Certification Problem
Input (TPDB SRS_Standard/ICFP_2010/264033)
The rewrite relation of the following TRS is considered.
|
0(0(1(0(2(x1))))) |
→ |
0(0(1(2(2(x1))))) |
(1) |
|
0(0(1(0(2(x1))))) |
→ |
0(0(2(1(2(x1))))) |
(2) |
|
0(0(1(0(2(x1))))) |
→ |
0(1(0(2(2(x1))))) |
(3) |
|
0(0(1(0(2(x1))))) |
→ |
0(1(1(2(2(x1))))) |
(4) |
|
0(0(1(0(2(x1))))) |
→ |
0(1(2(0(2(x1))))) |
(5) |
|
0(0(1(0(2(x1))))) |
→ |
0(1(2(2(0(x1))))) |
(6) |
|
0(0(1(0(2(x1))))) |
→ |
0(1(2(2(2(x1))))) |
(7) |
|
0(0(1(0(2(x1))))) |
→ |
0(2(1(0(2(x1))))) |
(8) |
|
0(0(1(0(2(x1))))) |
→ |
0(2(1(2(2(x1))))) |
(9) |
|
0(0(1(0(2(x1))))) |
→ |
0(2(2(1(0(x1))))) |
(10) |
|
0(0(1(0(2(x1))))) |
→ |
0(2(2(1(2(x1))))) |
(11) |
|
0(0(1(0(2(x1))))) |
→ |
1(0(0(2(2(x1))))) |
(12) |
|
0(0(1(0(2(x1))))) |
→ |
1(0(2(0(2(x1))))) |
(13) |
|
0(0(1(0(2(x1))))) |
→ |
1(0(2(2(0(x1))))) |
(14) |
|
0(0(1(0(2(x1))))) |
→ |
1(0(2(2(2(x1))))) |
(15) |
|
0(0(1(0(2(x1))))) |
→ |
1(1(0(2(2(x1))))) |
(16) |
|
0(0(1(0(2(x1))))) |
→ |
1(2(0(2(2(x1))))) |
(17) |
|
0(0(1(0(2(x1))))) |
→ |
1(2(1(0(2(x1))))) |
(18) |
|
0(0(1(0(2(x1))))) |
→ |
1(2(2(0(2(x1))))) |
(19) |
|
0(0(1(0(2(x1))))) |
→ |
1(2(2(2(0(x1))))) |
(20) |
|
0(0(1(0(2(x1))))) |
→ |
2(1(0(2(2(x1))))) |
(21) |
|
0(0(1(0(2(x1))))) |
→ |
2(2(1(0(2(x1))))) |
(22) |
|
0(0(1(0(2(x1))))) |
→ |
2(2(2(1(0(x1))))) |
(23) |
|
0(1(2(0(2(x1))))) |
→ |
0(1(0(2(2(x1))))) |
(24) |
|
0(1(2(0(2(x1))))) |
→ |
0(1(1(2(2(x1))))) |
(25) |
|
0(1(2(0(2(x1))))) |
→ |
0(1(2(2(2(x1))))) |
(26) |
|
0(1(2(0(2(x1))))) |
→ |
0(2(1(0(2(x1))))) |
(27) |
|
0(1(2(0(2(x1))))) |
→ |
0(2(1(2(2(x1))))) |
(28) |
|
0(1(2(0(2(x1))))) |
→ |
0(2(2(1(0(x1))))) |
(29) |
|
0(1(2(0(2(x1))))) |
→ |
0(2(2(1(2(x1))))) |
(30) |
|
0(1(2(0(2(x1))))) |
→ |
1(0(2(2(2(x1))))) |
(31) |
|
0(1(2(0(2(x1))))) |
→ |
1(2(0(2(2(x1))))) |
(32) |
|
0(1(2(0(2(x1))))) |
→ |
1(2(2(0(2(x1))))) |
(33) |
|
0(1(2(0(2(x1))))) |
→ |
1(2(2(2(0(x1))))) |
(34) |
|
