* Step 1: Bounds WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict TRS:
            active(adx(X)) -> adx(active(X))
            active(adx(cons(X,L))) -> mark(incr(cons(X,adx(L))))
            active(adx(nil())) -> mark(nil())
            active(cons(X1,X2)) -> cons(active(X1),X2)
            active(head(X)) -> head(active(X))
            active(head(cons(X,L))) -> mark(X)
            active(incr(X)) -> incr(active(X))
            active(incr(cons(X,L))) -> mark(cons(s(X),incr(L)))
            active(incr(nil())) -> mark(nil())
            active(nats()) -> mark(adx(zeros()))
            active(s(X)) -> s(active(X))
            active(tail(X)) -> tail(active(X))
            active(tail(cons(X,L))) -> mark(L)
            active(zeros()) -> mark(cons(0(),zeros()))
            adx(mark(X)) -> mark(adx(X))
            adx(ok(X)) -> ok(adx(X))
            cons(mark(X1),X2) -> mark(cons(X1,X2))
            cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
            head(mark(X)) -> mark(head(X))
            head(ok(X)) -> ok(head(X))
            incr(mark(X)) -> mark(incr(X))
            incr(ok(X)) -> ok(incr(X))
            proper(0()) -> ok(0())
            proper(adx(X)) -> adx(proper(X))
            proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
            proper(head(X)) -> head(proper(X))
            proper(incr(X)) -> incr(proper(X))
            proper(nats()) -> ok(nats())
            proper(nil()) -> ok(nil())
            proper(s(X)) -> s(proper(X))
            proper(tail(X)) -> tail(proper(X))
            proper(zeros()) -> ok(zeros())
            s(mark(X)) -> mark(s(X))
            s(ok(X)) -> ok(s(X))
            tail(mark(X)) -> mark(tail(X))
            tail(ok(X)) -> ok(tail(X))
            top(mark(X)) -> top(proper(X))
            top(ok(X)) -> top(active(X))
        - Signature:
            {active/1,adx/1,cons/2,head/1,incr/1,proper/1,s/1,tail/1,top/1} / {0/0,mark/1,nats/0,nil/0,ok/1,zeros/0}
        - Obligation:
             runtime complexity wrt. defined symbols {active,adx,cons,head,incr,proper,s,tail,top} and constructors {0
            ,mark,nats,nil,ok,zeros}
    + Applied Processor:
        Bounds {initialAutomaton = perSymbol, enrichment = match}
    + Details:
        The problem is match-bounded by 10.
        The enriched problem is compatible with follwoing automaton.
          0_0() -> 1
          0_1() -> 18
          0_2() -> 29
          0_3() -> 42
          0_4() -> 48
          0_5() -> 64
          0_6() -> 93
          0_7() -> 132
          0_8() -> 160
          active_0(1) -> 2
          active_0(7) -> 2
          active_0(8) -> 2
          active_0(9) -> 2
          active_0(10) -> 2
          active_0(15) -> 2
          active_1(1) -> 25
          active_1(7) -> 25
          active_1(8) -> 25
          active_1(9) -> 25
          active_1(10) -> 25
          active_1(15) -> 25
          active_2(17) -> 26
          active_2(18) -> 26
          active_3(34) -> 33
          active_4(28) -> 38
          active_4(29) -> 39
          active_4(32) -> 39
          active_4(44) -> 45
          active_5(37) -> 46
          active_5(42) -> 56
          active_5(61) -> 65
          active_5(62) -> 55
          active_5(66) -> 55
          active_6(48) -> 72
          active_6(49) -> 68
          active_6(63) -> 57
          active_6(75) -> 76
          active_6(106) -> 111
          active_6(107) -> 76
          active_7(64) -> 81
          active_7(67) -> 77
          active_7(99) -> 121
          active_7(100) -> 85
          active_7(144) -> 149
          active_7(148) -> 85
          active_8(93) -> 123
          active_8(98) -> 91
          active_8(109) -> 110
          active_8(142) -> 150
          active_8(166) -> 168
          active_8(167) -> 110
          active_9(108) -> 112
          active_9(119) -> 141
