The rewrite relation of the following TRS is considered.
active(eq(0,0)) | → | mark(true) | (1) |
active(eq(s(X),s(Y))) | → | mark(eq(X,Y)) | (2) |
active(eq(X,Y)) | → | mark(false) | (3) |
active(inf(X)) | → | mark(cons(X,inf(s(X)))) | (4) |
active(take(0,X)) | → | mark(nil) | (5) |
active(take(s(X),cons(Y,L))) | → | mark(cons(Y,take(X,L))) | (6) |
active(length(nil)) | → | mark(0) | (7) |
active(length(cons(X,L))) | → | mark(s(length(L))) | (8) |
active(inf(X)) | → | inf(active(X)) | (9) |
active(take(X1,X2)) | → | take(active(X1),X2) | (10) |
active(take(X1,X2)) | → | take(X1,active(X2)) | (11) |
active(length(X)) | → | length(active(X)) | (12) |
inf(mark(X)) | → | mark(inf(X)) | (13) |
take(mark(X1),X2) | → | mark(take(X1,X2)) | (14) |
take(X1,mark(X2)) | → | mark(take(X1,X2)) | (15) |
length(mark(X)) | → | mark(length(X)) | (16) |
proper(eq(X1,X2)) | → | eq(proper(X1),proper(X2)) | (17) |
proper(0) | → | ok(0) | (18) |
proper(true) | → | ok(true) | (19) |
proper(s(X)) | → | s(proper(X)) | (20) |
proper(false) | → | ok(false) | (21) |
proper(inf(X)) | → | inf(proper(X)) | (22) |
proper(cons(X1,X2)) | → | cons(proper(X1),proper(X2)) | (23) |
proper(take(X1,X2)) | → | take(proper(X1),proper(X2)) | (24) |
proper(nil) | → | ok(nil) | (25) |
proper(length(X)) | → | length(proper(X)) | (26) |
eq(ok(X1),ok(X2)) | → | ok(eq(X1,X2)) | (27) |
s(ok(X)) | → | ok(s(X)) | (28) |
inf(ok(X)) | → | ok(inf(X)) | (29) |
cons(ok(X1),ok(X2)) | → | ok(cons(X1,X2)) | (30) |
take(ok(X1),ok(X2)) | → | ok(take(X1,X2)) | (31) |
length(ok(X)) | → | ok(length(X)) | (32) |
top(mark(X)) | → | top(proper(X)) | (33) |
top(ok(X)) | → | top(active(X)) | (34) |
inf#(ok(X)) | → | inf#(X) | (35) |
active#(inf(X)) | → | cons#(X,inf(s(X))) | (36) |
proper#(inf(X)) | → | proper#(X) | (37) |
proper#(eq(X1,X2)) | → | proper#(X2) | (38) |
take#(X1,mark(X2)) | → | take#(X1,X2) | (39) |
active#(length(cons(X,L))) | → | length#(L) | (40) |
proper#(length(X)) | → | length#(proper(X)) | (41) |
proper#(length(X)) | → | proper#(X) | (42) |
active#(inf(X)) | → | inf#(active(X)) | (43) |
active#(length(cons(X,L))) | → | s#(length(L)) | (44) |
proper#(cons(X1,X2)) | → | cons#(proper(X1),proper(X2)) | (45) |
active#(take(X1,X2)) | → | active#(X2) | (46) |
proper#(take(X1,X2)) | → | proper#(X1) | (47) |
active#(take(X1,X2)) | → | active#(X1) | (48) |
active#(take(X1,X2)) | → | take#(active(X1),X2) | (49) |
active#(inf(X)) | → | s#(X) | (50) |
proper#(take(X1,X2)) | → | proper#(X2) | (51) |
top#(ok(X)) | → | active#(X) | (52) |
proper#(cons(X1,X2)) | → | proper#(X1) | (53) |
top#(ok(X)) | → | top#(active(X)) | (54) |
top#(mark(X)) | → | top#(proper(X)) | (55) |
cons#(ok(X1),ok(X2)) | → | cons#(X1,X2) | (56) |
active#(inf(X)) | → | active#(X) | (57) |
length#(mark(X)) | → | length#(X) | (58) |
proper#(take(X1,X2)) | → | take#(proper(X1),proper(X2)) | (59) |
proper#(eq(X1,X2)) | → | eq#(proper(X1),proper(X2)) | (60) |
inf#(mark(X)) | → | inf#(X) | (61) |
active#(inf(X)) | → | inf#(s(X)) | (62) |
proper#(inf(X)) | → | inf#(proper(X)) | (63) |
proper#(s(X)) | → | proper#(X) | (64) |
proper#(eq(X1,X2)) | → | proper#(X1) | (65) |
s#(ok(X)) | → | s#(X) | (66) |
active#(length(X)) | → | active#(X) | (67) |
eq#(ok(X1),ok(X2)) | → | eq#(X1,X2) | (68) |
take#(mark(X1),X2) | → | take#(X1,X2) | (69) |
top#(mark(X)) | → | proper#(X) | (70) |
length#(ok(X)) | → | length#(X) | (71) |
proper#(s(X)) | → | s#(proper(X)) | (72) |
active#(length(X)) | → | length#(active(X)) | (73) |
active#(take(s(X),cons(Y,L))) | → | cons#(Y,take(X,L)) | (74) |
active#(eq(s(X),s(Y))) | → | eq#(X,Y) | (75) |
active#(take(X1,X2)) | → | take#(X1,active(X2)) | (76) |
proper#(cons(X1,X2)) | → | proper#(X2) | (77) |
active#(take(s(X),cons(Y,L))) | → | take#(X,L) | (78) |
take#(ok(X1),ok(X2)) | → | take#(X1,X2) | (79) |
The dependency pairs are split into 9 components.
