The rewrite relation of the following TRS is considered.
active(from(X)) | → | mark(cons(X,from(s(X)))) | (1) |
active(sel(0,cons(X,Y))) | → | mark(X) | (2) |
active(sel(s(X),cons(Y,Z))) | → | mark(sel(X,Z)) | (3) |
mark(from(X)) | → | active(from(mark(X))) | (4) |
mark(cons(X1,X2)) | → | active(cons(mark(X1),X2)) | (5) |
mark(s(X)) | → | active(s(mark(X))) | (6) |
mark(sel(X1,X2)) | → | active(sel(mark(X1),mark(X2))) | (7) |
mark(0) | → | active(0) | (8) |
from(mark(X)) | → | from(X) | (9) |
from(active(X)) | → | from(X) | (10) |
cons(mark(X1),X2) | → | cons(X1,X2) | (11) |
cons(X1,mark(X2)) | → | cons(X1,X2) | (12) |
cons(active(X1),X2) | → | cons(X1,X2) | (13) |
cons(X1,active(X2)) | → | cons(X1,X2) | (14) |
s(mark(X)) | → | s(X) | (15) |
s(active(X)) | → | s(X) | (16) |
sel(mark(X1),X2) | → | sel(X1,X2) | (17) |
sel(X1,mark(X2)) | → | sel(X1,X2) | (18) |
sel(active(X1),X2) | → | sel(X1,X2) | (19) |
sel(X1,active(X2)) | → | sel(X1,X2) | (20) |
mark#(s(X)) | → | active#(s(mark(X))) | (21) |
s#(mark(X)) | → | s#(X) | (22) |
from#(mark(X)) | → | from#(X) | (23) |
mark#(sel(X1,X2)) | → | mark#(X1) | (24) |
cons#(X1,active(X2)) | → | cons#(X1,X2) | (25) |
mark#(sel(X1,X2)) | → | active#(sel(mark(X1),mark(X2))) | (26) |
active#(from(X)) | → | mark#(cons(X,from(s(X)))) | (27) |
active#(sel(s(X),cons(Y,Z))) | → | sel#(X,Z) | (28) |
mark#(sel(X1,X2)) | → | sel#(mark(X1),mark(X2)) | (29) |
mark#(from(X)) | → | from#(mark(X)) | (30) |
mark#(sel(X1,X2)) | → | mark#(X2) | (31) |
mark#(from(X)) | → | active#(from(mark(X))) | (32) |
active#(from(X)) | → | cons#(X,from(s(X))) | (33) |
sel#(active(X1),X2) | → | sel#(X1,X2) | (34) |
cons#(mark(X1),X2) | → | cons#(X1,X2) | (35) |
sel#(X1,active(X2)) | → | sel#(X1,X2) | (36) |
sel#(X1,mark(X2)) | → | sel#(X1,X2) | (37) |
cons#(active(X1),X2) | → | cons#(X1,X2) | (38) |
mark#(0) | → | active#(0) | (39) |
active#(sel(s(X),cons(Y,Z))) | → | mark#(sel(X,Z)) | (40) |
active#(from(X)) | → | s#(X) | (41) |
mark#(cons(X1,X2)) | → | cons#(mark(X1),X2) | (42) |
mark#(from(X)) | → | mark#(X) | (43) |
sel#(mark(X1),X2) | → | sel#(X1,X2) | (44) |
active#(from(X)) | → | from#(s(X)) | (45) |
s#(active(X)) | → | s#(X) | (46) |
mark#(cons(X1,X2)) | → | active#(cons(mark(X1),X2)) | (47) |
mark#(s(X)) | → | s#(mark(X)) | (48) |
active#(sel(0,cons(X,Y))) | → | mark#(X) | (49) |
cons#(X1,mark(X2)) | → | cons#(X1,X2) | (50) |
from#(active(X)) | → | from#(X) | (51) |
mark#(s(X)) | → | mark#(X) | (52) |
mark#(cons(X1,X2)) | → | mark#(X1) | (53) |
The dependency pairs are split into 5 components.
