MAYBE
Time: 3.034

Problem:
 Equations:
  plusAC(plusAC(x2,x3),x4) -> plusAC(x2,plusAC(x3,x4))
  plusAC(x2,x3) -> plusAC(x3,x2)
  timesAC(timesAC(x2,x3),x4) -> timesAC(x2,timesAC(x3,x4))
  timesAC(x2,x3) -> timesAC(x3,x2)
  plusAC(x2,plusAC(x3,x4)) -> plusAC(plusAC(x2,x3),x4)
  plusAC(x3,x2) -> plusAC(x2,x3)
  timesAC(x2,timesAC(x3,x4)) -> timesAC(timesAC(x2,x3),x4)
  timesAC(x3,x2) -> timesAC(x2,x3)
 TRS:
  0(S()) -> S()
  plusAC(S(),x) -> x
  plusAC(0(x),0(y)) -> 0(plusAC(x,y))
  plusAC(0(x),1(y)) -> 1(plusAC(x,y))
  plusAC(0(x),j(y)) -> j(plusAC(x,y))
  plusAC(1(x),1(y)) -> j(plusAC(1(S()),plusAC(x,y)))
  plusAC(j(x),j(y)) -> 1(plusAC(j(S()),plusAC(x,y)))
  plusAC(1(x),j(y)) -> 0(plusAC(x,y))
  opp(S()) -> S()
  opp(0(x)) -> 0(opp(x))
  opp(1(x)) -> j(opp(x))
  opp(j(x)) -> 1(opp(x))
  minus(x,y) -> plusAC(opp(y),x)
  timesAC(S(),x) -> S()
  timesAC(0(x),y) -> 0(timesAC(x,y))
  timesAC(1(x),y) -> plusAC(0(timesAC(x,y)),y)
  timesAC(j(x),y) -> minus(0(timesAC(x,y)),y)

Proof:
 DP Processor:
  Equations#:
   plus{AC,#}(plusAC(x2,x3),x4) -> plus{AC,#}(x2,plusAC(x3,x4))
   plus{AC,#}(x2,x3) -> plus{AC,#}(x3,x2)
   times{AC,#}(timesAC(x2,x3),x4) -> times{AC,#}(x2,timesAC(x3,x4))
   times{AC,#}(x2,x3) -> times{AC,#}(x3,x2)
   plus{AC,#}(x2,plusAC(x3,x4)) -> plus{AC,#}(plusAC(x2,x3),x4)
   plus{AC,#}(x3,x2) -> plus{AC,#}(x2,x3)
   times{AC,#}(x2,timesAC(x3,x4)) -> times{AC,#}(timesAC(x2,x3),x4)
   times{AC,#}(x3,x2) -> times{AC,#}(x2,x3)
  DPs:
   plus{AC,#}(0(x),0(y)) -> plus{AC,#}(x,y)
   plus{AC,#}(0(x),0(y)) -> 0#(plusAC(x,y))
   plus{AC,#}(0(x),1(y)) -> plus{AC,#}(x,y)
   plus{AC,#}(0(x),j(y)) -> plus{AC,#}(x,y)
   plus{AC,#}(1(x),1(y)) -> plus{AC,#}(x,y)
   plus{AC,#}(1(x),1(y)) -> plus{AC,#}(1(S()),plusAC(x,y))
   plus{AC,#}(j(x),j(y)) -> plus{AC,#}(x,y)
   plus{AC,#}(j(x),j(y)) -> plus{AC,#}(j(S()),plusAC(x,y))
   plus{AC,#}(1(x),j(y)) -> plus{AC,#}(x,y)
   plus{AC,#}(1(x),j(y)) -> 0#(plusAC(x,y))
   opp#(0(x)) -> opp#(x)
   opp#(0(x)) -> 0#(opp(x))
   opp#(1(x)) -> opp#(x)
   opp#(j(x)) -> opp#(x)
   minus#(x,y) -> opp#(y)
   minus#(x,y) -> plus{AC,#}(opp(y),x)
   times{AC,#}(0(x),y) -> times{AC,#}(x,y)
   times{AC,#}(0(x),y) -> 0#(timesAC(x,y))
   times{AC,#}(1(x),y) -> times{AC,#}(x,y)
   times{AC,#}(1(x),y) -> 0#(timesAC(x,y))
   times{AC,#}(1(x),y) -> plus{AC,#}(0(timesAC(x,y)),y)
   times{AC,#}(j(x),y) -> times{AC,#}(x,y)
   times{AC,#}(j(x),y) -> 0#(timesAC(x,y))
   times{AC,#}(j(x),y) -> minus#(0(timesAC(x,y)),y)
   plus{AC,#}(x5,plusAC(S(),x)) -> plus{AC,#}(x5,x)
   plus{AC,#}(x6,plusAC(0(x),0(y))) -> plus{AC,#}(x,y)