top#(mark(X)) | → | top#(proper(X)) | (55) |
top#(ok(X)) | → | top#(active(X)) | (54) |
[cons#(x1, x2)] | = |
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[s(x1)] | = |
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[take#(x1, x2)] | = |
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[take(x1, x2)] | = |
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[top(x1)] | = |
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[eq(x1, x2)] | = |
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[false] | = |
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[top#(x1)] | = |
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[true] | = |
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[eq#(x1, x2)] | = |
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[proper(x1)] | = |
x1 +
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[ok(x1)] | = |
x1 +
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[0] | = |
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[s#(x1)] | = |
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[nil] | = |
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[mark(x1)] | = |
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[proper#(x1)] | = |
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[inf#(x1)] | = |
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[active(x1)] | = |
x1 +
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[cons(x1, x2)] | = |
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[active#(x1)] | = |
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[length(x1)] | = |
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[length#(x1)] | = |
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[inf(x1)] | = |
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proper(0) | → | ok(0) | (18) |
active(inf(X)) | → | mark(cons(X,inf(s(X)))) | (4) |
take(X1,mark(X2)) | → | mark(take(X1,X2)) | (15) |
active(length(cons(X,L))) | → | mark(s(length(L))) | (8) |
active(eq(0,0)) | → | mark(true) | (1) |
active(eq(X,Y)) | → | mark(false) | (3) |
length(mark(X)) | → | mark(length(X)) | (16) |
proper(false) | → | ok(false) | (21) |
proper(length(X)) | → | length(proper(X)) | (26) |
proper(true) | → | ok(true) | (19) |
length(ok(X)) | → | ok(length(X)) | (32) |
proper(eq(X1,X2)) | → | eq(proper(X1),proper(X2)) | (17) |
eq(ok(X1),ok(X2)) | → | ok(eq(X1,X2)) | (27) |
proper(inf(X)) | → | inf(proper(X)) | (22) |
s(ok(X)) | → | ok(s(X)) | (28) |
active(take(0,X)) | → | mark(nil) | (5) |
active(take(X1,X2)) | → | take(active(X1),X2) | (10) |
active(length(nil)) | → | mark(0) | (7) |
proper(s(X)) | → | s(proper(X)) | (20) |
proper(nil) | → | ok(nil) | (25) |
cons(ok(X1),ok(X2)) | → | ok(cons(X1,X2)) | (30) |
take(mark(X1),X2) | → | mark(take(X1,X2)) | (14) |
take(ok(X1),ok(X2)) | → | ok(take(X1,X2)) | (31) |
active(length(X)) | → | length(active(X)) | (12) |
proper(cons(X1,X2)) | → | cons(proper(X1),proper(X2)) | (23) |
proper(take(X1,X2)) | → | take(proper(X1),proper(X2)) | (24) |
active(take(X1,X2)) | → | take(X1,active(X2)) | (11) |
active(inf(X)) | → | inf(active(X)) | (9) |
inf(mark(X)) | → | mark(inf(X)) | (13) |
active(take(s(X),cons(Y,L))) | → | mark(cons(Y,take(X,L))) | (6) |
inf(ok(X)) | → | ok(inf(X)) | (29) |
active(eq(s(X),s(Y))) | → | mark(eq(X,Y)) | (2) |
top#(mark(X)) | → | top#(proper(X)) | (55) |
The dependency pairs are split into 1 component.