mark#(cons(X1,X2)) | → | mark#(X1) | (53) |
mark#(s(X)) | → | mark#(X) | (52) |
mark#(from(X)) | → | active#(from(mark(X))) | (32) |
mark#(sel(X1,X2)) | → | mark#(X2) | (31) |
active#(sel(0,cons(X,Y))) | → | mark#(X) | (49) |
active#(from(X)) | → | mark#(cons(X,from(s(X)))) | (27) |
mark#(cons(X1,X2)) | → | active#(cons(mark(X1),X2)) | (47) |
mark#(sel(X1,X2)) | → | active#(sel(mark(X1),mark(X2))) | (26) |
mark#(sel(X1,X2)) | → | mark#(X1) | (24) |
mark#(from(X)) | → | mark#(X) | (43) |
active#(sel(s(X),cons(Y,Z))) | → | mark#(sel(X,Z)) | (40) |
mark#(s(X)) | → | active#(s(mark(X))) | (21) |
[cons#(x1, x2)] | = | 0 |
[s(x1)] | = | 20163 |
[mark#(x1)] | = | 29019 |
[0] | = | 1 |
[sel#(x1, x2)] | = | 0 |
[from(x1)] | = | 29019 |
[sel(x1, x2)] | = | 29019 |
[s#(x1)] | = | 0 |
[mark(x1)] | = | 1 |
[from#(x1)] | = | 0 |
[active(x1)] | = | 2 |
[cons(x1, x2)] | = | 1 |
[active#(x1)] | = | x1 + 0 |
sel(X1,mark(X2)) | → | sel(X1,X2) | (18) |
s(mark(X)) | → | s(X) | (15) |
s(active(X)) | → | s(X) | (16) |
sel(active(X1),X2) | → | sel(X1,X2) | (19) |
sel(mark(X1),X2) | → | sel(X1,X2) | (17) |
from(active(X)) | → | from(X) | (10) |
sel(X1,active(X2)) | → | sel(X1,X2) | (20) |
cons(X1,active(X2)) | → | cons(X1,X2) | (14) |
cons(X1,mark(X2)) | → | cons(X1,X2) | (12) |
cons(mark(X1),X2) | → | cons(X1,X2) | (11) |
from(mark(X)) | → | from(X) | (9) |
cons(active(X1),X2) | → | cons(X1,X2) | (13) |
mark#(cons(X1,X2)) | → | active#(cons(mark(X1),X2)) | (47) |
mark#(s(X)) | → | active#(s(mark(X))) | (21) |
The dependency pairs are split into 1 component.
mark#(from(X)) | → | mark#(X) | (43) |
mark#(from(X)) | → | active#(from(mark(X))) | (32) |
active#(from(X)) | → | mark#(cons(X,from(s(X)))) | (27) |
active#(sel(s(X),cons(Y,Z))) | → | mark#(sel(X,Z)) | (40) |
mark#(cons(X1,X2)) | → | mark#(X1) | (53) |
mark#(sel(X1,X2)) | → | mark#(X2) | (31) |
mark#(sel(X1,X2)) | → | mark#(X1) | (24) |
mark#(sel(X1,X2)) | → | active#(sel(mark(X1),mark(X2))) | (26) |
mark#(s(X)) | → | mark#(X) | (52) |
active#(sel(0,cons(X,Y))) | → | mark#(X) | (49) |
[cons#(x1, x2)] | = | max(0) |
[s(x1)] | = | x1 + 0 |
[mark#(x1)] | = | x1 + 0 |
[0] | = | 1 |
[sel#(x1, x2)] | = | max(0) |
[from(x1)] | = | x1 + 1144 |
[sel(x1, x2)] | = | max(x1 + 28101, x2 + 28102, 0) |
[s#(x1)] | = | 0 |
[mark(x1)] | = | x1 + 0 |
[from#(x1)] | = | 0 |
[active(x1)] | = | x1 + 0 |