          active_9(132) -> 147
          active_9(139) -> 120
          active_9(163) -> 169
          active_10(137) -> 146
          active_10(143) -> 145
          active_10(160) -> 170
          adx_0(1) -> 3
          adx_0(7) -> 3
          adx_0(8) -> 3
          adx_0(9) -> 3
          adx_0(10) -> 3
          adx_0(15) -> 3
          adx_1(1) -> 19
          adx_1(7) -> 19
          adx_1(8) -> 19
          adx_1(9) -> 19
          adx_1(10) -> 19
          adx_1(15) -> 19
          adx_1(17) -> 16
          adx_2(28) -> 27
          adx_2(30) -> 26
          adx_3(28) -> 34
          adx_3(35) -> 33
          adx_3(37) -> 40
          adx_4(37) -> 44
          adx_4(38) -> 33
          adx_4(41) -> 43
          adx_4(52) -> 53
          adx_5(46) -> 45
          adx_5(47) -> 50
          adx_5(49) -> 61
          adx_6(49) -> 71
          adx_6(57) -> 55
          adx_6(60) -> 97
          adx_6(63) -> 66
          adx_6(68) -> 65
          adx_6(73) -> 74
          adx_7(60) -> 80
          adx_7(67) -> 75
          adx_7(77) -> 76
          adx_7(86) -> 82
          adx_7(92) -> 105
          adx_7(94) -> 90
          adx_7(121) -> 111
          adx_7(124) -> 118
          adx_8(99) -> 106
          adx_8(101) -> 96
          adx_8(133) -> 130
          adx_8(133) -> 135
          adx_8(136) -> 138
          adx_9(161) -> 158
          adx_9(162) -> 164
          cons_0(1,1) -> 4
          cons_0(1,7) -> 4
          cons_0(1,8) -> 4
          cons_0(1,9) -> 4
          cons_0(1,10) -> 4
          cons_0(1,15) -> 4
          cons_0(7,1) -> 4
          cons_0(7,7) -> 4
          cons_0(7,8) -> 4
          cons_0(7,9) -> 4
          cons_0(7,10) -> 4
          cons_0(7,15) -> 4
          cons_0(8,1) -> 4
          cons_0(8,7) -> 4
          cons_0(8,8) -> 4
          cons_0(8,9) -> 4
          cons_0(8,10) -> 4
          cons_0(8,15) -> 4
          cons_0(9,1) -> 4
          cons_0(9,7) -> 4
          cons_0(9,8) -> 4
          cons_0(9,9) -> 4
          cons_0(9,10) -> 4
          cons_0(9,15) -> 4
          cons_0(10,1) -> 4
          cons_0(10,7) -> 4
          cons_0(10,8) -> 4
          cons_0(10,9) -> 4
          cons_0(10,10) -> 4
          cons_0(10,15) -> 4
          cons_0(15,1) -> 4
          cons_0(15,7) -> 4
          cons_0(15,8) -> 4
          cons_0(15,9) -> 4
          cons_0(15,10) -> 4
          cons_0(15,15) -> 4
          cons_1(1,1) -> 20
          cons_1(1,7) -> 20
          cons_1(1,8) -> 20
          cons_1(1,9) -> 20
          cons_1(1,10) -> 20
          cons_1(1,15) -> 20
          cons_1(7,1) -> 20
          cons_1(7,7) -> 20
          cons_1(7,8) -> 20
          cons_1(7,9) -> 20
          cons_1(7,10) -> 20
          cons_1(7,15) -> 20
          cons_1(8,1) -> 20
          cons_1(8,7) -> 20
          cons_1(8,8) -> 20
          cons_1(8,9) -> 20
          cons_1(8,10) -> 20
          cons_1(8,15) -> 20
          cons_1(9,1) -> 20
          cons_1(9,7) -> 20
          cons_1(9,8) -> 20
          cons_1(9,9) -> 20
          cons_1(9,10) -> 20
          cons_1(9,15) -> 20
          cons_1(10,1) -> 20
          cons_1(10,7) -> 20
          cons_1(10,8) -> 20
          cons_1(10,9) -> 20
          cons_1(10,10) -> 20
          cons_1(10,15) -> 20
          cons_1(15,1) -> 20
          cons_1(15,7) -> 20
          cons_1(15,8) -> 20
          cons_1(15,9) -> 20
          cons_1(15,10) -> 20
          cons_1(15,15) -> 20
          cons_1(18,17) -> 16
          cons_2(29,28) -> 27
          cons_2(31,30) -> 26
          cons_3(29,28) -> 34
          cons_3(32,28) -> 34
          cons_3(36,35) -> 33
          cons_3(42,37) -> 41
          cons_4(39,28) -> 33
          cons_4(40,28) -> 43
          cons_4(42,37) -> 44
          cons_4(48,49) -> 47
          cons_4(51,52) -> 46
          cons_4(61,37) -> 62
          cons_5(48,49) -> 63
          cons_5(53,54) -> 45
