The rewrite relation of the following TRS is considered.
a__from(X) | → | cons(mark(X),from(s(X))) | (1) |
a__2ndspos(0,Z) | → | rnil | (2) |
a__2ndspos(s(N),cons(X,cons(Y,Z))) | → | rcons(posrecip(mark(Y)),a__2ndsneg(mark(N),mark(Z))) | (3) |
a__2ndsneg(0,Z) | → | rnil | (4) |
a__2ndsneg(s(N),cons(X,cons(Y,Z))) | → | rcons(negrecip(mark(Y)),a__2ndspos(mark(N),mark(Z))) | (5) |
a__pi(X) | → | a__2ndspos(mark(X),a__from(0)) | (6) |
a__plus(0,Y) | → | mark(Y) | (7) |
a__plus(s(X),Y) | → | s(a__plus(mark(X),mark(Y))) | (8) |
a__times(0,Y) | → | 0 | (9) |
a__times(s(X),Y) | → | a__plus(mark(Y),a__times(mark(X),mark(Y))) | (10) |
a__square(X) | → | a__times(mark(X),mark(X)) | (11) |
mark(from(X)) | → | a__from(mark(X)) | (12) |
mark(2ndspos(X1,X2)) | → | a__2ndspos(mark(X1),mark(X2)) | (13) |
mark(2ndsneg(X1,X2)) | → | a__2ndsneg(mark(X1),mark(X2)) | (14) |
mark(pi(X)) | → | a__pi(mark(X)) | (15) |
mark(plus(X1,X2)) | → | a__plus(mark(X1),mark(X2)) | (16) |
mark(times(X1,X2)) | → | a__times(mark(X1),mark(X2)) | (17) |
mark(square(X)) | → | a__square(mark(X)) | (18) |
mark(0) | → | 0 | (19) |
mark(s(X)) | → | s(mark(X)) | (20) |
mark(posrecip(X)) | → | posrecip(mark(X)) | (21) |
mark(negrecip(X)) | → | negrecip(mark(X)) | (22) |
mark(nil) | → | nil | (23) |
mark(cons(X1,X2)) | → | cons(mark(X1),X2) | (24) |
mark(rnil) | → | rnil | (25) |
mark(rcons(X1,X2)) | → | rcons(mark(X1),mark(X2)) | (26) |
a__from(X) | → | from(X) | (27) |
a__2ndspos(X1,X2) | → | 2ndspos(X1,X2) | (28) |
a__2ndsneg(X1,X2) | → | 2ndsneg(X1,X2) | (29) |
a__pi(X) | → | pi(X) | (30) |
a__plus(X1,X2) | → | plus(X1,X2) | (31) |
a__times(X1,X2) | → | times(X1,X2) | (32) |
a__square(X) | → | square(X) | (33) |
a__pi#(X) | → | mark#(X) | (34) |
a__plus#(s(X),Y) | → | mark#(X) | (35) |
mark#(times(X1,X2)) | → | mark#(X1) | (36) |
mark#(plus(X1,X2)) | → | mark#(X1) | (37) |
mark#(pi(X)) | → | mark#(X) | (38) |
a__plus#(s(X),Y) | → | a__plus#(mark(X),mark(Y)) | (39) |
a__from#(X) | → | mark#(X) | (40) |
a__2ndspos#(s(N),cons(X,cons(Y,Z))) | → | mark#(Y) | (41) |
mark#(square(X)) | → | a__square#(mark(X)) | (42) |
mark#(square(X)) | → | mark#(X) | (43) |
a__2ndspos#(s(N),cons(X,cons(Y,Z))) | → | a__2ndsneg#(mark(N),mark(Z)) | (44) |
mark#(2ndspos(X1,X2)) | → | mark#(X2) | (45) |
a__2ndspos#(s(N),cons(X,cons(Y,Z))) | → | mark#(Z) | (46) |
mark#(2ndsneg(X1,X2)) | → | a__2ndsneg#(mark(X1),mark(X2)) | (47) |
a__square#(X) | → | mark#(X) | (48) |
mark#(from(X)) | → | a__from#(mark(X)) | (49) |
a__2ndsneg#(s(N),cons(X,cons(Y,Z))) | → | a__2ndspos#(mark(N),mark(Z)) | (50) |
a__2ndsneg#(s(N),cons(X,cons(Y,Z))) | → | mark#(Y) | (51) |
mark#(pi(X)) | → | a__pi#(mark(X)) | (52) |
mark#(from(X)) | → | mark#(X) | (53) |
mark#(rcons(X1,X2)) | → | mark#(X1) | (54) |
mark#(2ndsneg(X1,X2)) | → | mark#(X1) | (55) |
