Certification Problem

Input (TPDB SRS_Standard/ICFP_2010/3533)

The rewrite relation of the following TRS is considered.

1(0(4(0(x1)))) 2(2(2(3(3(1(5(5(2(0(x1)))))))))) (1)
0(4(1(5(5(x1))))) 2(4(2(0(2(4(3(0(1(5(x1)))))))))) (2)
1(4(2(5(2(x1))))) 4(3(5(0(2(2(0(0(5(3(x1)))))))))) (3)
3(1(0(3(0(x1))))) 3(2(2(2(4(3(3(5(2(0(x1)))))))))) (4)
5(0(1(4(3(x1))))) 3(5(4(2(2(0(4(3(3(0(x1)))))))))) (5)
5(5(5(5(2(x1))))) 5(2(2(0(3(3(1(5(0(0(x1)))))))))) (6)
0(5(0(1(1(3(x1)))))) 0(2(5(3(4(3(1(0(1(3(x1)))))))))) (7)
0(5(0(5(2(5(x1)))))) 4(2(0(0(2(5(1(3(4(1(x1)))))))))) (8)
1(5(4(0(1(1(x1)))))) 4(3(4(4(0(0(0(5(3(3(x1)))))))))) (9)
2(4(0(1(0(4(x1)))))) 0(2(3(3(3(3(5(0(2(5(x1)))))))))) (10)
2(4(1(3(1(4(x1)))))) 5(5(3(4(3(2(1(4(4(4(x1)))))))))) (11)
2(5(2(5(4(0(x1)))))) 4(2(5(3(5(5(2(2(3(0(x1)))))))))) (12)
3(4(2(4(2(5(x1)))))) 3(5(2(2(0(5(2(4(3(2(x1)))))))))) (13)
4(1(3(0(4(0(x1)))))) 5(0(1(2(3(1(2(3(5(2(x1)))))))))) (14)
5(4(3(2(4(0(x1)))))) 5(0(1(2(0(2(2(3(0(2(x1)))))))))) (15)
5(5(0(4(0(3(x1)))))) 5(2(2(2(2(2(4(4(3(2(x1)))))))))) (16)
0(0(5(0(4(0(5(x1))))))) 0(5(5(3(5(3(0(5(2(5(x1)))))))))) (17)
0(0(5(1(2(5(1(x1))))))) 0(1(2(4(3(5(0(1(3(3(x1)))))))))) (18)
0(0(5(5(5(0(5(x1))))))) 0(1(2(3(5(3(0(0(4(1(x1)))))))))) (19)
0(1(1(1(3(0(1(x1))))))) 4(2(2(3(3(0(4(0(0(3(x1)))))))))) (20)
0(3(1(0(3(1(1(x1))))))) 0(3(5(3(5(4(4(5(4(0(x1)))))))))) (21)
0(4(1(2(5(0(5(x1))))))) 2(0(1(5(1(5(0(2(0(5(x1)))))))))) (22)
0(4(2(4(2(3(4(x1))))))) 2(0(0(0(5(5(2(0(4(4(x1)))))))))) (23)
0(5(0(3(5(2(0(x1))))))) 2(2(3(3(1(4(2(2(0(2(x1)))))))))) (24)
1(0(4(0(4(0(5(x1))))))) 2(2(2(2(3(5(4(2(2(4(x1)))))))))) (25)
1(0(4(2(4(2(4(x1))))))) 1(2(0(0(4(4(2(2(2(2(x1)))))))))) (26)
1(0(5(0(4(3(4(x1))))))) 0(4(5(3(5(2(0(3(1(2(x1)))))))))) (27)
1(0(5(5(0(4(2(x1))))))) 1(0(2(1(5(4(5(2(0(2(x1)))))))))) (28)
1(2(4(4(2(4(0(x1))))))) 0(2(4(2(3(0(4(3(4(3(x1)))))))))) (29)
2(1(1(4(4(1(4(x1))))))) 4(2(4(3(4(3(5(4(5(4(x1)))))))))) (30)
2(4(2(3(3(4(1(x1))))))) 4(4(3(5(4(0(2(2(4(4(x1)))))))))) (31)
3(4(0(5(2(3(5(x1))))))) 3(3(5(0(0(2(2(3(3(5(x1)))))))))) (32)
3(4(2(0(5(1(2(x1))))))) 3(3(3(3(3(2(0(1(5(3(x1)))))))))) (33)

Property / Task

Prove or disprove termination.

