MAYBE

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

Strict Trs:
  { a__a() -> a__c()
  , a__a() -> a__d()
  , a__a() -> a()
  , a__c() -> e()
  , a__c() -> l()
  , a__c() -> c()
  , a__b() -> a__c()
  , a__b() -> a__d()
  , a__b() -> b()
  , a__k() -> l()
  , a__k() -> m()
  , a__k() -> k()
  , a__d() -> m()
  , a__d() -> d()
  , a__A() -> a__h(a__f(a__a()), a__f(a__b()))
  , a__A() -> A()
  , a__h(X, X) -> a__g(mark(X), mark(X), a__f(a__k()))
  , a__h(X1, X2) -> h(X1, X2)
  , a__f(X) -> a__z(mark(X), X)
  , a__f(X) -> f(X)
  , a__g(X1, X2, X3) -> g(X1, X2, X3)
  , a__g(d(), X, X) -> a__A()
  , mark(e()) -> e()
  , mark(l()) -> l()
  , mark(m()) -> m()
  , mark(d()) -> a__d()
  , mark(A()) -> a__A()
  , mark(a()) -> a__a()
  , mark(b()) -> a__b()
  , mark(c()) -> a__c()
  , mark(k()) -> a__k()
  , mark(z(X1, X2)) -> a__z(mark(X1), X2)
  , mark(f(X)) -> a__f(mark(X))
  , mark(h(X1, X2)) -> a__h(mark(X1), mark(X2))
  , mark(g(X1, X2, X3)) -> a__g(mark(X1), mark(X2), mark(X3))
  , a__z(X1, X2) -> z(X1, X2)
  , a__z(e(), X) -> mark(X) }
Obligation:
  innermost runtime complexity
Answer:
  MAYBE

We add following dependency tuples:

Strict DPs:
  { a__a^#() -> c_1(a__c^#())
  , a__a^#() -> c_2(a__d^#())
  , a__a^#() -> c_3()
  , a__c^#() -> c_4()
  , a__c^#() -> c_5()
  , a__c^#() -> c_6()
  , a__d^#() -> c_13()
  , a__d^#() -> c_14()
  , a__b^#() -> c_7(a__c^#())
  , a__b^#() -> c_8(a__d^#())
  , a__b^#() -> c_9()
  , a__k^#() -> c_10()
  , a__k^#() -> c_11()
  , a__k^#() -> c_12()
  , a__A^#() ->
    c_15(a__h^#(a__f(a__a()), a__f(a__b())),
         a__f^#(a__a()),
         a__a^#(),
         a__f^#(a__b()),
         a__b^#())
  , a__A^#() -> c_16()
  , a__h^#(X, X) ->
    c_17(a__g^#(mark(X), mark(X), a__f(a__k())),
         mark^#(X),
         mark^#(X),
         a__f^#(a__k()),
         a__k^#())
  , a__h^#(X1, X2) -> c_18()
  , a__f^#(X) -> c_19(a__z^#(mark(X), X), mark^#(X))
  , a__f^#(X) -> c_20()
  , a__g^#(X1, X2, X3) -> c_21()
  , a__g^#(d(), X, X) -> c_22(a__A^#())
  , mark^#(e()) -> c_23()
  , mark^#(l()) -> c_24()
  , mark^#(m()) -> c_25()
  , mark^#(d()) -> c_26(a__d^#())
  , mark^#(A()) -> c_27(a__A^#())
  , mark^#(a()) -> c_28(a__a^#())
  , mark^#(b()) -> c_29(a__b^#())
  , mark^#(c()) -> c_30(a__c^#())
  , mark^#(k()) -> c_31(a__k^#())
  , mark^#(z(X1, X2)) -> c_32(a__z^#(mark(X1), X2), mark^#(X1))
  , mark^#(f(X)) -> c_33(a__f^#(mark(X)), mark^#(X))
  , mark^#(h(X1, X2)) ->
    c_34(a__h^#(mark(X1), mark(X2)), mark^#(X1), mark^#(X2))
  , mark^#(g(X1, X2, X3)) ->
    c_35(a__g^#(mark(X1), mark(X2), mark(X3)),
         mark^#(X1),
         mark^#(X2),
         mark^#(X3))
  , a__z^#(X1, X2) -> c_36()
  , a__z^#(e(), X) -> c_37(mark^#(X)) }

and mark the set of starting terms.

