The rewrite relation of the following TRS is considered.
a__dbl(0) | → | 0 | (1) |
a__dbl(s(X)) | → | s(s(dbl(X))) | (2) |
a__dbls(nil) | → | nil | (3) |
a__dbls(cons(X,Y)) | → | cons(dbl(X),dbls(Y)) | (4) |
a__sel(0,cons(X,Y)) | → | mark(X) | (5) |
a__sel(s(X),cons(Y,Z)) | → | a__sel(mark(X),mark(Z)) | (6) |
a__indx(nil,X) | → | nil | (7) |
a__indx(cons(X,Y),Z) | → | cons(sel(X,Z),indx(Y,Z)) | (8) |
a__from(X) | → | cons(X,from(s(X))) | (9) |
mark(dbl(X)) | → | a__dbl(mark(X)) | (10) |
mark(dbls(X)) | → | a__dbls(mark(X)) | (11) |
mark(sel(X1,X2)) | → | a__sel(mark(X1),mark(X2)) | (12) |
mark(indx(X1,X2)) | → | a__indx(mark(X1),X2) | (13) |
mark(from(X)) | → | a__from(X) | (14) |
mark(0) | → | 0 | (15) |
mark(s(X)) | → | s(X) | (16) |
mark(nil) | → | nil | (17) |
mark(cons(X1,X2)) | → | cons(X1,X2) | (18) |
a__dbl(X) | → | dbl(X) | (19) |
a__dbls(X) | → | dbls(X) | (20) |
a__sel(X1,X2) | → | sel(X1,X2) | (21) |
a__indx(X1,X2) | → | indx(X1,X2) | (22) |
a__from(X) | → | from(X) | (23) |
a__sel#(s(X),cons(Y,Z)) | → | mark#(X) | (24) |
mark#(dbls(X)) | → | a__dbls#(mark(X)) | (25) |
mark#(dbl(X)) | → | mark#(X) | (26) |
mark#(sel(X1,X2)) | → | mark#(X1) | (27) |
mark#(from(X)) | → | a__from#(X) | (28) |
mark#(dbl(X)) | → | a__dbl#(mark(X)) | (29) |
a__sel#(0,cons(X,Y)) | → | mark#(X) | (30) |
mark#(dbls(X)) | → | mark#(X) | (31) |
mark#(sel(X1,X2)) | → | mark#(X2) | (32) |
mark#(indx(X1,X2)) | → | mark#(X1) | (33) |
a__sel#(s(X),cons(Y,Z)) | → | mark#(Z) | (34) |
a__sel#(s(X),cons(Y,Z)) | → | a__sel#(mark(X),mark(Z)) | (35) |
mark#(sel(X1,X2)) | → | a__sel#(mark(X1),mark(X2)) | (36) |
mark#(indx(X1,X2)) | → | a__indx#(mark(X1),X2) | (37) |
The dependency pairs are split into 1 component.
a__sel#(0,cons(X,Y)) | → | mark#(X) | (30) |
mark#(sel(X1,X2)) | → | a__sel#(mark(X1),mark(X2)) | (36) |
a__sel#(s(X),cons(Y,Z)) | → | a__sel#(mark(X),mark(Z)) | (35) |
a__sel#(s(X),cons(Y,Z)) | → | mark#(Z) | (34) |
mark#(sel(X1,X2)) | → | mark#(X1) | (27) |
mark#(dbl(X)) | → | mark#(X) | (26) |
mark#(indx(X1,X2)) | → | mark#(X1) | (33) |
mark#(sel(X1,X2)) | → | mark#(X2) | (32) |
mark#(dbls(X)) | → | mark#(X) | (31) |
