The rewrite relation of the following TRS is considered.
active(terms(N)) | → | mark(cons(recip(sqr(N)),terms(s(N)))) | (1) |
active(sqr(0)) | → | mark(0) | (2) |
active(sqr(s(X))) | → | mark(s(add(sqr(X),dbl(X)))) | (3) |
active(dbl(0)) | → | mark(0) | (4) |
active(dbl(s(X))) | → | mark(s(s(dbl(X)))) | (5) |
active(add(0,X)) | → | mark(X) | (6) |
active(add(s(X),Y)) | → | mark(s(add(X,Y))) | (7) |
active(first(0,X)) | → | mark(nil) | (8) |
active(first(s(X),cons(Y,Z))) | → | mark(cons(Y,first(X,Z))) | (9) |
mark(terms(X)) | → | active(terms(mark(X))) | (10) |
mark(cons(X1,X2)) | → | active(cons(mark(X1),X2)) | (11) |
mark(recip(X)) | → | active(recip(mark(X))) | (12) |
mark(sqr(X)) | → | active(sqr(mark(X))) | (13) |
mark(s(X)) | → | active(s(mark(X))) | (14) |
mark(0) | → | active(0) | (15) |
mark(add(X1,X2)) | → | active(add(mark(X1),mark(X2))) | (16) |
mark(dbl(X)) | → | active(dbl(mark(X))) | (17) |
mark(first(X1,X2)) | → | active(first(mark(X1),mark(X2))) | (18) |
mark(nil) | → | active(nil) | (19) |
terms(mark(X)) | → | terms(X) | (20) |
terms(active(X)) | → | terms(X) | (21) |
cons(mark(X1),X2) | → | cons(X1,X2) | (22) |
cons(X1,mark(X2)) | → | cons(X1,X2) | (23) |
cons(active(X1),X2) | → | cons(X1,X2) | (24) |
cons(X1,active(X2)) | → | cons(X1,X2) | (25) |
recip(mark(X)) | → | recip(X) | (26) |
recip(active(X)) | → | recip(X) | (27) |
sqr(mark(X)) | → | sqr(X) | (28) |
sqr(active(X)) | → | sqr(X) | (29) |
s(mark(X)) | → | s(X) | (30) |
s(active(X)) | → | s(X) | (31) |
add(mark(X1),X2) | → | add(X1,X2) | (32) |
add(X1,mark(X2)) | → | add(X1,X2) | (33) |
add(active(X1),X2) | → | add(X1,X2) | (34) |
add(X1,active(X2)) | → | add(X1,X2) | (35) |
dbl(mark(X)) | → | dbl(X) | (36) |
dbl(active(X)) | → | dbl(X) | (37) |
first(mark(X1),X2) | → | first(X1,X2) | (38) |
first(X1,mark(X2)) | → | first(X1,X2) | (39) |
first(active(X1),X2) | → | first(X1,X2) | (40) |
first(X1,active(X2)) | → | first(X1,X2) | (41) |
sqr#(active(X)) | → | sqr#(X) | (42) |
cons#(mark(X1),X2) | → | cons#(X1,X2) | (43) |
terms#(mark(X)) | → | terms#(X) | (44) |
mark#(terms(X)) | → | terms#(mark(X)) | (45) |
active#(terms(N)) | → | sqr#(N) | (46) |
mark#(dbl(X)) | → | active#(dbl(mark(X))) | (47) |
sqr#(mark(X)) | → | sqr#(X) | (48) |
active#(dbl(s(X))) | → | dbl#(X) | (49) |
add#(X1,mark(X2)) | → | add#(X1,X2) | (50) |
mark#(first(X1,X2)) | → | first#(mark(X1),mark(X2)) | (51) |
mark#(dbl(X)) | → | dbl#(mark(X)) | (52) |
terms#(active(X)) | → | terms#(X) | (53) |
active#(dbl(0)) | → | mark#(0) | (54) |
mark#(dbl(X)) | → | mark#(X) | (55) |
mark#(first(X1,X2)) | → | mark#(X2) | (56) |
mark#(first(X1,X2)) | → | mark#(X1) | (57) |
active#(sqr(s(X))) | → | mark#(s(add(sqr(X),dbl(X)))) | (58) |
active#(sqr(s(X))) | → | sqr#(X) | (59) |
active#(dbl(s(X))) | → | mark#(s(s(dbl(X)))) | (60) |
first#(mark(X1),X2) | → | first#(X1,X2) | (61) |
active#(sqr(s(X))) | → | s#(add(sqr(X),dbl(X))) | (62) |
mark#(add(X1,X2)) | → | add#(mark(X1),mark(X2)) | (63) |
active#(terms(N)) | → | terms#(s(N)) | (64) |
active#(dbl(s(X))) | → | s#(dbl(X)) | (65) |
recip#(mark(X)) | → | recip#(X) | (66) |
active#(first(s(X),cons(Y,Z))) | → | cons#(Y,first(X,Z)) | (67) |
mark#(sqr(X)) | → | active#(sqr(mark(X))) | (68) |
mark#(sqr(X)) | → | mark#(X) | (69) |
mark#(add(X1,X2)) | → | mark#(X2) | (70) |
mark#(s(X)) | → | active#(s(mark(X))) | (71) |
mark#(0) | → | active#(0) | (72) |
s#(active(X)) | → | s#(X) | (73) |
recip#(active(X)) | → | recip#(X) | (74) |
active#(first(0,X)) | → | mark#(nil) | (75) |
active#(first(s(X),cons(Y,Z))) | → | mark#(cons(Y,first(X,Z))) | (76) |
active#(add(s(X),Y)) | → | s#(add(X,Y)) | (77) |
mark#(add(X1,X2)) | → | mark#(X1) | (78) |
active#(first(s(X),cons(Y,Z))) | → | first#(X,Z) | (79) |
active#(sqr(s(X))) | → | dbl#(X) | (80) |
active#(add(s(X),Y)) | → | mark#(s(add(X,Y))) | (81) |
dbl#(mark(X)) | → | dbl#(X) | (82) |
add#(mark(X1),X2) | → | add#(X1,X2) | (83) |
mark#(s(X)) | → | s#(mark(X)) | (84) |
mark#(recip(X)) | → | active#(recip(mark(X))) | (85) |
active#(add(0,X)) | → | mark#(X) | (86) |
active#(dbl(s(X))) | → | s#(s(dbl(X))) | (87) |
mark#(sqr(X)) | → | sqr#(mark(X)) | (88) |
active#(terms(N)) | → | cons#(recip(sqr(N)),terms(s(N))) | (89) |
