The rewrite relation of the following TRS is considered.
a__from(X) | → | cons(mark(X),from(s(X))) | (1) |
a__after(0,XS) | → | mark(XS) | (2) |
a__after(s(N),cons(X,XS)) | → | a__after(mark(N),mark(XS)) | (3) |
mark(from(X)) | → | a__from(mark(X)) | (4) |
mark(after(X1,X2)) | → | a__after(mark(X1),mark(X2)) | (5) |
mark(cons(X1,X2)) | → | cons(mark(X1),X2) | (6) |
mark(s(X)) | → | s(mark(X)) | (7) |
mark(0) | → | 0 | (8) |
a__from(X) | → | from(X) | (9) |
a__after(X1,X2) | → | after(X1,X2) | (10) |
mark#(cons(X1,X2)) | → | mark#(X1) | (11) |
mark#(after(X1,X2)) | → | mark#(X2) | (12) |
a__after#(s(N),cons(X,XS)) | → | mark#(XS) | (13) |
mark#(from(X)) | → | a__from#(mark(X)) | (14) |
mark#(from(X)) | → | mark#(X) | (15) |
a__after#(s(N),cons(X,XS)) | → | a__after#(mark(N),mark(XS)) | (16) |
a__from#(X) | → | mark#(X) | (17) |
mark#(after(X1,X2)) | → | mark#(X1) | (18) |
mark#(s(X)) | → | mark#(X) | (19) |
a__after#(0,XS) | → | mark#(XS) | (20) |
a__after#(s(N),cons(X,XS)) | → | mark#(N) | (21) |
mark#(after(X1,X2)) | → | a__after#(mark(X1),mark(X2)) | (22) |
The dependency pairs are split into 1 component.
mark#(after(X1,X2)) | → | a__after#(mark(X1),mark(X2)) | (22) |
mark#(from(X)) | → | mark#(X) | (15) |
a__after#(s(N),cons(X,XS)) | → | mark#(N) | (21) |
a__after#(0,XS) | → | mark#(XS) | (20) |
mark#(s(X)) | → | mark#(X) | (19) |
mark#(from(X)) | → | a__from#(mark(X)) | (14) |
a__after#(s(N),cons(X,XS)) | → | mark#(XS) | (13) |
mark#(after(X1,X2)) | → | mark#(X2) | (12) |
mark#(after(X1,X2)) | → | mark#(X1) | (18) |
a__from#(X) | → | mark#(X) | (17) |
a__after#(s(N),cons(X,XS)) | → | a__after#(mark(N),mark(XS)) | (16) |
mark#(cons(X1,X2)) | → | mark#(X1) | (11) |
[s(x1)] | = | x1 + 0 |
[a__from#(x1)] | = | x1 + 5854 |
[a__from(x1)] | = | x1 + 41065 |
[after(x1, x2)] | = | max(x1 + 71680, x2 + 30614, 0) |
[a__after#(x1, x2)] | = | max(x1 + 46918, x2 + 5854, 0) |
[a__after(x1, x2)] | = | max(x1 + 71680, x2 + 30614, 0) |
[mark#(x1)] | = | x1 + 5853 |
[0] | = | 0 |
[from(x1)] | = | x1 + 41065 |
[mark(x1)] | = | x1 + 0 |
[cons(x1, x2)] | = | max(x1 + 41065, x2 + 0, 0) |
mark(from(X)) | → | a__from(mark(X)) | (4) |
mark(0) | → | 0 | (8) |
a__from(X) | → | cons(mark(X),from(s(X))) | (1) |
a__after(s(N),cons(X,XS)) | → | a__after(mark(N),mark(XS)) | (3) |
mark(after(X1,X2)) | → | a__after(mark(X1),mark(X2)) | (5) |
a__after(X1,X2) | → | after(X1,X2) | (10) |
mark(s(X)) | → | s(mark(X)) | (7) |
a__from(X) | → | from(X) | (9) |
mark(cons(X1,X2)) | → | cons(mark(X1),X2) | (6) |
a__after(0,XS) | → | mark(XS) | (2) |
mark#(after(X1,X2)) | → | a__after#(mark(X1),mark(X2)) | (22) |
mark#(from(X)) | → | mark#(X) | (15) |
a__after#(s(N),cons(X,XS)) | → | mark#(N) | (21) |
a__after#(0,XS) | → | mark#(XS) | (20) |
mark#(from(X)) | → | a__from#(mark(X)) | (14) |
a__after#(s(N),cons(X,XS)) | → | mark#(XS) | (13) |
mark#(after(X1,X2)) | → | mark#(X2) | (12) |
mark#(after(X1,X2)) | → | mark#(X1) | (18) |
a__from#(X) | → | mark#(X) | (17) |
mark#(cons(X1,X2)) | → | mark#(X1) | (11) |
The dependency pairs are split into 2 components.