mark#(times(X1,X2)) | → | mark#(X2) | (56) |
a__2ndsneg#(s(N),cons(X,cons(Y,Z))) | → | mark#(N) | (57) |
a__times#(s(X),Y) | → | a__times#(mark(X),mark(Y)) | (58) |
a__square#(X) | → | a__times#(mark(X),mark(X)) | (59) |
a__2ndspos#(s(N),cons(X,cons(Y,Z))) | → | mark#(N) | (60) |
mark#(cons(X1,X2)) | → | mark#(X1) | (61) |
mark#(posrecip(X)) | → | mark#(X) | (62) |
mark#(2ndspos(X1,X2)) | → | mark#(X1) | (63) |
a__plus#(s(X),Y) | → | mark#(Y) | (64) |
mark#(times(X1,X2)) | → | a__times#(mark(X1),mark(X2)) | (65) |
a__times#(s(X),Y) | → | mark#(Y) | (66) |
mark#(plus(X1,X2)) | → | a__plus#(mark(X1),mark(X2)) | (67) |
mark#(negrecip(X)) | → | mark#(X) | (68) |
a__plus#(0,Y) | → | mark#(Y) | (69) |
mark#(rcons(X1,X2)) | → | mark#(X2) | (70) |
a__times#(s(X),Y) | → | mark#(Y) | (66) |
a__2ndsneg#(s(N),cons(X,cons(Y,Z))) | → | mark#(Z) | (71) |
mark#(plus(X1,X2)) | → | mark#(X2) | (72) |
a__times#(s(X),Y) | → | mark#(X) | (73) |
mark#(s(X)) | → | mark#(X) | (74) |
a__pi#(X) | → | a__from#(0) | (75) |
a__pi#(X) | → | a__2ndspos#(mark(X),a__from(0)) | (76) |
a__square#(X) | → | mark#(X) | (48) |
mark#(2ndsneg(X1,X2)) | → | mark#(X2) | (77) |
mark#(2ndspos(X1,X2)) | → | a__2ndspos#(mark(X1),mark(X2)) | (78) |
a__times#(s(X),Y) | → | a__plus#(mark(Y),a__times(mark(X),mark(Y))) | (79) |
The dependency pairs are split into 1 component.
a__times#(s(X),Y) | → | a__plus#(mark(Y),a__times(mark(X),mark(Y))) | (79) |
a__2ndsneg#(s(N),cons(X,cons(Y,Z))) | → | mark#(N) | (57) |
mark#(2ndspos(X1,X2)) | → | a__2ndspos#(mark(X1),mark(X2)) | (78) |
mark#(times(X1,X2)) | → | mark#(X2) | (56) |
mark#(2ndsneg(X1,X2)) | → | mark#(X1) | (55) |
mark#(2ndsneg(X1,X2)) | → | mark#(X2) | (77) |
mark#(rcons(X1,X2)) | → | mark#(X1) | (54) |
mark#(from(X)) | → | mark#(X) | (53) |
a__square#(X) | → | mark#(X) | (48) |
mark#(pi(X)) | → | a__pi#(mark(X)) | (52) |
a__pi#(X) | → | a__2ndspos#(mark(X),a__from(0)) | (76) |
a__2ndsneg#(s(N),cons(X,cons(Y,Z))) | → | mark#(Y) | (51) |
a__pi#(X) | → | a__from#(0) | (75) |
a__2ndsneg#(s(N),cons(X,cons(Y,Z))) | → | a__2ndspos#(mark(N),mark(Z)) | (50) |
mark#(s(X)) | → | mark#(X) | (74) |
a__times#(s(X),Y) | → | mark#(X) | (73) |
mark#(plus(X1,X2)) | → | mark#(X2) | (72) |
a__2ndsneg#(s(N),cons(X,cons(Y,Z))) | → | mark#(Z) | (71) |
mark#(from(X)) | → | a__from#(mark(X)) | (49) |
a__square#(X) | → | mark#(X) | (48) |
mark#(2ndsneg(X1,X2)) | → | a__2ndsneg#(mark(X1),mark(X2)) | (47) |
mark#(rcons(X1,X2)) | → | mark#(X2) | (70) |
a__times#(s(X),Y) | → | mark#(Y) | (66) |
a__plus#(0,Y) | → | mark#(Y) | (69) |
a__2ndspos#(s(N),cons(X,cons(Y,Z))) | → | mark#(Z) | (46) |
mark#(2ndspos(X1,X2)) | → | mark#(X2) | (45) |
mark#(negrecip(X)) | → | mark#(X) | (68) |
a__2ndspos#(s(N),cons(X,cons(Y,Z))) | → | a__2ndsneg#(mark(N),mark(Z)) | (44) |
mark#(plus(X1,X2)) | → | a__plus#(mark(X1),mark(X2)) | (67) |
