Certification Problem

Input (TPDB SRS_Standard/ICFP_2010/130962)

The rewrite relation of the following TRS is considered.

0(0(0(0(1(0(1(2(2(3(3(4(1(2(3(2(3(3(2(2(x1))))))))))))))))))))	→	0(3(1(0(2(1(0(4(2(4(0(0(1(1(4(2(3(1(0(2(x1))))))))))))))))))))	(1)
0(1(1(1(0(4(1(0(1(2(1(0(1(4(1(1(2(4(4(2(x1))))))))))))))))))))	→	4(4(1(2(4(0(4(1(0(1(4(2(2(2(3(1(1(4(0(2(x1))))))))))))))))))))	(2)
0(1(1(1(1(2(4(4(0(3(4(4(0(2(0(4(1(1(2(1(x1))))))))))))))))))))	→	3(1(4(3(2(4(3(3(4(0(0(2(0(3(1(0(1(0(1(2(x1))))))))))))))))))))	(3)
0(1(2(0(4(0(2(0(3(0(2(2(3(2(0(4(3(0(1(2(x1))))))))))))))))))))	→	1(3(0(2(1(0(0(2(2(0(4(1(2(2(2(3(2(4(2(1(x1))))))))))))))))))))	(4)
0(1(2(2(0(3(1(1(3(2(1(1(1(1(3(4(2(3(0(2(x1))))))))))))))))))))	→	4(2(4(3(3(2(3(2(4(1(0(2(3(1(4(2(1(4(3(2(x1))))))))))))))))))))	(5)
0(1(3(1(1(2(3(2(4(3(4(1(1(2(3(1(0(4(2(2(x1))))))))))))))))))))	→	2(2(0(1(1(3(2(0(1(0(2(2(0(4(1(4(2(2(4(2(x1))))))))))))))))))))	(6)
0(1(3(2(3(1(0(0(0(3(3(2(3(3(2(1(0(2(1(2(x1))))))))))))))))))))	→	0(0(3(4(0(2(2(4(0(4(2(1(3(4(1(3(2(0(2(1(x1))))))))))))))))))))	(7)
0(1(3(3(3(3(0(1(1(2(0(0(4(4(4(3(1(0(0(2(x1))))))))))))))))))))	→	2(0(2(4(0(2(3(4(2(0(1(0(0(3(4(3(4(0(3(2(x1))))))))))))))))))))	(8)
0(2(0(0(0(4(0(3(1(2(2(4(4(3(3(2(2(2(3(2(x1))))))))))))))))))))	→	3(1(2(2(4(0(2(3(1(3(4(0(4(1(3(2(3(1(2(1(x1))))))))))))))))))))	(9)
0(2(0(1(2(1(1(0(2(2(0(0(3(4(4(3(1(2(2(1(x1))))))))))))))))))))	→	3(0(2(2(0(1(4(2(3(3(0(3(0(2(0(2(4(2(0(2(x1))))))))))))))))))))	(10)
0(2(0(2(2(1(3(2(2(0(2(0(0(2(1(0(4(3(3(2(x1))))))))))))))))))))	→	0(3(3(0(0(4(2(3(0(0(3(1(2(4(2(4(0(0(4(2(x1))))))))))))))))))))	(11)
0(2(1(1(3(3(4(4(0(4(3(3(3(0(0(4(1(2(1(1(x1))))))))))))))))))))	→	2(2(1(4(4(2(4(3(0(2(3(4(3(0(0(2(2(2(0(2(x1))))))))))))))))))))	(12)
0(2(2(3(4(2(3(2(3(0(1(3(1(3(2(2(2(1(1(2(x1))))))))))))))))))))	→	4(0(3(2(4(0(1(1(0(2(0(3(0(1(2(3(0(1(2(2(x1))))))))))))))))))))	(13)
0(3(1(0(1(1(2(3(3(1(4(3(3(3(2(1(4(0(2(2(x1))))))))))))))))))))	→	0(4(4(1(1(4(2(1(0(1(4(2(2(0(0(1(0(1(2(1(x1))))))))))))))))))))	(14)
0(3(3(4(1(4(2(3(2(3(0(4(2(3(3(2(2(2(2(1(x1))))))))))))))))))))	→	0(4(2(4(4(3(0(0(0(3(3(2(4(4(4(0(0(2(3(2(x1))))))))))))))))))))	(15)
0(3(4(0(2(0(1(2(3(1(0(4(4(3(1(4(1(3(0(2(x1))))))))))))))))))))	→	4(0(4(4(3(3(0(0(3(4(3(4(0(1(4(1(1(4(3(2(x1))))))))))))))))))))	(16)
0(3(4(3(2(0(1(1(0(2(3(3(2(1(3(1(1(2(3(2(x1))))))))))))))))))))	→	1(2(2(4(2(4(1(3(1(3(3(0(3(3(0(0(4(3(2(2(x1))))))))))))))))))))	(17)
0(4(0(2(0(1(2(1(4(3(1(4(3(3(1(0(3(3(1(2(x1))))))))))))))))))))	→	2(1(0(2(2(4(0(1(4(2(3(4(0(1(2(0(2(4(4(2(x1))))))))))))))))))))	(18)
0(4(2(0(0(4(2(3(2(3(4(3(4(4(3(3(2(0(2(2(x1))))))))))))))))))))	→	4(0(4(4(2(2(1(1(4(3(4(2(0(2(3(1(2(0(1(2(x1))))))))))))))))))))	(19)
0(4(3(2(4(4(3(4(1(3(3(2(3(1(0(1(2(1(2(2(x1))))))))))))))))))))	→	1(1(4(0(4(1(1(0(0(1(2(4(0(3(2(4(2(0(3(2(x1))))))))))))))))))))	(20)
0(4(4(0(4(3(0(2(1(2(3(2(2(0(2(0(0(2(2(1(x1))))))))))))))))))))	→	0(2(1(4(0(2(2(2(1(1(4(2(4(0(3(1(2(0(1(2(x1))))))))))))))))))))	(21)
1(0(2(1(3(2(3(1(3(3(4(1(3(2(2(0(1(2(3(2(x1))))))))))))))))))))	→	3(3(4(0(4(0(1(0(4(0(1(1(4(4(1(3(3(2(0(2(x1))))))))))))))))))))	(22)
1(0(3(0(0(0(2(3(3(0(4(4(4(0(3(1(1(1(2(1(x1))))))))))))))))))))	→	0(3(2(2(4(3(3(1(0(0(3(3(1(0(3(3(4(4(2(2(x1))))))))))))))))))))	(23)
1(0(3(4(4(4(4(4(1(3(0(1(2(0(2(0(1(1(3(2(x1))))))))))))))))))))	→	0(1(3(2(1(3(4(1(4(2(4(0(2(4(2(3(0(0(2(1(x1))))))))))))))))))))	(24)
1(0(4(1(4(1(2(2(0(0(0(4(0(1(1(2(3(3(3(2(x1))))))))))))))))))))	→	2(2(2(2(4(0(2(3(1(0(2(2(1(4(0(4(1(1(1(2(x1))))))))))))))))))))	(25)
1(1(0(3(4(3(2(3(2(3(4(3(2(1(4(4(2(3(0(2(x1))))))))))))))))))))	→	0(3(0(3(4(0(0(1(0(2(1(2(4(0(3(0(3(0(2(2(x1))))))))))))))))))))	(26)
1(1(2(3(0(3(4(2(1(2(4(0(3(2(3(4(4(4(3(2(x1))))))))))))))))))))	→	3(4(2(1(1(1(4(4(0(0(0(3(0(4(1(4(3(2(4(2(x1))))))))))))))))))))	(27)
1(1(3(4(0(1(4(2(0(3(4(4(0(0(3(0(1(2(3(2(x1))))))))))))))))))))	→	3(0(4(1(1(4(0(4(1(2(1(4(2(0(4(4(3(3(2(2(x1))))))))))))))))))))	(28)
1(2(0(4(1(4(3(0(0(0(3(2(4(4(1(3(0(2(3(2(x1))))))))))))))))))))	→	1(3(2(2(0(3(2(0(0(2(4(0(1(4(2(0(2(0(1(2(x1))))))))))))))))))))	(29)
1(2(2(1(0(3(2(4(4(1(4(0(0(0(3(1(3(3(2(1(x1))))))))))))))))))))	→	1(4(0(0(3(1(2(0(0(3(0(1(4(4(3(2(4(2(1(1(x1))))))))))))))))))))	(30)
1(2(3(4(2(4(2(3(2(0(2(1(0(2(2(0(4(2(0(2(x1))))))))))))))))))))	→	1(1(1(4(0(4(4(0(0(0(2(1(3(4(0(2(4(0(0(2(x1))))))))))))))))))))	(31)
1(2(4(4(4(3(1(0(0(2(0(0(4(0(4(4(3(1(0(2(x1))))))))))))))))))))	→	1(2(4(3(0(1(1(0(0(2(0(1(1(3(2(1(4(1(0(2(x1))))))))))))))))))))	(32)
1(3(0(1(3(2(0(4(0(2(0(4(2(0(4(0(2(4(0(2(x1))))))))))))))))))))	→	4(3(0(3(2(2(1(3(4(0(1(0(1(2(0(1(1(4(4(2(x1))))))))))))))))))))	(33)
1(3(3(1(0(0(1(1(3(2(3(0(0(0(1(1(1(1(0(2(x1))))))))))))))))))))	→	1(3(0(4(1(1(4(3(4(2(4(4(3(3(3(2(0(2(2(1(x1))))))))))))))))))))	(34)
1(4(0(2(3(0(0(4(4(1(0(0(1(0(2(2(1(1(3(2(x1))))))))))))))))))))	→	4(2(4(1(4(0(3(0(4(3(0(3(3(1(3(0(2(1(2(1(x1))))))))))))))))))))	(35)
1(4(1(3(1(1(0(0(0(0(4(3(0(0(2(0(2(1(1(1(x1))))))))))))))))))))	→	2(1(4(2(0(0(3(3(4(3(0(2(4(1(0(2(4(4(2(1(x1))))))))))))))))))))	(36)
2(0(0(1(2(3(2(3(0(1(2(4(2(2(1(0(0(3(2(1(x1))))))))))))))))))))	→	2(4(0(1(1(2(3(0(0(4(3(0(1(0(4(2(4(3(4(2(x1))))))))))))))))))))	(37)
2(0(1(1(0(0(4(2(3(1(0(2(3(0(3(4(0(3(3(2(x1))))))))))))))))))))	→	3(4(1(3(2(0(3(0(4(1(2(4(0(4(4(1(3(2(0(2(x1))))))))))))))))))))	(38)
2(0(1(2(0(1(0(1(0(4(3(1(4(4(4(0(2(3(3(2(x1))))))))))))))))))))	→	4(1(0(0(1(3(2(0(2(4(1(0(4(0(2(0(3(0(2(2(x1))))))))))))))))))))	(39)
2(0(1(2(0(1(3(2(2(0(4(3(2(2(4(3(0(1(2(1(x1))))))))))))))))))))	→	0(2(2(4(1(4(4(3(1(1(2(4(3(1(2(0(1(2(1(2(x1))))))))))))))))))))	(40)
2(0(2(1(3(3(4(0(1(1(2(0(3(1(3(0(1(2(1(2(x1))))))))))))))))))))	→	2(2(2(0(1(1(4(3(2(0(2(3(3(3(1(1(2(2(4(2(x1))))))))))))))))))))	(41)
2(0(4(3(4(0(2(1(3(2(0(3(2(0(1(0(4(4(2(2(x1))))))))))))))))))))	→	4(0(3(2(4(0(1(1(2(4(0(4(4(0(4(2(3(2(2(2(x1))))))))))))))))))))	(42)
2(0(4(4(0(3(3(2(4(0(1(4(2(4(4(4(2(2(2(2(x1))))))))))))))))))))	→	0(2(2(0(1(0(4(3(0(2(4(2(2(4(3(3(1(3(1(2(x1))))))))))))))))))))	(43)
2(0(4(4(2(1(3(3(3(2(0(0(2(3(3(1(4(2(3(2(x1))))))))))))))))))))	→	0(0(2(1(2(1(2(0(2(4(1(4(1(3(0(1(2(0(3(2(x1))))))))))))))))))))	(44)
2(1(0(1(0(4(2(1(1(1(3(0(4(2(2(0(2(3(2(2(x1))))))))))))))))))))	→	3(2(0(3(1(3(1(2(1(2(1(1(1(3(1(1(4(1(3(2(x1))))))))))))))))))))	(45)
2(1(0(3(1(4(4(0(4(3(0(4(3(3(4(1(2(3(4(2(x1))))))))))))))))))))	→	1(4(1(4(4(2(2(0(2(3(1(0(1(3(0(0(2(0(2(1(x1))))))))))))))))))))	(46)
2(1(2(0(3(1(4(2(3(0(1(1(4(4(2(0(4(3(2(1(x1))))))))))))))))))))	→	1(2(3(4(0(1(4(3(1(1(1(4(1(4(0(0(2(1(4(2(x1))))))))))))))))))))	(47)
2(1(2(3(3(2(2(1(2(3(3(2(0(4(3(4(1(0(1(2(x1))))))))))))))))))))	→	3(4(1(4(0(2(0(1(2(0(4(4(1(0(2(4(1(1(1(2(x1))))))))))))))))))))	(48)
2(1(2(3(4(4(0(2(3(2(0(3(2(4(4(4(2(4(2(2(x1))))))))))))))))))))	→	1(1(3(3(1(3(3(2(2(1(4(1(2(2(4(1(2(2(3(2(x1))))))))))))))))))))	(49)
