YES(?,O(n^1))

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:
 RT 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
   interpretation:
    [e](x0) = x0,
    
    [g](x0) = x0 + 5,
    
    [d](x0) = x0 + 20,
    
    [b] = 0,
    
    [c](x0) = x0 + 12,
    
    [f](x0) = x0 + 6,
    
    [a] = 14
   orientation:
    f(a()) = 20 >= 32 = f(c(a()))
    
    f(c(X)) = X + 18 >= X = X
    
    f(c(a())) = 32 >= 26 = f(d(b()))
    
    f(a()) = 20 >= 40 = f(d(a()))
    
    f(d(X)) = X + 26 >= X = X
    
    f(c(b())) = 18 >= 40 = f(d(a()))
    
    e(g(X)) = X + 5 >= X = e(X)
   problem:
    strict:
     f(a()) -> f(c(a()))
     f(a()) -> f(d(a()))
     f(c(b())) -> f(d(a()))
    weak:
     f(c(X)) -> X
     f(c(a())) -> f(d(b()))
     f(d(X)) -> X
     e(g(X)) -> e(X)
   Matrix Interpretation Processor:
    dimension: 1
    interpretation:
     [e](x0) = x0 + 23,
     
     [g](x0) = x0,
     
     [d](x0) = x0 + 14,
     
     [b] = 1,
     
     [c](x0) = x0 + 17,
     
     [f](x0) = x0,
     
     [a] = 0
    orientation:
     f(a()) = 0 >= 17 = f(c(a()))
     
     f(a()) = 0 >= 14 = f(d(a()))
     
     f(c(b())) = 18 >= 14 = f(d(a()))
     
     f(c(X)) = X + 17 >= X = X
     
     f(c(a())) = 17 >= 15 = f(d(b()))
     
     f(d(X)) = X + 14 >= X = X
     
     e(g(X)) = X + 23 >= X + 23 = e(X)
    problem:
     strict:
      f(a()) -> f(c(a()))
      f(a()) -> f(d(a()))
     weak:
      f(c(b())) -> f(d(a()))
      f(c(X)) -> X
      f(c(a())) -> f(d(b()))
      f(d(X)) -> X
      e(g(X)) -> e(X)
    Bounds Processor:
     bound: 1
     enrichment: match-rt
     automaton:
      final states: {9,8}
      transitions:
       f1(20) -> 21*
       c1(22) -> 23*
       a1() -> 19*
       d1(19) -> 20*
       b1() -> 31*
       f0(9) -> 8*
       f0(8) -> 8*
       a0() -> 8*
       c0(9) -> 8*
       c0(8) -> 8*
       d0(9) -> 8*
       d0(8) -> 8*
       b0() -> 8*
       e0(9) -> 8*
       e0(8) -> 8*
       g0(9) -> 9*
       g0(8) -> 9*
       9 -> 8*
       19 -> 21,8,22
       21 -> 8*
       22 -> 21,8
       23 -> 20*
       31 -> 19*
     problem:
      strict:
       f(a()) -> f(c(a()))
      weak:
       f(a()) -> f(d(a()))
       f(c(b())) -> f(d(a()))
       f(c(X)) -> X
       f(c(a())) -> f(d(b()))
       f(d(X)) -> X
       e(g(X)) -> e(X)
     Bounds Processor:
      bound: 1
      enrichment: match-rt
      automaton:
       final states: {9,8}
       transitions:
        f1(14) -> 15*
        c1(13) -> 14*
        a1() -> 13*
        d1(16) -> 17*
        b1() -> 20*
        f0(9) -> 8*
        f0(8) -> 8*
        a0() -> 8*
        c0(9) -> 8*
        c0(8) -> 8*
        d0(9) -> 8*
        d0(8) -> 8*
        b0() -> 8*
        e0(9) -> 8*
        e0(8) -> 8*
        g0(9) -> 9*
        g0(8) -> 9*
        9 -> 8*
        13 -> 15,8,16
        15 -> 8*
        16 -> 15,8
        17 -> 14*
        20 -> 16*
      problem:
       strict:
        
       weak:
        f(a()) -> f(c(a()))
        f(a()) -> f(d(a()))
        f(c(b())) -> f(d(a()))
        f(c(X)) -> X
        f(c(a())) -> f(d(b()))
        f(d(X)) -> X
        e(g(X)) -> e(X)
      Qed