WORST_CASE(Omega(n^1),O(n^2))
proof of input_f1GfDn3ipn.trs
# AProVE Commit ID: 5b976082cb74a395683ed8cc7acf94bd611ab29f fuhs 20230524 unpublished


The Runtime Complexity (parallel-innermost) of the given CpxRelTRS could be proven to be BOUNDS(n^1, n^2).

(0) CpxRelTRS
(1) SInnermostTerminationProof [BOTH CONCRETE BOUNDS(ID, ID), 277 ms]
(2) CpxRelTRS
(3) CpxTrsToCdtProof [UPPER BOUND(ID), 0 ms]
(4) CdtProblem
    (5) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms]
    (6) CdtProblem
    (7) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
    (8) CdtProblem
    (9) CdtGraphSplitRhsProof [BOTH BOUNDS(ID, ID), 0 ms]
    (10) CdtProblem
    (11) CdtLeafRemovalProof [ComplexityIfPolyImplication, 0 ms]
    (12) CdtProblem
    (13) CdtKnowledgeProof [BOTH BOUNDS(ID, ID), 0 ms]
    (14) CdtProblem
    (15) CdtUsableRulesProof [BOTH BOUNDS(ID, ID), 6 ms]
    (16) CdtProblem
    (17) CdtToCpxRelTrsProof [BOTH BOUNDS(ID, ID), 0 ms]
    (18) CpxRelTRS
    (19) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms]
    (20) CpxWeightedTrs
    (21) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms]
    (22) CpxTypedWeightedTrs
    (23) CompletionProof [UPPER BOUND(ID), 0 ms]
    (24) CpxTypedWeightedCompleteTrs
    (25) NarrowingProof [BOTH BOUNDS(ID, ID), 33 ms]
    (26) CpxTypedWeightedCompleteTrs
    (27) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms]
    (28) CpxRNTS
    (29) InliningProof [UPPER BOUND(ID), 987 ms]
    (30) CpxRNTS
    (31) SimplificationProof [BOTH BOUNDS(ID, ID), 0 ms]
    (32) CpxRNTS
    (33) CpxRntsAnalysisOrderProof [BOTH BOUNDS(ID, ID), 0 ms]
    (34) CpxRNTS
    (35) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
    (36) CpxRNTS
    (37) IntTrsBoundProof [UPPER BOUND(ID), 261 ms]
    (38) CpxRNTS
    (39) IntTrsBoundProof [UPPER BOUND(ID), 160 ms]
    (40) CpxRNTS
    (41) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
    (42) CpxRNTS
    (43) IntTrsBoundProof [UPPER BOUND(ID), 160 ms]
    (44) CpxRNTS
    (45) IntTrsBoundProof [UPPER BOUND(ID), 24 ms]
    (46) CpxRNTS
    (47) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
    (48) CpxRNTS
    (49) IntTrsBoundProof [UPPER BOUND(ID), 945 ms]
    (50) CpxRNTS
    (51) IntTrsBoundProof [UPPER BOUND(ID), 145 ms]
    (52) CpxRNTS
    (53) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
    (54) CpxRNTS
    (55) IntTrsBoundProof [UPPER BOUND(ID), 309 ms]
    (56) CpxRNTS
    (57) IntTrsBoundProof [UPPER BOUND(ID), 144 ms]
    (58) CpxRNTS
    (59) ResultPropagationProof [UPPER BOUND(ID), 2 ms]
    (60) CpxRNTS
    (61) IntTrsBoundProof [UPPER BOUND(ID), 630 ms]
    (62) CpxRNTS
    (63) IntTrsBoundProof [UPPER BOUND(ID), 104 ms]
    (64) CpxRNTS
    (65) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
    (66) CpxRNTS
    (67) IntTrsBoundProof [UPPER BOUND(ID), 528 ms]
    (68) CpxRNTS
    (69) IntTrsBoundProof [UPPER BOUND(ID), 67 ms]
    (70) CpxRNTS
    (71) ResultPropagationProof [UPPER BOUND(ID), 2 ms]
    (72) CpxRNTS
    (73) IntTrsBoundProof [UPPER BOUND(ID), 1852 ms]
    (74) CpxRNTS
    (75) IntTrsBoundProof [UPPER BOUND(ID), 316 ms]
    (76) CpxRNTS
    (77) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
    (78) CpxRNTS
    (79) IntTrsBoundProof [UPPER BOUND(ID), 156 ms]
    (80) CpxRNTS
    (81) IntTrsBoundProof [UPPER BOUND(ID), 62 ms]
    (82) CpxRNTS
    (83) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
    (84) CpxRNTS
    (85) IntTrsBoundProof [UPPER BOUND(ID), 601 ms]
    (86) CpxRNTS
    (87) IntTrsBoundProof [UPPER BOUND(ID), 85 ms]
    (88) CpxRNTS
    (89) ResultPropagationProof [UPPER BOUND(ID), 9 ms]
    (90) CpxRNTS
    (91) IntTrsBoundProof [UPPER BOUND(ID), 259 ms]
    (92) CpxRNTS
    (93) IntTrsBoundProof [UPPER BOUND(ID), 52 ms]
    (94) CpxRNTS
    (95) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
    (96) CpxRNTS
    (97) IntTrsBoundProof [UPPER BOUND(ID), 833 ms]
    (98) CpxRNTS
    (99) IntTrsBoundProof [UPPER BOUND(ID), 374 ms]
    (100) CpxRNTS
    (101) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
    (102) CpxRNTS
    (103) IntTrsBoundProof [UPPER BOUND(ID), 126 ms]
    (104) CpxRNTS
    (105) IntTrsBoundProof [UPPER BOUND(ID), 22 ms]
    (106) CpxRNTS
    (107) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
    (108) CpxRNTS
    (109) IntTrsBoundProof [UPPER BOUND(ID), 6249 ms]
    (110) CpxRNTS
    (111) IntTrsBoundProof [UPPER BOUND(ID), 4305 ms]
    (112) CpxRNTS
    (113) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
    (114) CpxRNTS
    (115) IntTrsBoundProof [UPPER BOUND(ID), 156 ms]
    (116) CpxRNTS
    (117) IntTrsBoundProof [UPPER BOUND(ID), 2 ms]
    (118) CpxRNTS
    (119) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
    (120) CpxRNTS
    (121) IntTrsBoundProof [UPPER BOUND(ID), 377 ms]
    (122) CpxRNTS
    (123) IntTrsBoundProof [UPPER BOUND(ID), 128 ms]
    (124) CpxRNTS
    (125) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
    (126) CpxRNTS
    (127) IntTrsBoundProof [UPPER BOUND(ID), 137 ms]
    (128) CpxRNTS
    (129) IntTrsBoundProof [UPPER BOUND(ID), 3 ms]
    (130) CpxRNTS
    (131) FinalProof [FINISHED, 0 ms]
    (132) BOUNDS(1, n^2)
(133) CpxTrsToCdtProof [BOTH BOUNDS(ID, ID), 0 ms]
(134) CdtProblem
    (135) CdtToCpxRelTrsProof [BOTH BOUNDS(ID, ID), 0 ms]
    (136) CpxRelTRS
    (137) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (138) CpxRelTRS
    (139) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms]
    (140) typed CpxTrs
    (141) OrderProof [LOWER BOUND(ID), 61 ms]
    (142) typed CpxTrs
    (143) RewriteLemmaProof [LOWER BOUND(ID), 1785 ms]
    (144) typed CpxTrs
    (145) RewriteLemmaProof [LOWER BOUND(ID), 1578 ms]
    (146) typed CpxTrs
    (147) RewriteLemmaProof [LOWER BOUND(ID), 606 ms]
    (148) typed CpxTrs
    (149) RewriteLemmaProof [LOWER BOUND(ID), 622 ms]
    (150) typed CpxTrs
    (151) RewriteLemmaProof [LOWER BOUND(ID), 607 ms]
    (152) typed CpxTrs
    (153) RewriteLemmaProof [LOWER BOUND(ID), 981 ms]
    (154) typed CpxTrs
    (155) RewriteLemmaProof [LOWER BOUND(ID), 113 ms]
    (156) typed CpxTrs
    (157) RewriteLemmaProof [LOWER BOUND(ID), 536 ms]
    (158) BEST
        (159) proven lower bound
            (160) LowerBoundPropagationProof [FINISHED, 0 ms]
            (161) BOUNDS(n^1, INF)
        (162) typed CpxTrs
            (163) RewriteLemmaProof [LOWER BOUND(ID), 517 ms]
            (164) typed CpxTrs
            (165) RewriteLemmaProof [LOWER BOUND(ID), 480 ms]
            (166) typed CpxTrs


----------------------------------------

(0)
Obligation:
The Runtime Complexity (parallel-innermost) of the given CpxRelTRS could be proven to be BOUNDS(n^1, n^2).


The TRS R consists of the following rules:

   #less(@x, @y) -> #cklt(#compare(@x, @y))
   append(@l1, @l2) -> append#1(@l1, @l2)
   append#1(::(@x, @xs), @l2) -> ::(@x, append(@xs, @l2))
   append#1(nil, @l2) -> @l2
   flatten(@t) -> flatten#1(@t)
   flatten#1(leaf) -> nil
   flatten#1(node(@l, @t1, @t2)) -> append(@l, append(flatten(@t1), flatten(@t2)))
   flattensort(@t) -> insertionsort(flatten(@t))
   insert(@x, @l) -> insert#1(@l, @x)
   insert#1(::(@y, @ys), @x) -> insert#2(#less(@y, @x), @x, @y, @ys)
   insert#1(nil, @x) -> ::(@x, nil)
   insert#2(#false, @x, @y, @ys) -> ::(@x, ::(@y, @ys))
   insert#2(#true, @x, @y, @ys) -> ::(@y, insert(@x, @ys))
   insertionsort(@l) -> insertionsort#1(@l)
   insertionsort#1(::(@x, @xs)) -> insert(@x, insertionsort(@xs))
   insertionsort#1(nil) -> nil

The (relative) TRS S consists of the following rules:

   #cklt(#EQ) -> #false
   #cklt(#GT) -> #false
   #cklt(#LT) -> #true
   #compare(#0, #0) -> #EQ
   #compare(#0, #neg(@y)) -> #GT
   #compare(#0, #pos(@y)) -> #LT
   #compare(#0, #s(@y)) -> #LT
   #compare(#neg(@x), #0) -> #LT
   #compare(#neg(@x), #neg(@y)) -> #compare(@y, @x)
   #compare(#neg(@x), #pos(@y)) -> #LT
   #compare(#pos(@x), #0) -> #GT
   #compare(#pos(@x), #neg(@y)) -> #GT
   #compare(#pos(@x), #pos(@y)) -> #compare(@x, @y)
   #compare(#s(@x), #0) -> #GT
   #compare(#s(@x), #s(@y)) -> #compare(@x, @y)

Rewrite Strategy: PARALLEL_INNERMOST
----------------------------------------

(1) SInnermostTerminationProof (BOTH CONCRETE BOUNDS(ID, ID))
proved innermost termination of relative rules
----------------------------------------

(2)
Obligation:
The Runtime Complexity (parallel-innermost) of the given CpxRelTRS could be proven to be BOUNDS(n^1, n^2).


The TRS R consists of the following rules:

   #less(@x, @y) -> #cklt(#compare(@x, @y))
   append(@l1, @l2) -> append#1(@l1, @l2)
   append#1(::(@x, @xs), @l2) -> ::(@x, append(@xs, @l2))
   append#1(nil, @l2) -> @l2
   flatten(@t) -> flatten#1(@t)
   flatten#1(leaf) -> nil
   flatten#1(node(@l, @t1, @t2)) -> append(@l, append(flatten(@t1), flatten(@t2)))
   flattensort(@t) -> insertionsort(flatten(@t))
   insert(@x, @l) -> insert#1(@l, @x)
   insert#1(::(@y, @ys), @x) -> insert#2(#less(@y, @x), @x, @y, @ys)
   insert#1(nil, @x) -> ::(@x, nil)
   insert#2(#false, @x, @y, @ys) -> ::(@x, ::(@y, @ys))
   insert#2(#true, @x, @y, @ys) -> ::(@y, insert(@x, @ys))
   insertionsort(@l) -> insertionsort#1(@l)
   insertionsort#1(::(@x, @xs)) -> insert(@x, insertionsort(@xs))
   insertionsort#1(nil) -> nil

The (relative) TRS S consists of the following rules:

   #cklt(#EQ) -> #false
   #cklt(#GT) -> #false
   #cklt(#LT) -> #true
   #compare(#0, #0) -> #EQ
   #compare(#0, #neg(@y)) -> #GT
   #compare(#0, #pos(@y)) -> #LT
   #compare(#0, #s(@y)) -> #LT
   #compare(#neg(@x), #0) -> #LT
   #compare(#neg(@x), #neg(@y)) -> #compare(@y, @x)
   #compare(#neg(@x), #pos(@y)) -> #LT
   #compare(#pos(@x), #0) -> #GT
   #compare(#pos(@x), #neg(@y)) -> #GT
   #compare(#pos(@x), #pos(@y)) -> #compare(@x, @y)
   #compare(#s(@x), #0) -> #GT
   #compare(#s(@x), #s(@y)) -> #compare(@x, @y)

Rewrite Strategy: PARALLEL_INNERMOST
----------------------------------------

(3) CpxTrsToCdtProof (UPPER BOUND(ID))
Converted Cpx (relative) TRS with rewrite strategy PARALLEL_INNERMOST to CDT
----------------------------------------

(4)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   #cklt(#EQ) -> #false
   #cklt(#GT) -> #false
   #cklt(#LT) -> #true
   #compare(#0, #0) -> #EQ
   #compare(#0, #neg(z0)) -> #GT
   #compare(#0, #pos(z0)) -> #LT
   #compare(#0, #s(z0)) -> #LT
   #compare(#neg(z0), #0) -> #LT
   #compare(#neg(z0), #neg(z1)) -> #compare(z1, z0)
   #compare(#neg(z0), #pos(z1)) -> #LT
   #compare(#pos(z0), #0) -> #GT
   #compare(#pos(z0), #neg(z1)) -> #GT
   #compare(#pos(z0), #pos(z1)) -> #compare(z0, z1)
   #compare(#s(z0), #0) -> #GT
   #compare(#s(z0), #s(z1)) -> #compare(z0, z1)
   #less(z0, z1) -> #cklt(#compare(z0, z1))
   append(z0, z1) -> append#1(z0, z1)
   append#1(::(z0, z1), z2) -> ::(z0, append(z1, z2))
   append#1(nil, z0) -> z0
   flatten(z0) -> flatten#1(z0)
   flatten#1(leaf) -> nil
   flatten#1(node(z0, z1, z2)) -> append(z0, append(flatten(z1), flatten(z2)))
   flattensort(z0) -> insertionsort(flatten(z0))
   insert(z0, z1) -> insert#1(z1, z0)
   insert#1(::(z0, z1), z2) -> insert#2(#less(z0, z2), z2, z0, z1)
   insert#1(nil, z0) -> ::(z0, nil)
   insert#2(#false, z0, z1, z2) -> ::(z0, ::(z1, z2))
   insert#2(#true, z0, z1, z2) -> ::(z1, insert(z0, z2))
   insertionsort(z0) -> insertionsort#1(z0)
   insertionsort#1(::(z0, z1)) -> insert(z0, insertionsort(z1))
   insertionsort#1(nil) -> nil
Tuples:
   #CKLT(#EQ) -> c
   #CKLT(#GT) -> c1
   #CKLT(#LT) -> c2
   #COMPARE(#0, #0) -> c3
   #COMPARE(#0, #neg(z0)) -> c4
   #COMPARE(#0, #pos(z0)) -> c5
   #COMPARE(#0, #s(z0)) -> c6
   #COMPARE(#neg(z0), #0) -> c7
   #COMPARE(#neg(z0), #neg(z1)) -> c8(#COMPARE(z1, z0))
   #COMPARE(#neg(z0), #pos(z1)) -> c9
   #COMPARE(#pos(z0), #0) -> c10
   #COMPARE(#pos(z0), #neg(z1)) -> c11
   #COMPARE(#pos(z0), #pos(z1)) -> c12(#COMPARE(z0, z1))
   #COMPARE(#s(z0), #0) -> c13
   #COMPARE(#s(z0), #s(z1)) -> c14(#COMPARE(z0, z1))
   #LESS(z0, z1) -> c15(#CKLT(#compare(z0, z1)), #COMPARE(z0, z1))
   APPEND(z0, z1) -> c16(APPEND#1(z0, z1))
   APPEND#1(::(z0, z1), z2) -> c17(APPEND(z1, z2))
   APPEND#1(nil, z0) -> c18
   FLATTEN(z0) -> c19(FLATTEN#1(z0))
   FLATTEN#1(leaf) -> c20
   FLATTEN#1(node(z0, z1, z2)) -> c21(APPEND(z0, append(flatten(z1), flatten(z2))), APPEND(flatten(z1), flatten(z2)), FLATTEN(z1))
   FLATTEN#1(node(z0, z1, z2)) -> c22(APPEND(z0, append(flatten(z1), flatten(z2))), APPEND(flatten(z1), flatten(z2)), FLATTEN(z2))
   FLATTENSORT(z0) -> c23(INSERTIONSORT(flatten(z0)), FLATTEN(z0))
   INSERT(z0, z1) -> c24(INSERT#1(z1, z0))
   INSERT#1(::(z0, z1), z2) -> c25(INSERT#2(#less(z0, z2), z2, z0, z1), #LESS(z0, z2))
   INSERT#1(nil, z0) -> c26
   INSERT#2(#false, z0, z1, z2) -> c27
   INSERT#2(#true, z0, z1, z2) -> c28(INSERT(z0, z2))
   INSERTIONSORT(z0) -> c29(INSERTIONSORT#1(z0))
   INSERTIONSORT#1(::(z0, z1)) -> c30(INSERT(z0, insertionsort(z1)), INSERTIONSORT(z1))
   INSERTIONSORT#1(nil) -> c31
S tuples:
   #LESS(z0, z1) -> c15(#CKLT(#compare(z0, z1)), #COMPARE(z0, z1))
   APPEND(z0, z1) -> c16(APPEND#1(z0, z1))
   APPEND#1(::(z0, z1), z2) -> c17(APPEND(z1, z2))
   APPEND#1(nil, z0) -> c18
   FLATTEN(z0) -> c19(FLATTEN#1(z0))
   FLATTEN#1(leaf) -> c20
   FLATTEN#1(node(z0, z1, z2)) -> c21(APPEND(z0, append(flatten(z1), flatten(z2))), APPEND(flatten(z1), flatten(z2)), FLATTEN(z1))
   FLATTEN#1(node(z0, z1, z2)) -> c22(APPEND(z0, append(flatten(z1), flatten(z2))), APPEND(flatten(z1), flatten(z2)), FLATTEN(z2))
   FLATTENSORT(z0) -> c23(INSERTIONSORT(flatten(z0)), FLATTEN(z0))
   INSERT(z0, z1) -> c24(INSERT#1(z1, z0))
   INSERT#1(::(z0, z1), z2) -> c25(INSERT#2(#less(z0, z2), z2, z0, z1), #LESS(z0, z2))
   INSERT#1(nil, z0) -> c26
   INSERT#2(#false, z0, z1, z2) -> c27
   INSERT#2(#true, z0, z1, z2) -> c28(INSERT(z0, z2))
   INSERTIONSORT(z0) -> c29(INSERTIONSORT#1(z0))
   INSERTIONSORT#1(::(z0, z1)) -> c30(INSERT(z0, insertionsort(z1)), INSERTIONSORT(z1))
   INSERTIONSORT#1(nil) -> c31
K tuples:none
Defined Rule Symbols:   #less_2, append_2, append#1_2, flatten_1, flatten#1_1, flattensort_1, insert_2, insert#1_2, insert#2_4, insertionsort_1, insertionsort#1_1, #cklt_1, #compare_2

Defined Pair Symbols:   #CKLT_1, #COMPARE_2, #LESS_2, APPEND_2, APPEND#1_2, FLATTEN_1, FLATTEN#1_1, FLATTENSORT_1, INSERT_2, INSERT#1_2, INSERT#2_4, INSERTIONSORT_1, INSERTIONSORT#1_1

Compound Symbols:   c, c1, c2, c3, c4, c5, c6, c7, c8_1, c9, c10, c11, c12_1, c13, c14_1, c15_2, c16_1, c17_1, c18, c19_1, c20, c21_3, c22_3, c23_2, c24_1, c25_2, c26, c27, c28_1, c29_1, c30_2, c31


----------------------------------------

(5) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 17 trailing nodes:
   #COMPARE(#s(z0), #0) -> c13
   FLATTEN#1(leaf) -> c20
   #CKLT(#GT) -> c1
   INSERT#1(nil, z0) -> c26
   INSERTIONSORT#1(nil) -> c31
   #COMPARE(#0, #neg(z0)) -> c4
   #COMPARE(#0, #pos(z0)) -> c5
   #COMPARE(#0, #0) -> c3
   #COMPARE(#neg(z0), #0) -> c7
   #COMPARE(#neg(z0), #pos(z1)) -> c9
   #CKLT(#EQ) -> c
   INSERT#2(#false, z0, z1, z2) -> c27
   #COMPARE(#pos(z0), #neg(z1)) -> c11
   APPEND#1(nil, z0) -> c18
   #COMPARE(#0, #s(z0)) -> c6
   #COMPARE(#pos(z0), #0) -> c10
   #CKLT(#LT) -> c2

----------------------------------------

(6)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   #cklt(#EQ) -> #false
   #cklt(#GT) -> #false
   #cklt(#LT) -> #true
   #compare(#0, #0) -> #EQ
   #compare(#0, #neg(z0)) -> #GT
   #compare(#0, #pos(z0)) -> #LT
   #compare(#0, #s(z0)) -> #LT
   #compare(#neg(z0), #0) -> #LT
   #compare(#neg(z0), #neg(z1)) -> #compare(z1, z0)
   #compare(#neg(z0), #pos(z1)) -> #LT
   #compare(#pos(z0), #0) -> #GT
   #compare(#pos(z0), #neg(z1)) -> #GT
   #compare(#pos(z0), #pos(z1)) -> #compare(z0, z1)
   #compare(#s(z0), #0) -> #GT
   #compare(#s(z0), #s(z1)) -> #compare(z0, z1)
   #less(z0, z1) -> #cklt(#compare(z0, z1))
   append(z0, z1) -> append#1(z0, z1)
   append#1(::(z0, z1), z2) -> ::(z0, append(z1, z2))
   append#1(nil, z0) -> z0
   flatten(z0) -> flatten#1(z0)
   flatten#1(leaf) -> nil
   flatten#1(node(z0, z1, z2)) -> append(z0, append(flatten(z1), flatten(z2)))
   flattensort(z0) -> insertionsort(flatten(z0))
   insert(z0, z1) -> insert#1(z1, z0)
   insert#1(::(z0, z1), z2) -> insert#2(#less(z0, z2), z2, z0, z1)
   insert#1(nil, z0) -> ::(z0, nil)
   insert#2(#false, z0, z1, z2) -> ::(z0, ::(z1, z2))
   insert#2(#true, z0, z1, z2) -> ::(z1, insert(z0, z2))
   insertionsort(z0) -> insertionsort#1(z0)
   insertionsort#1(::(z0, z1)) -> insert(z0, insertionsort(z1))
   insertionsort#1(nil) -> nil
Tuples:
   #COMPARE(#neg(z0), #neg(z1)) -> c8(#COMPARE(z1, z0))
   #COMPARE(#pos(z0), #pos(z1)) -> c12(#COMPARE(z0, z1))
   #COMPARE(#s(z0), #s(z1)) -> c14(#COMPARE(z0, z1))
   #LESS(z0, z1) -> c15(#CKLT(#compare(z0, z1)), #COMPARE(z0, z1))
   APPEND(z0, z1) -> c16(APPEND#1(z0, z1))
   APPEND#1(::(z0, z1), z2) -> c17(APPEND(z1, z2))
   FLATTEN(z0) -> c19(FLATTEN#1(z0))
   FLATTEN#1(node(z0, z1, z2)) -> c21(APPEND(z0, append(flatten(z1), flatten(z2))), APPEND(flatten(z1), flatten(z2)), FLATTEN(z1))
   FLATTEN#1(node(z0, z1, z2)) -> c22(APPEND(z0, append(flatten(z1), flatten(z2))), APPEND(flatten(z1), flatten(z2)), FLATTEN(z2))
   FLATTENSORT(z0) -> c23(INSERTIONSORT(flatten(z0)), FLATTEN(z0))
   INSERT(z0, z1) -> c24(INSERT#1(z1, z0))
   INSERT#1(::(z0, z1), z2) -> c25(INSERT#2(#less(z0, z2), z2, z0, z1), #LESS(z0, z2))
   INSERT#2(#true, z0, z1, z2) -> c28(INSERT(z0, z2))
   INSERTIONSORT(z0) -> c29(INSERTIONSORT#1(z0))
   INSERTIONSORT#1(::(z0, z1)) -> c30(INSERT(z0, insertionsort(z1)), INSERTIONSORT(z1))
S tuples:
   #LESS(z0, z1) -> c15(#CKLT(#compare(z0, z1)), #COMPARE(z0, z1))
   APPEND(z0, z1) -> c16(APPEND#1(z0, z1))
   APPEND#1(::(z0, z1), z2) -> c17(APPEND(z1, z2))
   FLATTEN(z0) -> c19(FLATTEN#1(z0))
   FLATTEN#1(node(z0, z1, z2)) -> c21(APPEND(z0, append(flatten(z1), flatten(z2))), APPEND(flatten(z1), flatten(z2)), FLATTEN(z1))
   FLATTEN#1(node(z0, z1, z2)) -> c22(APPEND(z0, append(flatten(z1), flatten(z2))), APPEND(flatten(z1), flatten(z2)), FLATTEN(z2))
   FLATTENSORT(z0) -> c23(INSERTIONSORT(flatten(z0)), FLATTEN(z0))
   INSERT(z0, z1) -> c24(INSERT#1(z1, z0))
   INSERT#1(::(z0, z1), z2) -> c25(INSERT#2(#less(z0, z2), z2, z0, z1), #LESS(z0, z2))
   INSERT#2(#true, z0, z1, z2) -> c28(INSERT(z0, z2))
   INSERTIONSORT(z0) -> c29(INSERTIONSORT#1(z0))
   INSERTIONSORT#1(::(z0, z1)) -> c30(INSERT(z0, insertionsort(z1)), INSERTIONSORT(z1))
K tuples:none
Defined Rule Symbols:   #less_2, append_2, append#1_2, flatten_1, flatten#1_1, flattensort_1, insert_2, insert#1_2, insert#2_4, insertionsort_1, insertionsort#1_1, #cklt_1, #compare_2

Defined Pair Symbols:   #COMPARE_2, #LESS_2, APPEND_2, APPEND#1_2, FLATTEN_1, FLATTEN#1_1, FLATTENSORT_1, INSERT_2, INSERT#1_2, INSERT#2_4, INSERTIONSORT_1, INSERTIONSORT#1_1

Compound Symbols:   c8_1, c12_1, c14_1, c15_2, c16_1, c17_1, c19_1, c21_3, c22_3, c23_2, c24_1, c25_2, c28_1, c29_1, c30_2


----------------------------------------

(7) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID))
Removed 1 trailing tuple parts
----------------------------------------

(8)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   #cklt(#EQ) -> #false
   #cklt(#GT) -> #false
   #cklt(#LT) -> #true
   #compare(#0, #0) -> #EQ
   #compare(#0, #neg(z0)) -> #GT
   #compare(#0, #pos(z0)) -> #LT
   #compare(#0, #s(z0)) -> #LT
   #compare(#neg(z0), #0) -> #LT
   #compare(#neg(z0), #neg(z1)) -> #compare(z1, z0)
   #compare(#neg(z0), #pos(z1)) -> #LT
   #compare(#pos(z0), #0) -> #GT
   #compare(#pos(z0), #neg(z1)) -> #GT
   #compare(#pos(z0), #pos(z1)) -> #compare(z0, z1)
   #compare(#s(z0), #0) -> #GT
   #compare(#s(z0), #s(z1)) -> #compare(z0, z1)
   #less(z0, z1) -> #cklt(#compare(z0, z1))
   append(z0, z1) -> append#1(z0, z1)
   append#1(::(z0, z1), z2) -> ::(z0, append(z1, z2))
   append#1(nil, z0) -> z0
   flatten(z0) -> flatten#1(z0)
   flatten#1(leaf) -> nil
   flatten#1(node(z0, z1, z2)) -> append(z0, append(flatten(z1), flatten(z2)))
   flattensort(z0) -> insertionsort(flatten(z0))
   insert(z0, z1) -> insert#1(z1, z0)
   insert#1(::(z0, z1), z2) -> insert#2(#less(z0, z2), z2, z0, z1)
   insert#1(nil, z0) -> ::(z0, nil)
   insert#2(#false, z0, z1, z2) -> ::(z0, ::(z1, z2))
   insert#2(#true, z0, z1, z2) -> ::(z1, insert(z0, z2))
   insertionsort(z0) -> insertionsort#1(z0)
   insertionsort#1(::(z0, z1)) -> insert(z0, insertionsort(z1))
   insertionsort#1(nil) -> nil
Tuples:
   #COMPARE(#neg(z0), #neg(z1)) -> c8(#COMPARE(z1, z0))
   #COMPARE(#pos(z0), #pos(z1)) -> c12(#COMPARE(z0, z1))
   #COMPARE(#s(z0), #s(z1)) -> c14(#COMPARE(z0, z1))
   APPEND(z0, z1) -> c16(APPEND#1(z0, z1))
   APPEND#1(::(z0, z1), z2) -> c17(APPEND(z1, z2))
   FLATTEN(z0) -> c19(FLATTEN#1(z0))
   FLATTEN#1(node(z0, z1, z2)) -> c21(APPEND(z0, append(flatten(z1), flatten(z2))), APPEND(flatten(z1), flatten(z2)), FLATTEN(z1))
   FLATTEN#1(node(z0, z1, z2)) -> c22(APPEND(z0, append(flatten(z1), flatten(z2))), APPEND(flatten(z1), flatten(z2)), FLATTEN(z2))
   FLATTENSORT(z0) -> c23(INSERTIONSORT(flatten(z0)), FLATTEN(z0))
   INSERT(z0, z1) -> c24(INSERT#1(z1, z0))
   INSERT#1(::(z0, z1), z2) -> c25(INSERT#2(#less(z0, z2), z2, z0, z1), #LESS(z0, z2))
   INSERT#2(#true, z0, z1, z2) -> c28(INSERT(z0, z2))
   INSERTIONSORT(z0) -> c29(INSERTIONSORT#1(z0))
   INSERTIONSORT#1(::(z0, z1)) -> c30(INSERT(z0, insertionsort(z1)), INSERTIONSORT(z1))
   #LESS(z0, z1) -> c15(#COMPARE(z0, z1))
S tuples:
   APPEND(z0, z1) -> c16(APPEND#1(z0, z1))
   APPEND#1(::(z0, z1), z2) -> c17(APPEND(z1, z2))
   FLATTEN(z0) -> c19(FLATTEN#1(z0))
   FLATTEN#1(node(z0, z1, z2)) -> c21(APPEND(z0, append(flatten(z1), flatten(z2))), APPEND(flatten(z1), flatten(z2)), FLATTEN(z1))
   FLATTEN#1(node(z0, z1, z2)) -> c22(APPEND(z0, append(flatten(z1), flatten(z2))), APPEND(flatten(z1), flatten(z2)), FLATTEN(z2))
   FLATTENSORT(z0) -> c23(INSERTIONSORT(flatten(z0)), FLATTEN(z0))
   INSERT(z0, z1) -> c24(INSERT#1(z1, z0))
   INSERT#1(::(z0, z1), z2) -> c25(INSERT#2(#less(z0, z2), z2, z0, z1), #LESS(z0, z2))
   INSERT#2(#true, z0, z1, z2) -> c28(INSERT(z0, z2))
   INSERTIONSORT(z0) -> c29(INSERTIONSORT#1(z0))
   INSERTIONSORT#1(::(z0, z1)) -> c30(INSERT(z0, insertionsort(z1)), INSERTIONSORT(z1))
   #LESS(z0, z1) -> c15(#COMPARE(z0, z1))
K tuples:none
Defined Rule Symbols:   #less_2, append_2, append#1_2, flatten_1, flatten#1_1, flattensort_1, insert_2, insert#1_2, insert#2_4, insertionsort_1, insertionsort#1_1, #cklt_1, #compare_2

Defined Pair Symbols:   #COMPARE_2, APPEND_2, APPEND#1_2, FLATTEN_1, FLATTEN#1_1, FLATTENSORT_1, INSERT_2, INSERT#1_2, INSERT#2_4, INSERTIONSORT_1, INSERTIONSORT#1_1, #LESS_2

Compound Symbols:   c8_1, c12_1, c14_1, c16_1, c17_1, c19_1, c21_3, c22_3, c23_2, c24_1, c25_2, c28_1, c29_1, c30_2, c15_1


----------------------------------------

(9) CdtGraphSplitRhsProof (BOTH BOUNDS(ID, ID))
Split RHS of tuples not part of any SCC
----------------------------------------

(10)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   #cklt(#EQ) -> #false
   #cklt(#GT) -> #false
   #cklt(#LT) -> #true
   #compare(#0, #0) -> #EQ
   #compare(#0, #neg(z0)) -> #GT
   #compare(#0, #pos(z0)) -> #LT
   #compare(#0, #s(z0)) -> #LT
   #compare(#neg(z0), #0) -> #LT
   #compare(#neg(z0), #neg(z1)) -> #compare(z1, z0)
   #compare(#neg(z0), #pos(z1)) -> #LT
   #compare(#pos(z0), #0) -> #GT
   #compare(#pos(z0), #neg(z1)) -> #GT
   #compare(#pos(z0), #pos(z1)) -> #compare(z0, z1)
   #compare(#s(z0), #0) -> #GT
   #compare(#s(z0), #s(z1)) -> #compare(z0, z1)
   #less(z0, z1) -> #cklt(#compare(z0, z1))
   append(z0, z1) -> append#1(z0, z1)
   append#1(::(z0, z1), z2) -> ::(z0, append(z1, z2))
   append#1(nil, z0) -> z0
   flatten(z0) -> flatten#1(z0)
   flatten#1(leaf) -> nil
   flatten#1(node(z0, z1, z2)) -> append(z0, append(flatten(z1), flatten(z2)))
   flattensort(z0) -> insertionsort(flatten(z0))
   insert(z0, z1) -> insert#1(z1, z0)
   insert#1(::(z0, z1), z2) -> insert#2(#less(z0, z2), z2, z0, z1)
   insert#1(nil, z0) -> ::(z0, nil)
   insert#2(#false, z0, z1, z2) -> ::(z0, ::(z1, z2))
   insert#2(#true, z0, z1, z2) -> ::(z1, insert(z0, z2))
   insertionsort(z0) -> insertionsort#1(z0)
   insertionsort#1(::(z0, z1)) -> insert(z0, insertionsort(z1))
   insertionsort#1(nil) -> nil
Tuples:
   #COMPARE(#neg(z0), #neg(z1)) -> c8(#COMPARE(z1, z0))
   #COMPARE(#pos(z0), #pos(z1)) -> c12(#COMPARE(z0, z1))
   #COMPARE(#s(z0), #s(z1)) -> c14(#COMPARE(z0, z1))
   APPEND(z0, z1) -> c16(APPEND#1(z0, z1))
   APPEND#1(::(z0, z1), z2) -> c17(APPEND(z1, z2))
   FLATTEN(z0) -> c19(FLATTEN#1(z0))
   FLATTEN#1(node(z0, z1, z2)) -> c21(APPEND(z0, append(flatten(z1), flatten(z2))), APPEND(flatten(z1), flatten(z2)), FLATTEN(z1))
   FLATTEN#1(node(z0, z1, z2)) -> c22(APPEND(z0, append(flatten(z1), flatten(z2))), APPEND(flatten(z1), flatten(z2)), FLATTEN(z2))
   INSERT(z0, z1) -> c24(INSERT#1(z1, z0))
   INSERT#1(::(z0, z1), z2) -> c25(INSERT#2(#less(z0, z2), z2, z0, z1), #LESS(z0, z2))
   INSERT#2(#true, z0, z1, z2) -> c28(INSERT(z0, z2))
   INSERTIONSORT(z0) -> c29(INSERTIONSORT#1(z0))
   INSERTIONSORT#1(::(z0, z1)) -> c30(INSERT(z0, insertionsort(z1)), INSERTIONSORT(z1))
   #LESS(z0, z1) -> c15(#COMPARE(z0, z1))
   FLATTENSORT(z0) -> c(INSERTIONSORT(flatten(z0)))
   FLATTENSORT(z0) -> c(FLATTEN(z0))
S tuples:
   APPEND(z0, z1) -> c16(APPEND#1(z0, z1))
   APPEND#1(::(z0, z1), z2) -> c17(APPEND(z1, z2))
   FLATTEN(z0) -> c19(FLATTEN#1(z0))
   FLATTEN#1(node(z0, z1, z2)) -> c21(APPEND(z0, append(flatten(z1), flatten(z2))), APPEND(flatten(z1), flatten(z2)), FLATTEN(z1))
   FLATTEN#1(node(z0, z1, z2)) -> c22(APPEND(z0, append(flatten(z1), flatten(z2))), APPEND(flatten(z1), flatten(z2)), FLATTEN(z2))
   INSERT(z0, z1) -> c24(INSERT#1(z1, z0))
   INSERT#1(::(z0, z1), z2) -> c25(INSERT#2(#less(z0, z2), z2, z0, z1), #LESS(z0, z2))
   INSERT#2(#true, z0, z1, z2) -> c28(INSERT(z0, z2))
   INSERTIONSORT(z0) -> c29(INSERTIONSORT#1(z0))
   INSERTIONSORT#1(::(z0, z1)) -> c30(INSERT(z0, insertionsort(z1)), INSERTIONSORT(z1))
   #LESS(z0, z1) -> c15(#COMPARE(z0, z1))
   FLATTENSORT(z0) -> c(INSERTIONSORT(flatten(z0)))
   FLATTENSORT(z0) -> c(FLATTEN(z0))
K tuples:none
Defined Rule Symbols:   #less_2, append_2, append#1_2, flatten_1, flatten#1_1, flattensort_1, insert_2, insert#1_2, insert#2_4, insertionsort_1, insertionsort#1_1, #cklt_1, #compare_2

Defined Pair Symbols:   #COMPARE_2, APPEND_2, APPEND#1_2, FLATTEN_1, FLATTEN#1_1, INSERT_2, INSERT#1_2, INSERT#2_4, INSERTIONSORT_1, INSERTIONSORT#1_1, #LESS_2, FLATTENSORT_1

Compound Symbols:   c8_1, c12_1, c14_1, c16_1, c17_1, c19_1, c21_3, c22_3, c24_1, c25_2, c28_1, c29_1, c30_2, c15_1, c_1


----------------------------------------

(11) CdtLeafRemovalProof (ComplexityIfPolyImplication)
Removed 1 leading nodes:
   FLATTENSORT(z0) -> c(FLATTEN(z0))

----------------------------------------

(12)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   #cklt(#EQ) -> #false
   #cklt(#GT) -> #false
   #cklt(#LT) -> #true
   #compare(#0, #0) -> #EQ
   #compare(#0, #neg(z0)) -> #GT
   #compare(#0, #pos(z0)) -> #LT
   #compare(#0, #s(z0)) -> #LT
   #compare(#neg(z0), #0) -> #LT
   #compare(#neg(z0), #neg(z1)) -> #compare(z1, z0)
   #compare(#neg(z0), #pos(z1)) -> #LT
   #compare(#pos(z0), #0) -> #GT
   #compare(#pos(z0), #neg(z1)) -> #GT
   #compare(#pos(z0), #pos(z1)) -> #compare(z0, z1)
   #compare(#s(z0), #0) -> #GT
   #compare(#s(z0), #s(z1)) -> #compare(z0, z1)
   #less(z0, z1) -> #cklt(#compare(z0, z1))
   append(z0, z1) -> append#1(z0, z1)
   append#1(::(z0, z1), z2) -> ::(z0, append(z1, z2))
   append#1(nil, z0) -> z0
   flatten(z0) -> flatten#1(z0)
   flatten#1(leaf) -> nil
   flatten#1(node(z0, z1, z2)) -> append(z0, append(flatten(z1), flatten(z2)))
   flattensort(z0) -> insertionsort(flatten(z0))
   insert(z0, z1) -> insert#1(z1, z0)
   insert#1(::(z0, z1), z2) -> insert#2(#less(z0, z2), z2, z0, z1)
   insert#1(nil, z0) -> ::(z0, nil)
   insert#2(#false, z0, z1, z2) -> ::(z0, ::(z1, z2))
   insert#2(#true, z0, z1, z2) -> ::(z1, insert(z0, z2))
   insertionsort(z0) -> insertionsort#1(z0)
   insertionsort#1(::(z0, z1)) -> insert(z0, insertionsort(z1))
   insertionsort#1(nil) -> nil
Tuples:
   #COMPARE(#neg(z0), #neg(z1)) -> c8(#COMPARE(z1, z0))
   #COMPARE(#pos(z0), #pos(z1)) -> c12(#COMPARE(z0, z1))
   #COMPARE(#s(z0), #s(z1)) -> c14(#COMPARE(z0, z1))
   APPEND(z0, z1) -> c16(APPEND#1(z0, z1))
   APPEND#1(::(z0, z1), z2) -> c17(APPEND(z1, z2))
   FLATTEN(z0) -> c19(FLATTEN#1(z0))
   FLATTEN#1(node(z0, z1, z2)) -> c21(APPEND(z0, append(flatten(z1), flatten(z2))), APPEND(flatten(z1), flatten(z2)), FLATTEN(z1))
   FLATTEN#1(node(z0, z1, z2)) -> c22(APPEND(z0, append(flatten(z1), flatten(z2))), APPEND(flatten(z1), flatten(z2)), FLATTEN(z2))
   INSERT(z0, z1) -> c24(INSERT#1(z1, z0))
   INSERT#1(::(z0, z1), z2) -> c25(INSERT#2(#less(z0, z2), z2, z0, z1), #LESS(z0, z2))
   INSERT#2(#true, z0, z1, z2) -> c28(INSERT(z0, z2))
   INSERTIONSORT(z0) -> c29(INSERTIONSORT#1(z0))
   INSERTIONSORT#1(::(z0, z1)) -> c30(INSERT(z0, insertionsort(z1)), INSERTIONSORT(z1))
   #LESS(z0, z1) -> c15(#COMPARE(z0, z1))
   FLATTENSORT(z0) -> c(INSERTIONSORT(flatten(z0)))
S tuples:
   APPEND(z0, z1) -> c16(APPEND#1(z0, z1))
   APPEND#1(::(z0, z1), z2) -> c17(APPEND(z1, z2))
   FLATTEN(z0) -> c19(FLATTEN#1(z0))
   FLATTEN#1(node(z0, z1, z2)) -> c21(APPEND(z0, append(flatten(z1), flatten(z2))), APPEND(flatten(z1), flatten(z2)), FLATTEN(z1))
   FLATTEN#1(node(z0, z1, z2)) -> c22(APPEND(z0, append(flatten(z1), flatten(z2))), APPEND(flatten(z1), flatten(z2)), FLATTEN(z2))
   INSERT(z0, z1) -> c24(INSERT#1(z1, z0))
   INSERT#1(::(z0, z1), z2) -> c25(INSERT#2(#less(z0, z2), z2, z0, z1), #LESS(z0, z2))
   INSERT#2(#true, z0, z1, z2) -> c28(INSERT(z0, z2))
   INSERTIONSORT(z0) -> c29(INSERTIONSORT#1(z0))
   INSERTIONSORT#1(::(z0, z1)) -> c30(INSERT(z0, insertionsort(z1)), INSERTIONSORT(z1))
   #LESS(z0, z1) -> c15(#COMPARE(z0, z1))
   FLATTENSORT(z0) -> c(INSERTIONSORT(flatten(z0)))
K tuples:none
Defined Rule Symbols:   #less_2, append_2, append#1_2, flatten_1, flatten#1_1, flattensort_1, insert_2, insert#1_2, insert#2_4, insertionsort_1, insertionsort#1_1, #cklt_1, #compare_2

Defined Pair Symbols:   #COMPARE_2, APPEND_2, APPEND#1_2, FLATTEN_1, FLATTEN#1_1, INSERT_2, INSERT#1_2, INSERT#2_4, INSERTIONSORT_1, INSERTIONSORT#1_1, #LESS_2, FLATTENSORT_1

Compound Symbols:   c8_1, c12_1, c14_1, c16_1, c17_1, c19_1, c21_3, c22_3, c24_1, c25_2, c28_1, c29_1, c30_2, c15_1, c_1


----------------------------------------

(13) CdtKnowledgeProof (BOTH BOUNDS(ID, ID))
The following tuples could be moved from S to K by knowledge propagation:
   FLATTENSORT(z0) -> c(INSERTIONSORT(flatten(z0)))

----------------------------------------

(14)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   #cklt(#EQ) -> #false
   #cklt(#GT) -> #false
   #cklt(#LT) -> #true
   #compare(#0, #0) -> #EQ
   #compare(#0, #neg(z0)) -> #GT
   #compare(#0, #pos(z0)) -> #LT
   #compare(#0, #s(z0)) -> #LT
   #compare(#neg(z0), #0) -> #LT
   #compare(#neg(z0), #neg(z1)) -> #compare(z1, z0)
   #compare(#neg(z0), #pos(z1)) -> #LT
   #compare(#pos(z0), #0) -> #GT
   #compare(#pos(z0), #neg(z1)) -> #GT
   #compare(#pos(z0), #pos(z1)) -> #compare(z0, z1)
   #compare(#s(z0), #0) -> #GT
   #compare(#s(z0), #s(z1)) -> #compare(z0, z1)
   #less(z0, z1) -> #cklt(#compare(z0, z1))
   append(z0, z1) -> append#1(z0, z1)
   append#1(::(z0, z1), z2) -> ::(z0, append(z1, z2))
   append#1(nil, z0) -> z0
   flatten(z0) -> flatten#1(z0)
   flatten#1(leaf) -> nil
   flatten#1(node(z0, z1, z2)) -> append(z0, append(flatten(z1), flatten(z2)))
   flattensort(z0) -> insertionsort(flatten(z0))
   insert(z0, z1) -> insert#1(z1, z0)
   insert#1(::(z0, z1), z2) -> insert#2(#less(z0, z2), z2, z0, z1)
   insert#1(nil, z0) -> ::(z0, nil)
   insert#2(#false, z0, z1, z2) -> ::(z0, ::(z1, z2))
   insert#2(#true, z0, z1, z2) -> ::(z1, insert(z0, z2))
   insertionsort(z0) -> insertionsort#1(z0)
   insertionsort#1(::(z0, z1)) -> insert(z0, insertionsort(z1))
   insertionsort#1(nil) -> nil
Tuples:
   #COMPARE(#neg(z0), #neg(z1)) -> c8(#COMPARE(z1, z0))
   #COMPARE(#pos(z0), #pos(z1)) -> c12(#COMPARE(z0, z1))
   #COMPARE(#s(z0), #s(z1)) -> c14(#COMPARE(z0, z1))
   APPEND(z0, z1) -> c16(APPEND#1(z0, z1))
   APPEND#1(::(z0, z1), z2) -> c17(APPEND(z1, z2))
   FLATTEN(z0) -> c19(FLATTEN#1(z0))
   FLATTEN#1(node(z0, z1, z2)) -> c21(APPEND(z0, append(flatten(z1), flatten(z2))), APPEND(flatten(z1), flatten(z2)), FLATTEN(z1))
   FLATTEN#1(node(z0, z1, z2)) -> c22(APPEND(z0, append(flatten(z1), flatten(z2))), APPEND(flatten(z1), flatten(z2)), FLATTEN(z2))
   INSERT(z0, z1) -> c24(INSERT#1(z1, z0))
   INSERT#1(::(z0, z1), z2) -> c25(INSERT#2(#less(z0, z2), z2, z0, z1), #LESS(z0, z2))
   INSERT#2(#true, z0, z1, z2) -> c28(INSERT(z0, z2))
   INSERTIONSORT(z0) -> c29(INSERTIONSORT#1(z0))
   INSERTIONSORT#1(::(z0, z1)) -> c30(INSERT(z0, insertionsort(z1)), INSERTIONSORT(z1))
   #LESS(z0, z1) -> c15(#COMPARE(z0, z1))
   FLATTENSORT(z0) -> c(INSERTIONSORT(flatten(z0)))
S tuples:
   APPEND(z0, z1) -> c16(APPEND#1(z0, z1))
   APPEND#1(::(z0, z1), z2) -> c17(APPEND(z1, z2))
   FLATTEN(z0) -> c19(FLATTEN#1(z0))
   FLATTEN#1(node(z0, z1, z2)) -> c21(APPEND(z0, append(flatten(z1), flatten(z2))), APPEND(flatten(z1), flatten(z2)), FLATTEN(z1))
   FLATTEN#1(node(z0, z1, z2)) -> c22(APPEND(z0, append(flatten(z1), flatten(z2))), APPEND(flatten(z1), flatten(z2)), FLATTEN(z2))
   INSERT(z0, z1) -> c24(INSERT#1(z1, z0))
   INSERT#1(::(z0, z1), z2) -> c25(INSERT#2(#less(z0, z2), z2, z0, z1), #LESS(z0, z2))
   INSERT#2(#true, z0, z1, z2) -> c28(INSERT(z0, z2))
   INSERTIONSORT(z0) -> c29(INSERTIONSORT#1(z0))
   INSERTIONSORT#1(::(z0, z1)) -> c30(INSERT(z0, insertionsort(z1)), INSERTIONSORT(z1))
   #LESS(z0, z1) -> c15(#COMPARE(z0, z1))
K tuples:
   FLATTENSORT(z0) -> c(INSERTIONSORT(flatten(z0)))
Defined Rule Symbols:   #less_2, append_2, append#1_2, flatten_1, flatten#1_1, flattensort_1, insert_2, insert#1_2, insert#2_4, insertionsort_1, insertionsort#1_1, #cklt_1, #compare_2

Defined Pair Symbols:   #COMPARE_2, APPEND_2, APPEND#1_2, FLATTEN_1, FLATTEN#1_1, INSERT_2, INSERT#1_2, INSERT#2_4, INSERTIONSORT_1, INSERTIONSORT#1_1, #LESS_2, FLATTENSORT_1

Compound Symbols:   c8_1, c12_1, c14_1, c16_1, c17_1, c19_1, c21_3, c22_3, c24_1, c25_2, c28_1, c29_1, c30_2, c15_1, c_1


----------------------------------------

(15) CdtUsableRulesProof (BOTH BOUNDS(ID, ID))
The following rules are not usable and were removed:
   flattensort(z0) -> insertionsort(flatten(z0))

----------------------------------------

(16)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   append(z0, z1) -> append#1(z0, z1)
   flatten(z0) -> flatten#1(z0)
   flatten#1(leaf) -> nil
   flatten#1(node(z0, z1, z2)) -> append(z0, append(flatten(z1), flatten(z2)))
   append#1(::(z0, z1), z2) -> ::(z0, append(z1, z2))
   append#1(nil, z0) -> z0
   #less(z0, z1) -> #cklt(#compare(z0, z1))
   #cklt(#EQ) -> #false
   #cklt(#GT) -> #false
   #cklt(#LT) -> #true
   #compare(#0, #0) -> #EQ
   #compare(#0, #neg(z0)) -> #GT
   #compare(#0, #pos(z0)) -> #LT
   #compare(#0, #s(z0)) -> #LT
   #compare(#neg(z0), #0) -> #LT
   #compare(#neg(z0), #neg(z1)) -> #compare(z1, z0)
   #compare(#neg(z0), #pos(z1)) -> #LT
   #compare(#pos(z0), #0) -> #GT
   #compare(#pos(z0), #neg(z1)) -> #GT
   #compare(#pos(z0), #pos(z1)) -> #compare(z0, z1)
   #compare(#s(z0), #0) -> #GT
   #compare(#s(z0), #s(z1)) -> #compare(z0, z1)
   insertionsort(z0) -> insertionsort#1(z0)
   insertionsort#1(::(z0, z1)) -> insert(z0, insertionsort(z1))
   insertionsort#1(nil) -> nil
   insert(z0, z1) -> insert#1(z1, z0)
   insert#1(::(z0, z1), z2) -> insert#2(#less(z0, z2), z2, z0, z1)
   insert#1(nil, z0) -> ::(z0, nil)
   insert#2(#false, z0, z1, z2) -> ::(z0, ::(z1, z2))
   insert#2(#true, z0, z1, z2) -> ::(z1, insert(z0, z2))
Tuples:
   #COMPARE(#neg(z0), #neg(z1)) -> c8(#COMPARE(z1, z0))
   #COMPARE(#pos(z0), #pos(z1)) -> c12(#COMPARE(z0, z1))
   #COMPARE(#s(z0), #s(z1)) -> c14(#COMPARE(z0, z1))
   APPEND(z0, z1) -> c16(APPEND#1(z0, z1))
   APPEND#1(::(z0, z1), z2) -> c17(APPEND(z1, z2))
   FLATTEN(z0) -> c19(FLATTEN#1(z0))
   FLATTEN#1(node(z0, z1, z2)) -> c21(APPEND(z0, append(flatten(z1), flatten(z2))), APPEND(flatten(z1), flatten(z2)), FLATTEN(z1))
   FLATTEN#1(node(z0, z1, z2)) -> c22(APPEND(z0, append(flatten(z1), flatten(z2))), APPEND(flatten(z1), flatten(z2)), FLATTEN(z2))
   INSERT(z0, z1) -> c24(INSERT#1(z1, z0))
   INSERT#1(::(z0, z1), z2) -> c25(INSERT#2(#less(z0, z2), z2, z0, z1), #LESS(z0, z2))
   INSERT#2(#true, z0, z1, z2) -> c28(INSERT(z0, z2))
   INSERTIONSORT(z0) -> c29(INSERTIONSORT#1(z0))
   INSERTIONSORT#1(::(z0, z1)) -> c30(INSERT(z0, insertionsort(z1)), INSERTIONSORT(z1))
   #LESS(z0, z1) -> c15(#COMPARE(z0, z1))
   FLATTENSORT(z0) -> c(INSERTIONSORT(flatten(z0)))
S tuples:
   APPEND(z0, z1) -> c16(APPEND#1(z0, z1))
   APPEND#1(::(z0, z1), z2) -> c17(APPEND(z1, z2))
   FLATTEN(z0) -> c19(FLATTEN#1(z0))
   FLATTEN#1(node(z0, z1, z2)) -> c21(APPEND(z0, append(flatten(z1), flatten(z2))), APPEND(flatten(z1), flatten(z2)), FLATTEN(z1))
   FLATTEN#1(node(z0, z1, z2)) -> c22(APPEND(z0, append(flatten(z1), flatten(z2))), APPEND(flatten(z1), flatten(z2)), FLATTEN(z2))
   INSERT(z0, z1) -> c24(INSERT#1(z1, z0))
   INSERT#1(::(z0, z1), z2) -> c25(INSERT#2(#less(z0, z2), z2, z0, z1), #LESS(z0, z2))
   INSERT#2(#true, z0, z1, z2) -> c28(INSERT(z0, z2))
   INSERTIONSORT(z0) -> c29(INSERTIONSORT#1(z0))
   INSERTIONSORT#1(::(z0, z1)) -> c30(INSERT(z0, insertionsort(z1)), INSERTIONSORT(z1))
   #LESS(z0, z1) -> c15(#COMPARE(z0, z1))
K tuples:
   FLATTENSORT(z0) -> c(INSERTIONSORT(flatten(z0)))
Defined Rule Symbols:   append_2, flatten_1, flatten#1_1, append#1_2, #less_2, #cklt_1, #compare_2, insertionsort_1, insertionsort#1_1, insert_2, insert#1_2, insert#2_4

Defined Pair Symbols:   #COMPARE_2, APPEND_2, APPEND#1_2, FLATTEN_1, FLATTEN#1_1, INSERT_2, INSERT#1_2, INSERT#2_4, INSERTIONSORT_1, INSERTIONSORT#1_1, #LESS_2, FLATTENSORT_1

Compound Symbols:   c8_1, c12_1, c14_1, c16_1, c17_1, c19_1, c21_3, c22_3, c24_1, c25_2, c28_1, c29_1, c30_2, c15_1, c_1


----------------------------------------

(17) CdtToCpxRelTrsProof (BOTH BOUNDS(ID, ID))
Converted S to standard rules, and D \ S as well as R to relative rules.
----------------------------------------

(18)
Obligation:
The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(1, n^2).


