YES
Time: 0.172

Problem:
 Equations:
  pAC(pAC(x3,x4),x5) -> pAC(x3,pAC(x4,x5))
  pAC(x3,x4) -> pAC(x4,x3)
  mAC(mAC(x3,x4),x5) -> mAC(x3,mAC(x4,x5))
  mAC(x3,x4) -> mAC(x4,x3)
  pAC(x3,pAC(x4,x5)) -> pAC(pAC(x3,x4),x5)
  pAC(x4,x3) -> pAC(x3,x4)
  mAC(x3,mAC(x4,x5)) -> mAC(mAC(x3,x4),x5)
  mAC(x4,x3) -> mAC(x3,x4)
 TRS:
  pAC(x,zero()) -> x
  pAC(i(x),x) -> zero()
  mAC(x,one()) -> x
  mAC(pAC(x,y),z) -> pAC(mAC(x,z),mAC(y,z))

Proof:
 DP Processor:
  Equations#:
   p{AC,#}(pAC(x3,x4),x5) -> p{AC,#}(x3,pAC(x4,x5))
   p{AC,#}(x3,x4) -> p{AC,#}(x4,x3)
   m{AC,#}(mAC(x3,x4),x5) -> m{AC,#}(x3,mAC(x4,x5))
   m{AC,#}(x3,x4) -> m{AC,#}(x4,x3)
   p{AC,#}(x3,pAC(x4,x5)) -> p{AC,#}(pAC(x3,x4),x5)
   p{AC,#}(x4,x3) -> p{AC,#}(x3,x4)
   m{AC,#}(x3,mAC(x4,x5)) -> m{AC,#}(mAC(x3,x4),x5)
   m{AC,#}(x4,x3) -> m{AC,#}(x3,x4)
  DPs:
   m{AC,#}(pAC(x,y),z) -> m{AC,#}(y,z)
   m{AC,#}(pAC(x,y),z) -> m{AC,#}(x,z)
   m{AC,#}(pAC(x,y),z) -> p{AC,#}(mAC(x,z),mAC(y,z))
   p{AC,#}(x6,pAC(x,zero())) -> p{AC,#}(x6,x)
   p{AC,#}(x7,pAC(i(x),x)) -> p{AC,#}(x7,zero())
   m{AC,#}(x8,mAC(x,one())) -> m{AC,#}(x8,x)
   m{AC,#}(x9,mAC(pAC(x,y),z)) -> m{AC,#}(y,z)
   m{AC,#}(x9,mAC(pAC(x,y),z)) -> m{AC,#}(x,z)
   m{AC,#}(x9,mAC(pAC(x,y),z)) -> p{AC,#}(mAC(x,z),mAC(y,z))
   m{AC,#}(x9,mAC(pAC(x,y),z)) -> m{AC,#}(x9,pAC(mAC(x,z),mAC(y,z)))
  Equations:
   pAC(pAC(x3,x4),x5) -> pAC(x3,pAC(x4,x5))
   pAC(x3,x4) -> pAC(x4,x3)
   mAC(mAC(x3,x4),x5) -> mAC(x3,mAC(x4,x5))
   mAC(x3,x4) -> mAC(x4,x3)
   pAC(x3,pAC(x4,x5)) -> pAC(pAC(x3,x4),x5)
   pAC(x4,x3) -> pAC(x3,x4)
   mAC(x3,mAC(x4,x5)) -> mAC(mAC(x3,x4),x5)
   mAC(x4,x3) -> mAC(x3,x4)
  TRS:
   pAC(x,zero()) -> x
   pAC(i(x),x) -> zero()
   mAC(x,one()) -> x
   mAC(pAC(x,y),z) -> pAC(mAC(x,z),mAC(y,z))
  S:
   p{AC,#}(pAC(x10,x11),x12) -> p{AC,#}(x10,x11)
   p{AC,#}(x10,pAC(x11,x12)) -> p{AC,#}(x11,x12)
   m{AC,#}(mAC(x10,x11),x12) -> m{AC,#}(x10,x11)
   m{AC,#}(x10,mAC(x11,x12)) -> m{AC,#}(x11,x12)
  AC-EDG Processor:
   Equations#:
    p{AC,#}(pAC(x3,x4),x5) -> p{AC,#}(x3,pAC(x4,x5))
    p{AC,#}(x3,x4) -> p{AC,#}(x4,x3)
    m{AC,#}(mAC(x3,x4),x5) -> m{AC,#}(x3,mAC(x4,x5))
    m{AC,#}(x3,x4) -> m{AC,#}(x4,x3)
    p{AC,#}(x3,pAC(x4,x5)) -> p{AC,#}(pAC(x3,x4),x5)
    p{AC,#}(x4,x3) -> p{AC,#}(x3,x4)
    m{AC,#}(x3,mAC(x4,x5)) -> m{AC,#}(mAC(x3,x4),x5)
    m{AC,#}(x4,x3) -> m{AC,#}(x3,x4)
   DPs:
    m{AC,#}(pAC(x,y),z) -> m{AC,#}(y,z)
