First, I prove that (0,0,0)(1,1,1)(2,1,1)(1,1,1) is standard...
- (0,0,0,0)(1,1,1,1)
- = (0,0,0)(1,1,1)(2,2,2)(3,3,3)(4,4,4)...
- > (0,0,0)(1,1,1)(2,2,2)
- = (0,0,0)(1,1,1)(2,2,1)(3,3,1)(4,4,1)...
- > (0,0,0)(1,1,1)(2,2,1)
- = (0,0,0)(1,1,1)(2,2,0)(3,3,1)(4,4,0)(5,5,1)...
- > (0,0,0)(1,1,1)(2,2,0)
- = (0,0,0)(1,1,1)(2,1,1)(3,1,1)(4,1,1)...
- > (0,0,0)(1,1,1)(2,1,1)(3,1,1)
- = (0,0,0)(1,1,1)(2,1,1)(3,1,0)(4,2,1)(5,1,1)(6,2,0)(7,3,1)(8,1,1)...
- > (0,0,0)(1,1,1)(2,1,1)(3,1,0)
- = (0,0,0)(1,1,1)(2,1,1)(3,0,0)(4,1,1)(5,1,1)(6,0,0)(7,1,1)(8,1,1)...
- > (0,0,0)(1,1,1)(2,1,1)(3,0,0)
- = (0,0,0)(1,1,1)(2,1,1)(2,1,1)(2,1,1)...
- > (0,0,0)(1,1,1)(2,1,1)(2,1,1)
- = (0,0,0)(1,1,1)(2,1,1)(2,1,0)(3,2,1)(4,1,1)(4,2,0)(5,3,1)(6,1,1)...
- > (0,0,0)(1,1,1)(2,1,1)(2,1,0)
- = (0,0,0)(1,1,1)(2,1,1)(2,0,0)(3,1,1)(4,1,1)(4,0,0)(5,1,1)(6,1,1)...
- > (0,0,0)(1,1,1)(2,1,1)(2,0,0)
- = (0,0,0)(1,1,1)(2,1,1)(1,1,1)(2,1,1)(1,1,1)(2,1,1)...
- > (0,0,0)(1,1,1)(2,1,1)(1,1,1)
...and then I prove that it doesn't terminate:
- = (0,0,0)(1,1,1)(2,1,1)(1,1,0)(2,2,1)(3,1,1)(2,2,0)(3,3,1)(4,1,1)(3,3,0)(4,4,1)(5,1,1)...
- > (0,0,0)(1,1,1)(2,1,1)(1,1,0)(2,2,1)(3,1,1)
- = (0,0,0)(1,1,1)(2,1,1)(1,1,0)(2,2,1)(3,1,0)(4,2,1)(5,1,1)(4,2,0)(5,3,1)(6,2,0)(7,3,1)(8,1,1)(9,3,0)...
- > (0,0,0)(1,1,1)(2,1,1)(1,1,0)(2,2,1)(3,1,0)(4,2,1)(5,1,1)
- = (0,0,0)(1,1,1)(2,1,1)(1,1,0)(2,2,1)(3,1,0)(4,2,1)(5,1,0)(6,2,1)(7,1,1)(6,2,0)(7,3,1)(8,1,0)(9,2,1)(10,2,0)...
- > (0,0,0)(1,1,1)(2,1,1)(1,1,0)(2,2,1)(3,1,0)(4,2,1)(5,1,0)(6,2,1)(7,1,1)
- = (0,0,0)(1,1,1)(2,1,1)(1,1,0)(2,2,1)(3,1,0)(4,2,1)(5,1,0)(6,2,1)(7,1,0)(8,2,1)(9,1,1)(8,2,0)(9,3,1)(10,1,0)(11,2,1)(12,1,0)(13,2,1)(14,2,0)...
- > (0,0,0)(1,1,1)(2,1,1)(1,1,0)(2,2,1)(3,1,0)(4,2,1)(5,1,0)(6,2,1)(7,1,0)(8,2,1)(9,1,1)
- ...