Tool Bounds
stdout:
YES(?,O(n^1))
We consider the following Problem:
Strict Trs:
{ 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1))))))))))))))))))))
-> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1))))))))))))))))))))
, 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1))))))))))))))))))) ->
3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1))))))))))))))))))
, 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1))))))))))))))) ->
5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1))))))))))))))
, 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1))))))))))))))) ->
5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1))))))))))))))
, 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1))))))))))))))) ->
4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1)))))))))))))))
, 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1)))))))))))))) ->
2(2(4(2(1(4(3(0(5(1(3(3(0(x1)))))))))))))
, 0(2(3(5(4(2(2(1(0(3(3(5(0(x1))))))))))))) ->
3(3(1(2(3(0(4(0(0(0(2(0(x1))))))))))))
, 2(4(1(2(5(2(4(1(3(2(0(3(x1)))))))))))) ->
4(3(0(4(2(3(4(3(4(2(0(x1)))))))))))
, 5(2(1(3(1(5(2(5(4(4(x1)))))))))) -> 5(3(4(5(0(1(4(0(3(x1)))))))))
, 5(4(4(5(0(1(4(5(4(x1))))))))) -> 1(5(5(0(4(1(4(5(4(x1)))))))))
, 3(4(2(1(1(2(2(5(4(x1))))))))) -> 3(3(3(1(3(3(4(x1)))))))
, 5(4(0(2(2(4(0(4(x1)))))))) -> 3(1(5(1(3(0(4(x1)))))))
, 2(1(5(2(1(3(4(4(x1)))))))) -> 4(0(3(4(0(1(2(x1)))))))
, 4(5(4(3(0(5(1(x1))))))) -> 4(3(3(5(4(1(x1))))))
, 1(3(5(4(1(2(2(x1))))))) -> 3(3(3(4(4(0(x1))))))
, 5(2(1(0(1(5(x1)))))) -> 5(4(2(4(5(1(x1))))))
, 3(5(2(2(4(5(x1)))))) -> 3(2(4(3(0(x1)))))
, 3(4(1(4(2(4(x1)))))) -> 1(3(3(3(x1))))
, 2(5(1(2(1(1(x1)))))) -> 5(2(1(2(4(1(x1))))))
, 2(2(5(3(2(2(x1)))))) -> 5(1(1(0(3(x1)))))
, 5(2(2(1(2(x1))))) -> 0(0(2(3(x1))))
, 1(3(5(5(2(x1))))) -> 1(3(2(3(x1))))
, 4(5(3(4(x1)))) -> 4(4(2(4(x1))))
, 4(2(5(2(x1)))) -> 1(4(0(x1)))
, 0(0(1(2(x1)))) -> 2(3(0(x1)))}
StartTerms: all
Strategy: none
Certificate: YES(?,O(n^1))
Proof:
The problem is match-bounded by 2.
The enriched problem is compatible with the following automaton:
{ 2_0(1) -> 1
, 2_1(1) -> 124
, 2_1(2) -> 91
, 2_1(3) -> 2
, 2_1(12) -> 11
, 2_1(17) -> 16
, 2_1(40) -> 39
, 2_1(45) -> 44
, 2_1(46) -> 45
, 2_1(47) -> 134
, 2_1(51) -> 50
, 2_1(57) -> 131
, 2_1(58) -> 124
, 2_1(61) -> 60
, 2_1(71) -> 91
, 2_1(72) -> 1
, 2_1(72) -> 124
, 2_1(73) -> 72
, 2_1(75) -> 74
, 2_1(81) -> 134
, 2_1(82) -> 1
, 2_1(82) -> 70
, 2_1(82) -> 71
, 2_1(85) -> 84
, 2_1(95) -> 94
, 2_1(99) -> 131
, 2_1(101) -> 91
, 2_1(112) -> 131
, 2_1(114) -> 124
, 2_1(124) -> 91
, 2_1(127) -> 91
