MAYBE
Time: 3.579

Problem:
 Equations:
  plusAC(plusAC(x4,x5),x6) -> plusAC(x4,plusAC(x5,x6))
  plusAC(x4,x5) -> plusAC(x5,x4)
  timesAC(timesAC(x4,x5),x6) -> timesAC(x4,timesAC(x5,x6))
  timesAC(x4,x5) -> timesAC(x5,x4)
  plusAC(x4,plusAC(x5,x6)) -> plusAC(plusAC(x4,x5),x6)
  plusAC(x5,x4) -> plusAC(x4,x5)
  timesAC(x4,timesAC(x5,x6)) -> timesAC(timesAC(x4,x5),x6)
  timesAC(x5,x4) -> timesAC(x4,x5)
 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)
  sign(x) -> if_sign(x,S())
  if_sign(S(),x) -> x
  if_sign(0(x),y) -> if_sign(x,y)
  if_sign(1(x),y) -> if_sign(x,1(S()))
  if_sign(j(x),y) -> if_sign(x,j(S()))
  abs(x) -> if_abs(x,x,S())
  if_abs(0(x),y,z) -> if_abs(x,y,z)
  if_abs(1(x),y,z) -> if_abs(x,y,1(S()))
  if_abs(j(x),y,z) -> if_abs(x,y,j(S()))
  if_abs(S(),x,S()) -> S()
  if_abs(S(),x,1(S())) -> x
  if_abs(S(),x,j(S())) -> opp(x)
  min(x,y) -> if_min(minus(abs(y),abs(x)),x,y,S())
  min'(x,y) -> if_min(minus(abs(1(y)),abs(1(x))),x,y,S())
  min''(x,y) -> if_min(minus(abs(j(y)),abs(j(x))),x,y,S())
  if_min(0(x),y,z,u) -> if_min(x,y,z,u)
  if_min(1(x),y,z,u) -> if_min(x,y,z,1(S()))
  if_min(j(x),y,z,u) -> if_min(x,y,z,j(S()))
  if_min(S(),x,y,S()) -> x
  if_min(S(),x,y,1(S())) -> x
  if_min(S(),x,y,j(S())) -> y

Proof:
 DP Processor:
  Equations#:
   plus{AC,#}(plusAC(x4,x5),x6) -> plus{AC,#}(x4,plusAC(x5,x6))
   plus{AC,#}(x4,x5) -> plus{AC,#}(x5,x4)
   times{AC,#}(timesAC(x4,x5),x6) -> times{AC,#}(x4,timesAC(x5,x6))
   times{AC,#}(x4,x5) -> times{AC,#}(x5,x4)
   plus{AC,#}(x4,plusAC(x5,x6)) -> plus{AC,#}(plusAC(x4,x5),x6)
   plus{AC,#}(x5,x4) -> plus{AC,#}(x4,x5)
   times{AC,#}(x4,timesAC(x5,x6)) -> times{AC,#}(timesAC(x4,x5),x6)
   times{AC,#}(x5,x4) -> times{AC,#}(x4,x5)
  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)
   sign#(x) -> if_sign#(x,S())
   if_sign#(0(x),y) -> if_sign#(x,y)
   if_sign#(1(x),y) -> if_sign#(x,1(S()))
   if_sign#(j(x),y) -> if_sign#(x,j(S()))
   abs#(x) -> if_abs#(x,x,S())
   if_abs#(0(x),y,z) -> if_abs#(x,y,z)
   if_abs#(1(x),y,z) -> if_abs#(x,y,1(S()))
   if_abs#(j(x),y,z) -> if_abs#(x,y,j(S()))
   if_abs#(S(),x,j(S())) -> opp#(x)
   min#(x,y) -> abs#(x)
   min#(x,y) -> abs#(y)
   min#(x,y) -> minus#(abs(y),abs(x))
   min#(x,y) -> if_min#(minus(abs(y),abs(x)),x,y,S())
   min'#(x,y) -> abs#(1(x))
   min'#(x,y) -> abs#(1(y))
   min'#(x,y) -> minus#(abs(1(y)),abs(1(x)))
   min'#(x,y) -> if_min#(minus(abs(1(y)),abs(1(x))),x,y,S())
   min''#(x,y) -> abs#(j(x))
   min''#(x,y) -> abs#(j(y))
   min''#(x,y) -> minus#(abs(j(y)),abs(j(x)))
   min''#(x,y) -> if_min#(minus(abs(j(y)),abs(j(x))),x,y,S())
   if_min#(0(x),y,z,u) -> if_min#(x,y,z,u)
   if_min#(1(x),y,z,u) -> if_min#(x,y,z,1(S()))
   if_min#(j(x),y,z,u) -> if_min#(x,y,z,j(S()))