1(0(1(0(2(x1))))) |
→ |
0(1(2(2(2(x1))))) |
(35) |
|
1(0(1(0(2(x1))))) |
→ |
0(2(1(2(2(x1))))) |
(36) |
|
1(0(1(0(2(x1))))) |
→ |
1(0(0(2(2(x1))))) |
(37) |
|
1(0(1(0(2(x1))))) |
→ |
1(0(1(2(2(x1))))) |
(38) |
|
1(0(1(0(2(x1))))) |
→ |
1(0(2(0(2(x1))))) |
(39) |
|
1(0(1(0(2(x1))))) |
→ |
1(0(2(1(2(x1))))) |
(40) |
|
1(0(1(0(2(x1))))) |
→ |
1(0(2(2(0(x1))))) |
(41) |
|
1(0(1(0(2(x1))))) |
→ |
1(0(2(2(2(x1))))) |
(42) |
|
1(0(1(0(2(x1))))) |
→ |
1(1(0(2(2(x1))))) |
(43) |
|
1(0(1(0(2(x1))))) |
→ |
1(2(0(2(2(x1))))) |
(44) |
|
1(0(1(0(2(x1))))) |
→ |
1(2(1(0(2(x1))))) |
(45) |
|
1(0(1(0(2(x1))))) |
→ |
1(2(2(0(2(x1))))) |
(46) |
|
1(0(1(0(2(x1))))) |
→ |
1(2(2(2(0(x1))))) |
(47) |
|
1(0(1(0(2(x1))))) |
→ |
2(0(1(2(2(x1))))) |
(48) |
|
1(0(1(0(2(x1))))) |
→ |
2(0(2(1(2(x1))))) |
(49) |
|
1(0(1(0(2(x1))))) |
→ |
2(1(0(2(2(x1))))) |
(50) |
|
1(0(1(0(2(x1))))) |
→ |
2(1(2(0(2(x1))))) |
(51) |
|
1(0(1(0(2(x1))))) |
→ |
2(1(2(2(0(x1))))) |
(52) |
|
1(0(1(0(2(x1))))) |
→ |
2(2(0(1(2(x1))))) |
(53) |
|
1(0(1(0(2(x1))))) |
→ |
2(2(1(0(2(x1))))) |
(54) |
|
1(0(1(0(2(x1))))) |
→ |
2(2(1(2(0(x1))))) |
(55) |
|
1(0(1(0(2(x1))))) |
→ |
2(2(2(1(0(x1))))) |
(56) |
|
1(0(2(0(2(x1))))) |
→ |
1(0(2(2(2(x1))))) |
(57) |
|
1(0(2(0(2(x1))))) |
→ |
1(2(0(2(2(x1))))) |
(58) |
|
1(0(2(0(2(x1))))) |
→ |
1(2(2(0(2(x1))))) |
(59) |
|
1(0(2(0(2(x1))))) |
→ |
1(2(2(2(0(x1))))) |
(60) |
|
1(0(2(0(2(x1))))) |
→ |
2(1(0(2(2(x1))))) |
(61) |
|
1(0(2(0(2(x1))))) |
→ |
2(2(1(0(2(x1))))) |
(62) |
|
1(1(2(0(2(x1))))) |
→ |
0(1(2(2(2(x1))))) |
(63) |
|
1(1(2(0(2(x1))))) |
→ |
0(2(1(2(2(x1))))) |
(64) |
|
1(1(2(0(2(x1))))) |
→ |
0(2(2(1(2(x1))))) |
(65) |
|
1(1(2(0(2(x1))))) |
→ |
1(0(0(2(2(x1))))) |
(66) |
|
1(1(2(0(2(x1))))) |
→ |
1(0(1(2(2(x1))))) |
(67) |
|
1(1(2(0(2(x1))))) |
→ |
1(0(2(0(2(x1))))) |
(68) |
|
1(1(2(0(2(x1))))) |
→ |
1(0(2(1(2(x1))))) |
(69) |
|
1(1(2(0(2(x1))))) |
→ |
1(0(2(2(0(x1))))) |
(70) |
|
