Certification Problem
Input (TPDB SRS_Standard/ICFP_2010/39849)
The rewrite relation of the following TRS is considered.
|
0(1(2(x1))) |
→ |
0(2(1(1(x1)))) |
(1) |
|
0(3(2(x1))) |
→ |
0(2(1(3(x1)))) |
(2) |
|
2(4(1(x1))) |
→ |
4(2(1(1(x1)))) |
(3) |
|
0(0(3(2(x1)))) |
→ |
0(0(2(1(3(x1))))) |
(4) |
|
0(1(0(3(x1)))) |
→ |
0(1(1(3(0(x1))))) |
(5) |
|
0(1(0(5(x1)))) |
→ |
0(0(1(1(5(x1))))) |
(6) |
|
0(1(2(2(x1)))) |
→ |
0(2(1(1(2(x1))))) |
(7) |
|
0(1(2(3(x1)))) |
→ |
0(2(1(3(1(x1))))) |
(8) |
|
0(1(2(5(x1)))) |
→ |
2(1(1(0(5(x1))))) |
(9) |
|
0(1(4(1(x1)))) |
→ |
0(4(1(1(1(x1))))) |
(10) |
|
0(1(4(2(x1)))) |
→ |
0(0(2(1(4(x1))))) |
(11) |
|
0(1(4(2(x1)))) |
→ |
0(4(0(2(1(x1))))) |
(12) |
|
0(1(4(3(x1)))) |
→ |
4(0(1(1(3(x1))))) |
(13) |
|
0(1(4(5(x1)))) |
→ |
0(1(1(5(4(x1))))) |
(14) |
|
0(1(5(2(x1)))) |
→ |
0(2(5(1(1(x1))))) |
(15) |
|
0(2(0(3(x1)))) |
→ |
0(0(2(3(1(x1))))) |
(16) |
|
0(3(0(1(x1)))) |
→ |
0(0(1(3(1(x1))))) |
(17) |
|
0(3(0(2(x1)))) |
→ |
0(0(2(3(1(x1))))) |
(18) |
|
0(3(0(3(x1)))) |
→ |
0(0(3(1(3(x1))))) |
(19) |
|
0(3(2(0(x1)))) |
→ |
0(2(1(3(0(x1))))) |
(20) |
|
0(3(5(1(x1)))) |
→ |
0(5(3(1(1(x1))))) |
(21) |
|
0(4(0(1(x1)))) |
→ |
0(0(4(1(1(x1))))) |
(22) |
|
0(5(2(0(x1)))) |
→ |
2(1(5(0(0(x1))))) |
(23) |
|
2(1(2(3(x1)))) |
→ |
2(1(1(3(2(x1))))) |
(24) |
|
2(1(4(1(x1)))) |
→ |
4(2(1(1(1(x1))))) |
(25) |
|
2(2(0(3(x1)))) |
→ |
2(0(2(1(3(x1))))) |
(26) |
|
2(2(4(1(x1)))) |
→ |
2(4(2(1(1(x1))))) |
(27) |
|
2(3(1(4(x1)))) |
→ |
2(1(1(3(4(x1))))) |
(28) |
|
2(4(1(4(x1)))) |
→ |
4(4(2(1(1(x1))))) |
(29) |
|
2(4(3(1(x1)))) |
→ |
4(2(3(1(1(x1))))) |
(30) |
|
2(5(0(1(x1)))) |
→ |
0(2(5(1(1(x1))))) |
(31) |
|
2(5(0(3(x1)))) |
→ |
5(0(2(1(3(x1))))) |
(32) |
|
3(0(1(0(x1)))) |
→ |
3(1(0(0(0(x1))))) |
(33) |
|
3(0(1(4(x1)))) |
→ |
3(1(1(0(4(x1))))) |
(34) |
|
3(0(3(0(x1)))) |
→ |
3(1(3(0(0(x1))))) |
(35) |
|
3(1(0(3(x1)))) |
→ |
3(1(1(3(0(x1))))) |
(36) |
|
3(1(2(1(x1)))) |
→ |
1(3(2(1(1(x1))))) |
(37) |
|
3(1(2(1(x1)))) |
→ |
3(2(1(1(1(x1))))) |
(38) |
|
3(2(0(1(x1)))) |
→ |
1(3(0(2(1(x1))))) |
(39) |
|
3(2(0(1(x1)))) |
→ |
3(1(0(2(1(x1))))) |
(40) |
|
3(4(1(2(x1)))) |
→ |
3(2(1(1(4(x1))))) |
(41) |
|
3(5(1(4(x1)))) |
→ |
3(1(1(5(4(x1))))) |
(42) |
|
4(1(0(1(x1)))) |
→ |
4(0(1(1(1(x1))))) |
(43) |
|
4(1(2(1(x1)))) |
→ |
2(4(1(1(1(x1))))) |
(44) |
|
4(1(4(3(x1)))) |
→ |
4(1(1(3(4(x1))))) |
(45) |
|
4(2(4(1(x1)))) |
→ |
4(4(2(1(1(x1))))) |
(46) |
|
4(4(1(2(x1)))) |
→ |
4(2(1(1(4(x1))))) |
(47) |
|
4(5(0(1(x1)))) |
→ |
5(0(4(1(1(x1))))) |
(48) |
|
5(1(0(3(x1)))) |
→ |
5(0(1(1(3(x1))))) |
(49) |
|
5(1(0(3(x1)))) |
→ |
5(1(1(3(0(x1))))) |
(50) |
|
5(1(3(1(x1)))) |
→ |
5(3(1(1(1(x1))))) |
(51) |
|
5(1(4(3(x1)))) |
→ |
4(1(1(3(5(x1))))) |
(52) |
|
5(1(4(4(x1)))) |
→ |
4(1(1(5(4(x1))))) |
(53) |
|
5(1(5(3(x1)))) |
→ |
5(5(1(1(3(x1))))) |
(54) |
|
5(2(0(1(x1)))) |
→ |
2(0(5(1(1(x1))))) |
(55) |
|
5(2(0(5(x1)))) |
→ |
5(0(2(1(5(x1))))) |
(56) |
|
5(3(4(1(x1)))) |
→ |
5(4(3(1(1(x1))))) |
(57) |
|
5(4(0(1(x1)))) |
→ |
5(0(4(1(1(x1))))) |
(58) |
|
5(4(1(0(x1)))) |
→ |
4(1(1(5(0(x1))))) |
(59) |
|
5(4(1(0(x1)))) |
→ |
5(1(1(4(0(x1))))) |
(60) |
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(1(0(x1))) |
→ |
