YES
Time: 0.604

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:
  s(p(x)) -> x
  p(s(x)) -> x
  plusAC(0(),y) -> y
  plusAC(s(x),y) -> s(plusAC(x,y))
  plusAC(p(x),y) -> p(plusAC(x,y))
  plusAC(i(x),x) -> 0()
  plusAC(x,plusAC(i(x),y)) -> y
  i(0()) -> 0()
  i(s(x)) -> p(i(x))
  i(p(x)) -> s(i(x))
  i(i(x)) -> x
  i(plusAC(x,y)) -> plusAC(i(y),i(x))
  timesAC(0(),y) -> 0()
  timesAC(s(x),y) -> plusAC(timesAC(x,y),y)
  timesAC(p(x),y) -> plusAC(timesAC(x,y),i(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,#}(s(x),y) -> plus{AC,#}(x,y)
   plus{AC,#}(s(x),y) -> s#(plusAC(x,y))
   plus{AC,#}(p(x),y) -> plus{AC,#}(x,y)
   plus{AC,#}(p(x),y) -> p#(plusAC(x,y))
   i#(s(x)) -> i#(x)
   i#(s(x)) -> p#(i(x))
   i#(p(x)) -> i#(x)
   i#(p(x)) -> s#(i(x))
   i#(plusAC(x,y)) -> i#(x)
   i#(plusAC(x,y)) -> i#(y)
   i#(plusAC(x,y)) -> plus{AC,#}(i(y),i(x))
   times{AC,#}(s(x),y) -> times{AC,#}(x,y)
   times{AC,#}(s(x),y) -> plus{AC,#}(timesAC(x,y),y)
   times{AC,#}(p(x),y) -> i#(y)
   times{AC,#}(p(x),y) -> times{AC,#}(x,y)
   times{AC,#}(p(x),y) -> plus{AC,#}(timesAC(x,y),i(y))
   plus{AC,#}(x5,plusAC(0(),y)) -> plus{AC,#}(x5,y)
   plus{AC,#}(x6,plusAC(s(x),y)) -> plus{AC,#}(x,y)
   plus{AC,#}(x6,plusAC(s(x),y)) -> s#(plusAC(x,y))
   plus{AC,#}(x6,plusAC(s(x),y)) -> plus{AC,#}(x6,s(plusAC(x,y)))
   plus{AC,#}(x7,plusAC(p(x),y)) -> plus{AC,#}(x,y)
   plus{AC,#}(x7,plusAC(p(x),y)) -> p#(plusAC(x,y))
   plus{AC,#}(x7,plusAC(p(x),y)) -> plus{AC,#}(x7,p(plusAC(x,y)))
   plus{AC,#}(x8,plusAC(i(x),x)) -> plus{AC,#}(x8,0())
   plus{AC,#}(x9,plusAC(x,plusAC(i(x),y))) -> plus{AC,#}(x9,y)
   times{AC,#}(x10,timesAC(0(),y)) -> times{AC,#}(x10,0())
   times{AC,#}(x11,timesAC(s(x),y)) -> times{AC,#}(x,y)
   times{AC,#}(x11,timesAC(s(x),y)) -> plus{AC,#}(timesAC(x,y),y)
   times{AC,#}(x11,timesAC(s(x),y)) -> times{AC,#}(x11,plusAC(timesAC(x,y),y))
   times{AC,#}(x12,timesAC(p(x),y)) -> i#(y)
   times{AC,#}(x12,timesAC(p(x),y)) -> times{AC,#}(x,y)
   times{AC,#}(x12,timesAC(p(x),y)) -> plus{AC,#}(timesAC(x,y),i(y))
   times{AC,#}(x12,timesAC(p(x),y)) -> times{AC,#}(x12,plusAC(timesAC(x,y),i(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:
   s(p(x)) -> x
   p(s(x)) -> x
   plusAC(0(),y) -> y
   plusAC(s(x),y) -> s(plusAC(x,y))
   plusAC(p(x),y) -> p(plusAC(x,y))
   plusAC(i(x),x) -> 0()
   plusAC(x,plusAC(i(x),y)) -> y
   i(0()) -> 0()
   i(s(x)) -> p(i(x))
   i(p(x)) -> s(i(x))
   i(i(x)) -> x
   i(plusAC(x,y)) -> plusAC(i(y),i(x))
   timesAC(0(),y) -> 0()
   timesAC(s(x),y) -> plusAC(timesAC(x,y),y)
   timesAC(p(x),y) -> plusAC(timesAC(x,y),i(y))
  S:
   plus{AC,#}(plusAC(x13,x14),x15) -> plus{AC,#}(x13,x14)
