3.03/1.25	YES
3.03/1.25	
3.03/1.25	Proof:
3.03/1.25	This system is confluent.
3.03/1.25	By \cite{ALS94}, Theorem 4.1.
3.03/1.25	This system is of type 3 or smaller.
3.03/1.25	This system is strongly deterministic.
3.03/1.25	This system is quasi-decreasing.
3.03/1.25	By \cite{A14}, Theorem 11.5.9.
3.03/1.25	This system is of type 3 or smaller.
3.03/1.25	This system is deterministic.
3.03/1.25	System R transformed to V(R) + Emb.
3.03/1.25	This system is terminating.
3.03/1.25	Call external tool:
3.03/1.25	./ttt2.sh
3.03/1.25	Input:
3.03/1.25	  f(x, y) -> x
3.03/1.25	  f(x, y) -> g(y)
3.03/1.25	  f(x, y) -> g(x)
3.03/1.25	  g(x) -> c
3.03/1.25	  g(x) -> d
3.03/1.25	  g(x) -> x
3.03/1.25	  f(x, y) -> x
3.03/1.25	  f(x, y) -> y
3.03/1.25	
3.03/1.25	 Polynomial Interpretation Processor:
3.03/1.25	  dimension: 1
3.03/1.25	  interpretation:
3.03/1.25	   [d] = 0,
3.03/1.25	   
3.03/1.25	   [c] = 0,
3.03/1.25	   
3.03/1.25	   [g](x0) = x0 + 1,
3.03/1.26	   
3.03/1.26	   [f](x0, x1) = x0 + 4x1 + 2
3.03/1.26	  orientation:
3.03/1.26	   f(x,y) = x + 4y + 2 >= x = x
3.03/1.26	   
3.03/1.26	   f(x,y) = x + 4y + 2 >= y + 1 = g(y)
3.03/1.26	   
3.03/1.26	   f(x,y) = x + 4y + 2 >= x + 1 = g(x)
3.03/1.26	   
3.03/1.26	   g(x) = x + 1 >= 0 = c()
3.03/1.26	   
3.03/1.26	   g(x) = x + 1 >= 0 = d()
3.03/1.26	   
3.03/1.26	   g(x) = x + 1 >= x = x
3.03/1.26	   
3.03/1.26	   f(x,y) = x + 4y + 2 >= y = y
3.03/1.26	  problem:
3.03/1.26	   
3.03/1.26	  Qed
3.03/1.26	All 0 critical pairs are joinable.
3.03/1.26	
4.14/1.55	EOF