Certification Problem

Input (TPDB SRS_Relative/ICFP_2010_relative/139167)

The relative rewrite relation R/S is considered where R is the following TRS

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

and S is the following TRS.

0(1(2(3(x1))))

→

0(1(2(3(x1))))

(81)

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(2(3(0(2(1(1(0(2(2(3(2(2(1(1(0(0(x1))))))))))))))))))	→	0(1(2(3(1(2(1(2(1(3(2(2(2(0(0(2(0(0(x1))))))))))))))))))	(82)
2(0(3(0(2(3(3(3(0(2(3(0(3(2(1(1(0(0(x1))))))))))))))))))	→	0(0(3(2(3(1(0(3(2(3(2(3(3(1(0(2(0(0(x1))))))))))))))))))	(83)
1(1(2(1(0(0(2(3(0(3(2(1(1(0(1(2(0(0(x1))))))))))))))))))	→	1(1(2(0(0(1(2(1(1(0(1(2(2(3(3(0(0(0(x1))))))))))))))))))	(84)
3(1(0(1(3(1(0(1(2(0(1(1(0(1(0(3(0(0(x1))))))))))))))))))	→	3(1(3(1(0(1(3(1(1(0(0(0(2(0(1(1(0(0(x1))))))))))))))))))	(85)
2(2(0(3(0(2(0(3(2(0(3(0(2(0(3(3(0(0(x1))))))))))))))))))	→	2(3(2(2(3(0(3(2(0(3(0(0(0(0(2(3(0(0(x1))))))))))))))))))	(86)
0(3(1(3(0(3(2(0(3(1(3(3(0(1(3(3(0(0(x1))))))))))))))))))	→	0(2(3(3(3(0(0(3(3(0(1(1(3(1(3(3(0(0(x1))))))))))))))))))	(87)
3(3(0(2(2(3(3(3(2(0(1(2(2(0(2(1(1(0(x1))))))))))))))))))	→	2(0(2(3(1(2(1(2(2(3(3(3(1(2(0(3(0(0(x1))))))))))))))))))	(88)
3(1(1(2(1(3(3(3(2(3(0(1(1(1(2(2(1(0(x1))))))))))))))))))	→	2(1(1(3(1(2(3(1(2(3(1(1(0(1(3(3(2(0(x1))))))))))))))))))	(89)
3(2(0(3(3(3(0(1(3(1(3(0(3(3(0(3(1(0(x1))))))))))))))))))	→	3(3(1(3(0(3(2(3(1(0(3(3(1(3(0(0(3(0(x1))))))))))))))))))	(90)
2(3(2(1(2(2(1(0(3(3(3(3(2(1(1(3(1(0(x1))))))))))))))))))	→	2(3(0(2(1(1(2(2(1(1(3(3(3(3(1(3(2(0(x1))))))))))))))))))	(91)
2(2(3(3(3(0(2(0(2(0(1(2(3(0(1(0(2(0(x1))))))))))))))))))	→	2(2(0(2(1(3(2(0(2(1(3(3(0(0(2(0(3(0(x1))))))))))))))))))	(92)
2(0(2(0(0(1(3(0(3(0(2(1(3(0(1(2(2(0(x1))))))))))))))))))	→	0(2(0(2(3(1(2(2(3(0(0(1(0(2(0(1(3(0(x1))))))))))))))))))	(93)
2(3(0(3(0(2(3(0(2(1(3(2(3(1(3(3(2(0(x1))))))))))))))))))	→	3(3(1(3(0(0(2(3(0(2(1(2(2(3(3(3(2(0(x1))))))))))))))))))	(94)
1(1(0(3(2(1(0(2(0(0(3(3(0(2(2(3(3(0(x1))))))))))))))))))	→	1(1(1(2(0(3(2(2(0(0(0(2(0(3(3(3(3(0(x1))))))))))))))))))	(95)
1(2(1(1(0(0(3(0(2(3(0(3(0(1(2(0(0(1(x1))))))))))))))))))	→	1(0(0(1(1(0(0(0(2(3(1(3(2(2(0(0(3(1(x1))))))))))))))))))	(96)
3(3(2(0(1(1(0(2(0(3(0(3(1(2(2(1(0(1(x1))))))))))))))))))	→	3(2(3(0(0(2(1(0(0(0(1(2(2(3(3(1(1(1(x1))))))))))))))))))	(97)
2(3(3(0(3(2(2(0(3(1(1(1(2(2(2(1(0(1(x1))))))))))))))))))	→	3(1(1(3(2(2(3(2(0(3(0(1(1(2(2(2(0(1(x1))))))))))))))))))	(98)
1(2(1(1(1(2(1(2(0(1(0(1(1(1(0(3(0(1(x1))))))))))))))))))	→	1(3(2(1(1(2(1(1(0(0(2(1(1(0(1(1(0(1(x1))))))))))))))))))	(99)
