The rewrite relation of the following TRS is considered.
active(app(nil,YS)) | → | mark(YS) | (1) |
active(app(cons(X,XS),YS)) | → | mark(cons(X,app(XS,YS))) | (2) |
active(from(X)) | → | mark(cons(X,from(s(X)))) | (3) |
active(zWadr(nil,YS)) | → | mark(nil) | (4) |
active(zWadr(XS,nil)) | → | mark(nil) | (5) |
active(zWadr(cons(X,XS),cons(Y,YS))) | → | mark(cons(app(Y,cons(X,nil)),zWadr(XS,YS))) | (6) |
active(prefix(L)) | → | mark(cons(nil,zWadr(L,prefix(L)))) | (7) |
active(app(X1,X2)) | → | app(active(X1),X2) | (8) |
active(app(X1,X2)) | → | app(X1,active(X2)) | (9) |
active(cons(X1,X2)) | → | cons(active(X1),X2) | (10) |
active(from(X)) | → | from(active(X)) | (11) |
active(s(X)) | → | s(active(X)) | (12) |
active(zWadr(X1,X2)) | → | zWadr(active(X1),X2) | (13) |
active(zWadr(X1,X2)) | → | zWadr(X1,active(X2)) | (14) |
active(prefix(X)) | → | prefix(active(X)) | (15) |
app(mark(X1),X2) | → | mark(app(X1,X2)) | (16) |
app(X1,mark(X2)) | → | mark(app(X1,X2)) | (17) |
cons(mark(X1),X2) | → | mark(cons(X1,X2)) | (18) |
from(mark(X)) | → | mark(from(X)) | (19) |
s(mark(X)) | → | mark(s(X)) | (20) |
zWadr(mark(X1),X2) | → | mark(zWadr(X1,X2)) | (21) |
zWadr(X1,mark(X2)) | → | mark(zWadr(X1,X2)) | (22) |
prefix(mark(X)) | → | mark(prefix(X)) | (23) |
proper(app(X1,X2)) | → | app(proper(X1),proper(X2)) | (24) |
proper(nil) | → | ok(nil) | (25) |
proper(cons(X1,X2)) | → | cons(proper(X1),proper(X2)) | (26) |
proper(from(X)) | → | from(proper(X)) | (27) |
proper(s(X)) | → | s(proper(X)) | (28) |
proper(zWadr(X1,X2)) | → | zWadr(proper(X1),proper(X2)) | (29) |
proper(prefix(X)) | → | prefix(proper(X)) | (30) |
app(ok(X1),ok(X2)) | → | ok(app(X1,X2)) | (31) |
cons(ok(X1),ok(X2)) | → | ok(cons(X1,X2)) | (32) |
from(ok(X)) | → | ok(from(X)) | (33) |
s(ok(X)) | → | ok(s(X)) | (34) |
zWadr(ok(X1),ok(X2)) | → | ok(zWadr(X1,X2)) | (35) |
prefix(ok(X)) | → | ok(prefix(X)) | (36) |
top(mark(X)) | → | top(proper(X)) | (37) |
top(ok(X)) | → | top(active(X)) | (38) |
active#(app(cons(X,XS),YS)) | → | app#(XS,YS) | (39) |
proper#(from(X)) | → | proper#(X) | (40) |
active#(zWadr(X1,X2)) | → | active#(X2) | (41) |
active#(cons(X1,X2)) | → | cons#(active(X1),X2) | (42) |
from#(mark(X)) | → | from#(X) | (43) |
proper#(from(X)) | → | from#(proper(X)) | (44) |
s#(ok(X)) | → | s#(X) | (45) |
from#(ok(X)) | → | from#(X) | (46) |
proper#(cons(X1,X2)) | → | cons#(proper(X1),proper(X2)) | (47) |
active#(from(X)) | → | cons#(X,from(s(X))) | (48) |
proper#(cons(X1,X2)) | → | proper#(X1) | (49) |
