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(n__filter(activate(Y),N,N))) | (4) |
nats(N) | → | cons(N,n__nats(n__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) |
s(X) | → | n__s(X) | (10) |
activate(n__filter(X1,X2,X3)) | → | filter(activate(X1),activate(X2),activate(X3)) | (11) |
activate(n__sieve(X)) | → | sieve(activate(X)) | (12) |
activate(n__nats(X)) | → | nats(activate(X)) | (13) |
activate(n__s(X)) | → | s(activate(X)) | (14) |
activate(X) | → | X | (15) |
zprimes# | → | sieve#(nats(s(s(0)))) | (16) |
activate#(n__nats(X)) | → | nats#(activate(X)) | (17) |
activate#(n__sieve(X)) | → | activate#(X) | (18) |
activate#(n__filter(X1,X2,X3)) | → | activate#(X1) | (19) |
activate#(n__filter(X1,X2,X3)) | → | activate#(X3) | (20) |
activate#(n__sieve(X)) | → | sieve#(activate(X)) | (21) |
activate#(n__s(X)) | → | s#(activate(X)) | (22) |
activate#(n__nats(X)) | → | activate#(X) | (23) |
activate#(n__filter(X1,X2,X3)) | → | activate#(X2) | (24) |
zprimes# | → | s#(0) | (25) |
filter#(cons(X,Y),0,M) | → | activate#(Y) | (26) |
sieve#(cons(0,Y)) | → | activate#(Y) | (27) |
zprimes# | → | nats#(s(s(0))) | (28) |
filter#(cons(X,Y),s(N),M) | → | activate#(Y) | (29) |
activate#(n__filter(X1,X2,X3)) | → | filter#(activate(X1),activate(X2),activate(X3)) | (30) |
activate#(n__s(X)) | → | activate#(X) | (31) |
zprimes# | → | s#(s(0)) | (32) |
sieve#(cons(s(N),Y)) | → | activate#(Y) | (33) |
The dependency pairs are split into 1 component.
sieve#(cons(s(N),Y)) | → | activate#(Y) | (33) |
activate#(n__s(X)) | → | activate#(X) | (31) |
activate#(n__sieve(X)) | → | sieve#(activate(X)) | (21) |
activate#(n__filter(X1,X2,X3)) | → | filter#(activate(X1),activate(X2),activate(X3)) | (30) |
filter#(cons(X,Y),s(N),M) | → | activate#(Y) | (29) |
sieve#(cons(0,Y)) | → | activate#(Y) | (27) |
activate#(n__filter(X1,X2,X3)) | → | activate#(X3) | (20) |
activate#(n__filter(X1,X2,X3)) | → | activate#(X1) | (19) |
activate#(n__sieve(X)) | → | activate#(X) | (18) |
filter#(cons(X,Y),0,M) | → | activate#(Y) | (26) |
activate#(n__filter(X1,X2,X3)) | → | activate#(X2) | (24) |
activate#(n__nats(X)) | → | activate#(X) | (23) |
[zprimes] | = | 0 |
[nats#(x1)] | = | 0 |
[s(x1)] | = | x1 + 0 |
[activate(x1)] | = | x1 + 0 |
[filter#(x1, x2, x3)] | = | max(x1 + 1, x2 + 2, x3 + 3, 0) |
[activate#(x1)] | = | x1 + 1 |
[zprimes#] | = | 0 |
[n__nats(x1)] | = | x1 + 40653 |
[n__s(x1)] | = | x1 + 0 |
[0] | = | 0 |
[s#(x1)] | = | 0 |
[n__filter(x1, x2, x3)] | = | max(x1 + 0, x2 + 1, x3 + 2, 0) |
[sieve(x1)] | = | x1 + 10452 |
[n__sieve(x1)] | = | x1 + 10452 |
[nats(x1)] | = | x1 + 40653 |
[cons(x1, x2)] | = | max(x1 + 32288, x2 + 0, 0) |
[filter(x1, x2, x3)] | = | max(x1 + 0, x2 + 1, x3 + 2, 0) |
[sieve#(x1)] | = | x1 + 2 |
