MAYBE

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

Strict Trs:
  { rev(nil()) -> nil()
  , rev(++(x, y)) -> ++(rev1(x, y), rev2(x, y))
  , rev1(x, nil()) -> x
  , rev1(x, ++(y, z)) -> rev1(y, z)
  , rev2(x, nil()) -> nil()
  , rev2(x, ++(y, z)) -> rev(++(x, rev(rev2(y, z)))) }
Obligation:
  innermost runtime complexity
Answer:
  MAYBE

We add following dependency tuples:

Strict DPs:
  { rev^#(nil()) -> c_1()
  , rev^#(++(x, y)) -> c_2(rev1^#(x, y), rev2^#(x, y))
  , rev1^#(x, nil()) -> c_3()
  , rev1^#(x, ++(y, z)) -> c_4(rev1^#(y, z))
  , rev2^#(x, nil()) -> c_5()
  , rev2^#(x, ++(y, z)) ->
    c_6(rev^#(++(x, rev(rev2(y, z)))),
        rev^#(rev2(y, z)),
        rev2^#(y, z)) }

and mark the set of starting terms.

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

Strict DPs:
  { rev^#(nil()) -> c_1()
  , rev^#(++(x, y)) -> c_2(rev1^#(x, y), rev2^#(x, y))
  , rev1^#(x, nil()) -> c_3()
  , rev1^#(x, ++(y, z)) -> c_4(rev1^#(y, z))
  , rev2^#(x, nil()) -> c_5()
  , rev2^#(x, ++(y, z)) ->
    c_6(rev^#(++(x, rev(rev2(y, z)))),
        rev^#(rev2(y, z)),
        rev2^#(y, z)) }
Weak Trs:
  { rev(nil()) -> nil()
  , rev(++(x, y)) -> ++(rev1(x, y), rev2(x, y))
  , rev1(x, nil()) -> x
  , rev1(x, ++(y, z)) -> rev1(y, z)
  , rev2(x, nil()) -> nil()
  , rev2(x, ++(y, z)) -> rev(++(x, rev(rev2(y, z)))) }
Obligation:
  innermost runtime complexity
Answer:
  MAYBE

We estimate the number of application of {1,3,5} by applications of
Pre({1,3,5}) = {2,4,6}. Here rules are labeled as follows:

  DPs:
    { 1: rev^#(nil()) -> c_1()
    , 2: rev^#(++(x, y)) -> c_2(rev1^#(x, y), rev2^#(x, y))
    , 3: rev1^#(x, nil()) -> c_3()
    , 4: rev1^#(x, ++(y, z)) -> c_4(rev1^#(y, z))
    , 5: rev2^#(x, nil()) -> c_5()
    , 6: rev2^#(x, ++(y, z)) ->
         c_6(rev^#(++(x, rev(rev2(y, z)))),
             rev^#(rev2(y, z)),
             rev2^#(y, z)) }

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

Strict DPs:
  { rev^#(++(x, y)) -> c_2(rev1^#(x, y), rev2^#(x, y))
  , rev1^#(x, ++(y, z)) -> c_4(rev1^#(y, z))
  , rev2^#(x, ++(y, z)) ->
    c_6(rev^#(++(x, rev(rev2(y, z)))),
        rev^#(rev2(y, z)),
        rev2^#(y, z)) }
Weak DPs:
  { rev^#(nil()) -> c_1()
  , rev1^#(x, nil()) -> c_3()
  , rev2^#(x, nil()) -> c_5() }
Weak Trs:
  { rev(nil()) -> nil()
  , rev(++(x, y)) -> ++(rev1(x, y), rev2(x, y))
  , rev1(x, nil()) -> x
  , rev1(x, ++(y, z)) -> rev1(y, z)
  , rev2(x, nil()) -> nil()
  , rev2(x, ++(y, z)) -> rev(++(x, rev(rev2(y, z)))) }
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.

{ rev^#(nil()) -> c_1()
, rev1^#(x, nil()) -> c_3()
, rev2^#(x, nil()) -> c_5() }

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

Strict DPs:
  { rev^#(++(x, y)) -> c_2(rev1^#(x, y), rev2^#(x, y))
  , rev1^#(x, ++(y, z)) -> c_4(rev1^#(y, z))
  , rev2^#(x, ++(y, z)) ->
    c_6(rev^#(++(x, rev(rev2(y, z)))),
        rev^#(rev2(y, z)),
        rev2^#(y, z)) }
Weak Trs:
  { rev(nil()) -> nil()
  , rev(++(x, y)) -> ++(rev1(x, y), rev2(x, y))
  , rev1(x, nil()) -> x
  , rev1(x, ++(y, z)) -> rev1(y, z)
  , rev2(x, nil()) -> nil()
  , rev2(x, ++(y, z)) -> rev(++(x, rev(rev2(y, z)))) }
Obligation:
  innermost runtime complexity
Answer:
  MAYBE

The input cannot be shown compatible

Arrrr..