11.91/13.33	YES
11.91/13.33	
11.91/13.33	Problem 1: 
11.91/13.33	
11.91/13.33	(VAR v_NonEmpty:S x1:S)
11.91/13.33	(RULES
11.91/13.33	e(r(x1:S)) -> e(w(x1:S))
11.91/13.33	e(w(x1:S)) -> r(i(x1:S))
11.91/13.33	i(t(x1:S)) -> e(r(x1:S))
11.91/13.33	r(e(x1:S)) -> w(r(x1:S))
11.91/13.33	r(i(t(e(r(x1:S))))) -> e(w(r(i(t(e(x1:S))))))
11.91/13.33	t(e(x1:S)) -> r(e(x1:S))
11.91/13.33	w(r(x1:S)) -> i(t(x1:S))
11.91/13.33	)
11.91/13.33	
11.91/13.33	Problem 1: 
11.91/13.33	
11.91/13.33	Dependency Pairs Processor:
11.91/13.33	-> Pairs:
11.91/13.33	 E(r(x1:S)) -> E(w(x1:S))
11.91/13.33	 E(r(x1:S)) -> W(x1:S)
11.91/13.33	 E(w(x1:S)) -> I(x1:S)
11.91/13.33	 E(w(x1:S)) -> R(i(x1:S))
11.91/13.33	 I(t(x1:S)) -> E(r(x1:S))
11.91/13.33	 I(t(x1:S)) -> R(x1:S)
11.91/13.33	 R(e(x1:S)) -> R(x1:S)
11.91/13.33	 R(e(x1:S)) -> W(r(x1:S))
11.91/13.33	 R(i(t(e(r(x1:S))))) -> E(w(r(i(t(e(x1:S))))))
11.91/13.33	 R(i(t(e(r(x1:S))))) -> E(x1:S)
11.91/13.33	 R(i(t(e(r(x1:S))))) -> I(t(e(x1:S)))
11.91/13.33	 R(i(t(e(r(x1:S))))) -> R(i(t(e(x1:S))))
11.91/13.33	 R(i(t(e(r(x1:S))))) -> T(e(x1:S))
11.91/13.33	 R(i(t(e(r(x1:S))))) -> W(r(i(t(e(x1:S)))))
11.91/13.33	 T(e(x1:S)) -> R(e(x1:S))
11.91/13.33	 W(r(x1:S)) -> I(t(x1:S))
11.91/13.33	 W(r(x1:S)) -> T(x1:S)
11.91/13.33	-> Rules:
11.91/13.33	 e(r(x1:S)) -> e(w(x1:S))
11.91/13.33	 e(w(x1:S)) -> r(i(x1:S))
11.91/13.33	 i(t(x1:S)) -> e(r(x1:S))
11.91/13.33	 r(e(x1:S)) -> w(r(x1:S))
11.91/13.33	 r(i(t(e(r(x1:S))))) -> e(w(r(i(t(e(x1:S))))))
11.91/13.33	 t(e(x1:S)) -> r(e(x1:S))
11.91/13.33	 w(r(x1:S)) -> i(t(x1:S))
11.91/13.33	
11.91/13.33	Problem 1: 
11.91/13.33	
11.91/13.33	SCC Processor:
11.91/13.33	-> Pairs:
11.91/13.33	 E(r(x1:S)) -> E(w(x1:S))
11.91/13.33	 E(r(x1:S)) -> W(x1:S)
11.91/13.33	 E(w(x1:S)) -> I(x1:S)
11.91/13.33	 E(w(x1:S)) -> R(i(x1:S))
11.91/13.33	 I(t(x1:S)) -> E(r(x1:S))
11.91/13.33	 I(t(x1:S)) -> R(x1:S)
11.91/13.33	 R(e(x1:S)) -> R(x1:S)
11.91/13.33	 R(e(x1:S)) -> W(r(x1:S))
11.91/13.33	 R(i(t(e(r(x1:S))))) -> E(w(r(i(t(e(x1:S))))))
11.91/13.33	 R(i(t(e(r(x1:S))))) -> E(x1:S)
11.91/13.33	 R(i(t(e(r(x1:S))))) -> I(t(e(x1:S)))
11.91/13.33	 R(i(t(e(r(x1:S))))) -> R(i(t(e(x1:S))))
11.91/13.33	 R(i(t(e(r(x1:S))))) -> T(e(x1:S))
11.91/13.33	 R(i(t(e(r(x1:S))))) -> W(r(i(t(e(x1:S)))))
11.91/13.33	 T(e(x1:S)) -> R(e(x1:S))
11.91/13.33	 W(r(x1:S)) -> I(t(x1:S))
11.91/13.33	 W(r(x1:S)) -> T(x1:S)
11.91/13.33	-> Rules:
11.91/13.33	 e(r(x1:S)) -> e(w(x1:S))
11.91/13.33	 e(w(x1:S)) -> r(i(x1:S))
11.91/13.33	 i(t(x1:S)) -> e(r(x1:S))
11.91/13.33	 r(e(x1:S)) -> w(r(x1:S))
11.91/13.33	 r(i(t(e(r(x1:S))))) -> e(w(r(i(t(e(x1:S))))))
11.91/13.33	 t(e(x1:S)) -> r(e(x1:S))
11.91/13.33	 w(r(x1:S)) -> i(t(x1:S))
11.91/13.33	->Strongly Connected Components:
11.91/13.33	->->Cycle:
11.91/13.33	->->-> Pairs:
11.91/13.33	 E(r(x1:S)) -> E(w(x1:S))
11.91/13.33	 E(r(x1:S)) -> W(x1:S)
11.91/13.33	 E(w(x1:S)) -> I(x1:S)
11.91/13.33	 E(w(x1:S)) -> R(i(x1:S))
11.91/13.33	 I(t(x1:S)) -> E(r(x1:S))
11.91/13.33	 I(t(x1:S)) -> R(x1:S)
11.91/13.33	 R(e(x1:S)) -> R(x1:S)
11.91/13.33	 R(e(x1:S)) -> W(r(x1:S))
11.91/13.33	 R(i(t(e(r(x1:S))))) -> E(w(r(i(t(e(x1:S))))))
11.91/13.33	 R(i(t(e(r(x1:S))))) -> E(x1:S)
11.91/13.33	 R(i(t(e(r(x1:S))))) -> I(t(e(x1:S)))
11.91/13.33	 R(i(t(e(r(x1:S))))) -> R(i(t(e(x1:S))))
11.91/13.33	 R(i(t(e(r(x1:S))))) -> T(e(x1:S))
11.91/13.33	 R(i(t(e(r(x1:S))))) -> W(r(i(t(e(x1:S)))))
11.91/13.33	 T(e(x1:S)) -> R(e(x1:S))
11.91/13.33	 W(r(x1:S)) -> I(t(x1:S))
11.91/13.33	 W(r(x1:S)) -> T(x1:S)
11.91/13.33	->->-> Rules:
11.91/13.33	 e(r(x1:S)) -> e(w(x1:S))
11.91/13.33	 e(w(x1:S)) -> r(i(x1:S))
11.91/13.33	 i(t(x1:S)) -> e(r(x1:S))
11.91/13.33	 r(e(x1:S)) -> w(r(x1:S))
11.91/13.33	 r(i(t(e(r(x1:S))))) -> e(w(r(i(t(e(x1:S))))))
11.91/13.33	 t(e(x1:S)) -> r(e(x1:S))
11.91/13.33	 w(r(x1:S)) -> i(t(x1:S))
11.91/13.33	
11.91/13.33	Problem 1: 
11.91/13.33	
11.91/13.33	Reduction Pair Processor:
11.91/13.33	-> Pairs:
11.91/13.33	 E(r(x1:S)) -> E(w(x1:S))
11.91/13.33	 E(r(x1:S)) -> W(x1:S)
11.91/13.33	 E(w(x1:S)) -> I(x1:S)
11.91/13.33	 E(w(x1:S)) -> R(i(x1:S))
11.91/13.33	 I(t(x1:S)) -> E(r(x1:S))
11.91/13.33	 I(t(x1:S)) -> R(x1:S)
11.91/13.33	 R(e(x1:S)) -> R(x1:S)
11.91/13.33	 R(e(x1:S)) -> W(r(x1:S))
11.91/13.33	 R(i(t(e(r(x1:S))))) -> E(w(r(i(t(e(x1:S))))))
11.91/13.33	 R(i(t(e(r(x1:S))))) -> E(x1:S)
11.91/13.33	 R(i(t(e(r(x1:S))))) -> I(t(e(x1:S)))
11.91/13.33	 R(i(t(e(r(x1:S))))) -> R(i(t(e(x1:S))))
11.91/13.33	 R(i(t(e(r(x1:S))))) -> T(e(x1:S))
