3.15/1.82	YES
3.15/1.82	
3.15/1.82	Proof:
3.15/1.82	This system is confluent.
3.15/1.82	By \cite{ALS94}, Theorem 4.1.
3.15/1.82	This system is of type 3 or smaller.
3.15/1.82	This system is strongly deterministic.
3.15/1.82	This system is quasi-decreasing.
3.15/1.82	By \cite{A14}, Theorem 11.5.9.
3.15/1.82	This system is of type 3 or smaller.
3.15/1.82	This system is deterministic.
3.15/1.82	System R transformed to V(R) + Emb.
3.15/1.82	This system is terminating.
3.15/1.82	Call external tool:
3.15/1.82	./ttt2.sh
3.15/1.82	Input:
3.15/1.82	(VAR x'' x z y x')
3.15/1.82	(RULES
3.15/1.82	  f(x, x') -> g(x, x)
3.15/1.82	  f(x, x') -> x'
3.15/1.82	  f(x, x') -> x
3.15/1.82	  h(x, x', x'') -> c
3.15/1.82	  h(x, x', x'') -> x''
3.15/1.82	  h(x, x', x'') -> x'
3.15/1.82	  h(x, x', x'') -> x
3.15/1.82	  h(x, y, z) -> x
3.15/1.82	  h(x, y, z) -> y
3.15/1.82	  h(x, y, z) -> z
3.15/1.82	  g(x, y) -> x
3.15/1.82	  g(x, y) -> y
3.15/1.82	  f(x, y) -> x
3.15/1.82	  f(x, y) -> y
3.15/1.82	)
3.15/1.82	
3.15/1.82	 Polynomial Interpretation Processor:
3.15/1.82	  dimension: 1
3.15/1.82	  interpretation:
3.15/1.82	   [c] = 0,
3.15/1.82	   
3.15/1.82	   [h](x0, x1, x2) = x0 + 4x1 + x2 + 1,
3.15/1.82	   
3.15/1.82	   [g](x0, x1) = 2x0 + 4x1 + x0x0 + 2x1x1 + 4,
3.15/1.82	   
3.15/1.82	   [f](x0, x1) = 6x0 + x1 + 3x0x0 + 5
3.15/1.82	  orientation:
3.15/1.82	   f(x,x') = 6x + 3x*x + x' + 5 >= 6x + 3x*x + 4 = g(x,x)
3.15/1.82	   
3.15/1.82	   f(x,x') = 6x + 3x*x + x' + 5 >= x' = x'
3.15/1.82	   
3.15/1.82	   f(x,x') = 6x + 3x*x + x' + 5 >= x = x
3.15/1.82	   
3.15/1.82	   h(x,x',x'') = x + 4x' + x'' + 1 >= 0 = c()
3.15/1.82	   
3.15/1.82	   h(x,x',x'') = x + 4x' + x'' + 1 >= x'' = x''
3.15/1.82	   
3.15/1.82	   h(x,x',x'') = x + 4x' + x'' + 1 >= x' = x'
3.15/1.82	   
3.15/1.82	   h(x,x',x'') = x + 4x' + x'' + 1 >= x = x
3.15/1.82	   
3.15/1.82	   h(x,y,z) = x + 4y + z + 1 >= x = x
3.15/1.82	   
3.15/1.82	   h(x,y,z) = x + 4y + z + 1 >= y = y
3.15/1.82	   
3.15/1.82	   h(x,y,z) = x + 4y + z + 1 >= z = z
3.15/1.82	   
3.15/1.82	   g(x,y) = 2x + x*x + 4y + 2y*y + 4 >= x = x
3.15/1.82	   
3.15/1.82	   g(x,y) = 2x + x*x + 4y + 2y*y + 4 >= y = y
3.15/1.82	   
3.15/1.82	   f(x,y) = 6x + 3x*x + y + 5 >= x = x
3.15/1.82	   
3.15/1.82	   f(x,y) = 6x + 3x*x + y + 5 >= y = y
3.15/1.82	  problem:
3.15/1.82	   
3.15/1.82	  Qed
3.15/1.82	All 0 critical pairs are joinable.
3.15/1.82	
3.15/1.84	EOF