1(1(2(0(x1)))) |
(61) |
|
2(3(0(x1))) |
→ |
3(1(2(0(x1)))) |
(62) |
|
1(4(2(x1))) |
→ |
1(1(2(4(x1)))) |
(63) |
|
2(3(0(0(x1)))) |
→ |
3(1(2(0(0(x1))))) |
(64) |
|
3(0(1(0(x1)))) |
→ |
0(3(1(1(0(x1))))) |
(65) |
|
5(0(1(0(x1)))) |
→ |
5(1(1(0(0(x1))))) |
(66) |
|
2(2(1(0(x1)))) |
→ |
2(1(1(2(0(x1))))) |
(67) |
|
3(2(1(0(x1)))) |
→ |
1(3(1(2(0(x1))))) |
(68) |
|
5(2(1(0(x1)))) |
→ |
5(0(1(1(2(x1))))) |
(69) |
|
1(4(1(0(x1)))) |
→ |
1(1(1(4(0(x1))))) |
(70) |
|
2(4(1(0(x1)))) |
→ |
4(1(2(0(0(x1))))) |
(71) |
|
2(4(1(0(x1)))) |
→ |
1(2(0(4(0(x1))))) |
(72) |
|
3(4(1(0(x1)))) |
→ |
3(1(1(0(4(x1))))) |
(73) |
|
5(4(1(0(x1)))) |
→ |
4(5(1(1(0(x1))))) |
(74) |
|
2(5(1(0(x1)))) |
→ |
1(1(5(2(0(x1))))) |
(75) |
|
3(0(2(0(x1)))) |
→ |
1(3(2(0(0(x1))))) |
(76) |
|
1(0(3(0(x1)))) |
→ |
1(3(1(0(0(x1))))) |
(77) |
|
2(0(3(0(x1)))) |
→ |
1(3(2(0(0(x1))))) |
(78) |
|
3(0(3(0(x1)))) |
→ |
3(1(3(0(0(x1))))) |
(35) |
|
0(2(3(0(x1)))) |
→ |
0(3(1(2(0(x1))))) |
(79) |
|
1(5(3(0(x1)))) |
→ |
1(1(3(5(0(x1))))) |
(80) |
|
1(0(4(0(x1)))) |
→ |
1(1(4(0(0(x1))))) |
(81) |
|
0(2(5(0(x1)))) |
→ |
0(0(5(1(2(x1))))) |
(82) |
|
3(2(1(2(x1)))) |
→ |
2(3(1(1(2(x1))))) |
(83) |
|
1(4(1(2(x1)))) |
→ |
1(1(1(2(4(x1))))) |
(84) |
|
3(0(2(2(x1)))) |
→ |
3(1(2(0(2(x1))))) |
(85) |
|
1(4(2(2(x1)))) |
→ |
1(1(2(4(2(x1))))) |
(86) |
|
4(1(3(2(x1)))) |
→ |
4(3(1(1(2(x1))))) |
(87) |
|
4(1(4(2(x1)))) |
→ |
1(1(2(4(4(x1))))) |
(88) |
|
1(3(4(2(x1)))) |
→ |
1(1(3(2(4(x1))))) |
(89) |
|
1(0(5(2(x1)))) |
→ |
1(1(5(2(0(x1))))) |
(90) |
|
3(0(5(2(x1)))) |
→ |
3(1(2(0(5(x1))))) |
(91) |
|
0(1(0(3(x1)))) |
→ |
0(0(0(1(3(x1))))) |
(92) |
|
4(1(0(3(x1)))) |
→ |
4(0(1(1(3(x1))))) |
(93) |
|
0(3(0(3(x1)))) |
→ |
0(0(3(1(3(x1))))) |
(19) |
|
3(0(1(3(x1)))) |
→ |
0(3(1(1(3(x1))))) |
(94) |
|
1(2(1(3(x1)))) |
→ |
1(1(2(3(1(x1))))) |
(95) |
|
1(2(1(3(x1)))) |
→ |
1(1(1(2(3(x1))))) |
(96) |
|
1(0(2(3(x1)))) |
→ |
1(2(0(3(1(x1))))) |
(97) |
|
1(0(2(3(x1)))) |
→ |
1(2(0(1(3(x1))))) |
(98) |
|
2(1(4(3(x1)))) |
→ |
4(1(1(2(3(x1))))) |
(99) |
|
4(1(5(3(x1)))) |
→ |
4(5(1(1(3(x1))))) |
(100) |
|
1(0(1(4(x1)))) |
→ |
1(1(1(0(4(x1))))) |
(101) |
|
1(2(1(4(x1)))) |
→ |
1(1(1(4(2(x1))))) |
(102) |
|
3(4(1(4(x1)))) |
→ |
4(3(1(1(4(x1))))) |
(103) |
|
1(4(2(4(x1)))) |
→ |
1(1(2(4(4(x1))))) |
(104) |
|
2(1(4(4(x1)))) |
→ |
4(1(1(2(4(x1))))) |
(105) |
|
1(0(5(4(x1)))) |
→ |
1(1(4(0(5(x1))))) |
(106) |
|
3(0(1(5(x1)))) |
→ |
3(1(1(0(5(x1))))) |
(107) |
|
3(0(1(5(x1)))) |
→ |
0(3(1(1(5(x1))))) |
(108) |
|
1(3(1(5(x1)))) |
→ |
1(1(1(3(5(x1))))) |
(109) |
|
3(4(1(5(x1)))) |
→ |
5(3(1(1(4(x1))))) |
(110) |
|
4(4(1(5(x1)))) |
→ |
4(5(1(1(4(x1))))) |
(111) |
|
3(5(1(5(x1)))) |
→ |
3(1(1(5(5(x1))))) |
(112) |
|
1(0(2(5(x1)))) |
→ |
1(1(5(0(2(x1))))) |
(113) |
|
5(0(2(5(x1)))) |
→ |
5(1(2(0(5(x1))))) |
(114) |
|
1(4(3(5(x1)))) |
→ |
1(1(3(4(5(x1))))) |
(115) |
|
1(0(4(5(x1)))) |
→ |
1(1(4(0(5(x1))))) |
(116) |
|
0(1(4(5(x1)))) |
→ |
0(5(1(1(4(x1))))) |
(117) |
|
0(1(4(5(x1)))) |
→ |
0(4(1(1(5(x1))))) |
(118) |
1.1 Closure Under Flat Contexts
Using the flat contexts
{2(☐), 1(☐), 0(☐), 3(☐), 4(☐), 5(☐)}
We obtain the transformed TRS
There are 153 ruless (increase limit for explicit display).
