MAYBE
Time: 0.010708
TRS:
 {  +(0(), y) -> y,
    +(s x, y) -> s +(x, y),
    *(x, 0()) -> 0(),
    *(x, s y) -> +(x, *(x, y)),
    twice 0() -> 0(),
    twice s x -> s s twice x,
    -(x, 0()) -> x,
  -(s x, s y) -> -(x, y),
        f s x -> f -(*(s s x, s s x), +(*(s x, s s x), s s 0()))}
 DP:
  DP:
   {  +#(s x, y) -> +#(x, y),
      *#(x, s y) -> +#(x, *(x, y)),
      *#(x, s y) -> *#(x, y),
      twice# s x -> twice# x,
    -#(s x, s y) -> -#(x, y),
          f# s x -> +#(*(s x, s s x), s s 0()),
          f# s x -> *#(s x, s s x),
          f# s x -> *#(s s x, s s x),
          f# s x -> -#(*(s s x, s s x), +(*(s x, s s x), s s 0())),
          f# s x -> f# -(*(s s x, s s x), +(*(s x, s s x), s s 0()))}
  TRS:
  {  +(0(), y) -> y,
     +(s x, y) -> s +(x, y),
     *(x, 0()) -> 0(),
     *(x, s y) -> +(x, *(x, y)),
     twice 0() -> 0(),
     twice s x -> s s twice x,
     -(x, 0()) -> x,
   -(s x, s y) -> -(x, y),
         f s x -> f -(*(s s x, s s x), +(*(s x, s s x), s s 0()))}
  UR:
   {  +(0(), y) -> y,
      +(s x, y) -> s +(x, y),
      *(x, 0()) -> 0(),
      *(x, s y) -> +(x, *(x, y)),
      -(x, 0()) -> x,
    -(s x, s y) -> -(x, y),
        a(z, w) -> z,
        a(z, w) -> w}
   EDG:
    {(*#(x, s y) -> +#(x, *(x, y)), +#(s x, y) -> +#(x, y))
     (f# s x -> +#(*(s x, s s x), s s 0()), +#(s x, y) -> +#(x, y))
     (f# s x -> *#(s s x, s s x), *#(x, s y) -> *#(x, y))
     (f# s x -> *#(s s x, s s x), *#(x, s y) -> +#(x, *(x, y)))
     (*#(x, s y) -> *#(x, y), *#(x, s y) -> *#(x, y))
     (*#(x, s y) -> *#(x, y), *#(x, s y) -> +#(x, *(x, y)))
     (f# s x -> f# -(*(s s x, s s x), +(*(s x, s s x), s s 0())), f# s x -> f# -(*(s s x, s s x), +(*(s x, s s x), s s 0())))
     (f# s x -> f# -(*(s s x, s s x), +(*(s x, s s x), s s 0())), f# s x -> -#(*(s s x, s s x), +(*(s x, s s x), s s 0())))
     (f# s x -> f# -(*(s s x, s s x), +(*(s x, s s x), s s 0())), f# s x -> *#(s s x, s s x))
     (f# s x -> f# -(*(s s x, s s x), +(*(s x, s s x), s s 0())), f# s x -> *#(s x, s s x))
     (f# s x -> f# -(*(s s x, s s x), +(*(s x, s s x), s s 0())), f# s x -> +#(*(s x, s s x), s s 0()))
     (-#(s x, s y) -> -#(x, y), -#(s x, s y) -> -#(x, y))
     (+#(s x, y) -> +#(x, y), +#(s x, y) -> +#(x, y))
     (f# s x -> *#(s x, s s x), *#(x, s y) -> +#(x, *(x, y)))
     (f# s x -> *#(s x, s s x), *#(x, s y) -> *#(x, y))
     (f# s x -> -#(*(s s x, s s x), +(*(s x, s s x), s s 0())), -#(s x, s y) -> -#(x, y))
     (twice# s x -> twice# x, twice# s x -> twice# x)}
    STATUS:
     arrows: 0.830000
     SCCS (5):
      Scc:
       {f# s x -> f# -(*(s s x, s s x), +(*(s x, s s x), s s 0()))}
      Scc:
       {*#(x, s y) -> *#(x, y)}
      Scc:
       {-#(s x, s y) -> -#(x, y)}
      Scc:
       {+#(s x, y) -> +#(x, y)}
      Scc:
       {twice# s x -> twice# x}
      
      SCC (1):
       Strict:
        {f# s x -> f# -(*(s s x, s s x), +(*(s x, s s x), s s 0()))}
       Weak:
       {  +(0(), y) -> y,
          +(s x, y) -> s +(x, y),
          *(x, 0()) -> 0(),
          *(x, s y) -> +(x, *(x, y)),
          twice 0() -> 0(),
          twice s x -> s s twice x,
          -(x, 0()) -> x,
        -(s x, s y) -> -(x, y),
              f s x -> f -(*(s s x, s s x), +(*(s x, s s x), s s 0()))}
       Open
      
      
      SCC (1):
       Strict:
        {*#(x, s y) -> *#(x, y)}
       Weak:
       {  +(0(), y) -> y,
          +(s x, y) -> s +(x, y),
          *(x, 0()) -> 0(),
          *(x, s y) -> +(x, *(x, y)),
          twice 0() -> 0(),
          twice s x -> s s twice x,
          -(x, 0()) -> x,
        -(s x, s y) -> -(x, y),
              f s x -> f -(*(s s x, s s x), +(*(s x, s s x), s s 0()))}
       Open
      
      
      SCC (1):
       Strict:
        {-#(s x, s y) -> -#(x, y)}
       Weak:
       {  +(0(), y) -> y,
          +(s x, y) -> s +(x, y),
          *(x, 0()) -> 0(),
          *(x, s y) -> +(x, *(x, y)),
          twice 0() -> 0(),
          twice s x -> s s twice x,
          -(x, 0()) -> x,
        -(s x, s y) -> -(x, y),
              f s x -> f -(*(s s x, s s x), +(*(s x, s s x), s s 0()))}
       Open
      
      SCC (1):
       Strict:
        {+#(s x, y) -> +#(x, y)}
       Weak:
       {  +(0(), y) -> y,
          +(s x, y) -> s +(x, y),
          *(x, 0()) -> 0(),
          *(x, s y) -> +(x, *(x, y)),
          twice 0() -> 0(),
          twice s x -> s s twice x,
          -(x, 0()) -> x,
        -(s x, s y) -> -(x, y),
              f s x -> f -(*(s s x, s s x), +(*(s x, s s x), s s 0()))}
       Open
      SCC (1):
       Strict:
        {twice# s x -> twice# x}
       Weak:
       {  +(0(), y) -> y,
          +(s x, y) -> s +(x, y),
          *(x, 0()) -> 0(),
          *(x, s y) -> +(x, *(x, y)),
          twice 0() -> 0(),
          twice s x -> s s twice x,
          -(x, 0()) -> x,
        -(s x, s y) -> -(x, y),
              f s x -> f -(*(s s x, s s x), +(*(s x, s s x), s s 0()))}
       Open