first#(X1,mark(X2)) | → | first#(X1,X2) | (90) |
mark#(first(X1,X2)) | → | active#(first(mark(X1),mark(X2))) | (91) |
dbl#(active(X)) | → | dbl#(X) | (92) |
add#(active(X1),X2) | → | add#(X1,X2) | (93) |
active#(terms(N)) | → | recip#(sqr(N)) | (94) |
cons#(X1,active(X2)) | → | cons#(X1,X2) | (95) |
mark#(recip(X)) | → | mark#(X) | (96) |
mark#(terms(X)) | → | active#(terms(mark(X))) | (97) |
s#(mark(X)) | → | s#(X) | (98) |
active#(sqr(s(X))) | → | add#(sqr(X),dbl(X)) | (99) |
mark#(cons(X1,X2)) | → | mark#(X1) | (100) |
active#(add(s(X),Y)) | → | add#(X,Y) | (101) |
cons#(X1,mark(X2)) | → | cons#(X1,X2) | (102) |
active#(terms(N)) | → | mark#(cons(recip(sqr(N)),terms(s(N)))) | (103) |
mark#(s(X)) | → | mark#(X) | (104) |
active#(terms(N)) | → | s#(N) | (105) |
mark#(terms(X)) | → | mark#(X) | (106) |
mark#(recip(X)) | → | recip#(mark(X)) | (107) |
mark#(cons(X1,X2)) | → | cons#(mark(X1),X2) | (108) |
add#(X1,active(X2)) | → | add#(X1,X2) | (109) |
active#(sqr(0)) | → | mark#(0) | (110) |
mark#(add(X1,X2)) | → | active#(add(mark(X1),mark(X2))) | (111) |
first#(active(X1),X2) | → | first#(X1,X2) | (112) |
mark#(cons(X1,X2)) | → | active#(cons(mark(X1),X2)) | (113) |
first#(X1,active(X2)) | → | first#(X1,X2) | (114) |
mark#(nil) | → | active#(nil) | (115) |
cons#(active(X1),X2) | → | cons#(X1,X2) | (116) |
The dependency pairs are split into 9 components.
active#(add(s(X),Y)) | → | mark#(s(add(X,Y))) | (81) |
mark#(cons(X1,X2)) | → | active#(cons(mark(X1),X2)) | (113) |
mark#(add(X1,X2)) | → | mark#(X1) | (78) |
active#(first(s(X),cons(Y,Z))) | → | mark#(cons(Y,first(X,Z))) | (76) |
mark#(add(X1,X2)) | → | active#(add(mark(X1),mark(X2))) | (111) |
mark#(s(X)) | → | active#(s(mark(X))) | (71) |
mark#(terms(X)) | → | mark#(X) | (106) |
mark#(add(X1,X2)) | → | mark#(X2) | (70) |
mark#(s(X)) | → | mark#(X) | (104) |
mark#(sqr(X)) | → | mark#(X) | (69) |
mark#(sqr(X)) | → | active#(sqr(mark(X))) | (68) |
active#(terms(N)) | → | mark#(cons(recip(sqr(N)),terms(s(N)))) | (103) |
mark#(cons(X1,X2)) | → | mark#(X1) | (100) |
active#(dbl(s(X))) | → | mark#(s(s(dbl(X)))) | (60) |
active#(sqr(s(X))) | → | mark#(s(add(sqr(X),dbl(X)))) | (58) |
mark#(first(X1,X2)) | → | mark#(X1) | (57) |
mark#(terms(X)) | → | active#(terms(mark(X))) | (97) |
mark#(first(X1,X2)) | → | mark#(X2) | (56) |
mark#(dbl(X)) | → | mark#(X) | (55) |
mark#(recip(X)) | → | mark#(X) | (96) |
mark#(first(X1,X2)) | → | active#(first(mark(X1),mark(X2))) | (91) |
mark#(dbl(X)) | → | active#(dbl(mark(X))) | (47) |
active#(add(0,X)) | → | mark#(X) | (86) |
mark#(recip(X)) | → | active#(recip(mark(X))) | (85) |
[cons#(x1, x2)] | = | 0 |
[s(x1)] | = | 1 |
[recip(x1)] | = | 1 |
[recip#(x1)] | = | 0 |
[dbl(x1)] | = | 2 |
[dbl#(x1)] | = | 0 |
[terms#(x1)] | = | 0 |
[sqr#(x1)] | = | 0 |
[mark#(x1)] | = | 2 |
[0] | = | 1 |
[s#(x1)] | = | 0 |
[first#(x1, x2)] | = | 0 |
[nil] | = | 2 |
[mark(x1)] | = | 2 |
[first(x1, x2)] | = | 2 |
[active(x1)] | = | x1 + 0 |
[cons(x1, x2)] | = | 1 |
[active#(x1)] | = | x1 + 0 |
[add#(x1, x2)] | = | 0 |
[add(x1, x2)] | = | 2 |
[sqr(x1)] | = | 2 |
[terms(x1)] | = | 2 |
mark(first(X1,X2)) | → | active(first(mark(X1),mark(X2))) | (18) |
active(dbl(0)) | → | mark(0) | (4) |
mark(0) | → | active(0) | (15) |
active(first(0,X)) | → | mark(nil) | (8) |
active(terms(N)) | → | mark(cons(recip(sqr(N)),terms(s(N)))) | (1) |
active(sqr(s(X))) | → | mark(s(add(sqr(X),dbl(X)))) | (3) |
mark(add(X1,X2)) | → | active(add(mark(X1),mark(X2))) | (16) |
terms(active(X)) | → | terms(X) | (21) |
dbl(mark(X)) | → | dbl(X) | (36) |
recip(mark(X)) | → | recip(X) | (26) |
mark(nil) | → | active(nil) | (19) |
add(mark(X1),X2) | → | add(X1,X2) | (32) |
mark(dbl(X)) | → | active(dbl(mark(X))) | (17) |
recip(active(X)) | → | recip(X) | (27) |
add(active(X1),X2) | → | add(X1,X2) | (34) |
cons(mark(X1),X2) | → | cons(X1,X2) | (22) |
sqr(mark(X)) | → | sqr(X) | (28) |
active(dbl(s(X))) | → | mark(s(s(dbl(X)))) | (5) |
add(X1,mark(X2)) | → | add(X1,X2) | (33) |
mark(terms(X)) | → | active(terms(mark(X))) | (10) |
first(X1,mark(X2)) | → | first(X1,X2) | (39) |
active(add(s(X),Y)) | → | mark(s(add(X,Y))) | (7) |
terms(mark(X)) | → | terms(X) | (20) |