top#(ok(X)) | → | top#(active(X)) | (54) |
[cons#(x1, x2)] | = | 0 |
[s(x1)] | = | x1 + 0 |
[take#(x1, x2)] | = | 0 |
[take(x1, x2)] | = | x1 + 0 |
[top(x1)] | = | 0 |
[eq(x1, x2)] | = | x2 + 0 |
[false] | = | 1 |
[top#(x1)] | = | x1 + 0 |
[true] | = | 1 |
[eq#(x1, x2)] | = | 0 |
[proper(x1)] | = | 33019 |
[ok(x1)] | = | x1 + 33018 |
[0] | = | 1 |
[s#(x1)] | = | 0 |
[nil] | = | 1 |
[mark(x1)] | = | 0 |
[proper#(x1)] | = | 0 |
[inf#(x1)] | = | 0 |
[active(x1)] | = | x1 + 33017 |
[cons(x1, x2)] | = | x1 + 0 |
[active#(x1)] | = | 0 |
[length(x1)] | = | x1 + 0 |
[length#(x1)] | = | 0 |
[inf(x1)] | = | x1 + 0 |
proper(0) | → | ok(0) | (18) |
active(inf(X)) | → | mark(cons(X,inf(s(X)))) | (4) |
take(X1,mark(X2)) | → | mark(take(X1,X2)) | (15) |
active(length(cons(X,L))) | → | mark(s(length(L))) | (8) |
active(eq(0,0)) | → | mark(true) | (1) |
active(eq(X,Y)) | → | mark(false) | (3) |
length(mark(X)) | → | mark(length(X)) | (16) |
proper(false) | → | ok(false) | (21) |
proper(length(X)) | → | length(proper(X)) | (26) |
proper(true) | → | ok(true) | (19) |
length(ok(X)) | → | ok(length(X)) | (32) |
proper(eq(X1,X2)) | → | eq(proper(X1),proper(X2)) | (17) |
eq(ok(X1),ok(X2)) | → | ok(eq(X1,X2)) | (27) |
proper(inf(X)) | → | inf(proper(X)) | (22) |
s(ok(X)) | → | ok(s(X)) | (28) |
active(take(0,X)) | → | mark(nil) | (5) |
active(take(X1,X2)) | → | take(active(X1),X2) | (10) |
active(length(nil)) | → | mark(0) | (7) |
proper(s(X)) | → | s(proper(X)) | (20) |
proper(nil) | → | ok(nil) | (25) |
cons(ok(X1),ok(X2)) | → | ok(cons(X1,X2)) | (30) |
take(mark(X1),X2) | → | mark(take(X1,X2)) | (14) |
take(ok(X1),ok(X2)) | → | ok(take(X1,X2)) | (31) |
active(length(X)) | → | length(active(X)) | (12) |
proper(cons(X1,X2)) | → | cons(proper(X1),proper(X2)) | (23) |
proper(take(X1,X2)) | → | take(proper(X1),proper(X2)) | (24) |
active(take(X1,X2)) | → | take(X1,active(X2)) | (11) |
active(inf(X)) | → | inf(active(X)) | (9) |
inf(mark(X)) | → | mark(inf(X)) | (13) |
active(take(s(X),cons(Y,L))) | → | mark(cons(Y,take(X,L))) | (6) |
inf(ok(X)) | → | ok(inf(X)) | (29) |
active(eq(s(X),s(Y))) | → | mark(eq(X,Y)) | (2) |
top#(ok(X)) | → | top#(active(X)) | (54) |
The dependency pairs are split into 0 components.
active#(take(X1,X2)) | → | active#(X1) | (48) |
active#(take(X1,X2)) | → | active#(X2) | (46) |
active#(length(X)) | → | active#(X) | (67) |
active#(inf(X)) | → | active#(X) | (57) |
[cons#(x1, x2)] | = | 0 |
[s(x1)] | = | x1 + 0 |
[take#(x1, x2)] | = | 0 |
[take(x1, x2)] | = | x1 + x2 + 0 |
[top(x1)] | = | 0 |
[eq(x1, x2)] | = | x2 + 0 |
[false] | = | 1 |
[top#(x1)] | = | 0 |
[true] | = | 1 |
[eq#(x1, x2)] | = | 0 |
[proper(x1)] | = | 3 |
[ok(x1)] | = | x1 + 1 |
[0] | = | 2 |
[s#(x1)] | = | 0 |
[nil] | = | 1 |
[mark(x1)] | = | x1 + 1 |
[proper#(x1)] | = | 0 |
[inf#(x1)] | = | 0 |
[active(x1)] | = | x1 + 0 |
[cons(x1, x2)] | = | x1 + x2 + 0 |
[active#(x1)] | = | x1 + 0 |
[length(x1)] | = | x1 + 0 |
[length#(x1)] | = | 0 |
[inf(x1)] | = | x1 + 1 |
proper(0) | → | ok(0) | (18) |
take(X1,mark(X2)) | → | mark(take(X1,X2)) | (15) |
active(eq(0,0)) | → | mark(true) | (1) |
length(mark(X)) | → | mark(length(X)) | (16) |
proper(false) | → | ok(false) | (21) |
proper(true) | → | ok(true) | (19) |
length(ok(X)) | → | ok(length(X)) | (32) |
eq(ok(X1),ok(X2)) | → | ok(eq(X1,X2)) | (27) |
s(ok(X)) | → | ok(s(X)) | (28) |
active(take(0,X)) | → | mark(nil) | (5) |
proper(nil) | → | ok(nil) | (25) |
cons(ok(X1),ok(X2)) | → | ok(cons(X1,X2)) | (30) |
take(mark(X1),X2) | → | mark(take(X1,X2)) | (14) |
take(ok(X1),ok(X2)) | → | ok(take(X1,X2)) | (31) |
inf(mark(X)) | → | mark(inf(X)) | (13) |
inf(ok(X)) | → | ok(inf(X)) | (29) |
active#(inf(X)) | → | active#(X) | (57) |
The dependency pairs are split into 1 component.
