The rewrite relation of the following TRS is considered.
from(X) | → | cons(X,n__from(n__s(X))) | (1) |
sel(0,cons(X,XS)) | → | X | (2) |
sel(s(N),cons(X,XS)) | → | sel(N,activate(XS)) | (3) |
minus(X,0) | → | 0 | (4) |
minus(s(X),s(Y)) | → | minus(X,Y) | (5) |
quot(0,s(Y)) | → | 0 | (6) |
quot(s(X),s(Y)) | → | s(quot(minus(X,Y),s(Y))) | (7) |
zWquot(XS,nil) | → | nil | (8) |
zWquot(nil,XS) | → | nil | (9) |
zWquot(cons(X,XS),cons(Y,YS)) | → | cons(quot(X,Y),n__zWquot(activate(XS),activate(YS))) | (10) |
from(X) | → | n__from(X) | (11) |
s(X) | → | n__s(X) | (12) |
zWquot(X1,X2) | → | n__zWquot(X1,X2) | (13) |
activate(n__from(X)) | → | from(activate(X)) | (14) |
activate(n__s(X)) | → | s(activate(X)) | (15) |
activate(n__zWquot(X1,X2)) | → | zWquot(activate(X1),activate(X2)) | (16) |
activate(X) | → | X | (17) |
activate#(n__from(X)) | → | activate#(X) | (18) |
zWquot#(cons(X,XS),cons(Y,YS)) | → | quot#(X,Y) | (19) |
sel#(s(N),cons(X,XS)) | → | sel#(N,activate(XS)) | (20) |
minus#(s(X),s(Y)) | → | minus#(X,Y) | (21) |
activate#(n__zWquot(X1,X2)) | → | activate#(X1) | (22) |
activate#(n__zWquot(X1,X2)) | → | activate#(X2) | (23) |
sel#(s(N),cons(X,XS)) | → | activate#(XS) | (24) |
zWquot#(cons(X,XS),cons(Y,YS)) | → | activate#(XS) | (25) |
activate#(n__zWquot(X1,X2)) | → | zWquot#(activate(X1),activate(X2)) | (26) |
quot#(s(X),s(Y)) | → | minus#(X,Y) | (27) |
activate#(n__s(X)) | → | activate#(X) | (28) |
quot#(s(X),s(Y)) | → | s#(quot(minus(X,Y),s(Y))) | (29) |
activate#(n__from(X)) | → | from#(activate(X)) | (30) |
zWquot#(cons(X,XS),cons(Y,YS)) | → | activate#(YS) | (31) |
activate#(n__s(X)) | → | s#(activate(X)) | (32) |
quot#(s(X),s(Y)) | → | quot#(minus(X,Y),s(Y)) | (33) |
The dependency pairs are split into 4 components.
sel#(s(N),cons(X,XS)) | → | sel#(N,activate(XS)) | (20) |
[s(x1)] | = | x1 + 1 |
[zWquot#(x1, x2)] | = | 0 |
[minus(x1, x2)] | = | x1 + 1 |
[activate(x1)] | = | 1 |
[n__from(x1)] | = | x1 + 3 |
[activate#(x1)] | = | 0 |
[zWquot(x1, x2)] | = | 2 |
[n__zWquot(x1, x2)] | = | x1 + x2 + 3 |
[n__s(x1)] | = | 2 |
[0] | = | 1 |
[quot(x1, x2)] | = | x1 + x2 + 2 |
[sel#(x1, x2)] | = | x1 + 0 |
[from(x1)] | = | 2 |
[sel(x1, x2)] | = | 0 |
[s#(x1)] | = | 0 |
[nil] | = | 3 |
[minus#(x1, x2)] | = | 0 |
[from#(x1)] | = | 0 |
[cons(x1, x2)] | = | x1 + 3 |
[quot#(x1, x2)] | = | 0 |
minus(X,0) | → | 0 | (4) |
minus(s(X),s(Y)) | → | minus(X,Y) | (5) |
sel#(s(N),cons(X,XS)) | → | sel#(N,activate(XS)) | (20) |
The dependency pairs are split into 0 components.