1(1(2(0(2(x1))))) |
→ |
1(0(2(2(2(x1))))) |
(71) |
|
1(1(2(0(2(x1))))) |
→ |
1(1(0(2(2(x1))))) |
(72) |
|
1(1(2(0(2(x1))))) |
→ |
1(2(0(2(2(x1))))) |
(73) |
|
1(1(2(0(2(x1))))) |
→ |
1(2(1(0(2(x1))))) |
(74) |
|
1(1(2(0(2(x1))))) |
→ |
1(2(2(0(2(x1))))) |
(75) |
|
1(1(2(0(2(x1))))) |
→ |
1(2(2(2(0(x1))))) |
(76) |
|
1(1(2(0(2(x1))))) |
→ |
2(0(1(2(2(x1))))) |
(77) |
|
1(1(2(0(2(x1))))) |
→ |
2(1(0(2(2(x1))))) |
(78) |
|
1(1(2(0(2(x1))))) |
→ |
2(1(2(0(2(x1))))) |
(79) |
|
1(1(2(0(2(x1))))) |
→ |
2(2(0(1(2(x1))))) |
(80) |
|
1(1(2(0(2(x1))))) |
→ |
2(2(1(0(2(x1))))) |
(81) |
|
1(1(2(0(2(x1))))) |
→ |
2(2(2(1(0(x1))))) |
(82) |
|
1(2(2(0(2(x1))))) |
→ |
1(0(2(2(2(x1))))) |
(83) |
|
2(0(1(0(2(x1))))) |
→ |
2(0(1(2(2(x1))))) |
(84) |
|
2(0(1(0(2(x1))))) |
→ |
2(0(2(1(2(x1))))) |
(85) |
|
2(0(1(0(2(x1))))) |
→ |
2(1(0(2(2(x1))))) |
(86) |
|
2(0(1(0(2(x1))))) |
→ |
2(1(2(0(2(x1))))) |
(87) |
|
2(0(1(0(2(x1))))) |
→ |
2(1(2(2(0(x1))))) |
(88) |
|
2(0(1(0(2(x1))))) |
→ |
2(2(0(1(2(x1))))) |
(89) |
|
2(0(1(0(2(x1))))) |
→ |
2(2(1(0(2(x1))))) |
(90) |
|
2(0(1(0(2(x1))))) |
→ |
2(2(1(2(0(x1))))) |
(91) |
|
2(0(1(0(2(x1))))) |
→ |
2(2(2(1(0(x1))))) |
(92) |
|
2(1(1(0(2(x1))))) |
→ |
2(0(1(0(2(x1))))) |
(93) |
|
2(1(1(0(2(x1))))) |
→ |
2(0(2(1(2(x1))))) |
(94) |
|
2(1(1(0(2(x1))))) |
→ |
2(1(2(0(2(x1))))) |
(95) |
|
2(1(1(0(2(x1))))) |
→ |
2(2(1(0(2(x1))))) |
(96) |
|
2(1(2(0(2(x1))))) |
→ |
2(0(1(2(2(x1))))) |
(97) |
|
2(1(2(0(2(x1))))) |
→ |
2(1(0(2(2(x1))))) |
(98) |
|
2(1(2(0(2(x1))))) |
→ |
2(2(1(0(2(x1))))) |
(99) |
|
2(1(2(0(2(x1))))) |
→ |
2(2(2(1(0(x1))))) |
(100) |
Property / Task
Prove or disprove termination.Answer / Result
Yes.Proof (by matchbox @ termCOMP 2023)
1 Rule Removal
Using the
matrix interpretations of dimension 1 with strict dimension 1 over the rationals with delta = 1
| [2(x1)] |
= |
x1 +
|
| [1(x1)] |
= |
x1 +
|
| [0(x1)] |
= |
x1 +
|
all of the following rules can be deleted.