    m{AC,#}(pAC(x,y),z) -> m{AC,#}(x,z)
    m{AC,#}(pAC(x,y),z) -> p{AC,#}(mAC(x,z),mAC(y,z))
    p{AC,#}(x6,pAC(x,zero())) -> p{AC,#}(x6,x)
    p{AC,#}(x7,pAC(i(x),x)) -> p{AC,#}(x7,zero())
    m{AC,#}(x8,mAC(x,one())) -> m{AC,#}(x8,x)
    m{AC,#}(x9,mAC(pAC(x,y),z)) -> m{AC,#}(y,z)
    m{AC,#}(x9,mAC(pAC(x,y),z)) -> m{AC,#}(x,z)
    m{AC,#}(x9,mAC(pAC(x,y),z)) -> p{AC,#}(mAC(x,z),mAC(y,z))
    m{AC,#}(x9,mAC(pAC(x,y),z)) -> m{AC,#}(x9,pAC(mAC(x,z),mAC(y,z)))
   Equations:
    pAC(pAC(x3,x4),x5) -> pAC(x3,pAC(x4,x5))
    pAC(x3,x4) -> pAC(x4,x3)
    mAC(mAC(x3,x4),x5) -> mAC(x3,mAC(x4,x5))
    mAC(x3,x4) -> mAC(x4,x3)
    pAC(x3,pAC(x4,x5)) -> pAC(pAC(x3,x4),x5)
    pAC(x4,x3) -> pAC(x3,x4)
    mAC(x3,mAC(x4,x5)) -> mAC(mAC(x3,x4),x5)
    mAC(x4,x3) -> mAC(x3,x4)
   TRS:
    pAC(x,zero()) -> x
    pAC(i(x),x) -> zero()
    mAC(x,one()) -> x
    mAC(pAC(x,y),z) -> pAC(mAC(x,z),mAC(y,z))
   S:
    p{AC,#}(pAC(x10,x11),x12) -> p{AC,#}(x10,x11)
    p{AC,#}(x10,pAC(x11,x12)) -> p{AC,#}(x11,x12)
    m{AC,#}(mAC(x10,x11),x12) -> m{AC,#}(x10,x11)
    m{AC,#}(x10,mAC(x11,x12)) -> m{AC,#}(x11,x12)
   SCC Processor:
    #sccs: 2
    #rules: 8
    #arcs: 56/100
    Equations#:
     p{AC,#}(pAC(x3,x4),x5) -> p{AC,#}(x3,pAC(x4,x5))
     p{AC,#}(x3,x4) -> p{AC,#}(x4,x3)
     m{AC,#}(mAC(x3,x4),x5) -> m{AC,#}(x3,mAC(x4,x5))
     m{AC,#}(x3,x4) -> m{AC,#}(x4,x3)
     p{AC,#}(x3,pAC(x4,x5)) -> p{AC,#}(pAC(x3,x4),x5)
     p{AC,#}(x4,x3) -> p{AC,#}(x3,x4)
     m{AC,#}(x3,mAC(x4,x5)) -> m{AC,#}(mAC(x3,x4),x5)
     m{AC,#}(x4,x3) -> m{AC,#}(x3,x4)
    DPs:
     m{AC,#}(pAC(x,y),z) -> m{AC,#}(y,z)
     m{AC,#}(x9,mAC(pAC(x,y),z)) -> m{AC,#}(x9,pAC(mAC(x,z),mAC(y,z)))
     m{AC,#}(x9,mAC(pAC(x,y),z)) -> m{AC,#}(x,z)
     m{AC,#}(x9,mAC(pAC(x,y),z)) -> m{AC,#}(y,z)
     m{AC,#}(x8,mAC(x,one())) -> m{AC,#}(x8,x)
     m{AC,#}(pAC(x,y),z) -> m{AC,#}(x,z)
    Equations:
     pAC(pAC(x3,x4),x5) -> pAC(x3,pAC(x4,x5))
     pAC(x3,x4) -> pAC(x4,x3)
     mAC(mAC(x3,x4),x5) -> mAC(x3,mAC(x4,x5))
     mAC(x3,x4) -> mAC(x4,x3)
     pAC(x3,pAC(x4,x5)) -> pAC(pAC(x3,x4),x5)
     pAC(x4,x3) -> pAC(x3,x4)
     mAC(x3,mAC(x4,x5)) -> mAC(mAC(x3,x4),x5)
     mAC(x4,x3) -> mAC(x3,x4)
    TRS:
     pAC(x,zero()) -> x
     pAC(i(x),x) -> zero()
     mAC(x,one()) -> x
     mAC(pAC(x,y),z) -> pAC(mAC(x,z),mAC(y,z))
    S:
     p{AC,#}(pAC(x10,x11),x12) -> p{AC,#}(x10,x11)
     p{AC,#}(x10,pAC(x11,x12)) -> p{AC,#}(x11,x12)
