0.69/1.56	YES
0.69/1.56	
0.69/1.56	Problem:
0.69/1.56	f(x, x) -> a() <= g(x) = b()
0.69/1.56	
0.69/1.56	Proof:
0.69/1.56	This system is confluent.
0.69/1.56	By \cite{ALS94}, Theorem 4.1.
0.69/1.56	This system is of type 3 or smaller.
0.69/1.56	This system is strongly deterministic.
0.69/1.56	All 0 critical pairs are joinable.
0.69/1.56	This system is quasi-decreasing.
0.69/1.56	By \cite{A14}, Theorem 11.5.9.
0.69/1.56	This system is of type 3 or smaller.
0.69/1.56	This system is deterministic.
0.69/1.56	System R transformed to V(R) + Emb.
0.69/1.56	This system is terminating.
0.69/1.56	Call external tool:
0.69/1.56	./ttt2.sh
0.69/1.56	Input:
0.69/1.56	  f(x, x) -> a()
0.69/1.56	  f(x, x) -> g(x)
0.69/1.56	  g(x) -> x
0.69/1.56	  f(x, y) -> x
0.69/1.56	  f(x, y) -> y
0.69/1.56	
0.69/1.56	 Polynomial Interpretation Processor:
0.69/1.57	  dimension: 1
0.69/1.57	  interpretation:
0.69/1.57	   [g](x0) = 2x0 + 2x0x0 + 4,
0.69/1.57	   
0.69/1.57	   [a] = 0,
0.69/1.57	   
0.69/1.57	   [f](x0, x1) = x0 + x1 + 2x0x0 + 5
0.69/1.57	  orientation:
0.69/1.57	   f(x,x) = 2x + 2x*x + 5 >= 0 = a()
0.69/1.57	   
0.69/1.57	   f(x,x) = 2x + 2x*x + 5 >= 2x + 2x*x + 4 = g(x)
0.69/1.57	   
0.69/1.57	   g(x) = 2x + 2x*x + 4 >= x = x
0.69/1.57	   
0.69/1.57	   f(x,y) = x + 2x*x + y + 5 >= x = x
0.69/1.57	   
0.69/1.57	   f(x,y) = x + 2x*x + y + 5 >= y = y
0.69/1.57	  problem:
0.69/1.57	   
0.69/1.57	  Qed
0.69/1.57	
0.69/1.58	EOF