YES
LCTRS
  Theories
    Core, Reals
  Signature
    lif: (Bool, Real, Real) -> Real
    log: (Real, Real) -> Real
  Rules
    lif(?14, ?15, ?16) -> +(1.0, log(/(?15, ?16), ?16)) [?14 = true]
    lif(?17, ?18, ?19) -> 0.0 [?17 = false]
    log(?20, ?21) -> lif(and(>=(?20, ?21), >(?21, 1.0)), ?20, ?21)
Confluent by Orthogonality with proof:
  no critical pairs

Elapsed Time:  37.90 ms