2(1(3(4(1(3(3(4(2(0(0(1(0(1(2(0(1(0(4(2(x1))))))))))))))))))))	→	2(1(1(2(1(1(0(1(4(0(1(3(2(1(2(4(0(1(2(2(x1))))))))))))))))))))	(50)
2(2(1(0(1(1(2(0(2(2(0(2(2(1(3(0(4(4(1(2(x1))))))))))))))))))))	→	1(2(1(2(4(0(2(1(2(0(3(1(1(2(2(4(4(3(1(2(x1))))))))))))))))))))	(51)
2(2(1(2(3(3(2(0(3(0(2(0(4(2(4(1(2(3(0(2(x1))))))))))))))))))))	→	0(4(1(0(2(2(1(0(3(3(4(2(1(4(1(2(1(4(1(2(x1))))))))))))))))))))	(52)
2(2(2(1(4(3(0(3(2(4(0(4(0(4(1(0(4(2(2(1(x1))))))))))))))))))))	→	1(1(4(2(4(4(2(1(2(0(3(2(1(4(3(1(3(2(4(2(x1))))))))))))))))))))	(53)
2(3(2(0(0(1(0(3(3(1(4(1(3(0(0(3(2(3(4(2(x1))))))))))))))))))))	→	1(2(4(4(0(1(1(4(4(4(2(2(4(4(3(2(0(3(4(2(x1))))))))))))))))))))	(54)
2(3(4(2(2(3(3(4(3(2(0(2(1(0(2(1(4(1(3(2(x1))))))))))))))))))))	→	1(4(0(4(1(3(1(1(1(1(3(0(1(0(4(1(4(2(1(1(x1))))))))))))))))))))	(55)
2(4(0(3(4(1(1(4(0(2(2(2(3(4(4(3(3(3(0(2(x1))))))))))))))))))))	→	0(1(0(0(1(1(4(3(3(0(4(2(4(1(1(3(2(2(2(2(x1))))))))))))))))))))	(56)
2(4(0(4(3(1(2(1(2(2(3(0(1(0(1(3(1(3(3(2(x1))))))))))))))))))))	→	0(2(4(4(1(4(1(4(2(2(2(4(3(3(3(1(1(0(1(2(x1))))))))))))))))))))	(57)
2(4(2(0(3(2(2(4(4(3(0(1(0(3(2(3(2(2(4(2(x1))))))))))))))))))))	→	3(0(4(0(2(4(1(0(3(2(3(0(0(2(4(2(4(1(0(2(x1))))))))))))))))))))	(58)
2(4(4(0(2(4(2(2(3(1(0(2(0(0(1(1(4(2(2(1(x1))))))))))))))))))))	→	0(2(4(1(4(4(0(2(4(1(1(4(1(3(3(0(3(2(1(2(x1))))))))))))))))))))	(59)
3(0(1(2(3(0(1(2(2(2(0(2(3(3(3(4(3(3(2(1(x1))))))))))))))))))))	→	0(2(3(1(3(1(0(1(2(1(1(1(1(3(3(4(4(0(3(2(x1))))))))))))))))))))	(60)
3(0(2(3(3(2(0(2(0(1(2(4(3(3(1(4(4(0(2(1(x1))))))))))))))))))))	→	2(0(2(1(1(1(3(3(0(4(2(4(3(0(1(1(1(4(1(2(x1))))))))))))))))))))	(61)
3(0(3(0(0(0(2(0(1(2(2(4(0(1(2(0(3(2(2(2(x1))))))))))))))))))))	→	4(4(2(4(4(2(4(1(4(4(2(0(3(2(1(4(4(2(4(2(x1))))))))))))))))))))	(62)
3(0(4(3(2(3(3(2(3(0(1(0(1(0(1(3(1(4(2(1(x1))))))))))))))))))))	→	4(1(3(2(1(4(1(0(1(3(3(1(4(4(0(4(2(1(1(2(x1))))))))))))))))))))	(63)
3(1(0(2(3(2(2(4(3(0(2(0(4(2(1(0(2(1(1(1(x1))))))))))))))))))))	→	1(4(0(1(0(4(1(1(3(4(3(2(4(4(3(2(1(1(2(2(x1))))))))))))))))))))	(64)
3(1(1(1(3(3(0(1(3(4(4(2(2(3(1(3(3(4(1(2(x1))))))))))))))))))))	→	1(4(1(1(2(1(1(3(4(1(4(2(0(0(2(2(3(2(2(2(x1))))))))))))))))))))	(65)
3(1(1(2(0(3(2(0(4(0(0(4(3(4(3(1(1(2(1(1(x1))))))))))))))))))))	→	4(2(0(1(2(4(3(4(4(3(3(3(1(1(3(0(4(3(4(2(x1))))))))))))))))))))	(66)
3(1(1(2(4(3(1(2(3(0(1(1(1(2(2(3(1(1(3(2(x1))))))))))))))))))))	→	4(0(0(1(3(0(1(1(2(4(2(4(3(4(1(4(0(0(0(2(x1))))))))))))))))))))	(67)
3(1(3(2(2(4(1(0(3(1(3(0(2(0(0(0(3(3(2(1(x1))))))))))))))))))))	→	1(3(0(2(1(3(2(1(4(2(2(2(3(4(4(0(2(4(3(2(x1))))))))))))))))))))	(68)
3(2(0(1(4(3(0(2(0(2(2(3(0(1(4(2(1(1(1(2(x1))))))))))))))))))))	→	0(3(1(2(2(2(4(0(3(0(0(3(2(4(4(2(4(3(2(1(x1))))))))))))))))))))	(69)
3(2(0(3(4(3(1(1(3(2(0(3(0(0(0(1(4(2(4(1(x1))))))))))))))))))))	→	3(3(2(0(2(4(3(0(0(3(3(0(1(2(4(1(0(0(2(1(x1))))))))))))))))))))	(70)
3(2(1(0(4(1(2(2(0(3(4(3(2(3(4(1(4(0(1(2(x1))))))))))))))))))))	→	0(2(4(3(3(2(4(3(3(3(1(2(2(3(4(3(4(3(4(2(x1))))))))))))))))))))	(71)
3(2(1(1(1(4(2(4(0(3(1(3(0(2(3(0(4(0(3(2(x1))))))))))))))))))))	→	3(0(3(0(4(3(2(2(1(1(4(4(4(3(0(2(4(2(2(2(x1))))))))))))))))))))	(72)
3(2(3(1(0(1(4(2(4(3(1(0(4(1(4(3(3(1(0(2(x1))))))))))))))))))))	→	0(0(1(2(2(0(4(4(4(1(0(2(4(1(4(4(0(1(1(2(x1))))))))))))))))))))	(73)
3(2(3(3(3(4(1(2(1(2(1(2(1(3(1(1(0(1(4(2(x1))))))))))))))))))))	→	3(0(1(0(0(4(4(4(4(2(4(4(4(3(0(0(2(1(4(2(x1))))))))))))))))))))	(74)
3(2(4(3(2(2(0(2(3(4(0(1(0(4(3(0(3(0(4(2(x1))))))))))))))))))))	→	0(1(2(0(4(2(3(1(4(0(1(1(0(0(1(1(0(1(1(2(x1))))))))))))))))))))	(75)
3(3(0(2(0(0(1(3(0(2(2(2(4(0(3(1(1(0(0(2(x1))))))))))))))))))))	→	4(0(2(1(3(2(4(0(1(4(1(1(0(2(0(0(2(2(4(2(x1))))))))))))))))))))	(76)
3(3(0(4(4(2(4(0(4(0(4(2(0(2(2(2(4(0(3(2(x1))))))))))))))))))))	→	0(1(0(1(1(1(4(4(0(1(3(2(2(4(1(4(3(4(2(2(x1))))))))))))))))))))	(77)
3(3(3(1(3(4(3(0(3(1(3(2(2(4(0(3(4(2(0(2(x1))))))))))))))))))))	→	4(0(4(1(0(2(4(3(4(2(3(2(3(3(3(0(1(0(4(2(x1))))))))))))))))))))	(78)
3(3(3(2(1(1(3(3(4(2(4(3(2(2(0(3(0(4(2(2(x1))))))))))))))))))))	→	1(3(4(2(4(4(4(3(2(4(4(0(3(3(4(0(4(2(2(1(x1))))))))))))))))))))	(79)
3(3(3(4(1(1(4(2(3(0(3(4(4(1(2(3(4(1(4(2(x1))))))))))))))))))))	→	0(2(4(3(1(2(3(4(1(2(0(1(1(3(3(4(1(0(1(2(x1))))))))))))))))))))	(80)
3(4(0(2(2(1(1(0(3(3(1(3(2(2(2(1(1(2(0(2(x1))))))))))))))))))))	→	3(0(2(3(4(2(0(2(1(4(0(3(3(2(4(1(2(4(1(2(x1))))))))))))))))))))	(81)
3(4(2(2(4(4(0(3(1(4(1(0(4(0(1(0(2(1(0(2(x1))))))))))))))))))))	→	0(2(4(1(2(0(3(0(2(3(4(1(1(4(0(3(3(2(4(2(x1))))))))))))))))))))	(82)
3(4(4(2(1(1(4(3(4(3(0(3(3(3(2(2(0(3(1(2(x1))))))))))))))))))))	→	2(4(0(3(2(3(1(4(3(2(2(2(0(1(0(2(3(2(3(2(x1))))))))))))))))))))	(83)
4(0(1(3(3(2(4(3(3(2(0(0(1(2(3(4(2(3(3(2(x1))))))))))))))))))))	→	2(4(3(0(3(0(1(4(2(1(4(3(2(1(3(2(3(1(2(2(x1))))))))))))))))))))	(84)
4(0(1(4(1(2(1(3(4(2(4(3(3(2(1(1(4(4(2(2(x1))))))))))))))))))))	→	4(2(3(4(2(4(1(1(1(2(0(1(1(4(0(0(1(3(2(1(x1))))))))))))))))))))	(85)
4(1(0(2(0(0(0(2(3(4(0(4(2(0(2(0(3(4(3(2(x1))))))))))))))))))))	→	2(1(1(1(4(2(2(0(0(4(1(2(2(2(0(0(2(4(0(2(x1))))))))))))))))))))	(86)
4(1(1(3(2(3(0(3(3(3(4(2(4(4(4(1(0(2(0(2(x1))))))))))))))))))))	→	4(4(4(4(1(0(0(3(1(4(0(4(4(0(3(0(1(3(2(2(x1))))))))))))))))))))	(87)
4(1(1(4(4(0(1(2(1(0(0(4(4(2(3(3(3(1(3(2(x1))))))))))))))))))))	→	3(1(0(4(2(4(4(1(2(4(3(3(2(2(1(4(3(3(4(2(x1))))))))))))))))))))	(88)
4(1(3(4(3(2(2(1(1(2(3(0(4(1(1(3(4(3(4(2(x1))))))))))))))))))))	→	2(4(2(1(1(4(0(2(3(0(0(4(2(4(4(0(3(3(1(2(x1))))))))))))))))))))	(89)
4(2(1(1(0(1(0(0(2(0(3(2(1(0(0(3(0(1(2(2(x1))))))))))))))))))))	→	0(0(4(1(0(1(4(2(4(1(0(0(0(1(4(1(3(3(2(1(x1))))))))))))))))))))	(90)
4(2(3(0(3(4(1(1(1(1(0(4(1(1(1(3(4(4(2(2(x1))))))))))))))))))))	→	2(0(3(3(2(4(4(2(1(1(4(1(1(0(0(2(4(0(0(2(x1))))))))))))))))))))	(91)
4(3(0(3(2(3(0(4(3(1(3(4(2(0(3(4(3(2(2(1(x1))))))))))))))))))))	→	0(3(4(3(3(2(4(1(0(0(1(0(0(2(0(3(2(0(2(2(x1))))))))))))))))))))	(92)
4(3(1(0(2(1(0(4(4(0(3(1(0(0(3(0(4(3(1(2(x1))))))))))))))))))))	→	0(1(3(4(0(2(0(0(3(0(0(3(1(2(4(3(1(1(3(2(x1))))))))))))))))))))	(93)
4(3(1(1(2(2(1(3(1(0(0(1(1(0(4(2(3(3(0(2(x1))))))))))))))))))))	→	0(3(3(1(4(1(1(2(1(2(1(3(1(3(1(4(2(2(4(2(x1))))))))))))))))))))	(94)
4(3(3(0(2(4(1(2(2(3(0(0(2(0(0(1(0(3(1(2(x1))))))))))))))))))))	→	4(0(2(3(1(1(4(3(3(1(1(4(0(2(3(2(2(0(1(2(x1))))))))))))))))))))	(95)
4(3(4(0(2(4(3(2(3(3(1(3(3(4(2(4(0(4(1(2(x1))))))))))))))))))))	→	4(4(3(4(1(0(4(4(3(0(2(1(4(2(1(1(4(4(1(2(x1))))))))))))))))))))	(96)
4(4(2(4(0(0(2(3(4(3(3(1(4(2(2(3(1(0(2(1(x1))))))))))))))))))))	→	4(4(1(4(4(4(1(1(4(0(2(3(2(3(1(2(2(1(2(1(x1))))))))))))))))))))	(97)
4(4(3(1(1(3(4(3(2(3(1(1(0(0(0(0(0(0(2(1(x1))))))))))))))))))))	→	0(4(0(1(3(0(2(4(3(1(2(2(3(2(0(0(4(4(1(2(x1))))))))))))))))))))	(98)
4(4(3(3(4(0(1(0(1(4(0(0(2(3(3(4(0(0(2(1(x1))))))))))))))))))))	→	1(0(1(2(0(1(1(1(1(2(0(0(1(4(3(2(2(4(3(2(x1))))))))))))))))))))	(99)