a__sel#(s(X),cons(Y,Z)) | → | mark#(X) | (24) |
[s(x1)] | = | x1 + 0 |
[a__from#(x1)] | = | 0 |
[dbls(x1)] | = | x1 + 282 |
[a__indx(x1, x2)] | = | max(x1 + 15945, x2 + 15944, 0) |
[a__from(x1)] | = | x1 + 5854 |
[a__indx#(x1, x2)] | = | max(0) |
[dbl(x1)] | = | x1 + 130 |
[indx(x1, x2)] | = | max(x1 + 15945, x2 + 15944, 0) |
[a__dbl(x1)] | = | x1 + 130 |
[a__dbls#(x1)] | = | 0 |
[mark#(x1)] | = | x1 + 26285 |
[0] | = | 48638 |
[sel(x1, x2)] | = | max(x1 + 15945, x2 + 10090, 0) |
[from(x1)] | = | x1 + 5854 |
[nil] | = | 15945 |
[a__dbl#(x1)] | = | 0 |
[a__sel#(x1, x2)] | = | max(x1 + 26286, x2 + 35232, 0) |
[mark(x1)] | = | x1 + 0 |
[a__sel(x1, x2)] | = | max(x1 + 15945, x2 + 10090, 0) |
[a__dbls(x1)] | = | x1 + 282 |
[cons(x1, x2)] | = | max(x1 + 5854, x2 + 0, 0) |
mark(cons(X1,X2)) | → | cons(X1,X2) | (18) |
a__dbls(cons(X,Y)) | → | cons(dbl(X),dbls(Y)) | (4) |
mark(0) | → | 0 | (15) |
a__indx(cons(X,Y),Z) | → | cons(sel(X,Z),indx(Y,Z)) | (8) |
a__dbl(0) | → | 0 | (1) |
a__dbls(nil) | → | nil | (3) |
mark(s(X)) | → | s(X) | (16) |
a__sel(X1,X2) | → | sel(X1,X2) | (21) |
a__dbl(X) | → | dbl(X) | (19) |
mark(nil) | → | nil | (17) |
a__indx(X1,X2) | → | indx(X1,X2) | (22) |
a__sel(0,cons(X,Y)) | → | mark(X) | (5) |
mark(dbl(X)) | → | a__dbl(mark(X)) | (10) |
a__indx(nil,X) | → | nil | (7) |
a__dbls(X) | → | dbls(X) | (20) |
mark(from(X)) | → | a__from(X) | (14) |
mark(sel(X1,X2)) | → | a__sel(mark(X1),mark(X2)) | (12) |
a__from(X) | → | from(X) | (23) |
mark(dbls(X)) | → | a__dbls(mark(X)) | (11) |
a__from(X) | → | cons(X,from(s(X))) | (9) |
mark(indx(X1,X2)) | → | a__indx(mark(X1),X2) | (13) |
a__sel(s(X),cons(Y,Z)) | → | a__sel(mark(X),mark(Z)) | (6) |
a__dbl(s(X)) | → | s(s(dbl(X))) | (2) |
a__sel#(0,cons(X,Y)) | → | mark#(X) | (30) |
mark#(sel(X1,X2)) | → | a__sel#(mark(X1),mark(X2)) | (36) |
a__sel#(s(X),cons(Y,Z)) | → | mark#(Z) | (34) |
mark#(sel(X1,X2)) | → | mark#(X1) | (27) |
mark#(dbl(X)) | → | mark#(X) | (26) |
mark#(indx(X1,X2)) | → | mark#(X1) | (33) |
mark#(sel(X1,X2)) | → | mark#(X2) | (32) |
mark#(dbls(X)) | → | mark#(X) | (31) |
a__sel#(s(X),cons(Y,Z)) | → | mark#(X) | (24) |
The dependency pairs are split into 1 component.