1.1.1 Semantic Labeling
Root-labeling is applied.
We obtain the labeled TRS
There are 918 ruless (increase limit for explicit display).
1.1.1.1 Rule Removal
Using the
linear polynomial interpretation over the naturals
| [14(x1)] |
= |
1 · x1 + 9 |
| [42(x1)] |
= |
1 · x1 + 13 |
| [21(x1)] |
= |
1 · x1 + 30 |
| [11(x1)] |
= |
1 · x1
|
| [12(x1)] |
= |
1 · x1
|
| [24(x1)] |
= |
1 · x1
|
| [41(x1)] |
= |
1 · x1 + 39 |
| [44(x1)] |
= |
1 · x1 + 9 |
| [22(x1)] |
= |
1 · x1 + 5 |
| [25(x1)] |
= |
1 · x1 + 17 |
| [45(x1)] |
= |
1 · x1 + 27 |
| [20(x1)] |
= |
1 · x1
|
| [40(x1)] |
= |
1 · x1 + 10 |
| [23(x1)] |
= |
1 · x1 + 27 |
| [43(x1)] |
= |
1 · x1 + 37 |
| [50(x1)] |
= |
1 · x1 + 23 |
| [01(x1)] |
= |
1 · x1 + 49 |
| [10(x1)] |
= |
1 · x1 + 45 |
| [51(x1)] |
= |
1 · x1 + 25 |
| [00(x1)] |
= |
1 · x1 + 36 |
| [04(x1)] |
= |
1 · x1 + 17 |
| [02(x1)] |
= |
1 · x1 + 39 |
| [05(x1)] |
= |
1 · x1 + 21 |
| [03(x1)] |
= |
1 · x1 + 48 |
| [52(x1)] |
= |
1 · x1
|
| [34(x1)] |
= |
1 · x1
|
| [31(x1)] |
= |
1 · x1 + 14 |
| [30(x1)] |
= |
1 · x1 + 37 |
| [13(x1)] |
= |
1 · x1 + 21 |
| [15(x1)] |
= |
1 · x1 + 29 |
| [53(x1)] |
= |
1 · x1 + 22 |
| [35(x1)] |
= |
1 · x1 + 20 |
| [32(x1)] |
= |
1 · x1 + 2 |
| [54(x1)] |
= |
1 · x1 + 9 |
| [55(x1)] |
= |
1 · x1 + 13 |
| [33(x1)] |
= |
1 · x1 + 13 |
all of the following rules can be deleted.
There are 814 ruless (increase limit for explicit display).
1.1.1.1.1 Rule Removal
Using the
linear polynomial interpretation over the naturals
| [30(x1)] |
= |
1 · x1
|
| [05(x1)] |
= |
1 · x1
|
| [52(x1)] |
= |
1 · x1 + 1 |
| [20(x1)] |
= |
1 · x1
|
| [31(x1)] |
= |
1 · x1
|
| [12(x1)] |
= |
1 · x1
|
| [50(x1)] |
= |
1 · x1
|
| [01(x1)] |
= |
1 · x1
|
| [10(x1)] |
= |
1 · x1
|
| [03(x1)] |
= |
1 · x1
|
| [00(x1)] |
= |
1 · x1
|
| [13(x1)] |
= |
1 · x1
|
| [34(x1)] |
= |
1 · x1
|
| [32(x1)] |
= |
1 · x1
|
| [35(x1)] |
= |
1 · x1
|
| [33(x1)] |
= |
1 · x1
|
| [14(x1)] |
= |
1 · x1
|
| [45(x1)] |
= |
1 · x1
|
| [51(x1)] |
= |
1 · x1 + 1 |
| [04(x1)] |
= |
1 · x1
|
| [41(x1)] |
= |
1 · x1
|
| [11(x1)] |
= |
1 · x1
|
| [15(x1)] |
= |
1 · x1
|
| [54(x1)] |
= |
1 · x1 + 1 |
| [55(x1)] |
= |
1 · x1 + 1 |
| [53(x1)] |
= |
1 · x1
|
| [02(x1)] |
= |
1 · x1
|
| [24(x1)] |
= |
1 · x1
|
| [42(x1)] |
= |
1 · x1
|
| [21(x1)] |
= |
1 · x1
|
| [23(x1)] |
= |
1 · x1
|
| [22(x1)] |
= |
1 · x1
|
| [25(x1)] |
= |
1 · x1
|
| [43(x1)] |
= |
1 · x1
|
| [44(x1)] |
= |
1 · x1
|
| [40(x1)] |
= |
1 · x1
|
all of the following rules can be deleted.
|
30(05(52(20(x1)))) |
→ |
31(12(20(05(50(x1))))) |
(343) |
1.1.1.1.1.1 Rule Removal
Using the
linear polynomial interpretation over the naturals
| [01(x1)] |
= |
1 · x1
|
| [10(x1)] |
= |
1 · x1 + 1 |
| [03(x1)] |
= |
1 · x1
|
| [31(x1)] |
= |
1 · x1
|
| [00(x1)] |
= |
1 · x1
|
| [13(x1)] |
= |
1 · x1
|
| [34(x1)] |
= |
1 · x1
|
| [32(x1)] |
= |
1 · x1 + 1 |
| [35(x1)] |
= |
1 · x1
|
| [30(x1)] |
= |
1 · x1 + 1 |
| [33(x1)] |
= |
1 · x1
|
| [14(x1)] |
= |
1 · x1
|
| [45(x1)] |
= |
1 · x1
|
| [51(x1)] |
= |
1 · x1
|
| [04(x1)] |
= |
1 · x1
|
| [41(x1)] |
= |
1 · x1
|
| [11(x1)] |
= |
1 · x1
|
| [15(x1)] |
= |
1 · x1
|
| [54(x1)] |
= |
1 · x1
|
| [52(x1)] |
= |
1 · x1
|
| [55(x1)] |
= |
1 · x1
|
| [50(x1)] |
= |
1 · x1
|
| [53(x1)] |
= |
1 · x1
|
| [02(x1)] |
= |
1 · x1
|
| [05(x1)] |
= |
1 · x1
|
| [12(x1)] |
= |
1 · x1
|
| [24(x1)] |
= |
1 · x1
|
| [20(x1)] |
= |
1 · x1 + 1 |
| [42(x1)] |
= |
1 · x1
|
| [21(x1)] |
= |
1 · x1
|
| [23(x1)] |
= |
1 · x1 + 1 |
| [22(x1)] |
= |
1 · x1
|
| [25(x1)] |
= |
1 · x1
|
| [43(x1)] |
= |
1 · x1
|
| [44(x1)] |
= |
1 · x1
|
| [40(x1)] |
= |
1 · x1
|
all of the following rules can be deleted.
