The rewrite relation of the following TRS is considered.
| fib(N) | → | sel(N,fib1(s(0),s(0))) | (1) |
| fib1(X,Y) | → | cons(X,n__fib1(Y,add(X,Y))) | (2) |
| add(0,X) | → | X | (3) |
| add(s(X),Y) | → | s(add(X,Y)) | (4) |
| sel(0,cons(X,XS)) | → | X | (5) |
| sel(s(N),cons(X,XS)) | → | sel(N,activate(XS)) | (6) |
| fib1(X1,X2) | → | n__fib1(X1,X2) | (7) |
| activate(n__fib1(X1,X2)) | → | fib1(X1,X2) | (8) |
| activate(X) | → | X | (9) |
| sel#(s(N),cons(X,XS)) | → | sel#(N,activate(XS)) | (10) |
| activate#(n__fib1(X1,X2)) | → | fib1#(X1,X2) | (11) |
| add#(s(X),Y) | → | add#(X,Y) | (12) |
| fib#(N) | → | fib1#(s(0),s(0)) | (13) |
| sel#(s(N),cons(X,XS)) | → | activate#(XS) | (14) |
| fib1#(X,Y) | → | add#(X,Y) | (15) |
| fib#(N) | → | sel#(N,fib1(s(0),s(0))) | (16) |
The dependency pairs are split into 2 components.
| sel#(s(N),cons(X,XS)) | → | sel#(N,activate(XS)) | (10) |
| [s(x1)] | = | x1 + 1 |
| [activate(x1)] | = | 1 |
| [activate#(x1)] | = | 0 |
| [fib1#(x1, x2)] | = | 0 |
| [n__fib1(x1, x2)] | = | x2 + 3 |
| [fib1(x1, x2)] | = | x1 + x2 + 2 |
| [fib(x1)] | = | 0 |
| [0] | = | 40651 |
| [sel#(x1, x2)] | = | x1 + 0 |
| [sel(x1, x2)] | = | 0 |
| [cons(x1, x2)] | = | x1 + 3 |
| [add#(x1, x2)] | = | 0 |
| [add(x1, x2)] | = | x1 + 1 |
| [fib#(x1)] | = | 0 |
| sel#(s(N),cons(X,XS)) | → | sel#(N,activate(XS)) | (10) |
The dependency pairs are split into 0 components.
| add#(s(X),Y) | → | add#(X,Y) | (12) |
| [s(x1)] | = | x1 + 1 |
| [activate(x1)] | = | 1 |
| [activate#(x1)] | = | 0 |
| [fib1#(x1, x2)] | = | 0 |
| [n__fib1(x1, x2)] | = | x2 + 3 |
| [fib1(x1, x2)] | = | x1 + x2 + 2 |
| [fib(x1)] | = | 0 |
| [0] | = | 40651 |
| [sel#(x1, x2)] | = | 0 |
| [sel(x1, x2)] | = | 0 |
| [cons(x1, x2)] | = | x1 + 3 |
| [add#(x1, x2)] | = | x1 + 0 |
| [add(x1, x2)] | = | x1 + 1 |
| [fib#(x1)] | = | 0 |
| add#(s(X),Y) | → | add#(X,Y) | (12) |
The dependency pairs are split into 0 components.