11.91/13.33	 R(i(t(e(r(x1:S))))) -> W(r(i(t(e(x1:S)))))
11.91/13.33	 T(e(x1:S)) -> R(e(x1:S))
11.91/13.33	 W(r(x1:S)) -> I(t(x1:S))
11.91/13.33	 W(r(x1:S)) -> T(x1:S)
11.91/13.33	-> Rules:
11.91/13.33	 e(r(x1:S)) -> e(w(x1:S))
11.91/13.33	 e(w(x1:S)) -> r(i(x1:S))
11.91/13.33	 i(t(x1:S)) -> e(r(x1:S))
11.91/13.33	 r(e(x1:S)) -> w(r(x1:S))
11.91/13.33	 r(i(t(e(r(x1:S))))) -> e(w(r(i(t(e(x1:S))))))
11.91/13.33	 t(e(x1:S)) -> r(e(x1:S))
11.91/13.33	 w(r(x1:S)) -> i(t(x1:S))
11.91/13.33	-> Usable rules:
11.91/13.33	 e(r(x1:S)) -> e(w(x1:S))
11.91/13.33	 e(w(x1:S)) -> r(i(x1:S))
11.91/13.33	 i(t(x1:S)) -> e(r(x1:S))
11.91/13.33	 r(e(x1:S)) -> w(r(x1:S))
11.91/13.33	 r(i(t(e(r(x1:S))))) -> e(w(r(i(t(e(x1:S))))))
11.91/13.33	 t(e(x1:S)) -> r(e(x1:S))
11.91/13.33	 w(r(x1:S)) -> i(t(x1:S))
11.91/13.33	->Interpretation type:
11.91/13.33	 Linear
11.91/13.33	->Coefficients:
11.91/13.33	 All rationals
11.91/13.33	->Dimension:
11.91/13.33	 1
11.91/13.33	->Bound:
11.91/13.33	 4
11.91/13.33	->Interpretation:
11.91/13.33	 
11.91/13.33	[e](X) = X + 1/2
11.91/13.33	[i](X) = 1/2.X
11.91/13.33	[r](X) = 3/2.X + 1
11.91/13.33	[t](X) = 3.X + 3
11.91/13.33	[w](X) = X + 3/4
11.91/13.33	[E](X) = 1/2.X + 1/3
11.91/13.33	[I](X) = 1/4.X + 1/4
11.91/13.33	[R](X) = 3/4.X + 2/3
11.91/13.33	[T](X) = 3/4.X + 2/3
11.91/13.33	[W](X) = 1/2.X + 1/2
11.91/13.33	
11.91/13.33	Problem 1: 
11.91/13.33	
11.91/13.33	SCC Processor:
11.91/13.33	-> Pairs:
11.91/13.33	 E(r(x1:S)) -> W(x1:S)
11.91/13.33	 E(w(x1:S)) -> I(x1:S)
11.91/13.33	 E(w(x1:S)) -> R(i(x1:S))
11.91/13.33	 I(t(x1:S)) -> E(r(x1:S))
11.91/13.33	 I(t(x1:S)) -> R(x1:S)
11.91/13.33	 R(e(x1:S)) -> R(x1:S)
11.91/13.33	 R(e(x1:S)) -> W(r(x1:S))
11.91/13.33	 R(i(t(e(r(x1:S))))) -> E(w(r(i(t(e(x1:S))))))
11.91/13.33	 R(i(t(e(r(x1:S))))) -> E(x1:S)
11.91/13.33	 R(i(t(e(r(x1:S))))) -> I(t(e(x1:S)))
11.91/13.33	 R(i(t(e(r(x1:S))))) -> R(i(t(e(x1:S))))
11.91/13.33	 R(i(t(e(r(x1:S))))) -> T(e(x1:S))
11.91/13.33	 R(i(t(e(r(x1:S))))) -> W(r(i(t(e(x1:S)))))
11.91/13.33	 T(e(x1:S)) -> R(e(x1:S))
11.91/13.33	 W(r(x1:S)) -> I(t(x1:S))
11.91/13.33	 W(r(x1:S)) -> T(x1:S)
11.91/13.33	-> Rules:
11.91/13.33	 e(r(x1:S)) -> e(w(x1:S))
11.91/13.33	 e(w(x1:S)) -> r(i(x1:S))
11.91/13.33	 i(t(x1:S)) -> e(r(x1:S))
11.91/13.33	 r(e(x1:S)) -> w(r(x1:S))
11.91/13.33	 r(i(t(e(r(x1:S))))) -> e(w(r(i(t(e(x1:S))))))
11.91/13.33	 t(e(x1:S)) -> r(e(x1:S))
11.91/13.33	 w(r(x1:S)) -> i(t(x1:S))
11.91/13.33	->Strongly Connected Components:
11.91/13.33	->->Cycle:
11.91/13.33	->->-> Pairs:
11.91/13.33	 E(r(x1:S)) -> W(x1:S)
11.91/13.33	 E(w(x1:S)) -> I(x1:S)
11.91/13.33	 E(w(x1:S)) -> R(i(x1:S))
11.91/13.33	 I(t(x1:S)) -> E(r(x1:S))
11.91/13.33	 I(t(x1:S)) -> R(x1:S)
11.91/13.33	 R(e(x1:S)) -> R(x1:S)
11.91/13.33	 R(e(x1:S)) -> W(r(x1:S))
11.91/13.33	 R(i(t(e(r(x1:S))))) -> E(w(r(i(t(e(x1:S))))))
11.91/13.33	 R(i(t(e(r(x1:S))))) -> E(x1:S)
11.91/13.33	 R(i(t(e(r(x1:S))))) -> I(t(e(x1:S)))
11.91/13.33	 R(i(t(e(r(x1:S))))) -> R(i(t(e(x1:S))))
11.91/13.33	 R(i(t(e(r(x1:S))))) -> T(e(x1:S))
11.91/13.33	 R(i(t(e(r(x1:S))))) -> W(r(i(t(e(x1:S)))))
11.91/13.33	 T(e(x1:S)) -> R(e(x1:S))
11.91/13.33	 W(r(x1:S)) -> I(t(x1:S))
11.91/13.33	 W(r(x1:S)) -> T(x1:S)
11.91/13.33	->->-> Rules:
11.91/13.33	 e(r(x1:S)) -> e(w(x1:S))
11.91/13.33	 e(w(x1:S)) -> r(i(x1:S))
11.91/13.33	 i(t(x1:S)) -> e(r(x1:S))
11.91/13.33	 r(e(x1:S)) -> w(r(x1:S))
11.91/13.33	 r(i(t(e(r(x1:S))))) -> e(w(r(i(t(e(x1:S))))))
11.91/13.33	 t(e(x1:S)) -> r(e(x1:S))
11.91/13.33	 w(r(x1:S)) -> i(t(x1:S))
11.91/13.33	
11.91/13.33	Problem 1: 
11.91/13.33	
11.91/13.33	Reduction Pair Processor:
11.91/13.33	-> Pairs:
11.91/13.33	 E(r(x1:S)) -> W(x1:S)
11.91/13.33	 E(w(x1:S)) -> I(x1:S)
11.91/13.33	 E(w(x1:S)) -> R(i(x1:S))
11.91/13.33	 I(t(x1:S)) -> E(r(x1:S))
11.91/13.33	 I(t(x1:S)) -> R(x1:S)
11.91/13.33	 R(e(x1:S)) -> R(x1:S)
11.91/13.33	 R(e(x1:S)) -> W(r(x1:S))
11.91/13.33	 R(i(t(e(r(x1:S))))) -> E(w(r(i(t(e(x1:S))))))
11.91/13.33	 R(i(t(e(r(x1:S))))) -> E(x1:S)
11.91/13.33	 R(i(t(e(r(x1:S))))) -> I(t(e(x1:S)))
11.91/13.33	 R(i(t(e(r(x1:S))))) -> R(i(t(e(x1:S))))
11.91/13.33	 R(i(t(e(r(x1:S))))) -> T(e(x1:S))
11.91/13.33	 R(i(t(e(r(x1:S))))) -> W(r(i(t(e(x1:S)))))
11.91/13.33	 T(e(x1:S)) -> R(e(x1:S))
11.91/13.33	 W(r(x1:S)) -> I(t(x1:S))
11.91/13.33	 W(r(x1:S)) -> T(x1:S)
11.91/13.33	-> Rules:
11.91/13.33	 e(r(x1:S)) -> e(w(x1:S))
11.91/13.33	 e(w(x1:S)) -> r(i(x1:S))
11.91/13.33	 i(t(x1:S)) -> e(r(x1:S))
