Time: 5.084531
TRS:
 {       plus_int(pos x, pos y) -> pos plus_nat(x, y),
         plus_int(pos x, neg y) -> minus_nat(x, y),
         plus_int(neg x, pos y) -> minus_nat(y, x),
         plus_int(neg x, neg y) -> neg plus_nat(x, y),
                     diff(x, y) -> cond1(equal_int(x, y), x, y),
           cond2(false(), x, y) -> plus_int(pos s 0(), diff(plus_int(pos s 0(), x), y)),
            cond2(true(), x, y) -> plus_int(pos s 0(), diff(x, plus_int(pos s 0(), y))),
           cond1(false(), x, y) -> cond2(greater_int(x, y), x, y),
            cond1(true(), x, y) -> pos 0(),
    equal_int(pos s x, pos s y) -> equal_int(pos x, pos y),
    equal_int(pos s x, pos 0()) -> false(),
    equal_int(pos s x, neg s y) -> false(),
    equal_int(pos s x, neg 0()) -> false(),
    equal_int(pos 0(), pos s y) -> false(),
    equal_int(pos 0(), pos 0()) -> true(),
    equal_int(pos 0(), neg s y) -> false(),
    equal_int(pos 0(), neg 0()) -> true(),
    equal_int(neg s x, pos s y) -> false(),
    equal_int(neg s x, pos 0()) -> false(),
    equal_int(neg s x, neg s y) -> equal_int(neg x, neg y),
    equal_int(neg s x, neg 0()) -> false(),
    equal_int(neg 0(), pos s y) -> false(),
    equal_int(neg 0(), pos 0()) -> true(),
    equal_int(neg 0(), neg s y) -> false(),
    equal_int(neg 0(), neg 0()) -> true(),
  greater_int(pos s x, pos s y) -> greater_int(pos x, pos y),
  greater_int(pos s x, pos 0()) -> true(),
  greater_int(pos s x, neg s y) -> true(),
  greater_int(pos s x, neg 0()) -> true(),
  greater_int(pos 0(), pos s y) -> false(),
  greater_int(pos 0(), pos 0()) -> false(),
  greater_int(pos 0(), neg s y) -> true(),
  greater_int(pos 0(), neg 0()) -> false(),
  greater_int(neg s x, pos s y) -> false(),
  greater_int(neg s x, pos 0()) -> false(),
  greater_int(neg s x, neg s y) -> greater_int(neg x, neg y),
  greater_int(neg s x, neg 0()) -> false(),
  greater_int(neg 0(), pos s y) -> false(),
  greater_int(neg 0(), pos 0()) -> false(),
  greater_int(neg 0(), neg s y) -> true(),
  greater_int(neg 0(), neg 0()) -> false(),
            minus_nat(s x, s y) -> minus_nat(x, y),
            minus_nat(s x, 0()) -> pos s x,
            minus_nat(0(), s y) -> neg s y,
            minus_nat(0(), 0()) -> pos 0(),
               plus_nat(s x, y) -> s plus_nat(x, y),
               plus_nat(0(), x) -> x}
 SRS: We consider a TRS.
  Trs:
   {       plus_int(pos x, pos y) -> pos plus_nat(x, y),
           plus_int(pos x, neg y) -> minus_nat(x, y),
           plus_int(neg x, pos y) -> minus_nat(y, x),
           plus_int(neg x, neg y) -> neg plus_nat(x, y),
                       diff(x, y) -> cond1(equal_int(x, y), x, y),
             cond2(false(), x, y) -> plus_int(pos s 0(), diff(plus_int(pos s 0(), x), y)),
              cond2(true(), x, y) -> plus_int(pos s 0(), diff(x, plus_int(pos s 0(), y))),
             cond1(false(), x, y) -> cond2(greater_int(x, y), x, y),
              cond1(true(), x, y) -> pos 0(),
      equal_int(pos s x, pos s y) -> equal_int(pos x, pos y),
      equal_int(pos s x, pos 0()) -> false(),
      equal_int(pos s x, neg s y) -> false(),
      equal_int(pos s x, neg 0()) -> false(),
      equal_int(pos 0(), pos s y) -> false(),
      equal_int(pos 0(), pos 0()) -> true(),
      equal_int(pos 0(), neg s y) -> false(),
      equal_int(pos 0(), neg 0()) -> true(),
      equal_int(neg s x, pos s y) -> false(),
      equal_int(neg s x, pos 0()) -> false(),
      equal_int(neg s x, neg s y) -> equal_int(neg x, neg y),
      equal_int(neg s x, neg 0()) -> false(),
      equal_int(neg 0(), pos s y) -> false(),
      equal_int(neg 0(), pos 0()) -> true(),
      equal_int(neg 0(), neg s y) -> false(),
      equal_int(neg 0(), neg 0()) -> true(),
    greater_int(pos s x, pos s y) -> greater_int(pos x, pos y),
    greater_int(pos s x, pos 0()) -> true(),
    greater_int(pos s x, neg s y) -> true(),
    greater_int(pos s x, neg 0()) -> true(),
    greater_int(pos 0(), pos s y) -> false(),
    greater_int(pos 0(), pos 0()) -> false(),
    greater_int(pos 0(), neg s y) -> true(),
    greater_int(pos 0(), neg 0()) -> false(),
    greater_int(neg s x, pos s y) -> false(),
    greater_int(neg s x, pos 0()) -> false(),
    greater_int(neg s x, neg s y) -> greater_int(neg x, neg y),
    greater_int(neg s x, neg 0()) -> false(),
    greater_int(neg 0(), pos s y) -> false(),
    greater_int(neg 0(), pos 0()) -> false(),
    greater_int(neg 0(), neg s y) -> true(),
    greater_int(neg 0(), neg 0()) -> false(),
              minus_nat(s x, s y) -> minus_nat(x, y),
              minus_nat(s x, 0()) -> pos s x,
              minus_nat(0(), s y) -> neg s y,
              minus_nat(0(), 0()) -> pos 0(),
                 plus_nat(s x, y) -> s plus_nat(x, y),
                 plus_nat(0(), x) -> x}
  Fail