2(1(2(3(3(0(2(2(3(0(1(0(2(0(2(0(1(1(x1))))))))))))))))))	→	2(1(0(0(3(3(1(3(2(2(2(0(0(1(2(2(0(1(x1))))))))))))))))))	(100)
2(2(0(3(1(2(1(1(1(2(0(0(2(3(0(1(1(1(x1))))))))))))))))))	→	2(1(2(3(1(1(1(1(1(2(2(3(2(0(0(0(0(1(x1))))))))))))))))))	(101)
3(2(1(1(3(1(1(0(2(2(3(0(2(0(1(1(1(1(x1))))))))))))))))))	→	3(1(0(1(1(2(2(0(1(0(2(1(3(3(1(1(2(1(x1))))))))))))))))))	(102)
1(0(1(1(0(2(1(3(0(0(3(2(3(2(2(1(1(1(x1))))))))))))))))))	→	1(3(2(0(2(1(3(1(3(1(0(0(0(1(1(2(1(2(x1))))))))))))))))))	(103)
1(0(2(2(3(1(1(1(0(1(1(2(2(3(2(1(1(1(x1))))))))))))))))))	→	1(2(3(2(0(1(1(0(1(1(1(2(3(1(2(2(1(1(x1))))))))))))))))))	(104)
2(1(1(1(1(0(2(0(2(2(3(0(3(2(3(1(1(1(x1))))))))))))))))))	→	2(0(0(2(1(3(1(3(3(1(0(1(2(1(1(2(1(2(x1))))))))))))))))))	(105)
3(0(1(3(0(0(3(1(1(1(0(3(2(3(2(2(1(1(x1))))))))))))))))))	→	3(0(3(2(3(0(1(2(3(3(1(1(1(2(0(0(1(1(x1))))))))))))))))))	(106)
3(0(3(3(0(1(2(1(1(2(0(1(2(0(3(2(1(1(x1))))))))))))))))))	→	0(3(1(2(3(0(0(2(1(1(2(1(1(3(3(2(0(1(x1))))))))))))))))))	(107)
3(2(0(3(3(1(3(3(2(1(1(0(3(1(3(2(1(1(x1))))))))))))))))))	→	3(3(3(1(3(0(2(1(3(0(2(3(1(1(3(1(2(1(x1))))))))))))))))))	(108)
3(2(3(0(0(0(3(3(3(0(1(3(0(3(3(2(1(1(x1))))))))))))))))))	→	3(0(0(1(3(2(3(0(3(2(3(1(3(0(0(1(3(3(x1))))))))))))))))))	(109)
0(3(1(3(2(1(0(1(3(2(1(0(2(3(0(3(1(1(x1))))))))))))))))))	→	0(1(1(2(3(1(0(0(3(1(2(1(3(2(3(0(3(1(x1))))))))))))))))))	(110)
0(2(3(0(2(0(2(1(3(2(2(0(3(0(0(0(2(1(x1))))))))))))))))))	→	0(0(2(3(2(2(0(0(0(2(0(2(0(3(1(3(1(2(x1))))))))))))))))))	(111)
2(3(1(2(0(2(1(1(1(1(3(2(0(3(2(0(2(1(x1))))))))))))))))))	→	2(2(3(2(1(0(1(3(1(0(3(1(2(2(2(0(1(1(x1))))))))))))))))))	(112)
0(3(1(2(3(3(3(3(0(1(1(2(3(0(3(0(2(1(x1))))))))))))))))))	→	0(2(3(3(3(1(3(1(0(3(2(0(1(2(0(3(3(1(x1))))))))))))))))))	(113)
1(3(0(1(1(1(3(0(2(3(3(3(3(3(0(1(2(1(x1))))))))))))))))))	→	3(1(3(0(1(3(3(1(3(1(3(2(2(1(0(0(3(1(x1))))))))))))))))))	(114)
1(1(2(0(2(1(1(3(3(0(3(1(1(3(3(3(2(1(x1))))))))))))))))))	→	2(3(1(1(1(1(1(3(2(0(0(3(1(3(3(3(2(1(x1))))))))))))))))))	(115)
3(3(2(3(3(3(1(1(0(1(0(3(3(2(1(0(3(1(x1))))))))))))))))))	→	3(1(3(3(3(0(0(2(3(1(1(2(3(0(3(1(3(1(x1))))))))))))))))))	(116)
2(3(0(0(2(0(3(1(1(1(3(0(2(0(3(0(3(1(x1))))))))))))))))))	→	3(3(1(0(3(1(0(0(0(3(1(2(0(0(2(3(2(1(x1))))))))))))))))))	(117)
3(0(1(2(1(0(2(3(0(2(2(1(1(2(0(1(0(2(x1))))))))))))))))))	→	2(0(3(2(1(0(1(1(2(2(2(3(2(0(1(0(0(1(x1))))))))))))))))))	(118)
0(2(2(0(3(2(2(0(1(1(0(1(0(3(0(1(0(2(x1))))))))))))))))))	→	0(0(1(2(0(1(2(1(0(1(2(0(3(2(3(0(0(2(x1))))))))))))))))))	(119)
0(2(1(2(1(0(1(0(2(0(0(3(3(2(1(1(0(2(x1))))))))))))))))))	→	0(0(1(1(1(2(0(2(1(0(0(1(2(3(3(2(0(2(x1))))))))))))))))))	(120)
