MAYBE

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

Strict Trs:
  { r(xs, ys, zs, nil()) -> xs
  , r(xs, nil(), zs, cons(w, ws)) ->
    r(xs, xs, cons(succ(zero()), zs), ws)
  , r(xs, cons(y, ys), nil(), cons(w, ws)) ->
    r(xs, xs, cons(succ(zero()), nil()), ws)
  , r(xs, cons(y, ys), cons(z, zs), cons(w, ws)) ->
    r(ys, cons(y, ys), zs, cons(succ(zero()), cons(w, ws))) }
Obligation:
  innermost runtime complexity
Answer:
  MAYBE

We add following weak dependency pairs:

Strict DPs:
  { r^#(xs, ys, zs, nil()) -> c_1()
  , r^#(xs, nil(), zs, cons(w, ws)) ->
    c_2(r^#(xs, xs, cons(succ(zero()), zs), ws))
  , r^#(xs, cons(y, ys), nil(), cons(w, ws)) ->
    c_3(r^#(xs, xs, cons(succ(zero()), nil()), ws))
  , r^#(xs, cons(y, ys), cons(z, zs), cons(w, ws)) ->
    c_4(r^#(ys, cons(y, ys), zs, cons(succ(zero()), cons(w, ws)))) }

and mark the set of starting terms.

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

Strict DPs:
  { r^#(xs, ys, zs, nil()) -> c_1()
  , r^#(xs, nil(), zs, cons(w, ws)) ->
    c_2(r^#(xs, xs, cons(succ(zero()), zs), ws))
  , r^#(xs, cons(y, ys), nil(), cons(w, ws)) ->
    c_3(r^#(xs, xs, cons(succ(zero()), nil()), ws))
  , r^#(xs, cons(y, ys), cons(z, zs), cons(w, ws)) ->
    c_4(r^#(ys, cons(y, ys), zs, cons(succ(zero()), cons(w, ws)))) }
Strict Trs:
  { r(xs, ys, zs, nil()) -> xs
  , r(xs, nil(), zs, cons(w, ws)) ->
    r(xs, xs, cons(succ(zero()), zs), ws)
  , r(xs, cons(y, ys), nil(), cons(w, ws)) ->
    r(xs, xs, cons(succ(zero()), nil()), ws)
  , r(xs, cons(y, ys), cons(z, zs), cons(w, ws)) ->
    r(ys, cons(y, ys), zs, cons(succ(zero()), cons(w, ws))) }
Obligation:
  innermost runtime complexity
Answer:
  MAYBE

No rule is usable, rules are removed from the input problem.

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

Strict DPs:
  { r^#(xs, ys, zs, nil()) -> c_1()
  , r^#(xs, nil(), zs, cons(w, ws)) ->
    c_2(r^#(xs, xs, cons(succ(zero()), zs), ws))
  , r^#(xs, cons(y, ys), nil(), cons(w, ws)) ->
    c_3(r^#(xs, xs, cons(succ(zero()), nil()), ws))
  , r^#(xs, cons(y, ys), cons(z, zs), cons(w, ws)) ->
    c_4(r^#(ys, cons(y, ys), zs, cons(succ(zero()), cons(w, ws)))) }
Obligation:
  innermost runtime complexity
Answer:
  MAYBE

The weightgap principle applies (using the following constant
growth matrix-interpretation)

The following argument positions are usable:
  Uargs(c_2) = {1}, Uargs(c_3) = {1}, Uargs(c_4) = {1}

TcT has computed following constructor-restricted matrix
interpretation.

                  [nil] = [0]         
                                      
         [cons](x1, x2) = [1] x2 + [0]
                                      
             [succ](x1) = [0]         
                                      
                 [zero] = [0]         
                                      
  [r^#](x1, x2, x3, x4) = [1]         
                                      
                  [c_1] = [0]         
                                      
              [c_2](x1) = [1] x1 + [0]
                                      
              [c_3](x1) = [1] x1 + [0]
                                      
              [c_4](x1) = [1] x1 + [0]

This order satisfies following ordering constraints:


Further, it can be verified that all rules not oriented are covered by the weightgap condition.

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

Strict DPs:
  { r^#(xs, nil(), zs, cons(w, ws)) ->
    c_2(r^#(xs, xs, cons(succ(zero()), zs), ws))
  , r^#(xs, cons(y, ys), nil(), cons(w, ws)) ->
    c_3(r^#(xs, xs, cons(succ(zero()), nil()), ws))
  , r^#(xs, cons(y, ys), cons(z, zs), cons(w, ws)) ->
    c_4(r^#(ys, cons(y, ys), zs, cons(succ(zero()), cons(w, ws)))) }
Weak DPs: { r^#(xs, ys, zs, nil()) -> c_1() }
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.

{ r^#(xs, ys, zs, nil()) -> c_1() }

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

Strict DPs:
  { r^#(xs, nil(), zs, cons(w, ws)) ->
    c_2(r^#(xs, xs, cons(succ(zero()), zs), ws))
  , r^#(xs, cons(y, ys), nil(), cons(w, ws)) ->
    c_3(r^#(xs, xs, cons(succ(zero()), nil()), ws))
  , r^#(xs, cons(y, ys), cons(z, zs), cons(w, ws)) ->
    c_4(r^#(ys, cons(y, ys), zs, cons(succ(zero()), cons(w, ws)))) }
Obligation:
  innermost runtime complexity
Answer:
  MAYBE

The input cannot be shown compatible

Arrrr..