Certification Problem

Input (TPDB SRS_Standard/ICFP_2010/132957)

The rewrite relation of the following TRS is considered.

0(0(0(2(3(0(2(2(0(3(0(1(2(3(3(0(2(0(x1))))))))))))))))))	→	0(1(3(2(3(2(2(2(0(0(3(3(2(0(0(0(0(0(x1))))))))))))))))))	(1)
0(0(0(3(0(1(3(0(2(0(3(0(3(0(3(1(0(3(x1))))))))))))))))))	→	0(0(1(0(0(1(0(3(3(0(0(3(2(0(3(0(3(3(x1))))))))))))))))))	(2)
0(0(2(0(3(0(3(1(1(0(0(1(3(0(3(0(0(2(x1))))))))))))))))))	→	0(0(1(1(1(0(3(0(3(3(0(0(2(0(3(0(0(2(x1))))))))))))))))))	(3)
0(0(2(0(3(1(3(2(1(1(2(3(3(0(2(2(2(2(x1))))))))))))))))))	→	3(2(3(1(2(0(1(3(2(0(2(0(2(3(0(1(2(2(x1))))))))))))))))))	(4)
0(0(2(3(0(2(1(2(2(3(0(3(3(1(1(0(2(0(x1))))))))))))))))))	→	0(0(1(2(2(3(3(2(0(3(1(0(2(1(0(3(2(0(x1))))))))))))))))))	(5)
0(0(3(1(2(3(1(0(2(3(3(0(2(1(3(0(2(2(x1))))))))))))))))))	→	0(3(2(0(3(3(1(2(2(0(1(3(0(0(2(1(3(2(x1))))))))))))))))))	(6)
0(1(0(0(2(2(1(1(3(0(0(1(2(0(1(2(2(0(x1))))))))))))))))))	→	0(1(1(0(0(0(2(2(1(2(0(1(1(0(3(2(2(0(x1))))))))))))))))))	(7)
0(1(0(2(3(0(2(1(2(2(1(1(3(3(2(0(3(3(x1))))))))))))))))))	→	0(1(2(0(2(2(3(3(2(0(1(3(2(3(0(1(1(3(x1))))))))))))))))))	(8)
0(1(1(3(0(2(0(3(0(1(2(3(0(2(0(3(0(3(x1))))))))))))))))))	→	0(0(0(2(3(3(1(0(1(2(0(0(0(1(3(3(2(3(x1))))))))))))))))))	(9)
0(1(2(3(2(0(2(3(1(0(3(0(2(2(1(1(3(3(x1))))))))))))))))))	→	0(1(2(2(3(2(3(1(1(2(3(3(2(0(0(1(0(3(x1))))))))))))))))))	(10)
0(1(2(3(2(2(1(3(0(2(1(3(3(1(0(0(2(1(x1))))))))))))))))))	→	0(3(2(1(0(1(0(2(3(0(1(3(2(1(3(2(2(1(x1))))))))))))))))))	(11)
0(2(1(3(0(3(3(3(3(1(1(1(3(3(3(2(1(2(x1))))))))))))))))))	→	1(3(2(3(3(3(1(0(1(3(1(3(3(3(2(0(1(2(x1))))))))))))))))))	(12)
0(2(2(0(3(1(3(3(0(1(0(3(3(1(1(0(1(2(x1))))))))))))))))))	→	0(3(1(2(0(3(2(3(1(0(0(3(1(0(1(3(1(2(x1))))))))))))))))))	(13)
0(3(0(0(1(3(0(0(1(3(0(3(3(1(1(1(1(0(x1))))))))))))))))))	→	0(3(0(3(0(0(3(1(0(1(3(1(1(0(3(1(1(0(x1))))))))))))))))))	(14)
0(3(0(0(3(1(0(3(0(0(0(1(2(1(2(0(2(0(x1))))))))))))))))))	→	0(3(0(0(1(1(0(2(2(3(0(0(1(0(0(3(2(0(x1))))))))))))))))))	(15)
0(3(0(2(0(0(0(0(2(2(0(2(1(0(2(2(2(0(x1))))))))))))))))))	→	0(2(2(2(1(2(0(0(3(2(2(0(0(2(0(0(0(0(x1))))))))))))))))))	(16)
0(3(0(3(0(3(0(1(3(0(0(3(2(0(2(1(0(3(x1))))))))))))))))))	→	1(3(2(3(0(0(1(0(0(3(2(0(3(0(0(3(0(3(x1))))))))))))))))))	(17)
0(3(0(3(1(3(0(1(3(0(2(2(3(1(2(0(3(1(x1))))))))))))))))))	→	1(0(3(0(3(0(0(3(2(3(0(1(2(3(1(2(3(1(x1))))))))))))))))))	(18)
0(3(0(3(2(2(0(0(2(3(2(1(3(3(0(2(0(2(x1))))))))))))))))))	→	0(3(3(1(0(0(2(2(0(0(0(2(3(2(3(2(3(2(x1))))))))))))))))))	(19)
0(3(1(2(3(2(1(2(3(3(2(1(2(3(3(2(2(2(x1))))))))))))))))))	→	1(2(3(2(3(1(2(0(3(3(1(3(2(2(3(2(2(2(x1))))))))))))))))))	(20)
0(3(2(0(1(0(1(1(1(0(0(2(1(1(2(2(1(1(x1))))))))))))))))))	→	0(3(2(1(0(1(2(1(2(0(0(1(1(0(1(2(1(1(x1))))))))))))))))))	(21)
1(0(1(1(1(2(2(3(0(2(0(3(2(3(0(3(0(0(x1))))))))))))))))))	→	1(3(2(0(3(1(1(0(3(2(0(3(2(0(2(1(0(0(x1))))))))))))))))))	(22)
1(0(1(2(2(2(0(3(3(2(1(2(0(2(0(1(2(2(x1))))))))))))))))))	→	1(0(2(2(1(2(0(2(2(1(1(0(0(2(3(2(3(2(x1))))))))))))))))))	(23)
1(0(3(0(3(3(0(2(1(2(3(3(1(0(2(2(3(3(x1))))))))))))))))))	→	1(0(3(1(2(3(3(1(0(2(2(3(0(0(3(2(3(3(x1))))))))))))))))))	(24)
1(1(0(1(3(0(3(1(3(1(1(3(3(1(2(2(3(3(x1))))))))))))))))))	→	1(3(1(3(1(0(3(1(3(1(3(1(3(2(3(2(1(0(x1))))))))))))))))))	(25)
1(1(1(0(2(1(3(2(2(2(1(3(3(1(0(0(2(0(x1))))))))))))))))))	→	1(0(1(3(2(1(2(1(1(3(2(2(3(0(0(1(2(0(x1))))))))))))))))))	(26)
1(1(1(1(1(1(2(1(2(2(2(2(2(0(3(3(1(0(x1))))))))))))))))))	→	1(1(3(2(2(3(1(2(1(1(2(0(1(0(2(1(1(2(x1))))))))))))))))))	(27)
1(1(1(2(0(1(2(1(3(1(0(3(3(0(0(2(1(3(x1))))))))))))))))))	→	1(1(1(1(2(2(0(3(1(0(3(2(0(0(1(3(1(3(x1))))))))))))))))))	(28)
1(1(1(2(3(0(3(0(2(2(1(0(1(3(3(3(3(1(x1))))))))))))))))))	→	1(2(3(0(1(2(3(1(3(3(2(0(1(3(1(3(0(1(x1))))))))))))))))))	(29)
1(1(1(3(0(1(0(1(3(1(1(0(2(3(1(1(1(3(x1))))))))))))))))))	→	1(1(3(1(3(0(1(1(0(1(0(1(3(1(2(1(1(3(x1))))))))))))))))))	(30)
1(1(1(3(0(2(0(3(3(3(0(0(0(1(2(0(2(1(x1))))))))))))))))))	→	1(2(3(2(0(1(0(3(0(0(1(3(0(1(0(3(2(1(x1))))))))))))))))))	(31)
1(1(2(2(2(2(3(0(2(1(3(0(0(0(2(2(2(1(x1))))))))))))))))))	→	1(2(2(3(0(1(2(0(0(2(3(1(0(2(2(2(2(1(x1))))))))))))))))))	(32)
1(1(3(0(2(1(2(1(0(3(1(0(3(2(3(0(2(1(x1))))))))))))))))))	→	1(1(0(2(3(3(3(3(0(1(1(0(1(2(2(0(2(1(x1))))))))))))))))))	(33)
1(1(3(1(1(2(0(2(1(3(0(2(3(3(3(2(1(3(x1))))))))))))))))))	→	1(0(3(2(1(3(3(1(2(1(1(3(2(2(3(0(1(3(x1))))))))))))))))))	(34)
1(3(0(2(0(1(1(1(1(3(0(0(1(1(2(3(1(1(x1))))))))))))))))))	→	1(0(1(1(2(1(3(2(3(1(3(0(1(1(0(0(1(1(x1))))))))))))))))))	(35)
1(3(0(2(1(1(3(1(1(0(3(2(3(3(1(1(2(2(x1))))))))))))))))))	→	1(2(3(0(3(3(3(2(1(1(0(1(1(1(3(1(2(2(x1))))))))))))))))))	(36)
1(3(0(2(1(3(0(1(2(2(1(1(0(2(3(3(3(2(x1))))))))))))))))))	→	3(2(1(1(3(2(1(3(2(3(1(0(0(1(0(2(3(2(x1))))))))))))))))))	(37)
1(3(0(2(1(3(1(2(1(1(0(2(1(1(1(1(1(1(x1))))))))))))))))))	→	1(3(1(1(1(1(0(1(2(1(1(0(1(2(3(2(1(1(x1))))))))))))))))))	(38)
1(3(0(2(1(3(2(0(0(3(0(1(2(3(3(2(2(2(x1))))))))))))))))))	→	1(3(1(0(0(2(0(1(3(3(2(2(3(2(0(2(3(2(x1))))))))))))))))))	(39)
1(3(1(3(0(1(3(0(0(0(3(3(0(1(2(2(2(3(x1))))))))))))))))))	→	1(0(0(2(3(1(0(3(1(3(2(3(2(0(1(3(0(3(x1))))))))))))))))))	(40)
