MAYBE

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

Strict Trs:
  { g(X) -> h(X)
  , h(d()) -> g(c())
  , c() -> d() }
Obligation:
  innermost runtime complexity
Answer:
  MAYBE

We add following weak dependency pairs:

Strict DPs:
  { g^#(X) -> c_1(h^#(X))
  , h^#(d()) -> c_2(g^#(c()))
  , c^#() -> c_3() }

and mark the set of starting terms.

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

Strict DPs:
  { g^#(X) -> c_1(h^#(X))
  , h^#(d()) -> c_2(g^#(c()))
  , c^#() -> c_3() }
Strict Trs:
  { g(X) -> h(X)
  , h(d()) -> g(c())
  , c() -> d() }
Obligation:
  innermost runtime complexity
Answer:
  MAYBE

We replace rewrite rules by usable rules:

  Strict Usable Rules: { c() -> d() }

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

Strict DPs:
  { g^#(X) -> c_1(h^#(X))
  , h^#(d()) -> c_2(g^#(c()))
  , c^#() -> c_3() }
Strict Trs: { c() -> d() }
Obligation:
  innermost runtime complexity
Answer:
  MAYBE

The weightgap principle applies (using the following constant
growth matrix-interpretation)

The following argument positions are usable:
  Uargs(g^#) = {1}, Uargs(c_1) = {1}, Uargs(c_2) = {1}

TcT has computed following constructor-restricted matrix
interpretation.

        [c] = [2]         
                          
        [d] = [1]         
                          
  [g^#](x1) = [1] x1 + [1]
                          
  [c_1](x1) = [1] x1 + [2]
                          
  [h^#](x1) = [1] x1 + [1]
                          
  [c_2](x1) = [1] x1 + [1]
                          
      [c^#] = [1]         
                          
      [c_3] = [1]         

This order satisfies following ordering constraints:

  [c()] = [2]  
        > [1]  
        = [d()]
               

Further, it can be verified that all rules not oriented are covered by the weightgap condition.

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

Strict DPs:
  { g^#(X) -> c_1(h^#(X))
  , h^#(d()) -> c_2(g^#(c()))
  , c^#() -> c_3() }
Weak Trs: { c() -> d() }
Obligation:
  innermost runtime complexity
Answer:
  MAYBE

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

  DPs:
    { 1: g^#(X) -> c_1(h^#(X))
    , 2: h^#(d()) -> c_2(g^#(c()))
    , 3: c^#() -> c_3() }

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

Strict DPs:
  { g^#(X) -> c_1(h^#(X))
  , h^#(d()) -> c_2(g^#(c())) }
Weak DPs: { c^#() -> c_3() }
Weak Trs: { c() -> d() }
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.

{ c^#() -> c_3() }

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

Strict DPs:
  { g^#(X) -> c_1(h^#(X))
  , h^#(d()) -> c_2(g^#(c())) }
Weak Trs: { c() -> d() }
Obligation:
  innermost runtime complexity
Answer:
  MAYBE

The input cannot be shown compatible

Arrrr..