The rewrite relation of the following TRS is considered.
active(2nd(cons(X,cons(Y,Z)))) | → | mark(Y) | (1) |
active(from(X)) | → | mark(cons(X,from(s(X)))) | (2) |
mark(2nd(X)) | → | active(2nd(mark(X))) | (3) |
mark(cons(X1,X2)) | → | active(cons(mark(X1),X2)) | (4) |
mark(from(X)) | → | active(from(mark(X))) | (5) |
mark(s(X)) | → | active(s(mark(X))) | (6) |
2nd(mark(X)) | → | 2nd(X) | (7) |
2nd(active(X)) | → | 2nd(X) | (8) |
cons(mark(X1),X2) | → | cons(X1,X2) | (9) |
cons(X1,mark(X2)) | → | cons(X1,X2) | (10) |
cons(active(X1),X2) | → | cons(X1,X2) | (11) |
cons(X1,active(X2)) | → | cons(X1,X2) | (12) |
from(mark(X)) | → | from(X) | (13) |
from(active(X)) | → | from(X) | (14) |
s(mark(X)) | → | s(X) | (15) |
s(active(X)) | → | s(X) | (16) |
active#(from(X)) | → | cons#(X,from(s(X))) | (17) |
mark#(s(X)) | → | s#(mark(X)) | (18) |
2nd#(mark(X)) | → | 2nd#(X) | (19) |
cons#(mark(X1),X2) | → | cons#(X1,X2) | (20) |
cons#(X1,active(X2)) | → | cons#(X1,X2) | (21) |
s#(mark(X)) | → | s#(X) | (22) |
2nd#(active(X)) | → | 2nd#(X) | (23) |
from#(active(X)) | → | from#(X) | (24) |
cons#(X1,mark(X2)) | → | cons#(X1,X2) | (25) |
mark#(cons(X1,X2)) | → | active#(cons(mark(X1),X2)) | (26) |
mark#(2nd(X)) | → | 2nd#(mark(X)) | (27) |
mark#(s(X)) | → | mark#(X) | (28) |
cons#(active(X1),X2) | → | cons#(X1,X2) | (29) |
mark#(s(X)) | → | active#(s(mark(X))) | (30) |
active#(2nd(cons(X,cons(Y,Z)))) | → | mark#(Y) | (31) |
mark#(cons(X1,X2)) | → | mark#(X1) | (32) |
mark#(from(X)) | → | mark#(X) | (33) |
mark#(2nd(X)) | → | active#(2nd(mark(X))) | (34) |
mark#(cons(X1,X2)) | → | cons#(mark(X1),X2) | (35) |
mark#(2nd(X)) | → | mark#(X) | (36) |
mark#(from(X)) | → | from#(mark(X)) | (37) |
active#(from(X)) | → | from#(s(X)) | (38) |
active#(from(X)) | → | mark#(cons(X,from(s(X)))) | (39) |
from#(mark(X)) | → | from#(X) | (40) |
mark#(from(X)) | → | active#(from(mark(X))) | (41) |
active#(from(X)) | → | s#(X) | (42) |
s#(active(X)) | → | s#(X) | (43) |
The dependency pairs are split into 5 components.
