MAYBE

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

Strict Trs:
  { a____(X1, X2) -> __(X1, X2)
  , a____(X, nil()) -> mark(X)
  , a____(__(X, Y), Z) -> a____(mark(X), a____(mark(Y), mark(Z)))
  , a____(nil(), X) -> mark(X)
  , mark(__(X1, X2)) -> a____(mark(X1), mark(X2))
  , mark(nil()) -> nil()
  , mark(tt()) -> tt()
  , mark(U11(X)) -> a__U11(mark(X))
  , mark(U12(X)) -> a__U12(mark(X))
  , mark(isNePal(X)) -> a__isNePal(mark(X))
  , a__U11(X) -> U11(X)
  , a__U11(tt()) -> a__U12(tt())
  , a__U12(X) -> U12(X)
  , a__U12(tt()) -> tt()
  , a__isNePal(X) -> isNePal(X)
  , a__isNePal(__(I, __(P, I))) -> a__U11(tt()) }
Obligation:
  innermost runtime complexity
Answer:
  MAYBE

We add following dependency tuples:

Strict DPs:
  { a____^#(X1, X2) -> c_1()
  , a____^#(X, nil()) -> c_2(mark^#(X))
  , a____^#(__(X, Y), Z) ->
    c_3(a____^#(mark(X), a____(mark(Y), mark(Z))),
        mark^#(X),
        a____^#(mark(Y), mark(Z)),
        mark^#(Y),
        mark^#(Z))
  , a____^#(nil(), X) -> c_4(mark^#(X))
  , mark^#(__(X1, X2)) ->
    c_5(a____^#(mark(X1), mark(X2)), mark^#(X1), mark^#(X2))
  , mark^#(nil()) -> c_6()
  , mark^#(tt()) -> c_7()
  , mark^#(U11(X)) -> c_8(a__U11^#(mark(X)), mark^#(X))
  , mark^#(U12(X)) -> c_9(a__U12^#(mark(X)), mark^#(X))
  , mark^#(isNePal(X)) -> c_10(a__isNePal^#(mark(X)), mark^#(X))
  , a__U11^#(X) -> c_11()
  , a__U11^#(tt()) -> c_12(a__U12^#(tt()))
  , a__U12^#(X) -> c_13()
  , a__U12^#(tt()) -> c_14()
  , a__isNePal^#(X) -> c_15()
  , a__isNePal^#(__(I, __(P, I))) -> c_16(a__U11^#(tt())) }

and mark the set of starting terms.

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

Strict DPs:
  { a____^#(X1, X2) -> c_1()
  , a____^#(X, nil()) -> c_2(mark^#(X))
  , a____^#(__(X, Y), Z) ->
    c_3(a____^#(mark(X), a____(mark(Y), mark(Z))),
        mark^#(X),
        a____^#(mark(Y), mark(Z)),
        mark^#(Y),
        mark^#(Z))
  , a____^#(nil(), X) -> c_4(mark^#(X))
  , mark^#(__(X1, X2)) ->
    c_5(a____^#(mark(X1), mark(X2)), mark^#(X1), mark^#(X2))
  , mark^#(nil()) -> c_6()
  , mark^#(tt()) -> c_7()
  , mark^#(U11(X)) -> c_8(a__U11^#(mark(X)), mark^#(X))
  , mark^#(U12(X)) -> c_9(a__U12^#(mark(X)), mark^#(X))
  , mark^#(isNePal(X)) -> c_10(a__isNePal^#(mark(X)), mark^#(X))
  , a__U11^#(X) -> c_11()
  , a__U11^#(tt()) -> c_12(a__U12^#(tt()))
  , a__U12^#(X) -> c_13()
  , a__U12^#(tt()) -> c_14()
  , a__isNePal^#(X) -> c_15()
  , a__isNePal^#(__(I, __(P, I))) -> c_16(a__U11^#(tt())) }
Weak Trs:
  { a____(X1, X2) -> __(X1, X2)
  , a____(X, nil()) -> mark(X)
  , a____(__(X, Y), Z) -> a____(mark(X), a____(mark(Y), mark(Z)))
  , a____(nil(), X) -> mark(X)
  , mark(__(X1, X2)) -> a____(mark(X1), mark(X2))
  , mark(nil()) -> nil()
  , mark(tt()) -> tt()
  , mark(U11(X)) -> a__U11(mark(X))
  , mark(U12(X)) -> a__U12(mark(X))
  , mark(isNePal(X)) -> a__isNePal(mark(X))
  , a__U11(X) -> U11(X)
  , a__U11(tt()) -> a__U12(tt())
  , a__U12(X) -> U12(X)
  , a__U12(tt()) -> tt()
  , a__isNePal(X) -> isNePal(X)
  , a__isNePal(__(I, __(P, I))) -> a__U11(tt()) }
Obligation:
  innermost runtime complexity
Answer:
  MAYBE