active#(take(X1,X2)) | → | active#(X1) | (48) |
active#(length(X)) | → | active#(X) | (67) |
active#(take(X1,X2)) | → | active#(X2) | (46) |
[cons#(x1, x2)] | = | 0 |
[s(x1)] | = | 0 |
[take#(x1, x2)] | = | 0 |
[take(x1, x2)] | = | x1 + x2 + 0 |
[top(x1)] | = | 0 |
[eq(x1, x2)] | = | x2 + 1 |
[false] | = | 1 |
[top#(x1)] | = | 0 |
[true] | = | 0 |
[eq#(x1, x2)] | = | 0 |
[proper(x1)] | = | x1 + 1 |
[ok(x1)] | = | 1 |
[0] | = | 1 |
[s#(x1)] | = | 0 |
[nil] | = | 0 |
[mark(x1)] | = | x1 + 1 |
[proper#(x1)] | = | 0 |
[inf#(x1)] | = | 0 |
[active(x1)] | = | 0 |
[cons(x1, x2)] | = | x1 + x2 + 0 |
[active#(x1)] | = | x1 + 0 |
[length(x1)] | = | x1 + 1 |
[length#(x1)] | = | 0 |
[inf(x1)] | = | x1 + 1 |
proper(0) | → | ok(0) | (18) |
take(X1,mark(X2)) | → | mark(take(X1,X2)) | (15) |
length(mark(X)) | → | mark(length(X)) | (16) |
proper(false) | → | ok(false) | (21) |
proper(true) | → | ok(true) | (19) |
length(ok(X)) | → | ok(length(X)) | (32) |
eq(ok(X1),ok(X2)) | → | ok(eq(X1,X2)) | (27) |
proper(nil) | → | ok(nil) | (25) |
cons(ok(X1),ok(X2)) | → | ok(cons(X1,X2)) | (30) |
take(mark(X1),X2) | → | mark(take(X1,X2)) | (14) |
take(ok(X1),ok(X2)) | → | ok(take(X1,X2)) | (31) |
inf(mark(X)) | → | mark(inf(X)) | (13) |
inf(ok(X)) | → | ok(inf(X)) | (29) |
active#(length(X)) | → | active#(X) | (67) |
The dependency pairs are split into 1 component.
active#(take(X1,X2)) | → | active#(X1) | (48) |
active#(take(X1,X2)) | → | active#(X2) | (46) |
[cons#(x1, x2)] | = | 0 |
[s(x1)] | = | x1 + 1 |
[take#(x1, x2)] | = | 0 |
[take(x1, x2)] | = | x1 + x2 + 1 |
[top(x1)] | = | 0 |
[eq(x1, x2)] | = | x1 + 1 |
[false] | = | 1 |
[top#(x1)] | = | 0 |
[true] | = | 1 |
[eq#(x1, x2)] | = | 0 |
[proper(x1)] | = | x1 + 0 |
[ok(x1)] | = | x1 + 0 |
[0] | = | 1 |
[s#(x1)] | = | 0 |
[nil] | = | 0 |
[mark(x1)] | = | 5 |
[proper#(x1)] | = | 0 |
[inf#(x1)] | = | 0 |
[active(x1)] | = | x1 + 1 |
[cons(x1, x2)] | = | 1 |
[active#(x1)] | = | x1 + 0 |
[length(x1)] | = | x1 + 1 |
[length#(x1)] | = | 0 |
[inf(x1)] | = | x1 + 1 |
proper(0) | → | ok(0) | (18) |
take(X1,mark(X2)) | → | mark(take(X1,X2)) | (15) |
length(mark(X)) | → | mark(length(X)) | (16) |
proper(false) | → | ok(false) | (21) |
proper(length(X)) | → | length(proper(X)) | (26) |
proper(true) | → | ok(true) | (19) |
length(ok(X)) | → | ok(length(X)) | (32) |
proper(eq(X1,X2)) | → | eq(proper(X1),proper(X2)) | (17) |
eq(ok(X1),ok(X2)) | → | ok(eq(X1,X2)) | (27) |
proper(inf(X)) | → | inf(proper(X)) | (22) |
s(ok(X)) | → | ok(s(X)) | (28) |
proper(s(X)) | → | s(proper(X)) | (20) |
proper(nil) | → | ok(nil) | (25) |
cons(ok(X1),ok(X2)) | → | ok(cons(X1,X2)) | (30) |
take(mark(X1),X2) | → | mark(take(X1,X2)) | (14) |
take(ok(X1),ok(X2)) | → | ok(take(X1,X2)) | (31) |
proper(cons(X1,X2)) | → | cons(proper(X1),proper(X2)) | (23) |
proper(take(X1,X2)) | → | take(proper(X1),proper(X2)) | (24) |
inf(mark(X)) | → | mark(inf(X)) | (13) |
inf(ok(X)) | → | ok(inf(X)) | (29) |
active#(take(X1,X2)) | → | active#(X1) | (48) |
active#(take(X1,X2)) | → | active#(X2) | (46) |
The dependency pairs are split into 0 components.
