MAYBE

Problem:
 f(0(x1)) -> s(0(x1))
 d(0(x1)) -> 0(x1)
 d(s(x1)) -> s(s(d(x1)))
 f(s(x1)) -> d(f(x1))

Proof:
 RT Transformation Processor:
  strict:
   f(0(x1)) -> s(0(x1))
   d(0(x1)) -> 0(x1)
   d(s(x1)) -> s(s(d(x1)))
   f(s(x1)) -> d(f(x1))
  weak:
   
  Matrix Interpretation Processor:
   dimension: 1
   interpretation:
    [d](x0) = x0 + 15,
    
    [s](x0) = x0 + 24,
    
    [f](x0) = x0 + 17,
    
    [0](x0) = x0
   orientation:
    f(0(x1)) = x1 + 17 >= x1 + 24 = s(0(x1))
    
    d(0(x1)) = x1 + 15 >= x1 = 0(x1)
    
    d(s(x1)) = x1 + 39 >= x1 + 63 = s(s(d(x1)))
    
    f(s(x1)) = x1 + 41 >= x1 + 32 = d(f(x1))
   problem:
    strict:
     f(0(x1)) -> s(0(x1))
     d(s(x1)) -> s(s(d(x1)))
    weak:
     d(0(x1)) -> 0(x1)
     f(s(x1)) -> d(f(x1))
   Matrix Interpretation Processor:
    dimension: 1
    interpretation:
     [d](x0) = x0,
     
     [s](x0) = x0 + 4,
     
     [f](x0) = x0 + 8,
     
     [0](x0) = x0 + 3
    orientation:
     f(0(x1)) = x1 + 11 >= x1 + 7 = s(0(x1))
     
     d(s(x1)) = x1 + 4 >= x1 + 8 = s(s(d(x1)))
     
     d(0(x1)) = x1 + 3 >= x1 + 3 = 0(x1)
     
     f(s(x1)) = x1 + 12 >= x1 + 8 = d(f(x1))
    problem:
     strict:
      d(s(x1)) -> s(s(d(x1)))
     weak:
      f(0(x1)) -> s(0(x1))
      d(0(x1)) -> 0(x1)
      f(s(x1)) -> d(f(x1))
    Open