          cons_5(56,37) -> 45
          cons_5(58,59) -> 57
          cons_5(64,60) -> 73
          cons_5(65,37) -> 55
          cons_5(106,49) -> 107
          cons_6(48,71) -> 70
          cons_6(64,60) -> 67
          cons_6(64,97) -> 98
          cons_6(72,49) -> 57
          cons_6(74,37) -> 69
          cons_6(87,88) -> 86
          cons_6(111,49) -> 76
          cons_6(144,60) -> 148
          cons_7(64,80) -> 79
          cons_7(81,60) -> 77
          cons_7(81,97) -> 91
          cons_7(82,83) -> 76
          cons_7(89,90) -> 84
          cons_7(93,92) -> 99
          cons_7(93,105) -> 108
          cons_7(103,104) -> 102
          cons_7(122,49) -> 78
          cons_7(149,60) -> 85
          cons_7(166,92) -> 167
          cons_8(95,96) -> 91
          cons_8(114,115) -> 113
          cons_8(116,117) -> 110
          cons_8(119,115) -> 139
          cons_8(123,92) -> 121
          cons_8(123,105) -> 112
          cons_8(125,126) -> 85
          cons_8(132,138) -> 142
          cons_8(134,135) -> 129
          cons_8(137,152) -> 151
          cons_8(151,60) -> 153
          cons_8(168,92) -> 110
          cons_9(127,128) -> 120
          cons_9(137,140) -> 143
          cons_9(141,115) -> 120
          cons_9(147,138) -> 150
          cons_9(154,155) -> 110
          cons_9(156,157) -> 154
          cons_9(169,165) -> 168
          cons_10(146,140) -> 145
          cons_10(163,165) -> 166
          head_0(1) -> 5
          head_0(7) -> 5
          head_0(8) -> 5
          head_0(9) -> 5
          head_0(10) -> 5
          head_0(15) -> 5
          head_1(1) -> 21
          head_1(7) -> 21
          head_1(8) -> 21
          head_1(9) -> 21
          head_1(10) -> 21
          head_1(15) -> 21
          incr_0(1) -> 6
          incr_0(7) -> 6
          incr_0(8) -> 6
          incr_0(9) -> 6
          incr_0(10) -> 6
          incr_0(15) -> 6
          incr_1(1) -> 22
          incr_1(7) -> 22
          incr_1(8) -> 22
          incr_1(9) -> 22
          incr_1(10) -> 22
          incr_1(15) -> 22
          incr_6(70) -> 69
          incr_7(79) -> 78
          incr_7(84) -> 76
          incr_7(97) -> 104
          incr_7(98) -> 100
          incr_7(108) -> 122
          incr_8(91) -> 85
          incr_8(105) -> 115
          incr_8(108) -> 109
          incr_8(118) -> 117
          incr_8(129) -> 125
          incr_8(138) -> 152
          incr_8(150) -> 149
          incr_9(112) -> 110
          incr_9(130) -> 128
          incr_9(138) -> 140
          incr_9(142) -> 144
          incr_9(158) -> 157
          incr_10(164) -> 165
          mark_0(1) -> 7
          mark_0(7) -> 7
          mark_0(8) -> 7
          mark_0(9) -> 7
          mark_0(10) -> 7
          mark_0(15) -> 7
          mark_1(16) -> 2
          mark_1(16) -> 25
          mark_1(19) -> 3
          mark_1(19) -> 19
          mark_1(20) -> 4
          mark_1(20) -> 20
          mark_1(21) -> 5
          mark_1(21) -> 21
          mark_1(22) -> 6
          mark_1(22) -> 22
          mark_1(23) -> 12
          mark_1(23) -> 23
          mark_1(24) -> 13
          mark_1(24) -> 24
          mark_2(27) -> 26
          mark_3(40) -> 39
          mark_3(41) -> 38
          mark_4(43) -> 33
          mark_4(47) -> 46
          mark_5(50) -> 45
          mark_5(73) -> 68
          mark_6(69) -> 55
          mark_6(74) -> 65
          mark_7(78) -> 76
          mark_7(102) -> 85
          mark_7(122) -> 111
          mark_8(113) -> 110
          mark_8(151) -> 149
          mark_8(153) -> 85
          nats_0() -> 8
          nats_1() -> 18
          nats_2() -> 32
          nil_0() -> 9
          nil_1() -> 18
          nil_2() -> 32
          ok_0(1) -> 10
          ok_0(7) -> 10
          ok_0(8) -> 10
          ok_0(9) -> 10
          ok_0(10) -> 10
          ok_0(15) -> 10
          ok_1(17) -> 11
          ok_1(17) -> 25
