),plus(x,a)),x3)
1.71/2.28	 TIMES(times(z,plus(x,f(y))),x3) -> TIMES(g(z,y),plus(x,a))
1.71/2.28	 TIMES(plus(x,y),z) -> TIMES(x,z)
1.71/2.28	 TIMES(plus(x,y),z) -> TIMES(y,z)
1.71/2.28	 TIMES(z,plus(x,f(y))) -> TIMES(g(z,y),plus(x,a))
1.71/2.28	-> EAxioms:
1.71/2.28	 times(times(x3,x4),x5) = times(x3,times(x4,x5))
1.71/2.28	 times(x3,x4) = times(x4,x3)
1.71/2.28	 plus(plus(x3,x4),x5) = plus(x3,plus(x4,x5))
1.71/2.28	 plus(x3,x4) = plus(x4,x3)
1.71/2.28	-> Rules:
1.71/2.28	 times(plus(x,y),z) -> plus(times(x,z),times(y,z))
1.71/2.28	 times(z,plus(x,f(y))) -> times(g(z,y),plus(x,a))
1.71/2.28	-> SRules:
1.71/2.28	 TIMES(times(x3,x4),x5) -> TIMES(x3,x4)
1.71/2.28	 TIMES(x3,times(x4,x5)) -> TIMES(x4,x5)
1.71/2.28	 PLUS(plus(x3,x4),x5) -> PLUS(x3,x4)
1.71/2.28	 PLUS(x3,plus(x4,x5)) -> PLUS(x4,x5)
1.71/2.28	
1.71/2.28	Problem 1: 
1.71/2.28	
1.71/2.28	SCC Processor:
1.71/2.28	-> FAxioms:
1.71/2.28	 TIMES(times(x3,x4),x5) = TIMES(x3,times(x4,x5))
1.71/2.28	 TIMES(x3,x4) = TIMES(x4,x3)
1.71/2.28	 PLUS(plus(x3,x4),x5) = PLUS(x3,plus(x4,x5))
1.71/2.28	 PLUS(x3,x4) = PLUS(x4,x3)
1.71/2.28	-> Pairs:
1.71/2.28	 TIMES(times(plus(x,y),z),x3) -> TIMES(plus(times(x,z),times(y,z)),x3)
1.71/2.28	 TIMES(times(plus(x,y),z),x3) -> TIMES(x,z)
1.71/2.28	 TIMES(times(plus(x,y),z),x3) -> TIMES(y,z)
1.71/2.28	 TIMES(times(z,plus(x,f(y))),x3) -> TIMES(times(g(z,y),plus(x,a)),x3)
1.71/2.28	 TIMES(times(z,plus(x,f(y))),x3) -> TIMES(g(z,y),plus(x,a))
1.71/2.28	 TIMES(plus(x,y),z) -> TIMES(x,z)
1.71/2.28	 TIMES(plus(x,y),z) -> TIMES(y,z)
1.71/2.28	 TIMES(z,plus(x,f(y))) -> TIMES(g(z,y),plus(x,a))
1.71/2.28	-> EAxioms:
1.71/2.28	 times(times(x3,x4),x5) = times(x3,times(x4,x5))
1.71/2.28	 times(x3,x4) = times(x4,x3)
1.71/2.28	 plus(plus(x3,x4),x5) = plus(x3,plus(x4,x5))
1.71/2.28	 plus(x3,x4) = plus(x4,x3)
1.71/2.28	-> Rules:
1.71/2.28	 times(plus(x,y),z) -> plus(times(x,z),times(y,z))
1.71/2.28	 times(z,plus(x,f(y))) -> times(g(z,y),plus(x,a))
1.71/2.28	-> SRules:
1.71/2.28	 TIMES(times(x3,x4),x5) -> TIMES(x3,x4)
1.71/2.28	 TIMES(x3,times(x4,x5)) -> TIMES(x4,x5)
1.71/2.28	 PLUS(plus(x3,x4),x5) -> PLUS(x3,x4)
1.71/2.28	 PLUS(x3,plus(x4,x5)) -> PLUS(x4,x5)
1.71/2.28	->Strongly Connected Components:
1.71/2.28	->->Cycle:
1.71/2.28	->->-> Pairs:
1.71/2.28	 TIMES(times(plus(x,y),z),x3) -> TIMES(plus(times(x,z),times(y,z)),x3)
1.71/2.28	 TIMES(times(plus(x,y),z),x3) -> TIMES(x,z)
1.71/2.28	 TIMES(times(plus(x,y),z),x3) -> TIMES(y,z)
1.71/2.28	 TIMES(times(z,plus(x,f(y))),x3) -> TIMES(times(g(z,y),plus(x,a)),x3)
1.71/2.28	 TIMES(times(z,plus(x,f(y))),x3) -> TIMES(g(z,y),plus(x,a))
1.71/2.28	 TIMES(plus(x,y),z) -> TIMES(x,z)
1.71/2.28	 TIMES(plus(x,y),z) -> TIMES(y,z)
1.71/2.28	 TIMES(z,plus(x,f(y))) -> TIMES(g(z,y),plus(x,a))
1.71/2.28	-> FAxioms:
1.71/2.28	 times(times(x3,x4),x5) -> times(x3,times(x4,x5))
1.71/2.28	 times(x3,x4) -> times(x4,x3)
1.71/2.28	 plus(plus(x3,x4),x5) -> plus(x3,plus(x4,x5))
1.71/2.28	 plus(x3,x4) -> plus(x4,x3)
1.71/2.28	 TIMES(times(x3,x4),x5) -> TIMES(x3,times(x4,x5))
1.71/2.28	 TIMES(x3,x4) -> TIMES(x4,x3)
1.71/2.28	-> EAxioms:
1.71/2.28	 times(times(x3,x4),x5) = times(x3,times(x4,x5))
1.71/2.28	 times(x3,x4) = times(x4,x3)
1.71/2.28	 plus(plus(x3,x4),x5) = plus(x3,plus(x4,x5))
1.71/2.28	 plus(x3,x4) = plus(x4,x3)
1.71/2.28	->->-> Rules:
1.71/2.28	 times(plus(x,y),z) -> plus(times(x,z),times(y,z))
1.71/2.28	 times(z,plus(x,f(y))) -> times(g(z,y),plus(x,a))
1.71/2.28	-> SRules:
1.71/2.28	 TIMES(times(x3,x4),x5) -> TIMES(x3,x4)
1.71/2.28	 TIMES(x3,times(x4,x5)) -> TIMES(x4,x5)
1.71/2.28	
1.71/2.28	Problem 1: 
1.71/2.28	
1.71/2.28	Reduction Pairs Processor:
1.71/2.28	-> FAxioms:
1.71/2.28	 TIMES(times(x3,x4),x5) = TIMES(x3,times(x4,x5))
1.71/2.28	 TIMES(x3,x4) = TIMES(x4,x3)
1.71/2.28	-> Pairs:
1.71/2.28	 TIMES(times(plus(x,y),z),x3) -> TIMES(plus(times(x,z),times(y,z)),x3)
1.71/2.28	 TIMES(times(plus(x,y),z),x3) -> TIMES(x,z)
1.71/2.28	 TIMES(times(plus(x,y),z),x3) -> TIMES(y,z)
1.71/2.28	 TIMES(times(z,plus(x,f(y))),x3) -> TIMES(times(g(z,y),plus(x,a)),x3)
1.71/2.28	 TIMES(times(z,plus(x,f(y))),x3) -> TIMES(g(z,y),plus(x,a))
1.71/2.28	 TIMES(plus(x,y),z) -> TIMES(x,z)
1.71/2.28	 TIMES(plus(x,y),z) -> TIMES(y,z)
1.71/2.28	 TIMES(z,plus(x,f(y))) -> TIMES(g(z,y),plus(x,a))
1.71/2.28	-> EAxioms:
1.71/2.28	 times(times(x3,x4),x5) = times(x3,times(x4,x5))
1.71/2.28	 times(x3,x4) = times(x4,x3)
1.71/2.28	 plus(plus(x3,x4),x5) = plus(x3,plus(x4,x5))
1.71/2.28	 plus(x3,x4) = plus(x4,x3)
1.71/2.28	-> Usable Equations:
1.71/2.28	 times(times(x3,x4),x5) = times(x3,times(x4,x5))
1.71/2.28	 times(x3,x4) = times(x4,x3)
1.71/2.28	 plus(plus(x3,x4),x5) = plus(x3,plus(x4,x5))
1.71/2.28	 plus(x3,x4) = plus(x4,x3)
1.71/2.28	-> Rules:
1.71/2.28	 times(plus(x,y),z) -> plus(times(x,z),times(y,z))
1.71/2.28	 times(z,plus(x,f(y))) -> times(g(z,y),plus(x,a))
1.71/2.28	-> Usable Rules:
1.71/2.28	 times(plus(x,y),z) -> plus(times(x,z),times(y,z))