1(1(1(0(1(3(3(0(0(3(2(2(2(2(2(1(0(2(x1))))))))))))))))))	→	1(2(1(2(2(2(0(3(2(0(0(0(1(3(3(1(2(1(x1))))))))))))))))))	(121)
0(1(3(2(1(1(1(0(0(1(3(0(2(3(2(1(0(2(x1))))))))))))))))))	→	0(1(2(1(2(3(0(2(1(2(3(3(0(0(0(1(1(1(x1))))))))))))))))))	(122)
3(3(1(3(2(2(1(3(3(1(1(2(0(3(0(2(0(2(x1))))))))))))))))))	→	3(1(0(0(1(2(2(3(3(3(1(3(2(0(3(2(2(1(x1))))))))))))))))))	(123)
0(2(3(0(1(3(0(2(1(3(3(0(3(3(3(2(0(2(x1))))))))))))))))))	→	0(0(3(2(3(0(0(2(3(3(2(3(2(3(0(3(1(1(x1))))))))))))))))))	(124)
2(0(3(3(3(2(0(3(1(1(1(2(0(2(0(3(0(2(x1))))))))))))))))))	→	3(1(1(3(3(0(0(2(2(2(2(3(1(0(2(0(0(3(x1))))))))))))))))))	(125)
1(2(1(2(0(3(3(2(3(2(3(1(0(3(2(3(0(2(x1))))))))))))))))))	→	2(3(2(3(3(1(3(2(2(0(0(3(3(1(2(0(2(1(x1))))))))))))))))))	(126)
1(1(3(0(1(2(3(0(1(0(1(0(2(1(3(3(0(2(x1))))))))))))))))))	→	2(0(3(0(1(2(3(3(1(1(2(1(3(1(0(0(0(1(x1))))))))))))))))))	(127)
3(0(2(0(2(0(1(1(2(0(3(0(2(2(3(0(1(2(x1))))))))))))))))))	→	2(2(3(1(1(0(0(1(2(2(0(0(0(0(2(2(3(3(x1))))))))))))))))))	(128)
2(2(0(0(3(3(0(0(3(2(1(2(2(1(2(1(1(2(x1))))))))))))))))))	→	2(0(0(2(3(1(2(2(3(2(1(2(2(3(1(0(0(1(x1))))))))))))))))))	(129)
2(1(0(2(2(2(0(3(1(3(0(0(0(2(2(1(1(2(x1))))))))))))))))))	→	2(1(1(2(2(2(0(0(0(0(0(2(3(1(2(3(2(1(x1))))))))))))))))))	(130)
1(0(0(2(1(1(3(1(3(2(1(3(2(3(2(1(1(2(x1))))))))))))))))))	→	1(2(3(2(0(1(3(1(2(0(1(3(1(2(1(3(1(2(x1))))))))))))))))))	(131)
3(2(1(3(2(3(0(3(2(1(1(2(2(2(3(1(1(2(x1))))))))))))))))))	→	3(0(1(1(1(1(2(3(3(3(2(3(1(2(2(2(2(2(x1))))))))))))))))))	(132)
2(0(3(3(2(0(3(2(1(3(0(1(2(1(1(2(1(2(x1))))))))))))))))))	→	2(3(2(1(0(2(2(0(1(3(2(3(1(0(2(1(3(1(x1))))))))))))))))))	(133)
0(3(2(0(3(1(1(2(3(3(3(2(3(0(2(2(1(2(x1))))))))))))))))))	→	0(1(1(3(2(2(3(3(2(2(3(2(0(2(3(0(3(1(x1))))))))))))))))))	(134)
1(1(0(1(3(2(2(1(3(0(0(3(1(2(2(2(1(2(x1))))))))))))))))))	→	1(1(0(0(2(0(2(1(2(1(2(3(1(2(3(3(1(2(x1))))))))))))))))))	(135)
3(0(0(1(0(3(0(1(0(3(2(1(1(3(3(2(1(2(x1))))))))))))))))))	→	0(1(1(3(3(1(0(0(3(2(1(2(3(3(2(0(0(1(x1))))))))))))))))))	(136)
3(1(2(0(3(3(0(3(2(3(2(1(2(3(0(3(1(2(x1))))))))))))))))))	→	1(2(3(3(1(0(2(3(2(3(2(3(2(0(0(1(3(3(x1))))))))))))))))))	(137)
1(3(3(2(1(0(2(2(0(1(2(3(2(1(1(0(2(2(x1))))))))))))))))))	→	1(2(3(3(1(1(2(0(0(2(0(1(3(1(2(2(2(2(x1))))))))))))))))))	(138)
0(2(3(3(0(1(1(2(0(3(0(1(3(3(2(0(2(2(x1))))))))))))))))))	→	0(0(3(3(3(2(0(0(1(2(3(2(3(2(0(2(1(1(x1))))))))))))))))))	(139)
3(0(3(0(3(0(3(1(0(2(3(2(2(2(0(1(2(2(x1))))))))))))))))))	→	3(2(2(1(3(2(0(0(0(0(2(0(1(3(2(3(3(2(x1))))))))))))))))))	(140)
