The rewrite relation of the following TRS is considered.
active(from(X)) | → | mark(cons(X,from(s(X)))) | (1) |
active(length(nil)) | → | mark(0) | (2) |
active(length(cons(X,Y))) | → | mark(s(length1(Y))) | (3) |
active(length1(X)) | → | mark(length(X)) | (4) |
mark(from(X)) | → | active(from(mark(X))) | (5) |
mark(cons(X1,X2)) | → | active(cons(mark(X1),X2)) | (6) |
mark(s(X)) | → | active(s(mark(X))) | (7) |
mark(length(X)) | → | active(length(X)) | (8) |
mark(nil) | → | active(nil) | (9) |
mark(0) | → | active(0) | (10) |
mark(length1(X)) | → | active(length1(X)) | (11) |
from(mark(X)) | → | from(X) | (12) |
from(active(X)) | → | from(X) | (13) |
cons(mark(X1),X2) | → | cons(X1,X2) | (14) |
cons(X1,mark(X2)) | → | cons(X1,X2) | (15) |
cons(active(X1),X2) | → | cons(X1,X2) | (16) |
cons(X1,active(X2)) | → | cons(X1,X2) | (17) |
s(mark(X)) | → | s(X) | (18) |
s(active(X)) | → | s(X) | (19) |
length(mark(X)) | → | length(X) | (20) |
length(active(X)) | → | length(X) | (21) |
length1(mark(X)) | → | length1(X) | (22) |
length1(active(X)) | → | length1(X) | (23) |
mark#(cons(X1,X2)) | → | active#(cons(mark(X1),X2)) | (24) |
active#(from(X)) | → | from#(s(X)) | (25) |
s#(mark(X)) | → | s#(X) | (26) |
mark#(nil) | → | active#(nil) | (27) |
mark#(s(X)) | → | s#(mark(X)) | (28) |
from#(mark(X)) | → | from#(X) | (29) |
length#(mark(X)) | → | length#(X) | (30) |
active#(length(cons(X,Y))) | → | mark#(s(length1(Y))) | (31) |
cons#(active(X1),X2) | → | cons#(X1,X2) | (32) |
mark#(s(X)) | → | active#(s(mark(X))) | (33) |
mark#(length(X)) | → | active#(length(X)) | (34) |
mark#(s(X)) | → | mark#(X) | (35) |
active#(from(X)) | → | s#(X) | (36) |
active#(length(cons(X,Y))) | → | s#(length1(Y)) | (37) |
cons#(X1,active(X2)) | → | cons#(X1,X2) | (38) |
mark#(length1(X)) | → | active#(length1(X)) | (39) |
cons#(mark(X1),X2) | → | cons#(X1,X2) | (40) |
active#(length1(X)) | → | mark#(length(X)) | (41) |
from#(active(X)) | → | from#(X) | (42) |
active#(from(X)) | → | cons#(X,from(s(X))) | (43) |
length#(active(X)) | → | length#(X) | (44) |
active#(length1(X)) | → | length#(X) | (45) |
active#(from(X)) | → | mark#(cons(X,from(s(X)))) | (46) |
mark#(from(X)) | → | from#(mark(X)) | (47) |
cons#(X1,mark(X2)) | → | cons#(X1,X2) | (48) |
length1#(mark(X)) | → | length1#(X) | (49) |
active#(length(cons(X,Y))) | → | length1#(Y) | (50) |
s#(active(X)) | → | s#(X) | (51) |
mark#(from(X)) | → | active#(from(mark(X))) | (52) |
mark#(cons(X1,X2)) | → | cons#(mark(X1),X2) | (53) |
active#(length(nil)) | → | mark#(0) | (54) |
length1#(active(X)) | → | length1#(X) | (55) |
mark#(0) | → | active#(0) | (56) |
mark#(cons(X1,X2)) | → | mark#(X1) | (57) |
mark#(from(X)) | → | mark#(X) | (58) |
The dependency pairs are split into 6 components.
