MAYBE

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

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

We add following dependency tuples:

Strict DPs:
  { minus^#(x, 0()) -> c_1()
  , minus^#(s(x), s(y)) -> c_2(minus^#(x, y))
  , double^#(0()) -> c_3()
  , double^#(s(x)) -> c_4(double^#(x))
  , plus^#(0(), y) -> c_5()
  , plus^#(s(x), y) -> c_6(plus^#(x, y))
  , plus^#(s(x), y) ->
    c_7(plus^#(minus(x, y), double(y)), minus^#(x, y), double^#(y))
  , plus^#(s(x), y) -> c_8(plus^#(x, s(y))) }

and mark the set of starting terms.

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

Strict DPs:
  { minus^#(x, 0()) -> c_1()
  , minus^#(s(x), s(y)) -> c_2(minus^#(x, y))
  , double^#(0()) -> c_3()
  , double^#(s(x)) -> c_4(double^#(x))
  , plus^#(0(), y) -> c_5()
  , plus^#(s(x), y) -> c_6(plus^#(x, y))
  , plus^#(s(x), y) ->
    c_7(plus^#(minus(x, y), double(y)), minus^#(x, y), double^#(y))
  , plus^#(s(x), y) -> c_8(plus^#(x, s(y))) }
Weak Trs:
  { minus(x, 0()) -> x
  , minus(s(x), s(y)) -> minus(x, y)
  , double(0()) -> 0()
  , double(s(x)) -> s(s(double(x)))
  , plus(0(), y) -> y
  , plus(s(x), y) -> s(plus(x, y))
  , plus(s(x), y) -> s(plus(minus(x, y), double(y)))
  , plus(s(x), y) -> plus(x, s(y)) }
Obligation:
  innermost runtime complexity
Answer:
  MAYBE

We estimate the number of application of {1,3,5} by applications of
Pre({1,3,5}) = {2,4,6,7,8}. Here rules are labeled as follows:

  DPs:
    { 1: minus^#(x, 0()) -> c_1()
    , 2: minus^#(s(x), s(y)) -> c_2(minus^#(x, y))
    , 3: double^#(0()) -> c_3()
    , 4: double^#(s(x)) -> c_4(double^#(x))
    , 5: plus^#(0(), y) -> c_5()
    , 6: plus^#(s(x), y) -> c_6(plus^#(x, y))
    , 7: plus^#(s(x), y) ->
         c_7(plus^#(minus(x, y), double(y)), minus^#(x, y), double^#(y))
    , 8: plus^#(s(x), y) -> c_8(plus^#(x, s(y))) }

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

Strict DPs:
  { minus^#(s(x), s(y)) -> c_2(minus^#(x, y))
  , double^#(s(x)) -> c_4(double^#(x))
  , plus^#(s(x), y) -> c_6(plus^#(x, y))
  , plus^#(s(x), y) ->
    c_7(plus^#(minus(x, y), double(y)), minus^#(x, y), double^#(y))
  , plus^#(s(x), y) -> c_8(plus^#(x, s(y))) }
Weak DPs:
  { minus^#(x, 0()) -> c_1()
  , double^#(0()) -> c_3()
  , plus^#(0(), y) -> c_5() }
Weak Trs:
  { minus(x, 0()) -> x
  , minus(s(x), s(y)) -> minus(x, y)
  , double(0()) -> 0()
  , double(s(x)) -> s(s(double(x)))
  , plus(0(), y) -> y
  , plus(s(x), y) -> s(plus(x, y))
  , plus(s(x), y) -> s(plus(minus(x, y), double(y)))
  , plus(s(x), y) -> plus(x, s(y)) }
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.

{ minus^#(x, 0()) -> c_1()
, double^#(0()) -> c_3()
, plus^#(0(), y) -> c_5() }

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

Strict DPs:
  { minus^#(s(x), s(y)) -> c_2(minus^#(x, y))
  , double^#(s(x)) -> c_4(double^#(x))
  , plus^#(s(x), y) -> c_6(plus^#(x, y))
  , plus^#(s(x), y) ->
    c_7(plus^#(minus(x, y), double(y)), minus^#(x, y), double^#(y))
  , plus^#(s(x), y) -> c_8(plus^#(x, s(y))) }
Weak Trs:
  { minus(x, 0()) -> x
  , minus(s(x), s(y)) -> minus(x, y)
  , double(0()) -> 0()
  , double(s(x)) -> s(s(double(x)))
  , plus(0(), y) -> y
  , plus(s(x), y) -> s(plus(x, y))
  , plus(s(x), y) -> s(plus(minus(x, y), double(y)))
  , plus(s(x), y) -> plus(x, s(y)) }
Obligation:
  innermost runtime complexity
Answer:
  MAYBE

We replace rewrite rules by usable rules:

  Weak Usable Rules:
    { minus(x, 0()) -> x
    , minus(s(x), s(y)) -> minus(x, y)
    , double(0()) -> 0()
    , double(s(x)) -> s(s(double(x))) }

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

Strict DPs:
  { minus^#(s(x), s(y)) -> c_2(minus^#(x, y))
  , double^#(s(x)) -> c_4(double^#(x))
  , plus^#(s(x), y) -> c_6(plus^#(x, y))
  , plus^#(s(x), y) ->
    c_7(plus^#(minus(x, y), double(y)), minus^#(x, y), double^#(y))
  , plus^#(s(x), y) -> c_8(plus^#(x, s(y))) }
Weak Trs:
  { minus(x, 0()) -> x
  , minus(s(x), s(y)) -> minus(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..