MAYBE

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

Strict Trs:
  { f(a(), g(y)) -> g(g(y))
  , f(g(x), a()) -> f(x, g(a()))
  , f(g(x), g(y)) -> h(g(y), x, g(y))
  , h(a(), y, z) -> z
  , h(g(x), y, z) -> f(y, h(x, y, z)) }
Obligation:
  innermost runtime complexity
Answer:
  MAYBE

We add following dependency tuples:

Strict DPs:
  { f^#(a(), g(y)) -> c_1()
  , f^#(g(x), a()) -> c_2(f^#(x, g(a())))
  , f^#(g(x), g(y)) -> c_3(h^#(g(y), x, g(y)))
  , h^#(a(), y, z) -> c_4()
  , h^#(g(x), y, z) -> c_5(f^#(y, h(x, y, z)), h^#(x, y, z)) }

and mark the set of starting terms.

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

Strict DPs:
  { f^#(a(), g(y)) -> c_1()
  , f^#(g(x), a()) -> c_2(f^#(x, g(a())))
  , f^#(g(x), g(y)) -> c_3(h^#(g(y), x, g(y)))
  , h^#(a(), y, z) -> c_4()
  , h^#(g(x), y, z) -> c_5(f^#(y, h(x, y, z)), h^#(x, y, z)) }
Weak Trs:
  { f(a(), g(y)) -> g(g(y))
  , f(g(x), a()) -> f(x, g(a()))
  , f(g(x), g(y)) -> h(g(y), x, g(y))
  , h(a(), y, z) -> z
  , h(g(x), y, z) -> f(y, h(x, y, z)) }
Obligation:
  innermost runtime complexity
Answer:
  MAYBE

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

  DPs:
    { 1: f^#(a(), g(y)) -> c_1()
    , 2: f^#(g(x), a()) -> c_2(f^#(x, g(a())))
    , 3: f^#(g(x), g(y)) -> c_3(h^#(g(y), x, g(y)))
    , 4: h^#(a(), y, z) -> c_4()
    , 5: h^#(g(x), y, z) -> c_5(f^#(y, h(x, y, z)), h^#(x, y, z)) }

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

Strict DPs:
  { f^#(g(x), a()) -> c_2(f^#(x, g(a())))
  , f^#(g(x), g(y)) -> c_3(h^#(g(y), x, g(y)))
  , h^#(g(x), y, z) -> c_5(f^#(y, h(x, y, z)), h^#(x, y, z)) }
Weak DPs:
  { f^#(a(), g(y)) -> c_1()
  , h^#(a(), y, z) -> c_4() }
Weak Trs:
  { f(a(), g(y)) -> g(g(y))
  , f(g(x), a()) -> f(x, g(a()))
  , f(g(x), g(y)) -> h(g(y), x, g(y))
  , h(a(), y, z) -> z
  , h(g(x), y, z) -> f(y, h(x, y, z)) }
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.

{ f^#(a(), g(y)) -> c_1()
, h^#(a(), y, z) -> c_4() }

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

Strict DPs:
  { f^#(g(x), a()) -> c_2(f^#(x, g(a())))
  , f^#(g(x), g(y)) -> c_3(h^#(g(y), x, g(y)))
  , h^#(g(x), y, z) -> c_5(f^#(y, h(x, y, z)), h^#(x, y, z)) }
Weak Trs:
  { f(a(), g(y)) -> g(g(y))
  , f(g(x), a()) -> f(x, g(a()))
  , f(g(x), g(y)) -> h(g(y), x, g(y))
  , h(a(), y, z) -> z
  , h(g(x), y, z) -> f(y, h(x, y, z)) }
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..