We estimate the number of application of {1,6,7,11,13,14,15} by
applications of Pre({1,6,7,11,13,14,15}) = {2,3,4,5,8,9,10,12,16}.
Here rules are labeled as follows:

  DPs:
    { 1: a____^#(X1, X2) -> c_1()
    , 2: a____^#(X, nil()) -> c_2(mark^#(X))
    , 3: a____^#(__(X, Y), Z) ->
         c_3(a____^#(mark(X), a____(mark(Y), mark(Z))),
             mark^#(X),
             a____^#(mark(Y), mark(Z)),
             mark^#(Y),
             mark^#(Z))
    , 4: a____^#(nil(), X) -> c_4(mark^#(X))
    , 5: mark^#(__(X1, X2)) ->
         c_5(a____^#(mark(X1), mark(X2)), mark^#(X1), mark^#(X2))
    , 6: mark^#(nil()) -> c_6()
    , 7: mark^#(tt()) -> c_7()
    , 8: mark^#(U11(X)) -> c_8(a__U11^#(mark(X)), mark^#(X))
    , 9: mark^#(U12(X)) -> c_9(a__U12^#(mark(X)), mark^#(X))
    , 10: mark^#(isNePal(X)) -> c_10(a__isNePal^#(mark(X)), mark^#(X))
    , 11: a__U11^#(X) -> c_11()
    , 12: a__U11^#(tt()) -> c_12(a__U12^#(tt()))
    , 13: a__U12^#(X) -> c_13()
    , 14: a__U12^#(tt()) -> c_14()
    , 15: a__isNePal^#(X) -> c_15()
    , 16: a__isNePal^#(__(I, __(P, I))) -> c_16(a__U11^#(tt())) }

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

Strict DPs:
  { a____^#(X, nil()) -> c_2(mark^#(X))
  , a____^#(__(X, Y), Z) ->
    c_3(a____^#(mark(X), a____(mark(Y), mark(Z))),
        mark^#(X),
        a____^#(mark(Y), mark(Z)),
        mark^#(Y),
        mark^#(Z))
  , a____^#(nil(), X) -> c_4(mark^#(X))
  , mark^#(__(X1, X2)) ->
    c_5(a____^#(mark(X1), mark(X2)), mark^#(X1), mark^#(X2))
  , mark^#(U11(X)) -> c_8(a__U11^#(mark(X)), mark^#(X))
  , mark^#(U12(X)) -> c_9(a__U12^#(mark(X)), mark^#(X))
  , mark^#(isNePal(X)) -> c_10(a__isNePal^#(mark(X)), mark^#(X))
  , a__U11^#(tt()) -> c_12(a__U12^#(tt()))
  , a__isNePal^#(__(I, __(P, I))) -> c_16(a__U11^#(tt())) }
Weak DPs:
  { a____^#(X1, X2) -> c_1()
  , mark^#(nil()) -> c_6()
  , mark^#(tt()) -> c_7()
  , a__U11^#(X) -> c_11()
  , a__U12^#(X) -> c_13()
  , a__U12^#(tt()) -> c_14()
  , a__isNePal^#(X) -> c_15() }
Weak Trs:
  { a____(X1, X2) -> __(X1, X2)
  , a____(X, nil()) -> mark(X)
  , a____(__(X, Y), Z) -> a____(mark(X), a____(mark(Y), mark(Z)))
  , a____(nil(), X) -> mark(X)
  , mark(__(X1, X2)) -> a____(mark(X1), mark(X2))
  , mark(nil()) -> nil()
  , mark(tt()) -> tt()
  , mark(U11(X)) -> a__U11(mark(X))
  , mark(U12(X)) -> a__U12(mark(X))
  , mark(isNePal(X)) -> a__isNePal(mark(X))
  , a__U11(X) -> U11(X)
  , a__U11(tt()) -> a__U12(tt())
  , a__U12(X) -> U12(X)
  , a__U12(tt()) -> tt()
  , a__isNePal(X) -> isNePal(X)
  , a__isNePal(__(I, __(P, I))) -> a__U11(tt()) }
Obligation:
  innermost runtime complexity
Answer:
  MAYBE

