MAYBE

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

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

We add following dependency tuples:

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

and mark the set of starting terms.

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

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

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

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

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

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

{ exp^#(x, 0()) -> c_1()
, *^#(0(), y) -> c_3()
, -^#(x, 0()) -> c_5()
, -^#(0(), y) -> c_6() }

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

Strict DPs:
  { exp^#(x, s(y)) -> c_2(*^#(x, exp(x, y)), exp^#(x, y))
  , *^#(s(x), y) -> c_4(*^#(x, y))
  , -^#(s(x), s(y)) -> c_7(-^#(x, y)) }
Weak Trs:
  { exp(x, 0()) -> s(0())
  , exp(x, s(y)) -> *(x, exp(x, y))
  , *(0(), y) -> 0()
  , *(s(x), y) -> +(y, *(x, y))
  , -(x, 0()) -> x
  , -(0(), y) -> 0()
  , -(s(x), s(y)) -> -(x, y) }
Obligation:
  innermost runtime complexity
Answer:
  MAYBE

We replace rewrite rules by usable rules:

  Weak Usable Rules:
    { exp(x, 0()) -> s(0())
    , exp(x, s(y)) -> *(x, exp(x, y))
    , *(0(), y) -> 0()
    , *(s(x), y) -> +(y, *(x, y)) }

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

Strict DPs:
  { exp^#(x, s(y)) -> c_2(*^#(x, exp(x, y)), exp^#(x, y))
  , *^#(s(x), y) -> c_4(*^#(x, y))
  , -^#(s(x), s(y)) -> c_7(-^#(x, y)) }
Weak Trs:
  { exp(x, 0()) -> s(0())
  , exp(x, s(y)) -> *(x, exp(x, y))
  , *(0(), y) -> 0()
  , *(s(x), y) -> +(y, *(x, y)) }
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..