a__after#(s(N),cons(X,XS)) | → | a__after#(mark(N),mark(XS)) | (16) |
[s(x1)] | = | x1 + 9727 |
[a__from#(x1)] | = | 0 |
[a__from(x1)] | = | 44245 |
[after(x1, x2)] | = | x2 + 9726 |
[a__after#(x1, x2)] | = | x1 + 0 |
[a__after(x1, x2)] | = | x2 + 9726 |
[mark#(x1)] | = | 0 |
[0] | = | 31328 |
[from(x1)] | = | 34519 |
[mark(x1)] | = | x1 + 9726 |
[cons(x1, x2)] | = | x2 + 9726 |
mark(from(X)) | → | a__from(mark(X)) | (4) |
mark(0) | → | 0 | (8) |
a__from(X) | → | cons(mark(X),from(s(X))) | (1) |
a__after(s(N),cons(X,XS)) | → | a__after(mark(N),mark(XS)) | (3) |
mark(after(X1,X2)) | → | a__after(mark(X1),mark(X2)) | (5) |
a__after(X1,X2) | → | after(X1,X2) | (10) |
mark(s(X)) | → | s(mark(X)) | (7) |
a__from(X) | → | from(X) | (9) |
mark(cons(X1,X2)) | → | cons(mark(X1),X2) | (6) |
a__after(0,XS) | → | mark(XS) | (2) |
a__after#(s(N),cons(X,XS)) | → | a__after#(mark(N),mark(XS)) | (16) |
The dependency pairs are split into 0 components.
mark#(s(X)) | → | mark#(X) | (19) |
[s(x1)] | = | x1 + 9727 |
[a__from#(x1)] | = | 0 |
[a__from(x1)] | = | 35496 |
[after(x1, x2)] | = | x2 + 1 |
[a__after#(x1, x2)] | = | x1 + 0 |
[a__after(x1, x2)] | = | x2 + 1 |
[mark#(x1)] | = | x1 + 0 |
[0] | = | 31328 |
[from(x1)] | = | 35495 |
[mark(x1)] | = | x1 + 1 |
[cons(x1, x2)] | = | x2 + 1 |
mark(from(X)) | → | a__from(mark(X)) | (4) |
mark(0) | → | 0 | (8) |
a__from(X) | → | cons(mark(X),from(s(X))) | (1) |
a__after(s(N),cons(X,XS)) | → | a__after(mark(N),mark(XS)) | (3) |
mark(after(X1,X2)) | → | a__after(mark(X1),mark(X2)) | (5) |
a__after(X1,X2) | → | after(X1,X2) | (10) |
mark(s(X)) | → | s(mark(X)) | (7) |
a__from(X) | → | from(X) | (9) |
mark(cons(X1,X2)) | → | cons(mark(X1),X2) | (6) |
a__after(0,XS) | → | mark(XS) | (2) |
mark#(s(X)) | → | mark#(X) | (19) |
The dependency pairs are split into 0 components.