Answer / Result

Yes.

Proof (by matchbox @ termCOMP 2023)

1 Closure Under Flat Contexts

Using the flat contexts

{5(), 4(), 3(), 2(), 1(), 0()}

We obtain the transformed TRS

There are 198 ruless (increase limit for explicit display).

1.1 Semantic Labeling

The following interpretations form a model of the rules.

As carrier we take the set {0,...,5}. Symbols are labeled by the interpretation of their arguments using the interpretations (modulo 6):

[5(x1)] = 6x1 + 0
[4(x1)] = 6x1 + 1
[3(x1)] = 6x1 + 2
[2(x1)] = 6x1 + 3
[1(x1)] = 6x1 + 4
[0(x1)] = 6x1 + 5

We obtain the labeled TRS

There are 1188 ruless (increase limit for explicit display).

1.1.1 Rule Removal

Using the matrix interpretations of dimension 1 with strict dimension 1 over the rationals with delta = 1
[50(x1)] = x1 +
22283/10
[51(x1)] = x1 +
282/5
[52(x1)] = x1 +
0
[53(x1)] = x1 +
58691/35
[54(x1)] = x1 +
0
[55(x1)] = x1 +
185722/35
[40(x1)] = x1 +
1
[41(x1)] = x1 +
0
[42(x1)] = x1 +
0
[43(x1)] = x1 +
19209/7
[44(x1)] = x1 +
373377/70
[45(x1)] = x1 +
186646/35
[30(x1)] = x1 +
0
[31(x1)] = x1 +
1917/2
[32(x1)] = x1 +
0
[33(x1)] = x1 +
0
[34(x1)] = x1 +
1794/35
[35(x1)] = x1 +
0
[20(x1)] = x1 +
184672/35
[21(x1)] = x1 +
19279/7
[22(x1)] = x1 +
24
[23(x1)] = x1 +
0
[24(x1)] = x1 +
6410/7
[25(x1)] = x1 +
0
[10(x1)] = x1 +
12829/10
[11(x1)] = x1 +
160404/35
[12(x1)] = x1 +
12829/10
[13(x1)] = x1 +
63974/35
[14(x1)] = x1 +
63687/14
[15(x1)] = x1 +
184672/35
[00(x1)] = x1 +
186191/35
[01(x1)] = x1 +
19104/7
[02(x1)] = x1 +
0
[03(x1)] = x1 +
0
[04(x1)] = x1 +
33604/35
[05(x1)] = x1 +
0
all of the following rules can be deleted.

There are 1146 ruless (increase limit for explicit display).

