YES

Problem:
 .(1(),x) -> x
 .(x,1()) -> x
 .(i(x),x) -> 1()
 .(x,i(x)) -> 1()
 i(1()) -> 1()
 i(i(x)) -> x
 .(i(y),.(y,z)) -> z
 .(y,.(i(y),z)) -> z

Proof:
 Matrix Interpretation Processor: dim=3
  
  interpretation:
             [1 0 0]     [0]
   [i](x0) = [0 0 1]x0 + [1]
             [0 1 0]     [0],
   
                 [1 1 0]       
   [.](x0, x1) = [1 1 0]x0 + x1
                 [0 1 1]       ,
   
         [0]
   [1] = [0]
         [0]
  orientation:
                        
   .(1(),x) = x >= x = x
                        
   
              [1 1 0]          
   .(x,1()) = [1 1 0]x >= x = x
              [0 1 1]          
   
               [2 0 1]    [1]    [0]      
   .(i(x),x) = [1 1 1]x + [1] >= [0] = 1()
               [0 1 2]    [1]    [0]      
   
               [2 1 0]    [0]    [0]      
   .(x,i(x)) = [1 1 1]x + [1] >= [0] = 1()
               [0 2 1]    [0]    [0]      
   
            [0]    [0]      
   i(1()) = [1] >= [0] = 1()
            [0]    [0]      
   
                 [0]         
   i(i(x)) = x + [1] >= x = x
                 [1]         
   
                    [2 1 1]        [1]         
   .(i(y),.(y,z)) = [2 1 1]y + z + [1] >= z = z
                    [0 2 2]        [1]         
   
                    [2 1 1]        [1]         
   .(y,.(i(y),z)) = [2 1 1]y + z + [1] >= z = z
                    [0 2 2]        [1]         
  problem:
   .(1(),x) -> x
   .(x,1()) -> x
   .(x,i(x)) -> 1()
   i(1()) -> 1()
   i(i(x)) -> x
  Matrix Interpretation Processor: dim=3
   
   interpretation:
              [1 0 0]     [0]
    [i](x0) = [0 0 1]x0 + [0]
              [0 1 0]     [1],
    
                  [1 0 1]     [1 1 1]     [0]
    [.](x0, x1) = [0 1 0]x0 + [0 1 0]x1 + [1]
                  [1 0 1]     [0 0 1]     [0],
    
          [1]
    [1] = [0]
          [0]
   orientation:
               [1 1 1]    [1]         
    .(1(),x) = [0 1 0]x + [1] >= x = x
               [0 0 1]    [1]         
    
               [1 0 1]    [1]         
    .(x,1()) = [0 1 0]x + [1] >= x = x
               [1 0 1]    [0]         
    
                [2 1 2]    [1]    [1]      
    .(x,i(x)) = [0 1 1]x + [1] >= [0] = 1()
                [1 1 1]    [1]    [0]      
    
             [1]    [1]      
    i(1()) = [0] >= [0] = 1()
             [1]    [0]      
    
                  [0]         
    i(i(x)) = x + [1] >= x = x
                  [1]         
   problem:
    .(x,i(x)) -> 1()
    i(1()) -> 1()
    i(i(x)) -> x
   Matrix Interpretation Processor: dim=3
    
    interpretation:
               [1 0 1]     [0]
     [i](x0) = [1 0 1]x0 + [1]
               [0 1 0]     [0],
     
                   [1 0 0]     [1 1 0]  
     [.](x0, x1) = [0 0 0]x0 + [0 0 0]x1
                   [0 0 0]     [0 0 0]  ,
     
           [0]
     [1] = [0]
           [0]
    orientation:
                 [3 0 2]    [1]    [0]      
     .(x,i(x)) = [0 0 0]x + [0] >= [0] = 1()
                 [0 0 0]    [0]    [0]      
     
              [0]    [0]      
     i(1()) = [1] >= [0] = 1()
              [0]    [0]      
     
               [1 1 1]    [0]         
     i(i(x)) = [1 1 1]x + [1] >= x = x
               [1 0 1]    [1]         
    problem:
     i(1()) -> 1()
     i(i(x)) -> x
    Matrix Interpretation Processor: dim=3
     
     interpretation:
                [1 0 1]  
      [i](x0) = [0 0 1]x0
                [0 1 0]  ,
      
            [0]
      [1] = [1]
            [1]
     orientation:
               [1]    [0]      
      i(1()) = [1] >= [1] = 1()
               [1]    [1]      
      
                [1 1 1]          
      i(i(x)) = [0 1 0]x >= x = x
                [0 0 1]          
     problem:
      i(i(x)) -> x
     Matrix Interpretation Processor: dim=3
      
      interpretation:
                 [1 1 0]     [0]
       [i](x0) = [0 0 1]x0 + [1]
                 [0 1 0]     [0]
      orientation:
                 [1 1 1]    [1]         
       i(i(x)) = [0 1 0]x + [1] >= x = x
                 [0 0 1]    [1]         
      problem:
       
      Qed