MAYBE

We are left with following problem, upon which TcT provides the
certificate MAYBE.

Strict Trs:
  { D(t()) -> 1()
  , D(constant()) -> 0()
  , D(+(x, y)) -> +(D(x), D(y))
  , D(*(x, y)) -> +(*(y, D(x)), *(x, D(y)))
  , D(-(x, y)) -> -(D(x), D(y))
  , D(minus(x)) -> minus(D(x))
  , D(div(x, y)) -> -(div(D(x), y), div(*(x, D(y)), pow(y, 2())))
  , D(pow(x, y)) ->
    +(*(*(y, pow(x, -(y, 1()))), D(x)), *(*(pow(x, y), ln(x)), D(y)))
  , D(ln(x)) -> div(D(x), x) }
Obligation:
  innermost runtime complexity
Answer:
  MAYBE

We add following weak dependency pairs:

Strict DPs:
  { D^#(t()) -> c_1()
  , D^#(constant()) -> c_2()
  , D^#(+(x, y)) -> c_3(D^#(x), D^#(y))
  , D^#(*(x, y)) -> c_4(D^#(x), D^#(y))
  , D^#(-(x, y)) -> c_5(D^#(x), D^#(y))
  , D^#(minus(x)) -> c_6(D^#(x))
  , D^#(div(x, y)) -> c_7(D^#(x), D^#(y))
  , D^#(pow(x, y)) -> c_8(D^#(x), D^#(y))
  , D^#(ln(x)) -> c_9(D^#(x)) }

and mark the set of starting terms.

We are left with following problem, upon which TcT provides the
certificate MAYBE.

Strict DPs:
  { D^#(t()) -> c_1()
  , D^#(constant()) -> c_2()
  , D^#(+(x, y)) -> c_3(D^#(x), D^#(y))
  , D^#(*(x, y)) -> c_4(D^#(x), D^#(y))
  , D^#(-(x, y)) -> c_5(D^#(x), D^#(y))
  , D^#(minus(x)) -> c_6(D^#(x))
  , D^#(div(x, y)) -> c_7(D^#(x), D^#(y))
  , D^#(pow(x, y)) -> c_8(D^#(x), D^#(y))
  , D^#(ln(x)) -> c_9(D^#(x)) }
Strict Trs:
  { D(t()) -> 1()
  , D(constant()) -> 0()
  , D(+(x, y)) -> +(D(x), D(y))
  , D(*(x, y)) -> +(*(y, D(x)), *(x, D(y)))
  , D(-(x, y)) -> -(D(x), D(y))
  , D(minus(x)) -> minus(D(x))
  , D(div(x, y)) -> -(div(D(x), y), div(*(x, D(y)), pow(y, 2())))
  , D(pow(x, y)) ->
    +(*(*(y, pow(x, -(y, 1()))), D(x)), *(*(pow(x, y), ln(x)), D(y)))
  , D(ln(x)) -> div(D(x), x) }
Obligation:
  innermost runtime complexity
Answer:
  MAYBE

No rule is usable, rules are removed from the input problem.

We are left with following problem, upon which TcT provides the
certificate MAYBE.

Strict DPs:
  { D^#(t()) -> c_1()
  , D^#(constant()) -> c_2()
  , D^#(+(x, y)) -> c_3(D^#(x), D^#(y))
  , D^#(*(x, y)) -> c_4(D^#(x), D^#(y))
  , D^#(-(x, y)) -> c_5(D^#(x), D^#(y))
  , D^#(minus(x)) -> c_6(D^#(x))
  , D^#(div(x, y)) -> c_7(D^#(x), D^#(y))
  , D^#(pow(x, y)) -> c_8(D^#(x), D^#(y))
  , D^#(ln(x)) -> c_9(D^#(x)) }
Obligation:
  innermost runtime complexity
Answer:
  MAYBE

The weightgap principle applies (using the following constant
growth matrix-interpretation)

The following argument positions are usable:
  Uargs(c_3) = {1, 2}, Uargs(c_4) = {1, 2}, Uargs(c_5) = {1, 2},
  Uargs(c_6) = {1}, Uargs(c_7) = {1, 2}, Uargs(c_8) = {1, 2},
  Uargs(c_9) = {1}

TcT has computed following constructor-restricted matrix
interpretation.

            [t] = [2]                  
                                       
     [constant] = [1]                  
                                       
    [+](x1, x2) = [1] x1 + [1] x2 + [1]
                                       
    [*](x1, x2) = [1] x1 + [1] x2 + [2]
                                       
    [-](x1, x2) = [1] x1 + [1] x2 + [2]
                                       
    [minus](x1) = [1] x1 + [1]         
                                       
  [div](x1, x2) = [1] x1 + [1] x2 + [1]
                                       
  [pow](x1, x2) = [1] x1 + [1] x2 + [2]
                                       
       [ln](x1) = [1] x1 + [2]         
                                       
      [D^#](x1) = [1]                  
                                       
          [c_1] = [0]                  
                                       
          [c_2] = [0]                  
                                       
  [c_3](x1, x2) = [1] x1 + [1] x2 + [2]
                                       
  [c_4](x1, x2) = [1] x1 + [1] x2 + [2]
                                       
  [c_5](x1, x2) = [1] x1 + [1] x2 + [2]
                                       
      [c_6](x1) = [1] x1 + [0]         
                                       
  [c_7](x1, x2) = [1] x1 + [1] x2 + [2]
                                       
  [c_8](x1, x2) = [1] x1 + [1] x2 + [2]
                                       
      [c_9](x1) = [1] x1 + [0]         

This order satisfies following ordering constraints:


Further, it can be verified that all rules not oriented are covered by the weightgap condition.

We are left with following problem, upon which TcT provides the
certificate MAYBE.

Strict DPs:
  { D^#(+(x, y)) -> c_3(D^#(x), D^#(y))
  , D^#(*(x, y)) -> c_4(D^#(x), D^#(y))
  , D^#(-(x, y)) -> c_5(D^#(x), D^#(y))
  , D^#(minus(x)) -> c_6(D^#(x))
  , D^#(div(x, y)) -> c_7(D^#(x), D^#(y))
  , D^#(pow(x, y)) -> c_8(D^#(x), D^#(y))
  , D^#(ln(x)) -> c_9(D^#(x)) }
Weak DPs:
  { D^#(t()) -> c_1()
  , D^#(constant()) -> c_2() }
Obligation:
  innermost runtime complexity
Answer:
  MAYBE

The following weak DPs constitute a sub-graph of the DG that is
closed under successors. The DPs are removed.

{ D^#(t()) -> c_1()
, D^#(constant()) -> c_2() }

We are left with following problem, upon which TcT provides the
certificate MAYBE.

Strict DPs:
  { D^#(+(x, y)) -> c_3(D^#(x), D^#(y))
  , D^#(*(x, y)) -> c_4(D^#(x), D^#(y))
  , D^#(-(x, y)) -> c_5(D^#(x), D^#(y))
  , D^#(minus(x)) -> c_6(D^#(x))
  , D^#(div(x, y)) -> c_7(D^#(x), D^#(y))
  , D^#(pow(x, y)) -> c_8(D^#(x), D^#(y))
  , D^#(ln(x)) -> c_9(D^#(x)) }
Obligation:
  innermost runtime complexity
Answer:
  MAYBE

The input cannot be shown compatible

Arrrr..