3.07/4.08	YES
3.07/4.08	
3.07/4.08	Problem 1: 
3.07/4.08	
3.07/4.08	(VAR x y z)
3.07/4.08	(THEORY 
3.07/4.08	(AC and or)
3.07/4.08	(C eq neq))
3.07/4.08	(RULES
3.07/4.08	and(x,or(x,y)) -> x
3.07/4.08	and(x,false) -> false
3.07/4.08	and(x,true) -> x
3.07/4.08	and(x,x) -> x
3.07/4.08	eq(x,x) -> true
3.07/4.08	neq(x,x) -> false
3.07/4.08	not(and(x,y)) -> or(not(x),not(y))
3.07/4.08	not(eq(x,y)) -> neq(x,y)
3.07/4.08	not(neq(x,y)) -> eq(x,y)
3.07/4.08	not(not(x)) -> x
3.07/4.08	not(or(x,y)) -> and(not(x),not(y))
3.07/4.08	not(false) -> true
3.07/4.08	not(true) -> false
3.07/4.08	or(and(x,y),z) -> and(or(x,z),or(y,z))
3.07/4.08	or(x,false) -> x
3.07/4.08	or(x,true) -> true
3.07/4.08	or(x,x) -> x
3.07/4.08	)
3.07/4.08	
3.07/4.08	Problem 1: 
3.07/4.08	
3.07/4.08	Dependency Pairs Processor:
3.07/4.08	-> FAxioms:
3.07/4.08	 AND(and(x3,x4),x5) = AND(x3,and(x4,x5))
3.07/4.08	 AND(x3,x4) = AND(x4,x3)
3.07/4.08	 EQ(x3,x4) = EQ(x4,x3)
3.07/4.08	 NEQ(x3,x4) = NEQ(x4,x3)
3.07/4.08	 OR(or(x3,x4),x5) = OR(x3,or(x4,x5))
3.07/4.08	 OR(x3,x4) = OR(x4,x3)
3.07/4.08	-> Pairs:
3.07/4.08	 AND(and(x,or(x,y)),x3) -> AND(x,x3)
3.07/4.08	 AND(and(x,false),x3) -> AND(false,x3)
3.07/4.08	 AND(and(x,true),x3) -> AND(x,x3)
3.07/4.08	 AND(and(x,x),x3) -> AND(x,x3)
3.07/4.08	 NOT(and(x,y)) -> NOT(x)
3.07/4.08	 NOT(and(x,y)) -> NOT(y)
3.07/4.08	 NOT(and(x,y)) -> OR(not(x),not(y))
3.07/4.08	 NOT(eq(x,y)) -> NEQ(x,y)
3.07/4.08	 NOT(neq(x,y)) -> EQ(x,y)
3.07/4.08	 NOT(or(x,y)) -> AND(not(x),not(y))
3.07/4.08	 NOT(or(x,y)) -> NOT(x)
3.07/4.08	 NOT(or(x,y)) -> NOT(y)
3.07/4.08	 OR(and(x,y),z) -> AND(or(x,z),or(y,z))
3.07/4.08	 OR(and(x,y),z) -> OR(x,z)
3.07/4.08	 OR(and(x,y),z) -> OR(y,z)
3.07/4.08	 OR(or(and(x,y),z),x3) -> AND(or(x,z),or(y,z))
3.07/4.08	 OR(or(and(x,y),z),x3) -> OR(and(or(x,z),or(y,z)),x3)
3.07/4.08	 OR(or(and(x,y),z),x3) -> OR(x,z)
3.07/4.08	 OR(or(and(x,y),z),x3) -> OR(y,z)
3.07/4.08	 OR(or(x,false),x3) -> OR(x,x3)
3.07/4.08	 OR(or(x,true),x3) -> OR(true,x3)
3.07/4.08	 OR(or(x,x),x3) -> OR(x,x3)
3.07/4.08	-> EAxioms:
3.07/4.08	 and(and(x3,x4),x5) = and(x3,and(x4,x5))
3.07/4.08	 and(x3,x4) = and(x4,x3)
3.07/4.08	 eq(x3,x4) = eq(x4,x3)
3.07/4.08	 neq(x3,x4) = neq(x4,x3)
3.07/4.08	 or(or(x3,x4),x5) = or(x3,or(x4,x5))
3.07/4.08	 or(x3,x4) = or(x4,x3)
3.07/4.08	-> Rules:
3.07/4.08	 and(x,or(x,y)) -> x
3.07/4.08	 and(x,false) -> false
3.07/4.08	 and(x,true) -> x
3.07/4.08	 and(x,x) -> x
3.07/4.08	 eq(x,x) -> true
3.07/4.08	 neq(x,x) -> false
3.07/4.08	 not(and(x,y)) -> or(not(x),not(y))
3.07/4.08	 not(eq(x,y)) -> neq(x,y)
3.07/4.08	 not(neq(x,y)) -> eq(x,y)
3.07/4.08	 not(not(x)) -> x
3.07/4.08	 not(or(x,y)) -> and(not(x),not(y))
3.07/4.08	 not(false) -> true
3.07/4.08	 not(true) -> false
3.07/4.08	 or(and(x,y),z) -> and(or(x,z),or(y,z))
3.07/4.08	 or(x,false) -> x
3.07/4.08	 or(x,true) -> true
3.07/4.08	 or(x,x) -> x
3.07/4.08	-> SRules:
3.07/4.08	 AND(and(x3,x4),x5) -> AND(x3,x4)
3.07/4.08	 AND(x3,and(x4,x5)) -> AND(x4,x5)
3.07/4.08	 OR(or(x3,x4),x5) -> OR(x3,x4)
3.07/4.08	 OR(x3,or(x4,x5)) -> OR(x4,x5)
3.07/4.08	
3.07/4.08	Problem 1: 
3.07/4.08	
3.07/4.08	SCC Processor:
3.07/4.08	-> FAxioms:
3.07/4.08	 AND(and(x3,x4),x5) = AND(x3,and(x4,x5))
3.07/4.08	 AND(x3,x4) = AND(x4,x3)
3.07/4.08	 EQ(x3,x4) = EQ(x4,x3)
3.07/4.08	 NEQ(x3,x4) = NEQ(x4,x3)
3.07/4.08	 OR(or(x3,x4),x5) = OR(x3,or(x4,x5))
3.07/4.08	 OR(x3,x4) = OR(x4,x3)
3.07/4.08	-> Pairs:
3.07/4.08	 AND(and(x,or(x,y)),x3) -> AND(x,x3)
3.07/4.08	 AND(and(x,false),x3) -> AND(false,x3)
3.07/4.08	 AND(and(x,true),x3) -> AND(x,x3)
3.07/4.08	 AND(and(x,x),x3) -> AND(x,x3)
3.07/4.08	 NOT(and(x,y)) -> NOT(x)
3.07/4.08	 NOT(and(x,y)) -> NOT(y)
3.07/4.08	 NOT(and(x,y)) -> OR(not(x),not(y))
3.07/4.08	 NOT(eq(x,y)) -> NEQ(x,y)
3.07/4.08	 NOT(neq(x,y)) -> EQ(x,y)
3.07/4.08	 NOT(or(x,y)) -> AND(not(x),not(y))
3.07/4.08	 NOT(or(x,y)) -> NOT(x)
3.07/4.08	 NOT(or(x,y)) -> NOT(y)
3.07/4.08	 OR(and(x,y),z) -> AND(or(x,z),or(y,z))
3.07/4.08	 OR(and(x,y),z) -> OR(x,z)
3.07/4.08	 OR(and(x,y),z) -> OR(y,z)
3.07/4.08	 OR(or(and(x,y),z),x3) -> AND(or(x,z),or(y,z))
3.07/4.08	 OR(or(and(x,y),z),x3) -> OR(and(or(x,z),or(y,z)),x3)
3.07/4.08	 OR(or(and(x,y),z),x3) -> OR(x,z)
3.07/4.08	 OR(or(and(x,y),z),x3) -> OR(y,z)
3.07/4.08	 OR(or(x,false),x3) -> OR(x,x3)
3.07/4.08	 OR(or(x,true),x3) -> OR(true,x3)
3.07/4.08	 OR(or(x,x),x3) -> OR(x,x3)
3.07/4.08	-> EAxioms:
3.07/4.08	 and(and(x3,x4),x5) = and(x3,and(x4,x5))
3.07/4.08	 and(x3,x4) = and(x4,x3)
3.07/4.08	 eq(x3,x4) = eq(x4,x3)
3.07/4.08	 neq(x3,x4) = neq(x4,x3)
3.07/4.08	 or(or(x3,x4),x5) = or(x3,or(x4,x5))
3.07/4.08	 or(x3,x4) = or(x4,x3)
3.07/4.08	-> Rules:
3.07/4.08	 and(x,or(x,y)) -> x
3.07/4.08	 and(x,false) -> false
3.07/4.08	 and(x,true) -> x
3.07/4.08	 and(x,x) -> x
3.07/4.08	 eq(x,x) -> true
3.07/4.08	 neq(x,x) -> false
3.07/4.08	 not(and(x,y)) -> or(not(x),not(y))
3.07/4.08	 not(eq(x,y)) -> neq(x,y)
3.07/4.08	 not(neq(x,y)) -> eq(x,y)
3.07/4.08	 not(not(x)) -> x
3.07/4.08	 not(or(x,y)) -> and(not(x),not(y))
3.07/4.08	 not(false) -> true
3.07/4.08	 not(true) -> false
3.07/4.08	 or(and(x,y),z) -> and(or(x,z),or(y,z))
3.07/4.08	 or(x,false) -> x
3.07/4.08	 or(x,true) -> true
3.07/4.08	 or(x,x) -> x
3.07/4.08	-> SRules:
3.07/4.08	 AND(and(x3,x4),x5) -> AND(x3,x4)
3.07/4.08	 AND(x3,and(x4,x5)) -> AND(x4,x5)
3.07/4.08	 OR(or(x3,x4),x5) -> OR(x3,x4)
3.07/4.08	 OR(x3,or(x4,x5)) -> OR(x4,x5)
3.07/4.08	->Strongly Connected Components:
3.07/4.08	->->Cycle:
3.07/4.08	->->-> Pairs:
3.07/4.08	 AND(and(x,or(x,y)),x3) -> AND(x,x3)
3.07/4.08	 AND(and(x,false),x3) -> AND(false,x3)
3.07/4.08	 AND(and(x,true),x3) -> AND(x,x3)
3.07/4.08	 AND(and(x,x),x3) -> AND(x,x3)
3.07/4.08	-> FAxioms:
3.07/4.08	 and(and(x3,x4),x5) -> and(x3,and(x4,x5))
3.07/4.08	 and(x3,x4) -> and(x4,x3)
3.07/4.08	 eq(x3,x4) -> eq(x4,x3)
3.07/4.08	 neq(x3,x4) -> neq(x4,x3)
3.07/4.08	 or(or(x3,x4),x5) -> or(x3,or(x4,x5))
3.07/4.08	 or(x3,x4) -> or(x4,x3)
3.07/4.08	 AND(and(x3,x4),x5) -> AND(x3,and(x4,x5))
3.07/4.08	 AND(x3,x4) -> AND(x4,x3)
3.07/4.08	-> EAxioms:
3.07/4.08	 and(and(x3,x4),x5) = and(x3,and(x4,x5))
3.07/4.08	 and(x3,x4) = and(x4,x3)
3.07/4.08	 eq(x3,x4) = eq(x4,x3)
3.07/4.08	 neq(x3,x4) = neq(x4,x3)
3.07/4.08	 or(or(x3,x4),x5) = or(x3,or(x4,x5))
3.07/4.08	 or(x3,x4) = or(x4,x3)
3.07/4.08	->->-> Rules:
3.07/4.08	 and(x,or(x,y)) -> x
3.07/4.08	 and(x,false) -> false
3.07/4.08	 and(x,true) -> x
3.07/4.08	 and(x,x) -> x
3.07/4.08	 eq(x,x) -> true
3.07/4.08	 neq(x,x) -> false
3.07/4.08	 not(and(x,y)) -> or(not(x),not(y))
3.07/4.08	 not(eq(x,y)) -> neq(x,y)
3.07/4.08	 not(neq(x,y)) -> eq(x,y)
3.07/4.08	 not(not(x)) -> x
3.07/4.08	 not(or(x,y)) -> and(not(x),not(y))
3.07/4.08	 not(false) -> true
3.07/4.08	 not(true) -> false
3.07/4.08	 or(and(x,y),z) -> and(or(x,z),or(y,z))
3.07/4.08	 or(x,false) -> x
3.07/4.08	 or(x,true) -> true
3.07/4.08	 or(x,x) -> x
3.07/4.08	-> SRules:
3.07/4.08	 AND(and(x3,x4),x5) -> AND(x3,x4)
3.07/4.08	 AND(x3,and(x4,x5)) -> AND(x4,x5)
3.07/4.08	->->Cycle:
3.07/4.08	->->-> Pairs:
3.07/4.08	 OR(and(x,y),z) -> OR(x,z)
3.07/4.08	 OR(and(x,y),z) -> OR(y,z)
3.07/4.08	 OR(or(and(x,y),z),x3) -> OR(and(or(x,z),or(y,z)),x3)
3.07/4.08	 OR(or(and(x,y),z),x3) -> OR(x,z)
3.07/4.08	 OR(or(and(x,y),z),x3) -> OR(y,z)
3.07/4.08	 OR(or(x,false),x3) -> OR(x,x3)
3.07/4.08	 OR(or(x,true),x3) -> OR(true,x3)
3.07/4.08	 OR(or(x,x),x3) -> OR(x,x3)
3.07/4.08	-> FAxioms:
3.07/4.08	 and(and(x3,x4),x5) -> and(x3,and(x4,x5))
3.07/4.08	 and(x3,x4) -> and(x4,x3)
3.07/4.08	 eq(x3,x4) -> eq(x4,x3)
3.07/4.08	 neq(x3,x4) -> neq(x4,x3)
3.07/4.08	 or(or(x3,x4),x5) -> or(x3,or(x4,x5))
3.07/4.08	 or(x3,x4) -> or(x4,x3)
3.07/4.08	 OR(or(x3,x4),x5) -> OR(x3,or(x4,x5))
3.07/4.08	 OR(x3,x4) -> OR(x4,x3)
3.07/4.08	-> EAxioms:
3.07/4.08	 and(and(x3,x4),x5) = and(x3,and(x4,x5))
3.07/4.08	 and(x3,x4) = and(x4,x3)
3.07/4.08	 eq(x3,x4) = eq(x4,x3)
3.07/4.08	 neq(x3,x4) = neq(x4,x3)
3.07/4.08	 or(or(x3,x4),x5) = or(x3,or(x4,x5))
3.07/4.08	 or(x3,x4) = or(x4,x3)
3.07/4.08	->->-> Rules:
3.07/4.08	 and(x,or(x,y)) -> x
3.07/4.08	 and(x,false) -> false
3.07/4.08	 and(x,true) -> x
3.07/4.08	 and(x,x) -> x
3.07/4.08	 eq(x,x) -> true
3.07/4.08	 neq(x,x) -> false
3.07/4.08	 not(and(x,y)) -> or(not(x),not(y))
3.07/4.08	 not(eq(x,y)) -> neq(x,y)
3.07/4.08	 not(neq(x,y)) -> eq(x,y)
3.07/4.08	 not(not(x)) -> x
3.07/4.08	 not(or(x,y)) -> and(not(x),not(y))
3.07/4.08	 not(false) -> true
3.07/4.08	 not(true) -> false
3.07/4.08	 or(and(x,y),z) -> and(or(x,z),or(y,z))
3.07/4.08	 or(x,false) -> x
3.07/4.08	 or(x,true) -> true
3.07/4.08	 or(x,x) -> x
3.07/4.08	-> SRules:
3.07/4.08	 OR(or(x3,x4),x5) -> OR(x3,x4)
3.07/4.08	 OR(x3,or(x4,x5)) -> OR(x4,x5)
3.07/4.08	->->Cycle:
3.07/4.08	->->-> Pairs:
3.07/4.08	 NOT(and(x,y)) -> NOT(x)
3.07/4.08	 NOT(and(x,y)) -> NOT(y)
3.07/4.08	 NOT(or(x,y)) -> NOT(x)
3.07/4.08	 NOT(or(x,y)) -> NOT(y)
3.07/4.08	-> FAxioms:
3.07/4.08	 and(and(x3,x4),x5) -> and(x3,and(x4,x5))
3.07/4.08	 and(x3,x4) -> and(x4,x3)
3.07/4.08	 eq(x3,x4) -> eq(x4,x3)
3.07/4.08	 neq(x3,x4) -> neq(x4,x3)
3.07/4.08	 or(or(x3,x4),x5) -> or(x3,or(x4,x5))
3.07/4.08	 or(x3,x4) -> or(x4,x3)
3.07/4.08	-> EAxioms:
3.07/4.08	 and(and(x3,x4),x5) = and(x3,and(x4,x5))
3.07/4.08	 and(x3,x4) = and(x4,x3)
3.07/4.08	 eq(x3,x4) = eq(x4,x3)
3.07/4.08	 neq(x3,x4) = neq(x4,x3)
3.07/4.08	 or(or(x3,x4),x5) = or(x3,or(x4,x5))
3.07/4.08	 or(x3,x4) = or(x4,x3)
3.07/4.08	->->-> Rules:
3.07/4.08	 and(x,or(x,y)) -> x
3.07/4.08	 and(x,false) -> false
3.07/4.08	 and(x,true) -> x
3.07/4.08	 and(x,x) -> x
3.07/4.08	 eq(x,x) -> true
3.07/4.08	 neq(x,x) -> false
3.07/4.08	 not(and(x,y)) -> or(not(x),not(y))
3.07/4.08	 not(eq(x,y)) -> neq(x,y)
3.07/4.08	 not(neq(x,y)) -> eq(x,y)
3.07/4.08	 not(not(x)) -> x
3.07/4.08	 not(or(x,y)) -> and(not(x),not(y))
3.07/4.08	 not(false) -> true
3.07/4.08	 not(true) -> false
3.07/4.08	 or(and(x,y),z) -> and(or(x,z),or(y,z))
3.07/4.08	 or(x,false) -> x
3.07/4.08	 or(x,true) -> true
3.07/4.08	 or(x,x) -> x
3.07/4.08	-> SRules:
3.07/4.08	 Empty
3.07/4.08	
3.07/4.08	
3.07/4.08	The problem is decomposed in 3 subproblems.