active#(prefix(X)) | → | prefix#(active(X)) | (50) |
proper#(s(X)) | → | s#(proper(X)) | (51) |
zWadr#(ok(X1),ok(X2)) | → | zWadr#(X1,X2) | (52) |
active#(prefix(X)) | → | active#(X) | (53) |
active#(from(X)) | → | s#(X) | (54) |
zWadr#(X1,mark(X2)) | → | zWadr#(X1,X2) | (55) |
zWadr#(mark(X1),X2) | → | zWadr#(X1,X2) | (56) |
active#(zWadr(cons(X,XS),cons(Y,YS))) | → | cons#(X,nil) | (57) |
top#(ok(X)) | → | top#(active(X)) | (58) |
active#(zWadr(cons(X,XS),cons(Y,YS))) | → | cons#(app(Y,cons(X,nil)),zWadr(XS,YS)) | (59) |
active#(app(X1,X2)) | → | active#(X1) | (60) |
prefix#(mark(X)) | → | prefix#(X) | (61) |
proper#(app(X1,X2)) | → | proper#(X2) | (62) |
cons#(ok(X1),ok(X2)) | → | cons#(X1,X2) | (63) |
active#(zWadr(cons(X,XS),cons(Y,YS))) | → | app#(Y,cons(X,nil)) | (64) |
proper#(prefix(X)) | → | proper#(X) | (65) |
active#(app(X1,X2)) | → | app#(active(X1),X2) | (66) |
active#(zWadr(cons(X,XS),cons(Y,YS))) | → | zWadr#(XS,YS) | (67) |
proper#(prefix(X)) | → | prefix#(proper(X)) | (68) |
app#(mark(X1),X2) | → | app#(X1,X2) | (69) |
proper#(cons(X1,X2)) | → | proper#(X2) | (70) |
active#(s(X)) | → | s#(active(X)) | (71) |
active#(from(X)) | → | active#(X) | (72) |
top#(mark(X)) | → | top#(proper(X)) | (73) |
proper#(s(X)) | → | proper#(X) | (74) |
top#(ok(X)) | → | active#(X) | (75) |
active#(prefix(L)) | → | cons#(nil,zWadr(L,prefix(L))) | (76) |
proper#(zWadr(X1,X2)) | → | proper#(X2) | (77) |
app#(X1,mark(X2)) | → | app#(X1,X2) | (78) |
active#(zWadr(X1,X2)) | → | zWadr#(X1,active(X2)) | (79) |
proper#(app(X1,X2)) | → | proper#(X1) | (80) |
active#(prefix(L)) | → | zWadr#(L,prefix(L)) | (81) |
app#(ok(X1),ok(X2)) | → | app#(X1,X2) | (82) |
cons#(mark(X1),X2) | → | cons#(X1,X2) | (83) |
active#(app(X1,X2)) | → | app#(X1,active(X2)) | (84) |
s#(mark(X)) | → | s#(X) | (85) |
active#(from(X)) | → | from#(active(X)) | (86) |
active#(s(X)) | → | active#(X) | (87) |
active#(cons(X1,X2)) | → | active#(X1) | (88) |
proper#(app(X1,X2)) | → | app#(proper(X1),proper(X2)) | (89) |
active#(zWadr(X1,X2)) | → | active#(X1) | (90) |
proper#(zWadr(X1,X2)) | → | zWadr#(proper(X1),proper(X2)) | (91) |
active#(app(cons(X,XS),YS)) | → | cons#(X,app(XS,YS)) | (92) |
active#(from(X)) | → | from#(s(X)) | (93) |
top#(mark(X)) | → | proper#(X) | (94) |
active#(zWadr(X1,X2)) | → | zWadr#(active(X1),X2) | (95) |
proper#(zWadr(X1,X2)) | → | proper#(X1) | (96) |
prefix#(ok(X)) | → | prefix#(X) | (97) |
active#(app(X1,X2)) | → | active#(X2) | (98) |
The dependency pairs are split into 9 components.
