Tool Bounds
stdout:
YES(?,O(n^1))
We consider the following Problem:
Strict Trs:
{ 5(0(4(x1))) -> 1(5(1(0(3(4(x1))))))
, 5(0(4(x1))) -> 1(0(3(2(4(4(x1))))))
, 5(0(2(x1))) -> 1(5(2(1(0(2(x1))))))
, 4(0(5(x1))) -> 4(2(1(4(3(5(x1))))))
, 4(0(5(x1))) -> 4(1(4(5(1(4(x1))))))
, 4(0(0(x1))) -> 2(5(2(1(1(1(x1))))))
, 3(0(5(x1))) -> 3(1(0(2(3(2(x1))))))
, 3(0(1(x1))) -> 3(1(4(3(4(1(x1))))))
, 2(0(4(x1))) -> 2(4(1(4(3(1(x1))))))
, 2(0(4(x1))) -> 2(0(2(1(4(3(x1))))))
, 2(0(1(x1))) -> 2(4(3(5(2(3(x1))))))
, 2(0(1(x1))) -> 2(1(5(1(0(1(x1))))))
, 2(0(0(x1))) -> 2(4(3(4(4(4(x1))))))
, 1(3(5(x1))) -> 1(1(4(3(3(2(x1))))))
, 1(3(3(x1))) -> 5(4(0(3(2(3(x1))))))
, 1(3(3(x1))) -> 0(2(1(1(0(5(x1))))))
, 1(2(3(x1))) -> 5(1(4(1(4(4(x1))))))
, 0(4(0(x1))) -> 0(1(2(1(0(3(x1))))))
, 0(2(4(x1))) -> 1(5(4(3(4(4(x1))))))
, 0(1(3(x1))) -> 0(2(4(3(4(4(x1))))))
, 0(1(1(x1))) -> 0(2(2(1(1(1(x1))))))
, 0(0(4(x1))) -> 1(1(5(2(3(4(x1))))))
, 0(4(x1)) -> 0(2(1(4(3(4(x1))))))
, 0(4(x1)) -> 0(1(4(2(3(3(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:
{ 4_0(1) -> 1
, 4_1(1) -> 6
, 4_1(2) -> 6
, 4_1(5) -> 27
, 4_1(6) -> 9
, 4_1(9) -> 39
, 4_1(13) -> 1
, 4_1(13) -> 6
, 4_1(16) -> 15
, 4_1(19) -> 18
, 4_1(21) -> 9
, 4_1(25) -> 31
, 4_1(26) -> 6
, 4_1(30) -> 27
, 4_1(32) -> 21
, 4_1(34) -> 33
, 4_1(35) -> 1
, 4_1(35) -> 6
, 4_1(38) -> 37
, 4_1(45) -> 44
, 4_1(46) -> 6
, 4_1(47) -> 46
, 4_1(49) -> 6
, 4_1(54) -> 53
, 4_1(58) -> 3
, 4_1(75) -> 55
, 4_2(13) -> 63
, 4_2(26) -> 68
, 4_2(32) -> 63
, 4_2(35) -> 63
, 4_2(47) -> 63
, 4_2(58) -> 107
, 4_2(61) -> 60
, 4_2(63) -> 62
, 4_2(66) -> 65
, 4_2(68) -> 67
, 4_2(74) -> 73
, 4_2(78) -> 77
, 4_2(92) -> 91
, 4_2(94) -> 93
, 4_2(95) -> 62
, 4_2(96) -> 95
, 4_2(105) -> 104
, 4_2(107) -> 106
, 4_3(66) -> 112
, 4_3(110) -> 109
, 4_3(112) -> 111
, 0_0(1) -> 1
, 0_1(1) -> 43
, 0_1(2) -> 43
, 0_1(5) -> 4
, 0_1(7) -> 2
, 0_1(12) -> 11
, 0_1(17) -> 52
, 0_1(25) -> 43
, 0_1(28) -> 27
, 0_1(29) -> 47
, 0_1(35) -> 21
, 0_1(38) -> 57
, 0_1(48) -> 47
, 0_1(49) -> 1
, 0_1(49) -> 25
, 0_1(49) -> 43
, 0_2(64) -> 43
, 0_2(64) -> 52
, 0_2(85) -> 84