1(3(1(3(0(2(1(0(1(3(0(2(1(2(1(1(3(1(x1))))))))))))))))))	→	1(0(1(0(1(3(2(2(0(3(1(2(1(1(1(3(3(1(x1))))))))))))))))))	(41)
1(3(3(1(3(3(1(0(2(1(1(3(1(2(2(3(2(3(x1))))))))))))))))))	→	1(3(1(2(1(1(0(3(1(2(3(3(1(2(3(3(2(3(x1))))))))))))))))))	(42)
2(0(0(3(0(3(2(0(2(0(1(2(0(1(3(1(0(3(x1))))))))))))))))))	→	2(0(0(3(0(3(2(2(3(0(1(2(0(0(1(1(0(3(x1))))))))))))))))))	(43)
2(0(1(3(1(3(0(2(1(3(0(2(1(1(0(2(3(2(x1))))))))))))))))))	→	3(0(1(1(2(1(3(2(3(1(2(0(0(1(2(0(3(2(x1))))))))))))))))))	(44)
2(0(2(1(3(0(0(0(3(1(0(2(2(3(0(2(0(0(x1))))))))))))))))))	→	2(0(3(2(0(2(1(2(0(3(0(0(3(0(1(2(0(0(x1))))))))))))))))))	(45)
2(0(2(2(1(0(2(0(2(2(2(1(3(0(2(0(0(0(x1))))))))))))))))))	→	2(0(0(1(0(0(0(2(3(0(1(2(2(2(2(2(2(0(x1))))))))))))))))))	(46)
2(0(2(2(2(2(1(3(1(2(3(0(3(0(3(3(3(3(x1))))))))))))))))))	→	2(0(3(0(2(1(3(3(0(1(3(2(2(2(2(3(3(3(x1))))))))))))))))))	(47)
2(1(1(3(0(0(3(2(1(2(1(2(3(3(0(3(1(0(x1))))))))))))))))))	→	2(1(1(3(2(3(0(1(1(2(0(0(3(3(0(3(1(2(x1))))))))))))))))))	(48)
2(1(2(2(1(0(2(1(2(2(1(3(0(2(2(1(1(1(x1))))))))))))))))))	→	2(0(2(1(2(2(3(2(2(1(0(2(1(1(1(2(1(1(x1))))))))))))))))))	(49)
2(1(2(2(2(0(2(0(2(1(3(3(2(2(3(1(3(3(x1))))))))))))))))))	→	2(1(3(2(3(2(3(3(2(0(2(2(0(1(1(3(2(2(x1))))))))))))))))))	(50)
2(1(2(2(2(2(0(3(0(3(2(0(1(0(0(2(0(2(x1))))))))))))))))))	→	2(2(3(2(2(0(0(1(0(2(0(2(2(1(0(3(0(2(x1))))))))))))))))))	(51)
2(1(3(2(3(2(1(2(2(1(3(0(0(0(3(1(1(2(x1))))))))))))))))))	→	2(3(2(0(0(1(1(3(2(2(1(3(1(2(0(1(3(2(x1))))))))))))))))))	(52)
2(2(0(1(0(2(3(3(2(0(1(3(2(1(2(2(3(2(x1))))))))))))))))))	→	2(2(1(3(2(2(2(3(2(3(1(2(0(0(0(1(3(2(x1))))))))))))))))))	(53)
2(2(1(0(1(3(0(2(1(0(2(1(0(2(1(1(0(1(x1))))))))))))))))))	→	2(2(0(1(1(0(1(3(0(1(1(2(1(2(0(2(0(1(x1))))))))))))))))))	(54)
2(2(1(2(1(3(0(1(0(2(2(0(1(3(3(0(2(1(x1))))))))))))))))))	→	2(2(2(1(3(2(2(1(1(2(3(0(0(1(3(0(0(1(x1))))))))))))))))))	(55)
2(2(3(0(0(3(1(3(0(2(3(0(3(3(1(2(3(2(x1))))))))))))))))))	→	1(0(2(3(2(3(0(0(3(0(3(3(1(3(2(2(3(2(x1))))))))))))))))))	(56)
2(3(0(1(1(0(2(1(2(0(3(1(0(3(2(1(3(1(x1))))))))))))))))))	→	2(0(1(1(1(3(3(1(2(3(2(0(0(1(2(0(3(1(x1))))))))))))))))))	(57)
2(3(0(2(1(2(0(0(3(0(0(2(0(2(3(1(2(0(x1))))))))))))))))))	→	3(2(0(1(0(2(2(0(0(0(3(1(0(2(3(2(2(0(x1))))))))))))))))))	(58)
2(3(1(1(1(1(2(0(0(2(0(2(2(1(3(3(1(2(x1))))))))))))))))))	→	2(3(2(3(0(2(1(3(1(2(1(2(1(0(0(1(1(2(x1))))))))))))))))))	(59)
3(0(0(0(0(1(2(2(3(0(3(0(3(1(3(3(3(3(x1))))))))))))))))))	→	3(2(3(0(0(0(3(2(3(0(0(0(1(1(3(3(3(3(x1))))))))))))))))))	(60)
3(0(1(1(2(3(0(0(3(0(3(1(2(1(3(1(1(0(x1))))))))))))))))))	→	3(0(1(2(3(3(1(0(3(0(1(0(3(2(1(1(1(0(x1))))))))))))))))))	(61)
3(0(2(1(1(1(3(1(3(2(1(3(0(0(3(2(3(2(x1))))))))))))))))))	→	3(3(0(1(2(2(0(1(1(1(3(2(3(3(0(1(3(2(x1))))))))))))))))))	(62)
3(0(2(2(0(0(2(1(2(0(2(1(0(1(2(0(1(0(x1))))))))))))))))))	→	0(1(0(2(0(2(0(0(1(2(1(2(3(2(2(0(1(0(x1))))))))))))))))))	(63)
3(0(2(3(1(2(3(3(0(0(0(3(2(2(2(1(2(1(x1))))))))))))))))))	→	3(0(3(3(2(3(2(3(0(2(0(2(0(1(2(1(2(1(x1))))))))))))))))))	(64)
3(0(2(3(2(1(0(1(3(3(2(2(3(0(3(2(0(0(x1))))))))))))))))))	→	3(0(3(2(3(3(1(2(3(2(2(0(1(2(0(0(3(0(x1))))))))))))))))))	(65)
3(0(3(0(3(3(1(0(3(0(3(3(1(3(1(1(0(3(x1))))))))))))))))))	→	0(1(3(1(3(3(3(3(1(0(0(1(3(3(3(0(0(3(x1))))))))))))))))))	(66)
3(0(3(1(0(0(3(1(3(0(2(0(2(3(0(0(0(0(x1))))))))))))))))))	→	0(0(0(2(3(1(1(0(0(0(0(0(3(3(2(3(3(0(x1))))))))))))))))))	(67)
3(1(0(1(2(2(1(3(3(3(0(2(3(1(0(1(2(3(x1))))))))))))))))))	→	3(1(0(1(1(2(2(3(2(2(0(0(3(1(3(3(1(3(x1))))))))))))))))))	(68)
3(1(2(2(3(3(1(0(2(1(3(3(2(1(1(2(0(0(x1))))))))))))))))))	→	3(1(3(0(2(2(2(1(1(3(1(3(2(3(1(2(0(0(x1))))))))))))))))))	(69)
3(1(3(0(2(0(2(2(2(2(2(1(3(0(0(3(0(0(x1))))))))))))))))))	→	2(1(3(2(0(3(1(3(0(0(3(2(2(0(2(2(0(0(x1))))))))))))))))))	(70)
3(1(3(0(2(1(2(3(2(2(3(2(3(2(3(0(0(3(x1))))))))))))))))))	→	0(1(1(3(2(3(3(2(3(2(3(2(2(0(3(0(2(3(x1))))))))))))))))))	(71)
3(1(3(0(2(3(3(0(1(3(2(2(2(3(2(1(0(2(x1))))))))))))))))))	→	3(2(1(3(2(3(2(3(0(1(3(3(1(2(0(2(0(2(x1))))))))))))))))))	(72)
3(2(1(3(3(1(3(0(3(0(2(2(2(2(1(1(0(2(x1))))))))))))))))))	→	3(3(2(2(1(0(0(3(0(2(1(1(2(1(2(3(3(2(x1))))))))))))))))))	(73)
3(3(0(2(0(2(0(3(1(3(0(2(0(0(2(2(0(3(x1))))))))))))))))))	→	0(2(3(0(0(2(0(3(3(2(1(0(2(0(3(2(0(3(x1))))))))))))))))))	(74)
3(3(0(2(1(0(3(2(2(2(3(3(0(1(3(3(0(2(x1))))))))))))))))))	→	3(3(2(2(3(3(3(3(0(3(1(2(1(0(2(0(0(2(x1))))))))))))))))))	(75)
3(3(1(0(0(0(3(3(0(3(0(0(3(2(1(2(3(3(x1))))))))))))))))))	→	3(0(0(1(0(1(3(2(3(3(3(2(3(0(3(0(0(3(x1))))))))))))))))))	(76)
3(3(1(1(3(3(0(0(2(0(3(1(2(1(2(3(0(0(x1))))))))))))))))))	→	3(0(1(1(3(3(0(3(0(1(3(0(1(2(3(2(2(0(x1))))))))))))))))))	(77)
3(3(2(0(0(0(3(0(1(0(3(1(2(1(2(1(2(2(x1))))))))))))))))))	→	0(2(2(0(1(1(0(3(1(3(2(0(1(0(3(2(3(2(x1))))))))))))))))))	(78)
3(3(2(0(2(1(3(1(2(2(2(2(1(2(1(0(3(2(x1))))))))))))))))))	→	3(0(2(2(3(1(1(2(1(3(2(2(1(2(0(2(3(2(x1))))))))))))))))))	(79)
3(3(3(0(1(2(1(3(1(1(1(3(0(3(0(0(3(0(x1))))))))))))))))))	→	3(3(3(1(3(2(1(3(1(1(0(0(3(1(3(0(0(0(x1))))))))))))))))))	(80)

