MAYBE
Time: 0.010

Problem:
 Equations:
  
 TRS:
  0(#()) -> #()
  +AC(#(),x) -> x
  +AC(0(x),0(y)) -> 0(+AC(x,y))
  +AC(0(x),1(y)) -> 1(+AC(x,y))
  +AC(1(x),1(y)) -> 0(+AC(1(#()),+AC(x,y)))
  *AC(#(),x) -> #()
  *AC(0(x),y) -> 0(*AC(x,y))
  *AC(1(x),y) -> +AC(0(*AC(x,y)),y)
  *AC(+AC(y,z),x) -> +AC(*AC(x,y),*AC(x,z))
  UAC(empty(),b) -> b
  sum(empty()) -> 0(#())
  sum(singl(x)) -> x
  sum(UAC(x,y)) -> +AC(sum(x),sum(y))
  prod(empty()) -> 1(#())
  prod(singl(x)) -> x
  prod(UAC(x,y)) -> *AC(prod(x),prod(y))

Proof:
 Open