2(0(3(3(0(1(0(3(0(3(1(1(3(0(1(3(2(2(x1))))))))))))))))))	→	3(1(3(1(0(3(0(0(3(1(1(2(2(0(0(3(2(3(x1))))))))))))))))))	(141)
1(1(1(1(3(1(0(3(2(1(2(1(0(2(3(0(3(2(x1))))))))))))))))))	→	1(2(3(3(3(1(1(0(0(1(2(2(3(1(0(1(1(2(x1))))))))))))))))))	(142)
1(1(2(1(1(2(3(0(3(1(0(0(3(2(3(0(3(2(x1))))))))))))))))))	→	1(3(1(1(3(1(3(0(2(0(0(0(2(2(3(1(3(2(x1))))))))))))))))))	(143)
2(1(0(3(0(2(0(2(1(1(2(3(3(2(3(0(3(2(x1))))))))))))))))))	→	3(2(2(3(3(2(0(0(1(1(0(3(0(2(2(3(1(2(x1))))))))))))))))))	(144)
2(3(0(3(3(2(2(2(2(1(1(2(3(3(0(2(3(2(x1))))))))))))))))))	→	0(2(0(1(3(2(3(2(2(3(2(2(3(2(3(3(1(2(x1))))))))))))))))))	(145)
2(3(0(3(3(0(3(2(2(0(1(1(0(1(0(2(0(3(x1))))))))))))))))))	→	3(2(2(3(3(1(0(0(3(1(0(0(2(1(0(3(0(2(x1))))))))))))))))))	(146)
0(2(1(3(0(1(3(2(2(1(3(0(2(1(1(3(0(3(x1))))))))))))))))))	→	0(3(1(0(1(2(3(3(2(0(0(3(1(2(1(1(2(3(x1))))))))))))))))))	(147)
0(0(1(3(0(3(0(1(1(3(2(1(1(0(2(3(0(3(x1))))))))))))))))))	→	0(0(2(0(3(1(2(1(3(1(0(3(3(1(1(0(0(3(x1))))))))))))))))))	(148)
2(0(1(2(1(2(1(0(3(1(0(3(1(2(2(3(0(3(x1))))))))))))))))))	→	2(3(2(3(1(3(2(0(3(1(0(1(2(1(0(0(1(2(x1))))))))))))))))))	(149)
3(1(2(1(0(1(3(2(2(3(3(0(2(2(2(3(0(3(x1))))))))))))))))))	→	3(1(1(2(3(1(2(0(2(2(3(3(2(3(3(0(0(2(x1))))))))))))))))))	(150)
2(3(3(2(0(2(2(3(0(1(1(1(2(1(3(0(1(3(x1))))))))))))))))))	→	2(3(2(1(1(3(1(3(1(3(0(2(0(2(0(1(2(3(x1))))))))))))))))))	(151)
1(1(1(1(0(1(3(3(2(1(2(1(2(1(1(1(1(3(x1))))))))))))))))))	→	1(1(2(1(2(2(3(1(3(1(1(1(1(0(1(1(1(3(x1))))))))))))))))))	(152)
0(0(3(0(0(0(0(1(3(3(1(2(0(2(1(1(1(3(x1))))))))))))))))))	→	0(0(3(2(0(0(1(3(0(0(0(1(1(1(1(3(2(3(x1))))))))))))))))))	(153)
1(1(0(2(0(1(0(1(0(3(0(0(2(0(3(0(2(3(x1))))))))))))))))))	→	3(1(3(1(0(0(1(0(0(2(0(1(2(0(0(0(2(3(x1))))))))))))))))))	(154)
0(3(2(3(3(0(2(2(0(2(2(1(0(2(0(1(2(3(x1))))))))))))))))))	→	0(1(2(2(3(0(2(0(2(2(3(2(1(2(0(0(3(3(x1))))))))))))))))))	(155)
1(3(3(3(0(3(0(3(3(3(2(2(2(3(0(1(2(3(x1))))))))))))))))))	→	1(0(3(3(3(2(3(2(2(0(0(2(1(3(3(3(3(3(x1))))))))))))))))))	(156)
2(3(0(3(1(0(2(3(0(1(3(3(3(3(0(2(2(3(x1))))))))))))))))))	→	2(2(3(3(0(2(3(0(2(3(3(0(0(1(3(3(1(3(x1))))))))))))))))))	(157)
2(3(2(2(3(2(0(3(3(0(3(3(1(2(1(3(2(3(x1))))))))))))))))))	→	2(3(2(3(0(0(1(2(3(3(3(2(3(3(1(2(2(3(x1))))))))))))))))))	(158)
1(3(0(3(3(0(3(1(2(3(0(1(0(3(3(3(2(3(x1))))))))))))))))))	→	1(0(0(2(0(1(3(1(3(3(3(3(0(3(3(2(3(3(x1))))))))))))))))))	(159)
2(2(3(0(3(3(2(3(3(1(0(3(0(3(2(2(3(3(x1))))))))))))))))))	→	2(0(0(3(2(1(0(3(3(2(2(2(3(3(3(3(3(3(x1))))))))))))))))))	(160)
0(2(0(2(1(3(1(0(0(3(3(3(0(1(3(2(3(3(x1))))))))))))))))))	→	0(3(3(0(2(1(0(0(3(1(2(3(1(0(2(3(3(3(x1))))))))))))))))))	(161)