1.1.1.1 String Reversal

Since only unary symbols occur, one can reverse all terms and obtains the TRS
30(42(11(04(55(10(x1)))))) 00(35(32(42(01(25(23(43(51(30(12(x1))))))))))) (1420)
30(42(11(04(55(30(x1)))))) 00(35(32(42(01(25(23(43(51(30(32(x1))))))))))) (1421)
24(53(50(50(50(10(x1)))))) 04(05(55(10(34(32(02(25(23(53(10(x1))))))))))) (1422)
24(53(50(50(50(00(x1)))))) 04(05(55(10(34(32(02(25(23(53(00(x1))))))))))) (1423)
24(53(50(50(50(40(x1)))))) 04(05(55(10(34(32(02(25(23(53(40(x1))))))))))) (1424)
24(53(50(50(50(20(x1)))))) 04(05(55(10(34(32(02(25(23(53(20(x1))))))))))) (1425)
24(53(50(50(50(30(x1)))))) 04(05(55(10(34(32(02(25(23(53(30(x1))))))))))) (1426)
24(53(50(50(50(50(x1)))))) 04(05(55(10(34(32(02(25(23(53(50(x1))))))))))) (1427)
54(20(53(00(55(00(25(x1))))))) 14(44(31(12(54(20(03(05(25(43(21(x1))))))))))) (1428)
44(11(34(12(44(21(03(x1))))))) 44(41(41(11(24(33(42(31(52(50(00(x1))))))))))) (1429)
45(11(34(12(44(21(03(x1))))))) 45(41(41(11(24(33(42(31(52(50(00(x1))))))))))) (1430)
41(11(34(12(44(21(03(x1))))))) 41(41(41(11(24(33(42(31(52(50(00(x1))))))))))) (1431)
43(11(34(12(44(21(03(x1))))))) 43(41(41(11(24(33(42(31(52(50(00(x1))))))))))) (1432)
42(11(34(12(44(21(03(x1))))))) 42(41(41(11(24(33(42(31(52(50(00(x1))))))))))) (1433)
40(11(34(12(44(21(03(x1))))))) 40(41(41(11(24(33(42(31(52(50(00(x1))))))))))) (1434)
01(45(21(33(42(51(10(x1))))))) 21(03(35(22(23(03(25(13(04(55(10(x1))))))))))) (1435)
01(45(21(33(42(51(00(x1))))))) 21(03(35(22(23(03(25(13(04(55(00(x1))))))))))) (1436)
01(45(21(33(42(51(40(x1))))))) 21(03(35(22(23(03(25(13(04(55(40(x1))))))))))) (1437)
01(45(21(33(42(51(20(x1))))))) 21(03(35(22(23(03(25(13(04(55(20(x1))))))))))) (1438)
01(45(21(33(42(51(30(x1))))))) 21(03(35(22(23(03(25(13(04(55(30(x1))))))))))) (1439)
01(45(21(33(42(51(50(x1))))))) 21(03(35(22(23(03(25(13(04(55(50(x1))))))))))) (1440)
12(04(35(12(14(14(04(25(x1)))))))) 32(02(05(45(01(35(32(22(23(43(21(x1))))))))))) (1441)
10(04(35(12(14(14(04(25(x1)))))))) 30(02(05(45(01(35(32(22(23(43(21(x1))))))))))) (1442)
44(31(22(43(21(43(01(05(x1)))))))) 44(41(01(25(53(50(00(05(05(25(03(x1))))))))))) (1443)
45(31(22(43(21(43(01(05(x1)))))))) 45(41(01(25(53(50(00(05(05(25(03(x1))))))))))) (1444)
41(31(22(43(21(43(01(05(x1)))))))) 41(41(01(25(53(50(00(05(05(25(03(x1))))))))))) (1445)
43(31(22(43(21(43(01(05(x1)))))))) 43(41(01(25(53(50(00(05(05(25(03(x1))))))))))) (1446)
42(31(22(43(21(43(01(05(x1)))))))) 42(41(01(25(53(50(00(05(05(25(03(x1))))))))))) (1447)
40(31(22(43(21(43(01(05(x1)))))))) 40(41(01(25(53(50(00(05(05(25(03(x1))))))))))) (1448)
44(31(22(43(21(43(01(25(x1)))))))) 44(41(01(25(53(50(00(05(05(25(23(x1))))))))))) (1449)
45(31(22(43(21(43(01(25(x1)))))))) 45(41(01(25(53(50(00(05(05(25(23(x1))))))))))) (1450)
41(31(22(43(21(43(01(25(x1)))))))) 41(41(01(25(53(50(00(05(05(25(23(x1))))))))))) (1451)
43(31(22(43(21(43(01(25(x1)))))))) 43(41(01(25(53(50(00(05(05(25(23(x1))))))))))) (1452)
42(31(22(43(21(43(01(25(x1)))))))) 42(41(01(25(53(50(00(05(05(25(23(x1))))))))))) (1453)
40(31(22(43(21(43(01(25(x1)))))))) 40(41(01(25(53(50(00(05(05(25(23(x1))))))))))) (1454)
44(31(22(43(21(43(01(35(x1)))))))) 44(41(01(25(53(50(00(05(05(25(33(x1))))))))))) (1455)
45(31(22(43(21(43(01(35(x1)))))))) 45(41(01(25(53(50(00(05(05(25(33(x1))))))))))) (1456)
41(31(22(43(21(43(01(35(x1)))))))) 41(41(01(25(53(50(00(05(05(25(33(x1))))))))))) (1457)
43(31(22(43(21(43(01(35(x1)))))))) 43(41(01(25(53(50(00(05(05(25(33(x1))))))))))) (1458)
42(31(22(43(21(43(01(35(x1)))))))) 42(41(01(25(53(50(00(05(05(25(33(x1))))))))))) (1459)
40(31(22(43(21(43(01(35(x1)))))))) 40(41(01(25(53(50(00(05(05(25(33(x1))))))))))) (1460)
13(44(31(32(22(43(21(13(x1)))))))) 43(41(21(23(03(45(51(30(42(41(11(x1))))))))))) (1461)

