MAYBE

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

Strict Trs:
  { cond(true(), x, y) -> cond(gr(x, y), p(x), y)
  , gr(0(), x) -> false()
  , gr(s(x), 0()) -> true()
  , gr(s(x), s(y)) -> gr(x, y)
  , p(0()) -> 0()
  , p(s(x)) -> x }
Obligation:
  innermost runtime complexity
Answer:
  MAYBE

We add following dependency tuples:

Strict DPs:
  { cond^#(true(), x, y) ->
    c_1(cond^#(gr(x, y), p(x), y), gr^#(x, y), p^#(x))
  , gr^#(0(), x) -> c_2()
  , gr^#(s(x), 0()) -> c_3()
  , gr^#(s(x), s(y)) -> c_4(gr^#(x, y))
  , p^#(0()) -> c_5()
  , p^#(s(x)) -> c_6() }

and mark the set of starting terms.

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

Strict DPs:
  { cond^#(true(), x, y) ->
    c_1(cond^#(gr(x, y), p(x), y), gr^#(x, y), p^#(x))
  , gr^#(0(), x) -> c_2()
  , gr^#(s(x), 0()) -> c_3()
  , gr^#(s(x), s(y)) -> c_4(gr^#(x, y))
  , p^#(0()) -> c_5()
  , p^#(s(x)) -> c_6() }
Weak Trs:
  { cond(true(), x, y) -> cond(gr(x, y), p(x), y)
  , gr(0(), x) -> false()
  , gr(s(x), 0()) -> true()
  , gr(s(x), s(y)) -> gr(x, y)
  , p(0()) -> 0()
  , p(s(x)) -> x }
Obligation:
  innermost runtime complexity
Answer:
  MAYBE

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

  DPs:
    { 1: cond^#(true(), x, y) ->
         c_1(cond^#(gr(x, y), p(x), y), gr^#(x, y), p^#(x))
    , 2: gr^#(0(), x) -> c_2()
    , 3: gr^#(s(x), 0()) -> c_3()
    , 4: gr^#(s(x), s(y)) -> c_4(gr^#(x, y))
    , 5: p^#(0()) -> c_5()
    , 6: p^#(s(x)) -> c_6() }

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

Strict DPs:
  { cond^#(true(), x, y) ->
    c_1(cond^#(gr(x, y), p(x), y), gr^#(x, y), p^#(x))
  , gr^#(s(x), s(y)) -> c_4(gr^#(x, y)) }
Weak DPs:
  { gr^#(0(), x) -> c_2()
  , gr^#(s(x), 0()) -> c_3()
  , p^#(0()) -> c_5()
  , p^#(s(x)) -> c_6() }
Weak Trs:
  { cond(true(), x, y) -> cond(gr(x, y), p(x), y)
  , gr(0(), x) -> false()
  , gr(s(x), 0()) -> true()
  , gr(s(x), s(y)) -> gr(x, y)
  , p(0()) -> 0()
  , p(s(x)) -> 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.

{ gr^#(0(), x) -> c_2()
, gr^#(s(x), 0()) -> c_3()
, p^#(0()) -> c_5()
, p^#(s(x)) -> c_6() }

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

Strict DPs:
  { cond^#(true(), x, y) ->
    c_1(cond^#(gr(x, y), p(x), y), gr^#(x, y), p^#(x))
  , gr^#(s(x), s(y)) -> c_4(gr^#(x, y)) }
Weak Trs:
  { cond(true(), x, y) -> cond(gr(x, y), p(x), y)
  , gr(0(), x) -> false()
  , gr(s(x), 0()) -> true()
  , gr(s(x), s(y)) -> gr(x, y)
  , p(0()) -> 0()
  , p(s(x)) -> x }
Obligation:
  innermost runtime complexity
Answer:
  MAYBE

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

  { cond^#(true(), x, y) ->
    c_1(cond^#(gr(x, y), p(x), y), gr^#(x, y), p^#(x)) }

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

Strict DPs:
  { cond^#(true(), x, y) ->
    c_1(cond^#(gr(x, y), p(x), y), gr^#(x, y))
  , gr^#(s(x), s(y)) -> c_2(gr^#(x, y)) }
Weak Trs:
  { cond(true(), x, y) -> cond(gr(x, y), p(x), y)
  , gr(0(), x) -> false()
  , gr(s(x), 0()) -> true()
  , gr(s(x), s(y)) -> gr(x, y)
  , p(0()) -> 0()
  , p(s(x)) -> x }
Obligation:
  innermost runtime complexity
Answer:
  MAYBE

We replace rewrite rules by usable rules:

  Weak Usable Rules:
    { gr(0(), x) -> false()
    , gr(s(x), 0()) -> true()
    , gr(s(x), s(y)) -> gr(x, y)
    , p(0()) -> 0()
    , p(s(x)) -> x }

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

Strict DPs:
  { cond^#(true(), x, y) ->
    c_1(cond^#(gr(x, y), p(x), y), gr^#(x, y))
  , gr^#(s(x), s(y)) -> c_2(gr^#(x, y)) }
Weak Trs:
  { gr(0(), x) -> false()
  , gr(s(x), 0()) -> true()
  , gr(s(x), s(y)) -> gr(x, y)
  , p(0()) -> 0()
  , p(s(x)) -> x }
Obligation:
  innermost runtime complexity
Answer:
  MAYBE

The input cannot be shown compatible

Arrrr..