   plus{AC,#}(x13,plusAC(x14,x15)) -> plus{AC,#}(x14,x15)
   times{AC,#}(timesAC(x13,x14),x15) -> times{AC,#}(x13,x14)
   times{AC,#}(x13,timesAC(x14,x15)) -> times{AC,#}(x14,x15)
  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,#}(s(x),y) -> plus{AC,#}(x,y)
    plus{AC,#}(s(x),y) -> s#(plusAC(x,y))
    plus{AC,#}(p(x),y) -> plus{AC,#}(x,y)
    plus{AC,#}(p(x),y) -> p#(plusAC(x,y))
    i#(s(x)) -> i#(x)
    i#(s(x)) -> p#(i(x))
    i#(p(x)) -> i#(x)
    i#(p(x)) -> s#(i(x))
    i#(plusAC(x,y)) -> i#(x)
    i#(plusAC(x,y)) -> i#(y)
    i#(plusAC(x,y)) -> plus{AC,#}(i(y),i(x))
    times{AC,#}(s(x),y) -> times{AC,#}(x,y)
    times{AC,#}(s(x),y) -> plus{AC,#}(timesAC(x,y),y)
    times{AC,#}(p(x),y) -> i#(y)
    times{AC,#}(p(x),y) -> times{AC,#}(x,y)
    times{AC,#}(p(x),y) -> plus{AC,#}(timesAC(x,y),i(y))
    plus{AC,#}(x5,plusAC(0(),y)) -> plus{AC,#}(x5,y)
    plus{AC,#}(x6,plusAC(s(x),y)) -> plus{AC,#}(x,y)
    plus{AC,#}(x6,plusAC(s(x),y)) -> s#(plusAC(x,y))
    plus{AC,#}(x6,plusAC(s(x),y)) -> plus{AC,#}(x6,s(plusAC(x,y)))
    plus{AC,#}(x7,plusAC(p(x),y)) -> plus{AC,#}(x,y)
    plus{AC,#}(x7,plusAC(p(x),y)) -> p#(plusAC(x,y))
    plus{AC,#}(x7,plusAC(p(x),y)) -> plus{AC,#}(x7,p(plusAC(x,y)))
    plus{AC,#}(x8,plusAC(i(x),x)) -> plus{AC,#}(x8,0())
    plus{AC,#}(x9,plusAC(x,plusAC(i(x),y))) -> plus{AC,#}(x9,y)
    times{AC,#}(x10,timesAC(0(),y)) -> times{AC,#}(x10,0())
    times{AC,#}(x11,timesAC(s(x),y)) -> times{AC,#}(x,y)
    times{AC,#}(x11,timesAC(s(x),y)) -> plus{AC,#}(timesAC(x,y),y)
    times{AC,#}(x11,timesAC(s(x),y)) -> times{AC,#}(x11,plusAC(timesAC(x,y),y))
    times{AC,#}(x12,timesAC(p(x),y)) -> i#(y)
    times{AC,#}(x12,timesAC(p(x),y)) -> times{AC,#}(x,y)
    times{AC,#}(x12,timesAC(p(x),y)) -> plus{AC,#}(timesAC(x,y),i(y))
    times{AC,#}(x12,timesAC(p(x),y)) -> times{AC,#}(x12,plusAC(timesAC(x,y),i(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:
    s(p(x)) -> x
    p(s(x)) -> x
    plusAC(0(),y) -> y
    plusAC(s(x),y) -> s(plusAC(x,y))
    plusAC(p(x),y) -> p(plusAC(x,y))
    plusAC(i(x),x) -> 0()
    plusAC(x,plusAC(i(x),y)) -> y
    i(0()) -> 0()
    i(s(x)) -> p(i(x))
    i(p(x)) -> s(i(x))
    i(i(x)) -> x
    i(plusAC(x,y)) -> plusAC(i(y),i(x))
    timesAC(0(),y) -> 0()
    timesAC(s(x),y) -> plusAC(timesAC(x,y),y)
    timesAC(p(x),y) -> plusAC(timesAC(x,y),i(y))
   S:
    plus{AC,#}(plusAC(x13,x14),x15) -> plus{AC,#}(x13,x14)
    plus{AC,#}(x13,plusAC(x14,x15)) -> plus{AC,#}(x14,x15)
    times{AC,#}(timesAC(x13,x14),x15) -> times{AC,#}(x13,x14)
    times{AC,#}(x13,timesAC(x14,x15)) -> times{AC,#}(x14,x15)
   SCC Processor:
    #sccs: 3
    #rules: 20
    #arcs: 315/1089
    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:
     times{AC,#}(s(x),y) -> times{AC,#}(x,y)
     times{AC,#}(x12,timesAC(p(x),y)) -> times{AC,#}(x12,plusAC(timesAC(x,y),i(y)))
     times{AC,#}(x12,timesAC(p(x),y)) -> times{AC,#}(x,y)
     times{AC,#}(x11,timesAC(s(x),y)) -> times{AC,#}(x11,plusAC(timesAC(x,y),y))
     times{AC,#}(x11,timesAC(s(x),y)) -> times{AC,#}(x,y)
     times{AC,#}(x10,timesAC(0(),y)) -> times{AC,#}(x10,0())
     times{AC,#}(p(x),y) -> times{AC,#}(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:
     s(p(x)) -> x
     p(s(x)) -> x
     plusAC(0(),y) -> y
     plusAC(s(x),y) -> s(plusAC(x,y))
     plusAC(p(x),y) -> p(plusAC(x,y))
     plusAC(i(x),x) -> 0()
     plusAC(x,plusAC(i(x),y)) -> y
     i(0()) -> 0()
     i(s(x)) -> p(i(x))
     i(p(x)) -> s(i(x))
     i(i(x)) -> x
     i(plusAC(x,y)) -> plusAC(i(y),i(x))
     timesAC(0(),y) -> 0()
     timesAC(s(x),y) -> plusAC(timesAC(x,y),y)
     timesAC(p(x),y) -> plusAC(timesAC(x,y),i(y))
    S:
     plus{AC,#}(plusAC(x13,x14),x15) -> plus{AC,#}(x13,x14)
     plus{AC,#}(x13,plusAC(x14,x15)) -> plus{AC,#}(x14,x15)
     times{AC,#}(timesAC(x13,x14),x15) -> times{AC,#}(x13,x14)
     times{AC,#}(x13,timesAC(x14,x15)) -> times{AC,#}(x14,x15)
    AC-DP unlabeling:
     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)
     DPs:
      timesAC(s(x),y) -> timesAC(x,y)
      timesAC(x12,timesAC(p(x),y)) -> timesAC(x12,plusAC(timesAC(x,y),i(y)))
      timesAC(x12,timesAC(p(x),y)) -> timesAC(x,y)
      timesAC(x11,timesAC(s(x),y)) -> timesAC(x11,plusAC(timesAC(x,y),y))
      timesAC(x11,timesAC(s(x),y)) -> timesAC(x,y)
      timesAC(x10,timesAC(0(),y)) -> timesAC(x10,0())
      timesAC(p(x),y) -> 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:
      s(p(x)) -> x
      p(s(x)) -> x
      plusAC(0(),y) -> y
      plusAC(s(x),y) -> s(plusAC(x,y))
      plusAC(p(x),y) -> p(plusAC(x,y))
      plusAC(i(x),x) -> 0()
      plusAC(x,plusAC(i(x),y)) -> y
      i(0()) -> 0()
      i(s(x)) -> p(i(x))
      i(p(x)) -> s(i(x))
      i(i(x)) -> x
      i(plusAC(x,y)) -> plusAC(i(y),i(x))
      timesAC(0(),y) -> 0()
      timesAC(s(x),y) -> plusAC(timesAC(x,y),y)
      timesAC(p(x),y) -> plusAC(timesAC(x,y),i(y))
     S:
      plusAC(plusAC(x13,x14),x15) -> plusAC(x13,x14)
      plusAC(x13,plusAC(x14,x15)) -> plusAC(x14,x15)
      timesAC(timesAC(x13,x14),x15) -> timesAC(x13,x14)
      timesAC(x13,timesAC(x14,x15)) -> timesAC(x14,x15)
     AC-RPO Processor:
      argument filtering:
       pi(plusAC) = [0,1]
       pi(timesAC) = [0,1]
       pi(p) = [0]
       pi(s) = [0]
       pi(0) = []
       pi(i) = [0]
      precedence:
       timesAC > i > plusAC > p > 0 > s
      status:
       