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

Strict DPs:
  { a__a^#() -> c_1(a__c^#())
  , a__a^#() -> c_2(a__d^#())
  , a__a^#() -> c_3()
  , a__c^#() -> c_4()
  , a__c^#() -> c_5()
  , a__c^#() -> c_6()
  , a__d^#() -> c_13()
  , a__d^#() -> c_14()
  , a__b^#() -> c_7(a__c^#())
  , a__b^#() -> c_8(a__d^#())
  , a__b^#() -> c_9()
  , a__k^#() -> c_10()
  , a__k^#() -> c_11()
  , a__k^#() -> c_12()
  , a__A^#() ->
    c_15(a__h^#(a__f(a__a()), a__f(a__b())),
         a__f^#(a__a()),
         a__a^#(),
         a__f^#(a__b()),
         a__b^#())
  , a__A^#() -> c_16()
  , a__h^#(X, X) ->
    c_17(a__g^#(mark(X), mark(X), a__f(a__k())),
         mark^#(X),
         mark^#(X),
         a__f^#(a__k()),
         a__k^#())
  , a__h^#(X1, X2) -> c_18()
  , a__f^#(X) -> c_19(a__z^#(mark(X), X), mark^#(X))
  , a__f^#(X) -> c_20()
  , a__g^#(X1, X2, X3) -> c_21()
  , a__g^#(d(), X, X) -> c_22(a__A^#())
  , mark^#(e()) -> c_23()
  , mark^#(l()) -> c_24()
  , mark^#(m()) -> c_25()
  , mark^#(d()) -> c_26(a__d^#())
  , mark^#(A()) -> c_27(a__A^#())
  , mark^#(a()) -> c_28(a__a^#())
  , mark^#(b()) -> c_29(a__b^#())
  , mark^#(c()) -> c_30(a__c^#())
  , mark^#(k()) -> c_31(a__k^#())
  , mark^#(z(X1, X2)) -> c_32(a__z^#(mark(X1), X2), mark^#(X1))
  , mark^#(f(X)) -> c_33(a__f^#(mark(X)), mark^#(X))
  , mark^#(h(X1, X2)) ->
    c_34(a__h^#(mark(X1), mark(X2)), mark^#(X1), mark^#(X2))
  , mark^#(g(X1, X2, X3)) ->
    c_35(a__g^#(mark(X1), mark(X2), mark(X3)),
         mark^#(X1),
         mark^#(X2),
         mark^#(X3))
  , a__z^#(X1, X2) -> c_36()
  , a__z^#(e(), X) -> c_37(mark^#(X)) }
Weak Trs:
  { a__a() -> a__c()
  , a__a() -> a__d()
  , a__a() -> a()
  , a__c() -> e()
  , a__c() -> l()
  , a__c() -> c()
  , a__b() -> a__c()
  , a__b() -> a__d()
  , a__b() -> b()
  , a__k() -> l()
  , a__k() -> m()
  , a__k() -> k()
  , a__d() -> m()
  , a__d() -> d()
  , a__A() -> a__h(a__f(a__a()), a__f(a__b()))
  , a__A() -> A()
  , a__h(X, X) -> a__g(mark(X), mark(X), a__f(a__k()))
  , a__h(X1, X2) -> h(X1, X2)
  , a__f(X) -> a__z(mark(X), X)
  , a__f(X) -> f(X)
  , a__g(X1, X2, X3) -> g(X1, X2, X3)
  , a__g(d(), X, X) -> a__A()
  , mark(e()) -> e()
  , mark(l()) -> l()
  , mark(m()) -> m()
  , mark(d()) -> a__d()
  , mark(A()) -> a__A()
  , mark(a()) -> a__a()
  , mark(b()) -> a__b()
  , mark(c()) -> a__c()
  , mark(k()) -> a__k()
  , mark(z(X1, X2)) -> a__z(mark(X1), X2)
  , mark(f(X)) -> a__f(mark(X))
  , mark(h(X1, X2)) -> a__h(mark(X1), mark(X2))
  , mark(g(X1, X2, X3)) -> a__g(mark(X1), mark(X2), mark(X3))
  , a__z(X1, X2) -> z(X1, X2)
  , a__z(e(), X) -> mark(X) }
Obligation:
  innermost runtime complexity
Answer:
  MAYBE

We estimate the number of application of
{3,4,5,6,7,8,11,12,13,14,16,18,20,21,23,24,25,36} by applications
of Pre({3,4,5,6,7,8,11,12,13,14,16,18,20,21,23,24,25,36}) =
{1,2,9,10,15,17,19,22,26,27,28,29,30,31,32,33,34,35,37}. Here rules
are labeled as follows:

  DPs:
    { 1: a__a^#() -> c_1(a__c^#())
    , 2: a__a^#() -> c_2(a__d^#())
    , 3: a__a^#() -> c_3()
    , 4: a__c^#() -> c_4()
    , 5: a__c^#() -> c_5()
    , 6: a__c^#() -> c_6()
    , 7: a__d^#() -> c_13()
    , 8: a__d^#() -> c_14()
    , 9: a__b^#() -> c_7(a__c^#())
    , 10: a__b^#() -> c_8(a__d^#())
    , 11: a__b^#() -> c_9()
    , 12: a__k^#() -> c_10()
    , 13: a__k^#() -> c_11()
    , 14: a__k^#() -> c_12()
    , 15: a__A^#() ->
          c_15(a__h^#(a__f(a__a()), a__f(a__b())),
               a__f^#(a__a()),
               a__a^#(),
               a__f^#(a__b()),
               a__b^#())
    , 16: a__A^#() -> c_16()
    , 17: a__h^#(X, X) ->
          c_17(a__g^#(mark(X), mark(X), a__f(a__k())),
               mark^#(X),
               mark^#(X),
               a__f^#(a__k()),
               a__k^#())
    , 18: a__h^#(X1, X2) -> c_18()
    , 19: a__f^#(X) -> c_19(a__z^#(mark(X), X), mark^#(X))
    , 20: a__f^#(X) -> c_20()
    , 21: a__g^#(X1, X2, X3) -> c_21()
    , 22: a__g^#(d(), X, X) -> c_22(a__A^#())
    , 23: mark^#(e()) -> c_23()
    , 24: mark^#(l()) -> c_24()
    , 25: mark^#(m()) -> c_25()
    , 26: mark^#(d()) -> c_26(a__d^#())
    , 27: mark^#(A()) -> c_27(a__A^#())
    , 28: mark^#(a()) -> c_28(a__a^#())
    , 29: mark^#(b()) -> c_29(a__b^#())
    , 30: mark^#(c()) -> c_30(a__c^#())
    , 31: mark^#(k()) -> c_31(a__k^#())
    , 32: mark^#(z(X1, X2)) -> c_32(a__z^#(mark(X1), X2), mark^#(X1))
    , 33: mark^#(f(X)) -> c_33(a__f^#(mark(X)), mark^#(X))
    , 34: mark^#(h(X1, X2)) ->
          c_34(a__h^#(mark(X1), mark(X2)), mark^#(X1), mark^#(X2))
    , 35: mark^#(g(X1, X2, X3)) ->
          c_35(a__g^#(mark(X1), mark(X2), mark(X3)),
               mark^#(X1),
               mark^#(X2),
               mark^#(X3))
    , 36: a__z^#(X1, X2) -> c_36()
    , 37: a__z^#(e(), X) -> c_37(mark^#(X)) }

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

Strict DPs:
  { a__a^#() -> c_1(a__c^#())
  , a__a^#() -> c_2(a__d^#())
  , a__b^#() -> c_7(a__c^#())
  , a__b^#() -> c_8(a__d^#())
  , a__A^#() ->
    c_15(a__h^#(a__f(a__a()), a__f(a__b())),
         a__f^#(a__a()),
         a__a^#(),
         a__f^#(a__b()),
         a__b^#())
  , a__h^#(X, X) ->
    c_17(a__g^#(mark(X), mark(X), a__f(a__k())),
         mark^#(X),
         mark^#(X),
         a__f^#(a__k()),
         a__k^#())
  , a__f^#(X) -> c_19(a__z^#(mark(X), X), mark^#(X))
  , a__g^#(d(), X, X) -> c_22(a__A^#())
  , mark^#(d()) -> c_26(a__d^#())
  , mark^#(A()) -> c_27(a__A^#())
  , mark^#(a()) -> c_28(a__a^#())
  , mark^#(b()) -> c_29(a__b^#())
  , mark^#(c()) -> c_30(a__c^#())
  , mark^#(k()) -> c_31(a__k^#())
  , mark^#(z(X1, X2)) -> c_32(a__z^#(mark(X1), X2), mark^#(X1))
  , mark^#(f(X)) -> c_33(a__f^#(mark(X)), mark^#(X))
  , mark^#(h(X1, X2)) ->
    c_34(a__h^#(mark(X1), mark(X2)), mark^#(X1), mark^#(X2))
  , mark^#(g(X1, X2, X3)) ->
    c_35(a__g^#(mark(X1), mark(X2), mark(X3)),
         mark^#(X1),
         mark^#(X2),
         mark^#(X3))
  , a__z^#(e(), X) -> c_37(mark^#(X)) }
Weak DPs:
  { a__a^#() -> c_3()
  , a__c^#() -> c_4()
  , a__c^#() -> c_5()
  , a__c^#() -> c_6()
  , a__d^#() -> c_13()
  , a__d^#() -> c_14()
  , a__b^#() -> c_9()
  , a__k^#() -> c_10()
  , a__k^#() -> c_11()
  , a__k^#() -> c_12()
  , a__A^#() -> c_16()
  , a__h^#(X1, X2) -> c_18()
  , a__f^#(X) -> c_20()
  , a__g^#(X1, X2, X3) -> c_21()
  , mark^#(e()) -> c_23()
  , mark^#(l()) -> c_24()
  , mark^#(m()) -> c_25()
  , a__z^#(X1, X2) -> c_36() }
Weak Trs:
  { a__a() -> a__c()
  , a__a() -> a__d()
  , a__a() -> a()
  , a__c() -> e()
  , a__c() -> l()
  , a__c() -> c()
  , a__b() -> a__c()
  , a__b() -> a__d()
  , a__b() -> b()
  , a__k() -> l()
  , a__k() -> m()
  , a__k() -> k()
  , a__d() -> m()
  , a__d() -> d()
  , a__A() -> a__h(a__f(a__a()), a__f(a__b()))
  , a__A() -> A()
  , a__h(X, X) -> a__g(mark(X), mark(X), a__f(a__k()))
  , a__h(X1, X2) -> h(X1, X2)
  , a__f(X) -> a__z(mark(X), X)
  , a__f(X) -> f(X)
  , a__g(X1, X2, X3) -> g(X1, X2, X3)
  , a__g(d(), X, X) -> a__A()
  , mark(e()) -> e()
  , mark(l()) -> l()
  , mark(m()) -> m()
  , mark(d()) -> a__d()
  , mark(A()) -> a__A()
  , mark(a()) -> a__a()
  , mark(b()) -> a__b()
  , mark(c()) -> a__c()
  , mark(k()) -> a__k()
  , mark(z(X1, X2)) -> a__z(mark(X1), X2)
  , mark(f(X)) -> a__f(mark(X))
  , mark(h(X1, X2)) -> a__h(mark(X1), mark(X2))
  , mark(g(X1, X2, X3)) -> a__g(mark(X1), mark(X2), mark(X3))
  , a__z(X1, X2) -> z(X1, X2)
  , a__z(e(), X) -> mark(X) }
Obligation:
  innermost runtime complexity
Answer:
  MAYBE

