3.74/1.89	MAYBE
3.74/1.89	
3.74/1.89	Proof:
3.74/1.89	ConCon could not decide confluence of the system.
3.74/1.89	Inlined conditions in System R.
3.74/1.89	\cite{ALS94}, Theorem 4.1 does not apply.
3.74/1.89	This system is of type 3 or smaller.
3.74/1.89	This system is strongly deterministic.
3.74/1.89	This system is quasi-decreasing.
3.74/1.89	By \cite{A14}, Theorem 11.5.9.
3.74/1.89	This system is of type 3 or smaller.
3.74/1.89	This system is deterministic.
3.74/1.89	System R transformed to V(R) + Emb.
3.74/1.89	This system is terminating.
3.74/1.89	Call external tool:
3.74/1.89	./ttt2.sh
3.74/1.89	Input:
3.74/1.89	(VAR x y)
3.74/1.89	(RULES
3.74/1.89	  f(x) -> c(x, g(x))
3.74/1.89	  f(x) -> g(x)
3.74/1.89	  a -> b
3.74/1.89	  g(a) -> h(b)
3.74/1.89	  h(x) -> x
3.74/1.89	  c(x, y) -> x
3.74/1.89	  c(x, y) -> y
3.74/1.89	  g(x) -> x
3.74/1.89	  f(x) -> x
3.74/1.89	)
3.74/1.89	
3.74/1.89	 Matrix Interpretation Processor: dim=1
3.74/1.89	  
3.74/1.89	  interpretation:
3.74/1.89	   [h](x0) = x0 + 1,
3.74/1.89	   
3.74/1.89	   [b] = 3,
3.74/1.89	   
3.74/1.89	   [a] = 5,
3.74/1.89	   
3.74/1.89	   [c](x0, x1) = x0 + x1 + 2,
3.74/1.89	   
3.74/1.89	   [g](x0) = 4x0,
3.74/1.89	   
3.74/1.89	   [f](x0) = 5x0 + 2
3.74/1.89	  orientation:
3.74/1.89	   f(x) = 5x + 2 >= 5x + 2 = c(x,g(x))
3.74/1.89	   
3.74/1.89	   f(x) = 5x + 2 >= 4x = g(x)
3.74/1.89	   
3.74/1.89	   a() = 5 >= 3 = b()
3.74/1.89	   
3.74/1.89	   g(a()) = 20 >= 4 = h(b())
3.74/1.89	   
3.74/1.89	   h(x) = x + 1 >= x = x
3.74/1.89	   
3.74/1.89	   c(x,y) = x + y + 2 >= x = x
3.74/1.90	   
3.74/1.90	   c(x,y) = x + y + 2 >= y = y
3.74/1.90	   
3.74/1.90	   g(x) = 4x >= x = x
3.74/1.90	   
3.74/1.90	   f(x) = 5x + 2 >= x = x
3.74/1.90	  problem:
3.74/1.90	   f(x) -> c(x,g(x))
3.74/1.90	   g(x) -> x
3.74/1.90	  Matrix Interpretation Processor: dim=1
3.74/1.90	   
3.74/1.90	   interpretation:
3.74/1.90	    [c](x0, x1) = 2x0 + 2x1,
3.74/1.90	    
3.74/1.90	    [g](x0) = 2x0 + 2,
3.74/1.90	    
3.74/1.90	    [f](x0) = 6x0 + 4
3.74/1.90	   orientation:
3.74/1.90	    f(x) = 6x + 4 >= 6x + 4 = c(x,g(x))
3.74/1.90	    
3.74/1.90	    g(x) = 2x + 2 >= x = x
3.74/1.90	   problem:
3.74/1.90	    f(x) -> c(x,g(x))
3.74/1.90	   Matrix Interpretation Processor: dim=1
3.74/1.90	    
3.74/1.90	    interpretation:
3.74/1.90	     [c](x0, x1) = x0 + x1,
3.74/1.90	     
3.74/1.90	     [g](x0) = 4x0,
3.74/1.90	     
3.74/1.90	     [f](x0) = 5x0 + 1
3.74/1.90	    orientation:
3.74/1.90	     f(x) = 5x + 1 >= 5x = c(x,g(x))
3.74/1.90	    problem:
3.74/1.90	     
3.74/1.90	    Qed
3.74/1.90	ConCon could not decide whether all 1 critical pairs are joinable or not.
3.74/1.90	Overlap: (rule1: g(a) -> h(b), rule2: a -> b, pos: 1, mgu: {})
3.74/1.90	CP: g(b) = h(b)
3.74/1.90	ConCon could not decide context-joinability of this critical pair.
3.74/1.90	
4.21/1.92	EOF