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

2(2(3(3(2(3(2(1(4(3(3(2(2(1(0(1(0(0(0(0(x1))))))))))))))))))))	→	2(0(1(3(2(4(1(1(0(0(4(2(4(0(1(2(0(1(3(0(x1))))))))))))))))))))	(100)
2(4(4(2(1(1(4(1(0(1(2(1(0(1(4(0(1(1(1(0(x1))))))))))))))))))))	→	2(0(4(1(1(3(2(2(2(4(1(0(1(4(0(4(2(1(4(4(x1))))))))))))))))))))	(101)
1(2(1(1(4(0(2(0(4(4(3(0(4(4(2(1(1(1(1(0(x1))))))))))))))))))))	→	2(1(0(1(0(1(3(0(2(0(0(4(3(3(4(2(3(4(1(3(x1))))))))))))))))))))	(102)
2(1(0(3(4(0(2(3(2(2(0(3(0(2(0(4(0(2(1(0(x1))))))))))))))))))))	→	1(2(4(2(3(2(2(2(1(4(0(2(2(0(0(1(2(0(3(1(x1))))))))))))))))))))	(103)
2(0(3(2(4(3(1(1(1(1(2(3(1(1(3(0(2(2(1(0(x1))))))))))))))))))))	→	2(3(4(1(2(4(1(3(2(0(1(4(2(3(2(3(3(4(2(4(x1))))))))))))))))))))	(104)
2(2(4(0(1(3(2(1(1(4(3(4(2(3(2(1(1(3(1(0(x1))))))))))))))))))))	→	2(4(2(2(4(1(4(0(2(2(0(1(0(2(3(1(1(0(2(2(x1))))))))))))))))))))	(105)
2(1(2(0(1(2(3(3(2(3(3(0(0(0(1(3(2(3(1(0(x1))))))))))))))))))))	→	1(2(0(2(3(1(4(3(1(2(4(0(4(2(2(0(4(3(0(0(x1))))))))))))))))))))	(106)
2(0(0(1(3(4(4(4(0(0(2(1(1(0(3(3(3(3(1(0(x1))))))))))))))))))))	→	2(3(0(4(3(4(3(0(0(1(0(2(4(3(2(0(4(2(0(2(x1))))))))))))))))))))	(107)
2(3(2(2(2(3(3(4(4(2(2(1(3(0(4(0(0(0(2(0(x1))))))))))))))))))))	→	1(2(1(3(2(3(1(4(0(4(3(1(3(2(0(4(2(2(1(3(x1))))))))))))))))))))	(108)
1(2(2(1(3(4(4(3(0(0(2(2(0(1(1(2(1(0(2(0(x1))))))))))))))))))))	→	2(0(2(4(2(0(2(0(3(0(3(3(2(4(1(0(2(2(0(3(x1))))))))))))))))))))	(109)
2(3(3(4(0(1(2(0(0(2(0(2(2(3(1(2(2(0(2(0(x1))))))))))))))))))))	→	2(4(0(0(4(2(4(2(1(3(0(0(3(2(4(0(0(3(3(0(x1))))))))))))))))))))	(110)
1(1(2(1(4(0(0(3(3(3(4(0(4(4(3(3(1(1(2(0(x1))))))))))))))))))))	→	2(0(2(2(2(0(0(3(4(3(2(0(3(4(2(4(4(1(2(2(x1))))))))))))))))))))	(111)
2(1(1(2(2(2(3(1(3(1(0(3(2(3(2(4(3(2(2(0(x1))))))))))))))))))))	→	2(2(1(0(3(2(1(0(3(0(2(0(1(1(0(4(2(3(0(4(x1))))))))))))))))))))	(112)
2(2(0(4(1(2(3(3(3(4(1(3(3(2(1(1(0(1(3(0(x1))))))))))))))))))))	→	1(2(1(0(1(0(0(2(2(4(1(0(1(2(4(1(1(4(4(0(x1))))))))))))))))))))	(113)
1(2(2(2(2(3(3(2(4(0(3(2(3(2(4(1(4(3(3(0(x1))))))))))))))))))))	→	2(3(2(0(0(4(4(4(2(3(3(0(0(0(3(4(4(2(4(0(x1))))))))))))))))))))	(114)
2(0(3(1(4(1(3(4(4(0(1(3(2(1(0(2(0(4(3(0(x1))))))))))))))))))))	→	2(3(4(1(1(4(1(0(4(3(4(3(0(0(3(3(4(4(0(4(x1))))))))))))))))))))	(115)
2(3(2(1(1(3(1(2(3(3(2(0(1(1(0(2(3(4(3(0(x1))))))))))))))))))))	→	2(2(3(4(0(0(3(3(0(3(3(1(3(1(4(2(4(2(2(1(x1))))))))))))))))))))	(116)
2(1(3(3(0(1(3(3(4(1(3(4(1(2(1(0(2(0(4(0(x1))))))))))))))))))))	→	2(4(4(2(0(2(1(0(4(3(2(4(1(0(4(2(2(0(1(2(x1))))))))))))))))))))	(117)
2(2(0(2(3(3(4(4(3(4(3(2(3(2(4(0(0(2(4(0(x1))))))))))))))))))))	→	2(1(0(2(1(3(2(0(2(4(3(4(1(1(2(2(4(4(0(4(x1))))))))))))))))))))	(118)
2(2(1(2(1(0(1(3(2(3(3(1(4(3(4(4(2(3(4(0(x1))))))))))))))))))))	→	2(3(0(2(4(2(3(0(4(2(1(0(0(1(1(4(0(4(1(1(x1))))))))))))))))))))	(119)
1(2(2(0(0(2(0(2(2(3(2(1(2(0(3(4(0(4(4(0(x1))))))))))))))))))))	→	2(1(0(2(1(3(0(4(2(4(1(1(2(2(2(0(4(1(2(0(x1))))))))))))))))))))	(120)
2(3(2(1(0(2(2(3(1(4(3(3(1(3(2(3(1(2(0(1(x1))))))))))))))))))))	→	2(0(2(3(3(1(4(4(1(1(0(4(0(1(0(4(0(4(3(3(x1))))))))))))))))))))	(121)
1(2(1(1(1(3(0(4(4(4(0(3(3(2(0(0(0(3(0(1(x1))))))))))))))))))))	→	2(2(4(4(3(3(0(1(3(3(0(0(1(3(3(4(2(2(3(0(x1))))))))))))))))))))	(122)
2(3(1(1(0(2(0(2(1(0(3(1(4(4(4(4(4(3(0(1(x1))))))))))))))))))))	→	1(2(0(0(3(2(4(2(0(4(2(4(1(4(3(1(2(3(1(0(x1))))))))))))))))))))	(123)
2(3(3(3(2(1(1(0(4(0(0(0(2(2(1(4(1(4(0(1(x1))))))))))))))))))))	→	2(1(1(1(4(0(4(1(2(2(0(1(3(2(0(4(2(2(2(2(x1))))))))))))))))))))	(124)
2(0(3(2(4(4(1(2(3(4(3(2(3(2(3(4(3(0(1(1(x1))))))))))))))))))))	→	2(2(0(3(0(3(0(4(2(1(2(0(1(0(0(4(3(0(3(0(x1))))))))))))))))))))	(125)
2(3(4(4(4(3(2(3(0(4(2(1(2(4(3(0(3(2(1(1(x1))))))))))))))))))))	→	2(4(2(3(4(1(4(0(3(0(0(0(4(4(1(1(1(2(4(3(x1))))))))))))))))))))	(126)
2(3(2(1(0(3(0(0(4(4(3(0(2(4(1(0(4(3(1(1(x1))))))))))))))))))))	→	2(2(3(3(4(4(0(2(4(1(2(1(4(0(4(1(1(4(0(3(x1))))))))))))))))))))	(127)
2(3(2(0(3(1(4(4(2(3(0(0(0(3(4(1(4(0(2(1(x1))))))))))))))))))))	→	2(1(0(2(0(2(4(1(0(4(2(0(0(2(3(0(2(2(3(1(x1))))))))))))))))))))	(128)
1(2(3(3(1(3(0(0(0(4(1(4(4(2(3(0(1(2(2(1(x1))))))))))))))))))))	→	1(1(2(4(2(3(4(4(1(0(3(0(0(2(1(3(0(0(4(1(x1))))))))))))))))))))	(129)
2(0(2(4(0(2(2(0(1(2(0(2(3(2(4(2(4(3(2(1(x1))))))))))))))))))))	→	2(0(0(4(2(0(4(3(1(2(0(0(0(4(4(0(4(1(1(1(x1))))))))))))))))))))	(130)
2(0(1(3(4(4(0(4(0(0(2(0(0(1(3(4(4(4(2(1(x1))))))))))))))))))))	→	2(0(1(4(1(2(3(1(1(0(2(0(0(1(1(0(3(4(2(1(x1))))))))))))))))))))	(131)
2(0(4(2(0(4(0(2(4(0(2(0(4(0(2(3(1(0(3(1(x1))))))))))))))))))))	→	2(4(4(1(1(0(2(1(0(1(0(4(3(1(2(2(3(0(3(4(x1))))))))))))))))))))	(132)
2(0(1(1(1(1(0(0(0(3(2(3(1(1(0(0(1(3(3(1(x1))))))))))))))))))))	→	1(2(2(0(2(3(3(3(4(4(2(4(3(4(1(1(4(0(3(1(x1))))))))))))))))))))	(133)
2(3(1(1(2(2(0(1(0(0(1(4(4(0(0(3(2(0(4(1(x1))))))))))))))))))))	→	1(2(1(2(0(3(1(3(3(0(3(4(0(3(0(4(1(4(2(4(x1))))))))))))))))))))	(134)
1(1(1(2(0(2(0(0(3(4(0(0(0(0(1(1(3(1(4(1(x1))))))))))))))))))))	→	1(2(4(4(2(0(1(4(2(0(3(4(3(3(0(0(2(4(1(2(x1))))))))))))))))))))	(135)
1(2(3(0(0(1(2(2(4(2(1(0(3(2(3(2(1(0(0(2(x1))))))))))))))))))))	→	2(4(3(4(2(4(0(1(0(3(4(0(0(3(2(1(1(0(4(2(x1))))))))))))))))))))	(136)
2(3(3(0(4(3(0(3(2(0(1(3(2(4(0(0(1(1(0(2(x1))))))))))))))))))))	→	2(0(2(3(1(4(4(0(4(2(1(4(0(3(0(2(3(1(4(3(x1))))))))))))))))))))	(137)
2(3(3(2(0(4(4(4(1(3(4(0(1(0(1(0(2(1(0(2(x1))))))))))))))))))))	→	2(2(0(3(0(2(0(4(0(1(4(2(0(2(3(1(0(0(1(4(x1))))))))))))))))))))	(138)
1(2(1(0(3(4(2(2(3(4(0(2(2(3(1(0(2(1(0(2(x1))))))))))))))))))))	→	2(1(2(1(0(2(1(3(4(2(1(1(3(4(4(1(4(2(2(0(x1))))))))))))))))))))	(139)
2(1(2(1(0(3(1(3(0(2(1(1(0(4(3(3(1(2(0(2(x1))))))))))))))))))))	→	2(4(2(2(1(1(3(3(3(2(0(2(3(4(1(1(0(2(2(2(x1))))))))))))))))))))	(140)
2(2(4(4(0(1(0(2(3(0(2(3(1(2(0(4(3(4(0(2(x1))))))))))))))))))))	→	2(2(2(3(2(4(0(4(4(0(4(2(1(1(0(4(2(3(0(4(x1))))))))))))))))))))	(141)
2(2(2(2(4(4(4(2(4(1(0(4(2(3(3(0(4(4(0(2(x1))))))))))))))))))))	→	2(1(3(1(3(3(4(2(2(4(2(0(3(4(0(1(0(2(2(0(x1))))))))))))))))))))	(142)
2(3(2(4(1(3(3(2(0(0(2(3(3(3(1(2(4(4(0(2(x1))))))))))))))))))))	→	2(3(0(2(1(0(3(1(4(1(4(2(0(2(1(2(1(2(0(0(x1))))))))))))))))))))	(143)
2(2(3(2(0(2(2(4(0(3(1(1(1(2(4(0(1(0(1(2(x1))))))))))))))))))))	→	2(3(1(4(1(1(3(1(1(1(2(1(2(1(3(1(3(0(2(3(x1))))))))))))))))))))	(144)
2(4(3(2(1(4(3(3(4(0(3(4(0(4(4(1(3(0(1(2(x1))))))))))))))))))))	→	1(2(0(2(0(0(3(1(0(1(3(2(0(2(2(4(4(1(4(1(x1))))))))))))))))))))	(145)
1(2(3(4(0(2(4(4(1(1(0(3(2(4(1(3(0(2(1(2(x1))))))))))))))))))))	→	2(4(1(2(0(0(4(1(4(1(1(1(3(4(1(0(4(3(2(1(x1))))))))))))))))))))	(146)
2(1(0(1(4(3(4(0(2(3(3(2(1(2(2(3(3(2(1(2(x1))))))))))))))))))))	→	2(1(1(1(4(2(0(1(4(4(0(2(1(0(2(0(4(1(4(3(x1))))))))))))))))))))	(147)
2(2(4(2(4(4(4(2(3(0(2(3(2(0(4(4(3(2(1(2(x1))))))))))))))))))))	→	2(3(2(2(1(4(2(2(1(4(1(2(2(3(3(1(3(3(1(1(x1))))))))))))))))))))	(148)
