The rewrite relation of the following TRS is considered.
2nd(cons1(X,cons(Y,Z))) | → | Y | (1) |
2nd(cons(X,X1)) | → | 2nd(cons1(X,activate(X1))) | (2) |
from(X) | → | cons(X,n__from(s(X))) | (3) |
from(X) | → | n__from(X) | (4) |
activate(n__from(X)) | → | from(X) | (5) |
activate(X) | → | X | (6) |
|
originates from |
|
||||||||
|
originates from |
|
||||||||
|
originates from |
|
||||||||
|
originates from |
|
||||||||
|
originates from |
|
||||||||
|
originates from |
|
2nd#(cons1(z0,cons(z1,z2))) |
2nd#(cons(z0,z1)) |
from#(z0) |
from#(z0) |
activate#(n__from(z0)) |
activate#(z0) |
2nd(cons1(z0,cons(z1,z2))) | → | z1 | (7) |
2nd(cons(z0,z1)) | → | 2nd(cons1(z0,activate(z1))) | (9) |
2nd#(cons1(z0,cons(z1,z2))) | → | c | (8) |
from#(z0) | → | c2 | (12) |
from#(z0) | → | c3 | (14) |
activate#(n__from(z0)) | → | c4(from#(z0)) | (16) |
activate#(z0) | → | c5 | (18) |
[c] | = | 0 |
[c1(x1, x2)] | = | 1 · x1 + 0 + 1 · x2 |
[c2] | = | 0 |
[c3] | = | 0 |
[c4(x1)] | = | 1 · x1 + 0 |
[c5] | = | 0 |
[activate(x1)] | = | 1 + 1 · x1 |
[from(x1)] | = | 1 + 1 · x1 |
[2nd#(x1)] | = | 1 + 1 · x1 |
[from#(x1)] | = | 1 + 1 · x1 |
[activate#(x1)] | = | 1 + 1 · x1 |
[n__from(x1)] | = | 1 + 1 · x1 |
[cons(x1, x2)] | = | 1 + 1 · x1 + 1 · x2 |
[s(x1)] | = | 1 + 1 · x1 |
[cons1(x1, x2)] | = | 1 · x1 + 0 |
2nd#(cons1(z0,cons(z1,z2))) | → | c | (8) |
2nd#(cons(z0,z1)) | → | c1(2nd#(cons1(z0,activate(z1))),activate#(z1)) | (10) |
from#(z0) | → | c2 | (12) |
from#(z0) | → | c3 | (14) |
activate#(n__from(z0)) | → | c4(from#(z0)) | (16) |
activate#(z0) | → | c5 | (18) |
2nd#(cons(z0,z1)) | → | c1(2nd#(cons1(z0,activate(z1))),activate#(z1)) | (10) |
[c] | = | 0 |
[c1(x1, x2)] | = | 1 · x1 + 0 + 1 · x2 |
[c2] | = | 0 |
[c3] | = | 0 |
[c4(x1)] | = | 1 · x1 + 0 |
[c5] | = | 0 |
[activate(x1)] | = | 3 |
[from(x1)] | = | 3 + 3 · x1 |
[2nd#(x1)] | = | 1 · x1 + 0 |
[from#(x1)] | = | 0 |
[activate#(x1)] | = | 0 |
[n__from(x1)] | = | 3 + 1 · x1 |
[cons(x1, x2)] | = | 1 + 1 · x1 |
[s(x1)] | = | 3 + 1 · x1 |
[cons1(x1, x2)] | = | 0 |
2nd#(cons1(z0,cons(z1,z2))) | → | c | (8) |
2nd#(cons(z0,z1)) | → | c1(2nd#(cons1(z0,activate(z1))),activate#(z1)) | (10) |
from#(z0) | → | c2 | (12) |
from#(z0) | → | c3 | (14) |
activate#(n__from(z0)) | → | c4(from#(z0)) | (16) |
activate#(z0) | → | c5 | (18) |
There are no rules in the TRS R. Hence, R/S has complexity O(1).