1.1 Closure Under Flat Contexts

Using the flat contexts

{0(☐), 2(☐), 3(☐), 1(☐)}

We obtain the transformed TRS

There are 146 ruless (increase limit for explicit display).

1.1.1 Semantic Labeling

Root-labeling is applied.

We obtain the labeled TRS

There are 584 ruless (increase limit for explicit display).

1.1.1.1 Rule Removal

Using the linear polynomial interpretation over the naturals

[0₂(x₁)]	=	1 · x₁
[2₂(x₁)]	=	1 · x₁ + 13
[2₃(x₁)]	=	1 · x₁
[3₀(x₁)]	=	1 · x₁ + 21
[2₁(x₁)]	=	1 · x₁ + 13
[1₁(x₁)]	=	1 · x₁ + 9
[1₀(x₁)]	=	1 · x₁ + 19
[3₂(x₁)]	=	1 · x₁ + 8
[0₀(x₁)]	=	1 · x₁
[0₁(x₁)]	=	1 · x₁ + 1
[1₂(x₁)]	=	1 · x₁ + 10
[3₁(x₁)]	=	1 · x₁
[1₃(x₁)]	=	1 · x₁
[2₀(x₁)]	=	1 · x₁ + 20
[0₃(x₁)]	=	1 · x₁
[3₃(x₁)]	=	1 · x₁ + 3

all of the following rules can be deleted.

There are 547 ruless (increase limit for explicit display).

1.1.1.1.1 Rule Removal

Using the linear polynomial interpretation over the naturals

[2₂(x₁)]	=	1 · x₁
[2₃(x₁)]	=	1 · x₁ + 1
[3₃(x₁)]	=	1 · x₁
[3₀(x₁)]	=	1 · x₁
[0₂(x₁)]	=	1 · x₁ + 3
[2₀(x₁)]	=	1 · x₁
[0₁(x₁)]	=	1 · x₁ + 3
[1₂(x₁)]	=	1 · x₁
[1₀(x₁)]	=	1 · x₁ + 2
[0₀(x₁)]	=	1 · x₁
[2₁(x₁)]	=	1 · x₁ + 2
[1₃(x₁)]	=	1 · x₁
[3₂(x₁)]	=	1 · x₁
[0₃(x₁)]	=	1 · x₁
[1₁(x₁)]	=	1 · x₁ + 1
[3₁(x₁)]	=	1 · x₁

all of the following rules can be deleted.

