MAYBE

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

Strict Trs:
  { and(tt(), X) -> activate(X)
  , activate(X) -> X
  , plus(N, 0()) -> N
  , plus(N, s(M)) -> s(plus(N, M))
  , x(N, 0()) -> 0()
  , x(N, s(M)) -> plus(x(N, M), N) }
Obligation:
  innermost runtime complexity
Answer:
  MAYBE

We add following dependency tuples:

Strict DPs:
  { and^#(tt(), X) -> c_1(activate^#(X))
  , activate^#(X) -> c_2()
  , plus^#(N, 0()) -> c_3()
  , plus^#(N, s(M)) -> c_4(plus^#(N, M))
  , x^#(N, 0()) -> c_5()
  , x^#(N, s(M)) -> c_6(plus^#(x(N, M), N), x^#(N, M)) }

and mark the set of starting terms.

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

Strict DPs:
  { and^#(tt(), X) -> c_1(activate^#(X))
  , activate^#(X) -> c_2()
  , plus^#(N, 0()) -> c_3()
  , plus^#(N, s(M)) -> c_4(plus^#(N, M))
  , x^#(N, 0()) -> c_5()
  , x^#(N, s(M)) -> c_6(plus^#(x(N, M), N), x^#(N, M)) }
Weak Trs:
  { and(tt(), X) -> activate(X)
  , activate(X) -> X
  , plus(N, 0()) -> N
  , plus(N, s(M)) -> s(plus(N, M))
  , x(N, 0()) -> 0()
  , x(N, s(M)) -> plus(x(N, M), N) }
Obligation:
  innermost runtime complexity
Answer:
  MAYBE

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

  DPs:
    { 1: and^#(tt(), X) -> c_1(activate^#(X))
    , 2: activate^#(X) -> c_2()
    , 3: plus^#(N, 0()) -> c_3()
    , 4: plus^#(N, s(M)) -> c_4(plus^#(N, M))
    , 5: x^#(N, 0()) -> c_5()
    , 6: x^#(N, s(M)) -> c_6(plus^#(x(N, M), N), x^#(N, M)) }

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

Strict DPs:
  { and^#(tt(), X) -> c_1(activate^#(X))
  , plus^#(N, s(M)) -> c_4(plus^#(N, M))
  , x^#(N, s(M)) -> c_6(plus^#(x(N, M), N), x^#(N, M)) }
Weak DPs:
  { activate^#(X) -> c_2()
  , plus^#(N, 0()) -> c_3()
  , x^#(N, 0()) -> c_5() }
Weak Trs:
  { and(tt(), X) -> activate(X)
  , activate(X) -> X
  , plus(N, 0()) -> N
  , plus(N, s(M)) -> s(plus(N, M))
  , x(N, 0()) -> 0()
  , x(N, s(M)) -> plus(x(N, M), N) }
Obligation:
  innermost runtime complexity
Answer:
  MAYBE

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

  DPs:
    { 1: and^#(tt(), X) -> c_1(activate^#(X))
    , 2: plus^#(N, s(M)) -> c_4(plus^#(N, M))
    , 3: x^#(N, s(M)) -> c_6(plus^#(x(N, M), N), x^#(N, M))
    , 4: activate^#(X) -> c_2()
    , 5: plus^#(N, 0()) -> c_3()
    , 6: x^#(N, 0()) -> c_5() }

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

Strict DPs:
  { plus^#(N, s(M)) -> c_4(plus^#(N, M))
  , x^#(N, s(M)) -> c_6(plus^#(x(N, M), N), x^#(N, M)) }
Weak DPs:
  { and^#(tt(), X) -> c_1(activate^#(X))
  , activate^#(X) -> c_2()
  , plus^#(N, 0()) -> c_3()
  , x^#(N, 0()) -> c_5() }
Weak Trs:
  { and(tt(), X) -> activate(X)
  , activate(X) -> X
  , plus(N, 0()) -> N
  , plus(N, s(M)) -> s(plus(N, M))
  , x(N, 0()) -> 0()
  , x(N, s(M)) -> plus(x(N, M), N) }
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.

{ and^#(tt(), X) -> c_1(activate^#(X))
, activate^#(X) -> c_2()
, plus^#(N, 0()) -> c_3()
, x^#(N, 0()) -> c_5() }

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

Strict DPs:
  { plus^#(N, s(M)) -> c_4(plus^#(N, M))
  , x^#(N, s(M)) -> c_6(plus^#(x(N, M), N), x^#(N, M)) }
Weak Trs:
  { and(tt(), X) -> activate(X)
  , activate(X) -> X
  , plus(N, 0()) -> N
  , plus(N, s(M)) -> s(plus(N, M))
  , x(N, 0()) -> 0()
  , x(N, s(M)) -> plus(x(N, M), N) }
Obligation:
  innermost runtime complexity
Answer:
  MAYBE

We replace rewrite rules by usable rules:

  Weak Usable Rules:
    { plus(N, 0()) -> N
    , plus(N, s(M)) -> s(plus(N, M))
    , x(N, 0()) -> 0()
    , x(N, s(M)) -> plus(x(N, M), N) }

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

Strict DPs:
  { plus^#(N, s(M)) -> c_4(plus^#(N, M))
  , x^#(N, s(M)) -> c_6(plus^#(x(N, M), N), x^#(N, M)) }
Weak Trs:
  { plus(N, 0()) -> N
  , plus(N, s(M)) -> s(plus(N, M))
  , x(N, 0()) -> 0()
  , x(N, s(M)) -> plus(x(N, M), N) }
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..