The rewrite relation of the following TRS is considered.
filter(cons(X,Y),0,M) | → | cons(0,n__filter(activate(Y),M,M)) | (1) |
filter(cons(X,Y),s(N),M) | → | cons(X,n__filter(activate(Y),N,M)) | (2) |
sieve(cons(0,Y)) | → | cons(0,n__sieve(activate(Y))) | (3) |
sieve(cons(s(N),Y)) | → | cons(s(N),n__sieve(filter(activate(Y),N,N))) | (4) |
nats(N) | → | cons(N,n__nats(s(N))) | (5) |
zprimes | → | sieve(nats(s(s(0)))) | (6) |
filter(X1,X2,X3) | → | n__filter(X1,X2,X3) | (7) |
sieve(X) | → | n__sieve(X) | (8) |
nats(X) | → | n__nats(X) | (9) |
activate(n__filter(X1,X2,X3)) | → | filter(X1,X2,X3) | (10) |
activate(n__sieve(X)) | → | sieve(X) | (11) |
activate(n__nats(X)) | → | nats(X) | (12) |
activate(X) | → | X | (13) |
zprimes# | → | sieve#(nats(s(s(0)))) | (14) |
activate#(n__filter(X1,X2,X3)) | → | filter#(X1,X2,X3) | (15) |
sieve#(cons(s(N),Y)) | → | filter#(activate(Y),N,N) | (16) |
sieve#(cons(0,Y)) | → | activate#(Y) | (17) |
sieve#(cons(s(N),Y)) | → | activate#(Y) | (18) |
activate#(n__nats(X)) | → | nats#(X) | (19) |
zprimes# | → | nats#(s(s(0))) | (20) |
filter#(cons(X,Y),s(N),M) | → | activate#(Y) | (21) |
filter#(cons(X,Y),0,M) | → | activate#(Y) | (22) |
activate#(n__sieve(X)) | → | sieve#(X) | (23) |
The dependency pairs are split into 1 component.
activate#(n__sieve(X)) | → | sieve#(X) | (23) |
filter#(cons(X,Y),0,M) | → | activate#(Y) | (22) |
filter#(cons(X,Y),s(N),M) | → | activate#(Y) | (21) |
sieve#(cons(s(N),Y)) | → | filter#(activate(Y),N,N) | (16) |
activate#(n__filter(X1,X2,X3)) | → | filter#(X1,X2,X3) | (15) |
sieve#(cons(s(N),Y)) | → | activate#(Y) | (18) |
sieve#(cons(0,Y)) | → | activate#(Y) | (17) |
[zprimes] | = | 0 |
[nats#(x1)] | = | 0 |
[s(x1)] | = | 1 |
[activate(x1)] | = | x1 + 0 |
[filter#(x1, x2, x3)] | = | x1 + 0 |
[activate#(x1)] | = | x1 + 0 |
[zprimes#] | = | 0 |
[n__nats(x1)] | = | 41063 |
[0] | = | 1 |
[n__filter(x1, x2, x3)] | = | x1 + 0 |
[sieve(x1)] | = | x1 + 32287 |
[n__sieve(x1)] | = | x1 + 32287 |
[nats(x1)] | = | 41063 |
[cons(x1, x2)] | = | x2 + 0 |
[filter(x1, x2, x3)] | = | x1 + 0 |
[sieve#(x1)] | = | x1 + 1 |
sieve(cons(s(N),Y)) | → | cons(s(N),n__sieve(filter(activate(Y),N,N))) | (4) |
sieve(X) | → | n__sieve(X) | (8) |
filter(cons(X,Y),0,M) | → | cons(0,n__filter(activate(Y),M,M)) | (1) |
sieve(cons(0,Y)) | → | cons(0,n__sieve(activate(Y))) | (3) |
nats(N) | → | cons(N,n__nats(s(N))) | (5) |
activate(n__filter(X1,X2,X3)) | → | filter(X1,X2,X3) | (10) |
filter(X1,X2,X3) | → | n__filter(X1,X2,X3) | (7) |
activate(n__nats(X)) | → | nats(X) | (12) |
activate(n__sieve(X)) | → | sieve(X) | (11) |
nats(X) | → | n__nats(X) | (9) |
activate(X) | → | X | (13) |
filter(cons(X,Y),s(N),M) | → | cons(X,n__filter(activate(Y),N,M)) | (2) |
activate#(n__sieve(X)) | → | sieve#(X) | (23) |
sieve#(cons(s(N),Y)) | → | filter#(activate(Y),N,N) | (16) |
sieve#(cons(s(N),Y)) | → | activate#(Y) | (18) |
sieve#(cons(0,Y)) | → | activate#(Y) | (17) |
The dependency pairs are split into 1 component.
filter#(cons(X,Y),0,M) | → | activate#(Y) | (22) |
activate#(n__filter(X1,X2,X3)) | → | filter#(X1,X2,X3) | (15) |
filter#(cons(X,Y),s(N),M) | → | activate#(Y) | (21) |
[zprimes] | = | 0 |
[nats#(x1)] | = | 0 |
[s(x1)] | = | 1 |
[activate(x1)] | = | x1 + 1 |
[filter#(x1, x2, x3)] | = | x1 + 0 |
[activate#(x1)] | = | x1 + 0 |
[zprimes#] | = | 0 |
[n__nats(x1)] | = | 24653 |
[0] | = | 2 |
[n__filter(x1, x2, x3)] | = | x1 + x3 + 14681 |
[sieve(x1)] | = | 52869 |
[n__sieve(x1)] | = | 52868 |
[nats(x1)] | = | 24654 |
[cons(x1, x2)] | = | x2 + 1 |
[filter(x1, x2, x3)] | = | x1 + x3 + 14682 |
[sieve#(x1)] | = | 1 |
sieve(cons(s(N),Y)) | → | cons(s(N),n__sieve(filter(activate(Y),N,N))) | (4) |
sieve(X) | → | n__sieve(X) | (8) |
filter(cons(X,Y),0,M) | → | cons(0,n__filter(activate(Y),M,M)) | (1) |
sieve(cons(0,Y)) | → | cons(0,n__sieve(activate(Y))) | (3) |
nats(N) | → | cons(N,n__nats(s(N))) | (5) |
activate(n__filter(X1,X2,X3)) | → | filter(X1,X2,X3) | (10) |
filter(X1,X2,X3) | → | n__filter(X1,X2,X3) | (7) |
activate(n__nats(X)) | → | nats(X) | (12) |
activate(n__sieve(X)) | → | sieve(X) | (11) |
nats(X) | → | n__nats(X) | (9) |
activate(X) | → | X | (13) |
filter(cons(X,Y),s(N),M) | → | cons(X,n__filter(activate(Y),N,M)) | (2) |
filter#(cons(X,Y),0,M) | → | activate#(Y) | (22) |
activate#(n__filter(X1,X2,X3)) | → | filter#(X1,X2,X3) | (15) |
filter#(cons(X,Y),s(N),M) | → | activate#(Y) | (21) |
The dependency pairs are split into 0 components.