MAYBE

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

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

We add following dependency tuples:

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

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

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

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

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

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), y, x), gr^#(x, y))
  , gr^#(s(x), s(y)) -> c_4(gr^#(x, y)) }
Weak Trs:
  { cond(true(), x, y) -> cond(gr(x, y), y, x)
  , gr(0(), x) -> false()
  , gr(s(x), 0()) -> true()
  , gr(s(x), s(y)) -> gr(x, y) }
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) }

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), y, x), gr^#(x, y))
  , gr^#(s(x), s(y)) -> c_4(gr^#(x, y)) }
Weak Trs:
  { gr(0(), x) -> false()
  , gr(s(x), 0()) -> true()
  , gr(s(x), s(y)) -> gr(x, y) }
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..