MAYBE

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

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

We add following weak dependency pairs:

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

and mark the set of starting terms.

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

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

TcT has computed following constructor-restricted matrix
interpretation.

                   [0] = [2]         
                                     
               [s](x1) = [1] x1 + [0]
                                     
  [quot^#](x1, x2, x3) = [2] x1 + [0]
                                     
             [c_1](x1) = [1] x1 + [1]
                                     
                 [c_2] = [1]         
                                     
             [c_3](x1) = [1] x1 + [2]

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:
  { quot^#(x, 0(), s(z)) -> c_1(quot^#(x, s(z), s(z)))
  , quot^#(s(x), s(y), z) -> c_3(quot^#(x, y, z)) }
Weak DPs: { quot^#(0(), s(y), s(z)) -> 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.

{ quot^#(0(), s(y), s(z)) -> c_2() }

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

Strict DPs:
  { quot^#(x, 0(), s(z)) -> c_1(quot^#(x, s(z), s(z)))
  , quot^#(s(x), s(y), z) -> c_3(quot^#(x, y, z)) }
Obligation:
  innermost runtime complexity
Answer:
  MAYBE

The input cannot be shown compatible

Arrrr..