, 2_1(128) -> 127
, 2_1(130) -> 21
, 2_1(131) -> 124
, 2_1(136) -> 91
, 2_1(137) -> 91
, 2_2(138) -> 137
, 2_2(139) -> 70
, 1_0(1) -> 1
, 1_1(1) -> 20
, 1_1(2) -> 20
, 1_1(5) -> 4
, 1_1(6) -> 5
, 1_1(9) -> 8
, 1_1(11) -> 10
, 1_1(16) -> 15
, 1_1(25) -> 24
, 1_1(26) -> 25
, 1_1(34) -> 33
, 1_1(37) -> 36
, 1_1(41) -> 40
, 1_1(42) -> 41
, 1_1(47) -> 46
, 1_1(52) -> 51
, 1_1(58) -> 20
, 1_1(62) -> 61
, 1_1(76) -> 75
, 1_1(81) -> 80
, 1_1(82) -> 117
, 1_1(84) -> 83
, 1_1(91) -> 123
, 1_1(103) -> 102
, 1_1(104) -> 132
, 1_1(105) -> 1
, 1_1(105) -> 20
, 1_1(105) -> 46
, 1_1(105) -> 47
, 1_1(105) -> 111
, 1_1(105) -> 115
, 1_1(106) -> 20
, 1_1(110) -> 109
, 1_1(114) -> 1
, 1_1(114) -> 47
, 1_1(114) -> 113
, 1_1(114) -> 115
, 1_1(116) -> 21
, 1_1(118) -> 117
, 1_1(124) -> 123
, 1_1(126) -> 1
, 1_1(126) -> 2
, 1_1(126) -> 112
, 1_1(127) -> 1
, 1_1(131) -> 3
, 1_1(132) -> 2
, 1_1(136) -> 1
, 1_1(137) -> 1
, 1_1(239) -> 1
, 1_1(413) -> 1
, 1_2(239) -> 2
, 1_2(239) -> 98
, 1_2(413) -> 115
, 0_0(1) -> 1
, 0_1(1) -> 71
, 0_1(2) -> 71
, 0_1(3) -> 71
, 0_1(10) -> 9
, 0_1(13) -> 12
, 0_1(15) -> 14
, 0_1(21) -> 2
, 0_1(22) -> 21
, 0_1(36) -> 2
, 0_1(38) -> 37
, 0_1(39) -> 38
, 0_1(43) -> 42
, 0_1(47) -> 104
, 0_1(53) -> 52
, 0_1(57) -> 56
, 0_1(59) -> 71
, 0_1(65) -> 64
, 0_1(66) -> 65
, 0_1(67) -> 66
, 0_1(71) -> 70
, 0_1(72) -> 71
, 0_1(73) -> 71
, 0_1(79) -> 78
, 0_1(81) -> 104
, 0_1(82) -> 71
, 0_1(87) -> 86
, 0_1(89) -> 88
, 0_1(90) -> 89
, 0_1(91) -> 90
, 0_1(93) -> 92
, 0_1(100) -> 2
, 0_1(102) -> 101
, 0_1(104) -> 70
, 0_1(105) -> 104
, 0_1(108) -> 107
, 0_1(112) -> 119
, 0_1(120) -> 58
, 0_1(123) -> 122
, 0_1(124) -> 90
, 0_1(128) -> 71
, 0_1(130) -> 71
, 0_1(133) -> 1
, 0_1(133) -> 111
, 0_1(134) -> 133
, 0_1(138) -> 71
, 0_2(3) -> 240
, 0_2(57) -> 140
, 0_2(99) -> 140
, 0_2(112) -> 140
, 0_2(128) -> 140
, 0_2(138) -> 140
, 3_0(1) -> 1
, 3_1(1) -> 47
, 3_1(2) -> 47
, 3_1(3) -> 47
, 3_1(4) -> 47
, 3_1(14) -> 13
, 3_1(18) -> 17
, 3_1(19) -> 35
, 3_1(20) -> 19
, 3_1(21) -> 1
, 3_1(21) -> 20
, 3_1(21) -> 46
, 3_1(21) -> 47
, 3_1(21) -> 71
, 3_1(21) -> 90
, 3_1(21) -> 92
, 3_1(21) -> 111
, 3_1(21) -> 115
, 3_1(21) -> 125
, 3_1(21) -> 133
, 3_1(27) -> 26
, 3_1(29) -> 28
, 3_1(44) -> 43
, 3_1(47) -> 114
, 3_1(50) -> 49
, 3_1(54) -> 53
, 3_1(55) -> 54
, 3_1(58) -> 47
, 3_1(60) -> 59
, 3_1(71) -> 82
, 3_1(72) -> 47
, 3_1(73) -> 47
, 3_1(78) -> 77
, 3_1(82) -> 81
, 3_1(83) -> 21
, 3_1(86) -> 85
, 3_1(92) -> 58
, 3_1(96) -> 95
, 3_1(98) -> 97
, 3_1(99) -> 2
, 3_1(100) -> 1
, 3_1(105) -> 47
, 3_1(111) -> 92
, 3_1(112) -> 115
, 3_1(113) -> 83