mark#(square(X)) | → | mark#(X) | (43) |
a__times#(s(X),Y) | → | mark#(Y) | (66) |
mark#(times(X1,X2)) | → | a__times#(mark(X1),mark(X2)) | (65) |
mark#(square(X)) | → | a__square#(mark(X)) | (42) |
a__plus#(s(X),Y) | → | mark#(Y) | (64) |
mark#(2ndspos(X1,X2)) | → | mark#(X1) | (63) |
a__2ndspos#(s(N),cons(X,cons(Y,Z))) | → | mark#(Y) | (41) |
mark#(posrecip(X)) | → | mark#(X) | (62) |
a__from#(X) | → | mark#(X) | (40) |
a__plus#(s(X),Y) | → | a__plus#(mark(X),mark(Y)) | (39) |
mark#(cons(X1,X2)) | → | mark#(X1) | (61) |
mark#(pi(X)) | → | mark#(X) | (38) |
a__2ndspos#(s(N),cons(X,cons(Y,Z))) | → | mark#(N) | (60) |
a__square#(X) | → | a__times#(mark(X),mark(X)) | (59) |
mark#(plus(X1,X2)) | → | mark#(X1) | (37) |
mark#(times(X1,X2)) | → | mark#(X1) | (36) |
a__plus#(s(X),Y) | → | mark#(X) | (35) |
a__pi#(X) | → | mark#(X) | (34) |
a__times#(s(X),Y) | → | a__times#(mark(X),mark(Y)) | (58) |
[a__plus(x1, x2)] | = | max(x1 + 14683, x2 + 0, 0) |
[a__2ndsneg(x1, x2)] | = | max(x1 + 15927, x2 + 15924, 0) |
[negrecip(x1)] | = | x1 + 9983 |
[s(x1)] | = | x1 + 0 |
[a__pi#(x1)] | = | x1 + 82871 |
[a__from#(x1)] | = | x1 + 4322 |
[2ndspos(x1, x2)] | = | max(x1 + 15927, x2 + 15924, 0) |
[a__from(x1)] | = | x1 + 21657 |
[rnil] | = | 15925 |
[square(x1)] | = | x1 + 49915 |
[a__times#(x1, x2)] | = | max(x1 + 19003, x2 + 45289, 0) |
[pi(x1)] | = | x1 + 78551 |
[rcons(x1, x2)] | = | max(x1 + 5942, x2 + 0, 0) |
[a__2ndspos(x1, x2)] | = | max(x1 + 15927, x2 + 15924, 0) |
[a__2ndsneg#(x1, x2)] | = | max(x1 + 20243, x2 + 20244, 0) |
[a__plus#(x1, x2)] | = | max(x1 + 4322, x2 + 4321, 0) |
[mark#(x1)] | = | x1 + 4321 |
[0] | = | 40969 |
[from(x1)] | = | x1 + 21657 |
[times(x1, x2)] | = | max(x1 + 14682, x2 + 40968, 0) |
[a__pi(x1)] | = | x1 + 78551 |
[nil] | = | 39434 |
[mark(x1)] | = | x1 + 0 |
[2ndsneg(x1, x2)] | = | max(x1 + 15927, x2 + 15924, 0) |
[plus(x1, x2)] | = | max(x1 + 14683, x2 + 0, 0) |
[a__square(x1)] | = | x1 + 49915 |
[cons(x1, x2)] | = | max(x1 + 2, x2 + 0, 0) |
[a__times(x1, x2)] | = | max(x1 + 14682, x2 + 40968, 0) |
[a__square#(x1)] | = | x1 + 45290 |
[a__2ndspos#(x1, x2)] | = | max(x1 + 20243, x2 + 20244, 0) |
[posrecip(x1)] | = | x1 + 9983 |
mark(square(X)) | → | a__square(mark(X)) | (18) |
a__2ndsneg(0,Z) | → | rnil | (4) |
mark(pi(X)) | → | a__pi(mark(X)) | (15) |
a__plus(s(X),Y) | → | s(a__plus(mark(X),mark(Y))) | (8) |
a__from(X) | → | cons(mark(X),from(s(X))) | (1) |
a__2ndspos(s(N),cons(X,cons(Y,Z))) | → | rcons(posrecip(mark(Y)),a__2ndsneg(mark(N),mark(Z))) | (3) |
mark(plus(X1,X2)) | → | a__plus(mark(X1),mark(X2)) | (16) |
mark(posrecip(X)) | → | posrecip(mark(X)) | (21) |
mark(rcons(X1,X2)) | → | rcons(mark(X1),mark(X2)) | (26) |
mark(0) | → | 0 | (19) |
a__times(X1,X2) | → | times(X1,X2) | (32) |