mark#(from(X)) | → | mark#(X) | (58) |
mark#(cons(X1,X2)) | → | mark#(X1) | (57) |
mark#(s(X)) | → | mark#(X) | (35) |
mark#(length(X)) | → | active#(length(X)) | (34) |
mark#(s(X)) | → | active#(s(mark(X))) | (33) |
active#(length(cons(X,Y))) | → | mark#(s(length1(Y))) | (31) |
mark#(from(X)) | → | active#(from(mark(X))) | (52) |
active#(from(X)) | → | mark#(cons(X,from(s(X)))) | (46) |
active#(length1(X)) | → | mark#(length(X)) | (41) |
mark#(length1(X)) | → | active#(length1(X)) | (39) |
mark#(cons(X1,X2)) | → | active#(cons(mark(X1),X2)) | (24) |
[cons#(x1, x2)] | = | 0 |
[s(x1)] | = | 1 |
[length1#(x1)] | = | 0 |
[length1(x1)] | = | 2 |
[mark#(x1)] | = | 2 |
[0] | = | 1 |
[from(x1)] | = | 2 |
[s#(x1)] | = | 0 |
[nil] | = | 1 |
[mark(x1)] | = | 2 |
[from#(x1)] | = | 0 |
[active(x1)] | = | x1 + 0 |
[cons(x1, x2)] | = | 1 |
[active#(x1)] | = | x1 + 0 |
[length(x1)] | = | 2 |
[length#(x1)] | = | 0 |
s(mark(X)) | → | s(X) | (18) |
active(length1(X)) | → | mark(length(X)) | (4) |
cons(X1,mark(X2)) | → | cons(X1,X2) | (15) |
mark(length(X)) | → | active(length(X)) | (8) |
active(from(X)) | → | mark(cons(X,from(s(X)))) | (1) |
active(length(cons(X,Y))) | → | mark(s(length1(Y))) | (3) |
cons(active(X1),X2) | → | cons(X1,X2) | (16) |
length(active(X)) | → | length(X) | (21) |
s(active(X)) | → | s(X) | (19) |
cons(X1,active(X2)) | → | cons(X1,X2) | (17) |
length1(mark(X)) | → | length1(X) | (22) |
mark(from(X)) | → | active(from(mark(X))) | (5) |
mark(0) | → | active(0) | (10) |
mark(s(X)) | → | active(s(mark(X))) | (7) |
length(mark(X)) | → | length(X) | (20) |
cons(mark(X1),X2) | → | cons(X1,X2) | (14) |
from(mark(X)) | → | from(X) | (12) |
length1(active(X)) | → | length1(X) | (23) |
mark(length1(X)) | → | active(length1(X)) | (11) |
mark(nil) | → | active(nil) | (9) |
from(active(X)) | → | from(X) | (13) |
mark(cons(X1,X2)) | → | active(cons(mark(X1),X2)) | (6) |
active(length(nil)) | → | mark(0) | (2) |
mark#(s(X)) | → | active#(s(mark(X))) | (33) |
mark#(cons(X1,X2)) | → | active#(cons(mark(X1),X2)) | (24) |
The dependency pairs are split into 1 component.
