4.46/2.71	YES
4.46/2.71	
4.46/2.71	Proof:
4.46/2.71	This system is confluent.
4.46/2.71	By \cite{ALS94}, Theorem 4.1.
4.46/2.71	This system is of type 3 or smaller.
4.46/2.71	This system is strongly deterministic.
4.46/2.71	This system is quasi-decreasing.
4.46/2.71	By \cite{O02}, p. 214, Proposition 7.2.50.
4.46/2.71	This system is of type 3 or smaller.
4.46/2.71	This system is deterministic.
4.46/2.71	System R transformed to U(R).
4.46/2.71	This system is terminating.
4.46/2.71	Call external tool:
4.46/2.71	./ttt2.sh
4.46/2.71	Input:
4.46/2.71	  a -> c
4.46/2.71	  a -> d
4.46/2.71	  b -> c
4.46/2.71	  b -> d
4.46/2.71	  c -> e
4.46/2.71	  d -> e
4.46/2.71	  k -> e
4.46/2.71	  l -> e
4.46/2.71	  s(c) -> t(k)
4.46/2.71	  s(c) -> t(l)
4.46/2.71	  s(e) -> t(e)
4.46/2.71	  g(x, x) -> h(x, x)
4.46/2.71	  ?1(t(y), x) -> pair(x, y)
4.46/2.71	  f(x) -> ?1(s(x), x)
4.46/2.71	
4.46/2.71	 Matrix Interpretation Processor: dim=1
4.46/2.71	  
4.46/2.71	  interpretation:
4.46/2.71	   [f](x0) = 7x0 + 4,
4.46/2.71	   
4.46/2.71	   [pair](x0, x1) = x0 + x1,
4.46/2.71	   
4.46/2.71	   [?1](x0, x1) = 2x0 + x1,
4.46/2.71	   
4.46/2.71	   [h](x0, x1) = 4x0 + 4x1,
4.46/2.71	   
4.46/2.71	   [g](x0, x1) = 6x0 + 2x1 + 4,
4.46/2.71	   
4.46/2.71	   [t](x0) = 2x0 + 2,
4.46/2.71	   
4.46/2.71	   [s](x0) = 3x0 + 2,
4.46/2.71	   
4.46/2.71	   [l] = 4,
4.46/2.71	   
4.46/2.71	   [k] = 3,
4.46/2.71	   
4.46/2.71	   [e] = 0,
4.46/2.71	   
4.46/2.71	   [b] = 3,
4.46/2.71	   
4.46/2.71	   [d] = 1,
4.46/2.71	   
4.46/2.71	   [c] = 3,
4.46/2.71	   
4.46/2.72	   [a] = 3
4.46/2.72	  orientation:
4.46/2.72	   a() = 3 >= 3 = c()
4.46/2.72	   
4.46/2.72	   a() = 3 >= 1 = d()
4.46/2.72	   
4.46/2.72	   b() = 3 >= 3 = c()
4.46/2.72	   
4.46/2.72	   b() = 3 >= 1 = d()
4.46/2.72	   
4.46/2.72	   c() = 3 >= 0 = e()
4.46/2.72	   
4.46/2.72	   d() = 1 >= 0 = e()
4.46/2.72	   
4.46/2.72	   k() = 3 >= 0 = e()
4.46/2.72	   
4.46/2.72	   l() = 4 >= 0 = e()
4.46/2.72	   
4.46/2.72	   s(c()) = 11 >= 8 = t(k())
4.46/2.72	   
4.46/2.72	   s(c()) = 11 >= 10 = t(l())
4.46/2.72	   
4.46/2.72	   s(e()) = 2 >= 2 = t(e())
4.46/2.72	   
4.46/2.72	   g(x,x) = 8x + 4 >= 8x = h(x,x)
4.46/2.72	   
4.46/2.72	   ?1(t(y),x) = x + 4y + 4 >= x + y = pair(x,y)
4.46/2.72	   
4.46/2.72	   f(x) = 7x + 4 >= 7x + 4 = ?1(s(x),x)
4.46/2.72	  problem:
4.46/2.72	   a() -> c()
4.46/2.72	   b() -> c()
4.46/2.72	   s(e()) -> t(e())
4.46/2.72	   f(x) -> ?1(s(x),x)
4.46/2.72	  Matrix Interpretation Processor: dim=1
4.46/2.72	   
4.46/2.72	   interpretation:
4.46/2.72	    [f](x0) = 6x0 + 1,
4.46/2.72	    
4.46/2.72	    [?1](x0, x1) = x0 + 5x1,
4.46/2.72	    
4.46/2.72	    [t](x0) = x0,
4.46/2.72	    
4.46/2.72	    [s](x0) = x0,
4.46/2.72	    
4.46/2.72	    [e] = 4,
4.46/2.72	    
4.46/2.72	    [b] = 0,
4.46/2.72	    
4.46/2.72	    [c] = 0,
4.46/2.72	    
4.46/2.72	    [a] = 0
4.46/2.72	   orientation:
4.46/2.72	    a() = 0 >= 0 = c()
4.46/2.72	    
4.46/2.72	    b() = 0 >= 0 = c()
4.46/2.72	    
4.46/2.72	    s(e()) = 4 >= 4 = t(e())
4.46/2.72	    
4.46/2.72	    f(x) = 6x + 1 >= 6x = ?1(s(x),x)
4.46/2.72	   problem:
4.46/2.72	    a() -> c()
4.46/2.72	    b() -> c()
4.46/2.72	    s(e()) -> t(e())
4.46/2.72	   Matrix Interpretation Processor: dim=3
4.46/2.72	    
4.46/2.72	    interpretation:
4.46/2.72	               [1 0 0]  
4.46/2.72	     [t](x0) = [0 0 0]x0
4.46/2.72	               [0 0 0]  ,
4.46/2.72	     