     m{AC,#}(mAC(x10,x11),x12) -> m{AC,#}(x10,x11)
     m{AC,#}(x10,mAC(x11,x12)) -> m{AC,#}(x11,x12)
    AC-DP unlabeling:
     Equations#:
      pAC(pAC(x3,x4),x5) -> pAC(x3,pAC(x4,x5))
      pAC(x3,x4) -> pAC(x4,x3)
      mAC(mAC(x3,x4),x5) -> mAC(x3,mAC(x4,x5))
      mAC(x3,x4) -> mAC(x4,x3)
      pAC(x3,pAC(x4,x5)) -> pAC(pAC(x3,x4),x5)
      pAC(x4,x3) -> pAC(x3,x4)
      mAC(x3,mAC(x4,x5)) -> mAC(mAC(x3,x4),x5)
      mAC(x4,x3) -> mAC(x3,x4)
     DPs:
      mAC(pAC(x,y),z) -> mAC(y,z)
      mAC(x9,mAC(pAC(x,y),z)) -> mAC(x9,pAC(mAC(x,z),mAC(y,z)))
      mAC(x9,mAC(pAC(x,y),z)) -> mAC(x,z)
      mAC(x9,mAC(pAC(x,y),z)) -> mAC(y,z)
      mAC(x8,mAC(x,one())) -> mAC(x8,x)
      mAC(pAC(x,y),z) -> mAC(x,z)
     Equations:
      pAC(pAC(x3,x4),x5) -> pAC(x3,pAC(x4,x5))
      pAC(x3,x4) -> pAC(x4,x3)
      mAC(mAC(x3,x4),x5) -> mAC(x3,mAC(x4,x5))
      mAC(x3,x4) -> mAC(x4,x3)
      pAC(x3,pAC(x4,x5)) -> pAC(pAC(x3,x4),x5)
      pAC(x4,x3) -> pAC(x3,x4)
      mAC(x3,mAC(x4,x5)) -> mAC(mAC(x3,x4),x5)
      mAC(x4,x3) -> mAC(x3,x4)
     TRS:
      pAC(x,zero()) -> x
      pAC(i(x),x) -> zero()
      mAC(x,one()) -> x
      mAC(pAC(x,y),z) -> pAC(mAC(x,z),mAC(y,z))
     S:
      pAC(pAC(x10,x11),x12) -> pAC(x10,x11)
      pAC(x10,pAC(x11,x12)) -> pAC(x11,x12)
      mAC(mAC(x10,x11),x12) -> mAC(x10,x11)
      mAC(x10,mAC(x11,x12)) -> mAC(x11,x12)
     AC-RPO Processor:
      argument filtering:
       pi(pAC) = [0,1]
       pi(mAC) = [0,1]
       pi(zero) = []
       pi(i) = []
       pi(one) = []
      precedence:
       i > zero > one > mAC > pAC
      status:
       
      problem:
       Equations#:
        pAC(pAC(x3,x4),x5) -> pAC(x3,pAC(x4,x5))
        pAC(x3,x4) -> pAC(x4,x3)
        mAC(mAC(x3,x4),x5) -> mAC(x3,mAC(x4,x5))
        mAC(x3,x4) -> mAC(x4,x3)
        pAC(x3,pAC(x4,x5)) -> pAC(pAC(x3,x4),x5)
        pAC(x4,x3) -> pAC(x3,x4)
        mAC(x3,mAC(x4,x5)) -> mAC(mAC(x3,x4),x5)
        mAC(x4,x3) -> mAC(x3,x4)
       DPs:
        
       Equations:
        pAC(pAC(x3,x4),x5) -> pAC(x3,pAC(x4,x5))
        pAC(x3,x4) -> pAC(x4,x3)
        mAC(mAC(x3,x4),x5) -> mAC(x3,mAC(x4,x5))
        mAC(x3,x4) -> mAC(x4,x3)
        pAC(x3,pAC(x4,x5)) -> pAC(pAC(x3,x4),x5)
        pAC(x4,x3) -> pAC(x3,x4)
        mAC(x3,mAC(x4,x5)) -> mAC(mAC(x3,x4),x5)
        mAC(x4,x3) -> mAC(x3,x4)
       TRS:
        pAC(x,zero()) -> x
        pAC(i(x),x) -> zero()
        mAC(x,one()) -> x
