MAYBE

Problem:
 f(s(x)) -> s(s(f(p(s(x)))))
 f(0()) -> 0()
 p(s(x)) -> x

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