mark#(cons(X1,X2)) | → | active#(cons(mark(X1),X2)) | (26) |
mark#(from(X)) | → | active#(from(mark(X))) | (41) |
active#(from(X)) | → | mark#(cons(X,from(s(X)))) | (39) |
mark#(2nd(X)) | → | mark#(X) | (36) |
mark#(2nd(X)) | → | active#(2nd(mark(X))) | (34) |
mark#(from(X)) | → | mark#(X) | (33) |
mark#(cons(X1,X2)) | → | mark#(X1) | (32) |
active#(2nd(cons(X,cons(Y,Z)))) | → | mark#(Y) | (31) |
mark#(s(X)) | → | active#(s(mark(X))) | (30) |
mark#(s(X)) | → | mark#(X) | (28) |
[cons#(x1, x2)] | = | 0 |
[s(x1)] | = | 8366 |
[2nd(x1)] | = | 8857 |
[mark#(x1)] | = | 8857 |
[from(x1)] | = | 8857 |
[s#(x1)] | = | 0 |
[2nd#(x1)] | = | 0 |
[mark(x1)] | = | 8857 |
[from#(x1)] | = | 0 |
[active(x1)] | = | x1 + 0 |
[cons(x1, x2)] | = | 8856 |
[active#(x1)] | = | x1 + 0 |
mark(cons(X1,X2)) | → | active(cons(mark(X1),X2)) | (4) |
s(mark(X)) | → | s(X) | (15) |
2nd(active(X)) | → | 2nd(X) | (8) |
active(2nd(cons(X,cons(Y,Z)))) | → | mark(Y) | (1) |
mark(2nd(X)) | → | active(2nd(mark(X))) | (3) |
s(active(X)) | → | s(X) | (16) |
mark(from(X)) | → | active(from(mark(X))) | (5) |
cons(X1,mark(X2)) | → | cons(X1,X2) | (10) |
2nd(mark(X)) | → | 2nd(X) | (7) |
from(active(X)) | → | from(X) | (14) |
cons(X1,active(X2)) | → | cons(X1,X2) | (12) |
cons(active(X1),X2) | → | cons(X1,X2) | (11) |
cons(mark(X1),X2) | → | cons(X1,X2) | (9) |
from(mark(X)) | → | from(X) | (13) |
mark(s(X)) | → | active(s(mark(X))) | (6) |
active(from(X)) | → | mark(cons(X,from(s(X)))) | (2) |
mark#(cons(X1,X2)) | → | active#(cons(mark(X1),X2)) | (26) |
mark#(s(X)) | → | active#(s(mark(X))) | (30) |
The dependency pairs are split into 1 component.
mark#(cons(X1,X2)) | → | mark#(X1) | (32) |
active#(2nd(cons(X,cons(Y,Z)))) | → | mark#(Y) | (31) |
mark#(2nd(X)) | → | mark#(X) | (36) |
mark#(2nd(X)) | → | active#(2nd(mark(X))) | (34) |
mark#(from(X)) | → | mark#(X) | (33) |
mark#(from(X)) | → | active#(from(mark(X))) | (41) |
mark#(s(X)) | → | mark#(X) | (28) |
active#(from(X)) | → | mark#(cons(X,from(s(X)))) | (39) |
[cons#(x1, x2)] | = | max(0) |
[s(x1)] | = | x1 + 0 |
[2nd(x1)] | = | x1 + 8366 |
[mark#(x1)] | = | x1 + 0 |
[from(x1)] | = | x1 + 11799 |
[s#(x1)] | = | 0 |
[2nd#(x1)] | = | 0 |
[mark(x1)] | = | x1 + 0 |
[from#(x1)] | = | 0 |
[active(x1)] | = | x1 + 0 |
[cons(x1, x2)] | = | max(x1 + 11798, x2 + 0, 0) |
[active#(x1)] | = | x1 + 0 |
mark(cons(X1,X2)) | → | active(cons(mark(X1),X2)) | (4) |
s(mark(X)) | → | s(X) | (15) |
2nd(active(X)) | → | 2nd(X) | (8) |
active(2nd(cons(X,cons(Y,Z)))) | → | mark(Y) | (1) |
mark(2nd(X)) | → | active(2nd(mark(X))) | (3) |
s(active(X)) | → | s(X) | (16) |
mark(from(X)) | → | active(from(mark(X))) | (5) |
cons(X1,mark(X2)) | → | cons(X1,X2) | (10) |
2nd(mark(X)) | → | 2nd(X) | (7) |
from(active(X)) | → | from(X) | (14) |
cons(X1,active(X2)) | → | cons(X1,X2) | (12) |
cons(active(X1),X2) | → | cons(X1,X2) | (11) |
cons(mark(X1),X2) | → | cons(X1,X2) | (9) |
from(mark(X)) | → | from(X) | (13) |
mark(s(X)) | → | active(s(mark(X))) | (6) |
active(from(X)) | → | mark(cons(X,from(s(X)))) | (2) |
mark#(cons(X1,X2)) | → | mark#(X1) | (32) |
active#(2nd(cons(X,cons(Y,Z)))) | → | mark#(Y) | (31) |
mark#(2nd(X)) | → | mark#(X) | (36) |
mark#(from(X)) | → | mark#(X) | (33) |
The dependency pairs are split into 1 component.
