MAYBE

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

Strict Trs:
  { not(true()) -> false()
  , not(false()) -> true()
  , evenodd(x, 0()) -> not(evenodd(x, s(0())))
  , evenodd(0(), s(0())) -> false()
  , evenodd(s(x), s(0())) -> evenodd(x, 0()) }
Obligation:
  innermost runtime complexity
Answer:
  MAYBE

We add following dependency tuples:

Strict DPs:
  { not^#(true()) -> c_1()
  , not^#(false()) -> c_2()
  , evenodd^#(x, 0()) ->
    c_3(not^#(evenodd(x, s(0()))), evenodd^#(x, s(0())))
  , evenodd^#(0(), s(0())) -> c_4()
  , evenodd^#(s(x), s(0())) -> c_5(evenodd^#(x, 0())) }

and mark the set of starting terms.

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

Strict DPs:
  { not^#(true()) -> c_1()
  , not^#(false()) -> c_2()
  , evenodd^#(x, 0()) ->
    c_3(not^#(evenodd(x, s(0()))), evenodd^#(x, s(0())))
  , evenodd^#(0(), s(0())) -> c_4()
  , evenodd^#(s(x), s(0())) -> c_5(evenodd^#(x, 0())) }
Weak Trs:
  { not(true()) -> false()
  , not(false()) -> true()
  , evenodd(x, 0()) -> not(evenodd(x, s(0())))
  , evenodd(0(), s(0())) -> false()
  , evenodd(s(x), s(0())) -> evenodd(x, 0()) }
Obligation:
  innermost runtime complexity
Answer:
  MAYBE

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

  DPs:
    { 1: not^#(true()) -> c_1()
    , 2: not^#(false()) -> c_2()
    , 3: evenodd^#(x, 0()) ->
         c_3(not^#(evenodd(x, s(0()))), evenodd^#(x, s(0())))
    , 4: evenodd^#(0(), s(0())) -> c_4()
    , 5: evenodd^#(s(x), s(0())) -> c_5(evenodd^#(x, 0())) }

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

Strict DPs:
  { evenodd^#(x, 0()) ->
    c_3(not^#(evenodd(x, s(0()))), evenodd^#(x, s(0())))
  , evenodd^#(s(x), s(0())) -> c_5(evenodd^#(x, 0())) }
Weak DPs:
  { not^#(true()) -> c_1()
  , not^#(false()) -> c_2()
  , evenodd^#(0(), s(0())) -> c_4() }
Weak Trs:
  { not(true()) -> false()
  , not(false()) -> true()
  , evenodd(x, 0()) -> not(evenodd(x, s(0())))
  , evenodd(0(), s(0())) -> false()
  , evenodd(s(x), s(0())) -> evenodd(x, 0()) }
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.

{ not^#(true()) -> c_1()
, not^#(false()) -> c_2()
, evenodd^#(0(), s(0())) -> c_4() }

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

Strict DPs:
  { evenodd^#(x, 0()) ->
    c_3(not^#(evenodd(x, s(0()))), evenodd^#(x, s(0())))
  , evenodd^#(s(x), s(0())) -> c_5(evenodd^#(x, 0())) }
Weak Trs:
  { not(true()) -> false()
  , not(false()) -> true()
  , evenodd(x, 0()) -> not(evenodd(x, s(0())))
  , evenodd(0(), s(0())) -> false()
  , evenodd(s(x), s(0())) -> evenodd(x, 0()) }
Obligation:
  innermost runtime complexity
Answer:
  MAYBE

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

  { evenodd^#(x, 0()) ->
    c_3(not^#(evenodd(x, s(0()))), evenodd^#(x, s(0()))) }

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

Strict DPs:
  { evenodd^#(x, 0()) -> c_1(evenodd^#(x, s(0())))
  , evenodd^#(s(x), s(0())) -> c_2(evenodd^#(x, 0())) }
Weak Trs:
  { not(true()) -> false()
  , not(false()) -> true()
  , evenodd(x, 0()) -> not(evenodd(x, s(0())))
  , evenodd(0(), s(0())) -> false()
  , evenodd(s(x), s(0())) -> evenodd(x, 0()) }
Obligation:
  innermost runtime complexity
Answer:
  MAYBE

No rule is usable, rules are removed from the input problem.

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

Strict DPs:
  { evenodd^#(x, 0()) -> c_1(evenodd^#(x, s(0())))
  , evenodd^#(s(x), s(0())) -> c_2(evenodd^#(x, 0())) }
Obligation:
  innermost runtime complexity
Answer:
  MAYBE

The input cannot be shown compatible

Arrrr..