MAYBE

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

Strict Trs:
  { pairNs() -> cons(0(), incr(oddNs()))
  , incr(cons(X, XS)) -> cons(s(X), incr(XS))
  , oddNs() -> incr(pairNs())
  , take(0(), XS) -> nil()
  , take(s(N), cons(X, XS)) -> cons(X, take(N, XS))
  , zip(X, nil()) -> nil()
  , zip(cons(X, XS), cons(Y, YS)) -> cons(pair(X, Y), zip(XS, YS))
  , zip(nil(), XS) -> nil()
  , tail(cons(X, XS)) -> XS
  , repItems(cons(X, XS)) -> cons(X, cons(X, repItems(XS)))
  , repItems(nil()) -> nil() }
Obligation:
  innermost runtime complexity
Answer:
  MAYBE

We add following dependency tuples:

Strict DPs:
  { pairNs^#() -> c_1(incr^#(oddNs()), oddNs^#())
  , incr^#(cons(X, XS)) -> c_2(incr^#(XS))
  , oddNs^#() -> c_3(incr^#(pairNs()), pairNs^#())
  , take^#(0(), XS) -> c_4()
  , take^#(s(N), cons(X, XS)) -> c_5(take^#(N, XS))
  , zip^#(X, nil()) -> c_6()
  , zip^#(cons(X, XS), cons(Y, YS)) -> c_7(zip^#(XS, YS))
  , zip^#(nil(), XS) -> c_8()
  , tail^#(cons(X, XS)) -> c_9()
  , repItems^#(cons(X, XS)) -> c_10(repItems^#(XS))
  , repItems^#(nil()) -> c_11() }

and mark the set of starting terms.

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

Strict DPs:
  { pairNs^#() -> c_1(incr^#(oddNs()), oddNs^#())
  , incr^#(cons(X, XS)) -> c_2(incr^#(XS))
  , oddNs^#() -> c_3(incr^#(pairNs()), pairNs^#())
  , take^#(0(), XS) -> c_4()
  , take^#(s(N), cons(X, XS)) -> c_5(take^#(N, XS))
  , zip^#(X, nil()) -> c_6()
  , zip^#(cons(X, XS), cons(Y, YS)) -> c_7(zip^#(XS, YS))
  , zip^#(nil(), XS) -> c_8()
  , tail^#(cons(X, XS)) -> c_9()
  , repItems^#(cons(X, XS)) -> c_10(repItems^#(XS))
  , repItems^#(nil()) -> c_11() }
Weak Trs:
  { pairNs() -> cons(0(), incr(oddNs()))
  , incr(cons(X, XS)) -> cons(s(X), incr(XS))
  , oddNs() -> incr(pairNs())
  , take(0(), XS) -> nil()
  , take(s(N), cons(X, XS)) -> cons(X, take(N, XS))
  , zip(X, nil()) -> nil()
  , zip(cons(X, XS), cons(Y, YS)) -> cons(pair(X, Y), zip(XS, YS))
  , zip(nil(), XS) -> nil()
  , tail(cons(X, XS)) -> XS
  , repItems(cons(X, XS)) -> cons(X, cons(X, repItems(XS)))
  , repItems(nil()) -> nil() }
Obligation:
  innermost runtime complexity
Answer:
  MAYBE

We estimate the number of application of {4,6,8,9,11} by
applications of Pre({4,6,8,9,11}) = {5,7,10}. Here rules are
labeled as follows:

  DPs:
    { 1: pairNs^#() -> c_1(incr^#(oddNs()), oddNs^#())
    , 2: incr^#(cons(X, XS)) -> c_2(incr^#(XS))
    , 3: oddNs^#() -> c_3(incr^#(pairNs()), pairNs^#())
    , 4: take^#(0(), XS) -> c_4()
    , 5: take^#(s(N), cons(X, XS)) -> c_5(take^#(N, XS))
    , 6: zip^#(X, nil()) -> c_6()
    , 7: zip^#(cons(X, XS), cons(Y, YS)) -> c_7(zip^#(XS, YS))
    , 8: zip^#(nil(), XS) -> c_8()
    , 9: tail^#(cons(X, XS)) -> c_9()
    , 10: repItems^#(cons(X, XS)) -> c_10(repItems^#(XS))
    , 11: repItems^#(nil()) -> c_11() }