11.91/13.33	 r(e(x1:S)) -> w(r(x1:S))
11.91/13.33	 r(i(t(e(r(x1:S))))) -> e(w(r(i(t(e(x1:S))))))
11.91/13.33	 t(e(x1:S)) -> r(e(x1:S))
11.91/13.33	 w(r(x1:S)) -> i(t(x1:S))
11.91/13.33	-> Usable rules:
11.91/13.33	 e(r(x1:S)) -> e(w(x1:S))
11.91/13.33	 e(w(x1:S)) -> r(i(x1:S))
11.91/13.33	 i(t(x1:S)) -> e(r(x1:S))
11.91/13.33	 r(e(x1:S)) -> w(r(x1:S))
11.91/13.33	 r(i(t(e(r(x1:S))))) -> e(w(r(i(t(e(x1:S))))))
11.91/13.33	 t(e(x1:S)) -> r(e(x1:S))
11.91/13.33	 w(r(x1:S)) -> i(t(x1:S))
11.91/13.33	->Interpretation type:
11.91/13.33	 Linear
11.91/13.33	->Coefficients:
11.91/13.33	 All rationals
11.91/13.33	->Dimension:
11.91/13.33	 1
11.91/13.33	->Bound:
11.91/13.33	 4
11.91/13.33	->Interpretation:
11.91/13.33	 
11.91/13.33	[e](X) = X + 1/3
11.91/13.33	[i](X) = 1/3.X
11.91/13.33	[r](X) = 4/3.X + 2/3
11.91/13.33	[t](X) = 4.X + 3
11.91/13.33	[w](X) = X + 1/3
11.91/13.33	[E](X) = 3/2.X + 3/2
11.91/13.33	[I](X) = 1/2.X + 1
11.91/13.33	[R](X) = 2.X + 2
11.91/13.33	[T](X) = 2.X + 2
11.91/13.33	[W](X) = 3/2.X + 3/2
11.91/13.33	
11.91/13.33	Problem 1: 
11.91/13.33	
11.91/13.33	SCC Processor:
11.91/13.33	-> Pairs:
11.91/13.33	 E(w(x1:S)) -> I(x1:S)
11.91/13.33	 E(w(x1:S)) -> R(i(x1:S))
11.91/13.33	 I(t(x1:S)) -> E(r(x1:S))
11.91/13.33	 I(t(x1:S)) -> R(x1:S)
11.91/13.33	 R(e(x1:S)) -> R(x1:S)
11.91/13.33	 R(e(x1:S)) -> W(r(x1:S))
11.91/13.33	 R(i(t(e(r(x1:S))))) -> E(w(r(i(t(e(x1:S))))))
11.91/13.33	 R(i(t(e(r(x1:S))))) -> E(x1:S)
11.91/13.33	 R(i(t(e(r(x1:S))))) -> I(t(e(x1:S)))
11.91/13.33	 R(i(t(e(r(x1:S))))) -> R(i(t(e(x1:S))))
11.91/13.33	 R(i(t(e(r(x1:S))))) -> T(e(x1:S))
11.91/13.33	 R(i(t(e(r(x1:S))))) -> W(r(i(t(e(x1:S)))))
11.91/13.33	 T(e(x1:S)) -> R(e(x1:S))
11.91/13.33	 W(r(x1:S)) -> I(t(x1:S))
11.91/13.33	 W(r(x1:S)) -> T(x1:S)
11.91/13.33	-> Rules:
11.91/13.33	 e(r(x1:S)) -> e(w(x1:S))
11.91/13.33	 e(w(x1:S)) -> r(i(x1:S))
11.91/13.33	 i(t(x1:S)) -> e(r(x1:S))
11.91/13.33	 r(e(x1:S)) -> w(r(x1:S))
11.91/13.33	 r(i(t(e(r(x1:S))))) -> e(w(r(i(t(e(x1:S))))))
11.91/13.33	 t(e(x1:S)) -> r(e(x1:S))
11.91/13.33	 w(r(x1:S)) -> i(t(x1:S))
11.91/13.33	->Strongly Connected Components:
11.91/13.33	->->Cycle:
11.91/13.33	->->-> Pairs:
11.91/13.33	 E(w(x1:S)) -> I(x1:S)
11.91/13.33	 E(w(x1:S)) -> R(i(x1:S))
11.91/13.33	 I(t(x1:S)) -> E(r(x1:S))
11.91/13.33	 I(t(x1:S)) -> R(x1:S)
11.91/13.33	 R(e(x1:S)) -> R(x1:S)
11.91/13.33	 R(e(x1:S)) -> W(r(x1:S))
11.91/13.33	 R(i(t(e(r(x1:S))))) -> E(w(r(i(t(e(x1:S))))))
11.91/13.33	 R(i(t(e(r(x1:S))))) -> E(x1:S)
11.91/13.33	 R(i(t(e(r(x1:S))))) -> I(t(e(x1:S)))
11.91/13.33	 R(i(t(e(r(x1:S))))) -> R(i(t(e(x1:S))))
11.91/13.33	 R(i(t(e(r(x1:S))))) -> T(e(x1:S))
11.91/13.33	 R(i(t(e(r(x1:S))))) -> W(r(i(t(e(x1:S)))))
11.91/13.33	 T(e(x1:S)) -> R(e(x1:S))
11.91/13.33	 W(r(x1:S)) -> I(t(x1:S))
11.91/13.33	 W(r(x1:S)) -> T(x1:S)
11.91/13.33	->->-> Rules:
11.91/13.33	 e(r(x1:S)) -> e(w(x1:S))
11.91/13.33	 e(w(x1:S)) -> r(i(x1:S))
11.91/13.33	 i(t(x1:S)) -> e(r(x1:S))
11.91/13.33	 r(e(x1:S)) -> w(r(x1:S))
11.91/13.33	 r(i(t(e(r(x1:S))))) -> e(w(r(i(t(e(x1:S))))))
11.91/13.33	 t(e(x1:S)) -> r(e(x1:S))
11.91/13.33	 w(r(x1:S)) -> i(t(x1:S))
11.91/13.33	
11.91/13.33	Problem 1: 
11.91/13.33	
11.91/13.33	Reduction Pair Processor:
11.91/13.33	-> Pairs:
11.91/13.33	 E(w(x1:S)) -> I(x1:S)
11.91/13.33	 E(w(x1:S)) -> R(i(x1:S))
11.91/13.33	 I(t(x1:S)) -> E(r(x1:S))
11.91/13.33	 I(t(x1:S)) -> R(x1:S)
11.91/13.33	 R(e(x1:S)) -> R(x1:S)
11.91/13.33	 R(e(x1:S)) -> W(r(x1:S))
11.91/13.33	 R(i(t(e(r(x1:S))))) -> E(w(r(i(t(e(x1:S))))))
11.91/13.33	 R(i(t(e(r(x1:S))))) -> E(x1:S)
11.91/13.33	 R(i(t(e(r(x1:S))))) -> I(t(e(x1:S)))
11.91/13.33	 R(i(t(e(r(x1:S))))) -> R(i(t(e(x1:S))))
11.91/13.33	 R(i(t(e(r(x1:S))))) -> T(e(x1:S))
11.91/13.33	 R(i(t(e(r(x1:S))))) -> W(r(i(t(e(x1:S)))))
11.91/13.33	 T(e(x1:S)) -> R(e(x1:S))
11.91/13.33	 W(r(x1:S)) -> I(t(x1:S))
11.91/13.33	 W(r(x1:S)) -> T(x1:S)
11.91/13.33	-> Rules:
11.91/13.33	 e(r(x1:S)) -> e(w(x1:S))
11.91/13.33	 e(w(x1:S)) -> r(i(x1:S))
11.91/13.33	 i(t(x1:S)) -> e(r(x1:S))
11.91/13.33	 r(e(x1:S)) -> w(r(x1:S))
11.91/13.33	 r(i(t(e(r(x1:S))))) -> e(w(r(i(t(e(x1:S))))))
11.91/13.33	 t(e(x1:S)) -> r(e(x1:S))
11.91/13.33	 w(r(x1:S)) -> i(t(x1:S))
11.91/13.33	-> Usable rules:
11.91/13.33	 e(r(x1:S)) -> e(w(x1:S))
11.91/13.33	 e(w(x1:S)) -> r(i(x1:S))
11.91/13.33	 i(t(x1:S)) -> e(r(x1:S))
11.91/13.33	 r(e(x1:S)) -> w(r(x1:S))
11.91/13.33	 r(i(t(e(r(x1:S))))) -> e(w(r(i(t(e(x1:S))))))