top#(ok(X)) | → | top#(active(X)) | (58) |
top#(mark(X)) | → | top#(proper(X)) | (73) |
[cons#(x1, x2)] | = | 0 |
[s(x1)] | = | x1 + 1 |
[top(x1)] | = | 0 |
[top#(x1)] | = | x1 + 0 |
[prefix(x1)] | = | x1 + 64283 |
[zWadr#(x1, x2)] | = | 0 |
[zWadr(x1, x2)] | = | x1 + x2 + 2 |
[proper(x1)] | = | x1 + 0 |
[ok(x1)] | = | x1 + 0 |
[from(x1)] | = | x1 + 49044 |
[s#(x1)] | = | 0 |
[nil] | = | 15239 |
[mark(x1)] | = | x1 + 1 |
[prefix#(x1)] | = | 0 |
[app#(x1, x2)] | = | 0 |
[proper#(x1)] | = | 0 |
[from#(x1)] | = | 0 |
[active(x1)] | = | x1 + 0 |
[cons(x1, x2)] | = | x1 + 49043 |
[active#(x1)] | = | 0 |
[app(x1, x2)] | = | x1 + x2 + 1 |
cons(mark(X1),X2) | → | mark(cons(X1,X2)) | (18) |
active(zWadr(nil,YS)) | → | mark(nil) | (4) |
active(prefix(X)) | → | prefix(active(X)) | (15) |
active(app(X1,X2)) | → | app(active(X1),X2) | (8) |
active(app(nil,YS)) | → | mark(YS) | (1) |
active(from(X)) | → | mark(cons(X,from(s(X)))) | (3) |
app(mark(X1),X2) | → | mark(app(X1,X2)) | (16) |
zWadr(mark(X1),X2) | → | mark(zWadr(X1,X2)) | (21) |
prefix(ok(X)) | → | ok(prefix(X)) | (36) |
proper(cons(X1,X2)) | → | cons(proper(X1),proper(X2)) | (26) |
from(mark(X)) | → | mark(from(X)) | (19) |
cons(ok(X1),ok(X2)) | → | ok(cons(X1,X2)) | (32) |
app(X1,mark(X2)) | → | mark(app(X1,X2)) | (17) |
proper(from(X)) | → | from(proper(X)) | (27) |
s(ok(X)) | → | ok(s(X)) | (34) |
zWadr(X1,mark(X2)) | → | mark(zWadr(X1,X2)) | (22) |
proper(s(X)) | → | s(proper(X)) | (28) |
active(zWadr(XS,nil)) | → | mark(nil) | (5) |
from(ok(X)) | → | ok(from(X)) | (33) |
active(cons(X1,X2)) | → | cons(active(X1),X2) | (10) |
active(prefix(L)) | → | mark(cons(nil,zWadr(L,prefix(L)))) | (7) |
s(mark(X)) | → | mark(s(X)) | (20) |
proper(nil) | → | ok(nil) | (25) |
proper(prefix(X)) | → | prefix(proper(X)) | (30) |
active(zWadr(X1,X2)) | → | zWadr(X1,active(X2)) | (14) |
app(ok(X1),ok(X2)) | → | ok(app(X1,X2)) | (31) |
active(s(X)) | → | s(active(X)) | (12) |
prefix(mark(X)) | → | mark(prefix(X)) | (23) |
proper(app(X1,X2)) | → | app(proper(X1),proper(X2)) | (24) |
active(from(X)) | → | from(active(X)) | (11) |
active(app(X1,X2)) | → | app(X1,active(X2)) | (9) |
active(zWadr(X1,X2)) | → | zWadr(active(X1),X2) | (13) |
active(zWadr(cons(X,XS),cons(Y,YS))) | → | mark(cons(app(Y,cons(X,nil)),zWadr(XS,YS))) | (6) |
zWadr(ok(X1),ok(X2)) | → | ok(zWadr(X1,X2)) | (35) |
proper(zWadr(X1,X2)) | → | zWadr(proper(X1),proper(X2)) | (29) |
active(app(cons(X,XS),YS)) | → | mark(cons(X,app(XS,YS))) | (2) |
top#(mark(X)) | → | top#(proper(X)) | (73) |
The dependency pairs are split into 1 component.
top#(ok(X)) | → | top#(active(X)) | (58) |
[cons#(x1, x2)] | = | 0 |
[s(x1)] | = | x1 + 6812 |
[top(x1)] | = | 0 |
[top#(x1)] | = | x1 + 0 |
[prefix(x1)] | = | x1 + 1 |
[zWadr#(x1, x2)] | = | 0 |
[zWadr(x1, x2)] | = | x2 + 24324 |