1.71/2.28	 times(z,plus(x,f(y))) -> times(g(z,y),plus(x,a))
1.71/2.28	-> SRules:
1.71/2.28	 TIMES(times(x3,x4),x5) -> TIMES(x3,x4)
1.71/2.28	 TIMES(x3,times(x4,x5)) -> TIMES(x4,x5)
1.71/2.28	->Interpretation type:
1.71/2.28	 Simple mixed
1.71/2.28	->Coefficients:
1.71/2.28	 Natural Numbers
1.71/2.28	->Dimension:
1.71/2.28	 1
1.71/2.28	->Bound:
1.71/2.28	 1
1.71/2.28	->Interpretation:
1.71/2.28	 
1.71/2.28	[times](X1,X2) = X1.X2 + X1 + X2
1.71/2.28	[a] = 1
1.71/2.28	[f](X) = X + 1
1.71/2.28	[g](X1,X2) = X1
1.71/2.28	[plus](X1,X2) = X1 + X2 + 1
1.71/2.28	[TIMES](X1,X2) = X1.X2 + X1 + X2
1.71/2.28	[PLUS](X1,X2) = 0
1.71/2.28	
1.71/2.28	Problem 1: 
1.71/2.28	
1.71/2.28	SCC Processor:
1.71/2.28	-> FAxioms:
1.71/2.28	 TIMES(times(x3,x4),x5) = TIMES(x3,times(x4,x5))
1.71/2.28	 TIMES(x3,x4) = TIMES(x4,x3)
1.71/2.28	-> Pairs:
1.71/2.28	 TIMES(times(plus(x,y),z),x3) -> TIMES(plus(times(x,z),times(y,z)),x3)
1.71/2.28	 TIMES(times(plus(x,y),z),x3) -> TIMES(y,z)
1.71/2.28	 TIMES(times(z,plus(x,f(y))),x3) -> TIMES(times(g(z,y),plus(x,a)),x3)
1.71/2.28	 TIMES(times(z,plus(x,f(y))),x3) -> TIMES(g(z,y),plus(x,a))
1.71/2.28	 TIMES(plus(x,y),z) -> TIMES(x,z)
1.71/2.28	 TIMES(plus(x,y),z) -> TIMES(y,z)
1.71/2.28	 TIMES(z,plus(x,f(y))) -> TIMES(g(z,y),plus(x,a))
1.71/2.28	-> EAxioms:
1.71/2.28	 times(times(x3,x4),x5) = times(x3,times(x4,x5))
1.71/2.28	 times(x3,x4) = times(x4,x3)
1.71/2.28	 plus(plus(x3,x4),x5) = plus(x3,plus(x4,x5))
1.71/2.28	 plus(x3,x4) = plus(x4,x3)
1.71/2.28	-> Rules:
1.71/2.28	 times(plus(x,y),z) -> plus(times(x,z),times(y,z))
1.71/2.28	 times(z,plus(x,f(y))) -> times(g(z,y),plus(x,a))
1.71/2.28	-> SRules:
1.71/2.28	 TIMES(times(x3,x4),x5) -> TIMES(x3,x4)
1.71/2.28	 TIMES(x3,times(x4,x5)) -> TIMES(x4,x5)
1.71/2.28	->Strongly Connected Components:
1.71/2.28	->->Cycle:
1.71/2.28	->->-> Pairs:
1.71/2.28	 TIMES(times(plus(x,y),z),x3) -> TIMES(plus(times(x,z),times(y,z)),x3)
1.71/2.28	 TIMES(times(plus(x,y),z),x3) -> TIMES(y,z)
1.71/2.28	 TIMES(times(z,plus(x,f(y))),x3) -> TIMES(times(g(z,y),plus(x,a)),x3)
1.71/2.28	 TIMES(times(z,plus(x,f(y))),x3) -> TIMES(g(z,y),plus(x,a))
1.71/2.28	 TIMES(plus(x,y),z) -> TIMES(x,z)
1.71/2.28	 TIMES(plus(x,y),z) -> TIMES(y,z)
1.71/2.28	 TIMES(z,plus(x,f(y))) -> TIMES(g(z,y),plus(x,a))
1.71/2.28	-> FAxioms:
1.71/2.28	 times(times(x3,x4),x5) -> times(x3,times(x4,x5))
1.71/2.28	 times(x3,x4) -> times(x4,x3)
1.71/2.28	 plus(plus(x3,x4),x5) -> plus(x3,plus(x4,x5))
1.71/2.28	 plus(x3,x4) -> plus(x4,x3)
1.71/2.28	 TIMES(times(x3,x4),x5) -> TIMES(x3,times(x4,x5))
1.71/2.28	 TIMES(x3,x4) -> TIMES(x4,x3)
1.71/2.28	-> EAxioms:
1.71/2.28	 times(times(x3,x4),x5) = times(x3,times(x4,x5))
1.71/2.28	 times(x3,x4) = times(x4,x3)
1.71/2.28	 plus(plus(x3,x4),x5) = plus(x3,plus(x4,x5))
1.71/2.28	 plus(x3,x4) = plus(x4,x3)
1.71/2.28	->->-> Rules:
1.71/2.28	 times(plus(x,y),z) -> plus(times(x,z),times(y,z))
1.71/2.28	 times(z,plus(x,f(y))) -> times(g(z,y),plus(x,a))
1.71/2.28	-> SRules:
1.71/2.28	 TIMES(times(x3,x4),x5) -> TIMES(x3,x4)
1.71/2.28	 TIMES(x3,times(x4,x5)) -> TIMES(x4,x5)
1.71/2.28	
1.71/2.28	Problem 1: 
1.71/2.28	
1.71/2.28	Reduction Pairs Processor:
1.71/2.28	-> FAxioms:
1.71/2.28	 TIMES(times(x3,x4),x5) = TIMES(x3,times(x4,x5))
1.71/2.28	 TIMES(x3,x4) = TIMES(x4,x3)
1.71/2.28	-> Pairs:
1.71/2.28	 TIMES(times(plus(x,y),z),x3) -> TIMES(plus(times(x,z),times(y,z)),x3)
1.71/2.28	 TIMES(times(plus(x,y),z),x3) -> TIMES(y,z)
1.71/2.28	 TIMES(times(z,plus(x,f(y))),x3) -> TIMES(times(g(z,y),plus(x,a)),x3)
1.71/2.28	 TIMES(times(z,plus(x,f(y))),x3) -> TIMES(g(z,y),plus(x,a))
1.71/2.28	 TIMES(plus(x,y),z) -> TIMES(x,z)
1.71/2.28	 TIMES(plus(x,y),z) -> TIMES(y,z)
1.71/2.28	 TIMES(z,plus(x,f(y))) -> TIMES(g(z,y),plus(x,a))
1.71/2.28	-> EAxioms:
1.71/2.28	 times(times(x3,x4),x5) = times(x3,times(x4,x5))
1.71/2.28	 times(x3,x4) = times(x4,x3)
1.71/2.28	 plus(plus(x3,x4),x5) = plus(x3,plus(x4,x5))
1.71/2.28	 plus(x3,x4) = plus(x4,x3)
1.71/2.28	-> Usable Equations:
1.71/2.28	 times(times(x3,x4),x5) = times(x3,times(x4,x5))
1.71/2.28	 times(x3,x4) = times(x4,x3)
1.71/2.28	 plus(plus(x3,x4),x5) = plus(x3,plus(x4,x5))
1.71/2.28	 plus(x3,x4) = plus(x4,x3)
1.71/2.28	-> Rules:
1.71/2.28	 times(plus(x,y),z) -> plus(times(x,z),times(y,z))
1.71/2.28	 times(z,plus(x,f(y))) -> times(g(z,y),plus(x,a))
1.71/2.28	-> Usable Rules:
1.71/2.28	 times(plus(x,y),z) -> plus(times(x,z),times(y,z))
1.71/2.28	 times(z,plus(x,f(y))) -> times(g(z,y),plus(x,a))
1.71/2.28	-> SRules:
1.71/2.28	 TIMES(times(x3,x4),x5) -> TIMES(x3,x4)
1.71/2.28	 TIMES(x3,times(x4,x5)) -> TIMES(x4,x5)
1.71/2.28	->Interpretation type:
1.71/2.28	 Simple mixed
1.71/2.28	->Coefficients:
1.71/2.28	 Natural Numbers
1.71/2.28	->Dimension:
1.71/2.28	 1
1.71/2.28	->Bound:
1.71/2.28	 1
1.71/2.28	->Interpretation:
1.71/2.28	 
1.71/2.28	[times](X1,X2) = X1.X2 + X1 + X2
1.71/2.28	[a] = 1
1.71/2.28	[f](X) = X + 1
