MAYBE

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

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

We add following dependency tuples:

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

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

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

{ minus^#(x, 0()) -> c_1()
, f^#(0()) -> c_3()
, g^#(0()) -> c_5() }

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

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

The input cannot be shown compatible

Arrrr..