MAYBE
Time: 0.429

Problem:
 Equations:
  plusAC(plusAC(x3,x4),x5) -> plusAC(x3,plusAC(x4,x5))
  plusAC(x3,x4) -> plusAC(x4,x3)
  timesAC(timesAC(x3,x4),x5) -> timesAC(x3,timesAC(x4,x5))
  timesAC(x3,x4) -> timesAC(x4,x3)
  plusAC(x3,plusAC(x4,x5)) -> plusAC(plusAC(x3,x4),x5)
  plusAC(x4,x3) -> plusAC(x3,x4)
  timesAC(x3,timesAC(x4,x5)) -> timesAC(timesAC(x3,x4),x5)
  timesAC(x4,x3) -> timesAC(x3,x4)
 TRS:
  plusAC(x,0()) -> x
  plusAC(0(),y) -> y
  plusAC(s(x),y) -> s(plusAC(x,y))
  timesAC(0(),y) -> 0()
  timesAC(s(0()),y) -> y
  timesAC(s(x),y) -> plusAC(y,timesAC(x,y))
  div(0(),y) -> 0()
  div(x,y) -> quot(x,y,y)
  quot(0(),s(y),z) -> 0()
  quot(s(x),s(y),z) -> quot(x,y,z)
  quot(x,0(),s(z)) -> s(div(x,s(z)))
  div(div(x,y),z) -> div(x,timesAC(y,z))

Proof:
 DP Processor:
  Equations#:
   plus{AC,#}(plusAC(x3,x4),x5) -> plus{AC,#}(x3,plusAC(x4,x5))
   plus{AC,#}(x3,x4) -> plus{AC,#}(x4,x3)
   times{AC,#}(timesAC(x3,x4),x5) -> times{AC,#}(x3,timesAC(x4,x5))
   times{AC,#}(x3,x4) -> times{AC,#}(x4,x3)
   plus{AC,#}(x3,plusAC(x4,x5)) -> plus{AC,#}(plusAC(x3,x4),x5)
   plus{AC,#}(x4,x3) -> plus{AC,#}(x3,x4)
   times{AC,#}(x3,timesAC(x4,x5)) -> times{AC,#}(timesAC(x3,x4),x5)
   times{AC,#}(x4,x3) -> times{AC,#}(x3,x4)
  DPs:
   plus{AC,#}(s(x),y) -> plus{AC,#}(x,y)
   times{AC,#}(s(x),y) -> times{AC,#}(x,y)
   times{AC,#}(s(x),y) -> plus{AC,#}(y,timesAC(x,y))
   div#(x,y) -> quot#(x,y,y)
   quot#(s(x),s(y),z) -> quot#(x,y,z)
   quot#(x,0(),s(z)) -> div#(x,s(z))
   div#(div(x,y),z) -> times{AC,#}(y,z)
   div#(div(x,y),z) -> div#(x,timesAC(y,z))
   plus{AC,#}(x6,plusAC(x,0())) -> plus{AC,#}(x6,x)
   plus{AC,#}(x7,plusAC(0(),y)) -> plus{AC,#}(x7,y)
   plus{AC,#}(x8,plusAC(s(x),y)) -> plus{AC,#}(x,y)
   plus{AC,#}(x8,plusAC(s(x),y)) -> plus{AC,#}(x8,s(plusAC(x,y)))
   times{AC,#}(x9,timesAC(0(),y)) -> times{AC,#}(x9,0())
   times{AC,#}(x10,timesAC(s(0()),y)) -> times{AC,#}(x10,y)
   times{AC,#}(x11,timesAC(s(x),y)) -> times{AC,#}(x,y)
   times{AC,#}(x11,timesAC(s(x),y)) -> plus{AC,#}(y,timesAC(x,y))
   times{AC,#}(x11,timesAC(s(x),y)) -> times{AC,#}(x11,plusAC(y,timesAC(x,y)))
  Equations:
   plusAC(plusAC(x3,x4),x5) -> plusAC(x3,plusAC(x4,x5))
   plusAC(x3,x4) -> plusAC(x4,x3)
   timesAC(timesAC(x3,x4),x5) -> timesAC(x3,timesAC(x4,x5))
   timesAC(x3,x4) -> timesAC(x4,x3)
   plusAC(x3,plusAC(x4,x5)) -> plusAC(plusAC(x3,x4),x5)
   plusAC(x4,x3) -> plusAC(x3,x4)
   timesAC(x3,timesAC(x4,x5)) -> timesAC(timesAC(x3,x4),x5)
   timesAC(x4,x3) -> timesAC(x3,x4)
  TRS:
   plusAC(x,0()) -> x
   plusAC(0(),y) -> y
   plusAC(s(x),y) -> s(plusAC(x,y))
   timesAC(0(),y) -> 0()
   timesAC(s(0()),y) -> y
   timesAC(s(x),y) -> plusAC(y,timesAC(x,y))
   div(0(),y) -> 0()
   div(x,y) -> quot(x,y,y)
   quot(0(),s(y),z) -> 0()
