Certification Problem

Input (TPDB SRS_Standard/ICFP_2010/160234)

The rewrite relation of the following TRS is considered.

0(1(2(x1)))	→	2(3(0(3(1(x1)))))	(1)
0(0(0(2(x1))))	→	3(0(0(3(0(2(x1))))))	(2)
0(0(2(2(x1))))	→	2(3(0(0(3(2(x1))))))	(3)
0(1(1(2(x1))))	→	2(3(0(3(1(1(x1))))))	(4)
0(1(2(1(x1))))	→	0(1(2(4(1(3(x1))))))	(5)
0(1(2(2(x1))))	→	2(3(0(3(1(2(x1))))))	(6)
0(1(2(5(x1))))	→	2(0(5(3(1(x1)))))	(7)
0(1(5(1(x1))))	→	1(0(3(5(3(1(x1))))))	(8)
0(1(5(2(x1))))	→	2(4(1(0(3(5(x1))))))	(9)
0(1(5(2(x1))))	→	2(4(3(1(0(5(x1))))))	(10)
0(1(5(2(x1))))	→	3(1(3(0(5(2(x1))))))	(11)
0(1(5(5(x1))))	→	1(3(0(5(5(x1)))))	(12)
0(2(1(2(x1))))	→	2(2(3(0(3(1(x1))))))	(13)
0(2(5(2(x1))))	→	2(2(3(0(5(x1)))))	(14)
1(1(4(5(x1))))	→	5(4(1(3(1(x1)))))	(15)
1(5(1(5(x1))))	→	1(3(5(5(3(1(x1))))))	(16)
1(5(5(1(x1))))	→	1(5(3(1(5(3(x1))))))	(17)
2(0(1(2(x1))))	→	2(2(3(0(3(1(x1))))))	(18)
2(0(1(5(x1))))	→	2(1(3(0(5(x1)))))	(19)
5(0(1(2(x1))))	→	3(0(5(3(1(2(x1))))))	(20)
5(0(1(2(x1))))	→	4(2(3(0(5(1(x1))))))	(21)
0(0(0(0(1(x1)))))	→	0(0(1(0(0(3(x1))))))	(22)
0(0(1(2(5(x1)))))	→	2(0(0(5(3(1(x1))))))	(23)
0(0(1(5(2(x1)))))	→	0(1(0(3(5(2(x1))))))	(24)
0(1(0(4(5(x1)))))	→	5(4(0(0(3(1(x1))))))	(25)
0(1(1(1(2(x1)))))	→	1(0(3(1(1(2(x1))))))	(26)
0(1(2(1(5(x1)))))	→	2(1(0(5(3(1(x1))))))	(27)
0(1(3(5(2(x1)))))	→	3(0(4(1(5(2(x1))))))	(28)
0(1(4(2(5(x1)))))	→	2(4(3(0(5(1(x1))))))	(29)
0(1(4(4(2(x1)))))	→	1(0(4(4(4(2(x1))))))	(30)
0(1(5(0(1(x1)))))	→	0(1(1(0(5(3(x1))))))	(31)
0(1(5(0(5(x1)))))	→	3(5(1(0(5(0(x1))))))	(32)
0(2(4(2(1(x1)))))	→	2(1(2(4(3(0(x1))))))	(33)
0(4(0(2(1(x1)))))	→	3(0(4(1(2(0(x1))))))	(34)
0(5(0(1(5(x1)))))	→	0(5(0(5(3(1(x1))))))	(35)
1(0(0(1(5(x1)))))	→	5(1(0(0(3(1(x1))))))	(36)
1(0(1(4(5(x1)))))	→	1(4(4(1(0(5(x1))))))	(37)
1(4(0(1(5(x1)))))	→	1(4(1(3(0(5(x1))))))	(38)
2(0(1(5(2(x1)))))	→	2(1(0(3(5(2(x1))))))	(39)
2(0(4(2(1(x1)))))	→	2(1(4(2(3(0(x1))))))	(40)
2(0(5(1(2(x1)))))	→	0(3(1(5(2(2(x1))))))	(41)
2(2(1(1(2(x1)))))	→	2(2(1(3(1(2(x1))))))	(42)
2(5(1(5(2(x1)))))	→	2(4(1(5(5(2(x1))))))	(43)
5(0(1(4(5(x1)))))	→	4(1(0(3(5(5(x1))))))	(44)
5(1(0(1(5(x1)))))	→	3(1(5(1(0(5(x1))))))	(45)
5(4(0(2(1(x1)))))	→	4(1(3(5(2(0(x1))))))	(46)
5(5(1(4(5(x1)))))	→	5(4(1(3(5(5(x1))))))	(47)

Property / Task

Prove or disprove termination.

