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) |
activate#(n__s(X)) | → | s#(activate(X)) | (11) |
activate#(n__first(X1,X2)) | → | activate#(X2) | (12) |
activate#(n__from(X)) | → | from#(activate(X)) | (13) |
activate#(n__first(X1,X2)) | → | activate#(X1) | (14) |
activate#(n__s(X)) | → | activate#(X) | (15) |
first#(s(X),cons(Y,Z)) | → | activate#(Z) | (16) |
activate#(n__from(X)) | → | activate#(X) | (17) |
activate#(n__first(X1,X2)) | → | first#(activate(X1),activate(X2)) | (18) |
The dependency pairs are split into 1 component.
activate#(n__first(X1,X2)) | → | first#(activate(X1),activate(X2)) | (18) |
activate#(n__from(X)) | → | activate#(X) | (17) |
first#(s(X),cons(Y,Z)) | → | activate#(Z) | (16) |
activate#(n__s(X)) | → | activate#(X) | (15) |
activate#(n__first(X1,X2)) | → | activate#(X2) | (12) |
activate#(n__first(X1,X2)) | → | activate#(X1) | (14) |
[s(x1)] | = | x1 + 0 |
[n__first(x1, x2)] | = | x1 + x2 + 30614 |
[activate(x1)] | = | x1 + 0 |
[n__from(x1)] | = | x1 + 10451 |
[activate#(x1)] | = | x1 + 0 |
[n__s(x1)] | = | x1 + 0 |
[0] | = | 40651 |
[from(x1)] | = | x1 + 10451 |
[s#(x1)] | = | 0 |
[first#(x1, x2)] | = | x2 + 1 |
[nil] | = | 0 |
[first(x1, x2)] | = | x1 + x2 + 30614 |
[from#(x1)] | = | 0 |
[cons(x1, x2)] | = | x2 + 0 |
first(X1,X2) | → | n__first(X1,X2) | (4) |
activate(n__from(X)) | → | from(activate(X)) | (8) |
first(0,X) | → | nil | (1) |
from(X) | → | cons(X,n__from(n__s(X))) | (3) |
from(X) | → | n__from(X) | (5) |
activate(X) | → | X | (10) |
activate(n__first(X1,X2)) | → | first(activate(X1),activate(X2)) | (7) |
activate(n__s(X)) | → | s(activate(X)) | (9) |
s(X) | → | n__s(X) | (6) |
first(s(X),cons(Y,Z)) | → | cons(Y,n__first(X,activate(Z))) | (2) |
activate#(n__first(X1,X2)) | → | first#(activate(X1),activate(X2)) | (18) |
activate#(n__from(X)) | → | activate#(X) | (17) |
first#(s(X),cons(Y,Z)) | → | activate#(Z) | (16) |
activate#(n__first(X1,X2)) | → | activate#(X2) | (12) |
activate#(n__first(X1,X2)) | → | activate#(X1) | (14) |
The dependency pairs are split into 1 component.
activate#(n__s(X)) | → | activate#(X) | (15) |
[s(x1)] | = | x1 + 1 |
[n__first(x1, x2)] | = | x1 + x2 + 1 |
[activate(x1)] | = | x1 + 0 |
[n__from(x1)] | = | 10451 |
[activate#(x1)] | = | x1 + 0 |
[n__s(x1)] | = | x1 + 1 |
[0] | = | 40651 |
[from(x1)] | = | 10451 |
[s#(x1)] | = | 0 |
[first#(x1, x2)] | = | x2 + 1 |
[nil] | = | 0 |
[first(x1, x2)] | = | x1 + x2 + 1 |
[from#(x1)] | = | 0 |
[cons(x1, x2)] | = | 0 |
first(X1,X2) | → | n__first(X1,X2) | (4) |
activate(n__from(X)) | → | from(activate(X)) | (8) |
first(0,X) | → | nil | (1) |
from(X) | → | cons(X,n__from(n__s(X))) | (3) |
from(X) | → | n__from(X) | (5) |
activate(X) | → | X | (10) |
activate(n__first(X1,X2)) | → | first(activate(X1),activate(X2)) | (7) |
activate(n__s(X)) | → | s(activate(X)) | (9) |
s(X) | → | n__s(X) | (6) |
first(s(X),cons(Y,Z)) | → | cons(Y,n__first(X,activate(Z))) | (2) |
activate#(n__s(X)) | → | activate#(X) | (15) |
The dependency pairs are split into 0 components.