MAYBE

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

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