      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)
       DPs:
        
       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:
        s(p(x)) -> x
        p(s(x)) -> x
        plusAC(0(),y) -> y
        plusAC(s(x),y) -> s(plusAC(x,y))
        plusAC(p(x),y) -> p(plusAC(x,y))
        plusAC(i(x),x) -> 0()
        plusAC(x,plusAC(i(x),y)) -> y
        i(0()) -> 0()
        i(s(x)) -> p(i(x))
        i(p(x)) -> s(i(x))
        i(i(x)) -> x
        i(plusAC(x,y)) -> plusAC(i(y),i(x))
        timesAC(0(),y) -> 0()
        timesAC(s(x),y) -> plusAC(timesAC(x,y),y)
        timesAC(p(x),y) -> plusAC(timesAC(x,y),i(y))
       S:
        plusAC(plusAC(x13,x14),x15) -> plusAC(x13,x14)
        plusAC(x13,plusAC(x14,x15)) -> plusAC(x14,x15)
        timesAC(timesAC(x13,x14),x15) -> timesAC(x13,x14)
        timesAC(x13,timesAC(x14,x15)) -> timesAC(x14,x15)
      Qed
    
    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:
     i#(plusAC(x,y)) -> i#(y)
     i#(plusAC(x,y)) -> i#(x)
     i#(p(x)) -> i#(x)
     i#(s(x)) -> i#(x)
    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:
     s(p(x)) -> x
     p(s(x)) -> x
     plusAC(0(),y) -> y
     plusAC(s(x),y) -> s(plusAC(x,y))
     plusAC(p(x),y) -> p(plusAC(x,y))
     plusAC(i(x),x) -> 0()
     plusAC(x,plusAC(i(x),y)) -> y
     i(0()) -> 0()
     i(s(x)) -> p(i(x))
     i(p(x)) -> s(i(x))
     i(i(x)) -> x
     i(plusAC(x,y)) -> plusAC(i(y),i(x))
     timesAC(0(),y) -> 0()
     timesAC(s(x),y) -> plusAC(timesAC(x,y),y)
     timesAC(p(x),y) -> plusAC(timesAC(x,y),i(y))
    S:
     plus{AC,#}(plusAC(x13,x14),x15) -> plus{AC,#}(x13,x14)
     plus{AC,#}(x13,plusAC(x14,x15)) -> plus{AC,#}(x14,x15)
     times{AC,#}(timesAC(x13,x14),x15) -> times{AC,#}(x13,x14)
     times{AC,#}(x13,timesAC(x14,x15)) -> times{AC,#}(x14,x15)
    AC-DP unlabeling:
     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)
     DPs:
      i#(plusAC(x,y)) -> i#(y)
      i#(plusAC(x,y)) -> i#(x)
      i#(p(x)) -> i#(x)
      i#(s(x)) -> i#(x)
     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:
      s(p(x)) -> x
      p(s(x)) -> x
      plusAC(0(),y) -> y
      plusAC(s(x),y) -> s(plusAC(x,y))
      plusAC(p(x),y) -> p(plusAC(x,y))
      plusAC(i(x),x) -> 0()
      plusAC(x,plusAC(i(x),y)) -> y
      i(0()) -> 0()
      i(s(x)) -> p(i(x))
      i(p(x)) -> s(i(x))
      i(i(x)) -> x
      i(plusAC(x,y)) -> plusAC(i(y),i(x))
      timesAC(0(),y) -> 0()
      timesAC(s(x),y) -> plusAC(timesAC(x,y),y)
      timesAC(p(x),y) -> plusAC(timesAC(x,y),i(y))
     S:
      plusAC(plusAC(x13,x14),x15) -> plusAC(x13,x14)
      plusAC(x13,plusAC(x14,x15)) -> plusAC(x14,x15)
      timesAC(timesAC(x13,x14),x15) -> timesAC(x13,x14)
      timesAC(x13,timesAC(x14,x15)) -> timesAC(x14,x15)
     Usable Rule Processor:
      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)
      DPs:
       i#(plusAC(x,y)) -> i#(y)
       i#(plusAC(x,y)) -> i#(x)
       i#(p(x)) -> i#(x)
       i#(s(x)) -> i#(x)
      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:
       