   plus{AC,#}(x7,plusAC(S(),x)) -> plus{AC,#}(x7,x)
   plus{AC,#}(x8,plusAC(0(x),0(y))) -> plus{AC,#}(x,y)
   plus{AC,#}(x8,plusAC(0(x),0(y))) -> 0#(plusAC(x,y))
   plus{AC,#}(x8,plusAC(0(x),0(y))) -> plus{AC,#}(x8,0(plusAC(x,y)))
   plus{AC,#}(x9,plusAC(0(x),1(y))) -> plus{AC,#}(x,y)
   plus{AC,#}(x9,plusAC(0(x),1(y))) -> plus{AC,#}(x9,1(plusAC(x,y)))
   plus{AC,#}(x10,plusAC(0(x),j(y))) -> plus{AC,#}(x,y)
   plus{AC,#}(x10,plusAC(0(x),j(y))) -> plus{AC,#}(x10,j(plusAC(x,y)))
   plus{AC,#}(x11,plusAC(1(x),1(y))) -> plus{AC,#}(x,y)
   plus{AC,#}(x11,plusAC(1(x),1(y))) -> plus{AC,#}(1(S()),plusAC(x,y))
   plus{AC,#}(x11,plusAC(1(x),1(y))) -> plus{AC,#}(x11,j(plusAC(1(S()),plusAC(x,y))))
   plus{AC,#}(x12,plusAC(j(x),j(y))) -> plus{AC,#}(x,y)
   plus{AC,#}(x12,plusAC(j(x),j(y))) -> plus{AC,#}(j(S()),plusAC(x,y))
   plus{AC,#}(x12,plusAC(j(x),j(y))) -> plus{AC,#}(x12,1(plusAC(j(S()),plusAC(x,y))))
   plus{AC,#}(x13,plusAC(1(x),j(y))) -> plus{AC,#}(x,y)
   plus{AC,#}(x13,plusAC(1(x),j(y))) -> 0#(plusAC(x,y))
   plus{AC,#}(x13,plusAC(1(x),j(y))) -> plus{AC,#}(x13,0(plusAC(x,y)))
   times{AC,#}(x14,timesAC(S(),x)) -> times{AC,#}(x14,S())
   times{AC,#}(x15,timesAC(0(x),y)) -> times{AC,#}(x,y)
   times{AC,#}(x15,timesAC(0(x),y)) -> 0#(timesAC(x,y))
   times{AC,#}(x15,timesAC(0(x),y)) -> times{AC,#}(x15,0(timesAC(x,y)))
   times{AC,#}(x16,timesAC(1(x),y)) -> times{AC,#}(x,y)
   times{AC,#}(x16,timesAC(1(x),y)) -> 0#(timesAC(x,y))
   times{AC,#}(x16,timesAC(1(x),y)) -> plus{AC,#}(0(timesAC(x,y)),y)
   times{AC,#}(x16,timesAC(1(x),y)) -> times{AC,#}(x16,plusAC(0(timesAC(x,y)),y))
   times{AC,#}(x17,timesAC(j(x),y)) -> times{AC,#}(x,y)
   times{AC,#}(x17,timesAC(j(x),y)) -> 0#(timesAC(x,y))
   times{AC,#}(x17,timesAC(j(x),y)) -> minus#(0(timesAC(x,y)),y)
   times{AC,#}(x17,timesAC(j(x),y)) -> times{AC,#}(x17,minus(0(timesAC(x,y)),y))
  Equations:
   plusAC(plusAC(x4,x5),x6) -> plusAC(x4,plusAC(x5,x6))
   plusAC(x4,x5) -> plusAC(x5,x4)
   timesAC(timesAC(x4,x5),x6) -> timesAC(x4,timesAC(x5,x6))
   timesAC(x4,x5) -> timesAC(x5,x4)
   plusAC(x4,plusAC(x5,x6)) -> plusAC(plusAC(x4,x5),x6)
   plusAC(x5,x4) -> plusAC(x4,x5)
   timesAC(x4,timesAC(x5,x6)) -> timesAC(timesAC(x4,x5),x6)
   timesAC(x5,x4) -> timesAC(x4,x5)
  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)
   sign(x) -> if_sign(x,S())
   if_sign(S(),x) -> x
   if_sign(0(x),y) -> if_sign(x,y)
   if_sign(1(x),y) -> if_sign(x,1(S()))
   if_sign(j(x),y) -> if_sign(x,j(S()))
   abs(x) -> if_abs(x,x,S())
   if_abs(0(x),y,z) -> if_abs(x,y,z)
   if_abs(1(x),y,z) -> if_abs(x,y,1(S()))
   if_abs(j(x),y,z) -> if_abs(x,y,j(S()))
   if_abs(S(),x,S()) -> S()
   if_abs(S(),x,1(S())) -> x
   if_abs(S(),x,j(S())) -> opp(x)
   min(x,y) -> if_min(minus(abs(y),abs(x)),x,y,S())
