MAYBE
TRS:
 {f(true(), x, y, z) -> f(gt(x, plus(y, z)), x, y, s(z)),
  f(true(), x, y, z) -> f(gt(x, plus(y, z)), x, s(y), z),
      gt(s(u), s(v)) -> gt(u, v),
       gt(s(u), 0()) -> true(),
          gt(0(), v) -> false(),
       plus(n, s(m)) -> s(plus(n, m)),
        plus(n, 0()) -> n}
 DP:
  Strict:
   {f#(true(), x, y, z) -> f#(gt(x, plus(y, z)), x, y, s(z)),
    f#(true(), x, y, z) -> f#(gt(x, plus(y, z)), x, s(y), z),
    f#(true(), x, y, z) -> gt#(x, plus(y, z)),
    f#(true(), x, y, z) -> plus#(y, z),
        gt#(s(u), s(v)) -> gt#(u, v),
         plus#(n, s(m)) -> plus#(n, m)}
  Weak:
  {f(true(), x, y, z) -> f(gt(x, plus(y, z)), x, y, s(z)),
   f(true(), x, y, z) -> f(gt(x, plus(y, z)), x, s(y), z),
       gt(s(u), s(v)) -> gt(u, v),
        gt(s(u), 0()) -> true(),
           gt(0(), v) -> false(),
        plus(n, s(m)) -> s(plus(n, m)),
         plus(n, 0()) -> n}
  EDG:
   {(f#(true(), x, y, z) -> gt#(x, plus(y, z)), gt#(s(u), s(v)) -> gt#(u, v))
    (f#(true(), x, y, z) -> plus#(y, z), plus#(n, s(m)) -> plus#(n, m))
    (gt#(s(u), s(v)) -> gt#(u, v), gt#(s(u), s(v)) -> gt#(u, v))
    (f#(true(), x, y, z) -> f#(gt(x, plus(y, z)), x, y, s(z)), f#(true(), x, y, z) -> f#(gt(x, plus(y, z)), x, y, s(z)))
    (f#(true(), x, y, z) -> f#(gt(x, plus(y, z)), x, y, s(z)), f#(true(), x, y, z) -> f#(gt(x, plus(y, z)), x, s(y), z))
    (f#(true(), x, y, z) -> f#(gt(x, plus(y, z)), x, y, s(z)), f#(true(), x, y, z) -> gt#(x, plus(y, z)))
    (f#(true(), x, y, z) -> f#(gt(x, plus(y, z)), x, y, s(z)), f#(true(), x, y, z) -> plus#(y, z))
    (f#(true(), x, y, z) -> f#(gt(x, plus(y, z)), x, s(y), z), f#(true(), x, y, z) -> f#(gt(x, plus(y, z)), x, y, s(z)))
    (f#(true(), x, y, z) -> f#(gt(x, plus(y, z)), x, s(y), z), f#(true(), x, y, z) -> f#(gt(x, plus(y, z)), x, s(y), z))
    (f#(true(), x, y, z) -> f#(gt(x, plus(y, z)), x, s(y), z), f#(true(), x, y, z) -> gt#(x, plus(y, z)))
    (f#(true(), x, y, z) -> f#(gt(x, plus(y, z)), x, s(y), z), f#(true(), x, y, z) -> plus#(y, z))
    (plus#(n, s(m)) -> plus#(n, m), plus#(n, s(m)) -> plus#(n, m))}
   SCCS:
    Scc:
     {plus#(n, s(m)) -> plus#(n, m)}
    Scc:
     {gt#(s(u), s(v)) -> gt#(u, v)}
    Scc:
     {f#(true(), x, y, z) -> f#(gt(x, plus(y, z)), x, y, s(z)),
      f#(true(), x, y, z) -> f#(gt(x, plus(y, z)), x, s(y), z)}
    SCC:
     Strict:
      {plus#(n, s(m)) -> plus#(n, m)}
     Weak:
     {f(true(), x, y, z) -> f(gt(x, plus(y, z)), x, y, s(z)),
      f(true(), x, y, z) -> f(gt(x, plus(y, z)), x, s(y), z),
          gt(s(u), s(v)) -> gt(u, v),
           gt(s(u), 0()) -> true(),
              gt(0(), v) -> false(),
           plus(n, s(m)) -> s(plus(n, m)),
            plus(n, 0()) -> n}
     SPSC:
      Simple Projection:
       pi(plus#) = 1
      Strict:
       {}
      Qed
    SCC:
     Strict:
      {gt#(s(u), s(v)) -> gt#(u, v)}
     Weak:
     {f(true(), x, y, z) -> f(gt(x, plus(y, z)), x, y, s(z)),
      f(true(), x, y, z) -> f(gt(x, plus(y, z)), x, s(y), z),
          gt(s(u), s(v)) -> gt(u, v),
           gt(s(u), 0()) -> true(),
              gt(0(), v) -> false(),
           plus(n, s(m)) -> s(plus(n, m)),
            plus(n, 0()) -> n}
     SPSC:
      Simple Projection:
       pi(gt#) = 0
      Strict:
       {}
      Qed
    SCC:
     Strict:
      {f#(true(), x, y, z) -> f#(gt(x, plus(y, z)), x, y, s(z)),
       f#(true(), x, y, z) -> f#(gt(x, plus(y, z)), x, s(y), z)}
     Weak:
     {f(true(), x, y, z) -> f(gt(x, plus(y, z)), x, y, s(z)),
      f(true(), x, y, z) -> f(gt(x, plus(y, z)), x, s(y), z),
          gt(s(u), s(v)) -> gt(u, v),
           gt(s(u), 0()) -> true(),
              gt(0(), v) -> false(),
           plus(n, s(m)) -> s(plus(n, m)),
            plus(n, 0()) -> n}
     Fail