1.71/2.28	[g](X1,X2) = X1
1.71/2.28	[plus](X1,X2) = X1 + X2 + 1
1.71/2.28	[TIMES](X1,X2) = X1.X2 + X1 + X2
1.71/2.28	[PLUS](X1,X2) = 0
1.71/2.28	
1.71/2.28	Problem 1: 
1.71/2.28	
1.71/2.28	SCC Processor:
1.71/2.28	-> FAxioms:
1.71/2.28	 TIMES(times(x3,x4),x5) = TIMES(x3,times(x4,x5))
1.71/2.28	 TIMES(x3,x4) = TIMES(x4,x3)
1.71/2.28	-> Pairs:
1.71/2.28	 TIMES(times(plus(x,y),z),x3) -> TIMES(plus(times(x,z),times(y,z)),x3)
1.71/2.28	 TIMES(times(z,plus(x,f(y))),x3) -> TIMES(times(g(z,y),plus(x,a)),x3)
1.71/2.28	 TIMES(times(z,plus(x,f(y))),x3) -> TIMES(g(z,y),plus(x,a))
1.71/2.28	 TIMES(plus(x,y),z) -> TIMES(x,z)
1.71/2.28	 TIMES(plus(x,y),z) -> TIMES(y,z)
1.71/2.28	 TIMES(z,plus(x,f(y))) -> TIMES(g(z,y),plus(x,a))
1.71/2.28	-> EAxioms:
1.71/2.28	 times(times(x3,x4),x5) = times(x3,times(x4,x5))
1.71/2.28	 times(x3,x4) = times(x4,x3)
1.71/2.28	 plus(plus(x3,x4),x5) = plus(x3,plus(x4,x5))
1.71/2.28	 plus(x3,x4) = plus(x4,x3)
1.71/2.28	-> Rules:
1.71/2.28	 times(plus(x,y),z) -> plus(times(x,z),times(y,z))
1.71/2.28	 times(z,plus(x,f(y))) -> times(g(z,y),plus(x,a))
1.71/2.28	-> SRules:
1.71/2.28	 TIMES(times(x3,x4),x5) -> TIMES(x3,x4)
1.71/2.28	 TIMES(x3,times(x4,x5)) -> TIMES(x4,x5)
1.71/2.28	->Strongly Connected Components:
1.71/2.28	->->Cycle:
1.71/2.28	->->-> Pairs:
1.71/2.28	 TIMES(times(plus(x,y),z),x3) -> TIMES(plus(times(x,z),times(y,z)),x3)
1.71/2.28	 TIMES(times(z,plus(x,f(y))),x3) -> TIMES(times(g(z,y),plus(x,a)),x3)
1.71/2.28	 TIMES(times(z,plus(x,f(y))),x3) -> TIMES(g(z,y),plus(x,a))
1.71/2.28	 TIMES(plus(x,y),z) -> TIMES(x,z)
1.71/2.28	 TIMES(plus(x,y),z) -> TIMES(y,z)
1.71/2.28	 TIMES(z,plus(x,f(y))) -> TIMES(g(z,y),plus(x,a))
1.71/2.28	-> FAxioms:
1.71/2.28	 times(times(x3,x4),x5) -> times(x3,times(x4,x5))
1.71/2.28	 times(x3,x4) -> times(x4,x3)
1.71/2.28	 plus(plus(x3,x4),x5) -> plus(x3,plus(x4,x5))
1.71/2.28	 plus(x3,x4) -> plus(x4,x3)
1.71/2.28	 TIMES(times(x3,x4),x5) -> TIMES(x3,times(x4,x5))
1.71/2.28	 TIMES(x3,x4) -> TIMES(x4,x3)
1.71/2.28	-> EAxioms:
1.71/2.28	 times(times(x3,x4),x5) = times(x3,times(x4,x5))
1.71/2.28	 times(x3,x4) = times(x4,x3)
1.71/2.28	 plus(plus(x3,x4),x5) = plus(x3,plus(x4,x5))
1.71/2.28	 plus(x3,x4) = plus(x4,x3)
1.71/2.28	->->-> Rules:
1.71/2.28	 times(plus(x,y),z) -> plus(times(x,z),times(y,z))
1.71/2.28	 times(z,plus(x,f(y))) -> times(g(z,y),plus(x,a))
1.71/2.28	-> SRules:
1.71/2.28	 TIMES(times(x3,x4),x5) -> TIMES(x3,x4)
1.71/2.28	 TIMES(x3,times(x4,x5)) -> TIMES(x4,x5)
1.71/2.28	
1.71/2.28	Problem 1: 
1.71/2.28	
1.71/2.28	Reduction Pairs Processor:
1.71/2.28	-> FAxioms:
1.71/2.28	 TIMES(times(x3,x4),x5) = TIMES(x3,times(x4,x5))
1.71/2.28	 TIMES(x3,x4) = TIMES(x4,x3)
1.71/2.28	-> Pairs:
1.71/2.28	 TIMES(times(plus(x,y),z),x3) -> TIMES(plus(times(x,z),times(y,z)),x3)
1.71/2.28	 TIMES(times(z,plus(x,f(y))),x3) -> TIMES(times(g(z,y),plus(x,a)),x3)
1.71/2.28	 TIMES(times(z,plus(x,f(y))),x3) -> TIMES(g(z,y),plus(x,a))
1.71/2.28	 TIMES(plus(x,y),z) -> TIMES(x,z)
1.71/2.28	 TIMES(plus(x,y),z) -> TIMES(y,z)
1.71/2.28	 TIMES(z,plus(x,f(y))) -> TIMES(g(z,y),plus(x,a))
1.71/2.28	-> EAxioms:
1.71/2.28	 times(times(x3,x4),x5) = times(x3,times(x4,x5))
1.71/2.28	 times(x3,x4) = times(x4,x3)
1.71/2.28	 plus(plus(x3,x4),x5) = plus(x3,plus(x4,x5))
1.71/2.28	 plus(x3,x4) = plus(x4,x3)
1.71/2.28	-> Usable Equations:
1.71/2.28	 times(times(x3,x4),x5) = times(x3,times(x4,x5))
1.71/2.28	 times(x3,x4) = times(x4,x3)
1.71/2.28	 plus(plus(x3,x4),x5) = plus(x3,plus(x4,x5))
1.71/2.28	 plus(x3,x4) = plus(x4,x3)
1.71/2.28	-> Rules:
1.71/2.28	 times(plus(x,y),z) -> plus(times(x,z),times(y,z))
1.71/2.28	 times(z,plus(x,f(y))) -> times(g(z,y),plus(x,a))
1.71/2.28	-> Usable Rules:
1.71/2.28	 times(plus(x,y),z) -> plus(times(x,z),times(y,z))
1.71/2.28	 times(z,plus(x,f(y))) -> times(g(z,y),plus(x,a))
1.71/2.28	-> SRules:
1.71/2.28	 TIMES(times(x3,x4),x5) -> TIMES(x3,x4)
1.71/2.28	 TIMES(x3,times(x4,x5)) -> TIMES(x4,x5)
1.71/2.28	->Interpretation type:
1.71/2.28	 Simple mixed
1.71/2.28	->Coefficients:
1.71/2.28	 Natural Numbers
1.71/2.28	->Dimension:
1.71/2.28	 1
1.71/2.28	->Bound:
1.71/2.28	 1
1.71/2.28	->Interpretation:
1.71/2.28	 
1.71/2.28	[times](X1,X2) = X1.X2 + X1 + X2
1.71/2.28	[a] = 0
1.71/2.28	[f](X) = X + 1
1.71/2.28	[g](X1,X2) = X1
1.71/2.28	[plus](X1,X2) = X1 + X2 + 1
1.71/2.28	[TIMES](X1,X2) = X1.X2 + X1 + X2
1.71/2.28	[PLUS](X1,X2) = 0
1.71/2.28	
1.71/2.28	Problem 1: 
1.71/2.28	
1.71/2.28	SCC Processor:
1.71/2.28	-> FAxioms:
1.71/2.28	 TIMES(times(x3,x4),x5) = TIMES(x3,times(x4,x5))
1.71/2.28	 TIMES(x3,x4) = TIMES(x4,x3)
1.71/2.28	-> Pairs:
1.71/2.28	 TIMES(times(plus(x,y),z),x3) -> TIMES(plus(times(x,z),times(y,z)),x3)
1.71/2.28	 TIMES(times(z,plus(x,f(y))),x3) -> TIMES(g(z,y),plus(x,a))
1.71/2.28	 TIMES(plus(x,y),z) -> TIMES(x,z)
1.71/2.28	 TIMES(plus(x,y),z) -> TIMES(y,z)
1.71/2.28	 TIMES(z,plus(x,f(y))) -> TIMES(g(z,y),plus(x,a))
1.71/2.28	-> EAxioms:
