MAYBE

Problem:
 -(x,0()) -> x
 -(s(x),s(y)) -> -(x,y)
 <=(0(),y) -> true()
 <=(s(x),0()) -> false()
 <=(s(x),s(y)) -> <=(x,y)
 if(true(),x,y) -> x
 if(false(),x,y) -> y
 perfectp(0()) -> false()
 perfectp(s(x)) -> f(x,s(0()),s(x),s(x))
 f(0(),y,0(),u) -> true()
 f(0(),y,s(z),u) -> false()
 f(s(x),0(),z,u) -> f(x,u,-(z,s(x)),u)
 f(s(x),s(y),z,u) -> if(<=(x,y),f(s(x),-(y,x),z,u),f(x,u,z,u))

Proof:
 DP Processor:
  DPs:
   -#(s(x),s(y)) -> -#(x,y)
   <=#(s(x),s(y)) -> <=#(x,y)
   perfectp#(s(x)) -> f#(x,s(0()),s(x),s(x))
   f#(s(x),0(),z,u) -> -#(z,s(x))
   f#(s(x),0(),z,u) -> f#(x,u,-(z,s(x)),u)
   f#(s(x),s(y),z,u) -> f#(x,u,z,u)
   f#(s(x),s(y),z,u) -> -#(y,x)
   f#(s(x),s(y),z,u) -> f#(s(x),-(y,x),z,u)
   f#(s(x),s(y),z,u) -> <=#(x,y)
   f#(s(x),s(y),z,u) -> if#(<=(x,y),f(s(x),-(y,x),z,u),f(x,u,z,u))
  TRS:
   -(x,0()) -> x
   -(s(x),s(y)) -> -(x,y)
   <=(0(),y) -> true()
   <=(s(x),0()) -> false()
   <=(s(x),s(y)) -> <=(x,y)
   if(true(),x,y) -> x
   if(false(),x,y) -> y
   perfectp(0()) -> false()
   perfectp(s(x)) -> f(x,s(0()),s(x),s(x))
   f(0(),y,0(),u) -> true()
   f(0(),y,s(z),u) -> false()
   f(s(x),0(),z,u) -> f(x,u,-(z,s(x)),u)
   f(s(x),s(y),z,u) -> if(<=(x,y),f(s(x),-(y,x),z,u),f(x,u,z,u))
  Usable Rule Processor:
   DPs:
    -#(s(x),s(y)) -> -#(x,y)
    <=#(s(x),s(y)) -> <=#(x,y)
    perfectp#(s(x)) -> f#(x,s(0()),s(x),s(x))
    f#(s(x),0(),z,u) -> -#(z,s(x))
    f#(s(x),0(),z,u) -> f#(x,u,-(z,s(x)),u)
    f#(s(x),s(y),z,u) -> f#(x,u,z,u)
    f#(s(x),s(y),z,u) -> -#(y,x)
    f#(s(x),s(y),z,u) -> f#(s(x),-(y,x),z,u)
    f#(s(x),s(y),z,u) -> <=#(x,y)
    f#(s(x),s(y),z,u) -> if#(<=(x,y),f(s(x),-(y,x),z,u),f(x,u,z,u))
   TRS:
    -(s(x),s(y)) -> -(x,y)
    -(x,0()) -> x
    f(0(),y,0(),u) -> true()
    f(0(),y,s(z),u) -> false()
    f(s(x),0(),z,u) -> f(x,u,-(z,s(x)),u)
    f(s(x),s(y),z,u) -> if(<=(x,y),f(s(x),-(y,x),z,u),f(x,u,z,u))
    if(true(),x,y) -> x
    if(false(),x,y) -> y
    <=(0(),y) -> true()
    <=(s(x),0()) -> false()
    <=(s(x),s(y)) -> <=(x,y)
   Open