11.91/13.33	 t(e(x1:S)) -> r(e(x1:S))
11.91/13.33	 w(r(x1:S)) -> i(t(x1:S))
11.91/13.33	->Interpretation type:
11.91/13.33	 Linear
11.91/13.33	->Coefficients:
11.91/13.33	 All rationals
11.91/13.33	->Dimension:
11.91/13.33	 1
11.91/13.33	->Bound:
11.91/13.33	 4
11.91/13.33	->Interpretation:
11.91/13.33	 
11.91/13.33	[e](X) = X + 2/3
11.91/13.33	[i](X) = X
11.91/13.33	[r](X) = X + 4/3
11.91/13.33	[t](X) = X + 2
11.91/13.33	[w](X) = X + 2/3
11.91/13.33	[E](X) = 1/4.X + 1/2
11.91/13.33	[I](X) = 1/4.X + 1/3
11.91/13.33	[R](X) = 1/4.X + 2/3
11.91/13.33	[T](X) = 1/4.X + 3/4
11.91/13.33	[W](X) = 1/4.X + 1/2
11.91/13.33	
11.91/13.33	Problem 1: 
11.91/13.33	
11.91/13.33	SCC Processor:
11.91/13.33	-> Pairs:
11.91/13.33	 E(w(x1:S)) -> R(i(x1:S))
11.91/13.33	 I(t(x1:S)) -> E(r(x1:S))
11.91/13.33	 I(t(x1:S)) -> R(x1:S)
11.91/13.33	 R(e(x1:S)) -> R(x1:S)
11.91/13.33	 R(e(x1:S)) -> W(r(x1:S))
11.91/13.33	 R(i(t(e(r(x1:S))))) -> E(w(r(i(t(e(x1:S))))))
11.91/13.33	 R(i(t(e(r(x1:S))))) -> E(x1:S)
11.91/13.33	 R(i(t(e(r(x1:S))))) -> I(t(e(x1:S)))
11.91/13.33	 R(i(t(e(r(x1:S))))) -> R(i(t(e(x1:S))))
11.91/13.33	 R(i(t(e(r(x1:S))))) -> T(e(x1:S))
11.91/13.33	 R(i(t(e(r(x1:S))))) -> W(r(i(t(e(x1:S)))))
11.91/13.33	 T(e(x1:S)) -> R(e(x1:S))
11.91/13.33	 W(r(x1:S)) -> I(t(x1:S))
11.91/13.33	 W(r(x1:S)) -> T(x1:S)
11.91/13.33	-> Rules:
11.91/13.33	 e(r(x1:S)) -> e(w(x1:S))
11.91/13.33	 e(w(x1:S)) -> r(i(x1:S))
11.91/13.33	 i(t(x1:S)) -> e(r(x1:S))
11.91/13.33	 r(e(x1:S)) -> w(r(x1:S))
11.91/13.33	 r(i(t(e(r(x1:S))))) -> e(w(r(i(t(e(x1:S))))))
11.91/13.33	 t(e(x1:S)) -> r(e(x1:S))
11.91/13.33	 w(r(x1:S)) -> i(t(x1:S))
11.91/13.33	->Strongly Connected Components:
11.91/13.33	->->Cycle:
11.91/13.33	->->-> Pairs:
11.91/13.33	 E(w(x1:S)) -> R(i(x1:S))
11.91/13.33	 I(t(x1:S)) -> E(r(x1:S))
11.91/13.33	 I(t(x1:S)) -> R(x1:S)
11.91/13.33	 R(e(x1:S)) -> R(x1:S)
11.91/13.33	 R(e(x1:S)) -> W(r(x1:S))
11.91/13.33	 R(i(t(e(r(x1:S))))) -> E(w(r(i(t(e(x1:S))))))
11.91/13.33	 R(i(t(e(r(x1:S))))) -> E(x1:S)
11.91/13.33	 R(i(t(e(r(x1:S))))) -> I(t(e(x1:S)))
11.91/13.34	 R(i(t(e(r(x1:S))))) -> R(i(t(e(x1:S))))
11.91/13.34	 R(i(t(e(r(x1:S))))) -> T(e(x1:S))
11.91/13.34	 R(i(t(e(r(x1:S))))) -> W(r(i(t(e(x1:S)))))
11.91/13.34	 T(e(x1:S)) -> R(e(x1:S))
11.91/13.34	 W(r(x1:S)) -> I(t(x1:S))
11.91/13.34	 W(r(x1:S)) -> T(x1:S)
11.91/13.34	->->-> Rules:
11.91/13.34	 e(r(x1:S)) -> e(w(x1:S))
11.91/13.34	 e(w(x1:S)) -> r(i(x1:S))
11.91/13.34	 i(t(x1:S)) -> e(r(x1:S))
11.91/13.34	 r(e(x1:S)) -> w(r(x1:S))
11.91/13.34	 r(i(t(e(r(x1:S))))) -> e(w(r(i(t(e(x1:S))))))
11.91/13.34	 t(e(x1:S)) -> r(e(x1:S))
11.91/13.34	 w(r(x1:S)) -> i(t(x1:S))
11.91/13.34	
11.91/13.34	Problem 1: 
11.91/13.34	
11.91/13.34	Reduction Pair Processor:
11.91/13.34	-> Pairs:
11.91/13.34	 E(w(x1:S)) -> R(i(x1:S))
11.91/13.34	 I(t(x1:S)) -> E(r(x1:S))
11.91/13.34	 I(t(x1:S)) -> R(x1:S)
11.91/13.34	 R(e(x1:S)) -> R(x1:S)
11.91/13.34	 R(e(x1:S)) -> W(r(x1:S))
11.91/13.34	 R(i(t(e(r(x1:S))))) -> E(w(r(i(t(e(x1:S))))))
11.91/13.34	 R(i(t(e(r(x1:S))))) -> E(x1:S)
11.91/13.34	 R(i(t(e(r(x1:S))))) -> I(t(e(x1:S)))
11.91/13.34	 R(i(t(e(r(x1:S))))) -> R(i(t(e(x1:S))))
11.91/13.34	 R(i(t(e(r(x1:S))))) -> T(e(x1:S))
11.91/13.34	 R(i(t(e(r(x1:S))))) -> W(r(i(t(e(x1:S)))))
11.91/13.34	 T(e(x1:S)) -> R(e(x1:S))
11.91/13.34	 W(r(x1:S)) -> I(t(x1:S))
11.91/13.34	 W(r(x1:S)) -> T(x1:S)
11.91/13.34	-> Rules:
11.91/13.34	 e(r(x1:S)) -> e(w(x1:S))
11.91/13.34	 e(w(x1:S)) -> r(i(x1:S))
11.91/13.34	 i(t(x1:S)) -> e(r(x1:S))
11.91/13.34	 r(e(x1:S)) -> w(r(x1:S))
11.91/13.34	 r(i(t(e(r(x1:S))))) -> e(w(r(i(t(e(x1:S))))))
11.91/13.34	 t(e(x1:S)) -> r(e(x1:S))
11.91/13.34	 w(r(x1:S)) -> i(t(x1:S))
11.91/13.34	-> Usable rules:
11.91/13.34	 e(r(x1:S)) -> e(w(x1:S))
11.91/13.34	 e(w(x1:S)) -> r(i(x1:S))
11.91/13.34	 i(t(x1:S)) -> e(r(x1:S))
11.91/13.34	 r(e(x1:S)) -> w(r(x1:S))
11.91/13.34	 r(i(t(e(r(x1:S))))) -> e(w(r(i(t(e(x1:S))))))
11.91/13.34	 t(e(x1:S)) -> r(e(x1:S))
11.91/13.34	 w(r(x1:S)) -> i(t(x1:S))
11.91/13.34	->Interpretation type:
11.91/13.34	 Linear
11.91/13.34	->Coefficients:
11.91/13.34	 All rationals
11.91/13.34	->Dimension:
11.91/13.34	 1
11.91/13.34	->Bound:
11.91/13.34	 4
11.91/13.34	->Interpretation:
11.91/13.34	 
11.91/13.34	[e](X) = 4/3.X + 1/3
11.91/13.34	[i](X) = 2/3.X
11.91/13.34	[r](X) = 2.X + 3/4
11.91/13.34	[t](X) = 4.X + 2
11.91/13.34	[w](X) = 4/3.X + 1/3
11.91/13.34	[E](X) = X + 3/4
11.91/13.34	[I](X) = 1/2.X + 2/3
