3.46/1.41	MAYBE
3.46/1.41	
3.46/1.41	Proof:
3.46/1.41	ConCon could not decide confluence of the system.
3.46/1.41	\cite{ALS94}, Theorem 4.1 does not apply.
3.46/1.42	This system is of type 3 or smaller.
3.46/1.42	This system is strongly deterministic.
3.46/1.42	This system is quasi-decreasing.
3.46/1.42	By \cite{A14}, Theorem 11.5.9.
3.46/1.42	This system is of type 3 or smaller.
3.46/1.42	This system is deterministic.
3.46/1.42	System R transformed to V(R) + Emb.
3.46/1.42	This system is terminating.
3.46/1.42	Call external tool:
3.46/1.42	./ttt2.sh
3.46/1.42	Input:
3.46/1.42	  f(x) -> c(x, g(x))
3.46/1.42	  f(x) -> g(x)
3.46/1.42	  a -> b
3.46/1.42	  g(a) -> h(b)
3.46/1.42	  h(x) -> x
3.46/1.42	  c(x, y) -> x
3.46/1.42	  c(x, y) -> y
3.46/1.42	  g(x) -> x
3.46/1.42	  f(x) -> x
3.46/1.42	
3.46/1.42	 Matrix Interpretation Processor: dim=1
3.46/1.42	  
3.46/1.42	  interpretation:
3.46/1.42	   [h](x0) = x0 + 1,
3.46/1.42	   
3.46/1.42	   [b] = 3,
3.46/1.42	   
3.46/1.42	   [a] = 5,
3.46/1.42	   
3.46/1.42	   [c](x0, x1) = x0 + x1 + 2,
3.46/1.42	   
3.46/1.42	   [g](x0) = 4x0,
3.46/1.42	   
3.46/1.42	   [f](x0) = 5x0 + 2
3.46/1.42	  orientation:
3.46/1.42	   f(x) = 5x + 2 >= 5x + 2 = c(x,g(x))
3.46/1.42	   
3.46/1.42	   f(x) = 5x + 2 >= 4x = g(x)
3.46/1.42	   
3.46/1.42	   a() = 5 >= 3 = b()
3.46/1.42	   
3.46/1.42	   g(a()) = 20 >= 4 = h(b())
3.46/1.42	   
3.46/1.42	   h(x) = x + 1 >= x = x
3.46/1.42	   
3.46/1.42	   c(x,y) = x + y + 2 >= x = x
3.46/1.42	   
3.46/1.42	   c(x,y) = x + y + 2 >= y = y
3.46/1.42	   
3.46/1.42	   g(x) = 4x >= x = x
3.46/1.42	   
3.46/1.42	   f(x) = 5x + 2 >= x = x
3.46/1.42	  problem:
3.46/1.42	   f(x) -> c(x,g(x))
3.46/1.42	   g(x) -> x
3.46/1.42	  Matrix Interpretation Processor: dim=1
3.46/1.42	   
3.46/1.42	   interpretation:
3.46/1.42	    [c](x0, x1) = 2x0 + 2x1,
3.46/1.42	    
3.46/1.42	    [g](x0) = 2x0 + 2,
3.46/1.42	    
3.46/1.42	    [f](x0) = 6x0 + 4
3.46/1.42	   orientation:
3.46/1.42	    f(x) = 6x + 4 >= 6x + 4 = c(x,g(x))
3.46/1.42	    
3.46/1.42	    g(x) = 2x + 2 >= x = x
3.46/1.42	   problem:
3.46/1.42	    f(x) -> c(x,g(x))
3.46/1.42	   Matrix Interpretation Processor: dim=1
3.46/1.42	    
3.46/1.42	    interpretation:
3.46/1.42	     [c](x0, x1) = x0 + x1,
3.46/1.42	     
3.46/1.42	     [g](x0) = 4x0,
3.46/1.42	     
3.46/1.42	     [f](x0) = 5x0 + 1
3.46/1.42	    orientation:
3.46/1.42	     f(x) = 5x + 1 >= 5x = c(x,g(x))
3.46/1.42	    problem:
3.46/1.42	     
3.46/1.42	    Qed
3.46/1.42	This critical pair is not joinable.
3.46/1.42	
3.46/1.44	EOF