|
0(0(1(0(2(x1))))) |
→ |
0(0(1(2(2(x1))))) |
(1) |
|
0(0(1(0(2(x1))))) |
→ |
0(0(2(1(2(x1))))) |
(2) |
|
0(0(1(0(2(x1))))) |
→ |
0(1(0(2(2(x1))))) |
(3) |
|
0(0(1(0(2(x1))))) |
→ |
0(1(1(2(2(x1))))) |
(4) |
|
0(0(1(0(2(x1))))) |
→ |
0(1(2(0(2(x1))))) |
(5) |
|
0(0(1(0(2(x1))))) |
→ |
0(1(2(2(0(x1))))) |
(6) |
|
0(0(1(0(2(x1))))) |
→ |
0(1(2(2(2(x1))))) |
(7) |
|
0(0(1(0(2(x1))))) |
→ |
0(2(1(0(2(x1))))) |
(8) |
|
0(0(1(0(2(x1))))) |
→ |
0(2(1(2(2(x1))))) |
(9) |
|
0(0(1(0(2(x1))))) |
→ |
0(2(2(1(0(x1))))) |
(10) |
|
0(0(1(0(2(x1))))) |
→ |
0(2(2(1(2(x1))))) |
(11) |
|
0(0(1(0(2(x1))))) |
→ |
1(0(0(2(2(x1))))) |
(12) |
|
0(0(1(0(2(x1))))) |
→ |
1(0(2(0(2(x1))))) |
(13) |
|
0(0(1(0(2(x1))))) |
→ |
1(0(2(2(0(x1))))) |
(14) |
|
0(0(1(0(2(x1))))) |
→ |
1(0(2(2(2(x1))))) |
(15) |
|
0(0(1(0(2(x1))))) |
→ |
1(1(0(2(2(x1))))) |
(16) |
|
0(0(1(0(2(x1))))) |
→ |
1(2(0(2(2(x1))))) |
(17) |
|
0(0(1(0(2(x1))))) |
→ |
1(2(1(0(2(x1))))) |
(18) |
|
0(0(1(0(2(x1))))) |
→ |
1(2(2(0(2(x1))))) |
(19) |
|
0(0(1(0(2(x1))))) |
→ |
1(2(2(2(0(x1))))) |
(20) |
|
0(0(1(0(2(x1))))) |
→ |
2(1(0(2(2(x1))))) |
(21) |
|
0(0(1(0(2(x1))))) |
→ |
2(2(1(0(2(x1))))) |
(22) |
|
0(0(1(0(2(x1))))) |
→ |
2(2(2(1(0(x1))))) |
(23) |
|
0(1(2(0(2(x1))))) |
→ |
0(1(2(2(2(x1))))) |
(26) |
|
0(1(2(0(2(x1))))) |
→ |
0(2(1(2(2(x1))))) |
(28) |
|
0(1(2(0(2(x1))))) |
→ |
0(2(2(1(2(x1))))) |
(30) |
|
0(1(2(0(2(x1))))) |
→ |
1(0(2(2(2(x1))))) |
(31) |
|
0(1(2(0(2(x1))))) |
→ |
1(2(0(2(2(x1))))) |
(32) |
|
0(1(2(0(2(x1))))) |
→ |
1(2(2(0(2(x1))))) |
(33) |
|
0(1(2(0(2(x1))))) |
→ |
1(2(2(2(0(x1))))) |
(34) |
|
1(0(1(0(2(x1))))) |
→ |
0(1(2(2(2(x1))))) |
(35) |
|
1(0(1(0(2(x1))))) |
→ |
0(2(1(2(2(x1))))) |
(36) |
|
1(0(1(0(2(x1))))) |
→ |
1(0(0(2(2(x1))))) |
(37) |
|
1(0(1(0(2(x1))))) |
→ |
1(0(1(2(2(x1))))) |
(38) |
|
1(0(1(0(2(x1))))) |
→ |
1(0(2(0(2(x1))))) |
(39) |
|
1(0(1(0(2(x1))))) |
→ |
1(0(2(1(2(x1))))) |
(40) |
|
1(0(1(0(2(x1))))) |
→ |
1(0(2(2(0(x1))))) |
(41) |
|
1(0(1(0(2(x1))))) |
→ |
1(0(2(2(2(x1))))) |
(42) |
|
1(0(1(0(2(x1))))) |
→ |
1(1(0(2(2(x1))))) |
(43) |
|
1(0(1(0(2(x1))))) |
→ |
1(2(0(2(2(x1))))) |
(44) |
|