2(4(0(1(0(2(1(0(1(0(0(2(4(3(3(1(4(3(1(2(x1))))))))))))))))))))	→	2(2(1(0(4(2(1(2(3(1(0(4(1(0(1(1(2(1(1(2(x1))))))))))))))))))))	(149)
2(1(4(4(0(3(1(2(2(0(2(2(0(2(1(1(0(1(2(2(x1))))))))))))))))))))	→	2(1(3(4(4(2(2(1(1(3(0(2(1(2(0(4(2(1(2(1(x1))))))))))))))))))))	(150)
2(0(3(2(1(4(2(4(0(2(0(3(0(2(3(3(2(1(2(2(x1))))))))))))))))))))	→	2(1(4(1(2(1(4(1(2(4(3(3(0(1(2(2(0(1(4(0(x1))))))))))))))))))))	(151)
1(2(2(4(0(1(4(0(4(0(4(2(3(0(3(4(1(2(2(2(x1))))))))))))))))))))	→	2(4(2(3(1(3(4(1(2(3(0(2(1(2(4(4(2(4(1(1(x1))))))))))))))))))))	(152)
2(4(3(2(3(0(0(3(1(4(1(3(3(0(1(0(0(2(3(2(x1))))))))))))))))))))	→	2(4(3(0(2(3(4(4(2(2(4(4(4(1(1(0(4(4(2(1(x1))))))))))))))))))))	(153)
2(3(1(4(1(2(0(1(2(0(2(3(4(3(3(2(2(4(3(2(x1))))))))))))))))))))	→	1(1(2(4(1(4(0(1(0(3(1(1(1(1(3(1(4(0(4(1(x1))))))))))))))))))))	(154)
2(0(3(3(3(4(4(3(2(2(2(0(4(1(1(4(3(0(4(2(x1))))))))))))))))))))	→	2(2(2(2(3(1(1(4(2(4(0(3(3(4(1(1(0(0(1(0(x1))))))))))))))))))))	(155)
2(3(3(1(3(1(0(1(0(3(2(2(1(2(1(3(4(0(4(2(x1))))))))))))))))))))	→	2(1(0(1(1(3(3(3(4(2(2(2(4(1(4(1(4(4(2(0(x1))))))))))))))))))))	(156)
2(4(2(2(3(2(3(0(1(0(3(4(4(2(2(3(0(2(4(2(x1))))))))))))))))))))	→	2(0(1(4(2(4(2(0(0(3(2(3(0(1(4(2(0(4(0(3(x1))))))))))))))))))))	(157)
1(2(2(4(1(1(0(0(2(0(1(3(2(2(4(2(0(4(4(2(x1))))))))))))))))))))	→	2(1(2(3(0(3(3(1(4(1(1(4(2(0(4(4(1(4(2(0(x1))))))))))))))))))))	(158)
1(2(3(3(4(3(3(3(2(0(2(2(2(1(0(3(2(1(0(3(x1))))))))))))))))))))	→	2(3(0(4(4(3(3(1(1(1(1(2(1(0(1(3(1(3(2(0(x1))))))))))))))))))))	(159)
1(2(0(4(4(1(3(3(4(2(1(0(2(0(2(3(3(2(0(3(x1))))))))))))))))))))	→	2(1(4(1(1(1(0(3(4(2(4(0(3(3(1(1(1(2(0(2(x1))))))))))))))))))))	(160)
2(2(2(3(0(2(1(0(4(2(2(1(0(2(0(0(0(3(0(3(x1))))))))))))))))))))	→	2(4(2(4(4(1(2(3(0(2(4(4(1(4(2(4(4(2(4(4(x1))))))))))))))))))))	(161)
1(2(4(1(3(1(0(1(0(1(0(3(2(3(3(2(3(4(0(3(x1))))))))))))))))))))	→	2(1(1(2(4(0(4(4(1(3(3(1(0(1(4(1(2(3(1(4(x1))))))))))))))))))))	(162)
1(1(1(2(0(1(2(4(0(2(0(3(4(2(2(3(2(0(1(3(x1))))))))))))))))))))	→	2(2(1(1(2(3(4(4(2(3(4(3(1(1(4(0(1(0(4(1(x1))))))))))))))))))))	(163)
2(1(4(3(3(1(3(2(2(4(4(3(1(0(3(3(1(1(1(3(x1))))))))))))))))))))	→	2(2(2(3(2(2(0(0(2(4(1(4(3(1(1(2(1(1(4(1(x1))))))))))))))))))))	(164)
1(1(2(1(1(3(4(3(4(0(0(4(0(2(3(0(2(1(1(3(x1))))))))))))))))))))	→	2(4(3(4(0(3(1(1(3(3(3(4(4(3(4(2(1(0(2(4(x1))))))))))))))))))))	(165)
2(3(1(1(3(2(2(1(1(1(0(3(2(1(3(4(2(1(1(3(x1))))))))))))))))))))	→	2(0(0(0(4(1(4(3(4(2(4(2(1(1(0(3(1(0(0(4(x1))))))))))))))))))))	(166)
1(2(3(3(0(0(0(2(0(3(1(3(0(1(4(2(2(3(1(3(x1))))))))))))))))))))	→	2(3(4(2(0(4(4(3(2(2(2(4(1(2(3(1(2(0(3(1(x1))))))))))))))))))))	(167)
2(1(1(1(2(4(1(0(3(2(2(0(2(0(3(4(1(0(2(3(x1))))))))))))))))))))	→	1(2(3(4(2(4(4(2(3(0(0(3(0(4(2(2(2(1(3(0(x1))))))))))))))))))))	(168)
1(4(2(4(1(0(0(0(3(0(2(3(1(1(3(4(3(0(2(3(x1))))))))))))))))))))	→	1(2(0(0(1(4(2(1(0(3(3(0(0(3(4(2(0(2(3(3(x1))))))))))))))))))))	(169)
2(1(0(4(1(4(3(2(3(4(3(0(2(2(1(4(0(1(2(3(x1))))))))))))))))))))	→	2(4(3(4(3(4(3(2(2(1(3(3(3(4(2(3(3(4(2(0(x1))))))))))))))))))))	(170)
2(3(0(4(0(3(2(0(3(1(3(0(4(2(4(1(1(1(2(3(x1))))))))))))))))))))	→	2(2(2(4(2(0(3(4(4(4(1(1(2(2(3(4(0(3(0(3(x1))))))))))))))))))))	(171)
2(0(1(3(3(4(1(4(0(1(3(4(2(4(1(0(1(3(2(3(x1))))))))))))))))))))	→	2(1(1(0(4(4(1(4(2(0(1(4(4(4(0(2(2(1(0(0(x1))))))))))))))))))))	(172)
2(4(1(0(1(1(3(1(2(1(2(1(2(1(4(3(3(3(2(3(x1))))))))))))))))))))	→	2(4(1(2(0(0(3(4(4(4(2(4(4(4(4(0(0(1(0(3(x1))))))))))))))))))))	(173)
2(4(0(3(0(3(4(0(1(0(4(3(2(0(2(2(3(4(2(3(x1))))))))))))))))))))	→	2(1(1(0(1(1(0(0(1(1(0(4(1(3(2(4(0(2(1(0(x1))))))))))))))))))))	(174)
2(0(0(1(1(3(0(4(2(2(2(0(3(1(0(0(2(0(3(3(x1))))))))))))))))))))	→	2(4(2(2(0(0(2(0(1(1(4(1(0(4(2(3(1(2(0(4(x1))))))))))))))))))))	(175)
2(3(0(4(2(2(2(0(2(4(0(4(0(4(2(4(4(0(3(3(x1))))))))))))))))))))	→	2(2(4(3(4(1(4(2(2(3(1(0(4(4(1(1(1(0(1(0(x1))))))))))))))))))))	(176)
2(0(2(4(3(0(4(2(2(3(1(3(0(3(4(3(1(3(3(3(x1))))))))))))))))))))	→	2(4(0(1(0(3(3(3(2(3(2(4(3(4(2(0(1(4(0(4(x1))))))))))))))))))))	(177)
2(2(4(0(3(0(2(2(3(4(2(4(3(3(1(1(2(3(3(3(x1))))))))))))))))))))	→	1(2(2(4(0(4(3(3(0(4(4(2(3(4(4(4(2(4(3(1(x1))))))))))))))))))))	(178)
2(4(1(4(3(2(1(4(4(3(0(3(2(4(1(1(4(3(3(3(x1))))))))))))))))))))	→	2(1(0(1(4(3(3(1(1(0(2(1(4(3(2(1(3(4(2(0(x1))))))))))))))))))))	(179)
2(0(2(1(1(2(2(2(3(1(3(3(0(1(1(2(2(0(4(3(x1))))))))))))))))))))	→	2(1(4(2(1(4(2(3(3(0(4(1(2(0(2(4(3(2(0(3(x1))))))))))))))))))))	(180)
2(0(1(2(0(1(0(4(0(1(4(1(3(0(4(4(2(2(4(3(x1))))))))))))))))))))	→	2(4(2(3(3(0(4(1(1(4(3(2(0(3(0(2(1(4(2(0(x1))))))))))))))))))))	(181)
2(1(3(0(2(2(3(3(3(0(3(4(3(4(1(1(2(4(4(3(x1))))))))))))))))))))	→	2(3(2(3(2(0(1(0(2(2(2(3(4(1(3(2(3(0(4(2(x1))))))))))))))))))))	(182)
2(3(3(2(4(3(2(1(0(0(2(3(3(4(2(3(3(1(0(4(x1))))))))))))))))))))	→	2(2(1(3(2(3(1(2(3(4(1(2(4(1(0(3(0(3(4(2(x1))))))))))))))))))))	(183)
2(2(4(4(1(1(2(3(3(4(2(4(3(1(2(1(4(1(0(4(x1))))))))))))))))))))	→	1(2(3(1(0(0(4(1(1(0(2(1(1(1(4(2(4(3(2(4(x1))))))))))))))))))))	(184)
2(3(4(3(0(2(0(2(4(0(4(3(2(0(0(0(2(0(1(4(x1))))))))))))))))))))	→	2(0(4(2(0(0(2(2(2(1(4(0(0(2(2(4(1(1(1(2(x1))))))))))))))))))))	(185)
2(0(2(0(1(4(4(4(2(4(3(3(3(0(3(2(3(1(1(4(x1))))))))))))))))))))	→	2(2(3(1(0(3(0(4(4(0(4(1(3(0(0(1(4(4(4(4(x1))))))))))))))))))))	(186)
2(3(1(3(3(3(2(4(4(0(0(1(2(1(0(4(4(1(1(4(x1))))))))))))))))))))	→	2(4(3(3(4(1(2(2(3(3(4(2(1(4(4(2(4(0(1(3(x1))))))))))))))))))))	(187)
2(4(3(4(3(1(1(4(0(3(2(1(1(2(2(3(4(3(1(4(x1))))))))))))))))))))	→	2(1(3(3(0(4(4(2(4(0(0(3(2(0(4(1(1(2(4(2(x1))))))))))))))))))))	(188)
2(2(1(0(3(0(0(1(2(3(0(2(0(0(1(0(1(1(2(4(x1))))))))))))))))))))	→	1(2(3(3(1(4(1(0(0(0(1(4(2(4(1(0(1(4(0(0(x1))))))))))))))))))))	(189)
2(2(4(4(3(1(1(1(4(0(1(1(1(1(4(3(0(3(2(4(x1))))))))))))))))))))	→	2(0(0(4(2(0(0(1(1(4(1(1(2(4(4(2(3(3(0(2(x1))))))))))))))))))))	(190)
1(2(2(3(4(3(0(2(4(3(1(3(4(0(3(2(3(0(3(4(x1))))))))))))))))))))	→	2(2(0(2(3(0(2(0(0(1(0(0(1(4(2(3(3(4(3(0(x1))))))))))))))))))))	(191)
2(1(3(4(0(3(0(0(1(3(0(4(4(0(1(2(0(1(3(4(x1))))))))))))))))))))	→	2(3(1(1(3(4(2(1(3(0(0(3(0(0(2(0(4(3(1(0(x1))))))))))))))))))))	(192)
2(0(3(3(2(4(0(1(1(0(0(1(3(1(2(2(1(1(3(4(x1))))))))))))))))))))	→	2(4(2(2(4(1(3(1(3(1(2(1(2(1(1(4(1(3(3(0(x1))))))))))))))))))))	(193)
2(1(3(0(1(0(0(2(0(0(3(2(2(1(4(2(0(3(3(4(x1))))))))))))))))))))	→	2(1(0(2(2(3(2(0(4(1(1(3(3(4(1(1(3(2(0(4(x1))))))))))))))))))))	(194)
2(1(4(0(4(2(4(3(3(1(3(3(2(3(4(2(0(4(3(4(x1))))))))))))))))))))	→	2(1(4(4(1(1(2(4(1(2(0(3(4(4(0(1(4(3(4(4(x1))))))))))))))))))))	(195)
1(2(0(1(3(2(2(4(1(3(3(4(3(2(0(0(4(2(4(4(x1))))))))))))))))))))	→	1(2(1(2(2(1(3(2(3(2(0(4(1(1(4(4(4(1(4(4(x1))))))))))))))))))))	(196)
1(2(0(0(0(0(0(0(1(1(3(2(3(4(3(1(1(3(4(4(x1))))))))))))))))))))	→	2(1(4(4(0(0(2(3(2(2(1(3(4(2(0(3(1(0(4(0(x1))))))))))))))))))))	(197)
1(2(0(0(4(3(3(2(0(0(4(1(0(1(0(4(3(3(4(4(x1))))))))))))))))))))	→	2(3(4(2(2(3(4(1(0(0(2(1(1(1(1(0(2(1(0(1(x1))))))))))))))))))))	(198)

