Descending dungeons of positional systems
Jelly, 9 bytes
Ż+⁵ṚDḅ¥@/

A monadic Link accepting a non-negative integer which yields a non-negative integer.
Try it online! Or see the test-suite.
How?
Ż+⁵ṚDḅ¥@/                  e.g. 5
Ż         - zero-range          [0,1,2,3,4,5]
  ⁵       - ten                 10
 +        - add                 [10,11,12,13,14,15]
   Ṛ      - reverse             [15,14,13,12,11,10]
        / - reduce by:          f(f(f(f(f(15,14),13),12),11),10)
       @  -   using swapped arguments:         e.g. f(y=15,x=14)
      ɗ   -     last two links as a dyad
    D     -       decimal (x)                       [1,4]            
     ḅ    -       convert (that) from base (y)      19
                           i.e. f(f(f(f(f(15,14),13),12),11),10)
                              = f(f(f(f(19,13),12),11),10)
                              = f(f(f(22,12),11),10)
                              = f(f(24,11),10)
                              = f(25,10)
                              = 25