We estimate the number of application of {1,2,3,4,9,13,14} by
applications of Pre({1,2,3,4,9,13,14}) =
{5,6,7,11,12,15,16,17,18,19}. Here rules are labeled as follows:

  DPs:
    { 1: a__a^#() -> c_1(a__c^#())
    , 2: a__a^#() -> c_2(a__d^#())
    , 3: a__b^#() -> c_7(a__c^#())
    , 4: a__b^#() -> c_8(a__d^#())
    , 5: a__A^#() ->
         c_15(a__h^#(a__f(a__a()), a__f(a__b())),
              a__f^#(a__a()),
              a__a^#(),
              a__f^#(a__b()),
              a__b^#())
    , 6: a__h^#(X, X) ->
         c_17(a__g^#(mark(X), mark(X), a__f(a__k())),
              mark^#(X),
              mark^#(X),
              a__f^#(a__k()),
              a__k^#())
    , 7: a__f^#(X) -> c_19(a__z^#(mark(X), X), mark^#(X))
    , 8: a__g^#(d(), X, X) -> c_22(a__A^#())
    , 9: mark^#(d()) -> c_26(a__d^#())
    , 10: mark^#(A()) -> c_27(a__A^#())
    , 11: mark^#(a()) -> c_28(a__a^#())
    , 12: mark^#(b()) -> c_29(a__b^#())
    , 13: mark^#(c()) -> c_30(a__c^#())
    , 14: mark^#(k()) -> c_31(a__k^#())
    , 15: mark^#(z(X1, X2)) -> c_32(a__z^#(mark(X1), X2), mark^#(X1))
    , 16: mark^#(f(X)) -> c_33(a__f^#(mark(X)), mark^#(X))
    , 17: mark^#(h(X1, X2)) ->
          c_34(a__h^#(mark(X1), mark(X2)), mark^#(X1), mark^#(X2))
    , 18: mark^#(g(X1, X2, X3)) ->
          c_35(a__g^#(mark(X1), mark(X2), mark(X3)),
               mark^#(X1),
               mark^#(X2),
               mark^#(X3))
    , 19: a__z^#(e(), X) -> c_37(mark^#(X))
    , 20: a__a^#() -> c_3()
    , 21: a__c^#() -> c_4()
    , 22: a__c^#() -> c_5()
    , 23: a__c^#() -> c_6()
    , 24: a__d^#() -> c_13()
    , 25: a__d^#() -> c_14()
    , 26: a__b^#() -> c_9()
    , 27: a__k^#() -> c_10()
    , 28: a__k^#() -> c_11()
    , 29: a__k^#() -> c_12()
    , 30: a__A^#() -> c_16()
    , 31: a__h^#(X1, X2) -> c_18()
    , 32: a__f^#(X) -> c_20()
    , 33: a__g^#(X1, X2, X3) -> c_21()
    , 34: mark^#(e()) -> c_23()
    , 35: mark^#(l()) -> c_24()
    , 36: mark^#(m()) -> c_25()
    , 37: a__z^#(X1, X2) -> c_36() }