3.07/4.08	
3.07/4.08	Problem 1.1: 
3.07/4.08	
3.07/4.08	Reduction Pairs Processor:
3.07/4.08	-> FAxioms:
3.07/4.08	 AND(and(x3,x4),x5) = AND(x3,and(x4,x5))
3.07/4.08	 AND(x3,x4) = AND(x4,x3)
3.07/4.08	-> Pairs:
3.07/4.08	 AND(and(x,or(x,y)),x3) -> AND(x,x3)
3.07/4.08	 AND(and(x,false),x3) -> AND(false,x3)
3.07/4.08	 AND(and(x,true),x3) -> AND(x,x3)
3.07/4.08	 AND(and(x,x),x3) -> AND(x,x3)
3.07/4.08	-> EAxioms:
3.07/4.08	 and(and(x3,x4),x5) = and(x3,and(x4,x5))
3.07/4.08	 and(x3,x4) = and(x4,x3)
3.07/4.08	 eq(x3,x4) = eq(x4,x3)
3.07/4.08	 neq(x3,x4) = neq(x4,x3)
3.07/4.08	 or(or(x3,x4),x5) = or(x3,or(x4,x5))
3.07/4.08	 or(x3,x4) = or(x4,x3)
3.07/4.08	-> Usable Equations:
3.07/4.08	 and(and(x3,x4),x5) = and(x3,and(x4,x5))
3.07/4.08	 and(x3,x4) = and(x4,x3)
3.07/4.08	-> Rules:
3.07/4.08	 and(x,or(x,y)) -> x
3.07/4.08	 and(x,false) -> false
3.07/4.08	 and(x,true) -> x
3.07/4.08	 and(x,x) -> x
3.07/4.08	 eq(x,x) -> true
3.07/4.08	 neq(x,x) -> false
3.07/4.08	 not(and(x,y)) -> or(not(x),not(y))
3.07/4.08	 not(eq(x,y)) -> neq(x,y)
3.07/4.08	 not(neq(x,y)) -> eq(x,y)
3.07/4.08	 not(not(x)) -> x
3.07/4.08	 not(or(x,y)) -> and(not(x),not(y))
3.07/4.08	 not(false) -> true
3.07/4.08	 not(true) -> false
3.07/4.08	 or(and(x,y),z) -> and(or(x,z),or(y,z))
3.07/4.08	 or(x,false) -> x
3.07/4.08	 or(x,true) -> true
3.07/4.08	 or(x,x) -> x
3.07/4.08	-> Usable Rules:
3.07/4.08	 and(x,or(x,y)) -> x
3.07/4.08	 and(x,false) -> false
3.07/4.08	 and(x,true) -> x
3.07/4.08	 and(x,x) -> x
3.07/4.08	-> SRules:
3.07/4.08	 AND(and(x3,x4),x5) -> AND(x3,x4)
3.07/4.08	 AND(x3,and(x4,x5)) -> AND(x4,x5)
3.07/4.08	->Interpretation type:
3.07/4.08	 Linear
3.07/4.08	->Coefficients:
3.07/4.08	 Natural Numbers
3.07/4.08	->Dimension:
3.07/4.08	 1
3.07/4.08	->Bound:
3.07/4.08	 2
3.07/4.08	->Interpretation:
3.07/4.08	 
3.07/4.08	[and](X1,X2) = X1 + X2 + 1
3.07/4.08	[eq](X1,X2) = 0
3.07/4.08	[neq](X1,X2) = 0
3.07/4.08	[not](X) = 0
3.07/4.08	[or](X1,X2) = 2.X1 + 2
3.07/4.08	[false] = 2
3.07/4.08	[true] = 0
3.07/4.08	[AND](X1,X2) = 2.X1 + 2.X2
3.07/4.08	[EQ](X1,X2) = 0
3.07/4.08	[NEQ](X1,X2) = 0
3.07/4.08	[NOT](X) = 0
3.07/4.08	[OR](X1,X2) = 0
3.07/4.08	
3.07/4.08	Problem 1.1: 
3.07/4.08	
3.07/4.08	SCC Processor:
3.07/4.08	-> FAxioms:
3.07/4.08	 AND(and(x3,x4),x5) = AND(x3,and(x4,x5))
3.07/4.08	 AND(x3,x4) = AND(x4,x3)
3.07/4.08	-> Pairs:
3.07/4.08	 AND(and(x,false),x3) -> AND(false,x3)
3.07/4.08	 AND(and(x,true),x3) -> AND(x,x3)
3.07/4.08	 AND(and(x,x),x3) -> AND(x,x3)
3.07/4.08	-> EAxioms:
3.07/4.08	 and(and(x3,x4),x5) = and(x3,and(x4,x5))
3.07/4.08	 and(x3,x4) = and(x4,x3)
3.07/4.08	 eq(x3,x4) = eq(x4,x3)
3.07/4.08	 neq(x3,x4) = neq(x4,x3)
3.07/4.08	 or(or(x3,x4),x5) = or(x3,or(x4,x5))
3.07/4.08	 or(x3,x4) = or(x4,x3)
3.07/4.08	-> Rules:
3.07/4.08	 and(x,or(x,y)) -> x
3.07/4.08	 and(x,false) -> false
3.07/4.08	 and(x,true) -> x
3.07/4.08	 and(x,x) -> x
3.07/4.08	 eq(x,x) -> true
3.07/4.08	 neq(x,x) -> false
3.07/4.08	 not(and(x,y)) -> or(not(x),not(y))
3.07/4.08	 not(eq(x,y)) -> neq(x,y)
3.07/4.08	 not(neq(x,y)) -> eq(x,y)
3.07/4.08	 not(not(x)) -> x
3.07/4.08	 not(or(x,y)) -> and(not(x),not(y))
3.07/4.08	 not(false) -> true
3.07/4.08	 not(true) -> false
3.07/4.08	 or(and(x,y),z) -> and(or(x,z),or(y,z))
3.07/4.08	 or(x,false) -> x
3.07/4.08	 or(x,true) -> true
3.07/4.08	 or(x,x) -> x
3.07/4.08	-> SRules:
3.07/4.08	 AND(and(x3,x4),x5) -> AND(x3,x4)
3.07/4.08	 AND(x3,and(x4,x5)) -> AND(x4,x5)
3.07/4.08	->Strongly Connected Components:
3.07/4.08	->->Cycle:
3.07/4.08	->->-> Pairs:
3.07/4.08	 AND(and(x,false),x3) -> AND(false,x3)
3.07/4.08	 AND(and(x,true),x3) -> AND(x,x3)
3.07/4.08	 AND(and(x,x),x3) -> AND(x,x3)
3.07/4.08	-> FAxioms:
3.07/4.08	 and(and(x3,x4),x5) -> and(x3,and(x4,x5))
3.07/4.08	 and(x3,x4) -> and(x4,x3)
3.07/4.08	 eq(x3,x4) -> eq(x4,x3)
3.07/4.08	 neq(x3,x4) -> neq(x4,x3)
3.07/4.08	 or(or(x3,x4),x5) -> or(x3,or(x4,x5))
3.07/4.08	 or(x3,x4) -> or(x4,x3)
3.07/4.08	 AND(and(x3,x4),x5) -> AND(x3,and(x4,x5))
3.07/4.08	 AND(x3,x4) -> AND(x4,x3)
3.07/4.08	-> EAxioms:
3.07/4.08	 and(and(x3,x4),x5) = and(x3,and(x4,x5))
3.07/4.08	 and(x3,x4) = and(x4,x3)
3.07/4.08	 eq(x3,x4) = eq(x4,x3)
3.07/4.08	 neq(x3,x4) = neq(x4,x3)
3.07/4.08	 or(or(x3,x4),x5) = or(x3,or(x4,x5))
3.07/4.08	 or(x3,x4) = or(x4,x3)
3.07/4.08	->->-> Rules:
3.07/4.08	 and(x,or(x,y)) -> x
3.07/4.08	 and(x,false) -> false
3.07/4.08	 and(x,true) -> x
3.07/4.08	 and(x,x) -> x
3.07/4.08	 eq(x,x) -> true
3.07/4.08	 neq(x,x) -> false
3.07/4.08	 not(and(x,y)) -> or(not(x),not(y))
3.07/4.08	 not(eq(x,y)) -> neq(x,y)
3.07/4.08	 not(neq(x,y)) -> eq(x,y)
3.07/4.08	 not(not(x)) -> x
3.07/4.08	 not(or(x,y)) -> and(not(x),not(y))
3.07/4.08	 not(false) -> true
3.07/4.08	 not(true) -> false
3.07/4.08	 or(and(x,y),z) -> and(or(x,z),or(y,z))
3.07/4.08	 or(x,false) -> x
3.07/4.08	 or(x,true) -> true
3.07/4.08	 or(x,x) -> x
3.07/4.08	-> SRules:
3.07/4.08	 AND(and(x3,x4),x5) -> AND(x3,x4)
3.07/4.08	 AND(x3,and(x4,x5)) -> AND(x4,x5)
3.07/4.08	
3.07/4.08	Problem 1.1: 
3.07/4.08	
3.07/4.08	Reduction Pairs Processor:
3.07/4.08	-> FAxioms:
3.07/4.08	 AND(and(x3,x4),x5) = AND(x3,and(x4,x5))
3.07/4.08	 AND(x3,x4) = AND(x4,x3)
3.07/4.08	-> Pairs:
3.07/4.08	 AND(and(x,false),x3) -> AND(false,x3)
3.07/4.08	 AND(and(x,true),x3) -> AND(x,x3)
3.07/4.08	 AND(and(x,x),x3) -> AND(x,x3)
3.07/4.08	-> EAxioms:
3.07/4.08	 and(and(x3,x4),x5) = and(x3,and(x4,x5))
3.07/4.08	 and(x3,x4) = and(x4,x3)
3.07/4.08	 eq(x3,x4) = eq(x4,x3)
3.07/4.08	 neq(x3,x4) = neq(x4,x3)
3.07/4.08	 or(or(x3,x4),x5) = or(x3,or(x4,x5))
3.07/4.08	 or(x3,x4) = or(x4,x3)
3.07/4.08	-> Usable Equations:
3.07/4.08	 and(and(x3,x4),x5) = and(x3,and(x4,x5))
3.07/4.08	 and(x3,x4) = and(x4,x3)
3.07/4.08	-> Rules:
3.07/4.08	 and(x,or(x,y)) -> x
3.07/4.08	 and(x,false) -> false
3.07/4.08	 and(x,true) -> x
3.07/4.08	 and(x,x) -> x
3.07/4.08	 eq(x,x) -> true
3.07/4.08	 neq(x,x) -> false
3.07/4.08	 not(and(x,y)) -> or(not(x),not(y))
3.07/4.08	 not(eq(x,y)) -> neq(x,y)
3.07/4.08	 not(neq(x,y)) -> eq(x,y)
3.07/4.08	 not(not(x)) -> x
3.07/4.08	 not(or(x,y)) -> and(not(x),not(y))
3.07/4.08	 not(false) -> true
3.07/4.08	 not(true) -> false
3.07/4.08	 or(and(x,y),z) -> and(or(x,z),or(y,z))
3.07/4.08	 or(x,false) -> x
3.07/4.08	 or(x,true) -> true
3.07/4.08	 or(x,x) -> x
3.07/4.08	-> Usable Rules:
3.07/4.08	 and(x,or(x,y)) -> x
3.07/4.08	 and(x,false) -> false
3.07/4.08	 and(x,true) -> x
3.07/4.08	 and(x,x) -> x
3.07/4.08	-> SRules:
3.07/4.08	 AND(and(x3,x4),x5) -> AND(x3,x4)
3.07/4.08	 AND(x3,and(x4,x5)) -> AND(x4,x5)
3.07/4.08	->Interpretation type:
3.07/4.08	 Linear
3.07/4.08	->Coefficients:
3.07/4.08	 Natural Numbers
3.07/4.08	->Dimension:
3.07/4.08	 1
3.07/4.08	->Bound:
3.07/4.08	 2
3.07/4.08	->Interpretation:
3.07/4.08	 
3.07/4.08	[and](X1,X2) = X1 + X2 + 2
3.07/4.08	[eq](X1,X2) = 0
3.07/4.08	[neq](X1,X2) = 0
3.07/4.08	[not](X) = 0
3.07/4.08	[or](X1,X2) = 2.X1
3.07/4.08	[false] = 2
3.07/4.08	[true] = 0
3.07/4.08	[AND](X1,X2) = 2.X1 + 2.X2
3.07/4.08	[EQ](X1,X2) = 0
3.07/4.08	[NEQ](X1,X2) = 0
3.07/4.08	[NOT](X) = 0
3.07/4.08	[OR](X1,X2) = 0
3.07/4.08	
3.07/4.08	Problem 1.1: 
3.07/4.08	
3.07/4.08	SCC Processor:
3.07/4.08	-> FAxioms:
3.07/4.08	 AND(and(x3,x4),x5) = AND(x3,and(x4,x5))
3.07/4.08	 AND(x3,x4) = AND(x4,x3)
3.07/4.08	-> Pairs:
3.07/4.08	 AND(and(x,true),x3) -> AND(x,x3)
3.07/4.08	 AND(and(x,x),x3) -> AND(x,x3)
3.07/4.08	-> EAxioms:
3.07/4.08	 and(and(x3,x4),x5) = and(x3,and(x4,x5))
3.07/4.08	 and(x3,x4) = and(x4,x3)
3.07/4.08	 eq(x3,x4) = eq(x4,x3)
3.07/4.08	 neq(x3,x4) = neq(x4,x3)
3.07/4.08	 or(or(x3,x4),x5) = or(x3,or(x4,x5))
3.07/4.08	 or(x3,x4) = or(x4,x3)
3.07/4.08	-> Rules:
3.07/4.08	 and(x,or(x,y)) -> x
3.07/4.08	 and(x,false) -> false
3.07/4.08	 and(x,true) -> x
3.07/4.08	 and(x,x) -> x
3.07/4.08	 eq(x,x) -> true
3.07/4.08	 neq(x,x) -> false
3.07/4.08	 not(and(x,y)) -> or(not(x),not(y))
3.07/4.08	 not(eq(x,y)) -> neq(x,y)
3.07/4.08	 not(neq(x,y)) -> eq(x,y)
3.07/4.08	 not(not(x)) -> x
3.07/4.08	 not(or(x,y)) -> and(not(x),not(y))
3.07/4.08	 not(false) -> true
3.07/4.08	 not(true) -> false
3.07/4.08	 or(and(x,y),z) -> and(or(x,z),or(y,z))
3.07/4.08	 or(x,false) -> x
3.07/4.08	 or(x,true) -> true
3.07/4.08	 or(x,x) -> x
3.07/4.08	-> SRules:
3.07/4.08	 AND(and(x3,x4),x5) -> AND(x3,x4)
3.07/4.08	 AND(x3,and(x4,x5)) -> AND(x4,x5)
3.07/4.08	->Strongly Connected Components:
3.07/4.08	->->Cycle:
3.07/4.08	->->-> Pairs:
3.07/4.08	 AND(and(x,true),x3) -> AND(x,x3)
3.07/4.08	 AND(and(x,x),x3) -> AND(x,x3)
3.07/4.08	-> FAxioms:
3.07/4.08	 and(and(x3,x4),x5) -> and(x3,and(x4,x5))
3.07/4.08	 and(x3,x4) -> and(x4,x3)
3.07/4.08	 eq(x3,x4) -> eq(x4,x3)
3.07/4.08	 neq(x3,x4) -> neq(x4,x3)
3.07/4.08	 or(or(x3,x4),x5) -> or(x3,or(x4,x5))
3.07/4.08	 or(x3,x4) -> or(x4,x3)
3.07/4.08	 AND(and(x3,x4),x5) -> AND(x3,and(x4,x5))
3.07/4.08	 AND(x3,x4) -> AND(x4,x3)
3.07/4.08	-> EAxioms:
3.07/4.08	 and(and(x3,x4),x5) = and(x3,and(x4,x5))