active#(length1(X)) | → | mark#(length(X)) | (41) |
mark#(length(X)) | → | active#(length(X)) | (34) |
active#(from(X)) | → | mark#(cons(X,from(s(X)))) | (46) |
active#(length(cons(X,Y))) | → | mark#(s(length1(Y))) | (31) |
mark#(from(X)) | → | mark#(X) | (58) |
mark#(from(X)) | → | active#(from(mark(X))) | (52) |
mark#(s(X)) | → | mark#(X) | (35) |
mark#(length1(X)) | → | active#(length1(X)) | (39) |
mark#(cons(X1,X2)) | → | mark#(X1) | (57) |
[cons#(x1, x2)] | = | 0 |
[s(x1)] | = | x1 + 0 |
[length1#(x1)] | = | 0 |
[length1(x1)] | = | 20977 |
[mark#(x1)] | = | x1 + 2 |
[0] | = | 679 |
[from(x1)] | = | x1 + 31894 |
[s#(x1)] | = | 0 |
[nil] | = | 40587 |
[mark(x1)] | = | x1 + 0 |
[from#(x1)] | = | 0 |
[active(x1)] | = | x1 + 0 |
[cons(x1, x2)] | = | x1 + 1 |
[active#(x1)] | = | x1 + 2 |
[length(x1)] | = | 20977 |
[length#(x1)] | = | 0 |
s(mark(X)) | → | s(X) | (18) |
active(length1(X)) | → | mark(length(X)) | (4) |
cons(X1,mark(X2)) | → | cons(X1,X2) | (15) |
mark(length(X)) | → | active(length(X)) | (8) |
active(from(X)) | → | mark(cons(X,from(s(X)))) | (1) |
active(length(cons(X,Y))) | → | mark(s(length1(Y))) | (3) |
cons(active(X1),X2) | → | cons(X1,X2) | (16) |
length(active(X)) | → | length(X) | (21) |
s(active(X)) | → | s(X) | (19) |
cons(X1,active(X2)) | → | cons(X1,X2) | (17) |
length1(mark(X)) | → | length1(X) | (22) |
mark(from(X)) | → | active(from(mark(X))) | (5) |
mark(0) | → | active(0) | (10) |
mark(s(X)) | → | active(s(mark(X))) | (7) |
length(mark(X)) | → | length(X) | (20) |
cons(mark(X1),X2) | → | cons(X1,X2) | (14) |
from(mark(X)) | → | from(X) | (12) |
length1(active(X)) | → | length1(X) | (23) |
mark(length1(X)) | → | active(length1(X)) | (11) |
mark(nil) | → | active(nil) | (9) |
from(active(X)) | → | from(X) | (13) |
mark(cons(X1,X2)) | → | active(cons(mark(X1),X2)) | (6) |
active(length(nil)) | → | mark(0) | (2) |
active#(from(X)) | → | mark#(cons(X,from(s(X)))) | (46) |
mark#(from(X)) | → | mark#(X) | (58) |
mark#(cons(X1,X2)) | → | mark#(X1) | (57) |
The dependency pairs are split into 1 component.
active#(length1(X)) | → | mark#(length(X)) | (41) |
mark#(length(X)) | → | active#(length(X)) | (34) |
active#(length(cons(X,Y))) | → | mark#(s(length1(Y))) | (31) |
mark#(from(X)) | → | active#(from(mark(X))) | (52) |
mark#(s(X)) | → | mark#(X) | (35) |
mark#(length1(X)) | → | active#(length1(X)) | (39) |
[cons#(x1, x2)] | = | 0 |
[s(x1)] | = | x1 + 0 |
[length1#(x1)] | = | 0 |
[length1(x1)] | = | 1 |
[mark#(x1)] | = | x1 + 1 |
[0] | = | 1 |
[from(x1)] | = | x1 + 6880 |
[s#(x1)] | = | 0 |
[nil] | = | 29091 |
[mark(x1)] | = | x1 + 2 |
[from#(x1)] | = | 0 |
[active(x1)] | = | x1 + 1 |
[cons(x1, x2)] | = | x1 + x2 + 29534 |
[active#(x1)] | = | 2 |
[length(x1)] | = | 1 |
[length#(x1)] | = | 0 |
s(mark(X)) | → | s(X) | (18) |
cons(X1,mark(X2)) | → | cons(X1,X2) | (15) |
cons(active(X1),X2) | → | cons(X1,X2) | (16) |
length(active(X)) | → | length(X) | (21) |
s(active(X)) | → | s(X) | (19) |
cons(X1,active(X2)) | → | cons(X1,X2) | (17) |
length1(mark(X)) | → | length1(X) | (22) |
length(mark(X)) | → | length(X) | (20) |
cons(mark(X1),X2) | → | cons(X1,X2) | (14) |
from(mark(X)) | → | from(X) | (12) |
length1(active(X)) | → | length1(X) | (23) |
from(active(X)) | → | from(X) | (13) |
mark#(from(X)) | → | active#(from(mark(X))) | (52) |
The dependency pairs are split into 1 component.