1.1 Dependency Pair Transformation

The following set of initial dependency pairs has been identified.

There are 883 ruless (increase limit for explicit display).

1.1.1 Dependency Graph Processor

The dependency pairs are split into 1 component.

The 1^st component contains the pair

2^#(4(4(2(1(1(4(1(0(1(2(1(0(1(4(0(1(1(1(0(x1))))))))))))))))))))	→	2^#(1(4(4(x1))))	(216)
2^#(1(4(4(0(3(1(2(2(0(2(2(0(2(1(1(0(1(2(2(x1))))))))))))))))))))	→	2^#(1(2(1(x1))))	(647)
2^#(1(2(1(0(3(1(3(0(2(1(1(0(4(3(3(1(2(0(2(x1))))))))))))))))))))	→	2^#(2(2(x1)))	(540)
2^#(2(2(2(4(4(4(2(4(1(0(4(2(3(3(0(4(4(0(2(x1))))))))))))))))))))	→	2^#(0(x1))	(558)
2^#(0(3(2(4(3(1(1(1(1(2(3(1(1(3(0(2(2(1(0(x1))))))))))))))))))))	→	2^#(0(1(4(2(3(2(3(3(4(2(4(x1))))))))))))	(241)
2^#(0(2(4(0(2(2(0(1(2(0(2(3(2(4(2(4(3(2(1(x1))))))))))))))))))))	→	1^#(1(1(x1)))	(456)
1^#(1(1(2(0(2(0(0(3(4(0(0(0(0(1(1(3(1(4(1(x1))))))))))))))))))))	→	1^#(2(x1))	(496)
1^#(2(2(1(3(4(4(3(0(0(2(2(0(1(1(2(1(0(2(0(x1))))))))))))))))))))	→	2^#(0(3(x1)))	(289)
2^#(0(3(2(4(3(1(1(1(1(2(3(1(1(3(0(2(2(1(0(x1))))))))))))))))))))	→	2^#(4(x1))	(245)
2^#(4(3(2(1(4(3(3(4(0(3(4(0(4(4(1(3(0(1(2(x1))))))))))))))))))))	→	2^#(0(2(2(4(4(1(4(1(x1)))))))))	(588)
2^#(0(2(4(0(2(2(0(1(2(0(2(3(2(4(2(4(3(2(1(x1))))))))))))))))))))	→	1^#(1(x1))	(457)
1^#(1(2(1(4(0(0(3(3(3(4(0(4(4(3(3(1(1(2(0(x1))))))))))))))))))))	→	1^#(2(2(x1)))	(301)
1^#(2(2(2(2(3(3(2(4(0(3(2(3(2(4(1(4(3(3(0(x1))))))))))))))))))))	→	2^#(4(0(x1)))	(327)
2^#(4(0(1(0(2(1(0(1(0(0(2(4(3(3(1(4(3(1(2(x1))))))))))))))))))))	→	1^#(1(2(x1)))	(637)
1^#(1(2(1(4(0(0(3(3(3(4(0(4(4(3(3(1(1(2(0(x1))))))))))))))))))))	→	2^#(2(x1))	(302)
2^#(2(4(0(1(3(2(1(1(4(3(4(2(3(2(1(1(3(1(0(x1))))))))))))))))))))	→	2^#(2(x1))	(256)
2^#(2(4(0(1(3(2(1(1(4(3(4(2(3(2(1(1(3(1(0(x1))))))))))))))))))))	→	2^#(x1)	(257)
2^#(1(0(3(4(0(2(3(2(2(0(3(0(2(0(4(0(2(1(0(x1))))))))))))))))))))	→	1^#(x1)	(236)
1^#(1(2(1(4(0(0(3(3(3(4(0(4(4(3(3(1(1(2(0(x1))))))))))))))))))))	→	2^#(x1)	(303)
2^#(0(0(1(3(4(4(4(0(0(2(1(1(0(3(3(3(3(1(0(x1))))))))))))))))))))	→	2^#(0(2(x1)))	(270)
2^#(0(2(1(1(2(2(2(3(1(3(3(0(1(1(2(2(0(4(3(x1))))))))))))))))))))	→	2^#(0(2(4(3(2(0(3(x1))))))))	(915)
2^#(0(2(1(1(2(2(2(3(1(3(3(0(1(1(2(2(0(4(3(x1))))))))))))))))))))	→	2^#(0(3(x1)))	(917)
2^#(0(0(1(3(4(4(4(0(0(2(1(1(0(3(3(3(3(1(0(x1))))))))))))))))))))	→	2^#(x1)	(271)
2^#(3(2(2(2(3(3(4(4(2(2(1(3(0(4(0(0(0(2(0(x1))))))))))))))))))))	→	2^#(1(3(x1)))	(280)
2^#(1(3(3(0(1(3(3(4(1(3(4(1(2(1(0(2(0(4(0(x1))))))))))))))))))))	→	2^#(0(1(2(x1))))	(347)
2^#(0(1(2(0(1(0(4(0(1(4(1(3(0(4(4(2(2(4(3(x1))))))))))))))))))))	→	2^#(0(x1))	(925)
2^#(0(0(1(1(3(0(4(2(2(2(0(3(1(0(0(2(0(3(3(x1))))))))))))))))))))	→	1^#(2(0(4(x1))))	(875)
1^#(2(0(4(4(1(3(3(4(2(1(0(2(0(2(3(3(2(0(3(x1))))))))))))))))))))	→	1^#(1(1(2(0(2(x1))))))	(744)
1^#(1(1(2(0(2(0(0(3(4(0(0(0(0(1(1(3(1(4(1(x1))))))))))))))))))))	→	2^#(x1)	(497)
2^#(3(2(1(1(3(1(2(3(3(2(0(1(1(0(2(3(4(3(0(x1))))))))))))))))))))	→	2^#(2(1(x1)))	(337)
2^#(2(1(2(1(0(1(3(2(3(3(1(4(3(4(4(2(3(4(0(x1))))))))))))))))))))	→	1^#(1(x1))	(367)
1^#(1(1(2(0(1(2(4(0(2(0(3(4(2(2(3(2(0(1(3(x1))))))))))))))))))))	→	1^#(x1)	(776)
1^#(2(2(0(0(2(0(2(2(3(2(1(2(0(3(4(0(4(4(0(x1))))))))))))))))))))	→	1^#(2(0(x1)))	(379)
1^#(2(0(4(4(1(3(3(4(2(1(0(2(0(2(3(3(2(0(3(x1))))))))))))))))))))	→	2^#(0(2(x1)))	(747)
1^#(2(0(4(4(1(3(3(4(2(1(0(2(0(2(3(3(2(0(3(x1))))))))))))))))))))	→	2^#(x1)	(748)
2^#(3(2(1(1(3(1(2(3(3(2(0(1(1(0(2(3(4(3(0(x1))))))))))))))))))))	→	2^#(1(x1))	(338)
2^#(1(3(3(0(1(3(3(4(1(3(4(1(2(1(0(2(0(4(0(x1))))))))))))))))))))	→	1^#(2(x1))	(348)
1^#(2(2(0(0(2(0(2(2(3(2(1(2(0(3(4(0(4(4(0(x1))))))))))))))))))))	→	2^#(0(x1))	(380)
1^#(2(1(0(3(4(2(2(3(4(0(2(2(3(1(0(2(1(0(2(x1))))))))))))))))))))	→	2^#(0(x1))	(530)
1^#(2(3(4(0(2(4(4(1(1(0(3(2(4(1(3(0(2(1(2(x1))))))))))))))))))))	→	2^#(1(x1))	(601)
2^#(1(3(3(0(1(3(3(4(1(3(4(1(2(1(0(2(0(4(0(x1))))))))))))))))))))	→	2^#(x1)	(349)
2^#(3(2(1(1(3(1(2(3(3(2(0(1(1(0(2(3(4(3(0(x1))))))))))))))))))))	→	1^#(x1)	(339)
1^#(2(3(4(0(2(4(4(1(1(0(3(2(4(1(3(0(2(1(2(x1))))))))))))))))))))	→	1^#(x1)	(602)
1^#(2(2(4(0(1(4(0(4(0(4(2(3(0(3(4(1(2(2(2(x1))))))))))))))))))))	→	1^#(1(x1))	(671)
1^#(1(2(1(1(3(4(3(4(0(0(4(0(2(3(0(2(1(1(3(x1))))))))))))))))))))	→	2^#(4(x1))	(795)
