MAYBE

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

Strict Trs:
  { div(x, y) -> quot(x, y, y)
  , div(0(), y) -> 0()
  , quot(x, 0(), s(z)) -> s(div(x, s(z)))
  , quot(0(), s(y), 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:
  { div^#(x, y) -> c_1(quot^#(x, y, y))
  , div^#(0(), y) -> c_2()
  , quot^#(x, 0(), s(z)) -> c_3(div^#(x, s(z)))
  , quot^#(0(), s(y), z) -> c_4()
  , quot^#(s(x), s(y), z) -> c_5(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:
  { div^#(x, y) -> c_1(quot^#(x, y, y))
  , div^#(0(), y) -> c_2()
  , quot^#(x, 0(), s(z)) -> c_3(div^#(x, s(z)))
  , quot^#(0(), s(y), z) -> c_4()
  , quot^#(s(x), s(y), z) -> c_5(quot^#(x, y, z)) }
Strict Trs:
  { div(x, y) -> quot(x, y, y)
  , div(0(), y) -> 0()
  , quot(x, 0(), s(z)) -> s(div(x, s(z)))
  , quot(0(), s(y), 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:
  { div^#(x, y) -> c_1(quot^#(x, y, y))
  , div^#(0(), y) -> c_2()
  , quot^#(x, 0(), s(z)) -> c_3(div^#(x, s(z)))
  , quot^#(0(), s(y), z) -> c_4()
  , quot^#(s(x), s(y), z) -> c_5(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}, Uargs(c_5) = {1}

TcT has computed following constructor-restricted matrix
interpretation.

                   [0] = [0]         
                                     
               [s](x1) = [0]         
                                     
       [div^#](x1, x2) = [1]         
                                     
             [c_1](x1) = [1] x1 + [2]
                                     
  [quot^#](x1, x2, x3) = [0]         
                                     
                 [c_2] = [0]         
                                     
             [c_3](x1) = [1] x1 + [0]
                                     
                 [c_4] = [1]         
                                     
             [c_5](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:
  { div^#(x, y) -> c_1(quot^#(x, y, y))
  , quot^#(x, 0(), s(z)) -> c_3(div^#(x, s(z)))
  , quot^#(0(), s(y), z) -> c_4()
  , quot^#(s(x), s(y), z) -> c_5(quot^#(x, y, z)) }
Weak DPs: { div^#(0(), y) -> c_2() }
Obligation:
  innermost runtime complexity
Answer:
  MAYBE

We estimate the number of application of {3} by applications of
Pre({3}) = {1,4}. Here rules are labeled as follows:

  DPs:
    { 1: div^#(x, y) -> c_1(quot^#(x, y, y))
    , 2: quot^#(x, 0(), s(z)) -> c_3(div^#(x, s(z)))
    , 3: quot^#(0(), s(y), z) -> c_4()
    , 4: quot^#(s(x), s(y), z) -> c_5(quot^#(x, y, z))
    , 5: div^#(0(), y) -> c_2() }

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

Strict DPs:
  { div^#(x, y) -> c_1(quot^#(x, y, y))
  , quot^#(x, 0(), s(z)) -> c_3(div^#(x, s(z)))
  , quot^#(s(x), s(y), z) -> c_5(quot^#(x, y, z)) }
Weak DPs:
  { div^#(0(), y) -> c_2()
  , quot^#(0(), s(y), z) -> 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.

{ div^#(0(), y) -> c_2()
, quot^#(0(), s(y), z) -> c_4() }

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

Strict DPs:
  { div^#(x, y) -> c_1(quot^#(x, y, y))
  , quot^#(x, 0(), s(z)) -> c_3(div^#(x, s(z)))
  , quot^#(s(x), s(y), z) -> c_5(quot^#(x, y, z)) }
Obligation:
  innermost runtime complexity
Answer:
  MAYBE

None of the processors succeeded.

Details of failed attempt(s):
-----------------------------
1) 'matrices' failed due to the following reason:
   
   None of the processors succeeded.
   
   Details of failed attempt(s):
   -----------------------------
   1) 'matrix interpretation of dimension 4' failed due to the
      following reason:
      
      The input cannot be shown compatible
   
   2) 'matrix interpretation of dimension 3' failed due to the
      following reason:
      
      The input cannot be shown compatible
   
   3) 'matrix interpretation of dimension 3' failed due to the
      following reason:
      
      The input cannot be shown compatible
   
   4) 'matrix interpretation of dimension 2' failed due to the
      following reason:
      
      The input cannot be shown compatible
   
   5) 'matrix interpretation of dimension 2' failed due to the
      following reason:
      
      The input cannot be shown compatible
   
   6) 'matrix interpretation of dimension 1' failed due to the
      following reason:
      
      The input cannot be shown compatible
   

2) 'empty' failed due to the following reason:
   
   Empty strict component of the problem is NOT empty.


Arrrr..