   plus{AC,#}(x6,plusAC(0(x),0(y))) -> 0#(plusAC(x,y))
   plus{AC,#}(x6,plusAC(0(x),0(y))) -> plus{AC,#}(x6,0(plusAC(x,y)))
   plus{AC,#}(x7,plusAC(0(x),1(y))) -> plus{AC,#}(x,y)
   plus{AC,#}(x7,plusAC(0(x),1(y))) -> plus{AC,#}(x7,1(plusAC(x,y)))
   plus{AC,#}(x8,plusAC(0(x),j(y))) -> plus{AC,#}(x,y)
   plus{AC,#}(x8,plusAC(0(x),j(y))) -> plus{AC,#}(x8,j(plusAC(x,y)))
   plus{AC,#}(x9,plusAC(1(x),1(y))) -> plus{AC,#}(x,y)
   plus{AC,#}(x9,plusAC(1(x),1(y))) -> plus{AC,#}(1(S()),plusAC(x,y))
   plus{AC,#}(x9,plusAC(1(x),1(y))) -> plus{AC,#}(x9,j(plusAC(1(S()),plusAC(x,y))))
   plus{AC,#}(x10,plusAC(j(x),j(y))) -> plus{AC,#}(x,y)
   plus{AC,#}(x10,plusAC(j(x),j(y))) -> plus{AC,#}(j(S()),plusAC(x,y))
   plus{AC,#}(x10,plusAC(j(x),j(y))) -> plus{AC,#}(x10,1(plusAC(j(S()),plusAC(x,y))))
   plus{AC,#}(x11,plusAC(1(x),j(y))) -> plus{AC,#}(x,y)
   plus{AC,#}(x11,plusAC(1(x),j(y))) -> 0#(plusAC(x,y))
   plus{AC,#}(x11,plusAC(1(x),j(y))) -> plus{AC,#}(x11,0(plusAC(x,y)))
   times{AC,#}(x12,timesAC(S(),x)) -> times{AC,#}(x12,S())
   times{AC,#}(x13,timesAC(0(x),y)) -> times{AC,#}(x,y)
   times{AC,#}(x13,timesAC(0(x),y)) -> 0#(timesAC(x,y))
   times{AC,#}(x13,timesAC(0(x),y)) -> times{AC,#}(x13,0(timesAC(x,y)))
   times{AC,#}(x14,timesAC(1(x),y)) -> times{AC,#}(x,y)
   times{AC,#}(x14,timesAC(1(x),y)) -> 0#(timesAC(x,y))
   times{AC,#}(x14,timesAC(1(x),y)) -> plus{AC,#}(0(timesAC(x,y)),y)
   times{AC,#}(x14,timesAC(1(x),y)) -> times{AC,#}(x14,plusAC(0(timesAC(x,y)),y))
   times{AC,#}(x15,timesAC(j(x),y)) -> times{AC,#}(x,y)
   times{AC,#}(x15,timesAC(j(x),y)) -> 0#(timesAC(x,y))
   times{AC,#}(x15,timesAC(j(x),y)) -> minus#(0(timesAC(x,y)),y)
   times{AC,#}(x15,timesAC(j(x),y)) -> times{AC,#}(x15,minus(0(timesAC(x,y)),y))
  Equations:
   plusAC(plusAC(x2,x3),x4) -> plusAC(x2,plusAC(x3,x4))
   plusAC(x2,x3) -> plusAC(x3,x2)
   timesAC(timesAC(x2,x3),x4) -> timesAC(x2,timesAC(x3,x4))
   timesAC(x2,x3) -> timesAC(x3,x2)
   plusAC(x2,plusAC(x3,x4)) -> plusAC(plusAC(x2,x3),x4)
   plusAC(x3,x2) -> plusAC(x2,x3)
   timesAC(x2,timesAC(x3,x4)) -> timesAC(timesAC(x2,x3),x4)
   timesAC(x3,x2) -> timesAC(x2,x3)
  TRS:
   0(S()) -> S()
   plusAC(S(),x) -> x
   plusAC(0(x),0(y)) -> 0(plusAC(x,y))
   plusAC(0(x),1(y)) -> 1(plusAC(x,y))
   plusAC(0(x),j(y)) -> j(plusAC(x,y))
   plusAC(1(x),1(y)) -> j(plusAC(1(S()),plusAC(x,y)))
   plusAC(j(x),j(y)) -> 1(plusAC(j(S()),plusAC(x,y)))
   plusAC(1(x),j(y)) -> 0(plusAC(x,y))
   opp(S()) -> S()
   opp(0(x)) -> 0(opp(x))
   opp(1(x)) -> j(opp(x))
   opp(j(x)) -> 1(opp(x))
