2.43/1.72	YES
2.43/1.72	
2.43/1.72	Proof:
2.43/1.72	This system is confluent.
2.43/1.72	By \cite{ALS94}, Theorem 4.1.
2.43/1.72	This system is of type 3 or smaller.
2.43/1.72	This system is strongly deterministic.
2.43/1.72	This system is quasi-decreasing.
2.43/1.72	By \cite{A14}, Theorem 11.5.9.
2.43/1.72	This system is of type 3 or smaller.
2.43/1.72	This system is deterministic.
2.43/1.72	System R transformed to V(R) + Emb.
2.43/1.72	This system is terminating.
2.43/1.72	Call external tool:
2.43/1.72	./ttt2.sh
2.43/1.72	Input:
2.43/1.72	(VAR x'' x z y x')
2.43/1.72	(RULES
2.43/1.72	  f(x, x') -> g(x, x)
2.43/1.72	  f(x, x') -> x'
2.43/1.72	  f(x, x') -> x
2.43/1.72	  h(x, x', x'') -> c
2.43/1.72	  h(x, x', x'') -> x''
2.43/1.72	  h(x, x', x'') -> x'
2.43/1.72	  h(x, x', x'') -> x
2.43/1.72	  h(x, y, z) -> x
2.43/1.72	  h(x, y, z) -> y
2.43/1.72	  h(x, y, z) -> z
2.43/1.72	  g(x, y) -> x
2.43/1.72	  g(x, y) -> y
2.43/1.72	  f(x, y) -> x
2.43/1.72	  f(x, y) -> y
2.43/1.72	)
2.43/1.72	
2.43/1.72	 Polynomial Interpretation Processor:
2.43/1.72	  dimension: 1
2.43/1.72	  interpretation:
2.43/1.72	   [c] = 0,
2.43/1.72	   
2.43/1.72	   [h](x0, x1, x2) = x0 + 4x1 + x2 + 1,
2.43/1.72	   
2.43/1.72	   [g](x0, x1) = 2x0 + 4x1 + x0x0 + 2x1x1 + 4,
2.43/1.72	   
2.43/1.72	   [f](x0, x1) = 6x0 + x1 + 3x0x0 + 5
2.43/1.72	  orientation:
2.43/1.72	   f(x,x') = 6x + 3x*x + x' + 5 >= 6x + 3x*x + 4 = g(x,x)
2.43/1.72	   
2.43/1.72	   f(x,x') = 6x + 3x*x + x' + 5 >= x' = x'
2.43/1.73	   
2.43/1.73	   f(x,x') = 6x + 3x*x + x' + 5 >= x = x
2.43/1.73	   
2.43/1.73	   h(x,x',x'') = x + 4x' + x'' + 1 >= 0 = c()
2.43/1.73	   
2.43/1.73	   h(x,x',x'') = x + 4x' + x'' + 1 >= x'' = x''
2.43/1.73	   
2.43/1.73	   h(x,x',x'') = x + 4x' + x'' + 1 >= x' = x'
2.43/1.73	   
2.43/1.73	   h(x,x',x'') = x + 4x' + x'' + 1 >= x = x
2.43/1.73	   
2.43/1.73	   h(x,y,z) = x + 4y + z + 1 >= x = x
2.43/1.73	   
2.43/1.73	   h(x,y,z) = x + 4y + z + 1 >= y = y
2.43/1.73	   
2.43/1.73	   h(x,y,z) = x + 4y + z + 1 >= z = z
2.43/1.73	   
2.43/1.73	   g(x,y) = 2x + x*x + 4y + 2y*y + 4 >= x = x
2.43/1.73	   
2.43/1.73	   g(x,y) = 2x + x*x + 4y + 2y*y + 4 >= y = y
2.43/1.73	   
2.43/1.73	   f(x,y) = 6x + 3x*x + y + 5 >= x = x
2.43/1.73	   
2.43/1.73	   f(x,y) = 6x + 3x*x + y + 5 >= y = y
2.43/1.73	  problem:
2.43/1.73	   
2.43/1.73	  Qed
2.43/1.73	All 0 critical pairs are joinable.
2.43/1.73	
2.43/1.76	EOF