|
01(10(03(31(x1)))) |
→ |
00(00(01(13(31(x1))))) |
(345) |
|
01(10(03(34(x1)))) |
→ |
00(00(01(13(34(x1))))) |
(346) |
|
01(10(03(32(x1)))) |
→ |
00(00(01(13(32(x1))))) |
(347) |
|
01(10(03(35(x1)))) |
→ |
00(00(01(13(35(x1))))) |
(348) |
|
01(10(03(30(x1)))) |
→ |
00(00(01(13(30(x1))))) |
(349) |
|
01(10(03(33(x1)))) |
→ |
00(00(01(13(33(x1))))) |
(350) |
1.1.1.1.1.1.1 Rule Removal
Using the
linear polynomial interpretation over the naturals
| [01(x1)] |
= |
1 · x1
|
| [14(x1)] |
= |
1 · x1
|
| [45(x1)] |
= |
1 · x1 + 1 |
| [51(x1)] |
= |
1 · x1
|
| [04(x1)] |
= |
1 · x1
|
| [41(x1)] |
= |
1 · x1
|
| [11(x1)] |
= |
1 · x1
|
| [15(x1)] |
= |
1 · x1
|
| [54(x1)] |
= |
1 · x1
|
| [52(x1)] |
= |
1 · x1
|
| [55(x1)] |
= |
1 · x1 + 1 |
| [50(x1)] |
= |
1 · x1
|
| [53(x1)] |
= |
1 · x1
|
| [13(x1)] |
= |
1 · x1
|
| [30(x1)] |
= |
1 · x1
|
| [10(x1)] |
= |
1 · x1
|
| [03(x1)] |
= |
1 · x1
|
| [31(x1)] |
= |
1 · x1
|
| [02(x1)] |
= |
1 · x1
|
| [05(x1)] |
= |
1 · x1 + 1 |
| [00(x1)] |
= |
1 · x1
|
| [33(x1)] |
= |
1 · x1
|
| [12(x1)] |
= |
1 · x1
|
| [24(x1)] |
= |
1 · x1
|
| [20(x1)] |
= |
1 · x1
|
| [42(x1)] |
= |
1 · x1
|
| [32(x1)] |
= |
1 · x1
|
| [21(x1)] |
= |
1 · x1
|
| [23(x1)] |
= |
1 · x1
|
| [22(x1)] |
= |
1 · x1
|
| [25(x1)] |
= |
1 · x1
|
| [34(x1)] |
= |
1 · x1
|
| [35(x1)] |
= |
1 · x1
|
| [43(x1)] |
= |
1 · x1
|
| [44(x1)] |
= |
1 · x1
|
| [40(x1)] |
= |
1 · x1
|
all of the following rules can be deleted.
|
01(14(45(51(x1)))) |
→ |
04(41(11(15(51(x1))))) |
(471) |
|
01(14(45(54(x1)))) |
→ |
04(41(11(15(54(x1))))) |
(472) |
|
01(14(45(52(x1)))) |
→ |
04(41(11(15(52(x1))))) |
(473) |
|
01(14(45(55(x1)))) |
→ |
04(41(11(15(55(x1))))) |
(474) |
|
01(14(45(50(x1)))) |
→ |
04(41(11(15(50(x1))))) |
(475) |
|
01(14(45(53(x1)))) |
→ |
04(41(11(15(53(x1))))) |
(476) |
1.1.1.1.1.1.1.1 Rule Removal
Using the
linear polynomial interpretation over the naturals
| [13(x1)] |
= |
1 · x1
|
| [30(x1)] |
= |
1 · x1 + 1 |
| [01(x1)] |
= |
1 · x1
|
| [10(x1)] |
= |
1 · x1 + 1 |
| [03(x1)] |
= |
1 · x1
|
| [31(x1)] |
= |
1 · x1
|
| [11(x1)] |
= |
1 · x1
|
| [04(x1)] |
= |
1 · x1
|
| [02(x1)] |
= |
1 · x1 + 1 |
| [05(x1)] |
= |
1 · x1
|
| [00(x1)] |
= |
1 · x1
|
| [33(x1)] |
= |
1 · x1
|
| [12(x1)] |
= |
1 · x1
|
| [24(x1)] |
= |
1 · x1
|
| [41(x1)] |
= |
1 · x1
|
| [14(x1)] |
= |
1 · x1
|
| [20(x1)] |
= |
1 · x1
|
| [52(x1)] |
= |
1 · x1
|
| [54(x1)] |
= |
1 · x1
|
| [45(x1)] |
= |
1 · x1
|
| [51(x1)] |
= |
1 · x1
|
| [55(x1)] |
= |
1 · x1
|
| [42(x1)] |
= |
1 · x1
|
| [32(x1)] |
= |
1 · x1 + 1 |
| [21(x1)] |
= |
1 · x1
|
| [23(x1)] |
= |
1 · x1
|
| [22(x1)] |
= |
1 · x1
|
| [25(x1)] |
= |
1 · x1
|
| [34(x1)] |
= |
1 · x1
|
| [35(x1)] |
= |
1 · x1
|
| [43(x1)] |
= |
1 · x1
|
| [44(x1)] |
= |
1 · x1
|
| [40(x1)] |
= |
1 · x1
|
| [15(x1)] |
= |
1 · x1
|
| [50(x1)] |
= |
1 · x1
|
| [53(x1)] |
= |
1 · x1
|
all of the following rules can be deleted.
