The rewrite relation of the following TRS is considered.
| and(true,X) | → | activate(X) | (1) |
| and(false,Y) | → | false | (2) |
| if(true,X,Y) | → | activate(X) | (3) |
| if(false,X,Y) | → | activate(Y) | (4) |
| add(0,X) | → | activate(X) | (5) |
| add(s(X),Y) | → | s(n__add(activate(X),activate(Y))) | (6) |
| first(0,X) | → | nil | (7) |
| first(s(X),cons(Y,Z)) | → | cons(activate(Y),n__first(activate(X),activate(Z))) | (8) |
| from(X) | → | cons(activate(X),n__from(n__s(activate(X)))) | (9) |
| add(X1,X2) | → | n__add(X1,X2) | (10) |
| first(X1,X2) | → | n__first(X1,X2) | (11) |
| from(X) | → | n__from(X) | (12) |
| s(X) | → | n__s(X) | (13) |
| activate(n__add(X1,X2)) | → | add(activate(X1),X2) | (14) |
| activate(n__first(X1,X2)) | → | first(activate(X1),activate(X2)) | (15) |
| activate(n__from(X)) | → | from(X) | (16) |
| activate(n__s(X)) | → | s(X) | (17) |
| activate(X) | → | X | (18) |
| add#(s(X),Y) | → | activate#(X) | (19) |
| activate#(n__add(X1,X2)) | → | add#(activate(X1),X2) | (20) |
| first#(s(X),cons(Y,Z)) | → | activate#(Y) | (21) |
| activate#(n__s(X)) | → | s#(X) | (22) |
| if#(true,X,Y) | → | activate#(X) | (23) |
| and#(true,X) | → | activate#(X) | (24) |
| first#(s(X),cons(Y,Z)) | → | activate#(X) | (25) |
| activate#(n__add(X1,X2)) | → | activate#(X1) | (26) |
| activate#(n__from(X)) | → | from#(X) | (27) |
| from#(X) | → | activate#(X) | (28) |
| activate#(n__first(X1,X2)) | → | activate#(X1) | (29) |
| if#(false,X,Y) | → | activate#(Y) | (30) |
| activate#(n__first(X1,X2)) | → | first#(activate(X1),activate(X2)) | (31) |
| add#(s(X),Y) | → | activate#(Y) | (32) |
| add#(s(X),Y) | → | s#(n__add(activate(X),activate(Y))) | (33) |
| add#(0,X) | → | activate#(X) | (34) |
| first#(s(X),cons(Y,Z)) | → | activate#(Z) | (35) |
| from#(X) | → | activate#(X) | (28) |
| activate#(n__first(X1,X2)) | → | activate#(X2) | (36) |
The dependency pairs are split into 1 component.
| activate#(n__first(X1,X2)) | → | activate#(X2) | (36) |
| from#(X) | → | activate#(X) | (28) |
| first#(s(X),cons(Y,Z)) | → | activate#(X) | (25) |
| first#(s(X),cons(Y,Z)) | → | activate#(Z) | (35) |
| add#(0,X) | → | activate#(X) | (34) |
| add#(s(X),Y) | → | activate#(Y) | (32) |
| activate#(n__first(X1,X2)) | → | first#(activate(X1),activate(X2)) | (31) |
| first#(s(X),cons(Y,Z)) | → | activate#(Y) | (21) |
| activate#(n__first(X1,X2)) | → | activate#(X1) | (29) |
| activate#(n__add(X1,X2)) | → | add#(activate(X1),X2) | (20) |
| from#(X) | → | activate#(X) | (28) |
| activate#(n__from(X)) | → | from#(X) | (27) |
| activate#(n__add(X1,X2)) | → | activate#(X1) | (26) |
| add#(s(X),Y) | → | activate#(X) | (19) |
| [s(x1)] | = | x1 + 0 |
| [n__first(x1, x2)] | = | max(x1 + 10452, x2 + 10453, 0) |
| [activate(x1)] | = | x1 + 0 |
| [and(x1, x2)] | = | max(0) |
| [n__from(x1)] | = | x1 + 10454 |
| [activate#(x1)] | = | x1 + 1142 |
| [false] | = | 0 |
| [n__add(x1, x2)] | = | max(x1 + 75976, x2 + 67610, 0) |
| [true] | = | 0 |
| [n__s(x1)] | = | x1 + 0 |
| [if(x1, x2, x3)] | = | max(0) |
| [0] | = | 0 |
| [from(x1)] | = | x1 + 10454 |
| [s#(x1)] | = | 0 |
| [first#(x1, x2)] | = | max(x1 + 1143, x2 + 1143, 0) |
| [nil] | = | 10453 |
| [first(x1, x2)] | = | max(x1 + 10452, x2 + 10453, 0) |
| [from#(x1)] | = | x1 + 1143 |
| [cons(x1, x2)] | = | max(x1 + 10454, x2 + 0, 0) |
| [if#(x1, x2, x3)] | = | max(0) |
| [add#(x1, x2)] | = | max(x1 + 36466, x2 + 68751, 0) |
| [add(x1, x2)] | = | max(x1 + 75976, x2 + 67610, 0) |
| [and#(x1, x2)] | = | max(0) |
| activate(X) | → | X | (18) |
| activate(n__first(X1,X2)) | → | first(activate(X1),activate(X2)) | (15) |
| first(s(X),cons(Y,Z)) | → | cons(activate(Y),n__first(activate(X),activate(Z))) | (8) |
| activate(n__from(X)) | → | from(X) | (16) |
| activate(n__s(X)) | → | s(X) | (17) |
| add(0,X) | → | activate(X) | (5) |
| add(X1,X2) | → | n__add(X1,X2) | (10) |
| first(0,X) | → | nil | (7) |
| activate(n__add(X1,X2)) | → | add(activate(X1),X2) | (14) |
| from(X) | → | n__from(X) | (12) |
| first(X1,X2) | → | n__first(X1,X2) | (11) |
| from(X) | → | cons(activate(X),n__from(n__s(activate(X)))) | (9) |
| s(X) | → | n__s(X) | (13) |
| add(s(X),Y) | → | s(n__add(activate(X),activate(Y))) | (6) |
| activate#(n__first(X1,X2)) | → | activate#(X2) | (36) |
| from#(X) | → | activate#(X) | (28) |
| first#(s(X),cons(Y,Z)) | → | activate#(X) | (25) |
| first#(s(X),cons(Y,Z)) | → | activate#(Z) | (35) |
| add#(0,X) | → | activate#(X) | (34) |
| add#(s(X),Y) | → | activate#(Y) | (32) |
| activate#(n__first(X1,X2)) | → | first#(activate(X1),activate(X2)) | (31) |
| first#(s(X),cons(Y,Z)) | → | activate#(Y) | (21) |
| activate#(n__first(X1,X2)) | → | activate#(X1) | (29) |
| activate#(n__add(X1,X2)) | → | add#(activate(X1),X2) | (20) |
| from#(X) | → | activate#(X) | (28) |
| activate#(n__from(X)) | → | from#(X) | (27) |
| activate#(n__add(X1,X2)) | → | activate#(X1) | (26) |
| add#(s(X),Y) | → | activate#(X) | (19) |
The dependency pairs are split into 0 components.