1.1.1.1.1 Dependency Pair Transformation

The following set of initial dependency pairs has been identified.

There are 122 ruless (increase limit for explicit display).

1.1.1.1.1.1 Monotonic Reduction Pair Processor with Usable Rules

Using the matrix interpretations of dimension 1 with strict dimension 1 over the rationals with delta = 1
[50(x1)] = x1 +
3
[51(x1)] = x1 +
0
[52(x1)] = x1 +
0
[53(x1)] = x1 +
3
[54(x1)] = x1 +
0
[55(x1)] = x1 +
3
[40(x1)] = x1 +
0
[41(x1)] = x1 +
0
[42(x1)] = x1 +
3
[43(x1)] = x1 +
3
[44(x1)] = x1 +
3
[45(x1)] = x1 +
3
[30(x1)] = x1 +
0
[31(x1)] = x1 +
0
[32(x1)] = x1 +
0
[33(x1)] = x1 +
0
[34(x1)] = x1 +
3
[35(x1)] = x1 +
0
[20(x1)] = x1 +
1
[21(x1)] = x1 +
3
[22(x1)] = x1 +
0
[23(x1)] = x1 +
0
[24(x1)] = x1 +
0
[25(x1)] = x1 +
0
[10(x1)] = x1 +
0
[11(x1)] = x1 +
3
[12(x1)] = x1 +
0
[13(x1)] = x1 +
3
[14(x1)] = x1 +
3
[00(x1)] = x1 +
3
[01(x1)] = x1 +
3
[02(x1)] = x1 +
0
[03(x1)] = x1 +
0
[04(x1)] = x1 +
3
[05(x1)] = x1 +
0
[54#(x1)] = x1 +
1
[40#(x1)] = x1 +
1
[41#(x1)] = x1 +
0
[42#(x1)] = x1 +
3
[43#(x1)] = x1 +
3
[44#(x1)] = x1 +
1
[45#(x1)] = x1 +
3
[30#(x1)] = x1 +
3
[24#(x1)] = x1 +
0
[10#(x1)] = x1 +
5
[12#(x1)] = x1 +
3
[13#(x1)] = x1 +
4
[01#(x1)] = x1 +
2
together with the usable rules
30(42(11(04(55(10(x1)))))) 00(35(32(42(01(25(23(43(51(30(12(x1))))))))))) (1420)
30(42(11(04(55(30(x1)))))) 00(35(32(42(01(25(23(43(51(30(32(x1))))))))))) (1421)
24(53(50(50(50(10(x1)))))) 04(05(55(10(34(32(02(25(23(53(10(x1))))))))))) (1422)
24(53(50(50(50(00(x1)))))) 04(05(55(10(34(32(02(25(23(53(00(x1))))))))))) (1423)
24(53(50(50(50(40(x1)))))) 04(05(55(10(34(32(02(25(23(53(40(x1))))))))))) (1424)
24(53(50(50(50(20(x1)))))) 04(05(55(10(34(32(02(25(23(53(20(x1))))))))))) (1425)
24(53(50(50(50(30(x1)))))) 04(05(55(10(34(32(02(25(23(53(30(x1))))))))))) (1426)
24(53(50(50(50(50(x1)))))) 04(05(55(10(34(32(02(25(23(53(50(x1))))))))))) (1427)
54(20(53(00(55(00(25(x1))))))) 14(44(31(12(54(20(03(05(25(43(21(x1))))))))))) (1428)
44(11(34(12(44(21(03(x1))))))) 44(41(41(11(24(33(42(31(52(50(00(x1))))))))))) (1429)
45(11(34(12(44(21(03(x1))))))) 45(41(41(11(24(33(42(31(52(50(00(x1))))))))))) (1430)
41(11(34(12(44(21(03(x1))))))) 41(41(41(11(24(33(42(31(52(50(00(x1))))))))))) (1431)
43(11(34(12(44(21(03(x1))))))) 43(41(41(11(24(33(42(31(52(50(00(x1))))))))))) (1432)
42(11(34(12(44(21(03(x1))))))) 42(41(41(11(24(33(42(31(52(50(00(x1))))))))))) (1433)
