The rewrite relation of the following TRS is considered.
f(0) | → | cons(0,n__f(n__s(n__0))) | (1) |
f(s(0)) | → | f(p(s(0))) | (2) |
p(s(X)) | → | X | (3) |
f(X) | → | n__f(X) | (4) |
s(X) | → | n__s(X) | (5) |
0 | → | n__0 | (6) |
activate(n__f(X)) | → | f(activate(X)) | (7) |
activate(n__s(X)) | → | s(activate(X)) | (8) |
activate(n__0) | → | 0 | (9) |
activate(X) | → | X | (10) |
f#(s(0)) | → | p#(s(0)) | (11) |
activate#(n__s(X)) | → | s#(activate(X)) | (12) |
activate#(n__s(X)) | → | activate#(X) | (13) |
activate#(n__f(X)) | → | activate#(X) | (14) |
activate#(n__0) | → | 0# | (15) |
f#(s(0)) | → | f#(p(s(0))) | (16) |
activate#(n__f(X)) | → | f#(activate(X)) | (17) |
The dependency pairs are split into 2 components.
activate#(n__f(X)) | → | activate#(X) | (14) |
activate#(n__s(X)) | → | activate#(X) | (13) |
[0#] | = | 0 |
[s(x1)] | = | 0 |
[activate(x1)] | = | 0 |
[activate#(x1)] | = | x1 + 0 |
[p#(x1)] | = | 0 |
[f(x1)] | = | 0 |
[n__s(x1)] | = | x1 + 1 |
[p(x1)] | = | 0 |
[0] | = | 0 |
[s#(x1)] | = | 0 |
[n__f(x1)] | = | x1 + 1 |
[f#(x1)] | = | 0 |
[n__0] | = | 0 |
[cons(x1, x2)] | = | 0 |
activate#(n__f(X)) | → | activate#(X) | (14) |
activate#(n__s(X)) | → | activate#(X) | (13) |
The dependency pairs are split into 0 components.
f#(s(0)) | → | f#(p(s(0))) | (16) |
π(p#) | = | 1 |
prec(0#) | = | 0 | status(0#) | = | [] | list-extension(0#) | = | Lex | ||
prec(s) | = | 1 | status(s) | = | [1] | list-extension(s) | = | Lex | ||
prec(activate) | = | 0 | status(activate) | = | [] | list-extension(activate) | = | Lex | ||
prec(activate#) | = | 0 | status(activate#) | = | [] | list-extension(activate#) | = | Lex | ||
prec(f) | = | 0 | status(f) | = | [] | list-extension(f) | = | Lex | ||
prec(n__s) | = | 1 | status(n__s) | = | [] | list-extension(n__s) | = | Lex | ||
prec(p) | = | 1 | status(p) | = | [] | list-extension(p) | = | Lex | ||
prec(0) | = | 0 | status(0) | = | [] | list-extension(0) | = | Lex | ||
prec(s#) | = | 0 | status(s#) | = | [] | list-extension(s#) | = | Lex | ||
prec(n__f) | = | 0 | status(n__f) | = | [] | list-extension(n__f) | = | Lex | ||
prec(f#) | = | 0 | status(f#) | = | [1] | list-extension(f#) | = | Lex | ||
prec(n__0) | = | 0 | status(n__0) | = | [] | list-extension(n__0) | = | Lex | ||
prec(cons) | = | 0 | status(cons) | = | [] | list-extension(cons) | = | Lex |
[0#] | = | 0 |
[s(x1)] | = | x1 + 7721 |
[activate(x1)] | = | 1 |
[activate#(x1)] | = | 1 |
[f(x1)] | = | 1 |
[n__s(x1)] | = | 1 |
[p(x1)] | = | x1 + 0 |
[0] | = | 1 |
[s#(x1)] | = | 1 |
[n__f(x1)] | = | 1 |
[f#(x1)] | = | x1 + 1 |
[n__0] | = | 1 |
[cons(x1, x2)] | = | x1 + 1 |
p(s(X)) | → | X | (3) |
s(X) | → | n__s(X) | (5) |
0 | → | n__0 | (6) |
f#(s(0)) | → | f#(p(s(0))) | (16) |
The dependency pairs are split into 0 components.