1(0(1(0(2(x1))))) |
→ |
1(2(1(0(2(x1))))) |
(45) |
|
1(0(1(0(2(x1))))) |
→ |
1(2(2(0(2(x1))))) |
(46) |
|
1(0(1(0(2(x1))))) |
→ |
1(2(2(2(0(x1))))) |
(47) |
|
1(0(1(0(2(x1))))) |
→ |
2(0(1(2(2(x1))))) |
(48) |
|
1(0(1(0(2(x1))))) |
→ |
2(0(2(1(2(x1))))) |
(49) |
|
1(0(1(0(2(x1))))) |
→ |
2(1(0(2(2(x1))))) |
(50) |
|
1(0(1(0(2(x1))))) |
→ |
2(1(2(0(2(x1))))) |
(51) |
|
1(0(1(0(2(x1))))) |
→ |
2(1(2(2(0(x1))))) |
(52) |
|
1(0(1(0(2(x1))))) |
→ |
2(2(0(1(2(x1))))) |
(53) |
|
1(0(1(0(2(x1))))) |
→ |
2(2(1(0(2(x1))))) |
(54) |
|
1(0(1(0(2(x1))))) |
→ |
2(2(1(2(0(x1))))) |
(55) |
|
1(0(1(0(2(x1))))) |
→ |
2(2(2(1(0(x1))))) |
(56) |
|
1(0(2(0(2(x1))))) |
→ |
1(0(2(2(2(x1))))) |
(57) |
|
1(0(2(0(2(x1))))) |
→ |
1(2(0(2(2(x1))))) |
(58) |
|
1(0(2(0(2(x1))))) |
→ |
1(2(2(0(2(x1))))) |
(59) |
|
1(0(2(0(2(x1))))) |
→ |
1(2(2(2(0(x1))))) |
(60) |
|
1(0(2(0(2(x1))))) |
→ |
2(1(0(2(2(x1))))) |
(61) |
|
1(0(2(0(2(x1))))) |
→ |
2(2(1(0(2(x1))))) |
(62) |
|
1(1(2(0(2(x1))))) |
→ |
0(1(2(2(2(x1))))) |
(63) |
|
1(1(2(0(2(x1))))) |
→ |
0(2(1(2(2(x1))))) |
(64) |
|
1(1(2(0(2(x1))))) |
→ |
0(2(2(1(2(x1))))) |
(65) |
|
1(1(2(0(2(x1))))) |
→ |
1(0(2(2(2(x1))))) |
(71) |
|
1(1(2(0(2(x1))))) |
→ |
1(2(0(2(2(x1))))) |
(73) |
|
1(1(2(0(2(x1))))) |
→ |
1(2(2(0(2(x1))))) |
(75) |
|
1(1(2(0(2(x1))))) |
→ |
1(2(2(2(0(x1))))) |
(76) |
|
1(1(2(0(2(x1))))) |
→ |
2(0(1(2(2(x1))))) |
(77) |
|
1(1(2(0(2(x1))))) |
→ |
2(1(0(2(2(x1))))) |
(78) |
|
1(1(2(0(2(x1))))) |
→ |
2(1(2(0(2(x1))))) |
(79) |
|
1(1(2(0(2(x1))))) |
→ |
2(2(0(1(2(x1))))) |
(80) |
|
1(1(2(0(2(x1))))) |
→ |
2(2(1(0(2(x1))))) |
(81) |
|
1(1(2(0(2(x1))))) |
→ |
2(2(2(1(0(x1))))) |
(82) |
|
2(0(1(0(2(x1))))) |
→ |
2(0(1(2(2(x1))))) |
(84) |
|
2(0(1(0(2(x1))))) |
→ |
2(0(2(1(2(x1))))) |
(85) |
|
2(0(1(0(2(x1))))) |
→ |
2(1(0(2(2(x1))))) |
(86) |
|
2(0(1(0(2(x1))))) |
→ |
2(1(2(0(2(x1))))) |
(87) |
|
2(0(1(0(2(x1))))) |
→ |
2(1(2(2(0(x1))))) |
(88) |
|
2(0(1(0(2(x1))))) |
→ |
2(2(0(1(2(x1))))) |
(89) |
|
2(0(1(0(2(x1))))) |
→ |
2(2(1(0(2(x1))))) |
(90) |
|
2(0(1(0(2(x1))))) |
→ |
2(2(1(2(0(x1))))) |
(91) |
|
2(0(1(0(2(x1))))) |
→ |
2(2(2(1(0(x1))))) |
(92) |
