3.51/1.74	YES
3.51/1.74	
3.51/1.74	Proof:
3.51/1.74	This system is confluent.
3.51/1.74	Removed infeasible rules from system R.
3.51/1.74	By \cite{ALS94}, Theorem 4.1.
3.51/1.74	This system is of type 3 or smaller.
3.51/1.74	This system is strongly deterministic.
3.51/1.74	This system is quasi-decreasing.
3.51/1.74	By \cite{A14}, Theorem 11.5.9.
3.51/1.74	This system is of type 3 or smaller.
3.51/1.74	This system is deterministic.
3.51/1.74	System R transformed to V(R) + Emb.
3.51/1.74	This system is terminating.
3.51/1.74	Call external tool:
3.51/1.74	./ttt2.sh
3.51/1.74	Input:
3.51/1.74	(VAR x y)
3.51/1.74	(RULES
3.51/1.74	  f(x, y) -> x
3.51/1.74	  f(x, y) -> g(y)
3.51/1.74	  f(x, y) -> g(x)
3.51/1.74	  g(x) -> x
3.51/1.74	  f(x, y) -> x
3.51/1.74	  f(x, y) -> y
3.51/1.74	)
3.51/1.74	
3.51/1.74	 Polynomial Interpretation Processor:
3.51/1.74	  dimension: 1
3.51/1.74	  interpretation:
3.51/1.74	   [g](x0) = x0 + 1,
3.51/1.74	   
3.51/1.74	   [f](x0, x1) = x0 + 4x1 + x0x0 + 2
3.51/1.74	  orientation:
3.51/1.74	   f(x,y) = x + x*x + 4y + 2 >= x = x
3.51/1.74	   
3.51/1.74	   f(x,y) = x + x*x + 4y + 2 >= y + 1 = g(y)
3.51/1.74	   
3.51/1.74	   f(x,y) = x + x*x + 4y + 2 >= x + 1 = g(x)
3.51/1.74	   
3.51/1.74	   g(x) = x + 1 >= x = x
3.51/1.74	   
3.51/1.74	   f(x,y) = x + x*x + 4y + 2 >= y = y
3.51/1.74	  problem:
3.51/1.74	   
3.51/1.74	  Qed
3.51/1.74	All 0 critical pairs are joinable.
3.51/1.74	
4.33/2.07	EOF