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) |
a__dbl1(0) | → | 01 | (10) |
a__dbl1(s(X)) | → | s1(s1(a__dbl1(mark(X)))) | (11) |
a__sel1(0,cons(X,Y)) | → | mark(X) | (12) |
a__sel1(s(X),cons(Y,Z)) | → | a__sel1(mark(X),mark(Z)) | (13) |
a__quote(0) | → | 01 | (14) |
a__quote(s(X)) | → | s1(a__quote(mark(X))) | (15) |
a__quote(dbl(X)) | → | a__dbl1(mark(X)) | (16) |
a__quote(sel(X,Y)) | → | a__sel1(mark(X),mark(Y)) | (17) |
mark(dbl(X)) | → | a__dbl(mark(X)) | (18) |
mark(dbls(X)) | → | a__dbls(mark(X)) | (19) |
mark(sel(X1,X2)) | → | a__sel(mark(X1),mark(X2)) | (20) |
mark(indx(X1,X2)) | → | a__indx(mark(X1),X2) | (21) |
mark(from(X)) | → | a__from(X) | (22) |
mark(dbl1(X)) | → | a__dbl1(mark(X)) | (23) |
mark(sel1(X1,X2)) | → | a__sel1(mark(X1),mark(X2)) | (24) |
mark(quote(X)) | → | a__quote(mark(X)) | (25) |
mark(0) | → | 0 | (26) |
mark(s(X)) | → | s(X) | (27) |
mark(nil) | → | nil | (28) |
mark(cons(X1,X2)) | → | cons(X1,X2) | (29) |
mark(01) | → | 01 | (30) |
mark(s1(X)) | → | s1(mark(X)) | (31) |
a__dbl(X) | → | dbl(X) | (32) |
a__dbls(X) | → | dbls(X) | (33) |
a__sel(X1,X2) | → | sel(X1,X2) | (34) |
a__indx(X1,X2) | → | indx(X1,X2) | (35) |
a__from(X) | → | from(X) | (36) |
a__dbl1(X) | → | dbl1(X) | (37) |
a__sel1(X1,X2) | → | sel1(X1,X2) | (38) |
a__quote(X) | → | quote(X) | (39) |
a__sel#(s(X),cons(Y,Z)) | → | mark#(X) | (40) |
mark#(indx(X1,X2)) | → | mark#(X1) | (41) |
mark#(dbl(X)) | → | mark#(X) | (42) |
a__sel1#(s(X),cons(Y,Z)) | → | mark#(Z) | (43) |
mark#(dbl1(X)) | → | mark#(X) | (44) |
mark#(sel1(X1,X2)) | → | a__sel1#(mark(X1),mark(X2)) | (45) |
mark#(sel1(X1,X2)) | → | mark#(X2) | (46) |
a__quote#(sel(X,Y)) | → | mark#(X) | (47) |
a__quote#(sel(X,Y)) | → | a__sel1#(mark(X),mark(Y)) | (48) |
mark#(dbl1(X)) | → | a__dbl1#(mark(X)) | (49) |
a__quote#(dbl(X)) | → | mark#(X) | (50) |
a__sel1#(0,cons(X,Y)) | → | mark#(X) | (51) |
a__quote#(dbl(X)) | → | a__dbl1#(mark(X)) | (52) |
a__quote#(sel(X,Y)) | → | mark#(Y) | (53) |
mark#(sel(X1,X2)) | → | mark#(X2) | (54) |
a__dbl1#(s(X)) | → | a__dbl1#(mark(X)) | (55) |
mark#(sel1(X1,X2)) | → | mark#(X1) | (56) |
a__quote#(s(X)) | → | mark#(X) | (57) |
a__sel1#(s(X),cons(Y,Z)) | → | mark#(X) | (58) |
mark#(indx(X1,X2)) | → | a__indx#(mark(X1),X2) | (59) |
mark#(from(X)) | → | a__from#(X) | (60) |
mark#(dbl(X)) | → | a__dbl#(mark(X)) | (61) |
mark#(dbls(X)) | → | mark#(X) | (62) |
mark#(quote(X)) | → | mark#(X) | (63) |
a__quote#(s(X)) | → | a__quote#(mark(X)) | (64) |
mark#(sel(X1,X2)) | → | mark#(X1) | (65) |
mark#(dbls(X)) | → | a__dbls#(mark(X)) | (66) |
a__sel#(0,cons(X,Y)) | → | mark#(X) | (67) |
mark#(quote(X)) | → | a__quote#(mark(X)) | (68) |
a__sel#(s(X),cons(Y,Z)) | → | mark#(Z) | (69) |
a__sel#(s(X),cons(Y,Z)) | → | a__sel#(mark(X),mark(Z)) | (70) |
a__dbl1#(s(X)) | → | mark#(X) | (71) |
mark#(s1(X)) | → | mark#(X) | (72) |
a__sel1#(s(X),cons(Y,Z)) | → | a__sel1#(mark(X),mark(Z)) | (73) |
mark#(sel(X1,X2)) | → | a__sel#(mark(X1),mark(X2)) | (74) |
The dependency pairs are split into 1 component.
