The rewrite relation of the following TRS is considered.
active(from(X)) | → | mark(cons(X,from(s(X)))) | (1) |
active(after(0,XS)) | → | mark(XS) | (2) |
active(after(s(N),cons(X,XS))) | → | mark(after(N,XS)) | (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(after(X1,X2)) | → | active(after(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) |
after(mark(X1),X2) | → | after(X1,X2) | (17) |
after(X1,mark(X2)) | → | after(X1,X2) | (18) |
after(active(X1),X2) | → | after(X1,X2) | (19) |
after(X1,active(X2)) | → | after(X1,X2) | (20) |
mark#(s(X)) | → | active#(s(mark(X))) | (21) |
s#(mark(X)) | → | s#(X) | (22) |
from#(mark(X)) | → | from#(X) | (23) |
mark#(after(X1,X2)) | → | mark#(X1) | (24) |
cons#(X1,active(X2)) | → | cons#(X1,X2) | (25) |
mark#(after(X1,X2)) | → | active#(after(mark(X1),mark(X2))) | (26) |
active#(from(X)) | → | mark#(cons(X,from(s(X)))) | (27) |
active#(after(s(N),cons(X,XS))) | → | after#(N,XS) | (28) |
mark#(after(X1,X2)) | → | after#(mark(X1),mark(X2)) | (29) |
mark#(from(X)) | → | from#(mark(X)) | (30) |
mark#(after(X1,X2)) | → | mark#(X2) | (31) |
mark#(from(X)) | → | active#(from(mark(X))) | (32) |
active#(from(X)) | → | cons#(X,from(s(X))) | (33) |
after#(active(X1),X2) | → | after#(X1,X2) | (34) |
cons#(mark(X1),X2) | → | cons#(X1,X2) | (35) |
after#(X1,active(X2)) | → | after#(X1,X2) | (36) |
after#(X1,mark(X2)) | → | after#(X1,X2) | (37) |
cons#(active(X1),X2) | → | cons#(X1,X2) | (38) |
mark#(0) | → | active#(0) | (39) |
active#(after(s(N),cons(X,XS))) | → | mark#(after(N,XS)) | (40) |
active#(from(X)) | → | s#(X) | (41) |
mark#(cons(X1,X2)) | → | cons#(mark(X1),X2) | (42) |
mark#(from(X)) | → | mark#(X) | (43) |
after#(mark(X1),X2) | → | after#(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#(after(0,XS)) | → | mark#(XS) | (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#(after(X1,X2)) | → | mark#(X2) | (31) |
active#(after(0,XS)) | → | mark#(XS) | (49) |
active#(from(X)) | → | mark#(cons(X,from(s(X)))) | (27) |
mark#(cons(X1,X2)) | → | active#(cons(mark(X1),X2)) | (47) |
mark#(after(X1,X2)) | → | active#(after(mark(X1),mark(X2))) | (26) |
mark#(after(X1,X2)) | → | mark#(X1) | (24) |
mark#(from(X)) | → | mark#(X) | (43) |
active#(after(s(N),cons(X,XS))) | → | mark#(after(N,XS)) | (40) |
mark#(s(X)) | → | active#(s(mark(X))) | (21) |
[cons#(x1, x2)] | = | 0 |
[s(x1)] | = | 40651 |
[after(x1, x2)] | = | 52449 |
[mark#(x1)] | = | 52449 |
[0] | = | 1 |
[from(x1)] | = | 52449 |
[s#(x1)] | = | 0 |
[mark(x1)] | = | 1 |
[after#(x1, x2)] | = | 0 |
[from#(x1)] | = | 0 |
[active(x1)] | = | 2 |
[cons(x1, x2)] | = | 1 |
[active#(x1)] | = | x1 + 0 |
after(X1,mark(X2)) | → | after(X1,X2) | (18) |
s(mark(X)) | → | s(X) | (15) |
s(active(X)) | → | s(X) | (16) |
after(active(X1),X2) | → | after(X1,X2) | (19) |
after(mark(X1),X2) | → | after(X1,X2) | (17) |
from(active(X)) | → | from(X) | (10) |
after(X1,active(X2)) | → | after(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#(after(s(N),cons(X,XS))) | → | mark#(after(N,XS)) | (40) |
mark#(cons(X1,X2)) | → | mark#(X1) | (53) |
mark#(after(X1,X2)) | → | mark#(X2) | (31) |
mark#(after(X1,X2)) | → | mark#(X1) | (24) |
mark#(after(X1,X2)) | → | active#(after(mark(X1),mark(X2))) | (26) |
mark#(s(X)) | → | mark#(X) | (52) |
active#(after(0,XS)) | → | mark#(XS) | (49) |
[cons#(x1, x2)] | = | max(0) |
[s(x1)] | = | x1 + 0 |
[after(x1, x2)] | = | max(x1 + 10452, x2 + 1, 0) |
[mark#(x1)] | = | x1 + 0 |
[0] | = | 44083 |
[from(x1)] | = | x1 + 18818 |
[s#(x1)] | = | 0 |
[mark(x1)] | = | x1 + 0 |
[after#(x1, x2)] | = | max(0) |