[proper(x1)] | = | x1 + 49760 |
[ok(x1)] | = | x1 + 49760 |
[from(x1)] | = | x1 + 0 |
[s#(x1)] | = | 0 |
[nil] | = | 15240 |
[mark(x1)] | = | 1 |
[prefix#(x1)] | = | 0 |
[app#(x1, x2)] | = | 0 |
[proper#(x1)] | = | 0 |
[from#(x1)] | = | 0 |
[active(x1)] | = | x1 + 34837 |
[cons(x1, x2)] | = | x2 + 1 |
[active#(x1)] | = | 0 |
[app(x1, x2)] | = | x1 + 1 |
cons(mark(X1),X2) | → | mark(cons(X1,X2)) | (18) |
active(zWadr(nil,YS)) | → | mark(nil) | (4) |
active(prefix(X)) | → | prefix(active(X)) | (15) |
active(app(X1,X2)) | → | app(active(X1),X2) | (8) |
active(app(nil,YS)) | → | mark(YS) | (1) |
active(from(X)) | → | mark(cons(X,from(s(X)))) | (3) |
app(mark(X1),X2) | → | mark(app(X1,X2)) | (16) |
zWadr(mark(X1),X2) | → | mark(zWadr(X1,X2)) | (21) |
prefix(ok(X)) | → | ok(prefix(X)) | (36) |
proper(cons(X1,X2)) | → | cons(proper(X1),proper(X2)) | (26) |
from(mark(X)) | → | mark(from(X)) | (19) |
cons(ok(X1),ok(X2)) | → | ok(cons(X1,X2)) | (32) |
app(X1,mark(X2)) | → | mark(app(X1,X2)) | (17) |
proper(from(X)) | → | from(proper(X)) | (27) |
s(ok(X)) | → | ok(s(X)) | (34) |
zWadr(X1,mark(X2)) | → | mark(zWadr(X1,X2)) | (22) |
proper(s(X)) | → | s(proper(X)) | (28) |
active(zWadr(XS,nil)) | → | mark(nil) | (5) |
from(ok(X)) | → | ok(from(X)) | (33) |
active(cons(X1,X2)) | → | cons(active(X1),X2) | (10) |
active(prefix(L)) | → | mark(cons(nil,zWadr(L,prefix(L)))) | (7) |
s(mark(X)) | → | mark(s(X)) | (20) |
proper(nil) | → | ok(nil) | (25) |
proper(prefix(X)) | → | prefix(proper(X)) | (30) |
active(zWadr(X1,X2)) | → | zWadr(X1,active(X2)) | (14) |
app(ok(X1),ok(X2)) | → | ok(app(X1,X2)) | (31) |
active(s(X)) | → | s(active(X)) | (12) |
prefix(mark(X)) | → | mark(prefix(X)) | (23) |
proper(app(X1,X2)) | → | app(proper(X1),proper(X2)) | (24) |
active(from(X)) | → | from(active(X)) | (11) |
active(app(X1,X2)) | → | app(X1,active(X2)) | (9) |
active(zWadr(X1,X2)) | → | zWadr(active(X1),X2) | (13) |
active(zWadr(cons(X,XS),cons(Y,YS))) | → | mark(cons(app(Y,cons(X,nil)),zWadr(XS,YS))) | (6) |
zWadr(ok(X1),ok(X2)) | → | ok(zWadr(X1,X2)) | (35) |
proper(zWadr(X1,X2)) | → | zWadr(proper(X1),proper(X2)) | (29) |
active(app(cons(X,XS),YS)) | → | mark(cons(X,app(XS,YS))) | (2) |
top#(ok(X)) | → | top#(active(X)) | (58) |
The dependency pairs are split into 0 components.
proper#(cons(X1,X2)) | → | proper#(X2) | (70) |
proper#(zWadr(X1,X2)) | → | proper#(X1) | (96) |
proper#(prefix(X)) | → | proper#(X) | (65) |
proper#(app(X1,X2)) | → | proper#(X2) | (62) |
proper#(cons(X1,X2)) | → | proper#(X1) | (49) |
proper#(app(X1,X2)) | → | proper#(X1) | (80) |
proper#(zWadr(X1,X2)) | → | proper#(X2) | (77) |
proper#(s(X)) | → | proper#(X) | (74) |
proper#(from(X)) | → | proper#(X) | (40) |
[cons#(x1, x2)] | = | 0 |
[s(x1)] | = | x1 + 1 |
[top(x1)] | = | 0 |