, 0_2(94) -> 102
, 3_0(1) -> 1
, 3_1(1) -> 38
, 3_1(2) -> 38
, 3_1(6) -> 5
, 3_1(8) -> 7
, 3_1(9) -> 58
, 3_1(12) -> 29
, 3_1(13) -> 38
, 3_1(17) -> 16
, 3_1(25) -> 34
, 3_1(26) -> 1
, 3_1(26) -> 38
, 3_1(29) -> 45
, 3_1(31) -> 30
, 3_1(35) -> 38
, 3_1(38) -> 76
, 3_1(39) -> 32
, 3_1(40) -> 48
, 3_1(49) -> 38
, 3_1(55) -> 38
, 3_1(103) -> 38
, 3_2(13) -> 80
, 3_2(35) -> 80
, 3_2(55) -> 99
, 3_2(62) -> 61
, 3_2(63) -> 74
, 3_2(67) -> 66
, 3_2(80) -> 79
, 3_2(90) -> 34
, 3_2(90) -> 38
, 3_2(93) -> 92
, 3_2(97) -> 96
, 3_2(106) -> 105
, 3_3(111) -> 110
, 2_0(1) -> 1
, 2_1(1) -> 12
, 2_1(3) -> 49
, 2_1(5) -> 72
, 2_1(9) -> 8
, 2_1(10) -> 3
, 2_1(14) -> 13
, 2_1(21) -> 1
, 2_1(21) -> 6
, 2_1(21) -> 12
, 2_1(22) -> 49
, 2_1(23) -> 22
, 2_1(26) -> 49
, 2_1(29) -> 28
, 2_1(36) -> 35
, 2_1(38) -> 40
, 2_1(42) -> 3
, 2_1(46) -> 12
, 2_1(50) -> 49
, 2_1(56) -> 55
, 2_1(76) -> 75
, 2_2(3) -> 85
, 2_2(22) -> 85
, 2_2(26) -> 85
, 2_2(50) -> 85
, 2_2(65) -> 64
, 2_2(69) -> 65
, 2_2(79) -> 78
, 2_2(83) -> 82
, 2_2(95) -> 12
, 2_2(99) -> 98
, 1_0(1) -> 1
, 1_1(1) -> 25
, 1_1(2) -> 1
, 1_1(2) -> 11
, 1_1(2) -> 17
, 1_1(2) -> 25
, 1_1(2) -> 43
, 1_1(4) -> 3
, 1_1(6) -> 20
, 1_1(9) -> 54
, 1_1(11) -> 10
, 1_1(13) -> 25
, 1_1(15) -> 14
, 1_1(18) -> 13
, 1_1(24) -> 23
, 1_1(25) -> 24
, 1_1(27) -> 26
, 1_1(33) -> 32
, 1_1(35) -> 25
, 1_1(37) -> 36
, 1_1(41) -> 21
, 1_1(43) -> 42
, 1_1(44) -> 2
, 1_1(49) -> 25
, 1_1(51) -> 50
, 1_1(52) -> 51
, 1_1(53) -> 46
, 1_1(55) -> 49
, 1_1(57) -> 56
, 1_1(103) -> 2
, 1_2(2) -> 71
, 1_2(18) -> 71
, 1_2(44) -> 71
, 1_2(55) -> 94
, 1_2(59) -> 11
, 1_2(59) -> 43
, 1_2(70) -> 69
, 1_2(71) -> 70
, 1_2(73) -> 65
, 1_2(77) -> 64
, 1_2(81) -> 17
, 1_2(83) -> 69
, 1_2(84) -> 83
, 1_2(91) -> 90
, 1_2(94) -> 70
, 1_2(100) -> 95
, 1_2(102) -> 101
, 1_2(103) -> 1
, 1_2(103) -> 25
, 1_2(103) -> 43
, 1_2(103) -> 84
, 1_3(108) -> 43
, 1_3(108) -> 52
, 5_0(1) -> 1
, 5_1(1) -> 17
, 5_1(3) -> 2
, 5_1(20) -> 19
, 5_1(22) -> 21
, 5_1(26) -> 17
, 5_1(40) -> 39
, 5_1(42) -> 41
, 5_1(46) -> 1
, 5_1(46) -> 25
, 5_1(72) -> 44
, 5_2(60) -> 59
