2.97/1.66	YES
2.97/1.66	
2.97/1.66	Proof:
2.97/1.66	This system is confluent.
2.97/1.66	Removed infeasible rules from system R.
2.97/1.66	By \cite{ALS94}, Theorem 4.1.
2.97/1.67	This system is of type 3 or smaller.
2.97/1.67	This system is strongly deterministic.
2.97/1.67	This system is quasi-decreasing.
2.97/1.67	By \cite{A14}, Theorem 11.5.9.
2.97/1.67	This system is of type 3 or smaller.
2.97/1.67	This system is deterministic.
2.97/1.67	System R transformed to V(R) + Emb.
2.97/1.67	This system is terminating.
2.97/1.67	Call external tool:
2.97/1.67	./ttt2.sh
2.97/1.67	Input:
2.97/1.67	(VAR x y)
2.97/1.67	(RULES
2.97/1.67	  f(x, y) -> x
2.97/1.67	  f(x, y) -> g(y)
2.97/1.67	  f(x, y) -> g(x)
2.97/1.67	  g(x) -> x
2.97/1.67	  f(x, y) -> x
2.97/1.67	  f(x, y) -> y
2.97/1.67	)
2.97/1.67	
2.97/1.67	 Polynomial Interpretation Processor:
2.97/1.67	  dimension: 1
2.97/1.67	  interpretation:
2.97/1.67	   [g](x0) = x0 + 1,
2.97/1.67	   
2.97/1.67	   [f](x0, x1) = x0 + 4x1 + x0x0 + 2
2.97/1.67	  orientation:
2.97/1.67	   f(x,y) = x + x*x + 4y + 2 >= x = x
2.97/1.67	   
2.97/1.67	   f(x,y) = x + x*x + 4y + 2 >= y + 1 = g(y)
2.97/1.67	   
2.97/1.67	   f(x,y) = x + x*x + 4y + 2 >= x + 1 = g(x)
2.97/1.67	   
2.97/1.67	   g(x) = x + 1 >= x = x
2.97/1.67	   
2.97/1.67	   f(x,y) = x + x*x + 4y + 2 >= y = y
2.97/1.67	  problem:
2.97/1.67	   
2.97/1.67	  Qed
2.97/1.67	All 0 critical pairs are joinable.
2.97/1.67	
3.37/1.76	EOF