11.91/13.34	[R](X) = 2.X + 1
11.91/13.34	[T](X) = 2.X + 3/2
11.91/13.34	[W](X) = 4/3.X + 2/3
11.91/13.34	
11.91/13.34	Problem 1: 
11.91/13.34	
11.91/13.34	SCC Processor:
11.91/13.34	-> Pairs:
11.91/13.34	 I(t(x1:S)) -> E(r(x1:S))
11.91/13.34	 I(t(x1:S)) -> R(x1:S)
11.91/13.34	 R(e(x1:S)) -> R(x1:S)
11.91/13.34	 R(e(x1:S)) -> W(r(x1:S))
11.91/13.34	 R(i(t(e(r(x1:S))))) -> E(w(r(i(t(e(x1:S))))))
11.91/13.34	 R(i(t(e(r(x1:S))))) -> E(x1:S)
11.91/13.34	 R(i(t(e(r(x1:S))))) -> I(t(e(x1:S)))
11.91/13.34	 R(i(t(e(r(x1:S))))) -> R(i(t(e(x1:S))))
11.91/13.34	 R(i(t(e(r(x1:S))))) -> T(e(x1:S))
11.91/13.34	 R(i(t(e(r(x1:S))))) -> W(r(i(t(e(x1:S)))))
11.91/13.34	 T(e(x1:S)) -> R(e(x1:S))
11.91/13.34	 W(r(x1:S)) -> I(t(x1:S))
11.91/13.34	 W(r(x1:S)) -> T(x1:S)
11.91/13.34	-> Rules:
11.91/13.34	 e(r(x1:S)) -> e(w(x1:S))
11.91/13.34	 e(w(x1:S)) -> r(i(x1:S))
11.91/13.34	 i(t(x1:S)) -> e(r(x1:S))
11.91/13.34	 r(e(x1:S)) -> w(r(x1:S))
11.91/13.34	 r(i(t(e(r(x1:S))))) -> e(w(r(i(t(e(x1:S))))))
11.91/13.34	 t(e(x1:S)) -> r(e(x1:S))
11.91/13.34	 w(r(x1:S)) -> i(t(x1:S))
11.91/13.34	->Strongly Connected Components:
11.91/13.34	->->Cycle:
11.91/13.34	->->-> Pairs:
11.91/13.34	 I(t(x1:S)) -> R(x1:S)
11.91/13.34	 R(e(x1:S)) -> R(x1:S)
11.91/13.34	 R(e(x1:S)) -> W(r(x1:S))
11.91/13.34	 R(i(t(e(r(x1:S))))) -> I(t(e(x1:S)))
11.91/13.34	 R(i(t(e(r(x1:S))))) -> R(i(t(e(x1:S))))
11.91/13.34	 R(i(t(e(r(x1:S))))) -> T(e(x1:S))
11.91/13.34	 R(i(t(e(r(x1:S))))) -> W(r(i(t(e(x1:S)))))
11.91/13.34	 T(e(x1:S)) -> R(e(x1:S))
11.91/13.34	 W(r(x1:S)) -> I(t(x1:S))
11.91/13.34	 W(r(x1:S)) -> T(x1:S)
11.91/13.34	->->-> Rules:
11.91/13.34	 e(r(x1:S)) -> e(w(x1:S))
11.91/13.34	 e(w(x1:S)) -> r(i(x1:S))
11.91/13.34	 i(t(x1:S)) -> e(r(x1:S))
11.91/13.34	 r(e(x1:S)) -> w(r(x1:S))
11.91/13.34	 r(i(t(e(r(x1:S))))) -> e(w(r(i(t(e(x1:S))))))
11.91/13.34	 t(e(x1:S)) -> r(e(x1:S))
11.91/13.34	 w(r(x1:S)) -> i(t(x1:S))
11.91/13.34	
11.91/13.34	Problem 1: 
11.91/13.34	
11.91/13.34	Reduction Pair Processor:
11.91/13.34	-> Pairs:
11.91/13.34	 I(t(x1:S)) -> R(x1:S)
11.91/13.34	 R(e(x1:S)) -> R(x1:S)
11.91/13.34	 R(e(x1:S)) -> W(r(x1:S))
11.91/13.34	 R(i(t(e(r(x1:S))))) -> I(t(e(x1:S)))
11.91/13.34	 R(i(t(e(r(x1:S))))) -> R(i(t(e(x1:S))))
11.91/13.34	 R(i(t(e(r(x1:S))))) -> T(e(x1:S))
11.91/13.34	 R(i(t(e(r(x1:S))))) -> W(r(i(t(e(x1:S)))))
11.91/13.34	 T(e(x1:S)) -> R(e(x1:S))
11.91/13.34	 W(r(x1:S)) -> I(t(x1:S))
11.91/13.34	 W(r(x1:S)) -> T(x1:S)
11.91/13.34	-> Rules:
11.91/13.34	 e(r(x1:S)) -> e(w(x1:S))
11.91/13.34	 e(w(x1:S)) -> r(i(x1:S))
11.91/13.34	 i(t(x1:S)) -> e(r(x1:S))
11.91/13.34	 r(e(x1:S)) -> w(r(x1:S))
11.91/13.34	 r(i(t(e(r(x1:S))))) -> e(w(r(i(t(e(x1:S))))))
11.91/13.34	 t(e(x1:S)) -> r(e(x1:S))
11.91/13.34	 w(r(x1:S)) -> i(t(x1:S))
11.91/13.34	-> Usable rules:
11.91/13.34	 e(r(x1:S)) -> e(w(x1:S))
11.91/13.34	 e(w(x1:S)) -> r(i(x1:S))
11.91/13.34	 i(t(x1:S)) -> e(r(x1:S))
11.91/13.34	 r(e(x1:S)) -> w(r(x1:S))
11.91/13.34	 r(i(t(e(r(x1:S))))) -> e(w(r(i(t(e(x1:S))))))
11.91/13.34	 t(e(x1:S)) -> r(e(x1:S))
11.91/13.34	 w(r(x1:S)) -> i(t(x1:S))
11.91/13.34	->Interpretation type:
11.91/13.34	 Linear
11.91/13.34	->Coefficients:
11.91/13.34	 All rationals
11.91/13.34	->Dimension:
11.91/13.34	 1
11.91/13.34	->Bound:
11.91/13.34	 4
11.91/13.34	->Interpretation:
11.91/13.34	 
11.91/13.34	[e](X) = X + 1/2
11.91/13.34	[i](X) = 1/2.X
11.91/13.34	[r](X) = X + 1
11.91/13.34	[t](X) = 2.X + 3
11.91/13.34	[w](X) = X + 1/2
11.91/13.34	[I](X) = 1/4.X + 1/3
11.91/13.34	[R](X) = 1/2.X + 1
11.91/13.34	[T](X) = 1/2.X + 1
11.91/13.34	[W](X) = 1/2.X + 2/3
11.91/13.34	
11.91/13.34	Problem 1: 
11.91/13.34	
11.91/13.34	SCC Processor:
11.91/13.34	-> Pairs:
11.91/13.34	 R(e(x1:S)) -> R(x1:S)
11.91/13.34	 R(e(x1:S)) -> W(r(x1:S))
11.91/13.34	 R(i(t(e(r(x1:S))))) -> I(t(e(x1:S)))
11.91/13.34	 R(i(t(e(r(x1:S))))) -> R(i(t(e(x1:S))))
11.91/13.34	 R(i(t(e(r(x1:S))))) -> T(e(x1:S))
11.91/13.34	 R(i(t(e(r(x1:S))))) -> W(r(i(t(e(x1:S)))))
11.91/13.34	 T(e(x1:S)) -> R(e(x1:S))
11.91/13.34	 W(r(x1:S)) -> I(t(x1:S))
11.91/13.34	 W(r(x1:S)) -> T(x1:S)
11.91/13.34	-> Rules:
11.91/13.34	 e(r(x1:S)) -> e(w(x1:S))
11.91/13.34	 e(w(x1:S)) -> r(i(x1:S))
11.91/13.34	 i(t(x1:S)) -> e(r(x1:S))
11.91/13.34	 r(e(x1:S)) -> w(r(x1:S))
11.91/13.34	 r(i(t(e(r(x1:S))))) -> e(w(r(i(t(e(x1:S))))))
11.91/13.34	 t(e(x1:S)) -> r(e(x1:S))
11.91/13.34	 w(r(x1:S)) -> i(t(x1:S))
11.91/13.34	->Strongly Connected Components:
11.91/13.34	->->Cycle:
