YES
LCTRS
  Theories
    Core, Reals
  Signature
    sqrt: Real -> Real
    sumroot: Real -> Real
  Rules
    sumroot(?7) -> +(sqrt(?7), sumroot(-(?7, 1.0))) [not(>=(0.0, ?7))]
    sumroot(?8) -> 0.0 [>=(0.0, ?8)]
Confluent by Orthogonality with proof:
  no critical pairs

Elapsed Time:  37.87 ms