MAYBE

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

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

We add following dependency tuples:

Strict DPs:
  { add^#(0(), x) -> c_1()
  , add^#(s(x), y) -> c_2(add^#(x, y))
  , mult^#(0(), x) -> c_3()
  , mult^#(s(x), y) -> c_4(add^#(y, mult(x, y)), mult^#(x, y)) }

and mark the set of starting terms.

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

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

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

  DPs:
    { 1: add^#(0(), x) -> c_1()
    , 2: add^#(s(x), y) -> c_2(add^#(x, y))
    , 3: mult^#(0(), x) -> c_3()
    , 4: mult^#(s(x), y) -> c_4(add^#(y, mult(x, y)), mult^#(x, y)) }

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

Strict DPs:
  { add^#(s(x), y) -> c_2(add^#(x, y))
  , mult^#(s(x), y) -> c_4(add^#(y, mult(x, y)), mult^#(x, y)) }
Weak DPs:
  { add^#(0(), x) -> c_1()
  , mult^#(0(), x) -> c_3() }
Weak Trs:
  { add(0(), x) -> x
  , add(s(x), y) -> s(add(x, y))
  , mult(0(), x) -> 0()
  , mult(s(x), y) -> add(y, mult(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.

{ add^#(0(), x) -> c_1()
, mult^#(0(), x) -> c_3() }

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

Strict DPs:
  { add^#(s(x), y) -> c_2(add^#(x, y))
  , mult^#(s(x), y) -> c_4(add^#(y, mult(x, y)), mult^#(x, y)) }
Weak Trs:
  { add(0(), x) -> x
  , add(s(x), y) -> s(add(x, y))
  , mult(0(), x) -> 0()
  , mult(s(x), y) -> add(y, mult(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..