3.03/1.79	YES
3.03/1.79	
3.03/1.79	Proof:
3.03/1.79	This system is confluent.
3.03/1.79	By \cite{ALS94}, Theorem 4.1.
3.03/1.79	This system is of type 3 or smaller.
3.03/1.79	This system is strongly deterministic.
3.03/1.79	This system is quasi-decreasing.
3.03/1.79	By \cite{O02}, p. 214, Proposition 7.2.50.
3.03/1.79	This system is of type 3 or smaller.
3.03/1.79	This system is deterministic.
3.03/1.80	System R transformed to optimized U(R).
3.03/1.80	This system is terminating.
3.03/1.80	Call external tool:
3.03/1.80	./ttt2.sh
3.03/1.80	Input:
3.03/1.80	(VAR x)
3.03/1.80	(RULES
3.03/1.80	  f(x) -> ?1(x, x)
3.03/1.80	  ?1(a, x) -> x
3.03/1.80	  g(x) -> ?2(A, x)
3.03/1.80	  ?2(B, x) -> C
3.03/1.80	  A -> B
3.03/1.80	)
3.03/1.80	
3.03/1.80	 Polynomial Interpretation Processor:
3.03/1.80	  dimension: 1
3.03/1.80	  interpretation:
3.03/1.80	   [C] = 0,
3.03/1.80	   
3.03/1.80	   [B] = 0,
3.03/1.80	   
3.03/1.80	   [?2](x0, x1) = x0 + 2x1 + x1x1 + 2,
3.03/1.80	   
3.03/1.80	   [A] = 1,
3.03/1.80	   
3.03/1.80	   [g](x0) = 7x0 + 4x0x0 + 4,
3.03/1.80	   
3.03/1.80	   [a] = 4,
3.03/1.80	   
3.03/1.80	   [?1](x0, x1) = -1x0 + 6x1 + 4x0x0 + x1x1 + 4,
3.03/1.80	   
3.03/1.80	   [f](x0) = 6x0 + 5x0x0 + 6
3.03/1.80	  orientation:
3.03/1.80	   f(x) = 6x + 5x*x + 6 >= 5x + 5x*x + 4 = ?1(x,x)
3.03/1.80	   
3.03/1.80	   ?1(a(),x) = 6x + x*x + 64 >= x = x
3.03/1.80	   
3.03/1.80	   g(x) = 7x + 4x*x + 4 >= 2x + x*x + 3 = ?2(A(),x)
3.03/1.80	   
3.03/1.80	   ?2(B(),x) = 2x + x*x + 2 >= 0 = C()
3.03/1.80	   
3.03/1.80	   A() = 1 >= 0 = B()
3.03/1.80	  problem:
3.03/1.80	   
3.03/1.80	  Qed
3.03/1.80	All 0 critical pairs are joinable.
3.03/1.80	
3.03/1.82	EOF