|
12(24(41(10(01(x1))))) |
→ |
14(41(12(20(00(01(x1)))))) |
(651) |
|
12(24(41(10(04(x1))))) |
→ |
14(41(12(20(00(04(x1)))))) |
(652) |
|
12(24(41(10(02(x1))))) |
→ |
14(41(12(20(00(02(x1)))))) |
(653) |
|
12(24(41(10(05(x1))))) |
→ |
14(41(12(20(00(05(x1)))))) |
(654) |
|
12(24(41(10(00(x1))))) |
→ |
14(41(12(20(00(00(x1)))))) |
(655) |
|
12(24(41(10(03(x1))))) |
→ |
14(41(12(20(00(03(x1)))))) |
(656) |
|
52(24(41(10(01(x1))))) |
→ |
54(41(12(20(00(01(x1)))))) |
(675) |
|
52(24(41(10(04(x1))))) |
→ |
54(41(12(20(00(04(x1)))))) |
(676) |
|
52(24(41(10(02(x1))))) |
→ |
54(41(12(20(00(02(x1)))))) |
(677) |
|
52(24(41(10(05(x1))))) |
→ |
54(41(12(20(00(05(x1)))))) |
(678) |
|
52(24(41(10(00(x1))))) |
→ |
54(41(12(20(00(00(x1)))))) |
(679) |
|
52(24(41(10(03(x1))))) |
→ |
54(41(12(20(00(03(x1)))))) |
(680) |
1.1.1.1.1.1.1.1.1 Rule Removal
Using the
linear polynomial interpretation over the naturals
| [13(x1)] |
= |
1 · x1
|
| [30(x1)] |
= |
1 · x1
|
| [01(x1)] |
= |
1 · x1
|
| [10(x1)] |
= |
1 · x1
|
| [03(x1)] |
= |
1 · x1
|
| [31(x1)] |
= |
1 · x1
|
| [11(x1)] |
= |
1 · x1
|
| [04(x1)] |
= |
1 · x1
|
| [02(x1)] |
= |
1 · x1
|
| [05(x1)] |
= |
1 · x1 + 1 |
| [00(x1)] |
= |
1 · x1
|
| [33(x1)] |
= |
1 · x1
|
| [54(x1)] |
= |
1 · x1
|
| [41(x1)] |
= |
1 · x1
|
| [45(x1)] |
= |
1 · x1
|
| [51(x1)] |
= |
1 · x1
|
| [55(x1)] |
= |
1 · x1
|
| [42(x1)] |
= |
1 · x1
|
| [20(x1)] |
= |
1 · x1
|
| [32(x1)] |
= |
1 · x1
|
| [21(x1)] |
= |
1 · x1
|
| [12(x1)] |
= |
1 · x1
|
| [23(x1)] |
= |
1 · x1
|
| [24(x1)] |
= |
1 · x1
|
| [22(x1)] |
= |
1 · x1
|
| [25(x1)] |
= |
1 · x1
|
| [34(x1)] |
= |
1 · x1
|
| [35(x1)] |
= |
1 · x1
|
| [14(x1)] |
= |
1 · x1
|
| [43(x1)] |
= |
1 · x1
|
| [44(x1)] |
= |
1 · x1
|
| [40(x1)] |
= |
1 · x1
|
| [52(x1)] |
= |
1 · x1
|
| [15(x1)] |
= |
1 · x1
|
| [50(x1)] |
= |
1 · x1
|
| [53(x1)] |
= |
1 · x1
|
all of the following rules can be deleted.
|
05(54(41(10(01(x1))))) |
→ |
04(45(51(11(10(01(x1)))))) |
(729) |
|
05(54(41(10(04(x1))))) |
→ |
04(45(51(11(10(04(x1)))))) |
(730) |
|
05(54(41(10(02(x1))))) |
→ |
04(45(51(11(10(02(x1)))))) |
(731) |
|
05(54(41(10(05(x1))))) |
→ |
04(45(51(11(10(05(x1)))))) |
(732) |
|
05(54(41(10(00(x1))))) |
→ |
04(45(51(11(10(00(x1)))))) |
(733) |
|
05(54(41(10(03(x1))))) |
→ |
04(45(51(11(10(03(x1)))))) |
(734) |
1.1.1.1.1.1.1.1.1.1 Rule Removal
Using the
linear polynomial interpretation over the naturals
| [13(x1)] |
= |
1 · x1
|
| [30(x1)] |
= |
1 · x1
|
| [01(x1)] |
= |
1 · x1
|
| [10(x1)] |
= |
1 · x1
|
| [03(x1)] |
= |
1 · x1
|
| [31(x1)] |
= |
1 · x1
|
| [11(x1)] |
= |
1 · x1
|
| [04(x1)] |
= |
1 · x1
|
| [02(x1)] |
= |
1 · x1
|
| [05(x1)] |
= |
1 · x1
|
| [00(x1)] |
= |
1 · x1
|
| [33(x1)] |
= |
1 · x1
|
| [55(x1)] |
= |
1 · x1 + 1 |
| [54(x1)] |
= |
1 · x1
|
| [41(x1)] |
= |
1 · x1
|
| [45(x1)] |
= |
1 · x1
|
| [51(x1)] |
= |
1 · x1
|
| [42(x1)] |
= |
1 · x1
|
| [20(x1)] |
= |
1 · x1
|
| [32(x1)] |
= |
1 · x1
|
| [21(x1)] |
= |
1 · x1
|
| [12(x1)] |
= |
1 · x1
|
| [23(x1)] |
= |
1 · x1
|
| [24(x1)] |
= |
1 · x1
|
| [22(x1)] |
= |
1 · x1
|
| [25(x1)] |
= |
1 · x1
|
| [34(x1)] |
= |
1 · x1
|
| [35(x1)] |
= |
1 · x1
|
| [14(x1)] |
= |
1 · x1
|
| [43(x1)] |
= |
1 · x1
|
| [44(x1)] |
= |
1 · x1
|
| [40(x1)] |
= |
1 · x1
|
| [52(x1)] |
= |
1 · x1
|
| [15(x1)] |
= |
1 · x1
|
| [50(x1)] |
= |
1 · x1
|
| [53(x1)] |
= |
1 · x1
|
all of the following rules can be deleted.
