MAYBE

Problem:
 a(f(),0()) -> a(s(),0())
 a(d(),0()) -> 0()
 a(d(),a(s(),x)) -> a(s(),a(s(),a(d(),a(p(),a(s(),x)))))
 a(f(),a(s(),x)) -> a(d(),a(f(),a(p(),a(s(),x))))
 a(p(),a(s(),x)) -> x

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