a__sel#(s(X),cons(Y,Z)) | → | a__sel#(mark(X),mark(Z)) | (35) |
π(a__dbls#) | = | 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(dbls) | = | 4 | status(dbls) | = | [1] | list-extension(dbls) | = | Lex | ||
prec(a__indx) | = | 5 | status(a__indx) | = | [] | list-extension(a__indx) | = | Lex | ||
prec(a__from) | = | 4 | status(a__from) | = | [1] | list-extension(a__from) | = | Lex | ||
prec(a__indx#) | = | 0 | status(a__indx#) | = | [] | list-extension(a__indx#) | = | Lex | ||
prec(dbl) | = | 3 | status(dbl) | = | [1] | list-extension(dbl) | = | Lex | ||
prec(indx) | = | 5 | status(indx) | = | [] | list-extension(indx) | = | Lex | ||
prec(a__dbl) | = | 3 | status(a__dbl) | = | [1] | list-extension(a__dbl) | = | Lex | ||
prec(mark#) | = | 0 | status(mark#) | = | [] | list-extension(mark#) | = | Lex | ||
prec(0) | = | 3 | status(0) | = | [] | list-extension(0) | = | Lex | ||
prec(sel) | = | 6 | status(sel) | = | [] | list-extension(sel) | = | Lex | ||
prec(from) | = | 4 | status(from) | = | [1] | list-extension(from) | = | Lex | ||
prec(nil) | = | 0 | status(nil) | = | [] | list-extension(nil) | = | Lex | ||
prec(a__dbl#) | = | 0 | status(a__dbl#) | = | [] | list-extension(a__dbl#) | = | Lex | ||
prec(a__sel#) | = | 0 | status(a__sel#) | = | [1] | list-extension(a__sel#) | = | Lex | ||
prec(a__sel) | = | 6 | status(a__sel) | = | [] | list-extension(a__sel) | = | Lex | ||
prec(a__dbls) | = | 4 | status(a__dbls) | = | [1] | list-extension(a__dbls) | = | Lex | ||
prec(cons) | = | 4 | status(cons) | = | [1] | list-extension(cons) | = | Lex |
[s(x1)] | = | x1 + 0 |
[a__from#(x1)] | = | 1 |
[dbls(x1)] | = | x1 + 19455 |
[a__indx(x1, x2)] | = | x2 + 19453 |
[a__from(x1)] | = | x1 + 9728 |
[a__indx#(x1, x2)] | = | x1 + 0 |
[dbl(x1)] | = | x1 + 9727 |
[indx(x1, x2)] | = | x2 + 19453 |
[a__dbl(x1)] | = | x1 + 9727 |
[mark#(x1)] | = | 1 |
[0] | = | 1 |
[sel(x1, x2)] | = | x2 + 9726 |
[from(x1)] | = | x1 + 9728 |
[nil] | = | 0 |
[a__dbl#(x1)] | = | 1 |
[a__sel#(x1, x2)] | = | x1 + 0 |
[a__sel(x1, x2)] | = | x2 + 9726 |
[a__dbls(x1)] | = | x1 + 19455 |
[cons(x1, x2)] | = | max(x1 + 9727, x2 + 0, 0) |
mark(cons(X1,X2)) | → | cons(X1,X2) | (18) |
a__dbls(cons(X,Y)) | → | cons(dbl(X),dbls(Y)) | (4) |
mark(0) | → | 0 | (15) |
a__indx(cons(X,Y),Z) | → | cons(sel(X,Z),indx(Y,Z)) | (8) |
a__dbl(0) | → | 0 | (1) |
a__dbls(nil) | → | nil | (3) |
mark(s(X)) | → | s(X) | (16) |
a__sel(X1,X2) | → | sel(X1,X2) | (21) |
a__dbl(X) | → | dbl(X) | (19) |
mark(nil) | → | nil | (17) |
a__indx(X1,X2) | → | indx(X1,X2) | (22) |
a__sel(0,cons(X,Y)) | → | mark(X) | (5) |
mark(dbl(X)) | → | a__dbl(mark(X)) | (10) |
a__indx(nil,X) | → | nil | (7) |
a__dbls(X) | → | dbls(X) | (20) |
mark(from(X)) | → | a__from(X) | (14) |
mark(sel(X1,X2)) | → | a__sel(mark(X1),mark(X2)) | (12) |
a__from(X) | → | from(X) | (23) |
mark(dbls(X)) | → | a__dbls(mark(X)) | (11) |
a__from(X) | → | cons(X,from(s(X))) | (9) |
mark(indx(X1,X2)) | → | a__indx(mark(X1),X2) | (13) |
a__sel(s(X),cons(Y,Z)) | → | a__sel(mark(X),mark(Z)) | (6) |
a__dbl(s(X)) | → | s(s(dbl(X))) | (2) |
a__sel#(s(X),cons(Y,Z)) | → | a__sel#(mark(X),mark(Z)) | (35) |
The dependency pairs are split into 0 components.