      S:
       plusAC(plusAC(x13,x14),x15) -> plusAC(x13,x14)
       plusAC(x13,plusAC(x14,x15)) -> plusAC(x14,x15)
       timesAC(timesAC(x13,x14),x15) -> timesAC(x13,x14)
       timesAC(x13,timesAC(x14,x15)) -> timesAC(x14,x15)
      AC-RPO Processor:
       argument filtering:
        pi(plusAC) = [0,1]
        pi(timesAC) = []
        pi(p) = [0]
        pi(s) = [0]
        pi(i#) = [0]
       precedence:
        s > timesAC > p > plusAC > i#
       status:
        
       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)
        DPs:
         
        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:
         
        S:
         plusAC(plusAC(x13,x14),x15) -> plusAC(x13,x14)
         plusAC(x13,plusAC(x14,x15)) -> plusAC(x14,x15)
         timesAC(timesAC(x13,x14),x15) -> timesAC(x13,x14)
         timesAC(x13,timesAC(x14,x15)) -> timesAC(x14,x15)
       Qed
    
    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,#}(x9,plusAC(x,plusAC(i(x),y))) -> plus{AC,#}(x9,y)
     plus{AC,#}(x8,plusAC(i(x),x)) -> plus{AC,#}(x8,0())
     plus{AC,#}(x7,plusAC(p(x),y)) -> plus{AC,#}(x7,p(plusAC(x,y)))
     plus{AC,#}(x7,plusAC(p(x),y)) -> plus{AC,#}(x,y)
     plus{AC,#}(x6,plusAC(s(x),y)) -> plus{AC,#}(x6,s(plusAC(x,y)))
     plus{AC,#}(x6,plusAC(s(x),y)) -> plus{AC,#}(x,y)
     plus{AC,#}(x5,plusAC(0(),y)) -> plus{AC,#}(x5,y)
     plus{AC,#}(p(x),y) -> plus{AC,#}(x,y)
     plus{AC,#}(s(x),y) -> plus{AC,#}(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:
     s(p(x)) -> x
     p(s(x)) -> x
     plusAC(0(),y) -> y
     plusAC(s(x),y) -> s(plusAC(x,y))
     plusAC(p(x),y) -> p(plusAC(x,y))
     plusAC(i(x),x) -> 0()
     plusAC(x,plusAC(i(x),y)) -> y
     i(0()) -> 0()
     i(s(x)) -> p(i(x))
     i(p(x)) -> s(i(x))
     i(i(x)) -> x
     i(plusAC(x,y)) -> plusAC(i(y),i(x))
     timesAC(0(),y) -> 0()
     timesAC(s(x),y) -> plusAC(timesAC(x,y),y)
     timesAC(p(x),y) -> plusAC(timesAC(x,y),i(y))
    S:
     plus{AC,#}(plusAC(x13,x14),x15) -> plus{AC,#}(x13,x14)
     plus{AC,#}(x13,plusAC(x14,x15)) -> plus{AC,#}(x14,x15)
     times{AC,#}(timesAC(x13,x14),x15) -> times{AC,#}(x13,x14)
     times{AC,#}(x13,timesAC(x14,x15)) -> times{AC,#}(x14,x15)
    AC-DP unlabeling:
     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)
     DPs:
      plusAC(x9,plusAC(x,plusAC(i(x),y))) -> plusAC(x9,y)
      plusAC(x8,plusAC(i(x),x)) -> plusAC(x8,0())
      plusAC(x7,plusAC(p(x),y)) -> plusAC(x7,p(plusAC(x,y)))
      plusAC(x7,plusAC(p(x),y)) -> plusAC(x,y)
      plusAC(x6,plusAC(s(x),y)) -> plusAC(x6,s(plusAC(x,y)))
      plusAC(x6,plusAC(s(x),y)) -> plusAC(x,y)
      plusAC(x5,plusAC(0(),y)) -> plusAC(x5,y)
      plusAC(p(x),y) -> plusAC(x,y)