3.07/4.08	 and(x3,x4) = and(x4,x3)
3.07/4.08	 eq(x3,x4) = eq(x4,x3)
3.07/4.08	 neq(x3,x4) = neq(x4,x3)
3.07/4.08	 or(or(x3,x4),x5) = or(x3,or(x4,x5))
3.07/4.08	 or(x3,x4) = or(x4,x3)
3.07/4.08	->->-> Rules:
3.07/4.08	 and(x,or(x,y)) -> x
3.07/4.08	 and(x,false) -> false
3.07/4.08	 and(x,true) -> x
3.07/4.08	 and(x,x) -> x
3.07/4.08	 eq(x,x) -> true
3.07/4.08	 neq(x,x) -> false
3.07/4.08	 not(and(x,y)) -> or(not(x),not(y))
3.07/4.08	 not(eq(x,y)) -> neq(x,y)
3.07/4.08	 not(neq(x,y)) -> eq(x,y)
3.07/4.08	 not(not(x)) -> x
3.07/4.08	 not(or(x,y)) -> and(not(x),not(y))
3.07/4.08	 not(false) -> true
3.07/4.08	 not(true) -> false
3.07/4.08	 or(and(x,y),z) -> and(or(x,z),or(y,z))
3.07/4.08	 or(x,false) -> x
3.07/4.08	 or(x,true) -> true
3.07/4.08	 or(x,x) -> x
3.07/4.08	-> SRules:
3.07/4.08	 AND(and(x3,x4),x5) -> AND(x3,x4)
3.07/4.08	 AND(x3,and(x4,x5)) -> AND(x4,x5)
3.07/4.08	
3.07/4.08	Problem 1.1: 
3.07/4.08	
3.07/4.08	Reduction Pairs Processor:
3.07/4.08	-> FAxioms:
3.07/4.08	 AND(and(x3,x4),x5) = AND(x3,and(x4,x5))
3.07/4.08	 AND(x3,x4) = AND(x4,x3)
3.07/4.08	-> Pairs:
3.07/4.08	 AND(and(x,true),x3) -> AND(x,x3)
3.07/4.08	 AND(and(x,x),x3) -> AND(x,x3)
3.07/4.08	-> EAxioms:
3.07/4.08	 and(and(x3,x4),x5) = and(x3,and(x4,x5))
3.07/4.08	 and(x3,x4) = and(x4,x3)
3.07/4.08	 eq(x3,x4) = eq(x4,x3)
3.07/4.08	 neq(x3,x4) = neq(x4,x3)
3.07/4.08	 or(or(x3,x4),x5) = or(x3,or(x4,x5))
3.07/4.08	 or(x3,x4) = or(x4,x3)
3.07/4.08	-> Usable Equations:
3.07/4.08	 and(and(x3,x4),x5) = and(x3,and(x4,x5))
3.07/4.08	 and(x3,x4) = and(x4,x3)
3.07/4.08	-> Rules:
3.07/4.08	 and(x,or(x,y)) -> x
3.07/4.08	 and(x,false) -> false
3.07/4.08	 and(x,true) -> x
3.07/4.08	 and(x,x) -> x
3.07/4.08	 eq(x,x) -> true
3.07/4.08	 neq(x,x) -> false
3.07/4.08	 not(and(x,y)) -> or(not(x),not(y))
3.07/4.08	 not(eq(x,y)) -> neq(x,y)
3.07/4.08	 not(neq(x,y)) -> eq(x,y)
3.07/4.08	 not(not(x)) -> x
3.07/4.08	 not(or(x,y)) -> and(not(x),not(y))
3.07/4.08	 not(false) -> true
3.07/4.08	 not(true) -> false
3.07/4.08	 or(and(x,y),z) -> and(or(x,z),or(y,z))
3.07/4.08	 or(x,false) -> x
3.07/4.08	 or(x,true) -> true
3.07/4.08	 or(x,x) -> x
3.07/4.08	-> Usable Rules:
3.07/4.08	 and(x,or(x,y)) -> x
3.07/4.08	 and(x,false) -> false
3.07/4.08	 and(x,true) -> x
3.07/4.08	 and(x,x) -> x
3.07/4.08	-> SRules:
3.07/4.08	 AND(and(x3,x4),x5) -> AND(x3,x4)
3.07/4.08	 AND(x3,and(x4,x5)) -> AND(x4,x5)
3.07/4.08	->Interpretation type:
3.07/4.08	 Linear
3.07/4.08	->Coefficients:
3.07/4.08	 Natural Numbers
3.07/4.08	->Dimension:
3.07/4.08	 1
3.07/4.08	->Bound:
3.07/4.08	 2
3.07/4.08	->Interpretation:
3.07/4.08	 
3.07/4.08	[and](X1,X2) = X1 + X2
3.07/4.08	[eq](X1,X2) = 0
3.07/4.08	[neq](X1,X2) = 0
3.07/4.08	[not](X) = 0
3.07/4.08	[or](X1,X2) = 2.X1
3.07/4.08	[false] = 2
3.07/4.08	[true] = 2
3.07/4.08	[AND](X1,X2) = 2.X1 + 2.X2
3.07/4.08	[EQ](X1,X2) = 0
3.07/4.08	[NEQ](X1,X2) = 0
3.07/4.08	[NOT](X) = 0
3.07/4.08	[OR](X1,X2) = 0
3.07/4.08	
3.07/4.08	Problem 1.1: 
3.07/4.08	
3.07/4.08	SCC Processor:
3.07/4.08	-> FAxioms:
3.07/4.08	 AND(and(x3,x4),x5) = AND(x3,and(x4,x5))
3.07/4.08	 AND(x3,x4) = AND(x4,x3)
3.07/4.08	-> Pairs:
3.07/4.08	 AND(and(x,x),x3) -> AND(x,x3)
3.07/4.08	-> EAxioms:
3.07/4.08	 and(and(x3,x4),x5) = and(x3,and(x4,x5))
3.07/4.08	 and(x3,x4) = and(x4,x3)
3.07/4.08	 eq(x3,x4) = eq(x4,x3)
3.07/4.08	 neq(x3,x4) = neq(x4,x3)
3.07/4.08	 or(or(x3,x4),x5) = or(x3,or(x4,x5))
3.07/4.08	 or(x3,x4) = or(x4,x3)
3.07/4.08	-> Rules:
3.07/4.08	 and(x,or(x,y)) -> x
3.07/4.08	 and(x,false) -> false
3.07/4.08	 and(x,true) -> x
3.07/4.08	 and(x,x) -> x
3.07/4.08	 eq(x,x) -> true
3.07/4.08	 neq(x,x) -> false
3.07/4.08	 not(and(x,y)) -> or(not(x),not(y))
3.07/4.08	 not(eq(x,y)) -> neq(x,y)
3.07/4.08	 not(neq(x,y)) -> eq(x,y)
3.07/4.08	 not(not(x)) -> x
3.07/4.08	 not(or(x,y)) -> and(not(x),not(y))
3.07/4.08	 not(false) -> true
3.07/4.08	 not(true) -> false
3.07/4.08	 or(and(x,y),z) -> and(or(x,z),or(y,z))
3.07/4.08	 or(x,false) -> x
3.07/4.08	 or(x,true) -> true
3.07/4.08	 or(x,x) -> x
3.07/4.08	-> SRules:
3.07/4.08	 AND(and(x3,x4),x5) -> AND(x3,x4)
3.07/4.08	 AND(x3,and(x4,x5)) -> AND(x4,x5)
3.07/4.08	->Strongly Connected Components:
3.07/4.08	->->Cycle:
3.07/4.08	->->-> Pairs:
3.07/4.08	 AND(and(x,x),x3) -> AND(x,x3)
3.07/4.08	-> FAxioms:
3.07/4.08	 and(and(x3,x4),x5) -> and(x3,and(x4,x5))
3.07/4.08	 and(x3,x4) -> and(x4,x3)
3.07/4.08	 eq(x3,x4) -> eq(x4,x3)
3.07/4.08	 neq(x3,x4) -> neq(x4,x3)
3.07/4.08	 or(or(x3,x4),x5) -> or(x3,or(x4,x5))
3.07/4.08	 or(x3,x4) -> or(x4,x3)
3.07/4.08	 AND(and(x3,x4),x5) -> AND(x3,and(x4,x5))
3.07/4.08	 AND(x3,x4) -> AND(x4,x3)
3.07/4.08	-> EAxioms:
3.07/4.08	 and(and(x3,x4),x5) = and(x3,and(x4,x5))
3.07/4.08	 and(x3,x4) = and(x4,x3)
3.07/4.08	 eq(x3,x4) = eq(x4,x3)
3.07/4.08	 neq(x3,x4) = neq(x4,x3)
3.07/4.08	 or(or(x3,x4),x5) = or(x3,or(x4,x5))
3.07/4.08	 or(x3,x4) = or(x4,x3)
3.07/4.08	->->-> Rules:
3.07/4.08	 and(x,or(x,y)) -> x
3.07/4.08	 and(x,false) -> false
3.07/4.08	 and(x,true) -> x
3.07/4.08	 and(x,x) -> x
3.07/4.08	 eq(x,x) -> true
3.07/4.08	 neq(x,x) -> false
3.07/4.08	 not(and(x,y)) -> or(not(x),not(y))
3.07/4.08	 not(eq(x,y)) -> neq(x,y)
3.07/4.08	 not(neq(x,y)) -> eq(x,y)
3.07/4.08	 not(not(x)) -> x
3.07/4.08	 not(or(x,y)) -> and(not(x),not(y))
3.07/4.08	 not(false) -> true
3.07/4.08	 not(true) -> false
3.07/4.08	 or(and(x,y),z) -> and(or(x,z),or(y,z))
3.07/4.08	 or(x,false) -> x
3.07/4.08	 or(x,true) -> true
3.07/4.08	 or(x,x) -> x
3.07/4.08	-> SRules:
3.07/4.08	 AND(and(x3,x4),x5) -> AND(x3,x4)
3.07/4.08	 AND(x3,and(x4,x5)) -> AND(x4,x5)
3.07/4.08	
3.07/4.08	Problem 1.1: 
3.07/4.08	
3.07/4.08	Reduction Pairs Processor:
3.07/4.08	-> FAxioms:
3.07/4.08	 AND(and(x3,x4),x5) = AND(x3,and(x4,x5))
3.07/4.08	 AND(x3,x4) = AND(x4,x3)
3.07/4.08	-> Pairs:
3.07/4.08	 AND(and(x,x),x3) -> AND(x,x3)
3.07/4.08	-> EAxioms:
3.07/4.08	 and(and(x3,x4),x5) = and(x3,and(x4,x5))
3.07/4.08	 and(x3,x4) = and(x4,x3)
3.07/4.08	 eq(x3,x4) = eq(x4,x3)
3.07/4.08	 neq(x3,x4) = neq(x4,x3)
3.07/4.08	 or(or(x3,x4),x5) = or(x3,or(x4,x5))
3.07/4.08	 or(x3,x4) = or(x4,x3)
3.07/4.08	-> Usable Equations:
3.07/4.08	 and(and(x3,x4),x5) = and(x3,and(x4,x5))
3.07/4.08	 and(x3,x4) = and(x4,x3)
3.07/4.08	-> Rules:
3.07/4.08	 and(x,or(x,y)) -> x
3.07/4.08	 and(x,false) -> false
3.07/4.08	 and(x,true) -> x
3.07/4.08	 and(x,x) -> x
3.07/4.08	 eq(x,x) -> true
3.07/4.08	 neq(x,x) -> false
3.07/4.08	 not(and(x,y)) -> or(not(x),not(y))
3.07/4.08	 not(eq(x,y)) -> neq(x,y)
3.07/4.08	 not(neq(x,y)) -> eq(x,y)
3.07/4.08	 not(not(x)) -> x
3.07/4.08	 not(or(x,y)) -> and(not(x),not(y))
3.07/4.08	 not(false) -> true
3.07/4.08	 not(true) -> false
3.07/4.08	 or(and(x,y),z) -> and(or(x,z),or(y,z))
3.07/4.08	 or(x,false) -> x
3.07/4.08	 or(x,true) -> true
3.07/4.08	 or(x,x) -> x
3.07/4.08	-> Usable Rules:
3.07/4.08	 and(x,or(x,y)) -> x
3.07/4.08	 and(x,false) -> false
3.07/4.08	 and(x,true) -> x
3.07/4.08	 and(x,x) -> x
3.07/4.08	-> SRules:
3.07/4.08	 AND(and(x3,x4),x5) -> AND(x3,x4)
3.07/4.08	 AND(x3,and(x4,x5)) -> AND(x4,x5)
3.07/4.08	->Interpretation type:
3.07/4.08	 Linear
3.07/4.08	->Coefficients:
3.07/4.08	 Natural Numbers
3.07/4.08	->Dimension:
3.07/4.08	 1
3.07/4.08	->Bound:
3.07/4.08	 2
3.07/4.08	->Interpretation:
3.07/4.08	 
3.07/4.08	[and](X1,X2) = X1 + X2 + 2
3.07/4.08	[eq](X1,X2) = 0
3.07/4.08	[neq](X1,X2) = 0
3.07/4.08	[not](X) = 0
3.07/4.08	[or](X1,X2) = 2.X1
3.07/4.08	[false] = 2
3.07/4.08	[true] = 0
3.07/4.08	[AND](X1,X2) = 2.X1 + 2.X2
3.07/4.08	[EQ](X1,X2) = 0
3.07/4.08	[NEQ](X1,X2) = 0
3.07/4.08	[NOT](X) = 0
3.07/4.08	[OR](X1,X2) = 0
3.07/4.08	
3.07/4.08	Problem 1.1: 
3.07/4.08	
3.07/4.08	SCC Processor:
3.07/4.08	-> FAxioms:
3.07/4.08	 AND(and(x3,x4),x5) = AND(x3,and(x4,x5))
3.07/4.08	 AND(x3,x4) = AND(x4,x3)
3.07/4.08	-> Pairs:
3.07/4.08	 Empty
3.07/4.08	-> EAxioms:
3.07/4.08	 and(and(x3,x4),x5) = and(x3,and(x4,x5))
3.07/4.08	 and(x3,x4) = and(x4,x3)
3.07/4.08	 eq(x3,x4) = eq(x4,x3)
3.07/4.08	 neq(x3,x4) = neq(x4,x3)
3.07/4.08	 or(or(x3,x4),x5) = or(x3,or(x4,x5))
3.07/4.08	 or(x3,x4) = or(x4,x3)
3.07/4.08	-> Rules:
3.07/4.08	 and(x,or(x,y)) -> x
3.07/4.08	 and(x,false) -> false
3.07/4.08	 and(x,true) -> x
3.07/4.08	 and(x,x) -> x
3.07/4.08	 eq(x,x) -> true
3.07/4.08	 neq(x,x) -> false
3.07/4.08	 not(and(x,y)) -> or(not(x),not(y))
3.07/4.08	 not(eq(x,y)) -> neq(x,y)
3.07/4.08	 not(neq(x,y)) -> eq(x,y)
3.07/4.08	 not(not(x)) -> x
3.07/4.08	 not(or(x,y)) -> and(not(x),not(y))
3.07/4.08	 not(false) -> true
3.07/4.08	 not(true) -> false
3.07/4.08	 or(and(x,y),z) -> and(or(x,z),or(y,z))
3.07/4.08	 or(x,false) -> x
3.07/4.08	 or(x,true) -> true
3.07/4.08	 or(x,x) -> x
3.07/4.08	-> SRules:
3.07/4.08	 AND(and(x3,x4),x5) -> AND(x3,x4)
3.07/4.08	 AND(x3,and(x4,x5)) -> AND(x4,x5)
3.07/4.08	->Strongly Connected Components:
3.07/4.08	 There is no strongly connected component
3.07/4.08	
3.07/4.08	The problem is finite.
