MAYBE

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

Strict Trs:
  { f(0(), 1(), X) -> h(X, X)
  , h(0(), X) -> f(0(), X, X)
  , g(X, Y) -> X
  , g(X, Y) -> Y }
Obligation:
  innermost runtime complexity
Answer:
  MAYBE

We add following weak dependency pairs:

Strict DPs:
  { f^#(0(), 1(), X) -> c_1(h^#(X, X))
  , h^#(0(), X) -> c_2(f^#(0(), X, X))
  , g^#(X, Y) -> c_3()
  , g^#(X, Y) -> c_4() }

and mark the set of starting terms.

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

Strict DPs:
  { f^#(0(), 1(), X) -> c_1(h^#(X, X))
  , h^#(0(), X) -> c_2(f^#(0(), X, X))
  , g^#(X, Y) -> c_3()
  , g^#(X, Y) -> c_4() }
Strict Trs:
  { f(0(), 1(), X) -> h(X, X)
  , h(0(), X) -> f(0(), X, X)
  , g(X, Y) -> X
  , g(X, Y) -> Y }
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^#(0(), 1(), X) -> c_1(h^#(X, X))
  , h^#(0(), X) -> c_2(f^#(0(), X, X))
  , g^#(X, Y) -> c_3()
  , g^#(X, Y) -> c_4() }
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}, Uargs(c_2) = {1}

TcT has computed following constructor-restricted matrix
interpretation.

                [0] = [2]                  
                                           
                [1] = [2]                  
                                           
  [f^#](x1, x2, x3) = [1] x1 + [1] x3 + [2]
                                           
          [c_1](x1) = [1] x1 + [1]         
                                           
      [h^#](x1, x2) = [1] x2 + [2]         
                                           
          [c_2](x1) = [1] x1 + [2]         
                                           
      [g^#](x1, x2) = [2]                  
                                           
              [c_3] = [1]                  
                                           
              [c_4] = [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: { h^#(0(), X) -> c_2(f^#(0(), X, X)) }
Weak DPs:
  { f^#(0(), 1(), X) -> c_1(h^#(X, X))
  , g^#(X, Y) -> c_3()
  , g^#(X, Y) -> c_4() }
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.

{ g^#(X, Y) -> c_3()
, g^#(X, Y) -> c_4() }

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

Strict DPs: { h^#(0(), X) -> c_2(f^#(0(), X, X)) }
Weak DPs: { f^#(0(), 1(), X) -> c_1(h^#(X, X)) }
Obligation:
  innermost runtime complexity
Answer:
  MAYBE

The input cannot be shown compatible

Arrrr..