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

We start by computing the following initial DP problem:

  P1. (1) plus#(s(Y), U) => plus#(Y, U)
      (2) add#(X{6}, X{7}) => plus#(X{8}, X{9})
      (3) add#(X{6}, X{7}) => curry#(plus, X{6}, X{7})

***** We apply the Graph Processor on P1.

There is only one SCC, so all DPs not inside the SCC can be removed:

  P2. (1) plus#(s(Y), U) => plus#(Y, U)

***** We apply the Subterm Criterion Processor on P2.

We use the following projection function:

  nu(plus#) = 1

We thus have:

  (1) s(Y) |>| Y

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