Answer / Result

Yes.

Proof (by NaTT @ termCOMP 2023)

1 Dependency Pair Transformation

The following set of initial dependency pairs has been identified.

There are 167 ruless (increase limit for explicit display).

1.1 Dependency Graph Processor

The dependency pairs are split into 1 component.

The 1^st component contains the pair

0^#(1(5(0(5(x1)))))	→	0^#(x1)	(141)
5^#(4(0(2(1(x1)))))	→	0^#(x1)	(213)
0^#(1(0(4(5(x1)))))	→	1^#(x1)	(211)
5^#(0(1(4(5(x1)))))	→	5^#(5(x1))	(210)
2^#(0(5(1(2(x1)))))	→	2^#(2(x1))	(137)
0^#(1(5(2(x1))))	→	5^#(x1)	(136)
2^#(5(1(5(2(x1)))))	→	1^#(5(5(2(x1))))	(209)
5^#(1(0(1(5(x1)))))	→	1^#(0(5(x1)))	(133)
0^#(1(3(5(2(x1)))))	→	1^#(5(2(x1)))	(132)
0^#(5(0(1(5(x1)))))	→	1^#(x1)	(131)
5^#(5(1(4(5(x1)))))	→	5^#(5(x1))	(123)
5^#(0(1(2(x1))))	→	0^#(5(1(x1)))	(203)
0^#(1(4(2(5(x1)))))	→	5^#(1(x1))	(201)
0^#(2(1(2(x1))))	→	1^#(x1)	(118)
0^#(1(5(0(5(x1)))))	→	5^#(0(x1))	(114)
2^#(0(5(1(2(x1)))))	→	1^#(5(2(2(x1))))	(113)
1^#(1(4(5(x1))))	→	1^#(x1)	(194)
2^#(0(5(1(2(x1)))))	→	5^#(2(2(x1)))	(110)
5^#(4(0(2(1(x1)))))	→	5^#(2(0(x1)))	(192)
2^#(0(1(2(x1))))	→	1^#(x1)	(107)
0^#(1(2(1(x1))))	→	0^#(1(2(4(1(3(x1))))))	(103)
0^#(1(3(5(2(x1)))))	→	0^#(4(1(5(2(x1)))))	(183)
0^#(1(4(2(5(x1)))))	→	1^#(x1)	(101)
5^#(1(0(1(5(x1)))))	→	0^#(5(x1))	(181)
0^#(1(5(2(x1))))	→	0^#(5(2(x1)))	(99)
0^#(1(5(0(5(x1)))))	→	5^#(1(0(5(0(x1)))))	(180)
5^#(0(1(2(x1))))	→	1^#(x1)	(179)
5^#(4(0(2(1(x1)))))	→	2^#(0(x1))	(176)
2^#(0(1(5(x1))))	→	0^#(5(x1))	(92)
5^#(1(0(1(5(x1)))))	→	1^#(5(1(0(5(x1)))))	(174)
0^#(0(1(2(5(x1)))))	→	1^#(x1)	(90)
5^#(0(1(2(x1))))	→	5^#(1(x1))	(171)
1^#(0(1(4(5(x1)))))	→	1^#(0(5(x1)))	(168)
5^#(1(0(1(5(x1)))))	→	5^#(1(0(5(x1))))	(82)
0^#(4(0(2(1(x1)))))	→	1^#(2(0(x1)))	(80)
0^#(4(0(2(1(x1)))))	→	0^#(4(1(2(0(x1)))))	(76)
0^#(2(5(2(x1))))	→	5^#(x1)	(77)
1^#(4(0(1(5(x1)))))	→	0^#(5(x1))	(164)
1^#(5(1(5(x1))))	→	1^#(x1)	(71)
1^#(0(0(1(5(x1)))))	→	1^#(x1)	(72)
0^#(1(5(0(5(x1)))))	→	0^#(5(0(x1)))	(163)
1^#(0(1(4(5(x1)))))	→	0^#(5(x1))	(161)
0^#(1(5(5(x1))))	→	0^#(5(5(x1)))	(159)
0^#(2(5(2(x1))))	→	0^#(5(x1))	(67)
0^#(1(5(2(x1))))	→	1^#(0(5(x1)))	(66)
0^#(1(2(1(5(x1)))))	→	1^#(x1)	(156)
2^#(5(1(5(2(x1)))))	→	5^#(5(2(x1)))	(157)
0^#(2(4(2(1(x1)))))	→	0^#(x1)	(65)
0^#(1(1(2(x1))))	→	1^#(x1)	(64)
0^#(1(1(2(x1))))	→	1^#(1(x1))	(155)
0^#(4(0(2(1(x1)))))	→	2^#(0(x1))	(62)
0^#(1(2(2(x1))))	→	1^#(2(x1))	(61)
0^#(1(5(2(x1))))	→	5^#(x1)	(136)
2^#(0(4(2(1(x1)))))	→	0^#(x1)	(60)
0^#(4(0(2(1(x1)))))	→	0^#(x1)	(57)
0^#(1(5(2(x1))))	→	0^#(5(x1))	(150)
0^#(1(2(x1)))	→	1^#(x1)	(147)
0^#(1(4(2(5(x1)))))	→	0^#(5(1(x1)))	(145)
0^#(1(5(0(5(x1)))))	→	1^#(0(5(0(x1))))	(143)
0^#(1(2(5(x1))))	→	1^#(x1)	(49)