40(11(34(12(44(21(03(x1))))))) 40(41(41(11(24(33(42(31(52(50(00(x1))))))))))) (1434)
01(45(21(33(42(51(10(x1))))))) 21(03(35(22(23(03(25(13(04(55(10(x1))))))))))) (1435)
01(45(21(33(42(51(00(x1))))))) 21(03(35(22(23(03(25(13(04(55(00(x1))))))))))) (1436)
01(45(21(33(42(51(40(x1))))))) 21(03(35(22(23(03(25(13(04(55(40(x1))))))))))) (1437)
01(45(21(33(42(51(20(x1))))))) 21(03(35(22(23(03(25(13(04(55(20(x1))))))))))) (1438)
01(45(21(33(42(51(30(x1))))))) 21(03(35(22(23(03(25(13(04(55(30(x1))))))))))) (1439)
01(45(21(33(42(51(50(x1))))))) 21(03(35(22(23(03(25(13(04(55(50(x1))))))))))) (1440)
12(04(35(12(14(14(04(25(x1)))))))) 32(02(05(45(01(35(32(22(23(43(21(x1))))))))))) (1441)
10(04(35(12(14(14(04(25(x1)))))))) 30(02(05(45(01(35(32(22(23(43(21(x1))))))))))) (1442)
44(31(22(43(21(43(01(05(x1)))))))) 44(41(01(25(53(50(00(05(05(25(03(x1))))))))))) (1443)
45(31(22(43(21(43(01(05(x1)))))))) 45(41(01(25(53(50(00(05(05(25(03(x1))))))))))) (1444)
41(31(22(43(21(43(01(05(x1)))))))) 41(41(01(25(53(50(00(05(05(25(03(x1))))))))))) (1445)
43(31(22(43(21(43(01(05(x1)))))))) 43(41(01(25(53(50(00(05(05(25(03(x1))))))))))) (1446)
42(31(22(43(21(43(01(05(x1)))))))) 42(41(01(25(53(50(00(05(05(25(03(x1))))))))))) (1447)
40(31(22(43(21(43(01(05(x1)))))))) 40(41(01(25(53(50(00(05(05(25(03(x1))))))))))) (1448)
44(31(22(43(21(43(01(25(x1)))))))) 44(41(01(25(53(50(00(05(05(25(23(x1))))))))))) (1449)
45(31(22(43(21(43(01(25(x1)))))))) 45(41(01(25(53(50(00(05(05(25(23(x1))))))))))) (1450)
41(31(22(43(21(43(01(25(x1)))))))) 41(41(01(25(53(50(00(05(05(25(23(x1))))))))))) (1451)
43(31(22(43(21(43(01(25(x1)))))))) 43(41(01(25(53(50(00(05(05(25(23(x1))))))))))) (1452)
42(31(22(43(21(43(01(25(x1)))))))) 42(41(01(25(53(50(00(05(05(25(23(x1))))))))))) (1453)
40(31(22(43(21(43(01(25(x1)))))))) 40(41(01(25(53(50(00(05(05(25(23(x1))))))))))) (1454)
44(31(22(43(21(43(01(35(x1)))))))) 44(41(01(25(53(50(00(05(05(25(33(x1))))))))))) (1455)
45(31(22(43(21(43(01(35(x1)))))))) 45(41(01(25(53(50(00(05(05(25(33(x1))))))))))) (1456)
41(31(22(43(21(43(01(35(x1)))))))) 41(41(01(25(53(50(00(05(05(25(33(x1))))))))))) (1457)
43(31(22(43(21(43(01(35(x1)))))))) 43(41(01(25(53(50(00(05(05(25(33(x1))))))))))) (1458)
42(31(22(43(21(43(01(35(x1)))))))) 42(41(01(25(53(50(00(05(05(25(33(x1))))))))))) (1459)
40(31(22(43(21(43(01(35(x1)))))))) 40(41(01(25(53(50(00(05(05(25(33(x1))))))))))) (1460)