3.07/4.08	
3.07/4.08	Problem 1.2: 
3.07/4.08	
3.07/4.08	Reduction Pairs Processor:
3.07/4.08	-> FAxioms:
3.07/4.08	 OR(or(x3,x4),x5) = OR(x3,or(x4,x5))
3.07/4.08	 OR(x3,x4) = OR(x4,x3)
3.07/4.08	-> Pairs:
3.07/4.08	 OR(and(x,y),z) -> OR(x,z)
3.07/4.08	 OR(and(x,y),z) -> OR(y,z)
3.07/4.08	 OR(or(and(x,y),z),x3) -> OR(and(or(x,z),or(y,z)),x3)
3.07/4.08	 OR(or(and(x,y),z),x3) -> OR(x,z)
3.07/4.08	 OR(or(and(x,y),z),x3) -> OR(y,z)
3.07/4.08	 OR(or(x,false),x3) -> OR(x,x3)
3.07/4.08	 OR(or(x,true),x3) -> OR(true,x3)
3.07/4.08	 OR(or(x,x),x3) -> OR(x,x3)
3.07/4.08	-> EAxioms:
3.07/4.08	 and(and(x3,x4),x5) = and(x3,and(x4,x5))
3.07/4.08	 and(x3,x4) = and(x4,x3)
3.07/4.08	 eq(x3,x4) = eq(x4,x3)
3.07/4.08	 neq(x3,x4) = neq(x4,x3)
3.07/4.08	 or(or(x3,x4),x5) = or(x3,or(x4,x5))
3.07/4.08	 or(x3,x4) = or(x4,x3)
3.07/4.08	-> Usable Equations:
3.07/4.08	 and(and(x3,x4),x5) = and(x3,and(x4,x5))
3.07/4.08	 and(x3,x4) = and(x4,x3)
3.07/4.08	 or(or(x3,x4),x5) = or(x3,or(x4,x5))
3.07/4.08	 or(x3,x4) = or(x4,x3)
3.07/4.08	-> Rules:
3.07/4.08	 and(x,or(x,y)) -> x
3.07/4.08	 and(x,false) -> false
3.07/4.08	 and(x,true) -> x
3.07/4.08	 and(x,x) -> x
3.07/4.08	 eq(x,x) -> true
3.07/4.08	 neq(x,x) -> false
3.07/4.08	 not(and(x,y)) -> or(not(x),not(y))
3.07/4.08	 not(eq(x,y)) -> neq(x,y)
3.07/4.08	 not(neq(x,y)) -> eq(x,y)
3.07/4.08	 not(not(x)) -> x
3.07/4.08	 not(or(x,y)) -> and(not(x),not(y))
3.07/4.08	 not(false) -> true
3.07/4.08	 not(true) -> false
3.07/4.08	 or(and(x,y),z) -> and(or(x,z),or(y,z))
3.07/4.08	 or(x,false) -> x
3.07/4.08	 or(x,true) -> true
3.07/4.08	 or(x,x) -> x
3.07/4.08	-> Usable Rules:
3.07/4.08	 and(x,or(x,y)) -> x
3.07/4.08	 and(x,false) -> false
3.07/4.08	 and(x,true) -> x
3.07/4.08	 and(x,x) -> x
3.07/4.08	 or(and(x,y),z) -> and(or(x,z),or(y,z))
3.07/4.08	 or(x,false) -> x
3.07/4.08	 or(x,true) -> true
3.07/4.08	 or(x,x) -> x
3.07/4.08	-> SRules:
3.07/4.08	 OR(or(x3,x4),x5) -> OR(x3,x4)
3.07/4.08	 OR(x3,or(x4,x5)) -> OR(x4,x5)
3.07/4.08	->Interpretation type:
3.07/4.08	 Simple mixed
3.07/4.08	->Coefficients:
3.07/4.08	 Natural Numbers
3.07/4.08	->Dimension:
3.07/4.08	 1
3.07/4.08	->Bound:
3.07/4.08	 1
3.07/4.08	->Interpretation:
3.07/4.08	 
3.07/4.08	[and](X1,X2) = X1 + X2 + 1
3.07/4.08	[eq](X1,X2) = 0
3.07/4.08	[neq](X1,X2) = 0
3.07/4.08	[not](X) = 0
3.07/4.08	[or](X1,X2) = X1.X2 + X1 + X2
3.07/4.08	[false] = 1
3.07/4.08	[true] = 1
3.07/4.08	[AND](X1,X2) = 0
3.07/4.08	[EQ](X1,X2) = 0
3.07/4.08	[NEQ](X1,X2) = 0
3.07/4.08	[NOT](X) = 0
3.07/4.08	[OR](X1,X2) = X1.X2 + X1 + X2
3.07/4.08	
3.07/4.08	Problem 1.2: 
3.07/4.08	
3.07/4.08	SCC Processor:
3.07/4.08	-> FAxioms:
3.07/4.08	 OR(or(x3,x4),x5) = OR(x3,or(x4,x5))
3.07/4.08	 OR(x3,x4) = OR(x4,x3)
3.07/4.08	-> Pairs:
3.07/4.08	 OR(and(x,y),z) -> OR(y,z)
3.07/4.08	 OR(or(and(x,y),z),x3) -> OR(and(or(x,z),or(y,z)),x3)
3.07/4.08	 OR(or(and(x,y),z),x3) -> OR(x,z)
3.07/4.08	 OR(or(and(x,y),z),x3) -> OR(y,z)
3.07/4.08	 OR(or(x,false),x3) -> OR(x,x3)
3.07/4.08	 OR(or(x,true),x3) -> OR(true,x3)
3.07/4.08	 OR(or(x,x),x3) -> OR(x,x3)
3.07/4.08	-> EAxioms:
3.07/4.08	 and(and(x3,x4),x5) = and(x3,and(x4,x5))
3.07/4.08	 and(x3,x4) = and(x4,x3)
3.07/4.08	 eq(x3,x4) = eq(x4,x3)
3.07/4.08	 neq(x3,x4) = neq(x4,x3)
3.07/4.08	 or(or(x3,x4),x5) = or(x3,or(x4,x5))
3.07/4.08	 or(x3,x4) = or(x4,x3)
3.07/4.08	-> Rules:
3.07/4.08	 and(x,or(x,y)) -> x
3.07/4.08	 and(x,false) -> false
3.07/4.08	 and(x,true) -> x
3.07/4.08	 and(x,x) -> x
3.07/4.08	 eq(x,x) -> true
3.07/4.08	 neq(x,x) -> false
3.07/4.08	 not(and(x,y)) -> or(not(x),not(y))
3.07/4.08	 not(eq(x,y)) -> neq(x,y)
3.07/4.08	 not(neq(x,y)) -> eq(x,y)
3.07/4.08	 not(not(x)) -> x
3.07/4.08	 not(or(x,y)) -> and(not(x),not(y))
3.07/4.08	 not(false) -> true
3.07/4.08	 not(true) -> false
3.07/4.08	 or(and(x,y),z) -> and(or(x,z),or(y,z))
3.07/4.08	 or(x,false) -> x
3.07/4.08	 or(x,true) -> true
3.07/4.08	 or(x,x) -> x
3.07/4.08	-> SRules:
3.07/4.08	 OR(or(x3,x4),x5) -> OR(x3,x4)
3.07/4.08	 OR(x3,or(x4,x5)) -> OR(x4,x5)
3.07/4.08	->Strongly Connected Components:
3.07/4.08	->->Cycle:
3.07/4.08	->->-> Pairs:
3.07/4.08	 OR(and(x,y),z) -> OR(y,z)
3.07/4.08	 OR(or(and(x,y),z),x3) -> OR(and(or(x,z),or(y,z)),x3)
3.07/4.08	 OR(or(and(x,y),z),x3) -> OR(x,z)
3.07/4.08	 OR(or(and(x,y),z),x3) -> OR(y,z)
3.07/4.08	 OR(or(x,false),x3) -> OR(x,x3)
3.07/4.08	 OR(or(x,true),x3) -> OR(true,x3)
3.07/4.08	 OR(or(x,x),x3) -> OR(x,x3)
3.07/4.08	-> FAxioms:
3.07/4.08	 and(and(x3,x4),x5) -> and(x3,and(x4,x5))
3.07/4.08	 and(x3,x4) -> and(x4,x3)
3.07/4.08	 eq(x3,x4) -> eq(x4,x3)
3.07/4.08	 neq(x3,x4) -> neq(x4,x3)
3.07/4.08	 or(or(x3,x4),x5) -> or(x3,or(x4,x5))
3.07/4.08	 or(x3,x4) -> or(x4,x3)
3.07/4.08	 OR(or(x3,x4),x5) -> OR(x3,or(x4,x5))
3.07/4.08	 OR(x3,x4) -> OR(x4,x3)
3.07/4.08	-> EAxioms:
3.07/4.08	 and(and(x3,x4),x5) = and(x3,and(x4,x5))
3.07/4.08	 and(x3,x4) = and(x4,x3)
3.07/4.08	 eq(x3,x4) = eq(x4,x3)
3.07/4.08	 neq(x3,x4) = neq(x4,x3)
3.07/4.08	 or(or(x3,x4),x5) = or(x3,or(x4,x5))
3.07/4.08	 or(x3,x4) = or(x4,x3)
3.07/4.08	->->-> Rules:
3.07/4.08	 and(x,or(x,y)) -> x
3.07/4.08	 and(x,false) -> false
3.07/4.08	 and(x,true) -> x
3.07/4.08	 and(x,x) -> x
3.07/4.08	 eq(x,x) -> true
3.07/4.08	 neq(x,x) -> false
3.07/4.08	 not(and(x,y)) -> or(not(x),not(y))
3.07/4.08	 not(eq(x,y)) -> neq(x,y)
3.07/4.08	 not(neq(x,y)) -> eq(x,y)
3.07/4.08	 not(not(x)) -> x
3.07/4.08	 not(or(x,y)) -> and(not(x),not(y))
3.07/4.08	 not(false) -> true
3.07/4.08	 not(true) -> false
3.07/4.08	 or(and(x,y),z) -> and(or(x,z),or(y,z))
3.07/4.08	 or(x,false) -> x
3.07/4.08	 or(x,true) -> true
3.07/4.08	 or(x,x) -> x
3.07/4.08	-> SRules:
3.07/4.08	 OR(or(x3,x4),x5) -> OR(x3,x4)
3.07/4.08	 OR(x3,or(x4,x5)) -> OR(x4,x5)
3.07/4.08	
3.07/4.08	Problem 1.2: 
3.07/4.08	
3.07/4.08	Reduction Pairs Processor:
3.07/4.08	-> FAxioms:
3.07/4.08	 OR(or(x3,x4),x5) = OR(x3,or(x4,x5))
3.07/4.08	 OR(x3,x4) = OR(x4,x3)
3.07/4.08	-> Pairs:
3.07/4.08	 OR(and(x,y),z) -> OR(y,z)
3.07/4.08	 OR(or(and(x,y),z),x3) -> OR(and(or(x,z),or(y,z)),x3)
3.07/4.08	 OR(or(and(x,y),z),x3) -> OR(x,z)
3.07/4.08	 OR(or(and(x,y),z),x3) -> OR(y,z)
3.07/4.08	 OR(or(x,false),x3) -> OR(x,x3)
3.07/4.08	 OR(or(x,true),x3) -> OR(true,x3)
3.07/4.08	 OR(or(x,x),x3) -> OR(x,x3)
3.07/4.08	-> EAxioms:
3.07/4.08	 and(and(x3,x4),x5) = and(x3,and(x4,x5))
3.07/4.08	 and(x3,x4) = and(x4,x3)
3.07/4.08	 eq(x3,x4) = eq(x4,x3)
3.07/4.08	 neq(x3,x4) = neq(x4,x3)
3.07/4.08	 or(or(x3,x4),x5) = or(x3,or(x4,x5))
3.07/4.08	 or(x3,x4) = or(x4,x3)
3.07/4.08	-> Usable Equations:
3.07/4.08	 and(and(x3,x4),x5) = and(x3,and(x4,x5))
3.07/4.08	 and(x3,x4) = and(x4,x3)
3.07/4.08	 or(or(x3,x4),x5) = or(x3,or(x4,x5))
3.07/4.08	 or(x3,x4) = or(x4,x3)
3.07/4.08	-> Rules:
3.07/4.08	 and(x,or(x,y)) -> x
3.07/4.08	 and(x,false) -> false
3.07/4.08	 and(x,true) -> x
3.07/4.08	 and(x,x) -> x
3.07/4.08	 eq(x,x) -> true
3.07/4.08	 neq(x,x) -> false
3.07/4.08	 not(and(x,y)) -> or(not(x),not(y))
3.07/4.08	 not(eq(x,y)) -> neq(x,y)
3.07/4.08	 not(neq(x,y)) -> eq(x,y)
3.07/4.08	 not(not(x)) -> x
3.07/4.08	 not(or(x,y)) -> and(not(x),not(y))
3.07/4.08	 not(false) -> true
3.07/4.08	 not(true) -> false
3.07/4.08	 or(and(x,y),z) -> and(or(x,z),or(y,z))
3.07/4.08	 or(x,false) -> x
3.07/4.08	 or(x,true) -> true
3.07/4.08	 or(x,x) -> x
3.07/4.08	-> Usable Rules:
3.07/4.08	 and(x,or(x,y)) -> x
3.07/4.08	 and(x,false) -> false
3.07/4.08	 and(x,true) -> x
3.07/4.08	 and(x,x) -> x
3.07/4.08	 or(and(x,y),z) -> and(or(x,z),or(y,z))
3.07/4.08	 or(x,false) -> x
3.07/4.08	 or(x,true) -> true
3.07/4.08	 or(x,x) -> x
3.07/4.08	-> SRules:
3.07/4.08	 OR(or(x3,x4),x5) -> OR(x3,x4)
3.07/4.08	 OR(x3,or(x4,x5)) -> OR(x4,x5)
3.07/4.08	->Interpretation type:
3.07/4.08	 Simple mixed
3.07/4.08	->Coefficients:
3.07/4.08	 Natural Numbers
3.07/4.08	->Dimension:
3.07/4.08	 1
3.07/4.08	->Bound:
3.07/4.08	 1
3.07/4.08	->Interpretation:
3.07/4.08	 
3.07/4.08	[and](X1,X2) = X1 + X2 + 1
3.07/4.08	[eq](X1,X2) = 0
3.07/4.08	[neq](X1,X2) = 0
3.07/4.08	[not](X) = 0
3.07/4.08	[or](X1,X2) = X1.X2 + X1 + X2
3.07/4.08	[false] = 1
3.07/4.08	[true] = 1
3.07/4.08	[AND](X1,X2) = 0
3.07/4.08	[EQ](X1,X2) = 0
3.07/4.08	[NEQ](X1,X2) = 0
3.07/4.08	[NOT](X) = 0
3.07/4.08	[OR](X1,X2) = X1.X2 + X1 + X2
3.07/4.08	
3.07/4.08	Problem 1.2: 
3.07/4.08	
3.07/4.08	SCC Processor:
3.07/4.08	-> FAxioms:
3.07/4.08	 OR(or(x3,x4),x5) = OR(x3,or(x4,x5))
3.07/4.08	 OR(x3,x4) = OR(x4,x3)
3.07/4.08	-> Pairs:
3.07/4.08	 OR(or(and(x,y),z),x3) -> OR(and(or(x,z),or(y,z)),x3)
3.07/4.08	 OR(or(and(x,y),z),x3) -> OR(x,z)
3.07/4.08	 OR(or(and(x,y),z),x3) -> OR(y,z)
3.07/4.08	 OR(or(x,false),x3) -> OR(x,x3)
3.07/4.08	 OR(or(x,true),x3) -> OR(true,x3)