mark#(sel(X1,X2)) | → | a__sel#(mark(X1),mark(X2)) | (74) |
a__quote#(sel(X,Y)) | → | mark#(Y) | (53) |
a__sel1#(s(X),cons(Y,Z)) | → | a__sel1#(mark(X),mark(Z)) | (73) |
a__quote#(dbl(X)) | → | a__dbl1#(mark(X)) | (52) |
a__sel1#(0,cons(X,Y)) | → | mark#(X) | (51) |
mark#(s1(X)) | → | mark#(X) | (72) |
a__quote#(dbl(X)) | → | mark#(X) | (50) |
mark#(dbl1(X)) | → | a__dbl1#(mark(X)) | (49) |
a__dbl1#(s(X)) | → | mark#(X) | (71) |
a__sel#(s(X),cons(Y,Z)) | → | a__sel#(mark(X),mark(Z)) | (70) |
a__quote#(sel(X,Y)) | → | a__sel1#(mark(X),mark(Y)) | (48) |
a__sel#(s(X),cons(Y,Z)) | → | mark#(Z) | (69) |
a__quote#(sel(X,Y)) | → | mark#(X) | (47) |
mark#(quote(X)) | → | a__quote#(mark(X)) | (68) |
a__sel#(0,cons(X,Y)) | → | mark#(X) | (67) |
mark#(sel1(X1,X2)) | → | mark#(X2) | (46) |
mark#(sel1(X1,X2)) | → | a__sel1#(mark(X1),mark(X2)) | (45) |
mark#(dbl1(X)) | → | mark#(X) | (44) |
a__quote#(s(X)) | → | a__quote#(mark(X)) | (64) |
mark#(sel(X1,X2)) | → | mark#(X1) | (65) |
mark#(quote(X)) | → | mark#(X) | (63) |
a__sel1#(s(X),cons(Y,Z)) | → | mark#(Z) | (43) |
mark#(dbls(X)) | → | mark#(X) | (62) |
a__sel1#(s(X),cons(Y,Z)) | → | mark#(X) | (58) |
a__quote#(s(X)) | → | mark#(X) | (57) |
mark#(sel1(X1,X2)) | → | mark#(X1) | (56) |
a__dbl1#(s(X)) | → | a__dbl1#(mark(X)) | (55) |
mark#(dbl(X)) | → | mark#(X) | (42) |
mark#(indx(X1,X2)) | → | mark#(X1) | (41) |
a__sel#(s(X),cons(Y,Z)) | → | mark#(X) | (40) |
mark#(sel(X1,X2)) | → | mark#(X2) | (54) |
[a__quote#(x1)] | = | x1 + 1 |
[a__dbl1(x1)] | = | x1 + 26435 |
[01] | = | 1 |
[s(x1)] | = | x1 + 0 |
[a__from#(x1)] | = | 0 |
[dbls(x1)] | = | x1 + 1 |
[a__indx(x1, x2)] | = | max(x1 + 98343, x2 + 98342, 0) |
[a__from(x1)] | = | x1 + 39057 |
[a__indx#(x1, x2)] | = | max(0) |
[dbl(x1)] | = | x1 + 1 |
[indx(x1, x2)] | = | max(x1 + 98343, x2 + 98342, 0) |
[a__dbl1#(x1)] | = | x1 + 1 |
[a__dbl(x1)] | = | x1 + 1 |
[a__sel1(x1, x2)] | = | max(x1 + 99938, x2 + 66509, 0) |
[a__dbls#(x1)] | = | 0 |
[mark#(x1)] | = | x1 + 0 |
[0] | = | 42410 |
[a__quote(x1)] | = | x1 + 32287 |
[sel(x1, x2)] | = | max(x1 + 98343, x2 + 67650, 0) |
[from(x1)] | = | x1 + 39057 |
[a__sel1#(x1, x2)] | = | max(x1 + 66508, x2 + 35815, 0) |
[nil] | = | 98343 |
[dbl1(x1)] | = | x1 + 26435 |
[a__dbl#(x1)] | = | 0 |
[a__sel#(x1, x2)] | = | max(x1 + 58794, x2 + 28101, 0) |
[mark(x1)] | = | x1 + 0 |
[a__sel(x1, x2)] | = | max(x1 + 98343, x2 + 67650, 0) |
[a__dbls(x1)] | = | x1 + 1 |
[quote(x1)] | = | x1 + 32287 |
[cons(x1, x2)] | = | max(x1 + 30692, x2 + 0, 0) |
[sel1(x1, x2)] | = | max(x1 + 99938, x2 + 66509, 0) |
[s1(x1)] | = | x1 + 0 |
mark(dbl(X)) | → | a__dbl(mark(X)) | (18) |
a__dbls(cons(X,Y)) | → | cons(dbl(X),dbls(Y)) | (4) |
a__quote(s(X)) | → | s1(a__quote(mark(X))) | (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) |
a__quote(dbl(X)) | → | a__dbl1(mark(X)) | (16) |
mark(indx(X1,X2)) | → | a__indx(mark(X1),X2) | (21) |
a__from(X) | → | from(X) | (36) |
mark(0) | → | 0 | (26) |
mark(dbls(X)) | → | a__dbls(mark(X)) | (19) |
a__dbl(X) | → | dbl(X) | (32) |
a__quote(sel(X,Y)) | → | a__sel1(mark(X),mark(Y)) | (17) |
mark(s(X)) | → | s(X) | (27) |
a__sel(X1,X2) | → | sel(X1,X2) | (34) |
mark(from(X)) | → | a__from(X) | (22) |
mark(nil) | → | nil | (28) |
a__sel(0,cons(X,Y)) | → | mark(X) | (5) |
a__dbls(X) | → | dbls(X) | (33) |
a__dbl1(0) | → | 01 | (10) |
a__quote(X) | → | quote(X) | (39) |
a__indx(nil,X) | → | nil | (7) |
mark(sel(X1,X2)) | → | a__sel(mark(X1),mark(X2)) | (20) |
mark(quote(X)) | → | a__quote(mark(X)) | (25) |
mark(01) | → | 01 | (30) |
a__quote(0) | → | 01 | (14) |
mark(s1(X)) | → | s1(mark(X)) | (31) |
a__sel1(0,cons(X,Y)) | → | mark(X) | (12) |
mark(dbl1(X)) | → | a__dbl1(mark(X)) | (23) |