2^#(4(3(2(1(4(3(3(4(0(3(4(0(4(4(1(3(0(1(2(x1))))))))))))))))))))	→	1^#(x1)	(592)
1^#(2(2(4(0(1(4(0(4(0(4(2(3(0(3(4(1(2(2(2(x1))))))))))))))))))))	→	1^#(x1)	(672)
1^#(2(2(4(1(1(0(0(2(0(1(3(2(2(4(2(0(4(4(2(x1))))))))))))))))))))	→	2^#(0(x1))	(727)
1^#(2(3(3(4(3(3(3(2(0(2(2(2(1(0(3(2(1(0(3(x1))))))))))))))))))))	→	2^#(0(x1))	(737)
1^#(2(4(1(3(1(0(1(0(1(0(3(2(3(3(2(3(4(0(3(x1))))))))))))))))))))	→	2^#(3(1(4(x1))))	(765)
2^#(3(1(4(1(2(0(1(2(0(2(3(4(3(3(2(2(4(3(2(x1))))))))))))))))))))	→	1^#(x1)	(691)
1^#(2(4(1(3(1(0(1(0(1(0(3(2(3(3(2(3(4(0(3(x1))))))))))))))))))))	→	1^#(4(x1))	(766)
1^#(4(2(4(1(0(0(0(3(0(2(3(1(1(3(4(3(0(2(3(x1))))))))))))))))))))	→	2^#(0(2(3(3(x1)))))	(826)
1^#(4(2(4(1(0(0(0(3(0(2(3(1(1(3(4(3(0(2(3(x1))))))))))))))))))))	→	2^#(3(3(x1)))	(827)
2^#(3(3(3(2(1(1(0(4(0(0(0(2(2(1(4(1(4(0(1(x1))))))))))))))))))))	→	2^#(2(2(2(x1))))	(411)
2^#(3(3(3(2(1(1(0(4(0(0(0(2(2(1(4(1(4(0(1(x1))))))))))))))))))))	→	2^#(2(2(x1)))	(412)
2^#(2(2(3(0(2(1(0(4(2(2(1(0(2(0(0(0(3(0(3(x1))))))))))))))))))))	→	2^#(4(4(x1)))	(756)
2^#(3(3(3(2(1(1(0(4(0(0(0(2(2(1(4(1(4(0(1(x1))))))))))))))))))))	→	2^#(2(x1))	(413)
2^#(2(1(2(1(0(1(3(2(3(3(1(4(3(4(4(2(3(4(0(x1))))))))))))))))))))	→	1^#(x1)	(368)
1^#(2(3(3(0(0(0(2(0(3(1(3(0(1(4(2(2(3(1(3(x1))))))))))))))))))))	→	1^#(x1)	(812)
1^#(2(0(0(4(3(3(2(0(0(4(1(0(1(0(4(3(3(4(4(x1))))))))))))))))))))	→	1^#(x1)	(1081)
2^#(2(3(2(0(2(2(4(0(3(1(1(1(2(4(0(1(0(1(2(x1))))))))))))))))))))	→	2^#(3(x1))	(582)
2^#(3(3(3(2(1(1(0(4(0(0(0(2(2(1(4(1(4(0(1(x1))))))))))))))))))))	→	2^#(x1)	(414)
2^#(3(4(4(4(3(2(3(0(4(2(1(2(4(3(0(3(2(1(1(x1))))))))))))))))))))	→	2^#(4(3(x1)))	(427)
2^#(4(3(2(3(0(0(3(1(4(1(3(3(0(1(0(0(2(3(2(x1))))))))))))))))))))	→	2^#(1(x1))	(679)
2^#(1(2(1(0(3(1(3(0(2(1(1(0(4(3(3(1(2(0(2(x1))))))))))))))))))))	→	2^#(2(x1))	(541)
2^#(2(4(2(4(4(4(2(3(0(2(3(2(0(4(4(3(2(1(2(x1))))))))))))))))))))	→	1^#(1(x1))	(624)
2^#(2(4(2(4(4(4(2(3(0(2(3(2(0(4(4(3(2(1(2(x1))))))))))))))))))))	→	1^#(x1)	(625)
2^#(2(4(0(3(0(2(2(3(4(2(4(3(3(1(1(2(3(3(3(x1))))))))))))))))))))	→	1^#(x1)	(898)
2^#(2(4(4(1(1(2(3(3(4(2(4(3(1(2(1(4(1(0(4(x1))))))))))))))))))))	→	2^#(4(x1))	(956)
2^#(4(3(2(3(0(0(3(1(4(1(3(3(0(1(0(0(2(3(2(x1))))))))))))))))))))	→	1^#(x1)	(680)
2^#(4(0(3(0(3(4(0(1(0(4(3(2(0(2(2(3(4(2(3(x1))))))))))))))))))))	→	2^#(1(0(x1)))	(865)
2^#(1(0(4(1(4(3(2(3(4(3(0(2(2(1(4(0(1(2(3(x1))))))))))))))))))))	→	2^#(0(x1))	(833)
2^#(4(1(4(3(2(1(4(4(3(0(3(2(4(1(1(4(3(3(3(x1))))))))))))))))))))	→	2^#(0(x1))	(908)
2^#(4(3(4(3(1(1(4(0(3(2(1(1(2(2(3(4(3(1(4(x1))))))))))))))))))))	→	2^#(x1)	(989)
2^#(3(2(0(3(1(4(4(2(3(0(0(0(3(4(1(4(0(2(1(x1))))))))))))))))))))	→	2^#(3(1(x1)))	(444)
2^#(3(1(1(2(2(0(1(0(0(1(4(4(0(0(3(2(0(4(1(x1))))))))))))))))))))	→	1^#(4(2(4(x1))))	(488)
2^#(3(1(1(2(2(0(1(0(0(1(4(4(0(0(3(2(0(4(1(x1))))))))))))))))))))	→	2^#(4(x1))	(489)
2^#(3(3(2(0(4(4(4(1(3(4(0(1(0(1(0(2(1(0(2(x1))))))))))))))))))))	→	1^#(4(x1))	(518)
2^#(3(2(4(1(3(3(2(0(0(2(3(3(3(1(2(4(4(0(2(x1))))))))))))))))))))	→	2^#(0(2(1(2(1(2(0(0(x1)))))))))	(564)
2^#(3(2(4(1(3(3(2(0(0(2(3(3(3(1(2(4(4(0(2(x1))))))))))))))))))))	→	1^#(2(0(0(x1))))	(568)
2^#(3(2(4(1(3(3(2(0(0(2(3(3(3(1(2(4(4(0(2(x1))))))))))))))))))))	→	2^#(0(0(x1)))	(569)
2^#(1(4(4(0(3(1(2(2(0(2(2(0(2(1(1(0(1(2(2(x1))))))))))))))))))))	→	1^#(2(1(x1)))	(648)
2^#(1(4(4(0(3(1(2(2(0(2(2(0(2(1(1(0(1(2(2(x1))))))))))))))))))))	→	2^#(1(x1))	(649)
2^#(1(4(4(0(3(1(2(2(0(2(2(0(2(1(1(0(1(2(2(x1))))))))))))))))))))	→	1^#(x1)	(650)
2^#(1(4(3(3(1(3(2(2(4(4(3(1(0(3(3(1(1(1(3(x1))))))))))))))))))))	→	1^#(x1)	(789)
2^#(1(1(1(2(4(1(0(3(2(2(0(2(0(3(4(1(0(2(3(x1))))))))))))))))))))	→	2^#(1(3(0(x1))))	(819)
2^#(1(3(0(2(2(3(3(3(0(3(4(3(4(1(1(2(4(4(3(x1))))))))))))))))))))	→	2^#(x1)	(935)
2^#(3(3(1(3(1(0(1(0(3(2(2(1(2(1(3(4(0(4(2(x1))))))))))))))))))))	→	2^#(0(x1))	(711)
2^#(3(3(2(4(3(2(1(0(0(2(3(3(4(2(3(3(1(0(4(x1))))))))))))))))))))	→	2^#(x1)	(945)
2^#(3(4(3(0(2(0(2(4(0(4(3(2(0(0(0(2(0(1(4(x1))))))))))))))))))))	→	1^#(1(1(2(x1))))	(965)
2^#(3(4(3(0(2(0(2(4(0(4(3(2(0(0(0(2(0(1(4(x1))))))))))))))))))))	→	1^#(1(2(x1)))	(966)
2^#(3(4(3(0(2(0(2(4(0(4(3(2(0(0(0(2(0(1(4(x1))))))))))))))))))))	→	1^#(2(x1))	(967)
2^#(3(4(3(0(2(0(2(4(0(4(3(2(0(0(0(2(0(1(4(x1))))))))))))))))))))	→	2^#(x1)	(968)
2^#(2(4(4(3(1(1(1(4(0(1(1(1(1(4(3(0(3(2(4(x1))))))))))))))))))))	→	2^#(x1)	(1006)