Property / Task

Prove or disprove termination.

Answer / Result

Yes.

Proof (by AProVE @ termCOMP 2023)

1 String Reversal

Since only unary symbols occur, one can reverse all terms and obtains the TRS

0(2(0(3(3(2(1(0(3(0(2(2(0(3(2(0(0(0(x1))))))))))))))))))	→	0(0(0(0(0(2(3(3(0(0(2(2(2(3(2(3(1(0(x1))))))))))))))))))	(81)
3(0(1(3(0(3(0(3(0(2(0(3(1(0(3(0(0(0(x1))))))))))))))))))	→	3(3(0(3(0(2(3(0(0(3(3(0(1(0(0(1(0(0(x1))))))))))))))))))	(82)
2(0(0(3(0(3(1(0(0(1(1(3(0(3(0(2(0(0(x1))))))))))))))))))	→	2(0(0(3(0(2(0(0(3(3(0(3(0(1(1(1(0(0(x1))))))))))))))))))	(83)
2(2(2(2(0(3(3(2(1(1(2(3(1(3(0(2(0(0(x1))))))))))))))))))	→	2(2(1(0(3(2(0(2(0(2(3(1(0(2(1(3(2(3(x1))))))))))))))))))	(84)
0(2(0(1(1(3(3(0(3(2(2(1(2(0(3(2(0(0(x1))))))))))))))))))	→	0(2(3(0(1(2(0(1(3(0(2(3(3(2(2(1(0(0(x1))))))))))))))))))	(85)
2(2(0(3(1(2(0(3(3(2(0(1(3(2(1(3(0(0(x1))))))))))))))))))	→	2(3(1(2(0(0(3(1(0(2(2(1(3(3(0(2(3(0(x1))))))))))))))))))	(86)
0(2(2(1(0(2(1(0(0(3(1(1(2(2(0(0(1(0(x1))))))))))))))))))	→	0(2(2(3(0(1(1(0(2(1(2(2(0(0(0(1(1(0(x1))))))))))))))))))	(87)
3(3(0(2(3(3(1(1(2(2(1(2(0(3(2(0(1(0(x1))))))))))))))))))	→	3(1(1(0(3(2(3(1(0(2(3(3(2(2(0(2(1(0(x1))))))))))))))))))	(88)
3(0(3(0(2(0(3(2(1(0(3(0(2(0(3(1(1(0(x1))))))))))))))))))	→	3(2(3(3(1(0(0(0(2(1(0(1(3(3(2(0(0(0(x1))))))))))))))))))	(89)
3(3(1(1(2(2(0(3(0(1(3(2(0(2(3(2(1(0(x1))))))))))))))))))	→	3(0(1(0(0(2(3(3(2(1(1(3(2(3(2(2(1(0(x1))))))))))))))))))	(90)
1(2(0(0(1(3(3(1(2(0(3(1(2(2(3(2(1(0(x1))))))))))))))))))	→	1(2(2(3(1(2(3(1(0(3(2(0(1(0(1(2(3(0(x1))))))))))))))))))	(91)
2(1(2(3(3(3(1(1(1(3(3(3(3(0(3(1(2(0(x1))))))))))))))))))	→	2(1(0(2(3(3(3(1(3(1(0(1(3(3(3(2(3(1(x1))))))))))))))))))	(92)
2(1(0(1(1(3(3(0(1(0(3(3(1(3(0(2(2(0(x1))))))))))))))))))	→	2(1(3(1(0(1(3(0(0(1(3(2(3(0(2(1(3(0(x1))))))))))))))))))	(93)
0(1(1(1(1(3(3(0(3(1(0(0(3(1(0(0(3(0(x1))))))))))))))))))	→	0(1(1(3(0(1(1(3(1(0(1(3(0(0(3(0(3(0(x1))))))))))))))))))	(94)
0(2(0(2(1(2(1(0(0(0(3(0(1(3(0(0(3(0(x1))))))))))))))))))	→	0(2(3(0(0(1(0(0(3(2(2(0(1(1(0(0(3(0(x1))))))))))))))))))	(95)
0(2(2(2(0(1(2(0(2(2(0(0(0(0(2(0(3(0(x1))))))))))))))))))	→	0(0(0(0(2(0(0(2(2(3(0(0(2(1(2(2(2(0(x1))))))))))))))))))	(96)
3(0(1(2(0(2(3(0(0(3(1(0(3(0(3(0(3(0(x1))))))))))))))))))	→	3(0(3(0(0(3(0(2(3(0(0(1(0(0(3(2(3(1(x1))))))))))))))))))	(97)
1(3(0(2(1(3(2(2(0(3(1(0(3(1(3(0(3(0(x1))))))))))))))))))	→	1(3(2(1(3(2(1(0(3(2(3(0(0(3(0(3(0(1(x1))))))))))))))))))	(98)
2(0(2(0(3(3(1(2(3(2(0(0(2(2(3(0(3(0(x1))))))))))))))))))	→	2(3(2(3(2(3(2(0(0(0(2(2(0(0(1(3(3(0(x1))))))))))))))))))	(99)
2(2(2(3(3(2(1(2(3(3(2(1(2(3(2(1(3(0(x1))))))))))))))))))	→	2(2(2(3(2(2(3(1(3(3(0(2(1(3(2(3(2(1(x1))))))))))))))))))	(100)
1(1(2(2(1(1(2(0(0(1(1(1(0(1(0(2(3(0(x1))))))))))))))))))	→	1(1(2(1(0(1(1(0(0(2(1(2(1(0(1(2(3(0(x1))))))))))))))))))	(101)
0(0(3(0(3(2(3(0(2(0(3(2(2(1(1(1(0(1(x1))))))))))))))))))	→	0(0(1(2(0(2(3(0(2(3(0(1(1(3(0(2(3(1(x1))))))))))))))))))	(102)
2(2(1(0(2(0(2(1(2(3(3(0(2(2(2(1(0(1(x1))))))))))))))))))	→	2(3(2(3(2(0(0(1(1(2(2(0(2(1(2(2(0(1(x1))))))))))))))))))	(103)
3(3(2(2(0(1(3(3(2(1(2(0(3(3(0(3(0(1(x1))))))))))))))))))	→	3(3(2(3(0(0(3(2(2(0(1(3(3(2(1(3(0(1(x1))))))))))))))))))	(104)
3(3(2(2(1(3(3(1(1(3(1(3(0(3(1(0(1(1(x1))))))))))))))))))	→	0(1(2(3(2(3(1(3(1(3(1(3(0(1(3(1(3(1(x1))))))))))))))))))	(105)
0(2(0(0(1(3(3(1(2(2(2(3(1(2(0(1(1(1(x1))))))))))))))))))	→	0(2(1(0(0(3(2(2(3(1(1(2(1(2(3(1(0(1(x1))))))))))))))))))	(106)
0(1(3(3(0(2(2(2(2(2(1(2(1(1(1(1(1(1(x1))))))))))))))))))	→	2(1(1(2(0(1(0(2(1(1(2(1(3(2(2(3(1(1(x1))))))))))))))))))	(107)
3(1(2(0(0(3(3(0(1(3(1(2(1(0(2(1(1(1(x1))))))))))))))))))	→	3(1(3(1(0(0(2(3(0(1(3(0(2(2(1(1(1(1(x1))))))))))))))))))	(108)
1(3(3(3(3(1(0(1(2(2(0(3(0(3(2(1(1(1(x1))))))))))))))))))	→	1(0(3(1(3(1(0(2(3(3(1(3(2(1(0(3(2(1(x1))))))))))))))))))	(109)
3(1(1(1(3(2(0(1(1(3(1(0(1(0(3(1(1(1(x1))))))))))))))))))	→	3(1(1(2(1(3(1(0(1(0(1(1(0(3(1(3(1(1(x1))))))))))))))))))	(110)
1(2(0(2(1(0(0(0(3(3(3(0(2(0(3(1(1(1(x1))))))))))))))))))	→	1(2(3(0(1(0(3(1(0(0(3(0(1(0(2(3(2(1(x1))))))))))))))))))	(111)
1(2(2(2(0(0(0(3(1(2(0(3(2(2(2(2(1(1(x1))))))))))))))))))	→	1(2(2(2(2(0(1(3(2(0(0(2(1(0(3(2(2(1(x1))))))))))))))))))	(112)
1(2(0(3(2(3(0(1(3(0(1(2(1(2(0(3(1(1(x1))))))))))))))))))	→	1(2(0(2(2(1(0(1(1(0(3(3(3(3(2(0(1(1(x1))))))))))))))))))	(113)
3(1(2(3(3(3(2(0(3(1(2(0(2(1(1(3(1(1(x1))))))))))))))))))	→	3(1(0(3(2(2(3(1(1(2(1(3(3(1(2(3(0(1(x1))))))))))))))))))	(114)
1(1(3(2(1(1(0(0(3(1(1(1(1(0(2(0(3(1(x1))))))))))))))))))	→	1(1(0(0(1(1(0(3(1(3(2(3(1(2(1(1(0(1(x1))))))))))))))))))	(115)
2(2(1(1(3(3(2(3(0(1(1(3(1(1(2(0(3(1(x1))))))))))))))))))	→	2(2(1(3(1(1(1(0(1(1(2(3(3(3(0(3(2(1(x1))))))))))))))))))	(116)
2(3(3(3(2(0(1(1(2(2(1(0(3(1(2(0(3(1(x1))))))))))))))))))	→	2(3(2(0(1(0(0(1(3(2(3(1(2(3(1(1(2(3(x1))))))))))))))))))	(117)
1(1(1(1(1(1(2(0(1(1(2(1(3(1(2(0(3(1(x1))))))))))))))))))	→	1(1(2(3(2(1(0(1(1(2(1(0(1(1(1(1(3(1(x1))))))))))))))))))	(118)
2(2(2(3(3(2(1(0(3(0(0(2(3(1(2(0(3(1(x1))))))))))))))))))	→	2(3(2(0(2(3(2(2(3(3(1(0(2(0(0(1(3(1(x1))))))))))))))))))	(119)