|
2(1(1(0(2(x1))))) |
→ |
2(0(2(1(2(x1))))) |
(94) |
|
2(1(1(0(2(x1))))) |
→ |
2(1(2(0(2(x1))))) |
(95) |
|
2(1(1(0(2(x1))))) |
→ |
2(2(1(0(2(x1))))) |
(96) |
1.1 Closure Under Flat Contexts
Using the flat contexts
{2(☐), 1(☐), 0(☐)}
We obtain the transformed TRS
|
2(0(1(2(0(2(x1)))))) |
→ |
2(0(1(0(2(2(x1)))))) |
(101) |
|
2(0(1(2(0(2(x1)))))) |
→ |
2(0(1(1(2(2(x1)))))) |
(102) |
|
2(0(1(2(0(2(x1)))))) |
→ |
2(0(2(1(0(2(x1)))))) |
(103) |
|
2(0(1(2(0(2(x1)))))) |
→ |
2(0(2(2(1(0(x1)))))) |
(104) |
|
2(1(1(2(0(2(x1)))))) |
→ |
2(1(0(0(2(2(x1)))))) |
(105) |
|
2(1(1(2(0(2(x1)))))) |
→ |
2(1(0(1(2(2(x1)))))) |
(106) |
|
2(1(1(2(0(2(x1)))))) |
→ |
2(1(0(2(0(2(x1)))))) |
(107) |
|
2(1(1(2(0(2(x1)))))) |
→ |
2(1(0(2(1(2(x1)))))) |
(108) |
|
2(1(1(2(0(2(x1)))))) |
→ |
2(1(0(2(2(0(x1)))))) |
(109) |
|
2(1(1(2(0(2(x1)))))) |
→ |
2(1(1(0(2(2(x1)))))) |
(110) |
|
2(1(1(2(0(2(x1)))))) |
→ |
2(1(2(1(0(2(x1)))))) |
(111) |
|
2(1(2(2(0(2(x1)))))) |
→ |
2(1(0(2(2(2(x1)))))) |
(112) |
|
2(2(1(1(0(2(x1)))))) |
→ |
2(2(0(1(0(2(x1)))))) |
(113) |
|
2(2(1(2(0(2(x1)))))) |
→ |
2(2(0(1(2(2(x1)))))) |
(114) |
|
2(2(1(2(0(2(x1)))))) |
→ |
2(2(1(0(2(2(x1)))))) |
(115) |
|
2(2(1(2(0(2(x1)))))) |
→ |
2(2(2(1(0(2(x1)))))) |
(116) |
|
2(2(1(2(0(2(x1)))))) |
→ |
2(2(2(2(1(0(x1)))))) |
(117) |
|
1(0(1(2(0(2(x1)))))) |
→ |
1(0(1(0(2(2(x1)))))) |
(118) |
|
1(0(1(2(0(2(x1)))))) |
→ |
1(0(1(1(2(2(x1)))))) |
(119) |
|
1(0(1(2(0(2(x1)))))) |
→ |
1(0(2(1(0(2(x1)))))) |
(120) |
|
1(0(1(2(0(2(x1)))))) |
→ |
1(0(2(2(1(0(x1)))))) |
(121) |
|
1(1(1(2(0(2(x1)))))) |
→ |
1(1(0(0(2(2(x1)))))) |
(122) |
|
1(1(1(2(0(2(x1)))))) |
→ |
1(1(0(1(2(2(x1)))))) |
(123) |
|
1(1(1(2(0(2(x1)))))) |
→ |
1(1(0(2(0(2(x1)))))) |
(124) |
|
1(1(1(2(0(2(x1)))))) |
→ |
1(1(0(2(1(2(x1)))))) |
(125) |
|
1(1(1(2(0(2(x1)))))) |
→ |
1(1(0(2(2(0(x1)))))) |
(126) |
|
1(1(1(2(0(2(x1)))))) |
→ |
1(1(1(0(2(2(x1)))))) |
(127) |
|
1(1(1(2(0(2(x1)))))) |
→ |
1(1(2(1(0(2(x1)))))) |
(128) |
|
1(1(2(2(0(2(x1)))))) |
→ |
1(1(0(2(2(2(x1)))))) |
(129) |
|
1(2(1(1(0(2(x1)))))) |
→ |
1(2(0(1(0(2(x1)))))) |
(130) |
|
1(2(1(2(0(2(x1)))))) |
→ |
1(2(0(1(2(2(x1)))))) |
