MAYBE

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

Proof:
 Complexity Transformation Processor:
  strict:
   f(0(x1)) -> s(0(x1))
   d(0(x1)) -> 0(x1)
   d(s(x1)) -> s(s(d(p(s(x1)))))
   f(s(x1)) -> d(f(p(s(x1))))
   p(s(x1)) -> x1
  weak:
   
  Matrix Interpretation Processor:
   dimension: 1
   max_matrix:
    1
    interpretation:
     [p](x0) = x0 + 1,
     
     [d](x0) = x0 + 1,
     
     [s](x0) = x0,
     
     [f](x0) = x0,
     
     [0](x0) = x0
    orientation:
     f(0(x1)) = x1 >= x1 = s(0(x1))
     
     d(0(x1)) = x1 + 1 >= x1 = 0(x1)
     
     d(s(x1)) = x1 + 1 >= x1 + 2 = s(s(d(p(s(x1)))))
     
     f(s(x1)) = x1 >= x1 + 2 = d(f(p(s(x1))))
     
     p(s(x1)) = x1 + 1 >= x1 = x1
    problem:
     strict:
      f(0(x1)) -> s(0(x1))
      d(s(x1)) -> s(s(d(p(s(x1)))))
      f(s(x1)) -> d(f(p(s(x1))))
     weak:
      d(0(x1)) -> 0(x1)
      p(s(x1)) -> x1
    Matrix Interpretation Processor:
     dimension: 1
     max_matrix:
      1
      interpretation:
       [p](x0) = x0,
       
       [d](x0) = x0,
       
       [s](x0) = x0,
       
       [f](x0) = x0 + 1,
       
       [0](x0) = x0
      orientation:
       f(0(x1)) = x1 + 1 >= x1 = s(0(x1))
       
       d(s(x1)) = x1 >= x1 = s(s(d(p(s(x1)))))
       
       f(s(x1)) = x1 + 1 >= x1 + 1 = d(f(p(s(x1))))
       
       d(0(x1)) = x1 >= x1 = 0(x1)
       
       p(s(x1)) = x1 >= x1 = x1
      problem:
       strict:
        d(s(x1)) -> s(s(d(p(s(x1)))))
        f(s(x1)) -> d(f(p(s(x1))))
       weak:
        f(0(x1)) -> s(0(x1))
        d(0(x1)) -> 0(x1)
        p(s(x1)) -> x1
      Open