mark#(2nd(X)) | → | active#(2nd(mark(X))) | (34) |
mark#(from(X)) | → | active#(from(mark(X))) | (41) |
mark#(s(X)) | → | mark#(X) | (28) |
active#(from(X)) | → | mark#(cons(X,from(s(X)))) | (39) |
[cons#(x1, x2)] | = | 0 |
[s(x1)] | = | 52870 |
[2nd(x1)] | = | 52868 |
[mark#(x1)] | = | 52870 |
[from(x1)] | = | 52870 |
[s#(x1)] | = | 0 |
[2nd#(x1)] | = | 0 |
[mark(x1)] | = | 52870 |
[from#(x1)] | = | 0 |
[active(x1)] | = | x1 + 1 |
[cons(x1, x2)] | = | 0 |
[active#(x1)] | = | x1 + 0 |
s(mark(X)) | → | s(X) | (15) |
2nd(active(X)) | → | 2nd(X) | (8) |
s(active(X)) | → | s(X) | (16) |
cons(X1,mark(X2)) | → | cons(X1,X2) | (10) |
2nd(mark(X)) | → | 2nd(X) | (7) |
from(active(X)) | → | from(X) | (14) |
cons(X1,active(X2)) | → | cons(X1,X2) | (12) |
cons(active(X1),X2) | → | cons(X1,X2) | (11) |
cons(mark(X1),X2) | → | cons(X1,X2) | (9) |
from(mark(X)) | → | from(X) | (13) |
mark#(2nd(X)) | → | active#(2nd(mark(X))) | (34) |
The dependency pairs are split into 1 component.
mark#(from(X)) | → | active#(from(mark(X))) | (41) |
mark#(s(X)) | → | mark#(X) | (28) |
active#(from(X)) | → | mark#(cons(X,from(s(X)))) | (39) |
[cons#(x1, x2)] | = | 0 |
[s(x1)] | = | x1 + 52870 |
[2nd(x1)] | = | 52868 |
[mark#(x1)] | = | x1 + 0 |
[from(x1)] | = | 42006 |
[s#(x1)] | = | 0 |
[2nd#(x1)] | = | 0 |
[mark(x1)] | = | 1 |
[from#(x1)] | = | 0 |
[active(x1)] | = | 1 |
[cons(x1, x2)] | = | 42004 |
[active#(x1)] | = | 42005 |
mark(cons(X1,X2)) | → | active(cons(mark(X1),X2)) | (4) |
active(2nd(cons(X,cons(Y,Z)))) | → | mark(Y) | (1) |
mark(2nd(X)) | → | active(2nd(mark(X))) | (3) |
mark(from(X)) | → | active(from(mark(X))) | (5) |
cons(X1,mark(X2)) | → | cons(X1,X2) | (10) |
cons(X1,active(X2)) | → | cons(X1,X2) | (12) |
cons(active(X1),X2) | → | cons(X1,X2) | (11) |
cons(mark(X1),X2) | → | cons(X1,X2) | (9) |
mark(s(X)) | → | active(s(mark(X))) | (6) |
active(from(X)) | → | mark(cons(X,from(s(X)))) | (2) |
mark#(from(X)) | → | active#(from(mark(X))) | (41) |
mark#(s(X)) | → | mark#(X) | (28) |
active#(from(X)) | → | mark#(cons(X,from(s(X)))) | (39) |
The dependency pairs are split into 0 components.
from#(active(X)) | → | from#(X) | (24) |
from#(mark(X)) | → | from#(X) | (40) |
[cons#(x1, x2)] | = | 0 |
[s(x1)] | = | x1 + 1 |
[2nd(x1)] | = | 0 |
[mark#(x1)] | = | x1 + 0 |
[from(x1)] | = | 0 |
[s#(x1)] | = | 0 |
[2nd#(x1)] | = | 0 |
[mark(x1)] | = | x1 + 12618 |
[from#(x1)] | = | x1 + 0 |
[active(x1)] | = | x1 + 12619 |
[cons(x1, x2)] | = | 0 |
[active#(x1)] | = | 42005 |
cons(X1,mark(X2)) | → | cons(X1,X2) | (10) |
cons(X1,active(X2)) | → | cons(X1,X2) | (12) |
cons(active(X1),X2) | → | cons(X1,X2) | (11) |
cons(mark(X1),X2) | → | cons(X1,X2) | (9) |
from#(active(X)) | → | from#(X) | (24) |
from#(mark(X)) | → | from#(X) | (40) |
The dependency pairs are split into 0 components.
