The rewrite relation of the following TRS is considered.
| a__fst(0,Z) | → | nil | (1) |
| a__fst(s(X),cons(Y,Z)) | → | cons(mark(Y),fst(X,Z)) | (2) |
| a__from(X) | → | cons(mark(X),from(s(X))) | (3) |
| a__add(0,X) | → | mark(X) | (4) |
| a__add(s(X),Y) | → | s(add(X,Y)) | (5) |
| a__len(nil) | → | 0 | (6) |
| a__len(cons(X,Z)) | → | s(len(Z)) | (7) |
| mark(fst(X1,X2)) | → | a__fst(mark(X1),mark(X2)) | (8) |
| mark(from(X)) | → | a__from(mark(X)) | (9) |
| mark(add(X1,X2)) | → | a__add(mark(X1),mark(X2)) | (10) |
| mark(len(X)) | → | a__len(mark(X)) | (11) |
| mark(0) | → | 0 | (12) |
| mark(s(X)) | → | s(X) | (13) |
| mark(nil) | → | nil | (14) |
| mark(cons(X1,X2)) | → | cons(mark(X1),X2) | (15) |
| a__fst(X1,X2) | → | fst(X1,X2) | (16) |
| a__from(X) | → | from(X) | (17) |
| a__add(X1,X2) | → | add(X1,X2) | (18) |
| a__len(X) | → | len(X) | (19) |
| prec(len) | = | 0 | status(len) | = | [1] | list-extension(len) | = | Lex | ||
| prec(a__len) | = | 1 | status(a__len) | = | [1] | list-extension(a__len) | = | Lex | ||
| prec(add) | = | 0 | status(add) | = | [2, 1] | list-extension(add) | = | Lex | ||
| prec(a__add) | = | 2 | status(a__add) | = | [2, 1] | list-extension(a__add) | = | Lex | ||
| prec(from) | = | 0 | status(from) | = | [1] | list-extension(from) | = | Lex | ||
| prec(a__from) | = | 2 | status(a__from) | = | [1] | list-extension(a__from) | = | Lex | ||
| prec(fst) | = | 0 | status(fst) | = | [1, 2] | list-extension(fst) | = | Lex | ||
| prec(mark) | = | 3 | status(mark) | = | [1] | list-extension(mark) | = | Lex | ||
| prec(cons) | = | 0 | status(cons) | = | [1, 2] | list-extension(cons) | = | Lex | ||
| prec(s) | = | 0 | status(s) | = | [1] | list-extension(s) | = | Lex | ||
| prec(nil) | = | 0 | status(nil) | = | [] | list-extension(nil) | = | Lex | ||
| prec(a__fst) | = | 1 | status(a__fst) | = | [1, 2] | list-extension(a__fst) | = | Lex | ||
| prec(0) | = | 0 | status(0) | = | [] | list-extension(0) | = | Lex |
| [len(x1)] | = | max(0, 0 + 1 · x1) |
| [a__len(x1)] | = | 0 + 1 · x1 |
| [add(x1, x2)] | = | max(0, 2 + 1 · x1, 1 + 1 · x2) |
| [a__add(x1, x2)] | = | max(0, 2 + 1 · x1, 1 + 1 · x2) |
| [from(x1)] | = | max(0, 2 + 1 · x1) |
| [a__from(x1)] | = | max(0, 2 + 1 · x1) |
| [fst(x1, x2)] | = | 0 + 1 · x1 + 1 · x2 |
| [mark(x1)] | = | max(0, 0 + 1 · x1) |
| [cons(x1, x2)] | = | max(2, 1 + 1 · x1, 0 + 1 · x2) |
| [s(x1)] | = | max(0, 0 + 1 · x1) |
| [nil] | = | max(2) |
| [a__fst(x1, x2)] | = | 0 + 1 · x1 + 1 · x2 |
| [0] | = | max(2) |
| a__fst(0,Z) | → | nil | (1) |
| a__fst(s(X),cons(Y,Z)) | → | cons(mark(Y),fst(X,Z)) | (2) |
| a__from(X) | → | cons(mark(X),from(s(X))) | (3) |
| a__add(0,X) | → | mark(X) | (4) |
| a__add(s(X),Y) | → | s(add(X,Y)) | (5) |
| a__len(nil) | → | 0 | (6) |
| a__len(cons(X,Z)) | → | s(len(Z)) | (7) |
| mark(fst(X1,X2)) | → | a__fst(mark(X1),mark(X2)) | (8) |
| mark(from(X)) | → | a__from(mark(X)) | (9) |
| mark(add(X1,X2)) | → | a__add(mark(X1),mark(X2)) | (10) |
| mark(len(X)) | → | a__len(mark(X)) | (11) |
| mark(0) | → | 0 | (12) |
| mark(s(X)) | → | s(X) | (13) |
| mark(nil) | → | nil | (14) |
| mark(cons(X1,X2)) | → | cons(mark(X1),X2) | (15) |
| a__fst(X1,X2) | → | fst(X1,X2) | (16) |
| a__from(X) | → | from(X) | (17) |
| a__add(X1,X2) | → | add(X1,X2) | (18) |
| a__len(X) | → | len(X) | (19) |
There are no rules in the TRS. Hence, it is terminating.