Problem:
 implies(not(x),y) -> or(x,y)
 implies(not(x),or(y,z)) -> implies(y,or(x,z))
 implies(x,or(y,z)) -> or(y,implies(x,z))

Proof:
 Complexity Transformation Processor:
  strict:
   implies(not(x),y) -> or(x,y)
   implies(not(x),or(y,z)) -> implies(y,or(x,z))
   implies(x,or(y,z)) -> or(y,implies(x,z))
  weak:
   
  Matrix Interpretation Processor:
   dimension: 1
   max_matrix:
    1
    interpretation:
     [or](x0, x1) = x0 + x1 + 4,
     
     [implies](x0, x1) = x0 + x1 + 78,
     
     [not](x0) = x0 + 128
    orientation:
     implies(not(x),y) = x + y + 206 >= x + y + 4 = or(x,y)
     
     implies(not(x),or(y,z)) = x + y + z + 210 >= x + y + z + 82 = implies(y,or(x,z))
     
     implies(x,or(y,z)) = x + y + z + 82 >= x + y + z + 82 = or(y,implies(x,z))
    problem:
     strict:
      implies(x,or(y,z)) -> or(y,implies(x,z))
     weak:
      implies(not(x),y) -> or(x,y)
      implies(not(x),or(y,z)) -> implies(y,or(x,z))
    Matrix Interpretation Processor:
     dimension: 4
     max_matrix:
      [1 1 1 1]
      [0 1 1 1]
      [0 0 0 0]
      [0 0 0 0]
      interpretation:
                      [1 1 1 0]     [1 0 0 0]     [0]
                      [0 1 1 0]     [0 1 1 0]     [0]
       [or](x0, x1) = [0 0 0 0]x0 + [0 0 0 0]x1 + [1]
                      [0 0 0 0]     [0 0 0 0]     [0],
       
                           [1 1 0 0]     [1 1 1 0]     [0]
                           [0 1 1 0]     [0 1 1 0]     [0]
       [implies](x0, x1) = [0 0 0 0]x0 + [0 0 0 0]x1 + [1]
                           [0 0 0 0]     [0 0 0 0]     [0],
       
                   [1 1 1 1]     [1]
                   [0 1 1 1]     [1]
       [not](x0) = [0 0 0 0]x0 + [1]
                   [0 0 0 0]     [0]
      orientation:
                            [1 1 0 0]    [1 2 2 0]    [1 1 1 0]    [1]    [1 1 0 0]    [1 1 1 0]    [1 1 1 0]    [0]                     
                            [0 1 1 0]    [0 1 1 0]    [0 1 1 0]    [1]    [0 1 1 0]    [0 1 1 0]    [0 1 1 0]    [1]                     
       implies(x,or(y,z)) = [0 0 0 0]x + [0 0 0 0]y + [0 0 0 0]z + [1] >= [0 0 0 0]x + [0 0 0 0]y + [0 0 0 0]z + [1] = or(y,implies(x,z))
                            [0 0 0 0]    [0 0 0 0]    [0 0 0 0]    [0]    [0 0 0 0]    [0 0 0 0]    [0 0 0 0]    [0]                     
       
                           [1 2 2 2]    [1 1 1 0]    [2]    [1 1 1 0]    [1 0 0 0]    [0]          
                           [0 1 1 1]    [0 1 1 0]    [2]    [0 1 1 0]    [0 1 1 0]    [0]          
       implies(not(x),y) = [0 0 0 0]x + [0 0 0 0]y + [1] >= [0 0 0 0]x + [0 0 0 0]y + [1] = or(x,y)
                           [0 0 0 0]    [0 0 0 0]    [0]    [0 0 0 0]    [0 0 0 0]    [0]          
       
                                 [1 2 2 2]    [1 2 2 0]    [1 1 1 0]    [3]    [1 2 2 0]    [1 1 0 0]    [1 1 1 0]    [1]                     
                                 [0 1 1 1]    [0 1 1 0]    [0 1 1 0]    [3]    [0 1 1 0]    [0 1 1 0]    [0 1 1 0]    [1]                     
       implies(not(x),or(y,z)) = [0 0 0 0]x + [0 0 0 0]y + [0 0 0 0]z + [1] >= [0 0 0 0]x + [0 0 0 0]y + [0 0 0 0]z + [1] = implies(y,or(x,z))
                                 [0 0 0 0]    [0 0 0 0]    [0 0 0 0]    [0]    [0 0 0 0]    [0 0 0 0]    [0 0 0 0]    [0]                     
      problem:
       strict:
        
       weak:
        implies(x,or(y,z)) -> or(y,implies(x,z))
        implies(not(x),y) -> or(x,y)
        implies(not(x),or(y,z)) -> implies(y,or(x,z))
      Qed