The rewrite relation of the following TRS is considered.
a__from(X) | → | cons(mark(X),from(s(X))) | (1) |
a__sel(0,cons(X,Y)) | → | mark(X) | (2) |
a__sel(s(X),cons(Y,Z)) | → | a__sel(mark(X),mark(Z)) | (3) |
mark(from(X)) | → | a__from(mark(X)) | (4) |
mark(sel(X1,X2)) | → | a__sel(mark(X1),mark(X2)) | (5) |
mark(cons(X1,X2)) | → | cons(mark(X1),X2) | (6) |
mark(s(X)) | → | s(mark(X)) | (7) |
mark(0) | → | 0 | (8) |
a__from(X) | → | from(X) | (9) |
a__sel(X1,X2) | → | sel(X1,X2) | (10) |
mark#(cons(X1,X2)) | → | mark#(X1) | (11) |
mark#(sel(X1,X2)) | → | mark#(X2) | (12) |
a__sel#(s(X),cons(Y,Z)) | → | mark#(Z) | (13) |
mark#(from(X)) | → | a__from#(mark(X)) | (14) |
mark#(from(X)) | → | mark#(X) | (15) |
a__sel#(s(X),cons(Y,Z)) | → | a__sel#(mark(X),mark(Z)) | (16) |
a__from#(X) | → | mark#(X) | (17) |
mark#(sel(X1,X2)) | → | mark#(X1) | (18) |
mark#(s(X)) | → | mark#(X) | (19) |
a__sel#(0,cons(X,Y)) | → | mark#(X) | (20) |
a__sel#(s(X),cons(Y,Z)) | → | mark#(X) | (21) |
mark#(sel(X1,X2)) | → | a__sel#(mark(X1),mark(X2)) | (22) |
The dependency pairs are split into 1 component.
mark#(sel(X1,X2)) | → | a__sel#(mark(X1),mark(X2)) | (22) |
mark#(from(X)) | → | mark#(X) | (15) |
a__sel#(s(X),cons(Y,Z)) | → | mark#(X) | (21) |
a__sel#(0,cons(X,Y)) | → | mark#(X) | (20) |
mark#(s(X)) | → | mark#(X) | (19) |
mark#(from(X)) | → | a__from#(mark(X)) | (14) |
a__sel#(s(X),cons(Y,Z)) | → | mark#(Z) | (13) |
mark#(sel(X1,X2)) | → | mark#(X2) | (12) |
mark#(sel(X1,X2)) | → | mark#(X1) | (18) |
a__from#(X) | → | mark#(X) | (17) |
a__sel#(s(X),cons(Y,Z)) | → | a__sel#(mark(X),mark(Z)) | (16) |
mark#(cons(X1,X2)) | → | mark#(X1) | (11) |
[s(x1)] | = | x1 + 0 |
[a__from#(x1)] | = | x1 + 35231 |
[a__from(x1)] | = | x1 + 20539 |
[mark#(x1)] | = | x1 + 35230 |
[0] | = | 1 |
[from(x1)] | = | x1 + 20539 |
[sel(x1, x2)] | = | max(x1 + 4902, x2 + 284, 0) |
[a__sel#(x1, x2)] | = | max(x1 + 40131, x2 + 35231, 0) |
[mark(x1)] | = | x1 + 0 |
[a__sel(x1, x2)] | = | max(x1 + 4902, x2 + 284, 0) |
[cons(x1, x2)] | = | max(x1 + 4618, x2 + 0, 0) |
mark(from(X)) | → | a__from(mark(X)) | (4) |
mark(0) | → | 0 | (8) |
a__from(X) | → | cons(mark(X),from(s(X))) | (1) |
a__sel(s(X),cons(Y,Z)) | → | a__sel(mark(X),mark(Z)) | (3) |
mark(sel(X1,X2)) | → | a__sel(mark(X1),mark(X2)) | (5) |
a__sel(X1,X2) | → | sel(X1,X2) | (10) |
mark(s(X)) | → | s(mark(X)) | (7) |
a__from(X) | → | from(X) | (9) |
mark(cons(X1,X2)) | → | cons(mark(X1),X2) | (6) |
a__sel(0,cons(X,Y)) | → | mark(X) | (2) |
mark#(sel(X1,X2)) | → | a__sel#(mark(X1),mark(X2)) | (22) |
mark#(from(X)) | → | mark#(X) | (15) |
a__sel#(s(X),cons(Y,Z)) | → | mark#(X) | (21) |
a__sel#(0,cons(X,Y)) | → | mark#(X) | (20) |
mark#(from(X)) | → | a__from#(mark(X)) | (14) |
a__sel#(s(X),cons(Y,Z)) | → | mark#(Z) | (13) |
mark#(sel(X1,X2)) | → | mark#(X2) | (12) |
mark#(sel(X1,X2)) | → | mark#(X1) | (18) |
a__from#(X) | → | mark#(X) | (17) |
mark#(cons(X1,X2)) | → | mark#(X1) | (11) |
The dependency pairs are split into 2 components.