          ok_1(18) -> 11
          ok_1(18) -> 25
          ok_1(19) -> 3
          ok_1(19) -> 19
          ok_1(20) -> 4
          ok_1(20) -> 20
          ok_1(21) -> 5
          ok_1(21) -> 21
          ok_1(22) -> 6
          ok_1(22) -> 22
          ok_1(23) -> 12
          ok_1(23) -> 23
          ok_1(24) -> 13
          ok_1(24) -> 24
          ok_2(28) -> 30
          ok_2(29) -> 31
          ok_2(32) -> 31
          ok_3(34) -> 26
          ok_3(37) -> 35
          ok_3(37) -> 54
          ok_3(42) -> 36
          ok_4(44) -> 33
          ok_4(48) -> 51
          ok_4(49) -> 52
          ok_4(49) -> 83
          ok_4(62) -> 45
          ok_5(60) -> 59
          ok_5(60) -> 94
          ok_5(60) -> 126
          ok_5(61) -> 53
          ok_5(63) -> 46
          ok_5(64) -> 58
          ok_5(64) -> 89
          ok_5(107) -> 76
          ok_6(66) -> 45
          ok_6(67) -> 57
          ok_6(92) -> 88
          ok_6(92) -> 101
          ok_6(92) -> 124
          ok_6(92) -> 155
          ok_6(93) -> 87
          ok_6(93) -> 95
          ok_6(97) -> 90
          ok_6(98) -> 84
          ok_6(148) -> 85
          ok_7(75) -> 55
          ok_7(99) -> 86
          ok_7(100) -> 76
          ok_7(105) -> 96
          ok_7(105) -> 118
          ok_7(108) -> 91
          ok_7(119) -> 116
          ok_7(132) -> 131
          ok_7(132) -> 134
          ok_7(136) -> 133
          ok_7(167) -> 110
          ok_8(106) -> 82
          ok_8(109) -> 85
          ok_8(115) -> 117
          ok_8(137) -> 127
          ok_8(138) -> 130
          ok_8(138) -> 135
          ok_8(139) -> 110
          ok_8(142) -> 129
          ok_8(160) -> 159
          ok_8(162) -> 161
          ok_9(140) -> 128
          ok_9(143) -> 120
          ok_9(144) -> 125
          ok_9(163) -> 156
          ok_9(164) -> 158
          ok_10(165) -> 157
          ok_10(166) -> 154
          proper_0(1) -> 11
          proper_0(7) -> 11
          proper_0(8) -> 11
          proper_0(9) -> 11
          proper_0(10) -> 11
          proper_0(15) -> 11
          proper_1(1) -> 25
          proper_1(7) -> 25
          proper_1(8) -> 25
          proper_1(9) -> 25
          proper_1(10) -> 25
          proper_1(15) -> 25
          proper_2(16) -> 26
          proper_2(17) -> 30
          proper_2(18) -> 31
          proper_3(27) -> 33
          proper_3(28) -> 35
          proper_3(29) -> 36
          proper_4(37) -> 52
          proper_4(42) -> 51
          proper_4(43) -> 45
          proper_5(28) -> 54
          proper_5(40) -> 53
          proper_5(41) -> 46
          proper_5(48) -> 58
          proper_5(49) -> 59
          proper_5(50) -> 55
          proper_6(47) -> 57
          proper_6(60) -> 88
          proper_6(64) -> 87
          proper_6(69) -> 76
          proper_7(37) -> 83
          proper_7(48) -> 89
          proper_7(49) -> 94
          proper_7(60) -> 124
          proper_7(70) -> 84
          proper_7(71) -> 90
          proper_7(73) -> 86
          proper_7(74) -> 82
          proper_7(78) -> 85
          proper_8(49) -> 126
          proper_8(60) -> 101
          proper_8(64) -> 95
          proper_8(79) -> 91
          proper_8(80) -> 96
          proper_8(92) -> 133
          proper_8(93) -> 134
          proper_8(97) -> 118
          proper_8(102) -> 110
          proper_8(103) -> 116
          proper_8(104) -> 117
          proper_8(105) -> 135
          proper_8(108) -> 129
          proper_8(122) -> 125
          proper_8(153) -> 110
          proper_9(60) -> 155
          proper_9(93) -> 131
          proper_9(105) -> 130
          proper_9(113) -> 120
          proper_9(114) -> 127
          proper_9(115) -> 128
          proper_9(132) -> 159
          proper_9(136) -> 161
          proper_9(137) -> 156
          proper_9(138) -> 158
          proper_9(151) -> 154
          proper_9(152) -> 157