cons(X1,active(X2)) | → | cons(X1,X2) | (25) |
s(mark(X)) | → | s(X) | (30) |
mark(s(X)) | → | active(s(mark(X))) | (14) |
s(active(X)) | → | s(X) | (31) |
mark(recip(X)) | → | active(recip(mark(X))) | (12) |
cons(X1,mark(X2)) | → | cons(X1,X2) | (23) |
cons(active(X1),X2) | → | cons(X1,X2) | (24) |
mark(cons(X1,X2)) | → | active(cons(mark(X1),X2)) | (11) |
active(first(s(X),cons(Y,Z))) | → | mark(cons(Y,first(X,Z))) | (9) |
mark(sqr(X)) | → | active(sqr(mark(X))) | (13) |
first(active(X1),X2) | → | first(X1,X2) | (40) |
active(add(0,X)) | → | mark(X) | (6) |
first(mark(X1),X2) | → | first(X1,X2) | (38) |
dbl(active(X)) | → | dbl(X) | (37) |
first(X1,active(X2)) | → | first(X1,X2) | (41) |
add(X1,active(X2)) | → | add(X1,X2) | (35) |
sqr(active(X)) | → | sqr(X) | (29) |
active(sqr(0)) | → | mark(0) | (2) |
mark#(cons(X1,X2)) | → | active#(cons(mark(X1),X2)) | (113) |
mark#(s(X)) | → | active#(s(mark(X))) | (71) |
mark#(recip(X)) | → | active#(recip(mark(X))) | (85) |
The dependency pairs are split into 1 component.
mark#(first(X1,X2)) | → | mark#(X2) | (56) |
mark#(first(X1,X2)) | → | mark#(X1) | (57) |
mark#(first(X1,X2)) | → | active#(first(mark(X1),mark(X2))) | (91) |
active#(terms(N)) | → | mark#(cons(recip(sqr(N)),terms(s(N)))) | (103) |
active#(sqr(s(X))) | → | mark#(s(add(sqr(X),dbl(X)))) | (58) |
mark#(add(X1,X2)) | → | mark#(X2) | (70) |
mark#(add(X1,X2)) | → | mark#(X1) | (78) |
mark#(add(X1,X2)) | → | active#(add(mark(X1),mark(X2))) | (111) |
mark#(dbl(X)) | → | mark#(X) | (55) |
mark#(dbl(X)) | → | active#(dbl(mark(X))) | (47) |
active#(dbl(s(X))) | → | mark#(s(s(dbl(X)))) | (60) |
mark#(terms(X)) | → | mark#(X) | (106) |
mark#(terms(X)) | → | active#(terms(mark(X))) | (97) |
active#(add(s(X),Y)) | → | mark#(s(add(X,Y))) | (81) |
mark#(s(X)) | → | mark#(X) | (104) |
mark#(recip(X)) | → | mark#(X) | (96) |
mark#(cons(X1,X2)) | → | mark#(X1) | (100) |
active#(first(s(X),cons(Y,Z))) | → | mark#(cons(Y,first(X,Z))) | (76) |
mark#(sqr(X)) | → | mark#(X) | (69) |
mark#(sqr(X)) | → | active#(sqr(mark(X))) | (68) |
active#(add(0,X)) | → | mark#(X) | (86) |
[cons#(x1, x2)] | = | max(0) |
[s(x1)] | = | x1 + 0 |
[recip(x1)] | = | x1 + 20977 |
[recip#(x1)] | = | 0 |
[dbl(x1)] | = | x1 + 26286 |
[dbl#(x1)] | = | 0 |
[terms#(x1)] | = | 0 |
[sqr#(x1)] | = | 0 |
[mark#(x1)] | = | x1 + 0 |
[0] | = | 2998 |
[s#(x1)] | = | 0 |
[first#(x1, x2)] | = | max(0) |
[nil] | = | 17680 |
[mark(x1)] | = | x1 + 0 |
[first(x1, x2)] | = | max(x1 + 14681, x2 + 17680, 0) |
[active(x1)] | = | x1 + 0 |
[cons(x1, x2)] | = | max(x1 + 17681, x2 + 0, 0) |
[active#(x1)] | = | x1 + 0 |
[add#(x1, x2)] | = | max(0) |
[add(x1, x2)] | = | max(x1 + 0, x2 + 1, 0) |
[sqr(x1)] | = | x1 + 26288 |
[terms(x1)] | = | x1 + 64947 |
mark(first(X1,X2)) | → | active(first(mark(X1),mark(X2))) | (18) |
active(dbl(0)) | → | mark(0) | (4) |
mark(0) | → | active(0) | (15) |
active(first(0,X)) | → | mark(nil) | (8) |
active(terms(N)) | → | mark(cons(recip(sqr(N)),terms(s(N)))) | (1) |
active(sqr(s(X))) | → | mark(s(add(sqr(X),dbl(X)))) | (3) |
mark(add(X1,X2)) | → | active(add(mark(X1),mark(X2))) | (16) |
terms(active(X)) | → | terms(X) | (21) |
dbl(mark(X)) | → | dbl(X) | (36) |
recip(mark(X)) | → | recip(X) | (26) |
mark(nil) | → | active(nil) | (19) |
add(mark(X1),X2) | → | add(X1,X2) | (32) |
mark(dbl(X)) | → | active(dbl(mark(X))) | (17) |
recip(active(X)) | → | recip(X) | (27) |
add(active(X1),X2) | → | add(X1,X2) | (34) |
cons(mark(X1),X2) | → | cons(X1,X2) | (22) |
sqr(mark(X)) | → | sqr(X) | (28) |
active(dbl(s(X))) | → | mark(s(s(dbl(X)))) | (5) |
add(X1,mark(X2)) | → | add(X1,X2) | (33) |
mark(terms(X)) | → | active(terms(mark(X))) | (10) |
first(X1,mark(X2)) | → | first(X1,X2) | (39) |
active(add(s(X),Y)) | → | mark(s(add(X,Y))) | (7) |
terms(mark(X)) | → | terms(X) | (20) |
cons(X1,active(X2)) | → | cons(X1,X2) | (25) |
s(mark(X)) | → | s(X) | (30) |
mark(s(X)) | → | active(s(mark(X))) | (14) |
s(active(X)) | → | s(X) | (31) |
mark(recip(X)) | → | active(recip(mark(X))) | (12) |
cons(X1,mark(X2)) | → | cons(X1,X2) | (23) |
cons(active(X1),X2) | → | cons(X1,X2) | (24) |
mark(cons(X1,X2)) | → | active(cons(mark(X1),X2)) | (11) |