3.07/4.08	 OR(or(x,x),x3) -> OR(x,x3)
3.07/4.08	-> EAxioms:
3.07/4.08	 and(and(x3,x4),x5) = and(x3,and(x4,x5))
3.07/4.08	 and(x3,x4) = and(x4,x3)
3.07/4.08	 eq(x3,x4) = eq(x4,x3)
3.07/4.08	 neq(x3,x4) = neq(x4,x3)
3.07/4.08	 or(or(x3,x4),x5) = or(x3,or(x4,x5))
3.07/4.08	 or(x3,x4) = or(x4,x3)
3.07/4.08	-> Rules:
3.07/4.08	 and(x,or(x,y)) -> x
3.07/4.08	 and(x,false) -> false
3.07/4.08	 and(x,true) -> x
3.07/4.08	 and(x,x) -> x
3.07/4.08	 eq(x,x) -> true
3.07/4.08	 neq(x,x) -> false
3.07/4.08	 not(and(x,y)) -> or(not(x),not(y))
3.07/4.08	 not(eq(x,y)) -> neq(x,y)
3.07/4.08	 not(neq(x,y)) -> eq(x,y)
3.07/4.08	 not(not(x)) -> x
3.07/4.08	 not(or(x,y)) -> and(not(x),not(y))
3.07/4.08	 not(false) -> true
3.07/4.08	 not(true) -> false
3.07/4.08	 or(and(x,y),z) -> and(or(x,z),or(y,z))
3.07/4.08	 or(x,false) -> x
3.07/4.08	 or(x,true) -> true
3.07/4.08	 or(x,x) -> x
3.07/4.08	-> SRules:
3.07/4.08	 OR(or(x3,x4),x5) -> OR(x3,x4)
3.07/4.08	 OR(x3,or(x4,x5)) -> OR(x4,x5)
3.07/4.08	->Strongly Connected Components:
3.07/4.08	->->Cycle:
3.07/4.08	->->-> Pairs:
3.07/4.08	 OR(or(and(x,y),z),x3) -> OR(and(or(x,z),or(y,z)),x3)
3.07/4.08	 OR(or(and(x,y),z),x3) -> OR(x,z)
3.07/4.08	 OR(or(and(x,y),z),x3) -> OR(y,z)
3.07/4.08	 OR(or(x,false),x3) -> OR(x,x3)
3.07/4.08	 OR(or(x,true),x3) -> OR(true,x3)
3.07/4.08	 OR(or(x,x),x3) -> OR(x,x3)
3.07/4.08	-> FAxioms:
3.07/4.08	 and(and(x3,x4),x5) -> and(x3,and(x4,x5))
3.07/4.08	 and(x3,x4) -> and(x4,x3)
3.07/4.08	 eq(x3,x4) -> eq(x4,x3)
3.07/4.08	 neq(x3,x4) -> neq(x4,x3)
3.07/4.08	 or(or(x3,x4),x5) -> or(x3,or(x4,x5))
3.07/4.08	 or(x3,x4) -> or(x4,x3)
3.07/4.08	 OR(or(x3,x4),x5) -> OR(x3,or(x4,x5))
3.07/4.08	 OR(x3,x4) -> OR(x4,x3)
3.07/4.08	-> EAxioms:
3.07/4.08	 and(and(x3,x4),x5) = and(x3,and(x4,x5))
3.07/4.08	 and(x3,x4) = and(x4,x3)
3.07/4.08	 eq(x3,x4) = eq(x4,x3)
3.07/4.08	 neq(x3,x4) = neq(x4,x3)
3.07/4.08	 or(or(x3,x4),x5) = or(x3,or(x4,x5))
3.07/4.08	 or(x3,x4) = or(x4,x3)
3.07/4.08	->->-> Rules:
3.07/4.08	 and(x,or(x,y)) -> x
3.07/4.08	 and(x,false) -> false
3.07/4.08	 and(x,true) -> x
3.07/4.08	 and(x,x) -> x
3.07/4.08	 eq(x,x) -> true
3.07/4.08	 neq(x,x) -> false
3.07/4.08	 not(and(x,y)) -> or(not(x),not(y))
3.07/4.08	 not(eq(x,y)) -> neq(x,y)
3.07/4.08	 not(neq(x,y)) -> eq(x,y)
3.07/4.08	 not(not(x)) -> x
3.07/4.08	 not(or(x,y)) -> and(not(x),not(y))
3.07/4.08	 not(false) -> true
3.07/4.08	 not(true) -> false
3.07/4.08	 or(and(x,y),z) -> and(or(x,z),or(y,z))
3.07/4.08	 or(x,false) -> x
3.07/4.08	 or(x,true) -> true
3.07/4.08	 or(x,x) -> x
3.07/4.08	-> SRules:
3.07/4.08	 OR(or(x3,x4),x5) -> OR(x3,x4)
3.07/4.08	 OR(x3,or(x4,x5)) -> OR(x4,x5)
3.07/4.08	
3.07/4.08	Problem 1.2: 
3.07/4.08	
3.07/4.08	Reduction Pairs Processor:
3.07/4.08	-> FAxioms:
3.07/4.08	 OR(or(x3,x4),x5) = OR(x3,or(x4,x5))
3.07/4.08	 OR(x3,x4) = OR(x4,x3)
3.07/4.08	-> Pairs:
3.07/4.08	 OR(or(and(x,y),z),x3) -> OR(and(or(x,z),or(y,z)),x3)
3.07/4.08	 OR(or(and(x,y),z),x3) -> OR(x,z)
3.07/4.08	 OR(or(and(x,y),z),x3) -> OR(y,z)
3.07/4.08	 OR(or(x,false),x3) -> OR(x,x3)
3.07/4.08	 OR(or(x,true),x3) -> OR(true,x3)
3.07/4.08	 OR(or(x,x),x3) -> OR(x,x3)
3.07/4.08	-> EAxioms:
3.07/4.08	 and(and(x3,x4),x5) = and(x3,and(x4,x5))
3.07/4.08	 and(x3,x4) = and(x4,x3)
3.07/4.08	 eq(x3,x4) = eq(x4,x3)
3.07/4.08	 neq(x3,x4) = neq(x4,x3)
3.07/4.08	 or(or(x3,x4),x5) = or(x3,or(x4,x5))
3.07/4.08	 or(x3,x4) = or(x4,x3)
3.07/4.08	-> Usable Equations:
3.07/4.08	 and(and(x3,x4),x5) = and(x3,and(x4,x5))
3.07/4.08	 and(x3,x4) = and(x4,x3)
3.07/4.08	 or(or(x3,x4),x5) = or(x3,or(x4,x5))
3.07/4.08	 or(x3,x4) = or(x4,x3)
3.07/4.08	-> Rules:
3.07/4.08	 and(x,or(x,y)) -> x
3.07/4.08	 and(x,false) -> false
3.07/4.08	 and(x,true) -> x
3.07/4.08	 and(x,x) -> x
3.07/4.08	 eq(x,x) -> true
3.07/4.08	 neq(x,x) -> false
3.07/4.08	 not(and(x,y)) -> or(not(x),not(y))
3.07/4.08	 not(eq(x,y)) -> neq(x,y)
3.07/4.08	 not(neq(x,y)) -> eq(x,y)
3.07/4.08	 not(not(x)) -> x
3.07/4.08	 not(or(x,y)) -> and(not(x),not(y))
3.07/4.08	 not(false) -> true
3.07/4.08	 not(true) -> false
3.07/4.08	 or(and(x,y),z) -> and(or(x,z),or(y,z))
3.07/4.08	 or(x,false) -> x
3.07/4.08	 or(x,true) -> true
3.07/4.08	 or(x,x) -> x
3.07/4.08	-> Usable Rules:
3.07/4.08	 and(x,or(x,y)) -> x
3.07/4.08	 and(x,false) -> false
3.07/4.08	 and(x,true) -> x
3.07/4.08	 and(x,x) -> x
3.07/4.08	 or(and(x,y),z) -> and(or(x,z),or(y,z))
3.07/4.08	 or(x,false) -> x
3.07/4.08	 or(x,true) -> true
3.07/4.08	 or(x,x) -> x
3.07/4.08	-> SRules:
3.07/4.08	 OR(or(x3,x4),x5) -> OR(x3,x4)
3.07/4.08	 OR(x3,or(x4,x5)) -> OR(x4,x5)
3.07/4.08	->Interpretation type:
3.07/4.08	 Simple mixed
3.07/4.08	->Coefficients:
3.07/4.08	 Natural Numbers
3.07/4.08	->Dimension:
3.07/4.08	 1
3.07/4.08	->Bound:
3.07/4.08	 1
3.07/4.08	->Interpretation:
3.07/4.08	 
3.07/4.08	[and](X1,X2) = X1 + X2 + 1
3.07/4.08	[eq](X1,X2) = 0
3.07/4.08	[neq](X1,X2) = 0
3.07/4.08	[not](X) = 0
3.07/4.08	[or](X1,X2) = X1.X2 + X1 + X2
3.07/4.08	[false] = 1
3.07/4.08	[true] = 1
3.07/4.08	[AND](X1,X2) = 0
3.07/4.08	[EQ](X1,X2) = 0
3.07/4.08	[NEQ](X1,X2) = 0
3.07/4.08	[NOT](X) = 0
3.07/4.08	[OR](X1,X2) = X1.X2 + X1 + X2
3.07/4.08	
3.07/4.08	Problem 1.2: 
3.07/4.08	
3.07/4.08	SCC Processor:
3.07/4.08	-> FAxioms:
3.07/4.08	 OR(or(x3,x4),x5) = OR(x3,or(x4,x5))
3.07/4.08	 OR(x3,x4) = OR(x4,x3)
3.07/4.08	-> Pairs:
3.07/4.08	 OR(or(and(x,y),z),x3) -> OR(and(or(x,z),or(y,z)),x3)
3.07/4.08	 OR(or(and(x,y),z),x3) -> OR(y,z)
3.07/4.08	 OR(or(x,false),x3) -> OR(x,x3)
3.07/4.08	 OR(or(x,true),x3) -> OR(true,x3)
3.07/4.08	 OR(or(x,x),x3) -> OR(x,x3)
3.07/4.08	-> EAxioms:
3.07/4.08	 and(and(x3,x4),x5) = and(x3,and(x4,x5))
3.07/4.08	 and(x3,x4) = and(x4,x3)
3.07/4.08	 eq(x3,x4) = eq(x4,x3)
3.07/4.08	 neq(x3,x4) = neq(x4,x3)
3.07/4.08	 or(or(x3,x4),x5) = or(x3,or(x4,x5))
3.07/4.08	 or(x3,x4) = or(x4,x3)
3.07/4.08	-> Rules:
3.07/4.08	 and(x,or(x,y)) -> x
3.07/4.08	 and(x,false) -> false
3.07/4.08	 and(x,true) -> x
3.07/4.08	 and(x,x) -> x
3.07/4.08	 eq(x,x) -> true
3.07/4.08	 neq(x,x) -> false
3.07/4.08	 not(and(x,y)) -> or(not(x),not(y))
3.07/4.08	 not(eq(x,y)) -> neq(x,y)
3.07/4.08	 not(neq(x,y)) -> eq(x,y)
3.07/4.08	 not(not(x)) -> x
3.07/4.08	 not(or(x,y)) -> and(not(x),not(y))
3.07/4.08	 not(false) -> true
3.07/4.08	 not(true) -> false
3.07/4.08	 or(and(x,y),z) -> and(or(x,z),or(y,z))
3.07/4.08	 or(x,false) -> x
3.07/4.08	 or(x,true) -> true
3.07/4.08	 or(x,x) -> x
3.07/4.08	-> SRules:
3.07/4.08	 OR(or(x3,x4),x5) -> OR(x3,x4)
3.07/4.08	 OR(x3,or(x4,x5)) -> OR(x4,x5)
3.07/4.08	->Strongly Connected Components:
3.07/4.08	->->Cycle:
3.07/4.08	->->-> Pairs:
3.07/4.08	 OR(or(and(x,y),z),x3) -> OR(and(or(x,z),or(y,z)),x3)
3.07/4.08	 OR(or(and(x,y),z),x3) -> OR(y,z)
3.07/4.08	 OR(or(x,false),x3) -> OR(x,x3)
3.07/4.08	 OR(or(x,true),x3) -> OR(true,x3)
3.07/4.08	 OR(or(x,x),x3) -> OR(x,x3)
3.07/4.08	-> FAxioms:
3.07/4.08	 and(and(x3,x4),x5) -> and(x3,and(x4,x5))
3.07/4.08	 and(x3,x4) -> and(x4,x3)
3.07/4.08	 eq(x3,x4) -> eq(x4,x3)
3.07/4.08	 neq(x3,x4) -> neq(x4,x3)
3.07/4.08	 or(or(x3,x4),x5) -> or(x3,or(x4,x5))
3.07/4.08	 or(x3,x4) -> or(x4,x3)
3.07/4.08	 OR(or(x3,x4),x5) -> OR(x3,or(x4,x5))
3.07/4.08	 OR(x3,x4) -> OR(x4,x3)
3.07/4.08	-> EAxioms:
3.07/4.08	 and(and(x3,x4),x5) = and(x3,and(x4,x5))
3.07/4.08	 and(x3,x4) = and(x4,x3)
3.07/4.08	 eq(x3,x4) = eq(x4,x3)
3.07/4.08	 neq(x3,x4) = neq(x4,x3)
3.07/4.08	 or(or(x3,x4),x5) = or(x3,or(x4,x5))
3.07/4.08	 or(x3,x4) = or(x4,x3)
3.07/4.08	->->-> Rules:
3.07/4.08	 and(x,or(x,y)) -> x
3.07/4.08	 and(x,false) -> false
3.07/4.08	 and(x,true) -> x
3.07/4.08	 and(x,x) -> x
3.07/4.08	 eq(x,x) -> true
3.07/4.08	 neq(x,x) -> false
3.07/4.08	 not(and(x,y)) -> or(not(x),not(y))
3.07/4.08	 not(eq(x,y)) -> neq(x,y)
3.07/4.08	 not(neq(x,y)) -> eq(x,y)
3.07/4.08	 not(not(x)) -> x
3.07/4.08	 not(or(x,y)) -> and(not(x),not(y))
3.07/4.08	 not(false) -> true
3.07/4.08	 not(true) -> false
3.07/4.08	 or(and(x,y),z) -> and(or(x,z),or(y,z))
3.07/4.08	 or(x,false) -> x
3.07/4.08	 or(x,true) -> true
3.07/4.08	 or(x,x) -> x
3.07/4.08	-> SRules:
3.07/4.08	 OR(or(x3,x4),x5) -> OR(x3,x4)
3.07/4.08	 OR(x3,or(x4,x5)) -> OR(x4,x5)
3.07/4.08	
3.07/4.08	Problem 1.2: 
3.07/4.08	
3.07/4.08	Reduction Pairs Processor:
3.07/4.08	-> FAxioms:
3.07/4.08	 OR(or(x3,x4),x5) = OR(x3,or(x4,x5))
3.07/4.08	 OR(x3,x4) = OR(x4,x3)
3.07/4.08	-> Pairs:
3.07/4.08	 OR(or(and(x,y),z),x3) -> OR(and(or(x,z),or(y,z)),x3)
3.07/4.08	 OR(or(and(x,y),z),x3) -> OR(y,z)
3.07/4.08	 OR(or(x,false),x3) -> OR(x,x3)
3.07/4.08	 OR(or(x,true),x3) -> OR(true,x3)
3.07/4.08	 OR(or(x,x),x3) -> OR(x,x3)
3.07/4.08	-> EAxioms:
3.07/4.08	 and(and(x3,x4),x5) = and(x3,and(x4,x5))