|
55(54(41(10(01(x1))))) |
→ |
54(45(51(11(10(01(x1)))))) |
(747) |
|
55(54(41(10(04(x1))))) |
→ |
54(45(51(11(10(04(x1)))))) |
(748) |
|
55(54(41(10(02(x1))))) |
→ |
54(45(51(11(10(02(x1)))))) |
(749) |
|
55(54(41(10(05(x1))))) |
→ |
54(45(51(11(10(05(x1)))))) |
(750) |
|
55(54(41(10(00(x1))))) |
→ |
54(45(51(11(10(00(x1)))))) |
(751) |
|
55(54(41(10(03(x1))))) |
→ |
54(45(51(11(10(03(x1)))))) |
(752) |
1.1.1.1.1.1.1.1.1.1.1 Rule Removal
Using the
linear polynomial interpretation over the naturals
| [13(x1)] |
= |
1 · x1
|
| [30(x1)] |
= |
1 · x1
|
| [01(x1)] |
= |
1 · x1
|
| [10(x1)] |
= |
1 · x1
|
| [03(x1)] |
= |
1 · x1
|
| [31(x1)] |
= |
1 · x1
|
| [11(x1)] |
= |
1 · x1
|
| [04(x1)] |
= |
1 · x1
|
| [02(x1)] |
= |
1 · x1
|
| [05(x1)] |
= |
1 · x1
|
| [00(x1)] |
= |
1 · x1
|
| [33(x1)] |
= |
1 · x1
|
| [42(x1)] |
= |
1 · x1 + 1 |
| [20(x1)] |
= |
1 · x1
|
| [41(x1)] |
= |
1 · x1
|
| [32(x1)] |
= |
1 · x1
|
| [21(x1)] |
= |
1 · x1
|
| [12(x1)] |
= |
1 · x1
|
| [23(x1)] |
= |
1 · x1
|
| [24(x1)] |
= |
1 · x1
|
| [22(x1)] |
= |
1 · x1
|
| [25(x1)] |
= |
1 · x1
|
| [34(x1)] |
= |
1 · x1
|
| [35(x1)] |
= |
1 · x1
|
| [14(x1)] |
= |
1 · x1
|
| [43(x1)] |
= |
1 · x1
|
| [44(x1)] |
= |
1 · x1
|
| [45(x1)] |
= |
1 · x1
|
| [40(x1)] |
= |
1 · x1
|
| [52(x1)] |
= |
1 · x1
|
| [54(x1)] |
= |
1 · x1
|
| [15(x1)] |
= |
1 · x1
|
| [51(x1)] |
= |
1 · x1
|
| [55(x1)] |
= |
1 · x1
|
| [50(x1)] |
= |
1 · x1
|
| [53(x1)] |
= |
1 · x1
|
all of the following rules can be deleted.
|
42(20(03(30(01(x1))))) |
→ |
41(13(32(20(00(01(x1)))))) |
(849) |
|
42(20(03(30(04(x1))))) |
→ |
41(13(32(20(00(04(x1)))))) |
(850) |
|
42(20(03(30(02(x1))))) |
→ |
41(13(32(20(00(02(x1)))))) |
(851) |
|
42(20(03(30(05(x1))))) |
→ |
41(13(32(20(00(05(x1)))))) |
(852) |
|
42(20(03(30(00(x1))))) |
→ |
41(13(32(20(00(00(x1)))))) |
(853) |
|
42(20(03(30(03(x1))))) |
→ |
41(13(32(20(00(03(x1)))))) |
(854) |
1.1.1.1.1.1.1.1.1.1.1.1 Rule Removal
Using the
linear polynomial interpretation over the naturals
| [13(x1)] |
= |
1 · x1
|
| [30(x1)] |
= |
1 · x1
|
| [01(x1)] |
= |
1 · x1
|
| [10(x1)] |
= |
1 · x1
|
| [03(x1)] |
= |
1 · x1
|
| [31(x1)] |
= |
1 · x1
|
| [11(x1)] |
= |
1 · x1
|
| [04(x1)] |
= |
1 · x1
|
| [02(x1)] |
= |
1 · x1
|
| [05(x1)] |
= |
1 · x1
|
| [00(x1)] |
= |
1 · x1
|
| [33(x1)] |
= |
1 · x1
|
| [32(x1)] |
= |
1 · x1 + 1 |
| [21(x1)] |
= |
1 · x1
|
| [12(x1)] |
= |
1 · x1
|
| [23(x1)] |
= |
1 · x1
|
| [24(x1)] |
= |
1 · x1
|
| [22(x1)] |
= |
1 · x1
|
| [25(x1)] |
= |
1 · x1
|
| [20(x1)] |
= |
1 · x1
|
| [34(x1)] |
= |
1 · x1
|
| [35(x1)] |
= |
1 · x1
|
| [41(x1)] |
= |
1 · x1
|
| [14(x1)] |
= |
1 · x1
|
| [43(x1)] |
= |
1 · x1
|
| [44(x1)] |
= |
1 · x1
|
| [42(x1)] |
= |
1 · x1
|
| [45(x1)] |
= |
1 · x1
|
| [40(x1)] |
= |
1 · x1
|
| [52(x1)] |
= |
1 · x1
|
| [54(x1)] |
= |
1 · x1
|
| [15(x1)] |
= |
1 · x1
|
| [51(x1)] |
= |
1 · x1
|
| [55(x1)] |
= |
1 · x1
|
| [50(x1)] |
= |
1 · x1
|
| [53(x1)] |
= |
1 · x1
|
all of the following rules can be deleted.
|
03(32(21(12(21(x1))))) |
→ |
02(23(31(11(12(21(x1)))))) |
(873) |
|
03(32(21(12(24(x1))))) |
→ |
02(23(31(11(12(24(x1)))))) |
(874) |
|
03(32(21(12(22(x1))))) |
→ |
02(23(31(11(12(22(x1)))))) |
(875) |
|
03(32(21(12(25(x1))))) |
→ |
02(23(31(11(12(25(x1)))))) |
(876) |
|
03(32(21(12(20(x1))))) |
→ |
02(23(31(11(12(20(x1)))))) |
(877) |
|
03(32(21(12(23(x1))))) |
→ |
02(23(31(11(12(23(x1)))))) |
(878) |
1.1.1.1.1.1.1.1.1.1.1.1.1 Rule Removal
Using the
linear polynomial interpretation over the naturals
| [13(x1)] |
= |
1 · x1
|
| [30(x1)] |
= |
1 · x1
|
| [01(x1)] |
= |
1 · x1
|
| [10(x1)] |
= |
1 · x1
|
| [03(x1)] |
= |
1 · x1
|
| [31(x1)] |
= |
1 · x1
|
| [11(x1)] |
= |
1 · x1
|
| [04(x1)] |
= |
1 · x1
|
| [02(x1)] |
= |
1 · x1
|
| [05(x1)] |
= |
1 · x1
|
| [00(x1)] |
= |
1 · x1
|
| [33(x1)] |
= |
1 · x1
|
| [34(x1)] |
= |
1 · x1
|
| [32(x1)] |
= |
1 · x1
|
| [35(x1)] |
= |
1 · x1
|
| [41(x1)] |
= |
1 · x1
|
| [14(x1)] |
= |
1 · x1
|
| [43(x1)] |
= |
1 · x1
|
| [44(x1)] |
= |
1 · x1
|
| [42(x1)] |
= |
1 · x1
|
| [45(x1)] |
= |
1 · x1
|
| [40(x1)] |
= |
1 · x1
|
| [12(x1)] |
= |
1 · x1 + 1 |
| [21(x1)] |
= |
1 · x1 + 1 |
| [24(x1)] |
= |
1 · x1
|
| [52(x1)] |
= |
1 · x1
|
| [54(x1)] |
= |
1 · x1
|
| [15(x1)] |
= |
1 · x1
|
| [51(x1)] |
= |
1 · x1
|
| [55(x1)] |
= |
1 · x1
|
| [50(x1)] |
= |
1 · x1
|
| [53(x1)] |
= |
1 · x1
|
all of the following rules can be deleted.