2₂(2₃(3₃(3₃(3₀(0₂(2₀(0₂(2₀(0₁(1₂(2₃(3₀(0₁(1₀(0₂(2₀(0₀(x1))))))))))))))))))	→	2₂(2₀(0₂(2₁(1₃(3₂(2₀(0₂(2₁(1₃(3₃(3₀(0₀(0₂(2₀(0₃(3₀(0₀(x1))))))))))))))))))	(278)
2₂(2₃(3₃(3₃(3₀(0₂(2₀(0₂(2₀(0₁(1₂(2₃(3₀(0₁(1₀(0₂(2₀(0₂(x1))))))))))))))))))	→	2₂(2₀(0₂(2₁(1₃(3₂(2₀(0₂(2₁(1₃(3₃(3₀(0₀(0₂(2₀(0₃(3₀(0₂(x1))))))))))))))))))	(279)
2₂(2₃(3₃(3₃(3₀(0₂(2₀(0₂(2₀(0₁(1₂(2₃(3₀(0₁(1₀(0₂(2₀(0₃(x1))))))))))))))))))	→	2₂(2₀(0₂(2₁(1₃(3₂(2₀(0₂(2₁(1₃(3₃(3₀(0₀(0₂(2₀(0₃(3₀(0₃(x1))))))))))))))))))	(280)
2₂(2₃(3₃(3₃(3₀(0₂(2₀(0₂(2₀(0₁(1₂(2₃(3₀(0₁(1₀(0₂(2₀(0₁(x1))))))))))))))))))	→	2₂(2₀(0₂(2₁(1₃(3₂(2₀(0₂(2₁(1₃(3₃(3₀(0₀(0₂(2₀(0₃(3₀(0₁(x1))))))))))))))))))	(281)
1₀(0₂(2₂(2₃(3₁(1₁(1₁(1₀(0₁(1₁(1₂(2₂(2₃(3₂(2₁(1₁(1₁(1₀(x1))))))))))))))))))	→	1₂(2₃(3₂(2₀(0₁(1₁(1₀(0₁(1₁(1₁(1₂(2₃(3₁(1₂(2₂(2₁(1₁(1₀(x1))))))))))))))))))	(314)
1₀(0₂(2₂(2₃(3₁(1₁(1₁(1₀(0₁(1₁(1₂(2₂(2₃(3₂(2₁(1₁(1₁(1₂(x1))))))))))))))))))	→	1₂(2₃(3₂(2₀(0₁(1₁(1₀(0₁(1₁(1₁(1₂(2₃(3₁(1₂(2₂(2₁(1₁(1₂(x1))))))))))))))))))	(315)
1₀(0₂(2₂(2₃(3₁(1₁(1₁(1₀(0₁(1₁(1₂(2₂(2₃(3₂(2₁(1₁(1₁(1₃(x1))))))))))))))))))	→	1₂(2₃(3₂(2₀(0₁(1₁(1₀(0₁(1₁(1₁(1₂(2₃(3₁(1₂(2₂(2₁(1₁(1₃(x1))))))))))))))))))	(316)
1₀(0₂(2₂(2₃(3₁(1₁(1₁(1₀(0₁(1₁(1₂(2₂(2₃(3₂(2₁(1₁(1₁(1₁(x1))))))))))))))))))	→	1₂(2₃(3₂(2₀(0₁(1₁(1₀(0₁(1₁(1₁(1₂(2₃(3₁(1₂(2₂(2₁(1₁(1₁(x1))))))))))))))))))	(317)
0₁(1₃(3₂(2₁(1₁(1₁(1₀(0₀(0₁(1₃(3₀(0₂(2₃(3₂(2₁(1₀(0₂(2₃(x1))))))))))))))))))	→	0₁(1₂(2₁(1₂(2₃(3₀(0₂(2₁(1₂(2₃(3₃(3₀(0₀(0₀(0₁(1₁(1₁(1₃(x1))))))))))))))))))	(368)
0₂(2₃(3₀(0₃(3₀(0₂(2₃(3₀(0₂(2₁(1₃(3₂(2₃(3₁(1₃(3₃(3₂(2₀(0₀(x1)))))))))))))))))))	→	0₃(3₃(3₁(1₃(3₀(0₀(0₂(2₃(3₀(0₂(2₁(1₂(2₂(2₃(3₃(3₃(3₂(2₀(0₀(x1)))))))))))))))))))	(546)
0₂(2₃(3₀(0₃(3₀(0₂(2₃(3₀(0₂(2₁(1₃(3₂(2₃(3₁(1₃(3₃(3₂(2₀(0₂(x1)))))))))))))))))))	→	0₃(3₃(3₁(1₃(3₀(0₀(0₂(2₃(3₀(0₂(2₁(1₂(2₂(2₃(3₃(3₃(3₂(2₀(0₂(x1)))))))))))))))))))	(547)
0₂(2₃(3₀(0₃(3₀(0₂(2₃(3₀(0₂(2₁(1₃(3₂(2₃(3₁(1₃(3₃(3₂(2₀(0₃(x1)))))))))))))))))))	→	0₃(3₃(3₁(1₃(3₀(0₀(0₂(2₃(3₀(0₂(2₁(1₂(2₂(2₃(3₃(3₃(3₂(2₀(0₃(x1)))))))))))))))))))	(548)
0₂(2₃(3₀(0₃(3₀(0₂(2₃(3₀(0₂(2₁(1₃(3₂(2₃(3₁(1₃(3₃(3₂(2₀(0₁(x1)))))))))))))))))))	→	0₃(3₃(3₁(1₃(3₀(0₀(0₂(2₃(3₀(0₂(2₁(1₂(2₂(2₃(3₃(3₃(3₂(2₀(0₁(x1)))))))))))))))))))	(549)

1.1.1.1.1.1 Rule Removal

Using the linear polynomial interpretation over the naturals

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

all of the following rules can be deleted.

3₂(2₁(1₁(1₃(3₁(1₁(1₀(0₂(2₂(2₃(3₀(0₂(2₀(0₁(1₁(1₁(1₁(1₀(x1))))))))))))))))))	→	3₁(1₀(0₁(1₁(1₂(2₂(2₀(0₁(1₀(0₂(2₁(1₃(3₃(3₁(1₁(1₂(2₁(1₀(x1))))))))))))))))))	(306)
3₂(2₁(1₁(1₃(3₁(1₁(1₀(0₂(2₂(2₃(3₀(0₂(2₀(0₁(1₁(1₁(1₁(1₂(x1))))))))))))))))))	→	3₁(1₀(0₁(1₁(1₂(2₂(2₀(0₁(1₀(0₂(2₁(1₃(3₃(3₁(1₁(1₂(2₁(1₂(x1))))))))))))))))))	(307)
3₂(2₁(1₁(1₃(3₁(1₁(1₀(0₂(2₂(2₃(3₀(0₂(2₀(0₁(1₁(1₁(1₁(1₃(x1))))))))))))))))))	→	3₁(1₀(0₁(1₁(1₂(2₂(2₀(0₁(1₀(0₂(2₁(1₃(3₃(3₁(1₁(1₂(2₁(1₃(x1))))))))))))))))))	(308)
3₂(2₁(1₁(1₃(3₁(1₁(1₀(0₂(2₂(2₃(3₀(0₂(2₀(0₁(1₁(1₁(1₁(1₁(x1))))))))))))))))))	→	3₁(1₀(0₁(1₁(1₂(2₂(2₀(0₁(1₀(0₂(2₁(1₃(3₃(3₁(1₁(1₂(2₁(1₁(x1))))))))))))))))))	(309)

