The rewrite relation of the following TRS is considered.
f(0) | → | cons(0,n__f(s(0))) | (1) |
f(s(0)) | → | f(p(s(0))) | (2) |
p(s(X)) | → | X | (3) |
f(X) | → | n__f(X) | (4) |
activate(n__f(X)) | → | f(X) | (5) |
activate(X) | → | X | (6) |
f#(s(0)) | → | p#(s(0)) | (7) |
activate#(n__f(X)) | → | f#(X) | (8) |
f#(s(0)) | → | f#(p(s(0))) | (9) |
The dependency pairs are split into 1 component.
f#(s(0)) | → | f#(p(s(0))) | (9) |
π(f#) | = | 1 |
prec(s) | = | 2 | status(s) | = | [] | list-extension(s) | = | Lex | ||
prec(activate) | = | 0 | status(activate) | = | [] | list-extension(activate) | = | Lex | ||
prec(activate#) | = | 0 | status(activate#) | = | [] | list-extension(activate#) | = | Lex | ||
prec(p#) | = | 0 | status(p#) | = | [] | list-extension(p#) | = | Lex | ||
prec(f) | = | 0 | status(f) | = | [] | list-extension(f) | = | Lex | ||
prec(p) | = | 0 | status(p) | = | [] | list-extension(p) | = | Lex | ||
prec(0) | = | 1 | status(0) | = | [] | list-extension(0) | = | Lex | ||
prec(n__f) | = | 0 | status(n__f) | = | [] | list-extension(n__f) | = | Lex | ||
prec(cons) | = | 0 | status(cons) | = | [1, 2] | list-extension(cons) | = | Lex |
[s(x1)] | = | x1 + 1 |
[activate(x1)] | = | 1 |
[activate#(x1)] | = | 1 |
[p#(x1)] | = | 1 |
[f(x1)] | = | 1 |
[p(x1)] | = | x1 + 0 |
[0] | = | 20653 |
[n__f(x1)] | = | 1 |
[cons(x1, x2)] | = | x1 + x2 + 1 |
p(s(X)) | → | X | (3) |
f#(s(0)) | → | f#(p(s(0))) | (9) |
The dependency pairs are split into 0 components.