5.64/2.22	YES
5.64/2.22	
5.64/2.22	Proof:
5.64/2.22	This system is confluent.
5.64/2.22	By \cite{ALS94}, Theorem 4.1.
5.64/2.22	This system is of type 3 or smaller.
5.64/2.22	This system is strongly deterministic.
5.64/2.22	This system is quasi-decreasing.
5.64/2.22	By \cite{A14}, Theorem 11.5.9.
5.64/2.22	This system is of type 3 or smaller.
5.64/2.22	This system is deterministic.
5.64/2.22	System R transformed to V(R) + Emb.
5.64/2.22	This system is terminating.
5.64/2.22	Call external tool:
5.64/2.22	./ttt2.sh
5.64/2.22	Input:
5.64/2.22	(VAR x)
5.64/2.22	(RULES
5.64/2.22	  f(g(x)) -> b
5.64/2.22	  f(g(x)) -> x
5.64/2.22	  g(x) -> c
5.64/2.22	  g(x) -> x
5.64/2.22	  g(x) -> x
5.64/2.22	  f(x) -> x
5.64/2.22	)
5.64/2.22	
5.64/2.22	 Matrix Interpretation Processor: dim=3
5.64/2.22	  
5.64/2.22	  interpretation:
5.64/2.22	         [0]
5.64/2.22	   [c] = [0]
5.64/2.22	         [0],
5.64/2.22	   
5.64/2.22	         [0]
5.64/2.22	   [b] = [0]
5.64/2.22	         [1],
5.64/2.22	   
5.64/2.22	             [1 0 0]  
5.64/2.22	   [f](x0) = [0 1 0]x0
5.64/2.22	             [1 0 1]  ,
5.64/2.22	   
5.64/2.22	                  [1]
5.64/2.22	   [g](x0) = x0 + [0]
5.64/2.22	                  [0]
5.64/2.22	  orientation:
5.64/2.22	             [1 0 0]    [1]    [0]      
5.64/2.22	   f(g(x)) = [0 1 0]x + [0] >= [0] = b()
5.64/2.22	             [1 0 1]    [1]    [1]      
5.64/2.22	   
5.64/2.22	             [1 0 0]    [1]         
5.64/2.22	   f(g(x)) = [0 1 0]x + [0] >= x = x
5.64/2.22	             [1 0 1]    [1]         
5.64/2.22	   
5.64/2.22	              [1]    [0]      
5.64/2.22	   g(x) = x + [0] >= [0] = c()
5.64/2.22	              [0]    [0]      
5.64/2.22	   
5.64/2.22	              [1]         
5.64/2.22	   g(x) = x + [0] >= x = x
5.64/2.22	              [0]         
5.64/2.22	   
5.64/2.22	          [1 0 0]          
5.64/2.22	   f(x) = [0 1 0]x >= x = x
5.64/2.22	          [1 0 1]          
5.64/2.22	  problem:
5.64/2.22	   f(x) -> x
5.64/2.22	  Matrix Interpretation Processor: dim=3
5.64/2.22	   
5.64/2.22	   interpretation:
5.64/2.22	                   [1]
5.64/2.22	    [f](x0) = x0 + [0]
5.64/2.22	                   [0]
5.64/2.22	   orientation:
5.64/2.22	               [1]         
5.64/2.22	    f(x) = x + [0] >= x = x
5.64/2.22	               [0]         
5.64/2.22	   problem:
5.64/2.22	    
5.64/2.22	   Qed
5.64/2.22	All 1 critical pairs are joinable.
5.64/2.22	Overlap: (rule1: f(g(y)) -> b <= y = a, rule2: g(z) -> c <= z = c, pos: 1, mgu: {(y,z)})
5.64/2.22	CP: f(c) = b <= z = a, z = c
5.64/2.22	This critical pair is unfeasible.
5.64/2.22	
5.64/2.25	EOF