The rewrite relation of the following TRS is considered.
active(f(a,X,X)) | → | mark(f(X,b,b)) | (1) |
active(b) | → | mark(a) | (2) |
mark(f(X1,X2,X3)) | → | active(f(X1,mark(X2),X3)) | (3) |
mark(a) | → | active(a) | (4) |
mark(b) | → | active(b) | (5) |
f(mark(X1),X2,X3) | → | f(X1,X2,X3) | (6) |
f(X1,mark(X2),X3) | → | f(X1,X2,X3) | (7) |
f(X1,X2,mark(X3)) | → | f(X1,X2,X3) | (8) |
f(active(X1),X2,X3) | → | f(X1,X2,X3) | (9) |
f(X1,active(X2),X3) | → | f(X1,X2,X3) | (10) |
f(X1,X2,active(X3)) | → | f(X1,X2,X3) | (11) |
f#(mark(X1),X2,X3) | → | f#(X1,X2,X3) | (12) |
f#(X1,active(X2),X3) | → | f#(X1,X2,X3) | (13) |
f#(X1,X2,mark(X3)) | → | f#(X1,X2,X3) | (14) |
mark#(f(X1,X2,X3)) | → | f#(X1,mark(X2),X3) | (15) |
active#(f(a,X,X)) | → | mark#(f(X,b,b)) | (16) |
active#(f(a,X,X)) | → | f#(X,b,b) | (17) |
mark#(a) | → | active#(a) | (18) |
mark#(b) | → | active#(b) | (19) |
mark#(f(X1,X2,X3)) | → | mark#(X2) | (20) |
f#(X1,mark(X2),X3) | → | f#(X1,X2,X3) | (21) |
f#(active(X1),X2,X3) | → | f#(X1,X2,X3) | (22) |
active#(b) | → | mark#(a) | (23) |
mark#(f(X1,X2,X3)) | → | active#(f(X1,mark(X2),X3)) | (24) |
f#(X1,X2,active(X3)) | → | f#(X1,X2,X3) | (25) |
The dependency pairs are split into 2 components.
mark#(f(X1,X2,X3)) | → | active#(f(X1,mark(X2),X3)) | (24) |
active#(f(a,X,X)) | → | mark#(f(X,b,b)) | (16) |
mark#(f(X1,X2,X3)) | → | mark#(X2) | (20) |
[a] | = | 2438 |
[b] | = | 2438 |
[f(x1, x2, x3)] | = | x1 + x2 + 8856 |
[mark#(x1)] | = | x1 + 0 |
[mark(x1)] | = | x1 + 0 |
[f#(x1, x2, x3)] | = | 0 |
[active(x1)] | = | x1 + 0 |
[active#(x1)] | = | x1 + 0 |
mark(a) | → | active(a) | (4) |
f(X1,X2,mark(X3)) | → | f(X1,X2,X3) | (8) |
active(f(a,X,X)) | → | mark(f(X,b,b)) | (1) |
mark(f(X1,X2,X3)) | → | active(f(X1,mark(X2),X3)) | (3) |
mark(b) | → | active(b) | (5) |
f(X1,active(X2),X3) | → | f(X1,X2,X3) | (10) |
f(X1,mark(X2),X3) | → | f(X1,X2,X3) | (7) |
f(X1,X2,active(X3)) | → | f(X1,X2,X3) | (11) |
f(active(X1),X2,X3) | → | f(X1,X2,X3) | (9) |
f(mark(X1),X2,X3) | → | f(X1,X2,X3) | (6) |
active(b) | → | mark(a) | (2) |
mark#(f(X1,X2,X3)) | → | mark#(X2) | (20) |
The dependency pairs are split into 1 component.
active#(f(a,X,X)) | → | mark#(f(X,b,b)) | (16) |
mark#(f(X1,X2,X3)) | → | active#(f(X1,mark(X2),X3)) | (24) |
[a] | = | 3 |
[b] | = | 1 |
[f(x1, x2, x3)] | = | x1 + x3 + 47562 |
[mark#(x1)] | = | x1 + 1 |
[mark(x1)] | = | x1 + 1 |
[f#(x1, x2, x3)] | = | 0 |
[active(x1)] | = | x1 + 2 |
[active#(x1)] | = | x1 + 0 |
f(X1,X2,mark(X3)) | → | f(X1,X2,X3) | (8) |
f(X1,active(X2),X3) | → | f(X1,X2,X3) | (10) |
f(X1,mark(X2),X3) | → | f(X1,X2,X3) | (7) |
f(X1,X2,active(X3)) | → | f(X1,X2,X3) | (11) |
f(active(X1),X2,X3) | → | f(X1,X2,X3) | (9) |
f(mark(X1),X2,X3) | → | f(X1,X2,X3) | (6) |
active#(f(a,X,X)) | → | mark#(f(X,b,b)) | (16) |
mark#(f(X1,X2,X3)) | → | active#(f(X1,mark(X2),X3)) | (24) |
The dependency pairs are split into 0 components.
f#(X1,X2,active(X3)) | → | f#(X1,X2,X3) | (25) |
f#(active(X1),X2,X3) | → | f#(X1,X2,X3) | (22) |
f#(X1,X2,mark(X3)) | → | f#(X1,X2,X3) | (14) |
f#(X1,active(X2),X3) | → | f#(X1,X2,X3) | (13) |
f#(X1,mark(X2),X3) | → | f#(X1,X2,X3) | (21) |
f#(mark(X1),X2,X3) | → | f#(X1,X2,X3) | (12) |
[a] | = | 3 |
[b] | = | 1 |
[f(x1, x2, x3)] | = | x1 + x3 + 47562 |
[mark#(x1)] | = | x1 + 1 |
[mark(x1)] | = | x1 + 1 |
[f#(x1, x2, x3)] | = | x1 + x2 + x3 + 0 |
[active(x1)] | = | x1 + 2 |
[active#(x1)] | = | x1 + 0 |
f(X1,X2,mark(X3)) | → | f(X1,X2,X3) | (8) |
f(X1,active(X2),X3) | → | f(X1,X2,X3) | (10) |
f(X1,mark(X2),X3) | → | f(X1,X2,X3) | (7) |
f(X1,X2,active(X3)) | → | f(X1,X2,X3) | (11) |
f(active(X1),X2,X3) | → | f(X1,X2,X3) | (9) |
f(mark(X1),X2,X3) | → | f(X1,X2,X3) | (6) |
f#(X1,X2,active(X3)) | → | f#(X1,X2,X3) | (25) |
f#(active(X1),X2,X3) | → | f#(X1,X2,X3) | (22) |
f#(X1,X2,mark(X3)) | → | f#(X1,X2,X3) | (14) |
f#(X1,active(X2),X3) | → | f#(X1,X2,X3) | (13) |
f#(X1,mark(X2),X3) | → | f#(X1,X2,X3) | (21) |
f#(mark(X1),X2,X3) | → | f#(X1,X2,X3) | (12) |
The dependency pairs are split into 0 components.