The rewrite relation of the following TRS is considered.
from(X) | → | cons(X,n__from(n__s(X))) | (1) |
sel(0,cons(X,Y)) | → | X | (2) |
sel(s(X),cons(Y,Z)) | → | sel(X,activate(Z)) | (3) |
from(X) | → | n__from(X) | (4) |
s(X) | → | n__s(X) | (5) |
activate(n__from(X)) | → | from(activate(X)) | (6) |
activate(n__s(X)) | → | s(activate(X)) | (7) |
activate(X) | → | X | (8) |
activate#(n__from(X)) | → | activate#(X) | (9) |
sel#(s(X),cons(Y,Z)) | → | activate#(Z) | (10) |
sel#(s(X),cons(Y,Z)) | → | sel#(X,activate(Z)) | (11) |
activate#(n__s(X)) | → | s#(activate(X)) | (12) |
activate#(n__from(X)) | → | from#(activate(X)) | (13) |
activate#(n__s(X)) | → | activate#(X) | (14) |
The dependency pairs are split into 2 components.
sel#(s(X),cons(Y,Z)) | → | sel#(X,activate(Z)) | (11) |
[s(x1)] | = | x1 + 1 |
[activate(x1)] | = | 8856 |
[n__from(x1)] | = | 8858 |
[activate#(x1)] | = | 0 |
[n__s(x1)] | = | 2 |
[0] | = | 0 |
[sel#(x1, x2)] | = | x1 + 0 |
[from(x1)] | = | 8857 |
[sel(x1, x2)] | = | 0 |
[s#(x1)] | = | 0 |
[from#(x1)] | = | 0 |
[cons(x1, x2)] | = | x1 + 8858 |
sel#(s(X),cons(Y,Z)) | → | sel#(X,activate(Z)) | (11) |
The dependency pairs are split into 0 components.
activate#(n__s(X)) | → | activate#(X) | (14) |
activate#(n__from(X)) | → | activate#(X) | (9) |
[s(x1)] | = | x1 + 1 |
[activate(x1)] | = | 8856 |
[n__from(x1)] | = | x1 + 8858 |
[activate#(x1)] | = | x1 + 0 |
[n__s(x1)] | = | x1 + 0 |
[0] | = | 0 |
[sel#(x1, x2)] | = | 0 |
[from(x1)] | = | 8857 |
[sel(x1, x2)] | = | 0 |
[s#(x1)] | = | 0 |
[from#(x1)] | = | 0 |
[cons(x1, x2)] | = | x1 + 8858 |
activate#(n__from(X)) | → | activate#(X) | (9) |
The dependency pairs are split into 1 component.
activate#(n__s(X)) | → | activate#(X) | (14) |
[s(x1)] | = | x1 + 1 |
[activate(x1)] | = | 8856 |
[n__from(x1)] | = | x1 + 8858 |
[activate#(x1)] | = | x1 + 0 |
[n__s(x1)] | = | x1 + 1 |
[0] | = | 0 |
[sel#(x1, x2)] | = | 0 |
[from(x1)] | = | 8857 |
[sel(x1, x2)] | = | 0 |
[s#(x1)] | = | 0 |
[from#(x1)] | = | 0 |
[cons(x1, x2)] | = | x1 + 8858 |
activate#(n__s(X)) | → | activate#(X) | (14) |
The dependency pairs are split into 0 components.