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

Strict DPs:
  { a__A^#() ->
    c_15(a__h^#(a__f(a__a()), a__f(a__b())),
         a__f^#(a__a()),
         a__a^#(),
         a__f^#(a__b()),
         a__b^#())
  , a__h^#(X, X) ->
    c_17(a__g^#(mark(X), mark(X), a__f(a__k())),
         mark^#(X),
         mark^#(X),
         a__f^#(a__k()),
         a__k^#())
  , a__f^#(X) -> c_19(a__z^#(mark(X), X), mark^#(X))
  , a__g^#(d(), X, X) -> c_22(a__A^#())
  , mark^#(A()) -> c_27(a__A^#())
  , mark^#(a()) -> c_28(a__a^#())
  , mark^#(b()) -> c_29(a__b^#())
  , mark^#(z(X1, X2)) -> c_32(a__z^#(mark(X1), X2), mark^#(X1))
  , mark^#(f(X)) -> c_33(a__f^#(mark(X)), mark^#(X))
  , mark^#(h(X1, X2)) ->
    c_34(a__h^#(mark(X1), mark(X2)), mark^#(X1), mark^#(X2))
  , mark^#(g(X1, X2, X3)) ->
    c_35(a__g^#(mark(X1), mark(X2), mark(X3)),
         mark^#(X1),
         mark^#(X2),
         mark^#(X3))
  , a__z^#(e(), X) -> c_37(mark^#(X)) }
Weak DPs:
  { a__a^#() -> c_1(a__c^#())
  , a__a^#() -> c_2(a__d^#())
  , a__a^#() -> c_3()
  , a__c^#() -> c_4()
  , a__c^#() -> c_5()
  , a__c^#() -> c_6()
  , a__d^#() -> c_13()
  , a__d^#() -> c_14()
  , a__b^#() -> c_7(a__c^#())
  , a__b^#() -> c_8(a__d^#())
  , a__b^#() -> c_9()
  , a__k^#() -> c_10()
  , a__k^#() -> c_11()
  , a__k^#() -> c_12()
  , a__A^#() -> c_16()
  , a__h^#(X1, X2) -> c_18()
  , a__f^#(X) -> c_20()
  , a__g^#(X1, X2, X3) -> c_21()
  , mark^#(e()) -> c_23()
  , mark^#(l()) -> c_24()
  , mark^#(m()) -> c_25()
  , mark^#(d()) -> c_26(a__d^#())
  , mark^#(c()) -> c_30(a__c^#())
  , mark^#(k()) -> c_31(a__k^#())
  , a__z^#(X1, X2) -> c_36() }
Weak Trs:
  { a__a() -> a__c()
  , a__a() -> a__d()
  , a__a() -> a()
  , a__c() -> e()
  , a__c() -> l()
  , a__c() -> c()
  , a__b() -> a__c()
  , a__b() -> a__d()
  , a__b() -> b()
  , a__k() -> l()
  , a__k() -> m()
  , a__k() -> k()
  , a__d() -> m()
  , a__d() -> d()
  , a__A() -> a__h(a__f(a__a()), a__f(a__b()))
  , a__A() -> A()
  , a__h(X, X) -> a__g(mark(X), mark(X), a__f(a__k()))
  , a__h(X1, X2) -> h(X1, X2)
  , a__f(X) -> a__z(mark(X), X)
  , a__f(X) -> f(X)
  , a__g(X1, X2, X3) -> g(X1, X2, X3)
  , a__g(d(), X, X) -> a__A()
  , mark(e()) -> e()
  , mark(l()) -> l()
  , mark(m()) -> m()
  , mark(d()) -> a__d()
  , mark(A()) -> a__A()
  , mark(a()) -> a__a()
  , mark(b()) -> a__b()
  , mark(c()) -> a__c()
  , mark(k()) -> a__k()
  , mark(z(X1, X2)) -> a__z(mark(X1), X2)
  , mark(f(X)) -> a__f(mark(X))
  , mark(h(X1, X2)) -> a__h(mark(X1), mark(X2))
  , mark(g(X1, X2, X3)) -> a__g(mark(X1), mark(X2), mark(X3))
  , a__z(X1, X2) -> z(X1, X2)
  , a__z(e(), X) -> mark(X) }
Obligation:
  innermost runtime complexity
Answer:
  MAYBE

We estimate the number of application of {6,7} by applications of
Pre({6,7}) = {2,3,8,9,10,11,12}. Here rules are labeled as follows:

