MAYBE

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

Strict Trs:
  { purge(nil()) -> nil()
  , purge(.(x, y)) -> .(x, purge(remove(x, y)))
  , remove(x, nil()) -> nil()
  , remove(x, .(y, z)) ->
    if(=(x, y), remove(x, z), .(y, remove(x, z))) }
Obligation:
  innermost runtime complexity
Answer:
  MAYBE

We add following dependency tuples:

Strict DPs:
  { purge^#(nil()) -> c_1()
  , purge^#(.(x, y)) -> c_2(purge^#(remove(x, y)), remove^#(x, y))
  , remove^#(x, nil()) -> c_3()
  , remove^#(x, .(y, z)) -> c_4(remove^#(x, z), remove^#(x, z)) }

and mark the set of starting terms.

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

Strict DPs:
  { purge^#(nil()) -> c_1()
  , purge^#(.(x, y)) -> c_2(purge^#(remove(x, y)), remove^#(x, y))
  , remove^#(x, nil()) -> c_3()
  , remove^#(x, .(y, z)) -> c_4(remove^#(x, z), remove^#(x, z)) }
Weak Trs:
  { purge(nil()) -> nil()
  , purge(.(x, y)) -> .(x, purge(remove(x, y)))
  , remove(x, nil()) -> nil()
  , remove(x, .(y, z)) ->
    if(=(x, y), remove(x, z), .(y, remove(x, z))) }
Obligation:
  innermost runtime complexity
Answer:
  MAYBE

We estimate the number of application of {1,3} by applications of
Pre({1,3}) = {2,4}. Here rules are labeled as follows:

  DPs:
    { 1: purge^#(nil()) -> c_1()
    , 2: purge^#(.(x, y)) -> c_2(purge^#(remove(x, y)), remove^#(x, y))
    , 3: remove^#(x, nil()) -> c_3()
    , 4: remove^#(x, .(y, z)) -> c_4(remove^#(x, z), remove^#(x, z)) }

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

Strict DPs:
  { purge^#(.(x, y)) -> c_2(purge^#(remove(x, y)), remove^#(x, y))
  , remove^#(x, .(y, z)) -> c_4(remove^#(x, z), remove^#(x, z)) }
Weak DPs:
  { purge^#(nil()) -> c_1()
  , remove^#(x, nil()) -> c_3() }
Weak Trs:
  { purge(nil()) -> nil()
  , purge(.(x, y)) -> .(x, purge(remove(x, y)))
  , remove(x, nil()) -> nil()
  , remove(x, .(y, z)) ->
    if(=(x, y), remove(x, z), .(y, remove(x, z))) }
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.

{ purge^#(nil()) -> c_1()
, remove^#(x, nil()) -> c_3() }

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

Strict DPs:
  { purge^#(.(x, y)) -> c_2(purge^#(remove(x, y)), remove^#(x, y))
  , remove^#(x, .(y, z)) -> c_4(remove^#(x, z), remove^#(x, z)) }
Weak Trs:
  { purge(nil()) -> nil()
  , purge(.(x, y)) -> .(x, purge(remove(x, y)))
  , remove(x, nil()) -> nil()
  , remove(x, .(y, z)) ->
    if(=(x, y), remove(x, z), .(y, remove(x, z))) }
Obligation:
  innermost runtime complexity
Answer:
  MAYBE

We replace rewrite rules by usable rules:

  Weak Usable Rules:
    { remove(x, nil()) -> nil()
    , remove(x, .(y, z)) ->
      if(=(x, y), remove(x, z), .(y, remove(x, z))) }

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

Strict DPs:
  { purge^#(.(x, y)) -> c_2(purge^#(remove(x, y)), remove^#(x, y))
  , remove^#(x, .(y, z)) -> c_4(remove^#(x, z), remove^#(x, z)) }
Weak Trs:
  { remove(x, nil()) -> nil()
  , remove(x, .(y, z)) ->
    if(=(x, y), remove(x, z), .(y, remove(x, z))) }
Obligation:
  innermost runtime complexity
Answer:
  MAYBE

The input cannot be shown compatible

Arrrr..