13(44(31(32(22(43(21(13(x1)))))))) 43(41(21(23(03(45(51(30(42(41(11(x1))))))))))) (1461)
(w.r.t. the implicit argument filter of the reduction pair), the pairs
54#(20(53(00(55(00(25(x1))))))) 54#(20(03(05(25(43(21(x1))))))) (1462)
54#(20(53(00(55(00(25(x1))))))) 43#(21(x1)) (1463)
54#(20(53(00(55(00(25(x1))))))) 44#(31(12(54(20(03(05(25(43(21(x1)))))))))) (1464)
54#(20(53(00(55(00(25(x1))))))) 12#(54(20(03(05(25(43(21(x1)))))))) (1465)
40#(31(22(43(21(43(01(35(x1)))))))) 41#(01(25(53(50(00(05(05(25(33(x1)))))))))) (1467)
40#(31(22(43(21(43(01(35(x1)))))))) 01#(25(53(50(00(05(05(25(33(x1))))))))) (1468)
40#(31(22(43(21(43(01(25(x1)))))))) 41#(01(25(53(50(00(05(05(25(23(x1)))))))))) (1470)
40#(31(22(43(21(43(01(25(x1)))))))) 01#(25(53(50(00(05(05(25(23(x1))))))))) (1471)
40#(31(22(43(21(43(01(05(x1)))))))) 41#(01(25(53(50(00(05(05(25(03(x1)))))))))) (1473)
40#(31(22(43(21(43(01(05(x1)))))))) 01#(25(53(50(00(05(05(25(03(x1))))))))) (1474)
40#(11(34(12(44(21(03(x1))))))) 41#(41(11(24(33(42(31(52(50(00(x1)))))))))) (1476)
40#(11(34(12(44(21(03(x1))))))) 41#(11(24(33(42(31(52(50(00(x1))))))))) (1477)
40#(11(34(12(44(21(03(x1))))))) 42#(31(52(50(00(x1))))) (1478)
40#(11(34(12(44(21(03(x1))))))) 24#(33(42(31(52(50(00(x1))))))) (1479)
41#(31(22(43(21(43(01(35(x1)))))))) 01#(25(53(50(00(05(05(25(33(x1))))))))) (1482)
41#(31(22(43(21(43(01(25(x1)))))))) 01#(25(53(50(00(05(05(25(23(x1))))))))) (1485)
41#(31(22(43(21(43(01(05(x1)))))))) 01#(25(53(50(00(05(05(25(03(x1))))))))) (1488)
41#(11(34(12(44(21(03(x1))))))) 42#(31(52(50(00(x1))))) (1492)
41#(11(34(12(44(21(03(x1))))))) 24#(33(42(31(52(50(00(x1))))))) (1493)
42#(31(22(43(21(43(01(35(x1)))))))) 41#(01(25(53(50(00(05(05(25(33(x1)))))))))) (1494)
42#(31(22(43(21(43(01(35(x1)))))))) 01#(25(53(50(00(05(05(25(33(x1))))))))) (1496)
42#(31(22(43(21(43(01(25(x1)))))))) 41#(01(25(53(50(00(05(05(25(23(x1)))))))))) (1497)
42#(31(22(43(21(43(01(25(x1)))))))) 01#(25(53(50(00(05(05(25(23(x1))))))))) (1499)
42#(31(22(43(21(43(01(05(x1)))))))) 41#(01(25(53(50(00(05(05(25(03(x1)))))))))) (1500)
42#(31(22(43(21(43(01(05(x1)))))))) 01#(25(53(50(00(05(05(25(03(x1))))))))) (1502)
42#(11(34(12(44(21(03(x1))))))) 41#(41(11(24(33(42(31(52(50(00(x1)))))))))) (1503)
42#(11(34(12(44(21(03(x1))))))) 41#(11(24(33(42(31(52(50(00(x1))))))))) (1504)
42#(11(34(12(44(21(03(x1))))))) 42#(31(52(50(00(x1))))) (1506)
42#(11(34(12(44(21(03(x1))))))) 24#(33(42(31(52(50(00(x1))))))) (1507)
