MAYBE

Problem:
 -(x,0()) -> x
 -(s(x),s(y)) -> -(x,y)
 +(0(),y) -> y
 +(s(x),y) -> s(+(x,y))
 *(x,0()) -> 0()
 *(x,s(y)) -> +(x,*(x,y))
 f(s(x)) -> f(-(+(*(s(x),s(x)),*(s(x),s(s(s(0()))))),*(s(s(x)),s(s(x)))))

Proof:
 DP Processor:
  DPs:
   -#(s(x),s(y)) -> -#(x,y)
   +#(s(x),y) -> +#(x,y)
   *#(x,s(y)) -> *#(x,y)
   *#(x,s(y)) -> +#(x,*(x,y))
   f#(s(x)) -> *#(s(s(x)),s(s(x)))
   f#(s(x)) -> *#(s(x),s(s(s(0()))))
   f#(s(x)) -> *#(s(x),s(x))
   f#(s(x)) -> +#(*(s(x),s(x)),*(s(x),s(s(s(0())))))
   f#(s(x)) -> -#(+(*(s(x),s(x)),*(s(x),s(s(s(0()))))),*(s(s(x)),s(s(x))))
   f#(s(x)) -> f#(-(+(*(s(x),s(x)),*(s(x),s(s(s(0()))))),*(s(s(x)),s(s(x)))))
  TRS:
   -(x,0()) -> x
   -(s(x),s(y)) -> -(x,y)
   +(0(),y) -> y
   +(s(x),y) -> s(+(x,y))
   *(x,0()) -> 0()
   *(x,s(y)) -> +(x,*(x,y))
   f(s(x)) -> f(-(+(*(s(x),s(x)),*(s(x),s(s(s(0()))))),*(s(s(x)),s(s(x)))))
  Usable Rule Processor:
   DPs:
    -#(s(x),s(y)) -> -#(x,y)
    +#(s(x),y) -> +#(x,y)
    *#(x,s(y)) -> *#(x,y)
    *#(x,s(y)) -> +#(x,*(x,y))
    f#(s(x)) -> *#(s(s(x)),s(s(x)))
    f#(s(x)) -> *#(s(x),s(s(s(0()))))
    f#(s(x)) -> *#(s(x),s(x))
    f#(s(x)) -> +#(*(s(x),s(x)),*(s(x),s(s(s(0())))))
    f#(s(x)) -> -#(+(*(s(x),s(x)),*(s(x),s(s(s(0()))))),*(s(s(x)),s(s(x))))
    f#(s(x)) -> f#(-(+(*(s(x),s(x)),*(s(x),s(s(s(0()))))),*(s(s(x)),s(s(x)))))
   TRS:
    *(x,0()) -> 0()
    *(x,s(y)) -> +(x,*(x,y))
    +(0(),y) -> y
    +(s(x),y) -> s(+(x,y))
    -(x,0()) -> x
    -(s(x),s(y)) -> -(x,y)
   Open