The rewrite relation of the following TRS is considered.
first(0,X) | → | nil | (1) |
first(s(X),cons(Y,Z)) | → | cons(Y,n__first(X,activate(Z))) | (2) |
from(X) | → | cons(X,n__from(n__s(X))) | (3) |
first(X1,X2) | → | n__first(X1,X2) | (4) |
from(X) | → | n__from(X) | (5) |
s(X) | → | n__s(X) | (6) |
activate(n__first(X1,X2)) | → | first(activate(X1),activate(X2)) | (7) |
activate(n__from(X)) | → | from(activate(X)) | (8) |
activate(n__s(X)) | → | s(activate(X)) | (9) |
activate(X) | → | X | (10) |
prec(n__from) | = | 0 | status(n__from) | = | [1] | list-extension(n__from) | = | Lex | ||
prec(n__s) | = | 0 | status(n__s) | = | [1] | list-extension(n__s) | = | Lex | ||
prec(from) | = | 1 | status(from) | = | [1] | list-extension(from) | = | Lex | ||
prec(n__first) | = | 0 | status(n__first) | = | [2, 1] | list-extension(n__first) | = | Lex | ||
prec(activate) | = | 2 | status(activate) | = | [1] | list-extension(activate) | = | Lex | ||
prec(cons) | = | 0 | status(cons) | = | [1, 2] | list-extension(cons) | = | Lex | ||
prec(s) | = | 1 | status(s) | = | [1] | list-extension(s) | = | Lex | ||
prec(nil) | = | 0 | status(nil) | = | [] | list-extension(nil) | = | Lex | ||
prec(first) | = | 1 | status(first) | = | [1, 2] | list-extension(first) | = | Lex | ||
prec(0) | = | 0 | status(0) | = | [] | list-extension(0) | = | Lex |
[n__from(x1)] | = | max(0, 0 + 1 · x1) |
[n__s(x1)] | = | max(0, 0 + 1 · x1) |
[from(x1)] | = | max(0, 0 + 1 · x1) |
[n__first(x1, x2)] | = | max(0, 0 + 1 · x1, 4 + 1 · x2) |
[activate(x1)] | = | max(0, 0 + 1 · x1) |
[cons(x1, x2)] | = | max(0, 0 + 1 · x1, 0 + 1 · x2) |
[s(x1)] | = | max(0, 0 + 1 · x1) |
[nil] | = | max(0) |
[first(x1, x2)] | = | max(0, 0 + 1 · x1, 4 + 1 · x2) |
[0] | = | max(0) |
first(0,X) | → | nil | (1) |
first(s(X),cons(Y,Z)) | → | cons(Y,n__first(X,activate(Z))) | (2) |
from(X) | → | cons(X,n__from(n__s(X))) | (3) |
first(X1,X2) | → | n__first(X1,X2) | (4) |
from(X) | → | n__from(X) | (5) |
s(X) | → | n__s(X) | (6) |
activate(n__first(X1,X2)) | → | first(activate(X1),activate(X2)) | (7) |
activate(n__from(X)) | → | from(activate(X)) | (8) |
activate(n__s(X)) | → | s(activate(X)) | (9) |
activate(X) | → | X | (10) |
There are no rules in the TRS. Hence, it is terminating.