6.04/2.18	YES
6.04/2.18	
6.04/2.18	Proof:
6.04/2.18	This system is confluent.
6.04/2.18	By \cite{ALS94}, Theorem 4.1.
6.04/2.18	This system is of type 3 or smaller.
6.04/2.18	This system is strongly deterministic.
6.04/2.18	This system is quasi-decreasing.
6.04/2.18	By \cite{O02}, p. 214, Proposition 7.2.50.
6.04/2.18	This system is of type 3 or smaller.
6.04/2.18	This system is deterministic.
6.04/2.18	System R transformed to optimized U(R).
6.04/2.18	This system is terminating.
6.04/2.18	Call external tool:
6.04/2.18	./ttt2.sh
6.04/2.18	Input:
6.04/2.18	  f(x', x'') -> ?1(x', x', x'')
6.04/2.18	  ?1(x, x', x'') -> ?2(x'', x', x'', x)
6.04/2.18	  ?2(x, x', x'', x) -> g(x)
6.04/2.18	  f(y', h(y'')) -> ?3(y', y', y'')
6.04/2.18	  ?3(y, y', y'') -> ?4(y'', y', y'', y)
6.04/2.18	  ?4(y, y', y'', y) -> g(y)
6.04/2.18	
6.04/2.18	 Matrix Interpretation Processor: dim=1
6.04/2.18	  
6.04/2.18	  interpretation:
6.04/2.18	   [?4](x0, x1, x2, x3) = x0 + x1 + 4x2 + 2x3 + 4,
6.04/2.18	   
6.04/2.18	   [?3](x0, x1, x2) = 2x0 + x1 + 6x2 + 5,
6.04/2.18	   
6.04/2.18	   [h](x0) = 3x0 + 4,
6.04/2.18	   
6.04/2.18	   [g](x0) = x0,
6.04/2.18	   
6.04/2.18	   [?2](x0, x1, x2, x3) = 2x0 + x1 + 2x2 + 2x3,
6.04/2.18	   
6.04/2.18	   [?1](x0, x1, x2) = 2x0 + x1 + 4x2,
6.04/2.18	   
6.04/2.18	   [f](x0, x1) = 3x0 + 5x1 + 3
6.04/2.18	  orientation:
6.04/2.18	   f(x',x'') = 3x' + 5x'' + 3 >= 3x' + 4x'' = ?1(x',x',x'')
6.04/2.18	   
6.04/2.18	   ?1(x,x',x'') = 2x + x' + 4x'' >= 2x + x' + 4x'' = ?2(x'',x',x'',x)
6.04/2.18	   
6.04/2.18	   ?2(x,x',x'',x) = 4x + x' + 2x'' >= x = g(x)
6.04/2.18	   
6.04/2.18	   f(y',h(y'')) = 3y' + 15y'' + 23 >= 3y' + 6y'' + 5 = ?3(y',y',y'')
6.04/2.18	   
6.04/2.18	   ?3(y,y',y'') = 2y + y' + 6y'' + 5 >= 2y + y' + 5y'' + 4 = ?4(y'',y',y'',y)
6.04/2.18	   
6.04/2.18	   ?4(y,y',y'',y) = 3y + y' + 4y'' + 4 >= y = g(y)
6.04/2.18	  problem:
6.04/2.18	   ?1(x,x',x'') -> ?2(x'',x',x'',x)
6.04/2.18	   ?2(x,x',x'',x) -> g(x)
6.04/2.18	  Matrix Interpretation Processor: dim=1
6.04/2.18	   
6.04/2.18	   interpretation:
6.04/2.18	    [g](x0) = 3x0,
6.04/2.18	    
6.04/2.18	    [?2](x0, x1, x2, x3) = x0 + 4x1 + 4x2 + 2x3,
6.04/2.18	    
6.04/2.18	    [?1](x0, x1, x2) = 2x0 + 4x1 + 5x2 + 4
6.04/2.18	   orientation:
6.04/2.18	    ?1(x,x',x'') = 2x + 4x' + 5x'' + 4 >= 2x + 4x' + 5x'' = ?2(x'',x',x'',x)
6.04/2.18	    
6.04/2.18	    ?2(x,x',x'',x) = 3x + 4x' + 4x'' >= 3x = g(x)
6.04/2.18	   problem:
6.04/2.18	    ?2(x,x',x'',x) -> g(x)
6.04/2.18	   Matrix Interpretation Processor: dim=3
6.04/2.18	    
6.04/2.18	    interpretation:
6.04/2.18	               [1 0 0]  
6.04/2.18	     [g](x0) = [0 0 0]x0
6.04/2.18	               [0 0 1]  ,
6.04/2.18	     
6.04/2.18	                            [1 0 0]     [1 0 0]     [1 0 0]     [1 0 0]     [1]
6.04/2.18	     [?2](x0, x1, x2, x3) = [0 0 0]x0 + [0 0 0]x1 + [0 0 0]x2 + [0 0 0]x3 + [0]
6.27/2.20	                            [0 0 0]     [0 0 0]     [0 0 0]     [0 0 1]     [0]
6.27/2.20	    orientation:
6.27/2.20	                      [2 0 0]    [1 0 0]     [1 0 0]      [1]    [1 0 0]        
6.27/2.20	     ?2(x,x',x'',x) = [0 0 0]x + [0 0 0]x' + [0 0 0]x'' + [0] >= [0 0 0]x = g(x)
6.27/2.20	                      [0 0 1]    [0 0 0]     [0 0 0]      [0]    [0 0 1]        
6.27/2.20	    problem:
6.27/2.20	     
6.27/2.20	    Qed
6.27/2.20	All 2 critical pairs are joinable.
6.27/2.22	Overlap: (rule1: f(z, h(x')) -> g(x) <= z = x, x' = x, rule2: f(y', z') -> g(y) <= y' = y, z' = y, pos: ε, mgu: {(y',z), (z',h(x'))})
6.27/2.22	CP: g(y) = g(x) <= z = x, x' = x, z = y, h(x') = y
6.27/2.22	This critical pair is infeasible.
6.27/2.22	This critical pair is conditional.
6.27/2.22	This critical pair has some non-trivial conditions.
6.27/2.22	Call external tool:
6.27/2.22	./waldmeister
6.27/2.22	Input:
6.27/2.22	  f(x', x'') -> g(x) <= x' = x, x'' = x
6.27/2.22	  f(y', h(y'')) -> g(y) <= y' = y, y'' = y
6.27/2.22	
6.27/2.22	By Waldmeister.
6.27/2.22	Overlap: (rule1: f(z, y') -> g(y) <= z = y, y' = y, rule2: f(x', h(z')) -> g(x) <= x' = x, z' = x, pos: ε, mgu: {(x',z), (y',h(z'))})
6.27/2.22	CP: g(x) = g(y) <= z = y, h(z') = y, z = x, z' = x
6.27/2.22	This critical pair is infeasible.
6.27/2.22	This critical pair is conditional.
6.27/2.22	This critical pair has some non-trivial conditions.
6.27/2.22	Call external tool:
6.27/2.22	./waldmeister
6.27/2.22	Input:
6.27/2.22	  f(x', x'') -> g(x) <= x' = x, x'' = x
6.27/2.22	  f(y', h(y'')) -> g(y) <= y' = y, y'' = y
6.27/2.22	
6.27/2.22	By Waldmeister.
6.27/2.22	
6.41/2.27	EOF