The TRS R consists of the following rules:

   APPEND(z0, z1) -> c16(APPEND#1(z0, z1))
   APPEND#1(::(z0, z1), z2) -> c17(APPEND(z1, z2))
   FLATTEN(z0) -> c19(FLATTEN#1(z0))
   FLATTEN#1(node(z0, z1, z2)) -> c21(APPEND(z0, append(flatten(z1), flatten(z2))), APPEND(flatten(z1), flatten(z2)), FLATTEN(z1))
   FLATTEN#1(node(z0, z1, z2)) -> c22(APPEND(z0, append(flatten(z1), flatten(z2))), APPEND(flatten(z1), flatten(z2)), FLATTEN(z2))
   INSERT(z0, z1) -> c24(INSERT#1(z1, z0))
   INSERT#1(::(z0, z1), z2) -> c25(INSERT#2(#less(z0, z2), z2, z0, z1), #LESS(z0, z2))
   INSERT#2(#true, z0, z1, z2) -> c28(INSERT(z0, z2))
   INSERTIONSORT(z0) -> c29(INSERTIONSORT#1(z0))
   INSERTIONSORT#1(::(z0, z1)) -> c30(INSERT(z0, insertionsort(z1)), INSERTIONSORT(z1))
   #LESS(z0, z1) -> c15(#COMPARE(z0, z1))

The (relative) TRS S consists of the following rules:

   #COMPARE(#neg(z0), #neg(z1)) -> c8(#COMPARE(z1, z0))
   #COMPARE(#pos(z0), #pos(z1)) -> c12(#COMPARE(z0, z1))
   #COMPARE(#s(z0), #s(z1)) -> c14(#COMPARE(z0, z1))
   FLATTENSORT(z0) -> c(INSERTIONSORT(flatten(z0)))
   append(z0, z1) -> append#1(z0, z1)
   flatten(z0) -> flatten#1(z0)
   flatten#1(leaf) -> nil
   flatten#1(node(z0, z1, z2)) -> append(z0, append(flatten(z1), flatten(z2)))
   append#1(::(z0, z1), z2) -> ::(z0, append(z1, z2))
   append#1(nil, z0) -> z0
   #less(z0, z1) -> #cklt(#compare(z0, z1))
   #cklt(#EQ) -> #false
   #cklt(#GT) -> #false
   #cklt(#LT) -> #true
   #compare(#0, #0) -> #EQ
   #compare(#0, #neg(z0)) -> #GT
   #compare(#0, #pos(z0)) -> #LT
   #compare(#0, #s(z0)) -> #LT
   #compare(#neg(z0), #0) -> #LT
   #compare(#neg(z0), #neg(z1)) -> #compare(z1, z0)
   #compare(#neg(z0), #pos(z1)) -> #LT
   #compare(#pos(z0), #0) -> #GT
   #compare(#pos(z0), #neg(z1)) -> #GT
   #compare(#pos(z0), #pos(z1)) -> #compare(z0, z1)
   #compare(#s(z0), #0) -> #GT
   #compare(#s(z0), #s(z1)) -> #compare(z0, z1)
   insertionsort(z0) -> insertionsort#1(z0)
   insertionsort#1(::(z0, z1)) -> insert(z0, insertionsort(z1))
   insertionsort#1(nil) -> nil
   insert(z0, z1) -> insert#1(z1, z0)
   insert#1(::(z0, z1), z2) -> insert#2(#less(z0, z2), z2, z0, z1)
   insert#1(nil, z0) -> ::(z0, nil)
   insert#2(#false, z0, z1, z2) -> ::(z0, ::(z1, z2))
   insert#2(#true, z0, z1, z2) -> ::(z1, insert(z0, z2))

Rewrite Strategy: INNERMOST
----------------------------------------

(19) RelTrsToWeightedTrsProof (BOTH BOUNDS(ID, ID))
Transformed relative TRS to weighted TRS
----------------------------------------

(20)
Obligation:
The Runtime Complexity (innermost) of the given CpxWeightedTrs could be proven to be BOUNDS(1, n^2).


The TRS R consists of the following rules:

   APPEND(z0, z1) -> c16(APPEND#1(z0, z1)) [1]
   APPEND#1(::(z0, z1), z2) -> c17(APPEND(z1, z2)) [1]
   FLATTEN(z0) -> c19(FLATTEN#1(z0)) [1]
   FLATTEN#1(node(z0, z1, z2)) -> c21(APPEND(z0, append(flatten(z1), flatten(z2))), APPEND(flatten(z1), flatten(z2)), FLATTEN(z1)) [1]
   FLATTEN#1(node(z0, z1, z2)) -> c22(APPEND(z0, append(flatten(z1), flatten(z2))), APPEND(flatten(z1), flatten(z2)), FLATTEN(z2)) [1]
   INSERT(z0, z1) -> c24(INSERT#1(z1, z0)) [1]
   INSERT#1(::(z0, z1), z2) -> c25(INSERT#2(#less(z0, z2), z2, z0, z1), #LESS(z0, z2)) [1]
   INSERT#2(#true, z0, z1, z2) -> c28(INSERT(z0, z2)) [1]
   INSERTIONSORT(z0) -> c29(INSERTIONSORT#1(z0)) [1]
   INSERTIONSORT#1(::(z0, z1)) -> c30(INSERT(z0, insertionsort(z1)), INSERTIONSORT(z1)) [1]
   #LESS(z0, z1) -> c15(#COMPARE(z0, z1)) [1]
   #COMPARE(#neg(z0), #neg(z1)) -> c8(#COMPARE(z1, z0)) [0]
   #COMPARE(#pos(z0), #pos(z1)) -> c12(#COMPARE(z0, z1)) [0]
   #COMPARE(#s(z0), #s(z1)) -> c14(#COMPARE(z0, z1)) [0]
   FLATTENSORT(z0) -> c(INSERTIONSORT(flatten(z0))) [0]
   append(z0, z1) -> append#1(z0, z1) [0]
   flatten(z0) -> flatten#1(z0) [0]
   flatten#1(leaf) -> nil [0]
   flatten#1(node(z0, z1, z2)) -> append(z0, append(flatten(z1), flatten(z2))) [0]
   append#1(::(z0, z1), z2) -> ::(z0, append(z1, z2)) [0]
   append#1(nil, z0) -> z0 [0]
   #less(z0, z1) -> #cklt(#compare(z0, z1)) [0]
   #cklt(#EQ) -> #false [0]
   #cklt(#GT) -> #false [0]
   #cklt(#LT) -> #true [0]
   #compare(#0, #0) -> #EQ [0]
   #compare(#0, #neg(z0)) -> #GT [0]
   #compare(#0, #pos(z0)) -> #LT [0]
   #compare(#0, #s(z0)) -> #LT [0]
   #compare(#neg(z0), #0) -> #LT [0]
   #compare(#neg(z0), #neg(z1)) -> #compare(z1, z0) [0]
   #compare(#neg(z0), #pos(z1)) -> #LT [0]
   #compare(#pos(z0), #0) -> #GT [0]
   #compare(#pos(z0), #neg(z1)) -> #GT [0]
   #compare(#pos(z0), #pos(z1)) -> #compare(z0, z1) [0]
   #compare(#s(z0), #0) -> #GT [0]
   #compare(#s(z0), #s(z1)) -> #compare(z0, z1) [0]
   insertionsort(z0) -> insertionsort#1(z0) [0]
   insertionsort#1(::(z0, z1)) -> insert(z0, insertionsort(z1)) [0]
   insertionsort#1(nil) -> nil [0]
   insert(z0, z1) -> insert#1(z1, z0) [0]
   insert#1(::(z0, z1), z2) -> insert#2(#less(z0, z2), z2, z0, z1) [0]
   insert#1(nil, z0) -> ::(z0, nil) [0]
   insert#2(#false, z0, z1, z2) -> ::(z0, ::(z1, z2)) [0]
   insert#2(#true, z0, z1, z2) -> ::(z1, insert(z0, z2)) [0]

Rewrite Strategy: INNERMOST
----------------------------------------

(21) TypeInferenceProof (BOTH BOUNDS(ID, ID))
Infered types.
----------------------------------------

(22)
Obligation:
Runtime Complexity Weighted TRS with Types.
The TRS R consists of the following rules:

   APPEND(z0, z1) -> c16(APPEND#1(z0, z1)) [1]
   APPEND#1(::(z0, z1), z2) -> c17(APPEND(z1, z2)) [1]
   FLATTEN(z0) -> c19(FLATTEN#1(z0)) [1]
   FLATTEN#1(node(z0, z1, z2)) -> c21(APPEND(z0, append(flatten(z1), flatten(z2))), APPEND(flatten(z1), flatten(z2)), FLATTEN(z1)) [1]
   FLATTEN#1(node(z0, z1, z2)) -> c22(APPEND(z0, append(flatten(z1), flatten(z2))), APPEND(flatten(z1), flatten(z2)), FLATTEN(z2)) [1]
   INSERT(z0, z1) -> c24(INSERT#1(z1, z0)) [1]
   INSERT#1(::(z0, z1), z2) -> c25(INSERT#2(#less(z0, z2), z2, z0, z1), #LESS(z0, z2)) [1]
   INSERT#2(#true, z0, z1, z2) -> c28(INSERT(z0, z2)) [1]
   INSERTIONSORT(z0) -> c29(INSERTIONSORT#1(z0)) [1]
   INSERTIONSORT#1(::(z0, z1)) -> c30(INSERT(z0, insertionsort(z1)), INSERTIONSORT(z1)) [1]
   #LESS(z0, z1) -> c15(#COMPARE(z0, z1)) [1]
   #COMPARE(#neg(z0), #neg(z1)) -> c8(#COMPARE(z1, z0)) [0]
   #COMPARE(#pos(z0), #pos(z1)) -> c12(#COMPARE(z0, z1)) [0]
   #COMPARE(#s(z0), #s(z1)) -> c14(#COMPARE(z0, z1)) [0]
   FLATTENSORT(z0) -> c(INSERTIONSORT(flatten(z0))) [0]
   append(z0, z1) -> append#1(z0, z1) [0]
   flatten(z0) -> flatten#1(z0) [0]
   flatten#1(leaf) -> nil [0]
   flatten#1(node(z0, z1, z2)) -> append(z0, append(flatten(z1), flatten(z2))) [0]
   append#1(::(z0, z1), z2) -> ::(z0, append(z1, z2)) [0]
   append#1(nil, z0) -> z0 [0]
   #less(z0, z1) -> #cklt(#compare(z0, z1)) [0]
   #cklt(#EQ) -> #false [0]
   #cklt(#GT) -> #false [0]
   #cklt(#LT) -> #true [0]
   #compare(#0, #0) -> #EQ [0]
   #compare(#0, #neg(z0)) -> #GT [0]
   #compare(#0, #pos(z0)) -> #LT [0]
   #compare(#0, #s(z0)) -> #LT [0]
   #compare(#neg(z0), #0) -> #LT [0]
   #compare(#neg(z0), #neg(z1)) -> #compare(z1, z0) [0]
   #compare(#neg(z0), #pos(z1)) -> #LT [0]
   #compare(#pos(z0), #0) -> #GT [0]
   #compare(#pos(z0), #neg(z1)) -> #GT [0]
   #compare(#pos(z0), #pos(z1)) -> #compare(z0, z1) [0]
   #compare(#s(z0), #0) -> #GT [0]
   #compare(#s(z0), #s(z1)) -> #compare(z0, z1) [0]
   insertionsort(z0) -> insertionsort#1(z0) [0]
   insertionsort#1(::(z0, z1)) -> insert(z0, insertionsort(z1)) [0]
   insertionsort#1(nil) -> nil [0]
   insert(z0, z1) -> insert#1(z1, z0) [0]
   insert#1(::(z0, z1), z2) -> insert#2(#less(z0, z2), z2, z0, z1) [0]
   insert#1(nil, z0) -> ::(z0, nil) [0]
   insert#2(#false, z0, z1, z2) -> ::(z0, ::(z1, z2)) [0]
   insert#2(#true, z0, z1, z2) -> ::(z1, insert(z0, z2)) [0]

The TRS has the following type information:
APPEND :: :::nil -> :::nil -> c16
c16 :: c17 -> c16
APPEND#1 :: :::nil -> :::nil -> c17
:: :: #neg:#pos:#s:#0 -> :::nil -> :::nil
c17 :: c16 -> c17
FLATTEN :: node:leaf -> c19
c19 :: c21:c22 -> c19
FLATTEN#1 :: node:leaf -> c21:c22
node :: :::nil -> node:leaf -> node:leaf -> node:leaf
c21 :: c16 -> c16 -> c19 -> c21:c22
append :: :::nil -> :::nil -> :::nil
flatten :: node:leaf -> :::nil
c22 :: c16 -> c16 -> c19 -> c21:c22
INSERT :: #neg:#pos:#s:#0 -> :::nil -> c24
c24 :: c25 -> c24
INSERT#1 :: :::nil -> #neg:#pos:#s:#0 -> c25
c25 :: c28 -> c15 -> c25
INSERT#2 :: #true:#false -> #neg:#pos:#s:#0 -> #neg:#pos:#s:#0 -> :::nil -> c28
#less :: #neg:#pos:#s:#0 -> #neg:#pos:#s:#0 -> #true:#false
#LESS :: #neg:#pos:#s:#0 -> #neg:#pos:#s:#0 -> c15
#true :: #true:#false
c28 :: c24 -> c28
INSERTIONSORT :: :::nil -> c29
c29 :: c30 -> c29
INSERTIONSORT#1 :: :::nil -> c30
c30 :: c24 -> c29 -> c30
insertionsort :: :::nil -> :::nil
c15 :: c8:c12:c14 -> c15
#COMPARE :: #neg:#pos:#s:#0 -> #neg:#pos:#s:#0 -> c8:c12:c14
#neg :: #neg:#pos:#s:#0 -> #neg:#pos:#s:#0
c8 :: c8:c12:c14 -> c8:c12:c14
#pos :: #neg:#pos:#s:#0 -> #neg:#pos:#s:#0
c12 :: c8:c12:c14 -> c8:c12:c14
#s :: #neg:#pos:#s:#0 -> #neg:#pos:#s:#0
c14 :: c8:c12:c14 -> c8:c12:c14
FLATTENSORT :: node:leaf -> c
c :: c29 -> c
append#1 :: :::nil -> :::nil -> :::nil
flatten#1 :: node:leaf -> :::nil
leaf :: node:leaf
nil :: :::nil
#cklt :: #EQ:#GT:#LT -> #true:#false
#compare :: #neg:#pos:#s:#0 -> #neg:#pos:#s:#0 -> #EQ:#GT:#LT
#EQ :: #EQ:#GT:#LT
#false :: #true:#false
#GT :: #EQ:#GT:#LT
#LT :: #EQ:#GT:#LT
#0 :: #neg:#pos:#s:#0
insertionsort#1 :: :::nil -> :::nil
insert :: #neg:#pos:#s:#0 -> :::nil -> :::nil
insert#1 :: :::nil -> #neg:#pos:#s:#0 -> :::nil
insert#2 :: #true:#false -> #neg:#pos:#s:#0 -> #neg:#pos:#s:#0 -> :::nil -> :::nil

Rewrite Strategy: INNERMOST
----------------------------------------

(23) CompletionProof (UPPER BOUND(ID))
The transformation into a RNTS is sound, since:

(a) The obligation is a constructor system where every type has a constant constructor,

(b) The following defined symbols do not have to be completely defined, as they can never occur inside other defined symbols:

   APPEND_2
   APPEND#1_2
   FLATTEN_1
   FLATTEN#1_1
   INSERT_2
   INSERT#1_2
   INSERT#2_4
   INSERTIONSORT_1
   INSERTIONSORT#1_1
   #LESS_2

(c) The following functions are completely defined:

   #COMPARE_2
   FLATTENSORT_1
   append_2
   flatten_1
   flatten#1_1
   append#1_2
   #less_2
   #cklt_1
   #compare_2
   insertionsort_1
   insertionsort#1_1
   insert_2
   insert#1_2
   insert#2_4

Due to the following rules being added:

   #COMPARE(v0, v1) -> const10 [0]
   FLATTENSORT(v0) -> const11 [0]
   append(v0, v1) -> nil [0]
   flatten(v0) -> nil [0]
   flatten#1(v0) -> nil [0]
   append#1(v0, v1) -> nil [0]
   #less(v0, v1) -> null_#less [0]
   #cklt(v0) -> null_#cklt [0]
   #compare(v0, v1) -> null_#compare [0]
   insertionsort(v0) -> nil [0]
   insertionsort#1(v0) -> nil [0]
   insert(v0, v1) -> nil [0]
   insert#1(v0, v1) -> nil [0]
   insert#2(v0, v1, v2, v3) -> nil [0]

And the following fresh constants:    const10, const11, null_#less, null_#cklt, null_#compare, const, const1, const2, const3, const4, const5, const6, const7, const8, const9

----------------------------------------

(24)
Obligation:
Runtime Complexity Weighted TRS where critical functions are completely defined. The underlying TRS is:

Runtime Complexity Weighted TRS with Types.
The TRS R consists of the following rules:

   APPEND(z0, z1) -> c16(APPEND#1(z0, z1)) [1]
   APPEND#1(::(z0, z1), z2) -> c17(APPEND(z1, z2)) [1]
   FLATTEN(z0) -> c19(FLATTEN#1(z0)) [1]
   FLATTEN#1(node(z0, z1, z2)) -> c21(APPEND(z0, append(flatten(z1), flatten(z2))), APPEND(flatten(z1), flatten(z2)), FLATTEN(z1)) [1]
   FLATTEN#1(node(z0, z1, z2)) -> c22(APPEND(z0, append(flatten(z1), flatten(z2))), APPEND(flatten(z1), flatten(z2)), FLATTEN(z2)) [1]
   INSERT(z0, z1) -> c24(INSERT#1(z1, z0)) [1]
   INSERT#1(::(z0, z1), z2) -> c25(INSERT#2(#less(z0, z2), z2, z0, z1), #LESS(z0, z2)) [1]
   INSERT#2(#true, z0, z1, z2) -> c28(INSERT(z0, z2)) [1]
   INSERTIONSORT(z0) -> c29(INSERTIONSORT#1(z0)) [1]
   INSERTIONSORT#1(::(z0, z1)) -> c30(INSERT(z0, insertionsort(z1)), INSERTIONSORT(z1)) [1]
   #LESS(z0, z1) -> c15(#COMPARE(z0, z1)) [1]
   #COMPARE(#neg(z0), #neg(z1)) -> c8(#COMPARE(z1, z0)) [0]
   #COMPARE(#pos(z0), #pos(z1)) -> c12(#COMPARE(z0, z1)) [0]
   #COMPARE(#s(z0), #s(z1)) -> c14(#COMPARE(z0, z1)) [0]
   FLATTENSORT(z0) -> c(INSERTIONSORT(flatten(z0))) [0]
   append(z0, z1) -> append#1(z0, z1) [0]
   flatten(z0) -> flatten#1(z0) [0]
   flatten#1(leaf) -> nil [0]
   flatten#1(node(z0, z1, z2)) -> append(z0, append(flatten(z1), flatten(z2))) [0]
   append#1(::(z0, z1), z2) -> ::(z0, append(z1, z2)) [0]
   append#1(nil, z0) -> z0 [0]
   #less(z0, z1) -> #cklt(#compare(z0, z1)) [0]
   #cklt(#EQ) -> #false [0]
   #cklt(#GT) -> #false [0]
   #cklt(#LT) -> #true [0]
   #compare(#0, #0) -> #EQ [0]
   #compare(#0, #neg(z0)) -> #GT [0]
   #compare(#0, #pos(z0)) -> #LT [0]
   #compare(#0, #s(z0)) -> #LT [0]
   #compare(#neg(z0), #0) -> #LT [0]
   #compare(#neg(z0), #neg(z1)) -> #compare(z1, z0) [0]
   #compare(#neg(z0), #pos(z1)) -> #LT [0]
   #compare(#pos(z0), #0) -> #GT [0]
   #compare(#pos(z0), #neg(z1)) -> #GT [0]
   #compare(#pos(z0), #pos(z1)) -> #compare(z0, z1) [0]
   #compare(#s(z0), #0) -> #GT [0]
   #compare(#s(z0), #s(z1)) -> #compare(z0, z1) [0]
   insertionsort(z0) -> insertionsort#1(z0) [0]
   insertionsort#1(::(z0, z1)) -> insert(z0, insertionsort(z1)) [0]
   insertionsort#1(nil) -> nil [0]
   insert(z0, z1) -> insert#1(z1, z0) [0]
   insert#1(::(z0, z1), z2) -> insert#2(#less(z0, z2), z2, z0, z1) [0]
   insert#1(nil, z0) -> ::(z0, nil) [0]
   insert#2(#false, z0, z1, z2) -> ::(z0, ::(z1, z2)) [0]
   insert#2(#true, z0, z1, z2) -> ::(z1, insert(z0, z2)) [0]
   #COMPARE(v0, v1) -> const10 [0]
   FLATTENSORT(v0) -> const11 [0]
   append(v0, v1) -> nil [0]
   flatten(v0) -> nil [0]
   flatten#1(v0) -> nil [0]
   append#1(v0, v1) -> nil [0]
   #less(v0, v1) -> null_#less [0]
   #cklt(v0) -> null_#cklt [0]
   #compare(v0, v1) -> null_#compare [0]
   insertionsort(v0) -> nil [0]
   insertionsort#1(v0) -> nil [0]
   insert(v0, v1) -> nil [0]
   insert#1(v0, v1) -> nil [0]
   insert#2(v0, v1, v2, v3) -> nil [0]

The TRS has the following type information:
APPEND :: :::nil -> :::nil -> c16
c16 :: c17 -> c16
APPEND#1 :: :::nil -> :::nil -> c17
:: :: #neg:#pos:#s:#0 -> :::nil -> :::nil
c17 :: c16 -> c17
FLATTEN :: node:leaf -> c19
c19 :: c21:c22 -> c19
FLATTEN#1 :: node:leaf -> c21:c22
node :: :::nil -> node:leaf -> node:leaf -> node:leaf
c21 :: c16 -> c16 -> c19 -> c21:c22
append :: :::nil -> :::nil -> :::nil
flatten :: node:leaf -> :::nil
c22 :: c16 -> c16 -> c19 -> c21:c22
INSERT :: #neg:#pos:#s:#0 -> :::nil -> c24
c24 :: c25 -> c24
INSERT#1 :: :::nil -> #neg:#pos:#s:#0 -> c25
c25 :: c28 -> c15 -> c25
INSERT#2 :: #true:#false:null_#less:null_#cklt -> #neg:#pos:#s:#0 -> #neg:#pos:#s:#0 -> :::nil -> c28
#less :: #neg:#pos:#s:#0 -> #neg:#pos:#s:#0 -> #true:#false:null_#less:null_#cklt
#LESS :: #neg:#pos:#s:#0 -> #neg:#pos:#s:#0 -> c15
#true :: #true:#false:null_#less:null_#cklt
c28 :: c24 -> c28
INSERTIONSORT :: :::nil -> c29
c29 :: c30 -> c29
INSERTIONSORT#1 :: :::nil -> c30
c30 :: c24 -> c29 -> c30
insertionsort :: :::nil -> :::nil
c15 :: c8:c12:c14:const10 -> c15
#COMPARE :: #neg:#pos:#s:#0 -> #neg:#pos:#s:#0 -> c8:c12:c14:const10
#neg :: #neg:#pos:#s:#0 -> #neg:#pos:#s:#0
c8 :: c8:c12:c14:const10 -> c8:c12:c14:const10
#pos :: #neg:#pos:#s:#0 -> #neg:#pos:#s:#0
c12 :: c8:c12:c14:const10 -> c8:c12:c14:const10
#s :: #neg:#pos:#s:#0 -> #neg:#pos:#s:#0
c14 :: c8:c12:c14:const10 -> c8:c12:c14:const10
FLATTENSORT :: node:leaf -> c:const11
c :: c29 -> c:const11
append#1 :: :::nil -> :::nil -> :::nil
flatten#1 :: node:leaf -> :::nil
leaf :: node:leaf
nil :: :::nil
#cklt :: #EQ:#GT:#LT:null_#compare -> #true:#false:null_#less:null_#cklt
#compare :: #neg:#pos:#s:#0 -> #neg:#pos:#s:#0 -> #EQ:#GT:#LT:null_#compare
#EQ :: #EQ:#GT:#LT:null_#compare
#false :: #true:#false:null_#less:null_#cklt
#GT :: #EQ:#GT:#LT:null_#compare
#LT :: #EQ:#GT:#LT:null_#compare
#0 :: #neg:#pos:#s:#0
insertionsort#1 :: :::nil -> :::nil
insert :: #neg:#pos:#s:#0 -> :::nil -> :::nil
insert#1 :: :::nil -> #neg:#pos:#s:#0 -> :::nil
insert#2 :: #true:#false:null_#less:null_#cklt -> #neg:#pos:#s:#0 -> #neg:#pos:#s:#0 -> :::nil -> :::nil
const10 :: c8:c12:c14:const10
const11 :: c:const11
null_#less :: #true:#false:null_#less:null_#cklt
null_#cklt :: #true:#false:null_#less:null_#cklt
null_#compare :: #EQ:#GT:#LT:null_#compare
const :: c16
const1 :: c17
const2 :: c19
const3 :: c21:c22
const4 :: c24
const5 :: c25
const6 :: c28
const7 :: c15
const8 :: c29
const9 :: c30

Rewrite Strategy: INNERMOST
----------------------------------------

(25) NarrowingProof (BOTH BOUNDS(ID, ID))
Narrowed the inner basic terms of all right-hand sides by a single narrowing step.
----------------------------------------

(26)
Obligation:
Runtime Complexity Weighted TRS where critical functions are completely defined. The underlying TRS is:

Runtime Complexity Weighted TRS with Types.
The TRS R consists of the following rules:

   APPEND(z0, z1) -> c16(APPEND#1(z0, z1)) [1]
   APPEND#1(::(z0, z1), z2) -> c17(APPEND(z1, z2)) [1]
   FLATTEN(z0) -> c19(FLATTEN#1(z0)) [1]
   FLATTEN#1(node(z0, z1, z2)) -> c21(APPEND(z0, append(flatten#1(z1), flatten#1(z2))), APPEND(flatten#1(z1), flatten#1(z2)), FLATTEN(z1)) [1]
   FLATTEN#1(node(z0, z1, z2)) -> c21(APPEND(z0, append(flatten#1(z1), flatten#1(z2))), APPEND(flatten#1(z1), nil), FLATTEN(z1)) [1]
   FLATTEN#1(node(z0, z1, z2)) -> c21(APPEND(z0, append(flatten#1(z1), flatten#1(z2))), APPEND(nil, flatten#1(z2)), FLATTEN(z1)) [1]
   FLATTEN#1(node(z0, z1, z2)) -> c21(APPEND(z0, append(flatten#1(z1), flatten#1(z2))), APPEND(nil, nil), FLATTEN(z1)) [1]
   FLATTEN#1(node(z0, z1, z2)) -> c21(APPEND(z0, append(flatten#1(z1), nil)), APPEND(flatten#1(z1), flatten#1(z2)), FLATTEN(z1)) [1]
   FLATTEN#1(node(z0, z1, z2)) -> c21(APPEND(z0, append(flatten#1(z1), nil)), APPEND(flatten#1(z1), nil), FLATTEN(z1)) [1]
   FLATTEN#1(node(z0, z1, z2)) -> c21(APPEND(z0, append(flatten#1(z1), nil)), APPEND(nil, flatten#1(z2)), FLATTEN(z1)) [1]
   FLATTEN#1(node(z0, z1, z2)) -> c21(APPEND(z0, append(flatten#1(z1), nil)), APPEND(nil, nil), FLATTEN(z1)) [1]
   FLATTEN#1(node(z0, z1, z2)) -> c21(APPEND(z0, append(nil, flatten#1(z2))), APPEND(flatten#1(z1), flatten#1(z2)), FLATTEN(z1)) [1]
   FLATTEN#1(node(z0, z1, z2)) -> c21(APPEND(z0, append(nil, flatten#1(z2))), APPEND(flatten#1(z1), nil), FLATTEN(z1)) [1]
   FLATTEN#1(node(z0, z1, z2)) -> c21(APPEND(z0, append(nil, flatten#1(z2))), APPEND(nil, flatten#1(z2)), FLATTEN(z1)) [1]
   FLATTEN#1(node(z0, z1, z2)) -> c21(APPEND(z0, append(nil, flatten#1(z2))), APPEND(nil, nil), FLATTEN(z1)) [1]
   FLATTEN#1(node(z0, z1, z2)) -> c21(APPEND(z0, append(nil, nil)), APPEND(flatten#1(z1), flatten#1(z2)), FLATTEN(z1)) [1]
   FLATTEN#1(node(z0, z1, z2)) -> c21(APPEND(z0, append(nil, nil)), APPEND(flatten#1(z1), nil), FLATTEN(z1)) [1]
   FLATTEN#1(node(z0, z1, z2)) -> c21(APPEND(z0, append(nil, nil)), APPEND(nil, flatten#1(z2)), FLATTEN(z1)) [1]
   FLATTEN#1(node(z0, z1, z2)) -> c21(APPEND(z0, append(nil, nil)), APPEND(nil, nil), FLATTEN(z1)) [1]
   FLATTEN#1(node(z0, z1, z2)) -> c22(APPEND(z0, append(flatten#1(z1), flatten#1(z2))), APPEND(flatten#1(z1), flatten#1(z2)), FLATTEN(z2)) [1]
   FLATTEN#1(node(z0, z1, z2)) -> c22(APPEND(z0, append(flatten#1(z1), flatten#1(z2))), APPEND(flatten#1(z1), nil), FLATTEN(z2)) [1]
   FLATTEN#1(node(z0, z1, z2)) -> c22(APPEND(z0, append(flatten#1(z1), flatten#1(z2))), APPEND(nil, flatten#1(z2)), FLATTEN(z2)) [1]
   FLATTEN#1(node(z0, z1, z2)) -> c22(APPEND(z0, append(flatten#1(z1), flatten#1(z2))), APPEND(nil, nil), FLATTEN(z2)) [1]
   FLATTEN#1(node(z0, z1, z2)) -> c22(APPEND(z0, append(flatten#1(z1), nil)), APPEND(flatten#1(z1), flatten#1(z2)), FLATTEN(z2)) [1]
   FLATTEN#1(node(z0, z1, z2)) -> c22(APPEND(z0, append(flatten#1(z1), nil)), APPEND(flatten#1(z1), nil), FLATTEN(z2)) [1]
   FLATTEN#1(node(z0, z1, z2)) -> c22(APPEND(z0, append(flatten#1(z1), nil)), APPEND(nil, flatten#1(z2)), FLATTEN(z2)) [1]
   FLATTEN#1(node(z0, z1, z2)) -> c22(APPEND(z0, append(flatten#1(z1), nil)), APPEND(nil, nil), FLATTEN(z2)) [1]
   FLATTEN#1(node(z0, z1, z2)) -> c22(APPEND(z0, append(nil, flatten#1(z2))), APPEND(flatten#1(z1), flatten#1(z2)), FLATTEN(z2)) [1]
   FLATTEN#1(node(z0, z1, z2)) -> c22(APPEND(z0, append(nil, flatten#1(z2))), APPEND(flatten#1(z1), nil), FLATTEN(z2)) [1]
   FLATTEN#1(node(z0, z1, z2)) -> c22(APPEND(z0, append(nil, flatten#1(z2))), APPEND(nil, flatten#1(z2)), FLATTEN(z2)) [1]
   FLATTEN#1(node(z0, z1, z2)) -> c22(APPEND(z0, append(nil, flatten#1(z2))), APPEND(nil, nil), FLATTEN(z2)) [1]
   FLATTEN#1(node(z0, z1, z2)) -> c22(APPEND(z0, append(nil, nil)), APPEND(flatten#1(z1), flatten#1(z2)), FLATTEN(z2)) [1]
   FLATTEN#1(node(z0, z1, z2)) -> c22(APPEND(z0, append(nil, nil)), APPEND(flatten#1(z1), nil), FLATTEN(z2)) [1]
   FLATTEN#1(node(z0, z1, z2)) -> c22(APPEND(z0, append(nil, nil)), APPEND(nil, flatten#1(z2)), FLATTEN(z2)) [1]
   FLATTEN#1(node(z0, z1, z2)) -> c22(APPEND(z0, append(nil, nil)), APPEND(nil, nil), FLATTEN(z2)) [1]
   INSERT(z0, z1) -> c24(INSERT#1(z1, z0)) [1]
   INSERT#1(::(z0, z1), z2) -> c25(INSERT#2(#cklt(#compare(z0, z2)), z2, z0, z1), #LESS(z0, z2)) [1]
   INSERT#1(::(z0, z1), z2) -> c25(INSERT#2(null_#less, z2, z0, z1), #LESS(z0, z2)) [1]
   INSERT#2(#true, z0, z1, z2) -> c28(INSERT(z0, z2)) [1]
   INSERTIONSORT(z0) -> c29(INSERTIONSORT#1(z0)) [1]
   INSERTIONSORT#1(::(z0, z1)) -> c30(INSERT(z0, insertionsort#1(z1)), INSERTIONSORT(z1)) [1]
   INSERTIONSORT#1(::(z0, z1)) -> c30(INSERT(z0, nil), INSERTIONSORT(z1)) [1]
   #LESS(z0, z1) -> c15(#COMPARE(z0, z1)) [1]
   #COMPARE(#neg(z0), #neg(z1)) -> c8(#COMPARE(z1, z0)) [0]
   #COMPARE(#pos(z0), #pos(z1)) -> c12(#COMPARE(z0, z1)) [0]
   #COMPARE(#s(z0), #s(z1)) -> c14(#COMPARE(z0, z1)) [0]
   FLATTENSORT(z0) -> c(INSERTIONSORT(flatten#1(z0))) [0]
   FLATTENSORT(z0) -> c(INSERTIONSORT(nil)) [0]
   append(z0, z1) -> append#1(z0, z1) [0]
   flatten(z0) -> flatten#1(z0) [0]
   flatten#1(leaf) -> nil [0]
   flatten#1(node(z0, z1, z2)) -> append(z0, append(flatten#1(z1), flatten#1(z2))) [0]
   flatten#1(node(z0, z1, z2)) -> append(z0, append(flatten#1(z1), nil)) [0]
   flatten#1(node(z0, z1, z2)) -> append(z0, append(nil, flatten#1(z2))) [0]
   flatten#1(node(z0, z1, z2)) -> append(z0, append(nil, nil)) [0]
   append#1(::(z0, z1), z2) -> ::(z0, append(z1, z2)) [0]
   append#1(nil, z0) -> z0 [0]
   #less(#0, #0) -> #cklt(#EQ) [0]
   #less(#0, #neg(z0')) -> #cklt(#GT) [0]
   #less(#0, #pos(z0'')) -> #cklt(#LT) [0]
   #less(#0, #s(z01)) -> #cklt(#LT) [0]
   #less(#neg(z02), #0) -> #cklt(#LT) [0]
   #less(#neg(z03), #neg(z1')) -> #cklt(#compare(z1', z03)) [0]
   #less(#neg(z04), #pos(z1'')) -> #cklt(#LT) [0]
   #less(#pos(z05), #0) -> #cklt(#GT) [0]
   #less(#pos(z06), #neg(z11)) -> #cklt(#GT) [0]
   #less(#pos(z07), #pos(z12)) -> #cklt(#compare(z07, z12)) [0]
   #less(#s(z08), #0) -> #cklt(#GT) [0]
   #less(#s(z09), #s(z13)) -> #cklt(#compare(z09, z13)) [0]
   #less(z0, z1) -> #cklt(null_#compare) [0]
   #cklt(#EQ) -> #false [0]
   #cklt(#GT) -> #false [0]
   #cklt(#LT) -> #true [0]
   #compare(#0, #0) -> #EQ [0]
   #compare(#0, #neg(z0)) -> #GT [0]
   #compare(#0, #pos(z0)) -> #LT [0]
   #compare(#0, #s(z0)) -> #LT [0]
   #compare(#neg(z0), #0) -> #LT [0]
   #compare(#neg(z0), #neg(z1)) -> #compare(z1, z0) [0]
   #compare(#neg(z0), #pos(z1)) -> #LT [0]
   #compare(#pos(z0), #0) -> #GT [0]
   #compare(#pos(z0), #neg(z1)) -> #GT [0]
   #compare(#pos(z0), #pos(z1)) -> #compare(z0, z1) [0]
   #compare(#s(z0), #0) -> #GT [0]
   #compare(#s(z0), #s(z1)) -> #compare(z0, z1) [0]
   insertionsort(z0) -> insertionsort#1(z0) [0]
   insertionsort#1(::(z0, z1)) -> insert(z0, insertionsort#1(z1)) [0]
   insertionsort#1(::(z0, z1)) -> insert(z0, nil) [0]
   insertionsort#1(nil) -> nil [0]
   insert(z0, z1) -> insert#1(z1, z0) [0]
   insert#1(::(z0, z1), z2) -> insert#2(#cklt(#compare(z0, z2)), z2, z0, z1) [0]
   insert#1(::(z0, z1), z2) -> insert#2(null_#less, z2, z0, z1) [0]
   insert#1(nil, z0) -> ::(z0, nil) [0]
   insert#2(#false, z0, z1, z2) -> ::(z0, ::(z1, z2)) [0]
   insert#2(#true, z0, z1, z2) -> ::(z1, insert(z0, z2)) [0]
   #COMPARE(v0, v1) -> const10 [0]
   FLATTENSORT(v0) -> const11 [0]
   append(v0, v1) -> nil [0]
   flatten(v0) -> nil [0]
   flatten#1(v0) -> nil [0]
   append#1(v0, v1) -> nil [0]
   #less(v0, v1) -> null_#less [0]
   #cklt(v0) -> null_#cklt [0]
   #compare(v0, v1) -> null_#compare [0]
   insertionsort(v0) -> nil [0]
   insertionsort#1(v0) -> nil [0]
   insert(v0, v1) -> nil [0]
   insert#1(v0, v1) -> nil [0]
   insert#2(v0, v1, v2, v3) -> nil [0]

The TRS has the following type information:
APPEND :: :::nil -> :::nil -> c16
c16 :: c17 -> c16
APPEND#1 :: :::nil -> :::nil -> c17
:: :: #neg:#pos:#s:#0 -> :::nil -> :::nil
c17 :: c16 -> c17
FLATTEN :: node:leaf -> c19
c19 :: c21:c22 -> c19
FLATTEN#1 :: node:leaf -> c21:c22
node :: :::nil -> node:leaf -> node:leaf -> node:leaf
c21 :: c16 -> c16 -> c19 -> c21:c22
append :: :::nil -> :::nil -> :::nil
flatten :: node:leaf -> :::nil
c22 :: c16 -> c16 -> c19 -> c21:c22
INSERT :: #neg:#pos:#s:#0 -> :::nil -> c24
c24 :: c25 -> c24
INSERT#1 :: :::nil -> #neg:#pos:#s:#0 -> c25
c25 :: c28 -> c15 -> c25
INSERT#2 :: #true:#false:null_#less:null_#cklt -> #neg:#pos:#s:#0 -> #neg:#pos:#s:#0 -> :::nil -> c28
#less :: #neg:#pos:#s:#0 -> #neg:#pos:#s:#0 -> #true:#false:null_#less:null_#cklt
#LESS :: #neg:#pos:#s:#0 -> #neg:#pos:#s:#0 -> c15
#true :: #true:#false:null_#less:null_#cklt
c28 :: c24 -> c28
INSERTIONSORT :: :::nil -> c29
c29 :: c30 -> c29
INSERTIONSORT#1 :: :::nil -> c30
c30 :: c24 -> c29 -> c30
insertionsort :: :::nil -> :::nil
c15 :: c8:c12:c14:const10 -> c15
#COMPARE :: #neg:#pos:#s:#0 -> #neg:#pos:#s:#0 -> c8:c12:c14:const10
#neg :: #neg:#pos:#s:#0 -> #neg:#pos:#s:#0
c8 :: c8:c12:c14:const10 -> c8:c12:c14:const10
#pos :: #neg:#pos:#s:#0 -> #neg:#pos:#s:#0
c12 :: c8:c12:c14:const10 -> c8:c12:c14:const10
#s :: #neg:#pos:#s:#0 -> #neg:#pos:#s:#0
c14 :: c8:c12:c14:const10 -> c8:c12:c14:const10
FLATTENSORT :: node:leaf -> c:const11
c :: c29 -> c:const11
append#1 :: :::nil -> :::nil -> :::nil
flatten#1 :: node:leaf -> :::nil
leaf :: node:leaf
nil :: :::nil
#cklt :: #EQ:#GT:#LT:null_#compare -> #true:#false:null_#less:null_#cklt
#compare :: #neg:#pos:#s:#0 -> #neg:#pos:#s:#0 -> #EQ:#GT:#LT:null_#compare
#EQ :: #EQ:#GT:#LT:null_#compare
#false :: #true:#false:null_#less:null_#cklt
#GT :: #EQ:#GT:#LT:null_#compare
#LT :: #EQ:#GT:#LT:null_#compare
#0 :: #neg:#pos:#s:#0
insertionsort#1 :: :::nil -> :::nil
insert :: #neg:#pos:#s:#0 -> :::nil -> :::nil
insert#1 :: :::nil -> #neg:#pos:#s:#0 -> :::nil
insert#2 :: #true:#false:null_#less:null_#cklt -> #neg:#pos:#s:#0 -> #neg:#pos:#s:#0 -> :::nil -> :::nil
const10 :: c8:c12:c14:const10
const11 :: c:const11
null_#less :: #true:#false:null_#less:null_#cklt
null_#cklt :: #true:#false:null_#less:null_#cklt
null_#compare :: #EQ:#GT:#LT:null_#compare
const :: c16
const1 :: c17
const2 :: c19
const3 :: c21:c22
const4 :: c24
const5 :: c25
const6 :: c28
const7 :: c15
const8 :: c29
const9 :: c30

Rewrite Strategy: INNERMOST
----------------------------------------

(27) CpxTypedWeightedTrsToRntsProof (UPPER BOUND(ID))
Transformed the TRS into an over-approximating RNTS by (improved) Size Abstraction.
The constant constructors are abstracted as follows:

   #true => 2
   leaf => 0
   nil => 0
   #EQ => 1
   #false => 1
   #GT => 2
   #LT => 3
   #0 => 0
   const10 => 0
   const11 => 0
   null_#less => 0
   null_#cklt => 0
   null_#compare => 0
   const => 0
   const1 => 0
   const2 => 0
   const3 => 0
   const4 => 0
   const5 => 0
   const6 => 0
   const7 => 0
   const8 => 0
   const9 => 0

----------------------------------------

(28)
Obligation:
Complexity RNTS consisting of the following rules:

   #COMPARE(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1
   #COMPARE(z, z') -{ 0 }-> 1 + #COMPARE(z0, z1) :|: z1 >= 0, z = 1 + z0, z0 >= 0, z' = 1 + z1
   #COMPARE(z, z') -{ 0 }-> 1 + #COMPARE(z1, z0) :|: z1 >= 0, z = 1 + z0, z0 >= 0, z' = 1 + z1
   #LESS(z, z') -{ 1 }-> 1 + #COMPARE(z0, z1) :|: z = z0, z1 >= 0, z' = z1, z0 >= 0
   #cklt(z) -{ 0 }-> 2 :|: z = 3
   #cklt(z) -{ 0 }-> 1 :|: z = 1
   #cklt(z) -{ 0 }-> 1 :|: z = 2
   #cklt(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0
   #compare(z, z') -{ 0 }-> 3 :|: z0 >= 0, z' = 1 + z0, z = 0
   #compare(z, z') -{ 0 }-> 3 :|: z = 1 + z0, z0 >= 0, z' = 0
   #compare(z, z') -{ 0 }-> 3 :|: z1 >= 0, z = 1 + z0, z0 >= 0, z' = 1 + z1
   #compare(z, z') -{ 0 }-> 2 :|: z0 >= 0, z' = 1 + z0, z = 0
   #compare(z, z') -{ 0 }-> 2 :|: z = 1 + z0, z0 >= 0, z' = 0
   #compare(z, z') -{ 0 }-> 2 :|: z1 >= 0, z = 1 + z0, z0 >= 0, z' = 1 + z1
   #compare(z, z') -{ 0 }-> 1 :|: z = 0, z' = 0
   #compare(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1
   #compare(z, z') -{ 0 }-> #compare(z0, z1) :|: z1 >= 0, z = 1 + z0, z0 >= 0, z' = 1 + z1
   #compare(z, z') -{ 0 }-> #compare(z1, z0) :|: z1 >= 0, z = 1 + z0, z0 >= 0, z' = 1 + z1
   #less(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1
   #less(z, z') -{ 0 }-> #cklt(3) :|: z' = 1 + z0'', z0'' >= 0, z = 0
   #less(z, z') -{ 0 }-> #cklt(3) :|: z01 >= 0, z' = 1 + z01, z = 0
   #less(z, z') -{ 0 }-> #cklt(3) :|: z = 1 + z02, z02 >= 0, z' = 0
   #less(z, z') -{ 0 }-> #cklt(3) :|: z04 >= 0, z' = 1 + z1'', z = 1 + z04, z1'' >= 0
   #less(z, z') -{ 0 }-> #cklt(2) :|: z0' >= 0, z = 0, z' = 1 + z0'
   #less(z, z') -{ 0 }-> #cklt(2) :|: z05 >= 0, z = 1 + z05, z' = 0
   #less(z, z') -{ 0 }-> #cklt(2) :|: z' = 1 + z11, z11 >= 0, z06 >= 0, z = 1 + z06
   #less(z, z') -{ 0 }-> #cklt(2) :|: z08 >= 0, z = 1 + z08, z' = 0
   #less(z, z') -{ 0 }-> #cklt(1) :|: z = 0, z' = 0
   #less(z, z') -{ 0 }-> #cklt(0) :|: z = z0, z1 >= 0, z' = z1, z0 >= 0
   #less(z, z') -{ 0 }-> #cklt(#compare(z07, z12)) :|: z' = 1 + z12, z07 >= 0, z = 1 + z07, z12 >= 0
   #less(z, z') -{ 0 }-> #cklt(#compare(z09, z13)) :|: z' = 1 + z13, z = 1 + z09, z09 >= 0, z13 >= 0
   #less(z, z') -{ 0 }-> #cklt(#compare(z1', z03)) :|: z' = 1 + z1', z1' >= 0, z = 1 + z03, z03 >= 0
   APPEND(z, z') -{ 1 }-> 1 + APPEND#1(z0, z1) :|: z = z0, z1 >= 0, z' = z1, z0 >= 0
   APPEND#1(z, z') -{ 1 }-> 1 + APPEND(z1, z2) :|: z1 >= 0, z' = z2, z0 >= 0, z = 1 + z0 + z1, z2 >= 0
   FLATTEN(z) -{ 1 }-> 1 + FLATTEN#1(z0) :|: z = z0, z0 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), flatten#1(z2))) + APPEND(flatten#1(z1), flatten#1(z2)) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), flatten#1(z2))) + APPEND(flatten#1(z1), flatten#1(z2)) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), flatten#1(z2))) + APPEND(flatten#1(z1), 0) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), flatten#1(z2))) + APPEND(flatten#1(z1), 0) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), flatten#1(z2))) + APPEND(0, flatten#1(z2)) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), flatten#1(z2))) + APPEND(0, flatten#1(z2)) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), flatten#1(z2))) + APPEND(0, 0) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), flatten#1(z2))) + APPEND(0, 0) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), 0)) + APPEND(flatten#1(z1), flatten#1(z2)) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), 0)) + APPEND(flatten#1(z1), flatten#1(z2)) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), 0)) + APPEND(flatten#1(z1), 0) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), 0)) + APPEND(flatten#1(z1), 0) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), 0)) + APPEND(0, flatten#1(z2)) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), 0)) + APPEND(0, flatten#1(z2)) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), 0)) + APPEND(0, 0) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), 0)) + APPEND(0, 0) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(0, flatten#1(z2))) + APPEND(flatten#1(z1), flatten#1(z2)) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(0, flatten#1(z2))) + APPEND(flatten#1(z1), flatten#1(z2)) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(0, flatten#1(z2))) + APPEND(flatten#1(z1), 0) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(0, flatten#1(z2))) + APPEND(flatten#1(z1), 0) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(0, flatten#1(z2))) + APPEND(0, flatten#1(z2)) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(0, flatten#1(z2))) + APPEND(0, flatten#1(z2)) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(0, flatten#1(z2))) + APPEND(0, 0) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(0, flatten#1(z2))) + APPEND(0, 0) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(0, 0)) + APPEND(flatten#1(z1), flatten#1(z2)) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(0, 0)) + APPEND(flatten#1(z1), flatten#1(z2)) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(0, 0)) + APPEND(flatten#1(z1), 0) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(0, 0)) + APPEND(flatten#1(z1), 0) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(0, 0)) + APPEND(0, flatten#1(z2)) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(0, 0)) + APPEND(0, flatten#1(z2)) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(0, 0)) + APPEND(0, 0) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(0, 0)) + APPEND(0, 0) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTENSORT(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0
   FLATTENSORT(z) -{ 0 }-> 1 + INSERTIONSORT(flatten#1(z0)) :|: z = z0, z0 >= 0
   FLATTENSORT(z) -{ 0 }-> 1 + INSERTIONSORT(0) :|: z = z0, z0 >= 0
   INSERT(z, z') -{ 1 }-> 1 + INSERT#1(z1, z0) :|: z = z0, z1 >= 0, z' = z1, z0 >= 0
   INSERT#1(z, z') -{ 1 }-> 1 + INSERT#2(0, z2, z0, z1) + #LESS(z0, z2) :|: z1 >= 0, z' = z2, z0 >= 0, z = 1 + z0 + z1, z2 >= 0
   INSERT#1(z, z') -{ 1 }-> 1 + INSERT#2(#cklt(#compare(z0, z2)), z2, z0, z1) + #LESS(z0, z2) :|: z1 >= 0, z' = z2, z0 >= 0, z = 1 + z0 + z1, z2 >= 0
   INSERT#2(z, z', z'', z3) -{ 1 }-> 1 + INSERT(z0, z2) :|: z = 2, z1 >= 0, z0 >= 0, z3 = z2, z' = z0, z2 >= 0, z'' = z1
   INSERTIONSORT(z) -{ 1 }-> 1 + INSERTIONSORT#1(z0) :|: z = z0, z0 >= 0
   INSERTIONSORT#1(z) -{ 1 }-> 1 + INSERT(z0, insertionsort#1(z1)) + INSERTIONSORT(z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   INSERTIONSORT#1(z) -{ 1 }-> 1 + INSERT(z0, 0) + INSERTIONSORT(z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   append(z, z') -{ 0 }-> append#1(z0, z1) :|: z = z0, z1 >= 0, z' = z1, z0 >= 0
   append(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1
   append#1(z, z') -{ 0 }-> z0 :|: z0 >= 0, z = 0, z' = z0
   append#1(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1
   append#1(z, z') -{ 0 }-> 1 + z0 + append(z1, z2) :|: z1 >= 0, z' = z2, z0 >= 0, z = 1 + z0 + z1, z2 >= 0
   flatten(z) -{ 0 }-> flatten#1(z0) :|: z = z0, z0 >= 0
   flatten(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0
   flatten#1(z) -{ 0 }-> append(z0, append(flatten#1(z1), flatten#1(z2))) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   flatten#1(z) -{ 0 }-> append(z0, append(flatten#1(z1), 0)) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   flatten#1(z) -{ 0 }-> append(z0, append(0, flatten#1(z2))) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   flatten#1(z) -{ 0 }-> append(z0, append(0, 0)) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   flatten#1(z) -{ 0 }-> 0 :|: z = 0
   flatten#1(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0
   insert(z, z') -{ 0 }-> insert#1(z1, z0) :|: z = z0, z1 >= 0, z' = z1, z0 >= 0
   insert(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1
   insert#1(z, z') -{ 0 }-> insert#2(0, z2, z0, z1) :|: z1 >= 0, z' = z2, z0 >= 0, z = 1 + z0 + z1, z2 >= 0
   insert#1(z, z') -{ 0 }-> insert#2(#cklt(#compare(z0, z2)), z2, z0, z1) :|: z1 >= 0, z' = z2, z0 >= 0, z = 1 + z0 + z1, z2 >= 0
   insert#1(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1
   insert#1(z, z') -{ 0 }-> 1 + z0 + 0 :|: z0 >= 0, z = 0, z' = z0
   insert#2(z, z', z'', z3) -{ 0 }-> 0 :|: v0 >= 0, z'' = v2, v1 >= 0, z = v0, z' = v1, z3 = v3, v2 >= 0, v3 >= 0
   insert#2(z, z', z'', z3) -{ 0 }-> 1 + z0 + (1 + z1 + z2) :|: z1 >= 0, z = 1, z0 >= 0, z3 = z2, z' = z0, z2 >= 0, z'' = z1
   insert#2(z, z', z'', z3) -{ 0 }-> 1 + z1 + insert(z0, z2) :|: z = 2, z1 >= 0, z0 >= 0, z3 = z2, z' = z0, z2 >= 0, z'' = z1
   insertionsort(z) -{ 0 }-> insertionsort#1(z0) :|: z = z0, z0 >= 0
   insertionsort(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0
   insertionsort#1(z) -{ 0 }-> insert(z0, insertionsort#1(z1)) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   insertionsort#1(z) -{ 0 }-> insert(z0, 0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   insertionsort#1(z) -{ 0 }-> 0 :|: z = 0
   insertionsort#1(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0


----------------------------------------

(29) InliningProof (UPPER BOUND(ID))
Inlined the following terminating rules on right-hand sides where appropriate:

   #cklt(z) -{ 0 }-> 1 :|: z = 1
   #cklt(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0
   #cklt(z) -{ 0 }-> 1 :|: z = 2
   #cklt(z) -{ 0 }-> 2 :|: z = 3

----------------------------------------

(30)
Obligation:
Complexity RNTS consisting of the following rules:

   #COMPARE(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1
   #COMPARE(z, z') -{ 0 }-> 1 + #COMPARE(z0, z1) :|: z1 >= 0, z = 1 + z0, z0 >= 0, z' = 1 + z1
   #COMPARE(z, z') -{ 0 }-> 1 + #COMPARE(z1, z0) :|: z1 >= 0, z = 1 + z0, z0 >= 0, z' = 1 + z1
   #LESS(z, z') -{ 1 }-> 1 + #COMPARE(z0, z1) :|: z = z0, z1 >= 0, z' = z1, z0 >= 0
   #cklt(z) -{ 0 }-> 2 :|: z = 3
   #cklt(z) -{ 0 }-> 1 :|: z = 1
   #cklt(z) -{ 0 }-> 1 :|: z = 2
   #cklt(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0
   #compare(z, z') -{ 0 }-> 3 :|: z0 >= 0, z' = 1 + z0, z = 0
   #compare(z, z') -{ 0 }-> 3 :|: z = 1 + z0, z0 >= 0, z' = 0
   #compare(z, z') -{ 0 }-> 3 :|: z1 >= 0, z = 1 + z0, z0 >= 0, z' = 1 + z1
   #compare(z, z') -{ 0 }-> 2 :|: z0 >= 0, z' = 1 + z0, z = 0
   #compare(z, z') -{ 0 }-> 2 :|: z = 1 + z0, z0 >= 0, z' = 0
   #compare(z, z') -{ 0 }-> 2 :|: z1 >= 0, z = 1 + z0, z0 >= 0, z' = 1 + z1
   #compare(z, z') -{ 0 }-> 1 :|: z = 0, z' = 0
   #compare(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1
   #compare(z, z') -{ 0 }-> #compare(z0, z1) :|: z1 >= 0, z = 1 + z0, z0 >= 0, z' = 1 + z1
   #compare(z, z') -{ 0 }-> #compare(z1, z0) :|: z1 >= 0, z = 1 + z0, z0 >= 0, z' = 1 + z1
   #less(z, z') -{ 0 }-> 2 :|: z' = 1 + z0'', z0'' >= 0, z = 0, 3 = 3
   #less(z, z') -{ 0 }-> 2 :|: z01 >= 0, z' = 1 + z01, z = 0, 3 = 3
   #less(z, z') -{ 0 }-> 2 :|: z = 1 + z02, z02 >= 0, z' = 0, 3 = 3
   #less(z, z') -{ 0 }-> 2 :|: z04 >= 0, z' = 1 + z1'', z = 1 + z04, z1'' >= 0, 3 = 3
   #less(z, z') -{ 0 }-> 1 :|: z = 0, z' = 0, 1 = 1
   #less(z, z') -{ 0 }-> 1 :|: z0' >= 0, z = 0, z' = 1 + z0', 2 = 2
   #less(z, z') -{ 0 }-> 1 :|: z05 >= 0, z = 1 + z05, z' = 0, 2 = 2
   #less(z, z') -{ 0 }-> 1 :|: z' = 1 + z11, z11 >= 0, z06 >= 0, z = 1 + z06, 2 = 2
   #less(z, z') -{ 0 }-> 1 :|: z08 >= 0, z = 1 + z08, z' = 0, 2 = 2
   #less(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1
   #less(z, z') -{ 0 }-> 0 :|: z = 0, z' = 0, v0 >= 0, 1 = v0
   #less(z, z') -{ 0 }-> 0 :|: z0' >= 0, z = 0, z' = 1 + z0', v0 >= 0, 2 = v0
   #less(z, z') -{ 0 }-> 0 :|: z' = 1 + z0'', z0'' >= 0, z = 0, v0 >= 0, 3 = v0
   #less(z, z') -{ 0 }-> 0 :|: z01 >= 0, z' = 1 + z01, z = 0, v0 >= 0, 3 = v0
   #less(z, z') -{ 0 }-> 0 :|: z = 1 + z02, z02 >= 0, z' = 0, v0 >= 0, 3 = v0
   #less(z, z') -{ 0 }-> 0 :|: z04 >= 0, z' = 1 + z1'', z = 1 + z04, z1'' >= 0, v0 >= 0, 3 = v0
   #less(z, z') -{ 0 }-> 0 :|: z05 >= 0, z = 1 + z05, z' = 0, v0 >= 0, 2 = v0
   #less(z, z') -{ 0 }-> 0 :|: z' = 1 + z11, z11 >= 0, z06 >= 0, z = 1 + z06, v0 >= 0, 2 = v0
   #less(z, z') -{ 0 }-> 0 :|: z08 >= 0, z = 1 + z08, z' = 0, v0 >= 0, 2 = v0
   #less(z, z') -{ 0 }-> 0 :|: z = z0, z1 >= 0, z' = z1, z0 >= 0, v0 >= 0, 0 = v0
   #less(z, z') -{ 0 }-> #cklt(#compare(z07, z12)) :|: z' = 1 + z12, z07 >= 0, z = 1 + z07, z12 >= 0
   #less(z, z') -{ 0 }-> #cklt(#compare(z09, z13)) :|: z' = 1 + z13, z = 1 + z09, z09 >= 0, z13 >= 0
   #less(z, z') -{ 0 }-> #cklt(#compare(z1', z03)) :|: z' = 1 + z1', z1' >= 0, z = 1 + z03, z03 >= 0
   APPEND(z, z') -{ 1 }-> 1 + APPEND#1(z0, z1) :|: z = z0, z1 >= 0, z' = z1, z0 >= 0
   APPEND#1(z, z') -{ 1 }-> 1 + APPEND(z1, z2) :|: z1 >= 0, z' = z2, z0 >= 0, z = 1 + z0 + z1, z2 >= 0
   FLATTEN(z) -{ 1 }-> 1 + FLATTEN#1(z0) :|: z = z0, z0 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), flatten#1(z2))) + APPEND(flatten#1(z1), flatten#1(z2)) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), flatten#1(z2))) + APPEND(flatten#1(z1), flatten#1(z2)) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), flatten#1(z2))) + APPEND(flatten#1(z1), 0) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), flatten#1(z2))) + APPEND(flatten#1(z1), 0) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), flatten#1(z2))) + APPEND(0, flatten#1(z2)) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), flatten#1(z2))) + APPEND(0, flatten#1(z2)) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), flatten#1(z2))) + APPEND(0, 0) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), flatten#1(z2))) + APPEND(0, 0) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), 0)) + APPEND(flatten#1(z1), flatten#1(z2)) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), 0)) + APPEND(flatten#1(z1), flatten#1(z2)) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), 0)) + APPEND(flatten#1(z1), 0) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), 0)) + APPEND(flatten#1(z1), 0) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), 0)) + APPEND(0, flatten#1(z2)) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), 0)) + APPEND(0, flatten#1(z2)) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), 0)) + APPEND(0, 0) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), 0)) + APPEND(0, 0) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(0, flatten#1(z2))) + APPEND(flatten#1(z1), flatten#1(z2)) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(0, flatten#1(z2))) + APPEND(flatten#1(z1), flatten#1(z2)) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(0, flatten#1(z2))) + APPEND(flatten#1(z1), 0) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(0, flatten#1(z2))) + APPEND(flatten#1(z1), 0) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(0, flatten#1(z2))) + APPEND(0, flatten#1(z2)) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(0, flatten#1(z2))) + APPEND(0, flatten#1(z2)) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(0, flatten#1(z2))) + APPEND(0, 0) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(0, flatten#1(z2))) + APPEND(0, 0) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(0, 0)) + APPEND(flatten#1(z1), flatten#1(z2)) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(0, 0)) + APPEND(flatten#1(z1), flatten#1(z2)) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(0, 0)) + APPEND(flatten#1(z1), 0) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(0, 0)) + APPEND(flatten#1(z1), 0) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(0, 0)) + APPEND(0, flatten#1(z2)) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(0, 0)) + APPEND(0, flatten#1(z2)) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(0, 0)) + APPEND(0, 0) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(0, 0)) + APPEND(0, 0) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTENSORT(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0
   FLATTENSORT(z) -{ 0 }-> 1 + INSERTIONSORT(flatten#1(z0)) :|: z = z0, z0 >= 0
   FLATTENSORT(z) -{ 0 }-> 1 + INSERTIONSORT(0) :|: z = z0, z0 >= 0
   INSERT(z, z') -{ 1 }-> 1 + INSERT#1(z1, z0) :|: z = z0, z1 >= 0, z' = z1, z0 >= 0
   INSERT#1(z, z') -{ 1 }-> 1 + INSERT#2(0, z2, z0, z1) + #LESS(z0, z2) :|: z1 >= 0, z' = z2, z0 >= 0, z = 1 + z0 + z1, z2 >= 0
   INSERT#1(z, z') -{ 1 }-> 1 + INSERT#2(#cklt(#compare(z0, z2)), z2, z0, z1) + #LESS(z0, z2) :|: z1 >= 0, z' = z2, z0 >= 0, z = 1 + z0 + z1, z2 >= 0
   INSERT#2(z, z', z'', z3) -{ 1 }-> 1 + INSERT(z0, z2) :|: z = 2, z1 >= 0, z0 >= 0, z3 = z2, z' = z0, z2 >= 0, z'' = z1
   INSERTIONSORT(z) -{ 1 }-> 1 + INSERTIONSORT#1(z0) :|: z = z0, z0 >= 0
   INSERTIONSORT#1(z) -{ 1 }-> 1 + INSERT(z0, insertionsort#1(z1)) + INSERTIONSORT(z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   INSERTIONSORT#1(z) -{ 1 }-> 1 + INSERT(z0, 0) + INSERTIONSORT(z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   append(z, z') -{ 0 }-> append#1(z0, z1) :|: z = z0, z1 >= 0, z' = z1, z0 >= 0
   append(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1
   append#1(z, z') -{ 0 }-> z0 :|: z0 >= 0, z = 0, z' = z0
   append#1(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1
   append#1(z, z') -{ 0 }-> 1 + z0 + append(z1, z2) :|: z1 >= 0, z' = z2, z0 >= 0, z = 1 + z0 + z1, z2 >= 0
   flatten(z) -{ 0 }-> flatten#1(z0) :|: z = z0, z0 >= 0
   flatten(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0
   flatten#1(z) -{ 0 }-> append(z0, append(flatten#1(z1), flatten#1(z2))) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   flatten#1(z) -{ 0 }-> append(z0, append(flatten#1(z1), 0)) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   flatten#1(z) -{ 0 }-> append(z0, append(0, flatten#1(z2))) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   flatten#1(z) -{ 0 }-> append(z0, append(0, 0)) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   flatten#1(z) -{ 0 }-> 0 :|: z = 0
   flatten#1(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0
   insert(z, z') -{ 0 }-> insert#1(z1, z0) :|: z = z0, z1 >= 0, z' = z1, z0 >= 0
   insert(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1
   insert#1(z, z') -{ 0 }-> insert#2(0, z2, z0, z1) :|: z1 >= 0, z' = z2, z0 >= 0, z = 1 + z0 + z1, z2 >= 0
   insert#1(z, z') -{ 0 }-> insert#2(#cklt(#compare(z0, z2)), z2, z0, z1) :|: z1 >= 0, z' = z2, z0 >= 0, z = 1 + z0 + z1, z2 >= 0
   insert#1(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1
   insert#1(z, z') -{ 0 }-> 1 + z0 + 0 :|: z0 >= 0, z = 0, z' = z0
   insert#2(z, z', z'', z3) -{ 0 }-> 0 :|: v0 >= 0, z'' = v2, v1 >= 0, z = v0, z' = v1, z3 = v3, v2 >= 0, v3 >= 0
   insert#2(z, z', z'', z3) -{ 0 }-> 1 + z0 + (1 + z1 + z2) :|: z1 >= 0, z = 1, z0 >= 0, z3 = z2, z' = z0, z2 >= 0, z'' = z1
   insert#2(z, z', z'', z3) -{ 0 }-> 1 + z1 + insert(z0, z2) :|: z = 2, z1 >= 0, z0 >= 0, z3 = z2, z' = z0, z2 >= 0, z'' = z1
   insertionsort(z) -{ 0 }-> insertionsort#1(z0) :|: z = z0, z0 >= 0
   insertionsort(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0
   insertionsort#1(z) -{ 0 }-> insert(z0, insertionsort#1(z1)) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   insertionsort#1(z) -{ 0 }-> insert(z0, 0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   insertionsort#1(z) -{ 0 }-> 0 :|: z = 0
   insertionsort#1(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0


----------------------------------------

(31) SimplificationProof (BOTH BOUNDS(ID, ID))
Simplified the RNTS by moving equalities from the constraints into the right-hand sides.
----------------------------------------

(32)
Obligation:
Complexity RNTS consisting of the following rules:

   #COMPARE(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   #COMPARE(z, z') -{ 0 }-> 1 + #COMPARE(z - 1, z' - 1) :|: z' - 1 >= 0, z - 1 >= 0
   #COMPARE(z, z') -{ 0 }-> 1 + #COMPARE(z' - 1, z - 1) :|: z' - 1 >= 0, z - 1 >= 0
   #LESS(z, z') -{ 1 }-> 1 + #COMPARE(z, z') :|: z' >= 0, z >= 0
   #cklt(z) -{ 0 }-> 2 :|: z = 3
   #cklt(z) -{ 0 }-> 1 :|: z = 1
   #cklt(z) -{ 0 }-> 1 :|: z = 2
   #cklt(z) -{ 0 }-> 0 :|: z >= 0
   #compare(z, z') -{ 0 }-> 3 :|: z' - 1 >= 0, z = 0
   #compare(z, z') -{ 0 }-> 3 :|: z - 1 >= 0, z' = 0
   #compare(z, z') -{ 0 }-> 3 :|: z' - 1 >= 0, z - 1 >= 0
   #compare(z, z') -{ 0 }-> 2 :|: z' - 1 >= 0, z = 0
   #compare(z, z') -{ 0 }-> 2 :|: z - 1 >= 0, z' = 0
   #compare(z, z') -{ 0 }-> 2 :|: z' - 1 >= 0, z - 1 >= 0
   #compare(z, z') -{ 0 }-> 1 :|: z = 0, z' = 0
   #compare(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   #compare(z, z') -{ 0 }-> #compare(z - 1, z' - 1) :|: z' - 1 >= 0, z - 1 >= 0
   #compare(z, z') -{ 0 }-> #compare(z' - 1, z - 1) :|: z' - 1 >= 0, z - 1 >= 0
   #less(z, z') -{ 0 }-> 2 :|: z' - 1 >= 0, z = 0, 3 = 3
   #less(z, z') -{ 0 }-> 2 :|: z - 1 >= 0, z' = 0, 3 = 3
   #less(z, z') -{ 0 }-> 2 :|: z - 1 >= 0, z' - 1 >= 0, 3 = 3
   #less(z, z') -{ 0 }-> 1 :|: z = 0, z' = 0, 1 = 1
   #less(z, z') -{ 0 }-> 1 :|: z' - 1 >= 0, z = 0, 2 = 2
   #less(z, z') -{ 0 }-> 1 :|: z - 1 >= 0, z' = 0, 2 = 2
   #less(z, z') -{ 0 }-> 1 :|: z' - 1 >= 0, z - 1 >= 0, 2 = 2
   #less(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   #less(z, z') -{ 0 }-> 0 :|: z = 0, z' = 0, v0 >= 0, 1 = v0
   #less(z, z') -{ 0 }-> 0 :|: z' - 1 >= 0, z = 0, v0 >= 0, 2 = v0
   #less(z, z') -{ 0 }-> 0 :|: z' - 1 >= 0, z = 0, v0 >= 0, 3 = v0
   #less(z, z') -{ 0 }-> 0 :|: z - 1 >= 0, z' = 0, v0 >= 0, 3 = v0
   #less(z, z') -{ 0 }-> 0 :|: z - 1 >= 0, z' - 1 >= 0, v0 >= 0, 3 = v0
   #less(z, z') -{ 0 }-> 0 :|: z - 1 >= 0, z' = 0, v0 >= 0, 2 = v0
   #less(z, z') -{ 0 }-> 0 :|: z' - 1 >= 0, z - 1 >= 0, v0 >= 0, 2 = v0
   #less(z, z') -{ 0 }-> 0 :|: z' >= 0, z >= 0, v0 >= 0, 0 = v0
   #less(z, z') -{ 0 }-> #cklt(#compare(z - 1, z' - 1)) :|: z - 1 >= 0, z' - 1 >= 0
   #less(z, z') -{ 0 }-> #cklt(#compare(z' - 1, z - 1)) :|: z' - 1 >= 0, z - 1 >= 0
   APPEND(z, z') -{ 1 }-> 1 + APPEND#1(z, z') :|: z' >= 0, z >= 0
   APPEND#1(z, z') -{ 1 }-> 1 + APPEND(z1, z') :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z' >= 0
   FLATTEN(z) -{ 1 }-> 1 + FLATTEN#1(z) :|: z >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), flatten#1(z2))) + APPEND(flatten#1(z1), flatten#1(z2)) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), flatten#1(z2))) + APPEND(flatten#1(z1), flatten#1(z2)) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), flatten#1(z2))) + APPEND(flatten#1(z1), 0) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), flatten#1(z2))) + APPEND(flatten#1(z1), 0) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), flatten#1(z2))) + APPEND(0, flatten#1(z2)) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), flatten#1(z2))) + APPEND(0, flatten#1(z2)) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), flatten#1(z2))) + APPEND(0, 0) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), flatten#1(z2))) + APPEND(0, 0) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), 0)) + APPEND(flatten#1(z1), flatten#1(z2)) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), 0)) + APPEND(flatten#1(z1), flatten#1(z2)) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), 0)) + APPEND(flatten#1(z1), 0) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), 0)) + APPEND(flatten#1(z1), 0) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), 0)) + APPEND(0, flatten#1(z2)) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), 0)) + APPEND(0, flatten#1(z2)) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), 0)) + APPEND(0, 0) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), 0)) + APPEND(0, 0) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(0, flatten#1(z2))) + APPEND(flatten#1(z1), flatten#1(z2)) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(0, flatten#1(z2))) + APPEND(flatten#1(z1), flatten#1(z2)) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(0, flatten#1(z2))) + APPEND(flatten#1(z1), 0) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(0, flatten#1(z2))) + APPEND(flatten#1(z1), 0) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(0, flatten#1(z2))) + APPEND(0, flatten#1(z2)) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(0, flatten#1(z2))) + APPEND(0, flatten#1(z2)) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(0, flatten#1(z2))) + APPEND(0, 0) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(0, flatten#1(z2))) + APPEND(0, 0) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(0, 0)) + APPEND(flatten#1(z1), flatten#1(z2)) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(0, 0)) + APPEND(flatten#1(z1), flatten#1(z2)) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(0, 0)) + APPEND(flatten#1(z1), 0) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(0, 0)) + APPEND(flatten#1(z1), 0) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(0, 0)) + APPEND(0, flatten#1(z2)) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(0, 0)) + APPEND(0, flatten#1(z2)) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(0, 0)) + APPEND(0, 0) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(0, 0)) + APPEND(0, 0) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTENSORT(z) -{ 0 }-> 0 :|: z >= 0
   FLATTENSORT(z) -{ 0 }-> 1 + INSERTIONSORT(flatten#1(z)) :|: z >= 0
   FLATTENSORT(z) -{ 0 }-> 1 + INSERTIONSORT(0) :|: z >= 0
   INSERT(z, z') -{ 1 }-> 1 + INSERT#1(z', z) :|: z' >= 0, z >= 0
   INSERT#1(z, z') -{ 1 }-> 1 + INSERT#2(0, z', z0, z1) + #LESS(z0, z') :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z' >= 0
   INSERT#1(z, z') -{ 1 }-> 1 + INSERT#2(#cklt(#compare(z0, z')), z', z0, z1) + #LESS(z0, z') :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z' >= 0
   INSERT#2(z, z', z'', z3) -{ 1 }-> 1 + INSERT(z', z3) :|: z = 2, z'' >= 0, z' >= 0, z3 >= 0
   INSERTIONSORT(z) -{ 1 }-> 1 + INSERTIONSORT#1(z) :|: z >= 0
   INSERTIONSORT#1(z) -{ 1 }-> 1 + INSERT(z0, insertionsort#1(z1)) + INSERTIONSORT(z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   INSERTIONSORT#1(z) -{ 1 }-> 1 + INSERT(z0, 0) + INSERTIONSORT(z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   append(z, z') -{ 0 }-> append#1(z, z') :|: z' >= 0, z >= 0
   append(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   append#1(z, z') -{ 0 }-> z' :|: z' >= 0, z = 0
   append#1(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   append#1(z, z') -{ 0 }-> 1 + z0 + append(z1, z') :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z' >= 0
   flatten(z) -{ 0 }-> flatten#1(z) :|: z >= 0
   flatten(z) -{ 0 }-> 0 :|: z >= 0
   flatten#1(z) -{ 0 }-> append(z0, append(flatten#1(z1), flatten#1(z2))) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   flatten#1(z) -{ 0 }-> append(z0, append(flatten#1(z1), 0)) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   flatten#1(z) -{ 0 }-> append(z0, append(0, flatten#1(z2))) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   flatten#1(z) -{ 0 }-> append(z0, append(0, 0)) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   flatten#1(z) -{ 0 }-> 0 :|: z = 0
   flatten#1(z) -{ 0 }-> 0 :|: z >= 0
   insert(z, z') -{ 0 }-> insert#1(z', z) :|: z' >= 0, z >= 0
   insert(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   insert#1(z, z') -{ 0 }-> insert#2(0, z', z0, z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z' >= 0
   insert#1(z, z') -{ 0 }-> insert#2(#cklt(#compare(z0, z')), z', z0, z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z' >= 0
   insert#1(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   insert#1(z, z') -{ 0 }-> 1 + z' + 0 :|: z' >= 0, z = 0
   insert#2(z, z', z'', z3) -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0, z3 >= 0
   insert#2(z, z', z'', z3) -{ 0 }-> 1 + z' + (1 + z'' + z3) :|: z'' >= 0, z = 1, z' >= 0, z3 >= 0
   insert#2(z, z', z'', z3) -{ 0 }-> 1 + z'' + insert(z', z3) :|: z = 2, z'' >= 0, z' >= 0, z3 >= 0
   insertionsort(z) -{ 0 }-> insertionsort#1(z) :|: z >= 0
   insertionsort(z) -{ 0 }-> 0 :|: z >= 0
   insertionsort#1(z) -{ 0 }-> insert(z0, insertionsort#1(z1)) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   insertionsort#1(z) -{ 0 }-> insert(z0, 0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   insertionsort#1(z) -{ 0 }-> 0 :|: z = 0
   insertionsort#1(z) -{ 0 }-> 0 :|: z >= 0


----------------------------------------

(33) CpxRntsAnalysisOrderProof (BOTH BOUNDS(ID, ID))
Found the following analysis order by SCC decomposition:

   { APPEND#1, APPEND }
   { #cklt }
   { #compare }
   { #COMPARE }
   { append#1, append }
   { #less }
   { insert#2, insert, insert#1 }
   { #LESS }
   { flatten#1 }
   { insertionsort#1 }
   { INSERT#1, INSERT#2, INSERT }
   { flatten }
   { FLATTEN, FLATTEN#1 }
   { insertionsort }
   { INSERTIONSORT, INSERTIONSORT#1 }
   { FLATTENSORT }

----------------------------------------

(34)
Obligation:
Complexity RNTS consisting of the following rules:

   #COMPARE(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   #COMPARE(z, z') -{ 0 }-> 1 + #COMPARE(z - 1, z' - 1) :|: z' - 1 >= 0, z - 1 >= 0
   #COMPARE(z, z') -{ 0 }-> 1 + #COMPARE(z' - 1, z - 1) :|: z' - 1 >= 0, z - 1 >= 0
   #LESS(z, z') -{ 1 }-> 1 + #COMPARE(z, z') :|: z' >= 0, z >= 0
   #cklt(z) -{ 0 }-> 2 :|: z = 3
   #cklt(z) -{ 0 }-> 1 :|: z = 1
   #cklt(z) -{ 0 }-> 1 :|: z = 2
   #cklt(z) -{ 0 }-> 0 :|: z >= 0
   #compare(z, z') -{ 0 }-> 3 :|: z' - 1 >= 0, z = 0
   #compare(z, z') -{ 0 }-> 3 :|: z - 1 >= 0, z' = 0
   #compare(z, z') -{ 0 }-> 3 :|: z' - 1 >= 0, z - 1 >= 0
   #compare(z, z') -{ 0 }-> 2 :|: z' - 1 >= 0, z = 0
   #compare(z, z') -{ 0 }-> 2 :|: z - 1 >= 0, z' = 0
   #compare(z, z') -{ 0 }-> 2 :|: z' - 1 >= 0, z - 1 >= 0
   #compare(z, z') -{ 0 }-> 1 :|: z = 0, z' = 0
   #compare(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   #compare(z, z') -{ 0 }-> #compare(z - 1, z' - 1) :|: z' - 1 >= 0, z - 1 >= 0
   #compare(z, z') -{ 0 }-> #compare(z' - 1, z - 1) :|: z' - 1 >= 0, z - 1 >= 0
   #less(z, z') -{ 0 }-> 2 :|: z' - 1 >= 0, z = 0, 3 = 3
   #less(z, z') -{ 0 }-> 2 :|: z - 1 >= 0, z' = 0, 3 = 3
   #less(z, z') -{ 0 }-> 2 :|: z - 1 >= 0, z' - 1 >= 0, 3 = 3
   #less(z, z') -{ 0 }-> 1 :|: z = 0, z' = 0, 1 = 1
   #less(z, z') -{ 0 }-> 1 :|: z' - 1 >= 0, z = 0, 2 = 2
   #less(z, z') -{ 0 }-> 1 :|: z - 1 >= 0, z' = 0, 2 = 2
   #less(z, z') -{ 0 }-> 1 :|: z' - 1 >= 0, z - 1 >= 0, 2 = 2
   #less(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   #less(z, z') -{ 0 }-> 0 :|: z = 0, z' = 0, v0 >= 0, 1 = v0
   #less(z, z') -{ 0 }-> 0 :|: z' - 1 >= 0, z = 0, v0 >= 0, 2 = v0
   #less(z, z') -{ 0 }-> 0 :|: z' - 1 >= 0, z = 0, v0 >= 0, 3 = v0
   #less(z, z') -{ 0 }-> 0 :|: z - 1 >= 0, z' = 0, v0 >= 0, 3 = v0
   #less(z, z') -{ 0 }-> 0 :|: z - 1 >= 0, z' - 1 >= 0, v0 >= 0, 3 = v0
   #less(z, z') -{ 0 }-> 0 :|: z - 1 >= 0, z' = 0, v0 >= 0, 2 = v0
   #less(z, z') -{ 0 }-> 0 :|: z' - 1 >= 0, z - 1 >= 0, v0 >= 0, 2 = v0
   #less(z, z') -{ 0 }-> 0 :|: z' >= 0, z >= 0, v0 >= 0, 0 = v0
   #less(z, z') -{ 0 }-> #cklt(#compare(z - 1, z' - 1)) :|: z - 1 >= 0, z' - 1 >= 0
   #less(z, z') -{ 0 }-> #cklt(#compare(z' - 1, z - 1)) :|: z' - 1 >= 0, z - 1 >= 0
   APPEND(z, z') -{ 1 }-> 1 + APPEND#1(z, z') :|: z' >= 0, z >= 0
   APPEND#1(z, z') -{ 1 }-> 1 + APPEND(z1, z') :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z' >= 0
   FLATTEN(z) -{ 1 }-> 1 + FLATTEN#1(z) :|: z >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), flatten#1(z2))) + APPEND(flatten#1(z1), flatten#1(z2)) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), flatten#1(z2))) + APPEND(flatten#1(z1), flatten#1(z2)) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), flatten#1(z2))) + APPEND(flatten#1(z1), 0) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), flatten#1(z2))) + APPEND(flatten#1(z1), 0) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), flatten#1(z2))) + APPEND(0, flatten#1(z2)) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), flatten#1(z2))) + APPEND(0, flatten#1(z2)) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), flatten#1(z2))) + APPEND(0, 0) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), flatten#1(z2))) + APPEND(0, 0) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), 0)) + APPEND(flatten#1(z1), flatten#1(z2)) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), 0)) + APPEND(flatten#1(z1), flatten#1(z2)) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), 0)) + APPEND(flatten#1(z1), 0) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), 0)) + APPEND(flatten#1(z1), 0) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), 0)) + APPEND(0, flatten#1(z2)) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), 0)) + APPEND(0, flatten#1(z2)) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), 0)) + APPEND(0, 0) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), 0)) + APPEND(0, 0) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(0, flatten#1(z2))) + APPEND(flatten#1(z1), flatten#1(z2)) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(0, flatten#1(z2))) + APPEND(flatten#1(z1), flatten#1(z2)) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(0, flatten#1(z2))) + APPEND(flatten#1(z1), 0) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(0, flatten#1(z2))) + APPEND(flatten#1(z1), 0) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(0, flatten#1(z2))) + APPEND(0, flatten#1(z2)) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(0, flatten#1(z2))) + APPEND(0, flatten#1(z2)) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(0, flatten#1(z2))) + APPEND(0, 0) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(0, flatten#1(z2))) + APPEND(0, 0) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(0, 0)) + APPEND(flatten#1(z1), flatten#1(z2)) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(0, 0)) + APPEND(flatten#1(z1), flatten#1(z2)) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(0, 0)) + APPEND(flatten#1(z1), 0) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(0, 0)) + APPEND(flatten#1(z1), 0) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(0, 0)) + APPEND(0, flatten#1(z2)) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(0, 0)) + APPEND(0, flatten#1(z2)) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(0, 0)) + APPEND(0, 0) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(0, 0)) + APPEND(0, 0) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTENSORT(z) -{ 0 }-> 0 :|: z >= 0
   FLATTENSORT(z) -{ 0 }-> 1 + INSERTIONSORT(flatten#1(z)) :|: z >= 0
   FLATTENSORT(z) -{ 0 }-> 1 + INSERTIONSORT(0) :|: z >= 0
   INSERT(z, z') -{ 1 }-> 1 + INSERT#1(z', z) :|: z' >= 0, z >= 0
   INSERT#1(z, z') -{ 1 }-> 1 + INSERT#2(0, z', z0, z1) + #LESS(z0, z') :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z' >= 0
   INSERT#1(z, z') -{ 1 }-> 1 + INSERT#2(#cklt(#compare(z0, z')), z', z0, z1) + #LESS(z0, z') :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z' >= 0
   INSERT#2(z, z', z'', z3) -{ 1 }-> 1 + INSERT(z', z3) :|: z = 2, z'' >= 0, z' >= 0, z3 >= 0
   INSERTIONSORT(z) -{ 1 }-> 1 + INSERTIONSORT#1(z) :|: z >= 0
   INSERTIONSORT#1(z) -{ 1 }-> 1 + INSERT(z0, insertionsort#1(z1)) + INSERTIONSORT(z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   INSERTIONSORT#1(z) -{ 1 }-> 1 + INSERT(z0, 0) + INSERTIONSORT(z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   append(z, z') -{ 0 }-> append#1(z, z') :|: z' >= 0, z >= 0
   append(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   append#1(z, z') -{ 0 }-> z' :|: z' >= 0, z = 0
   append#1(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   append#1(z, z') -{ 0 }-> 1 + z0 + append(z1, z') :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z' >= 0
   flatten(z) -{ 0 }-> flatten#1(z) :|: z >= 0
   flatten(z) -{ 0 }-> 0 :|: z >= 0
   flatten#1(z) -{ 0 }-> append(z0, append(flatten#1(z1), flatten#1(z2))) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   flatten#1(z) -{ 0 }-> append(z0, append(flatten#1(z1), 0)) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   flatten#1(z) -{ 0 }-> append(z0, append(0, flatten#1(z2))) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   flatten#1(z) -{ 0 }-> append(z0, append(0, 0)) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   flatten#1(z) -{ 0 }-> 0 :|: z = 0
   flatten#1(z) -{ 0 }-> 0 :|: z >= 0
   insert(z, z') -{ 0 }-> insert#1(z', z) :|: z' >= 0, z >= 0
   insert(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   insert#1(z, z') -{ 0 }-> insert#2(0, z', z0, z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z' >= 0
   insert#1(z, z') -{ 0 }-> insert#2(#cklt(#compare(z0, z')), z', z0, z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z' >= 0
   insert#1(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   insert#1(z, z') -{ 0 }-> 1 + z' + 0 :|: z' >= 0, z = 0
   insert#2(z, z', z'', z3) -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0, z3 >= 0
   insert#2(z, z', z'', z3) -{ 0 }-> 1 + z' + (1 + z'' + z3) :|: z'' >= 0, z = 1, z' >= 0, z3 >= 0
   insert#2(z, z', z'', z3) -{ 0 }-> 1 + z'' + insert(z', z3) :|: z = 2, z'' >= 0, z' >= 0, z3 >= 0
   insertionsort(z) -{ 0 }-> insertionsort#1(z) :|: z >= 0
   insertionsort(z) -{ 0 }-> 0 :|: z >= 0
   insertionsort#1(z) -{ 0 }-> insert(z0, insertionsort#1(z1)) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   insertionsort#1(z) -{ 0 }-> insert(z0, 0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   insertionsort#1(z) -{ 0 }-> 0 :|: z = 0
   insertionsort#1(z) -{ 0 }-> 0 :|: z >= 0

Function symbols to be analyzed: {APPEND#1,APPEND}, {#cklt}, {#compare}, {#COMPARE}, {append#1,append}, {#less}, {insert#2,insert,insert#1}, {#LESS}, {flatten#1}, {insertionsort#1}, {INSERT#1,INSERT#2,INSERT}, {flatten}, {FLATTEN,FLATTEN#1}, {insertionsort}, {INSERTIONSORT,INSERTIONSORT#1}, {FLATTENSORT}

----------------------------------------

(35) ResultPropagationProof (UPPER BOUND(ID))
Applied inner abstraction using the recently inferred runtime/size bounds where possible.
----------------------------------------

(36)
Obligation:
Complexity RNTS consisting of the following rules:

   #COMPARE(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   #COMPARE(z, z') -{ 0 }-> 1 + #COMPARE(z - 1, z' - 1) :|: z' - 1 >= 0, z - 1 >= 0
   #COMPARE(z, z') -{ 0 }-> 1 + #COMPARE(z' - 1, z - 1) :|: z' - 1 >= 0, z - 1 >= 0
   #LESS(z, z') -{ 1 }-> 1 + #COMPARE(z, z') :|: z' >= 0, z >= 0
   #cklt(z) -{ 0 }-> 2 :|: z = 3
   #cklt(z) -{ 0 }-> 1 :|: z = 1
   #cklt(z) -{ 0 }-> 1 :|: z = 2
   #cklt(z) -{ 0 }-> 0 :|: z >= 0
   #compare(z, z') -{ 0 }-> 3 :|: z' - 1 >= 0, z = 0
   #compare(z, z') -{ 0 }-> 3 :|: z - 1 >= 0, z' = 0
   #compare(z, z') -{ 0 }-> 3 :|: z' - 1 >= 0, z - 1 >= 0
   #compare(z, z') -{ 0 }-> 2 :|: z' - 1 >= 0, z = 0
   #compare(z, z') -{ 0 }-> 2 :|: z - 1 >= 0, z' = 0
   #compare(z, z') -{ 0 }-> 2 :|: z' - 1 >= 0, z - 1 >= 0
   #compare(z, z') -{ 0 }-> 1 :|: z = 0, z' = 0
   #compare(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   #compare(z, z') -{ 0 }-> #compare(z - 1, z' - 1) :|: z' - 1 >= 0, z - 1 >= 0
   #compare(z, z') -{ 0 }-> #compare(z' - 1, z - 1) :|: z' - 1 >= 0, z - 1 >= 0
   #less(z, z') -{ 0 }-> 2 :|: z' - 1 >= 0, z = 0, 3 = 3
   #less(z, z') -{ 0 }-> 2 :|: z - 1 >= 0, z' = 0, 3 = 3
   #less(z, z') -{ 0 }-> 2 :|: z - 1 >= 0, z' - 1 >= 0, 3 = 3
   #less(z, z') -{ 0 }-> 1 :|: z = 0, z' = 0, 1 = 1
   #less(z, z') -{ 0 }-> 1 :|: z' - 1 >= 0, z = 0, 2 = 2
   #less(z, z') -{ 0 }-> 1 :|: z - 1 >= 0, z' = 0, 2 = 2
   #less(z, z') -{ 0 }-> 1 :|: z' - 1 >= 0, z - 1 >= 0, 2 = 2
   #less(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   #less(z, z') -{ 0 }-> 0 :|: z = 0, z' = 0, v0 >= 0, 1 = v0
   #less(z, z') -{ 0 }-> 0 :|: z' - 1 >= 0, z = 0, v0 >= 0, 2 = v0
   #less(z, z') -{ 0 }-> 0 :|: z' - 1 >= 0, z = 0, v0 >= 0, 3 = v0
   #less(z, z') -{ 0 }-> 0 :|: z - 1 >= 0, z' = 0, v0 >= 0, 3 = v0
   #less(z, z') -{ 0 }-> 0 :|: z - 1 >= 0, z' - 1 >= 0, v0 >= 0, 3 = v0
   #less(z, z') -{ 0 }-> 0 :|: z - 1 >= 0, z' = 0, v0 >= 0, 2 = v0
   #less(z, z') -{ 0 }-> 0 :|: z' - 1 >= 0, z - 1 >= 0, v0 >= 0, 2 = v0
   #less(z, z') -{ 0 }-> 0 :|: z' >= 0, z >= 0, v0 >= 0, 0 = v0
   #less(z, z') -{ 0 }-> #cklt(#compare(z - 1, z' - 1)) :|: z - 1 >= 0, z' - 1 >= 0
   #less(z, z') -{ 0 }-> #cklt(#compare(z' - 1, z - 1)) :|: z' - 1 >= 0, z - 1 >= 0
   APPEND(z, z') -{ 1 }-> 1 + APPEND#1(z, z') :|: z' >= 0, z >= 0
   APPEND#1(z, z') -{ 1 }-> 1 + APPEND(z1, z') :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z' >= 0
   FLATTEN(z) -{ 1 }-> 1 + FLATTEN#1(z) :|: z >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), flatten#1(z2))) + APPEND(flatten#1(z1), flatten#1(z2)) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), flatten#1(z2))) + APPEND(flatten#1(z1), flatten#1(z2)) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), flatten#1(z2))) + APPEND(flatten#1(z1), 0) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), flatten#1(z2))) + APPEND(flatten#1(z1), 0) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), flatten#1(z2))) + APPEND(0, flatten#1(z2)) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), flatten#1(z2))) + APPEND(0, flatten#1(z2)) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), flatten#1(z2))) + APPEND(0, 0) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), flatten#1(z2))) + APPEND(0, 0) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), 0)) + APPEND(flatten#1(z1), flatten#1(z2)) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), 0)) + APPEND(flatten#1(z1), flatten#1(z2)) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), 0)) + APPEND(flatten#1(z1), 0) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), 0)) + APPEND(flatten#1(z1), 0) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), 0)) + APPEND(0, flatten#1(z2)) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), 0)) + APPEND(0, flatten#1(z2)) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), 0)) + APPEND(0, 0) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), 0)) + APPEND(0, 0) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(0, flatten#1(z2))) + APPEND(flatten#1(z1), flatten#1(z2)) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(0, flatten#1(z2))) + APPEND(flatten#1(z1), flatten#1(z2)) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(0, flatten#1(z2))) + APPEND(flatten#1(z1), 0) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(0, flatten#1(z2))) + APPEND(flatten#1(z1), 0) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(0, flatten#1(z2))) + APPEND(0, flatten#1(z2)) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(0, flatten#1(z2))) + APPEND(0, flatten#1(z2)) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(0, flatten#1(z2))) + APPEND(0, 0) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(0, flatten#1(z2))) + APPEND(0, 0) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(0, 0)) + APPEND(flatten#1(z1), flatten#1(z2)) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(0, 0)) + APPEND(flatten#1(z1), flatten#1(z2)) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(0, 0)) + APPEND(flatten#1(z1), 0) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(0, 0)) + APPEND(flatten#1(z1), 0) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(0, 0)) + APPEND(0, flatten#1(z2)) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(0, 0)) + APPEND(0, flatten#1(z2)) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(0, 0)) + APPEND(0, 0) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(0, 0)) + APPEND(0, 0) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTENSORT(z) -{ 0 }-> 0 :|: z >= 0
   FLATTENSORT(z) -{ 0 }-> 1 + INSERTIONSORT(flatten#1(z)) :|: z >= 0
   FLATTENSORT(z) -{ 0 }-> 1 + INSERTIONSORT(0) :|: z >= 0
   INSERT(z, z') -{ 1 }-> 1 + INSERT#1(z', z) :|: z' >= 0, z >= 0
   INSERT#1(z, z') -{ 1 }-> 1 + INSERT#2(0, z', z0, z1) + #LESS(z0, z') :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z' >= 0
   INSERT#1(z, z') -{ 1 }-> 1 + INSERT#2(#cklt(#compare(z0, z')), z', z0, z1) + #LESS(z0, z') :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z' >= 0
   INSERT#2(z, z', z'', z3) -{ 1 }-> 1 + INSERT(z', z3) :|: z = 2, z'' >= 0, z' >= 0, z3 >= 0
   INSERTIONSORT(z) -{ 1 }-> 1 + INSERTIONSORT#1(z) :|: z >= 0
   INSERTIONSORT#1(z) -{ 1 }-> 1 + INSERT(z0, insertionsort#1(z1)) + INSERTIONSORT(z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   INSERTIONSORT#1(z) -{ 1 }-> 1 + INSERT(z0, 0) + INSERTIONSORT(z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   append(z, z') -{ 0 }-> append#1(z, z') :|: z' >= 0, z >= 0
   append(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   append#1(z, z') -{ 0 }-> z' :|: z' >= 0, z = 0
   append#1(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   append#1(z, z') -{ 0 }-> 1 + z0 + append(z1, z') :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z' >= 0
   flatten(z) -{ 0 }-> flatten#1(z) :|: z >= 0
   flatten(z) -{ 0 }-> 0 :|: z >= 0
   flatten#1(z) -{ 0 }-> append(z0, append(flatten#1(z1), flatten#1(z2))) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   flatten#1(z) -{ 0 }-> append(z0, append(flatten#1(z1), 0)) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   flatten#1(z) -{ 0 }-> append(z0, append(0, flatten#1(z2))) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   flatten#1(z) -{ 0 }-> append(z0, append(0, 0)) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   flatten#1(z) -{ 0 }-> 0 :|: z = 0
   flatten#1(z) -{ 0 }-> 0 :|: z >= 0
   insert(z, z') -{ 0 }-> insert#1(z', z) :|: z' >= 0, z >= 0
   insert(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   insert#1(z, z') -{ 0 }-> insert#2(0, z', z0, z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z' >= 0
   insert#1(z, z') -{ 0 }-> insert#2(#cklt(#compare(z0, z')), z', z0, z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z' >= 0
   insert#1(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   insert#1(z, z') -{ 0 }-> 1 + z' + 0 :|: z' >= 0, z = 0
   insert#2(z, z', z'', z3) -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0, z3 >= 0
   insert#2(z, z', z'', z3) -{ 0 }-> 1 + z' + (1 + z'' + z3) :|: z'' >= 0, z = 1, z' >= 0, z3 >= 0
   insert#2(z, z', z'', z3) -{ 0 }-> 1 + z'' + insert(z', z3) :|: z = 2, z'' >= 0, z' >= 0, z3 >= 0
   insertionsort(z) -{ 0 }-> insertionsort#1(z) :|: z >= 0
   insertionsort(z) -{ 0 }-> 0 :|: z >= 0
   insertionsort#1(z) -{ 0 }-> insert(z0, insertionsort#1(z1)) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   insertionsort#1(z) -{ 0 }-> insert(z0, 0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   insertionsort#1(z) -{ 0 }-> 0 :|: z = 0
   insertionsort#1(z) -{ 0 }-> 0 :|: z >= 0