mark(times(X1,X2)) | → | a__times(mark(X1),mark(X2)) | (17) |
a__from(X) | → | from(X) | (27) |
mark(negrecip(X)) | → | negrecip(mark(X)) | (22) |
a__2ndspos(X1,X2) | → | 2ndspos(X1,X2) | (28) |
a__2ndsneg(s(N),cons(X,cons(Y,Z))) | → | rcons(negrecip(mark(Y)),a__2ndspos(mark(N),mark(Z))) | (5) |
a__square(X) | → | square(X) | (33) |
a__times(s(X),Y) | → | a__plus(mark(Y),a__times(mark(X),mark(Y))) | (10) |
a__plus(0,Y) | → | mark(Y) | (7) |
mark(s(X)) | → | s(mark(X)) | (20) |
mark(rnil) | → | rnil | (25) |
a__pi(X) | → | pi(X) | (30) |
mark(2ndsneg(X1,X2)) | → | a__2ndsneg(mark(X1),mark(X2)) | (14) |
a__plus(X1,X2) | → | plus(X1,X2) | (31) |
mark(from(X)) | → | a__from(mark(X)) | (12) |
mark(nil) | → | nil | (23) |
mark(cons(X1,X2)) | → | cons(mark(X1),X2) | (24) |
a__square(X) | → | a__times(mark(X),mark(X)) | (11) |
a__times(0,Y) | → | 0 | (9) |
mark(2ndspos(X1,X2)) | → | a__2ndspos(mark(X1),mark(X2)) | (13) |
a__pi(X) | → | a__2ndspos(mark(X),a__from(0)) | (6) |
a__2ndsneg(X1,X2) | → | 2ndsneg(X1,X2) | (29) |
a__2ndspos(0,Z) | → | rnil | (2) |
a__2ndsneg#(s(N),cons(X,cons(Y,Z))) | → | mark#(N) | (57) |
mark#(2ndspos(X1,X2)) | → | a__2ndspos#(mark(X1),mark(X2)) | (78) |
mark#(times(X1,X2)) | → | mark#(X2) | (56) |
mark#(2ndsneg(X1,X2)) | → | mark#(X1) | (55) |
mark#(2ndsneg(X1,X2)) | → | mark#(X2) | (77) |
mark#(rcons(X1,X2)) | → | mark#(X1) | (54) |
mark#(from(X)) | → | mark#(X) | (53) |
a__square#(X) | → | mark#(X) | (48) |
mark#(pi(X)) | → | a__pi#(mark(X)) | (52) |
a__pi#(X) | → | a__2ndspos#(mark(X),a__from(0)) | (76) |
a__2ndsneg#(s(N),cons(X,cons(Y,Z))) | → | mark#(Y) | (51) |
a__pi#(X) | → | a__from#(0) | (75) |
a__times#(s(X),Y) | → | mark#(X) | (73) |
a__2ndsneg#(s(N),cons(X,cons(Y,Z))) | → | mark#(Z) | (71) |
mark#(from(X)) | → | a__from#(mark(X)) | (49) |
a__square#(X) | → | mark#(X) | (48) |
mark#(2ndsneg(X1,X2)) | → | a__2ndsneg#(mark(X1),mark(X2)) | (47) |
a__times#(s(X),Y) | → | mark#(Y) | (66) |
a__2ndspos#(s(N),cons(X,cons(Y,Z))) | → | mark#(Z) | (46) |
mark#(2ndspos(X1,X2)) | → | mark#(X2) | (45) |
mark#(negrecip(X)) | → | mark#(X) | (68) |
mark#(square(X)) | → | mark#(X) | (43) |
a__times#(s(X),Y) | → | mark#(Y) | (66) |
mark#(square(X)) | → | a__square#(mark(X)) | (42) |
mark#(2ndspos(X1,X2)) | → | mark#(X1) | (63) |
a__2ndspos#(s(N),cons(X,cons(Y,Z))) | → | mark#(Y) | (41) |
mark#(posrecip(X)) | → | mark#(X) | (62) |
a__from#(X) | → | mark#(X) | (40) |
mark#(cons(X1,X2)) | → | mark#(X1) | (61) |
mark#(pi(X)) | → | mark#(X) | (38) |
a__2ndspos#(s(N),cons(X,cons(Y,Z))) | → | mark#(N) | (60) |
a__square#(X) | → | a__times#(mark(X),mark(X)) | (59) |
mark#(plus(X1,X2)) | → | mark#(X1) | (37) |
mark#(times(X1,X2)) | → | mark#(X1) | (36) |
a__plus#(s(X),Y) | → | mark#(X) | (35) |
a__pi#(X) | → | mark#(X) | (34) |
The dependency pairs are split into 2 components.