1.1.1 Reduction Pair Processor with Usable Rules

Using the Max-polynomial interpretation

[0^#(x₁)]	=	x₁ + 1740
[1(x₁)]	=	x₁ + 1104
[4(x₁)]	=	x₁ + 0
[5(x₁)]	=	x₁ + 26929
[3(x₁)]	=	x₁ + 0
[2^#(x₁)]	=	x₁ + 18171
[0(x₁)]	=	x₁ + 2842
[5^#(x₁)]	=	x₁ + 25826
[2(x₁)]	=	x₁ + 22116
[1^#(x₁)]	=	x₁ + 0

together with the usable rules

2(0(1(2(x1))))	→	2(2(3(0(3(1(x1))))))	(18)
0(1(1(2(x1))))	→	2(3(0(3(1(1(x1))))))	(4)
1(1(4(5(x1))))	→	5(4(1(3(1(x1)))))	(15)
0(1(5(1(x1))))	→	1(0(3(5(3(1(x1))))))	(8)
0(1(2(x1)))	→	2(3(0(3(1(x1)))))	(1)
0(0(2(2(x1))))	→	2(3(0(0(3(2(x1))))))	(3)
1(5(1(5(x1))))	→	1(3(5(5(3(1(x1))))))	(16)
5(0(1(2(x1))))	→	4(2(3(0(5(1(x1))))))	(21)
1(0(0(1(5(x1)))))	→	5(1(0(0(3(1(x1))))))	(36)
0(1(1(1(2(x1)))))	→	1(0(3(1(1(2(x1))))))	(26)
2(0(1(5(x1))))	→	2(1(3(0(5(x1)))))	(19)
0(1(5(0(5(x1)))))	→	3(5(1(0(5(0(x1))))))	(32)
1(5(5(1(x1))))	→	1(5(3(1(5(3(x1))))))	(17)
0(1(2(1(5(x1)))))	→	2(1(0(5(3(1(x1))))))	(27)
0(4(0(2(1(x1)))))	→	3(0(4(1(2(0(x1))))))	(34)
0(0(0(0(1(x1)))))	→	0(0(1(0(0(3(x1))))))	(22)
0(1(3(5(2(x1)))))	→	3(0(4(1(5(2(x1))))))	(28)
5(0(1(4(5(x1)))))	→	4(1(0(3(5(5(x1))))))	(44)
0(1(2(1(x1))))	→	0(1(2(4(1(3(x1))))))	(5)
0(2(4(2(1(x1)))))	→	2(1(2(4(3(0(x1))))))	(33)
0(1(5(2(x1))))	→	2(4(3(1(0(5(x1))))))	(10)
2(0(1(5(2(x1)))))	→	2(1(0(3(5(2(x1))))))	(39)
0(1(2(5(x1))))	→	2(0(5(3(1(x1)))))	(7)
5(0(1(2(x1))))	→	3(0(5(3(1(2(x1))))))	(20)
0(1(0(4(5(x1)))))	→	5(4(0(0(3(1(x1))))))	(25)
0(1(4(4(2(x1)))))	→	1(0(4(4(4(2(x1))))))	(30)
0(2(5(2(x1))))	→	2(2(3(0(5(x1)))))	(14)
0(1(5(0(1(x1)))))	→	0(1(1(0(5(3(x1))))))	(31)
0(1(5(5(x1))))	→	1(3(0(5(5(x1)))))	(12)
5(1(0(1(5(x1)))))	→	3(1(5(1(0(5(x1))))))	(45)
0(0(1(2(5(x1)))))	→	2(0(0(5(3(1(x1))))))	(23)
0(0(1(5(2(x1)))))	→	0(1(0(3(5(2(x1))))))	(24)
0(1(5(2(x1))))	→	3(1(3(0(5(2(x1))))))	(11)
0(1(5(2(x1))))	→	2(4(1(0(3(5(x1))))))	(9)
0(2(1(2(x1))))	→	2(2(3(0(3(1(x1))))))	(13)
2(0(4(2(1(x1)))))	→	2(1(4(2(3(0(x1))))))	(40)
0(1(2(2(x1))))	→	2(3(0(3(1(2(x1))))))	(6)
1(4(0(1(5(x1)))))	→	1(4(1(3(0(5(x1))))))	(38)
5(5(1(4(5(x1)))))	→	5(4(1(3(5(5(x1))))))	(47)
1(0(1(4(5(x1)))))	→	1(4(4(1(0(5(x1))))))	(37)
2(0(5(1(2(x1)))))	→	0(3(1(5(2(2(x1))))))	(41)
2(2(1(1(2(x1)))))	→	2(2(1(3(1(2(x1))))))	(42)
5(4(0(2(1(x1)))))	→	4(1(3(5(2(0(x1))))))	(46)
0(5(0(1(5(x1)))))	→	0(5(0(5(3(1(x1))))))	(35)
0(1(4(2(5(x1)))))	→	2(4(3(0(5(1(x1))))))	(29)
2(5(1(5(2(x1)))))	→	2(4(1(5(5(2(x1))))))	(43)
0(0(0(2(x1))))	→	3(0(0(3(0(2(x1))))))	(2)