|
12(21(14(44(41(x1))))) |
→ |
14(41(11(12(24(41(x1)))))) |
(1047) |
|
12(21(14(44(44(x1))))) |
→ |
14(41(11(12(24(44(x1)))))) |
(1048) |
|
12(21(14(44(42(x1))))) |
→ |
14(41(11(12(24(42(x1)))))) |
(1049) |
|
12(21(14(44(45(x1))))) |
→ |
14(41(11(12(24(45(x1)))))) |
(1050) |
|
12(21(14(44(40(x1))))) |
→ |
14(41(11(12(24(40(x1)))))) |
(1051) |
|
12(21(14(44(43(x1))))) |
→ |
14(41(11(12(24(43(x1)))))) |
(1052) |
1.1.1.1.1.1.1.1.1.1.1.1.1.1 Rule Removal
Using the
linear polynomial interpretation over the naturals
| [13(x1)] |
= |
1 · x1
|
| [30(x1)] |
= |
1 · x1
|
| [01(x1)] |
= |
1 · x1
|
| [10(x1)] |
= |
1 · x1
|
| [03(x1)] |
= |
1 · x1
|
| [31(x1)] |
= |
1 · x1
|
| [11(x1)] |
= |
1 · x1
|
| [04(x1)] |
= |
1 · x1
|
| [02(x1)] |
= |
1 · x1
|
| [05(x1)] |
= |
1 · x1
|
| [00(x1)] |
= |
1 · x1
|
| [33(x1)] |
= |
1 · x1
|
| [34(x1)] |
= |
1 · x1
|
| [32(x1)] |
= |
1 · x1
|
| [35(x1)] |
= |
1 · x1
|
| [41(x1)] |
= |
1 · x1
|
| [14(x1)] |
= |
1 · x1
|
| [43(x1)] |
= |
1 · x1
|
| [44(x1)] |
= |
1 · x1
|
| [42(x1)] |
= |
1 · x1
|
| [45(x1)] |
= |
1 · x1
|
| [40(x1)] |
= |
1 · x1
|
| [52(x1)] |
= |
1 · x1 + 1 |
| [21(x1)] |
= |
1 · x1
|
| [54(x1)] |
= |
1 · x1
|
| [12(x1)] |
= |
1 · x1
|
| [24(x1)] |
= |
1 · x1
|
| [15(x1)] |
= |
1 · x1
|
| [51(x1)] |
= |
1 · x1
|
| [55(x1)] |
= |
1 · x1
|
| [50(x1)] |
= |
1 · x1
|
| [53(x1)] |
= |
1 · x1
|
all of the following rules can be deleted.
|
52(21(14(44(41(x1))))) |
→ |
54(41(11(12(24(41(x1)))))) |
(1071) |
|
52(21(14(44(44(x1))))) |
→ |
54(41(11(12(24(44(x1)))))) |
(1072) |
|
52(21(14(44(42(x1))))) |
→ |
54(41(11(12(24(42(x1)))))) |
(1073) |
|
52(21(14(44(45(x1))))) |
→ |
54(41(11(12(24(45(x1)))))) |
(1074) |
|
52(21(14(44(40(x1))))) |
→ |
54(41(11(12(24(40(x1)))))) |
(1075) |
|
52(21(14(44(43(x1))))) |
→ |
54(41(11(12(24(43(x1)))))) |
(1076) |
1.1.1.1.1.1.1.1.1.1.1.1.1.1.1 Rule Removal
Using the
linear polynomial interpretation over the naturals
| [13(x1)] |
= |
1 · x1
|
| [30(x1)] |
= |
1 · x1 + 1 |
| [01(x1)] |
= |
1 · x1
|
| [10(x1)] |
= |
1 · x1
|
| [03(x1)] |
= |
1 · x1
|
| [31(x1)] |
= |
1 · x1
|
| [11(x1)] |
= |
1 · x1
|
| [04(x1)] |
= |
1 · x1
|
| [02(x1)] |
= |
1 · x1
|
| [05(x1)] |
= |
1 · x1
|
| [00(x1)] |
= |
1 · x1
|
| [33(x1)] |
= |
1 · x1
|
| [34(x1)] |
= |
1 · x1
|
| [32(x1)] |
= |
1 · x1
|
| [35(x1)] |
= |
1 · x1
|
| [41(x1)] |
= |
1 · x1
|
| [14(x1)] |
= |
1 · x1
|
| [43(x1)] |
= |
1 · x1
|
| [44(x1)] |
= |
1 · x1
|
| [42(x1)] |
= |
1 · x1
|
| [45(x1)] |
= |
1 · x1
|
| [40(x1)] |
= |
1 · x1
|
| [15(x1)] |
= |
1 · x1
|
| [51(x1)] |
= |
1 · x1
|
| [54(x1)] |
= |
1 · x1
|
| [52(x1)] |
= |
1 · x1
|
| [55(x1)] |
= |
1 · x1
|
| [50(x1)] |
= |
1 · x1
|
| [53(x1)] |
= |
1 · x1
|
all of the following rules can be deleted.