   minus(x,y) -> plusAC(opp(y),x)
   timesAC(S(),x) -> S()
   timesAC(0(x),y) -> 0(timesAC(x,y))
   timesAC(1(x),y) -> plusAC(0(timesAC(x,y)),y)
   timesAC(j(x),y) -> minus(0(timesAC(x,y)),y)
  S:
   plus{AC,#}(plusAC(x16,x17),x18) -> plus{AC,#}(x16,x17)
   plus{AC,#}(x16,plusAC(x17,x18)) -> plus{AC,#}(x17,x18)
   times{AC,#}(timesAC(x16,x17),x18) -> times{AC,#}(x16,x17)
   times{AC,#}(x16,timesAC(x17,x18)) -> times{AC,#}(x17,x18)
  AC-EDG Processor:
   Equations#:
    plus{AC,#}(plusAC(x2,x3),x4) -> plus{AC,#}(x2,plusAC(x3,x4))
    plus{AC,#}(x2,x3) -> plus{AC,#}(x3,x2)
    times{AC,#}(timesAC(x2,x3),x4) -> times{AC,#}(x2,timesAC(x3,x4))
    times{AC,#}(x2,x3) -> times{AC,#}(x3,x2)
    plus{AC,#}(x2,plusAC(x3,x4)) -> plus{AC,#}(plusAC(x2,x3),x4)
    plus{AC,#}(x3,x2) -> plus{AC,#}(x2,x3)
    times{AC,#}(x2,timesAC(x3,x4)) -> times{AC,#}(timesAC(x2,x3),x4)
    times{AC,#}(x3,x2) -> times{AC,#}(x2,x3)
   DPs:
    plus{AC,#}(0(x),0(y)) -> plus{AC,#}(x,y)
    plus{AC,#}(0(x),0(y)) -> 0#(plusAC(x,y))
    plus{AC,#}(0(x),1(y)) -> plus{AC,#}(x,y)
    plus{AC,#}(0(x),j(y)) -> plus{AC,#}(x,y)
    plus{AC,#}(1(x),1(y)) -> plus{AC,#}(x,y)
    plus{AC,#}(1(x),1(y)) -> plus{AC,#}(1(S()),plusAC(x,y))
    plus{AC,#}(j(x),j(y)) -> plus{AC,#}(x,y)
    plus{AC,#}(j(x),j(y)) -> plus{AC,#}(j(S()),plusAC(x,y))
    plus{AC,#}(1(x),j(y)) -> plus{AC,#}(x,y)
    plus{AC,#}(1(x),j(y)) -> 0#(plusAC(x,y))
    opp#(0(x)) -> opp#(x)
    opp#(0(x)) -> 0#(opp(x))
    opp#(1(x)) -> opp#(x)
    opp#(j(x)) -> opp#(x)
    minus#(x,y) -> opp#(y)
    minus#(x,y) -> plus{AC,#}(opp(y),x)
    times{AC,#}(0(x),y) -> times{AC,#}(x,y)
    times{AC,#}(0(x),y) -> 0#(timesAC(x,y))
    times{AC,#}(1(x),y) -> times{AC,#}(x,y)
    times{AC,#}(1(x),y) -> 0#(timesAC(x,y))
    times{AC,#}(1(x),y) -> plus{AC,#}(0(timesAC(x,y)),y)
    times{AC,#}(j(x),y) -> times{AC,#}(x,y)
    times{AC,#}(j(x),y) -> 0#(timesAC(x,y))
    times{AC,#}(j(x),y) -> minus#(0(timesAC(x,y)),y)
    plus{AC,#}(x5,plusAC(S(),x)) -> plus{AC,#}(x5,x)
    plus{AC,#}(x6,plusAC(0(x),0(y))) -> plus{AC,#}(x,y)
    plus{AC,#}(x6,plusAC(0(x),0(y))) -> 0#(plusAC(x,y))
    plus{AC,#}(x6,plusAC(0(x),0(y))) -> plus{AC,#}(x6,0(plusAC(x,y)))
    plus{AC,#}(x7,plusAC(0(x),1(y))) -> plus{AC,#}(x,y)
    plus{AC,#}(x7,plusAC(0(x),1(y))) -> plus{AC,#}(x7,1(plusAC(x,y)))
    plus{AC,#}(x8,plusAC(0(x),j(y))) -> plus{AC,#}(x,y)
    plus{AC,#}(x8,plusAC(0(x),j(y))) -> plus{AC,#}(x8,j(plusAC(x,y)))
    plus{AC,#}(x9,plusAC(1(x),1(y))) -> plus{AC,#}(x,y)
    plus{AC,#}(x9,plusAC(1(x),1(y))) -> plus{AC,#}(1(S()),plusAC(x,y))
