YES(?,O(n^2))
20.27/9.37	YES(?,O(n^2))
20.27/9.37	
20.27/9.37	Problem:
20.27/9.37	 ++(nil(),y) -> y
20.27/9.37	 ++(x,nil()) -> x
20.27/9.37	 ++(.(x,y),z) -> .(x,++(y,z))
20.27/9.37	 ++(++(x,y),z) -> ++(x,++(y,z))
20.27/9.37	
20.27/9.37	Proof:
20.27/9.37	 Complexity Transformation Processor:
20.27/9.37	  strict:
20.27/9.37	   ++(nil(),y) -> y
20.27/9.37	   ++(x,nil()) -> x
20.27/9.37	   ++(.(x,y),z) -> .(x,++(y,z))
20.27/9.37	   ++(++(x,y),z) -> ++(x,++(y,z))
20.27/9.37	  weak:
20.27/9.37	   
20.27/9.37	  Matrix Interpretation Processor: dim=1
20.27/9.37	   
20.27/9.37	   max_matrix:
20.27/9.37	    1
20.27/9.37	   interpretation:
20.27/9.37	    [.](x0, x1) = x0 + x1 + 19,
20.27/9.37	    
20.27/9.37	    [++](x0, x1) = x0 + x1 + 2,
20.27/9.37	    
20.27/9.37	    [nil] = 198
20.27/9.37	   orientation:
20.27/9.37	    ++(nil(),y) = y + 200 >= y = y
20.27/9.37	    
20.27/9.37	    ++(x,nil()) = x + 200 >= x = x
20.27/9.37	    
20.27/9.37	    ++(.(x,y),z) = x + y + z + 21 >= x + y + z + 21 = .(x,++(y,z))
20.27/9.37	    
20.27/9.37	    ++(++(x,y),z) = x + y + z + 4 >= x + y + z + 4 = ++(x,++(y,z))
20.27/9.37	   problem:
20.27/9.37	    strict:
20.27/9.37	     ++(.(x,y),z) -> .(x,++(y,z))
20.27/9.37	     ++(++(x,y),z) -> ++(x,++(y,z))
20.27/9.37	    weak:
20.27/9.37	     ++(nil(),y) -> y
20.27/9.37	     ++(x,nil()) -> x
20.27/9.37	   Splitting Processor:
20.27/9.37	    strict:
20.27/9.37	     ++(.(x,y),z) -> .(x,++(y,z))
20.27/9.37	    weak:
20.27/9.37	     ++(nil(),y) -> y
20.27/9.37	     ++(x,nil()) -> x
20.27/9.37	     ++(++(x,y),z) -> ++(x,++(y,z))
20.27/9.37	    Matrix Interpretation Processor: dim=2
20.27/9.37	     
20.27/9.37	     max_matrix:
20.27/9.37	      [1 1]
20.27/9.37	      [0 1]
20.27/9.37	     interpretation:
20.27/9.37	                              [1]
20.27/9.37	      [.](x0, x1) = x0 + x1 + [3],
20.27/9.37	      
20.27/9.37	                     [1 1]          [0]
20.27/9.37	      [++](x0, x1) = [0 1]x0 + x1 + [1],
20.27/9.37	      
20.27/9.37	              [0]
20.27/9.37	      [nil] = [1]
20.27/9.37	     orientation:
20.27/9.37	                      [1 2]    [1 1]        [1]    [1 1]    [1 1]        [0]                
20.27/9.37	      ++(++(x,y),z) = [0 1]x + [0 1]y + z + [2] >= [0 1]x + [0 1]y + z + [2] = ++(x,++(y,z))
20.27/9.37	      
20.27/9.37	                     [1 1]    [1 1]        [4]        [1 1]        [1]               
20.27/9.37	      ++(.(x,y),z) = [0 1]x + [0 1]y + z + [4] >= x + [0 1]y + z + [4] = .(x,++(y,z))
20.27/9.37	      
20.27/9.37	                        [1]         
20.27/9.37	      ++(nil(),y) = y + [2] >= y = y
20.27/9.37	      
20.27/9.37	                    [1 1]    [0]         
20.27/9.37	      ++(x,nil()) = [0 1]x + [2] >= x = x
20.27/9.37	     problem:
20.27/9.37	      strict:
20.27/9.37	       
20.27/9.37	      weak:
20.27/9.37	       ++(++(x,y),z) -> ++(x,++(y,z))
20.27/9.37	       ++(.(x,y),z) -> .(x,++(y,z))
20.27/9.37	       ++(nil(),y) -> y
20.27/9.37	       ++(x,nil()) -> x
20.27/9.37	     Qed
20.27/9.37	    
20.27/9.37	    strict:
20.27/9.37	     ++(++(x,y),z) -> ++(x,++(y,z))
20.27/9.37	    weak:
20.27/9.37	     ++(.(x,y),z) -> .(x,++(y,z))
20.27/9.37	     ++(nil(),y) -> y
20.27/9.37	     ++(x,nil()) -> x
20.27/9.37	    Matrix Interpretation Processor: dim=2
20.27/9.37	     
20.27/9.37	     max_matrix:
20.27/9.37	      [1 1]
20.27/9.37	      [0 1]
20.27/9.37	     interpretation:
20.27/9.37	                    [1 1]          [3]
20.27/9.37	      [.](x0, x1) = [0 0]x0 + x1 + [2],
20.27/9.37	      
20.27/9.37	                     [1 1]          [2]
20.27/9.37	      [++](x0, x1) = [0 1]x0 + x1 + [1],
20.27/9.37	      
20.27/9.37	              [0]
20.27/9.37	      [nil] = [0]
20.27/9.37	     orientation:
20.27/9.37	                     [1 1]    [1 1]        [7]    [1 1]    [1 1]        [5]               
20.27/9.37	      ++(.(x,y),z) = [0 0]x + [0 1]y + z + [3] >= [0 0]x + [0 1]y + z + [3] = .(x,++(y,z))
20.27/9.37	      
20.27/9.37	                        [2]         
20.27/9.37	      ++(nil(),y) = y + [1] >= y = y
20.27/9.37	      
20.27/9.37	                    [1 1]    [2]         
20.27/9.37	      ++(x,nil()) = [0 1]x + [1] >= x = x
20.27/9.37	      
20.27/9.37	                      [1 2]    [1 1]        [5]    [1 1]    [1 1]        [4]                
20.27/9.37	      ++(++(x,y),z) = [0 1]x + [0 1]y + z + [2] >= [0 1]x + [0 1]y + z + [2] = ++(x,++(y,z))
20.27/9.37	     problem:
20.27/9.37	      strict:
20.27/9.37	       
20.27/9.37	      weak:
20.27/9.37	       ++(.(x,y),z) -> .(x,++(y,z))
20.27/9.37	       ++(nil(),y) -> y
20.27/9.37	       ++(x,nil()) -> x
20.27/9.37	       ++(++(x,y),z) -> ++(x,++(y,z))
20.27/9.37	     Qed
20.27/9.38	EOF