MAYBE

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

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