The rewrite relation of the following TRS is considered.
a__f(0) | → | cons(0,f(s(0))) | (1) |
a__f(s(0)) | → | a__f(a__p(s(0))) | (2) |
a__p(s(X)) | → | mark(X) | (3) |
mark(f(X)) | → | a__f(mark(X)) | (4) |
mark(p(X)) | → | a__p(mark(X)) | (5) |
mark(0) | → | 0 | (6) |
mark(cons(X1,X2)) | → | cons(mark(X1),X2) | (7) |
mark(s(X)) | → | s(mark(X)) | (8) |
a__f(X) | → | f(X) | (9) |
a__p(X) | → | p(X) | (10) |
a__f#(s(0)) | → | a__p#(s(0)) | (11) |
a__p#(s(X)) | → | mark#(X) | (12) |
mark#(f(X)) | → | mark#(X) | (13) |
mark#(s(X)) | → | mark#(X) | (14) |
mark#(p(X)) | → | mark#(X) | (15) |
mark#(cons(X1,X2)) | → | mark#(X1) | (16) |
a__f#(s(0)) | → | a__f#(a__p(s(0))) | (17) |
mark#(f(X)) | → | a__f#(mark(X)) | (18) |
mark#(p(X)) | → | a__p#(mark(X)) | (19) |
The dependency pairs are split into 1 component.
mark#(p(X)) | → | a__p#(mark(X)) | (19) |
mark#(f(X)) | → | a__f#(mark(X)) | (18) |
a__f#(s(0)) | → | a__f#(a__p(s(0))) | (17) |
mark#(cons(X1,X2)) | → | mark#(X1) | (16) |
mark#(f(X)) | → | mark#(X) | (13) |
a__p#(s(X)) | → | mark#(X) | (12) |
mark#(p(X)) | → | mark#(X) | (15) |
mark#(s(X)) | → | mark#(X) | (14) |
a__f#(s(0)) | → | a__p#(s(0)) | (11) |
[s(x1)] | = | x1 + 29485 |
[a__f(x1)] | = | x1 + 4 |
[a__p(x1)] | = | x1 + 0 |
[f(x1)] | = | x1 + 4 |
[p(x1)] | = | x1 + 0 |
[mark#(x1)] | = | x1 + 29484 |
[0] | = | 1 |
[mark(x1)] | = | x1 + 29483 |
[a__p#(x1)] | = | x1 + 0 |
[cons(x1, x2)] | = | x1 + 2 |
[a__f#(x1)] | = | 29487 |
mark(f(X)) | → | a__f(mark(X)) | (4) |
mark(s(X)) | → | s(mark(X)) | (8) |
a__f(0) | → | cons(0,f(s(0))) | (1) |
a__p(s(X)) | → | mark(X) | (3) |
mark(p(X)) | → | a__p(mark(X)) | (5) |
a__p(X) | → | p(X) | (10) |
mark(cons(X1,X2)) | → | cons(mark(X1),X2) | (7) |
a__f(X) | → | f(X) | (9) |
mark(0) | → | 0 | (6) |
a__f(s(0)) | → | a__f(a__p(s(0))) | (2) |
mark#(p(X)) | → | a__p#(mark(X)) | (19) |
mark#(f(X)) | → | a__f#(mark(X)) | (18) |
mark#(cons(X1,X2)) | → | mark#(X1) | (16) |
mark#(f(X)) | → | mark#(X) | (13) |
a__p#(s(X)) | → | mark#(X) | (12) |
mark#(s(X)) | → | mark#(X) | (14) |
a__f#(s(0)) | → | a__p#(s(0)) | (11) |
The dependency pairs are split into 2 components.
mark#(p(X)) | → | mark#(X) | (15) |
[s(x1)] | = | x1 + 29480 |
[a__f(x1)] | = | 4 |
[a__p(x1)] | = | x1 + 1 |
[f(x1)] | = | 4 |
[p(x1)] | = | x1 + 1 |
[mark#(x1)] | = | x1 + 29484 |
[0] | = | 3 |
[mark(x1)] | = | x1 + 2241 |
[a__p#(x1)] | = | x1 + 0 |
[cons(x1, x2)] | = | x1 + 1 |
[a__f#(x1)] | = | 29487 |
mark(f(X)) | → | a__f(mark(X)) | (4) |
mark(s(X)) | → | s(mark(X)) | (8) |
a__f(0) | → | cons(0,f(s(0))) | (1) |
a__p(s(X)) | → | mark(X) | (3) |
mark(p(X)) | → | a__p(mark(X)) | (5) |
a__p(X) | → | p(X) | (10) |
mark(cons(X1,X2)) | → | cons(mark(X1),X2) | (7) |
a__f(X) | → | f(X) | (9) |
mark(0) | → | 0 | (6) |
a__f(s(0)) | → | a__f(a__p(s(0))) | (2) |
mark#(p(X)) | → | mark#(X) | (15) |
The dependency pairs are split into 0 components.
a__f#(s(0)) | → | a__f#(a__p(s(0))) | (17) |
π(mark) | = | 1 |
π(a__p#) | = | 1 |
prec(s) | = | 2 | status(s) | = | [] | list-extension(s) | = | Lex | ||
prec(a__f) | = | 1 | status(a__f) | = | [] | list-extension(a__f) | = | Lex | ||
prec(a__p) | = | 0 | status(a__p) | = | [] | list-extension(a__p) | = | Lex | ||
prec(f) | = | 1 | status(f) | = | [] | list-extension(f) | = | Lex | ||
prec(p) | = | 0 | status(p) | = | [] | list-extension(p) | = | Lex | ||
prec(mark#) | = | 0 | status(mark#) | = | [] | list-extension(mark#) | = | Lex | ||
prec(0) | = | 1 | status(0) | = | [] | list-extension(0) | = | Lex | ||
prec(cons) | = | 1 | status(cons) | = | [] | list-extension(cons) | = | Lex | ||
prec(a__f#) | = | 0 | status(a__f#) | = | [1] | list-extension(a__f#) | = | Lex |
[s(x1)] | = | x1 + 1 |
[a__f(x1)] | = | 32286 |
[a__p(x1)] | = | x1 + 0 |
[f(x1)] | = | 32286 |
[p(x1)] | = | x1 + 0 |
[mark#(x1)] | = | 1 |
[0] | = | 32287 |
[cons(x1, x2)] | = | 32286 |
[a__f#(x1)] | = | x1 + 1 |
mark(f(X)) | → | a__f(mark(X)) | (4) |
mark(s(X)) | → | s(mark(X)) | (8) |
a__f(0) | → | cons(0,f(s(0))) | (1) |
a__p(s(X)) | → | mark(X) | (3) |
mark(p(X)) | → | a__p(mark(X)) | (5) |
a__p(X) | → | p(X) | (10) |
mark(cons(X1,X2)) | → | cons(mark(X1),X2) | (7) |
a__f(X) | → | f(X) | (9) |
mark(0) | → | 0 | (6) |
a__f(s(0)) | → | a__f(a__p(s(0))) | (2) |
a__f#(s(0)) | → | a__f#(a__p(s(0))) | (17) |
The dependency pairs are split into 0 components.