MAYBE
Time: 1.024

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(x,S()) -> x
  plusAC(0(x),0(y)) -> 0(plusAC(x,y))
  plusAC(0(x),1(y)) -> 1(plusAC(x,y))
  plusAC(1(x),1(y)) -> 0(1(plusAC(plusAC(x,y),S())))
  timesAC(x,S()) -> S()
  timesAC(x,0(y)) -> 0(timesAC(x,y))
  timesAC(x,1(y)) -> plusAC(x,0(timesAC(x,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,#}(1(x),1(y)) -> plus{AC,#}(x,y)
   plus{AC,#}(1(x),1(y)) -> plus{AC,#}(plusAC(x,y),S())
   plus{AC,#}(1(x),1(y)) -> 0#(1(plusAC(plusAC(x,y),S())))
   times{AC,#}(x,0(y)) -> times{AC,#}(x,y)
   times{AC,#}(x,0(y)) -> 0#(timesAC(x,y))
   times{AC,#}(x,1(y)) -> times{AC,#}(x,y)
   times{AC,#}(x,1(y)) -> 0#(timesAC(x,y))
   times{AC,#}(x,1(y)) -> plus{AC,#}(x,0(timesAC(x,y)))
   plus{AC,#}(x5,plusAC(x,S())) -> 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(1(x),1(y))) -> plus{AC,#}(x,y)
   plus{AC,#}(x8,plusAC(1(x),1(y))) -> plus{AC,#}(plusAC(x,y),S())
   plus{AC,#}(x8,plusAC(1(x),1(y))) -> 0#(1(plusAC(plusAC(x,y),S())))
   plus{AC,#}(x8,plusAC(1(x),1(y))) -> plus{AC,#}(x8,0(1(plusAC(plusAC(x,y),S()))))
   times{AC,#}(x9,timesAC(x,S())) -> times{AC,#}(x9,S())
   times{AC,#}(x10,timesAC(x,0(y))) -> times{AC,#}(x,y)
   times{AC,#}(x10,timesAC(x,0(y))) -> 0#(timesAC(x,y))
   times{AC,#}(x10,timesAC(x,0(y))) -> times{AC,#}(x10,0(timesAC(x,y)))
   times{AC,#}(x11,timesAC(x,1(y))) -> times{AC,#}(x,y)
   times{AC,#}(x11,timesAC(x,1(y))) -> 0#(timesAC(x,y))
   times{AC,#}(x11,timesAC(x,1(y))) -> plus{AC,#}(x,0(timesAC(x,y)))
   times{AC,#}(x11,timesAC(x,1(y))) -> times{AC,#}(x11,plusAC(x,0(timesAC(x,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(x,S()) -> x
   plusAC(0(x),0(y)) -> 0(plusAC(x,y))
   plusAC(0(x),1(y)) -> 1(plusAC(x,y))
   plusAC(1(x),1(y)) -> 0(1(plusAC(plusAC(x,y),S())))
   timesAC(x,S()) -> S()
   timesAC(x,0(y)) -> 0(timesAC(x,y))
   timesAC(x,1(y)) -> plusAC(x,0(timesAC(x,y)))
  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(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,#}(1(x),1(y)) -> plus{AC,#}(x,y)
    plus{AC,#}(1(x),1(y)) -> plus{AC,#}(plusAC(x,y),S())
    plus{AC,#}(1(x),1(y)) -> 0#(1(plusAC(plusAC(x,y),S())))
    times{AC,#}(x,0(y)) -> times{AC,#}(x,y)
    times{AC,#}(x,0(y)) -> 0#(timesAC(x,y))
    times{AC,#}(x,1(y)) -> times{AC,#}(x,y)
    times{AC,#}(x,1(y)) -> 0#(timesAC(x,y))
    times{AC,#}(x,1(y)) -> plus{AC,#}(x,0(timesAC(x,y)))
    plus{AC,#}(x5,plusAC(x,S())) -> 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(1(x),1(y))) -> plus{AC,#}(x,y)
    plus{AC,#}(x8,plusAC(1(x),1(y))) -> plus{AC,#}(plusAC(x,y),S())
    plus{AC,#}(x8,plusAC(1(x),1(y))) -> 0#(1(plusAC(plusAC(x,y),S())))
    plus{AC,#}(x8,plusAC(1(x),1(y))) -> plus{AC,#}(x8,0(1(plusAC(plusAC(x,y),S()))))
    times{AC,#}(x9,timesAC(x,S())) -> times{AC,#}(x9,S())
    times{AC,#}(x10,timesAC(x,0(y))) -> times{AC,#}(x,y)
    times{AC,#}(x10,timesAC(x,0(y))) -> 0#(timesAC(x,y))
    times{AC,#}(x10,timesAC(x,0(y))) -> times{AC,#}(x10,0(timesAC(x,y)))
    times{AC,#}(x11,timesAC(x,1(y))) -> times{AC,#}(x,y)
    times{AC,#}(x11,timesAC(x,1(y))) -> 0#(timesAC(x,y))
    times{AC,#}(x11,timesAC(x,1(y))) -> plus{AC,#}(x,0(timesAC(x,y)))
    times{AC,#}(x11,timesAC(x,1(y))) -> times{AC,#}(x11,plusAC(x,0(timesAC(x,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(x,S()) -> x
    plusAC(0(x),0(y)) -> 0(plusAC(x,y))
    plusAC(0(x),1(y)) -> 1(plusAC(x,y))
    plusAC(1(x),1(y)) -> 0(1(plusAC(plusAC(x,y),S())))
    timesAC(x,S()) -> S()
    timesAC(x,0(y)) -> 0(timesAC(x,y))
    timesAC(x,1(y)) -> plusAC(x,0(timesAC(x,y)))
   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