proper#(cons(X1,X2)) | → | proper#(X1) | (53) |
proper#(cons(X1,X2)) | → | proper#(X2) | (77) |
proper#(take(X1,X2)) | → | proper#(X2) | (51) |
proper#(take(X1,X2)) | → | proper#(X1) | (47) |
proper#(length(X)) | → | proper#(X) | (42) |
proper#(eq(X1,X2)) | → | proper#(X1) | (65) |
proper#(s(X)) | → | proper#(X) | (64) |
proper#(eq(X1,X2)) | → | proper#(X2) | (38) |
proper#(inf(X)) | → | proper#(X) | (37) |
[cons#(x1, x2)] | = | 0 |
[s(x1)] | = | x1 + 1 |
[take#(x1, x2)] | = | 0 |
[take(x1, x2)] | = | x1 + x2 + 1 |
[top(x1)] | = | 0 |
[eq(x1, x2)] | = | x1 + x2 + 1 |
[false] | = | 1 |
[top#(x1)] | = | 0 |
[true] | = | 1 |
[eq#(x1, x2)] | = | 0 |
[proper(x1)] | = | x1 + 0 |
[ok(x1)] | = | x1 + 0 |
[0] | = | 1 |
[s#(x1)] | = | 0 |
[nil] | = | 0 |
[mark(x1)] | = | x1 + 26600 |
[proper#(x1)] | = | x1 + 0 |
[inf#(x1)] | = | 0 |
[active(x1)] | = | x1 + 26597 |
[cons(x1, x2)] | = | x1 + x2 + 1 |
[active#(x1)] | = | 0 |
[length(x1)] | = | x1 + 1 |
[length#(x1)] | = | 0 |
[inf(x1)] | = | x1 + 1 |
proper(0) | → | ok(0) | (18) |
take(X1,mark(X2)) | → | mark(take(X1,X2)) | (15) |
length(mark(X)) | → | mark(length(X)) | (16) |
proper(false) | → | ok(false) | (21) |
proper(length(X)) | → | length(proper(X)) | (26) |
proper(true) | → | ok(true) | (19) |
length(ok(X)) | → | ok(length(X)) | (32) |
proper(eq(X1,X2)) | → | eq(proper(X1),proper(X2)) | (17) |
eq(ok(X1),ok(X2)) | → | ok(eq(X1,X2)) | (27) |
proper(inf(X)) | → | inf(proper(X)) | (22) |
s(ok(X)) | → | ok(s(X)) | (28) |
proper(s(X)) | → | s(proper(X)) | (20) |
proper(nil) | → | ok(nil) | (25) |
cons(ok(X1),ok(X2)) | → | ok(cons(X1,X2)) | (30) |
take(mark(X1),X2) | → | mark(take(X1,X2)) | (14) |
take(ok(X1),ok(X2)) | → | ok(take(X1,X2)) | (31) |
proper(cons(X1,X2)) | → | cons(proper(X1),proper(X2)) | (23) |
proper(take(X1,X2)) | → | take(proper(X1),proper(X2)) | (24) |
inf(mark(X)) | → | mark(inf(X)) | (13) |
inf(ok(X)) | → | ok(inf(X)) | (29) |
proper#(cons(X1,X2)) | → | proper#(X1) | (53) |
proper#(cons(X1,X2)) | → | proper#(X2) | (77) |
proper#(take(X1,X2)) | → | proper#(X2) | (51) |
proper#(take(X1,X2)) | → | proper#(X1) | (47) |
proper#(length(X)) | → | proper#(X) | (42) |
proper#(eq(X1,X2)) | → | proper#(X1) | (65) |
proper#(s(X)) | → | proper#(X) | (64) |
proper#(eq(X1,X2)) | → | proper#(X2) | (38) |
proper#(inf(X)) | → | proper#(X) | (37) |
The dependency pairs are split into 0 components.