(w.r.t. the implicit argument filter of the reduction pair), the pairs

0^#(1(5(0(5(x1)))))	→	0^#(x1)	(141)
5^#(4(0(2(1(x1)))))	→	0^#(x1)	(213)
0^#(1(0(4(5(x1)))))	→	1^#(x1)	(211)
5^#(0(1(4(5(x1)))))	→	5^#(5(x1))	(210)
2^#(0(5(1(2(x1)))))	→	2^#(2(x1))	(137)
0^#(1(5(2(x1))))	→	5^#(x1)	(136)
2^#(5(1(5(2(x1)))))	→	1^#(5(5(2(x1))))	(209)
5^#(1(0(1(5(x1)))))	→	1^#(0(5(x1)))	(133)
0^#(1(3(5(2(x1)))))	→	1^#(5(2(x1)))	(132)
0^#(5(0(1(5(x1)))))	→	1^#(x1)	(131)
5^#(5(1(4(5(x1)))))	→	5^#(5(x1))	(123)
5^#(0(1(2(x1))))	→	0^#(5(1(x1)))	(203)
0^#(1(4(2(5(x1)))))	→	5^#(1(x1))	(201)
0^#(2(1(2(x1))))	→	1^#(x1)	(118)
0^#(1(5(0(5(x1)))))	→	5^#(0(x1))	(114)
2^#(0(5(1(2(x1)))))	→	1^#(5(2(2(x1))))	(113)
1^#(1(4(5(x1))))	→	1^#(x1)	(194)
2^#(0(5(1(2(x1)))))	→	5^#(2(2(x1)))	(110)
5^#(4(0(2(1(x1)))))	→	5^#(2(0(x1)))	(192)
2^#(0(1(2(x1))))	→	1^#(x1)	(107)
0^#(1(4(2(5(x1)))))	→	1^#(x1)	(101)
5^#(1(0(1(5(x1)))))	→	0^#(5(x1))	(181)
0^#(1(5(2(x1))))	→	0^#(5(2(x1)))	(99)
0^#(1(5(0(5(x1)))))	→	5^#(1(0(5(0(x1)))))	(180)
5^#(0(1(2(x1))))	→	1^#(x1)	(179)
5^#(4(0(2(1(x1)))))	→	2^#(0(x1))	(176)
2^#(0(1(5(x1))))	→	0^#(5(x1))	(92)
5^#(1(0(1(5(x1)))))	→	1^#(5(1(0(5(x1)))))	(174)
0^#(0(1(2(5(x1)))))	→	1^#(x1)	(90)
5^#(0(1(2(x1))))	→	5^#(1(x1))	(171)
1^#(0(1(4(5(x1)))))	→	1^#(0(5(x1)))	(168)
5^#(1(0(1(5(x1)))))	→	5^#(1(0(5(x1))))	(82)
0^#(4(0(2(1(x1)))))	→	1^#(2(0(x1)))	(80)