4.46/2.72	               [1 0 0]     [1]
4.46/2.72	     [s](x0) = [0 0 0]x0 + [0]
4.46/2.72	               [0 0 0]     [0],
4.46/2.72	     
4.46/2.72	           [0]
4.46/2.72	     [e] = [0]
4.46/2.72	           [0],
4.46/2.72	     
4.46/2.72	           [0]
4.46/2.72	     [b] = [0]
4.46/2.72	           [0],
4.46/2.72	     
4.46/2.72	           [0]
4.46/2.72	     [c] = [0]
4.46/2.72	           [0],
4.46/2.72	     
4.46/2.72	           [0]
4.46/2.72	     [a] = [0]
4.46/2.72	           [0]
4.46/2.72	    orientation:
4.46/2.72	           [0]    [0]      
4.46/2.72	     a() = [0] >= [0] = c()
4.46/2.72	           [0]    [0]      
4.46/2.72	     
4.46/2.72	           [0]    [0]      
4.46/2.72	     b() = [0] >= [0] = c()
4.46/2.72	           [0]    [0]      
4.46/2.72	     
4.46/2.72	              [1]    [0]         
4.46/2.72	     s(e()) = [0] >= [0] = t(e())
4.46/2.72	              [0]    [0]         
4.46/2.72	    problem:
4.46/2.72	     a() -> c()
4.46/2.72	     b() -> c()
4.46/2.72	    Matrix Interpretation Processor: dim=3
4.46/2.72	     
4.46/2.72	     interpretation:
4.46/2.72	            [1]
4.46/2.72	      [b] = [0]
4.46/2.72	            [0],
4.46/2.72	      
4.46/2.72	            [0]
4.46/2.72	      [c] = [0]
4.46/2.72	            [0],
4.46/2.72	      
4.46/2.72	            [0]
4.46/2.72	      [a] = [0]
4.46/2.72	            [0]
4.46/2.72	     orientation:
4.46/2.72	            [0]    [0]      
4.46/2.72	      a() = [0] >= [0] = c()
4.46/2.72	            [0]    [0]      
4.46/2.73	      
4.46/2.73	            [1]    [0]      
4.46/2.73	      b() = [0] >= [0] = c()
4.46/2.73	            [0]    [0]      
4.46/2.73	     problem:
4.46/2.73	      a() -> c()
4.46/2.73	     Matrix Interpretation Processor: dim=3
4.46/2.73	      
4.46/2.73	      interpretation:
4.46/2.73	             [0]
4.46/2.73	       [c] = [0]
4.46/2.73	             [0],
4.46/2.73	       
4.46/2.73	             [1]
4.46/2.73	       [a] = [0]
4.46/2.73	             [1]
4.46/2.73	      orientation:
4.46/2.73	             [1]    [0]      
4.46/2.73	       a() = [0] >= [0] = c()
4.46/2.73	             [1]    [0]      
4.46/2.73	      problem:
4.46/2.73	       
4.46/2.73	      Qed
4.46/2.73	All 8 critical pairs are joinable.
4.46/2.73	Overlap: (rule1: s(c) -> t(k), rule2: s(c) -> t(l), pos: ε, mgu: {})
4.46/2.73	CP: t(l) = t(k)
4.46/2.73	This critical pair is context-joinable.
4.46/2.73	Overlap: (rule1: b -> c, rule2: b -> d, pos: ε, mgu: {})
4.46/2.73	CP: d = c
4.46/2.73	This critical pair is context-joinable.
4.46/2.73	Overlap: (rule1: a -> d, rule2: a -> c, pos: ε, mgu: {})
4.46/2.73	CP: c = d
4.46/2.73	This critical pair is context-joinable.
4.46/2.73	Overlap: (rule1: b -> d, rule2: b -> c, pos: ε, mgu: {})
4.46/2.73	CP: c = d
4.46/2.73	This critical pair is context-joinable.
4.46/2.73	Overlap: (rule1: s(c) -> t(k), rule2: c -> e, pos: 1, mgu: {})
4.46/2.73	CP: s(e) = t(k)
4.46/2.73	This critical pair is context-joinable.
4.46/2.73	Overlap: (rule1: a -> c, rule2: a -> d, pos: ε, mgu: {})
4.46/2.73	CP: d = c
4.46/2.73	This critical pair is context-joinable.
4.46/2.73	Overlap: (rule1: s(c) -> t(l), rule2: s(c) -> t(k), pos: ε, mgu: {})
4.46/2.73	CP: t(k) = t(l)
4.46/2.73	This critical pair is context-joinable.
4.46/2.73	Overlap: (rule1: s(c) -> t(l), rule2: c -> e, pos: 1, mgu: {})
4.46/2.73	CP: s(e) = t(l)
4.46/2.73	This critical pair is context-joinable.
4.46/2.73	
4.65/2.75	EOF