mark(sel1(X1,X2)) | → | a__sel1(mark(X1),mark(X2)) | (24) |
a__dbl1(s(X)) | → | s1(s1(a__dbl1(mark(X)))) | (11) |
a__from(X) | → | cons(X,from(s(X))) | (9) |
a__sel1(s(X),cons(Y,Z)) | → | a__sel1(mark(X),mark(Z)) | (13) |
a__sel(s(X),cons(Y,Z)) | → | a__sel(mark(X),mark(Z)) | (6) |
a__sel1(X1,X2) | → | sel1(X1,X2) | (38) |
a__dbl1(X) | → | dbl1(X) | (37) |
a__indx(X1,X2) | → | indx(X1,X2) | (35) |
mark(cons(X1,X2)) | → | cons(X1,X2) | (29) |
a__dbl(s(X)) | → | s(s(dbl(X))) | (2) |
mark#(sel(X1,X2)) | → | a__sel#(mark(X1),mark(X2)) | (74) |
a__quote#(sel(X,Y)) | → | mark#(Y) | (53) |
a__quote#(dbl(X)) | → | a__dbl1#(mark(X)) | (52) |
a__sel1#(0,cons(X,Y)) | → | mark#(X) | (51) |
a__quote#(dbl(X)) | → | mark#(X) | (50) |
mark#(dbl1(X)) | → | a__dbl1#(mark(X)) | (49) |
a__dbl1#(s(X)) | → | mark#(X) | (71) |
a__quote#(sel(X,Y)) | → | a__sel1#(mark(X),mark(Y)) | (48) |
a__sel#(s(X),cons(Y,Z)) | → | mark#(Z) | (69) |
a__quote#(sel(X,Y)) | → | mark#(X) | (47) |
mark#(quote(X)) | → | a__quote#(mark(X)) | (68) |
a__sel#(0,cons(X,Y)) | → | mark#(X) | (67) |
mark#(sel1(X1,X2)) | → | mark#(X2) | (46) |
mark#(sel1(X1,X2)) | → | a__sel1#(mark(X1),mark(X2)) | (45) |
mark#(dbl1(X)) | → | mark#(X) | (44) |
mark#(sel(X1,X2)) | → | mark#(X1) | (65) |
mark#(quote(X)) | → | mark#(X) | (63) |
a__sel1#(s(X),cons(Y,Z)) | → | mark#(Z) | (43) |
mark#(dbls(X)) | → | mark#(X) | (62) |
a__sel1#(s(X),cons(Y,Z)) | → | mark#(X) | (58) |
a__quote#(s(X)) | → | mark#(X) | (57) |
mark#(sel1(X1,X2)) | → | mark#(X1) | (56) |
mark#(dbl(X)) | → | mark#(X) | (42) |
mark#(indx(X1,X2)) | → | mark#(X1) | (41) |
a__sel#(s(X),cons(Y,Z)) | → | mark#(X) | (40) |
mark#(sel(X1,X2)) | → | mark#(X2) | (54) |
The dependency pairs are split into 5 components.
a__quote#(s(X)) | → | a__quote#(mark(X)) | (64) |
π(a__quote#) | = | 1 |
π(a__from#) | = | 1 |
π(dbls) | = | 1 |
π(mark) | = | 1 |
π(a__dbls) | = | 1 |
π(s1) | = | 1 |
prec(a__dbl1) | = | 6 | status(a__dbl1) | = | [1] | list-extension(a__dbl1) | = | Lex | ||
prec(01) | = | 5 | status(01) | = | [] | list-extension(01) | = | Lex | ||
prec(s) | = | 4 | status(s) | = | [1] | list-extension(s) | = | Lex | ||
prec(a__indx) | = | 2 | status(a__indx) | = | [] | list-extension(a__indx) | = | Lex | ||
prec(a__from) | = | 1 | status(a__from) | = | [1] | list-extension(a__from) | = | Lex | ||
prec(a__indx#) | = | 0 | status(a__indx#) | = | [2, 1] | list-extension(a__indx#) | = | Lex | ||
prec(dbl) | = | 6 | status(dbl) | = | [1] | list-extension(dbl) | = | Lex | ||
prec(indx) | = | 2 | status(indx) | = | [] | list-extension(indx) | = | Lex | ||
prec(a__dbl1#) | = | 0 | status(a__dbl1#) | = | [] | list-extension(a__dbl1#) | = | Lex | ||
prec(a__dbl) | = | 6 | status(a__dbl) | = | [1] | list-extension(a__dbl) | = | Lex | ||
prec(a__sel1) | = | 2 | status(a__sel1) | = | [] | list-extension(a__sel1) | = | Lex | ||
prec(a__dbls#) | = | 0 | status(a__dbls#) | = | [] | list-extension(a__dbls#) | = | Lex | ||
prec(mark#) | = | 0 | status(mark#) | = | [] | list-extension(mark#) | = | Lex | ||
prec(0) | = | 7 | status(0) | = | [] | list-extension(0) | = | Lex | ||
prec(a__quote) | = | 3 | status(a__quote) | = | [1] | list-extension(a__quote) | = | Lex | ||
prec(sel) | = | 0 | status(sel) | = | [] | list-extension(sel) | = | Lex | ||
prec(from) | = | 1 | status(from) | = | [1] | list-extension(from) | = | Lex | ||
prec(a__sel1#) | = | 0 | status(a__sel1#) | = | [1] | list-extension(a__sel1#) | = | Lex | ||
prec(nil) | = | 7 | status(nil) | = | [] | list-extension(nil) | = | Lex | ||
prec(dbl1) | = | 6 | status(dbl1) | = | [1] | list-extension(dbl1) | = | 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) | = | 0 | status(a__sel) | = | [] | list-extension(a__sel) | = | Lex | ||