3(2(2(2(1(0(3(3(0(0(0(3(1(0(3(1(3(1(x1))))))))))))))))))	→	3(0(3(1(0(2(3(2(3(1(3(0(1(3(2(0(0(1(x1))))))))))))))))))	(120)
1(3(1(1(2(1(2(0(3(1(0(1(2(0(3(1(3(1(x1))))))))))))))))))	→	1(3(3(1(1(1(2(1(3(0(2(2(3(1(0(1(0(1(x1))))))))))))))))))	(121)
3(2(3(2(2(1(3(1(1(2(0(1(3(3(1(3(3(1(x1))))))))))))))))))	→	3(2(3(3(2(1(3(3(2(1(3(0(1(1(2(1(3(1(x1))))))))))))))))))	(122)
3(0(1(3(1(0(2(1(0(2(0(2(3(0(3(0(0(2(x1))))))))))))))))))	→	3(0(1(1(0(0(2(1(0(3(2(2(3(0(3(0(0(2(x1))))))))))))))))))	(123)
2(3(2(0(1(1(2(0(3(1(2(0(3(1(3(1(0(2(x1))))))))))))))))))	→	2(3(0(2(1(0(0(2(1(3(2(3(1(2(1(1(0(3(x1))))))))))))))))))	(124)
0(0(2(0(3(2(2(0(1(3(0(0(0(3(1(2(0(2(x1))))))))))))))))))	→	0(0(2(1(0(3(0(0(3(0(2(1(2(0(2(3(0(2(x1))))))))))))))))))	(125)
0(0(0(2(0(3(1(2(2(2(0(2(0(1(2(2(0(2(x1))))))))))))))))))	→	0(2(2(2(2(2(2(1(0(3(2(0(0(0(1(0(0(2(x1))))))))))))))))))	(126)
3(3(3(3(0(3(0(3(2(1(3(1(2(2(2(2(0(2(x1))))))))))))))))))	→	3(3(3(2(2(2(2(3(1(0(3(3(1(2(0(3(0(2(x1))))))))))))))))))	(127)
0(1(3(0(3(3(2(1(2(1(2(3(0(0(3(1(1(2(x1))))))))))))))))))	→	2(1(3(0(3(3(0(0(2(1(1(0(3(2(3(1(1(2(x1))))))))))))))))))	(128)
1(1(1(2(2(0(3(1(2(2(1(2(0(1(2(2(1(2(x1))))))))))))))))))	→	1(1(2(1(1(1(2(0(1(2(2(3(2(2(1(2(0(2(x1))))))))))))))))))	(129)
3(3(1(3(2(2(3(3(1(2(0(2(0(2(2(2(1(2(x1))))))))))))))))))	→	2(2(3(1(1(0(2(2(0(2(3(3(2(3(2(3(1(2(x1))))))))))))))))))	(130)
2(0(2(0(0(1(0(2(3(0(3(0(2(2(2(2(1(2(x1))))))))))))))))))	→	2(0(3(0(1(2(2(0(2(0(1(0(0(2(2(3(2(2(x1))))))))))))))))))	(131)
2(1(1(3(0(0(0(3(1(2(2(1(2(3(2(3(1(2(x1))))))))))))))))))	→	2(3(1(0(2(1(3(1(2(2(3(1(1(0(0(2(3(2(x1))))))))))))))))))	(132)
2(3(2(2(1(2(3(1(0(2(3(3(2(0(1(0(2(2(x1))))))))))))))))))	→	2(3(1(0(0(0(2(1(3(2(3(2(2(2(3(1(2(2(x1))))))))))))))))))	(133)
1(0(1(1(2(0(1(2(0(1(2(0(3(1(0(1(2(2(x1))))))))))))))))))	→	1(0(2(0(2(1(2(1(1(0(3(1(0(1(1(0(2(2(x1))))))))))))))))))	(134)
1(2(0(3(3(1(0(2(2(0(1(0(3(1(2(1(2(2(x1))))))))))))))))))	→	1(0(0(3(1(0(0(3(2(1(1(2(2(3(1(2(2(2(x1))))))))))))))))))	(135)
2(3(2(1(3(3(0(3(2(0(3(1(3(0(0(3(2(2(x1))))))))))))))))))	→	2(3(2(2(3(1(3(3(0(3(0(0(3(2(3(2(0(1(x1))))))))))))))))))	(136)
1(3(1(2(3(0(1(3(0(2(1(2(0(1(1(0(3(2(x1))))))))))))))))))	→	1(3(0(2(1(0(0(2(3(2(1(3(3(1(1(1(0(2(x1))))))))))))))))))	(137)
0(2(1(3(2(0(2(0(0(3(0(0(2(1(2(0(3(2(x1))))))))))))))))))	→	0(2(2(3(2(0(1(3(0(0(0(2(2(0(1(0(2(3(x1))))))))))))))))))	(138)
2(1(3(3(1(2(2(0(2(0(0(2(1(1(1(1(3(2(x1))))))))))))))))))	→	2(1(1(0(0(1(2(1(2(1(3(1(2(0(3(2(3(2(x1))))))))))))))))))	(139)
3(3(3(3(1(3(0(3(0(3(2(2(1(0(0(0(0(3(x1))))))))))))))))))	→	3(3(3(3(1(1(0(0(0(3(2(3(0(0(0(3(2(3(x1))))))))))))))))))	(140)
0(1(1(3(1(2(1(3(0(3(0(0(3(2(1(1(0(3(x1))))))))))))))))))	→	0(1(1(1(2(3(0(1(0(3(0(1(3(3(2(1(0(3(x1))))))))))))))))))	(141)
2(3(2(3(0(0(3(1(2(3(1(3(1(1(1(2(0(3(x1))))))))))))))))))	→	2(3(1(0(3(3(2(3(1(1(1(0(2(2(1(0(3(3(x1))))))))))))))))))	(142)
0(1(0(2(1(0(1(2(0(2(1(2(0(0(2(2(0(3(x1))))))))))))))))))	→	0(1(0(2(2(3(2(1(2(1(0(0(2(0(2(0(1(0(x1))))))))))))))))))	(143)
1(2(1(2(2(2(3(0(0(0(3(3(2(1(3(2(0(3(x1))))))))))))))))))	→	1(2(1(2(1(0(2(0(2(0(3(2(3(2(3(3(0(3(x1))))))))))))))))))	(144)
0(0(2(3(0(3(2(2(3(3(1(0(1(2(3(2(0(3(x1))))))))))))))))))	→	0(3(0(0(2(1(0(2(2(3(2(1(3(3(2(3(0(3(x1))))))))))))))))))	(145)
3(0(1(1(3(1(3(3(0(3(0(1(3(3(0(3(0(3(x1))))))))))))))))))	→	3(0(0(3(3(3(1(0(0(1(3(3(3(3(1(3(1(0(x1))))))))))))))))))	(146)
0(0(0(0(3(2(0(2(0(3(1(3(0(0(1(3(0(3(x1))))))))))))))))))	→	0(3(3(2(3(3(0(0(0(0(0(1(1(3(2(0(0(0(x1))))))))))))))))))	(147)
3(2(1(0(1(3(2(0(3(3(3(1(2(2(1(0(1(3(x1))))))))))))))))))	→	3(1(3(3(1(3(0(0(2(2(3(2(2(1(1(0(1(3(x1))))))))))))))))))	(148)
0(0(2(1(1(2(3(3(1(2(0(1(3(3(2(2(1(3(x1))))))))))))))))))	→	0(0(2(1(3(2(3(1(3(1(1(2(2(2(0(3(1(3(x1))))))))))))))))))	(149)
0(0(3(0(0(3(1(2(2(2(2(2(0(2(0(3(1(3(x1))))))))))))))))))	→	0(0(2(2(0(2(2(3(0(0(3(1(3(0(2(3(1(2(x1))))))))))))))))))	(150)
3(0(0(3(2(3(2(3(2(2(3(2(1(2(0(3(1(3(x1))))))))))))))))))	→	3(2(0(3(0(2(2(3(2(3(2(3(3(2(3(1(1(0(x1))))))))))))))))))	(151)
2(0(1(2(3(2(2(2(3(1(0(3(3(2(0(3(1(3(x1))))))))))))))))))	→	2(0(2(0(2(1(3(3(1(0(3(2(3(2(3(1(2(3(x1))))))))))))))))))	(152)
2(0(1(1(2(2(2(2(0(3(0(3(1(3(3(1(2(3(x1))))))))))))))))))	→	2(3(3(2(1(2(1(1(2(0(3(0(0(1(2(2(3(3(x1))))))))))))))))))	(153)
3(0(2(2(0(0(2(0(3(1(3(0(2(0(2(0(3(3(x1))))))))))))))))))	→	3(0(2(3(0(2(0(1(2(3(3(0(2(0(0(3(2(0(x1))))))))))))))))))	(154)
2(0(3(3(1(0(3(3(2(2(2(3(0(1(2(0(3(3(x1))))))))))))))))))	→	2(0(0(2(0(1(2(1(3(0(3(3(3(3(2(2(3(3(x1))))))))))))))))))	(155)
3(3(2(1(2(3(0(0(3(0(3(3(0(0(0(1(3(3(x1))))))))))))))))))	→	3(0(0(3(0(3(2(3(3(3(2(3(1(0(1(0(0(3(x1))))))))))))))))))	(156)
0(0(3(2(1(2(1(3(0(2(0(0(3(3(1(1(3(3(x1))))))))))))))))))	→	0(2(2(3(2(1(0(3(1(0(3(0(3(3(1(1(0(3(x1))))))))))))))))))	(157)
2(2(1(2(1(2(1(3(0(1(0(3(0(0(0(2(3(3(x1))))))))))))))))))	→	2(3(2(3(0(1(0(2(3(1(3(0(1(1(0(2(2(0(x1))))))))))))))))))	(158)
2(3(0(1(2(1(2(2(2(2(1(3(1(2(0(2(3(3(x1))))))))))))))))))	→	2(3(2(0(2(1(2(2(3(1(2(1(1(3(2(2(0(3(x1))))))))))))))))))	(159)
0(3(0(0(3(0(3(1(1(1(3(1(2(1(0(3(3(3(x1))))))))))))))))))	→	0(0(0(3(1(3(0(0(1(1(3(1(2(3(1(3(3(3(x1))))))))))))))))))	(160)