take#(ok(X1),ok(X2)) | → | take#(X1,X2) | (79) |
take#(mark(X1),X2) | → | take#(X1,X2) | (69) |
take#(X1,mark(X2)) | → | take#(X1,X2) | (39) |
[cons#(x1, x2)] | = | 0 |
[s(x1)] | = | x1 + 1 |
[take#(x1, x2)] | = | x2 + 0 |
[take(x1, x2)] | = | x1 + x2 + 1 |
[top(x1)] | = | 0 |
[eq(x1, x2)] | = | x1 + x2 + 1 |
[false] | = | 47313 |
[top#(x1)] | = | 0 |
[true] | = | 1 |
[eq#(x1, x2)] | = | 0 |
[proper(x1)] | = | x1 + 0 |
[ok(x1)] | = | x1 + 0 |
[0] | = | 1 |
[s#(x1)] | = | 0 |
[nil] | = | 0 |
[mark(x1)] | = | x1 + 45965 |
[proper#(x1)] | = | 0 |
[inf#(x1)] | = | 0 |
[active(x1)] | = | x1 + 45962 |
[cons(x1, x2)] | = | x1 + x2 + 1 |
[active#(x1)] | = | 0 |
[length(x1)] | = | x1 + 1 |
[length#(x1)] | = | 0 |
[inf(x1)] | = | x1 + 1 |
proper(0) | → | ok(0) | (18) |
take(X1,mark(X2)) | → | mark(take(X1,X2)) | (15) |
length(mark(X)) | → | mark(length(X)) | (16) |
proper(false) | → | ok(false) | (21) |
proper(length(X)) | → | length(proper(X)) | (26) |
proper(true) | → | ok(true) | (19) |
length(ok(X)) | → | ok(length(X)) | (32) |
proper(eq(X1,X2)) | → | eq(proper(X1),proper(X2)) | (17) |
eq(ok(X1),ok(X2)) | → | ok(eq(X1,X2)) | (27) |
proper(inf(X)) | → | inf(proper(X)) | (22) |
s(ok(X)) | → | ok(s(X)) | (28) |
proper(s(X)) | → | s(proper(X)) | (20) |
proper(nil) | → | ok(nil) | (25) |
cons(ok(X1),ok(X2)) | → | ok(cons(X1,X2)) | (30) |
take(mark(X1),X2) | → | mark(take(X1,X2)) | (14) |
take(ok(X1),ok(X2)) | → | ok(take(X1,X2)) | (31) |
proper(cons(X1,X2)) | → | cons(proper(X1),proper(X2)) | (23) |
proper(take(X1,X2)) | → | take(proper(X1),proper(X2)) | (24) |
inf(mark(X)) | → | mark(inf(X)) | (13) |
inf(ok(X)) | → | ok(inf(X)) | (29) |
take#(X1,mark(X2)) | → | take#(X1,X2) | (39) |
The dependency pairs are split into 1 component.
take#(mark(X1),X2) | → | take#(X1,X2) | (69) |
take#(ok(X1),ok(X2)) | → | take#(X1,X2) | (79) |
[cons#(x1, x2)] | = | 0 |
[s(x1)] | = | x1 + 1 |
[take#(x1, x2)] | = | x1 + 0 |
[take(x1, x2)] | = | x1 + x2 + 1 |
[top(x1)] | = | 0 |
[eq(x1, x2)] | = | x1 + x2 + 1 |
[false] | = | 1 |
[top#(x1)] | = | 0 |
[true] | = | 1 |
[eq#(x1, x2)] | = | 0 |
[proper(x1)] | = | x1 + 0 |
[ok(x1)] | = | x1 + 0 |
[0] | = | 1 |
[s#(x1)] | = | 0 |
[nil] | = | 0 |
[mark(x1)] | = | x1 + 4 |
[proper#(x1)] | = | 0 |
[inf#(x1)] | = | 0 |
[active(x1)] | = | x1 + 1 |
[cons(x1, x2)] | = | x1 + x2 + 1 |
[active#(x1)] | = | 0 |
[length(x1)] | = | x1 + 1 |
[length#(x1)] | = | 0 |
[inf(x1)] | = | x1 + 1 |
proper(0) | → | ok(0) | (18) |
take(X1,mark(X2)) | → | mark(take(X1,X2)) | (15) |
length(mark(X)) | → | mark(length(X)) | (16) |
proper(false) | → | ok(false) | (21) |
proper(length(X)) | → | length(proper(X)) | (26) |
proper(true) | → | ok(true) | (19) |
length(ok(X)) | → | ok(length(X)) | (32) |
proper(eq(X1,X2)) | → | eq(proper(X1),proper(X2)) | (17) |
eq(ok(X1),ok(X2)) | → | ok(eq(X1,X2)) | (27) |
proper(inf(X)) | → | inf(proper(X)) | (22) |
s(ok(X)) | → | ok(s(X)) | (28) |
proper(s(X)) | → | s(proper(X)) | (20) |
proper(nil) | → | ok(nil) | (25) |
cons(ok(X1),ok(X2)) | → | ok(cons(X1,X2)) | (30) |
take(mark(X1),X2) | → | mark(take(X1,X2)) | (14) |
take(ok(X1),ok(X2)) | → | ok(take(X1,X2)) | (31) |
proper(cons(X1,X2)) | → | cons(proper(X1),proper(X2)) | (23) |
proper(take(X1,X2)) | → | take(proper(X1),proper(X2)) | (24) |
inf(mark(X)) | → | mark(inf(X)) | (13) |
inf(ok(X)) | → | ok(inf(X)) | (29) |
take#(mark(X1),X2) | → | take#(X1,X2) | (69) |
The dependency pairs are split into 1 component.