   min'(x,y) -> if_min(minus(abs(1(y)),abs(1(x))),x,y,S())
   min''(x,y) -> if_min(minus(abs(j(y)),abs(j(x))),x,y,S())
   if_min(0(x),y,z,u) -> if_min(x,y,z,u)
   if_min(1(x),y,z,u) -> if_min(x,y,z,1(S()))
   if_min(j(x),y,z,u) -> if_min(x,y,z,j(S()))
   if_min(S(),x,y,S()) -> x
   if_min(S(),x,y,1(S())) -> x
   if_min(S(),x,y,j(S())) -> y
  S:
   plus{AC,#}(plusAC(x18,x19),x20) -> plus{AC,#}(x18,x19)
   plus{AC,#}(x18,plusAC(x19,x20)) -> plus{AC,#}(x19,x20)
   times{AC,#}(timesAC(x18,x19),x20) -> times{AC,#}(x18,x19)
   times{AC,#}(x18,timesAC(x19,x20)) -> times{AC,#}(x19,x20)
  AC-EDG Processor:
   Equations#:
    plus{AC,#}(plusAC(x4,x5),x6) -> plus{AC,#}(x4,plusAC(x5,x6))
    plus{AC,#}(x4,x5) -> plus{AC,#}(x5,x4)
    times{AC,#}(timesAC(x4,x5),x6) -> times{AC,#}(x4,timesAC(x5,x6))
    times{AC,#}(x4,x5) -> times{AC,#}(x5,x4)
    plus{AC,#}(x4,plusAC(x5,x6)) -> plus{AC,#}(plusAC(x4,x5),x6)
    plus{AC,#}(x5,x4) -> plus{AC,#}(x4,x5)
    times{AC,#}(x4,timesAC(x5,x6)) -> times{AC,#}(timesAC(x4,x5),x6)
    times{AC,#}(x5,x4) -> times{AC,#}(x4,x5)
   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)
    sign#(x) -> if_sign#(x,S())
    if_sign#(0(x),y) -> if_sign#(x,y)
    if_sign#(1(x),y) -> if_sign#(x,1(S()))
    if_sign#(j(x),y) -> if_sign#(x,j(S()))
    abs#(x) -> if_abs#(x,x,S())
    if_abs#(0(x),y,z) -> if_abs#(x,y,z)
    if_abs#(1(x),y,z) -> if_abs#(x,y,1(S()))
    if_abs#(j(x),y,z) -> if_abs#(x,y,j(S()))
    if_abs#(S(),x,j(S())) -> opp#(x)
    min#(x,y) -> abs#(x)
    min#(x,y) -> abs#(y)
    min#(x,y) -> minus#(abs(y),abs(x))
    min#(x,y) -> if_min#(minus(abs(y),abs(x)),x,y,S())
    min'#(x,y) -> abs#(1(x))
    min'#(x,y) -> abs#(1(y))
    min'#(x,y) -> minus#(abs(1(y)),abs(1(x)))
    min'#(x,y) -> if_min#(minus(abs(1(y)),abs(1(x))),x,y,S())
    min''#(x,y) -> abs#(j(x))
    min''#(x,y) -> abs#(j(y))
    min''#(x,y) -> minus#(abs(j(y)),abs(j(x)))
    min''#(x,y) -> if_min#(minus(abs(j(y)),abs(j(x))),x,y,S())
    if_min#(0(x),y,z,u) -> if_min#(x,y,z,u)
    if_min#(1(x),y,z,u) -> if_min#(x,y,z,1(S()))
    if_min#(j(x),y,z,u) -> if_min#(x,y,z,j(S()))
    plus{AC,#}(x7,plusAC(S(),x)) -> plus{AC,#}(x7,x)
    plus{AC,#}(x8,plusAC(0(x),0(y))) -> plus{AC,#}(x,y)
    plus{AC,#}(x8,plusAC(0(x),0(y))) -> 0#(plusAC(x,y))
    plus{AC,#}(x8,plusAC(0(x),0(y))) -> plus{AC,#}(x8,0(plusAC(x,y)))
    plus{AC,#}(x9,plusAC(0(x),1(y))) -> plus{AC,#}(x,y)
    plus{AC,#}(x9,plusAC(0(x),1(y))) -> plus{AC,#}(x9,1(plusAC(x,y)))
    plus{AC,#}(x10,plusAC(0(x),j(y))) -> plus{AC,#}(x,y)
    plus{AC,#}(x10,plusAC(0(x),j(y))) -> plus{AC,#}(x10,j(plusAC(x,y)))
    plus{AC,#}(x11,plusAC(1(x),1(y))) -> plus{AC,#}(x,y)
    plus{AC,#}(x11,plusAC(1(x),1(y))) -> plus{AC,#}(1(S()),plusAC(x,y))
    plus{AC,#}(x11,plusAC(1(x),1(y))) -> plus{AC,#}(x11,j(plusAC(1(S()),plusAC(x,y))))