11.91/13.34	->->-> Pairs:
11.91/13.34	 R(e(x1:S)) -> R(x1:S)
11.91/13.34	 R(e(x1:S)) -> W(r(x1:S))
11.91/13.34	 R(i(t(e(r(x1:S))))) -> R(i(t(e(x1:S))))
11.91/13.34	 R(i(t(e(r(x1:S))))) -> T(e(x1:S))
11.91/13.34	 R(i(t(e(r(x1:S))))) -> W(r(i(t(e(x1:S)))))
11.91/13.34	 T(e(x1:S)) -> R(e(x1:S))
11.91/13.34	 W(r(x1:S)) -> T(x1:S)
11.91/13.34	->->-> Rules:
11.91/13.34	 e(r(x1:S)) -> e(w(x1:S))
11.91/13.34	 e(w(x1:S)) -> r(i(x1:S))
11.91/13.34	 i(t(x1:S)) -> e(r(x1:S))
11.91/13.34	 r(e(x1:S)) -> w(r(x1:S))
11.91/13.34	 r(i(t(e(r(x1:S))))) -> e(w(r(i(t(e(x1:S))))))
11.91/13.34	 t(e(x1:S)) -> r(e(x1:S))
11.91/13.34	 w(r(x1:S)) -> i(t(x1:S))
11.91/13.34	
11.91/13.34	Problem 1: 
11.91/13.34	
11.91/13.34	Reduction Pair Processor:
11.91/13.34	-> Pairs:
11.91/13.34	 R(e(x1:S)) -> R(x1:S)
11.91/13.34	 R(e(x1:S)) -> W(r(x1:S))
11.91/13.34	 R(i(t(e(r(x1:S))))) -> R(i(t(e(x1:S))))
11.91/13.34	 R(i(t(e(r(x1:S))))) -> T(e(x1:S))
11.91/13.34	 R(i(t(e(r(x1:S))))) -> W(r(i(t(e(x1:S)))))
11.91/13.34	 T(e(x1:S)) -> R(e(x1:S))
11.91/13.34	 W(r(x1:S)) -> T(x1:S)
11.91/13.34	-> Rules:
11.91/13.34	 e(r(x1:S)) -> e(w(x1:S))
11.91/13.34	 e(w(x1:S)) -> r(i(x1:S))
11.91/13.34	 i(t(x1:S)) -> e(r(x1:S))
11.91/13.34	 r(e(x1:S)) -> w(r(x1:S))
11.91/13.34	 r(i(t(e(r(x1:S))))) -> e(w(r(i(t(e(x1:S))))))
11.91/13.34	 t(e(x1:S)) -> r(e(x1:S))
11.91/13.34	 w(r(x1:S)) -> i(t(x1:S))
11.91/13.34	-> Usable rules:
11.91/13.34	 e(r(x1:S)) -> e(w(x1:S))
11.91/13.34	 e(w(x1:S)) -> r(i(x1:S))
11.91/13.34	 i(t(x1:S)) -> e(r(x1:S))
11.91/13.34	 r(e(x1:S)) -> w(r(x1:S))
11.91/13.34	 r(i(t(e(r(x1:S))))) -> e(w(r(i(t(e(x1:S))))))
11.91/13.34	 t(e(x1:S)) -> r(e(x1:S))
11.91/13.34	 w(r(x1:S)) -> i(t(x1:S))
11.91/13.34	->Interpretation type:
11.91/13.34	 Linear
11.91/13.34	->Coefficients:
11.91/13.34	 All rationals
11.91/13.34	->Dimension:
11.91/13.34	 1
11.91/13.34	->Bound:
11.91/13.34	 4
11.91/13.34	->Interpretation:
11.91/13.34	 
11.91/13.34	[e](X) = X + 3/2
11.91/13.34	[i](X) = 1/2.X + 1
11.91/13.34	[r](X) = 3/2.X + 3/2
11.91/13.34	[t](X) = 3.X + 4
11.91/13.34	[w](X) = X + 3/2
11.91/13.34	[R](X) = 2.X + 4/3
11.91/13.34	[T](X) = 2.X + 2
11.91/13.34	[W](X) = 4/3.X + 2/3
11.91/13.34	
11.91/13.34	Problem 1: 
11.91/13.34	
11.91/13.34	SCC Processor:
11.91/13.34	-> Pairs:
11.91/13.34	 R(e(x1:S)) -> W(r(x1:S))
11.91/13.34	 R(i(t(e(r(x1:S))))) -> R(i(t(e(x1:S))))
11.91/13.34	 R(i(t(e(r(x1:S))))) -> T(e(x1:S))
11.91/13.34	 R(i(t(e(r(x1:S))))) -> W(r(i(t(e(x1:S)))))
11.91/13.34	 T(e(x1:S)) -> R(e(x1:S))
11.91/13.34	 W(r(x1:S)) -> T(x1:S)
11.91/13.34	-> Rules:
11.91/13.34	 e(r(x1:S)) -> e(w(x1:S))
11.91/13.34	 e(w(x1:S)) -> r(i(x1:S))
11.91/13.34	 i(t(x1:S)) -> e(r(x1:S))
11.91/13.34	 r(e(x1:S)) -> w(r(x1:S))
11.91/13.34	 r(i(t(e(r(x1:S))))) -> e(w(r(i(t(e(x1:S))))))
11.91/13.34	 t(e(x1:S)) -> r(e(x1:S))
11.91/13.34	 w(r(x1:S)) -> i(t(x1:S))
11.91/13.34	->Strongly Connected Components:
11.91/13.34	->->Cycle:
11.91/13.34	->->-> Pairs:
11.91/13.34	 R(e(x1:S)) -> W(r(x1:S))
11.91/13.34	 R(i(t(e(r(x1:S))))) -> R(i(t(e(x1:S))))
11.91/13.34	 R(i(t(e(r(x1:S))))) -> T(e(x1:S))
11.91/13.34	 R(i(t(e(r(x1:S))))) -> W(r(i(t(e(x1:S)))))
11.91/13.34	 T(e(x1:S)) -> R(e(x1:S))
11.91/13.34	 W(r(x1:S)) -> T(x1:S)
11.91/13.34	->->-> Rules:
11.91/13.34	 e(r(x1:S)) -> e(w(x1:S))
11.91/13.34	 e(w(x1:S)) -> r(i(x1:S))
11.91/13.34	 i(t(x1:S)) -> e(r(x1:S))
11.91/13.34	 r(e(x1:S)) -> w(r(x1:S))
11.91/13.34	 r(i(t(e(r(x1:S))))) -> e(w(r(i(t(e(x1:S))))))
11.91/13.34	 t(e(x1:S)) -> r(e(x1:S))
11.91/13.34	 w(r(x1:S)) -> i(t(x1:S))
11.91/13.34	
11.91/13.34	Problem 1: 
11.91/13.34	
11.91/13.34	Reduction Pair Processor:
11.91/13.34	-> Pairs:
11.91/13.34	 R(e(x1:S)) -> W(r(x1:S))
11.91/13.34	 R(i(t(e(r(x1:S))))) -> R(i(t(e(x1:S))))
11.91/13.34	 R(i(t(e(r(x1:S))))) -> T(e(x1:S))
11.91/13.34	 R(i(t(e(r(x1:S))))) -> W(r(i(t(e(x1:S)))))
11.91/13.34	 T(e(x1:S)) -> R(e(x1:S))
11.91/13.34	 W(r(x1:S)) -> T(x1:S)
11.91/13.34	-> Rules:
11.91/13.34	 e(r(x1:S)) -> e(w(x1:S))
11.91/13.34	 e(w(x1:S)) -> r(i(x1:S))
11.91/13.34	 i(t(x1:S)) -> e(r(x1:S))
11.91/13.34	 r(e(x1:S)) -> w(r(x1:S))
11.91/13.34	 r(i(t(e(r(x1:S))))) -> e(w(r(i(t(e(x1:S))))))
11.91/13.34	 t(e(x1:S)) -> r(e(x1:S))
11.91/13.34	 w(r(x1:S)) -> i(t(x1:S))
11.91/13.34	-> Usable rules:
11.91/13.34	 e(r(x1:S)) -> e(w(x1:S))
11.91/13.34	 e(w(x1:S)) -> r(i(x1:S))
11.91/13.34	 i(t(x1:S)) -> e(r(x1:S))
11.91/13.34	 r(e(x1:S)) -> w(r(x1:S))
11.91/13.34	 r(i(t(e(r(x1:S))))) -> e(w(r(i(t(e(x1:S))))))