        mAC(pAC(x,y),z) -> pAC(mAC(x,z),mAC(y,z))
       S:
        pAC(pAC(x10,x11),x12) -> pAC(x10,x11)
        pAC(x10,pAC(x11,x12)) -> pAC(x11,x12)
        mAC(mAC(x10,x11),x12) -> mAC(x10,x11)
        mAC(x10,mAC(x11,x12)) -> mAC(x11,x12)
      Qed
    
    Equations#:
     p{AC,#}(pAC(x3,x4),x5) -> p{AC,#}(x3,pAC(x4,x5))
     p{AC,#}(x3,x4) -> p{AC,#}(x4,x3)
     m{AC,#}(mAC(x3,x4),x5) -> m{AC,#}(x3,mAC(x4,x5))
     m{AC,#}(x3,x4) -> m{AC,#}(x4,x3)
     p{AC,#}(x3,pAC(x4,x5)) -> p{AC,#}(pAC(x3,x4),x5)
     p{AC,#}(x4,x3) -> p{AC,#}(x3,x4)
     m{AC,#}(x3,mAC(x4,x5)) -> m{AC,#}(mAC(x3,x4),x5)
     m{AC,#}(x4,x3) -> m{AC,#}(x3,x4)
    DPs:
     p{AC,#}(x7,pAC(i(x),x)) -> p{AC,#}(x7,zero())
     p{AC,#}(x6,pAC(x,zero())) -> p{AC,#}(x6,x)
    Equations:
     pAC(pAC(x3,x4),x5) -> pAC(x3,pAC(x4,x5))
     pAC(x3,x4) -> pAC(x4,x3)
     mAC(mAC(x3,x4),x5) -> mAC(x3,mAC(x4,x5))
     mAC(x3,x4) -> mAC(x4,x3)
     pAC(x3,pAC(x4,x5)) -> pAC(pAC(x3,x4),x5)
     pAC(x4,x3) -> pAC(x3,x4)
     mAC(x3,mAC(x4,x5)) -> mAC(mAC(x3,x4),x5)
     mAC(x4,x3) -> mAC(x3,x4)
    TRS:
     pAC(x,zero()) -> x
     pAC(i(x),x) -> zero()
     mAC(x,one()) -> x
     mAC(pAC(x,y),z) -> pAC(mAC(x,z),mAC(y,z))
    S:
     p{AC,#}(pAC(x10,x11),x12) -> p{AC,#}(x10,x11)
     p{AC,#}(x10,pAC(x11,x12)) -> p{AC,#}(x11,x12)
     m{AC,#}(mAC(x10,x11),x12) -> m{AC,#}(x10,x11)
     m{AC,#}(x10,mAC(x11,x12)) -> m{AC,#}(x11,x12)
    AC-DP unlabeling:
     Equations#:
      pAC(pAC(x3,x4),x5) -> pAC(x3,pAC(x4,x5))
      pAC(x3,x4) -> pAC(x4,x3)
      mAC(mAC(x3,x4),x5) -> mAC(x3,mAC(x4,x5))
      mAC(x3,x4) -> mAC(x4,x3)
      pAC(x3,pAC(x4,x5)) -> pAC(pAC(x3,x4),x5)
      pAC(x4,x3) -> pAC(x3,x4)
      mAC(x3,mAC(x4,x5)) -> mAC(mAC(x3,x4),x5)
      mAC(x4,x3) -> mAC(x3,x4)
     DPs:
      pAC(x7,pAC(i(x),x)) -> pAC(x7,zero())
      pAC(x6,pAC(x,zero())) -> pAC(x6,x)
     Equations:
      pAC(pAC(x3,x4),x5) -> pAC(x3,pAC(x4,x5))
      pAC(x3,x4) -> pAC(x4,x3)
      mAC(mAC(x3,x4),x5) -> mAC(x3,mAC(x4,x5))
      mAC(x3,x4) -> mAC(x4,x3)
      pAC(x3,pAC(x4,x5)) -> pAC(pAC(x3,x4),x5)
      pAC(x4,x3) -> pAC(x3,x4)
      mAC(x3,mAC(x4,x5)) -> mAC(mAC(x3,x4),x5)
      mAC(x4,x3) -> mAC(x3,x4)
     TRS:
      pAC(x,zero()) -> x
      pAC(i(x),x) -> zero()
      mAC(x,one()) -> x
      mAC(pAC(x,y),z) -> pAC(mAC(x,z),mAC(y,z))
     S:
      pAC(pAC(x10,x11),x12) -> pAC(x10,x11)
      pAC(x10,pAC(x11,x12)) -> pAC(x11,x12)