43#(31(22(43(21(43(01(35(x1)))))))) 41#(01(25(53(50(00(05(05(25(33(x1)))))))))) (1508)
43#(31(22(43(21(43(01(35(x1)))))))) 01#(25(53(50(00(05(05(25(33(x1))))))))) (1510)
43#(31(22(43(21(43(01(25(x1)))))))) 41#(01(25(53(50(00(05(05(25(23(x1)))))))))) (1511)
43#(31(22(43(21(43(01(25(x1)))))))) 01#(25(53(50(00(05(05(25(23(x1))))))))) (1513)
43#(31(22(43(21(43(01(05(x1)))))))) 41#(01(25(53(50(00(05(05(25(03(x1)))))))))) (1514)
43#(31(22(43(21(43(01(05(x1)))))))) 01#(25(53(50(00(05(05(25(03(x1))))))))) (1516)
43#(11(34(12(44(21(03(x1))))))) 41#(41(11(24(33(42(31(52(50(00(x1)))))))))) (1517)
43#(11(34(12(44(21(03(x1))))))) 41#(11(24(33(42(31(52(50(00(x1))))))))) (1518)
43#(11(34(12(44(21(03(x1))))))) 42#(31(52(50(00(x1))))) (1519)
43#(11(34(12(44(21(03(x1))))))) 24#(33(42(31(52(50(00(x1))))))) (1521)
44#(31(22(43(21(43(01(35(x1)))))))) 41#(01(25(53(50(00(05(05(25(33(x1)))))))))) (1522)
44#(31(22(43(21(43(01(35(x1)))))))) 01#(25(53(50(00(05(05(25(33(x1))))))))) (1524)
44#(31(22(43(21(43(01(25(x1)))))))) 41#(01(25(53(50(00(05(05(25(23(x1)))))))))) (1525)
44#(31(22(43(21(43(01(25(x1)))))))) 01#(25(53(50(00(05(05(25(23(x1))))))))) (1527)
44#(31(22(43(21(43(01(05(x1)))))))) 41#(01(25(53(50(00(05(05(25(03(x1)))))))))) (1528)
44#(31(22(43(21(43(01(05(x1)))))))) 01#(25(53(50(00(05(05(25(03(x1))))))))) (1530)
44#(11(34(12(44(21(03(x1))))))) 41#(41(11(24(33(42(31(52(50(00(x1)))))))))) (1531)
44#(11(34(12(44(21(03(x1))))))) 41#(11(24(33(42(31(52(50(00(x1))))))))) (1532)
44#(11(34(12(44(21(03(x1))))))) 42#(31(52(50(00(x1))))) (1533)
44#(11(34(12(44(21(03(x1))))))) 24#(33(42(31(52(50(00(x1))))))) (1535)
45#(31(22(43(21(43(01(35(x1)))))))) 41#(01(25(53(50(00(05(05(25(33(x1)))))))))) (1536)
45#(31(22(43(21(43(01(35(x1)))))))) 01#(25(53(50(00(05(05(25(33(x1))))))))) (1538)
45#(31(22(43(21(43(01(25(x1)))))))) 41#(01(25(53(50(00(05(05(25(23(x1)))))))))) (1539)
45#(31(22(43(21(43(01(25(x1)))))))) 01#(25(53(50(00(05(05(25(23(x1))))))))) (1541)
45#(31(22(43(21(43(01(05(x1)))))))) 41#(01(25(53(50(00(05(05(25(03(x1)))))))))) (1542)
45#(31(22(43(21(43(01(05(x1)))))))) 01#(25(53(50(00(05(05(25(03(x1))))))))) (1544)
45#(11(34(12(44(21(03(x1))))))) 41#(41(11(24(33(42(31(52(50(00(x1)))))))))) (1545)
45#(11(34(12(44(21(03(x1))))))) 41#(11(24(33(42(31(52(50(00(x1))))))))) (1546)
45#(11(34(12(44(21(03(x1))))))) 42#(31(52(50(00(x1))))) (1547)
