The rewrite relation of the following TRS is considered.
from(X) | → | cons(X,n__from(n__s(X))) | (1) |
head(cons(X,XS)) | → | X | (2) |
2nd(cons(X,XS)) | → | head(activate(XS)) | (3) |
take(0,XS) | → | nil | (4) |
take(s(N),cons(X,XS)) | → | cons(X,n__take(N,activate(XS))) | (5) |
sel(0,cons(X,XS)) | → | X | (6) |
sel(s(N),cons(X,XS)) | → | sel(N,activate(XS)) | (7) |
from(X) | → | n__from(X) | (8) |
s(X) | → | n__s(X) | (9) |
take(X1,X2) | → | n__take(X1,X2) | (10) |
activate(n__from(X)) | → | from(activate(X)) | (11) |
activate(n__s(X)) | → | s(activate(X)) | (12) |
activate(n__take(X1,X2)) | → | take(activate(X1),activate(X2)) | (13) |
activate(X) | → | X | (14) |
activate#(n__take(X1,X2)) | → | activate#(X1) | (15) |
activate#(n__s(X)) | → | s#(activate(X)) | (16) |
sel#(s(N),cons(X,XS)) | → | activate#(XS) | (17) |
2nd#(cons(X,XS)) | → | head#(activate(XS)) | (18) |
2nd#(cons(X,XS)) | → | activate#(XS) | (19) |
activate#(n__s(X)) | → | activate#(X) | (20) |
take#(s(N),cons(X,XS)) | → | activate#(XS) | (21) |
activate#(n__from(X)) | → | activate#(X) | (22) |
activate#(n__take(X1,X2)) | → | activate#(X2) | (23) |
activate#(n__take(X1,X2)) | → | take#(activate(X1),activate(X2)) | (24) |
sel#(s(N),cons(X,XS)) | → | sel#(N,activate(XS)) | (25) |
activate#(n__from(X)) | → | from#(activate(X)) | (26) |
The dependency pairs are split into 2 components.
sel#(s(N),cons(X,XS)) | → | sel#(N,activate(XS)) | (25) |
[s(x1)] | = | x1 + 1 |
[take#(x1, x2)] | = | 0 |
[activate(x1)] | = | x1 + 3 |
[take(x1, x2)] | = | x1 + x2 + 0 |
[n__from(x1)] | = | 1 |
[activate#(x1)] | = | 0 |
[2nd(x1)] | = | 0 |
[head#(x1)] | = | 0 |
[n__s(x1)] | = | 2 |
[0] | = | 23676 |
[n__take(x1, x2)] | = | 2 |
[sel#(x1, x2)] | = | x1 + 0 |
[from(x1)] | = | x1 + 2 |
[sel(x1, x2)] | = | 0 |
[s#(x1)] | = | 0 |
[nil] | = | 23677 |
[2nd#(x1)] | = | 0 |
[from#(x1)] | = | 0 |
[head(x1)] | = | 0 |
[cons(x1, x2)] | = | x1 + x2 + 2 |
sel#(s(N),cons(X,XS)) | → | sel#(N,activate(XS)) | (25) |
The dependency pairs are split into 0 components.
activate#(n__take(X1,X2)) | → | take#(activate(X1),activate(X2)) | (24) |
activate#(n__take(X1,X2)) | → | activate#(X2) | (23) |
activate#(n__from(X)) | → | activate#(X) | (22) |
take#(s(N),cons(X,XS)) | → | activate#(XS) | (21) |
activate#(n__s(X)) | → | activate#(X) | (20) |
activate#(n__take(X1,X2)) | → | activate#(X1) | (15) |
[s(x1)] | = | x1 + 0 |
[take#(x1, x2)] | = | x2 + 1 |
[activate(x1)] | = | x1 + 0 |
[take(x1, x2)] | = | x1 + x2 + 20539 |
[n__from(x1)] | = | x1 + 282 |
[activate#(x1)] | = | x1 + 0 |
[2nd(x1)] | = | 0 |
[head#(x1)] | = | 0 |
[n__s(x1)] | = | x1 + 0 |
[0] | = | 23676 |
[n__take(x1, x2)] | = | x1 + x2 + 20539 |
[sel#(x1, x2)] | = | 0 |
[from(x1)] | = | x1 + 282 |
[sel(x1, x2)] | = | 0 |
[s#(x1)] | = | 0 |
[nil] | = | 44215 |
[2nd#(x1)] | = | 0 |
[from#(x1)] | = | 0 |
[head(x1)] | = | 0 |
[cons(x1, x2)] | = | x2 + 0 |
take(0,XS) | → | nil | (4) |
from(X) | → | n__from(X) | (8) |
from(X) | → | cons(X,n__from(n__s(X))) | (1) |
take(s(N),cons(X,XS)) | → | cons(X,n__take(N,activate(XS))) | (5) |
take(X1,X2) | → | n__take(X1,X2) | (10) |
activate(X) | → | X | (14) |
activate(n__s(X)) | → | s(activate(X)) | (12) |
activate(n__from(X)) | → | from(activate(X)) | (11) |
s(X) | → | n__s(X) | (9) |
activate(n__take(X1,X2)) | → | take(activate(X1),activate(X2)) | (13) |
activate#(n__take(X1,X2)) | → | take#(activate(X1),activate(X2)) | (24) |
activate#(n__take(X1,X2)) | → | activate#(X2) | (23) |
activate#(n__from(X)) | → | activate#(X) | (22) |
take#(s(N),cons(X,XS)) | → | activate#(XS) | (21) |
activate#(n__take(X1,X2)) | → | activate#(X1) | (15) |
The dependency pairs are split into 1 component.
activate#(n__s(X)) | → | activate#(X) | (20) |
[s(x1)] | = | 0 |
[take#(x1, x2)] | = | 1 |
[activate(x1)] | = | 1 |
[take(x1, x2)] | = | 1 |
[n__from(x1)] | = | 1 |
[activate#(x1)] | = | x1 + 0 |
[2nd(x1)] | = | 0 |
[head#(x1)] | = | 0 |
[n__s(x1)] | = | x1 + 1 |
[0] | = | 23676 |
[n__take(x1, x2)] | = | 1 |
[sel#(x1, x2)] | = | 0 |
[from(x1)] | = | x1 + 0 |
[sel(x1, x2)] | = | 0 |
[s#(x1)] | = | 0 |
[nil] | = | 2 |
[2nd#(x1)] | = | 0 |
[from#(x1)] | = | 0 |
[head(x1)] | = | 0 |
[cons(x1, x2)] | = | x1 + 0 |
from(X) | → | cons(X,n__from(n__s(X))) | (1) |
take(X1,X2) | → | n__take(X1,X2) | (10) |
activate#(n__s(X)) | → | activate#(X) | (20) |
The dependency pairs are split into 0 components.