Tool Bounds
stdout:
YES(?,O(n^1))
We consider the following Problem:
Strict Trs:
{ 0(1(2(3(4(5(1(x1))))))) ->
1(2(3(4(5(1(1(0(1(2(3(4(5(0(1(2(3(4(5(0(1(2(3(4(5(x1)))))))))))))))))))))))))
, 0(1(2(3(4(5(1(x1))))))) ->
1(2(3(4(5(1(1(0(1(2(3(4(5(0(1(2(3(4(5(x1)))))))))))))))))))}
StartTerms: all
Strategy: none
Certificate: YES(?,O(n^1))
Proof:
The problem is match-bounded by 3.
The enriched problem is compatible with the following automaton:
{ 1_0(1) -> 1
, 1_1(2) -> 1
, 1_1(2) -> 20
, 1_1(7) -> 6
, 1_1(8) -> 7
, 1_1(10) -> 9
, 1_1(14) -> 7
, 1_1(16) -> 15
, 1_1(22) -> 21
, 1_2(31) -> 8
, 1_2(31) -> 14
, 1_2(31) -> 20
, 1_2(36) -> 35
, 1_2(37) -> 36
, 1_2(39) -> 38
, 1_2(45) -> 44
, 1_2(49) -> 8
, 1_2(49) -> 14
, 1_2(49) -> 20
, 1_2(54) -> 53
, 1_2(55) -> 54
, 1_2(57) -> 56
, 1_2(61) -> 8
, 1_2(61) -> 14
, 1_2(66) -> 65
, 1_2(67) -> 66
, 1_2(69) -> 68
, 1_2(75) -> 74
, 1_3(79) -> 43
, 1_3(84) -> 83
, 1_3(85) -> 84
, 1_3(87) -> 86
, 1_3(91) -> 84
, 1_3(93) -> 92
, 1_3(103) -> 102
, 1_3(107) -> 37
, 1_3(112) -> 111
, 1_3(113) -> 112
, 1_3(115) -> 114
, 1_3(119) -> 112
, 1_3(121) -> 120
, 1_3(127) -> 126
, 1_3(131) -> 55
, 1_3(136) -> 135
, 1_3(137) -> 136
, 1_3(139) -> 138
, 1_3(145) -> 144
, 5_0(1) -> 1
, 5_1(1) -> 25
, 5_1(2) -> 19
, 5_1(6) -> 5
, 5_1(7) -> 19
, 5_1(8) -> 13
, 5_1(14) -> 13
, 5_1(20) -> 19
, 5_2(2) -> 48
, 5_2(8) -> 48
, 5_2(14) -> 48
, 5_2(31) -> 48
, 5_2(35) -> 34
, 5_2(37) -> 60
, 5_2(43) -> 42
, 5_2(49) -> 78
, 5_2(53) -> 52
, 5_2(61) -> 48
, 5_2(65) -> 64
, 5_2(67) -> 60
, 5_2(73) -> 72
, 5_3(31) -> 106
, 5_3(49) -> 96
, 5_3(61) -> 90
, 5_3(79) -> 130
, 5_3(83) -> 82
, 5_3(85) -> 90
, 5_3(91) -> 90
, 5_3(107) -> 148
, 5_3(111) -> 110
, 5_3(119) -> 118
, 5_3(125) -> 124
, 5_3(135) -> 134
, 5_3(137) -> 142
, 5_3(143) -> 142
, 4_0(1) -> 1
, 4_1(5) -> 4
, 4_1(13) -> 12
, 4_1(19) -> 18
, 4_1(25) -> 24
, 4_2(34) -> 33
, 4_2(42) -> 41
, 4_2(48) -> 47
, 4_2(52) -> 51
, 4_2(60) -> 59
, 4_2(64) -> 63
, 4_2(72) -> 71
, 4_2(78) -> 77
, 4_3(82) -> 81
, 4_3(90) -> 89
, 4_3(96) -> 95
, 4_3(106) -> 105
, 4_3(110) -> 109
, 4_3(118) -> 117
, 4_3(124) -> 123
, 4_3(130) -> 129
, 4_3(134) -> 133
, 4_3(142) -> 141
, 4_3(148) -> 147
, 3_0(1) -> 1
, 3_1(4) -> 3
, 3_1(12) -> 11
, 3_1(18) -> 17
, 3_1(24) -> 23
, 3_2(33) -> 32