[top#(x1)] | = | x1 + 0 |
[prefix(x1)] | = | x1 + 32582 |
[zWadr#(x1, x2)] | = | 0 |
[zWadr(x1, x2)] | = | x1 + x2 + 1 |
[proper(x1)] | = | x1 + 0 |
[ok(x1)] | = | 1 |
[from(x1)] | = | x1 + 436 |
[s#(x1)] | = | 0 |
[nil] | = | 1 |
[mark(x1)] | = | 26815 |
[prefix#(x1)] | = | 0 |
[app#(x1, x2)] | = | 0 |
[proper#(x1)] | = | x1 + 0 |
[from#(x1)] | = | 0 |
[active(x1)] | = | x1 + 38803 |
[cons(x1, x2)] | = | x1 + x2 + 1 |
[active#(x1)] | = | 0 |
[app(x1, x2)] | = | x1 + x2 + 1 |
cons(mark(X1),X2) | → | mark(cons(X1,X2)) | (18) |
active(zWadr(nil,YS)) | → | mark(nil) | (4) |
active(prefix(X)) | → | prefix(active(X)) | (15) |
active(app(X1,X2)) | → | app(active(X1),X2) | (8) |
active(app(nil,YS)) | → | mark(YS) | (1) |
active(from(X)) | → | mark(cons(X,from(s(X)))) | (3) |
app(mark(X1),X2) | → | mark(app(X1,X2)) | (16) |
zWadr(mark(X1),X2) | → | mark(zWadr(X1,X2)) | (21) |
prefix(ok(X)) | → | ok(prefix(X)) | (36) |
proper(cons(X1,X2)) | → | cons(proper(X1),proper(X2)) | (26) |
from(mark(X)) | → | mark(from(X)) | (19) |
cons(ok(X1),ok(X2)) | → | ok(cons(X1,X2)) | (32) |
app(X1,mark(X2)) | → | mark(app(X1,X2)) | (17) |
proper(from(X)) | → | from(proper(X)) | (27) |
s(ok(X)) | → | ok(s(X)) | (34) |
zWadr(X1,mark(X2)) | → | mark(zWadr(X1,X2)) | (22) |
proper(s(X)) | → | s(proper(X)) | (28) |
active(zWadr(XS,nil)) | → | mark(nil) | (5) |
from(ok(X)) | → | ok(from(X)) | (33) |
active(cons(X1,X2)) | → | cons(active(X1),X2) | (10) |
active(prefix(L)) | → | mark(cons(nil,zWadr(L,prefix(L)))) | (7) |
s(mark(X)) | → | mark(s(X)) | (20) |
proper(nil) | → | ok(nil) | (25) |
proper(prefix(X)) | → | prefix(proper(X)) | (30) |
active(zWadr(X1,X2)) | → | zWadr(X1,active(X2)) | (14) |
app(ok(X1),ok(X2)) | → | ok(app(X1,X2)) | (31) |
active(s(X)) | → | s(active(X)) | (12) |
prefix(mark(X)) | → | mark(prefix(X)) | (23) |
proper(app(X1,X2)) | → | app(proper(X1),proper(X2)) | (24) |
active(from(X)) | → | from(active(X)) | (11) |
active(app(X1,X2)) | → | app(X1,active(X2)) | (9) |
active(zWadr(X1,X2)) | → | zWadr(active(X1),X2) | (13) |
active(zWadr(cons(X,XS),cons(Y,YS))) | → | mark(cons(app(Y,cons(X,nil)),zWadr(XS,YS))) | (6) |
zWadr(ok(X1),ok(X2)) | → | ok(zWadr(X1,X2)) | (35) |
proper(zWadr(X1,X2)) | → | zWadr(proper(X1),proper(X2)) | (29) |
active(app(cons(X,XS),YS)) | → | mark(cons(X,app(XS,YS))) | (2) |
proper#(cons(X1,X2)) | → | proper#(X2) | (70) |
proper#(zWadr(X1,X2)) | → | proper#(X1) | (96) |
proper#(prefix(X)) | → | proper#(X) | (65) |
proper#(app(X1,X2)) | → | proper#(X2) | (62) |
proper#(cons(X1,X2)) | → | proper#(X1) | (49) |
proper#(app(X1,X2)) | → | proper#(X1) | (80) |
proper#(zWadr(X1,X2)) | → | proper#(X2) | (77) |
proper#(s(X)) | → | proper#(X) | (74) |
proper#(from(X)) | → | proper#(X) | (40) |
The dependency pairs are split into 0 components.