active(first(s(X),cons(Y,Z))) | → | mark(cons(Y,first(X,Z))) | (9) |
mark(sqr(X)) | → | active(sqr(mark(X))) | (13) |
first(active(X1),X2) | → | first(X1,X2) | (40) |
active(add(0,X)) | → | mark(X) | (6) |
first(mark(X1),X2) | → | first(X1,X2) | (38) |
dbl(active(X)) | → | dbl(X) | (37) |
first(X1,active(X2)) | → | first(X1,X2) | (41) |
add(X1,active(X2)) | → | add(X1,X2) | (35) |
sqr(active(X)) | → | sqr(X) | (29) |
active(sqr(0)) | → | mark(0) | (2) |
mark#(first(X1,X2)) | → | mark#(X2) | (56) |
mark#(first(X1,X2)) | → | mark#(X1) | (57) |
mark#(add(X1,X2)) | → | mark#(X2) | (70) |
mark#(dbl(X)) | → | mark#(X) | (55) |
mark#(terms(X)) | → | mark#(X) | (106) |
mark#(recip(X)) | → | mark#(X) | (96) |
mark#(cons(X1,X2)) | → | mark#(X1) | (100) |
mark#(sqr(X)) | → | mark#(X) | (69) |
active#(add(0,X)) | → | mark#(X) | (86) |
The dependency pairs are split into 1 component.
mark#(first(X1,X2)) | → | active#(first(mark(X1),mark(X2))) | (91) |
active#(terms(N)) | → | mark#(cons(recip(sqr(N)),terms(s(N)))) | (103) |
active#(sqr(s(X))) | → | mark#(s(add(sqr(X),dbl(X)))) | (58) |
mark#(add(X1,X2)) | → | mark#(X1) | (78) |
mark#(add(X1,X2)) | → | active#(add(mark(X1),mark(X2))) | (111) |
mark#(dbl(X)) | → | active#(dbl(mark(X))) | (47) |
active#(dbl(s(X))) | → | mark#(s(s(dbl(X)))) | (60) |
mark#(terms(X)) | → | active#(terms(mark(X))) | (97) |
active#(add(s(X),Y)) | → | mark#(s(add(X,Y))) | (81) |
mark#(s(X)) | → | mark#(X) | (104) |
active#(first(s(X),cons(Y,Z))) | → | mark#(cons(Y,first(X,Z))) | (76) |
mark#(sqr(X)) | → | active#(sqr(mark(X))) | (68) |
[cons#(x1, x2)] | = | 0 |
[s(x1)] | = | x1 + 0 |
[recip(x1)] | = | 0 |
[recip#(x1)] | = | 0 |
[dbl(x1)] | = | 0 |
[dbl#(x1)] | = | 0 |
[terms#(x1)] | = | 0 |
[sqr#(x1)] | = | 0 |
[mark#(x1)] | = | x1 + 2 |
[0] | = | 0 |
[s#(x1)] | = | 0 |
[first#(x1, x2)] | = | 0 |
[nil] | = | 0 |
[mark(x1)] | = | x1 + 0 |
[first(x1, x2)] | = | 52195 |
[active(x1)] | = | x1 + 0 |
[cons(x1, x2)] | = | 52194 |
[active#(x1)] | = | x1 + 2 |
[add#(x1, x2)] | = | 0 |
[add(x1, x2)] | = | x1 + x2 + 0 |
[sqr(x1)] | = | 14003 |
[terms(x1)] | = | 52195 |
mark(first(X1,X2)) | → | active(first(mark(X1),mark(X2))) | (18) |
active(dbl(0)) | → | mark(0) | (4) |
mark(0) | → | active(0) | (15) |
active(first(0,X)) | → | mark(nil) | (8) |
active(terms(N)) | → | mark(cons(recip(sqr(N)),terms(s(N)))) | (1) |
active(sqr(s(X))) | → | mark(s(add(sqr(X),dbl(X)))) | (3) |
mark(add(X1,X2)) | → | active(add(mark(X1),mark(X2))) | (16) |
terms(active(X)) | → | terms(X) | (21) |
dbl(mark(X)) | → | dbl(X) | (36) |
recip(mark(X)) | → | recip(X) | (26) |
mark(nil) | → | active(nil) | (19) |
add(mark(X1),X2) | → | add(X1,X2) | (32) |
mark(dbl(X)) | → | active(dbl(mark(X))) | (17) |
recip(active(X)) | → | recip(X) | (27) |
add(active(X1),X2) | → | add(X1,X2) | (34) |
cons(mark(X1),X2) | → | cons(X1,X2) | (22) |
sqr(mark(X)) | → | sqr(X) | (28) |
active(dbl(s(X))) | → | mark(s(s(dbl(X)))) | (5) |
add(X1,mark(X2)) | → | add(X1,X2) | (33) |
mark(terms(X)) | → | active(terms(mark(X))) | (10) |
first(X1,mark(X2)) | → | first(X1,X2) | (39) |
active(add(s(X),Y)) | → | mark(s(add(X,Y))) | (7) |
terms(mark(X)) | → | terms(X) | (20) |
cons(X1,active(X2)) | → | cons(X1,X2) | (25) |
s(mark(X)) | → | s(X) | (30) |
mark(s(X)) | → | active(s(mark(X))) | (14) |
s(active(X)) | → | s(X) | (31) |
mark(recip(X)) | → | active(recip(mark(X))) | (12) |
cons(X1,mark(X2)) | → | cons(X1,X2) | (23) |
cons(active(X1),X2) | → | cons(X1,X2) | (24) |
mark(cons(X1,X2)) | → | active(cons(mark(X1),X2)) | (11) |
active(first(s(X),cons(Y,Z))) | → | mark(cons(Y,first(X,Z))) | (9) |
mark(sqr(X)) | → | active(sqr(mark(X))) | (13) |
first(active(X1),X2) | → | first(X1,X2) | (40) |
active(add(0,X)) | → | mark(X) | (6) |
first(mark(X1),X2) | → | first(X1,X2) | (38) |
dbl(active(X)) | → | dbl(X) | (37) |
first(X1,active(X2)) | → | first(X1,X2) | (41) |
add(X1,active(X2)) | → | add(X1,X2) | (35) |
sqr(active(X)) | → | sqr(X) | (29) |
active(sqr(0)) | → | mark(0) | (2) |
active#(terms(N)) | → | mark#(cons(recip(sqr(N)),terms(s(N)))) | (103) |
active#(first(s(X),cons(Y,Z))) | → | mark#(cons(Y,first(X,Z))) | (76) |
The dependency pairs are split into 1 component.