a__2ndspos#(s(N),cons(X,cons(Y,Z))) | → | a__2ndsneg#(mark(N),mark(Z)) | (44) |
a__2ndsneg#(s(N),cons(X,cons(Y,Z))) | → | a__2ndspos#(mark(N),mark(Z)) | (50) |
π(negrecip) | = | 1 |
π(a__times#) | = | 1 |
π(mark#) | = | 1 |
π(mark) | = | 1 |
π(a__2ndspos#) | = | 1 |
prec(a__plus) | = | 5 | status(a__plus) | = | [1, 2] | list-extension(a__plus) | = | Lex | ||
prec(a__2ndsneg) | = | 5 | status(a__2ndsneg) | = | [1, 2] | list-extension(a__2ndsneg) | = | Lex | ||
prec(s) | = | 4 | status(s) | = | [1] | list-extension(s) | = | Lex | ||
prec(a__pi#) | = | 0 | status(a__pi#) | = | [] | list-extension(a__pi#) | = | Lex | ||
prec(a__from#) | = | 0 | status(a__from#) | = | [] | list-extension(a__from#) | = | Lex | ||
prec(2ndspos) | = | 2 | status(2ndspos) | = | [] | list-extension(2ndspos) | = | Lex | ||
prec(a__from) | = | 3 | status(a__from) | = | [1] | list-extension(a__from) | = | Lex | ||
prec(rnil) | = | 2 | status(rnil) | = | [] | list-extension(rnil) | = | Lex | ||
prec(square) | = | 7 | status(square) | = | [1] | list-extension(square) | = | Lex | ||
prec(pi) | = | 6 | status(pi) | = | [] | list-extension(pi) | = | Lex | ||
prec(rcons) | = | 1 | status(rcons) | = | [] | list-extension(rcons) | = | Lex | ||
prec(a__2ndspos) | = | 2 | status(a__2ndspos) | = | [] | list-extension(a__2ndspos) | = | Lex | ||
prec(a__2ndsneg#) | = | 0 | status(a__2ndsneg#) | = | [1] | list-extension(a__2ndsneg#) | = | Lex | ||
prec(a__plus#) | = | 0 | status(a__plus#) | = | [2, 1] | list-extension(a__plus#) | = | Lex | ||
prec(0) | = | 6 | status(0) | = | [] | list-extension(0) | = | Lex | ||
prec(from) | = | 3 | status(from) | = | [1] | list-extension(from) | = | Lex | ||
prec(times) | = | 6 | status(times) | = | [1, 2] | list-extension(times) | = | Lex | ||
prec(a__pi) | = | 6 | status(a__pi) | = | [] | list-extension(a__pi) | = | Lex | ||
prec(nil) | = | 2 | status(nil) | = | [] | list-extension(nil) | = | Lex | ||
prec(2ndsneg) | = | 5 | status(2ndsneg) | = | [1, 2] | list-extension(2ndsneg) | = | Lex | ||
prec(plus) | = | 5 | status(plus) | = | [1, 2] | list-extension(plus) | = | Lex | ||
prec(a__square) | = | 7 | status(a__square) | = | [1] | list-extension(a__square) | = | Lex | ||
prec(cons) | = | 2 | status(cons) | = | [] | list-extension(cons) | = | Lex | ||
prec(a__times) | = | 6 | status(a__times) | = | [1, 2] | list-extension(a__times) | = | Lex | ||
prec(a__square#) | = | 0 | status(a__square#) | = | [] | list-extension(a__square#) | = | Lex | ||
prec(posrecip) | = | 2 | status(posrecip) | = | [] | list-extension(posrecip) | = | Lex |
[a__plus(x1, x2)] | = | max(x1 + 0, x2 + 0, 0) |
[a__2ndsneg(x1, x2)] | = | max(x1 + 0, x2 + 0, 0) |
[s(x1)] | = | x1 + 0 |
[a__pi#(x1)] | = | 0 |
[a__from#(x1)] | = | 0 |
[2ndspos(x1, x2)] | = | max(0) |
[a__from(x1)] | = | x1 + 0 |
[rnil] | = | 0 |
[square(x1)] | = | x1 + 0 |
[pi(x1)] | = | 0 |
[rcons(x1, x2)] | = | max(0) |
[a__2ndspos(x1, x2)] | = | max(0) |
[a__2ndsneg#(x1, x2)] | = | max(x1 + 0, 0) |
[a__plus#(x1, x2)] | = | max(x1 + 0, x2 + 0, 0) |
[0] | = | 0 |
[from(x1)] | = | x1 + 0 |
[times(x1, x2)] | = | max(x1 + 0, x2 + 0, 0) |