3.07/4.08	 and(x3,x4) = and(x4,x3)
3.07/4.08	 eq(x3,x4) = eq(x4,x3)
3.07/4.08	 neq(x3,x4) = neq(x4,x3)
3.07/4.08	 or(or(x3,x4),x5) = or(x3,or(x4,x5))
3.07/4.08	 or(x3,x4) = or(x4,x3)
3.07/4.08	-> Usable Equations:
3.07/4.08	 and(and(x3,x4),x5) = and(x3,and(x4,x5))
3.07/4.08	 and(x3,x4) = and(x4,x3)
3.07/4.08	 or(or(x3,x4),x5) = or(x3,or(x4,x5))
3.07/4.08	 or(x3,x4) = or(x4,x3)
3.07/4.08	-> Rules:
3.07/4.08	 and(x,or(x,y)) -> x
3.07/4.08	 and(x,false) -> false
3.07/4.08	 and(x,true) -> x
3.07/4.08	 and(x,x) -> x
3.07/4.08	 eq(x,x) -> true
3.07/4.08	 neq(x,x) -> false
3.07/4.08	 not(and(x,y)) -> or(not(x),not(y))
3.07/4.08	 not(eq(x,y)) -> neq(x,y)
3.07/4.08	 not(neq(x,y)) -> eq(x,y)
3.07/4.08	 not(not(x)) -> x
3.07/4.08	 not(or(x,y)) -> and(not(x),not(y))
3.07/4.08	 not(false) -> true
3.07/4.08	 not(true) -> false
3.07/4.08	 or(and(x,y),z) -> and(or(x,z),or(y,z))
3.07/4.08	 or(x,false) -> x
3.07/4.08	 or(x,true) -> true
3.07/4.08	 or(x,x) -> x
3.07/4.08	-> Usable Rules:
3.07/4.08	 and(x,or(x,y)) -> x
3.07/4.08	 and(x,false) -> false
3.07/4.08	 and(x,true) -> x
3.07/4.08	 and(x,x) -> x
3.07/4.08	 or(and(x,y),z) -> and(or(x,z),or(y,z))
3.07/4.08	 or(x,false) -> x
3.07/4.08	 or(x,true) -> true
3.07/4.08	 or(x,x) -> x
3.07/4.08	-> SRules:
3.07/4.08	 OR(or(x3,x4),x5) -> OR(x3,x4)
3.07/4.08	 OR(x3,or(x4,x5)) -> OR(x4,x5)
3.07/4.08	->Interpretation type:
3.07/4.08	 Simple mixed
3.07/4.08	->Coefficients:
3.07/4.08	 Natural Numbers
3.07/4.08	->Dimension:
3.07/4.08	 1
3.07/4.08	->Bound:
3.07/4.08	 1
3.07/4.08	->Interpretation:
3.07/4.08	 
3.07/4.08	[and](X1,X2) = X1 + X2 + 1
3.07/4.08	[eq](X1,X2) = 0
3.07/4.08	[neq](X1,X2) = 0
3.07/4.08	[not](X) = 0
3.07/4.08	[or](X1,X2) = X1.X2 + X1 + X2
3.07/4.08	[false] = 1
3.07/4.08	[true] = 1
3.07/4.08	[AND](X1,X2) = 0
3.07/4.08	[EQ](X1,X2) = 0
3.07/4.08	[NEQ](X1,X2) = 0
3.07/4.08	[NOT](X) = 0
3.07/4.08	[OR](X1,X2) = X1.X2 + X1 + X2
3.07/4.08	
3.07/4.08	Problem 1.2: 
3.07/4.08	
3.07/4.08	SCC Processor:
3.07/4.08	-> FAxioms:
3.07/4.08	 OR(or(x3,x4),x5) = OR(x3,or(x4,x5))
3.07/4.08	 OR(x3,x4) = OR(x4,x3)
3.07/4.08	-> Pairs:
3.07/4.08	 OR(or(and(x,y),z),x3) -> OR(and(or(x,z),or(y,z)),x3)
3.07/4.08	 OR(or(x,false),x3) -> OR(x,x3)
3.07/4.08	 OR(or(x,true),x3) -> OR(true,x3)
3.07/4.08	 OR(or(x,x),x3) -> OR(x,x3)
3.07/4.08	-> EAxioms:
3.07/4.08	 and(and(x3,x4),x5) = and(x3,and(x4,x5))
3.07/4.08	 and(x3,x4) = and(x4,x3)
3.07/4.08	 eq(x3,x4) = eq(x4,x3)
3.07/4.08	 neq(x3,x4) = neq(x4,x3)
3.07/4.09	 or(or(x3,x4),x5) = or(x3,or(x4,x5))
3.07/4.09	 or(x3,x4) = or(x4,x3)
3.07/4.09	-> Rules:
3.07/4.09	 and(x,or(x,y)) -> x
3.07/4.09	 and(x,false) -> false
3.07/4.09	 and(x,true) -> x
3.07/4.09	 and(x,x) -> x
3.07/4.09	 eq(x,x) -> true
3.07/4.09	 neq(x,x) -> false
3.07/4.09	 not(and(x,y)) -> or(not(x),not(y))
3.07/4.09	 not(eq(x,y)) -> neq(x,y)
3.07/4.09	 not(neq(x,y)) -> eq(x,y)
3.07/4.09	 not(not(x)) -> x
3.07/4.09	 not(or(x,y)) -> and(not(x),not(y))
3.07/4.09	 not(false) -> true
3.07/4.09	 not(true) -> false
3.07/4.09	 or(and(x,y),z) -> and(or(x,z),or(y,z))
3.07/4.09	 or(x,false) -> x
3.07/4.09	 or(x,true) -> true
3.07/4.09	 or(x,x) -> x
3.07/4.09	-> SRules:
3.07/4.09	 OR(or(x3,x4),x5) -> OR(x3,x4)
3.07/4.09	 OR(x3,or(x4,x5)) -> OR(x4,x5)
3.07/4.09	->Strongly Connected Components:
3.07/4.09	->->Cycle:
3.07/4.09	->->-> Pairs:
3.07/4.09	 OR(or(and(x,y),z),x3) -> OR(and(or(x,z),or(y,z)),x3)
3.07/4.09	 OR(or(x,false),x3) -> OR(x,x3)
3.07/4.09	 OR(or(x,true),x3) -> OR(true,x3)
3.07/4.09	 OR(or(x,x),x3) -> OR(x,x3)
3.07/4.09	-> FAxioms:
3.07/4.09	 and(and(x3,x4),x5) -> and(x3,and(x4,x5))
3.07/4.09	 and(x3,x4) -> and(x4,x3)
3.07/4.09	 eq(x3,x4) -> eq(x4,x3)
3.07/4.09	 neq(x3,x4) -> neq(x4,x3)
3.07/4.09	 or(or(x3,x4),x5) -> or(x3,or(x4,x5))
3.07/4.09	 or(x3,x4) -> or(x4,x3)
3.07/4.09	 OR(or(x3,x4),x5) -> OR(x3,or(x4,x5))
3.07/4.09	 OR(x3,x4) -> OR(x4,x3)
3.07/4.09	-> EAxioms:
3.07/4.09	 and(and(x3,x4),x5) = and(x3,and(x4,x5))
3.07/4.09	 and(x3,x4) = and(x4,x3)
3.07/4.09	 eq(x3,x4) = eq(x4,x3)
3.07/4.09	 neq(x3,x4) = neq(x4,x3)
3.07/4.09	 or(or(x3,x4),x5) = or(x3,or(x4,x5))
3.07/4.09	 or(x3,x4) = or(x4,x3)
3.07/4.09	->->-> Rules:
3.07/4.09	 and(x,or(x,y)) -> x
3.07/4.09	 and(x,false) -> false
3.07/4.09	 and(x,true) -> x
3.07/4.09	 and(x,x) -> x
3.07/4.09	 eq(x,x) -> true
3.07/4.09	 neq(x,x) -> false
3.07/4.09	 not(and(x,y)) -> or(not(x),not(y))
3.07/4.09	 not(eq(x,y)) -> neq(x,y)
3.07/4.09	 not(neq(x,y)) -> eq(x,y)
3.07/4.09	 not(not(x)) -> x
3.07/4.09	 not(or(x,y)) -> and(not(x),not(y))
3.07/4.09	 not(false) -> true
3.07/4.09	 not(true) -> false
3.07/4.09	 or(and(x,y),z) -> and(or(x,z),or(y,z))
3.07/4.09	 or(x,false) -> x
3.07/4.09	 or(x,true) -> true
3.07/4.09	 or(x,x) -> x
3.07/4.09	-> SRules:
3.07/4.09	 OR(or(x3,x4),x5) -> OR(x3,x4)
3.07/4.09	 OR(x3,or(x4,x5)) -> OR(x4,x5)
3.07/4.09	
3.07/4.09	Problem 1.2: 
3.07/4.09	
3.07/4.09	Reduction Pairs Processor:
3.07/4.09	-> FAxioms:
3.07/4.09	 OR(or(x3,x4),x5) = OR(x3,or(x4,x5))
3.07/4.09	 OR(x3,x4) = OR(x4,x3)
3.07/4.09	-> Pairs:
3.07/4.09	 OR(or(and(x,y),z),x3) -> OR(and(or(x,z),or(y,z)),x3)
3.07/4.09	 OR(or(x,false),x3) -> OR(x,x3)
3.07/4.09	 OR(or(x,true),x3) -> OR(true,x3)
3.07/4.09	 OR(or(x,x),x3) -> OR(x,x3)
3.07/4.09	-> EAxioms:
3.07/4.09	 and(and(x3,x4),x5) = and(x3,and(x4,x5))
3.07/4.09	 and(x3,x4) = and(x4,x3)
3.07/4.09	 eq(x3,x4) = eq(x4,x3)
3.07/4.09	 neq(x3,x4) = neq(x4,x3)
3.07/4.09	 or(or(x3,x4),x5) = or(x3,or(x4,x5))
3.07/4.09	 or(x3,x4) = or(x4,x3)
3.07/4.09	-> Usable Equations:
3.07/4.09	 and(and(x3,x4),x5) = and(x3,and(x4,x5))
3.07/4.09	 and(x3,x4) = and(x4,x3)
3.07/4.09	 or(or(x3,x4),x5) = or(x3,or(x4,x5))
3.07/4.09	 or(x3,x4) = or(x4,x3)
3.07/4.09	-> Rules:
3.07/4.09	 and(x,or(x,y)) -> x
3.07/4.09	 and(x,false) -> false
3.07/4.09	 and(x,true) -> x
3.07/4.09	 and(x,x) -> x
3.07/4.09	 eq(x,x) -> true
3.07/4.09	 neq(x,x) -> false
3.07/4.09	 not(and(x,y)) -> or(not(x),not(y))
3.07/4.09	 not(eq(x,y)) -> neq(x,y)
3.07/4.09	 not(neq(x,y)) -> eq(x,y)
3.07/4.09	 not(not(x)) -> x
3.07/4.09	 not(or(x,y)) -> and(not(x),not(y))
3.07/4.09	 not(false) -> true
3.07/4.09	 not(true) -> false
3.07/4.09	 or(and(x,y),z) -> and(or(x,z),or(y,z))
3.07/4.09	 or(x,false) -> x
3.07/4.09	 or(x,true) -> true
3.07/4.09	 or(x,x) -> x
3.07/4.09	-> Usable Rules:
3.07/4.09	 and(x,or(x,y)) -> x
3.07/4.09	 and(x,false) -> false
3.07/4.09	 and(x,true) -> x
3.07/4.09	 and(x,x) -> x
3.07/4.09	 or(and(x,y),z) -> and(or(x,z),or(y,z))
3.07/4.09	 or(x,false) -> x
3.07/4.09	 or(x,true) -> true
3.07/4.09	 or(x,x) -> x
3.07/4.09	-> SRules:
3.07/4.09	 OR(or(x3,x4),x5) -> OR(x3,x4)
3.07/4.09	 OR(x3,or(x4,x5)) -> OR(x4,x5)
3.07/4.09	->Interpretation type:
3.07/4.09	 Simple mixed
3.07/4.09	->Coefficients:
3.07/4.09	 Natural Numbers
3.07/4.09	->Dimension:
3.07/4.09	 1
3.07/4.09	->Bound:
3.07/4.09	 1
3.07/4.09	->Interpretation:
3.07/4.09	 
3.07/4.09	[and](X1,X2) = X1 + X2 + 1
3.07/4.09	[eq](X1,X2) = 0
3.07/4.09	[neq](X1,X2) = 0
3.07/4.09	[not](X) = 0
3.07/4.09	[or](X1,X2) = X1.X2 + X1 + X2
3.07/4.09	[false] = 1
3.07/4.09	[true] = 1
3.07/4.09	[AND](X1,X2) = 0
3.07/4.09	[EQ](X1,X2) = 0
3.07/4.09	[NEQ](X1,X2) = 0
3.07/4.09	[NOT](X) = 0
3.07/4.09	[OR](X1,X2) = X1.X2 + X1 + X2
3.07/4.09	
3.07/4.09	Problem 1.2: 
3.07/4.09	
3.07/4.09	SCC Processor:
3.07/4.09	-> FAxioms:
3.07/4.09	 OR(or(x3,x4),x5) = OR(x3,or(x4,x5))
3.07/4.09	 OR(x3,x4) = OR(x4,x3)
3.07/4.09	-> Pairs:
3.07/4.09	 OR(or(and(x,y),z),x3) -> OR(and(or(x,z),or(y,z)),x3)
3.07/4.09	 OR(or(x,true),x3) -> OR(true,x3)
3.07/4.09	 OR(or(x,x),x3) -> OR(x,x3)
3.07/4.09	-> EAxioms:
3.07/4.09	 and(and(x3,x4),x5) = and(x3,and(x4,x5))
3.07/4.09	 and(x3,x4) = and(x4,x3)
3.07/4.09	 eq(x3,x4) = eq(x4,x3)
3.07/4.09	 neq(x3,x4) = neq(x4,x3)
3.07/4.09	 or(or(x3,x4),x5) = or(x3,or(x4,x5))
3.07/4.09	 or(x3,x4) = or(x4,x3)
3.07/4.09	-> Rules:
3.07/4.09	 and(x,or(x,y)) -> x
3.07/4.09	 and(x,false) -> false
3.07/4.09	 and(x,true) -> x
3.07/4.09	 and(x,x) -> x
3.07/4.09	 eq(x,x) -> true
3.07/4.09	 neq(x,x) -> false
3.07/4.09	 not(and(x,y)) -> or(not(x),not(y))
3.07/4.09	 not(eq(x,y)) -> neq(x,y)
3.07/4.09	 not(neq(x,y)) -> eq(x,y)
3.07/4.09	 not(not(x)) -> x
3.07/4.09	 not(or(x,y)) -> and(not(x),not(y))
3.07/4.09	 not(false) -> true
3.07/4.09	 not(true) -> false
3.07/4.09	 or(and(x,y),z) -> and(or(x,z),or(y,z))
3.07/4.09	 or(x,false) -> x
3.07/4.09	 or(x,true) -> true
3.07/4.09	 or(x,x) -> x
3.07/4.09	-> SRules:
3.07/4.09	 OR(or(x3,x4),x5) -> OR(x3,x4)
3.07/4.09	 OR(x3,or(x4,x5)) -> OR(x4,x5)
3.07/4.09	->Strongly Connected Components:
3.07/4.09	->->Cycle:
3.07/4.09	->->-> Pairs:
3.07/4.09	 OR(or(and(x,y),z),x3) -> OR(and(or(x,z),or(y,z)),x3)