1.1 Closure Under Flat Contexts

Using the flat contexts

{0(☐), 2(☐), 3(☐), 1(☐)}

We obtain the transformed TRS

0(2(0(3(3(2(1(0(3(0(2(2(0(3(2(0(0(0(x1))))))))))))))))))	→	0(0(0(0(0(2(3(3(0(0(2(2(2(3(2(3(1(0(x1))))))))))))))))))	(81)
3(0(1(3(0(3(0(3(0(2(0(3(1(0(3(0(0(0(x1))))))))))))))))))	→	3(3(0(3(0(2(3(0(0(3(3(0(1(0(0(1(0(0(x1))))))))))))))))))	(82)
2(0(0(3(0(3(1(0(0(1(1(3(0(3(0(2(0(0(x1))))))))))))))))))	→	2(0(0(3(0(2(0(0(3(3(0(3(0(1(1(1(0(0(x1))))))))))))))))))	(83)
2(2(2(2(0(3(3(2(1(1(2(3(1(3(0(2(0(0(x1))))))))))))))))))	→	2(2(1(0(3(2(0(2(0(2(3(1(0(2(1(3(2(3(x1))))))))))))))))))	(84)
0(2(0(1(1(3(3(0(3(2(2(1(2(0(3(2(0(0(x1))))))))))))))))))	→	0(2(3(0(1(2(0(1(3(0(2(3(3(2(2(1(0(0(x1))))))))))))))))))	(85)
2(2(0(3(1(2(0(3(3(2(0(1(3(2(1(3(0(0(x1))))))))))))))))))	→	2(3(1(2(0(0(3(1(0(2(2(1(3(3(0(2(3(0(x1))))))))))))))))))	(86)
0(2(2(1(0(2(1(0(0(3(1(1(2(2(0(0(1(0(x1))))))))))))))))))	→	0(2(2(3(0(1(1(0(2(1(2(2(0(0(0(1(1(0(x1))))))))))))))))))	(87)
3(3(0(2(3(3(1(1(2(2(1(2(0(3(2(0(1(0(x1))))))))))))))))))	→	3(1(1(0(3(2(3(1(0(2(3(3(2(2(0(2(1(0(x1))))))))))))))))))	(88)
3(0(3(0(2(0(3(2(1(0(3(0(2(0(3(1(1(0(x1))))))))))))))))))	→	3(2(3(3(1(0(0(0(2(1(0(1(3(3(2(0(0(0(x1))))))))))))))))))	(89)
3(3(1(1(2(2(0(3(0(1(3(2(0(2(3(2(1(0(x1))))))))))))))))))	→	3(0(1(0(0(2(3(3(2(1(1(3(2(3(2(2(1(0(x1))))))))))))))))))	(90)
1(2(0(0(1(3(3(1(2(0(3(1(2(2(3(2(1(0(x1))))))))))))))))))	→	1(2(2(3(1(2(3(1(0(3(2(0(1(0(1(2(3(0(x1))))))))))))))))))	(91)
2(1(2(3(3(3(1(1(1(3(3(3(3(0(3(1(2(0(x1))))))))))))))))))	→	2(1(0(2(3(3(3(1(3(1(0(1(3(3(3(2(3(1(x1))))))))))))))))))	(92)
2(1(0(1(1(3(3(0(1(0(3(3(1(3(0(2(2(0(x1))))))))))))))))))	→	2(1(3(1(0(1(3(0(0(1(3(2(3(0(2(1(3(0(x1))))))))))))))))))	(93)
0(1(1(1(1(3(3(0(3(1(0(0(3(1(0(0(3(0(x1))))))))))))))))))	→	0(1(1(3(0(1(1(3(1(0(1(3(0(0(3(0(3(0(x1))))))))))))))))))	(94)
0(2(0(2(1(2(1(0(0(0(3(0(1(3(0(0(3(0(x1))))))))))))))))))	→	0(2(3(0(0(1(0(0(3(2(2(0(1(1(0(0(3(0(x1))))))))))))))))))	(95)
0(2(2(2(0(1(2(0(2(2(0(0(0(0(2(0(3(0(x1))))))))))))))))))	→	0(0(0(0(2(0(0(2(2(3(0(0(2(1(2(2(2(0(x1))))))))))))))))))	(96)
3(0(1(2(0(2(3(0(0(3(1(0(3(0(3(0(3(0(x1))))))))))))))))))	→	3(0(3(0(0(3(0(2(3(0(0(1(0(0(3(2(3(1(x1))))))))))))))))))	(97)
1(3(0(2(1(3(2(2(0(3(1(0(3(1(3(0(3(0(x1))))))))))))))))))	→	1(3(2(1(3(2(1(0(3(2(3(0(0(3(0(3(0(1(x1))))))))))))))))))	(98)
2(0(2(0(3(3(1(2(3(2(0(0(2(2(3(0(3(0(x1))))))))))))))))))	→	2(3(2(3(2(3(2(0(0(0(2(2(0(0(1(3(3(0(x1))))))))))))))))))	(99)
2(2(2(3(3(2(1(2(3(3(2(1(2(3(2(1(3(0(x1))))))))))))))))))	→	2(2(2(3(2(2(3(1(3(3(0(2(1(3(2(3(2(1(x1))))))))))))))))))	(100)
1(1(2(2(1(1(2(0(0(1(1(1(0(1(0(2(3(0(x1))))))))))))))))))	→	1(1(2(1(0(1(1(0(0(2(1(2(1(0(1(2(3(0(x1))))))))))))))))))	(101)
0(0(3(0(3(2(3(0(2(0(3(2(2(1(1(1(0(1(x1))))))))))))))))))	→	0(0(1(2(0(2(3(0(2(3(0(1(1(3(0(2(3(1(x1))))))))))))))))))	(102)
2(2(1(0(2(0(2(1(2(3(3(0(2(2(2(1(0(1(x1))))))))))))))))))	→	2(3(2(3(2(0(0(1(1(2(2(0(2(1(2(2(0(1(x1))))))))))))))))))	(103)
3(3(2(2(0(1(3(3(2(1(2(0(3(3(0(3(0(1(x1))))))))))))))))))	→	3(3(2(3(0(0(3(2(2(0(1(3(3(2(1(3(0(1(x1))))))))))))))))))	(104)
0(2(0(0(1(3(3(1(2(2(2(3(1(2(0(1(1(1(x1))))))))))))))))))	→	0(2(1(0(0(3(2(2(3(1(1(2(1(2(3(1(0(1(x1))))))))))))))))))	(106)
3(1(2(0(0(3(3(0(1(3(1(2(1(0(2(1(1(1(x1))))))))))))))))))	→	3(1(3(1(0(0(2(3(0(1(3(0(2(2(1(1(1(1(x1))))))))))))))))))	(108)
1(3(3(3(3(1(0(1(2(2(0(3(0(3(2(1(1(1(x1))))))))))))))))))	→	1(0(3(1(3(1(0(2(3(3(1(3(2(1(0(3(2(1(x1))))))))))))))))))	(109)
3(1(1(1(3(2(0(1(1(3(1(0(1(0(3(1(1(1(x1))))))))))))))))))	→	3(1(1(2(1(3(1(0(1(0(1(1(0(3(1(3(1(1(x1))))))))))))))))))	(110)
1(2(0(2(1(0(0(0(3(3(3(0(2(0(3(1(1(1(x1))))))))))))))))))	→	1(2(3(0(1(0(3(1(0(0(3(0(1(0(2(3(2(1(x1))))))))))))))))))	(111)
1(2(2(2(0(0(0(3(1(2(0(3(2(2(2(2(1(1(x1))))))))))))))))))	→	1(2(2(2(2(0(1(3(2(0(0(2(1(0(3(2(2(1(x1))))))))))))))))))	(112)
1(2(0(3(2(3(0(1(3(0(1(2(1(2(0(3(1(1(x1))))))))))))))))))	→	1(2(0(2(2(1(0(1(1(0(3(3(3(3(2(0(1(1(x1))))))))))))))))))	(113)
3(1(2(3(3(3(2(0(3(1(2(0(2(1(1(3(1(1(x1))))))))))))))))))	→	3(1(0(3(2(2(3(1(1(2(1(3(3(1(2(3(0(1(x1))))))))))))))))))	(114)
1(1(3(2(1(1(0(0(3(1(1(1(1(0(2(0(3(1(x1))))))))))))))))))	→	1(1(0(0(1(1(0(3(1(3(2(3(1(2(1(1(0(1(x1))))))))))))))))))	(115)
2(2(1(1(3(3(2(3(0(1(1(3(1(1(2(0(3(1(x1))))))))))))))))))	→	2(2(1(3(1(1(1(0(1(1(2(3(3(3(0(3(2(1(x1))))))))))))))))))	(116)
2(3(3(3(2(0(1(1(2(2(1(0(3(1(2(0(3(1(x1))))))))))))))))))	→	2(3(2(0(1(0(0(1(3(2(3(1(2(3(1(1(2(3(x1))))))))))))))))))	(117)
1(1(1(1(1(1(2(0(1(1(2(1(3(1(2(0(3(1(x1))))))))))))))))))	→	1(1(2(3(2(1(0(1(1(2(1(0(1(1(1(1(3(1(x1))))))))))))))))))	(118)
2(2(2(3(3(2(1(0(3(0(0(2(3(1(2(0(3(1(x1))))))))))))))))))	→	2(3(2(0(2(3(2(2(3(3(1(0(2(0(0(1(3(1(x1))))))))))))))))))	(119)
3(2(2(2(1(0(3(3(0(0(0(3(1(0(3(1(3(1(x1))))))))))))))))))	→	3(0(3(1(0(2(3(2(3(1(3(0(1(3(2(0(0(1(x1))))))))))))))))))	(120)
1(3(1(1(2(1(2(0(3(1(0(1(2(0(3(1(3(1(x1))))))))))))))))))	→	1(3(3(1(1(1(2(1(3(0(2(2(3(1(0(1(0(1(x1))))))))))))))))))	(121)
3(2(3(2(2(1(3(1(1(2(0(1(3(3(1(3(3(1(x1))))))))))))))))))	→	3(2(3(3(2(1(3(3(2(1(3(0(1(1(2(1(3(1(x1))))))))))))))))))	(122)
3(0(1(3(1(0(2(1(0(2(0(2(3(0(3(0(0(2(x1))))))))))))))))))	→	3(0(1(1(0(0(2(1(0(3(2(2(3(0(3(0(0(2(x1))))))))))))))))))	(123)
2(3(2(0(1(1(2(0(3(1(2(0(3(1(3(1(0(2(x1))))))))))))))))))	→	2(3(0(2(1(0(0(2(1(3(2(3(1(2(1(1(0(3(x1))))))))))))))))))	(124)
0(0(2(0(3(2(2(0(1(3(0(0(0(3(1(2(0(2(x1))))))))))))))))))	→	0(0(2(1(0(3(0(0(3(0(2(1(2(0(2(3(0(2(x1))))))))))))))))))	(125)
0(0(0(2(0(3(1(2(2(2(0(2(0(1(2(2(0(2(x1))))))))))))))))))	→	0(2(2(2(2(2(2(1(0(3(2(0(0(0(1(0(0(2(x1))))))))))))))))))	(126)
3(3(3(3(0(3(0(3(2(1(3(1(2(2(2(2(0(2(x1))))))))))))))))))	→	3(3(3(2(2(2(2(3(1(0(3(3(1(2(0(3(0(2(x1))))))))))))))))))	(127)
1(1(1(2(2(0(3(1(2(2(1(2(0(1(2(2(1(2(x1))))))))))))))))))	→	1(1(2(1(1(1(2(0(1(2(2(3(2(2(1(2(0(2(x1))))))))))))))))))	(129)