0^#(2(5(2(x1))))	→	5^#(x1)	(77)
1^#(4(0(1(5(x1)))))	→	0^#(5(x1))	(164)
1^#(5(1(5(x1))))	→	1^#(x1)	(71)
1^#(0(0(1(5(x1)))))	→	1^#(x1)	(72)
0^#(1(5(0(5(x1)))))	→	0^#(5(0(x1)))	(163)
1^#(0(1(4(5(x1)))))	→	0^#(5(x1))	(161)
0^#(1(5(5(x1))))	→	0^#(5(5(x1)))	(159)
0^#(2(5(2(x1))))	→	0^#(5(x1))	(67)
0^#(1(5(2(x1))))	→	1^#(0(5(x1)))	(66)
0^#(1(2(1(5(x1)))))	→	1^#(x1)	(156)
2^#(5(1(5(2(x1)))))	→	5^#(5(2(x1)))	(157)
0^#(2(4(2(1(x1)))))	→	0^#(x1)	(65)
0^#(1(1(2(x1))))	→	1^#(x1)	(64)
0^#(1(1(2(x1))))	→	1^#(1(x1))	(155)
0^#(4(0(2(1(x1)))))	→	2^#(0(x1))	(62)
0^#(1(2(2(x1))))	→	1^#(2(x1))	(61)
0^#(1(5(2(x1))))	→	5^#(x1)	(136)
2^#(0(4(2(1(x1)))))	→	0^#(x1)	(60)
0^#(4(0(2(1(x1)))))	→	0^#(x1)	(57)
0^#(1(5(2(x1))))	→	0^#(5(x1))	(150)
0^#(1(2(x1)))	→	1^#(x1)	(147)
0^#(1(4(2(5(x1)))))	→	0^#(5(1(x1)))	(145)
0^#(1(5(0(5(x1)))))	→	1^#(0(5(0(x1))))	(143)
0^#(1(2(5(x1))))	→	1^#(x1)	(49)

could be deleted.

1.1.1.1 Dependency Graph Processor

The dependency pairs are split into 1 component.

The 1^st component contains the pair

0^#(4(0(2(1(x1)))))

→

0^#(4(1(2(0(x1)))))

(76)

1.1.1.1.1 Reduction Pair Processor with Usable Rules

Using the Max-polynomial interpretation

[0^#(x₁)]	=	x₁ + 1740
[1(x₁)]	=	1
[4(x₁)]	=	x₁ + 0
[5(x₁)]	=	x₁ + 0
[3(x₁)]	=	x₁ + 0
[2^#(x₁)]	=	x₁ + 18171
[0(x₁)]	=	2
[5^#(x₁)]	=	x₁ + 25826
[2(x₁)]	=	2
[1^#(x₁)]	=	x₁ + 0