3.07/4.09	 OR(or(x,true),x3) -> OR(true,x3)
3.07/4.09	 OR(or(x,x),x3) -> OR(x,x3)
3.07/4.09	-> FAxioms:
3.07/4.09	 and(and(x3,x4),x5) -> and(x3,and(x4,x5))
3.07/4.09	 and(x3,x4) -> and(x4,x3)
3.07/4.09	 eq(x3,x4) -> eq(x4,x3)
3.07/4.09	 neq(x3,x4) -> neq(x4,x3)
3.07/4.09	 or(or(x3,x4),x5) -> or(x3,or(x4,x5))
3.07/4.09	 or(x3,x4) -> or(x4,x3)
3.07/4.09	 OR(or(x3,x4),x5) -> OR(x3,or(x4,x5))
3.07/4.09	 OR(x3,x4) -> OR(x4,x3)
3.07/4.09	-> EAxioms:
3.07/4.09	 and(and(x3,x4),x5) = and(x3,and(x4,x5))
3.07/4.09	 and(x3,x4) = and(x4,x3)
3.07/4.09	 eq(x3,x4) = eq(x4,x3)
3.07/4.09	 neq(x3,x4) = neq(x4,x3)
3.07/4.09	 or(or(x3,x4),x5) = or(x3,or(x4,x5))
3.07/4.09	 or(x3,x4) = or(x4,x3)
3.07/4.09	->->-> Rules:
3.07/4.09	 and(x,or(x,y)) -> x
3.07/4.09	 and(x,false) -> false
3.07/4.09	 and(x,true) -> x
3.07/4.09	 and(x,x) -> x
3.07/4.09	 eq(x,x) -> true
3.07/4.09	 neq(x,x) -> false
3.07/4.09	 not(and(x,y)) -> or(not(x),not(y))
3.07/4.09	 not(eq(x,y)) -> neq(x,y)
3.07/4.09	 not(neq(x,y)) -> eq(x,y)
3.07/4.09	 not(not(x)) -> x
3.07/4.09	 not(or(x,y)) -> and(not(x),not(y))
3.07/4.09	 not(false) -> true
3.07/4.09	 not(true) -> false
3.07/4.09	 or(and(x,y),z) -> and(or(x,z),or(y,z))
3.07/4.09	 or(x,false) -> x
3.07/4.09	 or(x,true) -> true
3.07/4.09	 or(x,x) -> x
3.07/4.09	-> SRules:
3.07/4.09	 OR(or(x3,x4),x5) -> OR(x3,x4)
3.07/4.09	 OR(x3,or(x4,x5)) -> OR(x4,x5)
3.07/4.09	
3.07/4.09	Problem 1.2: 
3.07/4.09	
3.07/4.09	Reduction Pairs Processor:
3.07/4.09	-> FAxioms:
3.07/4.09	 OR(or(x3,x4),x5) = OR(x3,or(x4,x5))
3.07/4.09	 OR(x3,x4) = OR(x4,x3)
3.07/4.09	-> Pairs:
3.07/4.09	 OR(or(and(x,y),z),x3) -> OR(and(or(x,z),or(y,z)),x3)
3.07/4.09	 OR(or(x,true),x3) -> OR(true,x3)
3.07/4.09	 OR(or(x,x),x3) -> OR(x,x3)
3.07/4.09	-> EAxioms:
3.07/4.09	 and(and(x3,x4),x5) = and(x3,and(x4,x5))
3.07/4.09	 and(x3,x4) = and(x4,x3)
3.07/4.09	 eq(x3,x4) = eq(x4,x3)
3.07/4.09	 neq(x3,x4) = neq(x4,x3)
3.07/4.09	 or(or(x3,x4),x5) = or(x3,or(x4,x5))
3.07/4.09	 or(x3,x4) = or(x4,x3)
3.07/4.09	-> Usable Equations:
3.07/4.09	 and(and(x3,x4),x5) = and(x3,and(x4,x5))
3.07/4.09	 and(x3,x4) = and(x4,x3)
3.07/4.09	 or(or(x3,x4),x5) = or(x3,or(x4,x5))
3.07/4.09	 or(x3,x4) = or(x4,x3)
3.07/4.09	-> Rules:
3.07/4.09	 and(x,or(x,y)) -> x
3.07/4.09	 and(x,false) -> false
3.07/4.09	 and(x,true) -> x
3.07/4.09	 and(x,x) -> x
3.07/4.09	 eq(x,x) -> true
3.07/4.09	 neq(x,x) -> false
3.07/4.09	 not(and(x,y)) -> or(not(x),not(y))
3.07/4.09	 not(eq(x,y)) -> neq(x,y)
3.07/4.09	 not(neq(x,y)) -> eq(x,y)
3.07/4.09	 not(not(x)) -> x
3.07/4.09	 not(or(x,y)) -> and(not(x),not(y))
3.07/4.09	 not(false) -> true
3.07/4.09	 not(true) -> false
3.07/4.09	 or(and(x,y),z) -> and(or(x,z),or(y,z))
3.07/4.09	 or(x,false) -> x
3.07/4.09	 or(x,true) -> true
3.07/4.09	 or(x,x) -> x
3.07/4.09	-> Usable Rules:
3.07/4.09	 and(x,or(x,y)) -> x
3.07/4.09	 and(x,false) -> false
3.07/4.09	 and(x,true) -> x
3.07/4.09	 and(x,x) -> x
3.07/4.09	 or(and(x,y),z) -> and(or(x,z),or(y,z))
3.07/4.09	 or(x,false) -> x
3.07/4.09	 or(x,true) -> true
3.07/4.09	 or(x,x) -> x
3.07/4.09	-> SRules:
3.07/4.09	 OR(or(x3,x4),x5) -> OR(x3,x4)
3.07/4.09	 OR(x3,or(x4,x5)) -> OR(x4,x5)
3.07/4.09	->Interpretation type:
3.07/4.09	 Simple mixed
3.07/4.09	->Coefficients:
3.07/4.09	 All rationals
3.07/4.09	->Dimension:
3.07/4.09	 1
3.07/4.09	->Bound:
3.07/4.09	 3
3.07/4.09	->Interpretation:
3.07/4.09	 
3.07/4.09	[and](X1,X2) = X1 + X2 + 3
3.07/4.09	[eq](X1,X2) = 0
3.07/4.09	[neq](X1,X2) = 0
3.07/4.09	[not](X) = 0
3.07/4.09	[or](X1,X2) = 2.X1.X2 + 3.X1 + 3.X2 + 3
3.07/4.09	[false] = 2
3.07/4.09	[true] = 0
3.07/4.09	[AND](X1,X2) = 0
3.07/4.09	[EQ](X1,X2) = 0
3.07/4.09	[NEQ](X1,X2) = 0
3.07/4.09	[NOT](X) = 0
3.07/4.09	[OR](X1,X2) = 2.X1.X2 + 3.X1 + 3.X2
3.07/4.09	
3.07/4.09	Problem 1.2: 
3.07/4.09	
3.07/4.09	SCC Processor:
3.07/4.09	-> FAxioms:
3.07/4.09	 OR(or(x3,x4),x5) = OR(x3,or(x4,x5))
3.07/4.09	 OR(x3,x4) = OR(x4,x3)
3.07/4.09	-> Pairs:
3.07/4.09	 OR(or(x,true),x3) -> OR(true,x3)
3.07/4.09	 OR(or(x,x),x3) -> OR(x,x3)
3.07/4.09	-> EAxioms:
3.07/4.09	 and(and(x3,x4),x5) = and(x3,and(x4,x5))
3.07/4.09	 and(x3,x4) = and(x4,x3)
3.07/4.09	 eq(x3,x4) = eq(x4,x3)
3.07/4.09	 neq(x3,x4) = neq(x4,x3)
3.07/4.09	 or(or(x3,x4),x5) = or(x3,or(x4,x5))
3.07/4.09	 or(x3,x4) = or(x4,x3)
3.07/4.09	-> Rules:
3.07/4.09	 and(x,or(x,y)) -> x
3.07/4.09	 and(x,false) -> false
3.07/4.09	 and(x,true) -> x
3.07/4.09	 and(x,x) -> x
3.07/4.09	 eq(x,x) -> true
3.07/4.09	 neq(x,x) -> false
3.07/4.09	 not(and(x,y)) -> or(not(x),not(y))
3.07/4.09	 not(eq(x,y)) -> neq(x,y)
3.07/4.09	 not(neq(x,y)) -> eq(x,y)
3.07/4.09	 not(not(x)) -> x
3.07/4.09	 not(or(x,y)) -> and(not(x),not(y))
3.07/4.09	 not(false) -> true
3.07/4.09	 not(true) -> false
3.07/4.09	 or(and(x,y),z) -> and(or(x,z),or(y,z))
3.07/4.09	 or(x,false) -> x
3.07/4.09	 or(x,true) -> true
3.07/4.09	 or(x,x) -> x
3.07/4.09	-> SRules:
3.07/4.09	 OR(or(x3,x4),x5) -> OR(x3,x4)
3.07/4.09	 OR(x3,or(x4,x5)) -> OR(x4,x5)
3.07/4.09	->Strongly Connected Components:
3.07/4.09	->->Cycle:
3.07/4.09	->->-> Pairs:
3.07/4.09	 OR(or(x,true),x3) -> OR(true,x3)
3.07/4.09	 OR(or(x,x),x3) -> OR(x,x3)
3.07/4.09	-> FAxioms:
3.07/4.09	 and(and(x3,x4),x5) -> and(x3,and(x4,x5))
3.07/4.09	 and(x3,x4) -> and(x4,x3)
3.07/4.09	 eq(x3,x4) -> eq(x4,x3)
3.07/4.09	 neq(x3,x4) -> neq(x4,x3)
3.07/4.09	 or(or(x3,x4),x5) -> or(x3,or(x4,x5))
3.07/4.09	 or(x3,x4) -> or(x4,x3)
3.07/4.09	 OR(or(x3,x4),x5) -> OR(x3,or(x4,x5))
3.07/4.09	 OR(x3,x4) -> OR(x4,x3)
3.07/4.09	-> EAxioms:
3.07/4.09	 and(and(x3,x4),x5) = and(x3,and(x4,x5))
3.07/4.09	 and(x3,x4) = and(x4,x3)
3.07/4.09	 eq(x3,x4) = eq(x4,x3)
3.07/4.09	 neq(x3,x4) = neq(x4,x3)
3.07/4.09	 or(or(x3,x4),x5) = or(x3,or(x4,x5))
3.07/4.09	 or(x3,x4) = or(x4,x3)
3.07/4.09	->->-> Rules:
3.07/4.09	 and(x,or(x,y)) -> x
3.07/4.09	 and(x,false) -> false
3.07/4.09	 and(x,true) -> x
3.07/4.09	 and(x,x) -> x
3.07/4.09	 eq(x,x) -> true
3.07/4.09	 neq(x,x) -> false
3.07/4.09	 not(and(x,y)) -> or(not(x),not(y))
3.07/4.09	 not(eq(x,y)) -> neq(x,y)
3.07/4.09	 not(neq(x,y)) -> eq(x,y)
3.07/4.09	 not(not(x)) -> x
3.07/4.09	 not(or(x,y)) -> and(not(x),not(y))
3.07/4.09	 not(false) -> true
3.07/4.09	 not(true) -> false
3.07/4.09	 or(and(x,y),z) -> and(or(x,z),or(y,z))
3.07/4.09	 or(x,false) -> x
3.07/4.09	 or(x,true) -> true
3.07/4.09	 or(x,x) -> x
3.07/4.09	-> SRules:
3.07/4.09	 OR(or(x3,x4),x5) -> OR(x3,x4)
3.07/4.09	 OR(x3,or(x4,x5)) -> OR(x4,x5)
3.07/4.09	
3.07/4.09	Problem 1.2: 
3.07/4.09	
3.07/4.09	Reduction Pairs Processor:
3.07/4.09	-> FAxioms:
3.07/4.09	 OR(or(x3,x4),x5) = OR(x3,or(x4,x5))
3.07/4.09	 OR(x3,x4) = OR(x4,x3)
3.07/4.09	-> Pairs:
3.07/4.09	 OR(or(x,true),x3) -> OR(true,x3)
3.07/4.09	 OR(or(x,x),x3) -> OR(x,x3)
3.07/4.09	-> EAxioms:
3.07/4.09	 and(and(x3,x4),x5) = and(x3,and(x4,x5))
3.07/4.09	 and(x3,x4) = and(x4,x3)
3.07/4.09	 eq(x3,x4) = eq(x4,x3)
3.07/4.09	 neq(x3,x4) = neq(x4,x3)
3.07/4.09	 or(or(x3,x4),x5) = or(x3,or(x4,x5))
3.07/4.09	 or(x3,x4) = or(x4,x3)
3.07/4.09	-> Usable Equations:
3.07/4.09	 and(and(x3,x4),x5) = and(x3,and(x4,x5))
3.07/4.09	 and(x3,x4) = and(x4,x3)
3.07/4.09	 or(or(x3,x4),x5) = or(x3,or(x4,x5))
3.07/4.09	 or(x3,x4) = or(x4,x3)
3.07/4.09	-> Rules:
3.07/4.09	 and(x,or(x,y)) -> x
3.07/4.09	 and(x,false) -> false
3.07/4.09	 and(x,true) -> x
3.07/4.09	 and(x,x) -> x
3.07/4.09	 eq(x,x) -> true
3.07/4.09	 neq(x,x) -> false
3.07/4.09	 not(and(x,y)) -> or(not(x),not(y))
3.07/4.09	 not(eq(x,y)) -> neq(x,y)
3.07/4.09	 not(neq(x,y)) -> eq(x,y)
3.07/4.09	 not(not(x)) -> x
3.07/4.09	 not(or(x,y)) -> and(not(x),not(y))
3.07/4.09	 not(false) -> true
3.07/4.09	 not(true) -> false
3.07/4.09	 or(and(x,y),z) -> and(or(x,z),or(y,z))
3.07/4.09	 or(x,false) -> x
3.07/4.09	 or(x,true) -> true
3.07/4.09	 or(x,x) -> x
3.07/4.09	-> Usable Rules:
3.07/4.09	 and(x,or(x,y)) -> x
3.07/4.09	 and(x,false) -> false
3.07/4.09	 and(x,true) -> x
3.07/4.09	 and(x,x) -> x
3.07/4.09	 or(and(x,y),z) -> and(or(x,z),or(y,z))
3.07/4.09	 or(x,false) -> x
3.07/4.09	 or(x,true) -> true
3.07/4.09	 or(x,x) -> x
3.07/4.09	-> SRules:
3.07/4.09	 OR(or(x3,x4),x5) -> OR(x3,x4)
3.07/4.09	 OR(x3,or(x4,x5)) -> OR(x4,x5)
3.07/4.09	->Interpretation type:
3.07/4.09	 Simple mixed
3.07/4.09	->Coefficients:
3.07/4.09	 All rationals
3.07/4.09	->Dimension:
3.07/4.09	 1
3.07/4.09	->Bound:
3.07/4.09	 3
3.07/4.09	->Interpretation:
3.07/4.09	 
3.07/4.09	[and](X1,X2) = X1 + X2 + 3
3.07/4.09	[eq](X1,X2) = 0
3.07/4.09	[neq](X1,X2) = 0
3.07/4.09	[not](X) = 0
3.07/4.09	[or](X1,X2) = 2.X1.X2 + 3.X1 + 3.X2 + 3
3.07/4.09	[false] = 1/3
3.07/4.09	[true] = 0
3.07/4.09	[AND](X1,X2) = 0
3.07/4.09	[EQ](X1,X2) = 0