[cons(x1, x2)] | = | max(x1 + 1143, x2 + 0, 0) |
[active#(x1)] | = | x1 + 0 |
sel(X1,mark(X2)) | → | sel(X1,X2) | (18) |
mark(from(X)) | → | active(from(mark(X))) | (4) |
s(mark(X)) | → | s(X) | (15) |
mark(0) | → | active(0) | (8) |
active(from(X)) | → | mark(cons(X,from(s(X)))) | (1) |
active(sel(s(X),cons(Y,Z))) | → | mark(sel(X,Z)) | (3) |
s(active(X)) | → | s(X) | (16) |
sel(active(X1),X2) | → | sel(X1,X2) | (19) |
sel(mark(X1),X2) | → | sel(X1,X2) | (17) |
mark(cons(X1,X2)) | → | active(cons(mark(X1),X2)) | (5) |
from(active(X)) | → | from(X) | (10) |
mark(sel(X1,X2)) | → | active(sel(mark(X1),mark(X2))) | (7) |
sel(X1,active(X2)) | → | sel(X1,X2) | (20) |
cons(X1,active(X2)) | → | cons(X1,X2) | (14) |
cons(X1,mark(X2)) | → | cons(X1,X2) | (12) |
cons(mark(X1),X2) | → | cons(X1,X2) | (11) |
from(mark(X)) | → | from(X) | (9) |
cons(active(X1),X2) | → | cons(X1,X2) | (13) |
mark(s(X)) | → | active(s(mark(X))) | (6) |
active(sel(0,cons(X,Y))) | → | mark(X) | (2) |
mark#(from(X)) | → | mark#(X) | (43) |
mark#(cons(X1,X2)) | → | mark#(X1) | (53) |
mark#(sel(X1,X2)) | → | mark#(X2) | (31) |
mark#(sel(X1,X2)) | → | mark#(X1) | (24) |
active#(sel(0,cons(X,Y))) | → | mark#(X) | (49) |
The dependency pairs are split into 1 component.
mark#(from(X)) | → | active#(from(mark(X))) | (32) |
active#(from(X)) | → | mark#(cons(X,from(s(X)))) | (27) |
active#(sel(s(X),cons(Y,Z))) | → | mark#(sel(X,Z)) | (40) |
mark#(sel(X1,X2)) | → | active#(sel(mark(X1),mark(X2))) | (26) |
mark#(s(X)) | → | mark#(X) | (52) |
[cons#(x1, x2)] | = | 0 |
[s(x1)] | = | x1 + 20163 |
[mark#(x1)] | = | x1 + 0 |
[0] | = | 1 |
[sel#(x1, x2)] | = | 0 |
[from(x1)] | = | 29021 |
[sel(x1, x2)] | = | 29020 |
[s#(x1)] | = | 0 |
[mark(x1)] | = | 0 |
[from#(x1)] | = | 0 |
[active(x1)] | = | 1 |
[cons(x1, x2)] | = | 1 |
[active#(x1)] | = | 29020 |
sel(X1,mark(X2)) | → | sel(X1,X2) | (18) |
sel(active(X1),X2) | → | sel(X1,X2) | (19) |
sel(mark(X1),X2) | → | sel(X1,X2) | (17) |
sel(X1,active(X2)) | → | sel(X1,X2) | (20) |
cons(X1,active(X2)) | → | cons(X1,X2) | (14) |
cons(X1,mark(X2)) | → | cons(X1,X2) | (12) |
cons(mark(X1),X2) | → | cons(X1,X2) | (11) |
cons(active(X1),X2) | → | cons(X1,X2) | (13) |
mark#(from(X)) | → | active#(from(mark(X))) | (32) |
active#(from(X)) | → | mark#(cons(X,from(s(X)))) | (27) |
mark#(s(X)) | → | mark#(X) | (52) |
The dependency pairs are split into 1 component.
