| 1: | x - 0 | → x | |
| 2: | s(x) - s(y) | → x - y | |
| 3: | 0 ≤ y | → true | |
| 4: | s(x) ≤ 0 | → false | |
| 5: | s(x) ≤ s(y) | → x ≤ y | |
| 6: | if(true,x,y) | → x | |
| 7: | if(false,x,y) | → y | |
| 8: | perfectp(0) | → false | |
| 9: | perfectp(s(x)) | → f(x,s(0),s(x),s(x)) | |
| 10: | f(0,y,0,u) | → true | |
| 11: | f(0,y,s(z),u) | → false | |
| 12: | f(s(x),0,z,u) | → f(x,u,z - s(x),u) | |
| 13: | f(s(x),s(y),z,u) | → if(x ≤ y,f(s(x),y - x,z,u),f(x,u,z,u)) | |
| 14: | s(x) -# s(y) | → x -# y | |
| 15: | s(x) <=# s(y) | → x <=# y | |
| 16: | PERFECTP(s(x)) | → F(x,s(0),s(x),s(x)) | |
| 17: | F(s(x),0,z,u) | → F(x,u,z - s(x),u) | |
| 18: | F(s(x),0,z,u) | → z -# s(x) | |
| 19: | F(s(x),s(y),z,u) | → IF(x ≤ y,f(s(x),y - x,z,u),f(x,u,z,u)) | |
| 20: | F(s(x),s(y),z,u) | → x <=# y | |
| 21: | F(s(x),s(y),z,u) | → F(s(x),y - x,z,u) | |
| 22: | F(s(x),s(y),z,u) | → y -# x | |
| 23: | F(s(x),s(y),z,u) | → F(x,u,z,u) | |