3.98/1.54	MAYBE
3.98/1.54	
3.98/1.54	Proof:
3.98/1.54	ConCon could not decide confluence of the system.
3.98/1.54	\cite{ALS94}, Theorem 4.1 does not apply.
3.98/1.54	This system is of type 3 or smaller.
3.98/1.54	This system is strongly deterministic.
3.98/1.54	This system is quasi-decreasing.
3.98/1.54	By \cite{O02}, p. 214, Proposition 7.2.50.
3.98/1.54	This system is of type 3 or smaller.
3.98/1.54	This system is deterministic.
3.98/1.54	System R transformed to U(R).
3.98/1.54	This system is terminating.
3.98/1.54	Call external tool:
3.98/1.54	./ttt2.sh
3.98/1.54	Input:
3.98/1.54	  a -> c
3.98/1.54	  a -> d
3.98/1.54	  b -> c
3.98/1.54	  b -> d
3.98/1.54	  s(c) -> t(k)
3.98/1.54	  s(c) -> t(l)
3.98/1.54	  g(x, x) -> h(x, x)
3.98/1.54	  ?1(t(y), x) -> pair(x, y)
3.98/1.54	  f(x) -> ?1(s(x), x)
3.98/1.54	
3.98/1.54	 Matrix Interpretation Processor: dim=1
3.98/1.54	  
3.98/1.54	  interpretation:
3.98/1.54	   [f](x0) = 7x0 + 7,
3.98/1.54	   
3.98/1.54	   [pair](x0, x1) = x0 + x1,
3.98/1.54	   
3.98/1.54	   [?1](x0, x1) = 3x0 + 4x1 + 1,
3.98/1.54	   
3.98/1.54	   [h](x0, x1) = x0 + x1,
3.98/1.54	   
3.98/1.54	   [g](x0, x1) = x0 + x1 + 2,
3.98/1.55	   
3.98/1.55	   [l] = 0,
3.98/1.55	   
3.98/1.55	   [t](x0) = x0 + 1,
3.98/1.55	   
3.98/1.55	   [k] = 0,
3.98/1.55	   
3.98/1.55	   [s](x0) = x0 + 2,
3.98/1.55	   
3.98/1.55	   [b] = 5,
3.98/1.55	   
3.98/1.55	   [d] = 5,
3.98/1.55	   
3.98/1.55	   [c] = 0,
3.98/1.55	   
3.98/1.55	   [a] = 5
3.98/1.55	  orientation:
3.98/1.55	   a() = 5 >= 0 = c()
3.98/1.55	   
3.98/1.55	   a() = 5 >= 5 = d()
3.98/1.55	   
3.98/1.55	   b() = 5 >= 0 = c()
3.98/1.55	   
3.98/1.55	   b() = 5 >= 5 = d()
3.98/1.55	   
3.98/1.55	   s(c()) = 2 >= 1 = t(k())
3.98/1.55	   
3.98/1.55	   s(c()) = 2 >= 1 = t(l())
3.98/1.55	   
3.98/1.55	   g(x,x) = 2x + 2 >= 2x = h(x,x)
3.98/1.55	   
3.98/1.55	   ?1(t(y),x) = 4x + 3y + 4 >= x + y = pair(x,y)
3.98/1.55	   
3.98/1.55	   f(x) = 7x + 7 >= 7x + 7 = ?1(s(x),x)
3.98/1.55	  problem:
3.98/1.55	   a() -> d()
3.98/1.55	   b() -> d()
3.98/1.55	   f(x) -> ?1(s(x),x)
3.98/1.55	  Matrix Interpretation Processor: dim=1
3.98/1.55	   
3.98/1.55	   interpretation:
3.98/1.55	    [f](x0) = 2x0 + 1,
3.98/1.55	    
3.98/1.55	    [?1](x0, x1) = x0 + x1,
3.98/1.55	    
3.98/1.55	    [s](x0) = x0,
3.98/1.55	    
3.98/1.55	    [b] = 0,
3.98/1.55	    
3.98/1.55	    [d] = 0,
3.98/1.55	    
3.98/1.55	    [a] = 0
3.98/1.55	   orientation:
3.98/1.55	    a() = 0 >= 0 = d()
3.98/1.55	    
3.98/1.55	    b() = 0 >= 0 = d()
3.98/1.55	    
3.98/1.55	    f(x) = 2x + 1 >= 2x = ?1(s(x),x)
3.98/1.55	   problem:
3.98/1.55	    a() -> d()
3.98/1.55	    b() -> d()
3.98/1.55	   Matrix Interpretation Processor: dim=3
3.98/1.55	    
3.98/1.55	    interpretation:
3.98/1.55	           [1]
3.98/1.55	     [b] = [0]
3.98/1.55	           [0],
3.98/1.55	     
3.98/1.55	           [0]
3.98/1.55	     [d] = [0]
3.98/1.55	           [0],
3.98/1.55	     
3.98/1.55	           [0]
3.98/1.55	     [a] = [0]
3.98/1.55	           [0]
3.98/1.55	    orientation:
3.98/1.55	           [0]    [0]      
3.98/1.55	     a() = [0] >= [0] = d()
3.98/1.55	           [0]    [0]      
3.98/1.55	     
3.98/1.55	           [1]    [0]      
3.98/1.55	     b() = [0] >= [0] = d()
3.98/1.55	           [0]    [0]      
3.98/1.55	    problem:
3.98/1.55	     a() -> d()
3.98/1.55	    Matrix Interpretation Processor: dim=3
3.98/1.55	     
3.98/1.55	     interpretation:
3.98/1.55	            [0]
3.98/1.55	      [d] = [0]
3.98/1.55	            [0],
3.98/1.55	      
3.98/1.55	            [1]
3.98/1.55	      [a] = [0]
3.98/1.55	            [1]
3.98/1.55	     orientation:
3.98/1.55	            [1]    [0]      
3.98/1.55	      a() = [0] >= [0] = d()
3.98/1.55	            [1]    [0]      
3.98/1.55	     problem:
3.98/1.55	      
3.98/1.55	     Qed
3.98/1.55	This critical pair is not context-joinable.
3.98/1.55	ConCon could not decide whether all 6 critical pairs are joinable or not.
3.98/1.55	Overlap: (rule1: s(c) -> t(k), rule2: s(c) -> t(l), pos: ε, mgu: {})
3.98/1.55	CP: t(l) = t(k)
3.98/1.55	This critical pair is not context-joinable.
3.98/1.55	
3.98/1.58	EOF