Tool Bounds
stdout:
YES(?,O(n^1))
We consider the following Problem:
Strict Trs:
{ n(s(x1)) -> a(l(a(t(x1))))
, s(a(x1)) -> l(a(t(o(m(a(t(e(x1))))))))
, o(m(a(x1))) -> t(e(n(x1)))
, a(l(x1)) -> a(t(x1))
, t(e(x1)) -> n(s(x1))
, t(o(x1)) -> m(a(x1))}
StartTerms: all
Strategy: none
Certificate: YES(?,O(n^1))
Proof:
The problem is match-bounded by 8.
The enriched problem is compatible with the following automaton:
{ o_0(1) -> 1
, o_1(8) -> 7
, o_2(37) -> 36
, o_3(44) -> 43
, o_4(77) -> 76
, t_0(1) -> 1
, t_1(1) -> 4
, t_1(5) -> 2
, t_1(7) -> 6
, t_1(11) -> 10
, t_1(12) -> 1
, t_2(1) -> 24
, t_2(3) -> 16
, t_2(5) -> 52
, t_2(14) -> 7
, t_2(36) -> 35
, t_2(40) -> 39
, t_3(1) -> 27
, t_3(2) -> 27
, t_3(4) -> 27
, t_3(13) -> 30
, t_3(16) -> 27
, t_3(23) -> 28
, t_3(28) -> 27
, t_3(43) -> 42
, t_3(47) -> 46
, t_3(48) -> 36
, t_3(54) -> 27
, t_4(2) -> 64
, t_4(4) -> 64
, t_4(15) -> 33
, t_4(16) -> 64
, t_4(26) -> 53
, t_4(28) -> 64
, t_4(29) -> 54
, t_4(50) -> 43
, t_4(54) -> 64
, t_4(76) -> 75
, t_4(80) -> 79
, t_5(16) -> 67
, t_5(28) -> 67
, t_5(32) -> 55
, t_5(49) -> 70
, t_5(54) -> 67
, t_5(63) -> 83
, t_5(81) -> 76
, t_6(28) -> 92
, t_6(51) -> 73
, t_6(54) -> 92
, t_6(66) -> 84
, t_6(69) -> 85
, t_7(72) -> 86
, t_7(82) -> 95
, t_7(91) -> 96
, t_8(94) -> 97
, a_0(1) -> 1
, a_1(1) -> 21
, a_1(2) -> 1
, a_1(2) -> 13
, a_1(4) -> 1
, a_1(4) -> 3
, a_1(4) -> 21
, a_1(6) -> 5
, a_1(10) -> 9
, a_2(8) -> 22
, a_2(16) -> 1
, a_2(16) -> 4
, a_2(16) -> 13
, a_2(16) -> 24
, a_2(16) -> 27
, a_2(24) -> 23
, a_2(35) -> 34
, a_2(39) -> 38
, a_2(52) -> 21
, a_3(25) -> 10
, a_3(27) -> 26
, a_3(28) -> 1
, a_3(28) -> 4
, a_3(28) -> 13
, a_3(28) -> 24
, a_3(28) -> 27
, a_3(30) -> 29
, a_3(37) -> 60
, a_3(42) -> 41
, a_3(46) -> 45
, a_4(31) -> 7
, a_4(33) -> 32
, a_4(44) -> 61
, a_4(53) -> 10
, a_4(54) -> 1
, a_4(54) -> 4
, a_4(54) -> 13
, a_4(54) -> 24
, a_4(54) -> 27
, a_4(62) -> 39
, a_4(64) -> 63
, a_4(75) -> 74
, a_4(79) -> 78
, a_5(55) -> 7
, a_5(65) -> 46
, a_5(67) -> 66
, a_5(68) -> 36
, a_5(70) -> 69
, a_5(77) -> 89
, a_5(83) -> 39
, a_6(71) -> 43
, a_6(73) -> 72
, a_6(84) -> 46
, a_6(85) -> 36
, a_6(90) -> 79
, a_6(92) -> 91
, a_7(86) -> 43
, a_7(93) -> 76
, a_7(95) -> 94
, a_7(96) -> 79
, a_8(97) -> 76
, m_0(1) -> 1
, m_1(9) -> 8
, m_1(21) -> 1
, m_1(21) -> 4
, m_1(21) -> 24
, m_1(21) -> 27
, m_2(22) -> 6
, m_2(38) -> 37
, m_3(45) -> 44
, m_3(60) -> 35
, m_4(61) -> 42
, m_4(78) -> 77
, m_5(89) -> 75
, e_0(1) -> 1
, e_1(1) -> 11
, e_1(2) -> 11
, e_1(4) -> 11
, e_1(13) -> 12
, e_1(16) -> 11
, e_1(28) -> 11
, e_1(54) -> 11
, e_2(2) -> 40
, e_2(4) -> 40
, e_2(15) -> 14
, e_2(16) -> 40
, e_2(28) -> 40
, e_2(54) -> 40
, e_3(16) -> 47
, e_3(28) -> 47
, e_3(49) -> 48
, e_3(54) -> 47
, e_4(28) -> 80
, e_4(51) -> 50
, e_4(54) -> 80
, e_5(82) -> 81
, s_0(1) -> 1
, s_1(1) -> 17
, s_2(1) -> 18
, s_2(2) -> 18
, s_2(4) -> 18
, s_2(13) -> 19
, s_2(16) -> 18
, s_2(28) -> 18
