MAYBE

Problem:
 norm(nil()) -> 0()
 norm(g(x,y)) -> s(norm(x))
 f(x,nil()) -> g(nil(),x)
 f(x,g(y,z)) -> g(f(x,y),z)
 rem(nil(),y) -> nil()
 rem(g(x,y),0()) -> g(x,y)
 rem(g(x,y),s(z)) -> rem(x,z)

Proof:
 DP Processor:
  DPs:
   norm#(g(x,y)) -> norm#(x)
   f#(x,g(y,z)) -> f#(x,y)
   rem#(g(x,y),s(z)) -> rem#(x,z)
  TRS:
   norm(nil()) -> 0()
   norm(g(x,y)) -> s(norm(x))
   f(x,nil()) -> g(nil(),x)
   f(x,g(y,z)) -> g(f(x,y),z)
   rem(nil(),y) -> nil()
   rem(g(x,y),0()) -> g(x,y)
   rem(g(x,y),s(z)) -> rem(x,z)
  Usable Rule Processor:
   DPs:
    norm#(g(x,y)) -> norm#(x)
    f#(x,g(y,z)) -> f#(x,y)
    rem#(g(x,y),s(z)) -> rem#(x,z)
   TRS:
    
   EDG Processor:
    DPs:
     norm#(g(x,y)) -> norm#(x)
     f#(x,g(y,z)) -> f#(x,y)
     rem#(g(x,y),s(z)) -> rem#(x,z)
    TRS:
     
    graph:
     rem#(g(x,y),s(z)) -> rem#(x,z) -> rem#(g(x,y),s(z)) -> rem#(x,z)
     f#(x,g(y,z)) -> f#(x,y) -> f#(x,g(y,z)) -> f#(x,y)
     norm#(g(x,y)) -> norm#(x) -> norm#(g(x,y)) -> norm#(x)
    Restore Modifier:
     DPs:
      norm#(g(x,y)) -> norm#(x)
      f#(x,g(y,z)) -> f#(x,y)
      rem#(g(x,y),s(z)) -> rem#(x,z)
     TRS:
      norm(nil()) -> 0()
      norm(g(x,y)) -> s(norm(x))
      f(x,nil()) -> g(nil(),x)
      f(x,g(y,z)) -> g(f(x,y),z)
      rem(nil(),y) -> nil()
      rem(g(x,y),0()) -> g(x,y)
      rem(g(x,y),s(z)) -> rem(x,z)
     SCC Processor:
      #sccs: 3
      #rules: 3
      #arcs: 3/9
      DPs:
       norm#(g(x,y)) -> norm#(x)
      TRS:
       norm(nil()) -> 0()
       norm(g(x,y)) -> s(norm(x))
       f(x,nil()) -> g(nil(),x)
       f(x,g(y,z)) -> g(f(x,y),z)
       rem(nil(),y) -> nil()
       rem(g(x,y),0()) -> g(x,y)
       rem(g(x,y),s(z)) -> rem(x,z)
      Open
      
      DPs:
       f#(x,g(y,z)) -> f#(x,y)
      TRS:
       norm(nil()) -> 0()
       norm(g(x,y)) -> s(norm(x))
       f(x,nil()) -> g(nil(),x)
       f(x,g(y,z)) -> g(f(x,y),z)
       rem(nil(),y) -> nil()
       rem(g(x,y),0()) -> g(x,y)
       rem(g(x,y),s(z)) -> rem(x,z)
      Open
      
      DPs:
       rem#(g(x,y),s(z)) -> rem#(x,z)
      TRS:
       norm(nil()) -> 0()
       norm(g(x,y)) -> s(norm(x))
       f(x,nil()) -> g(nil(),x)
       f(x,g(y,z)) -> g(f(x,y),z)
       rem(nil(),y) -> nil()
       rem(g(x,y),0()) -> g(x,y)
       rem(g(x,y),s(z)) -> rem(x,z)
      Open