4.87/2.06	YES
4.87/2.06	
4.87/2.06	Proof:
4.87/2.06	This system is confluent.
4.87/2.06	By \cite{ALS94}, Theorem 4.1.
4.87/2.06	This system is of type 3 or smaller.
4.87/2.06	This system is strongly deterministic.
4.87/2.06	This system is quasi-decreasing.
4.87/2.06	By \cite{A14}, Theorem 11.5.9.
4.87/2.06	This system is of type 3 or smaller.
4.87/2.06	This system is deterministic.
4.87/2.06	System R transformed to V(R) + Emb.
4.87/2.06	This system is terminating.
4.87/2.06	Call external tool:
4.87/2.06	./ttt2.sh
4.87/2.06	Input:
4.87/2.06	(VAR x)
4.87/2.06	(RULES
4.87/2.06	  f(g(x)) -> b
4.87/2.06	  f(g(x)) -> x
4.87/2.06	  g(x) -> c
4.87/2.06	  g(x) -> x
4.87/2.06	  g(x) -> x
4.87/2.06	  f(x) -> x
4.87/2.06	)
4.87/2.06	
4.87/2.06	 Matrix Interpretation Processor: dim=3
4.87/2.06	  
4.87/2.06	  interpretation:
4.87/2.06	         [0]
4.87/2.06	   [c] = [0]
4.87/2.06	         [0],
4.87/2.06	   
4.87/2.06	         [0]
4.87/2.06	   [b] = [0]
4.87/2.06	         [1],
4.87/2.06	   
4.87/2.06	             [1 0 0]  
4.87/2.06	   [f](x0) = [0 1 0]x0
4.87/2.06	             [1 0 1]  ,
4.87/2.06	   
4.87/2.06	                  [1]
4.87/2.06	   [g](x0) = x0 + [0]
4.87/2.06	                  [0]
4.87/2.06	  orientation:
4.87/2.06	             [1 0 0]    [1]    [0]      
4.87/2.06	   f(g(x)) = [0 1 0]x + [0] >= [0] = b()
4.87/2.06	             [1 0 1]    [1]    [1]      
4.87/2.06	   
4.87/2.06	             [1 0 0]    [1]         
4.87/2.06	   f(g(x)) = [0 1 0]x + [0] >= x = x
4.87/2.06	             [1 0 1]    [1]         
4.87/2.06	   
4.87/2.06	              [1]    [0]      
4.87/2.06	   g(x) = x + [0] >= [0] = c()
4.87/2.06	              [0]    [0]      
4.87/2.06	   
4.87/2.06	              [1]         
4.87/2.06	   g(x) = x + [0] >= x = x
4.87/2.06	              [0]         
4.87/2.06	   
4.87/2.06	          [1 0 0]          
4.87/2.06	   f(x) = [0 1 0]x >= x = x
4.87/2.06	          [1 0 1]          
4.87/2.06	  problem:
4.87/2.06	   f(x) -> x
4.87/2.06	  Matrix Interpretation Processor: dim=3
4.87/2.06	   
4.87/2.06	   interpretation:
4.87/2.06	                   [1]
4.87/2.06	    [f](x0) = x0 + [0]
4.87/2.06	                   [0]
4.87/2.06	   orientation:
4.87/2.06	               [1]         
4.87/2.06	    f(x) = x + [0] >= x = x
4.87/2.06	               [0]         
4.87/2.06	   problem:
4.87/2.06	    
4.87/2.06	   Qed
4.94/2.08	All 1 critical pairs are joinable.
4.94/2.08	Overlap: (rule1: f(g(y)) -> b <= y = a, rule2: g(z) -> c <= z = c, pos: 1, mgu: {(y,z)})
4.94/2.08	CP: f(c) = b <= z = a, z = c
4.94/2.08	This critical pair is unfeasible.
4.94/2.08	
5.57/2.24	EOF