1.91/1.07	YES
1.91/1.07	
1.91/1.07	Proof:
1.91/1.07	This system is confluent.
1.91/1.07	By \cite{ALS94}, Theorem 4.1.
1.91/1.07	This system is of type 3 or smaller.
1.91/1.07	This system is strongly deterministic.
1.91/1.07	This system is quasi-decreasing.
1.91/1.07	By \cite{O02}, p. 214, Proposition 7.2.50.
1.91/1.07	This system is of type 3 or smaller.
1.91/1.07	This system is deterministic.
1.91/1.07	System R transformed to U(R).
1.91/1.08	This system is terminating.
1.91/1.08	Call external tool:
1.91/1.08	./ttt2.sh
1.91/1.08	Input:
1.91/1.08	  ?1(y, x) -> y
1.91/1.08	  f(x) -> ?1(x, x)
1.91/1.08	  a -> b
1.91/1.08	  b -> c
1.91/1.08	
1.91/1.08	 Polynomial Interpretation Processor:
1.91/1.08	  dimension: 1
1.91/1.08	  interpretation:
1.91/1.08	   [c] = 0,
1.91/1.08	   
1.91/1.08	   [b] = 4,
1.91/1.08	   
1.91/1.08	   [a] = 5,
1.91/1.08	   
1.91/1.08	   [f](x0) = 5x0 + x0x0 + 6,
1.91/1.08	   
1.91/1.08	   [?1](x0, x1) = x0 + x1x1 + 4
1.91/1.08	  orientation:
1.91/1.08	   ?1(y,x) = x*x + y + 4 >= y = y
1.91/1.08	   
1.91/1.08	   f(x) = 5x + x*x + 6 >= x + x*x + 4 = ?1(x,x)
1.91/1.08	   
1.91/1.08	   a() = 5 >= 4 = b()
1.91/1.08	   
1.91/1.08	   b() = 4 >= 0 = c()
1.91/1.08	  problem:
1.91/1.08	   
1.91/1.08	  Qed
1.91/1.08	All 0 critical pairs are joinable.
1.91/1.08	
2.24/1.11	EOF