activate#(n__zWquot(X1,X2)) | → | activate#(X2) | (23) |
zWquot#(cons(X,XS),cons(Y,YS)) | → | activate#(YS) | (31) |
activate#(n__s(X)) | → | activate#(X) | (28) |
activate#(n__zWquot(X1,X2)) | → | activate#(X1) | (22) |
activate#(n__zWquot(X1,X2)) | → | zWquot#(activate(X1),activate(X2)) | (26) |
zWquot#(cons(X,XS),cons(Y,YS)) | → | activate#(XS) | (25) |
activate#(n__from(X)) | → | activate#(X) | (18) |
[s(x1)] | = | x1 + 0 |
[zWquot#(x1, x2)] | = | x1 + x2 + 1 |
[minus(x1, x2)] | = | 1 |
[activate(x1)] | = | x1 + 0 |
[n__from(x1)] | = | x1 + 20977 |
[activate#(x1)] | = | x1 + 0 |
[zWquot(x1, x2)] | = | x1 + x2 + 31893 |
[n__zWquot(x1, x2)] | = | x1 + x2 + 31893 |
[n__s(x1)] | = | x1 + 0 |
[0] | = | 1 |
[quot(x1, x2)] | = | 21656 |
[sel#(x1, x2)] | = | 0 |
[from(x1)] | = | x1 + 20977 |
[sel(x1, x2)] | = | 0 |
[s#(x1)] | = | 0 |
[nil] | = | 0 |
[minus#(x1, x2)] | = | 0 |
[from#(x1)] | = | 0 |
[cons(x1, x2)] | = | x2 + 0 |
[quot#(x1, x2)] | = | 0 |
minus(X,0) | → | 0 | (4) |
activate(n__s(X)) | → | s(activate(X)) | (15) |
zWquot(XS,nil) | → | nil | (8) |
from(X) | → | cons(X,n__from(n__s(X))) | (1) |
activate(n__zWquot(X1,X2)) | → | zWquot(activate(X1),activate(X2)) | (16) |
activate(X) | → | X | (17) |
minus(s(X),s(Y)) | → | minus(X,Y) | (5) |
zWquot(cons(X,XS),cons(Y,YS)) | → | cons(quot(X,Y),n__zWquot(activate(XS),activate(YS))) | (10) |
activate(n__from(X)) | → | from(activate(X)) | (14) |
s(X) | → | n__s(X) | (12) |
from(X) | → | n__from(X) | (11) |
zWquot(nil,XS) | → | nil | (9) |
zWquot(X1,X2) | → | n__zWquot(X1,X2) | (13) |
activate#(n__zWquot(X1,X2)) | → | activate#(X2) | (23) |
zWquot#(cons(X,XS),cons(Y,YS)) | → | activate#(YS) | (31) |
activate#(n__zWquot(X1,X2)) | → | activate#(X1) | (22) |
activate#(n__zWquot(X1,X2)) | → | zWquot#(activate(X1),activate(X2)) | (26) |
zWquot#(cons(X,XS),cons(Y,YS)) | → | activate#(XS) | (25) |
activate#(n__from(X)) | → | activate#(X) | (18) |
The dependency pairs are split into 1 component.
activate#(n__s(X)) | → | activate#(X) | (28) |
[s(x1)] | = | x1 + 0 |
[zWquot#(x1, x2)] | = | 1 |
[minus(x1, x2)] | = | 1 |
[activate(x1)] | = | 0 |
[n__from(x1)] | = | x1 + 1 |
[activate#(x1)] | = | x1 + 0 |
[zWquot(x1, x2)] | = | 0 |
[n__zWquot(x1, x2)] | = | 0 |
[n__s(x1)] | = | x1 + 1 |
[0] | = | 1 |
[quot(x1, x2)] | = | 23612 |
[sel#(x1, x2)] | = | 0 |
[from(x1)] | = | x1 + 2 |
[sel(x1, x2)] | = | 0 |
[s#(x1)] | = | 0 |
[nil] | = | 0 |
[minus#(x1, x2)] | = | 0 |
[from#(x1)] | = | 0 |
[cons(x1, x2)] | = | x2 + 0 |
[quot#(x1, x2)] | = | 0 |
minus(X,0) | → | 0 | (4) |
zWquot(XS,nil) | → | nil | (8) |
from(X) | → | cons(X,n__from(n__s(X))) | (1) |
activate(n__zWquot(X1,X2)) | → | zWquot(activate(X1),activate(X2)) | (16) |
minus(s(X),s(Y)) | → | minus(X,Y) | (5) |
zWquot(cons(X,XS),cons(Y,YS)) | → | cons(quot(X,Y),n__zWquot(activate(XS),activate(YS))) | (10) |
from(X) | → | n__from(X) | (11) |
zWquot(nil,XS) | → | nil | (9) |
zWquot(X1,X2) | → | n__zWquot(X1,X2) | (13) |
activate#(n__s(X)) | → | activate#(X) | (28) |
The dependency pairs are split into 0 components.
