The rewrite relation of the following TRS is considered.
from(X) | → | cons(X,n__from(n__s(X))) | (1) |
2ndspos(0,Z) | → | rnil | (2) |
2ndspos(s(N),cons(X,n__cons(Y,Z))) | → | rcons(posrecip(activate(Y)),2ndsneg(N,activate(Z))) | (3) |
2ndsneg(0,Z) | → | rnil | (4) |
2ndsneg(s(N),cons(X,n__cons(Y,Z))) | → | rcons(negrecip(activate(Y)),2ndspos(N,activate(Z))) | (5) |
pi(X) | → | 2ndspos(X,from(0)) | (6) |
plus(0,Y) | → | Y | (7) |
plus(s(X),Y) | → | s(plus(X,Y)) | (8) |
times(0,Y) | → | 0 | (9) |
times(s(X),Y) | → | plus(Y,times(X,Y)) | (10) |
square(X) | → | times(X,X) | (11) |
from(X) | → | n__from(X) | (12) |
s(X) | → | n__s(X) | (13) |
cons(X1,X2) | → | n__cons(X1,X2) | (14) |
activate(n__from(X)) | → | from(activate(X)) | (15) |
activate(n__s(X)) | → | s(activate(X)) | (16) |
activate(n__cons(X1,X2)) | → | cons(activate(X1),X2) | (17) |
activate(X) | → | X | (18) |
prec(from) | = | 4 | stat(from) | = | mul | |
prec(cons) | = | 1 | stat(cons) | = | mul | |
prec(n__from) | = | 2 | stat(n__from) | = | mul | |
prec(n__s) | = | 3 | stat(n__s) | = | mul | |
prec(2ndspos) | = | 9 | stat(2ndspos) | = | lex | |
prec(0) | = | 10 | stat(0) | = | mul | |
prec(rnil) | = | 5 | stat(rnil) | = | mul | |
prec(s) | = | 7 | stat(s) | = | mul | |
prec(n__cons) | = | 0 | stat(n__cons) | = | mul | |
prec(rcons) | = | 6 | stat(rcons) | = | mul | |
prec(activate) | = | 8 | stat(activate) | = | mul | |
prec(2ndsneg) | = | 9 | stat(2ndsneg) | = | lex | |
prec(pi) | = | 11 | stat(pi) | = | mul | |
prec(plus) | = | 12 | stat(plus) | = | mul | |
prec(times) | = | 13 | stat(times) | = | mul | |
prec(square) | = | 14 | stat(square) | = | lex |
π(from) | = | [1] |
π(cons) | = | [1,2] |
π(n__from) | = | [1] |
π(n__s) | = | [1] |
π(2ndspos) | = | [1,2] |
π(0) | = | [] |
π(rnil) | = | [] |
π(s) | = | [1] |
π(n__cons) | = | [1,2] |
π(rcons) | = | [1,2] |
π(posrecip) | = | 1 |
π(activate) | = | [1] |
π(2ndsneg) | = | [1,2] |
π(negrecip) | = | 1 |
π(pi) | = | [1] |
π(plus) | = | [1,2] |
π(times) | = | [1,2] |
π(square) | = | [1] |
from(X) | → | cons(X,n__from(n__s(X))) | (1) |
2ndspos(0,Z) | → | rnil | (2) |
2ndspos(s(N),cons(X,n__cons(Y,Z))) | → | rcons(posrecip(activate(Y)),2ndsneg(N,activate(Z))) | (3) |
2ndsneg(0,Z) | → | rnil | (4) |
2ndsneg(s(N),cons(X,n__cons(Y,Z))) | → | rcons(negrecip(activate(Y)),2ndspos(N,activate(Z))) | (5) |
pi(X) | → | 2ndspos(X,from(0)) | (6) |
plus(0,Y) | → | Y | (7) |
plus(s(X),Y) | → | s(plus(X,Y)) | (8) |
times(0,Y) | → | 0 | (9) |
times(s(X),Y) | → | plus(Y,times(X,Y)) | (10) |
square(X) | → | times(X,X) | (11) |
from(X) | → | n__from(X) | (12) |
s(X) | → | n__s(X) | (13) |
cons(X1,X2) | → | n__cons(X1,X2) | (14) |
activate(n__from(X)) | → | from(activate(X)) | (15) |
activate(n__s(X)) | → | s(activate(X)) | (16) |
activate(n__cons(X1,X2)) | → | cons(activate(X1),X2) | (17) |
activate(X) | → | X | (18) |
There are no rules in the TRS. Hence, it is terminating.