2.85/1.69	YES
2.85/1.69	
2.85/1.69	Proof:
2.85/1.69	This system is confluent.
2.85/1.69	By \cite{ALS94}, Theorem 4.1.
2.85/1.69	This system is of type 3 or smaller.
2.85/1.69	This system is strongly deterministic.
2.85/1.69	This system is quasi-decreasing.
2.85/1.69	By \cite{O02}, p. 214, Proposition 7.2.50.
2.85/1.69	This system is of type 3 or smaller.
2.85/1.69	This system is deterministic.
2.85/1.69	System R transformed to U(R).
2.85/1.69	This system is terminating.
2.85/1.69	Call external tool:
2.85/1.69	./ttt2.sh
2.85/1.69	Input:
2.85/1.69	(VAR x)
2.85/1.69	(RULES
2.85/1.69	  a -> b
2.85/1.69	  ?1(b, x) -> A
2.85/1.69	  f(x) -> ?1(x, x)
2.85/1.69	  g(x, x) -> h(x)
2.85/1.69	  h(x) -> i(x)
2.85/1.69	)
2.85/1.69	
2.85/1.69	 Polynomial Interpretation Processor:
2.85/1.69	  dimension: 1
2.85/1.70	  interpretation:
2.85/1.70	   [i](x0) = -3x0 + 4x0x0,
2.85/1.70	   
2.85/1.70	   [h](x0) = -3x0 + 4x0x0 + 1,
2.85/1.70	   
2.85/1.70	   [g](x0, x1) = 2x0 + x1 + 4x1x1 + 4,
2.85/1.70	   
2.85/1.70	   [f](x0) = 4x0 + 5x0x0 + 2,
2.85/1.70	   
2.85/1.70	   [A] = 0,
2.85/1.70	   
2.85/1.70	   [?1](x0, x1) = -3x0 + 4x0x0 + x1x1 + 1,
2.85/1.70	   
2.85/1.70	   [b] = 0,
2.85/1.70	   
2.85/1.70	   [a] = 1
2.85/1.70	  orientation:
2.85/1.70	   a() = 1 >= 0 = b()
2.85/1.70	   
2.85/1.70	   ?1(b(),x) = x*x + 1 >= 0 = A()
2.85/1.70	   
2.85/1.70	   f(x) = 4x + 5x*x + 2 >= -3x + 5x*x + 1 = ?1(x,x)
2.85/1.70	   
2.85/1.70	   g(x,x) = 3x + 4x*x + 4 >= -3x + 4x*x + 1 = h(x)
2.85/1.70	   
2.85/1.70	   h(x) = -3x + 4x*x + 1 >= -3x + 4x*x = i(x)
2.85/1.70	  problem:
2.85/1.70	   
2.85/1.70	  Qed
2.85/1.70	All 0 critical pairs are joinable.
2.85/1.70	
3.30/1.72	EOF