MAYBE

Problem:
 half(0()) -> 0()
 half(s(0())) -> 0()
 half(s(s(x))) -> s(half(x))
 bits(0()) -> 0()
 bits(s(x)) -> s(bits(half(s(x))))

Proof:
 Complexity Transformation Processor:
  strict:
   half(0()) -> 0()
   half(s(0())) -> 0()
   half(s(s(x))) -> s(half(x))
   bits(0()) -> 0()
   bits(s(x)) -> s(bits(half(s(x))))
  weak:
   
  Matrix Interpretation Processor:
   dimension: 1
   max_matrix:
    1
    interpretation:
     [bits](x0) = x0,
     
     [s](x0) = x0 + 1,
     
     [half](x0) = x0,
     
     [0] = 0
    orientation:
     half(0()) = 0 >= 0 = 0()
     
     half(s(0())) = 1 >= 0 = 0()
     
     half(s(s(x))) = x + 2 >= x + 1 = s(half(x))
     
     bits(0()) = 0 >= 0 = 0()
     
     bits(s(x)) = x + 1 >= x + 2 = s(bits(half(s(x))))
    problem:
     strict:
      half(0()) -> 0()
      bits(0()) -> 0()
      bits(s(x)) -> s(bits(half(s(x))))
     weak:
      half(s(0())) -> 0()
      half(s(s(x))) -> s(half(x))
    Matrix Interpretation Processor:
     dimension: 1
     max_matrix:
      1
      interpretation:
       [bits](x0) = x0,
       
       [s](x0) = x0 + 1,
       
       [half](x0) = x0 + 1,
       
       [0] = 0
      orientation:
       half(0()) = 1 >= 0 = 0()
       
       bits(0()) = 0 >= 0 = 0()
       
       bits(s(x)) = x + 1 >= x + 3 = s(bits(half(s(x))))
       
       half(s(0())) = 2 >= 0 = 0()
       
       half(s(s(x))) = x + 3 >= x + 2 = s(half(x))
      problem:
       strict:
        bits(0()) -> 0()
        bits(s(x)) -> s(bits(half(s(x))))
       weak:
        half(0()) -> 0()
        half(s(0())) -> 0()
        half(s(s(x))) -> s(half(x))
      Matrix Interpretation Processor:
       dimension: 1
       max_matrix:
        1
        interpretation:
         [bits](x0) = x0 + 1,
         
         [s](x0) = x0,
         
         [half](x0) = x0,
         
         [0] = 0
        orientation:
         bits(0()) = 1 >= 0 = 0()
         
         bits(s(x)) = x + 1 >= x + 1 = s(bits(half(s(x))))
         
         half(0()) = 0 >= 0 = 0()
         
         half(s(0())) = 0 >= 0 = 0()
         
         half(s(s(x))) = x >= x = s(half(x))
        problem:
         strict:
          bits(s(x)) -> s(bits(half(s(x))))
         weak:
          bits(0()) -> 0()
          half(0()) -> 0()
          half(s(0())) -> 0()
          half(s(s(x))) -> s(half(x))
        Open