5.28/2.23	MAYBE
5.28/2.23	
5.28/2.23	Proof:
5.28/2.23	ConCon could not decide confluence of the system.
5.28/2.23	\cite{ALS94}, Theorem 4.1 does not apply.
5.28/2.23	This system is of type 3 or smaller.
5.28/2.23	This system is strongly deterministic.
5.28/2.23	This system is quasi-decreasing.
5.28/2.23	By \cite{O02}, p. 214, Proposition 7.2.50.
5.28/2.23	This system is of type 3 or smaller.
5.28/2.23	This system is deterministic.
5.28/2.23	System R transformed to optimized U(R).
5.28/2.23	This system is terminating.
5.28/2.23	Call external tool:
5.28/2.24	./ttt2.sh
5.28/2.24	Input:
5.28/2.24	(VAR x z y)
5.28/2.24	(RULES
5.28/2.24	  pin(a) -> pout(b)
5.28/2.24	  pin(b) -> pout(c)
5.28/2.24	  tc(x) -> x
5.28/2.24	  tc(x) -> ?1(pin(x), x)
5.28/2.24	  ?1(pout(z), x) -> ?2(tc(z), x, z)
5.28/2.24	  ?2(y, x, z) -> y
5.28/2.24	)
5.28/2.24	
5.28/2.24	 Matrix Interpretation Processor: dim=1
5.28/2.24	  
5.28/2.24	  interpretation:
5.28/2.24	   [?2](x0, x1, x2) = x0 + 4x1 + x2 + 1,
5.28/2.24	   
5.28/2.24	   [?1](x0, x1) = 2x0 + 5x1 + 6,
5.28/2.24	   
5.28/2.24	   [tc](x0) = 7x0 + 6,
5.28/2.24	   
5.28/2.24	   [c] = 0,
5.28/2.24	   
5.28/2.24	   [pout](x0) = 4x0 + 1,
5.28/2.24	   
5.28/2.24	   [b] = 1,
5.28/2.24	   
5.28/2.24	   [pin](x0) = x0,
5.28/2.24	   
5.28/2.24	   [a] = 5
5.28/2.24	  orientation:
5.28/2.24	   pin(a()) = 5 >= 5 = pout(b())
5.28/2.24	   
5.28/2.24	   pin(b()) = 1 >= 1 = pout(c())
5.28/2.24	   
5.28/2.24	   tc(x) = 7x + 6 >= x = x
5.28/2.24	   
5.28/2.24	   tc(x) = 7x + 6 >= 7x + 6 = ?1(pin(x),x)
5.28/2.24	   
5.28/2.24	   ?1(pout(z),x) = 5x + 8z + 8 >= 4x + 8z + 7 = ?2(tc(z),x,z)
5.28/2.24	   
5.28/2.24	   ?2(y,x,z) = 4x + y + z + 1 >= y = y
5.28/2.24	  problem:
5.28/2.24	   pin(a()) -> pout(b())
5.28/2.24	   pin(b()) -> pout(c())
5.28/2.24	   tc(x) -> ?1(pin(x),x)
5.28/2.24	  Matrix Interpretation Processor: dim=1
5.28/2.24	   
5.28/2.24	   interpretation:
5.28/2.24	    [?1](x0, x1) = x0 + x1,
5.28/2.24	    
5.28/2.24	    [tc](x0) = 5x0 + 2,
5.28/2.24	    
5.28/2.24	    [c] = 4,
5.28/2.24	    
5.28/2.24	    [pout](x0) = 4x0,
5.28/2.24	    
5.28/2.24	    [b] = 4,
5.28/2.24	    
5.28/2.24	    [pin](x0) = 4x0,
5.28/2.24	    
5.28/2.24	    [a] = 5
5.28/2.24	   orientation:
5.28/2.24	    pin(a()) = 20 >= 16 = pout(b())
5.28/2.24	    
5.28/2.24	    pin(b()) = 16 >= 16 = pout(c())
5.28/2.24	    
5.28/2.24	    tc(x) = 5x + 2 >= 5x = ?1(pin(x),x)
5.28/2.24	   problem:
5.28/2.24	    pin(b()) -> pout(c())
5.28/2.24	   Matrix Interpretation Processor: dim=3
5.28/2.24	    
5.28/2.24	    interpretation:
5.28/2.24	           [0]
5.28/2.24	     [c] = [0]
5.28/2.24	           [0],
5.28/2.24	     
5.28/2.24	                  [1 0 0]  
5.28/2.24	     [pout](x0) = [0 0 0]x0
5.28/2.24	                  [0 0 0]  ,
5.28/2.24	     
5.28/2.24	           [0]
5.28/2.24	     [b] = [0]
5.28/2.24	           [0],
5.28/2.24	     
5.28/2.24	                 [1 0 0]     [1]
5.28/2.24	     [pin](x0) = [0 0 0]x0 + [0]
5.28/2.24	                 [0 0 0]     [0]
5.28/2.24	    orientation:
5.28/2.24	                [1]    [0]            
5.28/2.24	     pin(b()) = [0] >= [0] = pout(c())
5.28/2.24	                [0]    [0]            
5.28/2.24	    problem:
5.28/2.24	     
5.28/2.24	    Qed
5.28/2.24	This critical pair is conditional.
5.28/2.24	This critical pair has some non-trivial conditions.
5.28/2.24	ConCon could not decide whether all 2 critical pairs are joinable or not.
5.28/2.24	Overlap: (rule1: tc(x') -> y' <= pin(x') = pout(z'), tc(z') = y', rule2: tc(y) -> y, pos: ε, mgu: {(x',y)})
5.28/2.24	CP: y = y' <= pin(y) = pout(z'), tc(z') = y'
5.28/2.24	ConCon could not decide infeasibility of this critical pair.
5.28/2.24	
5.28/2.26	EOF