MAYBE
MAYBE
TRS:
 {
       active(minus(0(), Y)) -> mark(0()),
   active(minus(s(X), s(Y))) -> mark(minus(X, Y)),
                active(s(X)) -> s(active(X)),
         active(geq(X, 0())) -> mark(true()),
      active(geq(0(), s(Y))) -> mark(false()),
     active(geq(s(X), s(Y))) -> mark(geq(X, Y)),
         active(div(X1, X2)) -> div(active(X1), X2),
      active(div(0(), s(Y))) -> mark(0()),
     active(div(s(X), s(Y))) ->
  mark(if(geq(X, Y), s(div(minus(X, Y), s(Y))), 0())),
      active(if(X1, X2, X3)) -> if(active(X1), X2, X3),
    active(if(true(), X, Y)) -> mark(X),
   active(if(false(), X, Y)) -> mark(Y),
       minus(ok(X1), ok(X2)) -> ok(minus(X1, X2)),
                  s(mark(X)) -> mark(s(X)),
                    s(ok(X)) -> ok(s(X)),
         geq(ok(X1), ok(X2)) -> ok(geq(X1, X2)),
           div(mark(X1), X2) -> mark(div(X1, X2)),
         div(ok(X1), ok(X2)) -> ok(div(X1, X2)),
        if(mark(X1), X2, X3) -> mark(if(X1, X2, X3)),
  if(ok(X1), ok(X2), ok(X3)) -> ok(if(X1, X2, X3)),
                 proper(0()) -> ok(0()),
       proper(minus(X1, X2)) -> minus(proper(X1), proper(X2)),
                proper(s(X)) -> s(proper(X)),
              proper(true()) -> ok(true()),
         proper(geq(X1, X2)) -> geq(proper(X1), proper(X2)),
             proper(false()) -> ok(false()),
         proper(div(X1, X2)) -> div(proper(X1), proper(X2)),
      proper(if(X1, X2, X3)) -> if(proper(X1), proper(X2), proper(X3)),
                top(mark(X)) -> top(proper(X)),
                  top(ok(X)) -> top(active(X))
 }
 DUP: We consider a duplicating system.
  Trs:
   {
         active(minus(0(), Y)) -> mark(0()),
     active(minus(s(X), s(Y))) -> mark(minus(X, Y)),
                  active(s(X)) -> s(active(X)),
           active(geq(X, 0())) -> mark(true()),
        active(geq(0(), s(Y))) -> mark(false()),
       active(geq(s(X), s(Y))) -> mark(geq(X, Y)),
           active(div(X1, X2)) -> div(active(X1), X2),
        active(div(0(), s(Y))) -> mark(0()),
       active(div(s(X), s(Y))) ->
    mark(if(geq(X, Y), s(div(minus(X, Y), s(Y))), 0())),
        active(if(X1, X2, X3)) -> if(active(X1), X2, X3),
      active(if(true(), X, Y)) -> mark(X),
     active(if(false(), X, Y)) -> mark(Y),
         minus(ok(X1), ok(X2)) -> ok(minus(X1, X2)),
                    s(mark(X)) -> mark(s(X)),
                      s(ok(X)) -> ok(s(X)),
           geq(ok(X1), ok(X2)) -> ok(geq(X1, X2)),
             div(mark(X1), X2) -> mark(div(X1, X2)),
           div(ok(X1), ok(X2)) -> ok(div(X1, X2)),
          if(mark(X1), X2, X3) -> mark(if(X1, X2, X3)),
    if(ok(X1), ok(X2), ok(X3)) -> ok(if(X1, X2, X3)),
                   proper(0()) -> ok(0()),
         proper(minus(X1, X2)) -> minus(proper(X1), proper(X2)),
                  proper(s(X)) -> s(proper(X)),
                proper(true()) -> ok(true()),
           proper(geq(X1, X2)) -> geq(proper(X1), proper(X2)),
               proper(false()) -> ok(false()),
           proper(div(X1, X2)) -> div(proper(X1), proper(X2)),
        proper(if(X1, X2, X3)) -> if(proper(X1), proper(X2), proper(X3)),
                  top(mark(X)) -> top(proper(X)),
                    top(ok(X)) -> top(active(X))
   }
  Fail