    plus{AC,#}(x12,plusAC(j(x),j(y))) -> plus{AC,#}(x,y)
    plus{AC,#}(x12,plusAC(j(x),j(y))) -> plus{AC,#}(j(S()),plusAC(x,y))
    plus{AC,#}(x12,plusAC(j(x),j(y))) -> plus{AC,#}(x12,1(plusAC(j(S()),plusAC(x,y))))
    plus{AC,#}(x13,plusAC(1(x),j(y))) -> plus{AC,#}(x,y)
    plus{AC,#}(x13,plusAC(1(x),j(y))) -> 0#(plusAC(x,y))
    plus{AC,#}(x13,plusAC(1(x),j(y))) -> plus{AC,#}(x13,0(plusAC(x,y)))
    times{AC,#}(x14,timesAC(S(),x)) -> times{AC,#}(x14,S())
    times{AC,#}(x15,timesAC(0(x),y)) -> times{AC,#}(x,y)
    times{AC,#}(x15,timesAC(0(x),y)) -> 0#(timesAC(x,y))
    times{AC,#}(x15,timesAC(0(x),y)) -> times{AC,#}(x15,0(timesAC(x,y)))
    times{AC,#}(x16,timesAC(1(x),y)) -> times{AC,#}(x,y)
    times{AC,#}(x16,timesAC(1(x),y)) -> 0#(timesAC(x,y))
    times{AC,#}(x16,timesAC(1(x),y)) -> plus{AC,#}(0(timesAC(x,y)),y)
    times{AC,#}(x16,timesAC(1(x),y)) -> times{AC,#}(x16,plusAC(0(timesAC(x,y)),y))
    times{AC,#}(x17,timesAC(j(x),y)) -> times{AC,#}(x,y)
    times{AC,#}(x17,timesAC(j(x),y)) -> 0#(timesAC(x,y))
    times{AC,#}(x17,timesAC(j(x),y)) -> minus#(0(timesAC(x,y)),y)
    times{AC,#}(x17,timesAC(j(x),y)) -> times{AC,#}(x17,minus(0(timesAC(x,y)),y))
   Equations:
    plusAC(plusAC(x4,x5),x6) -> plusAC(x4,plusAC(x5,x6))
    plusAC(x4,x5) -> plusAC(x5,x4)
    timesAC(timesAC(x4,x5),x6) -> timesAC(x4,timesAC(x5,x6))
    timesAC(x4,x5) -> timesAC(x5,x4)
    plusAC(x4,plusAC(x5,x6)) -> plusAC(plusAC(x4,x5),x6)
    plusAC(x5,x4) -> plusAC(x4,x5)
    timesAC(x4,timesAC(x5,x6)) -> timesAC(timesAC(x4,x5),x6)
    timesAC(x5,x4) -> timesAC(x4,x5)
   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)
    sign(x) -> if_sign(x,S())
    if_sign(S(),x) -> x
    if_sign(0(x),y) -> if_sign(x,y)
    if_sign(1(x),y) -> if_sign(x,1(S()))
    if_sign(j(x),y) -> if_sign(x,j(S()))
    abs(x) -> if_abs(x,x,S())
    if_abs(0(x),y,z) -> if_abs(x,y,z)
    if_abs(1(x),y,z) -> if_abs(x,y,1(S()))
    if_abs(j(x),y,z) -> if_abs(x,y,j(S()))
    if_abs(S(),x,S()) -> S()
    if_abs(S(),x,1(S())) -> x
    if_abs(S(),x,j(S())) -> opp(x)
    min(x,y) -> if_min(minus(abs(y),abs(x)),x,y,S())
    min'(x,y) -> if_min(minus(abs(1(y)),abs(1(x))),x,y,S())
    min''(x,y) -> if_min(minus(abs(j(y)),abs(j(x))),x,y,S())
    if_min(0(x),y,z,u) -> if_min(x,y,z,u)
    if_min(1(x),y,z,u) -> if_min(x,y,z,1(S()))
    if_min(j(x),y,z,u) -> if_min(x,y,z,j(S()))
    if_min(S(),x,y,S()) -> x
    if_min(S(),x,y,1(S())) -> x
    if_min(S(),x,y,j(S())) -> y
   S:
    plus{AC,#}(plusAC(x18,x19),x20) -> plus{AC,#}(x18,x19)
    plus{AC,#}(x18,plusAC(x19,x20)) -> plus{AC,#}(x19,x20)
    times{AC,#}(timesAC(x18,x19),x20) -> times{AC,#}(x18,x19)
    times{AC,#}(x18,timesAC(x19,x20)) -> times{AC,#}(x19,x20)
   Open