3.07/4.09	[NEQ](X1,X2) = 0
3.07/4.09	[NOT](X) = 0
3.07/4.09	[OR](X1,X2) = 1/3.X1.X2 + 1/2.X1 + 1/2.X2
3.07/4.09	
3.07/4.09	Problem 1.2: 
3.07/4.09	
3.07/4.09	SCC Processor:
3.07/4.09	-> FAxioms:
3.07/4.09	 OR(or(x3,x4),x5) = OR(x3,or(x4,x5))
3.07/4.09	 OR(x3,x4) = OR(x4,x3)
3.07/4.09	-> Pairs:
3.07/4.09	 OR(or(x,x),x3) -> OR(x,x3)
3.07/4.09	-> EAxioms:
3.07/4.09	 and(and(x3,x4),x5) = and(x3,and(x4,x5))
3.07/4.09	 and(x3,x4) = and(x4,x3)
3.07/4.09	 eq(x3,x4) = eq(x4,x3)
3.07/4.09	 neq(x3,x4) = neq(x4,x3)
3.07/4.09	 or(or(x3,x4),x5) = or(x3,or(x4,x5))
3.07/4.09	 or(x3,x4) = or(x4,x3)
3.07/4.09	-> Rules:
3.07/4.09	 and(x,or(x,y)) -> x
3.07/4.09	 and(x,false) -> false
3.07/4.09	 and(x,true) -> x
3.07/4.09	 and(x,x) -> x
3.07/4.09	 eq(x,x) -> true
3.07/4.09	 neq(x,x) -> false
3.07/4.09	 not(and(x,y)) -> or(not(x),not(y))
3.07/4.09	 not(eq(x,y)) -> neq(x,y)
3.07/4.09	 not(neq(x,y)) -> eq(x,y)
3.07/4.09	 not(not(x)) -> x
3.07/4.09	 not(or(x,y)) -> and(not(x),not(y))
3.07/4.09	 not(false) -> true
3.07/4.09	 not(true) -> false
3.07/4.09	 or(and(x,y),z) -> and(or(x,z),or(y,z))
3.07/4.09	 or(x,false) -> x
3.07/4.09	 or(x,true) -> true
3.07/4.09	 or(x,x) -> x
3.07/4.09	-> SRules:
3.07/4.09	 OR(or(x3,x4),x5) -> OR(x3,x4)
3.07/4.09	 OR(x3,or(x4,x5)) -> OR(x4,x5)
3.07/4.09	->Strongly Connected Components:
3.07/4.09	->->Cycle:
3.07/4.09	->->-> Pairs:
3.07/4.09	 OR(or(x,x),x3) -> OR(x,x3)
3.07/4.09	-> FAxioms:
3.07/4.09	 and(and(x3,x4),x5) -> and(x3,and(x4,x5))
3.07/4.09	 and(x3,x4) -> and(x4,x3)
3.07/4.09	 eq(x3,x4) -> eq(x4,x3)
3.07/4.09	 neq(x3,x4) -> neq(x4,x3)
3.07/4.09	 or(or(x3,x4),x5) -> or(x3,or(x4,x5))
3.07/4.09	 or(x3,x4) -> or(x4,x3)
3.07/4.09	 OR(or(x3,x4),x5) -> OR(x3,or(x4,x5))
3.07/4.09	 OR(x3,x4) -> OR(x4,x3)
3.07/4.09	-> EAxioms:
3.07/4.09	 and(and(x3,x4),x5) = and(x3,and(x4,x5))
3.07/4.09	 and(x3,x4) = and(x4,x3)
3.07/4.09	 eq(x3,x4) = eq(x4,x3)
3.07/4.09	 neq(x3,x4) = neq(x4,x3)
3.07/4.09	 or(or(x3,x4),x5) = or(x3,or(x4,x5))
3.07/4.09	 or(x3,x4) = or(x4,x3)
3.07/4.09	->->-> Rules:
3.07/4.09	 and(x,or(x,y)) -> x
3.07/4.09	 and(x,false) -> false
3.07/4.09	 and(x,true) -> x
3.07/4.09	 and(x,x) -> x
3.07/4.09	 eq(x,x) -> true
3.07/4.09	 neq(x,x) -> false
3.07/4.09	 not(and(x,y)) -> or(not(x),not(y))
3.07/4.09	 not(eq(x,y)) -> neq(x,y)
3.07/4.09	 not(neq(x,y)) -> eq(x,y)
3.07/4.09	 not(not(x)) -> x
3.07/4.09	 not(or(x,y)) -> and(not(x),not(y))
3.07/4.09	 not(false) -> true
3.07/4.09	 not(true) -> false
3.07/4.09	 or(and(x,y),z) -> and(or(x,z),or(y,z))
3.07/4.09	 or(x,false) -> x
3.07/4.09	 or(x,true) -> true
3.07/4.09	 or(x,x) -> x
3.07/4.09	-> SRules:
3.07/4.09	 OR(or(x3,x4),x5) -> OR(x3,x4)
3.07/4.09	 OR(x3,or(x4,x5)) -> OR(x4,x5)
3.07/4.09	
3.07/4.09	Problem 1.2: 
3.07/4.09	
3.07/4.09	Reduction Pairs Processor:
3.07/4.09	-> FAxioms:
3.07/4.09	 OR(or(x3,x4),x5) = OR(x3,or(x4,x5))
3.07/4.09	 OR(x3,x4) = OR(x4,x3)
3.07/4.09	-> Pairs:
3.07/4.09	 OR(or(x,x),x3) -> OR(x,x3)
3.07/4.09	-> EAxioms:
3.07/4.09	 and(and(x3,x4),x5) = and(x3,and(x4,x5))
3.07/4.09	 and(x3,x4) = and(x4,x3)
3.07/4.09	 eq(x3,x4) = eq(x4,x3)
3.07/4.09	 neq(x3,x4) = neq(x4,x3)
3.07/4.09	 or(or(x3,x4),x5) = or(x3,or(x4,x5))
3.07/4.09	 or(x3,x4) = or(x4,x3)
3.07/4.09	-> Usable Equations:
3.07/4.09	 and(and(x3,x4),x5) = and(x3,and(x4,x5))
3.07/4.09	 and(x3,x4) = and(x4,x3)
3.07/4.09	 or(or(x3,x4),x5) = or(x3,or(x4,x5))
3.07/4.09	 or(x3,x4) = or(x4,x3)
3.07/4.09	-> Rules:
3.07/4.09	 and(x,or(x,y)) -> x
3.07/4.09	 and(x,false) -> false
3.07/4.09	 and(x,true) -> x
3.07/4.09	 and(x,x) -> x
3.07/4.09	 eq(x,x) -> true
3.07/4.09	 neq(x,x) -> false
3.07/4.09	 not(and(x,y)) -> or(not(x),not(y))
3.07/4.09	 not(eq(x,y)) -> neq(x,y)
3.07/4.09	 not(neq(x,y)) -> eq(x,y)
3.07/4.09	 not(not(x)) -> x
3.07/4.09	 not(or(x,y)) -> and(not(x),not(y))
3.07/4.09	 not(false) -> true
3.07/4.09	 not(true) -> false
3.07/4.09	 or(and(x,y),z) -> and(or(x,z),or(y,z))
3.07/4.09	 or(x,false) -> x
3.07/4.09	 or(x,true) -> true
3.07/4.09	 or(x,x) -> x
3.07/4.09	-> Usable Rules:
3.07/4.09	 and(x,or(x,y)) -> x
3.07/4.09	 and(x,false) -> false
3.07/4.09	 and(x,true) -> x
3.07/4.09	 and(x,x) -> x
3.07/4.09	 or(and(x,y),z) -> and(or(x,z),or(y,z))
3.07/4.09	 or(x,false) -> x
3.07/4.09	 or(x,true) -> true
3.07/4.09	 or(x,x) -> x
3.07/4.09	-> SRules:
3.07/4.09	 OR(or(x3,x4),x5) -> OR(x3,x4)
3.07/4.09	 OR(x3,or(x4,x5)) -> OR(x4,x5)
3.07/4.09	->Interpretation type:
3.07/4.09	 Simple mixed
3.07/4.09	->Coefficients:
3.07/4.09	 All rationals
3.07/4.09	->Dimension:
3.07/4.09	 1
3.07/4.09	->Bound:
3.07/4.09	 3
3.07/4.09	->Interpretation:
3.07/4.09	 
3.07/4.09	[and](X1,X2) = X1 + X2 + 2
3.07/4.09	[eq](X1,X2) = 0
3.07/4.09	[neq](X1,X2) = 0
3.07/4.09	[not](X) = 0
3.07/4.09	[or](X1,X2) = 3/2.X1.X2 + 3/2.X1 + 3/2.X2 + 1/2
3.07/4.09	[false] = 3/2
3.07/4.09	[true] = 3/2
3.07/4.09	[AND](X1,X2) = 0
3.07/4.09	[EQ](X1,X2) = 0
3.07/4.09	[NEQ](X1,X2) = 0
3.07/4.09	[NOT](X) = 0
3.07/4.09	[OR](X1,X2) = X1.X2 + X1 + X2
3.07/4.09	
3.07/4.09	Problem 1.2: 
3.07/4.09	
3.07/4.09	SCC Processor:
3.07/4.09	-> FAxioms:
3.07/4.09	 OR(or(x3,x4),x5) = OR(x3,or(x4,x5))
3.07/4.09	 OR(x3,x4) = OR(x4,x3)
3.07/4.09	-> Pairs:
3.07/4.09	 Empty
3.07/4.09	-> EAxioms:
3.07/4.09	 and(and(x3,x4),x5) = and(x3,and(x4,x5))
3.07/4.09	 and(x3,x4) = and(x4,x3)
3.07/4.09	 eq(x3,x4) = eq(x4,x3)
3.07/4.09	 neq(x3,x4) = neq(x4,x3)
3.07/4.09	 or(or(x3,x4),x5) = or(x3,or(x4,x5))
3.07/4.09	 or(x3,x4) = or(x4,x3)
3.07/4.09	-> Rules:
3.07/4.09	 and(x,or(x,y)) -> x
3.07/4.09	 and(x,false) -> false
3.07/4.09	 and(x,true) -> x
3.07/4.09	 and(x,x) -> x
3.07/4.09	 eq(x,x) -> true
3.07/4.09	 neq(x,x) -> false
3.07/4.09	 not(and(x,y)) -> or(not(x),not(y))
3.07/4.09	 not(eq(x,y)) -> neq(x,y)
3.07/4.09	 not(neq(x,y)) -> eq(x,y)
3.07/4.09	 not(not(x)) -> x
3.07/4.09	 not(or(x,y)) -> and(not(x),not(y))
3.07/4.09	 not(false) -> true
3.07/4.09	 not(true) -> false
3.07/4.09	 or(and(x,y),z) -> and(or(x,z),or(y,z))
3.07/4.09	 or(x,false) -> x
3.07/4.09	 or(x,true) -> true
3.07/4.09	 or(x,x) -> x
3.07/4.09	-> SRules:
3.07/4.09	 OR(or(x3,x4),x5) -> OR(x3,x4)
3.07/4.09	 OR(x3,or(x4,x5)) -> OR(x4,x5)
3.07/4.09	->Strongly Connected Components:
3.07/4.09	 There is no strongly connected component
3.07/4.09	
3.07/4.09	The problem is finite.
3.07/4.09	
3.07/4.09	Problem 1.3: 
3.07/4.09	
3.07/4.09	Subterm Processor:
3.07/4.09	-> FAxioms:
3.07/4.09	 Empty
3.07/4.09	-> Pairs:
3.07/4.09	 NOT(and(x,y)) -> NOT(x)
3.07/4.09	 NOT(and(x,y)) -> NOT(y)
3.07/4.09	 NOT(or(x,y)) -> NOT(x)
3.07/4.09	 NOT(or(x,y)) -> NOT(y)
3.07/4.09	-> EAxioms:
3.07/4.09	 and(and(x3,x4),x5) = and(x3,and(x4,x5))
3.07/4.09	 and(x3,x4) = and(x4,x3)
3.07/4.09	 eq(x3,x4) = eq(x4,x3)
3.07/4.09	 neq(x3,x4) = neq(x4,x3)
3.07/4.09	 or(or(x3,x4),x5) = or(x3,or(x4,x5))
3.07/4.09	 or(x3,x4) = or(x4,x3)
3.07/4.09	-> Rules:
3.07/4.09	 and(x,or(x,y)) -> x
3.07/4.09	 and(x,false) -> false
3.07/4.09	 and(x,true) -> x
3.07/4.09	 and(x,x) -> x
3.07/4.09	 eq(x,x) -> true
3.07/4.09	 neq(x,x) -> false
3.07/4.09	 not(and(x,y)) -> or(not(x),not(y))
3.07/4.09	 not(eq(x,y)) -> neq(x,y)
3.07/4.09	 not(neq(x,y)) -> eq(x,y)
3.07/4.09	 not(not(x)) -> x
3.07/4.09	 not(or(x,y)) -> and(not(x),not(y))
3.07/4.09	 not(false) -> true
3.07/4.09	 not(true) -> false
3.07/4.09	 or(and(x,y),z) -> and(or(x,z),or(y,z))
3.07/4.09	 or(x,false) -> x
3.07/4.09	 or(x,true) -> true
3.07/4.09	 or(x,x) -> x
3.07/4.09	-> SRules:
3.07/4.09	 Empty
3.07/4.09	->Projection:
3.07/4.09	 pi(NOT) = [1]
3.07/4.09	
3.07/4.09	Problem 1.3: 
3.07/4.09	
3.07/4.09	SCC Processor:
3.07/4.09	-> FAxioms:
3.07/4.09	 Empty
3.07/4.09	-> Pairs:
3.07/4.09	 Empty
3.07/4.09	-> EAxioms:
3.07/4.09	 and(and(x3,x4),x5) = and(x3,and(x4,x5))
3.07/4.09	 and(x3,x4) = and(x4,x3)
3.07/4.09	 eq(x3,x4) = eq(x4,x3)
3.07/4.09	 neq(x3,x4) = neq(x4,x3)
3.07/4.09	 or(or(x3,x4),x5) = or(x3,or(x4,x5))
3.07/4.09	 or(x3,x4) = or(x4,x3)
3.07/4.09	-> Rules:
3.07/4.09	 and(x,or(x,y)) -> x
3.07/4.09	 and(x,false) -> false
3.07/4.09	 and(x,true) -> x
3.07/4.09	 and(x,x) -> x
3.07/4.09	 eq(x,x) -> true
3.07/4.09	 neq(x,x) -> false
3.07/4.09	 not(and(x,y)) -> or(not(x),not(y))
3.07/4.09	 not(eq(x,y)) -> neq(x,y)
3.07/4.09	 not(neq(x,y)) -> eq(x,y)
3.07/4.09	 not(not(x)) -> x
3.07/4.09	 not(or(x,y)) -> and(not(x),not(y))
3.07/4.09	 not(false) -> true
3.07/4.09	 not(true) -> false
3.07/4.09	 or(and(x,y),z) -> and(or(x,z),or(y,z))
3.07/4.09	 or(x,false) -> x
3.07/4.09	 or(x,true) -> true
3.07/4.09	 or(x,x) -> x
3.07/4.09	-> SRules:
3.07/4.09	 Empty
3.07/4.09	->Strongly Connected Components:
3.07/4.09	 There is no strongly connected component
3.07/4.09	
3.07/4.09	The problem is finite.
3.07/4.09	EOF