Function symbols to be analyzed: {APPEND#1,APPEND}, {#cklt}, {#compare}, {#COMPARE}, {append#1,append}, {#less}, {insert#2,insert,insert#1}, {#LESS}, {flatten#1}, {insertionsort#1}, {INSERT#1,INSERT#2,INSERT}, {flatten}, {FLATTEN,FLATTEN#1}, {insertionsort}, {INSERTIONSORT,INSERTIONSORT#1}, {FLATTENSORT}

----------------------------------------

(37) IntTrsBoundProof (UPPER BOUND(ID))

Computed SIZE bound using CoFloCo for: APPEND#1
after applying outer abstraction to obtain an ITS,
resulting in: O(1) with polynomial bound: 0

Computed SIZE bound using CoFloCo for: APPEND
after applying outer abstraction to obtain an ITS,
resulting in: O(1) with polynomial bound: 1

----------------------------------------

(38)
Obligation:
Complexity RNTS consisting of the following rules:

   #COMPARE(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   #COMPARE(z, z') -{ 0 }-> 1 + #COMPARE(z - 1, z' - 1) :|: z' - 1 >= 0, z - 1 >= 0
   #COMPARE(z, z') -{ 0 }-> 1 + #COMPARE(z' - 1, z - 1) :|: z' - 1 >= 0, z - 1 >= 0
   #LESS(z, z') -{ 1 }-> 1 + #COMPARE(z, z') :|: z' >= 0, z >= 0
   #cklt(z) -{ 0 }-> 2 :|: z = 3
   #cklt(z) -{ 0 }-> 1 :|: z = 1
   #cklt(z) -{ 0 }-> 1 :|: z = 2
   #cklt(z) -{ 0 }-> 0 :|: z >= 0
   #compare(z, z') -{ 0 }-> 3 :|: z' - 1 >= 0, z = 0
   #compare(z, z') -{ 0 }-> 3 :|: z - 1 >= 0, z' = 0
   #compare(z, z') -{ 0 }-> 3 :|: z' - 1 >= 0, z - 1 >= 0
   #compare(z, z') -{ 0 }-> 2 :|: z' - 1 >= 0, z = 0
   #compare(z, z') -{ 0 }-> 2 :|: z - 1 >= 0, z' = 0
   #compare(z, z') -{ 0 }-> 2 :|: z' - 1 >= 0, z - 1 >= 0
   #compare(z, z') -{ 0 }-> 1 :|: z = 0, z' = 0
   #compare(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   #compare(z, z') -{ 0 }-> #compare(z - 1, z' - 1) :|: z' - 1 >= 0, z - 1 >= 0
   #compare(z, z') -{ 0 }-> #compare(z' - 1, z - 1) :|: z' - 1 >= 0, z - 1 >= 0
   #less(z, z') -{ 0 }-> 2 :|: z' - 1 >= 0, z = 0, 3 = 3
   #less(z, z') -{ 0 }-> 2 :|: z - 1 >= 0, z' = 0, 3 = 3
   #less(z, z') -{ 0 }-> 2 :|: z - 1 >= 0, z' - 1 >= 0, 3 = 3
   #less(z, z') -{ 0 }-> 1 :|: z = 0, z' = 0, 1 = 1
   #less(z, z') -{ 0 }-> 1 :|: z' - 1 >= 0, z = 0, 2 = 2
   #less(z, z') -{ 0 }-> 1 :|: z - 1 >= 0, z' = 0, 2 = 2
   #less(z, z') -{ 0 }-> 1 :|: z' - 1 >= 0, z - 1 >= 0, 2 = 2
   #less(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   #less(z, z') -{ 0 }-> 0 :|: z = 0, z' = 0, v0 >= 0, 1 = v0
   #less(z, z') -{ 0 }-> 0 :|: z' - 1 >= 0, z = 0, v0 >= 0, 2 = v0
   #less(z, z') -{ 0 }-> 0 :|: z' - 1 >= 0, z = 0, v0 >= 0, 3 = v0
   #less(z, z') -{ 0 }-> 0 :|: z - 1 >= 0, z' = 0, v0 >= 0, 3 = v0
   #less(z, z') -{ 0 }-> 0 :|: z - 1 >= 0, z' - 1 >= 0, v0 >= 0, 3 = v0
   #less(z, z') -{ 0 }-> 0 :|: z - 1 >= 0, z' = 0, v0 >= 0, 2 = v0
   #less(z, z') -{ 0 }-> 0 :|: z' - 1 >= 0, z - 1 >= 0, v0 >= 0, 2 = v0
   #less(z, z') -{ 0 }-> 0 :|: z' >= 0, z >= 0, v0 >= 0, 0 = v0
   #less(z, z') -{ 0 }-> #cklt(#compare(z - 1, z' - 1)) :|: z - 1 >= 0, z' - 1 >= 0
   #less(z, z') -{ 0 }-> #cklt(#compare(z' - 1, z - 1)) :|: z' - 1 >= 0, z - 1 >= 0
   APPEND(z, z') -{ 1 }-> 1 + APPEND#1(z, z') :|: z' >= 0, z >= 0
   APPEND#1(z, z') -{ 1 }-> 1 + APPEND(z1, z') :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z' >= 0
   FLATTEN(z) -{ 1 }-> 1 + FLATTEN#1(z) :|: z >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), flatten#1(z2))) + APPEND(flatten#1(z1), flatten#1(z2)) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), flatten#1(z2))) + APPEND(flatten#1(z1), flatten#1(z2)) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), flatten#1(z2))) + APPEND(flatten#1(z1), 0) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), flatten#1(z2))) + APPEND(flatten#1(z1), 0) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), flatten#1(z2))) + APPEND(0, flatten#1(z2)) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), flatten#1(z2))) + APPEND(0, flatten#1(z2)) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), flatten#1(z2))) + APPEND(0, 0) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), flatten#1(z2))) + APPEND(0, 0) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), 0)) + APPEND(flatten#1(z1), flatten#1(z2)) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), 0)) + APPEND(flatten#1(z1), flatten#1(z2)) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), 0)) + APPEND(flatten#1(z1), 0) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), 0)) + APPEND(flatten#1(z1), 0) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), 0)) + APPEND(0, flatten#1(z2)) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), 0)) + APPEND(0, flatten#1(z2)) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), 0)) + APPEND(0, 0) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), 0)) + APPEND(0, 0) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(0, flatten#1(z2))) + APPEND(flatten#1(z1), flatten#1(z2)) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(0, flatten#1(z2))) + APPEND(flatten#1(z1), flatten#1(z2)) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(0, flatten#1(z2))) + APPEND(flatten#1(z1), 0) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(0, flatten#1(z2))) + APPEND(flatten#1(z1), 0) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(0, flatten#1(z2))) + APPEND(0, flatten#1(z2)) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(0, flatten#1(z2))) + APPEND(0, flatten#1(z2)) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(0, flatten#1(z2))) + APPEND(0, 0) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(0, flatten#1(z2))) + APPEND(0, 0) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(0, 0)) + APPEND(flatten#1(z1), flatten#1(z2)) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(0, 0)) + APPEND(flatten#1(z1), flatten#1(z2)) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(0, 0)) + APPEND(flatten#1(z1), 0) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(0, 0)) + APPEND(flatten#1(z1), 0) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(0, 0)) + APPEND(0, flatten#1(z2)) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(0, 0)) + APPEND(0, flatten#1(z2)) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(0, 0)) + APPEND(0, 0) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(0, 0)) + APPEND(0, 0) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTENSORT(z) -{ 0 }-> 0 :|: z >= 0
   FLATTENSORT(z) -{ 0 }-> 1 + INSERTIONSORT(flatten#1(z)) :|: z >= 0
   FLATTENSORT(z) -{ 0 }-> 1 + INSERTIONSORT(0) :|: z >= 0
   INSERT(z, z') -{ 1 }-> 1 + INSERT#1(z', z) :|: z' >= 0, z >= 0
   INSERT#1(z, z') -{ 1 }-> 1 + INSERT#2(0, z', z0, z1) + #LESS(z0, z') :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z' >= 0
   INSERT#1(z, z') -{ 1 }-> 1 + INSERT#2(#cklt(#compare(z0, z')), z', z0, z1) + #LESS(z0, z') :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z' >= 0
   INSERT#2(z, z', z'', z3) -{ 1 }-> 1 + INSERT(z', z3) :|: z = 2, z'' >= 0, z' >= 0, z3 >= 0
   INSERTIONSORT(z) -{ 1 }-> 1 + INSERTIONSORT#1(z) :|: z >= 0
   INSERTIONSORT#1(z) -{ 1 }-> 1 + INSERT(z0, insertionsort#1(z1)) + INSERTIONSORT(z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   INSERTIONSORT#1(z) -{ 1 }-> 1 + INSERT(z0, 0) + INSERTIONSORT(z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   append(z, z') -{ 0 }-> append#1(z, z') :|: z' >= 0, z >= 0
   append(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   append#1(z, z') -{ 0 }-> z' :|: z' >= 0, z = 0
   append#1(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   append#1(z, z') -{ 0 }-> 1 + z0 + append(z1, z') :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z' >= 0
   flatten(z) -{ 0 }-> flatten#1(z) :|: z >= 0
   flatten(z) -{ 0 }-> 0 :|: z >= 0
   flatten#1(z) -{ 0 }-> append(z0, append(flatten#1(z1), flatten#1(z2))) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   flatten#1(z) -{ 0 }-> append(z0, append(flatten#1(z1), 0)) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   flatten#1(z) -{ 0 }-> append(z0, append(0, flatten#1(z2))) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   flatten#1(z) -{ 0 }-> append(z0, append(0, 0)) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   flatten#1(z) -{ 0 }-> 0 :|: z = 0
   flatten#1(z) -{ 0 }-> 0 :|: z >= 0
   insert(z, z') -{ 0 }-> insert#1(z', z) :|: z' >= 0, z >= 0
   insert(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   insert#1(z, z') -{ 0 }-> insert#2(0, z', z0, z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z' >= 0
   insert#1(z, z') -{ 0 }-> insert#2(#cklt(#compare(z0, z')), z', z0, z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z' >= 0
   insert#1(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   insert#1(z, z') -{ 0 }-> 1 + z' + 0 :|: z' >= 0, z = 0
   insert#2(z, z', z'', z3) -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0, z3 >= 0
   insert#2(z, z', z'', z3) -{ 0 }-> 1 + z' + (1 + z'' + z3) :|: z'' >= 0, z = 1, z' >= 0, z3 >= 0
   insert#2(z, z', z'', z3) -{ 0 }-> 1 + z'' + insert(z', z3) :|: z = 2, z'' >= 0, z' >= 0, z3 >= 0
   insertionsort(z) -{ 0 }-> insertionsort#1(z) :|: z >= 0
   insertionsort(z) -{ 0 }-> 0 :|: z >= 0
   insertionsort#1(z) -{ 0 }-> insert(z0, insertionsort#1(z1)) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   insertionsort#1(z) -{ 0 }-> insert(z0, 0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   insertionsort#1(z) -{ 0 }-> 0 :|: z = 0
   insertionsort#1(z) -{ 0 }-> 0 :|: z >= 0

Function symbols to be analyzed: {APPEND#1,APPEND}, {#cklt}, {#compare}, {#COMPARE}, {append#1,append}, {#less}, {insert#2,insert,insert#1}, {#LESS}, {flatten#1}, {insertionsort#1}, {INSERT#1,INSERT#2,INSERT}, {flatten}, {FLATTEN,FLATTEN#1}, {insertionsort}, {INSERTIONSORT,INSERTIONSORT#1}, {FLATTENSORT}
Previous analysis results are:
  APPEND#1: runtime: ?, size: O(1) [0]
  APPEND: runtime: ?, size: O(1) [1]

----------------------------------------

(39) IntTrsBoundProof (UPPER BOUND(ID))

Computed RUNTIME bound using KoAT for: APPEND#1
after applying outer abstraction to obtain an ITS,
resulting in: O(n^1) with polynomial bound: 4*z

Computed RUNTIME bound using CoFloCo for: APPEND
after applying outer abstraction to obtain an ITS,
resulting in: O(n^1) with polynomial bound: 1 + 4*z

----------------------------------------

(40)
Obligation:
Complexity RNTS consisting of the following rules:

   #COMPARE(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   #COMPARE(z, z') -{ 0 }-> 1 + #COMPARE(z - 1, z' - 1) :|: z' - 1 >= 0, z - 1 >= 0
   #COMPARE(z, z') -{ 0 }-> 1 + #COMPARE(z' - 1, z - 1) :|: z' - 1 >= 0, z - 1 >= 0
   #LESS(z, z') -{ 1 }-> 1 + #COMPARE(z, z') :|: z' >= 0, z >= 0
   #cklt(z) -{ 0 }-> 2 :|: z = 3
   #cklt(z) -{ 0 }-> 1 :|: z = 1
   #cklt(z) -{ 0 }-> 1 :|: z = 2
   #cklt(z) -{ 0 }-> 0 :|: z >= 0
   #compare(z, z') -{ 0 }-> 3 :|: z' - 1 >= 0, z = 0
   #compare(z, z') -{ 0 }-> 3 :|: z - 1 >= 0, z' = 0
   #compare(z, z') -{ 0 }-> 3 :|: z' - 1 >= 0, z - 1 >= 0
   #compare(z, z') -{ 0 }-> 2 :|: z' - 1 >= 0, z = 0
   #compare(z, z') -{ 0 }-> 2 :|: z - 1 >= 0, z' = 0
   #compare(z, z') -{ 0 }-> 2 :|: z' - 1 >= 0, z - 1 >= 0
   #compare(z, z') -{ 0 }-> 1 :|: z = 0, z' = 0
   #compare(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   #compare(z, z') -{ 0 }-> #compare(z - 1, z' - 1) :|: z' - 1 >= 0, z - 1 >= 0
   #compare(z, z') -{ 0 }-> #compare(z' - 1, z - 1) :|: z' - 1 >= 0, z - 1 >= 0
   #less(z, z') -{ 0 }-> 2 :|: z' - 1 >= 0, z = 0, 3 = 3
   #less(z, z') -{ 0 }-> 2 :|: z - 1 >= 0, z' = 0, 3 = 3
   #less(z, z') -{ 0 }-> 2 :|: z - 1 >= 0, z' - 1 >= 0, 3 = 3
   #less(z, z') -{ 0 }-> 1 :|: z = 0, z' = 0, 1 = 1
   #less(z, z') -{ 0 }-> 1 :|: z' - 1 >= 0, z = 0, 2 = 2
   #less(z, z') -{ 0 }-> 1 :|: z - 1 >= 0, z' = 0, 2 = 2
   #less(z, z') -{ 0 }-> 1 :|: z' - 1 >= 0, z - 1 >= 0, 2 = 2
   #less(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   #less(z, z') -{ 0 }-> 0 :|: z = 0, z' = 0, v0 >= 0, 1 = v0
   #less(z, z') -{ 0 }-> 0 :|: z' - 1 >= 0, z = 0, v0 >= 0, 2 = v0
   #less(z, z') -{ 0 }-> 0 :|: z' - 1 >= 0, z = 0, v0 >= 0, 3 = v0
   #less(z, z') -{ 0 }-> 0 :|: z - 1 >= 0, z' = 0, v0 >= 0, 3 = v0
   #less(z, z') -{ 0 }-> 0 :|: z - 1 >= 0, z' - 1 >= 0, v0 >= 0, 3 = v0
   #less(z, z') -{ 0 }-> 0 :|: z - 1 >= 0, z' = 0, v0 >= 0, 2 = v0
   #less(z, z') -{ 0 }-> 0 :|: z' - 1 >= 0, z - 1 >= 0, v0 >= 0, 2 = v0
   #less(z, z') -{ 0 }-> 0 :|: z' >= 0, z >= 0, v0 >= 0, 0 = v0
   #less(z, z') -{ 0 }-> #cklt(#compare(z - 1, z' - 1)) :|: z - 1 >= 0, z' - 1 >= 0
   #less(z, z') -{ 0 }-> #cklt(#compare(z' - 1, z - 1)) :|: z' - 1 >= 0, z - 1 >= 0
   APPEND(z, z') -{ 1 }-> 1 + APPEND#1(z, z') :|: z' >= 0, z >= 0
   APPEND#1(z, z') -{ 1 }-> 1 + APPEND(z1, z') :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z' >= 0
   FLATTEN(z) -{ 1 }-> 1 + FLATTEN#1(z) :|: z >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), flatten#1(z2))) + APPEND(flatten#1(z1), flatten#1(z2)) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), flatten#1(z2))) + APPEND(flatten#1(z1), flatten#1(z2)) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), flatten#1(z2))) + APPEND(flatten#1(z1), 0) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), flatten#1(z2))) + APPEND(flatten#1(z1), 0) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), flatten#1(z2))) + APPEND(0, flatten#1(z2)) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), flatten#1(z2))) + APPEND(0, flatten#1(z2)) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), flatten#1(z2))) + APPEND(0, 0) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), flatten#1(z2))) + APPEND(0, 0) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), 0)) + APPEND(flatten#1(z1), flatten#1(z2)) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), 0)) + APPEND(flatten#1(z1), flatten#1(z2)) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), 0)) + APPEND(flatten#1(z1), 0) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), 0)) + APPEND(flatten#1(z1), 0) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), 0)) + APPEND(0, flatten#1(z2)) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), 0)) + APPEND(0, flatten#1(z2)) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), 0)) + APPEND(0, 0) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), 0)) + APPEND(0, 0) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(0, flatten#1(z2))) + APPEND(flatten#1(z1), flatten#1(z2)) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(0, flatten#1(z2))) + APPEND(flatten#1(z1), flatten#1(z2)) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(0, flatten#1(z2))) + APPEND(flatten#1(z1), 0) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(0, flatten#1(z2))) + APPEND(flatten#1(z1), 0) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(0, flatten#1(z2))) + APPEND(0, flatten#1(z2)) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(0, flatten#1(z2))) + APPEND(0, flatten#1(z2)) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(0, flatten#1(z2))) + APPEND(0, 0) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(0, flatten#1(z2))) + APPEND(0, 0) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(0, 0)) + APPEND(flatten#1(z1), flatten#1(z2)) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(0, 0)) + APPEND(flatten#1(z1), flatten#1(z2)) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(0, 0)) + APPEND(flatten#1(z1), 0) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(0, 0)) + APPEND(flatten#1(z1), 0) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(0, 0)) + APPEND(0, flatten#1(z2)) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(0, 0)) + APPEND(0, flatten#1(z2)) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(0, 0)) + APPEND(0, 0) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(0, 0)) + APPEND(0, 0) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTENSORT(z) -{ 0 }-> 0 :|: z >= 0
   FLATTENSORT(z) -{ 0 }-> 1 + INSERTIONSORT(flatten#1(z)) :|: z >= 0
   FLATTENSORT(z) -{ 0 }-> 1 + INSERTIONSORT(0) :|: z >= 0
   INSERT(z, z') -{ 1 }-> 1 + INSERT#1(z', z) :|: z' >= 0, z >= 0
   INSERT#1(z, z') -{ 1 }-> 1 + INSERT#2(0, z', z0, z1) + #LESS(z0, z') :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z' >= 0
   INSERT#1(z, z') -{ 1 }-> 1 + INSERT#2(#cklt(#compare(z0, z')), z', z0, z1) + #LESS(z0, z') :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z' >= 0
   INSERT#2(z, z', z'', z3) -{ 1 }-> 1 + INSERT(z', z3) :|: z = 2, z'' >= 0, z' >= 0, z3 >= 0
   INSERTIONSORT(z) -{ 1 }-> 1 + INSERTIONSORT#1(z) :|: z >= 0
   INSERTIONSORT#1(z) -{ 1 }-> 1 + INSERT(z0, insertionsort#1(z1)) + INSERTIONSORT(z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   INSERTIONSORT#1(z) -{ 1 }-> 1 + INSERT(z0, 0) + INSERTIONSORT(z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   append(z, z') -{ 0 }-> append#1(z, z') :|: z' >= 0, z >= 0
   append(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   append#1(z, z') -{ 0 }-> z' :|: z' >= 0, z = 0
   append#1(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   append#1(z, z') -{ 0 }-> 1 + z0 + append(z1, z') :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z' >= 0
   flatten(z) -{ 0 }-> flatten#1(z) :|: z >= 0
   flatten(z) -{ 0 }-> 0 :|: z >= 0
   flatten#1(z) -{ 0 }-> append(z0, append(flatten#1(z1), flatten#1(z2))) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   flatten#1(z) -{ 0 }-> append(z0, append(flatten#1(z1), 0)) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   flatten#1(z) -{ 0 }-> append(z0, append(0, flatten#1(z2))) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   flatten#1(z) -{ 0 }-> append(z0, append(0, 0)) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   flatten#1(z) -{ 0 }-> 0 :|: z = 0
   flatten#1(z) -{ 0 }-> 0 :|: z >= 0
   insert(z, z') -{ 0 }-> insert#1(z', z) :|: z' >= 0, z >= 0
   insert(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   insert#1(z, z') -{ 0 }-> insert#2(0, z', z0, z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z' >= 0
   insert#1(z, z') -{ 0 }-> insert#2(#cklt(#compare(z0, z')), z', z0, z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z' >= 0
   insert#1(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   insert#1(z, z') -{ 0 }-> 1 + z' + 0 :|: z' >= 0, z = 0
   insert#2(z, z', z'', z3) -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0, z3 >= 0
   insert#2(z, z', z'', z3) -{ 0 }-> 1 + z' + (1 + z'' + z3) :|: z'' >= 0, z = 1, z' >= 0, z3 >= 0
   insert#2(z, z', z'', z3) -{ 0 }-> 1 + z'' + insert(z', z3) :|: z = 2, z'' >= 0, z' >= 0, z3 >= 0
   insertionsort(z) -{ 0 }-> insertionsort#1(z) :|: z >= 0
   insertionsort(z) -{ 0 }-> 0 :|: z >= 0
   insertionsort#1(z) -{ 0 }-> insert(z0, insertionsort#1(z1)) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   insertionsort#1(z) -{ 0 }-> insert(z0, 0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   insertionsort#1(z) -{ 0 }-> 0 :|: z = 0
   insertionsort#1(z) -{ 0 }-> 0 :|: z >= 0

Function symbols to be analyzed: {#cklt}, {#compare}, {#COMPARE}, {append#1,append}, {#less}, {insert#2,insert,insert#1}, {#LESS}, {flatten#1}, {insertionsort#1}, {INSERT#1,INSERT#2,INSERT}, {flatten}, {FLATTEN,FLATTEN#1}, {insertionsort}, {INSERTIONSORT,INSERTIONSORT#1}, {FLATTENSORT}
Previous analysis results are:
  APPEND#1: runtime: O(n^1) [4*z], size: O(1) [0]
  APPEND: runtime: O(n^1) [1 + 4*z], size: O(1) [1]

----------------------------------------

(41) ResultPropagationProof (UPPER BOUND(ID))
Applied inner abstraction using the recently inferred runtime/size bounds where possible.
----------------------------------------

(42)
Obligation:
Complexity RNTS consisting of the following rules:

   #COMPARE(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   #COMPARE(z, z') -{ 0 }-> 1 + #COMPARE(z - 1, z' - 1) :|: z' - 1 >= 0, z - 1 >= 0
   #COMPARE(z, z') -{ 0 }-> 1 + #COMPARE(z' - 1, z - 1) :|: z' - 1 >= 0, z - 1 >= 0
   #LESS(z, z') -{ 1 }-> 1 + #COMPARE(z, z') :|: z' >= 0, z >= 0
   #cklt(z) -{ 0 }-> 2 :|: z = 3
   #cklt(z) -{ 0 }-> 1 :|: z = 1
   #cklt(z) -{ 0 }-> 1 :|: z = 2
   #cklt(z) -{ 0 }-> 0 :|: z >= 0
   #compare(z, z') -{ 0 }-> 3 :|: z' - 1 >= 0, z = 0
   #compare(z, z') -{ 0 }-> 3 :|: z - 1 >= 0, z' = 0
   #compare(z, z') -{ 0 }-> 3 :|: z' - 1 >= 0, z - 1 >= 0
   #compare(z, z') -{ 0 }-> 2 :|: z' - 1 >= 0, z = 0
   #compare(z, z') -{ 0 }-> 2 :|: z - 1 >= 0, z' = 0
   #compare(z, z') -{ 0 }-> 2 :|: z' - 1 >= 0, z - 1 >= 0
   #compare(z, z') -{ 0 }-> 1 :|: z = 0, z' = 0
   #compare(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   #compare(z, z') -{ 0 }-> #compare(z - 1, z' - 1) :|: z' - 1 >= 0, z - 1 >= 0
   #compare(z, z') -{ 0 }-> #compare(z' - 1, z - 1) :|: z' - 1 >= 0, z - 1 >= 0
   #less(z, z') -{ 0 }-> 2 :|: z' - 1 >= 0, z = 0, 3 = 3
   #less(z, z') -{ 0 }-> 2 :|: z - 1 >= 0, z' = 0, 3 = 3
   #less(z, z') -{ 0 }-> 2 :|: z - 1 >= 0, z' - 1 >= 0, 3 = 3
   #less(z, z') -{ 0 }-> 1 :|: z = 0, z' = 0, 1 = 1
   #less(z, z') -{ 0 }-> 1 :|: z' - 1 >= 0, z = 0, 2 = 2
   #less(z, z') -{ 0 }-> 1 :|: z - 1 >= 0, z' = 0, 2 = 2
   #less(z, z') -{ 0 }-> 1 :|: z' - 1 >= 0, z - 1 >= 0, 2 = 2
   #less(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   #less(z, z') -{ 0 }-> 0 :|: z = 0, z' = 0, v0 >= 0, 1 = v0
   #less(z, z') -{ 0 }-> 0 :|: z' - 1 >= 0, z = 0, v0 >= 0, 2 = v0
   #less(z, z') -{ 0 }-> 0 :|: z' - 1 >= 0, z = 0, v0 >= 0, 3 = v0
   #less(z, z') -{ 0 }-> 0 :|: z - 1 >= 0, z' = 0, v0 >= 0, 3 = v0
   #less(z, z') -{ 0 }-> 0 :|: z - 1 >= 0, z' - 1 >= 0, v0 >= 0, 3 = v0
   #less(z, z') -{ 0 }-> 0 :|: z - 1 >= 0, z' = 0, v0 >= 0, 2 = v0
   #less(z, z') -{ 0 }-> 0 :|: z' - 1 >= 0, z - 1 >= 0, v0 >= 0, 2 = v0
   #less(z, z') -{ 0 }-> 0 :|: z' >= 0, z >= 0, v0 >= 0, 0 = v0
   #less(z, z') -{ 0 }-> #cklt(#compare(z - 1, z' - 1)) :|: z - 1 >= 0, z' - 1 >= 0
   #less(z, z') -{ 0 }-> #cklt(#compare(z' - 1, z - 1)) :|: z' - 1 >= 0, z - 1 >= 0
   APPEND(z, z') -{ 1 + 4*z }-> 1 + s :|: s >= 0, s <= 0, z' >= 0, z >= 0
   APPEND#1(z, z') -{ 2 + 4*z1 }-> 1 + s' :|: s' >= 0, s' <= 1, z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z' >= 0
   FLATTEN(z) -{ 1 }-> 1 + FLATTEN#1(z) :|: z >= 0
   FLATTEN#1(z) -{ 2 }-> 1 + APPEND(z0, append(flatten#1(z1), flatten#1(z2))) + s'' + FLATTEN(z1) :|: s'' >= 0, s'' <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 2 }-> 1 + APPEND(z0, append(flatten#1(z1), flatten#1(z2))) + s4 + FLATTEN(z2) :|: s4 >= 0, s4 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), flatten#1(z2))) + APPEND(flatten#1(z1), flatten#1(z2)) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), flatten#1(z2))) + APPEND(flatten#1(z1), flatten#1(z2)) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), flatten#1(z2))) + APPEND(flatten#1(z1), 0) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), flatten#1(z2))) + APPEND(flatten#1(z1), 0) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), flatten#1(z2))) + APPEND(0, flatten#1(z2)) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), flatten#1(z2))) + APPEND(0, flatten#1(z2)) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 2 }-> 1 + APPEND(z0, append(flatten#1(z1), 0)) + s1 + FLATTEN(z1) :|: s1 >= 0, s1 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 2 }-> 1 + APPEND(z0, append(flatten#1(z1), 0)) + s5 + FLATTEN(z2) :|: s5 >= 0, s5 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), 0)) + APPEND(flatten#1(z1), flatten#1(z2)) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), 0)) + APPEND(flatten#1(z1), flatten#1(z2)) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), 0)) + APPEND(flatten#1(z1), 0) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), 0)) + APPEND(flatten#1(z1), 0) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), 0)) + APPEND(0, flatten#1(z2)) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), 0)) + APPEND(0, flatten#1(z2)) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 2 }-> 1 + APPEND(z0, append(0, flatten#1(z2))) + s2 + FLATTEN(z1) :|: s2 >= 0, s2 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 2 }-> 1 + APPEND(z0, append(0, flatten#1(z2))) + s6 + FLATTEN(z2) :|: s6 >= 0, s6 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(0, flatten#1(z2))) + APPEND(flatten#1(z1), flatten#1(z2)) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(0, flatten#1(z2))) + APPEND(flatten#1(z1), flatten#1(z2)) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(0, flatten#1(z2))) + APPEND(flatten#1(z1), 0) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(0, flatten#1(z2))) + APPEND(flatten#1(z1), 0) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(0, flatten#1(z2))) + APPEND(0, flatten#1(z2)) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(0, flatten#1(z2))) + APPEND(0, flatten#1(z2)) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 2 }-> 1 + APPEND(z0, append(0, 0)) + s3 + FLATTEN(z1) :|: s3 >= 0, s3 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 2 }-> 1 + APPEND(z0, append(0, 0)) + s7 + FLATTEN(z2) :|: s7 >= 0, s7 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(0, 0)) + APPEND(flatten#1(z1), flatten#1(z2)) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(0, 0)) + APPEND(flatten#1(z1), flatten#1(z2)) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(0, 0)) + APPEND(flatten#1(z1), 0) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(0, 0)) + APPEND(flatten#1(z1), 0) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(0, 0)) + APPEND(0, flatten#1(z2)) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(0, 0)) + APPEND(0, flatten#1(z2)) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTENSORT(z) -{ 0 }-> 0 :|: z >= 0
   FLATTENSORT(z) -{ 0 }-> 1 + INSERTIONSORT(flatten#1(z)) :|: z >= 0
   FLATTENSORT(z) -{ 0 }-> 1 + INSERTIONSORT(0) :|: z >= 0
   INSERT(z, z') -{ 1 }-> 1 + INSERT#1(z', z) :|: z' >= 0, z >= 0
   INSERT#1(z, z') -{ 1 }-> 1 + INSERT#2(0, z', z0, z1) + #LESS(z0, z') :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z' >= 0
   INSERT#1(z, z') -{ 1 }-> 1 + INSERT#2(#cklt(#compare(z0, z')), z', z0, z1) + #LESS(z0, z') :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z' >= 0
   INSERT#2(z, z', z'', z3) -{ 1 }-> 1 + INSERT(z', z3) :|: z = 2, z'' >= 0, z' >= 0, z3 >= 0
   INSERTIONSORT(z) -{ 1 }-> 1 + INSERTIONSORT#1(z) :|: z >= 0
   INSERTIONSORT#1(z) -{ 1 }-> 1 + INSERT(z0, insertionsort#1(z1)) + INSERTIONSORT(z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   INSERTIONSORT#1(z) -{ 1 }-> 1 + INSERT(z0, 0) + INSERTIONSORT(z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   append(z, z') -{ 0 }-> append#1(z, z') :|: z' >= 0, z >= 0
   append(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   append#1(z, z') -{ 0 }-> z' :|: z' >= 0, z = 0
   append#1(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   append#1(z, z') -{ 0 }-> 1 + z0 + append(z1, z') :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z' >= 0
   flatten(z) -{ 0 }-> flatten#1(z) :|: z >= 0
   flatten(z) -{ 0 }-> 0 :|: z >= 0
   flatten#1(z) -{ 0 }-> append(z0, append(flatten#1(z1), flatten#1(z2))) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   flatten#1(z) -{ 0 }-> append(z0, append(flatten#1(z1), 0)) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   flatten#1(z) -{ 0 }-> append(z0, append(0, flatten#1(z2))) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   flatten#1(z) -{ 0 }-> append(z0, append(0, 0)) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   flatten#1(z) -{ 0 }-> 0 :|: z = 0
   flatten#1(z) -{ 0 }-> 0 :|: z >= 0
   insert(z, z') -{ 0 }-> insert#1(z', z) :|: z' >= 0, z >= 0
   insert(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   insert#1(z, z') -{ 0 }-> insert#2(0, z', z0, z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z' >= 0
   insert#1(z, z') -{ 0 }-> insert#2(#cklt(#compare(z0, z')), z', z0, z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z' >= 0
   insert#1(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   insert#1(z, z') -{ 0 }-> 1 + z' + 0 :|: z' >= 0, z = 0
   insert#2(z, z', z'', z3) -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0, z3 >= 0
   insert#2(z, z', z'', z3) -{ 0 }-> 1 + z' + (1 + z'' + z3) :|: z'' >= 0, z = 1, z' >= 0, z3 >= 0
   insert#2(z, z', z'', z3) -{ 0 }-> 1 + z'' + insert(z', z3) :|: z = 2, z'' >= 0, z' >= 0, z3 >= 0
   insertionsort(z) -{ 0 }-> insertionsort#1(z) :|: z >= 0
   insertionsort(z) -{ 0 }-> 0 :|: z >= 0
   insertionsort#1(z) -{ 0 }-> insert(z0, insertionsort#1(z1)) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   insertionsort#1(z) -{ 0 }-> insert(z0, 0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   insertionsort#1(z) -{ 0 }-> 0 :|: z = 0
   insertionsort#1(z) -{ 0 }-> 0 :|: z >= 0

Function symbols to be analyzed: {#cklt}, {#compare}, {#COMPARE}, {append#1,append}, {#less}, {insert#2,insert,insert#1}, {#LESS}, {flatten#1}, {insertionsort#1}, {INSERT#1,INSERT#2,INSERT}, {flatten}, {FLATTEN,FLATTEN#1}, {insertionsort}, {INSERTIONSORT,INSERTIONSORT#1}, {FLATTENSORT}
Previous analysis results are:
  APPEND#1: runtime: O(n^1) [4*z], size: O(1) [0]
  APPEND: runtime: O(n^1) [1 + 4*z], size: O(1) [1]

----------------------------------------

(43) IntTrsBoundProof (UPPER BOUND(ID))

Computed SIZE bound using CoFloCo for: #cklt
after applying outer abstraction to obtain an ITS,
resulting in: O(1) with polynomial bound: 2

----------------------------------------

(44)
Obligation:
Complexity RNTS consisting of the following rules:

   #COMPARE(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   #COMPARE(z, z') -{ 0 }-> 1 + #COMPARE(z - 1, z' - 1) :|: z' - 1 >= 0, z - 1 >= 0
   #COMPARE(z, z') -{ 0 }-> 1 + #COMPARE(z' - 1, z - 1) :|: z' - 1 >= 0, z - 1 >= 0
   #LESS(z, z') -{ 1 }-> 1 + #COMPARE(z, z') :|: z' >= 0, z >= 0
   #cklt(z) -{ 0 }-> 2 :|: z = 3
   #cklt(z) -{ 0 }-> 1 :|: z = 1
   #cklt(z) -{ 0 }-> 1 :|: z = 2
   #cklt(z) -{ 0 }-> 0 :|: z >= 0
   #compare(z, z') -{ 0 }-> 3 :|: z' - 1 >= 0, z = 0
   #compare(z, z') -{ 0 }-> 3 :|: z - 1 >= 0, z' = 0
   #compare(z, z') -{ 0 }-> 3 :|: z' - 1 >= 0, z - 1 >= 0
   #compare(z, z') -{ 0 }-> 2 :|: z' - 1 >= 0, z = 0
   #compare(z, z') -{ 0 }-> 2 :|: z - 1 >= 0, z' = 0
   #compare(z, z') -{ 0 }-> 2 :|: z' - 1 >= 0, z - 1 >= 0
   #compare(z, z') -{ 0 }-> 1 :|: z = 0, z' = 0
   #compare(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   #compare(z, z') -{ 0 }-> #compare(z - 1, z' - 1) :|: z' - 1 >= 0, z - 1 >= 0
   #compare(z, z') -{ 0 }-> #compare(z' - 1, z - 1) :|: z' - 1 >= 0, z - 1 >= 0
   #less(z, z') -{ 0 }-> 2 :|: z' - 1 >= 0, z = 0, 3 = 3
   #less(z, z') -{ 0 }-> 2 :|: z - 1 >= 0, z' = 0, 3 = 3
   #less(z, z') -{ 0 }-> 2 :|: z - 1 >= 0, z' - 1 >= 0, 3 = 3
   #less(z, z') -{ 0 }-> 1 :|: z = 0, z' = 0, 1 = 1
   #less(z, z') -{ 0 }-> 1 :|: z' - 1 >= 0, z = 0, 2 = 2
   #less(z, z') -{ 0 }-> 1 :|: z - 1 >= 0, z' = 0, 2 = 2
   #less(z, z') -{ 0 }-> 1 :|: z' - 1 >= 0, z - 1 >= 0, 2 = 2
   #less(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   #less(z, z') -{ 0 }-> 0 :|: z = 0, z' = 0, v0 >= 0, 1 = v0
   #less(z, z') -{ 0 }-> 0 :|: z' - 1 >= 0, z = 0, v0 >= 0, 2 = v0
   #less(z, z') -{ 0 }-> 0 :|: z' - 1 >= 0, z = 0, v0 >= 0, 3 = v0
   #less(z, z') -{ 0 }-> 0 :|: z - 1 >= 0, z' = 0, v0 >= 0, 3 = v0
   #less(z, z') -{ 0 }-> 0 :|: z - 1 >= 0, z' - 1 >= 0, v0 >= 0, 3 = v0
   #less(z, z') -{ 0 }-> 0 :|: z - 1 >= 0, z' = 0, v0 >= 0, 2 = v0
   #less(z, z') -{ 0 }-> 0 :|: z' - 1 >= 0, z - 1 >= 0, v0 >= 0, 2 = v0
   #less(z, z') -{ 0 }-> 0 :|: z' >= 0, z >= 0, v0 >= 0, 0 = v0
   #less(z, z') -{ 0 }-> #cklt(#compare(z - 1, z' - 1)) :|: z - 1 >= 0, z' - 1 >= 0
   #less(z, z') -{ 0 }-> #cklt(#compare(z' - 1, z - 1)) :|: z' - 1 >= 0, z - 1 >= 0
   APPEND(z, z') -{ 1 + 4*z }-> 1 + s :|: s >= 0, s <= 0, z' >= 0, z >= 0
   APPEND#1(z, z') -{ 2 + 4*z1 }-> 1 + s' :|: s' >= 0, s' <= 1, z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z' >= 0
   FLATTEN(z) -{ 1 }-> 1 + FLATTEN#1(z) :|: z >= 0
   FLATTEN#1(z) -{ 2 }-> 1 + APPEND(z0, append(flatten#1(z1), flatten#1(z2))) + s'' + FLATTEN(z1) :|: s'' >= 0, s'' <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 2 }-> 1 + APPEND(z0, append(flatten#1(z1), flatten#1(z2))) + s4 + FLATTEN(z2) :|: s4 >= 0, s4 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), flatten#1(z2))) + APPEND(flatten#1(z1), flatten#1(z2)) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), flatten#1(z2))) + APPEND(flatten#1(z1), flatten#1(z2)) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), flatten#1(z2))) + APPEND(flatten#1(z1), 0) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), flatten#1(z2))) + APPEND(flatten#1(z1), 0) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), flatten#1(z2))) + APPEND(0, flatten#1(z2)) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), flatten#1(z2))) + APPEND(0, flatten#1(z2)) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 2 }-> 1 + APPEND(z0, append(flatten#1(z1), 0)) + s1 + FLATTEN(z1) :|: s1 >= 0, s1 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 2 }-> 1 + APPEND(z0, append(flatten#1(z1), 0)) + s5 + FLATTEN(z2) :|: s5 >= 0, s5 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), 0)) + APPEND(flatten#1(z1), flatten#1(z2)) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), 0)) + APPEND(flatten#1(z1), flatten#1(z2)) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), 0)) + APPEND(flatten#1(z1), 0) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), 0)) + APPEND(flatten#1(z1), 0) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), 0)) + APPEND(0, flatten#1(z2)) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), 0)) + APPEND(0, flatten#1(z2)) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 2 }-> 1 + APPEND(z0, append(0, flatten#1(z2))) + s2 + FLATTEN(z1) :|: s2 >= 0, s2 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 2 }-> 1 + APPEND(z0, append(0, flatten#1(z2))) + s6 + FLATTEN(z2) :|: s6 >= 0, s6 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(0, flatten#1(z2))) + APPEND(flatten#1(z1), flatten#1(z2)) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(0, flatten#1(z2))) + APPEND(flatten#1(z1), flatten#1(z2)) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(0, flatten#1(z2))) + APPEND(flatten#1(z1), 0) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(0, flatten#1(z2))) + APPEND(flatten#1(z1), 0) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(0, flatten#1(z2))) + APPEND(0, flatten#1(z2)) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(0, flatten#1(z2))) + APPEND(0, flatten#1(z2)) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 2 }-> 1 + APPEND(z0, append(0, 0)) + s3 + FLATTEN(z1) :|: s3 >= 0, s3 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 2 }-> 1 + APPEND(z0, append(0, 0)) + s7 + FLATTEN(z2) :|: s7 >= 0, s7 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(0, 0)) + APPEND(flatten#1(z1), flatten#1(z2)) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(0, 0)) + APPEND(flatten#1(z1), flatten#1(z2)) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(0, 0)) + APPEND(flatten#1(z1), 0) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(0, 0)) + APPEND(flatten#1(z1), 0) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(0, 0)) + APPEND(0, flatten#1(z2)) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(0, 0)) + APPEND(0, flatten#1(z2)) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTENSORT(z) -{ 0 }-> 0 :|: z >= 0
   FLATTENSORT(z) -{ 0 }-> 1 + INSERTIONSORT(flatten#1(z)) :|: z >= 0
   FLATTENSORT(z) -{ 0 }-> 1 + INSERTIONSORT(0) :|: z >= 0
   INSERT(z, z') -{ 1 }-> 1 + INSERT#1(z', z) :|: z' >= 0, z >= 0
   INSERT#1(z, z') -{ 1 }-> 1 + INSERT#2(0, z', z0, z1) + #LESS(z0, z') :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z' >= 0
   INSERT#1(z, z') -{ 1 }-> 1 + INSERT#2(#cklt(#compare(z0, z')), z', z0, z1) + #LESS(z0, z') :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z' >= 0
   INSERT#2(z, z', z'', z3) -{ 1 }-> 1 + INSERT(z', z3) :|: z = 2, z'' >= 0, z' >= 0, z3 >= 0
   INSERTIONSORT(z) -{ 1 }-> 1 + INSERTIONSORT#1(z) :|: z >= 0
   INSERTIONSORT#1(z) -{ 1 }-> 1 + INSERT(z0, insertionsort#1(z1)) + INSERTIONSORT(z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   INSERTIONSORT#1(z) -{ 1 }-> 1 + INSERT(z0, 0) + INSERTIONSORT(z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   append(z, z') -{ 0 }-> append#1(z, z') :|: z' >= 0, z >= 0
   append(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   append#1(z, z') -{ 0 }-> z' :|: z' >= 0, z = 0
   append#1(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   append#1(z, z') -{ 0 }-> 1 + z0 + append(z1, z') :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z' >= 0
   flatten(z) -{ 0 }-> flatten#1(z) :|: z >= 0
   flatten(z) -{ 0 }-> 0 :|: z >= 0
   flatten#1(z) -{ 0 }-> append(z0, append(flatten#1(z1), flatten#1(z2))) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   flatten#1(z) -{ 0 }-> append(z0, append(flatten#1(z1), 0)) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   flatten#1(z) -{ 0 }-> append(z0, append(0, flatten#1(z2))) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   flatten#1(z) -{ 0 }-> append(z0, append(0, 0)) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   flatten#1(z) -{ 0 }-> 0 :|: z = 0
   flatten#1(z) -{ 0 }-> 0 :|: z >= 0
   insert(z, z') -{ 0 }-> insert#1(z', z) :|: z' >= 0, z >= 0
   insert(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   insert#1(z, z') -{ 0 }-> insert#2(0, z', z0, z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z' >= 0
   insert#1(z, z') -{ 0 }-> insert#2(#cklt(#compare(z0, z')), z', z0, z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z' >= 0
   insert#1(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   insert#1(z, z') -{ 0 }-> 1 + z' + 0 :|: z' >= 0, z = 0
   insert#2(z, z', z'', z3) -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0, z3 >= 0
   insert#2(z, z', z'', z3) -{ 0 }-> 1 + z' + (1 + z'' + z3) :|: z'' >= 0, z = 1, z' >= 0, z3 >= 0
   insert#2(z, z', z'', z3) -{ 0 }-> 1 + z'' + insert(z', z3) :|: z = 2, z'' >= 0, z' >= 0, z3 >= 0
   insertionsort(z) -{ 0 }-> insertionsort#1(z) :|: z >= 0
   insertionsort(z) -{ 0 }-> 0 :|: z >= 0
   insertionsort#1(z) -{ 0 }-> insert(z0, insertionsort#1(z1)) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   insertionsort#1(z) -{ 0 }-> insert(z0, 0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   insertionsort#1(z) -{ 0 }-> 0 :|: z = 0
   insertionsort#1(z) -{ 0 }-> 0 :|: z >= 0

Function symbols to be analyzed: {#cklt}, {#compare}, {#COMPARE}, {append#1,append}, {#less}, {insert#2,insert,insert#1}, {#LESS}, {flatten#1}, {insertionsort#1}, {INSERT#1,INSERT#2,INSERT}, {flatten}, {FLATTEN,FLATTEN#1}, {insertionsort}, {INSERTIONSORT,INSERTIONSORT#1}, {FLATTENSORT}
Previous analysis results are:
  APPEND#1: runtime: O(n^1) [4*z], size: O(1) [0]
  APPEND: runtime: O(n^1) [1 + 4*z], size: O(1) [1]
  #cklt: runtime: ?, size: O(1) [2]

----------------------------------------

(45) IntTrsBoundProof (UPPER BOUND(ID))