active#(length1(X)) | → | mark#(length(X)) | (41) |
mark#(length(X)) | → | active#(length(X)) | (34) |
active#(length(cons(X,Y))) | → | mark#(s(length1(Y))) | (31) |
mark#(s(X)) | → | mark#(X) | (35) |
mark#(length1(X)) | → | active#(length1(X)) | (39) |
[cons#(x1, x2)] | = | max(0) |
[s(x1)] | = | x1 + 2438 |
[length1#(x1)] | = | 0 |
[length1(x1)] | = | x1 + 3 |
[mark#(x1)] | = | x1 + 1 |
[0] | = | 0 |
[from(x1)] | = | 0 |
[s#(x1)] | = | 0 |
[nil] | = | 0 |
[mark(x1)] | = | x1 + 0 |
[from#(x1)] | = | 0 |
[active(x1)] | = | x1 + 0 |
[cons(x1, x2)] | = | max(x1 + 2442, x2 + 2442, 0) |
[active#(x1)] | = | x1 + 0 |
[length(x1)] | = | x1 + 1 |
[length#(x1)] | = | 0 |
s(mark(X)) | → | s(X) | (18) |
length(active(X)) | → | length(X) | (21) |
s(active(X)) | → | s(X) | (19) |
length1(mark(X)) | → | length1(X) | (22) |
length(mark(X)) | → | length(X) | (20) |
length1(active(X)) | → | length1(X) | (23) |
active#(length1(X)) | → | mark#(length(X)) | (41) |
mark#(length(X)) | → | active#(length(X)) | (34) |
active#(length(cons(X,Y))) | → | mark#(s(length1(Y))) | (31) |
mark#(s(X)) | → | mark#(X) | (35) |
mark#(length1(X)) | → | active#(length1(X)) | (39) |
The dependency pairs are split into 0 components.
length1#(active(X)) | → | length1#(X) | (55) |
length1#(mark(X)) | → | length1#(X) | (49) |
[cons#(x1, x2)] | = | 0 |
[s(x1)] | = | 26448 |
[length1#(x1)] | = | x1 + 0 |
[length1(x1)] | = | 1 |
[mark#(x1)] | = | 0 |
[0] | = | 43715 |
[from(x1)] | = | 7177 |
[s#(x1)] | = | 0 |
[nil] | = | 24446 |
[mark(x1)] | = | x1 + 1 |
[from#(x1)] | = | 0 |
[active(x1)] | = | x1 + 2 |
[cons(x1, x2)] | = | x1 + 7179 |
[active#(x1)] | = | 0 |
[length(x1)] | = | x1 + 19267 |
[length#(x1)] | = | 0 |
s(mark(X)) | → | s(X) | (18) |
s(active(X)) | → | s(X) | (19) |
length1(mark(X)) | → | length1(X) | (22) |
length1(active(X)) | → | length1(X) | (23) |
length1#(active(X)) | → | length1#(X) | (55) |
length1#(mark(X)) | → | length1#(X) | (49) |
The dependency pairs are split into 0 components.
from#(mark(X)) | → | from#(X) | (29) |
from#(active(X)) | → | from#(X) | (42) |
[cons#(x1, x2)] | = | 0 |
[s(x1)] | = | 91980 |
[length1#(x1)] | = | 0 |
[length1(x1)] | = | 1 |
[mark#(x1)] | = | 0 |
[0] | = | 85653 |
[from(x1)] | = | 8405 |
[s#(x1)] | = | 0 |
[nil] | = | 29936 |
[mark(x1)] | = | x1 + 1 |
[from#(x1)] | = | x1 + 0 |
[active(x1)] | = | x1 + 27858 |
[cons(x1, x2)] | = | x1 + 36263 |
[active#(x1)] | = | 0 |
[length(x1)] | = | x1 + 27859 |
[length#(x1)] | = | 0 |
s(mark(X)) | → | s(X) | (18) |
s(active(X)) | → | s(X) | (19) |
length1(mark(X)) | → | length1(X) | (22) |
length1(active(X)) | → | length1(X) | (23) |
from#(mark(X)) | → | from#(X) | (29) |
from#(active(X)) | → | from#(X) | (42) |
The dependency pairs are split into 0 components.