a__sel#(s(X),cons(Y,Z)) | → | a__sel#(mark(X),mark(Z)) | (16) |
π(a__sel#) | = | 1 |
π(mark) | = | 1 |
prec(s) | = | 2 | status(s) | = | [1] | list-extension(s) | = | Lex | ||
prec(a__from#) | = | 0 | status(a__from#) | = | [] | list-extension(a__from#) | = | Lex | ||
prec(a__from) | = | 1 | status(a__from) | = | [] | list-extension(a__from) | = | Lex | ||
prec(mark#) | = | 0 | status(mark#) | = | [] | list-extension(mark#) | = | Lex | ||
prec(0) | = | 0 | status(0) | = | [] | list-extension(0) | = | Lex | ||
prec(from) | = | 1 | status(from) | = | [] | list-extension(from) | = | Lex | ||
prec(sel) | = | 3 | status(sel) | = | [1, 2] | list-extension(sel) | = | Lex | ||
prec(a__sel) | = | 3 | status(a__sel) | = | [1, 2] | list-extension(a__sel) | = | Lex | ||
prec(cons) | = | 0 | status(cons) | = | [] | list-extension(cons) | = | Lex |
[s(x1)] | = | x1 + 0 |
[a__from#(x1)] | = | 1 |
[a__from(x1)] | = | x1 + 8858 |
[mark#(x1)] | = | 1 |
[0] | = | 1 |
[from(x1)] | = | x1 + 8858 |
[sel(x1, x2)] | = | x1 + x2 + 8856 |
[a__sel(x1, x2)] | = | x1 + x2 + 8856 |
[cons(x1, x2)] | = | max(x1 + 8857, x2 + 0, 0) |
mark(from(X)) | → | a__from(mark(X)) | (4) |
mark(0) | → | 0 | (8) |
a__from(X) | → | cons(mark(X),from(s(X))) | (1) |
a__sel(s(X),cons(Y,Z)) | → | a__sel(mark(X),mark(Z)) | (3) |
mark(sel(X1,X2)) | → | a__sel(mark(X1),mark(X2)) | (5) |
a__sel(X1,X2) | → | sel(X1,X2) | (10) |
mark(s(X)) | → | s(mark(X)) | (7) |
a__from(X) | → | from(X) | (9) |
mark(cons(X1,X2)) | → | cons(mark(X1),X2) | (6) |
a__sel(0,cons(X,Y)) | → | mark(X) | (2) |
a__sel#(s(X),cons(Y,Z)) | → | a__sel#(mark(X),mark(Z)) | (16) |
The dependency pairs are split into 0 components.
mark#(s(X)) | → | mark#(X) | (19) |
[s(x1)] | = | x1 + 1 |
[a__from#(x1)] | = | 2 |
[a__from(x1)] | = | 2 |
[mark#(x1)] | = | x1 + 2 |
[0] | = | 2 |
[from(x1)] | = | 3 |
[sel(x1, x2)] | = | x1 + 3 |
[a__sel#(x1, x2)] | = | 0 |
[mark(x1)] | = | 1 |
[a__sel(x1, x2)] | = | 2 |
[cons(x1, x2)] | = | 3 |
mark#(s(X)) | → | mark#(X) | (19) |
The dependency pairs are split into 0 components.