, s_2(54) -> 18
, s_3(2) -> 56
, s_3(4) -> 56
, s_3(15) -> 20
, s_3(16) -> 56
, s_3(28) -> 56
, s_3(54) -> 56
, s_4(16) -> 57
, s_4(28) -> 57
, s_4(49) -> 58
, s_4(54) -> 57
, s_5(28) -> 87
, s_5(51) -> 59
, s_5(54) -> 87
, s_6(82) -> 88
, n_0(1) -> 1
, n_1(1) -> 13
, n_1(2) -> 13
, n_1(4) -> 13
, n_1(16) -> 13
, n_1(17) -> 1
, n_1(17) -> 4
, n_1(17) -> 24
, n_1(17) -> 27
, n_1(28) -> 13
, n_1(52) -> 13
, n_1(54) -> 13
, n_2(10) -> 15
, n_2(18) -> 10
, n_2(19) -> 1
, n_3(20) -> 7
, n_3(39) -> 49
, n_3(56) -> 39
, n_4(46) -> 51
, n_4(57) -> 46
, n_4(58) -> 36
, n_5(59) -> 43
, n_5(79) -> 82
, n_5(87) -> 79
, n_6(88) -> 76
, l_0(1) -> 1
, l_1(3) -> 2
, l_1(5) -> 1
, l_1(5) -> 17
, l_1(5) -> 18
, l_2(23) -> 16
, l_2(34) -> 17
, l_2(34) -> 18
, l_2(34) -> 19
, l_3(26) -> 25
, l_3(29) -> 28
, l_3(41) -> 18
, l_3(41) -> 19
, l_3(41) -> 56
, l_4(32) -> 31
, l_4(63) -> 62
, l_4(74) -> 56
, l_5(66) -> 65
, l_5(69) -> 68
, l_6(72) -> 71
, l_6(91) -> 90
, l_7(94) -> 93}
Hurray, we answered YES(?,O(n^1))Tool CDI
stdout:
TIMEOUT
Statistics:
Number of monomials: 0
Last formula building started for bound 0
Last SAT solving started for bound 0Tool EDA
stdout:
TIMEOUT
We consider the following Problem:
Strict Trs:
{ n(s(x1)) -> a(l(a(t(x1))))
, s(a(x1)) -> l(a(t(o(m(a(t(e(x1))))))))
, o(m(a(x1))) -> t(e(n(x1)))
, a(l(x1)) -> a(t(x1))
, t(e(x1)) -> n(s(x1))
, t(o(x1)) -> m(a(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:
{ n(s(x1)) -> a(l(a(t(x1))))
, s(a(x1)) -> l(a(t(o(m(a(t(e(x1))))))))
, o(m(a(x1))) -> t(e(n(x1)))
, a(l(x1)) -> a(t(x1))
, t(e(x1)) -> n(s(x1))
, t(o(x1)) -> m(a(x1))}
StartTerms: all
Strategy: none
Certificate: TIMEOUT
Proof:
Computation stopped due to timeout after 60.0 seconds.
Arrrr..Tool TRI
stdout:
YES(?,O(n^3))
We consider the following Problem:
Strict Trs:
{ n(s(x1)) -> a(l(a(t(x1))))
, s(a(x1)) -> l(a(t(o(m(a(t(e(x1))))))))
, o(m(a(x1))) -> t(e(n(x1)))
, a(l(x1)) -> a(t(x1))
, t(e(x1)) -> n(s(x1))
, t(o(x1)) -> m(a(x1))}
StartTerms: all
Strategy: none
Certificate: YES(?,O(n^3))
Proof:
We have the following triangular matrix interpretation:
Interpretation Functions:
o(x1) = [1 3 3] x1 + [2]
[0 1 0] [3]
[0 0 1] [0]
t(x1) = [1 0 1] x1 + [0]
[0 0 1] [1]
[0 0 0] [0]
a(x1) = [1 0 0] x1 + [0]
[0 1 0] [3]
[0 0 1] [0]
m(x1) = [1 0 3] x1 + [0]
[0 0 1] [1]
[0 0 0] [0]
e(x1) = [1 3 2] x1 + [1]
[0 0 0] [0]
[0 0 0] [3]
s(x1) = [1 3 2] x1 + [3]
[0 0 0] [1]
[0 0 0] [2]
n(x1) = [1 0 0] x1 + [0]
[0 0 2] [0]
[0 0 0] [0]
l(x1) = [1 0 2] x1 + [2]
[0 0 1] [1]
[0 0 0] [0]
Hurray, we answered YES(?,O(n^3))Tool TRI2
stdout:
MAYBE
We consider the following Problem:
Strict Trs:
{ n(s(x1)) -> a(l(a(t(x1))))
, s(a(x1)) -> l(a(t(o(m(a(t(e(x1))))))))
, o(m(a(x1))) -> t(e(n(x1)))
, a(l(x1)) -> a(t(x1))
, t(e(x1)) -> n(s(x1))
, t(o(x1)) -> m(a(x1))}
StartTerms: all
Strategy: none
Certificate: MAYBE
Proof:
The input cannot be shown compatible
Arrrr..