[from#(x1)] | = | 0 |
[active(x1)] | = | x1 + 0 |
[cons(x1, x2)] | = | max(x1 + 18817, x2 + 0, 0) |
[active#(x1)] | = | x1 + 0 |
after(X1,mark(X2)) | → | after(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(after(s(N),cons(X,XS))) | → | mark(after(N,XS)) | (3) |
s(active(X)) | → | s(X) | (16) |
after(active(X1),X2) | → | after(X1,X2) | (19) |
after(mark(X1),X2) | → | after(X1,X2) | (17) |
mark(cons(X1,X2)) | → | active(cons(mark(X1),X2)) | (5) |
from(active(X)) | → | from(X) | (10) |
mark(after(X1,X2)) | → | active(after(mark(X1),mark(X2))) | (7) |
after(X1,active(X2)) | → | after(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(after(0,XS)) | → | mark(XS) | (2) |
mark#(from(X)) | → | mark#(X) | (43) |
mark#(cons(X1,X2)) | → | mark#(X1) | (53) |
mark#(after(X1,X2)) | → | mark#(X2) | (31) |
mark#(after(X1,X2)) | → | mark#(X1) | (24) |
active#(after(0,XS)) | → | mark#(XS) | (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#(after(s(N),cons(X,XS))) | → | mark#(after(N,XS)) | (40) |
mark#(after(X1,X2)) | → | active#(after(mark(X1),mark(X2))) | (26) |
mark#(s(X)) | → | mark#(X) | (52) |
[cons#(x1, x2)] | = | 0 |
[s(x1)] | = | x1 + 40651 |
[after(x1, x2)] | = | 21657 |
[mark#(x1)] | = | x1 + 30792 |
[0] | = | 1 |
[from(x1)] | = | 21658 |
[s#(x1)] | = | 0 |
[mark(x1)] | = | 1 |
[after#(x1, x2)] | = | 0 |
[from#(x1)] | = | 0 |
[active(x1)] | = | 2 |
[cons(x1, x2)] | = | 21656 |
[active#(x1)] | = | 52449 |
after(X1,mark(X2)) | → | after(X1,X2) | (18) |
after(active(X1),X2) | → | after(X1,X2) | (19) |
after(mark(X1),X2) | → | after(X1,X2) | (17) |
from(active(X)) | → | from(X) | (10) |
after(X1,active(X2)) | → | after(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#(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#(after(s(N),cons(X,XS))) | → | mark#(after(N,XS)) | (40) |
mark#(after(X1,X2)) | → | active#(after(mark(X1),mark(X2))) | (26) |
[cons#(x1, x2)] | = | 0 |
[s(x1)] | = | x1 + 16909 |
[after(x1, x2)] | = | x1 + x2 + 19428 |
[mark#(x1)] | = | x1 + 30792 |
[0] | = | 53516 |
[from(x1)] | = | 3037 |
[s#(x1)] | = | 0 |
[mark(x1)] | = | x1 + 0 |
[after#(x1, x2)] | = | 0 |
[from#(x1)] | = | 0 |
[active(x1)] | = | x1 + 0 |
[cons(x1, x2)] | = | x2 + 0 |
[active#(x1)] | = | x1 + 30791 |
after(X1,mark(X2)) | → | after(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(after(s(N),cons(X,XS))) | → | mark(after(N,XS)) | (3) |
s(active(X)) | → | s(X) | (16) |
after(active(X1),X2) | → | after(X1,X2) | (19) |
after(mark(X1),X2) | → | after(X1,X2) | (17) |
mark(cons(X1,X2)) | → | active(cons(mark(X1),X2)) | (5) |
from(active(X)) | → | from(X) | (10) |
mark(after(X1,X2)) | → | active(after(mark(X1),mark(X2))) | (7) |
after(X1,active(X2)) | → | after(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(after(0,XS)) | → | mark(XS) | (2) |
active#(after(s(N),cons(X,XS))) | → | mark#(after(N,XS)) | (40) |
mark#(after(X1,X2)) | → | active#(after(mark(X1),mark(X2))) | (26) |
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)] | = | x1 + x2 + 0 |
[s(x1)] | = | 29405 |
[after(x1, x2)] | = | x1 + 48664 |
[mark#(x1)] | = | 30792 |
[0] | = | 51696 |
[from(x1)] | = | 19791 |
[s#(x1)] | = | 0 |
[mark(x1)] | = | x1 + 0 |
[after#(x1, x2)] | = | 0 |
[from#(x1)] | = | 0 |
[active(x1)] | = | x1 + 7630 |
[cons(x1, x2)] | = | x1 + x2 + 7631 |
[active#(x1)] | = | 30791 |
from(active(X)) | → | from(X) | (10) |
from(mark(X)) | → | from(X) | (9) |
cons#(X1,active(X2)) | → | cons#(X1,X2) | (25) |
cons#(active(X1),X2) | → | cons#(X1,X2) | (38) |
The dependency pairs are split into 1 component.