active#(app(X1,X2)) | → | active#(X2) | (98) |
active#(zWadr(X1,X2)) | → | active#(X1) | (90) |
active#(cons(X1,X2)) | → | active#(X1) | (88) |
active#(app(X1,X2)) | → | active#(X1) | (60) |
active#(s(X)) | → | active#(X) | (87) |
active#(prefix(X)) | → | active#(X) | (53) |
active#(zWadr(X1,X2)) | → | active#(X2) | (41) |
active#(from(X)) | → | active#(X) | (72) |
[cons#(x1, x2)] | = | 0 |
[s(x1)] | = | x1 + 1 |
[top(x1)] | = | 0 |
[top#(x1)] | = | x1 + 0 |
[prefix(x1)] | = | x1 + 30808 |
[zWadr#(x1, x2)] | = | 0 |
[zWadr(x1, x2)] | = | x1 + x2 + 1 |
[proper(x1)] | = | x1 + 0 |
[ok(x1)] | = | 1 |
[from(x1)] | = | x1 + 1 |
[s#(x1)] | = | 0 |
[nil] | = | 1 |
[mark(x1)] | = | 1 |
[prefix#(x1)] | = | 0 |
[app#(x1, x2)] | = | 0 |
[proper#(x1)] | = | 0 |
[from#(x1)] | = | 0 |
[active(x1)] | = | x1 + 1 |
[cons(x1, x2)] | = | x1 + x2 + 1 |
[active#(x1)] | = | x1 + 0 |
[app(x1, x2)] | = | x1 + x2 + 1 |
cons(mark(X1),X2) | → | mark(cons(X1,X2)) | (18) |
active(zWadr(nil,YS)) | → | mark(nil) | (4) |
active(prefix(X)) | → | prefix(active(X)) | (15) |
active(app(X1,X2)) | → | app(active(X1),X2) | (8) |
active(app(nil,YS)) | → | mark(YS) | (1) |
active(from(X)) | → | mark(cons(X,from(s(X)))) | (3) |
app(mark(X1),X2) | → | mark(app(X1,X2)) | (16) |
zWadr(mark(X1),X2) | → | mark(zWadr(X1,X2)) | (21) |
prefix(ok(X)) | → | ok(prefix(X)) | (36) |
proper(cons(X1,X2)) | → | cons(proper(X1),proper(X2)) | (26) |
from(mark(X)) | → | mark(from(X)) | (19) |
cons(ok(X1),ok(X2)) | → | ok(cons(X1,X2)) | (32) |
app(X1,mark(X2)) | → | mark(app(X1,X2)) | (17) |
proper(from(X)) | → | from(proper(X)) | (27) |
s(ok(X)) | → | ok(s(X)) | (34) |
zWadr(X1,mark(X2)) | → | mark(zWadr(X1,X2)) | (22) |
proper(s(X)) | → | s(proper(X)) | (28) |
active(zWadr(XS,nil)) | → | mark(nil) | (5) |
from(ok(X)) | → | ok(from(X)) | (33) |
active(cons(X1,X2)) | → | cons(active(X1),X2) | (10) |
active(prefix(L)) | → | mark(cons(nil,zWadr(L,prefix(L)))) | (7) |
s(mark(X)) | → | mark(s(X)) | (20) |
proper(nil) | → | ok(nil) | (25) |
proper(prefix(X)) | → | prefix(proper(X)) | (30) |
active(zWadr(X1,X2)) | → | zWadr(X1,active(X2)) | (14) |
app(ok(X1),ok(X2)) | → | ok(app(X1,X2)) | (31) |
active(s(X)) | → | s(active(X)) | (12) |
prefix(mark(X)) | → | mark(prefix(X)) | (23) |
proper(app(X1,X2)) | → | app(proper(X1),proper(X2)) | (24) |
active(from(X)) | → | from(active(X)) | (11) |
active(app(X1,X2)) | → | app(X1,active(X2)) | (9) |
active(zWadr(X1,X2)) | → | zWadr(active(X1),X2) | (13) |
active(zWadr(cons(X,XS),cons(Y,YS))) | → | mark(cons(app(Y,cons(X,nil)),zWadr(XS,YS))) | (6) |
zWadr(ok(X1),ok(X2)) | → | ok(zWadr(X1,X2)) | (35) |
proper(zWadr(X1,X2)) | → | zWadr(proper(X1),proper(X2)) | (29) |
active(app(cons(X,XS),YS)) | → | mark(cons(X,app(XS,YS))) | (2) |
active#(app(X1,X2)) | → | active#(X2) | (98) |
active#(zWadr(X1,X2)) | → | active#(X1) | (90) |
active#(cons(X1,X2)) | → | active#(X1) | (88) |
active#(app(X1,X2)) | → | active#(X1) | (60) |
active#(s(X)) | → | active#(X) | (87) |
active#(prefix(X)) | → | active#(X) | (53) |
active#(zWadr(X1,X2)) | → | active#(X2) | (41) |
active#(from(X)) | → | active#(X) | (72) |
The dependency pairs are split into 0 components.
