Time: 5.148165
TRS:
 {                       eval x -> Cond_eval(and(equal_int(mod_int(x, pos s s 0()), pos 0()), greater_int(x, pos 0())), x),
        minus_int(pos x, pos y) -> minus_nat(x, y),
        minus_int(pos x, neg y) -> pos plus_nat(x, y),
        minus_int(neg x, pos y) -> neg plus_nat(x, y),
        minus_int(neg x, neg y) -> minus_nat(y, x),
           Cond_eval(true(), x) -> eval minus_int(x, pos s 0()),
            and(true(), true()) -> true(),
           and(true(), false()) -> false(),
           and(false(), true()) -> false(),
          and(false(), false()) -> false(),
    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(),
          mod_int(pos x, pos y) -> pos mod_nat(x, y),
          mod_int(pos x, neg y) -> pos mod_nat(x, y),
          mod_int(neg x, pos y) -> neg mod_nat(x, y),
          mod_int(neg x, neg y) -> neg mod_nat(x, y),
  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,
              mod_nat(s x, s y) -> if(greatereq_int(pos x, pos y), mod_nat(minus_nat_s(x, y), s y), s x),
              mod_nat(0(), s x) -> 0(),
               if(true(), x, y) -> x,
              if(false(), x, y) -> y,
            minus_nat_s(x, 0()) -> x,
          minus_nat_s(s x, s y) -> minus_nat_s(x, y),
          minus_nat_s(0(), s y) -> 0()}
 SRS: We consider a TRS.
  Trs:
   {                       eval x -> Cond_eval(and(equal_int(mod_int(x, pos s s 0()), pos 0()), greater_int(x, pos 0())), x),
          minus_int(pos x, pos y) -> minus_nat(x, y),
          minus_int(pos x, neg y) -> pos plus_nat(x, y),
          minus_int(neg x, pos y) -> neg plus_nat(x, y),
          minus_int(neg x, neg y) -> minus_nat(y, x),
             Cond_eval(true(), x) -> eval minus_int(x, pos s 0()),
              and(true(), true()) -> true(),
             and(true(), false()) -> false(),
             and(false(), true()) -> false(),
            and(false(), false()) -> false(),
      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(),
            mod_int(pos x, pos y) -> pos mod_nat(x, y),
            mod_int(pos x, neg y) -> pos mod_nat(x, y),
            mod_int(neg x, pos y) -> neg mod_nat(x, y),
            mod_int(neg x, neg y) -> neg mod_nat(x, y),
    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,
                mod_nat(s x, s y) -> if(greatereq_int(pos x, pos y), mod_nat(minus_nat_s(x, y), s y), s x),
                mod_nat(0(), s x) -> 0(),
                 if(true(), x, y) -> x,
                if(false(), x, y) -> y,
              minus_nat_s(x, 0()) -> x,
            minus_nat_s(s x, s y) -> minus_nat_s(x, y),
            minus_nat_s(0(), s y) -> 0()}
  Fail