MAYBE

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

Strict Trs:
  { empty(nil()) -> true()
  , empty(cons(x, l)) -> false()
  , head(cons(x, l)) -> x
  , tail(nil()) -> nil()
  , tail(cons(x, l)) -> l
  , rev(nil()) -> nil()
  , rev(cons(x, l)) -> cons(rev1(x, l), rev2(x, l))
  , rev2(x, nil()) -> nil()
  , rev2(x, cons(y, l)) -> rev(cons(x, rev2(y, l)))
  , last(x, l) -> if(empty(l), x, l)
  , if(true(), x, l) -> x
  , if(false(), x, l) -> last(head(l), tail(l)) }
Obligation:
  innermost runtime complexity
Answer:
  MAYBE

We add following dependency tuples:

Strict DPs:
  { empty^#(nil()) -> c_1()
  , empty^#(cons(x, l)) -> c_2()
  , head^#(cons(x, l)) -> c_3()
  , tail^#(nil()) -> c_4()
  , tail^#(cons(x, l)) -> c_5()
  , rev^#(nil()) -> c_6()
  , rev^#(cons(x, l)) -> c_7(rev2^#(x, l))
  , rev2^#(x, nil()) -> c_8()
  , rev2^#(x, cons(y, l)) ->
    c_9(rev^#(cons(x, rev2(y, l))), rev2^#(y, l))
  , last^#(x, l) -> c_10(if^#(empty(l), x, l), empty^#(l))
  , if^#(true(), x, l) -> c_11()
  , if^#(false(), x, l) ->
    c_12(last^#(head(l), tail(l)), head^#(l), tail^#(l)) }

and mark the set of starting terms.

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

Strict DPs:
  { empty^#(nil()) -> c_1()
  , empty^#(cons(x, l)) -> c_2()
  , head^#(cons(x, l)) -> c_3()
  , tail^#(nil()) -> c_4()
  , tail^#(cons(x, l)) -> c_5()
  , rev^#(nil()) -> c_6()
  , rev^#(cons(x, l)) -> c_7(rev2^#(x, l))
  , rev2^#(x, nil()) -> c_8()
  , rev2^#(x, cons(y, l)) ->
    c_9(rev^#(cons(x, rev2(y, l))), rev2^#(y, l))
  , last^#(x, l) -> c_10(if^#(empty(l), x, l), empty^#(l))
  , if^#(true(), x, l) -> c_11()
  , if^#(false(), x, l) ->
    c_12(last^#(head(l), tail(l)), head^#(l), tail^#(l)) }
Weak Trs:
  { empty(nil()) -> true()
  , empty(cons(x, l)) -> false()
  , head(cons(x, l)) -> x
  , tail(nil()) -> nil()
  , tail(cons(x, l)) -> l
  , rev(nil()) -> nil()
  , rev(cons(x, l)) -> cons(rev1(x, l), rev2(x, l))
  , rev2(x, nil()) -> nil()
  , rev2(x, cons(y, l)) -> rev(cons(x, rev2(y, l)))
  , last(x, l) -> if(empty(l), x, l)
  , if(true(), x, l) -> x
  , if(false(), x, l) -> last(head(l), tail(l)) }
Obligation:
  innermost runtime complexity
Answer:
  MAYBE

We estimate the number of application of {1,2,3,4,5,6,8,11} by
applications of Pre({1,2,3,4,5,6,8,11}) = {7,9,10,12}. Here rules
are labeled as follows:

  DPs:
    { 1: empty^#(nil()) -> c_1()
    , 2: empty^#(cons(x, l)) -> c_2()
    , 3: head^#(cons(x, l)) -> c_3()
    , 4: tail^#(nil()) -> c_4()
    , 5: tail^#(cons(x, l)) -> c_5()
    , 6: rev^#(nil()) -> c_6()
    , 7: rev^#(cons(x, l)) -> c_7(rev2^#(x, l))
    , 8: rev2^#(x, nil()) -> c_8()
    , 9: rev2^#(x, cons(y, l)) ->
         c_9(rev^#(cons(x, rev2(y, l))), rev2^#(y, l))
    , 10: last^#(x, l) -> c_10(if^#(empty(l), x, l), empty^#(l))
    , 11: if^#(true(), x, l) -> c_11()
    , 12: if^#(false(), x, l) ->
          c_12(last^#(head(l), tail(l)), head^#(l), tail^#(l)) }