zWadr#(mark(X1),X2) | → | zWadr#(X1,X2) | (56) |
zWadr#(X1,mark(X2)) | → | zWadr#(X1,X2) | (55) |
zWadr#(ok(X1),ok(X2)) | → | zWadr#(X1,X2) | (52) |
[cons#(x1, x2)] | = | 0 |
[s(x1)] | = | x1 + 0 |
[top(x1)] | = | 0 |
[top#(x1)] | = | 0 |
[prefix(x1)] | = | 32797 |
[zWadr#(x1, x2)] | = | x1 + 0 |
[zWadr(x1, x2)] | = | x2 + 0 |
[proper(x1)] | = | 32798 |
[ok(x1)] | = | x1 + 4 |
[from(x1)] | = | x1 + 0 |
[s#(x1)] | = | 0 |
[nil] | = | 32796 |
[mark(x1)] | = | x1 + 1 |
[prefix#(x1)] | = | 0 |
[app#(x1, x2)] | = | 0 |
[proper#(x1)] | = | 0 |
[from#(x1)] | = | 0 |
[active(x1)] | = | 32796 |
[cons(x1, x2)] | = | x1 + 0 |
[active#(x1)] | = | 0 |
[app(x1, x2)] | = | x1 + 0 |
zWadr#(mark(X1),X2) | → | zWadr#(X1,X2) | (56) |
zWadr#(ok(X1),ok(X2)) | → | zWadr#(X1,X2) | (52) |
The dependency pairs are split into 1 component.
zWadr#(X1,mark(X2)) | → | zWadr#(X1,X2) | (55) |
[cons#(x1, x2)] | = | 0 |
[s(x1)] | = | x1 + 0 |
[top(x1)] | = | 0 |
[top#(x1)] | = | 0 |
[prefix(x1)] | = | 2 |
[zWadr#(x1, x2)] | = | x2 + 0 |
[zWadr(x1, x2)] | = | x2 + 0 |
[proper(x1)] | = | 2 |
[ok(x1)] | = | x1 + 1 |
[from(x1)] | = | x1 + 0 |
[s#(x1)] | = | 0 |
[nil] | = | 6390 |
[mark(x1)] | = | x1 + 1 |
[prefix#(x1)] | = | 0 |
[app#(x1, x2)] | = | 0 |
[proper#(x1)] | = | 0 |
[from#(x1)] | = | 0 |
[active(x1)] | = | 1 |
[cons(x1, x2)] | = | x1 + 0 |
[active#(x1)] | = | 0 |
[app(x1, x2)] | = | x1 + 0 |
zWadr#(X1,mark(X2)) | → | zWadr#(X1,X2) | (55) |
The dependency pairs are split into 0 components.
cons#(ok(X1),ok(X2)) | → | cons#(X1,X2) | (63) |
cons#(mark(X1),X2) | → | cons#(X1,X2) | (83) |
[cons#(x1, x2)] | = | x1 + 0 |
[s(x1)] | = | x1 + 0 |
[top(x1)] | = | 0 |
[top#(x1)] | = | 0 |
[prefix(x1)] | = | 2 |
[zWadr#(x1, x2)] | = | 0 |
[zWadr(x1, x2)] | = | x2 + 0 |
[proper(x1)] | = | 2 |
[ok(x1)] | = | x1 + 20039 |
[from(x1)] | = | x1 + 0 |
[s#(x1)] | = | 0 |
[nil] | = | 6168 |
[mark(x1)] | = | x1 + 1 |
[prefix#(x1)] | = | 0 |
[app#(x1, x2)] | = | 0 |
[proper#(x1)] | = | 0 |
[from#(x1)] | = | 0 |
[active(x1)] | = | 1 |
[cons(x1, x2)] | = | x1 + 0 |
[active#(x1)] | = | 0 |
[app(x1, x2)] | = | x1 + 0 |
cons#(ok(X1),ok(X2)) | → | cons#(X1,X2) | (63) |
cons#(mark(X1),X2) | → | cons#(X1,X2) | (83) |
The dependency pairs are split into 0 components.
from#(ok(X)) | → | from#(X) | (46) |
from#(mark(X)) | → | from#(X) | (43) |
[cons#(x1, x2)] | = | 0 |
[s(x1)] | = | x1 + 0 |
[top(x1)] | = | 0 |
[top#(x1)] | = | 0 |
[prefix(x1)] | = | 2 |
[zWadr#(x1, x2)] | = | 0 |
[zWadr(x1, x2)] | = | x2 + 0 |
[proper(x1)] | = | 2 |
[ok(x1)] | = | x1 + 1 |
[from(x1)] | = | x1 + 0 |
[s#(x1)] | = | 0 |
[nil] | = | 2 |
[mark(x1)] | = | x1 + 1 |
[prefix#(x1)] | = | 0 |
[app#(x1, x2)] | = | 0 |
[proper#(x1)] | = | 0 |
[from#(x1)] | = | x1 + 0 |
[active(x1)] | = | 1 |
[cons(x1, x2)] | = | x1 + 0 |
[active#(x1)] | = | 0 |
[app(x1, x2)] | = | x1 + 0 |
from#(ok(X)) | → | from#(X) | (46) |
from#(mark(X)) | → | from#(X) | (43) |
The dependency pairs are split into 0 components.
