MAYBE

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

Strict Trs:
  { app(nil(), YS) -> YS
  , app(cons(X, XS), YS) -> cons(X, app(XS, YS))
  , from(X) -> cons(X, from(s(X)))
  , zWadr(XS, nil()) -> nil()
  , zWadr(nil(), YS) -> nil()
  , zWadr(cons(X, XS), cons(Y, YS)) ->
    cons(app(Y, cons(X, nil())), zWadr(XS, YS))
  , prefix(L) -> cons(nil(), zWadr(L, prefix(L))) }
Obligation:
  innermost runtime complexity
Answer:
  MAYBE

We add following dependency tuples:

Strict DPs:
  { app^#(nil(), YS) -> c_1()
  , app^#(cons(X, XS), YS) -> c_2(app^#(XS, YS))
  , from^#(X) -> c_3(from^#(s(X)))
  , zWadr^#(XS, nil()) -> c_4()
  , zWadr^#(nil(), YS) -> c_5()
  , zWadr^#(cons(X, XS), cons(Y, YS)) ->
    c_6(app^#(Y, cons(X, nil())), zWadr^#(XS, YS))
  , prefix^#(L) -> c_7(zWadr^#(L, prefix(L)), prefix^#(L)) }

and mark the set of starting terms.

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

Strict DPs:
  { app^#(nil(), YS) -> c_1()
  , app^#(cons(X, XS), YS) -> c_2(app^#(XS, YS))
  , from^#(X) -> c_3(from^#(s(X)))
  , zWadr^#(XS, nil()) -> c_4()
  , zWadr^#(nil(), YS) -> c_5()
  , zWadr^#(cons(X, XS), cons(Y, YS)) ->
    c_6(app^#(Y, cons(X, nil())), zWadr^#(XS, YS))
  , prefix^#(L) -> c_7(zWadr^#(L, prefix(L)), prefix^#(L)) }
Weak Trs:
  { app(nil(), YS) -> YS
  , app(cons(X, XS), YS) -> cons(X, app(XS, YS))
  , from(X) -> cons(X, from(s(X)))
  , zWadr(XS, nil()) -> nil()
  , zWadr(nil(), YS) -> nil()
  , zWadr(cons(X, XS), cons(Y, YS)) ->
    cons(app(Y, cons(X, nil())), zWadr(XS, YS))
  , prefix(L) -> cons(nil(), zWadr(L, prefix(L))) }
Obligation:
  innermost runtime complexity
Answer:
  MAYBE

We estimate the number of application of {1,4,5} by applications of
Pre({1,4,5}) = {2,6,7}. Here rules are labeled as follows:

  DPs:
    { 1: app^#(nil(), YS) -> c_1()
    , 2: app^#(cons(X, XS), YS) -> c_2(app^#(XS, YS))
    , 3: from^#(X) -> c_3(from^#(s(X)))
    , 4: zWadr^#(XS, nil()) -> c_4()
    , 5: zWadr^#(nil(), YS) -> c_5()
    , 6: zWadr^#(cons(X, XS), cons(Y, YS)) ->
         c_6(app^#(Y, cons(X, nil())), zWadr^#(XS, YS))
    , 7: prefix^#(L) -> c_7(zWadr^#(L, prefix(L)), prefix^#(L)) }

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

Strict DPs:
  { app^#(cons(X, XS), YS) -> c_2(app^#(XS, YS))
  , from^#(X) -> c_3(from^#(s(X)))
  , zWadr^#(cons(X, XS), cons(Y, YS)) ->
    c_6(app^#(Y, cons(X, nil())), zWadr^#(XS, YS))
  , prefix^#(L) -> c_7(zWadr^#(L, prefix(L)), prefix^#(L)) }
Weak DPs:
  { app^#(nil(), YS) -> c_1()
  , zWadr^#(XS, nil()) -> c_4()
  , zWadr^#(nil(), YS) -> c_5() }
Weak Trs:
  { app(nil(), YS) -> YS
  , app(cons(X, XS), YS) -> cons(X, app(XS, YS))
  , from(X) -> cons(X, from(s(X)))
  , zWadr(XS, nil()) -> nil()
  , zWadr(nil(), YS) -> nil()
  , zWadr(cons(X, XS), cons(Y, YS)) ->
    cons(app(Y, cons(X, nil())), zWadr(XS, YS))
  , prefix(L) -> cons(nil(), zWadr(L, prefix(L))) }
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.

{ app^#(nil(), YS) -> c_1()
, zWadr^#(XS, nil()) -> c_4()
, zWadr^#(nil(), YS) -> c_5() }

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

Strict DPs:
  { app^#(cons(X, XS), YS) -> c_2(app^#(XS, YS))
  , from^#(X) -> c_3(from^#(s(X)))
  , zWadr^#(cons(X, XS), cons(Y, YS)) ->
    c_6(app^#(Y, cons(X, nil())), zWadr^#(XS, YS))
  , prefix^#(L) -> c_7(zWadr^#(L, prefix(L)), prefix^#(L)) }
Weak Trs:
  { app(nil(), YS) -> YS
  , app(cons(X, XS), YS) -> cons(X, app(XS, YS))
  , from(X) -> cons(X, from(s(X)))
  , zWadr(XS, nil()) -> nil()
  , zWadr(nil(), YS) -> nil()
  , zWadr(cons(X, XS), cons(Y, YS)) ->
    cons(app(Y, cons(X, nil())), zWadr(XS, YS))
  , prefix(L) -> cons(nil(), zWadr(L, prefix(L))) }
Obligation:
  innermost runtime complexity
Answer:
  MAYBE

We replace rewrite rules by usable rules:

  Weak Usable Rules:
    { app(nil(), YS) -> YS
    , app(cons(X, XS), YS) -> cons(X, app(XS, YS))
    , zWadr(XS, nil()) -> nil()
    , zWadr(nil(), YS) -> nil()
    , zWadr(cons(X, XS), cons(Y, YS)) ->
      cons(app(Y, cons(X, nil())), zWadr(XS, YS))
    , prefix(L) -> cons(nil(), zWadr(L, prefix(L))) }

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

Strict DPs:
  { app^#(cons(X, XS), YS) -> c_2(app^#(XS, YS))
  , from^#(X) -> c_3(from^#(s(X)))
  , zWadr^#(cons(X, XS), cons(Y, YS)) ->
    c_6(app^#(Y, cons(X, nil())), zWadr^#(XS, YS))
  , prefix^#(L) -> c_7(zWadr^#(L, prefix(L)), prefix^#(L)) }
Weak Trs:
  { app(nil(), YS) -> YS
  , app(cons(X, XS), YS) -> cons(X, app(XS, YS))
  , zWadr(XS, nil()) -> nil()
  , zWadr(nil(), YS) -> nil()
  , zWadr(cons(X, XS), cons(Y, YS)) ->
    cons(app(Y, cons(X, nil())), zWadr(XS, YS))
  , prefix(L) -> cons(nil(), zWadr(L, prefix(L))) }
Obligation:
  innermost runtime complexity
Answer:
  MAYBE

The input cannot be shown compatible

Arrrr..