|
13(30(01(10(01(x1))))) |
→ |
10(03(31(11(10(01(x1)))))) |
(579) |
|
13(30(01(10(04(x1))))) |
→ |
10(03(31(11(10(04(x1)))))) |
(580) |
|
13(30(01(10(02(x1))))) |
→ |
10(03(31(11(10(02(x1)))))) |
(581) |
|
13(30(01(10(05(x1))))) |
→ |
10(03(31(11(10(05(x1)))))) |
(582) |
|
13(30(01(10(00(x1))))) |
→ |
10(03(31(11(10(00(x1)))))) |
(583) |
|
13(30(01(10(03(x1))))) |
→ |
10(03(31(11(10(03(x1)))))) |
(584) |
|
13(30(01(13(31(x1))))) |
→ |
10(03(31(11(13(31(x1)))))) |
(939) |
|
13(30(01(13(34(x1))))) |
→ |
10(03(31(11(13(34(x1)))))) |
(940) |
|
13(30(01(13(32(x1))))) |
→ |
10(03(31(11(13(32(x1)))))) |
(941) |
|
13(30(01(13(35(x1))))) |
→ |
10(03(31(11(13(35(x1)))))) |
(942) |
|
13(30(01(13(30(x1))))) |
→ |
10(03(31(11(13(30(x1)))))) |
(943) |
|
13(30(01(13(33(x1))))) |
→ |
10(03(31(11(13(33(x1)))))) |
(944) |
|
13(30(01(15(51(x1))))) |
→ |
10(03(31(11(15(51(x1)))))) |
(1083) |
|
13(30(01(15(54(x1))))) |
→ |
10(03(31(11(15(54(x1)))))) |
(1084) |
|
13(30(01(15(52(x1))))) |
→ |
10(03(31(11(15(52(x1)))))) |
(1085) |
|
13(30(01(15(55(x1))))) |
→ |
10(03(31(11(15(55(x1)))))) |
(1086) |
|
13(30(01(15(50(x1))))) |
→ |
10(03(31(11(15(50(x1)))))) |
(1087) |
|
13(30(01(15(53(x1))))) |
→ |
10(03(31(11(15(53(x1)))))) |
(1088) |
1.1.1.1.1.1.1.1.1.1.1.1.1.1.1.1 Rule Removal
Using the
linear polynomial interpretation over the naturals
| [33(x1)] |
= |
1 · x1
|
| [30(x1)] |
= |
1 · x1
|
| [01(x1)] |
= |
1 · x1 + 1 |
| [10(x1)] |
= |
1 · x1
|
| [03(x1)] |
= |
1 · x1
|
| [31(x1)] |
= |
1 · x1
|
| [11(x1)] |
= |
1 · x1
|
| [04(x1)] |
= |
1 · x1
|
| [02(x1)] |
= |
1 · x1
|
| [05(x1)] |
= |
1 · x1
|
| [00(x1)] |
= |
1 · x1
|
| [13(x1)] |
= |
1 · x1
|
| [34(x1)] |
= |
1 · x1
|
| [32(x1)] |
= |
1 · x1
|
| [35(x1)] |
= |
1 · x1
|
| [41(x1)] |
= |
1 · x1
|
| [14(x1)] |
= |
1 · x1
|
| [43(x1)] |
= |
1 · x1
|
| [44(x1)] |
= |
1 · x1
|
| [42(x1)] |
= |
1 · x1
|
| [45(x1)] |
= |
1 · x1
|
| [40(x1)] |
= |
1 · x1
|
| [15(x1)] |
= |
1 · x1
|
| [51(x1)] |
= |
1 · x1
|
| [54(x1)] |
= |
1 · x1
|
| [52(x1)] |
= |
1 · x1
|
| [55(x1)] |
= |
1 · x1
|
| [50(x1)] |
= |
1 · x1
|
| [53(x1)] |
= |
1 · x1
|
all of the following rules can be deleted.
|
33(30(01(10(01(x1))))) |
→ |
30(03(31(11(10(01(x1)))))) |
(591) |
|
33(30(01(10(04(x1))))) |
→ |
30(03(31(11(10(04(x1)))))) |
(592) |
|
33(30(01(10(02(x1))))) |
→ |
30(03(31(11(10(02(x1)))))) |
(593) |
|
33(30(01(10(05(x1))))) |
→ |
30(03(31(11(10(05(x1)))))) |
(594) |
|
33(30(01(10(00(x1))))) |
→ |
30(03(31(11(10(00(x1)))))) |
(595) |
|
33(30(01(10(03(x1))))) |
→ |
30(03(31(11(10(03(x1)))))) |
(596) |
|
33(30(01(13(31(x1))))) |
→ |
30(03(31(11(13(31(x1)))))) |
(951) |
|
33(30(01(13(34(x1))))) |
→ |
30(03(31(11(13(34(x1)))))) |
(952) |
|
33(30(01(13(32(x1))))) |
→ |
30(03(31(11(13(32(x1)))))) |
(953) |
|
33(30(01(13(35(x1))))) |
→ |
30(03(31(11(13(35(x1)))))) |
(954) |
|
33(30(01(13(30(x1))))) |
→ |
30(03(31(11(13(30(x1)))))) |
(955) |
|
33(30(01(13(33(x1))))) |
→ |
30(03(31(11(13(33(x1)))))) |
(956) |
|
33(30(01(15(51(x1))))) |
→ |
30(03(31(11(15(51(x1)))))) |
(1095) |
|
33(30(01(15(54(x1))))) |
→ |
30(03(31(11(15(54(x1)))))) |
(1096) |
|
33(30(01(15(52(x1))))) |
→ |
30(03(31(11(15(52(x1)))))) |
(1097) |
|
33(30(01(15(55(x1))))) |
→ |
30(03(31(11(15(55(x1)))))) |
(1098) |
|
33(30(01(15(50(x1))))) |
→ |
30(03(31(11(15(50(x1)))))) |
(1099) |
|
33(30(01(15(53(x1))))) |
→ |
30(03(31(11(15(53(x1)))))) |
(1100) |
1.1.1.1.1.1.1.1.1.1.1.1.1.1.1.1.1 Rule Removal
Using the
linear polynomial interpretation over the naturals
| [13(x1)] |
= |
1 · x1
|
| [34(x1)] |
= |
1 · x1 + 1 |
| [41(x1)] |
= |
1 · x1
|
| [14(x1)] |
= |
1 · x1
|
| [43(x1)] |
= |
1 · x1
|
| [31(x1)] |
= |
1 · x1
|
| [11(x1)] |
= |
1 · x1
|
| [44(x1)] |
= |
1 · x1
|
| [42(x1)] |
= |
1 · x1
|
| [45(x1)] |
= |
1 · x1
|
| [40(x1)] |
= |
1 · x1
|
| [15(x1)] |
= |
1 · x1
|
| [53(x1)] |
= |
1 · x1
|
all of the following rules can be deleted.
|
13(34(41(14(41(x1))))) |
→ |
14(43(31(11(14(41(x1)))))) |
(1011) |
|
13(34(41(14(44(x1))))) |
→ |
14(43(31(11(14(44(x1)))))) |
(1012) |
|
13(34(41(14(42(x1))))) |
→ |
14(43(31(11(14(42(x1)))))) |
(1013) |
|
13(34(41(14(45(x1))))) |
→ |
14(43(31(11(14(45(x1)))))) |
(1014) |
|
13(34(41(14(40(x1))))) |
→ |
14(43(31(11(14(40(x1)))))) |
(1015) |
|
13(34(41(14(43(x1))))) |
→ |
14(43(31(11(14(43(x1)))))) |
(1016) |
|
13(34(41(15(53(x1))))) |
→ |
15(53(31(11(14(43(x1)))))) |
(1124) |
1.1.1.1.1.1.1.1.1.1.1.1.1.1.1.1.1.1 R is empty
There are no rules in the TRS. Hence, it is terminating.