, 3_1(114) -> 105
, 3_1(115) -> 114
, 3_1(119) -> 118
, 3_1(121) -> 120
, 3_1(123) -> 19
, 3_1(124) -> 47
, 3_1(125) -> 92
, 3_1(126) -> 47
, 3_1(127) -> 47
, 3_1(128) -> 47
, 3_1(131) -> 47
, 3_1(132) -> 47
, 3_1(134) -> 105
, 3_1(136) -> 47
, 3_1(137) -> 47
, 3_1(138) -> 47
, 3_1(239) -> 47
, 3_1(413) -> 47
, 3_2(100) -> 415
, 3_2(140) -> 139
, 3_2(414) -> 413
, 3_2(415) -> 414
, 5_0(1) -> 1
, 5_1(1) -> 111
, 5_1(2) -> 1
, 5_1(2) -> 91
, 5_1(2) -> 111
, 5_1(2) -> 124
, 5_1(8) -> 7
, 5_1(20) -> 129
, 5_1(24) -> 23
, 5_1(28) -> 27
, 5_1(33) -> 32
, 5_1(48) -> 36
, 5_1(56) -> 55
, 5_1(57) -> 125
, 5_1(59) -> 58
, 5_1(64) -> 63
, 5_1(69) -> 68
, 5_1(80) -> 79
, 5_1(101) -> 100
, 5_1(106) -> 105
, 5_1(107) -> 106
, 5_1(112) -> 111
, 5_1(117) -> 116
, 5_1(119) -> 55
, 4_0(1) -> 1
, 4_1(1) -> 112
, 4_1(2) -> 1
, 4_1(2) -> 110
, 4_1(2) -> 112
, 4_1(4) -> 3
, 4_1(7) -> 6
, 4_1(19) -> 18
, 4_1(20) -> 57
, 4_1(23) -> 22
, 4_1(30) -> 29
, 4_1(31) -> 30
, 4_1(32) -> 31
, 4_1(35) -> 34
, 4_1(47) -> 18
, 4_1(49) -> 48
, 4_1(58) -> 1
, 4_1(58) -> 110
, 4_1(58) -> 112
, 4_1(58) -> 124
, 4_1(58) -> 131
, 4_1(63) -> 62
, 4_1(68) -> 67
, 4_1(70) -> 69
, 4_1(71) -> 126
, 4_1(74) -> 73
, 4_1(77) -> 76
, 4_1(82) -> 130
, 4_1(88) -> 87
, 4_1(91) -> 98
, 4_1(94) -> 93
, 4_1(97) -> 96
, 4_1(100) -> 99
, 4_1(104) -> 103
, 4_1(109) -> 108
, 4_1(111) -> 110
, 4_1(114) -> 1
, 4_1(122) -> 121
, 4_1(124) -> 2
, 4_1(126) -> 113
, 4_1(127) -> 2
, 4_1(128) -> 30
, 4_1(129) -> 128
, 4_1(131) -> 58
, 4_1(136) -> 1
, 4_2(100) -> 138
, 4_2(136) -> 2
, 4_2(136) -> 98
, 4_2(136) -> 110
, 4_2(136) -> 112
, 4_2(137) -> 136
, 4_2(240) -> 239}
Hurray, we answered YES(?,O(n^1))Tool EDA
stdout:
TIMEOUT
We consider the following Problem:
Strict Trs:
{ 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1))))))))))))))))))))
-> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1))))))))))))))))))))
, 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1))))))))))))))))))) ->
3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1))))))))))))))))))
, 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1))))))))))))))) ->
5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1))))))))))))))
, 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1))))))))))))))) ->
5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1))))))))))))))
, 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1))))))))))))))) ->
4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1)))))))))))))))
, 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1)))))))))))))) ->
2(2(4(2(1(4(3(0(5(1(3(3(0(x1)))))))))))))
