Term Rewriting System R:

   [x, y]
   bin(x, 0) -> s(0)
   bin(0, s(y)) -> 0
   bin(s(x), s(y)) -> +(bin(x, s(y)), bin(x, y))

Termination of R to be shown.


This program has no overlaps, so it is sufficient to show innermost termination. 


R contains the following Dependency Pairs: 


   BIN(s(x), s(y)) -> BIN(x, s(y))
   BIN(s(x), s(y)) -> BIN(x, y)

Furthermore, R contains one SCC.


SCC1:

BIN(s(x), s(y)) -> BIN(x, y)
BIN(s(x), s(y)) -> BIN(x, s(y))

Removing rules from R by ordering and analyzing Dependency Pairs, Usable Rules, and Usable Equations.

This is possible by using the following (C_E-compatible) Polynomial ordering.

Polynomial interpretation:
POL(BIN(x_1, x_2)) = 1 + x_1 + x_2
POL(s(x_1)) = 1 + x_1

The following Dependency Pairs can be deleted:

   BIN(s(x), s(y)) -> BIN(x, y)
   BIN(s(x), s(y)) -> BIN(x, s(y))



 This transformation is resulting in no new subcycles.




Termination of R successfully shown.


Duration: 0.476 seconds.