1.71/2.28	 times(times(x3,x4),x5) = times(x3,times(x4,x5))
1.71/2.28	 times(x3,x4) = times(x4,x3)
1.71/2.28	 plus(plus(x3,x4),x5) = plus(x3,plus(x4,x5))
1.71/2.28	 plus(x3,x4) = plus(x4,x3)
1.71/2.28	-> Rules:
1.71/2.28	 times(plus(x,y),z) -> plus(times(x,z),times(y,z))
1.71/2.28	 times(z,plus(x,f(y))) -> times(g(z,y),plus(x,a))
1.71/2.28	-> SRules:
1.71/2.28	 TIMES(times(x3,x4),x5) -> TIMES(x3,x4)
1.71/2.28	 TIMES(x3,times(x4,x5)) -> TIMES(x4,x5)
1.71/2.28	->Strongly Connected Components:
1.71/2.28	->->Cycle:
1.71/2.28	->->-> Pairs:
1.71/2.28	 TIMES(times(plus(x,y),z),x3) -> TIMES(plus(times(x,z),times(y,z)),x3)
1.71/2.28	 TIMES(times(z,plus(x,f(y))),x3) -> TIMES(g(z,y),plus(x,a))
1.71/2.28	 TIMES(plus(x,y),z) -> TIMES(x,z)
1.71/2.28	 TIMES(plus(x,y),z) -> TIMES(y,z)
1.71/2.28	 TIMES(z,plus(x,f(y))) -> TIMES(g(z,y),plus(x,a))
1.71/2.28	-> FAxioms:
1.71/2.28	 times(times(x3,x4),x5) -> times(x3,times(x4,x5))
1.71/2.28	 times(x3,x4) -> times(x4,x3)
1.71/2.28	 plus(plus(x3,x4),x5) -> plus(x3,plus(x4,x5))
1.71/2.28	 plus(x3,x4) -> plus(x4,x3)
1.71/2.28	 TIMES(times(x3,x4),x5) -> TIMES(x3,times(x4,x5))
1.71/2.28	 TIMES(x3,x4) -> TIMES(x4,x3)
1.71/2.28	-> EAxioms:
1.71/2.28	 times(times(x3,x4),x5) = times(x3,times(x4,x5))
1.71/2.28	 times(x3,x4) = times(x4,x3)
1.71/2.28	 plus(plus(x3,x4),x5) = plus(x3,plus(x4,x5))
1.71/2.28	 plus(x3,x4) = plus(x4,x3)
1.71/2.28	->->-> Rules:
1.71/2.28	 times(plus(x,y),z) -> plus(times(x,z),times(y,z))
1.71/2.28	 times(z,plus(x,f(y))) -> times(g(z,y),plus(x,a))
1.71/2.28	-> SRules:
1.71/2.28	 TIMES(times(x3,x4),x5) -> TIMES(x3,x4)
1.71/2.28	 TIMES(x3,times(x4,x5)) -> TIMES(x4,x5)
1.71/2.28	
1.71/2.28	Problem 1: 
1.71/2.28	
1.71/2.28	Reduction Pairs Processor:
1.71/2.28	-> FAxioms:
1.71/2.28	 TIMES(times(x3,x4),x5) = TIMES(x3,times(x4,x5))
1.71/2.28	 TIMES(x3,x4) = TIMES(x4,x3)
1.71/2.28	-> Pairs:
1.71/2.28	 TIMES(times(plus(x,y),z),x3) -> TIMES(plus(times(x,z),times(y,z)),x3)
1.71/2.28	 TIMES(times(z,plus(x,f(y))),x3) -> TIMES(g(z,y),plus(x,a))
1.71/2.28	 TIMES(plus(x,y),z) -> TIMES(x,z)
1.71/2.28	 TIMES(plus(x,y),z) -> TIMES(y,z)
1.71/2.28	 TIMES(z,plus(x,f(y))) -> TIMES(g(z,y),plus(x,a))
1.71/2.28	-> EAxioms:
1.71/2.28	 times(times(x3,x4),x5) = times(x3,times(x4,x5))
1.71/2.28	 times(x3,x4) = times(x4,x3)
1.71/2.28	 plus(plus(x3,x4),x5) = plus(x3,plus(x4,x5))
1.71/2.28	 plus(x3,x4) = plus(x4,x3)
1.71/2.28	-> Usable Equations:
1.71/2.28	 times(times(x3,x4),x5) = times(x3,times(x4,x5))
1.71/2.28	 times(x3,x4) = times(x4,x3)
1.71/2.28	 plus(plus(x3,x4),x5) = plus(x3,plus(x4,x5))
1.71/2.28	 plus(x3,x4) = plus(x4,x3)
1.71/2.28	-> Rules:
1.71/2.28	 times(plus(x,y),z) -> plus(times(x,z),times(y,z))
1.71/2.28	 times(z,plus(x,f(y))) -> times(g(z,y),plus(x,a))
1.71/2.28	-> Usable Rules:
1.71/2.28	 times(plus(x,y),z) -> plus(times(x,z),times(y,z))
1.71/2.28	 times(z,plus(x,f(y))) -> times(g(z,y),plus(x,a))
1.71/2.28	-> SRules:
1.71/2.28	 TIMES(times(x3,x4),x5) -> TIMES(x3,x4)
1.71/2.28	 TIMES(x3,times(x4,x5)) -> TIMES(x4,x5)
1.71/2.28	->Interpretation type:
1.71/2.28	 Simple mixed
1.71/2.28	->Coefficients:
1.71/2.28	 Natural Numbers
1.71/2.28	->Dimension:
1.71/2.28	 1
1.71/2.28	->Bound:
1.71/2.28	 1
1.71/2.28	->Interpretation:
1.71/2.28	 
1.71/2.28	[times](X1,X2) = X1.X2 + X1 + X2
1.71/2.28	[a] = 0
1.71/2.28	[f](X) = X + 1
1.71/2.28	[g](X1,X2) = X1
1.71/2.28	[plus](X1,X2) = X1 + X2 + 1
1.71/2.28	[TIMES](X1,X2) = X1.X2 + X1 + X2
1.71/2.28	[PLUS](X1,X2) = 0
1.71/2.28	
1.71/2.28	Problem 1: 
1.71/2.28	
1.71/2.28	SCC Processor:
1.71/2.28	-> FAxioms:
1.71/2.28	 TIMES(times(x3,x4),x5) = TIMES(x3,times(x4,x5))
1.71/2.28	 TIMES(x3,x4) = TIMES(x4,x3)
1.71/2.28	-> Pairs:
1.71/2.28	 TIMES(times(plus(x,y),z),x3) -> TIMES(plus(times(x,z),times(y,z)),x3)
1.71/2.28	 TIMES(plus(x,y),z) -> TIMES(x,z)
1.71/2.28	 TIMES(plus(x,y),z) -> TIMES(y,z)
1.71/2.28	 TIMES(z,plus(x,f(y))) -> TIMES(g(z,y),plus(x,a))
1.71/2.28	-> EAxioms:
1.71/2.28	 times(times(x3,x4),x5) = times(x3,times(x4,x5))
1.71/2.28	 times(x3,x4) = times(x4,x3)
1.71/2.28	 plus(plus(x3,x4),x5) = plus(x3,plus(x4,x5))
1.71/2.28	 plus(x3,x4) = plus(x4,x3)
1.71/2.28	-> Rules:
1.71/2.28	 times(plus(x,y),z) -> plus(times(x,z),times(y,z))
1.71/2.28	 times(z,plus(x,f(y))) -> times(g(z,y),plus(x,a))
1.71/2.28	-> SRules:
1.71/2.28	 TIMES(times(x3,x4),x5) -> TIMES(x3,x4)
1.71/2.28	 TIMES(x3,times(x4,x5)) -> TIMES(x4,x5)
1.71/2.28	->Strongly Connected Components:
1.71/2.28	->->Cycle:
1.71/2.28	->->-> Pairs:
1.71/2.28	 TIMES(times(plus(x,y),z),x3) -> TIMES(plus(times(x,z),times(y,z)),x3)
1.71/2.28	 TIMES(plus(x,y),z) -> TIMES(x,z)
1.71/2.28	 TIMES(plus(x,y),z) -> TIMES(y,z)
1.71/2.28	 TIMES(z,plus(x,f(y))) -> TIMES(g(z,y),plus(x,a))
1.71/2.28	-> FAxioms:
1.71/2.28	 times(times(x3,x4),x5) -> times(x3,times(x4,x5))
1.71/2.28	 times(x3,x4) -> times(x4,x3)
1.71/2.28	 plus(plus(x3,x4),x5) -> plus(x3,plus(x4,x5))
1.71/2.28	 plus(x3,x4) -> plus(x4,x3)