  DPs:
    { 1: a__A^#() ->
         c_15(a__h^#(a__f(a__a()), a__f(a__b())),
              a__f^#(a__a()),
              a__a^#(),
              a__f^#(a__b()),
              a__b^#())
    , 2: a__h^#(X, X) ->
         c_17(a__g^#(mark(X), mark(X), a__f(a__k())),
              mark^#(X),
              mark^#(X),
              a__f^#(a__k()),
              a__k^#())
    , 3: a__f^#(X) -> c_19(a__z^#(mark(X), X), mark^#(X))
    , 4: a__g^#(d(), X, X) -> c_22(a__A^#())
    , 5: mark^#(A()) -> c_27(a__A^#())
    , 6: mark^#(a()) -> c_28(a__a^#())
    , 7: mark^#(b()) -> c_29(a__b^#())
    , 8: mark^#(z(X1, X2)) -> c_32(a__z^#(mark(X1), X2), mark^#(X1))
    , 9: mark^#(f(X)) -> c_33(a__f^#(mark(X)), mark^#(X))
    , 10: mark^#(h(X1, X2)) ->
          c_34(a__h^#(mark(X1), mark(X2)), mark^#(X1), mark^#(X2))
    , 11: mark^#(g(X1, X2, X3)) ->
          c_35(a__g^#(mark(X1), mark(X2), mark(X3)),
               mark^#(X1),
               mark^#(X2),
               mark^#(X3))
    , 12: a__z^#(e(), X) -> c_37(mark^#(X))
    , 13: a__a^#() -> c_1(a__c^#())
    , 14: a__a^#() -> c_2(a__d^#())
    , 15: a__a^#() -> c_3()
    , 16: a__c^#() -> c_4()
    , 17: a__c^#() -> c_5()
    , 18: a__c^#() -> c_6()
    , 19: a__d^#() -> c_13()
    , 20: a__d^#() -> c_14()
    , 21: a__b^#() -> c_7(a__c^#())
    , 22: a__b^#() -> c_8(a__d^#())
    , 23: a__b^#() -> c_9()
    , 24: a__k^#() -> c_10()
    , 25: a__k^#() -> c_11()
    , 26: a__k^#() -> c_12()
    , 27: a__A^#() -> c_16()
    , 28: a__h^#(X1, X2) -> c_18()
    , 29: a__f^#(X) -> c_20()
    , 30: a__g^#(X1, X2, X3) -> c_21()
    , 31: mark^#(e()) -> c_23()
    , 32: mark^#(l()) -> c_24()
    , 33: mark^#(m()) -> c_25()
    , 34: mark^#(d()) -> c_26(a__d^#())
    , 35: mark^#(c()) -> c_30(a__c^#())
    , 36: mark^#(k()) -> c_31(a__k^#())
    , 37: a__z^#(X1, X2) -> c_36() }