1.1.1.1 Reduction Pair Processor

Using the linear polynomial interpretation over the naturals

[2^#(x₁)]	=	1 · x₁
[4(x₁)]	=	1 + 1 · x₁
[2(x₁)]	=	1 + 1 · x₁
[1(x₁)]	=	1 + 1 · x₁
[0(x₁)]	=	1 + 1 · x₁
[3(x₁)]	=	1 + 1 · x₁
[1^#(x₁)]	=	1 + 1 · x₁

the pairs

2^#(4(4(2(1(1(4(1(0(1(2(1(0(1(4(0(1(1(1(0(x1))))))))))))))))))))	→	2^#(1(4(4(x1))))	(216)
2^#(1(4(4(0(3(1(2(2(0(2(2(0(2(1(1(0(1(2(2(x1))))))))))))))))))))	→	2^#(1(2(1(x1))))	(647)
2^#(1(2(1(0(3(1(3(0(2(1(1(0(4(3(3(1(2(0(2(x1))))))))))))))))))))	→	2^#(2(2(x1)))	(540)
2^#(2(2(2(4(4(4(2(4(1(0(4(2(3(3(0(4(4(0(2(x1))))))))))))))))))))	→	2^#(0(x1))	(558)
2^#(0(3(2(4(3(1(1(1(1(2(3(1(1(3(0(2(2(1(0(x1))))))))))))))))))))	→	2^#(0(1(4(2(3(2(3(3(4(2(4(x1))))))))))))	(241)
2^#(0(2(4(0(2(2(0(1(2(0(2(3(2(4(2(4(3(2(1(x1))))))))))))))))))))	→	1^#(1(1(x1)))	(456)
1^#(1(1(2(0(2(0(0(3(4(0(0(0(0(1(1(3(1(4(1(x1))))))))))))))))))))	→	1^#(2(x1))	(496)
1^#(2(2(1(3(4(4(3(0(0(2(2(0(1(1(2(1(0(2(0(x1))))))))))))))))))))	→	2^#(0(3(x1)))	(289)
2^#(0(3(2(4(3(1(1(1(1(2(3(1(1(3(0(2(2(1(0(x1))))))))))))))))))))	→	2^#(4(x1))	(245)
2^#(4(3(2(1(4(3(3(4(0(3(4(0(4(4(1(3(0(1(2(x1))))))))))))))))))))	→	2^#(0(2(2(4(4(1(4(1(x1)))))))))	(588)
2^#(0(2(4(0(2(2(0(1(2(0(2(3(2(4(2(4(3(2(1(x1))))))))))))))))))))	→	1^#(1(x1))	(457)
1^#(1(2(1(4(0(0(3(3(3(4(0(4(4(3(3(1(1(2(0(x1))))))))))))))))))))	→	1^#(2(2(x1)))	(301)
1^#(2(2(2(2(3(3(2(4(0(3(2(3(2(4(1(4(3(3(0(x1))))))))))))))))))))	→	2^#(4(0(x1)))	(327)
2^#(4(0(1(0(2(1(0(1(0(0(2(4(3(3(1(4(3(1(2(x1))))))))))))))))))))	→	1^#(1(2(x1)))	(637)
1^#(1(2(1(4(0(0(3(3(3(4(0(4(4(3(3(1(1(2(0(x1))))))))))))))))))))	→	2^#(2(x1))	(302)
2^#(2(4(0(1(3(2(1(1(4(3(4(2(3(2(1(1(3(1(0(x1))))))))))))))))))))	→	2^#(2(x1))	(256)
2^#(2(4(0(1(3(2(1(1(4(3(4(2(3(2(1(1(3(1(0(x1))))))))))))))))))))	→	2^#(x1)	(257)
2^#(1(0(3(4(0(2(3(2(2(0(3(0(2(0(4(0(2(1(0(x1))))))))))))))))))))	→	1^#(x1)	(236)
1^#(1(2(1(4(0(0(3(3(3(4(0(4(4(3(3(1(1(2(0(x1))))))))))))))))))))	→	2^#(x1)	(303)
2^#(0(0(1(3(4(4(4(0(0(2(1(1(0(3(3(3(3(1(0(x1))))))))))))))))))))	→	2^#(0(2(x1)))	(270)
2^#(0(2(1(1(2(2(2(3(1(3(3(0(1(1(2(2(0(4(3(x1))))))))))))))))))))	→	2^#(0(2(4(3(2(0(3(x1))))))))	(915)
2^#(0(2(1(1(2(2(2(3(1(3(3(0(1(1(2(2(0(4(3(x1))))))))))))))))))))	→	2^#(0(3(x1)))	(917)
2^#(0(0(1(3(4(4(4(0(0(2(1(1(0(3(3(3(3(1(0(x1))))))))))))))))))))	→	2^#(x1)	(271)
2^#(3(2(2(2(3(3(4(4(2(2(1(3(0(4(0(0(0(2(0(x1))))))))))))))))))))	→	2^#(1(3(x1)))	(280)
2^#(1(3(3(0(1(3(3(4(1(3(4(1(2(1(0(2(0(4(0(x1))))))))))))))))))))	→	2^#(0(1(2(x1))))	(347)
2^#(0(1(2(0(1(0(4(0(1(4(1(3(0(4(4(2(2(4(3(x1))))))))))))))))))))	→	2^#(0(x1))	(925)
2^#(0(0(1(1(3(0(4(2(2(2(0(3(1(0(0(2(0(3(3(x1))))))))))))))))))))	→	1^#(2(0(4(x1))))	(875)
1^#(2(0(4(4(1(3(3(4(2(1(0(2(0(2(3(3(2(0(3(x1))))))))))))))))))))	→	1^#(1(1(2(0(2(x1))))))	(744)
1^#(1(1(2(0(2(0(0(3(4(0(0(0(0(1(1(3(1(4(1(x1))))))))))))))))))))	→	2^#(x1)	(497)
2^#(3(2(1(1(3(1(2(3(3(2(0(1(1(0(2(3(4(3(0(x1))))))))))))))))))))	→	2^#(2(1(x1)))	(337)
2^#(2(1(2(1(0(1(3(2(3(3(1(4(3(4(4(2(3(4(0(x1))))))))))))))))))))	→	1^#(1(x1))	(367)
1^#(1(1(2(0(1(2(4(0(2(0(3(4(2(2(3(2(0(1(3(x1))))))))))))))))))))	→	1^#(x1)	(776)
1^#(2(2(0(0(2(0(2(2(3(2(1(2(0(3(4(0(4(4(0(x1))))))))))))))))))))	→	1^#(2(0(x1)))	(379)
1^#(2(0(4(4(1(3(3(4(2(1(0(2(0(2(3(3(2(0(3(x1))))))))))))))))))))	→	2^#(0(2(x1)))	(747)
1^#(2(0(4(4(1(3(3(4(2(1(0(2(0(2(3(3(2(0(3(x1))))))))))))))))))))	→	2^#(x1)	(748)
2^#(3(2(1(1(3(1(2(3(3(2(0(1(1(0(2(3(4(3(0(x1))))))))))))))))))))	→	2^#(1(x1))	(338)
2^#(1(3(3(0(1(3(3(4(1(3(4(1(2(1(0(2(0(4(0(x1))))))))))))))))))))	→	1^#(2(x1))	(348)
1^#(2(2(0(0(2(0(2(2(3(2(1(2(0(3(4(0(4(4(0(x1))))))))))))))))))))	→	2^#(0(x1))	(380)
1^#(2(1(0(3(4(2(2(3(4(0(2(2(3(1(0(2(1(0(2(x1))))))))))))))))))))	→	2^#(0(x1))	(530)
1^#(2(3(4(0(2(4(4(1(1(0(3(2(4(1(3(0(2(1(2(x1))))))))))))))))))))	→	2^#(1(x1))	(601)
2^#(1(3(3(0(1(3(3(4(1(3(4(1(2(1(0(2(0(4(0(x1))))))))))))))))))))	→	2^#(x1)	(349)
2^#(3(2(1(1(3(1(2(3(3(2(0(1(1(0(2(3(4(3(0(x1))))))))))))))))))))	→	1^#(x1)	(339)
1^#(2(3(4(0(2(4(4(1(1(0(3(2(4(1(3(0(2(1(2(x1))))))))))))))))))))	→	1^#(x1)	(602)
1^#(2(2(4(0(1(4(0(4(0(4(2(3(0(3(4(1(2(2(2(x1))))))))))))))))))))	→	1^#(1(x1))	(671)
1^#(1(2(1(1(3(4(3(4(0(0(4(0(2(3(0(2(1(1(3(x1))))))))))))))))))))	→	2^#(4(x1))	(795)
2^#(4(3(2(1(4(3(3(4(0(3(4(0(4(4(1(3(0(1(2(x1))))))))))))))))))))	→	1^#(x1)	(592)