mark#(first(X1,X2)) | → | active#(first(mark(X1),mark(X2))) | (91) |
active#(sqr(s(X))) | → | mark#(s(add(sqr(X),dbl(X)))) | (58) |
mark#(add(X1,X2)) | → | mark#(X1) | (78) |
mark#(add(X1,X2)) | → | active#(add(mark(X1),mark(X2))) | (111) |
mark#(dbl(X)) | → | active#(dbl(mark(X))) | (47) |
active#(dbl(s(X))) | → | mark#(s(s(dbl(X)))) | (60) |
mark#(terms(X)) | → | active#(terms(mark(X))) | (97) |
active#(add(s(X),Y)) | → | mark#(s(add(X,Y))) | (81) |
mark#(s(X)) | → | mark#(X) | (104) |
mark#(sqr(X)) | → | active#(sqr(mark(X))) | (68) |
[cons#(x1, x2)] | = | 0 |
[s(x1)] | = | 1 |
[recip(x1)] | = | 1 |
[recip#(x1)] | = | 0 |
[dbl(x1)] | = | 23506 |
[dbl#(x1)] | = | 0 |
[terms#(x1)] | = | 0 |
[sqr#(x1)] | = | 0 |
[mark#(x1)] | = | 23506 |
[0] | = | 1 |
[s#(x1)] | = | 0 |
[first#(x1, x2)] | = | 0 |
[nil] | = | 1 |
[mark(x1)] | = | 1 |
[first(x1, x2)] | = | 1 |
[active(x1)] | = | 2 |
[cons(x1, x2)] | = | 1 |
[active#(x1)] | = | x1 + 0 |
[add#(x1, x2)] | = | 0 |
[add(x1, x2)] | = | 23506 |
[sqr(x1)] | = | 23506 |
[terms(x1)] | = | 4187 |
terms(active(X)) | → | terms(X) | (21) |
dbl(mark(X)) | → | dbl(X) | (36) |
recip(mark(X)) | → | recip(X) | (26) |
add(mark(X1),X2) | → | add(X1,X2) | (32) |
recip(active(X)) | → | recip(X) | (27) |
add(active(X1),X2) | → | add(X1,X2) | (34) |
cons(mark(X1),X2) | → | cons(X1,X2) | (22) |
sqr(mark(X)) | → | sqr(X) | (28) |
add(X1,mark(X2)) | → | add(X1,X2) | (33) |
first(X1,mark(X2)) | → | first(X1,X2) | (39) |
terms(mark(X)) | → | terms(X) | (20) |
cons(X1,active(X2)) | → | cons(X1,X2) | (25) |
s(mark(X)) | → | s(X) | (30) |
s(active(X)) | → | s(X) | (31) |
cons(X1,mark(X2)) | → | cons(X1,X2) | (23) |
cons(active(X1),X2) | → | cons(X1,X2) | (24) |
first(active(X1),X2) | → | first(X1,X2) | (40) |
first(mark(X1),X2) | → | first(X1,X2) | (38) |
dbl(active(X)) | → | dbl(X) | (37) |
first(X1,active(X2)) | → | first(X1,X2) | (41) |
add(X1,active(X2)) | → | add(X1,X2) | (35) |
sqr(active(X)) | → | sqr(X) | (29) |
mark#(first(X1,X2)) | → | active#(first(mark(X1),mark(X2))) | (91) |
mark#(terms(X)) | → | active#(terms(mark(X))) | (97) |
The dependency pairs are split into 1 component.