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

Strict DPs:
  { a__A^#() ->
    c_15(a__h^#(a__f(a__a()), a__f(a__b())),
         a__f^#(a__a()),
         a__a^#(),
         a__f^#(a__b()),
         a__b^#())
  , a__h^#(X, X) ->
    c_17(a__g^#(mark(X), mark(X), a__f(a__k())),
         mark^#(X),
         mark^#(X),
         a__f^#(a__k()),
         a__k^#())
  , a__f^#(X) -> c_19(a__z^#(mark(X), X), mark^#(X))
  , a__g^#(d(), X, X) -> c_22(a__A^#())
  , mark^#(A()) -> c_27(a__A^#())
  , mark^#(z(X1, X2)) -> c_32(a__z^#(mark(X1), X2), mark^#(X1))
  , mark^#(f(X)) -> c_33(a__f^#(mark(X)), mark^#(X))
  , mark^#(h(X1, X2)) ->
    c_34(a__h^#(mark(X1), mark(X2)), mark^#(X1), mark^#(X2))
  , mark^#(g(X1, X2, X3)) ->
    c_35(a__g^#(mark(X1), mark(X2), mark(X3)),
         mark^#(X1),
         mark^#(X2),
         mark^#(X3))
  , a__z^#(e(), X) -> c_37(mark^#(X)) }
Weak DPs:
  { a__a^#() -> c_1(a__c^#())
  , a__a^#() -> c_2(a__d^#())
  , a__a^#() -> c_3()
  , a__c^#() -> c_4()
  , a__c^#() -> c_5()
  , a__c^#() -> c_6()
  , a__d^#() -> c_13()
  , a__d^#() -> c_14()
  , a__b^#() -> c_7(a__c^#())
  , a__b^#() -> c_8(a__d^#())
  , a__b^#() -> c_9()
  , a__k^#() -> c_10()
  , a__k^#() -> c_11()
  , a__k^#() -> c_12()
  , a__A^#() -> c_16()
  , a__h^#(X1, X2) -> c_18()
  , a__f^#(X) -> c_20()
  , a__g^#(X1, X2, X3) -> c_21()
  , mark^#(e()) -> c_23()
  , mark^#(l()) -> c_24()
  , mark^#(m()) -> c_25()
  , mark^#(d()) -> c_26(a__d^#())
  , mark^#(a()) -> c_28(a__a^#())
  , mark^#(b()) -> c_29(a__b^#())
  , mark^#(c()) -> c_30(a__c^#())
  , mark^#(k()) -> c_31(a__k^#())
  , a__z^#(X1, X2) -> c_36() }
Weak Trs:
  { a__a() -> a__c()
  , a__a() -> a__d()
  , a__a() -> a()
  , a__c() -> e()
  , a__c() -> l()
  , a__c() -> c()
  , a__b() -> a__c()
  , a__b() -> a__d()
  , a__b() -> b()
  , a__k() -> l()
  , a__k() -> m()
  , a__k() -> k()
  , a__d() -> m()
  , a__d() -> d()
  , a__A() -> a__h(a__f(a__a()), a__f(a__b()))
  , a__A() -> A()
  , a__h(X, X) -> a__g(mark(X), mark(X), a__f(a__k()))
  , a__h(X1, X2) -> h(X1, X2)
  , a__f(X) -> a__z(mark(X), X)
  , a__f(X) -> f(X)
  , a__g(X1, X2, X3) -> g(X1, X2, X3)
  , a__g(d(), X, X) -> a__A()
  , mark(e()) -> e()
  , mark(l()) -> l()
  , mark(m()) -> m()
  , mark(d()) -> a__d()
  , mark(A()) -> a__A()
  , mark(a()) -> a__a()
  , mark(b()) -> a__b()
  , mark(c()) -> a__c()
  , mark(k()) -> a__k()
  , mark(z(X1, X2)) -> a__z(mark(X1), X2)
  , mark(f(X)) -> a__f(mark(X))
  , mark(h(X1, X2)) -> a__h(mark(X1), mark(X2))
  , mark(g(X1, X2, X3)) -> a__g(mark(X1), mark(X2), mark(X3))
  , a__z(X1, X2) -> z(X1, X2)
  , a__z(e(), X) -> mark(X) }
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__a^#() -> c_1(a__c^#())
, a__a^#() -> c_2(a__d^#())
, a__a^#() -> c_3()
, a__c^#() -> c_4()
, a__c^#() -> c_5()
, a__c^#() -> c_6()
, a__d^#() -> c_13()
, a__d^#() -> c_14()
, a__b^#() -> c_7(a__c^#())
, a__b^#() -> c_8(a__d^#())
, a__b^#() -> c_9()
, a__k^#() -> c_10()
, a__k^#() -> c_11()
, a__k^#() -> c_12()
, a__A^#() -> c_16()
, a__h^#(X1, X2) -> c_18()
, a__f^#(X) -> c_20()
, a__g^#(X1, X2, X3) -> c_21()
, mark^#(e()) -> c_23()
, mark^#(l()) -> c_24()
, mark^#(m()) -> c_25()
, mark^#(d()) -> c_26(a__d^#())
, mark^#(a()) -> c_28(a__a^#())
, mark^#(b()) -> c_29(a__b^#())
, mark^#(c()) -> c_30(a__c^#())
, mark^#(k()) -> c_31(a__k^#())
, a__z^#(X1, X2) -> c_36() }

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

Strict DPs:
  { a__A^#() ->
    c_15(a__h^#(a__f(a__a()), a__f(a__b())),
         a__f^#(a__a()),
         a__a^#(),
         a__f^#(a__b()),
         a__b^#())
  , a__h^#(X, X) ->
    c_17(a__g^#(mark(X), mark(X), a__f(a__k())),
         mark^#(X),
         mark^#(X),
         a__f^#(a__k()),
         a__k^#())
  , a__f^#(X) -> c_19(a__z^#(mark(X), X), mark^#(X))
  , a__g^#(d(), X, X) -> c_22(a__A^#())
  , mark^#(A()) -> c_27(a__A^#())
  , mark^#(z(X1, X2)) -> c_32(a__z^#(mark(X1), X2), mark^#(X1))
  , mark^#(f(X)) -> c_33(a__f^#(mark(X)), mark^#(X))
  , mark^#(h(X1, X2)) ->
    c_34(a__h^#(mark(X1), mark(X2)), mark^#(X1), mark^#(X2))
  , mark^#(g(X1, X2, X3)) ->
    c_35(a__g^#(mark(X1), mark(X2), mark(X3)),
         mark^#(X1),
         mark^#(X2),
         mark^#(X3))
  , a__z^#(e(), X) -> c_37(mark^#(X)) }
Weak Trs:
  { a__a() -> a__c()
  , a__a() -> a__d()
  , a__a() -> a()
  , a__c() -> e()
  , a__c() -> l()
  , a__c() -> c()
  , a__b() -> a__c()
  , a__b() -> a__d()
  , a__b() -> b()
  , a__k() -> l()
  , a__k() -> m()
  , a__k() -> k()
  , a__d() -> m()
  , a__d() -> d()
  , a__A() -> a__h(a__f(a__a()), a__f(a__b()))
  , a__A() -> A()
  , a__h(X, X) -> a__g(mark(X), mark(X), a__f(a__k()))
  , a__h(X1, X2) -> h(X1, X2)
  , a__f(X) -> a__z(mark(X), X)
  , a__f(X) -> f(X)
  , a__g(X1, X2, X3) -> g(X1, X2, X3)
  , a__g(d(), X, X) -> a__A()
  , mark(e()) -> e()
  , mark(l()) -> l()
  , mark(m()) -> m()
  , mark(d()) -> a__d()
  , mark(A()) -> a__A()
  , mark(a()) -> a__a()
  , mark(b()) -> a__b()
  , mark(c()) -> a__c()
  , mark(k()) -> a__k()
  , mark(z(X1, X2)) -> a__z(mark(X1), X2)
  , mark(f(X)) -> a__f(mark(X))
  , mark(h(X1, X2)) -> a__h(mark(X1), mark(X2))
  , mark(g(X1, X2, X3)) -> a__g(mark(X1), mark(X2), mark(X3))
  , a__z(X1, X2) -> z(X1, X2)
  , a__z(e(), X) -> mark(X) }
Obligation:
  innermost runtime complexity
Answer:
  MAYBE

