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

  Signature: + :: o -> o -> o
             0 :: o
             s :: o -> o

  Rules: +(x, 0) -> x
         +(x, s(y)) -> s(+(x, 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) +#(x, s(y)) => +#(x, y)

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

We use the following projection function:

  nu(+#) = 2

We thus have:

  (1) s(y) |>| y

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

Processor output: { }.