11.91/13.34	 t(e(x1:S)) -> r(e(x1:S))
11.91/13.34	 w(r(x1:S)) -> i(t(x1:S))
11.91/13.34	->Interpretation type:
11.91/13.34	 Linear
11.91/13.34	->Coefficients:
11.91/13.34	 All rationals
11.91/13.34	->Dimension:
11.91/13.34	 1
11.91/13.34	->Bound:
11.91/13.34	 4
11.91/13.34	->Interpretation:
11.91/13.34	 
11.91/13.34	[e](X) = X + 1/2
11.91/13.34	[i](X) = 1/2.X
11.91/13.34	[r](X) = 3/2.X + 1/2
11.91/13.34	[t](X) = 3.X + 2
11.91/13.34	[w](X) = X + 1/2
11.91/13.34	[R](X) = 3.X + 1/2
11.91/13.34	[T](X) = 3.X + 2/3
11.91/13.34	[W](X) = 2.X
11.91/13.34	
11.91/13.34	Problem 1: 
11.91/13.34	
11.91/13.34	SCC Processor:
11.91/13.34	-> Pairs:
11.91/13.34	 R(i(t(e(r(x1:S))))) -> R(i(t(e(x1:S))))
11.91/13.34	 R(i(t(e(r(x1:S))))) -> T(e(x1:S))
11.91/13.34	 R(i(t(e(r(x1:S))))) -> W(r(i(t(e(x1:S)))))
11.91/13.34	 T(e(x1:S)) -> R(e(x1:S))
11.91/13.34	 W(r(x1:S)) -> T(x1:S)
11.91/13.34	-> Rules:
11.91/13.34	 e(r(x1:S)) -> e(w(x1:S))
11.91/13.34	 e(w(x1:S)) -> r(i(x1:S))
11.91/13.34	 i(t(x1:S)) -> e(r(x1:S))
11.91/13.34	 r(e(x1:S)) -> w(r(x1:S))
11.91/13.34	 r(i(t(e(r(x1:S))))) -> e(w(r(i(t(e(x1:S))))))
11.91/13.34	 t(e(x1:S)) -> r(e(x1:S))
11.91/13.34	 w(r(x1:S)) -> i(t(x1:S))
11.91/13.34	->Strongly Connected Components:
11.91/13.34	->->Cycle:
11.91/13.34	->->-> Pairs:
11.91/13.34	 R(i(t(e(r(x1:S))))) -> R(i(t(e(x1:S))))
11.91/13.34	 R(i(t(e(r(x1:S))))) -> T(e(x1:S))
11.91/13.34	 R(i(t(e(r(x1:S))))) -> W(r(i(t(e(x1:S)))))
11.91/13.34	 T(e(x1:S)) -> R(e(x1:S))
11.91/13.34	 W(r(x1:S)) -> T(x1:S)
11.91/13.34	->->-> Rules:
11.91/13.34	 e(r(x1:S)) -> e(w(x1:S))
11.91/13.34	 e(w(x1:S)) -> r(i(x1:S))
11.91/13.34	 i(t(x1:S)) -> e(r(x1:S))
11.91/13.34	 r(e(x1:S)) -> w(r(x1:S))
11.91/13.34	 r(i(t(e(r(x1:S))))) -> e(w(r(i(t(e(x1:S))))))
11.91/13.34	 t(e(x1:S)) -> r(e(x1:S))
11.91/13.34	 w(r(x1:S)) -> i(t(x1:S))
11.91/13.34	
11.91/13.34	Problem 1: 
11.91/13.34	
11.91/13.34	Reduction Pair Processor:
11.91/13.34	-> Pairs:
11.91/13.34	 R(i(t(e(r(x1:S))))) -> R(i(t(e(x1:S))))
11.91/13.34	 R(i(t(e(r(x1:S))))) -> T(e(x1:S))
11.91/13.34	 R(i(t(e(r(x1:S))))) -> W(r(i(t(e(x1:S)))))
11.91/13.34	 T(e(x1:S)) -> R(e(x1:S))
11.91/13.34	 W(r(x1:S)) -> T(x1:S)
11.91/13.34	-> Rules:
11.91/13.34	 e(r(x1:S)) -> e(w(x1:S))
11.91/13.34	 e(w(x1:S)) -> r(i(x1:S))
11.91/13.34	 i(t(x1:S)) -> e(r(x1:S))
11.91/13.34	 r(e(x1:S)) -> w(r(x1:S))
11.91/13.34	 r(i(t(e(r(x1:S))))) -> e(w(r(i(t(e(x1:S))))))
11.91/13.34	 t(e(x1:S)) -> r(e(x1:S))
11.91/13.34	 w(r(x1:S)) -> i(t(x1:S))
11.91/13.34	-> Usable rules:
11.91/13.34	 e(r(x1:S)) -> e(w(x1:S))
11.91/13.34	 e(w(x1:S)) -> r(i(x1:S))
11.91/13.34	 i(t(x1:S)) -> e(r(x1:S))
11.91/13.34	 r(e(x1:S)) -> w(r(x1:S))
11.91/13.34	 r(i(t(e(r(x1:S))))) -> e(w(r(i(t(e(x1:S))))))
11.91/13.34	 t(e(x1:S)) -> r(e(x1:S))
11.91/13.34	 w(r(x1:S)) -> i(t(x1:S))
11.91/13.34	->Interpretation type:
11.91/13.34	 Linear
11.91/13.34	->Coefficients:
11.91/13.34	 All rationals
11.91/13.34	->Dimension:
11.91/13.34	 1
11.91/13.34	->Bound:
11.91/13.34	 4
11.91/13.34	->Interpretation:
11.91/13.34	 
11.91/13.34	[e](X) = 3/4.X + 1/2
11.91/13.34	[i](X) = 1/4.X + 1/4
11.91/13.34	[r](X) = 4/3.X + 2/3
11.91/13.34	[t](X) = 4.X + 3
11.91/13.34	[w](X) = 3/4.X + 2/3
11.91/13.34	[R](X) = 3.X + 4
11.91/13.34	[T](X) = 4.X + 4
11.91/13.34	[W](X) = 3.X + 2
11.91/13.34	
11.91/13.34	Problem 1: 
11.91/13.34	
11.91/13.34	SCC Processor:
11.91/13.34	-> Pairs:
11.91/13.34	 R(i(t(e(r(x1:S))))) -> T(e(x1:S))
11.91/13.34	 R(i(t(e(r(x1:S))))) -> W(r(i(t(e(x1:S)))))
11.91/13.34	 T(e(x1:S)) -> R(e(x1:S))
11.91/13.34	 W(r(x1:S)) -> T(x1:S)
11.91/13.34	-> Rules:
11.91/13.34	 e(r(x1:S)) -> e(w(x1:S))
11.91/13.34	 e(w(x1:S)) -> r(i(x1:S))
11.91/13.34	 i(t(x1:S)) -> e(r(x1:S))
11.91/13.34	 r(e(x1:S)) -> w(r(x1:S))
11.91/13.34	 r(i(t(e(r(x1:S))))) -> e(w(r(i(t(e(x1:S))))))
11.91/13.34	 t(e(x1:S)) -> r(e(x1:S))
11.91/13.34	 w(r(x1:S)) -> i(t(x1:S))
11.91/13.34	->Strongly Connected Components:
11.91/13.34	->->Cycle:
11.91/13.34	->->-> Pairs:
11.91/13.34	 R(i(t(e(r(x1:S))))) -> T(e(x1:S))
11.91/13.34	 R(i(t(e(r(x1:S))))) -> W(r(i(t(e(x1:S)))))
11.91/13.34	 T(e(x1:S)) -> R(e(x1:S))
11.91/13.34	 W(r(x1:S)) -> T(x1:S)
11.91/13.34	->->-> Rules:
11.91/13.34	 e(r(x1:S)) -> e(w(x1:S))
11.91/13.34	 e(w(x1:S)) -> r(i(x1:S))
11.91/13.34	 i(t(x1:S)) -> e(r(x1:S))
11.91/13.34	 r(e(x1:S)) -> w(r(x1:S))
11.91/13.34	 r(i(t(e(r(x1:S))))) -> e(w(r(i(t(e(x1:S))))))
11.91/13.34	 t(e(x1:S)) -> r(e(x1:S))
11.91/13.34	 w(r(x1:S)) -> i(t(x1:S))