active#(sqr(s(X))) | → | mark#(s(add(sqr(X),dbl(X)))) | (58) |
mark#(add(X1,X2)) | → | mark#(X1) | (78) |
mark#(add(X1,X2)) | → | active#(add(mark(X1),mark(X2))) | (111) |
mark#(dbl(X)) | → | active#(dbl(mark(X))) | (47) |
active#(dbl(s(X))) | → | mark#(s(s(dbl(X)))) | (60) |
active#(add(s(X),Y)) | → | mark#(s(add(X,Y))) | (81) |
mark#(s(X)) | → | mark#(X) | (104) |
mark#(sqr(X)) | → | active#(sqr(mark(X))) | (68) |
π(recip) | = | 1 |
π(sqr#) | = | 1 |
π(s#) | = | 1 |
π(mark) | = | 1 |
π(active) | = | 1 |
π(cons) | = | 2 |
prec(cons#) | = | 0 | status(cons#) | = | [1, 2] | list-extension(cons#) | = | Lex | ||
prec(s) | = | 0 | status(s) | = | [1] | list-extension(s) | = | Lex | ||
prec(recip#) | = | 0 | status(recip#) | = | [] | list-extension(recip#) | = | Lex | ||
prec(dbl) | = | 2 | status(dbl) | = | [1] | list-extension(dbl) | = | Lex | ||
prec(dbl#) | = | 0 | status(dbl#) | = | [] | list-extension(dbl#) | = | Lex | ||
prec(terms#) | = | 0 | status(terms#) | = | [] | list-extension(terms#) | = | Lex | ||
prec(mark#) | = | 0 | status(mark#) | = | [1] | list-extension(mark#) | = | Lex | ||
prec(0) | = | 2 | status(0) | = | [] | list-extension(0) | = | Lex | ||
prec(first#) | = | 0 | status(first#) | = | [1, 2] | list-extension(first#) | = | Lex | ||
prec(nil) | = | 1 | status(nil) | = | [] | list-extension(nil) | = | Lex | ||
prec(first) | = | 0 | status(first) | = | [1, 2] | list-extension(first) | = | Lex | ||
prec(active#) | = | 0 | status(active#) | = | [1] | list-extension(active#) | = | Lex | ||
prec(add#) | = | 0 | status(add#) | = | [2, 1] | list-extension(add#) | = | Lex | ||
prec(add) | = | 1 | status(add) | = | [2, 1] | list-extension(add) | = | Lex | ||
prec(sqr) | = | 2 | status(sqr) | = | [1] | list-extension(sqr) | = | Lex | ||
prec(terms) | = | 0 | status(terms) | = | [] | list-extension(terms) | = | Lex |
[cons#(x1, x2)] | = | max(x1 + 0, x2 + 0, 0) |
[s(x1)] | = | x1 + 0 |
[recip#(x1)] | = | 0 |
[dbl(x1)] | = | x1 + 0 |
[dbl#(x1)] | = | 0 |
[terms#(x1)] | = | 0 |
[mark#(x1)] | = | x1 + 0 |
[0] | = | 0 |
[first#(x1, x2)] | = | max(x1 + 0, x2 + 0, 0) |
[nil] | = | 0 |
[first(x1, x2)] | = | max(x1 + 0, x2 + 0, 0) |
[active#(x1)] | = | x1 + 0 |
[add#(x1, x2)] | = | max(x1 + 0, x2 + 0, 0) |
[add(x1, x2)] | = | max(x1 + 0, x2 + 0, 0) |
[sqr(x1)] | = | x1 + 0 |
[terms(x1)] | = | 0 |
mark(first(X1,X2)) | → | active(first(mark(X1),mark(X2))) | (18) |
active(dbl(0)) | → | mark(0) | (4) |
mark(0) | → | active(0) | (15) |
active(first(0,X)) | → | mark(nil) | (8) |
active(terms(N)) | → | mark(cons(recip(sqr(N)),terms(s(N)))) | (1) |
active(sqr(s(X))) | → | mark(s(add(sqr(X),dbl(X)))) | (3) |
mark(add(X1,X2)) | → | active(add(mark(X1),mark(X2))) | (16) |
terms(active(X)) | → | terms(X) | (21) |
dbl(mark(X)) | → | dbl(X) | (36) |
recip(mark(X)) | → | recip(X) | (26) |
mark(nil) | → | active(nil) | (19) |
add(mark(X1),X2) | → | add(X1,X2) | (32) |
mark(dbl(X)) | → | active(dbl(mark(X))) | (17) |
recip(active(X)) | → | recip(X) | (27) |
add(active(X1),X2) | → | add(X1,X2) | (34) |
cons(mark(X1),X2) | → | cons(X1,X2) | (22) |
sqr(mark(X)) | → | sqr(X) | (28) |
active(dbl(s(X))) | → | mark(s(s(dbl(X)))) | (5) |
add(X1,mark(X2)) | → | add(X1,X2) | (33) |
mark(terms(X)) | → | active(terms(mark(X))) | (10) |
first(X1,mark(X2)) | → | first(X1,X2) | (39) |
active(add(s(X),Y)) | → | mark(s(add(X,Y))) | (7) |
terms(mark(X)) | → | terms(X) | (20) |
cons(X1,active(X2)) | → | cons(X1,X2) | (25) |
s(mark(X)) | → | s(X) | (30) |
mark(s(X)) | → | active(s(mark(X))) | (14) |
s(active(X)) | → | s(X) | (31) |
mark(recip(X)) | → | active(recip(mark(X))) | (12) |
cons(X1,mark(X2)) | → | cons(X1,X2) | (23) |
cons(active(X1),X2) | → | cons(X1,X2) | (24) |
mark(cons(X1,X2)) | → | active(cons(mark(X1),X2)) | (11) |
active(first(s(X),cons(Y,Z))) | → | mark(cons(Y,first(X,Z))) | (9) |
mark(sqr(X)) | → | active(sqr(mark(X))) | (13) |
first(active(X1),X2) | → | first(X1,X2) | (40) |
active(add(0,X)) | → | mark(X) | (6) |
first(mark(X1),X2) | → | first(X1,X2) | (38) |
dbl(active(X)) | → | dbl(X) | (37) |
first(X1,active(X2)) | → | first(X1,X2) | (41) |
add(X1,active(X2)) | → | add(X1,X2) | (35) |
sqr(active(X)) | → | sqr(X) | (29) |
active(sqr(0)) | → | mark(0) | (2) |
active#(sqr(s(X))) | → | mark#(s(add(sqr(X),dbl(X)))) | (58) |
mark#(add(X1,X2)) | → | mark#(X1) | (78) |
active#(dbl(s(X))) | → | mark#(s(s(dbl(X)))) | (60) |
active#(add(s(X),Y)) | → | mark#(s(add(X,Y))) | (81) |
mark#(s(X)) | → | mark#(X) | (104) |
The dependency pairs are split into 0 components.