, 3_2(41) -> 40
, 3_2(47) -> 46
, 3_2(51) -> 50
, 3_2(59) -> 58
, 3_2(63) -> 62
, 3_2(71) -> 70
, 3_2(77) -> 76
, 3_3(81) -> 80
, 3_3(89) -> 88
, 3_3(95) -> 94
, 3_3(105) -> 104
, 3_3(109) -> 108
, 3_3(117) -> 116
, 3_3(123) -> 122
, 3_3(129) -> 128
, 3_3(133) -> 132
, 3_3(141) -> 140
, 3_3(147) -> 146
, 2_0(1) -> 1
, 2_1(3) -> 2
, 2_1(11) -> 10
, 2_1(17) -> 16
, 2_1(23) -> 22
, 2_2(32) -> 31
, 2_2(40) -> 39
, 2_2(46) -> 45
, 2_2(50) -> 49
, 2_2(58) -> 57
, 2_2(62) -> 61
, 2_2(70) -> 69
, 2_2(76) -> 75
, 2_3(80) -> 79
, 2_3(88) -> 87
, 2_3(94) -> 93
, 2_3(104) -> 103
, 2_3(108) -> 107
, 2_3(116) -> 115
, 2_3(122) -> 121
, 2_3(128) -> 127
, 2_3(132) -> 131
, 2_3(140) -> 139
, 2_3(146) -> 145
, 0_0(1) -> 1
, 0_1(9) -> 8
, 0_1(15) -> 14
, 0_1(21) -> 20
, 0_2(38) -> 37
, 0_2(44) -> 43
, 0_2(56) -> 55
, 0_2(68) -> 67
, 0_2(74) -> 73
, 0_3(86) -> 85
, 0_3(92) -> 91
, 0_3(102) -> 49
, 0_3(114) -> 113
, 0_3(120) -> 119
, 0_3(126) -> 125
, 0_3(138) -> 137
, 0_3(144) -> 143}
Hurray, we answered YES(?,O(n^1))Tool EDA
stdout:
TIMEOUT
We consider the following Problem:
Strict Trs:
{ 0(1(2(3(4(5(1(x1))))))) ->
1(2(3(4(5(1(1(0(1(2(3(4(5(0(1(2(3(4(5(0(1(2(3(4(5(x1)))))))))))))))))))))))))
, 0(1(2(3(4(5(1(x1))))))) ->
1(2(3(4(5(1(1(0(1(2(3(4(5(0(1(2(3(4(5(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:
{ 0(1(2(3(4(5(1(x1))))))) ->
1(2(3(4(5(1(1(0(1(2(3(4(5(0(1(2(3(4(5(0(1(2(3(4(5(x1)))))))))))))))))))))))))
, 0(1(2(3(4(5(1(x1))))))) ->
1(2(3(4(5(1(1(0(1(2(3(4(5(0(1(2(3(4(5(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:
{ 0(1(2(3(4(5(1(x1))))))) ->
1(2(3(4(5(1(1(0(1(2(3(4(5(0(1(2(3(4(5(0(1(2(3(4(5(x1)))))))))))))))))))))))))
, 0(1(2(3(4(5(1(x1))))))) ->
1(2(3(4(5(1(1(0(1(2(3(4(5(0(1(2(3(4(5(x1)))))))))))))))))))}
StartTerms: all
Strategy: none
Certificate: TIMEOUT
Proof:
Computation stopped due to timeout after 60.0 seconds.
Arrrr..Tool TRI2
stdout:
TIMEOUT
We consider the following Problem:
Strict Trs:
{ 0(1(2(3(4(5(1(x1))))))) ->
1(2(3(4(5(1(1(0(1(2(3(4(5(0(1(2(3(4(5(0(1(2(3(4(5(x1)))))))))))))))))))))))))
, 0(1(2(3(4(5(1(x1))))))) ->
1(2(3(4(5(1(1(0(1(2(3(4(5(0(1(2(3(4(5(x1)))))))))))))))))))}
StartTerms: all
Strategy: none
Certificate: TIMEOUT
Proof:
Computation stopped due to timeout after 60.0 seconds.
Arrrr..