3.28/1.70	YES
3.28/1.70	
3.28/1.70	Proof:
3.28/1.70	This system is confluent.
3.28/1.70	By \cite{ALS94}, Theorem 4.1.
3.28/1.70	This system is of type 3 or smaller.
3.28/1.70	This system is strongly deterministic.
3.28/1.70	This system is quasi-decreasing.
3.28/1.70	By \cite{O02}, p. 214, Proposition 7.2.50.
3.28/1.70	This system is of type 3 or smaller.
3.28/1.70	This system is deterministic.
3.28/1.70	System R transformed to optimized U(R).
3.28/1.70	This system is terminating.
3.28/1.70	Call external tool:
3.28/1.70	./ttt2.sh
3.28/1.70	Input:
3.28/1.70	(VAR x)
3.28/1.70	(RULES
3.28/1.70	  a -> b
3.28/1.70	  f(x) -> ?1(x, x)
3.28/1.70	  ?1(b, x) -> A
3.28/1.70	  g(x, x) -> h(x)
3.28/1.70	  h(x) -> i(x)
3.28/1.70	)
3.28/1.70	
3.28/1.70	 Polynomial Interpretation Processor:
3.28/1.70	  dimension: 1
3.28/1.70	  interpretation:
3.28/1.70	   [i](x0) = -3x0 + 4x0x0,
3.28/1.70	   
3.28/1.70	   [h](x0) = 4x0x0 + 1,
3.28/1.70	   
3.28/1.70	   [g](x0, x1) = 4x0 + 5x1x1 + 4,
3.28/1.70	   
3.28/1.70	   [A] = 0,
3.28/1.70	   
3.28/1.70	   [?1](x0, x1) = -1x0 + 2x0x0 + x1x1 + 4,
3.28/1.70	   
3.28/1.70	   [f](x0) = 3x0x0 + 5,
3.28/1.70	   
3.28/1.70	   [b] = 0,
3.28/1.70	   
3.28/1.70	   [a] = 1
3.28/1.70	  orientation:
3.28/1.70	   a() = 1 >= 0 = b()
3.28/1.70	   
3.28/1.70	   f(x) = 3x*x + 5 >= -1x + 3x*x + 4 = ?1(x,x)
3.28/1.70	   
3.28/1.70	   ?1(b(),x) = x*x + 4 >= 0 = A()
3.28/1.70	   
3.28/1.70	   g(x,x) = 4x + 5x*x + 4 >= 4x*x + 1 = h(x)
3.28/1.70	   
3.28/1.70	   h(x) = 4x*x + 1 >= -3x + 4x*x = i(x)
3.28/1.70	  problem:
3.28/1.70	   
3.28/1.70	  Qed
3.28/1.70	All 0 critical pairs are joinable.
3.28/1.70	
3.28/1.73	EOF