, 0(2(3(5(4(2(2(1(0(3(3(5(0(x1))))))))))))) ->
3(3(1(2(3(0(4(0(0(0(2(0(x1))))))))))))
, 2(4(1(2(5(2(4(1(3(2(0(3(x1)))))))))))) ->
4(3(0(4(2(3(4(3(4(2(0(x1)))))))))))
, 5(2(1(3(1(5(2(5(4(4(x1)))))))))) -> 5(3(4(5(0(1(4(0(3(x1)))))))))
, 5(4(4(5(0(1(4(5(4(x1))))))))) -> 1(5(5(0(4(1(4(5(4(x1)))))))))
, 3(4(2(1(1(2(2(5(4(x1))))))))) -> 3(3(3(1(3(3(4(x1)))))))
, 5(4(0(2(2(4(0(4(x1)))))))) -> 3(1(5(1(3(0(4(x1)))))))
, 2(1(5(2(1(3(4(4(x1)))))))) -> 4(0(3(4(0(1(2(x1)))))))
, 4(5(4(3(0(5(1(x1))))))) -> 4(3(3(5(4(1(x1))))))
, 1(3(5(4(1(2(2(x1))))))) -> 3(3(3(4(4(0(x1))))))
, 5(2(1(0(1(5(x1)))))) -> 5(4(2(4(5(1(x1))))))
, 3(5(2(2(4(5(x1)))))) -> 3(2(4(3(0(x1)))))
, 3(4(1(4(2(4(x1)))))) -> 1(3(3(3(x1))))
, 2(5(1(2(1(1(x1)))))) -> 5(2(1(2(4(1(x1))))))
, 2(2(5(3(2(2(x1)))))) -> 5(1(1(0(3(x1)))))
, 5(2(2(1(2(x1))))) -> 0(0(2(3(x1))))
, 1(3(5(5(2(x1))))) -> 1(3(2(3(x1))))
, 4(5(3(4(x1)))) -> 4(4(2(4(x1))))
, 4(2(5(2(x1)))) -> 1(4(0(x1)))
, 0(0(1(2(x1)))) -> 2(3(0(x1)))}
StartTerms: all
Strategy: none
Certificate: TIMEOUT
Proof:
Computation stopped due to timeout after 60.0 seconds.
Arrrr..Tool IDA
stdout:
TIMEOUT
We consider the following Problem:
Strict Trs:
{ 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1))))))))))))))))))))
-> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1))))))))))))))))))))
, 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1))))))))))))))))))) ->
3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1))))))))))))))))))
, 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1))))))))))))))) ->
5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1))))))))))))))
, 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1))))))))))))))) ->
5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1))))))))))))))
, 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1))))))))))))))) ->
4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1)))))))))))))))
, 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1)))))))))))))) ->
2(2(4(2(1(4(3(0(5(1(3(3(0(x1)))))))))))))
, 0(2(3(5(4(2(2(1(0(3(3(5(0(x1))))))))))))) ->
3(3(1(2(3(0(4(0(0(0(2(0(x1))))))))))))
, 2(4(1(2(5(2(4(1(3(2(0(3(x1)))))))))))) ->
4(3(0(4(2(3(4(3(4(2(0(x1)))))))))))
, 5(2(1(3(1(5(2(5(4(4(x1)))))))))) -> 5(3(4(5(0(1(4(0(3(x1)))))))))
, 5(4(4(5(0(1(4(5(4(x1))))))))) -> 1(5(5(0(4(1(4(5(4(x1)))))))))
, 3(4(2(1(1(2(2(5(4(x1))))))))) -> 3(3(3(1(3(3(4(x1)))))))
, 5(4(0(2(2(4(0(4(x1)))))))) -> 3(1(5(1(3(0(4(x1)))))))
, 2(1(5(2(1(3(4(4(x1)))))))) -> 4(0(3(4(0(1(2(x1)))))))
, 4(5(4(3(0(5(1(x1))))))) -> 4(3(3(5(4(1(x1))))))