sieve(cons(s(N),Y)) | → | cons(s(N),n__sieve(n__filter(activate(Y),N,N))) | (4) |
activate(X) | → | X | (15) |
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(n__s(N))) | (5) |
s(X) | → | n__s(X) | (10) |
filter(X1,X2,X3) | → | n__filter(X1,X2,X3) | (7) |
activate(n__s(X)) | → | s(activate(X)) | (14) |
activate(n__sieve(X)) | → | sieve(activate(X)) | (12) |
activate(n__filter(X1,X2,X3)) | → | filter(activate(X1),activate(X2),activate(X3)) | (11) |
nats(X) | → | n__nats(X) | (9) |
activate(n__nats(X)) | → | nats(activate(X)) | (13) |
filter(cons(X,Y),s(N),M) | → | cons(X,n__filter(activate(Y),N,M)) | (2) |
sieve#(cons(s(N),Y)) | → | activate#(Y) | (33) |
activate#(n__sieve(X)) | → | sieve#(activate(X)) | (21) |
sieve#(cons(0,Y)) | → | activate#(Y) | (27) |
activate#(n__filter(X1,X2,X3)) | → | activate#(X3) | (20) |
activate#(n__sieve(X)) | → | activate#(X) | (18) |
activate#(n__filter(X1,X2,X3)) | → | activate#(X2) | (24) |
activate#(n__nats(X)) | → | activate#(X) | (23) |
The dependency pairs are split into 1 component.
filter#(cons(X,Y),0,M) | → | activate#(Y) | (26) |
activate#(n__s(X)) | → | activate#(X) | (31) |
activate#(n__filter(X1,X2,X3)) | → | activate#(X1) | (19) |
activate#(n__filter(X1,X2,X3)) | → | filter#(activate(X1),activate(X2),activate(X3)) | (30) |
filter#(cons(X,Y),s(N),M) | → | activate#(Y) | (29) |
[zprimes] | = | 0 |
[nats#(x1)] | = | 0 |
[s(x1)] | = | x1 + 31892 |
[activate(x1)] | = | x1 + 0 |
[filter#(x1, x2, x3)] | = | x1 + 25907 |
[activate#(x1)] | = | x1 + 0 |
[zprimes#] | = | 0 |
[n__nats(x1)] | = | 19781 |
[n__s(x1)] | = | x1 + 31892 |
[0] | = | 0 |
[s#(x1)] | = | 0 |
[n__filter(x1, x2, x3)] | = | x1 + 25908 |
[sieve(x1)] | = | 50537 |
[n__sieve(x1)] | = | 50537 |
[nats(x1)] | = | 19781 |
[cons(x1, x2)] | = | x2 + 0 |
[filter(x1, x2, x3)] | = | x1 + 25908 |
[sieve#(x1)] | = | 0 |
sieve(cons(s(N),Y)) | → | cons(s(N),n__sieve(n__filter(activate(Y),N,N))) | (4) |
activate(X) | → | X | (15) |
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(n__s(N))) | (5) |
s(X) | → | n__s(X) | (10) |
filter(X1,X2,X3) | → | n__filter(X1,X2,X3) | (7) |
activate(n__s(X)) | → | s(activate(X)) | (14) |
activate(n__sieve(X)) | → | sieve(activate(X)) | (12) |
activate(n__filter(X1,X2,X3)) | → | filter(activate(X1),activate(X2),activate(X3)) | (11) |
nats(X) | → | n__nats(X) | (9) |
activate(n__nats(X)) | → | nats(activate(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) | (26) |
activate#(n__s(X)) | → | activate#(X) | (31) |
activate#(n__filter(X1,X2,X3)) | → | activate#(X1) | (19) |
activate#(n__filter(X1,X2,X3)) | → | filter#(activate(X1),activate(X2),activate(X3)) | (30) |
filter#(cons(X,Y),s(N),M) | → | activate#(Y) | (29) |
The dependency pairs are split into 0 components.