1.1.1.1.1.1.1 Rule Removal

Using the linear polynomial interpretation over the naturals

[2₃(x₁)]	=	1 · x₁ + 7
[3₁(x₁)]	=	1 · x₁
[1₂(x₁)]	=	1 · x₁
[2₀(x₁)]	=	1 · x₁
[0₂(x₁)]	=	1 · x₁ + 1
[2₁(x₁)]	=	1 · x₁ + 2
[1₁(x₁)]	=	1 · x₁
[1₃(x₁)]	=	1 · x₁ + 4
[3₂(x₁)]	=	1 · x₁
[0₃(x₁)]	=	1 · x₁
[1₀(x₁)]	=	1 · x₁ + 1
[2₂(x₁)]	=	1 · x₁
[0₁(x₁)]	=	1 · x₁
[3₀(x₁)]	=	1 · x₁
[3₃(x₁)]	=	1 · x₁ + 4
[0₀(x₁)]	=	1 · x₁

all of the following rules can be deleted.

2₃(3₁(1₂(2₀(0₂(2₁(1₁(1₁(1₁(1₃(3₂(2₀(0₃(3₂(2₀(0₂(2₁(1₀(x1))))))))))))))))))	→	2₂(2₃(3₂(2₁(1₀(0₁(1₃(3₁(1₀(0₃(3₁(1₂(2₂(2₂(2₀(0₁(1₁(1₀(x1))))))))))))))))))	(342)
2₃(3₁(1₂(2₀(0₂(2₁(1₁(1₁(1₁(1₃(3₂(2₀(0₃(3₂(2₀(0₂(2₁(1₂(x1))))))))))))))))))	→	2₂(2₃(3₂(2₁(1₀(0₁(1₃(3₁(1₀(0₃(3₁(1₂(2₂(2₂(2₀(0₁(1₁(1₂(x1))))))))))))))))))	(343)
2₃(3₁(1₂(2₀(0₂(2₁(1₁(1₁(1₁(1₃(3₂(2₀(0₃(3₂(2₀(0₂(2₁(1₃(x1))))))))))))))))))	→	2₂(2₃(3₂(2₁(1₀(0₁(1₃(3₁(1₀(0₃(3₁(1₂(2₂(2₂(2₀(0₁(1₁(1₃(x1))))))))))))))))))	(344)
2₃(3₁(1₂(2₀(0₂(2₁(1₁(1₁(1₁(1₃(3₂(2₀(0₃(3₂(2₀(0₂(2₁(1₁(x1))))))))))))))))))	→	2₂(2₃(3₂(2₁(1₀(0₁(1₃(3₁(1₀(0₃(3₁(1₂(2₂(2₂(2₀(0₁(1₁(1₁(x1))))))))))))))))))	(345)

1.1.1.1.1.1.1.1 Rule Removal

Using the linear polynomial interpretation over the naturals

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

all of the following rules can be deleted.

3₂(2₁(1₃(3₂(2₃(3₀(0₃(3₂(2₁(1₁(1₂(2₂(2₂(2₃(3₁(1₁(1₂(2₀(x1))))))))))))))))))	→	3₀(0₁(1₁(1₁(1₁(1₂(2₃(3₃(3₃(3₂(2₃(3₁(1₂(2₂(2₂(2₂(2₂(2₀(x1))))))))))))))))))	(390)
3₂(2₁(1₃(3₂(2₃(3₀(0₃(3₂(2₁(1₁(1₂(2₂(2₂(2₃(3₁(1₁(1₂(2₂(x1))))))))))))))))))	→	3₀(0₁(1₁(1₁(1₁(1₂(2₃(3₃(3₃(3₂(2₃(3₁(1₂(2₂(2₂(2₂(2₂(2₂(x1))))))))))))))))))	(391)
3₂(2₁(1₃(3₂(2₃(3₀(0₃(3₂(2₁(1₁(1₂(2₂(2₂(2₃(3₁(1₁(1₂(2₃(x1))))))))))))))))))	→	3₀(0₁(1₁(1₁(1₁(1₂(2₃(3₃(3₃(3₂(2₃(3₁(1₂(2₂(2₂(2₂(2₂(2₃(x1))))))))))))))))))	(392)
3₂(2₁(1₃(3₂(2₃(3₀(0₃(3₂(2₁(1₁(1₂(2₂(2₂(2₃(3₁(1₁(1₂(2₁(x1))))))))))))))))))	→	3₀(0₁(1₁(1₁(1₁(1₂(2₃(3₃(3₃(3₂(2₃(3₁(1₂(2₂(2₂(2₂(2₂(2₁(x1))))))))))))))))))	(393)

1.1.1.1.1.1.1.1.1 Rule Removal

Using the linear polynomial interpretation over the naturals

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

all of the following rules can be deleted.

