YES
LCTRS
  Theories
    Core, Reals
  Signature
    sqrt: Real -> Real
    sumroot: Real -> Real
  Rules
    sumroot(!x) -> 0.0 [>=(0.0, !x)]
    sumroot(!x) -> +(sqrt(!x), sumroot(-(!x, 1.0))) [not(>=(0.0, !x))]
DPGraph with indexed dependency pairs
  {1: sumroot#(!x) -> sumroot#(-(!x, 1.0)) [not(>=(0.0, !x))]}
and edges
  1 -> {1}
with 1 SCC(s)
  SCC:
    {sumroot#(!x) -> sumroot#(-(!x, 1.0)) [not(>=(0.0, !x))]}
Value criterion after 1 iteration(s) with the projections:
  Iteration 1:
    projection(s):
      v(sumroot#) = 1
    removing the rule(s):
      {sumroot#(!x) -> sumroot#(-(!x, 1.0)) [not(>=(0.0, !x))]}

Elapsed Time:  36.73 ms