2(0(2(0(0(1(0(2(3(0(3(0(2(2(2(2(1(2(x1))))))))))))))))))	→	2(0(3(0(1(2(2(0(2(0(1(0(0(2(2(3(2(2(x1))))))))))))))))))	(131)
2(1(1(3(0(0(0(3(1(2(2(1(2(3(2(3(1(2(x1))))))))))))))))))	→	2(3(1(0(2(1(3(1(2(2(3(1(1(0(0(2(3(2(x1))))))))))))))))))	(132)
2(3(2(2(1(2(3(1(0(2(3(3(2(0(1(0(2(2(x1))))))))))))))))))	→	2(3(1(0(0(0(2(1(3(2(3(2(2(2(3(1(2(2(x1))))))))))))))))))	(133)
1(0(1(1(2(0(1(2(0(1(2(0(3(1(0(1(2(2(x1))))))))))))))))))	→	1(0(2(0(2(1(2(1(1(0(3(1(0(1(1(0(2(2(x1))))))))))))))))))	(134)
1(2(0(3(3(1(0(2(2(0(1(0(3(1(2(1(2(2(x1))))))))))))))))))	→	1(0(0(3(1(0(0(3(2(1(1(2(2(3(1(2(2(2(x1))))))))))))))))))	(135)
2(3(2(1(3(3(0(3(2(0(3(1(3(0(0(3(2(2(x1))))))))))))))))))	→	2(3(2(2(3(1(3(3(0(3(0(0(3(2(3(2(0(1(x1))))))))))))))))))	(136)
1(3(1(2(3(0(1(3(0(2(1(2(0(1(1(0(3(2(x1))))))))))))))))))	→	1(3(0(2(1(0(0(2(3(2(1(3(3(1(1(1(0(2(x1))))))))))))))))))	(137)
0(2(1(3(2(0(2(0(0(3(0(0(2(1(2(0(3(2(x1))))))))))))))))))	→	0(2(2(3(2(0(1(3(0(0(0(2(2(0(1(0(2(3(x1))))))))))))))))))	(138)
2(1(3(3(1(2(2(0(2(0(0(2(1(1(1(1(3(2(x1))))))))))))))))))	→	2(1(1(0(0(1(2(1(2(1(3(1(2(0(3(2(3(2(x1))))))))))))))))))	(139)
3(3(3(3(1(3(0(3(0(3(2(2(1(0(0(0(0(3(x1))))))))))))))))))	→	3(3(3(3(1(1(0(0(0(3(2(3(0(0(0(3(2(3(x1))))))))))))))))))	(140)
0(1(1(3(1(2(1(3(0(3(0(0(3(2(1(1(0(3(x1))))))))))))))))))	→	0(1(1(1(2(3(0(1(0(3(0(1(3(3(2(1(0(3(x1))))))))))))))))))	(141)
2(3(2(3(0(0(3(1(2(3(1(3(1(1(1(2(0(3(x1))))))))))))))))))	→	2(3(1(0(3(3(2(3(1(1(1(0(2(2(1(0(3(3(x1))))))))))))))))))	(142)
0(1(0(2(1(0(1(2(0(2(1(2(0(0(2(2(0(3(x1))))))))))))))))))	→	0(1(0(2(2(3(2(1(2(1(0(0(2(0(2(0(1(0(x1))))))))))))))))))	(143)
1(2(1(2(2(2(3(0(0(0(3(3(2(1(3(2(0(3(x1))))))))))))))))))	→	1(2(1(2(1(0(2(0(2(0(3(2(3(2(3(3(0(3(x1))))))))))))))))))	(144)
0(0(2(3(0(3(2(2(3(3(1(0(1(2(3(2(0(3(x1))))))))))))))))))	→	0(3(0(0(2(1(0(2(2(3(2(1(3(3(2(3(0(3(x1))))))))))))))))))	(145)
3(0(1(1(3(1(3(3(0(3(0(1(3(3(0(3(0(3(x1))))))))))))))))))	→	3(0(0(3(3(3(1(0(0(1(3(3(3(3(1(3(1(0(x1))))))))))))))))))	(146)
0(0(0(0(3(2(0(2(0(3(1(3(0(0(1(3(0(3(x1))))))))))))))))))	→	0(3(3(2(3(3(0(0(0(0(0(1(1(3(2(0(0(0(x1))))))))))))))))))	(147)
3(2(1(0(1(3(2(0(3(3(3(1(2(2(1(0(1(3(x1))))))))))))))))))	→	3(1(3(3(1(3(0(0(2(2(3(2(2(1(1(0(1(3(x1))))))))))))))))))	(148)
0(0(2(1(1(2(3(3(1(2(0(1(3(3(2(2(1(3(x1))))))))))))))))))	→	0(0(2(1(3(2(3(1(3(1(1(2(2(2(0(3(1(3(x1))))))))))))))))))	(149)
0(0(3(0(0(3(1(2(2(2(2(2(0(2(0(3(1(3(x1))))))))))))))))))	→	0(0(2(2(0(2(2(3(0(0(3(1(3(0(2(3(1(2(x1))))))))))))))))))	(150)
3(0(0(3(2(3(2(3(2(2(3(2(1(2(0(3(1(3(x1))))))))))))))))))	→	3(2(0(3(0(2(2(3(2(3(2(3(3(2(3(1(1(0(x1))))))))))))))))))	(151)
2(0(1(2(3(2(2(2(3(1(0(3(3(2(0(3(1(3(x1))))))))))))))))))	→	2(0(2(0(2(1(3(3(1(0(3(2(3(2(3(1(2(3(x1))))))))))))))))))	(152)
2(0(1(1(2(2(2(2(0(3(0(3(1(3(3(1(2(3(x1))))))))))))))))))	→	2(3(3(2(1(2(1(1(2(0(3(0(0(1(2(2(3(3(x1))))))))))))))))))	(153)
3(0(2(2(0(0(2(0(3(1(3(0(2(0(2(0(3(3(x1))))))))))))))))))	→	3(0(2(3(0(2(0(1(2(3(3(0(2(0(0(3(2(0(x1))))))))))))))))))	(154)
2(0(3(3(1(0(3(3(2(2(2(3(0(1(2(0(3(3(x1))))))))))))))))))	→	2(0(0(2(0(1(2(1(3(0(3(3(3(3(2(2(3(3(x1))))))))))))))))))	(155)
3(3(2(1(2(3(0(0(3(0(3(3(0(0(0(1(3(3(x1))))))))))))))))))	→	3(0(0(3(0(3(2(3(3(3(2(3(1(0(1(0(0(3(x1))))))))))))))))))	(156)
0(0(3(2(1(2(1(3(0(2(0(0(3(3(1(1(3(3(x1))))))))))))))))))	→	0(2(2(3(2(1(0(3(1(0(3(0(3(3(1(1(0(3(x1))))))))))))))))))	(157)
2(2(1(2(1(2(1(3(0(1(0(3(0(0(0(2(3(3(x1))))))))))))))))))	→	2(3(2(3(0(1(0(2(3(1(3(0(1(1(0(2(2(0(x1))))))))))))))))))	(158)
2(3(0(1(2(1(2(2(2(2(1(3(1(2(0(2(3(3(x1))))))))))))))))))	→	2(3(2(0(2(1(2(2(3(1(2(1(1(3(2(2(0(3(x1))))))))))))))))))	(159)
0(3(0(0(3(0(3(1(1(1(3(1(2(1(0(3(3(3(x1))))))))))))))))))	→	0(0(0(3(1(3(0(0(1(1(3(1(2(3(1(3(3(3(x1))))))))))))))))))	(160)
0(3(3(2(2(1(3(3(1(1(3(1(3(0(3(1(0(1(1(x1)))))))))))))))))))	→	0(0(1(2(3(2(3(1(3(1(3(1(3(0(1(3(1(3(1(x1)))))))))))))))))))	(161)
2(3(3(2(2(1(3(3(1(1(3(1(3(0(3(1(0(1(1(x1)))))))))))))))))))	→	2(0(1(2(3(2(3(1(3(1(3(1(3(0(1(3(1(3(1(x1)))))))))))))))))))	(162)
3(3(3(2(2(1(3(3(1(1(3(1(3(0(3(1(0(1(1(x1)))))))))))))))))))	→	3(0(1(2(3(2(3(1(3(1(3(1(3(0(1(3(1(3(1(x1)))))))))))))))))))	(163)
1(3(3(2(2(1(3(3(1(1(3(1(3(0(3(1(0(1(1(x1)))))))))))))))))))	→	1(0(1(2(3(2(3(1(3(1(3(1(3(0(1(3(1(3(1(x1)))))))))))))))))))	(164)
0(0(1(3(3(0(2(2(2(2(2(1(2(1(1(1(1(1(1(x1)))))))))))))))))))	→	0(2(1(1(2(0(1(0(2(1(1(2(1(3(2(2(3(1(1(x1)))))))))))))))))))	(165)
2(0(1(3(3(0(2(2(2(2(2(1(2(1(1(1(1(1(1(x1)))))))))))))))))))	→	2(2(1(1(2(0(1(0(2(1(1(2(1(3(2(2(3(1(1(x1)))))))))))))))))))	(166)
3(0(1(3(3(0(2(2(2(2(2(1(2(1(1(1(1(1(1(x1)))))))))))))))))))	→	3(2(1(1(2(0(1(0(2(1(1(2(1(3(2(2(3(1(1(x1)))))))))))))))))))	(167)
1(0(1(3(3(0(2(2(2(2(2(1(2(1(1(1(1(1(1(x1)))))))))))))))))))	→	1(2(1(1(2(0(1(0(2(1(1(2(1(3(2(2(3(1(1(x1)))))))))))))))))))	(168)
0(0(1(3(0(3(3(2(1(2(1(2(3(0(0(3(1(1(2(x1)))))))))))))))))))	→	0(2(1(3(0(3(3(0(0(2(1(1(0(3(2(3(1(1(2(x1)))))))))))))))))))	(169)
2(0(1(3(0(3(3(2(1(2(1(2(3(0(0(3(1(1(2(x1)))))))))))))))))))	→	2(2(1(3(0(3(3(0(0(2(1(1(0(3(2(3(1(1(2(x1)))))))))))))))))))	(170)
3(0(1(3(0(3(3(2(1(2(1(2(3(0(0(3(1(1(2(x1)))))))))))))))))))	→	3(2(1(3(0(3(3(0(0(2(1(1(0(3(2(3(1(1(2(x1)))))))))))))))))))	(171)
1(0(1(3(0(3(3(2(1(2(1(2(3(0(0(3(1(1(2(x1)))))))))))))))))))	→	1(2(1(3(0(3(3(0(0(2(1(1(0(3(2(3(1(1(2(x1)))))))))))))))))))	(172)
0(3(3(1(3(2(2(3(3(1(2(0(2(0(2(2(2(1(2(x1)))))))))))))))))))	→	0(2(2(3(1(1(0(2(2(0(2(3(3(2(3(2(3(1(2(x1)))))))))))))))))))	(173)
2(3(3(1(3(2(2(3(3(1(2(0(2(0(2(2(2(1(2(x1)))))))))))))))))))	→	2(2(2(3(1(1(0(2(2(0(2(3(3(2(3(2(3(1(2(x1)))))))))))))))))))	(174)
3(3(3(1(3(2(2(3(3(1(2(0(2(0(2(2(2(1(2(x1)))))))))))))))))))	→	3(2(2(3(1(1(0(2(2(0(2(3(3(2(3(2(3(1(2(x1)))))))))))))))))))	(175)
1(3(3(1(3(2(2(3(3(1(2(0(2(0(2(2(2(1(2(x1)))))))))))))))))))	→	1(2(2(3(1(1(0(2(2(0(2(3(3(2(3(2(3(1(2(x1)))))))))))))))))))	(176)

