MAYBE

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

Strict Trs:
  { a(x1) -> x1
  , a(b(b(x1))) -> b(b(b(c(x1))))
  , c(b(x1)) -> a(a(x1)) }
Obligation:
  innermost runtime complexity
Answer:
  MAYBE

We add following dependency tuples:

Strict DPs:
  { a^#(x1) -> c_1()
  , a^#(b(b(x1))) -> c_2(c^#(x1))
  , c^#(b(x1)) -> c_3(a^#(a(x1)), a^#(x1)) }

and mark the set of starting terms.

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

Strict DPs:
  { a^#(x1) -> c_1()
  , a^#(b(b(x1))) -> c_2(c^#(x1))
  , c^#(b(x1)) -> c_3(a^#(a(x1)), a^#(x1)) }
Weak Trs:
  { a(x1) -> x1
  , a(b(b(x1))) -> b(b(b(c(x1))))
  , c(b(x1)) -> a(a(x1)) }
Obligation:
  innermost runtime complexity
Answer:
  MAYBE

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

  DPs:
    { 1: a^#(x1) -> c_1()
    , 2: a^#(b(b(x1))) -> c_2(c^#(x1))
    , 3: c^#(b(x1)) -> c_3(a^#(a(x1)), a^#(x1)) }

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

Strict DPs:
  { a^#(b(b(x1))) -> c_2(c^#(x1))
  , c^#(b(x1)) -> c_3(a^#(a(x1)), a^#(x1)) }
Weak DPs: { a^#(x1) -> c_1() }
Weak Trs:
  { a(x1) -> x1
  , a(b(b(x1))) -> b(b(b(c(x1))))
  , c(b(x1)) -> a(a(x1)) }
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.

{ a^#(x1) -> c_1() }

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

Strict DPs:
  { a^#(b(b(x1))) -> c_2(c^#(x1))
  , c^#(b(x1)) -> c_3(a^#(a(x1)), a^#(x1)) }
Weak Trs:
  { a(x1) -> x1
  , a(b(b(x1))) -> b(b(b(c(x1))))
  , c(b(x1)) -> a(a(x1)) }
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..