The rewrite relation of the following TRS is considered.
terms(N) | → | cons(recip(sqr(N)),n__terms(s(N))) | (1) |
sqr(0) | → | 0 | (2) |
sqr(s(X)) | → | s(add(sqr(X),dbl(X))) | (3) |
dbl(0) | → | 0 | (4) |
dbl(s(X)) | → | s(s(dbl(X))) | (5) |
add(0,X) | → | X | (6) |
add(s(X),Y) | → | s(add(X,Y)) | (7) |
first(0,X) | → | nil | (8) |
first(s(X),cons(Y,Z)) | → | cons(Y,n__first(X,activate(Z))) | (9) |
terms(X) | → | n__terms(X) | (10) |
first(X1,X2) | → | n__first(X1,X2) | (11) |
activate(n__terms(X)) | → | terms(X) | (12) |
activate(n__first(X1,X2)) | → | first(X1,X2) | (13) |
activate(X) | → | X | (14) |
first#(s(X),cons(Y,Z)) | → | activate#(Z) | (15) |
sqr#(s(X)) | → | add#(sqr(X),dbl(X)) | (16) |
terms#(N) | → | sqr#(N) | (17) |
sqr#(s(X)) | → | sqr#(X) | (18) |
dbl#(s(X)) | → | dbl#(X) | (19) |
activate#(n__terms(X)) | → | terms#(X) | (20) |
activate#(n__first(X1,X2)) | → | first#(X1,X2) | (21) |
sqr#(s(X)) | → | dbl#(X) | (22) |
add#(s(X),Y) | → | add#(X,Y) | (23) |
The dependency pairs are split into 4 components.
activate#(n__first(X1,X2)) | → | first#(X1,X2) | (21) |
first#(s(X),cons(Y,Z)) | → | activate#(Z) | (15) |
[s(x1)] | = | 1 |
[n__first(x1, x2)] | = | x2 + 1 |
[recip(x1)] | = | 0 |
[activate(x1)] | = | 0 |
[dbl(x1)] | = | 0 |
[dbl#(x1)] | = | 0 |
[terms#(x1)] | = | 0 |
[activate#(x1)] | = | x1 + 0 |
[sqr#(x1)] | = | 0 |
[0] | = | 0 |
[first#(x1, x2)] | = | x2 + 0 |
[nil] | = | 0 |
[first(x1, x2)] | = | 0 |
[n__terms(x1)] | = | 0 |
[cons(x1, x2)] | = | x2 + 1 |
[add#(x1, x2)] | = | 0 |
[add(x1, x2)] | = | 0 |
[sqr(x1)] | = | 0 |
[terms(x1)] | = | 0 |
activate#(n__first(X1,X2)) | → | first#(X1,X2) | (21) |
first#(s(X),cons(Y,Z)) | → | activate#(Z) | (15) |
The dependency pairs are split into 0 components.
sqr#(s(X)) | → | sqr#(X) | (18) |
[s(x1)] | = | x1 + 1 |
[n__first(x1, x2)] | = | 1 |
[recip(x1)] | = | 0 |
[activate(x1)] | = | 0 |
[dbl(x1)] | = | 0 |
[dbl#(x1)] | = | 0 |
[terms#(x1)] | = | 0 |
[activate#(x1)] | = | 0 |
[sqr#(x1)] | = | x1 + 0 |
[0] | = | 0 |
[first#(x1, x2)] | = | 0 |
[nil] | = | 0 |
[first(x1, x2)] | = | 0 |
[n__terms(x1)] | = | 0 |
[cons(x1, x2)] | = | 1 |
[add#(x1, x2)] | = | 0 |
[add(x1, x2)] | = | 0 |
[sqr(x1)] | = | 0 |
[terms(x1)] | = | 0 |
sqr#(s(X)) | → | sqr#(X) | (18) |
The dependency pairs are split into 0 components.
add#(s(X),Y) | → | add#(X,Y) | (23) |
[s(x1)] | = | x1 + 1 |
[n__first(x1, x2)] | = | 1 |
[recip(x1)] | = | 0 |
[activate(x1)] | = | 0 |
[dbl(x1)] | = | 0 |
[dbl#(x1)] | = | 0 |
[terms#(x1)] | = | 0 |
[activate#(x1)] | = | 0 |
[sqr#(x1)] | = | 0 |
[0] | = | 0 |
[first#(x1, x2)] | = | 0 |
[nil] | = | 0 |
[first(x1, x2)] | = | 0 |
[n__terms(x1)] | = | 0 |
[cons(x1, x2)] | = | 1 |
[add#(x1, x2)] | = | x1 + 0 |
[add(x1, x2)] | = | 0 |
[sqr(x1)] | = | 0 |
[terms(x1)] | = | 0 |
add#(s(X),Y) | → | add#(X,Y) | (23) |
The dependency pairs are split into 0 components.
dbl#(s(X)) | → | dbl#(X) | (19) |
[s(x1)] | = | x1 + 1 |
[n__first(x1, x2)] | = | 1 |
[recip(x1)] | = | 0 |
[activate(x1)] | = | 0 |
[dbl(x1)] | = | 0 |
[dbl#(x1)] | = | x1 + 0 |
[terms#(x1)] | = | 0 |
[activate#(x1)] | = | 0 |
[sqr#(x1)] | = | 0 |
[0] | = | 0 |
[first#(x1, x2)] | = | 0 |
[nil] | = | 0 |
[first(x1, x2)] | = | 0 |
[n__terms(x1)] | = | 0 |
[cons(x1, x2)] | = | 1 |
[add#(x1, x2)] | = | 0 |
[add(x1, x2)] | = | 0 |
[sqr(x1)] | = | 0 |
[terms(x1)] | = | 0 |
dbl#(s(X)) | → | dbl#(X) | (19) |
The dependency pairs are split into 0 components.