add#(mark(X1),X2) | → | add#(X1,X2) | (83) |
add#(X1,active(X2)) | → | add#(X1,X2) | (109) |
add#(active(X1),X2) | → | add#(X1,X2) | (93) |
add#(X1,mark(X2)) | → | add#(X1,X2) | (50) |
[cons#(x1, x2)] | = | 0 |
[s(x1)] | = | 1 |
[recip(x1)] | = | 25967 |
[recip#(x1)] | = | 0 |
[dbl(x1)] | = | x1 + 1 |
[dbl#(x1)] | = | 0 |
[terms#(x1)] | = | 0 |
[sqr#(x1)] | = | 0 |
[mark#(x1)] | = | 0 |
[0] | = | 1 |
[s#(x1)] | = | 0 |
[first#(x1, x2)] | = | 0 |
[nil] | = | 0 |
[mark(x1)] | = | x1 + 46596 |
[first(x1, x2)] | = | x1 + x2 + 46593 |
[active(x1)] | = | x1 + 1 |
[cons(x1, x2)] | = | 40940 |
[active#(x1)] | = | 0 |
[add#(x1, x2)] | = | x1 + 0 |
[add(x1, x2)] | = | x1 + x2 + 32582 |
[sqr(x1)] | = | 0 |
[terms(x1)] | = | x1 + 0 |
add#(mark(X1),X2) | → | add#(X1,X2) | (83) |
add#(active(X1),X2) | → | add#(X1,X2) | (93) |
The dependency pairs are split into 1 component.
add#(X1,mark(X2)) | → | add#(X1,X2) | (50) |
add#(X1,active(X2)) | → | add#(X1,X2) | (109) |
[cons#(x1, x2)] | = | 0 |
[s(x1)] | = | 1 |
[recip(x1)] | = | 32885 |
[recip#(x1)] | = | 0 |
[dbl(x1)] | = | 12703 |
[dbl#(x1)] | = | 0 |
[terms#(x1)] | = | 0 |
[sqr#(x1)] | = | 0 |
[mark#(x1)] | = | 0 |
[0] | = | 1 |
[s#(x1)] | = | 0 |
[first#(x1, x2)] | = | 0 |
[nil] | = | 0 |
[mark(x1)] | = | x1 + 14025 |
[first(x1, x2)] | = | x1 + x2 + 14022 |
[active(x1)] | = | x1 + 1 |
[cons(x1, x2)] | = | 31870 |
[active#(x1)] | = | 0 |
[add#(x1, x2)] | = | x2 + 0 |
[add(x1, x2)] | = | x1 + x2 + 242 |
[sqr(x1)] | = | 0 |
[terms(x1)] | = | x1 + 0 |
add#(X1,mark(X2)) | → | add#(X1,X2) | (50) |
add#(X1,active(X2)) | → | add#(X1,X2) | (109) |
The dependency pairs are split into 0 components.
dbl#(mark(X)) | → | dbl#(X) | (82) |
dbl#(active(X)) | → | dbl#(X) | (92) |
[cons#(x1, x2)] | = | 0 |
[s(x1)] | = | 1 |
[recip(x1)] | = | 17943 |
[recip#(x1)] | = | 0 |
[dbl(x1)] | = | 1 |
[dbl#(x1)] | = | x1 + 0 |
[terms#(x1)] | = | 0 |
[sqr#(x1)] | = | 0 |
[mark#(x1)] | = | 0 |
[0] | = | 1 |
[s#(x1)] | = | 0 |
[first#(x1, x2)] | = | 0 |
[nil] | = | 0 |
[mark(x1)] | = | x1 + 4 |
[first(x1, x2)] | = | x1 + x2 + 1 |
[active(x1)] | = | x1 + 1 |
[cons(x1, x2)] | = | 1 |
[active#(x1)] | = | 0 |
[add#(x1, x2)] | = | 0 |
[add(x1, x2)] | = | x1 + x2 + 1 |
[sqr(x1)] | = | 0 |
[terms(x1)] | = | x1 + 0 |
dbl#(mark(X)) | → | dbl#(X) | (82) |
dbl#(active(X)) | → | dbl#(X) | (92) |
The dependency pairs are split into 0 components.
first#(X1,active(X2)) | → | first#(X1,X2) | (114) |
first#(active(X1),X2) | → | first#(X1,X2) | (112) |
first#(mark(X1),X2) | → | first#(X1,X2) | (61) |
first#(X1,mark(X2)) | → | first#(X1,X2) | (90) |
[cons#(x1, x2)] | = | 0 |
[s(x1)] | = | 1 |
[recip(x1)] | = | 51071 |
[recip#(x1)] | = | 0 |
[dbl(x1)] | = | 1 |
[dbl#(x1)] | = | 0 |
[terms#(x1)] | = | 0 |
[sqr#(x1)] | = | 0 |
[mark#(x1)] | = | 0 |
[0] | = | 1 |
[s#(x1)] | = | 0 |
[first#(x1, x2)] | = | x1 + x2 + 0 |
[nil] | = | 0 |
[mark(x1)] | = | x1 + 4 |
[first(x1, x2)] | = | x1 + x2 + 1 |
[active(x1)] | = | x1 + 1 |
[cons(x1, x2)] | = | 13363 |
[active#(x1)] | = | 0 |
[add#(x1, x2)] | = | 0 |
[add(x1, x2)] | = | x1 + x2 + 1 |
[sqr(x1)] | = | 0 |
[terms(x1)] | = | x1 + 0 |
first#(X1,active(X2)) | → | first#(X1,X2) | (114) |
first#(active(X1),X2) | → | first#(X1,X2) | (112) |
first#(mark(X1),X2) | → | first#(X1,X2) | (61) |
first#(X1,mark(X2)) | → | first#(X1,X2) | (90) |
The dependency pairs are split into 0 components.
