MAYBE

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

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

We add following dependency tuples:

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

{ odd^#(0()) -> c_2()
, odd^#(s(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) -> c_1(cond^#(odd(x), p(x)), odd^#(x), p^#(x))
  , odd^#(s(s(x))) -> c_4(odd^#(x)) }
Weak Trs:
  { cond(true(), x) -> cond(odd(x), p(x))
  , odd(0()) -> false()
  , odd(s(0())) -> true()
  , odd(s(s(x))) -> odd(x)
  , 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) ->
    c_1(cond^#(odd(x), p(x)), odd^#(x), p^#(x)) }

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

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

We replace rewrite rules by usable rules:

  Weak Usable Rules:
    { odd(0()) -> false()
    , odd(s(0())) -> true()
    , odd(s(s(x))) -> odd(x)
    , 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) -> c_1(cond^#(odd(x), p(x)), odd^#(x))
  , odd^#(s(s(x))) -> c_2(odd^#(x)) }
Weak Trs:
  { odd(0()) -> false()
  , odd(s(0())) -> true()
  , odd(s(s(x))) -> odd(x)
  , p(0()) -> 0()
  , p(s(x)) -> x }
Obligation:
  innermost runtime complexity
Answer:
  MAYBE

None of the processors succeeded.

Details of failed attempt(s):
-----------------------------
1) 'matrices' failed due to the following reason:
   
   None of the processors succeeded.
   
   Details of failed attempt(s):
   -----------------------------
   1) 'matrix interpretation of dimension 4' failed due to the
      following reason:
      
      The input cannot be shown compatible
   
   2) 'matrix interpretation of dimension 3' failed due to the
      following reason:
      
      The input cannot be shown compatible
   
   3) 'matrix interpretation of dimension 3' failed due to the
      following reason:
      
      The input cannot be shown compatible
   
   4) 'matrix interpretation of dimension 2' failed due to the
      following reason:
      
      The input cannot be shown compatible
   
   5) 'matrix interpretation of dimension 2' failed due to the
      following reason:
      
      The input cannot be shown compatible
   
   6) 'matrix interpretation of dimension 1' failed due to the
      following reason:
      
      The input cannot be shown compatible
   

2) 'empty' failed due to the following reason:
   
   Empty strict component of the problem is NOT empty.


Arrrr..