1.1.1 Semantic Labeling

Root-labeling is applied.

We obtain the labeled TRS

There are 368 ruless (increase limit for explicit display).

1.1.1.1 Rule Removal

Using the linear polynomial interpretation over the naturals

[0₂(x₁)]	=	1 · x₁ + 3
[2₀(x₁)]	=	1 · x₁ + 6
[0₃(x₁)]	=	1 · x₁ + 14
[3₃(x₁)]	=	1 · x₁ + 13
[3₂(x₁)]	=	1 · x₁
[2₁(x₁)]	=	1 · x₁
[1₀(x₁)]	=	1 · x₁
[3₀(x₁)]	=	1 · x₁ + 4
[2₂(x₁)]	=	1 · x₁ + 1
[0₀(x₁)]	=	1 · x₁
[2₃(x₁)]	=	1 · x₁
[3₁(x₁)]	=	1 · x₁ + 4
[0₁(x₁)]	=	1 · x₁ + 1
[1₃(x₁)]	=	1 · x₁ + 12
[1₁(x₁)]	=	1 · x₁ + 3
[1₂(x₁)]	=	1 · x₁ + 8

all of the following rules can be deleted.

There are 332 ruless (increase limit for explicit display).

1.1.1.1.1 Rule Removal

Using the linear polynomial interpretation over the naturals

[2₀(x₁)]	=	1 · x₁ + 2
[0₀(x₁)]	=	1 · x₁ + 2
[0₃(x₁)]	=	1 · x₁
[3₀(x₁)]	=	1 · x₁
[3₁(x₁)]	=	1 · x₁ + 1
[1₀(x₁)]	=	1 · x₁
[0₁(x₁)]	=	1 · x₁
[1₁(x₁)]	=	1 · x₁
[1₃(x₁)]	=	1 · x₁
[0₂(x₁)]	=	1 · x₁ + 1
[3₃(x₁)]	=	1 · x₁ + 1
[2₂(x₁)]	=	1 · x₁ + 1
[2₁(x₁)]	=	1 · x₁ + 1
[1₂(x₁)]	=	1 · x₁
[2₃(x₁)]	=	1 · x₁
[3₂(x₁)]	=	1 · x₁

all of the following rules can be deleted.