      plusAC(s(x),y) -> plusAC(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:
      s(p(x)) -> x
      p(s(x)) -> x
      plusAC(0(),y) -> y
      plusAC(s(x),y) -> s(plusAC(x,y))
      plusAC(p(x),y) -> p(plusAC(x,y))
      plusAC(i(x),x) -> 0()
      plusAC(x,plusAC(i(x),y)) -> y
      i(0()) -> 0()
      i(s(x)) -> p(i(x))
      i(p(x)) -> s(i(x))
      i(i(x)) -> x
      i(plusAC(x,y)) -> plusAC(i(y),i(x))
      timesAC(0(),y) -> 0()
      timesAC(s(x),y) -> plusAC(timesAC(x,y),y)
      timesAC(p(x),y) -> plusAC(timesAC(x,y),i(y))
     S:
      plusAC(plusAC(x13,x14),x15) -> plusAC(x13,x14)
      plusAC(x13,plusAC(x14,x15)) -> plusAC(x14,x15)
      timesAC(timesAC(x13,x14),x15) -> timesAC(x13,x14)
      timesAC(x13,timesAC(x14,x15)) -> timesAC(x14,x15)
     Usable Rule Processor:
      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)
      DPs:
       plusAC(x9,plusAC(x,plusAC(i(x),y))) -> plusAC(x9,y)
       plusAC(x8,plusAC(i(x),x)) -> plusAC(x8,0())
       plusAC(x7,plusAC(p(x),y)) -> plusAC(x7,p(plusAC(x,y)))
       plusAC(x7,plusAC(p(x),y)) -> plusAC(x,y)
       plusAC(x6,plusAC(s(x),y)) -> plusAC(x6,s(plusAC(x,y)))
       plusAC(x6,plusAC(s(x),y)) -> plusAC(x,y)
       plusAC(x5,plusAC(0(),y)) -> plusAC(x5,y)
       plusAC(p(x),y) -> plusAC(x,y)
       plusAC(s(x),y) -> plusAC(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:
       plusAC(0(),y) -> y
       plusAC(s(x),y) -> s(plusAC(x,y))
       plusAC(p(x),y) -> p(plusAC(x,y))
       plusAC(i(x),x) -> 0()
       plusAC(x,plusAC(i(x),y)) -> y
       s(p(x)) -> x
       p(s(x)) -> x
      S:
       plusAC(plusAC(x13,x14),x15) -> plusAC(x13,x14)
       plusAC(x13,plusAC(x14,x15)) -> plusAC(x14,x15)
       timesAC(timesAC(x13,x14),x15) -> timesAC(x13,x14)
       timesAC(x13,timesAC(x14,x15)) -> timesAC(x14,x15)
      AC-RPO Processor:
       argument filtering:
        pi(plusAC) = [0,1]
        pi(timesAC) = [0,1]
        pi(p) = [0]
        pi(s) = [0]
        pi(0) = []
        pi(i) = []
       precedence:
        i > 0 > plusAC > s > p > timesAC
       status:
        
       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)
        DPs:
         
        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:
         plusAC(0(),y) -> y
         plusAC(s(x),y) -> s(plusAC(x,y))
         plusAC(p(x),y) -> p(plusAC(x,y))
         plusAC(i(x),x) -> 0()
         plusAC(x,plusAC(i(x),y)) -> y
         s(p(x)) -> x
         p(s(x)) -> x
        S:
         plusAC(plusAC(x13,x14),x15) -> plusAC(x13,x14)
         plusAC(x13,plusAC(x14,x15)) -> plusAC(x14,x15)
         timesAC(timesAC(x13,x14),x15) -> timesAC(x13,x14)
         timesAC(x13,timesAC(x14,x15)) -> timesAC(x14,x15)
       Qed