We consider termination of the MSTRS with no additional rule schemes:

  Signature: 0   :: nat
             add :: nat -> nat -> nat
             s   :: nat -> nat

  Rules: add(0, y) -> y
         add(s(x), y) -> add(x, s(y))

The system is accessible function passing by a sort ordering that equates all sorts.

We start by computing the initial DP problem D1 = (P1, R, i, c), where:

  P1. (1) add#(s(x), y) => add#(x, s(y))

***** We apply the Subterm Criterion Processor on D1 = (P1, R, i, c).

We use the following projection function:

  nu(add#) = 1

We thus have:

  (1) s(x) |>| x

All DPs are strictly oriented, and may be removed.  Hence, this DP problem is finite.

Processor output: { }.