1.71/2.28	 TIMES(times(x3,x4),x5) -> TIMES(x3,times(x4,x5))
1.71/2.28	 TIMES(x3,x4) -> TIMES(x4,x3)
1.71/2.28	-> EAxioms:
1.71/2.28	 times(times(x3,x4),x5) = times(x3,times(x4,x5))
1.71/2.28	 times(x3,x4) = times(x4,x3)
1.71/2.28	 plus(plus(x3,x4),x5) = plus(x3,plus(x4,x5))
1.71/2.28	 plus(x3,x4) = plus(x4,x3)
1.71/2.28	->->-> Rules:
1.71/2.28	 times(plus(x,y),z) -> plus(times(x,z),times(y,z))
1.71/2.28	 times(z,plus(x,f(y))) -> times(g(z,y),plus(x,a))
1.71/2.28	-> SRules:
1.71/2.28	 TIMES(times(x3,x4),x5) -> TIMES(x3,x4)
1.71/2.28	 TIMES(x3,times(x4,x5)) -> TIMES(x4,x5)
1.71/2.28	
1.71/2.28	Problem 1: 
1.71/2.28	
1.71/2.28	Reduction Pairs Processor:
1.71/2.28	-> FAxioms:
1.71/2.28	 TIMES(times(x3,x4),x5) = TIMES(x3,times(x4,x5))
1.71/2.28	 TIMES(x3,x4) = TIMES(x4,x3)
1.71/2.28	-> Pairs:
1.71/2.28	 TIMES(times(plus(x,y),z),x3) -> TIMES(plus(times(x,z),times(y,z)),x3)
1.71/2.28	 TIMES(plus(x,y),z) -> TIMES(x,z)
1.71/2.28	 TIMES(plus(x,y),z) -> TIMES(y,z)
1.71/2.28	 TIMES(z,plus(x,f(y))) -> TIMES(g(z,y),plus(x,a))
1.71/2.28	-> EAxioms:
1.71/2.28	 times(times(x3,x4),x5) = times(x3,times(x4,x5))
1.71/2.28	 times(x3,x4) = times(x4,x3)
1.71/2.28	 plus(plus(x3,x4),x5) = plus(x3,plus(x4,x5))
1.71/2.28	 plus(x3,x4) = plus(x4,x3)
1.71/2.28	-> Usable Equations:
1.71/2.28	 times(times(x3,x4),x5) = times(x3,times(x4,x5))
1.71/2.28	 times(x3,x4) = times(x4,x3)
1.71/2.28	 plus(plus(x3,x4),x5) = plus(x3,plus(x4,x5))
1.71/2.28	 plus(x3,x4) = plus(x4,x3)
1.71/2.28	-> Rules:
1.71/2.28	 times(plus(x,y),z) -> plus(times(x,z),times(y,z))
1.71/2.28	 times(z,plus(x,f(y))) -> times(g(z,y),plus(x,a))
1.71/2.28	-> Usable Rules:
1.71/2.28	 times(plus(x,y),z) -> plus(times(x,z),times(y,z))
1.71/2.28	 times(z,plus(x,f(y))) -> times(g(z,y),plus(x,a))
1.71/2.28	-> SRules:
1.71/2.28	 TIMES(times(x3,x4),x5) -> TIMES(x3,x4)
1.71/2.28	 TIMES(x3,times(x4,x5)) -> TIMES(x4,x5)
1.71/2.28	->Interpretation type:
1.71/2.28	 Simple mixed
1.71/2.28	->Coefficients:
1.71/2.28	 Natural Numbers
1.71/2.28	->Dimension:
1.71/2.28	 1
1.71/2.28	->Bound:
1.71/2.28	 1
1.71/2.28	->Interpretation:
1.71/2.28	 
1.71/2.28	[times](X1,X2) = X1.X2 + X1 + X2
1.71/2.28	[a] = 1
1.71/2.28	[f](X) = X + 1
1.71/2.28	[g](X1,X2) = X1
1.71/2.28	[plus](X1,X2) = X1 + X2 + 1
1.71/2.28	[TIMES](X1,X2) = X1.X2 + X1 + X2
1.71/2.28	[PLUS](X1,X2) = 0
1.71/2.28	
1.71/2.28	Problem 1: 
1.71/2.28	
1.71/2.28	SCC Processor:
1.71/2.28	-> FAxioms:
1.71/2.28	 TIMES(times(x3,x4),x5) = TIMES(x3,times(x4,x5))
1.71/2.28	 TIMES(x3,x4) = TIMES(x4,x3)
1.71/2.28	-> Pairs:
1.71/2.28	 TIMES(times(plus(x,y),z),x3) -> TIMES(plus(times(x,z),times(y,z)),x3)
1.71/2.28	 TIMES(plus(x,y),z) -> TIMES(y,z)
1.71/2.28	 TIMES(z,plus(x,f(y))) -> TIMES(g(z,y),plus(x,a))
1.71/2.28	-> EAxioms:
1.71/2.28	 times(times(x3,x4),x5) = times(x3,times(x4,x5))
1.71/2.28	 times(x3,x4) = times(x4,x3)
1.71/2.28	 plus(plus(x3,x4),x5) = plus(x3,plus(x4,x5))
1.71/2.28	 plus(x3,x4) = plus(x4,x3)
1.71/2.28	-> Rules:
1.71/2.28	 times(plus(x,y),z) -> plus(times(x,z),times(y,z))
1.71/2.28	 times(z,plus(x,f(y))) -> times(g(z,y),plus(x,a))
1.71/2.28	-> SRules:
1.71/2.28	 TIMES(times(x3,x4),x5) -> TIMES(x3,x4)
1.71/2.28	 TIMES(x3,times(x4,x5)) -> TIMES(x4,x5)
1.71/2.28	->Strongly Connected Components:
1.71/2.28	->->Cycle:
1.71/2.28	->->-> Pairs:
1.71/2.28	 TIMES(times(plus(x,y),z),x3) -> TIMES(plus(times(x,z),times(y,z)),x3)
1.71/2.28	 TIMES(plus(x,y),z) -> TIMES(y,z)
1.71/2.28	 TIMES(z,plus(x,f(y))) -> TIMES(g(z,y),plus(x,a))
1.71/2.28	-> FAxioms:
1.71/2.28	 times(times(x3,x4),x5) -> times(x3,times(x4,x5))
1.71/2.28	 times(x3,x4) -> times(x4,x3)
1.71/2.28	 plus(plus(x3,x4),x5) -> plus(x3,plus(x4,x5))
1.71/2.28	 plus(x3,x4) -> plus(x4,x3)
1.71/2.28	 TIMES(times(x3,x4),x5) -> TIMES(x3,times(x4,x5))
1.71/2.28	 TIMES(x3,x4) -> TIMES(x4,x3)
1.71/2.28	-> EAxioms:
1.71/2.28	 times(times(x3,x4),x5) = times(x3,times(x4,x5))
1.71/2.28	 times(x3,x4) = times(x4,x3)
1.71/2.28	 plus(plus(x3,x4),x5) = plus(x3,plus(x4,x5))
1.71/2.28	 plus(x3,x4) = plus(x4,x3)
1.71/2.28	->->-> Rules:
1.71/2.28	 times(plus(x,y),z) -> plus(times(x,z),times(y,z))
1.71/2.28	 times(z,plus(x,f(y))) -> times(g(z,y),plus(x,a))
1.71/2.28	-> SRules:
1.71/2.28	 TIMES(times(x3,x4),x5) -> TIMES(x3,x4)
1.71/2.28	 TIMES(x3,times(x4,x5)) -> TIMES(x4,x5)
1.71/2.28	
1.71/2.28	Problem 1: 
1.71/2.28	
1.71/2.28	Reduction Pairs Processor:
1.71/2.28	-> FAxioms:
1.71/2.28	 TIMES(times(x3,x4),x5) = TIMES(x3,times(x4,x5))
1.71/2.28	 TIMES(x3,x4) = TIMES(x4,x3)
1.71/2.28	-> Pairs:
1.71/2.28	 TIMES(times(plus(x,y),z),x3) -> TIMES(plus(times(x,z),times(y,z)),x3)
1.71/2.28	 TIMES(plus(x,y),z) -> TIMES(y,z)
1.71/2.28	 TIMES(z,plus(x,f(y))) -> TIMES(g(z,y),plus(x,a))
1.71/2.28	-> EAxioms:
1.71/2.28	 times(times(x3,x4),x5) = times(x3,times(x4,x5))
1.71/2.28	 times(x3,x4) = times(x4,x3)
1.71/2.28	 plus(plus(x3,x4),x5) = plus(x3,plus(x4,x5))
1.71/2.28	 plus(x3,x4) = plus(x4,x3)