0₀(0₃(3₀(0₀(0₀(0₀(0₁(1₃(3₃(3₁(1₂(2₀(0₂(2₁(1₁(1₁(1₃(3₀(x1))))))))))))))))))	→	0₀(0₃(3₂(2₀(0₀(0₁(1₃(3₀(0₀(0₀(0₁(1₁(1₁(1₁(1₃(3₂(2₃(3₀(x1))))))))))))))))))	(450)
0₀(0₃(3₀(0₀(0₀(0₀(0₁(1₃(3₃(3₁(1₂(2₀(0₂(2₁(1₁(1₁(1₃(3₂(x1))))))))))))))))))	→	0₀(0₃(3₂(2₀(0₀(0₁(1₃(3₀(0₀(0₀(0₁(1₁(1₁(1₁(1₃(3₂(2₃(3₂(x1))))))))))))))))))	(451)
0₀(0₃(3₀(0₀(0₀(0₀(0₁(1₃(3₃(3₁(1₂(2₀(0₂(2₁(1₁(1₁(1₃(3₃(x1))))))))))))))))))	→	0₀(0₃(3₂(2₀(0₀(0₁(1₃(3₀(0₀(0₀(0₁(1₁(1₁(1₁(1₃(3₂(2₃(3₃(x1))))))))))))))))))	(452)
0₀(0₃(3₀(0₀(0₀(0₀(0₁(1₃(3₃(3₁(1₂(2₀(0₂(2₁(1₁(1₁(1₃(3₁(x1))))))))))))))))))	→	0₀(0₃(3₂(2₀(0₀(0₁(1₃(3₀(0₀(0₀(0₁(1₁(1₁(1₁(1₃(3₂(2₃(3₁(x1))))))))))))))))))	(453)

1.1.1.1.1.1.1.1.1.1 Rule Removal

Using the linear polynomial interpretation over the naturals

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

all of the following rules can be deleted.

2₂(2₃(3₀(0₃(3₃(3₂(2₃(3₃(3₁(1₀(0₃(3₀(0₃(3₂(2₂(2₃(3₃(3₀(x1))))))))))))))))))	→	2₀(0₀(0₃(3₂(2₁(1₀(0₃(3₃(3₂(2₂(2₂(2₃(3₃(3₃(3₃(3₃(3₃(3₀(x1))))))))))))))))))	(474)
2₂(2₃(3₀(0₃(3₃(3₂(2₃(3₃(3₁(1₀(0₃(3₀(0₃(3₂(2₂(2₃(3₃(3₂(x1))))))))))))))))))	→	2₀(0₀(0₃(3₂(2₁(1₀(0₃(3₃(3₂(2₂(2₂(2₃(3₃(3₃(3₃(3₃(3₃(3₂(x1))))))))))))))))))	(475)
2₂(2₃(3₀(0₃(3₃(3₂(2₃(3₃(3₁(1₀(0₃(3₀(0₃(3₂(2₂(2₃(3₃(3₃(x1))))))))))))))))))	→	2₀(0₀(0₃(3₂(2₁(1₀(0₃(3₃(3₂(2₂(2₂(2₃(3₃(3₃(3₃(3₃(3₃(3₃(x1))))))))))))))))))	(476)
2₂(2₃(3₀(0₃(3₃(3₂(2₃(3₃(3₁(1₀(0₃(3₀(0₃(3₂(2₂(2₃(3₃(3₁(x1))))))))))))))))))	→	2₀(0₀(0₃(3₂(2₁(1₀(0₃(3₃(3₂(2₂(2₂(2₃(3₃(3₃(3₃(3₃(3₃(3₁(x1))))))))))))))))))	(477)

1.1.1.1.1.1.1.1.1.1.1 Rule Removal

Using the linear polynomial interpretation over the naturals

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

all of the following rules can be deleted.

0₂(2₀(0₂(2₁(1₃(3₁(1₀(0₀(0₃(3₃(3₃(3₀(0₁(1₃(3₂(2₃(3₃(3₀(x1))))))))))))))))))	→	0₃(3₃(3₀(0₂(2₁(1₀(0₀(0₃(3₁(1₂(2₃(3₁(1₀(0₂(2₃(3₃(3₃(3₀(x1))))))))))))))))))	(478)
0₂(2₀(0₂(2₁(1₃(3₁(1₀(0₀(0₃(3₃(3₃(3₀(0₁(1₃(3₂(2₃(3₃(3₂(x1))))))))))))))))))	→	0₃(3₃(3₀(0₂(2₁(1₀(0₀(0₃(3₁(1₂(2₃(3₁(1₀(0₂(2₃(3₃(3₃(3₂(x1))))))))))))))))))	(479)
0₂(2₀(0₂(2₁(1₃(3₁(1₀(0₀(0₃(3₃(3₃(3₀(0₁(1₃(3₂(2₃(3₃(3₃(x1))))))))))))))))))	→	0₃(3₃(3₀(0₂(2₁(1₀(0₀(0₃(3₁(1₂(2₃(3₁(1₀(0₂(2₃(3₃(3₃(3₃(x1))))))))))))))))))	(480)
0₂(2₀(0₂(2₁(1₃(3₁(1₀(0₀(0₃(3₃(3₃(3₀(0₁(1₃(3₂(2₃(3₃(3₁(x1))))))))))))))))))	→	0₃(3₃(3₀(0₂(2₁(1₀(0₀(0₃(3₁(1₂(2₃(3₁(1₀(0₂(2₃(3₃(3₃(3₁(x1))))))))))))))))))	(481)

1.1.1.1.1.1.1.1.1.1.1.1 R is empty

There are no rules in the TRS. Hence, it is terminating.