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

Strict DPs:
  { pairNs^#() -> c_1(incr^#(oddNs()), oddNs^#())
  , incr^#(cons(X, XS)) -> c_2(incr^#(XS))
  , oddNs^#() -> c_3(incr^#(pairNs()), pairNs^#())
  , take^#(s(N), cons(X, XS)) -> c_5(take^#(N, XS))
  , zip^#(cons(X, XS), cons(Y, YS)) -> c_7(zip^#(XS, YS))
  , repItems^#(cons(X, XS)) -> c_10(repItems^#(XS)) }
Weak DPs:
  { take^#(0(), XS) -> c_4()
  , zip^#(X, nil()) -> c_6()
  , zip^#(nil(), XS) -> c_8()
  , tail^#(cons(X, XS)) -> c_9()
  , repItems^#(nil()) -> c_11() }
Weak Trs:
  { pairNs() -> cons(0(), incr(oddNs()))
  , incr(cons(X, XS)) -> cons(s(X), incr(XS))
  , oddNs() -> incr(pairNs())
  , take(0(), XS) -> nil()
  , take(s(N), cons(X, XS)) -> cons(X, take(N, XS))
  , zip(X, nil()) -> nil()
  , zip(cons(X, XS), cons(Y, YS)) -> cons(pair(X, Y), zip(XS, YS))
  , zip(nil(), XS) -> nil()
  , tail(cons(X, XS)) -> XS
  , repItems(cons(X, XS)) -> cons(X, cons(X, repItems(XS)))
  , repItems(nil()) -> nil() }
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.

{ take^#(0(), XS) -> c_4()
, zip^#(X, nil()) -> c_6()
, zip^#(nil(), XS) -> c_8()
, tail^#(cons(X, XS)) -> c_9()
, repItems^#(nil()) -> c_11() }

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

Strict DPs:
  { pairNs^#() -> c_1(incr^#(oddNs()), oddNs^#())
  , incr^#(cons(X, XS)) -> c_2(incr^#(XS))
  , oddNs^#() -> c_3(incr^#(pairNs()), pairNs^#())
  , take^#(s(N), cons(X, XS)) -> c_5(take^#(N, XS))
  , zip^#(cons(X, XS), cons(Y, YS)) -> c_7(zip^#(XS, YS))
  , repItems^#(cons(X, XS)) -> c_10(repItems^#(XS)) }
Weak Trs:
  { pairNs() -> cons(0(), incr(oddNs()))
  , incr(cons(X, XS)) -> cons(s(X), incr(XS))
  , oddNs() -> incr(pairNs())
  , take(0(), XS) -> nil()
  , take(s(N), cons(X, XS)) -> cons(X, take(N, XS))
  , zip(X, nil()) -> nil()
  , zip(cons(X, XS), cons(Y, YS)) -> cons(pair(X, Y), zip(XS, YS))
  , zip(nil(), XS) -> nil()
  , tail(cons(X, XS)) -> XS
  , repItems(cons(X, XS)) -> cons(X, cons(X, repItems(XS)))
  , repItems(nil()) -> nil() }
Obligation:
  innermost runtime complexity
Answer:
  MAYBE

We replace rewrite rules by usable rules:

  Weak Usable Rules:
    { pairNs() -> cons(0(), incr(oddNs()))
    , incr(cons(X, XS)) -> cons(s(X), incr(XS))
    , oddNs() -> incr(pairNs()) }

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

Strict DPs:
  { pairNs^#() -> c_1(incr^#(oddNs()), oddNs^#())
  , incr^#(cons(X, XS)) -> c_2(incr^#(XS))
  , oddNs^#() -> c_3(incr^#(pairNs()), pairNs^#())
  , take^#(s(N), cons(X, XS)) -> c_5(take^#(N, XS))
  , zip^#(cons(X, XS), cons(Y, YS)) -> c_7(zip^#(XS, YS))
  , repItems^#(cons(X, XS)) -> c_10(repItems^#(XS)) }
Weak Trs:
  { pairNs() -> cons(0(), incr(oddNs()))
  , incr(cons(X, XS)) -> cons(s(X), incr(XS))
  , oddNs() -> incr(pairNs()) }
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..