   quot(s(x),s(y),z) -> quot(x,y,z)
   quot(x,0(),s(z)) -> s(div(x,s(z)))
   div(div(x,y),z) -> div(x,timesAC(y,z))
  S:
   plus{AC,#}(plusAC(x12,x13),x14) -> plus{AC,#}(x12,x13)
   plus{AC,#}(x12,plusAC(x13,x14)) -> plus{AC,#}(x13,x14)
   times{AC,#}(timesAC(x12,x13),x14) -> times{AC,#}(x12,x13)
   times{AC,#}(x12,timesAC(x13,x14)) -> times{AC,#}(x13,x14)
  AC-EDG Processor:
   Equations#:
    plus{AC,#}(plusAC(x3,x4),x5) -> plus{AC,#}(x3,plusAC(x4,x5))
    plus{AC,#}(x3,x4) -> plus{AC,#}(x4,x3)
    times{AC,#}(timesAC(x3,x4),x5) -> times{AC,#}(x3,timesAC(x4,x5))
    times{AC,#}(x3,x4) -> times{AC,#}(x4,x3)
    plus{AC,#}(x3,plusAC(x4,x5)) -> plus{AC,#}(plusAC(x3,x4),x5)
    plus{AC,#}(x4,x3) -> plus{AC,#}(x3,x4)
    times{AC,#}(x3,timesAC(x4,x5)) -> times{AC,#}(timesAC(x3,x4),x5)
    times{AC,#}(x4,x3) -> times{AC,#}(x3,x4)
   DPs:
    plus{AC,#}(s(x),y) -> plus{AC,#}(x,y)
    times{AC,#}(s(x),y) -> times{AC,#}(x,y)
    times{AC,#}(s(x),y) -> plus{AC,#}(y,timesAC(x,y))
    div#(x,y) -> quot#(x,y,y)
    quot#(s(x),s(y),z) -> quot#(x,y,z)
    quot#(x,0(),s(z)) -> div#(x,s(z))
    div#(div(x,y),z) -> times{AC,#}(y,z)
    div#(div(x,y),z) -> div#(x,timesAC(y,z))
    plus{AC,#}(x6,plusAC(x,0())) -> plus{AC,#}(x6,x)
    plus{AC,#}(x7,plusAC(0(),y)) -> plus{AC,#}(x7,y)
    plus{AC,#}(x8,plusAC(s(x),y)) -> plus{AC,#}(x,y)
    plus{AC,#}(x8,plusAC(s(x),y)) -> plus{AC,#}(x8,s(plusAC(x,y)))
    times{AC,#}(x9,timesAC(0(),y)) -> times{AC,#}(x9,0())
    times{AC,#}(x10,timesAC(s(0()),y)) -> times{AC,#}(x10,y)
    times{AC,#}(x11,timesAC(s(x),y)) -> times{AC,#}(x,y)
    times{AC,#}(x11,timesAC(s(x),y)) -> plus{AC,#}(y,timesAC(x,y))
    times{AC,#}(x11,timesAC(s(x),y)) -> times{AC,#}(x11,plusAC(y,timesAC(x,y)))
   Equations:
    plusAC(plusAC(x3,x4),x5) -> plusAC(x3,plusAC(x4,x5))
    plusAC(x3,x4) -> plusAC(x4,x3)
    timesAC(timesAC(x3,x4),x5) -> timesAC(x3,timesAC(x4,x5))
    timesAC(x3,x4) -> timesAC(x4,x3)
    plusAC(x3,plusAC(x4,x5)) -> plusAC(plusAC(x3,x4),x5)
    plusAC(x4,x3) -> plusAC(x3,x4)
    timesAC(x3,timesAC(x4,x5)) -> timesAC(timesAC(x3,x4),x5)
    timesAC(x4,x3) -> timesAC(x3,x4)
   TRS:
    plusAC(x,0()) -> x
    plusAC(0(),y) -> y
    plusAC(s(x),y) -> s(plusAC(x,y))
    timesAC(0(),y) -> 0()
    timesAC(s(0()),y) -> y
    timesAC(s(x),y) -> plusAC(y,timesAC(x,y))
    div(0(),y) -> 0()
    div(x,y) -> quot(x,y,y)
    quot(0(),s(y),z) -> 0()
    quot(s(x),s(y),z) -> quot(x,y,z)
    quot(x,0(),s(z)) -> s(div(x,s(z)))
    div(div(x,y),z) -> div(x,timesAC(y,z))
   S:
    plus{AC,#}(plusAC(x12,x13),x14) -> plus{AC,#}(x12,x13)
    plus{AC,#}(x12,plusAC(x13,x14)) -> plus{AC,#}(x13,x14)
    times{AC,#}(timesAC(x12,x13),x14) -> times{AC,#}(x12,x13)
    times{AC,#}(x12,timesAC(x13,x14)) -> times{AC,#}(x13,x14)
   Open