prec(quote) | = | 3 | status(quote) | = | [1] | list-extension(quote) | = | Lex | ||
prec(cons) | = | 1 | status(cons) | = | [] | list-extension(cons) | = | Lex | ||
prec(sel1) | = | 2 | status(sel1) | = | [] | list-extension(sel1) | = | Lex |
[a__dbl1(x1)] | = | x1 + 15923 |
[01] | = | 2 |
[s(x1)] | = | x1 + 0 |
[a__indx(x1, x2)] | = | x2 + 4 |
[a__from(x1)] | = | x1 + 4 |
[a__indx#(x1, x2)] | = | x1 + x2 + 1 |
[dbl(x1)] | = | x1 + 0 |
[indx(x1, x2)] | = | x2 + 4 |
[a__dbl1#(x1)] | = | 1 |
[a__dbl(x1)] | = | x1 + 0 |
[a__sel1(x1, x2)] | = | x2 + 2 |
[a__dbls#(x1)] | = | 1 |
[mark#(x1)] | = | 1 |
[0] | = | 1 |
[a__quote(x1)] | = | x1 + 15924 |
[sel(x1, x2)] | = | x2 + 0 |
[from(x1)] | = | x1 + 4 |
[a__sel1#(x1, x2)] | = | x1 + 1 |
[nil] | = | 3 |
[dbl1(x1)] | = | x1 + 15923 |
[a__dbl#(x1)] | = | 1 |
[a__sel#(x1, x2)] | = | x1 + 1 |
[a__sel(x1, x2)] | = | x2 + 0 |
[quote(x1)] | = | x1 + 15924 |
[cons(x1, x2)] | = | max(x1 + 3, x2 + 0, 0) |
[sel1(x1, x2)] | = | x2 + 2 |
mark(dbl(X)) | → | a__dbl(mark(X)) | (18) |
a__dbls(cons(X,Y)) | → | cons(dbl(X),dbls(Y)) | (4) |
a__quote(s(X)) | → | s1(a__quote(mark(X))) | (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) |
a__quote(dbl(X)) | → | a__dbl1(mark(X)) | (16) |
mark(indx(X1,X2)) | → | a__indx(mark(X1),X2) | (21) |
a__from(X) | → | from(X) | (36) |
mark(0) | → | 0 | (26) |
mark(dbls(X)) | → | a__dbls(mark(X)) | (19) |
a__dbl(X) | → | dbl(X) | (32) |
a__quote(sel(X,Y)) | → | a__sel1(mark(X),mark(Y)) | (17) |
mark(s(X)) | → | s(X) | (27) |
a__sel(X1,X2) | → | sel(X1,X2) | (34) |
mark(from(X)) | → | a__from(X) | (22) |
mark(nil) | → | nil | (28) |
a__sel(0,cons(X,Y)) | → | mark(X) | (5) |
a__dbls(X) | → | dbls(X) | (33) |
a__dbl1(0) | → | 01 | (10) |
a__quote(X) | → | quote(X) | (39) |
a__indx(nil,X) | → | nil | (7) |
mark(sel(X1,X2)) | → | a__sel(mark(X1),mark(X2)) | (20) |
mark(quote(X)) | → | a__quote(mark(X)) | (25) |
mark(01) | → | 01 | (30) |
a__quote(0) | → | 01 | (14) |
mark(s1(X)) | → | s1(mark(X)) | (31) |
a__sel1(0,cons(X,Y)) | → | mark(X) | (12) |
mark(dbl1(X)) | → | a__dbl1(mark(X)) | (23) |
mark(sel1(X1,X2)) | → | a__sel1(mark(X1),mark(X2)) | (24) |
a__dbl1(s(X)) | → | s1(s1(a__dbl1(mark(X)))) | (11) |
a__from(X) | → | cons(X,from(s(X))) | (9) |
a__sel1(s(X),cons(Y,Z)) | → | a__sel1(mark(X),mark(Z)) | (13) |
a__sel(s(X),cons(Y,Z)) | → | a__sel(mark(X),mark(Z)) | (6) |
a__sel1(X1,X2) | → | sel1(X1,X2) | (38) |
a__dbl1(X) | → | dbl1(X) | (37) |
a__indx(X1,X2) | → | indx(X1,X2) | (35) |
mark(cons(X1,X2)) | → | cons(X1,X2) | (29) |
a__dbl(s(X)) | → | s(s(dbl(X))) | (2) |
a__quote#(s(X)) | → | a__quote#(mark(X)) | (64) |
The dependency pairs are split into 0 components.
mark#(s1(X)) | → | mark#(X) | (72) |
[a__quote#(x1)] | = | 2 |
[a__dbl1(x1)] | = | x1 + 1 |
[01] | = | 4 |
[s(x1)] | = | 1 |
[a__from#(x1)] | = | 0 |
[dbls(x1)] | = | 21653 |
[a__indx(x1, x2)] | = | x1 + x2 + 0 |
[a__from(x1)] | = | 14008 |
[a__indx#(x1, x2)] | = | 0 |
[dbl(x1)] | = | 1 |
[indx(x1, x2)] | = | 1 |
[a__dbl1#(x1)] | = | 2 |
[a__dbl(x1)] | = | x1 + 2 |
[a__sel1(x1, x2)] | = | x1 + x2 + 0 |
[a__dbls#(x1)] | = | 0 |
[mark#(x1)] | = | x1 + 2 |
[0] | = | 1 |
[a__quote(x1)] | = | x1 + 2 |
[sel(x1, x2)] | = | x1 + x2 + 1 |
[from(x1)] | = | 14003 |
[a__sel1#(x1, x2)] | = | 2 |
[nil] | = | 1 |
[dbl1(x1)] | = | 24339 |
[a__dbl#(x1)] | = | 0 |
[a__sel#(x1, x2)] | = | 0 |
[mark(x1)] | = | x1 + 4 |
[a__sel(x1, x2)] | = | x1 + 0 |
[a__dbls(x1)] | = | x1 + 21652 |
[quote(x1)] | = | 1 |
[cons(x1, x2)] | = | x1 + x2 + 6 |
[sel1(x1, x2)] | = | 1 |
[s1(x1)] | = | x1 + 27857 |
mark#(s1(X)) | → | mark#(X) | (72) |
The dependency pairs are split into 0 components.