s#(active(X)) | → | s#(X) | (51) |
s#(mark(X)) | → | s#(X) | (26) |
[cons#(x1, x2)] | = | 0 |
[s(x1)] | = | 92124 |
[length1#(x1)] | = | 0 |
[length1(x1)] | = | 1 |
[mark#(x1)] | = | 0 |
[0] | = | 85653 |
[from(x1)] | = | 18005 |
[s#(x1)] | = | x1 + 0 |
[nil] | = | 33088 |
[mark(x1)] | = | x1 + 16674 |
[from#(x1)] | = | 0 |
[active(x1)] | = | x1 + 41379 |
[cons(x1, x2)] | = | x1 + 42711 |
[active#(x1)] | = | 0 |
[length(x1)] | = | x1 + 24707 |
[length#(x1)] | = | 0 |
s(mark(X)) | → | s(X) | (18) |
s(active(X)) | → | s(X) | (19) |
length1(mark(X)) | → | length1(X) | (22) |
length1(active(X)) | → | length1(X) | (23) |
s#(active(X)) | → | s#(X) | (51) |
s#(mark(X)) | → | s#(X) | (26) |
The dependency pairs are split into 0 components.
length#(mark(X)) | → | length#(X) | (30) |
length#(active(X)) | → | length#(X) | (44) |
[cons#(x1, x2)] | = | 0 |
[s(x1)] | = | 34772 |
[length1#(x1)] | = | 0 |
[length1(x1)] | = | 28938 |
[mark#(x1)] | = | 0 |
[0] | = | 32095 |
[from(x1)] | = | 5828 |
[s#(x1)] | = | 0 |
[nil] | = | 1 |
[mark(x1)] | = | x1 + 16674 |
[from#(x1)] | = | 0 |
[active(x1)] | = | x1 + 16675 |
[cons(x1, x2)] | = | x1 + 5830 |
[active#(x1)] | = | 0 |
[length(x1)] | = | x1 + 28940 |
[length#(x1)] | = | x1 + 0 |
s(mark(X)) | → | s(X) | (18) |
s(active(X)) | → | s(X) | (19) |
length1(mark(X)) | → | length1(X) | (22) |
length1(active(X)) | → | length1(X) | (23) |
length#(mark(X)) | → | length#(X) | (30) |
length#(active(X)) | → | length#(X) | (44) |
The dependency pairs are split into 0 components.
cons#(active(X1),X2) | → | cons#(X1,X2) | (32) |
cons#(X1,mark(X2)) | → | cons#(X1,X2) | (48) |
cons#(mark(X1),X2) | → | cons#(X1,X2) | (40) |
cons#(X1,active(X2)) | → | cons#(X1,X2) | (38) |
[cons#(x1, x2)] | = | x1 + x2 + 0 |
[s(x1)] | = | 34772 |
[length1#(x1)] | = | 0 |
[length1(x1)] | = | 1 |
[mark#(x1)] | = | 0 |
[0] | = | 6 |
[from(x1)] | = | 1 |
[s#(x1)] | = | 0 |
[nil] | = | 1 |
[mark(x1)] | = | x1 + 16674 |
[from#(x1)] | = | 0 |
[active(x1)] | = | x1 + 16675 |
[cons(x1, x2)] | = | x1 + 3 |
[active#(x1)] | = | 0 |
[length(x1)] | = | x1 + 3 |
[length#(x1)] | = | 0 |
s(mark(X)) | → | s(X) | (18) |
s(active(X)) | → | s(X) | (19) |
length1(mark(X)) | → | length1(X) | (22) |
length1(active(X)) | → | length1(X) | (23) |
cons#(active(X1),X2) | → | cons#(X1,X2) | (32) |
cons#(X1,mark(X2)) | → | cons#(X1,X2) | (48) |
cons#(mark(X1),X2) | → | cons#(X1,X2) | (40) |
cons#(X1,active(X2)) | → | cons#(X1,X2) | (38) |
The dependency pairs are split into 0 components.