  Let K be a number field, let f: P_1 --> P_1 be a nonconstant rational map of
degree greater than 1, let S be a finite set of places of K, and suppose that
u, w in P_1(K) are not preperiodic under f. We prove that the set of (m,n) in
N^2 such that f^m(u) is S-integral relative to f^n(w) is finite and effectively
computable. This may be thought of as a two-parameter analog of a result of
Silverman on integral points in orbits of rational maps.
  This issue can be translated in terms of integral points on an open subset of
P_1^2; then one can apply a modern version of the method of Runge, after
increasing the number of components at infinity by iterating the rational map.
Alternatively, an ineffective result comes from a well-known theorem of Vojta.