Due to missing edges in the dependency-graph, the right-hand sides
of following rules could be simplified:

  { a__A^#() ->
    c_15(a__h^#(a__f(a__a()), a__f(a__b())),
         a__f^#(a__a()),
         a__a^#(),
         a__f^#(a__b()),
         a__b^#())
  , a__h^#(X, X) ->
    c_17(a__g^#(mark(X), mark(X), a__f(a__k())),
         mark^#(X),
         mark^#(X),
         a__f^#(a__k()),
         a__k^#()) }

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

Strict DPs:
  { a__A^#() ->
    c_1(a__h^#(a__f(a__a()), a__f(a__b())),
        a__f^#(a__a()),
        a__f^#(a__b()))
  , a__h^#(X, X) ->
    c_2(a__g^#(mark(X), mark(X), a__f(a__k())),
        mark^#(X),
        mark^#(X),
        a__f^#(a__k()))
  , a__f^#(X) -> c_3(a__z^#(mark(X), X), mark^#(X))
  , a__g^#(d(), X, X) -> c_4(a__A^#())
  , mark^#(A()) -> c_5(a__A^#())
  , mark^#(z(X1, X2)) -> c_6(a__z^#(mark(X1), X2), mark^#(X1))
  , mark^#(f(X)) -> c_7(a__f^#(mark(X)), mark^#(X))
  , mark^#(h(X1, X2)) ->
    c_8(a__h^#(mark(X1), mark(X2)), mark^#(X1), mark^#(X2))
  , mark^#(g(X1, X2, X3)) ->
    c_9(a__g^#(mark(X1), mark(X2), mark(X3)),
        mark^#(X1),
        mark^#(X2),
        mark^#(X3))
  , a__z^#(e(), X) -> c_10(mark^#(X)) }
Weak Trs:
  { a__a() -> a__c()
  , a__a() -> a__d()
  , a__a() -> a()
  , a__c() -> e()
  , a__c() -> l()
  , a__c() -> c()
  , a__b() -> a__c()
  , a__b() -> a__d()
  , a__b() -> b()
  , a__k() -> l()
  , a__k() -> m()
  , a__k() -> k()
  , a__d() -> m()
  , a__d() -> d()
  , a__A() -> a__h(a__f(a__a()), a__f(a__b()))
  , a__A() -> A()
  , a__h(X, X) -> a__g(mark(X), mark(X), a__f(a__k()))
  , a__h(X1, X2) -> h(X1, X2)
  , a__f(X) -> a__z(mark(X), X)
  , a__f(X) -> f(X)
  , a__g(X1, X2, X3) -> g(X1, X2, X3)
  , a__g(d(), X, X) -> a__A()
  , mark(e()) -> e()
  , mark(l()) -> l()
  , mark(m()) -> m()
  , mark(d()) -> a__d()
  , mark(A()) -> a__A()
  , mark(a()) -> a__a()
  , mark(b()) -> a__b()
  , mark(c()) -> a__c()
  , mark(k()) -> a__k()
  , mark(z(X1, X2)) -> a__z(mark(X1), X2)
  , mark(f(X)) -> a__f(mark(X))
  , mark(h(X1, X2)) -> a__h(mark(X1), mark(X2))
  , mark(g(X1, X2, X3)) -> a__g(mark(X1), mark(X2), mark(X3))
  , a__z(X1, X2) -> z(X1, X2)
  , a__z(e(), X) -> mark(X) }
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:
      
      Following exception was raised:
        stack overflow
   
   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..