MAYBE

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

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

We add following weak dependency pairs:

Strict DPs:
  { bin^#(x, 0()) -> c_1()
  , bin^#(0(), s(y)) -> c_2()
  , bin^#(s(x), s(y)) -> c_3(bin^#(x, s(y)), bin^#(x, y)) }

and mark the set of starting terms.

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

Strict DPs:
  { bin^#(x, 0()) -> c_1()
  , bin^#(0(), s(y)) -> c_2()
  , bin^#(s(x), s(y)) -> c_3(bin^#(x, s(y)), bin^#(x, y)) }
Strict Trs:
  { bin(x, 0()) -> s(0())
  , bin(0(), s(y)) -> 0()
  , bin(s(x), s(y)) -> +(bin(x, s(y)), bin(x, 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:
  { bin^#(x, 0()) -> c_1()
  , bin^#(0(), s(y)) -> c_2()
  , bin^#(s(x), s(y)) -> c_3(bin^#(x, s(y)), bin^#(x, y)) }
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_3) = {1, 2}

TcT has computed following constructor-restricted matrix
interpretation.

              [0] = [1]                  
                                         
          [s](x1) = [1] x1 + [1]         
                                         
  [bin^#](x1, x2) = [1]                  
                                         
            [c_1] = [0]                  
                                         
            [c_2] = [0]                  
                                         
    [c_3](x1, x2) = [1] x1 + [1] x2 + [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:
  { bin^#(s(x), s(y)) -> c_3(bin^#(x, s(y)), bin^#(x, y)) }
Weak DPs:
  { bin^#(x, 0()) -> c_1()
  , bin^#(0(), s(y)) -> c_2() }
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.

{ bin^#(x, 0()) -> c_1()
, bin^#(0(), s(y)) -> c_2() }

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

Strict DPs:
  { bin^#(s(x), s(y)) -> c_3(bin^#(x, s(y)), bin^#(x, y)) }
Obligation:
  innermost runtime complexity
Answer:
  MAYBE

The input cannot be shown compatible

Arrrr..