active#(sel(s(X),cons(Y,Z))) | → | mark#(sel(X,Z)) | (40) |
mark#(sel(X1,X2)) | → | active#(sel(mark(X1),mark(X2))) | (26) |
π(mark#) | = | 1 |
π(mark) | = | 1 |
π(from#) | = | 1 |
π(active) | = | 1 |
π(active#) | = | 1 |
prec(cons#) | = | 0 | status(cons#) | = | [] | list-extension(cons#) | = | Lex | ||
prec(s) | = | 0 | status(s) | = | [1] | list-extension(s) | = | Lex | ||
prec(0) | = | 3 | status(0) | = | [] | list-extension(0) | = | Lex | ||
prec(sel#) | = | 0 | status(sel#) | = | [1, 2] | list-extension(sel#) | = | Lex | ||
prec(from) | = | 2 | status(from) | = | [1] | list-extension(from) | = | Lex | ||
prec(sel) | = | 2 | status(sel) | = | [1] | list-extension(sel) | = | Lex | ||
prec(s#) | = | 0 | status(s#) | = | [] | list-extension(s#) | = | Lex | ||
prec(cons) | = | 2 | status(cons) | = | [] | list-extension(cons) | = | Lex |
[cons#(x1, x2)] | = | max(x1 + 1, 0) |
[s(x1)] | = | x1 + 0 |
[0] | = | 1 |
[sel#(x1, x2)] | = | x1 + x2 + 1 |
[from(x1)] | = | x1 + 2999 |
[sel(x1, x2)] | = | x1 + x2 + 2998 |
[s#(x1)] | = | 1 |
[cons(x1, x2)] | = | max(x1 + 2999, x2 + 0, 0) |
sel(X1,mark(X2)) | → | sel(X1,X2) | (18) |
mark(from(X)) | → | active(from(mark(X))) | (4) |
s(mark(X)) | → | s(X) | (15) |
mark(0) | → | active(0) | (8) |
active(from(X)) | → | mark(cons(X,from(s(X)))) | (1) |
active(sel(s(X),cons(Y,Z))) | → | mark(sel(X,Z)) | (3) |
s(active(X)) | → | s(X) | (16) |
sel(active(X1),X2) | → | sel(X1,X2) | (19) |
sel(mark(X1),X2) | → | sel(X1,X2) | (17) |
mark(cons(X1,X2)) | → | active(cons(mark(X1),X2)) | (5) |
from(active(X)) | → | from(X) | (10) |
mark(sel(X1,X2)) | → | active(sel(mark(X1),mark(X2))) | (7) |
sel(X1,active(X2)) | → | sel(X1,X2) | (20) |
cons(X1,active(X2)) | → | cons(X1,X2) | (14) |
cons(X1,mark(X2)) | → | cons(X1,X2) | (12) |
cons(mark(X1),X2) | → | cons(X1,X2) | (11) |
from(mark(X)) | → | from(X) | (9) |
cons(active(X1),X2) | → | cons(X1,X2) | (13) |
mark(s(X)) | → | active(s(mark(X))) | (6) |
active(sel(0,cons(X,Y))) | → | mark(X) | (2) |
active#(sel(s(X),cons(Y,Z))) | → | mark#(sel(X,Z)) | (40) |
The dependency pairs are split into 0 components.
cons#(X1,mark(X2)) | → | cons#(X1,X2) | (50) |
cons#(X1,active(X2)) | → | cons#(X1,X2) | (25) |
cons#(active(X1),X2) | → | cons#(X1,X2) | (38) |
cons#(mark(X1),X2) | → | cons#(X1,X2) | (35) |
[cons#(x1, x2)] | = | x2 + 0 |
[s(x1)] | = | 0 |
[mark#(x1)] | = | 0 |
[0] | = | 1 |
[sel#(x1, x2)] | = | 0 |
[from(x1)] | = | 0 |
[sel(x1, x2)] | = | 35495 |
[s#(x1)] | = | 0 |
[mark(x1)] | = | x1 + 35497 |
[from#(x1)] | = | 0 |
[active(x1)] | = | x1 + 1 |
[cons(x1, x2)] | = | 1 |
[active#(x1)] | = | 0 |
from(active(X)) | → | from(X) | (10) |
from(mark(X)) | → | from(X) | (9) |
cons#(X1,mark(X2)) | → | cons#(X1,X2) | (50) |
cons#(X1,active(X2)) | → | cons#(X1,X2) | (25) |
The dependency pairs are split into 1 component.