, 5_2(82) -> 81
, 5_2(98) -> 97
, 5_2(101) -> 100
, 5_2(104) -> 103
, 5_3(109) -> 108}
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:
{ 5(0(4(x1))) -> 1(5(1(0(3(4(x1))))))
, 5(0(4(x1))) -> 1(0(3(2(4(4(x1))))))
, 5(0(2(x1))) -> 1(5(2(1(0(2(x1))))))
, 4(0(5(x1))) -> 4(2(1(4(3(5(x1))))))
, 4(0(5(x1))) -> 4(1(4(5(1(4(x1))))))
, 4(0(0(x1))) -> 2(5(2(1(1(1(x1))))))
, 3(0(5(x1))) -> 3(1(0(2(3(2(x1))))))
, 3(0(1(x1))) -> 3(1(4(3(4(1(x1))))))
, 2(0(4(x1))) -> 2(4(1(4(3(1(x1))))))
, 2(0(4(x1))) -> 2(0(2(1(4(3(x1))))))
, 2(0(1(x1))) -> 2(4(3(5(2(3(x1))))))
, 2(0(1(x1))) -> 2(1(5(1(0(1(x1))))))
, 2(0(0(x1))) -> 2(4(3(4(4(4(x1))))))
, 1(3(5(x1))) -> 1(1(4(3(3(2(x1))))))
, 1(3(3(x1))) -> 5(4(0(3(2(3(x1))))))
, 1(3(3(x1))) -> 0(2(1(1(0(5(x1))))))
, 1(2(3(x1))) -> 5(1(4(1(4(4(x1))))))
, 0(4(0(x1))) -> 0(1(2(1(0(3(x1))))))
, 0(2(4(x1))) -> 1(5(4(3(4(4(x1))))))
, 0(1(3(x1))) -> 0(2(4(3(4(4(x1))))))
, 0(1(1(x1))) -> 0(2(2(1(1(1(x1))))))
, 0(0(4(x1))) -> 1(1(5(2(3(4(x1))))))
, 0(4(x1)) -> 0(2(1(4(3(4(x1))))))
, 0(4(x1)) -> 0(1(4(2(3(3(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:
{ 5(0(4(x1))) -> 1(5(1(0(3(4(x1))))))
, 5(0(4(x1))) -> 1(0(3(2(4(4(x1))))))
, 5(0(2(x1))) -> 1(5(2(1(0(2(x1))))))
, 4(0(5(x1))) -> 4(2(1(4(3(5(x1))))))
, 4(0(5(x1))) -> 4(1(4(5(1(4(x1))))))
, 4(0(0(x1))) -> 2(5(2(1(1(1(x1))))))
, 3(0(5(x1))) -> 3(1(0(2(3(2(x1))))))
, 3(0(1(x1))) -> 3(1(4(3(4(1(x1))))))
, 2(0(4(x1))) -> 2(4(1(4(3(1(x1))))))
, 2(0(4(x1))) -> 2(0(2(1(4(3(x1))))))
, 2(0(1(x1))) -> 2(4(3(5(2(3(x1))))))
, 2(0(1(x1))) -> 2(1(5(1(0(1(x1))))))
, 2(0(0(x1))) -> 2(4(3(4(4(4(x1))))))
, 1(3(5(x1))) -> 1(1(4(3(3(2(x1))))))
, 1(3(3(x1))) -> 5(4(0(3(2(3(x1))))))
, 1(3(3(x1))) -> 0(2(1(1(0(5(x1))))))
, 1(2(3(x1))) -> 5(1(4(1(4(4(x1))))))
, 0(4(0(x1))) -> 0(1(2(1(0(3(x1))))))
, 0(2(4(x1))) -> 1(5(4(3(4(4(x1))))))
, 0(1(3(x1))) -> 0(2(4(3(4(4(x1))))))
, 0(1(1(x1))) -> 0(2(2(1(1(1(x1))))))
, 0(0(4(x1))) -> 1(1(5(2(3(4(x1))))))
, 0(4(x1)) -> 0(2(1(4(3(4(x1))))))
, 0(4(x1)) -> 0(1(4(2(3(3(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:
{ 5(0(4(x1))) -> 1(5(1(0(3(4(x1))))))
