MAYBE

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

Strict Trs:
  { -(x, 0()) -> x
  , -(0(), s(y)) -> 0()
  , -(s(x), s(y)) -> -(x, y)
  , f(0()) -> 0()
  , f(s(x)) -> -(s(x), g(f(x)))
  , g(0()) -> s(0())
  , g(s(x)) -> -(s(x), f(g(x))) }
Obligation:
  innermost runtime complexity
Answer:
  MAYBE

We add following dependency tuples:

Strict DPs:
  { -^#(x, 0()) -> c_1()
  , -^#(0(), s(y)) -> c_2()
  , -^#(s(x), s(y)) -> c_3(-^#(x, y))
  , f^#(0()) -> c_4()
  , f^#(s(x)) -> c_5(-^#(s(x), g(f(x))), g^#(f(x)), f^#(x))
  , g^#(0()) -> c_6()
  , g^#(s(x)) -> c_7(-^#(s(x), f(g(x))), f^#(g(x)), g^#(x)) }

and mark the set of starting terms.

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

Strict DPs:
  { -^#(x, 0()) -> c_1()
  , -^#(0(), s(y)) -> c_2()
  , -^#(s(x), s(y)) -> c_3(-^#(x, y))
  , f^#(0()) -> c_4()
  , f^#(s(x)) -> c_5(-^#(s(x), g(f(x))), g^#(f(x)), f^#(x))
  , g^#(0()) -> c_6()
  , g^#(s(x)) -> c_7(-^#(s(x), f(g(x))), f^#(g(x)), g^#(x)) }
Weak Trs:
  { -(x, 0()) -> x
  , -(0(), s(y)) -> 0()
  , -(s(x), s(y)) -> -(x, y)
  , f(0()) -> 0()
  , f(s(x)) -> -(s(x), g(f(x)))
  , g(0()) -> s(0())
  , g(s(x)) -> -(s(x), f(g(x))) }
Obligation:
  innermost runtime complexity
Answer:
  MAYBE

We estimate the number of application of {1,2,4,6} by applications
of Pre({1,2,4,6}) = {3,5,7}. Here rules are labeled as follows:

  DPs:
    { 1: -^#(x, 0()) -> c_1()
    , 2: -^#(0(), s(y)) -> c_2()
    , 3: -^#(s(x), s(y)) -> c_3(-^#(x, y))
    , 4: f^#(0()) -> c_4()
    , 5: f^#(s(x)) -> c_5(-^#(s(x), g(f(x))), g^#(f(x)), f^#(x))
    , 6: g^#(0()) -> c_6()
    , 7: g^#(s(x)) -> c_7(-^#(s(x), f(g(x))), f^#(g(x)), g^#(x)) }

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

Strict DPs:
  { -^#(s(x), s(y)) -> c_3(-^#(x, y))
  , f^#(s(x)) -> c_5(-^#(s(x), g(f(x))), g^#(f(x)), f^#(x))
  , g^#(s(x)) -> c_7(-^#(s(x), f(g(x))), f^#(g(x)), g^#(x)) }
Weak DPs:
  { -^#(x, 0()) -> c_1()
  , -^#(0(), s(y)) -> c_2()
  , f^#(0()) -> c_4()
  , g^#(0()) -> c_6() }
Weak Trs:
  { -(x, 0()) -> x
  , -(0(), s(y)) -> 0()
  , -(s(x), s(y)) -> -(x, y)
  , f(0()) -> 0()
  , f(s(x)) -> -(s(x), g(f(x)))
  , g(0()) -> s(0())
  , g(s(x)) -> -(s(x), f(g(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.

{ -^#(x, 0()) -> c_1()
, -^#(0(), s(y)) -> c_2()
, f^#(0()) -> c_4()
, g^#(0()) -> c_6() }

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

Strict DPs:
  { -^#(s(x), s(y)) -> c_3(-^#(x, y))
  , f^#(s(x)) -> c_5(-^#(s(x), g(f(x))), g^#(f(x)), f^#(x))
  , g^#(s(x)) -> c_7(-^#(s(x), f(g(x))), f^#(g(x)), g^#(x)) }
Weak Trs:
  { -(x, 0()) -> x
  , -(0(), s(y)) -> 0()
  , -(s(x), s(y)) -> -(x, y)
  , f(0()) -> 0()
  , f(s(x)) -> -(s(x), g(f(x)))
  , g(0()) -> s(0())
  , g(s(x)) -> -(s(x), f(g(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..