cons#(X1,mark(X2)) | → | cons#(X1,X2) | (50) |
cons#(mark(X1),X2) | → | cons#(X1,X2) | (35) |
[cons#(x1, x2)] | = | x1 + 0 |
[s(x1)] | = | 1 |
[after(x1, x2)] | = | x1 + 22541 |
[mark#(x1)] | = | 30792 |
[0] | = | 1 |
[from(x1)] | = | 48581 |
[s#(x1)] | = | 0 |
[mark(x1)] | = | x1 + 1103 |
[after#(x1, x2)] | = | 0 |
[from#(x1)] | = | 0 |
[active(x1)] | = | x1 + 1104 |
[cons(x1, x2)] | = | x1 + x2 + 2 |
[active#(x1)] | = | 30791 |
from(active(X)) | → | from(X) | (10) |
from(mark(X)) | → | from(X) | (9) |
cons#(mark(X1),X2) | → | cons#(X1,X2) | (35) |
The dependency pairs are split into 1 component.
cons#(X1,mark(X2)) | → | cons#(X1,X2) | (50) |
[cons#(x1, x2)] | = | x2 + 0 |
[s(x1)] | = | 11820 |
[after(x1, x2)] | = | x1 + 19095 |
[mark#(x1)] | = | 30792 |
[0] | = | 20752 |
[from(x1)] | = | 44049 |
[s#(x1)] | = | 0 |
[mark(x1)] | = | x1 + 28872 |
[after#(x1, x2)] | = | 0 |
[from#(x1)] | = | 0 |
[active(x1)] | = | x1 + 28873 |
[cons(x1, x2)] | = | x1 + x2 + 2 |
[active#(x1)] | = | 30791 |
from(active(X)) | → | from(X) | (10) |
from(mark(X)) | → | from(X) | (9) |
cons#(X1,mark(X2)) | → | cons#(X1,X2) | (50) |
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)] | = | 1 |
[after(x1, x2)] | = | x1 + 14598 |
[mark#(x1)] | = | 30792 |
[0] | = | 31729 |
[from(x1)] | = | 36554 |
[s#(x1)] | = | 0 |
[mark(x1)] | = | x1 + 28872 |
[after#(x1, x2)] | = | 0 |
[from#(x1)] | = | x1 + 0 |
[active(x1)] | = | x1 + 28873 |
[cons(x1, x2)] | = | x1 + x2 + 2 |
[active#(x1)] | = | 30791 |
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)] | = | 1 |
[after(x1, x2)] | = | x1 + 31233 |
[mark#(x1)] | = | 30792 |
[0] | = | 1 |
[from(x1)] | = | 40400 |
[s#(x1)] | = | x1 + 0 |
[mark(x1)] | = | x1 + 28872 |
[after#(x1, x2)] | = | 0 |
[from#(x1)] | = | 0 |
[active(x1)] | = | x1 + 28873 |
[cons(x1, x2)] | = | x1 + x2 + 2 |
[active#(x1)] | = | 30791 |
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.
after#(mark(X1),X2) | → | after#(X1,X2) | (44) |
after#(X1,mark(X2)) | → | after#(X1,X2) | (37) |
after#(X1,active(X2)) | → | after#(X1,X2) | (36) |
after#(active(X1),X2) | → | after#(X1,X2) | (34) |
[cons#(x1, x2)] | = | 0 |
[s(x1)] | = | 3566 |
[after(x1, x2)] | = | x1 + 37790 |
[mark#(x1)] | = | 30792 |
[0] | = | 35475 |
[from(x1)] | = | 31135 |
[s#(x1)] | = | 0 |
[mark(x1)] | = | x1 + 14923 |
[after#(x1, x2)] | = | x1 + x2 + 0 |
[from#(x1)] | = | 0 |
[active(x1)] | = | x1 + 14924 |
[cons(x1, x2)] | = | x1 + x2 + 2 |
[active#(x1)] | = | 30791 |
from(active(X)) | → | from(X) | (10) |
from(mark(X)) | → | from(X) | (9) |
after#(mark(X1),X2) | → | after#(X1,X2) | (44) |
after#(X1,mark(X2)) | → | after#(X1,X2) | (37) |
after#(X1,active(X2)) | → | after#(X1,X2) | (36) |
after#(active(X1),X2) | → | after#(X1,X2) | (34) |
The dependency pairs are split into 0 components.