The rewrite relation of the following TRS is considered.
| fst(0,Z) | → | nil | (1) |
| fst(s(X),cons(Y,Z)) | → | cons(Y,n__fst(activate(X),activate(Z))) | (2) |
| from(X) | → | cons(X,n__from(n__s(X))) | (3) |
| add(0,X) | → | X | (4) |
| add(s(X),Y) | → | s(n__add(activate(X),Y)) | (5) |
| len(nil) | → | 0 | (6) |
| len(cons(X,Z)) | → | s(n__len(activate(Z))) | (7) |
| fst(X1,X2) | → | n__fst(X1,X2) | (8) |
| from(X) | → | n__from(X) | (9) |
| s(X) | → | n__s(X) | (10) |
| add(X1,X2) | → | n__add(X1,X2) | (11) |
| len(X) | → | n__len(X) | (12) |
| activate(n__fst(X1,X2)) | → | fst(activate(X1),activate(X2)) | (13) |
| activate(n__from(X)) | → | from(activate(X)) | (14) |
| activate(n__s(X)) | → | s(X) | (15) |
| activate(n__add(X1,X2)) | → | add(activate(X1),activate(X2)) | (16) |
| activate(n__len(X)) | → | len(activate(X)) | (17) |
| activate(X) | → | X | (18) |
| fst#(s(X),cons(Y,Z)) | → | activate#(X) | (19) |
| fst#(s(X),cons(Y,Z)) | → | activate#(Z) | (20) |
| add#(s(X),Y) | → | s#(n__add(activate(X),Y)) | (21) |
| add#(s(X),Y) | → | activate#(X) | (22) |
| len#(cons(X,Z)) | → | s#(n__len(activate(Z))) | (23) |
| len#(cons(X,Z)) | → | activate#(Z) | (24) |
| activate#(n__fst(X1,X2)) | → | fst#(activate(X1),activate(X2)) | (25) |
| activate#(n__fst(X1,X2)) | → | activate#(X1) | (26) |
| activate#(n__fst(X1,X2)) | → | activate#(X2) | (27) |
| activate#(n__from(X)) | → | from#(activate(X)) | (28) |
| activate#(n__from(X)) | → | activate#(X) | (29) |
| activate#(n__s(X)) | → | s#(X) | (30) |
| activate#(n__add(X1,X2)) | → | add#(activate(X1),activate(X2)) | (31) |
| activate#(n__add(X1,X2)) | → | activate#(X1) | (32) |
| activate#(n__add(X1,X2)) | → | activate#(X2) | (33) |
| activate#(n__len(X)) | → | len#(activate(X)) | (34) |
| activate#(n__len(X)) | → | activate#(X) | (35) |
The dependency pairs are split into 1 component.
| activate#(n__fst(X1,X2)) | → | fst#(activate(X1),activate(X2)) | (25) |
| fst#(s(X),cons(Y,Z)) | → | activate#(X) | (19) |
| activate#(n__fst(X1,X2)) | → | activate#(X1) | (26) |
| activate#(n__fst(X1,X2)) | → | activate#(X2) | (27) |
| activate#(n__from(X)) | → | activate#(X) | (29) |
| activate#(n__add(X1,X2)) | → | add#(activate(X1),activate(X2)) | (31) |
| add#(s(X),Y) | → | activate#(X) | (22) |
| activate#(n__add(X1,X2)) | → | activate#(X1) | (32) |
| activate#(n__add(X1,X2)) | → | activate#(X2) | (33) |
| activate#(n__len(X)) | → | len#(activate(X)) | (34) |
| len#(cons(X,Z)) | → | activate#(Z) | (24) |
| activate#(n__len(X)) | → | activate#(X) | (35) |
| fst#(s(X),cons(Y,Z)) | → | activate#(Z) | (20) |
| [add#(x1, x2)] | = | 2 + 2 · x1 |
| [fst#(x1, x2)] | = | 2 · x1 + 2 · x2 |
| [len#(x1)] | = | 2 · x1 |
| [activate(x1)] | = | x1 |
| [n__fst(x1, x2)] | = | 2 · x1 + x2 |
| [fst(x1, x2)] | = | 2 · x1 + x2 |
| [n__from(x1)] | = | 2 + 2 · x1 |
| [from(x1)] | = | 2 + 2 · x1 |
| [n__s(x1)] | = | x1 |
| [s(x1)] | = | x1 |
| [n__add(x1, x2)] | = | 2 + x1 + 2 · x2 |
| [add(x1, x2)] | = | 2 + x1 + 2 · x2 |
| [n__len(x1)] | = | x1 |
| [len(x1)] | = | x1 |
| [cons(x1, x2)] | = | x2 |
| [0] | = | 2 |
| [nil] | = | 2 |
| [activate#(x1)] | = | 2 · x1 |
| activate#(n__from(X)) | → | activate#(X) | (29) |
| activate#(n__add(X1,X2)) | → | add#(activate(X1),activate(X2)) | (31) |
| add#(s(X),Y) | → | activate#(X) | (22) |
| activate#(n__add(X1,X2)) | → | activate#(X1) | (32) |
| activate#(n__add(X1,X2)) | → | activate#(X2) | (33) |
| [fst#(x1, x2)] | = | 2 · x1 + 2 · x2 |
| [len#(x1)] | = | 2 + x1 |
| [activate(x1)] | = | x1 |
| [n__fst(x1, x2)] | = | 2 + 2 · x1 + 2 · x2 |
| [fst(x1, x2)] | = | 2 + 2 · x1 + 2 · x2 |
| [n__from(x1)] | = | -2 |
| [from(x1)] | = | -2 |
| [n__s(x1)] | = | x1 |
| [s(x1)] | = | x1 |
| [n__add(x1, x2)] | = | x2 |
| [add(x1, x2)] | = | x2 |
| [n__len(x1)] | = | 2 + 2 · x1 |
| [len(x1)] | = | 2 + 2 · x1 |
| [cons(x1, x2)] | = | x2 |
| [0] | = | 2 |
| [nil] | = | 2 |
| [activate#(x1)] | = | x1 |
| activate#(n__fst(X1,X2)) | → | fst#(activate(X1),activate(X2)) | (25) |
| activate#(n__fst(X1,X2)) | → | activate#(X1) | (26) |
| activate#(n__fst(X1,X2)) | → | activate#(X2) | (27) |
| len#(cons(X,Z)) | → | activate#(Z) | (24) |
| activate#(n__len(X)) | → | activate#(X) | (35) |
The dependency pairs are split into 0 components.