MAYBE

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

Strict Trs:
  { and(false(), false()) -> false()
  , and(false(), true()) -> false()
  , and(true(), false()) -> false()
  , and(true(), true()) -> true()
  , eq(nil(), nil()) -> true()
  , eq(nil(), cons(T, L)) -> false()
  , eq(cons(T, L), nil()) -> false()
  , eq(cons(T, L), cons(Tp, Lp)) -> and(eq(T, Tp), eq(L, Lp))
  , eq(var(L), var(Lp)) -> eq(L, Lp)
  , eq(var(L), apply(T, S)) -> false()
  , eq(var(L), lambda(X, T)) -> false()
  , eq(apply(T, S), var(L)) -> false()
  , eq(apply(T, S), apply(Tp, Sp)) -> and(eq(T, Tp), eq(S, Sp))
  , eq(apply(T, S), lambda(X, Tp)) -> false()
  , eq(lambda(X, T), var(L)) -> false()
  , eq(lambda(X, T), apply(Tp, Sp)) -> false()
  , eq(lambda(X, T), lambda(Xp, Tp)) -> and(eq(T, Tp), eq(X, Xp))
  , if(false(), var(K), var(L)) -> var(L)
  , if(true(), var(K), var(L)) -> var(K)
  , ren(X, Y, apply(T, S)) -> apply(ren(X, Y, T), ren(X, Y, S))
  , ren(X, Y, lambda(Z, T)) ->
    lambda(var(cons(X, cons(Y, cons(lambda(Z, T), nil())))),
           ren(X,
               Y,
               ren(Z, var(cons(X, cons(Y, cons(lambda(Z, T), nil())))), T)))
  , ren(var(L), var(K), var(Lp)) -> if(eq(L, Lp), var(K), var(Lp)) }
Obligation:
  innermost runtime complexity
Answer:
  MAYBE

The input cannot be shown compatible

Arrrr..