          s_0(1) -> 12
          s_0(7) -> 12
          s_0(8) -> 12
          s_0(9) -> 12
          s_0(10) -> 12
          s_0(15) -> 12
          s_1(1) -> 23
          s_1(7) -> 23
          s_1(8) -> 23
          s_1(9) -> 23
          s_1(10) -> 23
          s_1(15) -> 23
          s_7(64) -> 103
          s_7(93) -> 119
          s_8(93) -> 114
          s_8(95) -> 116
          s_8(123) -> 141
          s_8(132) -> 137
          s_9(131) -> 127
          s_9(147) -> 146
          s_9(159) -> 156
          s_9(160) -> 163
          s_10(170) -> 169
          tail_0(1) -> 13
          tail_0(7) -> 13
          tail_0(8) -> 13
          tail_0(9) -> 13
          tail_0(10) -> 13
          tail_0(15) -> 13
          tail_1(1) -> 24
          tail_1(7) -> 24
          tail_1(8) -> 24
          tail_1(9) -> 24
          tail_1(10) -> 24
          tail_1(15) -> 24
          top_0(1) -> 14
          top_0(7) -> 14
          top_0(8) -> 14
          top_0(9) -> 14
          top_0(10) -> 14
          top_0(15) -> 14
          top_1(25) -> 14
          top_2(26) -> 14
          top_3(33) -> 14
          top_4(45) -> 14
          top_5(55) -> 14
          top_6(76) -> 14
          top_7(85) -> 14
          top_8(110) -> 14
          top_9(120) -> 14
          top_10(145) -> 14
          zeros_0() -> 15
          zeros_1() -> 17
          zeros_2() -> 28
          zeros_3() -> 37
          zeros_4() -> 49
          zeros_5() -> 60
          zeros_6() -> 92
          zeros_7() -> 136
          zeros_8() -> 162
* Step 2: EmptyProcessor WORST_CASE(?,O(1))
    + Considered Problem:
        - Weak TRS:
            active(adx(X)) -> adx(active(X))
            active(adx(cons(X,L))) -> mark(incr(cons(X,adx(L))))
            active(adx(nil())) -> mark(nil())
            active(cons(X1,X2)) -> cons(active(X1),X2)
            active(head(X)) -> head(active(X))
            active(head(cons(X,L))) -> mark(X)
            active(incr(X)) -> incr(active(X))
            active(incr(cons(X,L))) -> mark(cons(s(X),incr(L)))
            active(incr(nil())) -> mark(nil())
            active(nats()) -> mark(adx(zeros()))
            active(s(X)) -> s(active(X))
            active(tail(X)) -> tail(active(X))
            active(tail(cons(X,L))) -> mark(L)
            active(zeros()) -> mark(cons(0(),zeros()))
            adx(mark(X)) -> mark(adx(X))
            adx(ok(X)) -> ok(adx(X))
            cons(mark(X1),X2) -> mark(cons(X1,X2))
            cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
            head(mark(X)) -> mark(head(X))
            head(ok(X)) -> ok(head(X))
            incr(mark(X)) -> mark(incr(X))
            incr(ok(X)) -> ok(incr(X))
            proper(0()) -> ok(0())
            proper(adx(X)) -> adx(proper(X))
            proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
            proper(head(X)) -> head(proper(X))
            proper(incr(X)) -> incr(proper(X))
            proper(nats()) -> ok(nats())
            proper(nil()) -> ok(nil())
            proper(s(X)) -> s(proper(X))
            proper(tail(X)) -> tail(proper(X))
            proper(zeros()) -> ok(zeros())
            s(mark(X)) -> mark(s(X))
            s(ok(X)) -> ok(s(X))
            tail(mark(X)) -> mark(tail(X))
            tail(ok(X)) -> ok(tail(X))
            top(mark(X)) -> top(proper(X))
            top(ok(X)) -> top(active(X))
        - Signature:
            {active/1,adx/1,cons/2,head/1,incr/1,proper/1,s/1,tail/1,top/1} / {0/0,mark/1,nats/0,nil/0,ok/1,zeros/0}
        - Obligation:
             runtime complexity wrt. defined symbols {active,adx,cons,head,incr,proper,s,tail,top} and constructors {0
            ,mark,nats,nil,ok,zeros}
    + Applied Processor:
        EmptyProcessor
    + Details:
        The problem is already closed. The intended complexity is O(1).

WORST_CASE(?,O(n^1))