[a__pi(x1)] | = | 0 |
[nil] | = | 0 |
[2ndsneg(x1, x2)] | = | max(x1 + 0, x2 + 0, 0) |
[plus(x1, x2)] | = | max(x1 + 0, x2 + 0, 0) |
[a__square(x1)] | = | x1 + 0 |
[cons(x1, x2)] | = | max(0) |
[a__times(x1, x2)] | = | max(x1 + 0, x2 + 0, 0) |
[a__square#(x1)] | = | 0 |
[posrecip(x1)] | = | 0 |
mark(square(X)) | → | a__square(mark(X)) | (18) |
a__2ndsneg(0,Z) | → | rnil | (4) |
mark(pi(X)) | → | a__pi(mark(X)) | (15) |
a__plus(s(X),Y) | → | s(a__plus(mark(X),mark(Y))) | (8) |
a__from(X) | → | cons(mark(X),from(s(X))) | (1) |
a__2ndspos(s(N),cons(X,cons(Y,Z))) | → | rcons(posrecip(mark(Y)),a__2ndsneg(mark(N),mark(Z))) | (3) |
mark(plus(X1,X2)) | → | a__plus(mark(X1),mark(X2)) | (16) |
mark(posrecip(X)) | → | posrecip(mark(X)) | (21) |
mark(rcons(X1,X2)) | → | rcons(mark(X1),mark(X2)) | (26) |
mark(0) | → | 0 | (19) |
a__times(X1,X2) | → | times(X1,X2) | (32) |
mark(times(X1,X2)) | → | a__times(mark(X1),mark(X2)) | (17) |
a__from(X) | → | from(X) | (27) |
mark(negrecip(X)) | → | negrecip(mark(X)) | (22) |
a__2ndspos(X1,X2) | → | 2ndspos(X1,X2) | (28) |
a__2ndsneg(s(N),cons(X,cons(Y,Z))) | → | rcons(negrecip(mark(Y)),a__2ndspos(mark(N),mark(Z))) | (5) |
a__square(X) | → | square(X) | (33) |
a__times(s(X),Y) | → | a__plus(mark(Y),a__times(mark(X),mark(Y))) | (10) |
a__plus(0,Y) | → | mark(Y) | (7) |
mark(s(X)) | → | s(mark(X)) | (20) |
mark(rnil) | → | rnil | (25) |
a__pi(X) | → | pi(X) | (30) |
mark(2ndsneg(X1,X2)) | → | a__2ndsneg(mark(X1),mark(X2)) | (14) |
a__plus(X1,X2) | → | plus(X1,X2) | (31) |
mark(from(X)) | → | a__from(mark(X)) | (12) |
mark(nil) | → | nil | (23) |
mark(cons(X1,X2)) | → | cons(mark(X1),X2) | (24) |
a__square(X) | → | a__times(mark(X),mark(X)) | (11) |
a__times(0,Y) | → | 0 | (9) |
mark(2ndspos(X1,X2)) | → | a__2ndspos(mark(X1),mark(X2)) | (13) |
a__pi(X) | → | a__2ndspos(mark(X),a__from(0)) | (6) |
a__2ndsneg(X1,X2) | → | 2ndsneg(X1,X2) | (29) |
a__2ndspos(0,Z) | → | rnil | (2) |
a__2ndspos#(s(N),cons(X,cons(Y,Z))) | → | a__2ndsneg#(mark(N),mark(Z)) | (44) |
a__2ndsneg#(s(N),cons(X,cons(Y,Z))) | → | a__2ndspos#(mark(N),mark(Z)) | (50) |
The dependency pairs are split into 0 components.
a__plus#(s(X),Y) | → | mark#(Y) | (64) |
a__plus#(s(X),Y) | → | a__plus#(mark(X),mark(Y)) | (39) |
mark#(plus(X1,X2)) | → | mark#(X2) | (72) |
mark#(plus(X1,X2)) | → | a__plus#(mark(X1),mark(X2)) | (67) |
mark#(rcons(X1,X2)) | → | mark#(X2) | (70) |
mark#(times(X1,X2)) | → | a__times#(mark(X1),mark(X2)) | (65) |
a__times#(s(X),Y) | → | a__times#(mark(X),mark(Y)) | (58) |
a__times#(s(X),Y) | → | a__plus#(mark(Y),a__times(mark(X),mark(Y))) | (79) |
a__plus#(0,Y) | → | mark#(Y) | (69) |
mark#(s(X)) | → | mark#(X) | (74) |
π(rcons) | = | 2 |
π(mark) | = | 1 |
π(cons) | = | 2 |
π(a__2ndspos#) | = | 1 |
prec(a__plus) | = | 10 | status(a__plus) | = | [2, 1] | list-extension(a__plus) | = | Lex | ||
prec(a__2ndsneg) | = | 5 | status(a__2ndsneg) | = | [1, 2] | list-extension(a__2ndsneg) | = | Lex | ||
prec(negrecip) | = | 4 | status(negrecip) | = | [] | list-extension(negrecip) | = | Lex | ||
prec(s) | = | 4 | status(s) | = | [1] | list-extension(s) | = | Lex | ||
