MAYBE
Time: 0.294

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
  mAC(x,zero()) -> zero()
  pAC(s(x),y) -> s(pAC(x,y))
  mAC(s(x),y) -> pAC(mAC(x,y),y)
  mAC(x,pAC(y,z)) -> pAC(mAC(x,y),mAC(x,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:
   p{AC,#}(s(x),y) -> p{AC,#}(x,y)
   m{AC,#}(s(x),y) -> m{AC,#}(x,y)
   m{AC,#}(s(x),y) -> p{AC,#}(mAC(x,y),y)
   m{AC,#}(x,pAC(y,z)) -> m{AC,#}(x,z)
   m{AC,#}(x,pAC(y,z)) -> m{AC,#}(x,y)
   m{AC,#}(x,pAC(y,z)) -> p{AC,#}(mAC(x,y),mAC(x,z))
   p{AC,#}(x6,pAC(x,zero())) -> p{AC,#}(x6,x)
   m{AC,#}(x7,mAC(x,zero())) -> m{AC,#}(x7,zero())
   p{AC,#}(x8,pAC(s(x),y)) -> p{AC,#}(x,y)
   p{AC,#}(x8,pAC(s(x),y)) -> p{AC,#}(x8,s(pAC(x,y)))
   m{AC,#}(x9,mAC(s(x),y)) -> m{AC,#}(x,y)
   m{AC,#}(x9,mAC(s(x),y)) -> p{AC,#}(mAC(x,y),y)
   m{AC,#}(x9,mAC(s(x),y)) -> m{AC,#}(x9,pAC(mAC(x,y),y))
   m{AC,#}(x10,mAC(x,pAC(y,z))) -> m{AC,#}(x,z)
   m{AC,#}(x10,mAC(x,pAC(y,z))) -> m{AC,#}(x,y)
   m{AC,#}(x10,mAC(x,pAC(y,z))) -> p{AC,#}(mAC(x,y),mAC(x,z))
   m{AC,#}(x10,mAC(x,pAC(y,z))) -> m{AC,#}(x10,pAC(mAC(x,y),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
   mAC(x,zero()) -> zero()
   pAC(s(x),y) -> s(pAC(x,y))
   mAC(s(x),y) -> pAC(mAC(x,y),y)
   mAC(x,pAC(y,z)) -> pAC(mAC(x,y),mAC(x,z))
  S:
   p{AC,#}(pAC(x11,x12),x13) -> p{AC,#}(x11,x12)
   p{AC,#}(x11,pAC(x12,x13)) -> p{AC,#}(x12,x13)
   m{AC,#}(mAC(x11,x12),x13) -> m{AC,#}(x11,x12)
   m{AC,#}(x11,mAC(x12,x13)) -> m{AC,#}(x12,x13)
  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:
    p{AC,#}(s(x),y) -> p{AC,#}(x,y)
    m{AC,#}(s(x),y) -> m{AC,#}(x,y)
    m{AC,#}(s(x),y) -> p{AC,#}(mAC(x,y),y)
    m{AC,#}(x,pAC(y,z)) -> m{AC,#}(x,z)
    m{AC,#}(x,pAC(y,z)) -> m{AC,#}(x,y)
    m{AC,#}(x,pAC(y,z)) -> p{AC,#}(mAC(x,y),mAC(x,z))
    p{AC,#}(x6,pAC(x,zero())) -> p{AC,#}(x6,x)
    m{AC,#}(x7,mAC(x,zero())) -> m{AC,#}(x7,zero())
    p{AC,#}(x8,pAC(s(x),y)) -> p{AC,#}(x,y)
    p{AC,#}(x8,pAC(s(x),y)) -> p{AC,#}(x8,s(pAC(x,y)))
    m{AC,#}(x9,mAC(s(x),y)) -> m{AC,#}(x,y)
    m{AC,#}(x9,mAC(s(x),y)) -> p{AC,#}(mAC(x,y),y)
    m{AC,#}(x9,mAC(s(x),y)) -> m{AC,#}(x9,pAC(mAC(x,y),y))
    m{AC,#}(x10,mAC(x,pAC(y,z))) -> m{AC,#}(x,z)
    m{AC,#}(x10,mAC(x,pAC(y,z))) -> m{AC,#}(x,y)
    m{AC,#}(x10,mAC(x,pAC(y,z))) -> p{AC,#}(mAC(x,y),mAC(x,z))
    m{AC,#}(x10,mAC(x,pAC(y,z))) -> m{AC,#}(x10,pAC(mAC(x,y),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
    mAC(x,zero()) -> zero()
    pAC(s(x),y) -> s(pAC(x,y))
    mAC(s(x),y) -> pAC(mAC(x,y),y)
    mAC(x,pAC(y,z)) -> pAC(mAC(x,y),mAC(x,z))
   S:
    p{AC,#}(pAC(x11,x12),x13) -> p{AC,#}(x11,x12)
    p{AC,#}(x11,pAC(x12,x13)) -> p{AC,#}(x12,x13)
    m{AC,#}(mAC(x11,x12),x13) -> m{AC,#}(x11,x12)
    m{AC,#}(x11,mAC(x12,x13)) -> m{AC,#}(x12,x13)
   Open