cons#(mark(X1),X2) | → | cons#(X1,X2) | (35) |
cons#(active(X1),X2) | → | cons#(X1,X2) | (38) |
[cons#(x1, x2)] | = | x1 + 0 |
[s(x1)] | = | 0 |
[mark#(x1)] | = | 0 |
[0] | = | 1 |
[sel#(x1, x2)] | = | 0 |
[from(x1)] | = | 0 |
[sel(x1, x2)] | = | 30401 |
[s#(x1)] | = | 0 |
[mark(x1)] | = | x1 + 30403 |
[from#(x1)] | = | 0 |
[active(x1)] | = | x1 + 1 |
[cons(x1, x2)] | = | 1 |
[active#(x1)] | = | 0 |
from(active(X)) | → | from(X) | (10) |
from(mark(X)) | → | from(X) | (9) |
cons#(mark(X1),X2) | → | cons#(X1,X2) | (35) |
cons#(active(X1),X2) | → | cons#(X1,X2) | (38) |
The dependency pairs are split into 0 components.
from#(active(X)) | → | from#(X) | (51) |
from#(mark(X)) | → | from#(X) | (23) |
[cons#(x1, x2)] | = | 0 |
[s(x1)] | = | 0 |
[mark#(x1)] | = | 0 |
[0] | = | 1 |
[sel#(x1, x2)] | = | 0 |
[from(x1)] | = | 0 |
[sel(x1, x2)] | = | 49485 |
[s#(x1)] | = | 0 |
[mark(x1)] | = | x1 + 49487 |
[from#(x1)] | = | x1 + 0 |
[active(x1)] | = | x1 + 1 |
[cons(x1, x2)] | = | 1 |
[active#(x1)] | = | 0 |
from(active(X)) | → | from(X) | (10) |
from(mark(X)) | → | from(X) | (9) |
from#(active(X)) | → | from#(X) | (51) |
from#(mark(X)) | → | from#(X) | (23) |
The dependency pairs are split into 0 components.
s#(active(X)) | → | s#(X) | (46) |
s#(mark(X)) | → | s#(X) | (22) |
[cons#(x1, x2)] | = | 0 |
[s(x1)] | = | 0 |
[mark#(x1)] | = | 0 |
[0] | = | 1 |
[sel#(x1, x2)] | = | 0 |
[from(x1)] | = | 0 |
[sel(x1, x2)] | = | 15208 |
[s#(x1)] | = | x1 + 0 |
[mark(x1)] | = | x1 + 15210 |
[from#(x1)] | = | 0 |
[active(x1)] | = | x1 + 1 |
[cons(x1, x2)] | = | 46471 |
[active#(x1)] | = | 0 |
from(active(X)) | → | from(X) | (10) |
from(mark(X)) | → | from(X) | (9) |
s#(active(X)) | → | s#(X) | (46) |
s#(mark(X)) | → | s#(X) | (22) |
The dependency pairs are split into 0 components.
sel#(mark(X1),X2) | → | sel#(X1,X2) | (44) |
sel#(X1,mark(X2)) | → | sel#(X1,X2) | (37) |
sel#(X1,active(X2)) | → | sel#(X1,X2) | (36) |
sel#(active(X1),X2) | → | sel#(X1,X2) | (34) |
[cons#(x1, x2)] | = | 0 |
[s(x1)] | = | 0 |
[mark#(x1)] | = | 0 |
[0] | = | 1 |
[sel#(x1, x2)] | = | x1 + x2 + 0 |
[from(x1)] | = | 0 |
[sel(x1, x2)] | = | 1 |
[s#(x1)] | = | 0 |
[mark(x1)] | = | x1 + 3 |
[from#(x1)] | = | 0 |
[active(x1)] | = | x1 + 1 |
[cons(x1, x2)] | = | 1 |
[active#(x1)] | = | 0 |
from(active(X)) | → | from(X) | (10) |
from(mark(X)) | → | from(X) | (9) |
sel#(mark(X1),X2) | → | sel#(X1,X2) | (44) |
sel#(X1,mark(X2)) | → | sel#(X1,X2) | (37) |
sel#(X1,active(X2)) | → | sel#(X1,X2) | (36) |
sel#(active(X1),X2) | → | sel#(X1,X2) | (34) |
The dependency pairs are split into 0 components.