a__dbl1#(s(X)) | → | a__dbl1#(mark(X)) | (55) |
π(a__quote#) | = | 1 |
π(a__from#) | = | 1 |
π(a__dbl1#) | = | 1 |
π(mark) | = | 1 |
π(s1) | = | 1 |
prec(a__dbl1) | = | 5 | status(a__dbl1) | = | [] | list-extension(a__dbl1) | = | Lex | ||
prec(01) | = | 4 | status(01) | = | [] | list-extension(01) | = | Lex | ||
prec(s) | = | 5 | status(s) | = | [1] | list-extension(s) | = | Lex | ||
prec(dbls) | = | 5 | status(dbls) | = | [] | list-extension(dbls) | = | Lex | ||
prec(a__indx) | = | 2 | status(a__indx) | = | [1] | list-extension(a__indx) | = | Lex | ||
prec(a__from) | = | 2 | status(a__from) | = | [] | list-extension(a__from) | = | Lex | ||
prec(a__indx#) | = | 0 | status(a__indx#) | = | [2, 1] | list-extension(a__indx#) | = | Lex | ||
prec(dbl) | = | 6 | status(dbl) | = | [1] | list-extension(dbl) | = | Lex | ||
prec(indx) | = | 2 | status(indx) | = | [1] | list-extension(indx) | = | Lex | ||
prec(a__dbl) | = | 6 | status(a__dbl) | = | [1] | list-extension(a__dbl) | = | Lex | ||
prec(a__sel1) | = | 3 | status(a__sel1) | = | [] | list-extension(a__sel1) | = | Lex | ||
prec(a__dbls#) | = | 0 | status(a__dbls#) | = | [] | list-extension(a__dbls#) | = | Lex | ||
prec(mark#) | = | 0 | status(mark#) | = | [] | list-extension(mark#) | = | Lex | ||
prec(0) | = | 7 | status(0) | = | [] | list-extension(0) | = | Lex | ||
prec(a__quote) | = | 3 | status(a__quote) | = | [] | list-extension(a__quote) | = | Lex | ||
prec(sel) | = | 0 | status(sel) | = | [] | list-extension(sel) | = | Lex | ||
prec(from) | = | 2 | status(from) | = | [] | list-extension(from) | = | Lex | ||
prec(a__sel1#) | = | 0 | status(a__sel1#) | = | [1] | list-extension(a__sel1#) | = | Lex | ||
prec(nil) | = | 4 | status(nil) | = | [] | list-extension(nil) | = | Lex | ||
prec(dbl1) | = | 5 | status(dbl1) | = | [] | list-extension(dbl1) | = | 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) | = | 0 | status(a__sel) | = | [] | list-extension(a__sel) | = | Lex | ||
prec(a__dbls) | = | 5 | status(a__dbls) | = | [] | list-extension(a__dbls) | = | Lex | ||
prec(quote) | = | 3 | status(quote) | = | [] | list-extension(quote) | = | Lex | ||
prec(cons) | = | 1 | status(cons) | = | [1] | list-extension(cons) | = | Lex | ||
prec(sel1) | = | 3 | status(sel1) | = | [] | list-extension(sel1) | = | Lex |
[a__dbl1(x1)] | = | 15924 |
[01] | = | 2 |
[s(x1)] | = | x1 + 0 |
[dbls(x1)] | = | x1 + 0 |
[a__indx(x1, x2)] | = | x1 + x2 + 0 |
[a__from(x1)] | = | x1 + 36231 |
[a__indx#(x1, x2)] | = | x1 + x2 + 1 |
[dbl(x1)] | = | x1 + 0 |
[indx(x1, x2)] | = | x1 + x2 + 0 |
[a__dbl(x1)] | = | x1 + 0 |
[a__sel1(x1, x2)] | = | x2 + 12618 |
[a__dbls#(x1)] | = | 1 |
[mark#(x1)] | = | 1 |
[0] | = | 1 |
[a__quote(x1)] | = | x1 + 15925 |
[sel(x1, x2)] | = | x2 + 0 |
[from(x1)] | = | x1 + 36231 |
[a__sel1#(x1, x2)] | = | x1 + 1 |
[nil] | = | 33694 |
[dbl1(x1)] | = | 15924 |
[a__dbl#(x1)] | = | 1 |
[a__sel#(x1, x2)] | = | x1 + 1 |
[a__sel(x1, x2)] | = | x2 + 0 |
[a__dbls(x1)] | = | x1 + 0 |
[quote(x1)] | = | x1 + 15925 |
[cons(x1, x2)] | = | max(x1 + 36230, x2 + 0, 0) |
[sel1(x1, x2)] | = | x2 + 12618 |
mark(dbl(X)) | → | a__dbl(mark(X)) | (18) |
a__dbls(cons(X,Y)) | → | cons(dbl(X),dbls(Y)) | (4) |
a__quote(s(X)) | → | s1(a__quote(mark(X))) | (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) |
a__quote(dbl(X)) | → | a__dbl1(mark(X)) | (16) |
mark(indx(X1,X2)) | → | a__indx(mark(X1),X2) | (21) |
a__from(X) | → | from(X) | (36) |
mark(0) | → | 0 | (26) |
mark(dbls(X)) | → | a__dbls(mark(X)) | (19) |
a__dbl(X) | → | dbl(X) | (32) |
a__quote(sel(X,Y)) | → | a__sel1(mark(X),mark(Y)) | (17) |
