MAYBE

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

Strict Trs:
  { rev(nil()) -> nil()
  , rev(cons(x, l)) -> cons(rev1(x, l), rev2(x, l))
  , rev1(x, cons(y, l)) -> rev1(y, l)
  , rev1(0(), nil()) -> 0()
  , rev1(s(x), nil()) -> s(x)
  , rev2(x, nil()) -> nil()
  , rev2(x, cons(y, l)) -> rev(cons(x, rev2(y, l))) }
Obligation:
  innermost runtime complexity
Answer:
  MAYBE

We add following dependency tuples:

Strict DPs:
  { rev^#(nil()) -> c_1()
  , rev^#(cons(x, l)) -> c_2(rev1^#(x, l), rev2^#(x, l))
  , rev1^#(x, cons(y, l)) -> c_3(rev1^#(y, l))
  , rev1^#(0(), nil()) -> c_4()
  , rev1^#(s(x), nil()) -> c_5()
  , rev2^#(x, nil()) -> c_6()
  , rev2^#(x, cons(y, l)) ->
    c_7(rev^#(cons(x, rev2(y, l))), rev2^#(y, l)) }

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^#(cons(x, l)) -> c_2(rev1^#(x, l), rev2^#(x, l))
  , rev1^#(x, cons(y, l)) -> c_3(rev1^#(y, l))
  , rev1^#(0(), nil()) -> c_4()
  , rev1^#(s(x), nil()) -> c_5()
  , rev2^#(x, nil()) -> c_6()
  , rev2^#(x, cons(y, l)) ->
    c_7(rev^#(cons(x, rev2(y, l))), rev2^#(y, l)) }
Weak Trs:
  { rev(nil()) -> nil()
  , rev(cons(x, l)) -> cons(rev1(x, l), rev2(x, l))
  , rev1(x, cons(y, l)) -> rev1(y, l)
  , rev1(0(), nil()) -> 0()
  , rev1(s(x), nil()) -> s(x)
  , rev2(x, nil()) -> nil()
  , rev2(x, cons(y, l)) -> rev(cons(x, rev2(y, l))) }
Obligation:
  innermost runtime complexity
Answer:
  MAYBE

We estimate the number of application of {1,4,5,6} by applications
of Pre({1,4,5,6}) = {2,3,7}. Here rules are labeled as follows:

  DPs:
    { 1: rev^#(nil()) -> c_1()
    , 2: rev^#(cons(x, l)) -> c_2(rev1^#(x, l), rev2^#(x, l))
    , 3: rev1^#(x, cons(y, l)) -> c_3(rev1^#(y, l))
    , 4: rev1^#(0(), nil()) -> c_4()
    , 5: rev1^#(s(x), nil()) -> c_5()
    , 6: rev2^#(x, nil()) -> c_6()
    , 7: rev2^#(x, cons(y, l)) ->
         c_7(rev^#(cons(x, rev2(y, l))), rev2^#(y, l)) }

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

Strict DPs:
  { rev^#(cons(x, l)) -> c_2(rev1^#(x, l), rev2^#(x, l))
  , rev1^#(x, cons(y, l)) -> c_3(rev1^#(y, l))
  , rev2^#(x, cons(y, l)) ->
    c_7(rev^#(cons(x, rev2(y, l))), rev2^#(y, l)) }
Weak DPs:
  { rev^#(nil()) -> c_1()
  , rev1^#(0(), nil()) -> c_4()
  , rev1^#(s(x), nil()) -> c_5()
  , rev2^#(x, nil()) -> c_6() }
Weak Trs:
  { rev(nil()) -> nil()
  , rev(cons(x, l)) -> cons(rev1(x, l), rev2(x, l))
  , rev1(x, cons(y, l)) -> rev1(y, l)
  , rev1(0(), nil()) -> 0()
  , rev1(s(x), nil()) -> s(x)
  , rev2(x, nil()) -> nil()
  , rev2(x, cons(y, l)) -> rev(cons(x, rev2(y, l))) }
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^#(0(), nil()) -> c_4()
, rev1^#(s(x), nil()) -> c_5()
, rev2^#(x, nil()) -> c_6() }

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

Strict DPs:
  { rev^#(cons(x, l)) -> c_2(rev1^#(x, l), rev2^#(x, l))
  , rev1^#(x, cons(y, l)) -> c_3(rev1^#(y, l))
  , rev2^#(x, cons(y, l)) ->
    c_7(rev^#(cons(x, rev2(y, l))), rev2^#(y, l)) }
Weak Trs:
  { rev(nil()) -> nil()
  , rev(cons(x, l)) -> cons(rev1(x, l), rev2(x, l))
  , rev1(x, cons(y, l)) -> rev1(y, l)
  , rev1(0(), nil()) -> 0()
  , rev1(s(x), nil()) -> s(x)
  , rev2(x, nil()) -> nil()
  , rev2(x, cons(y, l)) -> rev(cons(x, rev2(y, l))) }
Obligation:
  innermost runtime complexity
Answer:
  MAYBE

The input cannot be shown compatible

Arrrr..