We estimate the number of application of {8} by applications of
Pre({8}) = {5,9}. Here rules are labeled as follows:

  DPs:
    { 1: a____^#(X, nil()) -> c_2(mark^#(X))
    , 2: a____^#(__(X, Y), Z) ->
         c_3(a____^#(mark(X), a____(mark(Y), mark(Z))),
             mark^#(X),
             a____^#(mark(Y), mark(Z)),
             mark^#(Y),
             mark^#(Z))
    , 3: a____^#(nil(), X) -> c_4(mark^#(X))
    , 4: mark^#(__(X1, X2)) ->
         c_5(a____^#(mark(X1), mark(X2)), mark^#(X1), mark^#(X2))
    , 5: mark^#(U11(X)) -> c_8(a__U11^#(mark(X)), mark^#(X))
    , 6: mark^#(U12(X)) -> c_9(a__U12^#(mark(X)), mark^#(X))
    , 7: mark^#(isNePal(X)) -> c_10(a__isNePal^#(mark(X)), mark^#(X))
    , 8: a__U11^#(tt()) -> c_12(a__U12^#(tt()))
    , 9: a__isNePal^#(__(I, __(P, I))) -> c_16(a__U11^#(tt()))
    , 10: a____^#(X1, X2) -> c_1()
    , 11: mark^#(nil()) -> c_6()
    , 12: mark^#(tt()) -> c_7()
    , 13: a__U11^#(X) -> c_11()
    , 14: a__U12^#(X) -> c_13()
    , 15: a__U12^#(tt()) -> c_14()
    , 16: a__isNePal^#(X) -> c_15() }

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

Strict DPs:
  { a____^#(X, nil()) -> c_2(mark^#(X))
  , a____^#(__(X, Y), Z) ->
    c_3(a____^#(mark(X), a____(mark(Y), mark(Z))),
        mark^#(X),
        a____^#(mark(Y), mark(Z)),
        mark^#(Y),
        mark^#(Z))
  , a____^#(nil(), X) -> c_4(mark^#(X))
  , mark^#(__(X1, X2)) ->
    c_5(a____^#(mark(X1), mark(X2)), mark^#(X1), mark^#(X2))
  , mark^#(U11(X)) -> c_8(a__U11^#(mark(X)), mark^#(X))
  , mark^#(U12(X)) -> c_9(a__U12^#(mark(X)), mark^#(X))
  , mark^#(isNePal(X)) -> c_10(a__isNePal^#(mark(X)), mark^#(X))
  , a__isNePal^#(__(I, __(P, I))) -> c_16(a__U11^#(tt())) }
Weak DPs:
  { a____^#(X1, X2) -> c_1()
  , mark^#(nil()) -> c_6()
  , mark^#(tt()) -> c_7()
  , a__U11^#(X) -> c_11()
  , a__U11^#(tt()) -> c_12(a__U12^#(tt()))
  , a__U12^#(X) -> c_13()
  , a__U12^#(tt()) -> c_14()
  , a__isNePal^#(X) -> c_15() }
Weak Trs:
  { a____(X1, X2) -> __(X1, X2)
  , a____(X, nil()) -> mark(X)
  , a____(__(X, Y), Z) -> a____(mark(X), a____(mark(Y), mark(Z)))
  , a____(nil(), X) -> mark(X)
  , mark(__(X1, X2)) -> a____(mark(X1), mark(X2))
  , mark(nil()) -> nil()
  , mark(tt()) -> tt()
  , mark(U11(X)) -> a__U11(mark(X))
  , mark(U12(X)) -> a__U12(mark(X))
  , mark(isNePal(X)) -> a__isNePal(mark(X))
  , a__U11(X) -> U11(X)
  , a__U11(tt()) -> a__U12(tt())
  , a__U12(X) -> U12(X)
  , a__U12(tt()) -> tt()
  , a__isNePal(X) -> isNePal(X)
  , a__isNePal(__(I, __(P, I))) -> a__U11(tt()) }
Obligation:
  innermost runtime complexity
Answer:
  MAYBE

