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
      Bounds Processor:
       bound: 1
       enrichment: match
       automaton:
        final states: {5,4,3}
        transitions:
         s1(55) -> 56*
         s1(25) -> 26*
         s1(17) -> 18*
         s1(12) -> 13*
         s1(49) -> 50*
         s1(29) -> 30*
         s1(56) -> 57*
         s1(26) -> 27*
         s1(48) -> 49*
         d1(15) -> 16*
         d1(47) -> 48*
         d1(54) -> 55*
         d1(24) -> 25*
         p1(80) -> 81*
         p1(94) -> 95*
         p1(51) -> 52*
         p1(46) -> 47*
         p1(68) -> 69*
         p1(53) -> 54*
         p1(13) -> 14*
         f1(14) -> 15*
         01(40) -> 41*
         01(28) -> 29*
         d0(2) -> 3*
         d0(1) -> 3*
         s0(2) -> 1*
         s0(1) -> 1*
         p0(2) -> 5*
         p0(1) -> 5*
         f0(2) -> 4*
         f0(1) -> 4*
         00(2) -> 2*
         00(1) -> 2*
         1 -> 40,5,4,17
         2 -> 28,5,3,12
         12 -> 14*
         14 -> 24*
         16 -> 15,4
         17 -> 14*
         18 -> 13*
         25 -> 47*
         26 -> 54,46
         27 -> 53,25,3
         29 -> 55,48,25
         30 -> 15*
         41 -> 55,48,29
         48 -> 69*
         49 -> 68,52
         50 -> 55,51,16
         52 -> 47*
         55 -> 95*
         56 -> 94,81
         57 -> 80,48
         69 -> 54*
         81 -> 47*
         95 -> 54*
       problem:
        strict:
         d(s(x1)) -> s(s(d(p(s(x1)))))
        weak:
         f(s(x1)) -> d(f(p(s(x1))))
         f(0(x1)) -> s(0(x1))
         d(0(x1)) -> 0(x1)
         p(s(x1)) -> x1
       Open