MAYBE

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

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

We add following dependency tuples:

Strict DPs:
  { sqr^#(0()) -> c_1()
  , sqr^#(s(x)) -> c_2(+^#(sqr(x), double(x)), sqr^#(x), double^#(x))
  , sqr^#(s(x)) ->
    c_3(+^#(sqr(x), s(double(x))), sqr^#(x), double^#(x))
  , +^#(x, 0()) -> c_4()
  , +^#(x, s(y)) -> c_5(+^#(x, y))
  , double^#(0()) -> c_6()
  , double^#(s(x)) -> c_7(double^#(x)) }

and mark the set of starting terms.

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

Strict DPs:
  { sqr^#(0()) -> c_1()
  , sqr^#(s(x)) -> c_2(+^#(sqr(x), double(x)), sqr^#(x), double^#(x))
  , sqr^#(s(x)) ->
    c_3(+^#(sqr(x), s(double(x))), sqr^#(x), double^#(x))
  , +^#(x, 0()) -> c_4()
  , +^#(x, s(y)) -> c_5(+^#(x, y))
  , double^#(0()) -> c_6()
  , double^#(s(x)) -> c_7(double^#(x)) }
Weak Trs:
  { sqr(0()) -> 0()
  , sqr(s(x)) -> s(+(sqr(x), double(x)))
  , sqr(s(x)) -> +(sqr(x), s(double(x)))
  , +(x, 0()) -> x
  , +(x, s(y)) -> s(+(x, y))
  , double(0()) -> 0()
  , double(s(x)) -> s(s(double(x))) }
Obligation:
  innermost runtime complexity
Answer:
  MAYBE

We estimate the number of application of {1,4,6} by applications of
Pre({1,4,6}) = {2,3,5,7}. Here rules are labeled as follows:

  DPs:
    { 1: sqr^#(0()) -> c_1()
    , 2: sqr^#(s(x)) ->
         c_2(+^#(sqr(x), double(x)), sqr^#(x), double^#(x))
    , 3: sqr^#(s(x)) ->
         c_3(+^#(sqr(x), s(double(x))), sqr^#(x), double^#(x))
    , 4: +^#(x, 0()) -> c_4()
    , 5: +^#(x, s(y)) -> c_5(+^#(x, y))
    , 6: double^#(0()) -> c_6()
    , 7: double^#(s(x)) -> c_7(double^#(x)) }

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

Strict DPs:
  { sqr^#(s(x)) -> c_2(+^#(sqr(x), double(x)), sqr^#(x), double^#(x))
  , sqr^#(s(x)) ->
    c_3(+^#(sqr(x), s(double(x))), sqr^#(x), double^#(x))
  , +^#(x, s(y)) -> c_5(+^#(x, y))
  , double^#(s(x)) -> c_7(double^#(x)) }
Weak DPs:
  { sqr^#(0()) -> c_1()
  , +^#(x, 0()) -> c_4()
  , double^#(0()) -> c_6() }
Weak Trs:
  { sqr(0()) -> 0()
  , sqr(s(x)) -> s(+(sqr(x), double(x)))
  , sqr(s(x)) -> +(sqr(x), s(double(x)))
  , +(x, 0()) -> x
  , +(x, s(y)) -> s(+(x, y))
  , double(0()) -> 0()
  , double(s(x)) -> s(s(double(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.

{ sqr^#(0()) -> c_1()
, +^#(x, 0()) -> c_4()
, double^#(0()) -> c_6() }

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

Strict DPs:
  { sqr^#(s(x)) -> c_2(+^#(sqr(x), double(x)), sqr^#(x), double^#(x))
  , sqr^#(s(x)) ->
    c_3(+^#(sqr(x), s(double(x))), sqr^#(x), double^#(x))
  , +^#(x, s(y)) -> c_5(+^#(x, y))
  , double^#(s(x)) -> c_7(double^#(x)) }
Weak Trs:
  { sqr(0()) -> 0()
  , sqr(s(x)) -> s(+(sqr(x), double(x)))
  , sqr(s(x)) -> +(sqr(x), s(double(x)))
  , +(x, 0()) -> x
  , +(x, s(y)) -> s(+(x, y))
  , double(0()) -> 0()
  , double(s(x)) -> s(s(double(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..