45#(11(34(12(44(21(03(x1))))))) 24#(33(42(31(52(50(00(x1))))))) (1549)
30#(42(11(04(55(30(x1)))))) 42#(01(25(23(43(51(30(32(x1)))))))) (1550)
30#(42(11(04(55(30(x1)))))) 43#(51(30(32(x1)))) (1551)
30#(42(11(04(55(30(x1)))))) 30#(32(x1)) (1552)
30#(42(11(04(55(30(x1)))))) 01#(25(23(43(51(30(32(x1))))))) (1553)
30#(42(11(04(55(10(x1)))))) 42#(01(25(23(43(51(30(12(x1)))))))) (1554)
30#(42(11(04(55(10(x1)))))) 43#(51(30(12(x1)))) (1555)
30#(42(11(04(55(10(x1)))))) 30#(12(x1)) (1556)
30#(42(11(04(55(10(x1)))))) 12#(x1) (1557)
30#(42(11(04(55(10(x1)))))) 01#(25(23(43(51(30(12(x1))))))) (1558)
24#(53(50(50(50(50(x1)))))) 10#(34(32(02(25(23(53(50(x1)))))))) (1559)
24#(53(50(50(50(40(x1)))))) 10#(34(32(02(25(23(53(40(x1)))))))) (1560)
24#(53(50(50(50(30(x1)))))) 10#(34(32(02(25(23(53(30(x1)))))))) (1561)
24#(53(50(50(50(20(x1)))))) 10#(34(32(02(25(23(53(20(x1)))))))) (1562)
24#(53(50(50(50(10(x1)))))) 10#(34(32(02(25(23(53(10(x1)))))))) (1563)
24#(53(50(50(50(00(x1)))))) 10#(34(32(02(25(23(53(00(x1)))))))) (1564)
10#(04(35(12(14(14(04(25(x1)))))))) 43#(21(x1)) (1565)
10#(04(35(12(14(14(04(25(x1)))))))) 45#(01(35(32(22(23(43(21(x1)))))))) (1566)
10#(04(35(12(14(14(04(25(x1)))))))) 30#(02(05(45(01(35(32(22(23(43(21(x1))))))))))) (1567)
10#(04(35(12(14(14(04(25(x1)))))))) 01#(35(32(22(23(43(21(x1))))))) (1568)
12#(04(35(12(14(14(04(25(x1)))))))) 43#(21(x1)) (1569)
12#(04(35(12(14(14(04(25(x1)))))))) 45#(01(35(32(22(23(43(21(x1)))))))) (1570)
12#(04(35(12(14(14(04(25(x1)))))))) 01#(35(32(22(23(43(21(x1))))))) (1571)
13#(44(31(32(22(43(21(13(x1)))))))) 41#(21(23(03(45(51(30(42(41(11(x1)))))))))) (1572)
13#(44(31(32(22(43(21(13(x1)))))))) 41#(11(x1)) (1573)
13#(44(31(32(22(43(21(13(x1)))))))) 42#(41(11(x1))) (1574)
13#(44(31(32(22(43(21(13(x1)))))))) 43#(41(21(23(03(45(51(30(42(41(11(x1))))))))))) (1575)
13#(44(31(32(22(43(21(13(x1)))))))) 45#(51(30(42(41(11(x1)))))) (1576)
13#(44(31(32(22(43(21(13(x1)))))))) 30#(42(41(11(x1)))) (1577)
01#(45(21(33(42(51(50(x1))))))) 13#(04(55(50(x1)))) (1578)
01#(45(21(33(42(51(40(x1))))))) 13#(04(55(40(x1)))) (1579)
01#(45(21(33(42(51(30(x1))))))) 13#(04(55(30(x1)))) (1580)
01#(45(21(33(42(51(20(x1))))))) 13#(04(55(20(x1)))) (1581)
01#(45(21(33(42(51(10(x1))))))) 13#(04(55(10(x1)))) (1582)
01#(45(21(33(42(51(00(x1))))))) 13#(04(55(00(x1)))) (1583)
and no rules could be deleted.

1.1.1.1.1.1.1 Dependency Graph Processor

The dependency pairs are split into 0 components.