quot#(s(X),s(Y)) | → | quot#(minus(X,Y),s(Y)) | (33) |
[s(x1)] | = | x1 + 2 |
[zWquot#(x1, x2)] | = | 1 |
[minus(x1, x2)] | = | x1 + 1 |
[activate(x1)] | = | 0 |
[n__from(x1)] | = | x1 + 1 |
[activate#(x1)] | = | 0 |
[zWquot(x1, x2)] | = | 0 |
[n__zWquot(x1, x2)] | = | 0 |
[n__s(x1)] | = | x1 + 3 |
[0] | = | 1 |
[quot(x1, x2)] | = | 23612 |
[sel#(x1, x2)] | = | 0 |
[from(x1)] | = | x1 + 4 |
[sel(x1, x2)] | = | 0 |
[s#(x1)] | = | 0 |
[nil] | = | 0 |
[minus#(x1, x2)] | = | 0 |
[from#(x1)] | = | 0 |
[cons(x1, x2)] | = | x2 + 0 |
[quot#(x1, x2)] | = | x1 + 0 |
minus(X,0) | → | 0 | (4) |
zWquot(XS,nil) | → | nil | (8) |
from(X) | → | cons(X,n__from(n__s(X))) | (1) |
activate(n__zWquot(X1,X2)) | → | zWquot(activate(X1),activate(X2)) | (16) |
minus(s(X),s(Y)) | → | minus(X,Y) | (5) |
zWquot(cons(X,XS),cons(Y,YS)) | → | cons(quot(X,Y),n__zWquot(activate(XS),activate(YS))) | (10) |
from(X) | → | n__from(X) | (11) |
zWquot(nil,XS) | → | nil | (9) |
zWquot(X1,X2) | → | n__zWquot(X1,X2) | (13) |
quot#(s(X),s(Y)) | → | quot#(minus(X,Y),s(Y)) | (33) |
The dependency pairs are split into 0 components.
minus#(s(X),s(Y)) | → | minus#(X,Y) | (21) |
[s(x1)] | = | x1 + 1 |
[zWquot#(x1, x2)] | = | 1 |
[minus(x1, x2)] | = | x1 + 1 |
[activate(x1)] | = | 0 |
[n__from(x1)] | = | x1 + 2 |
[activate#(x1)] | = | 0 |
[zWquot(x1, x2)] | = | 0 |
[n__zWquot(x1, x2)] | = | 0 |
[n__s(x1)] | = | x1 + 2 |
[0] | = | 1 |
[quot(x1, x2)] | = | 23612 |
[sel#(x1, x2)] | = | 0 |
[from(x1)] | = | x1 + 4 |
[sel(x1, x2)] | = | 0 |
[s#(x1)] | = | 0 |
[nil] | = | 0 |
[minus#(x1, x2)] | = | x1 + 0 |
[from#(x1)] | = | 0 |
[cons(x1, x2)] | = | x2 + 0 |
[quot#(x1, x2)] | = | x1 + 0 |
minus(X,0) | → | 0 | (4) |
zWquot(XS,nil) | → | nil | (8) |
from(X) | → | cons(X,n__from(n__s(X))) | (1) |
activate(n__zWquot(X1,X2)) | → | zWquot(activate(X1),activate(X2)) | (16) |
minus(s(X),s(Y)) | → | minus(X,Y) | (5) |
zWquot(cons(X,XS),cons(Y,YS)) | → | cons(quot(X,Y),n__zWquot(activate(XS),activate(YS))) | (10) |
from(X) | → | n__from(X) | (11) |
zWquot(nil,XS) | → | nil | (9) |
zWquot(X1,X2) | → | n__zWquot(X1,X2) | (13) |
minus#(s(X),s(Y)) | → | minus#(X,Y) | (21) |
The dependency pairs are split into 0 components.