The rewrite relation of the following TRS is considered.
from(X) | → | cons(X,n__from(s(X))) | (1) |
after(0,XS) | → | XS | (2) |
after(s(N),cons(X,XS)) | → | after(N,activate(XS)) | (3) |
from(X) | → | n__from(X) | (4) |
activate(n__from(X)) | → | from(X) | (5) |
activate(X) | → | X | (6) |
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from#(z0) |
from#(z0) |
after#(0,z0) |
after#(s(z0),cons(z1,z2)) |
activate#(n__from(z0)) |
activate#(z0) |
after(0,z0) | → | z0 | (11) |
after(s(z0),cons(z1,z2)) | → | after(z0,activate(z2)) | (13) |
after#(0,z0) | → | c2 | (12) |
after#(s(z0),cons(z1,z2)) | → | c3(after#(z0,activate(z2)),activate#(z2)) | (14) |
[c] | = | 0 |
[c1] | = | 0 |
[c2] | = | 0 |
[c3(x1, x2)] | = | 1 · x1 + 0 + 1 · x2 |
[c4(x1)] | = | 1 · x1 + 0 |
[c5] | = | 0 |
[activate(x1)] | = | 3 |
[from(x1)] | = | 3 + 3 · x1 |
[from#(x1)] | = | 0 |
[after#(x1, x2)] | = | 3 + 2 · x1 |
[activate#(x1)] | = | 0 |
[n__from(x1)] | = | 3 + 1 · x1 |
[cons(x1, x2)] | = | 3 + 1 · x1 |
[s(x1)] | = | 1 + 1 · x1 |
[0] | = | 3 |
from#(z0) | → | c | (8) |
from#(z0) | → | c1 | (10) |
after#(0,z0) | → | c2 | (12) |
after#(s(z0),cons(z1,z2)) | → | c3(after#(z0,activate(z2)),activate#(z2)) | (14) |
activate#(n__from(z0)) | → | c4(from#(z0)) | (16) |
activate#(z0) | → | c5 | (18) |
activate#(n__from(z0)) | → | c4(from#(z0)) | (16) |
activate#(z0) | → | c5 | (18) |
[c] | = | 0 |
[c1] | = | 0 |
[c2] | = | 0 |
[c3(x1, x2)] | = | 1 · x1 + 0 + 1 · x2 |
[c4(x1)] | = | 1 · x1 + 0 |
[c5] | = | 0 |
[activate(x1)] | = | 3 |
[from(x1)] | = | 3 + 3 · x1 |
[from#(x1)] | = | 0 |
[after#(x1, x2)] | = | 2 · x1 + 0 |
[activate#(x1)] | = | 2 |
[n__from(x1)] | = | 3 + 1 · x1 |
[cons(x1, x2)] | = | 3 + 1 · x1 |
[s(x1)] | = | 1 + 1 · x1 |
[0] | = | 0 |
from#(z0) | → | c | (8) |
from#(z0) | → | c1 | (10) |
after#(0,z0) | → | c2 | (12) |
after#(s(z0),cons(z1,z2)) | → | c3(after#(z0,activate(z2)),activate#(z2)) | (14) |
activate#(n__from(z0)) | → | c4(from#(z0)) | (16) |
activate#(z0) | → | c5 | (18) |
from#(z0) | → | c | (8) |
from#(z0) | → | c1 | (10) |
[c] | = | 0 |
[c1] | = | 0 |
[c2] | = | 0 |
[c3(x1, x2)] | = | 1 · x1 + 0 + 1 · x2 |
[c4(x1)] | = | 1 · x1 + 0 |
[c5] | = | 0 |
[activate(x1)] | = | 3 |
[from(x1)] | = | 3 + 3 · x1 |
[from#(x1)] | = | 1 |
[after#(x1, x2)] | = | 2 · x1 + 0 |
[activate#(x1)] | = | 1 |
[n__from(x1)] | = | 3 + 1 · x1 |
[cons(x1, x2)] | = | 3 + 1 · x1 |
[s(x1)] | = | 3 + 1 · x1 |
[0] | = | 0 |
from#(z0) | → | c | (8) |
from#(z0) | → | c1 | (10) |
after#(0,z0) | → | c2 | (12) |
after#(s(z0),cons(z1,z2)) | → | c3(after#(z0,activate(z2)),activate#(z2)) | (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).