0₁(1₁(1₁(1₁(1₃(3₃(3₀(0₃(3₁(1₀(0₀(0₃(3₁(1₀(0₀(0₃(3₀(0₀(x1))))))))))))))))))	→	0₁(1₁(1₃(3₀(0₁(1₁(1₃(3₁(1₀(0₁(1₃(3₀(0₀(0₃(3₀(0₃(3₀(0₀(x1))))))))))))))))))	(229)
0₁(1₁(1₁(1₁(1₃(3₃(3₀(0₃(3₁(1₀(0₀(0₃(3₁(1₀(0₀(0₃(3₀(0₂(x1))))))))))))))))))	→	0₁(1₁(1₃(3₀(0₁(1₁(1₃(3₁(1₀(0₁(1₃(3₀(0₀(0₃(3₀(0₃(3₀(0₂(x1))))))))))))))))))	(230)
0₁(1₁(1₁(1₁(1₃(3₃(3₀(0₃(3₁(1₀(0₀(0₃(3₁(1₀(0₀(0₃(3₀(0₃(x1))))))))))))))))))	→	0₁(1₁(1₃(3₀(0₁(1₁(1₃(3₁(1₀(0₁(1₃(3₀(0₀(0₃(3₀(0₃(3₀(0₃(x1))))))))))))))))))	(231)
0₁(1₁(1₁(1₁(1₃(3₃(3₀(0₃(3₁(1₀(0₀(0₃(3₁(1₀(0₀(0₃(3₀(0₁(x1))))))))))))))))))	→	0₁(1₁(1₃(3₀(0₁(1₁(1₃(3₁(1₀(0₁(1₃(3₀(0₀(0₃(3₀(0₃(3₀(0₁(x1))))))))))))))))))	(232)

1.1.1.1.1.1 Rule Removal

Using the linear polynomial interpretation over the naturals

[2₀(x₁)]	=	1 · x₁ + 1
[0₀(x₁)]	=	1 · x₁
[0₃(x₁)]	=	1 · x₁
[3₀(x₁)]	=	1 · x₁ + 1
[3₁(x₁)]	=	1 · x₁
[1₀(x₁)]	=	1 · x₁ + 1
[0₁(x₁)]	=	1 · x₁
[1₁(x₁)]	=	1 · x₁
[1₃(x₁)]	=	1 · x₁
[0₂(x₁)]	=	1 · x₁
[3₃(x₁)]	=	1 · x₁
[2₂(x₁)]	=	1 · x₁
[2₁(x₁)]	=	1 · x₁
[1₂(x₁)]	=	1 · x₁
[2₃(x₁)]	=	1 · x₁
[3₂(x₁)]	=	1 · x₁

all of the following rules can be deleted.

2₂(2₁(1₀(0₂(2₀(0₂(2₁(1₂(2₃(3₃(3₀(0₂(2₂(2₂(2₁(1₀(0₁(1₀(x1))))))))))))))))))	→	2₃(3₂(2₃(3₂(2₀(0₀(0₁(1₁(1₂(2₂(2₀(0₂(2₁(1₂(2₂(2₀(0₁(1₀(x1))))))))))))))))))	(265)
2₂(2₁(1₀(0₂(2₀(0₂(2₁(1₂(2₃(3₃(3₀(0₂(2₂(2₂(2₁(1₀(0₁(1₂(x1))))))))))))))))))	→	2₃(3₂(2₃(3₂(2₀(0₀(0₁(1₁(1₂(2₂(2₀(0₂(2₁(1₂(2₂(2₀(0₁(1₂(x1))))))))))))))))))	(266)
2₂(2₁(1₀(0₂(2₀(0₂(2₁(1₂(2₃(3₃(3₀(0₂(2₂(2₂(2₁(1₀(0₁(1₃(x1))))))))))))))))))	→	2₃(3₂(2₃(3₂(2₀(0₀(0₁(1₁(1₂(2₂(2₀(0₂(2₁(1₂(2₂(2₀(0₁(1₃(x1))))))))))))))))))	(267)
2₂(2₁(1₀(0₂(2₀(0₂(2₁(1₂(2₃(3₃(3₀(0₂(2₂(2₂(2₁(1₀(0₁(1₁(x1))))))))))))))))))	→	2₃(3₂(2₃(3₂(2₀(0₀(0₁(1₁(1₂(2₂(2₀(0₂(2₁(1₂(2₂(2₀(0₁(1₁(x1))))))))))))))))))	(268)

1.1.1.1.1.1.1 Rule Removal

Using the linear polynomial interpretation over the naturals

[2₀(x₁)]	=	1 · x₁
[0₀(x₁)]	=	1 · x₁
[0₃(x₁)]	=	1 · x₁
[3₀(x₁)]	=	1 · x₁
[3₁(x₁)]	=	1 · x₁ + 1
[1₀(x₁)]	=	1 · x₁ + 1
[0₁(x₁)]	=	1 · x₁ + 1
[1₁(x₁)]	=	1 · x₁ + 1
[1₃(x₁)]	=	1 · x₁ + 1
[0₂(x₁)]	=	1 · x₁ + 1
[3₃(x₁)]	=	1 · x₁ + 1
[3₂(x₁)]	=	1 · x₁
[1₂(x₁)]	=	1 · x₁
[2₁(x₁)]	=	1 · x₁
[2₃(x₁)]	=	1 · x₁
[2₂(x₁)]	=	1 · x₁

all of the following rules can be deleted.

1₀(0₁(1₃(3₃(3₀(0₂(2₂(2₂(2₂(2₂(2₁(1₂(2₁(1₁(1₁(1₁(1₁(1₁(1₀(x1)))))))))))))))))))	→	1₂(2₁(1₁(1₂(2₀(0₁(1₀(0₂(2₁(1₁(1₂(2₁(1₃(3₂(2₂(2₃(3₁(1₁(1₀(x1)))))))))))))))))))	(509)
1₀(0₁(1₃(3₃(3₀(0₂(2₂(2₂(2₂(2₂(2₁(1₂(2₁(1₁(1₁(1₁(1₁(1₁(1₂(x1)))))))))))))))))))	→	1₂(2₁(1₁(1₂(2₀(0₁(1₀(0₂(2₁(1₁(1₂(2₁(1₃(3₂(2₂(2₃(3₁(1₁(1₂(x1)))))))))))))))))))	(510)
1₀(0₁(1₃(3₃(3₀(0₂(2₂(2₂(2₂(2₂(2₁(1₂(2₁(1₁(1₁(1₁(1₁(1₁(1₃(x1)))))))))))))))))))	→	1₂(2₁(1₁(1₂(2₀(0₁(1₀(0₂(2₁(1₁(1₂(2₁(1₃(3₂(2₂(2₃(3₁(1₁(1₃(x1)))))))))))))))))))	(511)
1₀(0₁(1₃(3₃(3₀(0₂(2₂(2₂(2₂(2₂(2₁(1₂(2₁(1₁(1₁(1₁(1₁(1₁(1₁(x1)))))))))))))))))))	→	1₂(2₁(1₁(1₂(2₀(0₁(1₀(0₂(2₁(1₁(1₂(2₁(1₃(3₂(2₂(2₃(3₁(1₁(1₁(x1)))))))))))))))))))	(512)

1.1.1.1.1.1.1.1 Dependency Pair Transformation

The following set of initial dependency pairs has been identified.

There are 120 ruless (increase limit for explicit display).

1.1.1.1.1.1.1.1.1 Dependency Graph Processor

The dependency pairs are split into 1 component.

The 1^st component contains the pair

3₁^#(1₁(1₁(1₃(3₂(2₀(0₁(1₁(1₃(3₁(1₀(0₁(1₀(0₃(3₁(1₁(1₁(1₁(x1))))))))))))))))))

→

3₁^#(1₁(1₁(x1)))

(576)

1.1.1.1.1.1.1.1.1.1 Monotonic Reduction Pair Processor with Usable Rules

Using the linear polynomial interpretation over the naturals

[1₁(x₁)]	=	1 · x₁
[1₃(x₁)]	=	1 · x₁
[3₂(x₁)]	=	1 · x₁
[2₀(x₁)]	=	1 · x₁
[0₁(x₁)]	=	1 · x₁
[3₁(x₁)]	=	1 · x₁
[1₀(x₁)]	=	1 · x₁
[0₃(x₁)]	=	1 · x₁
[3₁^#(x₁)]	=	1 · x₁

having no usable rules (w.r.t. the implicit argument filter of the reduction pair), the rule could be deleted.

1.1.1.1.1.1.1.1.1.1.1 Size-Change Termination

Using size-change termination in combination with the subterm criterion one obtains the following initial size-change graphs.

3₁^#(1₁(1₁(1₃(3₂(2₀(0₁(1₁(1₃(3₁(1₀(0₁(1₀(0₃(3₁(1₁(1₁(1₁(x1))))))))))))))))))	→	3₁^#(1₁(1₁(x1)))	(576)

1	>	1

As there is no critical graph in the transitive closure, there are no infinite chains.