11.91/13.34	
11.91/13.34	Problem 1: 
11.91/13.34	
11.91/13.34	Reduction Pair Processor:
11.91/13.34	-> Pairs:
11.91/13.34	 R(i(t(e(r(x1:S))))) -> T(e(x1:S))
11.91/13.34	 R(i(t(e(r(x1:S))))) -> W(r(i(t(e(x1:S)))))
11.91/13.34	 T(e(x1:S)) -> R(e(x1:S))
11.91/13.34	 W(r(x1:S)) -> T(x1:S)
11.91/13.34	-> Rules:
11.91/13.34	 e(r(x1:S)) -> e(w(x1:S))
11.91/13.34	 e(w(x1:S)) -> r(i(x1:S))
11.91/13.34	 i(t(x1:S)) -> e(r(x1:S))
11.91/13.34	 r(e(x1:S)) -> w(r(x1:S))
11.91/13.34	 r(i(t(e(r(x1:S))))) -> e(w(r(i(t(e(x1:S))))))
11.91/13.34	 t(e(x1:S)) -> r(e(x1:S))
11.91/13.34	 w(r(x1:S)) -> i(t(x1:S))
11.91/13.34	-> Usable rules:
11.91/13.34	 e(r(x1:S)) -> e(w(x1:S))
11.91/13.34	 e(w(x1:S)) -> r(i(x1:S))
11.91/13.34	 i(t(x1:S)) -> e(r(x1:S))
11.91/13.34	 r(e(x1:S)) -> w(r(x1:S))
11.91/13.34	 r(i(t(e(r(x1:S))))) -> e(w(r(i(t(e(x1:S))))))
11.91/13.34	 t(e(x1:S)) -> r(e(x1:S))
11.91/13.34	 w(r(x1:S)) -> i(t(x1:S))
11.91/13.34	->Interpretation type:
11.91/13.34	 Linear
11.91/13.34	->Coefficients:
11.91/13.34	 All rationals
11.91/13.34	->Dimension:
11.91/13.34	 1
11.91/13.34	->Bound:
11.91/13.34	 4
11.91/13.34	->Interpretation:
11.91/13.34	 
11.91/13.34	[e](X) = 3/4.X + 3/4
11.91/13.34	[i](X) = 1/3.X + 1/3
11.91/13.34	[r](X) = 4/3.X + 1
11.91/13.34	[t](X) = 3.X + 4
11.91/13.34	[w](X) = 3/4.X + 1
11.91/13.34	[R](X) = 2.X + 1/2
11.91/13.34	[T](X) = 2.X + 3/4
11.91/13.34	[W](X) = 3/2.X
11.91/13.34	
11.91/13.34	Problem 1: 
11.91/13.34	
11.91/13.34	SCC Processor:
11.91/13.34	-> Pairs:
11.91/13.34	 R(i(t(e(r(x1:S))))) -> W(r(i(t(e(x1:S)))))
11.91/13.34	 T(e(x1:S)) -> R(e(x1:S))
11.91/13.34	 W(r(x1:S)) -> T(x1:S)
11.91/13.34	-> Rules:
11.91/13.34	 e(r(x1:S)) -> e(w(x1:S))
11.91/13.34	 e(w(x1:S)) -> r(i(x1:S))
11.91/13.34	 i(t(x1:S)) -> e(r(x1:S))
11.91/13.34	 r(e(x1:S)) -> w(r(x1:S))
11.91/13.34	 r(i(t(e(r(x1:S))))) -> e(w(r(i(t(e(x1:S))))))
11.91/13.34	 t(e(x1:S)) -> r(e(x1:S))
11.91/13.34	 w(r(x1:S)) -> i(t(x1:S))
11.91/13.34	->Strongly Connected Components:
11.91/13.34	->->Cycle:
11.91/13.34	->->-> Pairs:
11.91/13.34	 R(i(t(e(r(x1:S))))) -> W(r(i(t(e(x1:S)))))
11.91/13.34	 T(e(x1:S)) -> R(e(x1:S))
11.91/13.34	 W(r(x1:S)) -> T(x1:S)
11.91/13.34	->->-> Rules:
11.91/13.34	 e(r(x1:S)) -> e(w(x1:S))
11.91/13.34	 e(w(x1:S)) -> r(i(x1:S))
11.91/13.34	 i(t(x1:S)) -> e(r(x1:S))
11.91/13.34	 r(e(x1:S)) -> w(r(x1:S))
11.91/13.34	 r(i(t(e(r(x1:S))))) -> e(w(r(i(t(e(x1:S))))))
11.91/13.34	 t(e(x1:S)) -> r(e(x1:S))
11.91/13.34	 w(r(x1:S)) -> i(t(x1:S))
11.91/13.34	
11.91/13.34	Problem 1: 
11.91/13.34	
11.91/13.34	Reduction Pair Processor:
11.91/13.34	-> Pairs:
11.91/13.34	 R(i(t(e(r(x1:S))))) -> W(r(i(t(e(x1:S)))))
11.91/13.34	 T(e(x1:S)) -> R(e(x1:S))
11.91/13.34	 W(r(x1:S)) -> T(x1:S)
11.91/13.34	-> Rules:
11.91/13.34	 e(r(x1:S)) -> e(w(x1:S))
11.91/13.34	 e(w(x1:S)) -> r(i(x1:S))
11.91/13.34	 i(t(x1:S)) -> e(r(x1:S))
11.91/13.34	 r(e(x1:S)) -> w(r(x1:S))
11.91/13.34	 r(i(t(e(r(x1:S))))) -> e(w(r(i(t(e(x1:S))))))
11.91/13.34	 t(e(x1:S)) -> r(e(x1:S))
11.91/13.34	 w(r(x1:S)) -> i(t(x1:S))
11.91/13.34	-> Usable rules:
11.91/13.34	 e(r(x1:S)) -> e(w(x1:S))
11.91/13.34	 e(w(x1:S)) -> r(i(x1:S))
11.91/13.34	 i(t(x1:S)) -> e(r(x1:S))
11.91/13.34	 r(e(x1:S)) -> w(r(x1:S))
11.91/13.34	 r(i(t(e(r(x1:S))))) -> e(w(r(i(t(e(x1:S))))))
11.91/13.34	 t(e(x1:S)) -> r(e(x1:S))
11.91/13.34	 w(r(x1:S)) -> i(t(x1:S))
11.91/13.34	->Interpretation type:
11.91/13.34	 Linear
11.91/13.34	->Coefficients:
11.91/13.34	 All rationals
11.91/13.34	->Dimension:
11.91/13.34	 1
11.91/13.34	->Bound:
11.91/13.34	 4
11.91/13.34	->Interpretation:
11.91/13.34	 
11.91/13.34	[e](X) = X + 1/3
11.91/13.34	[i](X) = 1/2.X
11.91/13.34	[r](X) = 2.X + 1/2
11.91/13.34	[t](X) = 4.X + 2
11.91/13.34	[w](X) = X + 1/2
11.91/13.34	[R](X) = 4.X + 3
11.91/13.34	[T](X) = 4.X + 3
11.91/13.34	[W](X) = 2.X + 2
11.91/13.34	
11.91/13.34	Problem 1: 
11.91/13.34	
11.91/13.34	SCC Processor:
11.91/13.34	-> Pairs:
11.91/13.34	 T(e(x1:S)) -> R(e(x1:S))
11.91/13.34	 W(r(x1:S)) -> T(x1:S)
11.91/13.34	-> Rules:
11.91/13.34	 e(r(x1:S)) -> e(w(x1:S))
11.91/13.34	 e(w(x1:S)) -> r(i(x1:S))
11.91/13.34	 i(t(x1:S)) -> e(r(x1:S))
11.91/13.34	 r(e(x1:S)) -> w(r(x1:S))
11.91/13.34	 r(i(t(e(r(x1:S))))) -> e(w(r(i(t(e(x1:S))))))
11.91/13.34	 t(e(x1:S)) -> r(e(x1:S))
11.91/13.34	 w(r(x1:S)) -> i(t(x1:S))
11.91/13.34	->Strongly Connected Components:
11.91/13.34	 There is no strongly connected component
11.91/13.34	
11.91/13.34	The problem is finite.
11.91/13.34	EOF