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

Strict DPs:
  { rev^#(cons(x, l)) -> c_7(rev2^#(x, l))
  , rev2^#(x, cons(y, l)) ->
    c_9(rev^#(cons(x, rev2(y, l))), rev2^#(y, l))
  , last^#(x, l) -> c_10(if^#(empty(l), x, l), empty^#(l))
  , if^#(false(), x, l) ->
    c_12(last^#(head(l), tail(l)), head^#(l), tail^#(l)) }
Weak DPs:
  { empty^#(nil()) -> c_1()
  , empty^#(cons(x, l)) -> c_2()
  , head^#(cons(x, l)) -> c_3()
  , tail^#(nil()) -> c_4()
  , tail^#(cons(x, l)) -> c_5()
  , rev^#(nil()) -> c_6()
  , rev2^#(x, nil()) -> c_8()
  , if^#(true(), x, l) -> c_11() }
Weak Trs:
  { empty(nil()) -> true()
  , empty(cons(x, l)) -> false()
  , head(cons(x, l)) -> x
  , tail(nil()) -> nil()
  , tail(cons(x, l)) -> l
  , rev(nil()) -> nil()
  , rev(cons(x, l)) -> cons(rev1(x, l), rev2(x, l))
  , rev2(x, nil()) -> nil()
  , rev2(x, cons(y, l)) -> rev(cons(x, rev2(y, l)))
  , last(x, l) -> if(empty(l), x, l)
  , if(true(), x, l) -> x
  , if(false(), x, l) -> last(head(l), tail(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.

{ empty^#(nil()) -> c_1()
, empty^#(cons(x, l)) -> c_2()
, head^#(cons(x, l)) -> c_3()
, tail^#(nil()) -> c_4()
, tail^#(cons(x, l)) -> c_5()
, rev^#(nil()) -> c_6()
, rev2^#(x, nil()) -> c_8()
, if^#(true(), x, l) -> c_11() }

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

Strict DPs:
  { rev^#(cons(x, l)) -> c_7(rev2^#(x, l))
  , rev2^#(x, cons(y, l)) ->
    c_9(rev^#(cons(x, rev2(y, l))), rev2^#(y, l))
  , last^#(x, l) -> c_10(if^#(empty(l), x, l), empty^#(l))
  , if^#(false(), x, l) ->
    c_12(last^#(head(l), tail(l)), head^#(l), tail^#(l)) }
Weak Trs:
  { empty(nil()) -> true()
  , empty(cons(x, l)) -> false()
  , head(cons(x, l)) -> x
  , tail(nil()) -> nil()
  , tail(cons(x, l)) -> l
  , rev(nil()) -> nil()
  , rev(cons(x, l)) -> cons(rev1(x, l), rev2(x, l))
  , rev2(x, nil()) -> nil()
  , rev2(x, cons(y, l)) -> rev(cons(x, rev2(y, l)))
  , last(x, l) -> if(empty(l), x, l)
  , if(true(), x, l) -> x
  , if(false(), x, l) -> last(head(l), tail(l)) }
Obligation:
  innermost runtime complexity
Answer:
  MAYBE

Due to missing edges in the dependency-graph, the right-hand sides
of following rules could be simplified:

  { last^#(x, l) -> c_10(if^#(empty(l), x, l), empty^#(l))
  , if^#(false(), x, l) ->
    c_12(last^#(head(l), tail(l)), head^#(l), tail^#(l)) }

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

Strict DPs:
  { rev^#(cons(x, l)) -> c_1(rev2^#(x, l))
  , rev2^#(x, cons(y, l)) ->
    c_2(rev^#(cons(x, rev2(y, l))), rev2^#(y, l))
  , last^#(x, l) -> c_3(if^#(empty(l), x, l))
  , if^#(false(), x, l) -> c_4(last^#(head(l), tail(l))) }
Weak Trs:
  { empty(nil()) -> true()
  , empty(cons(x, l)) -> false()
  , head(cons(x, l)) -> x
  , tail(nil()) -> nil()
  , tail(cons(x, l)) -> l
  , rev(nil()) -> nil()
  , rev(cons(x, l)) -> cons(rev1(x, l), rev2(x, l))
  , rev2(x, nil()) -> nil()
  , rev2(x, cons(y, l)) -> rev(cons(x, rev2(y, l)))
  , last(x, l) -> if(empty(l), x, l)
  , if(true(), x, l) -> x
  , if(false(), x, l) -> last(head(l), tail(l)) }
Obligation:
  innermost runtime complexity
Answer:
  MAYBE

We replace rewrite rules by usable rules:

  Weak Usable Rules:
    { empty(nil()) -> true()
    , empty(cons(x, l)) -> false()
    , head(cons(x, l)) -> x
    , tail(nil()) -> nil()
    , tail(cons(x, l)) -> l
    , rev(nil()) -> nil()
    , rev(cons(x, l)) -> cons(rev1(x, l), rev2(x, l))
    , rev2(x, nil()) -> nil()
    , rev2(x, cons(y, l)) -> rev(cons(x, rev2(y, l))) }

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

Strict DPs:
  { rev^#(cons(x, l)) -> c_1(rev2^#(x, l))
  , rev2^#(x, cons(y, l)) ->
    c_2(rev^#(cons(x, rev2(y, l))), rev2^#(y, l))
  , last^#(x, l) -> c_3(if^#(empty(l), x, l))
  , if^#(false(), x, l) -> c_4(last^#(head(l), tail(l))) }
Weak Trs:
  { empty(nil()) -> true()
  , empty(cons(x, l)) -> false()
  , head(cons(x, l)) -> x
  , tail(nil()) -> nil()
  , tail(cons(x, l)) -> l
  , rev(nil()) -> nil()
  , rev(cons(x, l)) -> cons(rev1(x, l), rev2(x, l))
  , 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..