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) merge#(nil, cons(Y, U), V) => merge#(U, nil, cons(Y, V))
      (2) merge#(cons(W, P), X1, Y1) => merge#(X1, P, cons(W, Y1))
      (3) map#(H1, cons(W1, P1)) => map#(H1, P1)

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

Considering the 2 SCCs, this DP problem is split into the following new problems.

  P2. (1) merge#(nil, cons(Y, U), V) => merge#(U, nil, cons(Y, V))
      (2) merge#(cons(W, P), X1, Y1) => merge#(X1, P, cons(W, Y1))

  P3. (1) map#(H1, cons(W1, P1)) => map#(H1, P1)

***** We apply the horpo Processor on P2.

Constrained HORPO yields:

  merge#(nil, cons(Y, U), V) (>) merge#(U, nil, cons(Y, V))
  merge#(cons(W, P), X1, Y1) (>) merge#(X1, P, cons(W, Y1))
  merge(nil, nil, X) (>=) X
  merge(nil, cons(Y, U), V) (>=) merge(U, nil, cons(Y, V))
  merge(cons(W, P), X1, Y1) (>=) merge(X1, P, cons(W, Y1))
  map(G1, nil) (>=) nil
  map(H1, cons(W1, P1)) (>=) cons(H1(W1), map(H1, P1))

We do this using the following settings:

* Precedence and status (for non-mentioned symbols the precedence is irrelevant and the status is Lex):

  merge#  (status: Mul_2) >
  merge   (status: Mul_2) >
  map     (status: Mul_2) >
  nil     (status: Lex)   >
  cons    (status: Mul_2)

* Well-founded theory orderings:

  [>]_{Bool} = {(true,false)}
  [>]_{Int}  = {(x,y) | x < 1000 /\ x < y }

* Filter:

  cons disregards argument(s) 1 
  map  disregards argument(s) 1 

All dependency pairs were removed.

***** We apply the Subterm Criterion Processor on P3.

We use the following projection function:

  nu(map#) = 2

We thus have:

  (1) cons(W1, P1) |>| P1

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