mark(s(X)) | → | s(X) | (27) |
a__sel(X1,X2) | → | sel(X1,X2) | (34) |
mark(from(X)) | → | a__from(X) | (22) |
mark(nil) | → | nil | (28) |
a__sel(0,cons(X,Y)) | → | mark(X) | (5) |
a__dbls(X) | → | dbls(X) | (33) |
a__dbl1(0) | → | 01 | (10) |
a__quote(X) | → | quote(X) | (39) |
a__indx(nil,X) | → | nil | (7) |
mark(sel(X1,X2)) | → | a__sel(mark(X1),mark(X2)) | (20) |
mark(quote(X)) | → | a__quote(mark(X)) | (25) |
mark(01) | → | 01 | (30) |
a__quote(0) | → | 01 | (14) |
mark(s1(X)) | → | s1(mark(X)) | (31) |
a__sel1(0,cons(X,Y)) | → | mark(X) | (12) |
mark(dbl1(X)) | → | a__dbl1(mark(X)) | (23) |
mark(sel1(X1,X2)) | → | a__sel1(mark(X1),mark(X2)) | (24) |
a__dbl1(s(X)) | → | s1(s1(a__dbl1(mark(X)))) | (11) |
a__from(X) | → | cons(X,from(s(X))) | (9) |
a__sel1(s(X),cons(Y,Z)) | → | a__sel1(mark(X),mark(Z)) | (13) |
a__sel(s(X),cons(Y,Z)) | → | a__sel(mark(X),mark(Z)) | (6) |
a__sel1(X1,X2) | → | sel1(X1,X2) | (38) |
a__dbl1(X) | → | dbl1(X) | (37) |
a__indx(X1,X2) | → | indx(X1,X2) | (35) |
mark(cons(X1,X2)) | → | cons(X1,X2) | (29) |
a__dbl(s(X)) | → | s(s(dbl(X))) | (2) |
a__dbl1#(s(X)) | → | a__dbl1#(mark(X)) | (55) |
The dependency pairs are split into 0 components.
a__sel1#(s(X),cons(Y,Z)) | → | a__sel1#(mark(X),mark(Z)) | (73) |
π(a__quote#) | = | 1 |
π(a__from#) | = | 1 |
π(a__dbl1#) | = | 1 |
π(a__sel1#) | = | 1 |
π(mark) | = | 1 |
π(s1) | = | 1 |
prec(a__dbl1) | = | 5 | status(a__dbl1) | = | [] | list-extension(a__dbl1) | = | Lex | ||
prec(01) | = | 4 | status(01) | = | [] | list-extension(01) | = | Lex | ||
prec(s) | = | 5 | status(s) | = | [1] | list-extension(s) | = | Lex | ||
prec(dbls) | = | 5 | status(dbls) | = | [] | list-extension(dbls) | = | Lex | ||
prec(a__indx) | = | 2 | status(a__indx) | = | [1] | list-extension(a__indx) | = | Lex | ||
prec(a__from) | = | 2 | status(a__from) | = | [] | list-extension(a__from) | = | Lex | ||
prec(a__indx#) | = | 0 | status(a__indx#) | = | [2, 1] | list-extension(a__indx#) | = | Lex | ||
prec(dbl) | = | 6 | status(dbl) | = | [1] | list-extension(dbl) | = | Lex | ||
prec(indx) | = | 2 | status(indx) | = | [1] | list-extension(indx) | = | Lex | ||
prec(a__dbl) | = | 6 | status(a__dbl) | = | [1] | list-extension(a__dbl) | = | Lex | ||
prec(a__sel1) | = | 3 | status(a__sel1) | = | [] | list-extension(a__sel1) | = | Lex | ||
prec(a__dbls#) | = | 0 | status(a__dbls#) | = | [] | list-extension(a__dbls#) | = | Lex | ||
prec(mark#) | = | 0 | status(mark#) | = | [] | list-extension(mark#) | = | Lex | ||
prec(0) | = | 7 | status(0) | = | [] | list-extension(0) | = | Lex | ||
prec(a__quote) | = | 3 | status(a__quote) | = | [] | list-extension(a__quote) | = | Lex | ||
prec(sel) | = | 0 | status(sel) | = | [] | list-extension(sel) | = | Lex | ||
prec(from) | = | 2 | status(from) | = | [] | list-extension(from) | = | Lex | ||
prec(nil) | = | 4 | status(nil) | = | [] | list-extension(nil) | = | Lex | ||
prec(dbl1) | = | 5 | status(dbl1) | = | [] | list-extension(dbl1) | = | 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) | = | 0 | status(a__sel) | = | [] | list-extension(a__sel) | = | Lex | ||
prec(a__dbls) | = | 5 | status(a__dbls) | = | [] | list-extension(a__dbls) | = | Lex | ||
prec(quote) | = | 3 | status(quote) | = | [] | list-extension(quote) | = | Lex | ||
prec(cons) | = | 1 | status(cons) | = | [1] | list-extension(cons) | = | Lex | ||
prec(sel1) | = | 3 | status(sel1) | = | [] | list-extension(sel1) | = | Lex |
[a__dbl1(x1)] | = | 28226 |
[01] | = | 2 |
[s(x1)] | = | x1 + 0 |
[dbls(x1)] | = | x1 + 0 |
[a__indx(x1, x2)] | = | x1 + x2 + 0 |