together with the usable rules

2(0(1(2(x1))))	→	2(2(3(0(3(1(x1))))))	(18)
0(1(1(2(x1))))	→	2(3(0(3(1(1(x1))))))	(4)
1(1(4(5(x1))))	→	5(4(1(3(1(x1)))))	(15)
0(1(5(1(x1))))	→	1(0(3(5(3(1(x1))))))	(8)
0(1(2(x1)))	→	2(3(0(3(1(x1)))))	(1)
0(0(2(2(x1))))	→	2(3(0(0(3(2(x1))))))	(3)
1(5(1(5(x1))))	→	1(3(5(5(3(1(x1))))))	(16)
5(0(1(2(x1))))	→	4(2(3(0(5(1(x1))))))	(21)
1(0(0(1(5(x1)))))	→	5(1(0(0(3(1(x1))))))	(36)
0(1(1(1(2(x1)))))	→	1(0(3(1(1(2(x1))))))	(26)
2(0(1(5(x1))))	→	2(1(3(0(5(x1)))))	(19)
0(1(5(0(5(x1)))))	→	3(5(1(0(5(0(x1))))))	(32)
1(5(5(1(x1))))	→	1(5(3(1(5(3(x1))))))	(17)
0(1(2(1(5(x1)))))	→	2(1(0(5(3(1(x1))))))	(27)
0(4(0(2(1(x1)))))	→	3(0(4(1(2(0(x1))))))	(34)
0(0(0(0(1(x1)))))	→	0(0(1(0(0(3(x1))))))	(22)
0(1(3(5(2(x1)))))	→	3(0(4(1(5(2(x1))))))	(28)
5(0(1(4(5(x1)))))	→	4(1(0(3(5(5(x1))))))	(44)
0(1(2(1(x1))))	→	0(1(2(4(1(3(x1))))))	(5)
0(2(4(2(1(x1)))))	→	2(1(2(4(3(0(x1))))))	(33)
0(1(5(2(x1))))	→	2(4(3(1(0(5(x1))))))	(10)
2(0(1(5(2(x1)))))	→	2(1(0(3(5(2(x1))))))	(39)
0(1(2(5(x1))))	→	2(0(5(3(1(x1)))))	(7)
5(0(1(2(x1))))	→	3(0(5(3(1(2(x1))))))	(20)
0(1(0(4(5(x1)))))	→	5(4(0(0(3(1(x1))))))	(25)
0(1(4(4(2(x1)))))	→	1(0(4(4(4(2(x1))))))	(30)
0(2(5(2(x1))))	→	2(2(3(0(5(x1)))))	(14)
0(1(5(0(1(x1)))))	→	0(1(1(0(5(3(x1))))))	(31)
0(1(5(5(x1))))	→	1(3(0(5(5(x1)))))	(12)
5(1(0(1(5(x1)))))	→	3(1(5(1(0(5(x1))))))	(45)
0(0(1(2(5(x1)))))	→	2(0(0(5(3(1(x1))))))	(23)
0(0(1(5(2(x1)))))	→	0(1(0(3(5(2(x1))))))	(24)
0(1(5(2(x1))))	→	3(1(3(0(5(2(x1))))))	(11)
0(1(5(2(x1))))	→	2(4(1(0(3(5(x1))))))	(9)
0(2(1(2(x1))))	→	2(2(3(0(3(1(x1))))))	(13)
2(0(4(2(1(x1)))))	→	2(1(4(2(3(0(x1))))))	(40)
0(1(2(2(x1))))	→	2(3(0(3(1(2(x1))))))	(6)
1(4(0(1(5(x1)))))	→	1(4(1(3(0(5(x1))))))	(38)
5(5(1(4(5(x1)))))	→	5(4(1(3(5(5(x1))))))	(47)
1(0(1(4(5(x1)))))	→	1(4(4(1(0(5(x1))))))	(37)
2(0(5(1(2(x1)))))	→	0(3(1(5(2(2(x1))))))	(41)
2(2(1(1(2(x1)))))	→	2(2(1(3(1(2(x1))))))	(42)
5(4(0(2(1(x1)))))	→	4(1(3(5(2(0(x1))))))	(46)
0(5(0(1(5(x1)))))	→	0(5(0(5(3(1(x1))))))	(35)
0(1(4(2(5(x1)))))	→	2(4(3(0(5(1(x1))))))	(29)
2(5(1(5(2(x1)))))	→	2(4(1(5(5(2(x1))))))	(43)
0(0(0(2(x1))))	→	3(0(0(3(0(2(x1))))))	(2)

(w.r.t. the implicit argument filter of the reduction pair), the pair

0^#(4(0(2(1(x1)))))

→

0^#(4(1(2(0(x1)))))

(76)

could be deleted.

1.1.1.1.1.1 Dependency Graph Processor

The dependency pairs are split into 0 components.