We estimate the number of application of {8} by applications of
Pre({8}) = {7}. Here rules are labeled as follows:

  DPs:
    { 1: a____^#(X, nil()) -> c_2(mark^#(X))
    , 2: a____^#(__(X, Y), Z) ->
         c_3(a____^#(mark(X), a____(mark(Y), mark(Z))),
             mark^#(X),
             a____^#(mark(Y), mark(Z)),
             mark^#(Y),
             mark^#(Z))
    , 3: a____^#(nil(), X) -> c_4(mark^#(X))
    , 4: mark^#(__(X1, X2)) ->
         c_5(a____^#(mark(X1), mark(X2)), mark^#(X1), mark^#(X2))
    , 5: mark^#(U11(X)) -> c_8(a__U11^#(mark(X)), mark^#(X))
    , 6: mark^#(U12(X)) -> c_9(a__U12^#(mark(X)), mark^#(X))
    , 7: mark^#(isNePal(X)) -> c_10(a__isNePal^#(mark(X)), mark^#(X))
    , 8: a__isNePal^#(__(I, __(P, I))) -> c_16(a__U11^#(tt()))
    , 9: a____^#(X1, X2) -> c_1()
    , 10: mark^#(nil()) -> c_6()
    , 11: mark^#(tt()) -> c_7()
    , 12: a__U11^#(X) -> c_11()
    , 13: a__U11^#(tt()) -> c_12(a__U12^#(tt()))
    , 14: a__U12^#(X) -> c_13()
    , 15: a__U12^#(tt()) -> c_14()
    , 16: a__isNePal^#(X) -> c_15() }

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

Strict DPs:
  { a____^#(X, nil()) -> c_2(mark^#(X))
  , a____^#(__(X, Y), Z) ->
    c_3(a____^#(mark(X), a____(mark(Y), mark(Z))),
        mark^#(X),
        a____^#(mark(Y), mark(Z)),
        mark^#(Y),
        mark^#(Z))
  , a____^#(nil(), X) -> c_4(mark^#(X))
  , mark^#(__(X1, X2)) ->
    c_5(a____^#(mark(X1), mark(X2)), mark^#(X1), mark^#(X2))
  , mark^#(U11(X)) -> c_8(a__U11^#(mark(X)), mark^#(X))
  , mark^#(U12(X)) -> c_9(a__U12^#(mark(X)), mark^#(X))
  , mark^#(isNePal(X)) -> c_10(a__isNePal^#(mark(X)), mark^#(X)) }
Weak DPs:
  { a____^#(X1, X2) -> c_1()
  , mark^#(nil()) -> c_6()
  , mark^#(tt()) -> c_7()
  , a__U11^#(X) -> c_11()
  , a__U11^#(tt()) -> c_12(a__U12^#(tt()))
  , a__U12^#(X) -> c_13()
  , a__U12^#(tt()) -> c_14()
  , a__isNePal^#(X) -> c_15()
  , a__isNePal^#(__(I, __(P, I))) -> c_16(a__U11^#(tt())) }
Weak Trs:
  { a____(X1, X2) -> __(X1, X2)
  , a____(X, nil()) -> mark(X)
  , a____(__(X, Y), Z) -> a____(mark(X), a____(mark(Y), mark(Z)))
  , a____(nil(), X) -> mark(X)
  , mark(__(X1, X2)) -> a____(mark(X1), mark(X2))
  , mark(nil()) -> nil()
  , mark(tt()) -> tt()
  , mark(U11(X)) -> a__U11(mark(X))
  , mark(U12(X)) -> a__U12(mark(X))
  , mark(isNePal(X)) -> a__isNePal(mark(X))
  , a__U11(X) -> U11(X)
  , a__U11(tt()) -> a__U12(tt())
  , a__U12(X) -> U12(X)
  , a__U12(tt()) -> tt()
  , a__isNePal(X) -> isNePal(X)
  , a__isNePal(__(I, __(P, I))) -> a__U11(tt()) }
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, X2) -> c_1()
, mark^#(nil()) -> c_6()
, mark^#(tt()) -> c_7()
, a__U11^#(X) -> c_11()
, a__U11^#(tt()) -> c_12(a__U12^#(tt()))
, a__U12^#(X) -> c_13()
, a__U12^#(tt()) -> c_14()
, a__isNePal^#(X) -> c_15()
, a__isNePal^#(__(I, __(P, I))) -> c_16(a__U11^#(tt())) }

