6.92/2.58	MAYBE
6.92/2.58	
6.92/2.58	Proof:
6.92/2.58	ConCon could not decide confluence of the system.
6.92/2.58	\cite{ALS94}, Theorem 4.1 does not apply.
6.92/2.58	This system is of type 3 or smaller.
6.92/2.58	This system is strongly deterministic.
6.92/2.58	This system is quasi-decreasing.
6.92/2.58	By \cite{O02}, p. 214, Proposition 7.2.50.
6.92/2.58	This system is of type 3 or smaller.
6.92/2.58	This system is deterministic.
6.92/2.58	System R transformed to optimized U(R).
6.92/2.58	This system is terminating.
6.92/2.58	Call external tool:
6.92/2.58	./ttt2.sh
6.92/2.58	Input:
6.92/2.58	(VAR x z y)
6.92/2.58	(RULES
6.92/2.58	  pin(a) -> pout(b)
6.92/2.58	  pin(b) -> pout(c)
6.92/2.58	  tc(x) -> x
6.92/2.58	  tc(x) -> ?1(pin(x), x)
6.92/2.58	  ?1(pout(z), x) -> ?2(tc(z), x, z)
6.92/2.58	  ?2(y, x, z) -> y
6.92/2.58	)
6.92/2.58	
6.92/2.58	 Matrix Interpretation Processor: dim=1
6.92/2.58	  
6.92/2.58	  interpretation:
6.92/2.58	   [?2](x0, x1, x2) = x0 + 4x1 + x2 + 1,
6.92/2.58	   
6.92/2.58	   [?1](x0, x1) = 2x0 + 5x1 + 6,
6.92/2.58	   
6.92/2.58	   [tc](x0) = 7x0 + 6,
6.92/2.58	   
6.92/2.58	   [c] = 0,
6.92/2.58	   
6.92/2.58	   [pout](x0) = 4x0 + 1,
6.92/2.58	   
6.92/2.58	   [b] = 1,
6.92/2.58	   
6.92/2.58	   [pin](x0) = x0,
6.92/2.58	   
6.92/2.58	   [a] = 5
6.92/2.58	  orientation:
6.92/2.58	   pin(a()) = 5 >= 5 = pout(b())
6.92/2.58	   
6.92/2.58	   pin(b()) = 1 >= 1 = pout(c())
6.92/2.58	   
6.92/2.58	   tc(x) = 7x + 6 >= x = x
6.92/2.58	   
6.92/2.58	   tc(x) = 7x + 6 >= 7x + 6 = ?1(pin(x),x)
6.92/2.58	   
6.92/2.58	   ?1(pout(z),x) = 5x + 8z + 8 >= 4x + 8z + 7 = ?2(tc(z),x,z)
6.92/2.58	   
6.92/2.58	   ?2(y,x,z) = 4x + y + z + 1 >= y = y
6.92/2.58	  problem:
6.92/2.58	   pin(a()) -> pout(b())
6.92/2.58	   pin(b()) -> pout(c())
6.92/2.58	   tc(x) -> ?1(pin(x),x)
6.92/2.58	  Matrix Interpretation Processor: dim=1
6.92/2.58	   
6.92/2.58	   interpretation:
6.92/2.58	    [?1](x0, x1) = x0 + x1,
6.92/2.58	    
6.92/2.58	    [tc](x0) = 5x0 + 2,
6.92/2.58	    
6.92/2.58	    [c] = 4,
6.92/2.58	    
6.92/2.58	    [pout](x0) = 4x0,
6.92/2.58	    
6.92/2.58	    [b] = 4,
6.92/2.58	    
6.92/2.58	    [pin](x0) = 4x0,
6.92/2.58	    
6.92/2.58	    [a] = 5
6.92/2.58	   orientation:
6.92/2.58	    pin(a()) = 20 >= 16 = pout(b())
6.92/2.58	    
6.92/2.58	    pin(b()) = 16 >= 16 = pout(c())
6.92/2.58	    
6.92/2.58	    tc(x) = 5x + 2 >= 5x = ?1(pin(x),x)
6.92/2.58	   problem:
6.92/2.58	    pin(b()) -> pout(c())
6.92/2.58	   Matrix Interpretation Processor: dim=3
6.92/2.58	    
6.92/2.58	    interpretation:
6.92/2.58	           [0]
6.92/2.58	     [c] = [0]
6.92/2.58	           [0],
6.92/2.58	     
6.92/2.58	                  [1 0 0]  
6.92/2.58	     [pout](x0) = [0 0 0]x0
6.92/2.58	                  [0 0 0]  ,
6.92/2.58	     
6.92/2.58	           [0]
6.92/2.58	     [b] = [0]
6.92/2.58	           [0],
6.92/2.58	     
6.92/2.58	                 [1 0 0]     [1]
6.92/2.58	     [pin](x0) = [0 0 0]x0 + [0]
6.92/2.58	                 [0 0 0]     [0]
6.92/2.58	    orientation:
6.92/2.58	                [1]    [0]            
6.92/2.58	     pin(b()) = [0] >= [0] = pout(c())
6.92/2.58	                [0]    [0]            
6.92/2.58	    problem:
6.92/2.58	     
6.92/2.58	    Qed
6.92/2.58	This critical pair is conditional.
6.92/2.58	This critical pair has some non-trivial conditions.
6.92/2.58	ConCon could not decide whether all 2 critical pairs are joinable or not.
6.92/2.58	Overlap: (rule1: tc(x') -> y' <= pin(x') = pout(z'), tc(z') = y', rule2: tc(y) -> y, pos: ε, mgu: {(x',y)})
6.92/2.58	CP: y = y' <= pin(y) = pout(z'), tc(z') = y'
6.92/2.58	ConCon could not decide infeasibility of this critical pair.
6.92/2.58	
6.92/2.64	EOF