cons#(active(X1),X2) | → | cons#(X1,X2) | (116) |
cons#(X1,mark(X2)) | → | cons#(X1,X2) | (102) |
cons#(X1,active(X2)) | → | cons#(X1,X2) | (95) |
cons#(mark(X1),X2) | → | cons#(X1,X2) | (43) |
[cons#(x1, x2)] | = | x1 + x2 + 0 |
[s(x1)] | = | 1 |
[recip(x1)] | = | 6437 |
[recip#(x1)] | = | 0 |
[dbl(x1)] | = | 2 |
[dbl#(x1)] | = | 0 |
[terms#(x1)] | = | 0 |
[sqr#(x1)] | = | 0 |
[mark#(x1)] | = | 0 |
[0] | = | 1 |
[s#(x1)] | = | 0 |
[first#(x1, x2)] | = | 0 |
[nil] | = | 0 |
[mark(x1)] | = | x1 + 4 |
[first(x1, x2)] | = | x1 + x2 + 1 |
[active(x1)] | = | x1 + 1 |
[cons(x1, x2)] | = | 1 |
[active#(x1)] | = | 0 |
[add#(x1, x2)] | = | 0 |
[add(x1, x2)] | = | x1 + x2 + 1 |
[sqr(x1)] | = | 0 |
[terms(x1)] | = | x1 + 0 |
cons#(active(X1),X2) | → | cons#(X1,X2) | (116) |
cons#(X1,mark(X2)) | → | cons#(X1,X2) | (102) |
cons#(X1,active(X2)) | → | cons#(X1,X2) | (95) |
cons#(mark(X1),X2) | → | cons#(X1,X2) | (43) |
The dependency pairs are split into 0 components.
recip#(active(X)) | → | recip#(X) | (74) |
recip#(mark(X)) | → | recip#(X) | (66) |
[cons#(x1, x2)] | = | 0 |
[s(x1)] | = | 1 |
[recip(x1)] | = | 30215 |
[recip#(x1)] | = | x1 + 0 |
[dbl(x1)] | = | 2 |
[dbl#(x1)] | = | 0 |
[terms#(x1)] | = | 0 |
[sqr#(x1)] | = | 0 |
[mark#(x1)] | = | 0 |
[0] | = | 1 |
[s#(x1)] | = | 0 |
[first#(x1, x2)] | = | 0 |
[nil] | = | 0 |
[mark(x1)] | = | x1 + 4 |
[first(x1, x2)] | = | x1 + x2 + 1 |
[active(x1)] | = | x1 + 1 |
[cons(x1, x2)] | = | 40758 |
[active#(x1)] | = | 0 |
[add#(x1, x2)] | = | 0 |
[add(x1, x2)] | = | x1 + x2 + 1 |
[sqr(x1)] | = | 0 |
[terms(x1)] | = | x1 + 0 |
recip#(active(X)) | → | recip#(X) | (74) |
recip#(mark(X)) | → | recip#(X) | (66) |
The dependency pairs are split into 0 components.
sqr#(mark(X)) | → | sqr#(X) | (48) |
sqr#(active(X)) | → | sqr#(X) | (42) |
[cons#(x1, x2)] | = | 0 |
[s(x1)] | = | 1 |
[recip(x1)] | = | 26953 |
[recip#(x1)] | = | 0 |
[dbl(x1)] | = | 3 |
[dbl#(x1)] | = | 0 |
[terms#(x1)] | = | 0 |
[sqr#(x1)] | = | x1 + 0 |
[mark#(x1)] | = | 0 |
[0] | = | 1 |
[s#(x1)] | = | 0 |
[first#(x1, x2)] | = | 0 |
[nil] | = | 0 |
[mark(x1)] | = | x1 + 4 |
[first(x1, x2)] | = | x1 + x2 + 1 |
[active(x1)] | = | x1 + 1 |
[cons(x1, x2)] | = | 26211 |
[active#(x1)] | = | 0 |
[add#(x1, x2)] | = | 0 |
[add(x1, x2)] | = | x1 + x2 + 1 |
[sqr(x1)] | = | 0 |
[terms(x1)] | = | x1 + 0 |
sqr#(mark(X)) | → | sqr#(X) | (48) |
sqr#(active(X)) | → | sqr#(X) | (42) |
The dependency pairs are split into 0 components.
terms#(active(X)) | → | terms#(X) | (53) |
terms#(mark(X)) | → | terms#(X) | (44) |
[cons#(x1, x2)] | = | 0 |
[s(x1)] | = | 1 |
[recip(x1)] | = | 28776 |
[recip#(x1)] | = | 0 |
[dbl(x1)] | = | 1 |
[dbl#(x1)] | = | 0 |
[terms#(x1)] | = | x1 + 0 |
[sqr#(x1)] | = | 0 |
[mark#(x1)] | = | 0 |
[0] | = | 1 |
[s#(x1)] | = | 0 |
[first#(x1, x2)] | = | 0 |
[nil] | = | 0 |
[mark(x1)] | = | x1 + 4 |
[first(x1, x2)] | = | x1 + x2 + 1 |
[active(x1)] | = | x1 + 1 |
[cons(x1, x2)] | = | 1 |
[active#(x1)] | = | 0 |
[add#(x1, x2)] | = | 0 |
[add(x1, x2)] | = | x1 + x2 + 1 |
[sqr(x1)] | = | 0 |
[terms(x1)] | = | x1 + 0 |
terms#(active(X)) | → | terms#(X) | (53) |
terms#(mark(X)) | → | terms#(X) | (44) |
The dependency pairs are split into 0 components.
s#(active(X)) | → | s#(X) | (73) |
s#(mark(X)) | → | s#(X) | (98) |
[cons#(x1, x2)] | = | 0 |
[s(x1)] | = | 1 |
[recip(x1)] | = | 50219 |
[recip#(x1)] | = | 0 |
[dbl(x1)] | = | 1 |
[dbl#(x1)] | = | 0 |
[terms#(x1)] | = | 0 |
[sqr#(x1)] | = | 0 |
[mark#(x1)] | = | 0 |
[0] | = | 1 |
[s#(x1)] | = | x1 + 0 |
[first#(x1, x2)] | = | 0 |
[nil] | = | 0 |
[mark(x1)] | = | x1 + 4 |
[first(x1, x2)] | = | x1 + x2 + 1 |
[active(x1)] | = | x1 + 1 |
[cons(x1, x2)] | = | 19198 |
[active#(x1)] | = | 0 |
[add#(x1, x2)] | = | 0 |
[add(x1, x2)] | = | x1 + x2 + 1 |
[sqr(x1)] | = | 0 |
[terms(x1)] | = | x1 + 0 |
s#(active(X)) | → | s#(X) | (73) |
s#(mark(X)) | → | s#(X) | (98) |
The dependency pairs are split into 0 components.