    plus{AC,#}(x9,plusAC(1(x),1(y))) -> plus{AC,#}(x9,j(plusAC(1(S()),plusAC(x,y))))
    plus{AC,#}(x10,plusAC(j(x),j(y))) -> plus{AC,#}(x,y)
    plus{AC,#}(x10,plusAC(j(x),j(y))) -> plus{AC,#}(j(S()),plusAC(x,y))
    plus{AC,#}(x10,plusAC(j(x),j(y))) -> plus{AC,#}(x10,1(plusAC(j(S()),plusAC(x,y))))
    plus{AC,#}(x11,plusAC(1(x),j(y))) -> plus{AC,#}(x,y)
    plus{AC,#}(x11,plusAC(1(x),j(y))) -> 0#(plusAC(x,y))
    plus{AC,#}(x11,plusAC(1(x),j(y))) -> plus{AC,#}(x11,0(plusAC(x,y)))
    times{AC,#}(x12,timesAC(S(),x)) -> times{AC,#}(x12,S())
    times{AC,#}(x13,timesAC(0(x),y)) -> times{AC,#}(x,y)
    times{AC,#}(x13,timesAC(0(x),y)) -> 0#(timesAC(x,y))
    times{AC,#}(x13,timesAC(0(x),y)) -> times{AC,#}(x13,0(timesAC(x,y)))
    times{AC,#}(x14,timesAC(1(x),y)) -> times{AC,#}(x,y)
    times{AC,#}(x14,timesAC(1(x),y)) -> 0#(timesAC(x,y))
    times{AC,#}(x14,timesAC(1(x),y)) -> plus{AC,#}(0(timesAC(x,y)),y)
    times{AC,#}(x14,timesAC(1(x),y)) -> times{AC,#}(x14,plusAC(0(timesAC(x,y)),y))
    times{AC,#}(x15,timesAC(j(x),y)) -> times{AC,#}(x,y)
    times{AC,#}(x15,timesAC(j(x),y)) -> 0#(timesAC(x,y))
    times{AC,#}(x15,timesAC(j(x),y)) -> minus#(0(timesAC(x,y)),y)
    times{AC,#}(x15,timesAC(j(x),y)) -> times{AC,#}(x15,minus(0(timesAC(x,y)),y))
   Equations:
    plusAC(plusAC(x2,x3),x4) -> plusAC(x2,plusAC(x3,x4))
    plusAC(x2,x3) -> plusAC(x3,x2)
    timesAC(timesAC(x2,x3),x4) -> timesAC(x2,timesAC(x3,x4))
    timesAC(x2,x3) -> timesAC(x3,x2)
    plusAC(x2,plusAC(x3,x4)) -> plusAC(plusAC(x2,x3),x4)
    plusAC(x3,x2) -> plusAC(x2,x3)
    timesAC(x2,timesAC(x3,x4)) -> timesAC(timesAC(x2,x3),x4)
    timesAC(x3,x2) -> timesAC(x2,x3)
   TRS:
    0(S()) -> S()
    plusAC(S(),x) -> x
    plusAC(0(x),0(y)) -> 0(plusAC(x,y))
    plusAC(0(x),1(y)) -> 1(plusAC(x,y))
    plusAC(0(x),j(y)) -> j(plusAC(x,y))
    plusAC(1(x),1(y)) -> j(plusAC(1(S()),plusAC(x,y)))
    plusAC(j(x),j(y)) -> 1(plusAC(j(S()),plusAC(x,y)))
    plusAC(1(x),j(y)) -> 0(plusAC(x,y))
    opp(S()) -> S()
    opp(0(x)) -> 0(opp(x))
    opp(1(x)) -> j(opp(x))
    opp(j(x)) -> 1(opp(x))
    minus(x,y) -> plusAC(opp(y),x)
    timesAC(S(),x) -> S()
    timesAC(0(x),y) -> 0(timesAC(x,y))
    timesAC(1(x),y) -> plusAC(0(timesAC(x,y)),y)
    timesAC(j(x),y) -> minus(0(timesAC(x,y)),y)
   S:
    plus{AC,#}(plusAC(x16,x17),x18) -> plus{AC,#}(x16,x17)
    plus{AC,#}(x16,plusAC(x17,x18)) -> plus{AC,#}(x17,x18)
    times{AC,#}(timesAC(x16,x17),x18) -> times{AC,#}(x16,x17)
    times{AC,#}(x16,timesAC(x17,x18)) -> times{AC,#}(x17,x18)
   Open