      mAC(mAC(x10,x11),x12) -> mAC(x10,x11)
      mAC(x10,mAC(x11,x12)) -> mAC(x11,x12)
     Usable Rule Processor:
      Equations#:
       pAC(pAC(x3,x4),x5) -> pAC(x3,pAC(x4,x5))
       pAC(x3,x4) -> pAC(x4,x3)
       mAC(mAC(x3,x4),x5) -> mAC(x3,mAC(x4,x5))
       mAC(x3,x4) -> mAC(x4,x3)
       pAC(x3,pAC(x4,x5)) -> pAC(pAC(x3,x4),x5)
       pAC(x4,x3) -> pAC(x3,x4)
       mAC(x3,mAC(x4,x5)) -> mAC(mAC(x3,x4),x5)
       mAC(x4,x3) -> mAC(x3,x4)
      DPs:
       pAC(x7,pAC(i(x),x)) -> pAC(x7,zero())
       pAC(x6,pAC(x,zero())) -> pAC(x6,x)
      Equations:
       pAC(pAC(x3,x4),x5) -> pAC(x3,pAC(x4,x5))
       pAC(x3,x4) -> pAC(x4,x3)
       mAC(mAC(x3,x4),x5) -> mAC(x3,mAC(x4,x5))
       mAC(x3,x4) -> mAC(x4,x3)
       pAC(x3,pAC(x4,x5)) -> pAC(pAC(x3,x4),x5)
       pAC(x4,x3) -> pAC(x3,x4)
       mAC(x3,mAC(x4,x5)) -> mAC(mAC(x3,x4),x5)
       mAC(x4,x3) -> mAC(x3,x4)
      TRS:
       pAC(x,zero()) -> x
       pAC(i(x),x) -> zero()
      S:
       pAC(pAC(x10,x11),x12) -> pAC(x10,x11)
       pAC(x10,pAC(x11,x12)) -> pAC(x11,x12)
       mAC(mAC(x10,x11),x12) -> mAC(x10,x11)
       mAC(x10,mAC(x11,x12)) -> mAC(x11,x12)
      AC-RPO Processor:
       argument filtering:
        pi(pAC) = [0,1]
        pi(mAC) = [0,1]
        pi(zero) = []
        pi(i) = []
       precedence:
        i > zero > pAC > mAC
       status:
        
       problem:
        Equations#:
         pAC(pAC(x3,x4),x5) -> pAC(x3,pAC(x4,x5))
         pAC(x3,x4) -> pAC(x4,x3)
         mAC(mAC(x3,x4),x5) -> mAC(x3,mAC(x4,x5))
         mAC(x3,x4) -> mAC(x4,x3)
         pAC(x3,pAC(x4,x5)) -> pAC(pAC(x3,x4),x5)
         pAC(x4,x3) -> pAC(x3,x4)
         mAC(x3,mAC(x4,x5)) -> mAC(mAC(x3,x4),x5)
         mAC(x4,x3) -> mAC(x3,x4)
        DPs:
         
        Equations:
         pAC(pAC(x3,x4),x5) -> pAC(x3,pAC(x4,x5))
         pAC(x3,x4) -> pAC(x4,x3)
         mAC(mAC(x3,x4),x5) -> mAC(x3,mAC(x4,x5))
         mAC(x3,x4) -> mAC(x4,x3)
         pAC(x3,pAC(x4,x5)) -> pAC(pAC(x3,x4),x5)
         pAC(x4,x3) -> pAC(x3,x4)
         mAC(x3,mAC(x4,x5)) -> mAC(mAC(x3,x4),x5)
         mAC(x4,x3) -> mAC(x3,x4)
        TRS:
         pAC(x,zero()) -> x
         pAC(i(x),x) -> zero()
        S:
         pAC(pAC(x10,x11),x12) -> pAC(x10,x11)
         pAC(x10,pAC(x11,x12)) -> pAC(x11,x12)
         mAC(mAC(x10,x11),x12) -> mAC(x10,x11)
         mAC(x10,mAC(x11,x12)) -> mAC(x11,x12)
       Qed