prec(a__pi#) | = | 0 | status(a__pi#) | = | [] | list-extension(a__pi#) | = | Lex | ||
prec(a__from#) | = | 0 | status(a__from#) | = | [] | list-extension(a__from#) | = | Lex | ||
prec(2ndspos) | = | 5 | status(2ndspos) | = | [1, 2] | list-extension(2ndspos) | = | Lex | ||
prec(a__from) | = | 3 | status(a__from) | = | [] | list-extension(a__from) | = | Lex | ||
prec(rnil) | = | 5 | status(rnil) | = | [] | list-extension(rnil) | = | Lex | ||
prec(square) | = | 12 | status(square) | = | [1] | list-extension(square) | = | Lex | ||
prec(a__times#) | = | 11 | status(a__times#) | = | [1, 2] | list-extension(a__times#) | = | Lex | ||
prec(pi) | = | 6 | status(pi) | = | [1] | list-extension(pi) | = | Lex | ||
prec(a__2ndspos) | = | 5 | status(a__2ndspos) | = | [1, 2] | list-extension(a__2ndspos) | = | Lex | ||
prec(a__2ndsneg#) | = | 0 | status(a__2ndsneg#) | = | [1] | list-extension(a__2ndsneg#) | = | Lex | ||
prec(a__plus#) | = | 9 | status(a__plus#) | = | [1, 2] | list-extension(a__plus#) | = | Lex | ||
prec(mark#) | = | 8 | status(mark#) | = | [1] | list-extension(mark#) | = | Lex | ||
prec(0) | = | 7 | status(0) | = | [] | list-extension(0) | = | Lex | ||
prec(from) | = | 3 | status(from) | = | [] | list-extension(from) | = | Lex | ||
prec(times) | = | 11 | status(times) | = | [1, 2] | list-extension(times) | = | Lex | ||
prec(a__pi) | = | 6 | status(a__pi) | = | [1] | list-extension(a__pi) | = | Lex | ||
prec(nil) | = | 2 | status(nil) | = | [] | list-extension(nil) | = | Lex | ||
prec(2ndsneg) | = | 5 | status(2ndsneg) | = | [1, 2] | list-extension(2ndsneg) | = | Lex | ||
prec(plus) | = | 10 | status(plus) | = | [2, 1] | list-extension(plus) | = | Lex | ||
prec(a__square) | = | 12 | status(a__square) | = | [1] | list-extension(a__square) | = | Lex | ||
prec(a__times) | = | 11 | status(a__times) | = | [1, 2] | list-extension(a__times) | = | Lex | ||
prec(a__square#) | = | 0 | status(a__square#) | = | [] | list-extension(a__square#) | = | Lex | ||
prec(posrecip) | = | 2 | status(posrecip) | = | [] | list-extension(posrecip) | = | Lex |
[a__plus(x1, x2)] | = | max(x1 + 0, x2 + 0, 0) |
[a__2ndsneg(x1, x2)] | = | max(x1 + 0, x2 + 0, 0) |
[negrecip(x1)] | = | 0 |
[s(x1)] | = | x1 + 0 |
[a__pi#(x1)] | = | 0 |
[a__from#(x1)] | = | 0 |
[2ndspos(x1, x2)] | = | max(x1 + 0, x2 + 0, 0) |
[a__from(x1)] | = | 0 |
[rnil] | = | 0 |
[square(x1)] | = | x1 + 0 |
[a__times#(x1, x2)] | = | max(x1 + 0, x2 + 0, 0) |
[pi(x1)] | = | x1 + 0 |
[a__2ndspos(x1, x2)] | = | max(x1 + 0, x2 + 0, 0) |
[a__2ndsneg#(x1, x2)] | = | max(x1 + 0, 0) |
[a__plus#(x1, x2)] | = | max(x1 + 0, x2 + 0, 0) |
[mark#(x1)] | = | x1 + 0 |
[0] | = | 0 |
[from(x1)] | = | 0 |
[times(x1, x2)] | = | max(x1 + 0, x2 + 0, 0) |
[a__pi(x1)] | = | x1 + 0 |
[nil] | = | 0 |
[2ndsneg(x1, x2)] | = | max(x1 + 0, x2 + 0, 0) |
[plus(x1, x2)] | = | max(x1 + 0, x2 + 0, 0) |
[a__square(x1)] | = | x1 + 0 |
[a__times(x1, x2)] | = | max(x1 + 0, x2 + 0, 0) |
[a__square#(x1)] | = | 0 |
[posrecip(x1)] | = | 0 |
mark(square(X)) | → | a__square(mark(X)) | (18) |
a__2ndsneg(0,Z) | → | rnil | (4) |