[a__from(x1)] | = | x1 + 17890 |
[a__indx#(x1, x2)] | = | x1 + x2 + 1 |
[dbl(x1)] | = | x1 + 0 |
[indx(x1, x2)] | = | x1 + x2 + 0 |
[a__dbl(x1)] | = | x1 + 0 |
[a__sel1(x1, x2)] | = | x2 + 17888 |
[a__dbls#(x1)] | = | 1 |
[mark#(x1)] | = | 1 |
[0] | = | 1 |
[a__quote(x1)] | = | x1 + 28227 |
[sel(x1, x2)] | = | x2 + 0 |
[from(x1)] | = | x1 + 17890 |
[nil] | = | 38476 |
[dbl1(x1)] | = | 28226 |
[a__dbl#(x1)] | = | 1 |
[a__sel#(x1, x2)] | = | x1 + 1 |
[a__sel(x1, x2)] | = | x2 + 0 |
[a__dbls(x1)] | = | x1 + 0 |
[quote(x1)] | = | x1 + 28227 |
[cons(x1, x2)] | = | max(x1 + 17889, x2 + 0, 0) |
[sel1(x1, x2)] | = | x2 + 17888 |
mark(dbl(X)) | → | a__dbl(mark(X)) | (18) |
a__dbls(cons(X,Y)) | → | cons(dbl(X),dbls(Y)) | (4) |
a__quote(s(X)) | → | s1(a__quote(mark(X))) | (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) |
a__quote(dbl(X)) | → | a__dbl1(mark(X)) | (16) |
mark(indx(X1,X2)) | → | a__indx(mark(X1),X2) | (21) |
a__from(X) | → | from(X) | (36) |
mark(0) | → | 0 | (26) |
mark(dbls(X)) | → | a__dbls(mark(X)) | (19) |
a__dbl(X) | → | dbl(X) | (32) |
a__quote(sel(X,Y)) | → | a__sel1(mark(X),mark(Y)) | (17) |
mark(s(X)) | → | s(X) | (27) |
a__sel(X1,X2) | → | sel(X1,X2) | (34) |
mark(from(X)) | → | a__from(X) | (22) |
mark(nil) | → | nil | (28) |
a__sel(0,cons(X,Y)) | → | mark(X) | (5) |
a__dbls(X) | → | dbls(X) | (33) |
a__dbl1(0) | → | 01 | (10) |
a__quote(X) | → | quote(X) | (39) |
a__indx(nil,X) | → | nil | (7) |
mark(sel(X1,X2)) | → | a__sel(mark(X1),mark(X2)) | (20) |
mark(quote(X)) | → | a__quote(mark(X)) | (25) |
mark(01) | → | 01 | (30) |
a__quote(0) | → | 01 | (14) |
mark(s1(X)) | → | s1(mark(X)) | (31) |
a__sel1(0,cons(X,Y)) | → | mark(X) | (12) |
mark(dbl1(X)) | → | a__dbl1(mark(X)) | (23) |
mark(sel1(X1,X2)) | → | a__sel1(mark(X1),mark(X2)) | (24) |
a__dbl1(s(X)) | → | s1(s1(a__dbl1(mark(X)))) | (11) |
a__from(X) | → | cons(X,from(s(X))) | (9) |
a__sel1(s(X),cons(Y,Z)) | → | a__sel1(mark(X),mark(Z)) | (13) |
a__sel(s(X),cons(Y,Z)) | → | a__sel(mark(X),mark(Z)) | (6) |
a__sel1(X1,X2) | → | sel1(X1,X2) | (38) |
a__dbl1(X) | → | dbl1(X) | (37) |
a__indx(X1,X2) | → | indx(X1,X2) | (35) |
mark(cons(X1,X2)) | → | cons(X1,X2) | (29) |
a__dbl(s(X)) | → | s(s(dbl(X))) | (2) |
a__sel1#(s(X),cons(Y,Z)) | → | a__sel1#(mark(X),mark(Z)) | (73) |
The dependency pairs are split into 0 components.
a__sel#(s(X),cons(Y,Z)) | → | a__sel#(mark(X),mark(Z)) | (70) |
π(a__quote#) | = | 1 |
π(a__from#) | = | 1 |
π(a__dbl1#) | = | 1 |
π(a__sel1#) | = | 1 |
π(mark) | = | 1 |
π(s1) | = | 1 |
prec(a__dbl1) | = | 6 | status(a__dbl1) | = | [] | list-extension(a__dbl1) | = | Lex | ||
prec(01) | = | 5 | status(01) | = | [] | list-extension(01) | = | Lex | ||
prec(s) | = | 6 | status(s) | = | [1] | list-extension(s) | = | Lex | ||
prec(dbls) | = | 6 | status(dbls) | = | [] | list-extension(dbls) | = | Lex | ||
prec(a__indx) | = | 3 | status(a__indx) | = | [1] | list-extension(a__indx) | = | Lex | ||
prec(a__from) | = | 3 | status(a__from) | = | [] | list-extension(a__from) | = | Lex | ||
prec(a__indx#) | = | 0 | status(a__indx#) | = | [2, 1] | list-extension(a__indx#) | = | Lex | ||
prec(dbl) | = | 7 | status(dbl) | = | [1] | list-extension(dbl) | = | Lex | ||
prec(indx) | = | 3 | status(indx) | = | [1] | list-extension(indx) | = | Lex | ||
prec(a__dbl) | = | 7 | status(a__dbl) | = | [1] | list-extension(a__dbl) | = | Lex | ||
prec(a__sel1) | = | 4 | status(a__sel1) | = | [] | list-extension(a__sel1) | = | Lex | ||
prec(a__dbls#) | = | 0 | status(a__dbls#) | = | [] | list-extension(a__dbls#) | = | Lex | ||
