9.52/3.41	YES
9.52/3.41	
9.52/3.41	Proof:
9.52/3.41	This system is confluent.
9.52/3.41	By \cite{ALS94}, Theorem 4.1.
9.52/3.41	This system is of type 3 or smaller.
9.52/3.41	This system is strongly deterministic.
9.52/3.41	This system is quasi-decreasing.
9.52/3.41	By \cite{O02}, p. 214, Proposition 7.2.50.
9.52/3.41	This system is of type 3 or smaller.
9.52/3.41	This system is deterministic.
9.52/3.41	System R transformed to optimized U(R).
9.52/3.41	This system is terminating.
9.52/3.41	Call external tool:
9.52/3.41	./ttt2.sh
9.52/3.41	Input:
9.52/3.41	(VAR y' x'' x y'' y x')
9.52/3.41	(RULES
9.52/3.41	  f(x', x'') -> ?1(x', x', x'')
9.52/3.41	  ?1(x, x', x'') -> ?2(x'', x', x'', x)
9.52/3.41	  ?2(x, x', x'', x) -> g(x)
9.52/3.41	  f(y', h(y'')) -> ?3(y', y', y'')
9.52/3.41	  ?3(y, y', y'') -> ?4(y'', y', y'', y)
9.52/3.41	  ?4(y, y', y'', y) -> g(y)
9.52/3.41	)
9.52/3.41	
9.52/3.41	 Matrix Interpretation Processor: dim=1
9.52/3.41	  
9.52/3.41	  interpretation:
9.52/3.41	   [?4](x0, x1, x2, x3) = x0 + x1 + 4x2 + 2x3 + 4,
9.52/3.41	   
9.52/3.41	   [?3](x0, x1, x2) = 2x0 + x1 + 6x2 + 5,
9.52/3.41	   
9.52/3.41	   [h](x0) = 3x0 + 4,
9.52/3.41	   
9.52/3.41	   [g](x0) = x0,
9.52/3.41	   
9.52/3.41	   [?2](x0, x1, x2, x3) = 2x0 + x1 + 2x2 + 2x3,
9.52/3.41	   
9.52/3.41	   [?1](x0, x1, x2) = 2x0 + x1 + 4x2,
9.52/3.41	   
9.52/3.41	   [f](x0, x1) = 3x0 + 5x1 + 3
9.52/3.41	  orientation:
9.52/3.41	   f(x',x'') = 3x' + 5x'' + 3 >= 3x' + 4x'' = ?1(x',x',x'')
9.52/3.41	   
9.52/3.41	   ?1(x,x',x'') = 2x + x' + 4x'' >= 2x + x' + 4x'' = ?2(x'',x',x'',x)
9.52/3.41	   
9.52/3.41	   ?2(x,x',x'',x) = 4x + x' + 2x'' >= x = g(x)
9.52/3.41	   
9.52/3.41	   f(y',h(y'')) = 3y' + 15y'' + 23 >= 3y' + 6y'' + 5 = ?3(y',y',y'')
9.52/3.41	   
9.52/3.41	   ?3(y,y',y'') = 2y + y' + 6y'' + 5 >= 2y + y' + 5y'' + 4 = ?4(y'',y',y'',y)
9.52/3.41	   
9.52/3.41	   ?4(y,y',y'',y) = 3y + y' + 4y'' + 4 >= y = g(y)
9.52/3.41	  problem:
9.52/3.41	   ?1(x,x',x'') -> ?2(x'',x',x'',x)
9.52/3.41	   ?2(x,x',x'',x) -> g(x)
9.52/3.41	  Matrix Interpretation Processor: dim=1
9.52/3.41	   
9.52/3.41	   interpretation:
9.52/3.41	    [g](x0) = 3x0,
9.52/3.41	    
9.52/3.41	    [?2](x0, x1, x2, x3) = x0 + 4x1 + 4x2 + 2x3,
9.52/3.41	    
9.52/3.42	    [?1](x0, x1, x2) = 2x0 + 4x1 + 5x2 + 4
9.52/3.42	   orientation:
9.52/3.42	    ?1(x,x',x'') = 2x + 4x' + 5x'' + 4 >= 2x + 4x' + 5x'' = ?2(x'',x',x'',x)
9.52/3.42	    
9.52/3.42	    ?2(x,x',x'',x) = 3x + 4x' + 4x'' >= 3x = g(x)
9.52/3.42	   problem:
9.52/3.42	    ?2(x,x',x'',x) -> g(x)
9.52/3.42	   Matrix Interpretation Processor: dim=1
9.52/3.42	    
9.52/3.42	    interpretation:
9.52/3.42	     [g](x0) = 3x0,
9.52/3.42	     
9.52/3.42	     [?2](x0, x1, x2, x3) = x0 + 4x1 + 2x2 + 2x3 + 1
9.52/3.42	    orientation:
9.52/3.42	     ?2(x,x',x'',x) = 3x + 4x' + 2x'' + 1 >= 3x = g(x)
9.52/3.42	    problem:
9.52/3.42	     
9.52/3.42	    Qed
9.52/3.42	All 2 critical pairs are joinable.
9.52/3.42	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: {(z,y'), (z',h(x'))})
9.52/3.42	CP: g(y) = g(x) <= y' = x, x' = x, y' = y, h(x') = y
9.52/3.42	This critical pair is infeasible.
9.52/3.42	This critical pair is conditional.
9.52/3.42	This critical pair has some non-trivial conditions.
9.52/3.42	Call external tool:
9.52/3.42	./waldmeister
9.52/3.42	Input:
9.52/3.42	  f(x', x'') -> g(x) <= x' = x, x'' = x
9.52/3.42	  f(y', h(y'')) -> g(y) <= y' = y, y'' = y
9.52/3.42	
9.52/3.42	By Waldmeister.
9.52/3.42	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: {(z,x'), (y',h(z'))})
9.52/3.42	CP: g(x) = g(y) <= x' = y, h(z') = y, x' = x, z' = x
9.52/3.42	This critical pair is infeasible.
9.52/3.42	This critical pair is conditional.
9.52/3.42	This critical pair has some non-trivial conditions.
9.52/3.42	Call external tool:
9.52/3.42	./waldmeister
9.52/3.42	Input:
9.52/3.42	  f(x', x'') -> g(x) <= x' = x, x'' = x
9.52/3.42	  f(y', h(y'')) -> g(y) <= y' = y, y'' = y
9.52/3.42	
9.52/3.42	By Waldmeister.
9.52/3.42	
9.86/3.46	EOF