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

Strict DPs:
  { a____^#(X, nil()) -> c_2(mark^#(X))
  , a____^#(__(X, Y), Z) ->
    c_3(a____^#(mark(X), a____(mark(Y), mark(Z))),
        mark^#(X),
        a____^#(mark(Y), mark(Z)),
        mark^#(Y),
        mark^#(Z))
  , a____^#(nil(), X) -> c_4(mark^#(X))
  , mark^#(__(X1, X2)) ->
    c_5(a____^#(mark(X1), mark(X2)), mark^#(X1), mark^#(X2))
  , mark^#(U11(X)) -> c_8(a__U11^#(mark(X)), mark^#(X))
  , mark^#(U12(X)) -> c_9(a__U12^#(mark(X)), mark^#(X))
  , mark^#(isNePal(X)) -> c_10(a__isNePal^#(mark(X)), mark^#(X)) }
Weak Trs:
  { a____(X1, X2) -> __(X1, X2)
  , a____(X, nil()) -> mark(X)
  , a____(__(X, Y), Z) -> a____(mark(X), a____(mark(Y), mark(Z)))
  , a____(nil(), X) -> mark(X)
  , mark(__(X1, X2)) -> a____(mark(X1), mark(X2))
  , mark(nil()) -> nil()
  , mark(tt()) -> tt()
  , mark(U11(X)) -> a__U11(mark(X))
  , mark(U12(X)) -> a__U12(mark(X))
  , mark(isNePal(X)) -> a__isNePal(mark(X))
  , a__U11(X) -> U11(X)
  , a__U11(tt()) -> a__U12(tt())
  , a__U12(X) -> U12(X)
  , a__U12(tt()) -> tt()
  , a__isNePal(X) -> isNePal(X)
  , a__isNePal(__(I, __(P, I))) -> a__U11(tt()) }
Obligation:
  innermost runtime complexity
Answer:
  MAYBE

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

  { mark^#(U11(X)) -> c_8(a__U11^#(mark(X)), mark^#(X))
  , mark^#(U12(X)) -> c_9(a__U12^#(mark(X)), mark^#(X))
  , mark^#(isNePal(X)) -> c_10(a__isNePal^#(mark(X)), mark^#(X)) }

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

Strict DPs:
  { a____^#(X, nil()) -> c_1(mark^#(X))
  , a____^#(__(X, Y), Z) ->
    c_2(a____^#(mark(X), a____(mark(Y), mark(Z))),
        mark^#(X),
        a____^#(mark(Y), mark(Z)),
        mark^#(Y),
        mark^#(Z))
  , a____^#(nil(), X) -> c_3(mark^#(X))
  , mark^#(__(X1, X2)) ->
    c_4(a____^#(mark(X1), mark(X2)), mark^#(X1), mark^#(X2))
  , mark^#(U11(X)) -> c_5(mark^#(X))
  , mark^#(U12(X)) -> c_6(mark^#(X))
  , mark^#(isNePal(X)) -> c_7(mark^#(X)) }
Weak Trs:
  { a____(X1, X2) -> __(X1, X2)
  , a____(X, nil()) -> mark(X)
  , a____(__(X, Y), Z) -> a____(mark(X), a____(mark(Y), mark(Z)))
  , a____(nil(), X) -> mark(X)
  , mark(__(X1, X2)) -> a____(mark(X1), mark(X2))
  , mark(nil()) -> nil()
  , mark(tt()) -> tt()
  , mark(U11(X)) -> a__U11(mark(X))
  , mark(U12(X)) -> a__U12(mark(X))
  , mark(isNePal(X)) -> a__isNePal(mark(X))
  , a__U11(X) -> U11(X)
  , a__U11(tt()) -> a__U12(tt())
  , a__U12(X) -> U12(X)
  , a__U12(tt()) -> tt()
  , a__isNePal(X) -> isNePal(X)
  , a__isNePal(__(I, __(P, I))) -> a__U11(tt()) }
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..