2.72/1.26	YES
2.72/1.26	
2.72/1.26	Proof:
2.72/1.26	This system is confluent.
2.72/1.26	By \cite{ALS94}, Theorem 4.1.
2.72/1.26	This system is of type 3 or smaller.
2.72/1.26	This system is strongly deterministic.
2.72/1.26	This system is quasi-decreasing.
2.72/1.26	By \cite{A14}, Theorem 11.5.9.
2.72/1.26	This system is of type 3 or smaller.
2.72/1.26	This system is deterministic.
2.72/1.26	System R transformed to V(R) + Emb.
2.72/1.26	This system is terminating.
2.72/1.26	Call external tool:
2.72/1.26	./ttt2.sh
2.72/1.26	Input:
2.72/1.26	  f(x, y) -> x
2.72/1.26	  f(x, y) -> g(y)
2.72/1.26	  f(x, y) -> g(x)
2.72/1.26	  g(x) -> c
2.72/1.26	  g(x) -> d
2.72/1.26	  g(x) -> x
2.72/1.26	  f(x, y) -> x
2.72/1.26	  f(x, y) -> y
2.72/1.26	
2.72/1.26	 Polynomial Interpretation Processor:
2.72/1.26	  dimension: 1
2.72/1.26	  interpretation:
2.72/1.26	   [d] = 0,
2.72/1.26	   
2.72/1.26	   [c] = 0,
2.72/1.26	   
2.72/1.26	   [g](x0) = x0 + 1,
2.72/1.26	   
2.72/1.26	   [f](x0, x1) = x0 + 4x1 + 2
2.72/1.26	  orientation:
2.72/1.26	   f(x,y) = x + 4y + 2 >= x = x
2.72/1.26	   
2.72/1.26	   f(x,y) = x + 4y + 2 >= y + 1 = g(y)
2.72/1.26	   
2.72/1.26	   f(x,y) = x + 4y + 2 >= x + 1 = g(x)
2.72/1.26	   
2.72/1.26	   g(x) = x + 1 >= 0 = c()
2.72/1.26	   
2.72/1.26	   g(x) = x + 1 >= 0 = d()
2.72/1.26	   
2.72/1.26	   g(x) = x + 1 >= x = x
2.72/1.26	   
2.72/1.26	   f(x,y) = x + 4y + 2 >= y = y
2.72/1.26	  problem:
2.72/1.26	   
2.72/1.26	  Qed
2.72/1.26	All 0 critical pairs are joinable.
2.72/1.26	
3.03/1.32	EOF