take#(ok(X1),ok(X2)) | → | take#(X1,X2) | (79) |
[cons#(x1, x2)] | = | 0 |
[s(x1)] | = | x1 + 1 |
[take#(x1, x2)] | = | x2 + 0 |
[take(x1, x2)] | = | x2 + 1 |
[top(x1)] | = | 0 |
[eq(x1, x2)] | = | x1 + 1 |
[false] | = | 1 |
[top#(x1)] | = | 0 |
[true] | = | 4003 |
[eq#(x1, x2)] | = | 0 |
[proper(x1)] | = | x1 + 1 |
[ok(x1)] | = | x1 + 1 |
[0] | = | 1 |
[s#(x1)] | = | 0 |
[nil] | = | 1 |
[mark(x1)] | = | x1 + 2 |
[proper#(x1)] | = | 0 |
[inf#(x1)] | = | 0 |
[active(x1)] | = | x1 + 0 |
[cons(x1, x2)] | = | x1 + 22498 |
[active#(x1)] | = | 0 |
[length(x1)] | = | 1 |
[length#(x1)] | = | 0 |
[inf(x1)] | = | x1 + 1 |
proper(0) | → | ok(0) | (18) |
proper(false) | → | ok(false) | (21) |
proper(true) | → | ok(true) | (19) |
eq(ok(X1),ok(X2)) | → | ok(eq(X1,X2)) | (27) |
s(ok(X)) | → | ok(s(X)) | (28) |
cons(ok(X1),ok(X2)) | → | ok(cons(X1,X2)) | (30) |
inf(mark(X)) | → | mark(inf(X)) | (13) |
inf(ok(X)) | → | ok(inf(X)) | (29) |
take#(ok(X1),ok(X2)) | → | take#(X1,X2) | (79) |
The dependency pairs are split into 0 components.
s#(ok(X)) | → | s#(X) | (66) |
[cons#(x1, x2)] | = | 0 |
[s(x1)] | = | x1 + 1 |
[take#(x1, x2)] | = | 0 |
[take(x1, x2)] | = | x2 + 1 |
[top(x1)] | = | 0 |
[eq(x1, x2)] | = | x1 + 1 |
[false] | = | 1 |
[top#(x1)] | = | 0 |
[true] | = | 1 |
[eq#(x1, x2)] | = | 0 |
[proper(x1)] | = | x1 + 5082 |
[ok(x1)] | = | x1 + 1 |
[0] | = | 1 |
[s#(x1)] | = | x1 + 0 |
[nil] | = | 1 |
[mark(x1)] | = | x1 + 2 |
[proper#(x1)] | = | 0 |
[inf#(x1)] | = | 0 |
[active(x1)] | = | x1 + 0 |
[cons(x1, x2)] | = | x1 + 42875 |
[active#(x1)] | = | 0 |
[length(x1)] | = | 1 |
[length#(x1)] | = | 0 |
[inf(x1)] | = | x1 + 2082 |
proper(0) | → | ok(0) | (18) |
proper(false) | → | ok(false) | (21) |
proper(true) | → | ok(true) | (19) |
eq(ok(X1),ok(X2)) | → | ok(eq(X1,X2)) | (27) |
s(ok(X)) | → | ok(s(X)) | (28) |
cons(ok(X1),ok(X2)) | → | ok(cons(X1,X2)) | (30) |
inf(mark(X)) | → | mark(inf(X)) | (13) |
inf(ok(X)) | → | ok(inf(X)) | (29) |
s#(ok(X)) | → | s#(X) | (66) |
The dependency pairs are split into 0 components.
eq#(ok(X1),ok(X2)) | → | eq#(X1,X2) | (68) |
[cons#(x1, x2)] | = | 0 |
[s(x1)] | = | x1 + 1 |
[take#(x1, x2)] | = | 0 |
[take(x1, x2)] | = | x2 + 1 |
[top(x1)] | = | 0 |
[eq(x1, x2)] | = | x1 + 1 |
[false] | = | 1 |
[top#(x1)] | = | 0 |
[true] | = | 1 |
[eq#(x1, x2)] | = | x2 + 0 |
[proper(x1)] | = | x1 + 1 |
[ok(x1)] | = | x1 + 1 |
[0] | = | 1 |
[s#(x1)] | = | 0 |
[nil] | = | 42433 |
[mark(x1)] | = | x1 + 2 |
[proper#(x1)] | = | 0 |
[inf#(x1)] | = | 0 |
[active(x1)] | = | x1 + 0 |
[cons(x1, x2)] | = | x1 + 1 |
[active#(x1)] | = | 0 |
[length(x1)] | = | 1 |
[length#(x1)] | = | 0 |
[inf(x1)] | = | x1 + 1 |
proper(0) | → | ok(0) | (18) |
proper(false) | → | ok(false) | (21) |
proper(true) | → | ok(true) | (19) |
eq(ok(X1),ok(X2)) | → | ok(eq(X1,X2)) | (27) |
s(ok(X)) | → | ok(s(X)) | (28) |
cons(ok(X1),ok(X2)) | → | ok(cons(X1,X2)) | (30) |
inf(mark(X)) | → | mark(inf(X)) | (13) |
inf(ok(X)) | → | ok(inf(X)) | (29) |
eq#(ok(X1),ok(X2)) | → | eq#(X1,X2) | (68) |
The dependency pairs are split into 0 components.
