MAYBE

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

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

We add following dependency tuples:

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

and mark the set of starting terms.

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

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

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

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

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

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

{ b^#(c(x1)) -> c_1() }

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

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

We replace rewrite rules by usable rules:

  Weak Usable Rules:
    { b(c(x1)) -> d(c(x1))
    , b(d(x1)) -> d(b(x1)) }

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

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

The input cannot be shown compatible

Arrrr..