, 1(3(5(4(1(2(2(x1))))))) -> 3(3(3(4(4(0(x1))))))
, 5(2(1(0(1(5(x1)))))) -> 5(4(2(4(5(1(x1))))))
, 3(5(2(2(4(5(x1)))))) -> 3(2(4(3(0(x1)))))
, 3(4(1(4(2(4(x1)))))) -> 1(3(3(3(x1))))
, 2(5(1(2(1(1(x1)))))) -> 5(2(1(2(4(1(x1))))))
, 2(2(5(3(2(2(x1)))))) -> 5(1(1(0(3(x1)))))
, 5(2(2(1(2(x1))))) -> 0(0(2(3(x1))))
, 1(3(5(5(2(x1))))) -> 1(3(2(3(x1))))
, 4(5(3(4(x1)))) -> 4(4(2(4(x1))))
, 4(2(5(2(x1)))) -> 1(4(0(x1)))
, 0(0(1(2(x1)))) -> 2(3(0(x1)))}
StartTerms: all
Strategy: none
Certificate: TIMEOUT
Proof:
Computation stopped due to timeout after 60.0 seconds.
Arrrr..Tool TRI
stdout:
TIMEOUT
We consider the following Problem:
Strict Trs:
{ 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1))))))))))))))))))))
-> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1))))))))))))))))))))
, 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1))))))))))))))))))) ->
3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1))))))))))))))))))
, 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1))))))))))))))) ->
5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1))))))))))))))
, 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1))))))))))))))) ->
5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1))))))))))))))
, 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1))))))))))))))) ->
4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1)))))))))))))))
, 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1)))))))))))))) ->
2(2(4(2(1(4(3(0(5(1(3(3(0(x1)))))))))))))
, 0(2(3(5(4(2(2(1(0(3(3(5(0(x1))))))))))))) ->
3(3(1(2(3(0(4(0(0(0(2(0(x1))))))))))))
, 2(4(1(2(5(2(4(1(3(2(0(3(x1)))))))))))) ->
4(3(0(4(2(3(4(3(4(2(0(x1)))))))))))
, 5(2(1(3(1(5(2(5(4(4(x1)))))))))) -> 5(3(4(5(0(1(4(0(3(x1)))))))))
, 5(4(4(5(0(1(4(5(4(x1))))))))) -> 1(5(5(0(4(1(4(5(4(x1)))))))))
, 3(4(2(1(1(2(2(5(4(x1))))))))) -> 3(3(3(1(3(3(4(x1)))))))
, 5(4(0(2(2(4(0(4(x1)))))))) -> 3(1(5(1(3(0(4(x1)))))))
, 2(1(5(2(1(3(4(4(x1)))))))) -> 4(0(3(4(0(1(2(x1)))))))
, 4(5(4(3(0(5(1(x1))))))) -> 4(3(3(5(4(1(x1))))))
, 1(3(5(4(1(2(2(x1))))))) -> 3(3(3(4(4(0(x1))))))
, 5(2(1(0(1(5(x1)))))) -> 5(4(2(4(5(1(x1))))))
, 3(5(2(2(4(5(x1)))))) -> 3(2(4(3(0(x1)))))
, 3(4(1(4(2(4(x1)))))) -> 1(3(3(3(x1))))
, 2(5(1(2(1(1(x1)))))) -> 5(2(1(2(4(1(x1))))))
, 2(2(5(3(2(2(x1)))))) -> 5(1(1(0(3(x1)))))
, 5(2(2(1(2(x1))))) -> 0(0(2(3(x1))))
, 1(3(5(5(2(x1))))) -> 1(3(2(3(x1))))
, 4(5(3(4(x1)))) -> 4(4(2(4(x1))))
, 4(2(5(2(x1)))) -> 1(4(0(x1)))
, 0(0(1(2(x1)))) -> 2(3(0(x1)))}
StartTerms: all
Strategy: none
Certificate: TIMEOUT
Proof:
Computation stopped due to timeout after 60.0 seconds.
Arrrr..