1.71/2.28	-> Usable Equations:
1.71/2.28	 times(times(x3,x4),x5) = times(x3,times(x4,x5))
1.71/2.28	 times(x3,x4) = times(x4,x3)
1.71/2.28	 plus(plus(x3,x4),x5) = plus(x3,plus(x4,x5))
1.71/2.28	 plus(x3,x4) = plus(x4,x3)
1.71/2.28	-> Rules:
1.71/2.28	 times(plus(x,y),z) -> plus(times(x,z),times(y,z))
1.71/2.28	 times(z,plus(x,f(y))) -> times(g(z,y),plus(x,a))
1.71/2.28	-> Usable Rules:
1.71/2.28	 times(plus(x,y),z) -> plus(times(x,z),times(y,z))
1.71/2.28	 times(z,plus(x,f(y))) -> times(g(z,y),plus(x,a))
1.71/2.28	-> SRules:
1.71/2.28	 TIMES(times(x3,x4),x5) -> TIMES(x3,x4)
1.71/2.28	 TIMES(x3,times(x4,x5)) -> TIMES(x4,x5)
1.71/2.28	->Interpretation type:
1.71/2.28	 Simple mixed
1.71/2.28	->Coefficients:
1.71/2.28	 Natural Numbers
1.71/2.28	->Dimension:
1.71/2.28	 1
1.71/2.28	->Bound:
1.71/2.28	 1
1.71/2.28	->Interpretation:
1.71/2.28	 
1.71/2.28	[times](X1,X2) = X1.X2 + X1 + X2
1.71/2.28	[a] = 1
1.71/2.28	[f](X) = X + 1
1.71/2.28	[g](X1,X2) = X1
1.71/2.28	[plus](X1,X2) = X1 + X2 + 1
1.71/2.28	[TIMES](X1,X2) = X1.X2 + X1 + X2
1.71/2.28	[PLUS](X1,X2) = 0
1.71/2.28	
1.71/2.28	Problem 1: 
1.71/2.28	
1.71/2.28	SCC Processor:
1.71/2.28	-> FAxioms:
1.71/2.28	 TIMES(times(x3,x4),x5) = TIMES(x3,times(x4,x5))
1.71/2.28	 TIMES(x3,x4) = TIMES(x4,x3)
1.71/2.28	-> Pairs:
1.71/2.28	 TIMES(times(plus(x,y),z),x3) -> TIMES(plus(times(x,z),times(y,z)),x3)
1.71/2.28	 TIMES(z,plus(x,f(y))) -> TIMES(g(z,y),plus(x,a))
1.71/2.28	-> EAxioms:
1.71/2.28	 times(times(x3,x4),x5) = times(x3,times(x4,x5))
1.71/2.28	 times(x3,x4) = times(x4,x3)
1.71/2.28	 plus(plus(x3,x4),x5) = plus(x3,plus(x4,x5))
1.71/2.28	 plus(x3,x4) = plus(x4,x3)
1.71/2.28	-> Rules:
1.71/2.28	 times(plus(x,y),z) -> plus(times(x,z),times(y,z))
1.71/2.28	 times(z,plus(x,f(y))) -> times(g(z,y),plus(x,a))
1.71/2.28	-> SRules:
1.71/2.28	 TIMES(times(x3,x4),x5) -> TIMES(x3,x4)
1.71/2.28	 TIMES(x3,times(x4,x5)) -> TIMES(x4,x5)
1.71/2.28	->Strongly Connected Components:
1.71/2.28	->->Cycle:
1.71/2.28	->->-> Pairs:
1.71/2.28	 TIMES(times(plus(x,y),z),x3) -> TIMES(plus(times(x,z),times(y,z)),x3)
1.83/2.28	 TIMES(z,plus(x,f(y))) -> TIMES(g(z,y),plus(x,a))
1.83/2.28	-> FAxioms:
1.83/2.28	 times(times(x3,x4),x5) -> times(x3,times(x4,x5))
1.83/2.28	 times(x3,x4) -> times(x4,x3)
1.83/2.28	 plus(plus(x3,x4),x5) -> plus(x3,plus(x4,x5))
1.83/2.28	 plus(x3,x4) -> plus(x4,x3)
1.83/2.28	 TIMES(times(x3,x4),x5) -> TIMES(x3,times(x4,x5))
1.83/2.28	 TIMES(x3,x4) -> TIMES(x4,x3)
1.83/2.28	-> EAxioms:
1.83/2.28	 times(times(x3,x4),x5) = times(x3,times(x4,x5))
1.83/2.28	 times(x3,x4) = times(x4,x3)
1.83/2.28	 plus(plus(x3,x4),x5) = plus(x3,plus(x4,x5))
1.83/2.28	 plus(x3,x4) = plus(x4,x3)
1.83/2.28	->->-> Rules:
1.83/2.28	 times(plus(x,y),z) -> plus(times(x,z),times(y,z))
1.83/2.28	 times(z,plus(x,f(y))) -> times(g(z,y),plus(x,a))
1.83/2.28	-> SRules:
1.83/2.28	 TIMES(times(x3,x4),x5) -> TIMES(x3,x4)
1.83/2.28	 TIMES(x3,times(x4,x5)) -> TIMES(x4,x5)
1.83/2.28	
1.83/2.28	Problem 1: 
1.83/2.28	
1.83/2.28	Reduction Pairs Processor:
1.83/2.28	-> FAxioms:
1.83/2.28	 TIMES(times(x3,x4),x5) = TIMES(x3,times(x4,x5))
1.83/2.28	 TIMES(x3,x4) = TIMES(x4,x3)
1.83/2.28	-> Pairs:
1.83/2.28	 TIMES(times(plus(x,y),z),x3) -> TIMES(plus(times(x,z),times(y,z)),x3)
1.83/2.28	 TIMES(z,plus(x,f(y))) -> TIMES(g(z,y),plus(x,a))
1.83/2.28	-> EAxioms:
1.83/2.28	 times(times(x3,x4),x5) = times(x3,times(x4,x5))
1.83/2.28	 times(x3,x4) = times(x4,x3)
1.83/2.28	 plus(plus(x3,x4),x5) = plus(x3,plus(x4,x5))
1.83/2.28	 plus(x3,x4) = plus(x4,x3)
1.83/2.28	-> Usable Equations:
1.83/2.28	 times(times(x3,x4),x5) = times(x3,times(x4,x5))
1.83/2.28	 times(x3,x4) = times(x4,x3)
1.83/2.28	 plus(plus(x3,x4),x5) = plus(x3,plus(x4,x5))
1.83/2.28	 plus(x3,x4) = plus(x4,x3)
1.83/2.28	-> Rules:
1.83/2.28	 times(plus(x,y),z) -> plus(times(x,z),times(y,z))
1.83/2.28	 times(z,plus(x,f(y))) -> times(g(z,y),plus(x,a))
1.83/2.28	-> Usable Rules:
1.83/2.28	 times(plus(x,y),z) -> plus(times(x,z),times(y,z))
1.83/2.28	 times(z,plus(x,f(y))) -> times(g(z,y),plus(x,a))
1.83/2.28	-> SRules:
1.83/2.28	 TIMES(times(x3,x4),x5) -> TIMES(x3,x4)
1.83/2.28	 TIMES(x3,times(x4,x5)) -> TIMES(x4,x5)
1.83/2.28	->Interpretation type:
1.83/2.28	 Linear
1.83/2.28	->Coefficients:
1.83/2.28	 Natural Numbers
1.83/2.28	->Dimension:
1.83/2.28	 1
1.83/2.28	->Bound:
1.83/2.28	 2
1.83/2.28	->Interpretation:
1.83/2.28	 
1.83/2.28	[times](X1,X2) = X1 + X2 + 2
1.83/2.28	[a] = 1
1.83/2.28	[f](X) = 2.X + 2
1.83/2.28	[g](X1,X2) = 0
1.83/2.28	[plus](X1,X2) = 2
1.83/2.28	[TIMES](X1,X2) = 2.X1 + 2.X2
1.83/2.28	[PLUS](X1,X2) = 0
1.83/2.28	
1.83/2.28	Problem 1: 
1.83/2.28	
1.83/2.28	SCC Processor:
1.83/2.28	-> FAxioms:
1.83/2.28	 TIMES(times(x3,x4),x5) = TIMES(x3,times(x4,x5))
1.83/2.28	 TIMES(x3,x4) = TIMES(x4,x3)
1.83/2.28	-> Pairs:
1.83/2.28	 TIMES(z,plus(x,f(y))) -> TIMES(g(z,y),plus(x,a))
1.83/2.28	-> EAxioms:
1.83/2.28	 times(times(x3,x4),x5) = times(x3,times(x4,x5))
