MAYBE

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

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

We add following dependency tuples:

Strict DPs:
  { plus^#(x, 0()) -> c_1()
  , plus^#(x, s(y)) -> c_2(plus^#(x, y))
  , d^#(0()) -> c_3()
  , d^#(s(x)) -> c_4(d^#(x))
  , q^#(0()) -> c_5()
  , q^#(s(x)) -> c_6(plus^#(q(x), d(x)), q^#(x), d^#(x)) }

and mark the set of starting terms.

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

Strict DPs:
  { plus^#(x, 0()) -> c_1()
  , plus^#(x, s(y)) -> c_2(plus^#(x, y))
  , d^#(0()) -> c_3()
  , d^#(s(x)) -> c_4(d^#(x))
  , q^#(0()) -> c_5()
  , q^#(s(x)) -> c_6(plus^#(q(x), d(x)), q^#(x), d^#(x)) }
Weak Trs:
  { plus(x, 0()) -> x
  , plus(x, s(y)) -> s(plus(x, y))
  , d(0()) -> 0()
  , d(s(x)) -> s(s(d(x)))
  , q(0()) -> 0()
  , q(s(x)) -> s(plus(q(x), d(x))) }
Obligation:
  innermost runtime complexity
Answer:
  MAYBE

We estimate the number of application of {1,3,5} by applications of
Pre({1,3,5}) = {2,4,6}. Here rules are labeled as follows:

  DPs:
    { 1: plus^#(x, 0()) -> c_1()
    , 2: plus^#(x, s(y)) -> c_2(plus^#(x, y))
    , 3: d^#(0()) -> c_3()
    , 4: d^#(s(x)) -> c_4(d^#(x))
    , 5: q^#(0()) -> c_5()
    , 6: q^#(s(x)) -> c_6(plus^#(q(x), d(x)), q^#(x), d^#(x)) }

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

Strict DPs:
  { plus^#(x, s(y)) -> c_2(plus^#(x, y))
  , d^#(s(x)) -> c_4(d^#(x))
  , q^#(s(x)) -> c_6(plus^#(q(x), d(x)), q^#(x), d^#(x)) }
Weak DPs:
  { plus^#(x, 0()) -> c_1()
  , d^#(0()) -> c_3()
  , q^#(0()) -> c_5() }
Weak Trs:
  { plus(x, 0()) -> x
  , plus(x, s(y)) -> s(plus(x, y))
  , d(0()) -> 0()
  , d(s(x)) -> s(s(d(x)))
  , q(0()) -> 0()
  , q(s(x)) -> s(plus(q(x), d(x))) }
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.

{ plus^#(x, 0()) -> c_1()
, d^#(0()) -> c_3()
, q^#(0()) -> c_5() }

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

Strict DPs:
  { plus^#(x, s(y)) -> c_2(plus^#(x, y))
  , d^#(s(x)) -> c_4(d^#(x))
  , q^#(s(x)) -> c_6(plus^#(q(x), d(x)), q^#(x), d^#(x)) }
Weak Trs:
  { plus(x, 0()) -> x
  , plus(x, s(y)) -> s(plus(x, y))
  , d(0()) -> 0()
  , d(s(x)) -> s(s(d(x)))
  , q(0()) -> 0()
  , q(s(x)) -> s(plus(q(x), d(x))) }
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..