MAYBE

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

Strict Trs:
  { f(a(), X) -> f(X, X)
  , c() -> a()
  , c() -> b() }
Obligation:
  innermost runtime complexity
Answer:
  MAYBE

We add following weak dependency pairs:

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

No rule is usable, rules are removed from the input problem.

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

Strict DPs:
  { f^#(a(), X) -> c_1(f^#(X, X))
  , c^#() -> c_2()
  , c^#() -> c_3() }
Obligation:
  innermost runtime complexity
Answer:
  MAYBE

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

The following argument positions are usable:
  Uargs(c_1) = {1}

TcT has computed following constructor-restricted matrix
interpretation.

            [a] = [1]         
                              
  [f^#](x1, x2) = [1] x2 + [2]
                              
      [c_1](x1) = [1] x1 + [1]
                              
          [c^#] = [2]         
                              
          [c_2] = [1]         
                              
          [c_3] = [1]         

This order satisfies following ordering constraints:


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: { f^#(a(), X) -> c_1(f^#(X, X)) }
Weak DPs:
  { c^#() -> c_2()
  , c^#() -> c_3() }
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_2()
, c^#() -> c_3() }

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

Strict DPs: { f^#(a(), X) -> c_1(f^#(X, X)) }
Obligation:
  innermost runtime complexity
Answer:
  MAYBE

The input cannot be shown compatible

Arrrr..