, 5(0(4(x1))) -> 1(0(3(2(4(4(x1))))))
, 5(0(2(x1))) -> 1(5(2(1(0(2(x1))))))
, 4(0(5(x1))) -> 4(2(1(4(3(5(x1))))))
, 4(0(5(x1))) -> 4(1(4(5(1(4(x1))))))
, 4(0(0(x1))) -> 2(5(2(1(1(1(x1))))))
, 3(0(5(x1))) -> 3(1(0(2(3(2(x1))))))
, 3(0(1(x1))) -> 3(1(4(3(4(1(x1))))))
, 2(0(4(x1))) -> 2(4(1(4(3(1(x1))))))
, 2(0(4(x1))) -> 2(0(2(1(4(3(x1))))))
, 2(0(1(x1))) -> 2(4(3(5(2(3(x1))))))
, 2(0(1(x1))) -> 2(1(5(1(0(1(x1))))))
, 2(0(0(x1))) -> 2(4(3(4(4(4(x1))))))
, 1(3(5(x1))) -> 1(1(4(3(3(2(x1))))))
, 1(3(3(x1))) -> 5(4(0(3(2(3(x1))))))
, 1(3(3(x1))) -> 0(2(1(1(0(5(x1))))))
, 1(2(3(x1))) -> 5(1(4(1(4(4(x1))))))
, 0(4(0(x1))) -> 0(1(2(1(0(3(x1))))))
, 0(2(4(x1))) -> 1(5(4(3(4(4(x1))))))
, 0(1(3(x1))) -> 0(2(4(3(4(4(x1))))))
, 0(1(1(x1))) -> 0(2(2(1(1(1(x1))))))
, 0(0(4(x1))) -> 1(1(5(2(3(4(x1))))))
, 0(4(x1)) -> 0(2(1(4(3(4(x1))))))
, 0(4(x1)) -> 0(1(4(2(3(3(x1))))))}
StartTerms: all
Strategy: none
Certificate: TIMEOUT
Proof:
Computation stopped due to timeout after 60.0 seconds.
Arrrr..Tool TRI2
stdout:
MAYBE
We consider the following Problem:
Strict Trs:
{ 5(0(4(x1))) -> 1(5(1(0(3(4(x1))))))
, 5(0(4(x1))) -> 1(0(3(2(4(4(x1))))))
, 5(0(2(x1))) -> 1(5(2(1(0(2(x1))))))
, 4(0(5(x1))) -> 4(2(1(4(3(5(x1))))))
, 4(0(5(x1))) -> 4(1(4(5(1(4(x1))))))
, 4(0(0(x1))) -> 2(5(2(1(1(1(x1))))))
, 3(0(5(x1))) -> 3(1(0(2(3(2(x1))))))
, 3(0(1(x1))) -> 3(1(4(3(4(1(x1))))))
, 2(0(4(x1))) -> 2(4(1(4(3(1(x1))))))
, 2(0(4(x1))) -> 2(0(2(1(4(3(x1))))))
, 2(0(1(x1))) -> 2(4(3(5(2(3(x1))))))
, 2(0(1(x1))) -> 2(1(5(1(0(1(x1))))))
, 2(0(0(x1))) -> 2(4(3(4(4(4(x1))))))
, 1(3(5(x1))) -> 1(1(4(3(3(2(x1))))))
, 1(3(3(x1))) -> 5(4(0(3(2(3(x1))))))
, 1(3(3(x1))) -> 0(2(1(1(0(5(x1))))))
, 1(2(3(x1))) -> 5(1(4(1(4(4(x1))))))
, 0(4(0(x1))) -> 0(1(2(1(0(3(x1))))))
, 0(2(4(x1))) -> 1(5(4(3(4(4(x1))))))
, 0(1(3(x1))) -> 0(2(4(3(4(4(x1))))))
, 0(1(1(x1))) -> 0(2(2(1(1(1(x1))))))
, 0(0(4(x1))) -> 1(1(5(2(3(4(x1))))))
, 0(4(x1)) -> 0(2(1(4(3(4(x1))))))
, 0(4(x1)) -> 0(1(4(2(3(3(x1))))))}
StartTerms: all
Strategy: none
Certificate: MAYBE
Proof:
The input cannot be shown compatible
Arrrr..