The rewrite relation of the following TRS is considered.
a__2nd(cons1(X,cons(Y,Z))) | → | mark(Y) | (1) |
a__2nd(cons(X,X1)) | → | a__2nd(cons1(mark(X),mark(X1))) | (2) |
a__from(X) | → | cons(mark(X),from(s(X))) | (3) |
mark(2nd(X)) | → | a__2nd(mark(X)) | (4) |
mark(from(X)) | → | a__from(mark(X)) | (5) |
mark(cons(X1,X2)) | → | cons(mark(X1),X2) | (6) |
mark(s(X)) | → | s(mark(X)) | (7) |
mark(cons1(X1,X2)) | → | cons1(mark(X1),mark(X2)) | (8) |
a__2nd(X) | → | 2nd(X) | (9) |
a__from(X) | → | from(X) | (10) |
a__2nd#(cons(X,X1)) | → | mark#(X) | (11) |
mark#(from(X)) | → | a__from#(mark(X)) | (12) |
mark#(2nd(X)) | → | mark#(X) | (13) |
a__2nd#(cons1(X,cons(Y,Z))) | → | mark#(Y) | (14) |
mark#(cons1(X1,X2)) | → | mark#(X2) | (15) |
mark#(2nd(X)) | → | a__2nd#(mark(X)) | (16) |
mark#(from(X)) | → | mark#(X) | (17) |
mark#(cons1(X1,X2)) | → | mark#(X1) | (18) |
mark#(s(X)) | → | mark#(X) | (19) |
a__2nd#(cons(X,X1)) | → | mark#(X1) | (20) |
a__2nd#(cons(X,X1)) | → | a__2nd#(cons1(mark(X),mark(X1))) | (21) |
a__from#(X) | → | mark#(X) | (22) |
mark#(cons(X1,X2)) | → | mark#(X1) | (23) |
The dependency pairs are split into 1 component.
mark#(cons(X1,X2)) | → | mark#(X1) | (23) |
mark#(2nd(X)) | → | a__2nd#(mark(X)) | (16) |
a__from#(X) | → | mark#(X) | (22) |
a__2nd#(cons(X,X1)) | → | a__2nd#(cons1(mark(X),mark(X1))) | (21) |
a__2nd#(cons(X,X1)) | → | mark#(X1) | (20) |
mark#(cons1(X1,X2)) | → | mark#(X2) | (15) |
a__2nd#(cons1(X,cons(Y,Z))) | → | mark#(Y) | (14) |
mark#(2nd(X)) | → | mark#(X) | (13) |
mark#(from(X)) | → | a__from#(mark(X)) | (12) |
mark#(s(X)) | → | mark#(X) | (19) |
mark#(cons1(X1,X2)) | → | mark#(X1) | (18) |
mark#(from(X)) | → | mark#(X) | (17) |
a__2nd#(cons(X,X1)) | → | mark#(X) | (11) |
[s(x1)] | = | x1 + 0 |
[a__from#(x1)] | = | x1 + 30614 |
[a__from(x1)] | = | x1 + 30614 |
[2nd(x1)] | = | x1 + 2 |
[a__2nd(x1)] | = | x1 + 2 |
[a__2nd#(x1)] | = | x1 + 2 |
[cons1(x1, x2)] | = | max(x1 + 5854, x2 + 0, 0) |
[mark#(x1)] | = | x1 + 1 |
[from(x1)] | = | x1 + 30614 |
[mark(x1)] | = | x1 + 0 |
[cons(x1, x2)] | = | max(x1 + 5855, x2 + 0, 0) |
mark(2nd(X)) | → | a__2nd(mark(X)) | (4) |
mark(cons1(X1,X2)) | → | cons1(mark(X1),mark(X2)) | (8) |
a__2nd(cons1(X,cons(Y,Z))) | → | mark(Y) | (1) |
a__from(X) | → | cons(mark(X),from(s(X))) | (3) |
mark(from(X)) | → | a__from(mark(X)) | (5) |
a__from(X) | → | from(X) | (10) |
mark(s(X)) | → | s(mark(X)) | (7) |
a__2nd(X) | → | 2nd(X) | (9) |
mark(cons(X1,X2)) | → | cons(mark(X1),X2) | (6) |
a__2nd(cons(X,X1)) | → | a__2nd(cons1(mark(X),mark(X1))) | (2) |
mark#(cons(X1,X2)) | → | mark#(X1) | (23) |
mark#(2nd(X)) | → | a__2nd#(mark(X)) | (16) |
a__from#(X) | → | mark#(X) | (22) |
a__2nd#(cons(X,X1)) | → | mark#(X1) | (20) |
a__2nd#(cons1(X,cons(Y,Z))) | → | mark#(Y) | (14) |
mark#(2nd(X)) | → | mark#(X) | (13) |
mark#(from(X)) | → | a__from#(mark(X)) | (12) |
mark#(cons1(X1,X2)) | → | mark#(X1) | (18) |
mark#(from(X)) | → | mark#(X) | (17) |
a__2nd#(cons(X,X1)) | → | mark#(X) | (11) |
The dependency pairs are split into 1 component.
mark#(cons1(X1,X2)) | → | mark#(X2) | (15) |
mark#(s(X)) | → | mark#(X) | (19) |
[s(x1)] | = | x1 + 0 |
[a__from#(x1)] | = | 0 |
[a__from(x1)] | = | 2 |
[2nd(x1)] | = | 3 |
[a__2nd(x1)] | = | 2 |
[a__2nd#(x1)] | = | 0 |
[cons1(x1, x2)] | = | x2 + 1 |
[mark#(x1)] | = | x1 + 0 |
[from(x1)] | = | x1 + 3 |
[mark(x1)] | = | 1 |
[cons(x1, x2)] | = | x2 + 2 |
mark#(cons1(X1,X2)) | → | mark#(X2) | (15) |
The dependency pairs are split into 1 component.
mark#(s(X)) | → | mark#(X) | (19) |
[s(x1)] | = | x1 + 1 |
[a__from#(x1)] | = | 0 |
[a__from(x1)] | = | 19782 |
[2nd(x1)] | = | 19783 |
[a__2nd(x1)] | = | 19782 |
[a__2nd#(x1)] | = | 0 |
[cons1(x1, x2)] | = | x2 + 1 |
[mark#(x1)] | = | x1 + 0 |
[from(x1)] | = | x1 + 19783 |
[mark(x1)] | = | 19781 |
[cons(x1, x2)] | = | x2 + 19782 |
mark#(s(X)) | → | mark#(X) | (19) |
The dependency pairs are split into 0 components.