MAYBE

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

Strict Trs:
  { isList(nil()) -> tt()
  , isList(Cons(x, xs)) -> isList(xs)
  , downfrom(0()) -> nil()
  , downfrom(s(x)) -> Cons(s(x), downfrom(x))
  , f(x) -> cond(isList(downfrom(x)), s(x))
  , cond(tt(), x) -> f(x) }
Obligation:
  innermost runtime complexity
Answer:
  MAYBE

We add following dependency tuples:

Strict DPs:
  { isList^#(nil()) -> c_1()
  , isList^#(Cons(x, xs)) -> c_2(isList^#(xs))
  , downfrom^#(0()) -> c_3()
  , downfrom^#(s(x)) -> c_4(downfrom^#(x))
  , f^#(x) ->
    c_5(cond^#(isList(downfrom(x)), s(x)),
        isList^#(downfrom(x)),
        downfrom^#(x))
  , cond^#(tt(), x) -> c_6(f^#(x)) }

and mark the set of starting terms.

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

Strict DPs:
  { isList^#(nil()) -> c_1()
  , isList^#(Cons(x, xs)) -> c_2(isList^#(xs))
  , downfrom^#(0()) -> c_3()
  , downfrom^#(s(x)) -> c_4(downfrom^#(x))
  , f^#(x) ->
    c_5(cond^#(isList(downfrom(x)), s(x)),
        isList^#(downfrom(x)),
        downfrom^#(x))
  , cond^#(tt(), x) -> c_6(f^#(x)) }
Weak Trs:
  { isList(nil()) -> tt()
  , isList(Cons(x, xs)) -> isList(xs)
  , downfrom(0()) -> nil()
  , downfrom(s(x)) -> Cons(s(x), downfrom(x))
  , f(x) -> cond(isList(downfrom(x)), s(x))
  , cond(tt(), x) -> f(x) }
Obligation:
  innermost runtime complexity
Answer:
  MAYBE

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

  DPs:
    { 1: isList^#(nil()) -> c_1()
    , 2: isList^#(Cons(x, xs)) -> c_2(isList^#(xs))
    , 3: downfrom^#(0()) -> c_3()
    , 4: downfrom^#(s(x)) -> c_4(downfrom^#(x))
    , 5: f^#(x) ->
         c_5(cond^#(isList(downfrom(x)), s(x)),
             isList^#(downfrom(x)),
             downfrom^#(x))
    , 6: cond^#(tt(), x) -> c_6(f^#(x)) }

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

Strict DPs:
  { isList^#(Cons(x, xs)) -> c_2(isList^#(xs))
  , downfrom^#(s(x)) -> c_4(downfrom^#(x))
  , f^#(x) ->
    c_5(cond^#(isList(downfrom(x)), s(x)),
        isList^#(downfrom(x)),
        downfrom^#(x))
  , cond^#(tt(), x) -> c_6(f^#(x)) }
Weak DPs:
  { isList^#(nil()) -> c_1()
  , downfrom^#(0()) -> c_3() }
Weak Trs:
  { isList(nil()) -> tt()
  , isList(Cons(x, xs)) -> isList(xs)
  , downfrom(0()) -> nil()
  , downfrom(s(x)) -> Cons(s(x), downfrom(x))
  , f(x) -> cond(isList(downfrom(x)), s(x))
  , cond(tt(), x) -> f(x) }
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.

{ isList^#(nil()) -> c_1()
, downfrom^#(0()) -> c_3() }

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

Strict DPs:
  { isList^#(Cons(x, xs)) -> c_2(isList^#(xs))
  , downfrom^#(s(x)) -> c_4(downfrom^#(x))
  , f^#(x) ->
    c_5(cond^#(isList(downfrom(x)), s(x)),
        isList^#(downfrom(x)),
        downfrom^#(x))
  , cond^#(tt(), x) -> c_6(f^#(x)) }
Weak Trs:
  { isList(nil()) -> tt()
  , isList(Cons(x, xs)) -> isList(xs)
  , downfrom(0()) -> nil()
  , downfrom(s(x)) -> Cons(s(x), downfrom(x))
  , f(x) -> cond(isList(downfrom(x)), s(x))
  , cond(tt(), x) -> f(x) }
Obligation:
  innermost runtime complexity
Answer:
  MAYBE

We replace rewrite rules by usable rules:

  Weak Usable Rules:
    { isList(nil()) -> tt()
    , isList(Cons(x, xs)) -> isList(xs)
    , downfrom(0()) -> nil()
    , downfrom(s(x)) -> Cons(s(x), downfrom(x)) }

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

Strict DPs:
  { isList^#(Cons(x, xs)) -> c_2(isList^#(xs))
  , downfrom^#(s(x)) -> c_4(downfrom^#(x))
  , f^#(x) ->
    c_5(cond^#(isList(downfrom(x)), s(x)),
        isList^#(downfrom(x)),
        downfrom^#(x))
  , cond^#(tt(), x) -> c_6(f^#(x)) }
Weak Trs:
  { isList(nil()) -> tt()
  , isList(Cons(x, xs)) -> isList(xs)
  , downfrom(0()) -> nil()
  , downfrom(s(x)) -> Cons(s(x), downfrom(x)) }
Obligation:
  innermost runtime complexity
Answer:
  MAYBE

The input cannot be shown compatible

Arrrr..