The rewrite relation of the following TRS is considered.
a__first(0,X) | → | nil | (1) |
a__first(s(X),cons(Y,Z)) | → | cons(mark(Y),first(X,Z)) | (2) |
a__from(X) | → | cons(mark(X),from(s(X))) | (3) |
mark(first(X1,X2)) | → | a__first(mark(X1),mark(X2)) | (4) |
mark(from(X)) | → | a__from(mark(X)) | (5) |
mark(0) | → | 0 | (6) |
mark(nil) | → | nil | (7) |
mark(s(X)) | → | s(mark(X)) | (8) |
mark(cons(X1,X2)) | → | cons(mark(X1),X2) | (9) |
a__first(X1,X2) | → | first(X1,X2) | (10) |
a__from(X) | → | from(X) | (11) |
mark#(cons(X1,X2)) | → | mark#(X1) | (12) |
mark#(s(X)) | → | mark#(X) | (13) |
mark#(first(X1,X2)) | → | mark#(X2) | (14) |
mark#(first(X1,X2)) | → | a__first#(mark(X1),mark(X2)) | (15) |
a__from#(X) | → | mark#(X) | (16) |
mark#(from(X)) | → | a__from#(mark(X)) | (17) |
a__first#(s(X),cons(Y,Z)) | → | mark#(Y) | (18) |
mark#(first(X1,X2)) | → | mark#(X1) | (19) |
mark#(from(X)) | → | mark#(X) | (20) |
The dependency pairs are split into 1 component.
mark#(from(X)) | → | mark#(X) | (20) |
mark#(first(X1,X2)) | → | mark#(X1) | (19) |
a__first#(s(X),cons(Y,Z)) | → | mark#(Y) | (18) |
mark#(from(X)) | → | a__from#(mark(X)) | (17) |
mark#(first(X1,X2)) | → | mark#(X2) | (14) |
mark#(s(X)) | → | mark#(X) | (13) |
a__from#(X) | → | mark#(X) | (16) |
mark#(first(X1,X2)) | → | a__first#(mark(X1),mark(X2)) | (15) |
mark#(cons(X1,X2)) | → | mark#(X1) | (12) |
[s(x1)] | = | x1 + 1 |
[a__from#(x1)] | = | x1 + 1 |
[a__first#(x1, x2)] | = | x1 + x2 + 0 |
[a__from(x1)] | = | x1 + 2 |
[mark#(x1)] | = | x1 + 0 |
[0] | = | 29604 |
[from(x1)] | = | x1 + 2 |
[nil] | = | 11798 |
[mark(x1)] | = | x1 + 0 |
[first(x1, x2)] | = | x1 + x2 + 1 |
[a__first(x1, x2)] | = | x1 + x2 + 1 |
[cons(x1, x2)] | = | x1 + 2 |
mark(first(X1,X2)) | → | a__first(mark(X1),mark(X2)) | (4) |
mark(s(X)) | → | s(mark(X)) | (8) |
a__first(0,X) | → | nil | (1) |
a__from(X) | → | cons(mark(X),from(s(X))) | (3) |
mark(from(X)) | → | a__from(mark(X)) | (5) |
a__first(X1,X2) | → | first(X1,X2) | (10) |
mark(nil) | → | nil | (7) |
a__from(X) | → | from(X) | (11) |
mark(cons(X1,X2)) | → | cons(mark(X1),X2) | (9) |
mark(0) | → | 0 | (6) |
a__first(s(X),cons(Y,Z)) | → | cons(mark(Y),first(X,Z)) | (2) |
mark#(from(X)) | → | mark#(X) | (20) |
mark#(first(X1,X2)) | → | mark#(X1) | (19) |
a__first#(s(X),cons(Y,Z)) | → | mark#(Y) | (18) |
mark#(from(X)) | → | a__from#(mark(X)) | (17) |
mark#(first(X1,X2)) | → | mark#(X2) | (14) |
mark#(s(X)) | → | mark#(X) | (13) |
a__from#(X) | → | mark#(X) | (16) |
mark#(first(X1,X2)) | → | a__first#(mark(X1),mark(X2)) | (15) |
mark#(cons(X1,X2)) | → | mark#(X1) | (12) |
The dependency pairs are split into 0 components.