YES(?,O(n^2))

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

Proof:
 RT Transformation Processor:
  strict:
   half(0()) -> 0()
   half(s(s(x))) -> s(half(x))
   log(s(0())) -> 0()
   log(s(s(x))) -> s(log(s(half(x))))
  weak:
   
  Matrix Interpretation Processor:
   dimension: 1
   interpretation:
    [log](x0) = x0 + 18,
    
    [s](x0) = x0 + 4,
    
    [half](x0) = x0 + 14,
    
    [0] = 12
   orientation:
    half(0()) = 26 >= 12 = 0()
    
    half(s(s(x))) = x + 22 >= x + 18 = s(half(x))
    
    log(s(0())) = 34 >= 12 = 0()
    
    log(s(s(x))) = x + 26 >= x + 40 = s(log(s(half(x))))
   problem:
    strict:
     log(s(s(x))) -> s(log(s(half(x))))
    weak:
     half(0()) -> 0()
     half(s(s(x))) -> s(half(x))
     log(s(0())) -> 0()
   Matrix Interpretation Processor:
    dimension: 2
    interpretation:
                 [1 1]     [6]
     [log](x0) = [0 1]x0 + [0],
     
               [1 1]     [0]
     [s](x0) = [0 1]x0 + [1],
     
                    
     [half](x0) = x0,
     
           [14]
     [0] = [2 ]
    orientation:
                    [1 3]    [9]    [1 3]    [8]                     
     log(s(s(x))) = [0 1]x + [2] >= [0 1]x + [2] = s(log(s(half(x))))
     
                 [14]    [14]      
     half(0()) = [2 ] >= [2 ] = 0()
     
                     [1 2]    [1]    [1 1]    [0]             
     half(s(s(x))) = [0 1]x + [2] >= [0 1]x + [1] = s(half(x))
     
                   [25]    [14]      
     log(s(0())) = [3 ] >= [2 ] = 0()
    problem:
     strict:
      
     weak:
      log(s(s(x))) -> s(log(s(half(x))))
      half(0()) -> 0()
      half(s(s(x))) -> s(half(x))
      log(s(0())) -> 0()
    Qed