(131) |
|
1(2(1(2(0(2(x1)))))) |
→ |
1(2(1(0(2(2(x1)))))) |
(132) |
|
1(2(1(2(0(2(x1)))))) |
→ |
1(2(2(1(0(2(x1)))))) |
(133) |
|
1(2(1(2(0(2(x1)))))) |
→ |
1(2(2(2(1(0(x1)))))) |
(134) |
|
0(0(1(2(0(2(x1)))))) |
→ |
0(0(1(0(2(2(x1)))))) |
(135) |
|
0(0(1(2(0(2(x1)))))) |
→ |
0(0(1(1(2(2(x1)))))) |
(136) |
|
0(0(1(2(0(2(x1)))))) |
→ |
0(0(2(1(0(2(x1)))))) |
(137) |
|
0(0(1(2(0(2(x1)))))) |
→ |
0(0(2(2(1(0(x1)))))) |
(138) |
|
0(1(1(2(0(2(x1)))))) |
→ |
0(1(0(0(2(2(x1)))))) |
(139) |
|
0(1(1(2(0(2(x1)))))) |
→ |
0(1(0(1(2(2(x1)))))) |
(140) |
|
0(1(1(2(0(2(x1)))))) |
→ |
0(1(0(2(0(2(x1)))))) |
(141) |
|
0(1(1(2(0(2(x1)))))) |
→ |
0(1(0(2(1(2(x1)))))) |
(142) |
|
0(1(1(2(0(2(x1)))))) |
→ |
0(1(0(2(2(0(x1)))))) |
(143) |
|
0(1(1(2(0(2(x1)))))) |
→ |
0(1(1(0(2(2(x1)))))) |
(144) |
|
0(1(1(2(0(2(x1)))))) |
→ |
0(1(2(1(0(2(x1)))))) |
(145) |
|
0(1(2(2(0(2(x1)))))) |
→ |
0(1(0(2(2(2(x1)))))) |
(146) |
|
0(2(1(1(0(2(x1)))))) |
→ |
0(2(0(1(0(2(x1)))))) |
(147) |
|
0(2(1(2(0(2(x1)))))) |
→ |
0(2(0(1(2(2(x1)))))) |
(148) |
|
0(2(1(2(0(2(x1)))))) |
→ |
0(2(1(0(2(2(x1)))))) |
(149) |
|
0(2(1(2(0(2(x1)))))) |
→ |
0(2(2(1(0(2(x1)))))) |
(150) |
|
0(2(1(2(0(2(x1)))))) |
→ |
0(2(2(2(1(0(x1)))))) |
(151) |
1.1.1 Semantic Labeling
The following interpretations form a
model
of the rules.
As carrier we take the set
{0,1,2}.
Symbols are labeled by the interpretation of their arguments using the interpretations
(modulo 3):
| [2(x1)] |
= |
3x1 + 0 |
| [1(x1)] |
= |
3x1 + 1 |
| [0(x1)] |
= |
3x1 + 2 |
We obtain the labeled TRS
There are 153 ruless (increase limit for explicit display).
1.1.1.1 Rule Removal
Using the
matrix interpretations of dimension 1 with strict dimension 1 over the rationals with delta = 1
| [20(x1)] |
= |
x1 +
|
| [21(x1)] |
= |
x1 +
|
| [22(x1)] |
= |
x1 +
|
| [10(x1)] |
= |
x1 +
|
| [11(x1)] |
= |
x1 +
|
| [12(x1)] |
= |
x1 +
|
| [00(x1)] |
= |
x1 +
|
| [01(x1)] |
= |
x1 +
|
| [02(x1)] |
= |
x1 +
|
all of the following rules can be deleted.
There are 153 ruless (increase limit for explicit display).
1.1.1.1.1 R is empty
There are no rules in the TRS. Hence, it is terminating.