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:
 RT 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
   interpretation:
    [p](x0) = x0 + 8,
    
    [d](x0) = x0 + 7,
    
    [s](x0) = x0 + 9,
    
    [f](x0) = x0 + 12,
    
    [0](x0) = x0 + 26
   orientation:
    f(0(x1)) = x1 + 38 >= x1 + 35 = s(0(x1))
    
    d(0(x1)) = x1 + 33 >= x1 + 26 = 0(x1)
    
    d(s(x1)) = x1 + 16 >= x1 + 42 = s(s(d(p(s(x1)))))
    
    f(s(x1)) = x1 + 21 >= x1 + 36 = d(f(p(s(x1))))
    
    p(s(x1)) = x1 + 17 >= 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