length#(ok(X)) | → | length#(X) | (71) |
length#(mark(X)) | → | length#(X) | (58) |
[cons#(x1, x2)] | = | 0 |
[s(x1)] | = | x1 + 1 |
[take#(x1, x2)] | = | 0 |
[take(x1, x2)] | = | x2 + 1 |
[top(x1)] | = | 0 |
[eq(x1, x2)] | = | x1 + 31226 |
[false] | = | 1 |
[top#(x1)] | = | 0 |
[true] | = | 28966 |
[eq#(x1, x2)] | = | 0 |
[proper(x1)] | = | x1 + 36242 |
[ok(x1)] | = | x1 + 8127 |
[0] | = | 56050 |
[s#(x1)] | = | 0 |
[nil] | = | 42433 |
[mark(x1)] | = | x1 + 58311 |
[proper#(x1)] | = | 0 |
[inf#(x1)] | = | 0 |
[active(x1)] | = | x1 + 0 |
[cons(x1, x2)] | = | x1 + 46686 |
[active#(x1)] | = | 0 |
[length(x1)] | = | 1 |
[length#(x1)] | = | x1 + 0 |
[inf(x1)] | = | x1 + 30727 |
proper(0) | → | ok(0) | (18) |
proper(false) | → | ok(false) | (21) |
proper(true) | → | ok(true) | (19) |
eq(ok(X1),ok(X2)) | → | ok(eq(X1,X2)) | (27) |
s(ok(X)) | → | ok(s(X)) | (28) |
cons(ok(X1),ok(X2)) | → | ok(cons(X1,X2)) | (30) |
inf(mark(X)) | → | mark(inf(X)) | (13) |
inf(ok(X)) | → | ok(inf(X)) | (29) |
length#(ok(X)) | → | length#(X) | (71) |
length#(mark(X)) | → | length#(X) | (58) |
The dependency pairs are split into 0 components.
inf#(mark(X)) | → | inf#(X) | (61) |
inf#(ok(X)) | → | inf#(X) | (35) |
[cons#(x1, x2)] | = | 0 |
[s(x1)] | = | x1 + 1 |
[take#(x1, x2)] | = | 0 |
[take(x1, x2)] | = | x2 + 1 |
[top(x1)] | = | 0 |
[eq(x1, x2)] | = | x1 + 1 |
[false] | = | 39220 |
[top#(x1)] | = | 0 |
[true] | = | 1 |
[eq#(x1, x2)] | = | 0 |
[proper(x1)] | = | x1 + 31320 |
[ok(x1)] | = | x1 + 10113 |
[0] | = | 1 |
[s#(x1)] | = | 0 |
[nil] | = | 6829 |
[mark(x1)] | = | x1 + 2 |
[proper#(x1)] | = | 0 |
[inf#(x1)] | = | x1 + 0 |
[active(x1)] | = | x1 + 0 |
[cons(x1, x2)] | = | x1 + 46686 |
[active#(x1)] | = | 0 |
[length(x1)] | = | 1 |
[length#(x1)] | = | 0 |
[inf(x1)] | = | x1 + 30727 |
proper(0) | → | ok(0) | (18) |
proper(false) | → | ok(false) | (21) |
proper(true) | → | ok(true) | (19) |
eq(ok(X1),ok(X2)) | → | ok(eq(X1,X2)) | (27) |
s(ok(X)) | → | ok(s(X)) | (28) |
cons(ok(X1),ok(X2)) | → | ok(cons(X1,X2)) | (30) |
inf(mark(X)) | → | mark(inf(X)) | (13) |
inf(ok(X)) | → | ok(inf(X)) | (29) |
inf#(mark(X)) | → | inf#(X) | (61) |
inf#(ok(X)) | → | inf#(X) | (35) |
The dependency pairs are split into 0 components.
cons#(ok(X1),ok(X2)) | → | cons#(X1,X2) | (56) |
[cons#(x1, x2)] | = | x2 + 0 |
[s(x1)] | = | x1 + 1 |
[take#(x1, x2)] | = | 0 |
[take(x1, x2)] | = | 2 |
[top(x1)] | = | 0 |
[eq(x1, x2)] | = | 32067 |
[false] | = | 1 |
[top#(x1)] | = | 0 |
[true] | = | 33242 |
[eq#(x1, x2)] | = | 0 |
[proper(x1)] | = | 1 |
[ok(x1)] | = | x1 + 23951 |
[0] | = | 24235 |
[s#(x1)] | = | 0 |
[nil] | = | 8517 |
[mark(x1)] | = | x1 + 1 |
[proper#(x1)] | = | 0 |
[inf#(x1)] | = | 0 |
[active(x1)] | = | 1 |
[cons(x1, x2)] | = | x1 + x2 + 41482 |
[active#(x1)] | = | 0 |
[length(x1)] | = | 26389 |
[length#(x1)] | = | 0 |
[inf(x1)] | = | x1 + 5552 |
cons#(ok(X1),ok(X2)) | → | cons#(X1,X2) | (56) |
The dependency pairs are split into 0 components.