prec(mark#) | = | 0 | status(mark#) | = | [] | list-extension(mark#) | = | Lex | ||
prec(0) | = | 8 | status(0) | = | [] | list-extension(0) | = | Lex | ||
prec(a__quote) | = | 4 | status(a__quote) | = | [] | list-extension(a__quote) | = | Lex | ||
prec(sel) | = | 0 | status(sel) | = | [] | list-extension(sel) | = | Lex | ||
prec(from) | = | 3 | status(from) | = | [] | list-extension(from) | = | Lex | ||
prec(nil) | = | 5 | status(nil) | = | [] | list-extension(nil) | = | Lex | ||
prec(dbl1) | = | 6 | status(dbl1) | = | [] | list-extension(dbl1) | = | Lex | ||
prec(a__dbl#) | = | 0 | status(a__dbl#) | = | [] | list-extension(a__dbl#) | = | Lex | ||
prec(a__sel#) | = | 2 | status(a__sel#) | = | [1, 2] | list-extension(a__sel#) | = | Lex | ||
prec(a__sel) | = | 0 | status(a__sel) | = | [] | list-extension(a__sel) | = | Lex | ||
prec(a__dbls) | = | 6 | status(a__dbls) | = | [] | list-extension(a__dbls) | = | Lex | ||
prec(quote) | = | 4 | status(quote) | = | [] | list-extension(quote) | = | Lex | ||
prec(cons) | = | 1 | status(cons) | = | [1] | list-extension(cons) | = | Lex | ||
prec(sel1) | = | 4 | status(sel1) | = | [] | list-extension(sel1) | = | Lex |
[a__dbl1(x1)] | = | 3 |
[01] | = | 2 |
[s(x1)] | = | x1 + 0 |
[dbls(x1)] | = | x1 + 0 |
[a__indx(x1, x2)] | = | x1 + x2 + 0 |
[a__from(x1)] | = | x1 + 7581 |
[a__indx#(x1, x2)] | = | x1 + x2 + 1 |
[dbl(x1)] | = | x1 + 0 |
[indx(x1, x2)] | = | x1 + x2 + 0 |
[a__dbl(x1)] | = | x1 + 0 |
[a__sel1(x1, x2)] | = | x2 + 1 |
[a__dbls#(x1)] | = | 1 |
[mark#(x1)] | = | 1 |
[0] | = | 1 |
[a__quote(x1)] | = | x1 + 28227 |
[sel(x1, x2)] | = | x2 + 0 |
[from(x1)] | = | x1 + 7581 |
[nil] | = | 43324 |
[dbl1(x1)] | = | 3 |
[a__dbl#(x1)] | = | 1 |
[a__sel#(x1, x2)] | = | x1 + x2 + 1 |
[a__sel(x1, x2)] | = | x2 + 0 |
[a__dbls(x1)] | = | x1 + 0 |
[quote(x1)] | = | x1 + 28227 |
[cons(x1, x2)] | = | max(x1 + 2, x2 + 0, 0) |
[sel1(x1, x2)] | = | x2 + 1 |
mark(dbl(X)) | → | a__dbl(mark(X)) | (18) |
a__dbls(cons(X,Y)) | → | cons(dbl(X),dbls(Y)) | (4) |
a__quote(s(X)) | → | s1(a__quote(mark(X))) | (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) |
a__quote(dbl(X)) | → | a__dbl1(mark(X)) | (16) |
mark(indx(X1,X2)) | → | a__indx(mark(X1),X2) | (21) |
a__from(X) | → | from(X) | (36) |
mark(0) | → | 0 | (26) |
mark(dbls(X)) | → | a__dbls(mark(X)) | (19) |
a__dbl(X) | → | dbl(X) | (32) |
a__quote(sel(X,Y)) | → | a__sel1(mark(X),mark(Y)) | (17) |
mark(s(X)) | → | s(X) | (27) |
a__sel(X1,X2) | → | sel(X1,X2) | (34) |
mark(from(X)) | → | a__from(X) | (22) |
mark(nil) | → | nil | (28) |
a__sel(0,cons(X,Y)) | → | mark(X) | (5) |
a__dbls(X) | → | dbls(X) | (33) |
a__dbl1(0) | → | 01 | (10) |
a__quote(X) | → | quote(X) | (39) |
a__indx(nil,X) | → | nil | (7) |
mark(sel(X1,X2)) | → | a__sel(mark(X1),mark(X2)) | (20) |
mark(quote(X)) | → | a__quote(mark(X)) | (25) |
mark(01) | → | 01 | (30) |
a__quote(0) | → | 01 | (14) |
mark(s1(X)) | → | s1(mark(X)) | (31) |
a__sel1(0,cons(X,Y)) | → | mark(X) | (12) |
mark(dbl1(X)) | → | a__dbl1(mark(X)) | (23) |
mark(sel1(X1,X2)) | → | a__sel1(mark(X1),mark(X2)) | (24) |
a__dbl1(s(X)) | → | s1(s1(a__dbl1(mark(X)))) | (11) |
a__from(X) | → | cons(X,from(s(X))) | (9) |
a__sel1(s(X),cons(Y,Z)) | → | a__sel1(mark(X),mark(Z)) | (13) |
a__sel(s(X),cons(Y,Z)) | → | a__sel(mark(X),mark(Z)) | (6) |
a__sel1(X1,X2) | → | sel1(X1,X2) | (38) |
a__dbl1(X) | → | dbl1(X) | (37) |
a__indx(X1,X2) | → | indx(X1,X2) | (35) |
mark(cons(X1,X2)) | → | cons(X1,X2) | (29) |
a__dbl(s(X)) | → | s(s(dbl(X))) | (2) |
a__sel#(s(X),cons(Y,Z)) | → | a__sel#(mark(X),mark(Z)) | (70) |
The dependency pairs are split into 0 components.