1^#(2(2(4(0(1(4(0(4(0(4(2(3(0(3(4(1(2(2(2(x1))))))))))))))))))))	→	1^#(x1)	(672)
1^#(2(2(4(1(1(0(0(2(0(1(3(2(2(4(2(0(4(4(2(x1))))))))))))))))))))	→	2^#(0(x1))	(727)
1^#(2(3(3(4(3(3(3(2(0(2(2(2(1(0(3(2(1(0(3(x1))))))))))))))))))))	→	2^#(0(x1))	(737)
1^#(2(4(1(3(1(0(1(0(1(0(3(2(3(3(2(3(4(0(3(x1))))))))))))))))))))	→	2^#(3(1(4(x1))))	(765)
2^#(3(1(4(1(2(0(1(2(0(2(3(4(3(3(2(2(4(3(2(x1))))))))))))))))))))	→	1^#(x1)	(691)
1^#(2(4(1(3(1(0(1(0(1(0(3(2(3(3(2(3(4(0(3(x1))))))))))))))))))))	→	1^#(4(x1))	(766)
1^#(4(2(4(1(0(0(0(3(0(2(3(1(1(3(4(3(0(2(3(x1))))))))))))))))))))	→	2^#(0(2(3(3(x1)))))	(826)
1^#(4(2(4(1(0(0(0(3(0(2(3(1(1(3(4(3(0(2(3(x1))))))))))))))))))))	→	2^#(3(3(x1)))	(827)
2^#(3(3(3(2(1(1(0(4(0(0(0(2(2(1(4(1(4(0(1(x1))))))))))))))))))))	→	2^#(2(2(2(x1))))	(411)
2^#(3(3(3(2(1(1(0(4(0(0(0(2(2(1(4(1(4(0(1(x1))))))))))))))))))))	→	2^#(2(2(x1)))	(412)
2^#(2(2(3(0(2(1(0(4(2(2(1(0(2(0(0(0(3(0(3(x1))))))))))))))))))))	→	2^#(4(4(x1)))	(756)
2^#(3(3(3(2(1(1(0(4(0(0(0(2(2(1(4(1(4(0(1(x1))))))))))))))))))))	→	2^#(2(x1))	(413)
2^#(2(1(2(1(0(1(3(2(3(3(1(4(3(4(4(2(3(4(0(x1))))))))))))))))))))	→	1^#(x1)	(368)
1^#(2(3(3(0(0(0(2(0(3(1(3(0(1(4(2(2(3(1(3(x1))))))))))))))))))))	→	1^#(x1)	(812)
1^#(2(0(0(4(3(3(2(0(0(4(1(0(1(0(4(3(3(4(4(x1))))))))))))))))))))	→	1^#(x1)	(1081)
2^#(2(3(2(0(2(2(4(0(3(1(1(1(2(4(0(1(0(1(2(x1))))))))))))))))))))	→	2^#(3(x1))	(582)
2^#(3(3(3(2(1(1(0(4(0(0(0(2(2(1(4(1(4(0(1(x1))))))))))))))))))))	→	2^#(x1)	(414)
2^#(3(4(4(4(3(2(3(0(4(2(1(2(4(3(0(3(2(1(1(x1))))))))))))))))))))	→	2^#(4(3(x1)))	(427)
2^#(4(3(2(3(0(0(3(1(4(1(3(3(0(1(0(0(2(3(2(x1))))))))))))))))))))	→	2^#(1(x1))	(679)
2^#(1(2(1(0(3(1(3(0(2(1(1(0(4(3(3(1(2(0(2(x1))))))))))))))))))))	→	2^#(2(x1))	(541)
2^#(2(4(2(4(4(4(2(3(0(2(3(2(0(4(4(3(2(1(2(x1))))))))))))))))))))	→	1^#(1(x1))	(624)
2^#(2(4(2(4(4(4(2(3(0(2(3(2(0(4(4(3(2(1(2(x1))))))))))))))))))))	→	1^#(x1)	(625)
2^#(2(4(0(3(0(2(2(3(4(2(4(3(3(1(1(2(3(3(3(x1))))))))))))))))))))	→	1^#(x1)	(898)
2^#(2(4(4(1(1(2(3(3(4(2(4(3(1(2(1(4(1(0(4(x1))))))))))))))))))))	→	2^#(4(x1))	(956)
2^#(4(3(2(3(0(0(3(1(4(1(3(3(0(1(0(0(2(3(2(x1))))))))))))))))))))	→	1^#(x1)	(680)
2^#(4(0(3(0(3(4(0(1(0(4(3(2(0(2(2(3(4(2(3(x1))))))))))))))))))))	→	2^#(1(0(x1)))	(865)
2^#(1(0(4(1(4(3(2(3(4(3(0(2(2(1(4(0(1(2(3(x1))))))))))))))))))))	→	2^#(0(x1))	(833)
2^#(4(1(4(3(2(1(4(4(3(0(3(2(4(1(1(4(3(3(3(x1))))))))))))))))))))	→	2^#(0(x1))	(908)
2^#(4(3(4(3(1(1(4(0(3(2(1(1(2(2(3(4(3(1(4(x1))))))))))))))))))))	→	2^#(x1)	(989)
2^#(3(2(0(3(1(4(4(2(3(0(0(0(3(4(1(4(0(2(1(x1))))))))))))))))))))	→	2^#(3(1(x1)))	(444)
2^#(3(1(1(2(2(0(1(0(0(1(4(4(0(0(3(2(0(4(1(x1))))))))))))))))))))	→	1^#(4(2(4(x1))))	(488)
2^#(3(1(1(2(2(0(1(0(0(1(4(4(0(0(3(2(0(4(1(x1))))))))))))))))))))	→	2^#(4(x1))	(489)
2^#(3(3(2(0(4(4(4(1(3(4(0(1(0(1(0(2(1(0(2(x1))))))))))))))))))))	→	1^#(4(x1))	(518)
2^#(3(2(4(1(3(3(2(0(0(2(3(3(3(1(2(4(4(0(2(x1))))))))))))))))))))	→	2^#(0(2(1(2(1(2(0(0(x1)))))))))	(564)
2^#(3(2(4(1(3(3(2(0(0(2(3(3(3(1(2(4(4(0(2(x1))))))))))))))))))))	→	1^#(2(0(0(x1))))	(568)
2^#(3(2(4(1(3(3(2(0(0(2(3(3(3(1(2(4(4(0(2(x1))))))))))))))))))))	→	2^#(0(0(x1)))	(569)
2^#(1(4(4(0(3(1(2(2(0(2(2(0(2(1(1(0(1(2(2(x1))))))))))))))))))))	→	1^#(2(1(x1)))	(648)
2^#(1(4(4(0(3(1(2(2(0(2(2(0(2(1(1(0(1(2(2(x1))))))))))))))))))))	→	2^#(1(x1))	(649)
2^#(1(4(4(0(3(1(2(2(0(2(2(0(2(1(1(0(1(2(2(x1))))))))))))))))))))	→	1^#(x1)	(650)
2^#(1(4(3(3(1(3(2(2(4(4(3(1(0(3(3(1(1(1(3(x1))))))))))))))))))))	→	1^#(x1)	(789)
2^#(1(1(1(2(4(1(0(3(2(2(0(2(0(3(4(1(0(2(3(x1))))))))))))))))))))	→	2^#(1(3(0(x1))))	(819)
2^#(1(3(0(2(2(3(3(3(0(3(4(3(4(1(1(2(4(4(3(x1))))))))))))))))))))	→	2^#(x1)	(935)
2^#(3(3(1(3(1(0(1(0(3(2(2(1(2(1(3(4(0(4(2(x1))))))))))))))))))))	→	2^#(0(x1))	(711)
2^#(3(3(2(4(3(2(1(0(0(2(3(3(4(2(3(3(1(0(4(x1))))))))))))))))))))	→	2^#(x1)	(945)
2^#(3(4(3(0(2(0(2(4(0(4(3(2(0(0(0(2(0(1(4(x1))))))))))))))))))))	→	1^#(1(1(2(x1))))	(965)
2^#(3(4(3(0(2(0(2(4(0(4(3(2(0(0(0(2(0(1(4(x1))))))))))))))))))))	→	1^#(1(2(x1)))	(966)
2^#(3(4(3(0(2(0(2(4(0(4(3(2(0(0(0(2(0(1(4(x1))))))))))))))))))))	→	1^#(2(x1))	(967)
2^#(3(4(3(0(2(0(2(4(0(4(3(2(0(0(0(2(0(1(4(x1))))))))))))))))))))	→	2^#(x1)	(968)
2^#(2(4(4(3(1(1(1(4(0(1(1(1(1(4(3(0(3(2(4(x1))))))))))))))))))))	→	2^#(x1)	(1006)

could be deleted.

1.1.1.1.1 P is empty

There are no pairs anymore.