s#(mark(X)) | → | s#(X) | (85) |
s#(ok(X)) | → | s#(X) | (45) |
[cons#(x1, x2)] | = | 0 |
[s(x1)] | = | x1 + 0 |
[top(x1)] | = | 0 |
[top#(x1)] | = | 0 |
[prefix(x1)] | = | 2 |
[zWadr#(x1, x2)] | = | 0 |
[zWadr(x1, x2)] | = | x2 + 0 |
[proper(x1)] | = | 2 |
[ok(x1)] | = | x1 + 5360 |
[from(x1)] | = | x1 + 0 |
[s#(x1)] | = | x1 + 0 |
[nil] | = | 570 |
[mark(x1)] | = | x1 + 1 |
[prefix#(x1)] | = | 0 |
[app#(x1, x2)] | = | 0 |
[proper#(x1)] | = | 0 |
[from#(x1)] | = | 0 |
[active(x1)] | = | 1 |
[cons(x1, x2)] | = | x1 + 0 |
[active#(x1)] | = | 0 |
[app(x1, x2)] | = | x1 + 0 |
s#(mark(X)) | → | s#(X) | (85) |
s#(ok(X)) | → | s#(X) | (45) |
The dependency pairs are split into 0 components.
app#(mark(X1),X2) | → | app#(X1,X2) | (69) |
app#(ok(X1),ok(X2)) | → | app#(X1,X2) | (82) |
app#(X1,mark(X2)) | → | app#(X1,X2) | (78) |
[cons#(x1, x2)] | = | 0 |
[s(x1)] | = | x1 + 0 |
[top(x1)] | = | 0 |
[top#(x1)] | = | 0 |
[prefix(x1)] | = | 2 |
[zWadr#(x1, x2)] | = | 0 |
[zWadr(x1, x2)] | = | x2 + 0 |
[proper(x1)] | = | 2 |
[ok(x1)] | = | x1 + 1 |
[from(x1)] | = | x1 + 0 |
[s#(x1)] | = | 0 |
[nil] | = | 570 |
[mark(x1)] | = | x1 + 1 |
[prefix#(x1)] | = | 0 |
[app#(x1, x2)] | = | x1 + x2 + 0 |
[proper#(x1)] | = | 0 |
[from#(x1)] | = | 0 |
[active(x1)] | = | 1 |
[cons(x1, x2)] | = | x1 + 0 |
[active#(x1)] | = | 0 |
[app(x1, x2)] | = | x1 + 0 |
app#(mark(X1),X2) | → | app#(X1,X2) | (69) |
app#(ok(X1),ok(X2)) | → | app#(X1,X2) | (82) |
app#(X1,mark(X2)) | → | app#(X1,X2) | (78) |
The dependency pairs are split into 0 components.
prefix#(ok(X)) | → | prefix#(X) | (97) |
prefix#(mark(X)) | → | prefix#(X) | (61) |
[cons#(x1, x2)] | = | 0 |
[s(x1)] | = | x1 + 0 |
[top(x1)] | = | 0 |
[top#(x1)] | = | 0 |
[prefix(x1)] | = | 2 |
[zWadr#(x1, x2)] | = | 0 |
[zWadr(x1, x2)] | = | x2 + 0 |
[proper(x1)] | = | 191 |
[ok(x1)] | = | x1 + 1 |
[from(x1)] | = | x1 + 0 |
[s#(x1)] | = | 0 |
[nil] | = | 570 |
[mark(x1)] | = | x1 + 1 |
[prefix#(x1)] | = | x1 + 0 |
[app#(x1, x2)] | = | 0 |
[proper#(x1)] | = | 0 |
[from#(x1)] | = | 0 |
[active(x1)] | = | 1 |
[cons(x1, x2)] | = | x1 + 0 |
[active#(x1)] | = | 0 |
[app(x1, x2)] | = | x1 + 0 |
prefix#(ok(X)) | → | prefix#(X) | (97) |
prefix#(mark(X)) | → | prefix#(X) | (61) |
The dependency pairs are split into 0 components.