1.83/2.28	 times(x3,x4) = times(x4,x3)
1.83/2.28	 plus(plus(x3,x4),x5) = plus(x3,plus(x4,x5))
1.83/2.28	 plus(x3,x4) = plus(x4,x3)
1.83/2.28	-> Rules:
1.83/2.28	 times(plus(x,y),z) -> plus(times(x,z),times(y,z))
1.83/2.28	 times(z,plus(x,f(y))) -> times(g(z,y),plus(x,a))
1.83/2.28	-> SRules:
1.83/2.28	 TIMES(times(x3,x4),x5) -> TIMES(x3,x4)
1.83/2.28	 TIMES(x3,times(x4,x5)) -> TIMES(x4,x5)
1.83/2.28	->Strongly Connected Components:
1.83/2.28	->->Cycle:
1.83/2.28	->->-> Pairs:
1.83/2.28	 TIMES(z,plus(x,f(y))) -> TIMES(g(z,y),plus(x,a))
1.83/2.28	-> FAxioms:
1.83/2.28	 times(times(x3,x4),x5) -> times(x3,times(x4,x5))
1.83/2.28	 times(x3,x4) -> times(x4,x3)
1.83/2.28	 plus(plus(x3,x4),x5) -> plus(x3,plus(x4,x5))
1.83/2.28	 plus(x3,x4) -> plus(x4,x3)
1.83/2.28	 TIMES(times(x3,x4),x5) -> TIMES(x3,times(x4,x5))
1.83/2.28	 TIMES(x3,x4) -> TIMES(x4,x3)
1.83/2.28	-> EAxioms:
1.83/2.28	 times(times(x3,x4),x5) = times(x3,times(x4,x5))
1.83/2.28	 times(x3,x4) = times(x4,x3)
1.83/2.28	 plus(plus(x3,x4),x5) = plus(x3,plus(x4,x5))
1.83/2.28	 plus(x3,x4) = plus(x4,x3)
1.83/2.28	->->-> Rules:
1.83/2.28	 times(plus(x,y),z) -> plus(times(x,z),times(y,z))
1.83/2.28	 times(z,plus(x,f(y))) -> times(g(z,y),plus(x,a))
1.83/2.28	-> SRules:
1.83/2.28	 TIMES(times(x3,x4),x5) -> TIMES(x3,x4)
1.83/2.28	 TIMES(x3,times(x4,x5)) -> TIMES(x4,x5)
1.83/2.28	
1.83/2.28	Problem 1: 
1.83/2.28	
1.83/2.28	Reduction Pairs Processor:
1.83/2.28	-> FAxioms:
1.83/2.28	 TIMES(times(x3,x4),x5) = TIMES(x3,times(x4,x5))
1.83/2.28	 TIMES(x3,x4) = TIMES(x4,x3)
1.83/2.28	-> Pairs:
1.83/2.28	 TIMES(z,plus(x,f(y))) -> TIMES(g(z,y),plus(x,a))
1.83/2.28	-> EAxioms:
1.83/2.28	 times(times(x3,x4),x5) = times(x3,times(x4,x5))
1.83/2.28	 times(x3,x4) = times(x4,x3)
1.83/2.28	 plus(plus(x3,x4),x5) = plus(x3,plus(x4,x5))
1.83/2.28	 plus(x3,x4) = plus(x4,x3)
1.83/2.28	-> Usable Equations:
1.83/2.28	 times(times(x3,x4),x5) = times(x3,times(x4,x5))
1.83/2.28	 times(x3,x4) = times(x4,x3)
1.83/2.28	 plus(plus(x3,x4),x5) = plus(x3,plus(x4,x5))
1.83/2.28	 plus(x3,x4) = plus(x4,x3)
1.83/2.28	-> Rules:
1.83/2.28	 times(plus(x,y),z) -> plus(times(x,z),times(y,z))
1.83/2.28	 times(z,plus(x,f(y))) -> times(g(z,y),plus(x,a))
1.83/2.28	-> Usable Rules:
1.83/2.28	 times(plus(x,y),z) -> plus(times(x,z),times(y,z))
1.83/2.28	 times(z,plus(x,f(y))) -> times(g(z,y),plus(x,a))
1.83/2.28	-> SRules:
1.83/2.28	 TIMES(times(x3,x4),x5) -> TIMES(x3,x4)
1.83/2.28	 TIMES(x3,times(x4,x5)) -> TIMES(x4,x5)
1.83/2.28	->Interpretation type:
1.83/2.28	 Linear
1.83/2.28	->Coefficients:
1.83/2.28	 Natural Numbers
1.83/2.28	->Dimension:
1.83/2.28	 1
1.83/2.28	->Bound:
1.83/2.28	 2
1.83/2.28	->Interpretation:
1.83/2.28	 
1.83/2.28	[times](X1,X2) = X1 + X2 + 2
1.83/2.28	[a] = 2
1.83/2.28	[f](X) = 2.X + 2
1.83/2.28	[g](X1,X2) = 0
1.83/2.28	[plus](X1,X2) = 0
1.83/2.28	[TIMES](X1,X2) = X1 + X2
1.83/2.28	[PLUS](X1,X2) = 0
1.83/2.28	
1.83/2.28	Problem 1: 
1.83/2.28	
1.83/2.28	SCC Processor:
1.83/2.28	-> FAxioms:
1.83/2.28	 TIMES(times(x3,x4),x5) = TIMES(x3,times(x4,x5))
1.83/2.28	 TIMES(x3,x4) = TIMES(x4,x3)
1.83/2.28	-> Pairs:
1.83/2.28	 TIMES(z,plus(x,f(y))) -> TIMES(g(z,y),plus(x,a))
1.83/2.28	-> EAxioms:
1.83/2.28	 times(times(x3,x4),x5) = times(x3,times(x4,x5))
1.83/2.28	 times(x3,x4) = times(x4,x3)
1.83/2.28	 plus(plus(x3,x4),x5) = plus(x3,plus(x4,x5))
1.83/2.28	 plus(x3,x4) = plus(x4,x3)
1.83/2.28	-> Rules:
1.83/2.28	 times(plus(x,y),z) -> plus(times(x,z),times(y,z))
1.83/2.28	 times(z,plus(x,f(y))) -> times(g(z,y),plus(x,a))
1.83/2.28	-> SRules:
1.83/2.28	 TIMES(x3,times(x4,x5)) -> TIMES(x4,x5)
1.83/2.28	->Strongly Connected Components:
1.83/2.28	->->Cycle:
1.83/2.28	->->-> Pairs:
1.83/2.28	 TIMES(z,plus(x,f(y))) -> TIMES(g(z,y),plus(x,a))
1.83/2.28	-> FAxioms:
1.83/2.28	 times(times(x3,x4),x5) -> times(x3,times(x4,x5))
1.83/2.28	 times(x3,x4) -> times(x4,x3)
1.83/2.28	 plus(plus(x3,x4),x5) -> plus(x3,plus(x4,x5))
1.83/2.28	 plus(x3,x4) -> plus(x4,x3)
1.83/2.28	 TIMES(times(x3,x4),x5) -> TIMES(x3,times(x4,x5))
1.83/2.28	 TIMES(x3,x4) -> TIMES(x4,x3)
1.83/2.28	-> EAxioms:
1.83/2.28	 times(times(x3,x4),x5) = times(x3,times(x4,x5))
1.83/2.28	 times(x3,x4) = times(x4,x3)
1.83/2.28	 plus(plus(x3,x4),x5) = plus(x3,plus(x4,x5))
1.83/2.28	 plus(x3,x4) = plus(x4,x3)
1.83/2.28	->->-> Rules:
1.83/2.28	 times(plus(x,y),z) -> plus(times(x,z),times(y,z))
1.83/2.28	 times(z,plus(x,f(y))) -> times(g(z,y),plus(x,a))
1.83/2.28	-> SRules:
1.83/2.28	 TIMES(x3,times(x4,x5)) -> TIMES(x4,x5)
1.83/2.28	
1.83/2.28	Problem 1: 
1.83/2.28	
1.83/2.28	Reduction Pairs Processor:
1.83/2.28	-> FAxioms:
1.83/2.28	 TIMES(times(x3,x4),x5) = TIMES(x3,times(x4,x5))
1.83/2.28	 TIMES(x3,x4) = TIMES(x4,x3)
1.83/2.28	-> Pairs:
1.83/2.28	 TIMES(z,plus(x,f(y))) -> TIMES(g(z,y),plus(x,a))
1.83/2.28	-> EAxioms:
1.83/2.28	 times(times(x3,x4),x5) = times(x3,times(x4,x5))
1.83/2.28	 times(x3,x4) = times(x4,x3)