s#(active(X)) | → | s#(X) | (43) |
s#(mark(X)) | → | s#(X) | (22) |
[cons#(x1, x2)] | = | 0 |
[s(x1)] | = | x1 + 1 |
[2nd(x1)] | = | 0 |
[mark#(x1)] | = | x1 + 0 |
[from(x1)] | = | 0 |
[s#(x1)] | = | x1 + 0 |
[2nd#(x1)] | = | 0 |
[mark(x1)] | = | x1 + 868 |
[from#(x1)] | = | 0 |
[active(x1)] | = | x1 + 869 |
[cons(x1, x2)] | = | 0 |
[active#(x1)] | = | 42005 |
cons(X1,mark(X2)) | → | cons(X1,X2) | (10) |
cons(X1,active(X2)) | → | cons(X1,X2) | (12) |
cons(active(X1),X2) | → | cons(X1,X2) | (11) |
cons(mark(X1),X2) | → | cons(X1,X2) | (9) |
s#(active(X)) | → | s#(X) | (43) |
s#(mark(X)) | → | s#(X) | (22) |
The dependency pairs are split into 0 components.
cons#(X1,mark(X2)) | → | cons#(X1,X2) | (25) |
cons#(X1,active(X2)) | → | cons#(X1,X2) | (21) |
cons#(mark(X1),X2) | → | cons#(X1,X2) | (20) |
cons#(active(X1),X2) | → | cons#(X1,X2) | (29) |
[cons#(x1, x2)] | = | x2 + 0 |
[s(x1)] | = | x1 + 1 |
[2nd(x1)] | = | 0 |
[mark#(x1)] | = | x1 + 0 |
[from(x1)] | = | 0 |
[s#(x1)] | = | 0 |
[2nd#(x1)] | = | 0 |
[mark(x1)] | = | x1 + 868 |
[from#(x1)] | = | 0 |
[active(x1)] | = | x1 + 869 |
[cons(x1, x2)] | = | 0 |
[active#(x1)] | = | 42005 |
cons(X1,mark(X2)) | → | cons(X1,X2) | (10) |
cons(X1,active(X2)) | → | cons(X1,X2) | (12) |
cons(active(X1),X2) | → | cons(X1,X2) | (11) |
cons(mark(X1),X2) | → | cons(X1,X2) | (9) |
cons#(X1,mark(X2)) | → | cons#(X1,X2) | (25) |
cons#(X1,active(X2)) | → | cons#(X1,X2) | (21) |
The dependency pairs are split into 1 component.
cons#(active(X1),X2) | → | cons#(X1,X2) | (29) |
cons#(mark(X1),X2) | → | cons#(X1,X2) | (20) |
[cons#(x1, x2)] | = | x1 + 0 |
[s(x1)] | = | x1 + 1 |
[2nd(x1)] | = | 0 |
[mark#(x1)] | = | x1 + 0 |
[from(x1)] | = | 0 |
[s#(x1)] | = | 0 |
[2nd#(x1)] | = | 0 |
[mark(x1)] | = | x1 + 868 |
[from#(x1)] | = | 0 |
[active(x1)] | = | x1 + 869 |
[cons(x1, x2)] | = | 0 |
[active#(x1)] | = | 42005 |
cons(X1,mark(X2)) | → | cons(X1,X2) | (10) |
cons(X1,active(X2)) | → | cons(X1,X2) | (12) |
cons(active(X1),X2) | → | cons(X1,X2) | (11) |
cons(mark(X1),X2) | → | cons(X1,X2) | (9) |
cons#(active(X1),X2) | → | cons#(X1,X2) | (29) |
cons#(mark(X1),X2) | → | cons#(X1,X2) | (20) |
The dependency pairs are split into 0 components.
2nd#(active(X)) | → | 2nd#(X) | (23) |
2nd#(mark(X)) | → | 2nd#(X) | (19) |
[cons#(x1, x2)] | = | 0 |
[s(x1)] | = | x1 + 1 |
[2nd(x1)] | = | 0 |
[mark#(x1)] | = | x1 + 0 |
[from(x1)] | = | 0 |
[s#(x1)] | = | 0 |
[2nd#(x1)] | = | x1 + 0 |
[mark(x1)] | = | x1 + 868 |
[from#(x1)] | = | 0 |
[active(x1)] | = | x1 + 869 |
[cons(x1, x2)] | = | 0 |
[active#(x1)] | = | 42005 |
cons(X1,mark(X2)) | → | cons(X1,X2) | (10) |
cons(X1,active(X2)) | → | cons(X1,X2) | (12) |
cons(active(X1),X2) | → | cons(X1,X2) | (11) |
cons(mark(X1),X2) | → | cons(X1,X2) | (9) |
2nd#(active(X)) | → | 2nd#(X) | (23) |
2nd#(mark(X)) | → | 2nd#(X) | (19) |
The dependency pairs are split into 0 components.