MAYBE

Problem:
 f(a()) -> f(c(a()))
 f(c(X)) -> X
 f(c(a())) -> f(d(b()))
 f(a()) -> f(d(a()))
 f(d(X)) -> X
 f(c(b())) -> f(d(a()))
 e(g(X)) -> e(X)

Proof:
 Complexity Transformation Processor:
  strict:
   f(a()) -> f(c(a()))
   f(c(X)) -> X
   f(c(a())) -> f(d(b()))
   f(a()) -> f(d(a()))
   f(d(X)) -> X
   f(c(b())) -> f(d(a()))
   e(g(X)) -> e(X)
  weak:
   
  Matrix Interpretation Processor:
   dimension: 1
   max_matrix:
    1
    interpretation:
     [e](x0) = x0 + 1,
     
     [g](x0) = x0 + 1,
     
     [d](x0) = x0,
     
     [b] = 0,
     
     [c](x0) = x0,
     
     [f](x0) = x0,
     
     [a] = 0
    orientation:
     f(a()) = 0 >= 0 = f(c(a()))
     
     f(c(X)) = X >= X = X
     
     f(c(a())) = 0 >= 0 = f(d(b()))
     
     f(a()) = 0 >= 0 = f(d(a()))
     
     f(d(X)) = X >= X = X
     
     f(c(b())) = 0 >= 0 = f(d(a()))
     
     e(g(X)) = X + 2 >= X + 1 = e(X)
    problem:
     strict:
      f(a()) -> f(c(a()))
      f(c(X)) -> X
      f(c(a())) -> f(d(b()))
      f(a()) -> f(d(a()))
      f(d(X)) -> X
      f(c(b())) -> f(d(a()))
     weak:
      e(g(X)) -> e(X)
    Matrix Interpretation Processor:
     dimension: 1
     max_matrix:
      1
      interpretation:
       [e](x0) = x0,
       
       [g](x0) = x0,
       
       [d](x0) = x0,
       
       [b] = 0,
       
       [c](x0) = x0 + 1,
       
       [f](x0) = x0,
       
       [a] = 0
      orientation:
       f(a()) = 0 >= 1 = f(c(a()))
       
       f(c(X)) = X + 1 >= X = X
       
       f(c(a())) = 1 >= 0 = f(d(b()))
       
       f(a()) = 0 >= 0 = f(d(a()))
       
       f(d(X)) = X >= X = X
       
       f(c(b())) = 1 >= 0 = f(d(a()))
       
       e(g(X)) = X >= X = e(X)
      problem:
       strict:
        f(a()) -> f(c(a()))
        f(a()) -> f(d(a()))
        f(d(X)) -> X
       weak:
        f(c(X)) -> X
        f(c(a())) -> f(d(b()))
        f(c(b())) -> f(d(a()))
        e(g(X)) -> e(X)
      Matrix Interpretation Processor:
       dimension: 1
       max_matrix:
        1
        interpretation:
         [e](x0) = x0,
         
         [g](x0) = x0,
         
         [d](x0) = x0 + 1,
         
         [b] = 0,
         
         [c](x0) = x0 + 1,
         
         [f](x0) = x0,
         
         [a] = 0
        orientation:
         f(a()) = 0 >= 1 = f(c(a()))
         
         f(a()) = 0 >= 1 = f(d(a()))
         
         f(d(X)) = X + 1 >= X = X
         
         f(c(X)) = X + 1 >= X = X
         
         f(c(a())) = 1 >= 1 = f(d(b()))
         
         f(c(b())) = 1 >= 1 = f(d(a()))
         
         e(g(X)) = X >= X = e(X)
        problem:
         strict:
          f(a()) -> f(c(a()))
          f(a()) -> f(d(a()))
         weak:
          f(d(X)) -> X
          f(c(X)) -> X
          f(c(a())) -> f(d(b()))
          f(c(b())) -> f(d(a()))
          e(g(X)) -> e(X)
        Open