1.83/2.28	 plus(plus(x3,x4),x5) = plus(x3,plus(x4,x5))
1.83/2.28	 plus(x3,x4) = plus(x4,x3)
1.83/2.28	-> Usable Equations:
1.83/2.28	 times(times(x3,x4),x5) = times(x3,times(x4,x5))
1.83/2.28	 times(x3,x4) = times(x4,x3)
1.83/2.28	 plus(plus(x3,x4),x5) = plus(x3,plus(x4,x5))
1.83/2.28	 plus(x3,x4) = plus(x4,x3)
1.83/2.28	-> Rules:
1.83/2.28	 times(plus(x,y),z) -> plus(times(x,z),times(y,z))
1.83/2.28	 times(z,plus(x,f(y))) -> times(g(z,y),plus(x,a))
1.83/2.28	-> Usable Rules:
1.83/2.28	 times(plus(x,y),z) -> plus(times(x,z),times(y,z))
1.83/2.28	 times(z,plus(x,f(y))) -> times(g(z,y),plus(x,a))
1.83/2.28	-> SRules:
1.83/2.28	 TIMES(x3,times(x4,x5)) -> TIMES(x4,x5)
1.83/2.28	->Interpretation type:
1.83/2.28	 Linear
1.83/2.28	->Coefficients:
1.83/2.28	 Natural Numbers
1.83/2.28	->Dimension:
1.83/2.28	 1
1.83/2.28	->Bound:
1.83/2.28	 2
1.83/2.28	->Interpretation:
1.83/2.28	 
1.83/2.28	[times](X1,X2) = X1 + X2 + 1
1.83/2.28	[a] = 2
1.83/2.28	[f](X) = 2.X + 1
1.83/2.28	[g](X1,X2) = 0
1.83/2.28	[plus](X1,X2) = 0
1.83/2.28	[TIMES](X1,X2) = 2.X1 + 2.X2
1.83/2.28	[PLUS](X1,X2) = 0
1.83/2.28	
1.83/2.28	Problem 1: 
1.83/2.28	
1.83/2.28	SCC Processor:
1.83/2.28	-> FAxioms:
1.83/2.28	 TIMES(times(x3,x4),x5) = TIMES(x3,times(x4,x5))
1.83/2.28	 TIMES(x3,x4) = TIMES(x4,x3)
1.83/2.28	-> Pairs:
1.83/2.28	 TIMES(z,plus(x,f(y))) -> TIMES(g(z,y),plus(x,a))
1.83/2.28	-> EAxioms:
1.83/2.28	 times(times(x3,x4),x5) = times(x3,times(x4,x5))
1.83/2.28	 times(x3,x4) = times(x4,x3)
1.83/2.28	 plus(plus(x3,x4),x5) = plus(x3,plus(x4,x5))
1.83/2.28	 plus(x3,x4) = plus(x4,x3)
1.83/2.28	-> Rules:
1.83/2.28	 times(plus(x,y),z) -> plus(times(x,z),times(y,z))
1.83/2.28	 times(z,plus(x,f(y))) -> times(g(z,y),plus(x,a))
1.83/2.28	-> SRules:
1.83/2.28	 Empty
1.83/2.28	->Strongly Connected Components:
1.83/2.28	->->Cycle:
1.83/2.28	->->-> Pairs:
1.83/2.28	 TIMES(z,plus(x,f(y))) -> TIMES(g(z,y),plus(x,a))
1.83/2.28	-> FAxioms:
1.83/2.28	 times(times(x3,x4),x5) -> times(x3,times(x4,x5))
1.83/2.28	 times(x3,x4) -> times(x4,x3)
1.83/2.28	 plus(plus(x3,x4),x5) -> plus(x3,plus(x4,x5))
1.83/2.28	 plus(x3,x4) -> plus(x4,x3)
1.83/2.28	 TIMES(times(x3,x4),x5) -> TIMES(x3,times(x4,x5))
1.83/2.28	 TIMES(x3,x4) -> TIMES(x4,x3)
1.83/2.28	-> EAxioms:
1.83/2.28	 times(times(x3,x4),x5) = times(x3,times(x4,x5))
1.83/2.28	 times(x3,x4) = times(x4,x3)
1.83/2.28	 plus(plus(x3,x4),x5) = plus(x3,plus(x4,x5))
1.83/2.28	 plus(x3,x4) = plus(x4,x3)
1.83/2.28	->->-> Rules:
1.83/2.28	 times(plus(x,y),z) -> plus(times(x,z),times(y,z))
1.83/2.28	 times(z,plus(x,f(y))) -> times(g(z,y),plus(x,a))
1.83/2.28	-> SRules:
1.83/2.28	 Empty
1.83/2.28	
1.83/2.28	Problem 1: 
1.83/2.28	
1.83/2.28	Reduction Pairs Processor:
1.83/2.28	-> FAxioms:
1.83/2.28	 TIMES(times(x3,x4),x5) = TIMES(x3,times(x4,x5))
1.83/2.28	 TIMES(x3,x4) = TIMES(x4,x3)
1.83/2.28	-> Pairs:
1.83/2.28	 TIMES(z,plus(x,f(y))) -> TIMES(g(z,y),plus(x,a))
1.83/2.28	-> EAxioms:
1.83/2.28	 times(times(x3,x4),x5) = times(x3,times(x4,x5))
1.83/2.28	 times(x3,x4) = times(x4,x3)
1.83/2.28	 plus(plus(x3,x4),x5) = plus(x3,plus(x4,x5))
1.83/2.28	 plus(x3,x4) = plus(x4,x3)
1.83/2.28	-> Usable Equations:
1.83/2.28	 times(times(x3,x4),x5) = times(x3,times(x4,x5))
1.83/2.28	 times(x3,x4) = times(x4,x3)
1.83/2.28	 plus(plus(x3,x4),x5) = plus(x3,plus(x4,x5))
1.83/2.28	 plus(x3,x4) = plus(x4,x3)
1.83/2.28	-> Rules:
1.83/2.28	 times(plus(x,y),z) -> plus(times(x,z),times(y,z))
1.83/2.28	 times(z,plus(x,f(y))) -> times(g(z,y),plus(x,a))
1.83/2.28	-> Usable Rules:
1.83/2.28	 times(plus(x,y),z) -> plus(times(x,z),times(y,z))
1.83/2.28	 times(z,plus(x,f(y))) -> times(g(z,y),plus(x,a))
1.83/2.28	-> SRules:
1.83/2.28	 Empty
1.83/2.28	->Interpretation type:
1.83/2.28	 Simple mixed
1.83/2.28	->Coefficients:
1.83/2.28	 Natural Numbers
1.83/2.28	->Dimension:
1.83/2.28	 1
1.83/2.28	->Bound:
1.83/2.28	 1
1.83/2.28	->Interpretation:
1.83/2.28	 
1.83/2.28	[times](X1,X2) = X1.X2 + X1 + X2
1.83/2.28	[a] = 0
1.83/2.28	[f](X) = X + 1
1.83/2.28	[g](X1,X2) = X1
1.83/2.28	[plus](X1,X2) = X1 + X2 + 1
1.83/2.28	[TIMES](X1,X2) = X1.X2 + X1 + X2
1.83/2.28	[PLUS](X1,X2) = 0
1.83/2.28	
1.83/2.28	Problem 1: 
1.83/2.28	
1.83/2.28	SCC Processor:
1.83/2.28	-> FAxioms:
1.83/2.28	 TIMES(times(x3,x4),x5) = TIMES(x3,times(x4,x5))
1.83/2.28	 TIMES(x3,x4) = TIMES(x4,x3)
1.83/2.28	-> Pairs:
1.83/2.28	 Empty
1.83/2.28	-> EAxioms:
1.83/2.28	 times(times(x3,x4),x5) = times(x3,times(x4,x5))
1.83/2.28	 times(x3,x4) = times(x4,x3)
1.83/2.28	 plus(plus(x3,x4),x5) = plus(x3,plus(x4,x5))
1.83/2.28	 plus(x3,x4) = plus(x4,x3)
1.83/2.28	-> Rules:
1.83/2.28	 times(plus(x,y),z) -> plus(times(x,z),times(y,z))
1.83/2.28	 times(z,plus(x,f(y))) -> times(g(z,y),plus(x,a))
1.83/2.28	-> SRules:
1.83/2.28	 Empty
1.83/2.28	->Strongly Connected Components:
1.83/2.28	 There is no strongly connected component
1.83/2.28	
1.83/2.28	The problem is finite.
1.83/2.28	EOF