MAYBE

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

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

We add following dependency tuples:

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

and mark the set of starting terms.

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

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

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

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

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

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

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

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

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

The input cannot be shown compatible

Arrrr..