mark(pi(X)) | → | a__pi(mark(X)) | (15) |
a__plus(s(X),Y) | → | s(a__plus(mark(X),mark(Y))) | (8) |
a__from(X) | → | cons(mark(X),from(s(X))) | (1) |
a__2ndspos(s(N),cons(X,cons(Y,Z))) | → | rcons(posrecip(mark(Y)),a__2ndsneg(mark(N),mark(Z))) | (3) |
mark(plus(X1,X2)) | → | a__plus(mark(X1),mark(X2)) | (16) |
mark(posrecip(X)) | → | posrecip(mark(X)) | (21) |
mark(rcons(X1,X2)) | → | rcons(mark(X1),mark(X2)) | (26) |
mark(0) | → | 0 | (19) |
a__times(X1,X2) | → | times(X1,X2) | (32) |
mark(times(X1,X2)) | → | a__times(mark(X1),mark(X2)) | (17) |
a__from(X) | → | from(X) | (27) |
mark(negrecip(X)) | → | negrecip(mark(X)) | (22) |
a__2ndspos(X1,X2) | → | 2ndspos(X1,X2) | (28) |
a__2ndsneg(s(N),cons(X,cons(Y,Z))) | → | rcons(negrecip(mark(Y)),a__2ndspos(mark(N),mark(Z))) | (5) |
a__square(X) | → | square(X) | (33) |
a__times(s(X),Y) | → | a__plus(mark(Y),a__times(mark(X),mark(Y))) | (10) |
a__plus(0,Y) | → | mark(Y) | (7) |
mark(s(X)) | → | s(mark(X)) | (20) |
mark(rnil) | → | rnil | (25) |
a__pi(X) | → | pi(X) | (30) |
mark(2ndsneg(X1,X2)) | → | a__2ndsneg(mark(X1),mark(X2)) | (14) |
a__plus(X1,X2) | → | plus(X1,X2) | (31) |
mark(from(X)) | → | a__from(mark(X)) | (12) |
mark(nil) | → | nil | (23) |
mark(cons(X1,X2)) | → | cons(mark(X1),X2) | (24) |
a__square(X) | → | a__times(mark(X),mark(X)) | (11) |
a__times(0,Y) | → | 0 | (9) |
mark(2ndspos(X1,X2)) | → | a__2ndspos(mark(X1),mark(X2)) | (13) |
a__pi(X) | → | a__2ndspos(mark(X),a__from(0)) | (6) |
a__2ndsneg(X1,X2) | → | 2ndsneg(X1,X2) | (29) |
a__2ndspos(0,Z) | → | rnil | (2) |
a__plus#(s(X),Y) | → | mark#(Y) | (64) |
a__plus#(s(X),Y) | → | a__plus#(mark(X),mark(Y)) | (39) |
mark#(plus(X1,X2)) | → | mark#(X2) | (72) |
mark#(plus(X1,X2)) | → | a__plus#(mark(X1),mark(X2)) | (67) |
mark#(times(X1,X2)) | → | a__times#(mark(X1),mark(X2)) | (65) |
a__times#(s(X),Y) | → | a__times#(mark(X),mark(Y)) | (58) |
a__times#(s(X),Y) | → | a__plus#(mark(Y),a__times(mark(X),mark(Y))) | (79) |
a__plus#(0,Y) | → | mark#(Y) | (69) |
mark#(s(X)) | → | mark#(X) | (74) |
The dependency pairs are split into 1 component.
mark#(rcons(X1,X2)) | → | mark#(X2) | (70) |
[a__plus(x1, x2)] | = | x1 + x2 + 0 |
[a__2ndsneg(x1, x2)] | = | 21275 |
[negrecip(x1)] | = | 1 |
[s(x1)] | = | x1 + 8350 |
[a__pi#(x1)] | = | 0 |
[a__from#(x1)] | = | 0 |
[2ndspos(x1, x2)] | = | 21277 |
[a__from(x1)] | = | x1 + 61389 |
[rnil] | = | 40731 |
[square(x1)] | = | 4 |
[a__times#(x1, x2)] | = | 1 |
[pi(x1)] | = | 6 |
[rcons(x1, x2)] | = | x2 + 2 |
[a__2ndspos(x1, x2)] | = | 21276 |
[a__2ndsneg#(x1, x2)] | = | 0 |
[a__plus#(x1, x2)] | = | 0 |
[mark#(x1)] | = | x1 + 0 |
[0] | = | 3 |
[from(x1)] | = | 61388 |
[times(x1, x2)] | = | x1 + 1 |
[a__pi(x1)] | = | x1 + 5 |
[nil] | = | 32533 |
[mark(x1)] | = | x1 + 4 |
[2ndsneg(x1, x2)] | = | x1 + x2 + 21276 |
[plus(x1, x2)] | = | 3 |
[a__square(x1)] | = | x1 + 5 |
[cons(x1, x2)] | = | 61390 |
[a__times(x1, x2)] | = | x2 + 2 |
[a__square#(x1)] | = | 0 |
[a__2ndspos#(x1, x2)] | = | 1 |
[posrecip(x1)] | = | 29178 |
mark#(rcons(X1,X2)) | → | mark#(X2) | (70) |
The dependency pairs are split into 0 components.