MAYBE
TRS:
 {                   le(0(), y) -> true(),
                  le(s(x), 0()) -> false(),
                 le(s(x), s(y)) -> le(x, y),
                      zero(0()) -> true(),
                     zero(s(x)) -> false(),
                        id(0()) -> 0(),
                       id(s(x)) -> s(id(x)),
                  minus(x, 0()) -> x,
              minus(s(x), s(y)) -> minus(x, y),
   if_mod(true(), b1, b2, x, y) -> 0(),
  if_mod(false(), b1, b2, x, y) -> if2(b1, b2, x, y),
                      mod(x, y) -> if_mod(zero(x), zero(y), le(y, x), id(x), id(y)),
          if2(true(), b2, x, y) -> 0(),
         if2(false(), b2, x, y) -> if3(b2, x, y),
              if3(true(), x, y) -> mod(minus(x, y), s(y)),
             if3(false(), x, y) -> x}
 DP:
  Strict:
   {               le#(s(x), s(y)) -> le#(x, y),
                         id#(s(x)) -> id#(x),
                minus#(s(x), s(y)) -> minus#(x, y),
    if_mod#(false(), b1, b2, x, y) -> if2#(b1, b2, x, y),
                        mod#(x, y) -> le#(y, x),
                        mod#(x, y) -> zero#(y),
                        mod#(x, y) -> zero#(x),
                        mod#(x, y) -> id#(y),
                        mod#(x, y) -> id#(x),
                        mod#(x, y) -> if_mod#(zero(x), zero(y), le(y, x), id(x), id(y)),
           if2#(false(), b2, x, y) -> if3#(b2, x, y),
                if3#(true(), x, y) -> minus#(x, y),
                if3#(true(), x, y) -> mod#(minus(x, y), s(y))}
  Weak:
  {                   le(0(), y) -> true(),
                   le(s(x), 0()) -> false(),
                  le(s(x), s(y)) -> le(x, y),
                       zero(0()) -> true(),
                      zero(s(x)) -> false(),
                         id(0()) -> 0(),
                        id(s(x)) -> s(id(x)),
                   minus(x, 0()) -> x,
               minus(s(x), s(y)) -> minus(x, y),
    if_mod(true(), b1, b2, x, y) -> 0(),
   if_mod(false(), b1, b2, x, y) -> if2(b1, b2, x, y),
                       mod(x, y) -> if_mod(zero(x), zero(y), le(y, x), id(x), id(y)),
           if2(true(), b2, x, y) -> 0(),
          if2(false(), b2, x, y) -> if3(b2, x, y),
               if3(true(), x, y) -> mod(minus(x, y), s(y)),
              if3(false(), x, y) -> x}
  EDG:
   {(mod#(x, y) -> id#(y), id#(s(x)) -> id#(x))
    (if3#(true(), x, y) -> mod#(minus(x, y), s(y)), mod#(x, y) -> if_mod#(zero(x), zero(y), le(y, x), id(x), id(y)))
    (if3#(true(), x, y) -> mod#(minus(x, y), s(y)), mod#(x, y) -> id#(x))
    (if3#(true(), x, y) -> mod#(minus(x, y), s(y)), mod#(x, y) -> id#(y))
    (if3#(true(), x, y) -> mod#(minus(x, y), s(y)), mod#(x, y) -> zero#(x))
    (if3#(true(), x, y) -> mod#(minus(x, y), s(y)), mod#(x, y) -> zero#(y))
    (if3#(true(), x, y) -> mod#(minus(x, y), s(y)), mod#(x, y) -> le#(y, x))
    (minus#(s(x), s(y)) -> minus#(x, y), minus#(s(x), s(y)) -> minus#(x, y))
    (if2#(false(), b2, x, y) -> if3#(b2, x, y), if3#(true(), x, y) -> mod#(minus(x, y), s(y)))
    (if2#(false(), b2, x, y) -> if3#(b2, x, y), if3#(true(), x, y) -> minus#(x, y))
    (mod#(x, y) -> if_mod#(zero(x), zero(y), le(y, x), id(x), id(y)), if_mod#(false(), b1, b2, x, y) -> if2#(b1, b2, x, y))
    (mod#(x, y) -> le#(y, x), le#(s(x), s(y)) -> le#(x, y))
    (if3#(true(), x, y) -> minus#(x, y), minus#(s(x), s(y)) -> minus#(x, y))
    (if_mod#(false(), b1, b2, x, y) -> if2#(b1, b2, x, y), if2#(false(), b2, x, y) -> if3#(b2, x, y))
    (le#(s(x), s(y)) -> le#(x, y), le#(s(x), s(y)) -> le#(x, y))
    (mod#(x, y) -> id#(x), id#(s(x)) -> id#(x))
    (id#(s(x)) -> id#(x), id#(s(x)) -> id#(x))}
   SCCS:
    Scc:
     {if_mod#(false(), b1, b2, x, y) -> if2#(b1, b2, x, y),
                          mod#(x, y) -> if_mod#(zero(x), zero(y), le(y, x), id(x), id(y)),
             if2#(false(), b2, x, y) -> if3#(b2, x, y),
                  if3#(true(), x, y) -> mod#(minus(x, y), s(y))}
    Scc:
     {minus#(s(x), s(y)) -> minus#(x, y)}
    Scc:
     {id#(s(x)) -> id#(x)}
    Scc:
     {le#(s(x), s(y)) -> le#(x, y)}
    SCC:
     Strict:
      {if_mod#(false(), b1, b2, x, y) -> if2#(b1, b2, x, y),
                           mod#(x, y) -> if_mod#(zero(x), zero(y), le(y, x), id(x), id(y)),
              if2#(false(), b2, x, y) -> if3#(b2, x, y),
                   if3#(true(), x, y) -> mod#(minus(x, y), s(y))}
     Weak:
     {                   le(0(), y) -> true(),
                      le(s(x), 0()) -> false(),
                     le(s(x), s(y)) -> le(x, y),
                          zero(0()) -> true(),
                         zero(s(x)) -> false(),
                            id(0()) -> 0(),
                           id(s(x)) -> s(id(x)),
                      minus(x, 0()) -> x,
                  minus(s(x), s(y)) -> minus(x, y),
       if_mod(true(), b1, b2, x, y) -> 0(),
      if_mod(false(), b1, b2, x, y) -> if2(b1, b2, x, y),
                          mod(x, y) -> if_mod(zero(x), zero(y), le(y, x), id(x), id(y)),
              if2(true(), b2, x, y) -> 0(),
             if2(false(), b2, x, y) -> if3(b2, x, y),
                  if3(true(), x, y) -> mod(minus(x, y), s(y)),
                 if3(false(), x, y) -> x}
     Fail
    SCC:
     Strict:
      {minus#(s(x), s(y)) -> minus#(x, y)}
     Weak:
     {                   le(0(), y) -> true(),
                      le(s(x), 0()) -> false(),
                     le(s(x), s(y)) -> le(x, y),
                          zero(0()) -> true(),
                         zero(s(x)) -> false(),
                            id(0()) -> 0(),
                           id(s(x)) -> s(id(x)),
                      minus(x, 0()) -> x,
                  minus(s(x), s(y)) -> minus(x, y),
       if_mod(true(), b1, b2, x, y) -> 0(),
      if_mod(false(), b1, b2, x, y) -> if2(b1, b2, x, y),
                          mod(x, y) -> if_mod(zero(x), zero(y), le(y, x), id(x), id(y)),
              if2(true(), b2, x, y) -> 0(),
             if2(false(), b2, x, y) -> if3(b2, x, y),
                  if3(true(), x, y) -> mod(minus(x, y), s(y)),
                 if3(false(), x, y) -> x}
     SPSC:
      Simple Projection:
       pi(minus#) = 0
      Strict:
       {}
      Qed
    SCC:
     Strict:
      {id#(s(x)) -> id#(x)}
     Weak:
     {                   le(0(), y) -> true(),
                      le(s(x), 0()) -> false(),
                     le(s(x), s(y)) -> le(x, y),
                          zero(0()) -> true(),
                         zero(s(x)) -> false(),
                            id(0()) -> 0(),
                           id(s(x)) -> s(id(x)),
                      minus(x, 0()) -> x,
                  minus(s(x), s(y)) -> minus(x, y),
       if_mod(true(), b1, b2, x, y) -> 0(),
      if_mod(false(), b1, b2, x, y) -> if2(b1, b2, x, y),
                          mod(x, y) -> if_mod(zero(x), zero(y), le(y, x), id(x), id(y)),
              if2(true(), b2, x, y) -> 0(),
             if2(false(), b2, x, y) -> if3(b2, x, y),
                  if3(true(), x, y) -> mod(minus(x, y), s(y)),
                 if3(false(), x, y) -> x}
     SPSC:
      Simple Projection:
       pi(id#) = 0
      Strict:
       {}
      Qed
    SCC:
     Strict:
      {le#(s(x), s(y)) -> le#(x, y)}
     Weak:
     {                   le(0(), y) -> true(),
                      le(s(x), 0()) -> false(),
                     le(s(x), s(y)) -> le(x, y),
                          zero(0()) -> true(),
                         zero(s(x)) -> false(),
                            id(0()) -> 0(),
                           id(s(x)) -> s(id(x)),
                      minus(x, 0()) -> x,
                  minus(s(x), s(y)) -> minus(x, y),
       if_mod(true(), b1, b2, x, y) -> 0(),
      if_mod(false(), b1, b2, x, y) -> if2(b1, b2, x, y),
                          mod(x, y) -> if_mod(zero(x), zero(y), le(y, x), id(x), id(y)),
              if2(true(), b2, x, y) -> 0(),
             if2(false(), b2, x, y) -> if3(b2, x, y),
                  if3(true(), x, y) -> mod(minus(x, y), s(y)),
                 if3(false(), x, y) -> x}
     SPSC:
      Simple Projection:
       pi(le#) = 0
      Strict:
       {}
      Qed