Computed RUNTIME bound using CoFloCo for: #cklt
after applying outer abstraction to obtain an ITS,
resulting in: O(1) with polynomial bound: 0

----------------------------------------

(46)
Obligation:
Complexity RNTS consisting of the following rules:

   #COMPARE(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   #COMPARE(z, z') -{ 0 }-> 1 + #COMPARE(z - 1, z' - 1) :|: z' - 1 >= 0, z - 1 >= 0
   #COMPARE(z, z') -{ 0 }-> 1 + #COMPARE(z' - 1, z - 1) :|: z' - 1 >= 0, z - 1 >= 0
   #LESS(z, z') -{ 1 }-> 1 + #COMPARE(z, z') :|: z' >= 0, z >= 0
   #cklt(z) -{ 0 }-> 2 :|: z = 3
   #cklt(z) -{ 0 }-> 1 :|: z = 1
   #cklt(z) -{ 0 }-> 1 :|: z = 2
   #cklt(z) -{ 0 }-> 0 :|: z >= 0
   #compare(z, z') -{ 0 }-> 3 :|: z' - 1 >= 0, z = 0
   #compare(z, z') -{ 0 }-> 3 :|: z - 1 >= 0, z' = 0
   #compare(z, z') -{ 0 }-> 3 :|: z' - 1 >= 0, z - 1 >= 0
   #compare(z, z') -{ 0 }-> 2 :|: z' - 1 >= 0, z = 0
   #compare(z, z') -{ 0 }-> 2 :|: z - 1 >= 0, z' = 0
   #compare(z, z') -{ 0 }-> 2 :|: z' - 1 >= 0, z - 1 >= 0
   #compare(z, z') -{ 0 }-> 1 :|: z = 0, z' = 0
   #compare(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   #compare(z, z') -{ 0 }-> #compare(z - 1, z' - 1) :|: z' - 1 >= 0, z - 1 >= 0
   #compare(z, z') -{ 0 }-> #compare(z' - 1, z - 1) :|: z' - 1 >= 0, z - 1 >= 0
   #less(z, z') -{ 0 }-> 2 :|: z' - 1 >= 0, z = 0, 3 = 3
   #less(z, z') -{ 0 }-> 2 :|: z - 1 >= 0, z' = 0, 3 = 3
   #less(z, z') -{ 0 }-> 2 :|: z - 1 >= 0, z' - 1 >= 0, 3 = 3
   #less(z, z') -{ 0 }-> 1 :|: z = 0, z' = 0, 1 = 1
   #less(z, z') -{ 0 }-> 1 :|: z' - 1 >= 0, z = 0, 2 = 2
   #less(z, z') -{ 0 }-> 1 :|: z - 1 >= 0, z' = 0, 2 = 2
   #less(z, z') -{ 0 }-> 1 :|: z' - 1 >= 0, z - 1 >= 0, 2 = 2
   #less(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   #less(z, z') -{ 0 }-> 0 :|: z = 0, z' = 0, v0 >= 0, 1 = v0
   #less(z, z') -{ 0 }-> 0 :|: z' - 1 >= 0, z = 0, v0 >= 0, 2 = v0
   #less(z, z') -{ 0 }-> 0 :|: z' - 1 >= 0, z = 0, v0 >= 0, 3 = v0
   #less(z, z') -{ 0 }-> 0 :|: z - 1 >= 0, z' = 0, v0 >= 0, 3 = v0
   #less(z, z') -{ 0 }-> 0 :|: z - 1 >= 0, z' - 1 >= 0, v0 >= 0, 3 = v0
   #less(z, z') -{ 0 }-> 0 :|: z - 1 >= 0, z' = 0, v0 >= 0, 2 = v0
   #less(z, z') -{ 0 }-> 0 :|: z' - 1 >= 0, z - 1 >= 0, v0 >= 0, 2 = v0
   #less(z, z') -{ 0 }-> 0 :|: z' >= 0, z >= 0, v0 >= 0, 0 = v0
   #less(z, z') -{ 0 }-> #cklt(#compare(z - 1, z' - 1)) :|: z - 1 >= 0, z' - 1 >= 0
   #less(z, z') -{ 0 }-> #cklt(#compare(z' - 1, z - 1)) :|: z' - 1 >= 0, z - 1 >= 0
   APPEND(z, z') -{ 1 + 4*z }-> 1 + s :|: s >= 0, s <= 0, z' >= 0, z >= 0
   APPEND#1(z, z') -{ 2 + 4*z1 }-> 1 + s' :|: s' >= 0, s' <= 1, z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z' >= 0
   FLATTEN(z) -{ 1 }-> 1 + FLATTEN#1(z) :|: z >= 0
   FLATTEN#1(z) -{ 2 }-> 1 + APPEND(z0, append(flatten#1(z1), flatten#1(z2))) + s'' + FLATTEN(z1) :|: s'' >= 0, s'' <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 2 }-> 1 + APPEND(z0, append(flatten#1(z1), flatten#1(z2))) + s4 + FLATTEN(z2) :|: s4 >= 0, s4 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), flatten#1(z2))) + APPEND(flatten#1(z1), flatten#1(z2)) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), flatten#1(z2))) + APPEND(flatten#1(z1), flatten#1(z2)) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), flatten#1(z2))) + APPEND(flatten#1(z1), 0) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), flatten#1(z2))) + APPEND(flatten#1(z1), 0) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), flatten#1(z2))) + APPEND(0, flatten#1(z2)) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), flatten#1(z2))) + APPEND(0, flatten#1(z2)) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 2 }-> 1 + APPEND(z0, append(flatten#1(z1), 0)) + s1 + FLATTEN(z1) :|: s1 >= 0, s1 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 2 }-> 1 + APPEND(z0, append(flatten#1(z1), 0)) + s5 + FLATTEN(z2) :|: s5 >= 0, s5 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), 0)) + APPEND(flatten#1(z1), flatten#1(z2)) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), 0)) + APPEND(flatten#1(z1), flatten#1(z2)) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), 0)) + APPEND(flatten#1(z1), 0) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), 0)) + APPEND(flatten#1(z1), 0) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), 0)) + APPEND(0, flatten#1(z2)) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), 0)) + APPEND(0, flatten#1(z2)) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 2 }-> 1 + APPEND(z0, append(0, flatten#1(z2))) + s2 + FLATTEN(z1) :|: s2 >= 0, s2 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 2 }-> 1 + APPEND(z0, append(0, flatten#1(z2))) + s6 + FLATTEN(z2) :|: s6 >= 0, s6 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(0, flatten#1(z2))) + APPEND(flatten#1(z1), flatten#1(z2)) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(0, flatten#1(z2))) + APPEND(flatten#1(z1), flatten#1(z2)) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(0, flatten#1(z2))) + APPEND(flatten#1(z1), 0) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(0, flatten#1(z2))) + APPEND(flatten#1(z1), 0) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(0, flatten#1(z2))) + APPEND(0, flatten#1(z2)) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(0, flatten#1(z2))) + APPEND(0, flatten#1(z2)) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 2 }-> 1 + APPEND(z0, append(0, 0)) + s3 + FLATTEN(z1) :|: s3 >= 0, s3 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 2 }-> 1 + APPEND(z0, append(0, 0)) + s7 + FLATTEN(z2) :|: s7 >= 0, s7 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(0, 0)) + APPEND(flatten#1(z1), flatten#1(z2)) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(0, 0)) + APPEND(flatten#1(z1), flatten#1(z2)) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(0, 0)) + APPEND(flatten#1(z1), 0) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(0, 0)) + APPEND(flatten#1(z1), 0) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(0, 0)) + APPEND(0, flatten#1(z2)) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(0, 0)) + APPEND(0, flatten#1(z2)) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTENSORT(z) -{ 0 }-> 0 :|: z >= 0
   FLATTENSORT(z) -{ 0 }-> 1 + INSERTIONSORT(flatten#1(z)) :|: z >= 0
   FLATTENSORT(z) -{ 0 }-> 1 + INSERTIONSORT(0) :|: z >= 0
   INSERT(z, z') -{ 1 }-> 1 + INSERT#1(z', z) :|: z' >= 0, z >= 0
   INSERT#1(z, z') -{ 1 }-> 1 + INSERT#2(0, z', z0, z1) + #LESS(z0, z') :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z' >= 0
   INSERT#1(z, z') -{ 1 }-> 1 + INSERT#2(#cklt(#compare(z0, z')), z', z0, z1) + #LESS(z0, z') :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z' >= 0
   INSERT#2(z, z', z'', z3) -{ 1 }-> 1 + INSERT(z', z3) :|: z = 2, z'' >= 0, z' >= 0, z3 >= 0
   INSERTIONSORT(z) -{ 1 }-> 1 + INSERTIONSORT#1(z) :|: z >= 0
   INSERTIONSORT#1(z) -{ 1 }-> 1 + INSERT(z0, insertionsort#1(z1)) + INSERTIONSORT(z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   INSERTIONSORT#1(z) -{ 1 }-> 1 + INSERT(z0, 0) + INSERTIONSORT(z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   append(z, z') -{ 0 }-> append#1(z, z') :|: z' >= 0, z >= 0
   append(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   append#1(z, z') -{ 0 }-> z' :|: z' >= 0, z = 0
   append#1(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   append#1(z, z') -{ 0 }-> 1 + z0 + append(z1, z') :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z' >= 0
   flatten(z) -{ 0 }-> flatten#1(z) :|: z >= 0
   flatten(z) -{ 0 }-> 0 :|: z >= 0
   flatten#1(z) -{ 0 }-> append(z0, append(flatten#1(z1), flatten#1(z2))) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   flatten#1(z) -{ 0 }-> append(z0, append(flatten#1(z1), 0)) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   flatten#1(z) -{ 0 }-> append(z0, append(0, flatten#1(z2))) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   flatten#1(z) -{ 0 }-> append(z0, append(0, 0)) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   flatten#1(z) -{ 0 }-> 0 :|: z = 0
   flatten#1(z) -{ 0 }-> 0 :|: z >= 0
   insert(z, z') -{ 0 }-> insert#1(z', z) :|: z' >= 0, z >= 0
   insert(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   insert#1(z, z') -{ 0 }-> insert#2(0, z', z0, z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z' >= 0
   insert#1(z, z') -{ 0 }-> insert#2(#cklt(#compare(z0, z')), z', z0, z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z' >= 0
   insert#1(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   insert#1(z, z') -{ 0 }-> 1 + z' + 0 :|: z' >= 0, z = 0
   insert#2(z, z', z'', z3) -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0, z3 >= 0
   insert#2(z, z', z'', z3) -{ 0 }-> 1 + z' + (1 + z'' + z3) :|: z'' >= 0, z = 1, z' >= 0, z3 >= 0
   insert#2(z, z', z'', z3) -{ 0 }-> 1 + z'' + insert(z', z3) :|: z = 2, z'' >= 0, z' >= 0, z3 >= 0
   insertionsort(z) -{ 0 }-> insertionsort#1(z) :|: z >= 0
   insertionsort(z) -{ 0 }-> 0 :|: z >= 0
   insertionsort#1(z) -{ 0 }-> insert(z0, insertionsort#1(z1)) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   insertionsort#1(z) -{ 0 }-> insert(z0, 0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   insertionsort#1(z) -{ 0 }-> 0 :|: z = 0
   insertionsort#1(z) -{ 0 }-> 0 :|: z >= 0

Function symbols to be analyzed: {#compare}, {#COMPARE}, {append#1,append}, {#less}, {insert#2,insert,insert#1}, {#LESS}, {flatten#1}, {insertionsort#1}, {INSERT#1,INSERT#2,INSERT}, {flatten}, {FLATTEN,FLATTEN#1}, {insertionsort}, {INSERTIONSORT,INSERTIONSORT#1}, {FLATTENSORT}
Previous analysis results are:
  APPEND#1: runtime: O(n^1) [4*z], size: O(1) [0]
  APPEND: runtime: O(n^1) [1 + 4*z], size: O(1) [1]
  #cklt: runtime: O(1) [0], size: O(1) [2]

----------------------------------------

(47) ResultPropagationProof (UPPER BOUND(ID))
Applied inner abstraction using the recently inferred runtime/size bounds where possible.
----------------------------------------

(48)
Obligation:
Complexity RNTS consisting of the following rules:

   #COMPARE(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   #COMPARE(z, z') -{ 0 }-> 1 + #COMPARE(z - 1, z' - 1) :|: z' - 1 >= 0, z - 1 >= 0
   #COMPARE(z, z') -{ 0 }-> 1 + #COMPARE(z' - 1, z - 1) :|: z' - 1 >= 0, z - 1 >= 0
   #LESS(z, z') -{ 1 }-> 1 + #COMPARE(z, z') :|: z' >= 0, z >= 0
   #cklt(z) -{ 0 }-> 2 :|: z = 3
   #cklt(z) -{ 0 }-> 1 :|: z = 1
   #cklt(z) -{ 0 }-> 1 :|: z = 2
   #cklt(z) -{ 0 }-> 0 :|: z >= 0
   #compare(z, z') -{ 0 }-> 3 :|: z' - 1 >= 0, z = 0
   #compare(z, z') -{ 0 }-> 3 :|: z - 1 >= 0, z' = 0
   #compare(z, z') -{ 0 }-> 3 :|: z' - 1 >= 0, z - 1 >= 0
   #compare(z, z') -{ 0 }-> 2 :|: z' - 1 >= 0, z = 0
   #compare(z, z') -{ 0 }-> 2 :|: z - 1 >= 0, z' = 0
   #compare(z, z') -{ 0 }-> 2 :|: z' - 1 >= 0, z - 1 >= 0
   #compare(z, z') -{ 0 }-> 1 :|: z = 0, z' = 0
   #compare(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   #compare(z, z') -{ 0 }-> #compare(z - 1, z' - 1) :|: z' - 1 >= 0, z - 1 >= 0
   #compare(z, z') -{ 0 }-> #compare(z' - 1, z - 1) :|: z' - 1 >= 0, z - 1 >= 0
   #less(z, z') -{ 0 }-> 2 :|: z' - 1 >= 0, z = 0, 3 = 3
   #less(z, z') -{ 0 }-> 2 :|: z - 1 >= 0, z' = 0, 3 = 3
   #less(z, z') -{ 0 }-> 2 :|: z - 1 >= 0, z' - 1 >= 0, 3 = 3
   #less(z, z') -{ 0 }-> 1 :|: z = 0, z' = 0, 1 = 1
   #less(z, z') -{ 0 }-> 1 :|: z' - 1 >= 0, z = 0, 2 = 2
   #less(z, z') -{ 0 }-> 1 :|: z - 1 >= 0, z' = 0, 2 = 2
   #less(z, z') -{ 0 }-> 1 :|: z' - 1 >= 0, z - 1 >= 0, 2 = 2
   #less(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   #less(z, z') -{ 0 }-> 0 :|: z = 0, z' = 0, v0 >= 0, 1 = v0
   #less(z, z') -{ 0 }-> 0 :|: z' - 1 >= 0, z = 0, v0 >= 0, 2 = v0
   #less(z, z') -{ 0 }-> 0 :|: z' - 1 >= 0, z = 0, v0 >= 0, 3 = v0
   #less(z, z') -{ 0 }-> 0 :|: z - 1 >= 0, z' = 0, v0 >= 0, 3 = v0
   #less(z, z') -{ 0 }-> 0 :|: z - 1 >= 0, z' - 1 >= 0, v0 >= 0, 3 = v0
   #less(z, z') -{ 0 }-> 0 :|: z - 1 >= 0, z' = 0, v0 >= 0, 2 = v0
   #less(z, z') -{ 0 }-> 0 :|: z' - 1 >= 0, z - 1 >= 0, v0 >= 0, 2 = v0
   #less(z, z') -{ 0 }-> 0 :|: z' >= 0, z >= 0, v0 >= 0, 0 = v0
   #less(z, z') -{ 0 }-> #cklt(#compare(z - 1, z' - 1)) :|: z - 1 >= 0, z' - 1 >= 0
   #less(z, z') -{ 0 }-> #cklt(#compare(z' - 1, z - 1)) :|: z' - 1 >= 0, z - 1 >= 0
   APPEND(z, z') -{ 1 + 4*z }-> 1 + s :|: s >= 0, s <= 0, z' >= 0, z >= 0
   APPEND#1(z, z') -{ 2 + 4*z1 }-> 1 + s' :|: s' >= 0, s' <= 1, z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z' >= 0
   FLATTEN(z) -{ 1 }-> 1 + FLATTEN#1(z) :|: z >= 0
   FLATTEN#1(z) -{ 2 }-> 1 + APPEND(z0, append(flatten#1(z1), flatten#1(z2))) + s'' + FLATTEN(z1) :|: s'' >= 0, s'' <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 2 }-> 1 + APPEND(z0, append(flatten#1(z1), flatten#1(z2))) + s4 + FLATTEN(z2) :|: s4 >= 0, s4 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), flatten#1(z2))) + APPEND(flatten#1(z1), flatten#1(z2)) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), flatten#1(z2))) + APPEND(flatten#1(z1), flatten#1(z2)) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), flatten#1(z2))) + APPEND(flatten#1(z1), 0) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), flatten#1(z2))) + APPEND(flatten#1(z1), 0) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), flatten#1(z2))) + APPEND(0, flatten#1(z2)) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), flatten#1(z2))) + APPEND(0, flatten#1(z2)) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 2 }-> 1 + APPEND(z0, append(flatten#1(z1), 0)) + s1 + FLATTEN(z1) :|: s1 >= 0, s1 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 2 }-> 1 + APPEND(z0, append(flatten#1(z1), 0)) + s5 + FLATTEN(z2) :|: s5 >= 0, s5 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), 0)) + APPEND(flatten#1(z1), flatten#1(z2)) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), 0)) + APPEND(flatten#1(z1), flatten#1(z2)) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), 0)) + APPEND(flatten#1(z1), 0) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), 0)) + APPEND(flatten#1(z1), 0) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), 0)) + APPEND(0, flatten#1(z2)) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), 0)) + APPEND(0, flatten#1(z2)) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 2 }-> 1 + APPEND(z0, append(0, flatten#1(z2))) + s2 + FLATTEN(z1) :|: s2 >= 0, s2 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 2 }-> 1 + APPEND(z0, append(0, flatten#1(z2))) + s6 + FLATTEN(z2) :|: s6 >= 0, s6 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(0, flatten#1(z2))) + APPEND(flatten#1(z1), flatten#1(z2)) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(0, flatten#1(z2))) + APPEND(flatten#1(z1), flatten#1(z2)) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(0, flatten#1(z2))) + APPEND(flatten#1(z1), 0) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(0, flatten#1(z2))) + APPEND(flatten#1(z1), 0) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(0, flatten#1(z2))) + APPEND(0, flatten#1(z2)) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(0, flatten#1(z2))) + APPEND(0, flatten#1(z2)) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 2 }-> 1 + APPEND(z0, append(0, 0)) + s3 + FLATTEN(z1) :|: s3 >= 0, s3 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 2 }-> 1 + APPEND(z0, append(0, 0)) + s7 + FLATTEN(z2) :|: s7 >= 0, s7 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(0, 0)) + APPEND(flatten#1(z1), flatten#1(z2)) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(0, 0)) + APPEND(flatten#1(z1), flatten#1(z2)) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(0, 0)) + APPEND(flatten#1(z1), 0) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(0, 0)) + APPEND(flatten#1(z1), 0) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(0, 0)) + APPEND(0, flatten#1(z2)) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(0, 0)) + APPEND(0, flatten#1(z2)) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTENSORT(z) -{ 0 }-> 0 :|: z >= 0
   FLATTENSORT(z) -{ 0 }-> 1 + INSERTIONSORT(flatten#1(z)) :|: z >= 0
   FLATTENSORT(z) -{ 0 }-> 1 + INSERTIONSORT(0) :|: z >= 0
   INSERT(z, z') -{ 1 }-> 1 + INSERT#1(z', z) :|: z' >= 0, z >= 0
   INSERT#1(z, z') -{ 1 }-> 1 + INSERT#2(0, z', z0, z1) + #LESS(z0, z') :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z' >= 0
   INSERT#1(z, z') -{ 1 }-> 1 + INSERT#2(#cklt(#compare(z0, z')), z', z0, z1) + #LESS(z0, z') :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z' >= 0
   INSERT#2(z, z', z'', z3) -{ 1 }-> 1 + INSERT(z', z3) :|: z = 2, z'' >= 0, z' >= 0, z3 >= 0
   INSERTIONSORT(z) -{ 1 }-> 1 + INSERTIONSORT#1(z) :|: z >= 0
   INSERTIONSORT#1(z) -{ 1 }-> 1 + INSERT(z0, insertionsort#1(z1)) + INSERTIONSORT(z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   INSERTIONSORT#1(z) -{ 1 }-> 1 + INSERT(z0, 0) + INSERTIONSORT(z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   append(z, z') -{ 0 }-> append#1(z, z') :|: z' >= 0, z >= 0
   append(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   append#1(z, z') -{ 0 }-> z' :|: z' >= 0, z = 0
   append#1(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   append#1(z, z') -{ 0 }-> 1 + z0 + append(z1, z') :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z' >= 0
   flatten(z) -{ 0 }-> flatten#1(z) :|: z >= 0
   flatten(z) -{ 0 }-> 0 :|: z >= 0
   flatten#1(z) -{ 0 }-> append(z0, append(flatten#1(z1), flatten#1(z2))) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   flatten#1(z) -{ 0 }-> append(z0, append(flatten#1(z1), 0)) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   flatten#1(z) -{ 0 }-> append(z0, append(0, flatten#1(z2))) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   flatten#1(z) -{ 0 }-> append(z0, append(0, 0)) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   flatten#1(z) -{ 0 }-> 0 :|: z = 0
   flatten#1(z) -{ 0 }-> 0 :|: z >= 0
   insert(z, z') -{ 0 }-> insert#1(z', z) :|: z' >= 0, z >= 0
   insert(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   insert#1(z, z') -{ 0 }-> insert#2(0, z', z0, z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z' >= 0
   insert#1(z, z') -{ 0 }-> insert#2(#cklt(#compare(z0, z')), z', z0, z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z' >= 0
   insert#1(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   insert#1(z, z') -{ 0 }-> 1 + z' + 0 :|: z' >= 0, z = 0
   insert#2(z, z', z'', z3) -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0, z3 >= 0
   insert#2(z, z', z'', z3) -{ 0 }-> 1 + z' + (1 + z'' + z3) :|: z'' >= 0, z = 1, z' >= 0, z3 >= 0
   insert#2(z, z', z'', z3) -{ 0 }-> 1 + z'' + insert(z', z3) :|: z = 2, z'' >= 0, z' >= 0, z3 >= 0
   insertionsort(z) -{ 0 }-> insertionsort#1(z) :|: z >= 0
   insertionsort(z) -{ 0 }-> 0 :|: z >= 0
   insertionsort#1(z) -{ 0 }-> insert(z0, insertionsort#1(z1)) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   insertionsort#1(z) -{ 0 }-> insert(z0, 0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   insertionsort#1(z) -{ 0 }-> 0 :|: z = 0
   insertionsort#1(z) -{ 0 }-> 0 :|: z >= 0

Function symbols to be analyzed: {#compare}, {#COMPARE}, {append#1,append}, {#less}, {insert#2,insert,insert#1}, {#LESS}, {flatten#1}, {insertionsort#1}, {INSERT#1,INSERT#2,INSERT}, {flatten}, {FLATTEN,FLATTEN#1}, {insertionsort}, {INSERTIONSORT,INSERTIONSORT#1}, {FLATTENSORT}
Previous analysis results are:
  APPEND#1: runtime: O(n^1) [4*z], size: O(1) [0]
  APPEND: runtime: O(n^1) [1 + 4*z], size: O(1) [1]
  #cklt: runtime: O(1) [0], size: O(1) [2]

----------------------------------------

(49) IntTrsBoundProof (UPPER BOUND(ID))

Computed SIZE bound using CoFloCo for: #compare
after applying outer abstraction to obtain an ITS,
resulting in: O(1) with polynomial bound: 3

----------------------------------------

(50)
Obligation:
Complexity RNTS consisting of the following rules:

   #COMPARE(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   #COMPARE(z, z') -{ 0 }-> 1 + #COMPARE(z - 1, z' - 1) :|: z' - 1 >= 0, z - 1 >= 0
   #COMPARE(z, z') -{ 0 }-> 1 + #COMPARE(z' - 1, z - 1) :|: z' - 1 >= 0, z - 1 >= 0
   #LESS(z, z') -{ 1 }-> 1 + #COMPARE(z, z') :|: z' >= 0, z >= 0
   #cklt(z) -{ 0 }-> 2 :|: z = 3
   #cklt(z) -{ 0 }-> 1 :|: z = 1
   #cklt(z) -{ 0 }-> 1 :|: z = 2
   #cklt(z) -{ 0 }-> 0 :|: z >= 0
   #compare(z, z') -{ 0 }-> 3 :|: z' - 1 >= 0, z = 0
   #compare(z, z') -{ 0 }-> 3 :|: z - 1 >= 0, z' = 0
   #compare(z, z') -{ 0 }-> 3 :|: z' - 1 >= 0, z - 1 >= 0
   #compare(z, z') -{ 0 }-> 2 :|: z' - 1 >= 0, z = 0
   #compare(z, z') -{ 0 }-> 2 :|: z - 1 >= 0, z' = 0
   #compare(z, z') -{ 0 }-> 2 :|: z' - 1 >= 0, z - 1 >= 0
   #compare(z, z') -{ 0 }-> 1 :|: z = 0, z' = 0
   #compare(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   #compare(z, z') -{ 0 }-> #compare(z - 1, z' - 1) :|: z' - 1 >= 0, z - 1 >= 0
   #compare(z, z') -{ 0 }-> #compare(z' - 1, z - 1) :|: z' - 1 >= 0, z - 1 >= 0
   #less(z, z') -{ 0 }-> 2 :|: z' - 1 >= 0, z = 0, 3 = 3
   #less(z, z') -{ 0 }-> 2 :|: z - 1 >= 0, z' = 0, 3 = 3
   #less(z, z') -{ 0 }-> 2 :|: z - 1 >= 0, z' - 1 >= 0, 3 = 3
   #less(z, z') -{ 0 }-> 1 :|: z = 0, z' = 0, 1 = 1
   #less(z, z') -{ 0 }-> 1 :|: z' - 1 >= 0, z = 0, 2 = 2
   #less(z, z') -{ 0 }-> 1 :|: z - 1 >= 0, z' = 0, 2 = 2
   #less(z, z') -{ 0 }-> 1 :|: z' - 1 >= 0, z - 1 >= 0, 2 = 2
   #less(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   #less(z, z') -{ 0 }-> 0 :|: z = 0, z' = 0, v0 >= 0, 1 = v0
   #less(z, z') -{ 0 }-> 0 :|: z' - 1 >= 0, z = 0, v0 >= 0, 2 = v0
   #less(z, z') -{ 0 }-> 0 :|: z' - 1 >= 0, z = 0, v0 >= 0, 3 = v0
   #less(z, z') -{ 0 }-> 0 :|: z - 1 >= 0, z' = 0, v0 >= 0, 3 = v0
   #less(z, z') -{ 0 }-> 0 :|: z - 1 >= 0, z' - 1 >= 0, v0 >= 0, 3 = v0
   #less(z, z') -{ 0 }-> 0 :|: z - 1 >= 0, z' = 0, v0 >= 0, 2 = v0
   #less(z, z') -{ 0 }-> 0 :|: z' - 1 >= 0, z - 1 >= 0, v0 >= 0, 2 = v0
   #less(z, z') -{ 0 }-> 0 :|: z' >= 0, z >= 0, v0 >= 0, 0 = v0
   #less(z, z') -{ 0 }-> #cklt(#compare(z - 1, z' - 1)) :|: z - 1 >= 0, z' - 1 >= 0
   #less(z, z') -{ 0 }-> #cklt(#compare(z' - 1, z - 1)) :|: z' - 1 >= 0, z - 1 >= 0
   APPEND(z, z') -{ 1 + 4*z }-> 1 + s :|: s >= 0, s <= 0, z' >= 0, z >= 0
   APPEND#1(z, z') -{ 2 + 4*z1 }-> 1 + s' :|: s' >= 0, s' <= 1, z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z' >= 0
   FLATTEN(z) -{ 1 }-> 1 + FLATTEN#1(z) :|: z >= 0
   FLATTEN#1(z) -{ 2 }-> 1 + APPEND(z0, append(flatten#1(z1), flatten#1(z2))) + s'' + FLATTEN(z1) :|: s'' >= 0, s'' <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 2 }-> 1 + APPEND(z0, append(flatten#1(z1), flatten#1(z2))) + s4 + FLATTEN(z2) :|: s4 >= 0, s4 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), flatten#1(z2))) + APPEND(flatten#1(z1), flatten#1(z2)) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), flatten#1(z2))) + APPEND(flatten#1(z1), flatten#1(z2)) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), flatten#1(z2))) + APPEND(flatten#1(z1), 0) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), flatten#1(z2))) + APPEND(flatten#1(z1), 0) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), flatten#1(z2))) + APPEND(0, flatten#1(z2)) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), flatten#1(z2))) + APPEND(0, flatten#1(z2)) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 2 }-> 1 + APPEND(z0, append(flatten#1(z1), 0)) + s1 + FLATTEN(z1) :|: s1 >= 0, s1 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 2 }-> 1 + APPEND(z0, append(flatten#1(z1), 0)) + s5 + FLATTEN(z2) :|: s5 >= 0, s5 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), 0)) + APPEND(flatten#1(z1), flatten#1(z2)) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), 0)) + APPEND(flatten#1(z1), flatten#1(z2)) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), 0)) + APPEND(flatten#1(z1), 0) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), 0)) + APPEND(flatten#1(z1), 0) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), 0)) + APPEND(0, flatten#1(z2)) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), 0)) + APPEND(0, flatten#1(z2)) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 2 }-> 1 + APPEND(z0, append(0, flatten#1(z2))) + s2 + FLATTEN(z1) :|: s2 >= 0, s2 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 2 }-> 1 + APPEND(z0, append(0, flatten#1(z2))) + s6 + FLATTEN(z2) :|: s6 >= 0, s6 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(0, flatten#1(z2))) + APPEND(flatten#1(z1), flatten#1(z2)) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(0, flatten#1(z2))) + APPEND(flatten#1(z1), flatten#1(z2)) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(0, flatten#1(z2))) + APPEND(flatten#1(z1), 0) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(0, flatten#1(z2))) + APPEND(flatten#1(z1), 0) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(0, flatten#1(z2))) + APPEND(0, flatten#1(z2)) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(0, flatten#1(z2))) + APPEND(0, flatten#1(z2)) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 2 }-> 1 + APPEND(z0, append(0, 0)) + s3 + FLATTEN(z1) :|: s3 >= 0, s3 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 2 }-> 1 + APPEND(z0, append(0, 0)) + s7 + FLATTEN(z2) :|: s7 >= 0, s7 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(0, 0)) + APPEND(flatten#1(z1), flatten#1(z2)) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(0, 0)) + APPEND(flatten#1(z1), flatten#1(z2)) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(0, 0)) + APPEND(flatten#1(z1), 0) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(0, 0)) + APPEND(flatten#1(z1), 0) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(0, 0)) + APPEND(0, flatten#1(z2)) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(0, 0)) + APPEND(0, flatten#1(z2)) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTENSORT(z) -{ 0 }-> 0 :|: z >= 0
   FLATTENSORT(z) -{ 0 }-> 1 + INSERTIONSORT(flatten#1(z)) :|: z >= 0
   FLATTENSORT(z) -{ 0 }-> 1 + INSERTIONSORT(0) :|: z >= 0
   INSERT(z, z') -{ 1 }-> 1 + INSERT#1(z', z) :|: z' >= 0, z >= 0
   INSERT#1(z, z') -{ 1 }-> 1 + INSERT#2(0, z', z0, z1) + #LESS(z0, z') :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z' >= 0
   INSERT#1(z, z') -{ 1 }-> 1 + INSERT#2(#cklt(#compare(z0, z')), z', z0, z1) + #LESS(z0, z') :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z' >= 0
   INSERT#2(z, z', z'', z3) -{ 1 }-> 1 + INSERT(z', z3) :|: z = 2, z'' >= 0, z' >= 0, z3 >= 0
   INSERTIONSORT(z) -{ 1 }-> 1 + INSERTIONSORT#1(z) :|: z >= 0
   INSERTIONSORT#1(z) -{ 1 }-> 1 + INSERT(z0, insertionsort#1(z1)) + INSERTIONSORT(z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   INSERTIONSORT#1(z) -{ 1 }-> 1 + INSERT(z0, 0) + INSERTIONSORT(z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   append(z, z') -{ 0 }-> append#1(z, z') :|: z' >= 0, z >= 0
   append(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   append#1(z, z') -{ 0 }-> z' :|: z' >= 0, z = 0
   append#1(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   append#1(z, z') -{ 0 }-> 1 + z0 + append(z1, z') :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z' >= 0
   flatten(z) -{ 0 }-> flatten#1(z) :|: z >= 0
   flatten(z) -{ 0 }-> 0 :|: z >= 0
   flatten#1(z) -{ 0 }-> append(z0, append(flatten#1(z1), flatten#1(z2))) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   flatten#1(z) -{ 0 }-> append(z0, append(flatten#1(z1), 0)) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   flatten#1(z) -{ 0 }-> append(z0, append(0, flatten#1(z2))) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   flatten#1(z) -{ 0 }-> append(z0, append(0, 0)) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   flatten#1(z) -{ 0 }-> 0 :|: z = 0
   flatten#1(z) -{ 0 }-> 0 :|: z >= 0
   insert(z, z') -{ 0 }-> insert#1(z', z) :|: z' >= 0, z >= 0
   insert(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   insert#1(z, z') -{ 0 }-> insert#2(0, z', z0, z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z' >= 0
   insert#1(z, z') -{ 0 }-> insert#2(#cklt(#compare(z0, z')), z', z0, z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z' >= 0
   insert#1(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   insert#1(z, z') -{ 0 }-> 1 + z' + 0 :|: z' >= 0, z = 0
   insert#2(z, z', z'', z3) -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0, z3 >= 0
   insert#2(z, z', z'', z3) -{ 0 }-> 1 + z' + (1 + z'' + z3) :|: z'' >= 0, z = 1, z' >= 0, z3 >= 0
   insert#2(z, z', z'', z3) -{ 0 }-> 1 + z'' + insert(z', z3) :|: z = 2, z'' >= 0, z' >= 0, z3 >= 0
   insertionsort(z) -{ 0 }-> insertionsort#1(z) :|: z >= 0
   insertionsort(z) -{ 0 }-> 0 :|: z >= 0
   insertionsort#1(z) -{ 0 }-> insert(z0, insertionsort#1(z1)) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   insertionsort#1(z) -{ 0 }-> insert(z0, 0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   insertionsort#1(z) -{ 0 }-> 0 :|: z = 0
   insertionsort#1(z) -{ 0 }-> 0 :|: z >= 0

Function symbols to be analyzed: {#compare}, {#COMPARE}, {append#1,append}, {#less}, {insert#2,insert,insert#1}, {#LESS}, {flatten#1}, {insertionsort#1}, {INSERT#1,INSERT#2,INSERT}, {flatten}, {FLATTEN,FLATTEN#1}, {insertionsort}, {INSERTIONSORT,INSERTIONSORT#1}, {FLATTENSORT}
Previous analysis results are:
  APPEND#1: runtime: O(n^1) [4*z], size: O(1) [0]
  APPEND: runtime: O(n^1) [1 + 4*z], size: O(1) [1]
  #cklt: runtime: O(1) [0], size: O(1) [2]
  #compare: runtime: ?, size: O(1) [3]

----------------------------------------

(51) IntTrsBoundProof (UPPER BOUND(ID))

Computed RUNTIME bound using CoFloCo for: #compare
after applying outer abstraction to obtain an ITS,
resulting in: O(1) with polynomial bound: 0

----------------------------------------

(52)
Obligation:
Complexity RNTS consisting of the following rules:

   #COMPARE(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   #COMPARE(z, z') -{ 0 }-> 1 + #COMPARE(z - 1, z' - 1) :|: z' - 1 >= 0, z - 1 >= 0
   #COMPARE(z, z') -{ 0 }-> 1 + #COMPARE(z' - 1, z - 1) :|: z' - 1 >= 0, z - 1 >= 0
   #LESS(z, z') -{ 1 }-> 1 + #COMPARE(z, z') :|: z' >= 0, z >= 0
   #cklt(z) -{ 0 }-> 2 :|: z = 3
   #cklt(z) -{ 0 }-> 1 :|: z = 1
   #cklt(z) -{ 0 }-> 1 :|: z = 2
   #cklt(z) -{ 0 }-> 0 :|: z >= 0
   #compare(z, z') -{ 0 }-> 3 :|: z' - 1 >= 0, z = 0
   #compare(z, z') -{ 0 }-> 3 :|: z - 1 >= 0, z' = 0
   #compare(z, z') -{ 0 }-> 3 :|: z' - 1 >= 0, z - 1 >= 0
   #compare(z, z') -{ 0 }-> 2 :|: z' - 1 >= 0, z = 0
   #compare(z, z') -{ 0 }-> 2 :|: z - 1 >= 0, z' = 0
   #compare(z, z') -{ 0 }-> 2 :|: z' - 1 >= 0, z - 1 >= 0
   #compare(z, z') -{ 0 }-> 1 :|: z = 0, z' = 0
   #compare(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   #compare(z, z') -{ 0 }-> #compare(z - 1, z' - 1) :|: z' - 1 >= 0, z - 1 >= 0
   #compare(z, z') -{ 0 }-> #compare(z' - 1, z - 1) :|: z' - 1 >= 0, z - 1 >= 0
   #less(z, z') -{ 0 }-> 2 :|: z' - 1 >= 0, z = 0, 3 = 3
   #less(z, z') -{ 0 }-> 2 :|: z - 1 >= 0, z' = 0, 3 = 3
   #less(z, z') -{ 0 }-> 2 :|: z - 1 >= 0, z' - 1 >= 0, 3 = 3
   #less(z, z') -{ 0 }-> 1 :|: z = 0, z' = 0, 1 = 1
   #less(z, z') -{ 0 }-> 1 :|: z' - 1 >= 0, z = 0, 2 = 2
   #less(z, z') -{ 0 }-> 1 :|: z - 1 >= 0, z' = 0, 2 = 2
   #less(z, z') -{ 0 }-> 1 :|: z' - 1 >= 0, z - 1 >= 0, 2 = 2
   #less(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   #less(z, z') -{ 0 }-> 0 :|: z = 0, z' = 0, v0 >= 0, 1 = v0
   #less(z, z') -{ 0 }-> 0 :|: z' - 1 >= 0, z = 0, v0 >= 0, 2 = v0
   #less(z, z') -{ 0 }-> 0 :|: z' - 1 >= 0, z = 0, v0 >= 0, 3 = v0
   #less(z, z') -{ 0 }-> 0 :|: z - 1 >= 0, z' = 0, v0 >= 0, 3 = v0
   #less(z, z') -{ 0 }-> 0 :|: z - 1 >= 0, z' - 1 >= 0, v0 >= 0, 3 = v0
   #less(z, z') -{ 0 }-> 0 :|: z - 1 >= 0, z' = 0, v0 >= 0, 2 = v0
   #less(z, z') -{ 0 }-> 0 :|: z' - 1 >= 0, z - 1 >= 0, v0 >= 0, 2 = v0
   #less(z, z') -{ 0 }-> 0 :|: z' >= 0, z >= 0, v0 >= 0, 0 = v0
   #less(z, z') -{ 0 }-> #cklt(#compare(z - 1, z' - 1)) :|: z - 1 >= 0, z' - 1 >= 0
   #less(z, z') -{ 0 }-> #cklt(#compare(z' - 1, z - 1)) :|: z' - 1 >= 0, z - 1 >= 0
   APPEND(z, z') -{ 1 + 4*z }-> 1 + s :|: s >= 0, s <= 0, z' >= 0, z >= 0
   APPEND#1(z, z') -{ 2 + 4*z1 }-> 1 + s' :|: s' >= 0, s' <= 1, z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z' >= 0
   FLATTEN(z) -{ 1 }-> 1 + FLATTEN#1(z) :|: z >= 0
   FLATTEN#1(z) -{ 2 }-> 1 + APPEND(z0, append(flatten#1(z1), flatten#1(z2))) + s'' + FLATTEN(z1) :|: s'' >= 0, s'' <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 2 }-> 1 + APPEND(z0, append(flatten#1(z1), flatten#1(z2))) + s4 + FLATTEN(z2) :|: s4 >= 0, s4 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), flatten#1(z2))) + APPEND(flatten#1(z1), flatten#1(z2)) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), flatten#1(z2))) + APPEND(flatten#1(z1), flatten#1(z2)) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), flatten#1(z2))) + APPEND(flatten#1(z1), 0) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), flatten#1(z2))) + APPEND(flatten#1(z1), 0) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), flatten#1(z2))) + APPEND(0, flatten#1(z2)) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), flatten#1(z2))) + APPEND(0, flatten#1(z2)) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 2 }-> 1 + APPEND(z0, append(flatten#1(z1), 0)) + s1 + FLATTEN(z1) :|: s1 >= 0, s1 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 2 }-> 1 + APPEND(z0, append(flatten#1(z1), 0)) + s5 + FLATTEN(z2) :|: s5 >= 0, s5 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), 0)) + APPEND(flatten#1(z1), flatten#1(z2)) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), 0)) + APPEND(flatten#1(z1), flatten#1(z2)) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), 0)) + APPEND(flatten#1(z1), 0) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), 0)) + APPEND(flatten#1(z1), 0) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), 0)) + APPEND(0, flatten#1(z2)) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), 0)) + APPEND(0, flatten#1(z2)) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 2 }-> 1 + APPEND(z0, append(0, flatten#1(z2))) + s2 + FLATTEN(z1) :|: s2 >= 0, s2 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 2 }-> 1 + APPEND(z0, append(0, flatten#1(z2))) + s6 + FLATTEN(z2) :|: s6 >= 0, s6 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(0, flatten#1(z2))) + APPEND(flatten#1(z1), flatten#1(z2)) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(0, flatten#1(z2))) + APPEND(flatten#1(z1), flatten#1(z2)) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(0, flatten#1(z2))) + APPEND(flatten#1(z1), 0) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(0, flatten#1(z2))) + APPEND(flatten#1(z1), 0) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(0, flatten#1(z2))) + APPEND(0, flatten#1(z2)) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(0, flatten#1(z2))) + APPEND(0, flatten#1(z2)) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 2 }-> 1 + APPEND(z0, append(0, 0)) + s3 + FLATTEN(z1) :|: s3 >= 0, s3 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 2 }-> 1 + APPEND(z0, append(0, 0)) + s7 + FLATTEN(z2) :|: s7 >= 0, s7 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(0, 0)) + APPEND(flatten#1(z1), flatten#1(z2)) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(0, 0)) + APPEND(flatten#1(z1), flatten#1(z2)) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(0, 0)) + APPEND(flatten#1(z1), 0) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(0, 0)) + APPEND(flatten#1(z1), 0) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(0, 0)) + APPEND(0, flatten#1(z2)) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(0, 0)) + APPEND(0, flatten#1(z2)) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTENSORT(z) -{ 0 }-> 0 :|: z >= 0
   FLATTENSORT(z) -{ 0 }-> 1 + INSERTIONSORT(flatten#1(z)) :|: z >= 0
   FLATTENSORT(z) -{ 0 }-> 1 + INSERTIONSORT(0) :|: z >= 0
   INSERT(z, z') -{ 1 }-> 1 + INSERT#1(z', z) :|: z' >= 0, z >= 0
   INSERT#1(z, z') -{ 1 }-> 1 + INSERT#2(0, z', z0, z1) + #LESS(z0, z') :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z' >= 0
   INSERT#1(z, z') -{ 1 }-> 1 + INSERT#2(#cklt(#compare(z0, z')), z', z0, z1) + #LESS(z0, z') :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z' >= 0
   INSERT#2(z, z', z'', z3) -{ 1 }-> 1 + INSERT(z', z3) :|: z = 2, z'' >= 0, z' >= 0, z3 >= 0
   INSERTIONSORT(z) -{ 1 }-> 1 + INSERTIONSORT#1(z) :|: z >= 0
   INSERTIONSORT#1(z) -{ 1 }-> 1 + INSERT(z0, insertionsort#1(z1)) + INSERTIONSORT(z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   INSERTIONSORT#1(z) -{ 1 }-> 1 + INSERT(z0, 0) + INSERTIONSORT(z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   append(z, z') -{ 0 }-> append#1(z, z') :|: z' >= 0, z >= 0
   append(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   append#1(z, z') -{ 0 }-> z' :|: z' >= 0, z = 0
   append#1(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   append#1(z, z') -{ 0 }-> 1 + z0 + append(z1, z') :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z' >= 0
   flatten(z) -{ 0 }-> flatten#1(z) :|: z >= 0
   flatten(z) -{ 0 }-> 0 :|: z >= 0
   flatten#1(z) -{ 0 }-> append(z0, append(flatten#1(z1), flatten#1(z2))) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   flatten#1(z) -{ 0 }-> append(z0, append(flatten#1(z1), 0)) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   flatten#1(z) -{ 0 }-> append(z0, append(0, flatten#1(z2))) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   flatten#1(z) -{ 0 }-> append(z0, append(0, 0)) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   flatten#1(z) -{ 0 }-> 0 :|: z = 0
   flatten#1(z) -{ 0 }-> 0 :|: z >= 0
   insert(z, z') -{ 0 }-> insert#1(z', z) :|: z' >= 0, z >= 0
   insert(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   insert#1(z, z') -{ 0 }-> insert#2(0, z', z0, z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z' >= 0
   insert#1(z, z') -{ 0 }-> insert#2(#cklt(#compare(z0, z')), z', z0, z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z' >= 0
   insert#1(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   insert#1(z, z') -{ 0 }-> 1 + z' + 0 :|: z' >= 0, z = 0
   insert#2(z, z', z'', z3) -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0, z3 >= 0
   insert#2(z, z', z'', z3) -{ 0 }-> 1 + z' + (1 + z'' + z3) :|: z'' >= 0, z = 1, z' >= 0, z3 >= 0
   insert#2(z, z', z'', z3) -{ 0 }-> 1 + z'' + insert(z', z3) :|: z = 2, z'' >= 0, z' >= 0, z3 >= 0
   insertionsort(z) -{ 0 }-> insertionsort#1(z) :|: z >= 0
   insertionsort(z) -{ 0 }-> 0 :|: z >= 0
   insertionsort#1(z) -{ 0 }-> insert(z0, insertionsort#1(z1)) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   insertionsort#1(z) -{ 0 }-> insert(z0, 0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   insertionsort#1(z) -{ 0 }-> 0 :|: z = 0
   insertionsort#1(z) -{ 0 }-> 0 :|: z >= 0

Function symbols to be analyzed: {#COMPARE}, {append#1,append}, {#less}, {insert#2,insert,insert#1}, {#LESS}, {flatten#1}, {insertionsort#1}, {INSERT#1,INSERT#2,INSERT}, {flatten}, {FLATTEN,FLATTEN#1}, {insertionsort}, {INSERTIONSORT,INSERTIONSORT#1}, {FLATTENSORT}
Previous analysis results are:
  APPEND#1: runtime: O(n^1) [4*z], size: O(1) [0]
  APPEND: runtime: O(n^1) [1 + 4*z], size: O(1) [1]
  #cklt: runtime: O(1) [0], size: O(1) [2]
  #compare: runtime: O(1) [0], size: O(1) [3]

----------------------------------------

(53) ResultPropagationProof (UPPER BOUND(ID))
Applied inner abstraction using the recently inferred runtime/size bounds where possible.
----------------------------------------

(54)
Obligation:
Complexity RNTS consisting of the following rules:

   #COMPARE(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   #COMPARE(z, z') -{ 0 }-> 1 + #COMPARE(z - 1, z' - 1) :|: z' - 1 >= 0, z - 1 >= 0
   #COMPARE(z, z') -{ 0 }-> 1 + #COMPARE(z' - 1, z - 1) :|: z' - 1 >= 0, z - 1 >= 0
   #LESS(z, z') -{ 1 }-> 1 + #COMPARE(z, z') :|: z' >= 0, z >= 0
   #cklt(z) -{ 0 }-> 2 :|: z = 3
   #cklt(z) -{ 0 }-> 1 :|: z = 1
   #cklt(z) -{ 0 }-> 1 :|: z = 2
   #cklt(z) -{ 0 }-> 0 :|: z >= 0
   #compare(z, z') -{ 0 }-> s8 :|: s8 >= 0, s8 <= 3, z' - 1 >= 0, z - 1 >= 0
   #compare(z, z') -{ 0 }-> s9 :|: s9 >= 0, s9 <= 3, z' - 1 >= 0, z - 1 >= 0
   #compare(z, z') -{ 0 }-> 3 :|: z' - 1 >= 0, z = 0
   #compare(z, z') -{ 0 }-> 3 :|: z - 1 >= 0, z' = 0
   #compare(z, z') -{ 0 }-> 3 :|: z' - 1 >= 0, z - 1 >= 0
   #compare(z, z') -{ 0 }-> 2 :|: z' - 1 >= 0, z = 0
   #compare(z, z') -{ 0 }-> 2 :|: z - 1 >= 0, z' = 0
   #compare(z, z') -{ 0 }-> 2 :|: z' - 1 >= 0, z - 1 >= 0
   #compare(z, z') -{ 0 }-> 1 :|: z = 0, z' = 0
   #compare(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   #less(z, z') -{ 0 }-> s13 :|: s12 >= 0, s12 <= 3, s13 >= 0, s13 <= 2, z' - 1 >= 0, z - 1 >= 0
   #less(z, z') -{ 0 }-> s15 :|: s14 >= 0, s14 <= 3, s15 >= 0, s15 <= 2, z - 1 >= 0, z' - 1 >= 0
   #less(z, z') -{ 0 }-> 2 :|: z' - 1 >= 0, z = 0, 3 = 3
   #less(z, z') -{ 0 }-> 2 :|: z - 1 >= 0, z' = 0, 3 = 3
   #less(z, z') -{ 0 }-> 2 :|: z - 1 >= 0, z' - 1 >= 0, 3 = 3
   #less(z, z') -{ 0 }-> 1 :|: z = 0, z' = 0, 1 = 1
   #less(z, z') -{ 0 }-> 1 :|: z' - 1 >= 0, z = 0, 2 = 2
   #less(z, z') -{ 0 }-> 1 :|: z - 1 >= 0, z' = 0, 2 = 2
   #less(z, z') -{ 0 }-> 1 :|: z' - 1 >= 0, z - 1 >= 0, 2 = 2
   #less(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   #less(z, z') -{ 0 }-> 0 :|: z = 0, z' = 0, v0 >= 0, 1 = v0
   #less(z, z') -{ 0 }-> 0 :|: z' - 1 >= 0, z = 0, v0 >= 0, 2 = v0
   #less(z, z') -{ 0 }-> 0 :|: z' - 1 >= 0, z = 0, v0 >= 0, 3 = v0
   #less(z, z') -{ 0 }-> 0 :|: z - 1 >= 0, z' = 0, v0 >= 0, 3 = v0
   #less(z, z') -{ 0 }-> 0 :|: z - 1 >= 0, z' - 1 >= 0, v0 >= 0, 3 = v0
   #less(z, z') -{ 0 }-> 0 :|: z - 1 >= 0, z' = 0, v0 >= 0, 2 = v0
   #less(z, z') -{ 0 }-> 0 :|: z' - 1 >= 0, z - 1 >= 0, v0 >= 0, 2 = v0
   #less(z, z') -{ 0 }-> 0 :|: z' >= 0, z >= 0, v0 >= 0, 0 = v0
   APPEND(z, z') -{ 1 + 4*z }-> 1 + s :|: s >= 0, s <= 0, z' >= 0, z >= 0
   APPEND#1(z, z') -{ 2 + 4*z1 }-> 1 + s' :|: s' >= 0, s' <= 1, z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z' >= 0
   FLATTEN(z) -{ 1 }-> 1 + FLATTEN#1(z) :|: z >= 0
   FLATTEN#1(z) -{ 2 }-> 1 + APPEND(z0, append(flatten#1(z1), flatten#1(z2))) + s'' + FLATTEN(z1) :|: s'' >= 0, s'' <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 2 }-> 1 + APPEND(z0, append(flatten#1(z1), flatten#1(z2))) + s4 + FLATTEN(z2) :|: s4 >= 0, s4 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), flatten#1(z2))) + APPEND(flatten#1(z1), flatten#1(z2)) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), flatten#1(z2))) + APPEND(flatten#1(z1), flatten#1(z2)) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), flatten#1(z2))) + APPEND(flatten#1(z1), 0) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), flatten#1(z2))) + APPEND(flatten#1(z1), 0) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), flatten#1(z2))) + APPEND(0, flatten#1(z2)) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), flatten#1(z2))) + APPEND(0, flatten#1(z2)) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 2 }-> 1 + APPEND(z0, append(flatten#1(z1), 0)) + s1 + FLATTEN(z1) :|: s1 >= 0, s1 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 2 }-> 1 + APPEND(z0, append(flatten#1(z1), 0)) + s5 + FLATTEN(z2) :|: s5 >= 0, s5 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), 0)) + APPEND(flatten#1(z1), flatten#1(z2)) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), 0)) + APPEND(flatten#1(z1), flatten#1(z2)) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), 0)) + APPEND(flatten#1(z1), 0) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), 0)) + APPEND(flatten#1(z1), 0) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), 0)) + APPEND(0, flatten#1(z2)) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), 0)) + APPEND(0, flatten#1(z2)) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 2 }-> 1 + APPEND(z0, append(0, flatten#1(z2))) + s2 + FLATTEN(z1) :|: s2 >= 0, s2 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 2 }-> 1 + APPEND(z0, append(0, flatten#1(z2))) + s6 + FLATTEN(z2) :|: s6 >= 0, s6 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(0, flatten#1(z2))) + APPEND(flatten#1(z1), flatten#1(z2)) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(0, flatten#1(z2))) + APPEND(flatten#1(z1), flatten#1(z2)) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(0, flatten#1(z2))) + APPEND(flatten#1(z1), 0) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(0, flatten#1(z2))) + APPEND(flatten#1(z1), 0) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(0, flatten#1(z2))) + APPEND(0, flatten#1(z2)) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(0, flatten#1(z2))) + APPEND(0, flatten#1(z2)) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 2 }-> 1 + APPEND(z0, append(0, 0)) + s3 + FLATTEN(z1) :|: s3 >= 0, s3 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 2 }-> 1 + APPEND(z0, append(0, 0)) + s7 + FLATTEN(z2) :|: s7 >= 0, s7 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(0, 0)) + APPEND(flatten#1(z1), flatten#1(z2)) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(0, 0)) + APPEND(flatten#1(z1), flatten#1(z2)) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(0, 0)) + APPEND(flatten#1(z1), 0) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(0, 0)) + APPEND(flatten#1(z1), 0) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(0, 0)) + APPEND(0, flatten#1(z2)) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(0, 0)) + APPEND(0, flatten#1(z2)) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTENSORT(z) -{ 0 }-> 0 :|: z >= 0
   FLATTENSORT(z) -{ 0 }-> 1 + INSERTIONSORT(flatten#1(z)) :|: z >= 0
   FLATTENSORT(z) -{ 0 }-> 1 + INSERTIONSORT(0) :|: z >= 0
   INSERT(z, z') -{ 1 }-> 1 + INSERT#1(z', z) :|: z' >= 0, z >= 0
   INSERT#1(z, z') -{ 1 }-> 1 + INSERT#2(s11, z', z0, z1) + #LESS(z0, z') :|: s10 >= 0, s10 <= 3, s11 >= 0, s11 <= 2, z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z' >= 0
   INSERT#1(z, z') -{ 1 }-> 1 + INSERT#2(0, z', z0, z1) + #LESS(z0, z') :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z' >= 0
   INSERT#2(z, z', z'', z3) -{ 1 }-> 1 + INSERT(z', z3) :|: z = 2, z'' >= 0, z' >= 0, z3 >= 0
   INSERTIONSORT(z) -{ 1 }-> 1 + INSERTIONSORT#1(z) :|: z >= 0
   INSERTIONSORT#1(z) -{ 1 }-> 1 + INSERT(z0, insertionsort#1(z1)) + INSERTIONSORT(z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   INSERTIONSORT#1(z) -{ 1 }-> 1 + INSERT(z0, 0) + INSERTIONSORT(z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   append(z, z') -{ 0 }-> append#1(z, z') :|: z' >= 0, z >= 0
   append(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   append#1(z, z') -{ 0 }-> z' :|: z' >= 0, z = 0
   append#1(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   append#1(z, z') -{ 0 }-> 1 + z0 + append(z1, z') :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z' >= 0
   flatten(z) -{ 0 }-> flatten#1(z) :|: z >= 0
   flatten(z) -{ 0 }-> 0 :|: z >= 0
   flatten#1(z) -{ 0 }-> append(z0, append(flatten#1(z1), flatten#1(z2))) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   flatten#1(z) -{ 0 }-> append(z0, append(flatten#1(z1), 0)) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   flatten#1(z) -{ 0 }-> append(z0, append(0, flatten#1(z2))) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   flatten#1(z) -{ 0 }-> append(z0, append(0, 0)) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   flatten#1(z) -{ 0 }-> 0 :|: z = 0
   flatten#1(z) -{ 0 }-> 0 :|: z >= 0
   insert(z, z') -{ 0 }-> insert#1(z', z) :|: z' >= 0, z >= 0
   insert(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   insert#1(z, z') -{ 0 }-> insert#2(s17, z', z0, z1) :|: s16 >= 0, s16 <= 3, s17 >= 0, s17 <= 2, z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z' >= 0
   insert#1(z, z') -{ 0 }-> insert#2(0, z', z0, z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z' >= 0
   insert#1(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   insert#1(z, z') -{ 0 }-> 1 + z' + 0 :|: z' >= 0, z = 0
   insert#2(z, z', z'', z3) -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0, z3 >= 0
   insert#2(z, z', z'', z3) -{ 0 }-> 1 + z' + (1 + z'' + z3) :|: z'' >= 0, z = 1, z' >= 0, z3 >= 0
   insert#2(z, z', z'', z3) -{ 0 }-> 1 + z'' + insert(z', z3) :|: z = 2, z'' >= 0, z' >= 0, z3 >= 0
   insertionsort(z) -{ 0 }-> insertionsort#1(z) :|: z >= 0
   insertionsort(z) -{ 0 }-> 0 :|: z >= 0
   insertionsort#1(z) -{ 0 }-> insert(z0, insertionsort#1(z1)) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   insertionsort#1(z) -{ 0 }-> insert(z0, 0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   insertionsort#1(z) -{ 0 }-> 0 :|: z = 0
   insertionsort#1(z) -{ 0 }-> 0 :|: z >= 0

Function symbols to be analyzed: {#COMPARE}, {append#1,append}, {#less}, {insert#2,insert,insert#1}, {#LESS}, {flatten#1}, {insertionsort#1}, {INSERT#1,INSERT#2,INSERT}, {flatten}, {FLATTEN,FLATTEN#1}, {insertionsort}, {INSERTIONSORT,INSERTIONSORT#1}, {FLATTENSORT}
Previous analysis results are:
  APPEND#1: runtime: O(n^1) [4*z], size: O(1) [0]
  APPEND: runtime: O(n^1) [1 + 4*z], size: O(1) [1]
  #cklt: runtime: O(1) [0], size: O(1) [2]
  #compare: runtime: O(1) [0], size: O(1) [3]

----------------------------------------

(55) IntTrsBoundProof (UPPER BOUND(ID))

Computed SIZE bound using CoFloCo for: #COMPARE
after applying outer abstraction to obtain an ITS,
resulting in: O(n^1) with polynomial bound: z + z'

----------------------------------------

(56)
Obligation:
Complexity RNTS consisting of the following rules:

   #COMPARE(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   #COMPARE(z, z') -{ 0 }-> 1 + #COMPARE(z - 1, z' - 1) :|: z' - 1 >= 0, z - 1 >= 0
   #COMPARE(z, z') -{ 0 }-> 1 + #COMPARE(z' - 1, z - 1) :|: z' - 1 >= 0, z - 1 >= 0
   #LESS(z, z') -{ 1 }-> 1 + #COMPARE(z, z') :|: z' >= 0, z >= 0
   #cklt(z) -{ 0 }-> 2 :|: z = 3
   #cklt(z) -{ 0 }-> 1 :|: z = 1
   #cklt(z) -{ 0 }-> 1 :|: z = 2
   #cklt(z) -{ 0 }-> 0 :|: z >= 0
   #compare(z, z') -{ 0 }-> s8 :|: s8 >= 0, s8 <= 3, z' - 1 >= 0, z - 1 >= 0
   #compare(z, z') -{ 0 }-> s9 :|: s9 >= 0, s9 <= 3, z' - 1 >= 0, z - 1 >= 0
   #compare(z, z') -{ 0 }-> 3 :|: z' - 1 >= 0, z = 0
   #compare(z, z') -{ 0 }-> 3 :|: z - 1 >= 0, z' = 0
   #compare(z, z') -{ 0 }-> 3 :|: z' - 1 >= 0, z - 1 >= 0
   #compare(z, z') -{ 0 }-> 2 :|: z' - 1 >= 0, z = 0
   #compare(z, z') -{ 0 }-> 2 :|: z - 1 >= 0, z' = 0
   #compare(z, z') -{ 0 }-> 2 :|: z' - 1 >= 0, z - 1 >= 0
   #compare(z, z') -{ 0 }-> 1 :|: z = 0, z' = 0
   #compare(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   #less(z, z') -{ 0 }-> s13 :|: s12 >= 0, s12 <= 3, s13 >= 0, s13 <= 2, z' - 1 >= 0, z - 1 >= 0
   #less(z, z') -{ 0 }-> s15 :|: s14 >= 0, s14 <= 3, s15 >= 0, s15 <= 2, z - 1 >= 0, z' - 1 >= 0
   #less(z, z') -{ 0 }-> 2 :|: z' - 1 >= 0, z = 0, 3 = 3
   #less(z, z') -{ 0 }-> 2 :|: z - 1 >= 0, z' = 0, 3 = 3
   #less(z, z') -{ 0 }-> 2 :|: z - 1 >= 0, z' - 1 >= 0, 3 = 3
   #less(z, z') -{ 0 }-> 1 :|: z = 0, z' = 0, 1 = 1
   #less(z, z') -{ 0 }-> 1 :|: z' - 1 >= 0, z = 0, 2 = 2
   #less(z, z') -{ 0 }-> 1 :|: z - 1 >= 0, z' = 0, 2 = 2
   #less(z, z') -{ 0 }-> 1 :|: z' - 1 >= 0, z - 1 >= 0, 2 = 2
   #less(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   #less(z, z') -{ 0 }-> 0 :|: z = 0, z' = 0, v0 >= 0, 1 = v0
   #less(z, z') -{ 0 }-> 0 :|: z' - 1 >= 0, z = 0, v0 >= 0, 2 = v0
   #less(z, z') -{ 0 }-> 0 :|: z' - 1 >= 0, z = 0, v0 >= 0, 3 = v0
   #less(z, z') -{ 0 }-> 0 :|: z - 1 >= 0, z' = 0, v0 >= 0, 3 = v0
   #less(z, z') -{ 0 }-> 0 :|: z - 1 >= 0, z' - 1 >= 0, v0 >= 0, 3 = v0
   #less(z, z') -{ 0 }-> 0 :|: z - 1 >= 0, z' = 0, v0 >= 0, 2 = v0
   #less(z, z') -{ 0 }-> 0 :|: z' - 1 >= 0, z - 1 >= 0, v0 >= 0, 2 = v0
   #less(z, z') -{ 0 }-> 0 :|: z' >= 0, z >= 0, v0 >= 0, 0 = v0
   APPEND(z, z') -{ 1 + 4*z }-> 1 + s :|: s >= 0, s <= 0, z' >= 0, z >= 0
   APPEND#1(z, z') -{ 2 + 4*z1 }-> 1 + s' :|: s' >= 0, s' <= 1, z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z' >= 0
   FLATTEN(z) -{ 1 }-> 1 + FLATTEN#1(z) :|: z >= 0
   FLATTEN#1(z) -{ 2 }-> 1 + APPEND(z0, append(flatten#1(z1), flatten#1(z2))) + s'' + FLATTEN(z1) :|: s'' >= 0, s'' <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 2 }-> 1 + APPEND(z0, append(flatten#1(z1), flatten#1(z2))) + s4 + FLATTEN(z2) :|: s4 >= 0, s4 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), flatten#1(z2))) + APPEND(flatten#1(z1), flatten#1(z2)) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), flatten#1(z2))) + APPEND(flatten#1(z1), flatten#1(z2)) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), flatten#1(z2))) + APPEND(flatten#1(z1), 0) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), flatten#1(z2))) + APPEND(flatten#1(z1), 0) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), flatten#1(z2))) + APPEND(0, flatten#1(z2)) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), flatten#1(z2))) + APPEND(0, flatten#1(z2)) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 2 }-> 1 + APPEND(z0, append(flatten#1(z1), 0)) + s1 + FLATTEN(z1) :|: s1 >= 0, s1 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 2 }-> 1 + APPEND(z0, append(flatten#1(z1), 0)) + s5 + FLATTEN(z2) :|: s5 >= 0, s5 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), 0)) + APPEND(flatten#1(z1), flatten#1(z2)) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), 0)) + APPEND(flatten#1(z1), flatten#1(z2)) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), 0)) + APPEND(flatten#1(z1), 0) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), 0)) + APPEND(flatten#1(z1), 0) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), 0)) + APPEND(0, flatten#1(z2)) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), 0)) + APPEND(0, flatten#1(z2)) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 2 }-> 1 + APPEND(z0, append(0, flatten#1(z2))) + s2 + FLATTEN(z1) :|: s2 >= 0, s2 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 2 }-> 1 + APPEND(z0, append(0, flatten#1(z2))) + s6 + FLATTEN(z2) :|: s6 >= 0, s6 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(0, flatten#1(z2))) + APPEND(flatten#1(z1), flatten#1(z2)) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(0, flatten#1(z2))) + APPEND(flatten#1(z1), flatten#1(z2)) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(0, flatten#1(z2))) + APPEND(flatten#1(z1), 0) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(0, flatten#1(z2))) + APPEND(flatten#1(z1), 0) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(0, flatten#1(z2))) + APPEND(0, flatten#1(z2)) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(0, flatten#1(z2))) + APPEND(0, flatten#1(z2)) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 2 }-> 1 + APPEND(z0, append(0, 0)) + s3 + FLATTEN(z1) :|: s3 >= 0, s3 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 2 }-> 1 + APPEND(z0, append(0, 0)) + s7 + FLATTEN(z2) :|: s7 >= 0, s7 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(0, 0)) + APPEND(flatten#1(z1), flatten#1(z2)) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(0, 0)) + APPEND(flatten#1(z1), flatten#1(z2)) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(0, 0)) + APPEND(flatten#1(z1), 0) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(0, 0)) + APPEND(flatten#1(z1), 0) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(0, 0)) + APPEND(0, flatten#1(z2)) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(0, 0)) + APPEND(0, flatten#1(z2)) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTENSORT(z) -{ 0 }-> 0 :|: z >= 0
   FLATTENSORT(z) -{ 0 }-> 1 + INSERTIONSORT(flatten#1(z)) :|: z >= 0
   FLATTENSORT(z) -{ 0 }-> 1 + INSERTIONSORT(0) :|: z >= 0
   INSERT(z, z') -{ 1 }-> 1 + INSERT#1(z', z) :|: z' >= 0, z >= 0
   INSERT#1(z, z') -{ 1 }-> 1 + INSERT#2(s11, z', z0, z1) + #LESS(z0, z') :|: s10 >= 0, s10 <= 3, s11 >= 0, s11 <= 2, z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z' >= 0
   INSERT#1(z, z') -{ 1 }-> 1 + INSERT#2(0, z', z0, z1) + #LESS(z0, z') :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z' >= 0
   INSERT#2(z, z', z'', z3) -{ 1 }-> 1 + INSERT(z', z3) :|: z = 2, z'' >= 0, z' >= 0, z3 >= 0
   INSERTIONSORT(z) -{ 1 }-> 1 + INSERTIONSORT#1(z) :|: z >= 0
   INSERTIONSORT#1(z) -{ 1 }-> 1 + INSERT(z0, insertionsort#1(z1)) + INSERTIONSORT(z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   INSERTIONSORT#1(z) -{ 1 }-> 1 + INSERT(z0, 0) + INSERTIONSORT(z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   append(z, z') -{ 0 }-> append#1(z, z') :|: z' >= 0, z >= 0
   append(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   append#1(z, z') -{ 0 }-> z' :|: z' >= 0, z = 0
   append#1(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   append#1(z, z') -{ 0 }-> 1 + z0 + append(z1, z') :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z' >= 0
   flatten(z) -{ 0 }-> flatten#1(z) :|: z >= 0
   flatten(z) -{ 0 }-> 0 :|: z >= 0
   flatten#1(z) -{ 0 }-> append(z0, append(flatten#1(z1), flatten#1(z2))) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   flatten#1(z) -{ 0 }-> append(z0, append(flatten#1(z1), 0)) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   flatten#1(z) -{ 0 }-> append(z0, append(0, flatten#1(z2))) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   flatten#1(z) -{ 0 }-> append(z0, append(0, 0)) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   flatten#1(z) -{ 0 }-> 0 :|: z = 0
   flatten#1(z) -{ 0 }-> 0 :|: z >= 0
   insert(z, z') -{ 0 }-> insert#1(z', z) :|: z' >= 0, z >= 0
   insert(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   insert#1(z, z') -{ 0 }-> insert#2(s17, z', z0, z1) :|: s16 >= 0, s16 <= 3, s17 >= 0, s17 <= 2, z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z' >= 0
   insert#1(z, z') -{ 0 }-> insert#2(0, z', z0, z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z' >= 0
   insert#1(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   insert#1(z, z') -{ 0 }-> 1 + z' + 0 :|: z' >= 0, z = 0
   insert#2(z, z', z'', z3) -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0, z3 >= 0
   insert#2(z, z', z'', z3) -{ 0 }-> 1 + z' + (1 + z'' + z3) :|: z'' >= 0, z = 1, z' >= 0, z3 >= 0
   insert#2(z, z', z'', z3) -{ 0 }-> 1 + z'' + insert(z', z3) :|: z = 2, z'' >= 0, z' >= 0, z3 >= 0
   insertionsort(z) -{ 0 }-> insertionsort#1(z) :|: z >= 0
   insertionsort(z) -{ 0 }-> 0 :|: z >= 0
   insertionsort#1(z) -{ 0 }-> insert(z0, insertionsort#1(z1)) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   insertionsort#1(z) -{ 0 }-> insert(z0, 0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   insertionsort#1(z) -{ 0 }-> 0 :|: z = 0
   insertionsort#1(z) -{ 0 }-> 0 :|: z >= 0

Function symbols to be analyzed: {#COMPARE}, {append#1,append}, {#less}, {insert#2,insert,insert#1}, {#LESS}, {flatten#1}, {insertionsort#1}, {INSERT#1,INSERT#2,INSERT}, {flatten}, {FLATTEN,FLATTEN#1}, {insertionsort}, {INSERTIONSORT,INSERTIONSORT#1}, {FLATTENSORT}
Previous analysis results are:
  APPEND#1: runtime: O(n^1) [4*z], size: O(1) [0]
  APPEND: runtime: O(n^1) [1 + 4*z], size: O(1) [1]
  #cklt: runtime: O(1) [0], size: O(1) [2]
  #compare: runtime: O(1) [0], size: O(1) [3]
  #COMPARE: runtime: ?, size: O(n^1) [z + z']

----------------------------------------

(57) IntTrsBoundProof (UPPER BOUND(ID))

Computed RUNTIME bound using CoFloCo for: #COMPARE
after applying outer abstraction to obtain an ITS,
resulting in: O(1) with polynomial bound: 0

----------------------------------------

(58)
Obligation:
Complexity RNTS consisting of the following rules:

   #COMPARE(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   #COMPARE(z, z') -{ 0 }-> 1 + #COMPARE(z - 1, z' - 1) :|: z' - 1 >= 0, z - 1 >= 0
   #COMPARE(z, z') -{ 0 }-> 1 + #COMPARE(z' - 1, z - 1) :|: z' - 1 >= 0, z - 1 >= 0
   #LESS(z, z') -{ 1 }-> 1 + #COMPARE(z, z') :|: z' >= 0, z >= 0
   #cklt(z) -{ 0 }-> 2 :|: z = 3
   #cklt(z) -{ 0 }-> 1 :|: z = 1
   #cklt(z) -{ 0 }-> 1 :|: z = 2
   #cklt(z) -{ 0 }-> 0 :|: z >= 0
   #compare(z, z') -{ 0 }-> s8 :|: s8 >= 0, s8 <= 3, z' - 1 >= 0, z - 1 >= 0
   #compare(z, z') -{ 0 }-> s9 :|: s9 >= 0, s9 <= 3, z' - 1 >= 0, z - 1 >= 0
   #compare(z, z') -{ 0 }-> 3 :|: z' - 1 >= 0, z = 0
   #compare(z, z') -{ 0 }-> 3 :|: z - 1 >= 0, z' = 0
   #compare(z, z') -{ 0 }-> 3 :|: z' - 1 >= 0, z - 1 >= 0
   #compare(z, z') -{ 0 }-> 2 :|: z' - 1 >= 0, z = 0
   #compare(z, z') -{ 0 }-> 2 :|: z - 1 >= 0, z' = 0
   #compare(z, z') -{ 0 }-> 2 :|: z' - 1 >= 0, z - 1 >= 0
   #compare(z, z') -{ 0 }-> 1 :|: z = 0, z' = 0
   #compare(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   #less(z, z') -{ 0 }-> s13 :|: s12 >= 0, s12 <= 3, s13 >= 0, s13 <= 2, z' - 1 >= 0, z - 1 >= 0
   #less(z, z') -{ 0 }-> s15 :|: s14 >= 0, s14 <= 3, s15 >= 0, s15 <= 2, z - 1 >= 0, z' - 1 >= 0
   #less(z, z') -{ 0 }-> 2 :|: z' - 1 >= 0, z = 0, 3 = 3
   #less(z, z') -{ 0 }-> 2 :|: z - 1 >= 0, z' = 0, 3 = 3
   #less(z, z') -{ 0 }-> 2 :|: z - 1 >= 0, z' - 1 >= 0, 3 = 3
   #less(z, z') -{ 0 }-> 1 :|: z = 0, z' = 0, 1 = 1
   #less(z, z') -{ 0 }-> 1 :|: z' - 1 >= 0, z = 0, 2 = 2
   #less(z, z') -{ 0 }-> 1 :|: z - 1 >= 0, z' = 0, 2 = 2
   #less(z, z') -{ 0 }-> 1 :|: z' - 1 >= 0, z - 1 >= 0, 2 = 2
   #less(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   #less(z, z') -{ 0 }-> 0 :|: z = 0, z' = 0, v0 >= 0, 1 = v0
   #less(z, z') -{ 0 }-> 0 :|: z' - 1 >= 0, z = 0, v0 >= 0, 2 = v0
   #less(z, z') -{ 0 }-> 0 :|: z' - 1 >= 0, z = 0, v0 >= 0, 3 = v0
   #less(z, z') -{ 0 }-> 0 :|: z - 1 >= 0, z' = 0, v0 >= 0, 3 = v0
   #less(z, z') -{ 0 }-> 0 :|: z - 1 >= 0, z' - 1 >= 0, v0 >= 0, 3 = v0
   #less(z, z') -{ 0 }-> 0 :|: z - 1 >= 0, z' = 0, v0 >= 0, 2 = v0
   #less(z, z') -{ 0 }-> 0 :|: z' - 1 >= 0, z - 1 >= 0, v0 >= 0, 2 = v0
   #less(z, z') -{ 0 }-> 0 :|: z' >= 0, z >= 0, v0 >= 0, 0 = v0
   APPEND(z, z') -{ 1 + 4*z }-> 1 + s :|: s >= 0, s <= 0, z' >= 0, z >= 0
   APPEND#1(z, z') -{ 2 + 4*z1 }-> 1 + s' :|: s' >= 0, s' <= 1, z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z' >= 0
   FLATTEN(z) -{ 1 }-> 1 + FLATTEN#1(z) :|: z >= 0
   FLATTEN#1(z) -{ 2 }-> 1 + APPEND(z0, append(flatten#1(z1), flatten#1(z2))) + s'' + FLATTEN(z1) :|: s'' >= 0, s'' <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 2 }-> 1 + APPEND(z0, append(flatten#1(z1), flatten#1(z2))) + s4 + FLATTEN(z2) :|: s4 >= 0, s4 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), flatten#1(z2))) + APPEND(flatten#1(z1), flatten#1(z2)) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), flatten#1(z2))) + APPEND(flatten#1(z1), flatten#1(z2)) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), flatten#1(z2))) + APPEND(flatten#1(z1), 0) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), flatten#1(z2))) + APPEND(flatten#1(z1), 0) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), flatten#1(z2))) + APPEND(0, flatten#1(z2)) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), flatten#1(z2))) + APPEND(0, flatten#1(z2)) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 2 }-> 1 + APPEND(z0, append(flatten#1(z1), 0)) + s1 + FLATTEN(z1) :|: s1 >= 0, s1 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 2 }-> 1 + APPEND(z0, append(flatten#1(z1), 0)) + s5 + FLATTEN(z2) :|: s5 >= 0, s5 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), 0)) + APPEND(flatten#1(z1), flatten#1(z2)) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), 0)) + APPEND(flatten#1(z1), flatten#1(z2)) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), 0)) + APPEND(flatten#1(z1), 0) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), 0)) + APPEND(flatten#1(z1), 0) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), 0)) + APPEND(0, flatten#1(z2)) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), 0)) + APPEND(0, flatten#1(z2)) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 2 }-> 1 + APPEND(z0, append(0, flatten#1(z2))) + s2 + FLATTEN(z1) :|: s2 >= 0, s2 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 2 }-> 1 + APPEND(z0, append(0, flatten#1(z2))) + s6 + FLATTEN(z2) :|: s6 >= 0, s6 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(0, flatten#1(z2))) + APPEND(flatten#1(z1), flatten#1(z2)) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(0, flatten#1(z2))) + APPEND(flatten#1(z1), flatten#1(z2)) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(0, flatten#1(z2))) + APPEND(flatten#1(z1), 0) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(0, flatten#1(z2))) + APPEND(flatten#1(z1), 0) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(0, flatten#1(z2))) + APPEND(0, flatten#1(z2)) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(0, flatten#1(z2))) + APPEND(0, flatten#1(z2)) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 2 }-> 1 + APPEND(z0, append(0, 0)) + s3 + FLATTEN(z1) :|: s3 >= 0, s3 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 2 }-> 1 + APPEND(z0, append(0, 0)) + s7 + FLATTEN(z2) :|: s7 >= 0, s7 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(0, 0)) + APPEND(flatten#1(z1), flatten#1(z2)) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(0, 0)) + APPEND(flatten#1(z1), flatten#1(z2)) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(0, 0)) + APPEND(flatten#1(z1), 0) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(0, 0)) + APPEND(flatten#1(z1), 0) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(0, 0)) + APPEND(0, flatten#1(z2)) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(0, 0)) + APPEND(0, flatten#1(z2)) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTENSORT(z) -{ 0 }-> 0 :|: z >= 0
   FLATTENSORT(z) -{ 0 }-> 1 + INSERTIONSORT(flatten#1(z)) :|: z >= 0
   FLATTENSORT(z) -{ 0 }-> 1 + INSERTIONSORT(0) :|: z >= 0
   INSERT(z, z') -{ 1 }-> 1 + INSERT#1(z', z) :|: z' >= 0, z >= 0
   INSERT#1(z, z') -{ 1 }-> 1 + INSERT#2(s11, z', z0, z1) + #LESS(z0, z') :|: s10 >= 0, s10 <= 3, s11 >= 0, s11 <= 2, z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z' >= 0
   INSERT#1(z, z') -{ 1 }-> 1 + INSERT#2(0, z', z0, z1) + #LESS(z0, z') :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z' >= 0
   INSERT#2(z, z', z'', z3) -{ 1 }-> 1 + INSERT(z', z3) :|: z = 2, z'' >= 0, z' >= 0, z3 >= 0
   INSERTIONSORT(z) -{ 1 }-> 1 + INSERTIONSORT#1(z) :|: z >= 0
   INSERTIONSORT#1(z) -{ 1 }-> 1 + INSERT(z0, insertionsort#1(z1)) + INSERTIONSORT(z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   INSERTIONSORT#1(z) -{ 1 }-> 1 + INSERT(z0, 0) + INSERTIONSORT(z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   append(z, z') -{ 0 }-> append#1(z, z') :|: z' >= 0, z >= 0
   append(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   append#1(z, z') -{ 0 }-> z' :|: z' >= 0, z = 0
   append#1(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   append#1(z, z') -{ 0 }-> 1 + z0 + append(z1, z') :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z' >= 0
   flatten(z) -{ 0 }-> flatten#1(z) :|: z >= 0
   flatten(z) -{ 0 }-> 0 :|: z >= 0
   flatten#1(z) -{ 0 }-> append(z0, append(flatten#1(z1), flatten#1(z2))) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   flatten#1(z) -{ 0 }-> append(z0, append(flatten#1(z1), 0)) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   flatten#1(z) -{ 0 }-> append(z0, append(0, flatten#1(z2))) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   flatten#1(z) -{ 0 }-> append(z0, append(0, 0)) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   flatten#1(z) -{ 0 }-> 0 :|: z = 0
   flatten#1(z) -{ 0 }-> 0 :|: z >= 0
   insert(z, z') -{ 0 }-> insert#1(z', z) :|: z' >= 0, z >= 0
   insert(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   insert#1(z, z') -{ 0 }-> insert#2(s17, z', z0, z1) :|: s16 >= 0, s16 <= 3, s17 >= 0, s17 <= 2, z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z' >= 0
   insert#1(z, z') -{ 0 }-> insert#2(0, z', z0, z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z' >= 0
   insert#1(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   insert#1(z, z') -{ 0 }-> 1 + z' + 0 :|: z' >= 0, z = 0
   insert#2(z, z', z'', z3) -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0, z3 >= 0
   insert#2(z, z', z'', z3) -{ 0 }-> 1 + z' + (1 + z'' + z3) :|: z'' >= 0, z = 1, z' >= 0, z3 >= 0
   insert#2(z, z', z'', z3) -{ 0 }-> 1 + z'' + insert(z', z3) :|: z = 2, z'' >= 0, z' >= 0, z3 >= 0
   insertionsort(z) -{ 0 }-> insertionsort#1(z) :|: z >= 0
   insertionsort(z) -{ 0 }-> 0 :|: z >= 0
   insertionsort#1(z) -{ 0 }-> insert(z0, insertionsort#1(z1)) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   insertionsort#1(z) -{ 0 }-> insert(z0, 0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   insertionsort#1(z) -{ 0 }-> 0 :|: z = 0
   insertionsort#1(z) -{ 0 }-> 0 :|: z >= 0

Function symbols to be analyzed: {append#1,append}, {#less}, {insert#2,insert,insert#1}, {#LESS}, {flatten#1}, {insertionsort#1}, {INSERT#1,INSERT#2,INSERT}, {flatten}, {FLATTEN,FLATTEN#1}, {insertionsort}, {INSERTIONSORT,INSERTIONSORT#1}, {FLATTENSORT}
Previous analysis results are:
  APPEND#1: runtime: O(n^1) [4*z], size: O(1) [0]
  APPEND: runtime: O(n^1) [1 + 4*z], size: O(1) [1]
  #cklt: runtime: O(1) [0], size: O(1) [2]
  #compare: runtime: O(1) [0], size: O(1) [3]
  #COMPARE: runtime: O(1) [0], size: O(n^1) [z + z']

----------------------------------------

(59) ResultPropagationProof (UPPER BOUND(ID))
Applied inner abstraction using the recently inferred runtime/size bounds where possible.
----------------------------------------

(60)
Obligation:
Complexity RNTS consisting of the following rules:

   #COMPARE(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   #COMPARE(z, z') -{ 0 }-> 1 + s19 :|: s19 >= 0, s19 <= z' - 1 + (z - 1), z' - 1 >= 0, z - 1 >= 0
   #COMPARE(z, z') -{ 0 }-> 1 + s20 :|: s20 >= 0, s20 <= z - 1 + (z' - 1), z' - 1 >= 0, z - 1 >= 0
   #LESS(z, z') -{ 1 }-> 1 + s18 :|: s18 >= 0, s18 <= z + z', z' >= 0, z >= 0
   #cklt(z) -{ 0 }-> 2 :|: z = 3
   #cklt(z) -{ 0 }-> 1 :|: z = 1
   #cklt(z) -{ 0 }-> 1 :|: z = 2
   #cklt(z) -{ 0 }-> 0 :|: z >= 0
   #compare(z, z') -{ 0 }-> s8 :|: s8 >= 0, s8 <= 3, z' - 1 >= 0, z - 1 >= 0
   #compare(z, z') -{ 0 }-> s9 :|: s9 >= 0, s9 <= 3, z' - 1 >= 0, z - 1 >= 0
   #compare(z, z') -{ 0 }-> 3 :|: z' - 1 >= 0, z = 0
   #compare(z, z') -{ 0 }-> 3 :|: z - 1 >= 0, z' = 0
   #compare(z, z') -{ 0 }-> 3 :|: z' - 1 >= 0, z - 1 >= 0
   #compare(z, z') -{ 0 }-> 2 :|: z' - 1 >= 0, z = 0
   #compare(z, z') -{ 0 }-> 2 :|: z - 1 >= 0, z' = 0
   #compare(z, z') -{ 0 }-> 2 :|: z' - 1 >= 0, z - 1 >= 0
   #compare(z, z') -{ 0 }-> 1 :|: z = 0, z' = 0
   #compare(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   #less(z, z') -{ 0 }-> s13 :|: s12 >= 0, s12 <= 3, s13 >= 0, s13 <= 2, z' - 1 >= 0, z - 1 >= 0
   #less(z, z') -{ 0 }-> s15 :|: s14 >= 0, s14 <= 3, s15 >= 0, s15 <= 2, z - 1 >= 0, z' - 1 >= 0
   #less(z, z') -{ 0 }-> 2 :|: z' - 1 >= 0, z = 0, 3 = 3
   #less(z, z') -{ 0 }-> 2 :|: z - 1 >= 0, z' = 0, 3 = 3
   #less(z, z') -{ 0 }-> 2 :|: z - 1 >= 0, z' - 1 >= 0, 3 = 3
   #less(z, z') -{ 0 }-> 1 :|: z = 0, z' = 0, 1 = 1
   #less(z, z') -{ 0 }-> 1 :|: z' - 1 >= 0, z = 0, 2 = 2
   #less(z, z') -{ 0 }-> 1 :|: z - 1 >= 0, z' = 0, 2 = 2
   #less(z, z') -{ 0 }-> 1 :|: z' - 1 >= 0, z - 1 >= 0, 2 = 2
   #less(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   #less(z, z') -{ 0 }-> 0 :|: z = 0, z' = 0, v0 >= 0, 1 = v0
   #less(z, z') -{ 0 }-> 0 :|: z' - 1 >= 0, z = 0, v0 >= 0, 2 = v0
   #less(z, z') -{ 0 }-> 0 :|: z' - 1 >= 0, z = 0, v0 >= 0, 3 = v0
   #less(z, z') -{ 0 }-> 0 :|: z - 1 >= 0, z' = 0, v0 >= 0, 3 = v0
   #less(z, z') -{ 0 }-> 0 :|: z - 1 >= 0, z' - 1 >= 0, v0 >= 0, 3 = v0
   #less(z, z') -{ 0 }-> 0 :|: z - 1 >= 0, z' = 0, v0 >= 0, 2 = v0
   #less(z, z') -{ 0 }-> 0 :|: z' - 1 >= 0, z - 1 >= 0, v0 >= 0, 2 = v0
   #less(z, z') -{ 0 }-> 0 :|: z' >= 0, z >= 0, v0 >= 0, 0 = v0
   APPEND(z, z') -{ 1 + 4*z }-> 1 + s :|: s >= 0, s <= 0, z' >= 0, z >= 0
   APPEND#1(z, z') -{ 2 + 4*z1 }-> 1 + s' :|: s' >= 0, s' <= 1, z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z' >= 0
   FLATTEN(z) -{ 1 }-> 1 + FLATTEN#1(z) :|: z >= 0
   FLATTEN#1(z) -{ 2 }-> 1 + APPEND(z0, append(flatten#1(z1), flatten#1(z2))) + s'' + FLATTEN(z1) :|: s'' >= 0, s'' <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 2 }-> 1 + APPEND(z0, append(flatten#1(z1), flatten#1(z2))) + s4 + FLATTEN(z2) :|: s4 >= 0, s4 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), flatten#1(z2))) + APPEND(flatten#1(z1), flatten#1(z2)) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), flatten#1(z2))) + APPEND(flatten#1(z1), flatten#1(z2)) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), flatten#1(z2))) + APPEND(flatten#1(z1), 0) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), flatten#1(z2))) + APPEND(flatten#1(z1), 0) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), flatten#1(z2))) + APPEND(0, flatten#1(z2)) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), flatten#1(z2))) + APPEND(0, flatten#1(z2)) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 2 }-> 1 + APPEND(z0, append(flatten#1(z1), 0)) + s1 + FLATTEN(z1) :|: s1 >= 0, s1 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 2 }-> 1 + APPEND(z0, append(flatten#1(z1), 0)) + s5 + FLATTEN(z2) :|: s5 >= 0, s5 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), 0)) + APPEND(flatten#1(z1), flatten#1(z2)) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), 0)) + APPEND(flatten#1(z1), flatten#1(z2)) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), 0)) + APPEND(flatten#1(z1), 0) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), 0)) + APPEND(flatten#1(z1), 0) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), 0)) + APPEND(0, flatten#1(z2)) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), 0)) + APPEND(0, flatten#1(z2)) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 2 }-> 1 + APPEND(z0, append(0, flatten#1(z2))) + s2 + FLATTEN(z1) :|: s2 >= 0, s2 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 2 }-> 1 + APPEND(z0, append(0, flatten#1(z2))) + s6 + FLATTEN(z2) :|: s6 >= 0, s6 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(0, flatten#1(z2))) + APPEND(flatten#1(z1), flatten#1(z2)) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(0, flatten#1(z2))) + APPEND(flatten#1(z1), flatten#1(z2)) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(0, flatten#1(z2))) + APPEND(flatten#1(z1), 0) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(0, flatten#1(z2))) + APPEND(flatten#1(z1), 0) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(0, flatten#1(z2))) + APPEND(0, flatten#1(z2)) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(0, flatten#1(z2))) + APPEND(0, flatten#1(z2)) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 2 }-> 1 + APPEND(z0, append(0, 0)) + s3 + FLATTEN(z1) :|: s3 >= 0, s3 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 2 }-> 1 + APPEND(z0, append(0, 0)) + s7 + FLATTEN(z2) :|: s7 >= 0, s7 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(0, 0)) + APPEND(flatten#1(z1), flatten#1(z2)) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(0, 0)) + APPEND(flatten#1(z1), flatten#1(z2)) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(0, 0)) + APPEND(flatten#1(z1), 0) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(0, 0)) + APPEND(flatten#1(z1), 0) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(0, 0)) + APPEND(0, flatten#1(z2)) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(0, 0)) + APPEND(0, flatten#1(z2)) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTENSORT(z) -{ 0 }-> 0 :|: z >= 0
   FLATTENSORT(z) -{ 0 }-> 1 + INSERTIONSORT(flatten#1(z)) :|: z >= 0
   FLATTENSORT(z) -{ 0 }-> 1 + INSERTIONSORT(0) :|: z >= 0
   INSERT(z, z') -{ 1 }-> 1 + INSERT#1(z', z) :|: z' >= 0, z >= 0
   INSERT#1(z, z') -{ 1 }-> 1 + INSERT#2(s11, z', z0, z1) + #LESS(z0, z') :|: s10 >= 0, s10 <= 3, s11 >= 0, s11 <= 2, z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z' >= 0
   INSERT#1(z, z') -{ 1 }-> 1 + INSERT#2(0, z', z0, z1) + #LESS(z0, z') :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z' >= 0
   INSERT#2(z, z', z'', z3) -{ 1 }-> 1 + INSERT(z', z3) :|: z = 2, z'' >= 0, z' >= 0, z3 >= 0
   INSERTIONSORT(z) -{ 1 }-> 1 + INSERTIONSORT#1(z) :|: z >= 0
   INSERTIONSORT#1(z) -{ 1 }-> 1 + INSERT(z0, insertionsort#1(z1)) + INSERTIONSORT(z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   INSERTIONSORT#1(z) -{ 1 }-> 1 + INSERT(z0, 0) + INSERTIONSORT(z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   append(z, z') -{ 0 }-> append#1(z, z') :|: z' >= 0, z >= 0
   append(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   append#1(z, z') -{ 0 }-> z' :|: z' >= 0, z = 0
   append#1(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   append#1(z, z') -{ 0 }-> 1 + z0 + append(z1, z') :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z' >= 0
   flatten(z) -{ 0 }-> flatten#1(z) :|: z >= 0
   flatten(z) -{ 0 }-> 0 :|: z >= 0
   flatten#1(z) -{ 0 }-> append(z0, append(flatten#1(z1), flatten#1(z2))) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   flatten#1(z) -{ 0 }-> append(z0, append(flatten#1(z1), 0)) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   flatten#1(z) -{ 0 }-> append(z0, append(0, flatten#1(z2))) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   flatten#1(z) -{ 0 }-> append(z0, append(0, 0)) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   flatten#1(z) -{ 0 }-> 0 :|: z = 0
   flatten#1(z) -{ 0 }-> 0 :|: z >= 0
   insert(z, z') -{ 0 }-> insert#1(z', z) :|: z' >= 0, z >= 0
   insert(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   insert#1(z, z') -{ 0 }-> insert#2(s17, z', z0, z1) :|: s16 >= 0, s16 <= 3, s17 >= 0, s17 <= 2, z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z' >= 0
   insert#1(z, z') -{ 0 }-> insert#2(0, z', z0, z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z' >= 0
   insert#1(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   insert#1(z, z') -{ 0 }-> 1 + z' + 0 :|: z' >= 0, z = 0
   insert#2(z, z', z'', z3) -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0, z3 >= 0
   insert#2(z, z', z'', z3) -{ 0 }-> 1 + z' + (1 + z'' + z3) :|: z'' >= 0, z = 1, z' >= 0, z3 >= 0
   insert#2(z, z', z'', z3) -{ 0 }-> 1 + z'' + insert(z', z3) :|: z = 2, z'' >= 0, z' >= 0, z3 >= 0
   insertionsort(z) -{ 0 }-> insertionsort#1(z) :|: z >= 0
   insertionsort(z) -{ 0 }-> 0 :|: z >= 0
   insertionsort#1(z) -{ 0 }-> insert(z0, insertionsort#1(z1)) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   insertionsort#1(z) -{ 0 }-> insert(z0, 0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   insertionsort#1(z) -{ 0 }-> 0 :|: z = 0
   insertionsort#1(z) -{ 0 }-> 0 :|: z >= 0

Function symbols to be analyzed: {append#1,append}, {#less}, {insert#2,insert,insert#1}, {#LESS}, {flatten#1}, {insertionsort#1}, {INSERT#1,INSERT#2,INSERT}, {flatten}, {FLATTEN,FLATTEN#1}, {insertionsort}, {INSERTIONSORT,INSERTIONSORT#1}, {FLATTENSORT}
Previous analysis results are:
  APPEND#1: runtime: O(n^1) [4*z], size: O(1) [0]
  APPEND: runtime: O(n^1) [1 + 4*z], size: O(1) [1]
  #cklt: runtime: O(1) [0], size: O(1) [2]
  #compare: runtime: O(1) [0], size: O(1) [3]
  #COMPARE: runtime: O(1) [0], size: O(n^1) [z + z']

----------------------------------------

(61) IntTrsBoundProof (UPPER BOUND(ID))

Computed SIZE bound using CoFloCo for: append#1
after applying outer abstraction to obtain an ITS,
resulting in: O(n^1) with polynomial bound: z + z'

Computed SIZE bound using CoFloCo for: append
after applying outer abstraction to obtain an ITS,
resulting in: O(n^1) with polynomial bound: z + z'

----------------------------------------

(62)
Obligation:
Complexity RNTS consisting of the following rules:

   #COMPARE(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   #COMPARE(z, z') -{ 0 }-> 1 + s19 :|: s19 >= 0, s19 <= z' - 1 + (z - 1), z' - 1 >= 0, z - 1 >= 0
   #COMPARE(z, z') -{ 0 }-> 1 + s20 :|: s20 >= 0, s20 <= z - 1 + (z' - 1), z' - 1 >= 0, z - 1 >= 0
   #LESS(z, z') -{ 1 }-> 1 + s18 :|: s18 >= 0, s18 <= z + z', z' >= 0, z >= 0
   #cklt(z) -{ 0 }-> 2 :|: z = 3
   #cklt(z) -{ 0 }-> 1 :|: z = 1
   #cklt(z) -{ 0 }-> 1 :|: z = 2
   #cklt(z) -{ 0 }-> 0 :|: z >= 0
   #compare(z, z') -{ 0 }-> s8 :|: s8 >= 0, s8 <= 3, z' - 1 >= 0, z - 1 >= 0
   #compare(z, z') -{ 0 }-> s9 :|: s9 >= 0, s9 <= 3, z' - 1 >= 0, z - 1 >= 0
   #compare(z, z') -{ 0 }-> 3 :|: z' - 1 >= 0, z = 0
   #compare(z, z') -{ 0 }-> 3 :|: z - 1 >= 0, z' = 0
   #compare(z, z') -{ 0 }-> 3 :|: z' - 1 >= 0, z - 1 >= 0
   #compare(z, z') -{ 0 }-> 2 :|: z' - 1 >= 0, z = 0
   #compare(z, z') -{ 0 }-> 2 :|: z - 1 >= 0, z' = 0
   #compare(z, z') -{ 0 }-> 2 :|: z' - 1 >= 0, z - 1 >= 0
   #compare(z, z') -{ 0 }-> 1 :|: z = 0, z' = 0
   #compare(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   #less(z, z') -{ 0 }-> s13 :|: s12 >= 0, s12 <= 3, s13 >= 0, s13 <= 2, z' - 1 >= 0, z - 1 >= 0
   #less(z, z') -{ 0 }-> s15 :|: s14 >= 0, s14 <= 3, s15 >= 0, s15 <= 2, z - 1 >= 0, z' - 1 >= 0
   #less(z, z') -{ 0 }-> 2 :|: z' - 1 >= 0, z = 0, 3 = 3
   #less(z, z') -{ 0 }-> 2 :|: z - 1 >= 0, z' = 0, 3 = 3
   #less(z, z') -{ 0 }-> 2 :|: z - 1 >= 0, z' - 1 >= 0, 3 = 3
   #less(z, z') -{ 0 }-> 1 :|: z = 0, z' = 0, 1 = 1
   #less(z, z') -{ 0 }-> 1 :|: z' - 1 >= 0, z = 0, 2 = 2
   #less(z, z') -{ 0 }-> 1 :|: z - 1 >= 0, z' = 0, 2 = 2
   #less(z, z') -{ 0 }-> 1 :|: z' - 1 >= 0, z - 1 >= 0, 2 = 2
   #less(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   #less(z, z') -{ 0 }-> 0 :|: z = 0, z' = 0, v0 >= 0, 1 = v0
   #less(z, z') -{ 0 }-> 0 :|: z' - 1 >= 0, z = 0, v0 >= 0, 2 = v0
   #less(z, z') -{ 0 }-> 0 :|: z' - 1 >= 0, z = 0, v0 >= 0, 3 = v0
   #less(z, z') -{ 0 }-> 0 :|: z - 1 >= 0, z' = 0, v0 >= 0, 3 = v0
   #less(z, z') -{ 0 }-> 0 :|: z - 1 >= 0, z' - 1 >= 0, v0 >= 0, 3 = v0
   #less(z, z') -{ 0 }-> 0 :|: z - 1 >= 0, z' = 0, v0 >= 0, 2 = v0
   #less(z, z') -{ 0 }-> 0 :|: z' - 1 >= 0, z - 1 >= 0, v0 >= 0, 2 = v0
   #less(z, z') -{ 0 }-> 0 :|: z' >= 0, z >= 0, v0 >= 0, 0 = v0
   APPEND(z, z') -{ 1 + 4*z }-> 1 + s :|: s >= 0, s <= 0, z' >= 0, z >= 0
   APPEND#1(z, z') -{ 2 + 4*z1 }-> 1 + s' :|: s' >= 0, s' <= 1, z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z' >= 0
   FLATTEN(z) -{ 1 }-> 1 + FLATTEN#1(z) :|: z >= 0
   FLATTEN#1(z) -{ 2 }-> 1 + APPEND(z0, append(flatten#1(z1), flatten#1(z2))) + s'' + FLATTEN(z1) :|: s'' >= 0, s'' <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 2 }-> 1 + APPEND(z0, append(flatten#1(z1), flatten#1(z2))) + s4 + FLATTEN(z2) :|: s4 >= 0, s4 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), flatten#1(z2))) + APPEND(flatten#1(z1), flatten#1(z2)) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), flatten#1(z2))) + APPEND(flatten#1(z1), flatten#1(z2)) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), flatten#1(z2))) + APPEND(flatten#1(z1), 0) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), flatten#1(z2))) + APPEND(flatten#1(z1), 0) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), flatten#1(z2))) + APPEND(0, flatten#1(z2)) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), flatten#1(z2))) + APPEND(0, flatten#1(z2)) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 2 }-> 1 + APPEND(z0, append(flatten#1(z1), 0)) + s1 + FLATTEN(z1) :|: s1 >= 0, s1 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 2 }-> 1 + APPEND(z0, append(flatten#1(z1), 0)) + s5 + FLATTEN(z2) :|: s5 >= 0, s5 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), 0)) + APPEND(flatten#1(z1), flatten#1(z2)) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), 0)) + APPEND(flatten#1(z1), flatten#1(z2)) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), 0)) + APPEND(flatten#1(z1), 0) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), 0)) + APPEND(flatten#1(z1), 0) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), 0)) + APPEND(0, flatten#1(z2)) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), 0)) + APPEND(0, flatten#1(z2)) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 2 }-> 1 + APPEND(z0, append(0, flatten#1(z2))) + s2 + FLATTEN(z1) :|: s2 >= 0, s2 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 2 }-> 1 + APPEND(z0, append(0, flatten#1(z2))) + s6 + FLATTEN(z2) :|: s6 >= 0, s6 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(0, flatten#1(z2))) + APPEND(flatten#1(z1), flatten#1(z2)) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(0, flatten#1(z2))) + APPEND(flatten#1(z1), flatten#1(z2)) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(0, flatten#1(z2))) + APPEND(flatten#1(z1), 0) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(0, flatten#1(z2))) + APPEND(flatten#1(z1), 0) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(0, flatten#1(z2))) + APPEND(0, flatten#1(z2)) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(0, flatten#1(z2))) + APPEND(0, flatten#1(z2)) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 2 }-> 1 + APPEND(z0, append(0, 0)) + s3 + FLATTEN(z1) :|: s3 >= 0, s3 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 2 }-> 1 + APPEND(z0, append(0, 0)) + s7 + FLATTEN(z2) :|: s7 >= 0, s7 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(0, 0)) + APPEND(flatten#1(z1), flatten#1(z2)) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(0, 0)) + APPEND(flatten#1(z1), flatten#1(z2)) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(0, 0)) + APPEND(flatten#1(z1), 0) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(0, 0)) + APPEND(flatten#1(z1), 0) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(0, 0)) + APPEND(0, flatten#1(z2)) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(0, 0)) + APPEND(0, flatten#1(z2)) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTENSORT(z) -{ 0 }-> 0 :|: z >= 0
   FLATTENSORT(z) -{ 0 }-> 1 + INSERTIONSORT(flatten#1(z)) :|: z >= 0
   FLATTENSORT(z) -{ 0 }-> 1 + INSERTIONSORT(0) :|: z >= 0
   INSERT(z, z') -{ 1 }-> 1 + INSERT#1(z', z) :|: z' >= 0, z >= 0
   INSERT#1(z, z') -{ 1 }-> 1 + INSERT#2(s11, z', z0, z1) + #LESS(z0, z') :|: s10 >= 0, s10 <= 3, s11 >= 0, s11 <= 2, z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z' >= 0
   INSERT#1(z, z') -{ 1 }-> 1 + INSERT#2(0, z', z0, z1) + #LESS(z0, z') :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z' >= 0
   INSERT#2(z, z', z'', z3) -{ 1 }-> 1 + INSERT(z', z3) :|: z = 2, z'' >= 0, z' >= 0, z3 >= 0
   INSERTIONSORT(z) -{ 1 }-> 1 + INSERTIONSORT#1(z) :|: z >= 0
   INSERTIONSORT#1(z) -{ 1 }-> 1 + INSERT(z0, insertionsort#1(z1)) + INSERTIONSORT(z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   INSERTIONSORT#1(z) -{ 1 }-> 1 + INSERT(z0, 0) + INSERTIONSORT(z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   append(z, z') -{ 0 }-> append#1(z, z') :|: z' >= 0, z >= 0
   append(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   append#1(z, z') -{ 0 }-> z' :|: z' >= 0, z = 0
   append#1(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   append#1(z, z') -{ 0 }-> 1 + z0 + append(z1, z') :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z' >= 0
   flatten(z) -{ 0 }-> flatten#1(z) :|: z >= 0
   flatten(z) -{ 0 }-> 0 :|: z >= 0
   flatten#1(z) -{ 0 }-> append(z0, append(flatten#1(z1), flatten#1(z2))) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   flatten#1(z) -{ 0 }-> append(z0, append(flatten#1(z1), 0)) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   flatten#1(z) -{ 0 }-> append(z0, append(0, flatten#1(z2))) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   flatten#1(z) -{ 0 }-> append(z0, append(0, 0)) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   flatten#1(z) -{ 0 }-> 0 :|: z = 0
   flatten#1(z) -{ 0 }-> 0 :|: z >= 0
   insert(z, z') -{ 0 }-> insert#1(z', z) :|: z' >= 0, z >= 0
   insert(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   insert#1(z, z') -{ 0 }-> insert#2(s17, z', z0, z1) :|: s16 >= 0, s16 <= 3, s17 >= 0, s17 <= 2, z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z' >= 0
   insert#1(z, z') -{ 0 }-> insert#2(0, z', z0, z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z' >= 0
   insert#1(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   insert#1(z, z') -{ 0 }-> 1 + z' + 0 :|: z' >= 0, z = 0
   insert#2(z, z', z'', z3) -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0, z3 >= 0
   insert#2(z, z', z'', z3) -{ 0 }-> 1 + z' + (1 + z'' + z3) :|: z'' >= 0, z = 1, z' >= 0, z3 >= 0
   insert#2(z, z', z'', z3) -{ 0 }-> 1 + z'' + insert(z', z3) :|: z = 2, z'' >= 0, z' >= 0, z3 >= 0
   insertionsort(z) -{ 0 }-> insertionsort#1(z) :|: z >= 0
   insertionsort(z) -{ 0 }-> 0 :|: z >= 0
   insertionsort#1(z) -{ 0 }-> insert(z0, insertionsort#1(z1)) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   insertionsort#1(z) -{ 0 }-> insert(z0, 0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   insertionsort#1(z) -{ 0 }-> 0 :|: z = 0
   insertionsort#1(z) -{ 0 }-> 0 :|: z >= 0

Function symbols to be analyzed: {append#1,append}, {#less}, {insert#2,insert,insert#1}, {#LESS}, {flatten#1}, {insertionsort#1}, {INSERT#1,INSERT#2,INSERT}, {flatten}, {FLATTEN,FLATTEN#1}, {insertionsort}, {INSERTIONSORT,INSERTIONSORT#1}, {FLATTENSORT}
Previous analysis results are:
  APPEND#1: runtime: O(n^1) [4*z], size: O(1) [0]
  APPEND: runtime: O(n^1) [1 + 4*z], size: O(1) [1]
  #cklt: runtime: O(1) [0], size: O(1) [2]
  #compare: runtime: O(1) [0], size: O(1) [3]
  #COMPARE: runtime: O(1) [0], size: O(n^1) [z + z']
  append#1: runtime: ?, size: O(n^1) [z + z']
  append: runtime: ?, size: O(n^1) [z + z']

----------------------------------------

(63) IntTrsBoundProof (UPPER BOUND(ID))

Computed RUNTIME bound using CoFloCo for: append#1
after applying outer abstraction to obtain an ITS,
resulting in: O(1) with polynomial bound: 0

Computed RUNTIME bound using CoFloCo for: append
after applying outer abstraction to obtain an ITS,
resulting in: O(1) with polynomial bound: 0

----------------------------------------

(64)
Obligation:
Complexity RNTS consisting of the following rules:

   #COMPARE(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   #COMPARE(z, z') -{ 0 }-> 1 + s19 :|: s19 >= 0, s19 <= z' - 1 + (z - 1), z' - 1 >= 0, z - 1 >= 0
   #COMPARE(z, z') -{ 0 }-> 1 + s20 :|: s20 >= 0, s20 <= z - 1 + (z' - 1), z' - 1 >= 0, z - 1 >= 0
   #LESS(z, z') -{ 1 }-> 1 + s18 :|: s18 >= 0, s18 <= z + z', z' >= 0, z >= 0
   #cklt(z) -{ 0 }-> 2 :|: z = 3
   #cklt(z) -{ 0 }-> 1 :|: z = 1
   #cklt(z) -{ 0 }-> 1 :|: z = 2
   #cklt(z) -{ 0 }-> 0 :|: z >= 0
   #compare(z, z') -{ 0 }-> s8 :|: s8 >= 0, s8 <= 3, z' - 1 >= 0, z - 1 >= 0
   #compare(z, z') -{ 0 }-> s9 :|: s9 >= 0, s9 <= 3, z' - 1 >= 0, z - 1 >= 0
   #compare(z, z') -{ 0 }-> 3 :|: z' - 1 >= 0, z = 0
   #compare(z, z') -{ 0 }-> 3 :|: z - 1 >= 0, z' = 0
   #compare(z, z') -{ 0 }-> 3 :|: z' - 1 >= 0, z - 1 >= 0
   #compare(z, z') -{ 0 }-> 2 :|: z' - 1 >= 0, z = 0
   #compare(z, z') -{ 0 }-> 2 :|: z - 1 >= 0, z' = 0
   #compare(z, z') -{ 0 }-> 2 :|: z' - 1 >= 0, z - 1 >= 0
   #compare(z, z') -{ 0 }-> 1 :|: z = 0, z' = 0
   #compare(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   #less(z, z') -{ 0 }-> s13 :|: s12 >= 0, s12 <= 3, s13 >= 0, s13 <= 2, z' - 1 >= 0, z - 1 >= 0
   #less(z, z') -{ 0 }-> s15 :|: s14 >= 0, s14 <= 3, s15 >= 0, s15 <= 2, z - 1 >= 0, z' - 1 >= 0
   #less(z, z') -{ 0 }-> 2 :|: z' - 1 >= 0, z = 0, 3 = 3
   #less(z, z') -{ 0 }-> 2 :|: z - 1 >= 0, z' = 0, 3 = 3
   #less(z, z') -{ 0 }-> 2 :|: z - 1 >= 0, z' - 1 >= 0, 3 = 3
   #less(z, z') -{ 0 }-> 1 :|: z = 0, z' = 0, 1 = 1
   #less(z, z') -{ 0 }-> 1 :|: z' - 1 >= 0, z = 0, 2 = 2
   #less(z, z') -{ 0 }-> 1 :|: z - 1 >= 0, z' = 0, 2 = 2
   #less(z, z') -{ 0 }-> 1 :|: z' - 1 >= 0, z - 1 >= 0, 2 = 2
   #less(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   #less(z, z') -{ 0 }-> 0 :|: z = 0, z' = 0, v0 >= 0, 1 = v0
   #less(z, z') -{ 0 }-> 0 :|: z' - 1 >= 0, z = 0, v0 >= 0, 2 = v0
   #less(z, z') -{ 0 }-> 0 :|: z' - 1 >= 0, z = 0, v0 >= 0, 3 = v0
   #less(z, z') -{ 0 }-> 0 :|: z - 1 >= 0, z' = 0, v0 >= 0, 3 = v0
   #less(z, z') -{ 0 }-> 0 :|: z - 1 >= 0, z' - 1 >= 0, v0 >= 0, 3 = v0
   #less(z, z') -{ 0 }-> 0 :|: z - 1 >= 0, z' = 0, v0 >= 0, 2 = v0
   #less(z, z') -{ 0 }-> 0 :|: z' - 1 >= 0, z - 1 >= 0, v0 >= 0, 2 = v0
   #less(z, z') -{ 0 }-> 0 :|: z' >= 0, z >= 0, v0 >= 0, 0 = v0
   APPEND(z, z') -{ 1 + 4*z }-> 1 + s :|: s >= 0, s <= 0, z' >= 0, z >= 0
   APPEND#1(z, z') -{ 2 + 4*z1 }-> 1 + s' :|: s' >= 0, s' <= 1, z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z' >= 0
   FLATTEN(z) -{ 1 }-> 1 + FLATTEN#1(z) :|: z >= 0
   FLATTEN#1(z) -{ 2 }-> 1 + APPEND(z0, append(flatten#1(z1), flatten#1(z2))) + s'' + FLATTEN(z1) :|: s'' >= 0, s'' <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 2 }-> 1 + APPEND(z0, append(flatten#1(z1), flatten#1(z2))) + s4 + FLATTEN(z2) :|: s4 >= 0, s4 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), flatten#1(z2))) + APPEND(flatten#1(z1), flatten#1(z2)) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), flatten#1(z2))) + APPEND(flatten#1(z1), flatten#1(z2)) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), flatten#1(z2))) + APPEND(flatten#1(z1), 0) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), flatten#1(z2))) + APPEND(flatten#1(z1), 0) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), flatten#1(z2))) + APPEND(0, flatten#1(z2)) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), flatten#1(z2))) + APPEND(0, flatten#1(z2)) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 2 }-> 1 + APPEND(z0, append(flatten#1(z1), 0)) + s1 + FLATTEN(z1) :|: s1 >= 0, s1 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 2 }-> 1 + APPEND(z0, append(flatten#1(z1), 0)) + s5 + FLATTEN(z2) :|: s5 >= 0, s5 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), 0)) + APPEND(flatten#1(z1), flatten#1(z2)) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), 0)) + APPEND(flatten#1(z1), flatten#1(z2)) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), 0)) + APPEND(flatten#1(z1), 0) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), 0)) + APPEND(flatten#1(z1), 0) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), 0)) + APPEND(0, flatten#1(z2)) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), 0)) + APPEND(0, flatten#1(z2)) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 2 }-> 1 + APPEND(z0, append(0, flatten#1(z2))) + s2 + FLATTEN(z1) :|: s2 >= 0, s2 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 2 }-> 1 + APPEND(z0, append(0, flatten#1(z2))) + s6 + FLATTEN(z2) :|: s6 >= 0, s6 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(0, flatten#1(z2))) + APPEND(flatten#1(z1), flatten#1(z2)) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(0, flatten#1(z2))) + APPEND(flatten#1(z1), flatten#1(z2)) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(0, flatten#1(z2))) + APPEND(flatten#1(z1), 0) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(0, flatten#1(z2))) + APPEND(flatten#1(z1), 0) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(0, flatten#1(z2))) + APPEND(0, flatten#1(z2)) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(0, flatten#1(z2))) + APPEND(0, flatten#1(z2)) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 2 }-> 1 + APPEND(z0, append(0, 0)) + s3 + FLATTEN(z1) :|: s3 >= 0, s3 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 2 }-> 1 + APPEND(z0, append(0, 0)) + s7 + FLATTEN(z2) :|: s7 >= 0, s7 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(0, 0)) + APPEND(flatten#1(z1), flatten#1(z2)) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(0, 0)) + APPEND(flatten#1(z1), flatten#1(z2)) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(0, 0)) + APPEND(flatten#1(z1), 0) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(0, 0)) + APPEND(flatten#1(z1), 0) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(0, 0)) + APPEND(0, flatten#1(z2)) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(0, 0)) + APPEND(0, flatten#1(z2)) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTENSORT(z) -{ 0 }-> 0 :|: z >= 0
   FLATTENSORT(z) -{ 0 }-> 1 + INSERTIONSORT(flatten#1(z)) :|: z >= 0
   FLATTENSORT(z) -{ 0 }-> 1 + INSERTIONSORT(0) :|: z >= 0
   INSERT(z, z') -{ 1 }-> 1 + INSERT#1(z', z) :|: z' >= 0, z >= 0
   INSERT#1(z, z') -{ 1 }-> 1 + INSERT#2(s11, z', z0, z1) + #LESS(z0, z') :|: s10 >= 0, s10 <= 3, s11 >= 0, s11 <= 2, z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z' >= 0
   INSERT#1(z, z') -{ 1 }-> 1 + INSERT#2(0, z', z0, z1) + #LESS(z0, z') :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z' >= 0
   INSERT#2(z, z', z'', z3) -{ 1 }-> 1 + INSERT(z', z3) :|: z = 2, z'' >= 0, z' >= 0, z3 >= 0
   INSERTIONSORT(z) -{ 1 }-> 1 + INSERTIONSORT#1(z) :|: z >= 0
   INSERTIONSORT#1(z) -{ 1 }-> 1 + INSERT(z0, insertionsort#1(z1)) + INSERTIONSORT(z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   INSERTIONSORT#1(z) -{ 1 }-> 1 + INSERT(z0, 0) + INSERTIONSORT(z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   append(z, z') -{ 0 }-> append#1(z, z') :|: z' >= 0, z >= 0
   append(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   append#1(z, z') -{ 0 }-> z' :|: z' >= 0, z = 0
   append#1(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   append#1(z, z') -{ 0 }-> 1 + z0 + append(z1, z') :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z' >= 0
   flatten(z) -{ 0 }-> flatten#1(z) :|: z >= 0
   flatten(z) -{ 0 }-> 0 :|: z >= 0
   flatten#1(z) -{ 0 }-> append(z0, append(flatten#1(z1), flatten#1(z2))) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   flatten#1(z) -{ 0 }-> append(z0, append(flatten#1(z1), 0)) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   flatten#1(z) -{ 0 }-> append(z0, append(0, flatten#1(z2))) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   flatten#1(z) -{ 0 }-> append(z0, append(0, 0)) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   flatten#1(z) -{ 0 }-> 0 :|: z = 0
   flatten#1(z) -{ 0 }-> 0 :|: z >= 0
   insert(z, z') -{ 0 }-> insert#1(z', z) :|: z' >= 0, z >= 0
   insert(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   insert#1(z, z') -{ 0 }-> insert#2(s17, z', z0, z1) :|: s16 >= 0, s16 <= 3, s17 >= 0, s17 <= 2, z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z' >= 0
   insert#1(z, z') -{ 0 }-> insert#2(0, z', z0, z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z' >= 0
   insert#1(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   insert#1(z, z') -{ 0 }-> 1 + z' + 0 :|: z' >= 0, z = 0
   insert#2(z, z', z'', z3) -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0, z3 >= 0
   insert#2(z, z', z'', z3) -{ 0 }-> 1 + z' + (1 + z'' + z3) :|: z'' >= 0, z = 1, z' >= 0, z3 >= 0
   insert#2(z, z', z'', z3) -{ 0 }-> 1 + z'' + insert(z', z3) :|: z = 2, z'' >= 0, z' >= 0, z3 >= 0
   insertionsort(z) -{ 0 }-> insertionsort#1(z) :|: z >= 0
   insertionsort(z) -{ 0 }-> 0 :|: z >= 0
   insertionsort#1(z) -{ 0 }-> insert(z0, insertionsort#1(z1)) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   insertionsort#1(z) -{ 0 }-> insert(z0, 0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   insertionsort#1(z) -{ 0 }-> 0 :|: z = 0
   insertionsort#1(z) -{ 0 }-> 0 :|: z >= 0

Function symbols to be analyzed: {#less}, {insert#2,insert,insert#1}, {#LESS}, {flatten#1}, {insertionsort#1}, {INSERT#1,INSERT#2,INSERT}, {flatten}, {FLATTEN,FLATTEN#1}, {insertionsort}, {INSERTIONSORT,INSERTIONSORT#1}, {FLATTENSORT}
Previous analysis results are:
  APPEND#1: runtime: O(n^1) [4*z], size: O(1) [0]
  APPEND: runtime: O(n^1) [1 + 4*z], size: O(1) [1]
  #cklt: runtime: O(1) [0], size: O(1) [2]
  #compare: runtime: O(1) [0], size: O(1) [3]
  #COMPARE: runtime: O(1) [0], size: O(n^1) [z + z']
  append#1: runtime: O(1) [0], size: O(n^1) [z + z']
  append: runtime: O(1) [0], size: O(n^1) [z + z']

----------------------------------------

(65) ResultPropagationProof (UPPER BOUND(ID))
Applied inner abstraction using the recently inferred runtime/size bounds where possible.
----------------------------------------

(66)
Obligation:
Complexity RNTS consisting of the following rules:

   #COMPARE(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   #COMPARE(z, z') -{ 0 }-> 1 + s19 :|: s19 >= 0, s19 <= z' - 1 + (z - 1), z' - 1 >= 0, z - 1 >= 0
   #COMPARE(z, z') -{ 0 }-> 1 + s20 :|: s20 >= 0, s20 <= z - 1 + (z' - 1), z' - 1 >= 0, z - 1 >= 0
   #LESS(z, z') -{ 1 }-> 1 + s18 :|: s18 >= 0, s18 <= z + z', z' >= 0, z >= 0
   #cklt(z) -{ 0 }-> 2 :|: z = 3
   #cklt(z) -{ 0 }-> 1 :|: z = 1
   #cklt(z) -{ 0 }-> 1 :|: z = 2
   #cklt(z) -{ 0 }-> 0 :|: z >= 0
   #compare(z, z') -{ 0 }-> s8 :|: s8 >= 0, s8 <= 3, z' - 1 >= 0, z - 1 >= 0
   #compare(z, z') -{ 0 }-> s9 :|: s9 >= 0, s9 <= 3, z' - 1 >= 0, z - 1 >= 0
   #compare(z, z') -{ 0 }-> 3 :|: z' - 1 >= 0, z = 0
   #compare(z, z') -{ 0 }-> 3 :|: z - 1 >= 0, z' = 0
   #compare(z, z') -{ 0 }-> 3 :|: z' - 1 >= 0, z - 1 >= 0
   #compare(z, z') -{ 0 }-> 2 :|: z' - 1 >= 0, z = 0
   #compare(z, z') -{ 0 }-> 2 :|: z - 1 >= 0, z' = 0
   #compare(z, z') -{ 0 }-> 2 :|: z' - 1 >= 0, z - 1 >= 0
   #compare(z, z') -{ 0 }-> 1 :|: z = 0, z' = 0
   #compare(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   #less(z, z') -{ 0 }-> s13 :|: s12 >= 0, s12 <= 3, s13 >= 0, s13 <= 2, z' - 1 >= 0, z - 1 >= 0
   #less(z, z') -{ 0 }-> s15 :|: s14 >= 0, s14 <= 3, s15 >= 0, s15 <= 2, z - 1 >= 0, z' - 1 >= 0
   #less(z, z') -{ 0 }-> 2 :|: z' - 1 >= 0, z = 0, 3 = 3
   #less(z, z') -{ 0 }-> 2 :|: z - 1 >= 0, z' = 0, 3 = 3
   #less(z, z') -{ 0 }-> 2 :|: z - 1 >= 0, z' - 1 >= 0, 3 = 3
   #less(z, z') -{ 0 }-> 1 :|: z = 0, z' = 0, 1 = 1
   #less(z, z') -{ 0 }-> 1 :|: z' - 1 >= 0, z = 0, 2 = 2
   #less(z, z') -{ 0 }-> 1 :|: z - 1 >= 0, z' = 0, 2 = 2
   #less(z, z') -{ 0 }-> 1 :|: z' - 1 >= 0, z - 1 >= 0, 2 = 2
   #less(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   #less(z, z') -{ 0 }-> 0 :|: z = 0, z' = 0, v0 >= 0, 1 = v0
   #less(z, z') -{ 0 }-> 0 :|: z' - 1 >= 0, z = 0, v0 >= 0, 2 = v0
   #less(z, z') -{ 0 }-> 0 :|: z' - 1 >= 0, z = 0, v0 >= 0, 3 = v0
   #less(z, z') -{ 0 }-> 0 :|: z - 1 >= 0, z' = 0, v0 >= 0, 3 = v0
   #less(z, z') -{ 0 }-> 0 :|: z - 1 >= 0, z' - 1 >= 0, v0 >= 0, 3 = v0
   #less(z, z') -{ 0 }-> 0 :|: z - 1 >= 0, z' = 0, v0 >= 0, 2 = v0
   #less(z, z') -{ 0 }-> 0 :|: z' - 1 >= 0, z - 1 >= 0, v0 >= 0, 2 = v0
   #less(z, z') -{ 0 }-> 0 :|: z' >= 0, z >= 0, v0 >= 0, 0 = v0
   APPEND(z, z') -{ 1 + 4*z }-> 1 + s :|: s >= 0, s <= 0, z' >= 0, z >= 0
   APPEND#1(z, z') -{ 2 + 4*z1 }-> 1 + s' :|: s' >= 0, s' <= 1, z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z' >= 0
   FLATTEN(z) -{ 1 }-> 1 + FLATTEN#1(z) :|: z >= 0
   FLATTEN#1(z) -{ 2 + 4*z0 }-> 1 + s22 + APPEND(flatten#1(z1), flatten#1(z2)) + FLATTEN(z1) :|: s21 >= 0, s21 <= 0 + 0, s22 >= 0, s22 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 2 + 4*z0 }-> 1 + s24 + APPEND(flatten#1(z1), 0) + FLATTEN(z1) :|: s23 >= 0, s23 <= 0 + 0, s24 >= 0, s24 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 2 + 4*z0 }-> 1 + s26 + APPEND(0, flatten#1(z2)) + FLATTEN(z1) :|: s25 >= 0, s25 <= 0 + 0, s26 >= 0, s26 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*z0 }-> 1 + s28 + s3 + FLATTEN(z1) :|: s27 >= 0, s27 <= 0 + 0, s28 >= 0, s28 <= 1, s3 >= 0, s3 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 2 + 4*z0 }-> 1 + s30 + APPEND(flatten#1(z1), flatten#1(z2)) + FLATTEN(z2) :|: s29 >= 0, s29 <= 0 + 0, s30 >= 0, s30 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 2 + 4*z0 }-> 1 + s32 + APPEND(flatten#1(z1), 0) + FLATTEN(z2) :|: s31 >= 0, s31 <= 0 + 0, s32 >= 0, s32 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 2 + 4*z0 }-> 1 + s34 + APPEND(0, flatten#1(z2)) + FLATTEN(z2) :|: s33 >= 0, s33 <= 0 + 0, s34 >= 0, s34 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*z0 }-> 1 + s36 + s7 + FLATTEN(z2) :|: s35 >= 0, s35 <= 0 + 0, s36 >= 0, s36 <= 1, s7 >= 0, s7 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 2 }-> 1 + APPEND(z0, append(flatten#1(z1), flatten#1(z2))) + s'' + FLATTEN(z1) :|: s'' >= 0, s'' <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 2 }-> 1 + APPEND(z0, append(flatten#1(z1), flatten#1(z2))) + s4 + FLATTEN(z2) :|: s4 >= 0, s4 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), flatten#1(z2))) + APPEND(flatten#1(z1), flatten#1(z2)) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), flatten#1(z2))) + APPEND(flatten#1(z1), flatten#1(z2)) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), flatten#1(z2))) + APPEND(flatten#1(z1), 0) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), flatten#1(z2))) + APPEND(flatten#1(z1), 0) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), flatten#1(z2))) + APPEND(0, flatten#1(z2)) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), flatten#1(z2))) + APPEND(0, flatten#1(z2)) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 2 }-> 1 + APPEND(z0, append(flatten#1(z1), 0)) + s1 + FLATTEN(z1) :|: s1 >= 0, s1 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 2 }-> 1 + APPEND(z0, append(flatten#1(z1), 0)) + s5 + FLATTEN(z2) :|: s5 >= 0, s5 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), 0)) + APPEND(flatten#1(z1), flatten#1(z2)) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), 0)) + APPEND(flatten#1(z1), flatten#1(z2)) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), 0)) + APPEND(flatten#1(z1), 0) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), 0)) + APPEND(flatten#1(z1), 0) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), 0)) + APPEND(0, flatten#1(z2)) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), 0)) + APPEND(0, flatten#1(z2)) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 2 }-> 1 + APPEND(z0, append(0, flatten#1(z2))) + s2 + FLATTEN(z1) :|: s2 >= 0, s2 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 2 }-> 1 + APPEND(z0, append(0, flatten#1(z2))) + s6 + FLATTEN(z2) :|: s6 >= 0, s6 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(0, flatten#1(z2))) + APPEND(flatten#1(z1), flatten#1(z2)) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(0, flatten#1(z2))) + APPEND(flatten#1(z1), flatten#1(z2)) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(0, flatten#1(z2))) + APPEND(flatten#1(z1), 0) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(0, flatten#1(z2))) + APPEND(flatten#1(z1), 0) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(0, flatten#1(z2))) + APPEND(0, flatten#1(z2)) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(0, flatten#1(z2))) + APPEND(0, flatten#1(z2)) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTENSORT(z) -{ 0 }-> 0 :|: z >= 0
   FLATTENSORT(z) -{ 0 }-> 1 + INSERTIONSORT(flatten#1(z)) :|: z >= 0
   FLATTENSORT(z) -{ 0 }-> 1 + INSERTIONSORT(0) :|: z >= 0
   INSERT(z, z') -{ 1 }-> 1 + INSERT#1(z', z) :|: z' >= 0, z >= 0
   INSERT#1(z, z') -{ 1 }-> 1 + INSERT#2(s11, z', z0, z1) + #LESS(z0, z') :|: s10 >= 0, s10 <= 3, s11 >= 0, s11 <= 2, z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z' >= 0
   INSERT#1(z, z') -{ 1 }-> 1 + INSERT#2(0, z', z0, z1) + #LESS(z0, z') :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z' >= 0
   INSERT#2(z, z', z'', z3) -{ 1 }-> 1 + INSERT(z', z3) :|: z = 2, z'' >= 0, z' >= 0, z3 >= 0
   INSERTIONSORT(z) -{ 1 }-> 1 + INSERTIONSORT#1(z) :|: z >= 0
   INSERTIONSORT#1(z) -{ 1 }-> 1 + INSERT(z0, insertionsort#1(z1)) + INSERTIONSORT(z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   INSERTIONSORT#1(z) -{ 1 }-> 1 + INSERT(z0, 0) + INSERTIONSORT(z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   append(z, z') -{ 0 }-> s37 :|: s37 >= 0, s37 <= z + z', z' >= 0, z >= 0
   append(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   append#1(z, z') -{ 0 }-> z' :|: z' >= 0, z = 0
   append#1(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   append#1(z, z') -{ 0 }-> 1 + z0 + s40 :|: s40 >= 0, s40 <= z1 + z', z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z' >= 0
   flatten(z) -{ 0 }-> flatten#1(z) :|: z >= 0
   flatten(z) -{ 0 }-> 0 :|: z >= 0
   flatten#1(z) -{ 0 }-> s39 :|: s38 >= 0, s38 <= 0 + 0, s39 >= 0, s39 <= z0 + s38, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   flatten#1(z) -{ 0 }-> append(z0, append(flatten#1(z1), flatten#1(z2))) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   flatten#1(z) -{ 0 }-> append(z0, append(flatten#1(z1), 0)) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   flatten#1(z) -{ 0 }-> append(z0, append(0, flatten#1(z2))) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   flatten#1(z) -{ 0 }-> 0 :|: z = 0
   flatten#1(z) -{ 0 }-> 0 :|: z >= 0
   insert(z, z') -{ 0 }-> insert#1(z', z) :|: z' >= 0, z >= 0
   insert(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   insert#1(z, z') -{ 0 }-> insert#2(s17, z', z0, z1) :|: s16 >= 0, s16 <= 3, s17 >= 0, s17 <= 2, z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z' >= 0
   insert#1(z, z') -{ 0 }-> insert#2(0, z', z0, z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z' >= 0
   insert#1(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   insert#1(z, z') -{ 0 }-> 1 + z' + 0 :|: z' >= 0, z = 0
   insert#2(z, z', z'', z3) -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0, z3 >= 0
   insert#2(z, z', z'', z3) -{ 0 }-> 1 + z' + (1 + z'' + z3) :|: z'' >= 0, z = 1, z' >= 0, z3 >= 0
   insert#2(z, z', z'', z3) -{ 0 }-> 1 + z'' + insert(z', z3) :|: z = 2, z'' >= 0, z' >= 0, z3 >= 0
   insertionsort(z) -{ 0 }-> insertionsort#1(z) :|: z >= 0
   insertionsort(z) -{ 0 }-> 0 :|: z >= 0
   insertionsort#1(z) -{ 0 }-> insert(z0, insertionsort#1(z1)) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   insertionsort#1(z) -{ 0 }-> insert(z0, 0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   insertionsort#1(z) -{ 0 }-> 0 :|: z = 0
   insertionsort#1(z) -{ 0 }-> 0 :|: z >= 0

Function symbols to be analyzed: {#less}, {insert#2,insert,insert#1}, {#LESS}, {flatten#1}, {insertionsort#1}, {INSERT#1,INSERT#2,INSERT}, {flatten}, {FLATTEN,FLATTEN#1}, {insertionsort}, {INSERTIONSORT,INSERTIONSORT#1}, {FLATTENSORT}
Previous analysis results are:
  APPEND#1: runtime: O(n^1) [4*z], size: O(1) [0]
  APPEND: runtime: O(n^1) [1 + 4*z], size: O(1) [1]
  #cklt: runtime: O(1) [0], size: O(1) [2]
  #compare: runtime: O(1) [0], size: O(1) [3]
  #COMPARE: runtime: O(1) [0], size: O(n^1) [z + z']
  append#1: runtime: O(1) [0], size: O(n^1) [z + z']
  append: runtime: O(1) [0], size: O(n^1) [z + z']

----------------------------------------

(67) IntTrsBoundProof (UPPER BOUND(ID))

Computed SIZE bound using CoFloCo for: #less
after applying outer abstraction to obtain an ITS,
resulting in: O(1) with polynomial bound: 2

----------------------------------------

(68)
Obligation:
Complexity RNTS consisting of the following rules:

   #COMPARE(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   #COMPARE(z, z') -{ 0 }-> 1 + s19 :|: s19 >= 0, s19 <= z' - 1 + (z - 1), z' - 1 >= 0, z - 1 >= 0
   #COMPARE(z, z') -{ 0 }-> 1 + s20 :|: s20 >= 0, s20 <= z - 1 + (z' - 1), z' - 1 >= 0, z - 1 >= 0
   #LESS(z, z') -{ 1 }-> 1 + s18 :|: s18 >= 0, s18 <= z + z', z' >= 0, z >= 0
   #cklt(z) -{ 0 }-> 2 :|: z = 3
   #cklt(z) -{ 0 }-> 1 :|: z = 1
   #cklt(z) -{ 0 }-> 1 :|: z = 2
   #cklt(z) -{ 0 }-> 0 :|: z >= 0
   #compare(z, z') -{ 0 }-> s8 :|: s8 >= 0, s8 <= 3, z' - 1 >= 0, z - 1 >= 0
   #compare(z, z') -{ 0 }-> s9 :|: s9 >= 0, s9 <= 3, z' - 1 >= 0, z - 1 >= 0
   #compare(z, z') -{ 0 }-> 3 :|: z' - 1 >= 0, z = 0
   #compare(z, z') -{ 0 }-> 3 :|: z - 1 >= 0, z' = 0
   #compare(z, z') -{ 0 }-> 3 :|: z' - 1 >= 0, z - 1 >= 0
   #compare(z, z') -{ 0 }-> 2 :|: z' - 1 >= 0, z = 0
   #compare(z, z') -{ 0 }-> 2 :|: z - 1 >= 0, z' = 0
   #compare(z, z') -{ 0 }-> 2 :|: z' - 1 >= 0, z - 1 >= 0
   #compare(z, z') -{ 0 }-> 1 :|: z = 0, z' = 0
   #compare(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   #less(z, z') -{ 0 }-> s13 :|: s12 >= 0, s12 <= 3, s13 >= 0, s13 <= 2, z' - 1 >= 0, z - 1 >= 0
   #less(z, z') -{ 0 }-> s15 :|: s14 >= 0, s14 <= 3, s15 >= 0, s15 <= 2, z - 1 >= 0, z' - 1 >= 0
   #less(z, z') -{ 0 }-> 2 :|: z' - 1 >= 0, z = 0, 3 = 3
   #less(z, z') -{ 0 }-> 2 :|: z - 1 >= 0, z' = 0, 3 = 3
   #less(z, z') -{ 0 }-> 2 :|: z - 1 >= 0, z' - 1 >= 0, 3 = 3
   #less(z, z') -{ 0 }-> 1 :|: z = 0, z' = 0, 1 = 1
   #less(z, z') -{ 0 }-> 1 :|: z' - 1 >= 0, z = 0, 2 = 2
   #less(z, z') -{ 0 }-> 1 :|: z - 1 >= 0, z' = 0, 2 = 2
   #less(z, z') -{ 0 }-> 1 :|: z' - 1 >= 0, z - 1 >= 0, 2 = 2
   #less(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   #less(z, z') -{ 0 }-> 0 :|: z = 0, z' = 0, v0 >= 0, 1 = v0
   #less(z, z') -{ 0 }-> 0 :|: z' - 1 >= 0, z = 0, v0 >= 0, 2 = v0
   #less(z, z') -{ 0 }-> 0 :|: z' - 1 >= 0, z = 0, v0 >= 0, 3 = v0
   #less(z, z') -{ 0 }-> 0 :|: z - 1 >= 0, z' = 0, v0 >= 0, 3 = v0
   #less(z, z') -{ 0 }-> 0 :|: z - 1 >= 0, z' - 1 >= 0, v0 >= 0, 3 = v0
   #less(z, z') -{ 0 }-> 0 :|: z - 1 >= 0, z' = 0, v0 >= 0, 2 = v0
   #less(z, z') -{ 0 }-> 0 :|: z' - 1 >= 0, z - 1 >= 0, v0 >= 0, 2 = v0
   #less(z, z') -{ 0 }-> 0 :|: z' >= 0, z >= 0, v0 >= 0, 0 = v0
   APPEND(z, z') -{ 1 + 4*z }-> 1 + s :|: s >= 0, s <= 0, z' >= 0, z >= 0
   APPEND#1(z, z') -{ 2 + 4*z1 }-> 1 + s' :|: s' >= 0, s' <= 1, z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z' >= 0
   FLATTEN(z) -{ 1 }-> 1 + FLATTEN#1(z) :|: z >= 0
   FLATTEN#1(z) -{ 2 + 4*z0 }-> 1 + s22 + APPEND(flatten#1(z1), flatten#1(z2)) + FLATTEN(z1) :|: s21 >= 0, s21 <= 0 + 0, s22 >= 0, s22 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 2 + 4*z0 }-> 1 + s24 + APPEND(flatten#1(z1), 0) + FLATTEN(z1) :|: s23 >= 0, s23 <= 0 + 0, s24 >= 0, s24 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 2 + 4*z0 }-> 1 + s26 + APPEND(0, flatten#1(z2)) + FLATTEN(z1) :|: s25 >= 0, s25 <= 0 + 0, s26 >= 0, s26 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*z0 }-> 1 + s28 + s3 + FLATTEN(z1) :|: s27 >= 0, s27 <= 0 + 0, s28 >= 0, s28 <= 1, s3 >= 0, s3 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 2 + 4*z0 }-> 1 + s30 + APPEND(flatten#1(z1), flatten#1(z2)) + FLATTEN(z2) :|: s29 >= 0, s29 <= 0 + 0, s30 >= 0, s30 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 2 + 4*z0 }-> 1 + s32 + APPEND(flatten#1(z1), 0) + FLATTEN(z2) :|: s31 >= 0, s31 <= 0 + 0, s32 >= 0, s32 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 2 + 4*z0 }-> 1 + s34 + APPEND(0, flatten#1(z2)) + FLATTEN(z2) :|: s33 >= 0, s33 <= 0 + 0, s34 >= 0, s34 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*z0 }-> 1 + s36 + s7 + FLATTEN(z2) :|: s35 >= 0, s35 <= 0 + 0, s36 >= 0, s36 <= 1, s7 >= 0, s7 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 2 }-> 1 + APPEND(z0, append(flatten#1(z1), flatten#1(z2))) + s'' + FLATTEN(z1) :|: s'' >= 0, s'' <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 2 }-> 1 + APPEND(z0, append(flatten#1(z1), flatten#1(z2))) + s4 + FLATTEN(z2) :|: s4 >= 0, s4 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), flatten#1(z2))) + APPEND(flatten#1(z1), flatten#1(z2)) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), flatten#1(z2))) + APPEND(flatten#1(z1), flatten#1(z2)) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), flatten#1(z2))) + APPEND(flatten#1(z1), 0) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), flatten#1(z2))) + APPEND(flatten#1(z1), 0) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), flatten#1(z2))) + APPEND(0, flatten#1(z2)) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), flatten#1(z2))) + APPEND(0, flatten#1(z2)) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 2 }-> 1 + APPEND(z0, append(flatten#1(z1), 0)) + s1 + FLATTEN(z1) :|: s1 >= 0, s1 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 2 }-> 1 + APPEND(z0, append(flatten#1(z1), 0)) + s5 + FLATTEN(z2) :|: s5 >= 0, s5 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), 0)) + APPEND(flatten#1(z1), flatten#1(z2)) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), 0)) + APPEND(flatten#1(z1), flatten#1(z2)) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), 0)) + APPEND(flatten#1(z1), 0) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), 0)) + APPEND(flatten#1(z1), 0) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), 0)) + APPEND(0, flatten#1(z2)) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), 0)) + APPEND(0, flatten#1(z2)) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 2 }-> 1 + APPEND(z0, append(0, flatten#1(z2))) + s2 + FLATTEN(z1) :|: s2 >= 0, s2 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 2 }-> 1 + APPEND(z0, append(0, flatten#1(z2))) + s6 + FLATTEN(z2) :|: s6 >= 0, s6 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(0, flatten#1(z2))) + APPEND(flatten#1(z1), flatten#1(z2)) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(0, flatten#1(z2))) + APPEND(flatten#1(z1), flatten#1(z2)) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(0, flatten#1(z2))) + APPEND(flatten#1(z1), 0) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(0, flatten#1(z2))) + APPEND(flatten#1(z1), 0) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(0, flatten#1(z2))) + APPEND(0, flatten#1(z2)) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(0, flatten#1(z2))) + APPEND(0, flatten#1(z2)) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTENSORT(z) -{ 0 }-> 0 :|: z >= 0
   FLATTENSORT(z) -{ 0 }-> 1 + INSERTIONSORT(flatten#1(z)) :|: z >= 0
   FLATTENSORT(z) -{ 0 }-> 1 + INSERTIONSORT(0) :|: z >= 0
   INSERT(z, z') -{ 1 }-> 1 + INSERT#1(z', z) :|: z' >= 0, z >= 0
   INSERT#1(z, z') -{ 1 }-> 1 + INSERT#2(s11, z', z0, z1) + #LESS(z0, z') :|: s10 >= 0, s10 <= 3, s11 >= 0, s11 <= 2, z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z' >= 0
   INSERT#1(z, z') -{ 1 }-> 1 + INSERT#2(0, z', z0, z1) + #LESS(z0, z') :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z' >= 0
   INSERT#2(z, z', z'', z3) -{ 1 }-> 1 + INSERT(z', z3) :|: z = 2, z'' >= 0, z' >= 0, z3 >= 0
   INSERTIONSORT(z) -{ 1 }-> 1 + INSERTIONSORT#1(z) :|: z >= 0
   INSERTIONSORT#1(z) -{ 1 }-> 1 + INSERT(z0, insertionsort#1(z1)) + INSERTIONSORT(z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   INSERTIONSORT#1(z) -{ 1 }-> 1 + INSERT(z0, 0) + INSERTIONSORT(z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   append(z, z') -{ 0 }-> s37 :|: s37 >= 0, s37 <= z + z', z' >= 0, z >= 0
   append(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   append#1(z, z') -{ 0 }-> z' :|: z' >= 0, z = 0
   append#1(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   append#1(z, z') -{ 0 }-> 1 + z0 + s40 :|: s40 >= 0, s40 <= z1 + z', z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z' >= 0
   flatten(z) -{ 0 }-> flatten#1(z) :|: z >= 0
   flatten(z) -{ 0 }-> 0 :|: z >= 0
   flatten#1(z) -{ 0 }-> s39 :|: s38 >= 0, s38 <= 0 + 0, s39 >= 0, s39 <= z0 + s38, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   flatten#1(z) -{ 0 }-> append(z0, append(flatten#1(z1), flatten#1(z2))) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   flatten#1(z) -{ 0 }-> append(z0, append(flatten#1(z1), 0)) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   flatten#1(z) -{ 0 }-> append(z0, append(0, flatten#1(z2))) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   flatten#1(z) -{ 0 }-> 0 :|: z = 0
   flatten#1(z) -{ 0 }-> 0 :|: z >= 0
   insert(z, z') -{ 0 }-> insert#1(z', z) :|: z' >= 0, z >= 0
   insert(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   insert#1(z, z') -{ 0 }-> insert#2(s17, z', z0, z1) :|: s16 >= 0, s16 <= 3, s17 >= 0, s17 <= 2, z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z' >= 0
   insert#1(z, z') -{ 0 }-> insert#2(0, z', z0, z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z' >= 0
   insert#1(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   insert#1(z, z') -{ 0 }-> 1 + z' + 0 :|: z' >= 0, z = 0
   insert#2(z, z', z'', z3) -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0, z3 >= 0
   insert#2(z, z', z'', z3) -{ 0 }-> 1 + z' + (1 + z'' + z3) :|: z'' >= 0, z = 1, z' >= 0, z3 >= 0
   insert#2(z, z', z'', z3) -{ 0 }-> 1 + z'' + insert(z', z3) :|: z = 2, z'' >= 0, z' >= 0, z3 >= 0
   insertionsort(z) -{ 0 }-> insertionsort#1(z) :|: z >= 0
   insertionsort(z) -{ 0 }-> 0 :|: z >= 0
   insertionsort#1(z) -{ 0 }-> insert(z0, insertionsort#1(z1)) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   insertionsort#1(z) -{ 0 }-> insert(z0, 0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   insertionsort#1(z) -{ 0 }-> 0 :|: z = 0
   insertionsort#1(z) -{ 0 }-> 0 :|: z >= 0

Function symbols to be analyzed: {#less}, {insert#2,insert,insert#1}, {#LESS}, {flatten#1}, {insertionsort#1}, {INSERT#1,INSERT#2,INSERT}, {flatten}, {FLATTEN,FLATTEN#1}, {insertionsort}, {INSERTIONSORT,INSERTIONSORT#1}, {FLATTENSORT}
Previous analysis results are:
  APPEND#1: runtime: O(n^1) [4*z], size: O(1) [0]
  APPEND: runtime: O(n^1) [1 + 4*z], size: O(1) [1]
  #cklt: runtime: O(1) [0], size: O(1) [2]
  #compare: runtime: O(1) [0], size: O(1) [3]
  #COMPARE: runtime: O(1) [0], size: O(n^1) [z + z']
  append#1: runtime: O(1) [0], size: O(n^1) [z + z']
  append: runtime: O(1) [0], size: O(n^1) [z + z']
  #less: runtime: ?, size: O(1) [2]

----------------------------------------

(69) IntTrsBoundProof (UPPER BOUND(ID))

Computed RUNTIME bound using CoFloCo for: #less
after applying outer abstraction to obtain an ITS,
resulting in: O(1) with polynomial bound: 0

----------------------------------------

(70)
Obligation:
Complexity RNTS consisting of the following rules:

   #COMPARE(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   #COMPARE(z, z') -{ 0 }-> 1 + s19 :|: s19 >= 0, s19 <= z' - 1 + (z - 1), z' - 1 >= 0, z - 1 >= 0
   #COMPARE(z, z') -{ 0 }-> 1 + s20 :|: s20 >= 0, s20 <= z - 1 + (z' - 1), z' - 1 >= 0, z - 1 >= 0
   #LESS(z, z') -{ 1 }-> 1 + s18 :|: s18 >= 0, s18 <= z + z', z' >= 0, z >= 0
   #cklt(z) -{ 0 }-> 2 :|: z = 3
   #cklt(z) -{ 0 }-> 1 :|: z = 1
   #cklt(z) -{ 0 }-> 1 :|: z = 2
   #cklt(z) -{ 0 }-> 0 :|: z >= 0
   #compare(z, z') -{ 0 }-> s8 :|: s8 >= 0, s8 <= 3, z' - 1 >= 0, z - 1 >= 0
   #compare(z, z') -{ 0 }-> s9 :|: s9 >= 0, s9 <= 3, z' - 1 >= 0, z - 1 >= 0
   #compare(z, z') -{ 0 }-> 3 :|: z' - 1 >= 0, z = 0
   #compare(z, z') -{ 0 }-> 3 :|: z - 1 >= 0, z' = 0
   #compare(z, z') -{ 0 }-> 3 :|: z' - 1 >= 0, z - 1 >= 0
   #compare(z, z') -{ 0 }-> 2 :|: z' - 1 >= 0, z = 0
   #compare(z, z') -{ 0 }-> 2 :|: z - 1 >= 0, z' = 0
   #compare(z, z') -{ 0 }-> 2 :|: z' - 1 >= 0, z - 1 >= 0
   #compare(z, z') -{ 0 }-> 1 :|: z = 0, z' = 0
   #compare(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   #less(z, z') -{ 0 }-> s13 :|: s12 >= 0, s12 <= 3, s13 >= 0, s13 <= 2, z' - 1 >= 0, z - 1 >= 0
   #less(z, z') -{ 0 }-> s15 :|: s14 >= 0, s14 <= 3, s15 >= 0, s15 <= 2, z - 1 >= 0, z' - 1 >= 0
   #less(z, z') -{ 0 }-> 2 :|: z' - 1 >= 0, z = 0, 3 = 3
   #less(z, z') -{ 0 }-> 2 :|: z - 1 >= 0, z' = 0, 3 = 3
   #less(z, z') -{ 0 }-> 2 :|: z - 1 >= 0, z' - 1 >= 0, 3 = 3
   #less(z, z') -{ 0 }-> 1 :|: z = 0, z' = 0, 1 = 1
   #less(z, z') -{ 0 }-> 1 :|: z' - 1 >= 0, z = 0, 2 = 2
   #less(z, z') -{ 0 }-> 1 :|: z - 1 >= 0, z' = 0, 2 = 2
   #less(z, z') -{ 0 }-> 1 :|: z' - 1 >= 0, z - 1 >= 0, 2 = 2
   #less(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   #less(z, z') -{ 0 }-> 0 :|: z = 0, z' = 0, v0 >= 0, 1 = v0
   #less(z, z') -{ 0 }-> 0 :|: z' - 1 >= 0, z = 0, v0 >= 0, 2 = v0
   #less(z, z') -{ 0 }-> 0 :|: z' - 1 >= 0, z = 0, v0 >= 0, 3 = v0
   #less(z, z') -{ 0 }-> 0 :|: z - 1 >= 0, z' = 0, v0 >= 0, 3 = v0
   #less(z, z') -{ 0 }-> 0 :|: z - 1 >= 0, z' - 1 >= 0, v0 >= 0, 3 = v0
   #less(z, z') -{ 0 }-> 0 :|: z - 1 >= 0, z' = 0, v0 >= 0, 2 = v0
   #less(z, z') -{ 0 }-> 0 :|: z' - 1 >= 0, z - 1 >= 0, v0 >= 0, 2 = v0
   #less(z, z') -{ 0 }-> 0 :|: z' >= 0, z >= 0, v0 >= 0, 0 = v0
   APPEND(z, z') -{ 1 + 4*z }-> 1 + s :|: s >= 0, s <= 0, z' >= 0, z >= 0
   APPEND#1(z, z') -{ 2 + 4*z1 }-> 1 + s' :|: s' >= 0, s' <= 1, z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z' >= 0
   FLATTEN(z) -{ 1 }-> 1 + FLATTEN#1(z) :|: z >= 0
   FLATTEN#1(z) -{ 2 + 4*z0 }-> 1 + s22 + APPEND(flatten#1(z1), flatten#1(z2)) + FLATTEN(z1) :|: s21 >= 0, s21 <= 0 + 0, s22 >= 0, s22 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 2 + 4*z0 }-> 1 + s24 + APPEND(flatten#1(z1), 0) + FLATTEN(z1) :|: s23 >= 0, s23 <= 0 + 0, s24 >= 0, s24 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 2 + 4*z0 }-> 1 + s26 + APPEND(0, flatten#1(z2)) + FLATTEN(z1) :|: s25 >= 0, s25 <= 0 + 0, s26 >= 0, s26 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*z0 }-> 1 + s28 + s3 + FLATTEN(z1) :|: s27 >= 0, s27 <= 0 + 0, s28 >= 0, s28 <= 1, s3 >= 0, s3 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 2 + 4*z0 }-> 1 + s30 + APPEND(flatten#1(z1), flatten#1(z2)) + FLATTEN(z2) :|: s29 >= 0, s29 <= 0 + 0, s30 >= 0, s30 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 2 + 4*z0 }-> 1 + s32 + APPEND(flatten#1(z1), 0) + FLATTEN(z2) :|: s31 >= 0, s31 <= 0 + 0, s32 >= 0, s32 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 2 + 4*z0 }-> 1 + s34 + APPEND(0, flatten#1(z2)) + FLATTEN(z2) :|: s33 >= 0, s33 <= 0 + 0, s34 >= 0, s34 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*z0 }-> 1 + s36 + s7 + FLATTEN(z2) :|: s35 >= 0, s35 <= 0 + 0, s36 >= 0, s36 <= 1, s7 >= 0, s7 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 2 }-> 1 + APPEND(z0, append(flatten#1(z1), flatten#1(z2))) + s'' + FLATTEN(z1) :|: s'' >= 0, s'' <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 2 }-> 1 + APPEND(z0, append(flatten#1(z1), flatten#1(z2))) + s4 + FLATTEN(z2) :|: s4 >= 0, s4 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), flatten#1(z2))) + APPEND(flatten#1(z1), flatten#1(z2)) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), flatten#1(z2))) + APPEND(flatten#1(z1), flatten#1(z2)) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), flatten#1(z2))) + APPEND(flatten#1(z1), 0) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), flatten#1(z2))) + APPEND(flatten#1(z1), 0) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), flatten#1(z2))) + APPEND(0, flatten#1(z2)) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), flatten#1(z2))) + APPEND(0, flatten#1(z2)) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 2 }-> 1 + APPEND(z0, append(flatten#1(z1), 0)) + s1 + FLATTEN(z1) :|: s1 >= 0, s1 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 2 }-> 1 + APPEND(z0, append(flatten#1(z1), 0)) + s5 + FLATTEN(z2) :|: s5 >= 0, s5 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), 0)) + APPEND(flatten#1(z1), flatten#1(z2)) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), 0)) + APPEND(flatten#1(z1), flatten#1(z2)) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), 0)) + APPEND(flatten#1(z1), 0) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), 0)) + APPEND(flatten#1(z1), 0) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), 0)) + APPEND(0, flatten#1(z2)) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), 0)) + APPEND(0, flatten#1(z2)) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 2 }-> 1 + APPEND(z0, append(0, flatten#1(z2))) + s2 + FLATTEN(z1) :|: s2 >= 0, s2 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 2 }-> 1 + APPEND(z0, append(0, flatten#1(z2))) + s6 + FLATTEN(z2) :|: s6 >= 0, s6 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(0, flatten#1(z2))) + APPEND(flatten#1(z1), flatten#1(z2)) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(0, flatten#1(z2))) + APPEND(flatten#1(z1), flatten#1(z2)) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(0, flatten#1(z2))) + APPEND(flatten#1(z1), 0) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(0, flatten#1(z2))) + APPEND(flatten#1(z1), 0) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(0, flatten#1(z2))) + APPEND(0, flatten#1(z2)) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(0, flatten#1(z2))) + APPEND(0, flatten#1(z2)) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTENSORT(z) -{ 0 }-> 0 :|: z >= 0
   FLATTENSORT(z) -{ 0 }-> 1 + INSERTIONSORT(flatten#1(z)) :|: z >= 0
   FLATTENSORT(z) -{ 0 }-> 1 + INSERTIONSORT(0) :|: z >= 0
   INSERT(z, z') -{ 1 }-> 1 + INSERT#1(z', z) :|: z' >= 0, z >= 0
   INSERT#1(z, z') -{ 1 }-> 1 + INSERT#2(s11, z', z0, z1) + #LESS(z0, z') :|: s10 >= 0, s10 <= 3, s11 >= 0, s11 <= 2, z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z' >= 0
   INSERT#1(z, z') -{ 1 }-> 1 + INSERT#2(0, z', z0, z1) + #LESS(z0, z') :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z' >= 0
   INSERT#2(z, z', z'', z3) -{ 1 }-> 1 + INSERT(z', z3) :|: z = 2, z'' >= 0, z' >= 0, z3 >= 0
   INSERTIONSORT(z) -{ 1 }-> 1 + INSERTIONSORT#1(z) :|: z >= 0
   INSERTIONSORT#1(z) -{ 1 }-> 1 + INSERT(z0, insertionsort#1(z1)) + INSERTIONSORT(z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   INSERTIONSORT#1(z) -{ 1 }-> 1 + INSERT(z0, 0) + INSERTIONSORT(z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   append(z, z') -{ 0 }-> s37 :|: s37 >= 0, s37 <= z + z', z' >= 0, z >= 0
   append(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   append#1(z, z') -{ 0 }-> z' :|: z' >= 0, z = 0
   append#1(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   append#1(z, z') -{ 0 }-> 1 + z0 + s40 :|: s40 >= 0, s40 <= z1 + z', z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z' >= 0
   flatten(z) -{ 0 }-> flatten#1(z) :|: z >= 0
   flatten(z) -{ 0 }-> 0 :|: z >= 0
   flatten#1(z) -{ 0 }-> s39 :|: s38 >= 0, s38 <= 0 + 0, s39 >= 0, s39 <= z0 + s38, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   flatten#1(z) -{ 0 }-> append(z0, append(flatten#1(z1), flatten#1(z2))) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   flatten#1(z) -{ 0 }-> append(z0, append(flatten#1(z1), 0)) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   flatten#1(z) -{ 0 }-> append(z0, append(0, flatten#1(z2))) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   flatten#1(z) -{ 0 }-> 0 :|: z = 0
   flatten#1(z) -{ 0 }-> 0 :|: z >= 0
   insert(z, z') -{ 0 }-> insert#1(z', z) :|: z' >= 0, z >= 0
   insert(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   insert#1(z, z') -{ 0 }-> insert#2(s17, z', z0, z1) :|: s16 >= 0, s16 <= 3, s17 >= 0, s17 <= 2, z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z' >= 0
   insert#1(z, z') -{ 0 }-> insert#2(0, z', z0, z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z' >= 0
   insert#1(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   insert#1(z, z') -{ 0 }-> 1 + z' + 0 :|: z' >= 0, z = 0
   insert#2(z, z', z'', z3) -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0, z3 >= 0
   insert#2(z, z', z'', z3) -{ 0 }-> 1 + z' + (1 + z'' + z3) :|: z'' >= 0, z = 1, z' >= 0, z3 >= 0
   insert#2(z, z', z'', z3) -{ 0 }-> 1 + z'' + insert(z', z3) :|: z = 2, z'' >= 0, z' >= 0, z3 >= 0
   insertionsort(z) -{ 0 }-> insertionsort#1(z) :|: z >= 0
   insertionsort(z) -{ 0 }-> 0 :|: z >= 0
   insertionsort#1(z) -{ 0 }-> insert(z0, insertionsort#1(z1)) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   insertionsort#1(z) -{ 0 }-> insert(z0, 0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   insertionsort#1(z) -{ 0 }-> 0 :|: z = 0
   insertionsort#1(z) -{ 0 }-> 0 :|: z >= 0

Function symbols to be analyzed: {insert#2,insert,insert#1}, {#LESS}, {flatten#1}, {insertionsort#1}, {INSERT#1,INSERT#2,INSERT}, {flatten}, {FLATTEN,FLATTEN#1}, {insertionsort}, {INSERTIONSORT,INSERTIONSORT#1}, {FLATTENSORT}
Previous analysis results are:
  APPEND#1: runtime: O(n^1) [4*z], size: O(1) [0]
  APPEND: runtime: O(n^1) [1 + 4*z], size: O(1) [1]
  #cklt: runtime: O(1) [0], size: O(1) [2]
  #compare: runtime: O(1) [0], size: O(1) [3]
  #COMPARE: runtime: O(1) [0], size: O(n^1) [z + z']
  append#1: runtime: O(1) [0], size: O(n^1) [z + z']
  append: runtime: O(1) [0], size: O(n^1) [z + z']
  #less: runtime: O(1) [0], size: O(1) [2]

----------------------------------------

(71) ResultPropagationProof (UPPER BOUND(ID))
Applied inner abstraction using the recently inferred runtime/size bounds where possible.
----------------------------------------

(72)
Obligation:
Complexity RNTS consisting of the following rules:

   #COMPARE(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   #COMPARE(z, z') -{ 0 }-> 1 + s19 :|: s19 >= 0, s19 <= z' - 1 + (z - 1), z' - 1 >= 0, z - 1 >= 0
   #COMPARE(z, z') -{ 0 }-> 1 + s20 :|: s20 >= 0, s20 <= z - 1 + (z' - 1), z' - 1 >= 0, z - 1 >= 0
   #LESS(z, z') -{ 1 }-> 1 + s18 :|: s18 >= 0, s18 <= z + z', z' >= 0, z >= 0
   #cklt(z) -{ 0 }-> 2 :|: z = 3
   #cklt(z) -{ 0 }-> 1 :|: z = 1
   #cklt(z) -{ 0 }-> 1 :|: z = 2
   #cklt(z) -{ 0 }-> 0 :|: z >= 0
   #compare(z, z') -{ 0 }-> s8 :|: s8 >= 0, s8 <= 3, z' - 1 >= 0, z - 1 >= 0
   #compare(z, z') -{ 0 }-> s9 :|: s9 >= 0, s9 <= 3, z' - 1 >= 0, z - 1 >= 0
   #compare(z, z') -{ 0 }-> 3 :|: z' - 1 >= 0, z = 0
   #compare(z, z') -{ 0 }-> 3 :|: z - 1 >= 0, z' = 0
   #compare(z, z') -{ 0 }-> 3 :|: z' - 1 >= 0, z - 1 >= 0
   #compare(z, z') -{ 0 }-> 2 :|: z' - 1 >= 0, z = 0
   #compare(z, z') -{ 0 }-> 2 :|: z - 1 >= 0, z' = 0
   #compare(z, z') -{ 0 }-> 2 :|: z' - 1 >= 0, z - 1 >= 0
   #compare(z, z') -{ 0 }-> 1 :|: z = 0, z' = 0
   #compare(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   #less(z, z') -{ 0 }-> s13 :|: s12 >= 0, s12 <= 3, s13 >= 0, s13 <= 2, z' - 1 >= 0, z - 1 >= 0
   #less(z, z') -{ 0 }-> s15 :|: s14 >= 0, s14 <= 3, s15 >= 0, s15 <= 2, z - 1 >= 0, z' - 1 >= 0
   #less(z, z') -{ 0 }-> 2 :|: z' - 1 >= 0, z = 0, 3 = 3
   #less(z, z') -{ 0 }-> 2 :|: z - 1 >= 0, z' = 0, 3 = 3
   #less(z, z') -{ 0 }-> 2 :|: z - 1 >= 0, z' - 1 >= 0, 3 = 3
   #less(z, z') -{ 0 }-> 1 :|: z = 0, z' = 0, 1 = 1
   #less(z, z') -{ 0 }-> 1 :|: z' - 1 >= 0, z = 0, 2 = 2
   #less(z, z') -{ 0 }-> 1 :|: z - 1 >= 0, z' = 0, 2 = 2
   #less(z, z') -{ 0 }-> 1 :|: z' - 1 >= 0, z - 1 >= 0, 2 = 2
   #less(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   #less(z, z') -{ 0 }-> 0 :|: z = 0, z' = 0, v0 >= 0, 1 = v0
   #less(z, z') -{ 0 }-> 0 :|: z' - 1 >= 0, z = 0, v0 >= 0, 2 = v0
   #less(z, z') -{ 0 }-> 0 :|: z' - 1 >= 0, z = 0, v0 >= 0, 3 = v0
   #less(z, z') -{ 0 }-> 0 :|: z - 1 >= 0, z' = 0, v0 >= 0, 3 = v0
   #less(z, z') -{ 0 }-> 0 :|: z - 1 >= 0, z' - 1 >= 0, v0 >= 0, 3 = v0
   #less(z, z') -{ 0 }-> 0 :|: z - 1 >= 0, z' = 0, v0 >= 0, 2 = v0
   #less(z, z') -{ 0 }-> 0 :|: z' - 1 >= 0, z - 1 >= 0, v0 >= 0, 2 = v0
   #less(z, z') -{ 0 }-> 0 :|: z' >= 0, z >= 0, v0 >= 0, 0 = v0
   APPEND(z, z') -{ 1 + 4*z }-> 1 + s :|: s >= 0, s <= 0, z' >= 0, z >= 0
   APPEND#1(z, z') -{ 2 + 4*z1 }-> 1 + s' :|: s' >= 0, s' <= 1, z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z' >= 0
   FLATTEN(z) -{ 1 }-> 1 + FLATTEN#1(z) :|: z >= 0
   FLATTEN#1(z) -{ 2 + 4*z0 }-> 1 + s22 + APPEND(flatten#1(z1), flatten#1(z2)) + FLATTEN(z1) :|: s21 >= 0, s21 <= 0 + 0, s22 >= 0, s22 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 2 + 4*z0 }-> 1 + s24 + APPEND(flatten#1(z1), 0) + FLATTEN(z1) :|: s23 >= 0, s23 <= 0 + 0, s24 >= 0, s24 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 2 + 4*z0 }-> 1 + s26 + APPEND(0, flatten#1(z2)) + FLATTEN(z1) :|: s25 >= 0, s25 <= 0 + 0, s26 >= 0, s26 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*z0 }-> 1 + s28 + s3 + FLATTEN(z1) :|: s27 >= 0, s27 <= 0 + 0, s28 >= 0, s28 <= 1, s3 >= 0, s3 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 2 + 4*z0 }-> 1 + s30 + APPEND(flatten#1(z1), flatten#1(z2)) + FLATTEN(z2) :|: s29 >= 0, s29 <= 0 + 0, s30 >= 0, s30 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 2 + 4*z0 }-> 1 + s32 + APPEND(flatten#1(z1), 0) + FLATTEN(z2) :|: s31 >= 0, s31 <= 0 + 0, s32 >= 0, s32 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 2 + 4*z0 }-> 1 + s34 + APPEND(0, flatten#1(z2)) + FLATTEN(z2) :|: s33 >= 0, s33 <= 0 + 0, s34 >= 0, s34 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*z0 }-> 1 + s36 + s7 + FLATTEN(z2) :|: s35 >= 0, s35 <= 0 + 0, s36 >= 0, s36 <= 1, s7 >= 0, s7 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 2 }-> 1 + APPEND(z0, append(flatten#1(z1), flatten#1(z2))) + s'' + FLATTEN(z1) :|: s'' >= 0, s'' <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 2 }-> 1 + APPEND(z0, append(flatten#1(z1), flatten#1(z2))) + s4 + FLATTEN(z2) :|: s4 >= 0, s4 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), flatten#1(z2))) + APPEND(flatten#1(z1), flatten#1(z2)) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), flatten#1(z2))) + APPEND(flatten#1(z1), flatten#1(z2)) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), flatten#1(z2))) + APPEND(flatten#1(z1), 0) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), flatten#1(z2))) + APPEND(flatten#1(z1), 0) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), flatten#1(z2))) + APPEND(0, flatten#1(z2)) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), flatten#1(z2))) + APPEND(0, flatten#1(z2)) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 2 }-> 1 + APPEND(z0, append(flatten#1(z1), 0)) + s1 + FLATTEN(z1) :|: s1 >= 0, s1 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 2 }-> 1 + APPEND(z0, append(flatten#1(z1), 0)) + s5 + FLATTEN(z2) :|: s5 >= 0, s5 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), 0)) + APPEND(flatten#1(z1), flatten#1(z2)) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), 0)) + APPEND(flatten#1(z1), flatten#1(z2)) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), 0)) + APPEND(flatten#1(z1), 0) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), 0)) + APPEND(flatten#1(z1), 0) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), 0)) + APPEND(0, flatten#1(z2)) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), 0)) + APPEND(0, flatten#1(z2)) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 2 }-> 1 + APPEND(z0, append(0, flatten#1(z2))) + s2 + FLATTEN(z1) :|: s2 >= 0, s2 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 2 }-> 1 + APPEND(z0, append(0, flatten#1(z2))) + s6 + FLATTEN(z2) :|: s6 >= 0, s6 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(0, flatten#1(z2))) + APPEND(flatten#1(z1), flatten#1(z2)) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(0, flatten#1(z2))) + APPEND(flatten#1(z1), flatten#1(z2)) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(0, flatten#1(z2))) + APPEND(flatten#1(z1), 0) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(0, flatten#1(z2))) + APPEND(flatten#1(z1), 0) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(0, flatten#1(z2))) + APPEND(0, flatten#1(z2)) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(0, flatten#1(z2))) + APPEND(0, flatten#1(z2)) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTENSORT(z) -{ 0 }-> 0 :|: z >= 0
   FLATTENSORT(z) -{ 0 }-> 1 + INSERTIONSORT(flatten#1(z)) :|: z >= 0
   FLATTENSORT(z) -{ 0 }-> 1 + INSERTIONSORT(0) :|: z >= 0
   INSERT(z, z') -{ 1 }-> 1 + INSERT#1(z', z) :|: z' >= 0, z >= 0
   INSERT#1(z, z') -{ 1 }-> 1 + INSERT#2(s11, z', z0, z1) + #LESS(z0, z') :|: s10 >= 0, s10 <= 3, s11 >= 0, s11 <= 2, z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z' >= 0
   INSERT#1(z, z') -{ 1 }-> 1 + INSERT#2(0, z', z0, z1) + #LESS(z0, z') :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z' >= 0
   INSERT#2(z, z', z'', z3) -{ 1 }-> 1 + INSERT(z', z3) :|: z = 2, z'' >= 0, z' >= 0, z3 >= 0
   INSERTIONSORT(z) -{ 1 }-> 1 + INSERTIONSORT#1(z) :|: z >= 0
   INSERTIONSORT#1(z) -{ 1 }-> 1 + INSERT(z0, insertionsort#1(z1)) + INSERTIONSORT(z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   INSERTIONSORT#1(z) -{ 1 }-> 1 + INSERT(z0, 0) + INSERTIONSORT(z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   append(z, z') -{ 0 }-> s37 :|: s37 >= 0, s37 <= z + z', z' >= 0, z >= 0
   append(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   append#1(z, z') -{ 0 }-> z' :|: z' >= 0, z = 0
   append#1(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   append#1(z, z') -{ 0 }-> 1 + z0 + s40 :|: s40 >= 0, s40 <= z1 + z', z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z' >= 0
   flatten(z) -{ 0 }-> flatten#1(z) :|: z >= 0
   flatten(z) -{ 0 }-> 0 :|: z >= 0
   flatten#1(z) -{ 0 }-> s39 :|: s38 >= 0, s38 <= 0 + 0, s39 >= 0, s39 <= z0 + s38, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   flatten#1(z) -{ 0 }-> append(z0, append(flatten#1(z1), flatten#1(z2))) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   flatten#1(z) -{ 0 }-> append(z0, append(flatten#1(z1), 0)) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   flatten#1(z) -{ 0 }-> append(z0, append(0, flatten#1(z2))) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   flatten#1(z) -{ 0 }-> 0 :|: z = 0
   flatten#1(z) -{ 0 }-> 0 :|: z >= 0
   insert(z, z') -{ 0 }-> insert#1(z', z) :|: z' >= 0, z >= 0
   insert(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   insert#1(z, z') -{ 0 }-> insert#2(s17, z', z0, z1) :|: s16 >= 0, s16 <= 3, s17 >= 0, s17 <= 2, z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z' >= 0
   insert#1(z, z') -{ 0 }-> insert#2(0, z', z0, z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z' >= 0
   insert#1(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   insert#1(z, z') -{ 0 }-> 1 + z' + 0 :|: z' >= 0, z = 0
   insert#2(z, z', z'', z3) -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0, z3 >= 0
   insert#2(z, z', z'', z3) -{ 0 }-> 1 + z' + (1 + z'' + z3) :|: z'' >= 0, z = 1, z' >= 0, z3 >= 0
   insert#2(z, z', z'', z3) -{ 0 }-> 1 + z'' + insert(z', z3) :|: z = 2, z'' >= 0, z' >= 0, z3 >= 0
   insertionsort(z) -{ 0 }-> insertionsort#1(z) :|: z >= 0
   insertionsort(z) -{ 0 }-> 0 :|: z >= 0
   insertionsort#1(z) -{ 0 }-> insert(z0, insertionsort#1(z1)) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   insertionsort#1(z) -{ 0 }-> insert(z0, 0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   insertionsort#1(z) -{ 0 }-> 0 :|: z = 0
   insertionsort#1(z) -{ 0 }-> 0 :|: z >= 0

Function symbols to be analyzed: {insert#2,insert,insert#1}, {#LESS}, {flatten#1}, {insertionsort#1}, {INSERT#1,INSERT#2,INSERT}, {flatten}, {FLATTEN,FLATTEN#1}, {insertionsort}, {INSERTIONSORT,INSERTIONSORT#1}, {FLATTENSORT}
Previous analysis results are:
  APPEND#1: runtime: O(n^1) [4*z], size: O(1) [0]
  APPEND: runtime: O(n^1) [1 + 4*z], size: O(1) [1]
  #cklt: runtime: O(1) [0], size: O(1) [2]
  #compare: runtime: O(1) [0], size: O(1) [3]
  #COMPARE: runtime: O(1) [0], size: O(n^1) [z + z']
  append#1: runtime: O(1) [0], size: O(n^1) [z + z']
  append: runtime: O(1) [0], size: O(n^1) [z + z']
  #less: runtime: O(1) [0], size: O(1) [2]

----------------------------------------

(73) IntTrsBoundProof (UPPER BOUND(ID))

Computed SIZE bound using CoFloCo for: insert#2
after applying outer abstraction to obtain an ITS,
resulting in: O(n^1) with polynomial bound: 2 + z' + z'' + z3

Computed SIZE bound using CoFloCo for: insert
after applying outer abstraction to obtain an ITS,
resulting in: O(n^1) with polynomial bound: 1 + z + z'

Computed SIZE bound using CoFloCo for: insert#1
after applying outer abstraction to obtain an ITS,
resulting in: O(n^1) with polynomial bound: 1 + z + z'

----------------------------------------

(74)
Obligation:
Complexity RNTS consisting of the following rules:

   #COMPARE(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   #COMPARE(z, z') -{ 0 }-> 1 + s19 :|: s19 >= 0, s19 <= z' - 1 + (z - 1), z' - 1 >= 0, z - 1 >= 0
   #COMPARE(z, z') -{ 0 }-> 1 + s20 :|: s20 >= 0, s20 <= z - 1 + (z' - 1), z' - 1 >= 0, z - 1 >= 0
   #LESS(z, z') -{ 1 }-> 1 + s18 :|: s18 >= 0, s18 <= z + z', z' >= 0, z >= 0
   #cklt(z) -{ 0 }-> 2 :|: z = 3
   #cklt(z) -{ 0 }-> 1 :|: z = 1
   #cklt(z) -{ 0 }-> 1 :|: z = 2
   #cklt(z) -{ 0 }-> 0 :|: z >= 0
   #compare(z, z') -{ 0 }-> s8 :|: s8 >= 0, s8 <= 3, z' - 1 >= 0, z - 1 >= 0
   #compare(z, z') -{ 0 }-> s9 :|: s9 >= 0, s9 <= 3, z' - 1 >= 0, z - 1 >= 0
   #compare(z, z') -{ 0 }-> 3 :|: z' - 1 >= 0, z = 0
   #compare(z, z') -{ 0 }-> 3 :|: z - 1 >= 0, z' = 0
   #compare(z, z') -{ 0 }-> 3 :|: z' - 1 >= 0, z - 1 >= 0
   #compare(z, z') -{ 0 }-> 2 :|: z' - 1 >= 0, z = 0
   #compare(z, z') -{ 0 }-> 2 :|: z - 1 >= 0, z' = 0
   #compare(z, z') -{ 0 }-> 2 :|: z' - 1 >= 0, z - 1 >= 0
   #compare(z, z') -{ 0 }-> 1 :|: z = 0, z' = 0
   #compare(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   #less(z, z') -{ 0 }-> s13 :|: s12 >= 0, s12 <= 3, s13 >= 0, s13 <= 2, z' - 1 >= 0, z - 1 >= 0
   #less(z, z') -{ 0 }-> s15 :|: s14 >= 0, s14 <= 3, s15 >= 0, s15 <= 2, z - 1 >= 0, z' - 1 >= 0
   #less(z, z') -{ 0 }-> 2 :|: z' - 1 >= 0, z = 0, 3 = 3
   #less(z, z') -{ 0 }-> 2 :|: z - 1 >= 0, z' = 0, 3 = 3
   #less(z, z') -{ 0 }-> 2 :|: z - 1 >= 0, z' - 1 >= 0, 3 = 3
   #less(z, z') -{ 0 }-> 1 :|: z = 0, z' = 0, 1 = 1
   #less(z, z') -{ 0 }-> 1 :|: z' - 1 >= 0, z = 0, 2 = 2
   #less(z, z') -{ 0 }-> 1 :|: z - 1 >= 0, z' = 0, 2 = 2
   #less(z, z') -{ 0 }-> 1 :|: z' - 1 >= 0, z - 1 >= 0, 2 = 2
   #less(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   #less(z, z') -{ 0 }-> 0 :|: z = 0, z' = 0, v0 >= 0, 1 = v0
   #less(z, z') -{ 0 }-> 0 :|: z' - 1 >= 0, z = 0, v0 >= 0, 2 = v0
   #less(z, z') -{ 0 }-> 0 :|: z' - 1 >= 0, z = 0, v0 >= 0, 3 = v0
   #less(z, z') -{ 0 }-> 0 :|: z - 1 >= 0, z' = 0, v0 >= 0, 3 = v0
   #less(z, z') -{ 0 }-> 0 :|: z - 1 >= 0, z' - 1 >= 0, v0 >= 0, 3 = v0
   #less(z, z') -{ 0 }-> 0 :|: z - 1 >= 0, z' = 0, v0 >= 0, 2 = v0
   #less(z, z') -{ 0 }-> 0 :|: z' - 1 >= 0, z - 1 >= 0, v0 >= 0, 2 = v0
   #less(z, z') -{ 0 }-> 0 :|: z' >= 0, z >= 0, v0 >= 0, 0 = v0
   APPEND(z, z') -{ 1 + 4*z }-> 1 + s :|: s >= 0, s <= 0, z' >= 0, z >= 0
   APPEND#1(z, z') -{ 2 + 4*z1 }-> 1 + s' :|: s' >= 0, s' <= 1, z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z' >= 0
   FLATTEN(z) -{ 1 }-> 1 + FLATTEN#1(z) :|: z >= 0
   FLATTEN#1(z) -{ 2 + 4*z0 }-> 1 + s22 + APPEND(flatten#1(z1), flatten#1(z2)) + FLATTEN(z1) :|: s21 >= 0, s21 <= 0 + 0, s22 >= 0, s22 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 2 + 4*z0 }-> 1 + s24 + APPEND(flatten#1(z1), 0) + FLATTEN(z1) :|: s23 >= 0, s23 <= 0 + 0, s24 >= 0, s24 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 2 + 4*z0 }-> 1 + s26 + APPEND(0, flatten#1(z2)) + FLATTEN(z1) :|: s25 >= 0, s25 <= 0 + 0, s26 >= 0, s26 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*z0 }-> 1 + s28 + s3 + FLATTEN(z1) :|: s27 >= 0, s27 <= 0 + 0, s28 >= 0, s28 <= 1, s3 >= 0, s3 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 2 + 4*z0 }-> 1 + s30 + APPEND(flatten#1(z1), flatten#1(z2)) + FLATTEN(z2) :|: s29 >= 0, s29 <= 0 + 0, s30 >= 0, s30 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 2 + 4*z0 }-> 1 + s32 + APPEND(flatten#1(z1), 0) + FLATTEN(z2) :|: s31 >= 0, s31 <= 0 + 0, s32 >= 0, s32 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 2 + 4*z0 }-> 1 + s34 + APPEND(0, flatten#1(z2)) + FLATTEN(z2) :|: s33 >= 0, s33 <= 0 + 0, s34 >= 0, s34 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*z0 }-> 1 + s36 + s7 + FLATTEN(z2) :|: s35 >= 0, s35 <= 0 + 0, s36 >= 0, s36 <= 1, s7 >= 0, s7 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 2 }-> 1 + APPEND(z0, append(flatten#1(z1), flatten#1(z2))) + s'' + FLATTEN(z1) :|: s'' >= 0, s'' <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 2 }-> 1 + APPEND(z0, append(flatten#1(z1), flatten#1(z2))) + s4 + FLATTEN(z2) :|: s4 >= 0, s4 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), flatten#1(z2))) + APPEND(flatten#1(z1), flatten#1(z2)) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), flatten#1(z2))) + APPEND(flatten#1(z1), flatten#1(z2)) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), flatten#1(z2))) + APPEND(flatten#1(z1), 0) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), flatten#1(z2))) + APPEND(flatten#1(z1), 0) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), flatten#1(z2))) + APPEND(0, flatten#1(z2)) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), flatten#1(z2))) + APPEND(0, flatten#1(z2)) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 2 }-> 1 + APPEND(z0, append(flatten#1(z1), 0)) + s1 + FLATTEN(z1) :|: s1 >= 0, s1 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 2 }-> 1 + APPEND(z0, append(flatten#1(z1), 0)) + s5 + FLATTEN(z2) :|: s5 >= 0, s5 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), 0)) + APPEND(flatten#1(z1), flatten#1(z2)) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), 0)) + APPEND(flatten#1(z1), flatten#1(z2)) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), 0)) + APPEND(flatten#1(z1), 0) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), 0)) + APPEND(flatten#1(z1), 0) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), 0)) + APPEND(0, flatten#1(z2)) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), 0)) + APPEND(0, flatten#1(z2)) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 2 }-> 1 + APPEND(z0, append(0, flatten#1(z2))) + s2 + FLATTEN(z1) :|: s2 >= 0, s2 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 2 }-> 1 + APPEND(z0, append(0, flatten#1(z2))) + s6 + FLATTEN(z2) :|: s6 >= 0, s6 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(0, flatten#1(z2))) + APPEND(flatten#1(z1), flatten#1(z2)) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(0, flatten#1(z2))) + APPEND(flatten#1(z1), flatten#1(z2)) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(0, flatten#1(z2))) + APPEND(flatten#1(z1), 0) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(0, flatten#1(z2))) + APPEND(flatten#1(z1), 0) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(0, flatten#1(z2))) + APPEND(0, flatten#1(z2)) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(0, flatten#1(z2))) + APPEND(0, flatten#1(z2)) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTENSORT(z) -{ 0 }-> 0 :|: z >= 0
   FLATTENSORT(z) -{ 0 }-> 1 + INSERTIONSORT(flatten#1(z)) :|: z >= 0
   FLATTENSORT(z) -{ 0 }-> 1 + INSERTIONSORT(0) :|: z >= 0
   INSERT(z, z') -{ 1 }-> 1 + INSERT#1(z', z) :|: z' >= 0, z >= 0
   INSERT#1(z, z') -{ 1 }-> 1 + INSERT#2(s11, z', z0, z1) + #LESS(z0, z') :|: s10 >= 0, s10 <= 3, s11 >= 0, s11 <= 2, z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z' >= 0
   INSERT#1(z, z') -{ 1 }-> 1 + INSERT#2(0, z', z0, z1) + #LESS(z0, z') :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z' >= 0
   INSERT#2(z, z', z'', z3) -{ 1 }-> 1 + INSERT(z', z3) :|: z = 2, z'' >= 0, z' >= 0, z3 >= 0
   INSERTIONSORT(z) -{ 1 }-> 1 + INSERTIONSORT#1(z) :|: z >= 0
   INSERTIONSORT#1(z) -{ 1 }-> 1 + INSERT(z0, insertionsort#1(z1)) + INSERTIONSORT(z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   INSERTIONSORT#1(z) -{ 1 }-> 1 + INSERT(z0, 0) + INSERTIONSORT(z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   append(z, z') -{ 0 }-> s37 :|: s37 >= 0, s37 <= z + z', z' >= 0, z >= 0
   append(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   append#1(z, z') -{ 0 }-> z' :|: z' >= 0, z = 0
   append#1(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   append#1(z, z') -{ 0 }-> 1 + z0 + s40 :|: s40 >= 0, s40 <= z1 + z', z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z' >= 0
   flatten(z) -{ 0 }-> flatten#1(z) :|: z >= 0
   flatten(z) -{ 0 }-> 0 :|: z >= 0
   flatten#1(z) -{ 0 }-> s39 :|: s38 >= 0, s38 <= 0 + 0, s39 >= 0, s39 <= z0 + s38, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   flatten#1(z) -{ 0 }-> append(z0, append(flatten#1(z1), flatten#1(z2))) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   flatten#1(z) -{ 0 }-> append(z0, append(flatten#1(z1), 0)) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   flatten#1(z) -{ 0 }-> append(z0, append(0, flatten#1(z2))) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   flatten#1(z) -{ 0 }-> 0 :|: z = 0
   flatten#1(z) -{ 0 }-> 0 :|: z >= 0
   insert(z, z') -{ 0 }-> insert#1(z', z) :|: z' >= 0, z >= 0
   insert(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   insert#1(z, z') -{ 0 }-> insert#2(s17, z', z0, z1) :|: s16 >= 0, s16 <= 3, s17 >= 0, s17 <= 2, z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z' >= 0
   insert#1(z, z') -{ 0 }-> insert#2(0, z', z0, z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z' >= 0
   insert#1(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   insert#1(z, z') -{ 0 }-> 1 + z' + 0 :|: z' >= 0, z = 0
   insert#2(z, z', z'', z3) -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0, z3 >= 0
   insert#2(z, z', z'', z3) -{ 0 }-> 1 + z' + (1 + z'' + z3) :|: z'' >= 0, z = 1, z' >= 0, z3 >= 0
   insert#2(z, z', z'', z3) -{ 0 }-> 1 + z'' + insert(z', z3) :|: z = 2, z'' >= 0, z' >= 0, z3 >= 0
   insertionsort(z) -{ 0 }-> insertionsort#1(z) :|: z >= 0
   insertionsort(z) -{ 0 }-> 0 :|: z >= 0
   insertionsort#1(z) -{ 0 }-> insert(z0, insertionsort#1(z1)) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   insertionsort#1(z) -{ 0 }-> insert(z0, 0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   insertionsort#1(z) -{ 0 }-> 0 :|: z = 0
   insertionsort#1(z) -{ 0 }-> 0 :|: z >= 0

Function symbols to be analyzed: {insert#2,insert,insert#1}, {#LESS}, {flatten#1}, {insertionsort#1}, {INSERT#1,INSERT#2,INSERT}, {flatten}, {FLATTEN,FLATTEN#1}, {insertionsort}, {INSERTIONSORT,INSERTIONSORT#1}, {FLATTENSORT}
Previous analysis results are:
  APPEND#1: runtime: O(n^1) [4*z], size: O(1) [0]
  APPEND: runtime: O(n^1) [1 + 4*z], size: O(1) [1]
  #cklt: runtime: O(1) [0], size: O(1) [2]
  #compare: runtime: O(1) [0], size: O(1) [3]
  #COMPARE: runtime: O(1) [0], size: O(n^1) [z + z']
  append#1: runtime: O(1) [0], size: O(n^1) [z + z']
  append: runtime: O(1) [0], size: O(n^1) [z + z']
  #less: runtime: O(1) [0], size: O(1) [2]
  insert#2: runtime: ?, size: O(n^1) [2 + z' + z'' + z3]
  insert: runtime: ?, size: O(n^1) [1 + z + z']
  insert#1: runtime: ?, size: O(n^1) [1 + z + z']

----------------------------------------

(75) IntTrsBoundProof (UPPER BOUND(ID))

Computed RUNTIME bound using CoFloCo for: insert#2
after applying outer abstraction to obtain an ITS,
resulting in: O(1) with polynomial bound: 0

Computed RUNTIME bound using CoFloCo for: insert
after applying outer abstraction to obtain an ITS,
resulting in: O(1) with polynomial bound: 0

Computed RUNTIME bound using CoFloCo for: insert#1
after applying outer abstraction to obtain an ITS,
resulting in: O(1) with polynomial bound: 0

----------------------------------------

(76)
Obligation:
Complexity RNTS consisting of the following rules:

   #COMPARE(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   #COMPARE(z, z') -{ 0 }-> 1 + s19 :|: s19 >= 0, s19 <= z' - 1 + (z - 1), z' - 1 >= 0, z - 1 >= 0
   #COMPARE(z, z') -{ 0 }-> 1 + s20 :|: s20 >= 0, s20 <= z - 1 + (z' - 1), z' - 1 >= 0, z - 1 >= 0
   #LESS(z, z') -{ 1 }-> 1 + s18 :|: s18 >= 0, s18 <= z + z', z' >= 0, z >= 0
   #cklt(z) -{ 0 }-> 2 :|: z = 3
   #cklt(z) -{ 0 }-> 1 :|: z = 1
   #cklt(z) -{ 0 }-> 1 :|: z = 2
   #cklt(z) -{ 0 }-> 0 :|: z >= 0
   #compare(z, z') -{ 0 }-> s8 :|: s8 >= 0, s8 <= 3, z' - 1 >= 0, z - 1 >= 0
   #compare(z, z') -{ 0 }-> s9 :|: s9 >= 0, s9 <= 3, z' - 1 >= 0, z - 1 >= 0
   #compare(z, z') -{ 0 }-> 3 :|: z' - 1 >= 0, z = 0
   #compare(z, z') -{ 0 }-> 3 :|: z - 1 >= 0, z' = 0
   #compare(z, z') -{ 0 }-> 3 :|: z' - 1 >= 0, z - 1 >= 0
   #compare(z, z') -{ 0 }-> 2 :|: z' - 1 >= 0, z = 0
   #compare(z, z') -{ 0 }-> 2 :|: z - 1 >= 0, z' = 0
   #compare(z, z') -{ 0 }-> 2 :|: z' - 1 >= 0, z - 1 >= 0
   #compare(z, z') -{ 0 }-> 1 :|: z = 0, z' = 0
   #compare(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   #less(z, z') -{ 0 }-> s13 :|: s12 >= 0, s12 <= 3, s13 >= 0, s13 <= 2, z' - 1 >= 0, z - 1 >= 0
   #less(z, z') -{ 0 }-> s15 :|: s14 >= 0, s14 <= 3, s15 >= 0, s15 <= 2, z - 1 >= 0, z' - 1 >= 0
   #less(z, z') -{ 0 }-> 2 :|: z' - 1 >= 0, z = 0, 3 = 3
   #less(z, z') -{ 0 }-> 2 :|: z - 1 >= 0, z' = 0, 3 = 3
   #less(z, z') -{ 0 }-> 2 :|: z - 1 >= 0, z' - 1 >= 0, 3 = 3
   #less(z, z') -{ 0 }-> 1 :|: z = 0, z' = 0, 1 = 1
   #less(z, z') -{ 0 }-> 1 :|: z' - 1 >= 0, z = 0, 2 = 2
   #less(z, z') -{ 0 }-> 1 :|: z - 1 >= 0, z' = 0, 2 = 2
   #less(z, z') -{ 0 }-> 1 :|: z' - 1 >= 0, z - 1 >= 0, 2 = 2
   #less(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   #less(z, z') -{ 0 }-> 0 :|: z = 0, z' = 0, v0 >= 0, 1 = v0
   #less(z, z') -{ 0 }-> 0 :|: z' - 1 >= 0, z = 0, v0 >= 0, 2 = v0
   #less(z, z') -{ 0 }-> 0 :|: z' - 1 >= 0, z = 0, v0 >= 0, 3 = v0
   #less(z, z') -{ 0 }-> 0 :|: z - 1 >= 0, z' = 0, v0 >= 0, 3 = v0
   #less(z, z') -{ 0 }-> 0 :|: z - 1 >= 0, z' - 1 >= 0, v0 >= 0, 3 = v0
   #less(z, z') -{ 0 }-> 0 :|: z - 1 >= 0, z' = 0, v0 >= 0, 2 = v0
   #less(z, z') -{ 0 }-> 0 :|: z' - 1 >= 0, z - 1 >= 0, v0 >= 0, 2 = v0
   #less(z, z') -{ 0 }-> 0 :|: z' >= 0, z >= 0, v0 >= 0, 0 = v0
   APPEND(z, z') -{ 1 + 4*z }-> 1 + s :|: s >= 0, s <= 0, z' >= 0, z >= 0
   APPEND#1(z, z') -{ 2 + 4*z1 }-> 1 + s' :|: s' >= 0, s' <= 1, z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z' >= 0
   FLATTEN(z) -{ 1 }-> 1 + FLATTEN#1(z) :|: z >= 0
   FLATTEN#1(z) -{ 2 + 4*z0 }-> 1 + s22 + APPEND(flatten#1(z1), flatten#1(z2)) + FLATTEN(z1) :|: s21 >= 0, s21 <= 0 + 0, s22 >= 0, s22 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 2 + 4*z0 }-> 1 + s24 + APPEND(flatten#1(z1), 0) + FLATTEN(z1) :|: s23 >= 0, s23 <= 0 + 0, s24 >= 0, s24 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 2 + 4*z0 }-> 1 + s26 + APPEND(0, flatten#1(z2)) + FLATTEN(z1) :|: s25 >= 0, s25 <= 0 + 0, s26 >= 0, s26 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*z0 }-> 1 + s28 + s3 + FLATTEN(z1) :|: s27 >= 0, s27 <= 0 + 0, s28 >= 0, s28 <= 1, s3 >= 0, s3 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 2 + 4*z0 }-> 1 + s30 + APPEND(flatten#1(z1), flatten#1(z2)) + FLATTEN(z2) :|: s29 >= 0, s29 <= 0 + 0, s30 >= 0, s30 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 2 + 4*z0 }-> 1 + s32 + APPEND(flatten#1(z1), 0) + FLATTEN(z2) :|: s31 >= 0, s31 <= 0 + 0, s32 >= 0, s32 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 2 + 4*z0 }-> 1 + s34 + APPEND(0, flatten#1(z2)) + FLATTEN(z2) :|: s33 >= 0, s33 <= 0 + 0, s34 >= 0, s34 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*z0 }-> 1 + s36 + s7 + FLATTEN(z2) :|: s35 >= 0, s35 <= 0 + 0, s36 >= 0, s36 <= 1, s7 >= 0, s7 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 2 }-> 1 + APPEND(z0, append(flatten#1(z1), flatten#1(z2))) + s'' + FLATTEN(z1) :|: s'' >= 0, s'' <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 2 }-> 1 + APPEND(z0, append(flatten#1(z1), flatten#1(z2))) + s4 + FLATTEN(z2) :|: s4 >= 0, s4 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), flatten#1(z2))) + APPEND(flatten#1(z1), flatten#1(z2)) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), flatten#1(z2))) + APPEND(flatten#1(z1), flatten#1(z2)) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), flatten#1(z2))) + APPEND(flatten#1(z1), 0) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), flatten#1(z2))) + APPEND(flatten#1(z1), 0) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), flatten#1(z2))) + APPEND(0, flatten#1(z2)) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), flatten#1(z2))) + APPEND(0, flatten#1(z2)) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 2 }-> 1 + APPEND(z0, append(flatten#1(z1), 0)) + s1 + FLATTEN(z1) :|: s1 >= 0, s1 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 2 }-> 1 + APPEND(z0, append(flatten#1(z1), 0)) + s5 + FLATTEN(z2) :|: s5 >= 0, s5 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), 0)) + APPEND(flatten#1(z1), flatten#1(z2)) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), 0)) + APPEND(flatten#1(z1), flatten#1(z2)) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), 0)) + APPEND(flatten#1(z1), 0) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), 0)) + APPEND(flatten#1(z1), 0) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), 0)) + APPEND(0, flatten#1(z2)) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), 0)) + APPEND(0, flatten#1(z2)) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 2 }-> 1 + APPEND(z0, append(0, flatten#1(z2))) + s2 + FLATTEN(z1) :|: s2 >= 0, s2 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 2 }-> 1 + APPEND(z0, append(0, flatten#1(z2))) + s6 + FLATTEN(z2) :|: s6 >= 0, s6 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(0, flatten#1(z2))) + APPEND(flatten#1(z1), flatten#1(z2)) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(0, flatten#1(z2))) + APPEND(flatten#1(z1), flatten#1(z2)) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(0, flatten#1(z2))) + APPEND(flatten#1(z1), 0) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(0, flatten#1(z2))) + APPEND(flatten#1(z1), 0) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(0, flatten#1(z2))) + APPEND(0, flatten#1(z2)) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(0, flatten#1(z2))) + APPEND(0, flatten#1(z2)) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTENSORT(z) -{ 0 }-> 0 :|: z >= 0
   FLATTENSORT(z) -{ 0 }-> 1 + INSERTIONSORT(flatten#1(z)) :|: z >= 0
   FLATTENSORT(z) -{ 0 }-> 1 + INSERTIONSORT(0) :|: z >= 0
   INSERT(z, z') -{ 1 }-> 1 + INSERT#1(z', z) :|: z' >= 0, z >= 0
   INSERT#1(z, z') -{ 1 }-> 1 + INSERT#2(s11, z', z0, z1) + #LESS(z0, z') :|: s10 >= 0, s10 <= 3, s11 >= 0, s11 <= 2, z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z' >= 0
   INSERT#1(z, z') -{ 1 }-> 1 + INSERT#2(0, z', z0, z1) + #LESS(z0, z') :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z' >= 0
   INSERT#2(z, z', z'', z3) -{ 1 }-> 1 + INSERT(z', z3) :|: z = 2, z'' >= 0, z' >= 0, z3 >= 0
   INSERTIONSORT(z) -{ 1 }-> 1 + INSERTIONSORT#1(z) :|: z >= 0
   INSERTIONSORT#1(z) -{ 1 }-> 1 + INSERT(z0, insertionsort#1(z1)) + INSERTIONSORT(z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   INSERTIONSORT#1(z) -{ 1 }-> 1 + INSERT(z0, 0) + INSERTIONSORT(z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   append(z, z') -{ 0 }-> s37 :|: s37 >= 0, s37 <= z + z', z' >= 0, z >= 0
   append(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   append#1(z, z') -{ 0 }-> z' :|: z' >= 0, z = 0
   append#1(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   append#1(z, z') -{ 0 }-> 1 + z0 + s40 :|: s40 >= 0, s40 <= z1 + z', z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z' >= 0
   flatten(z) -{ 0 }-> flatten#1(z) :|: z >= 0
   flatten(z) -{ 0 }-> 0 :|: z >= 0
   flatten#1(z) -{ 0 }-> s39 :|: s38 >= 0, s38 <= 0 + 0, s39 >= 0, s39 <= z0 + s38, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   flatten#1(z) -{ 0 }-> append(z0, append(flatten#1(z1), flatten#1(z2))) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   flatten#1(z) -{ 0 }-> append(z0, append(flatten#1(z1), 0)) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   flatten#1(z) -{ 0 }-> append(z0, append(0, flatten#1(z2))) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   flatten#1(z) -{ 0 }-> 0 :|: z = 0
   flatten#1(z) -{ 0 }-> 0 :|: z >= 0
   insert(z, z') -{ 0 }-> insert#1(z', z) :|: z' >= 0, z >= 0
   insert(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   insert#1(z, z') -{ 0 }-> insert#2(s17, z', z0, z1) :|: s16 >= 0, s16 <= 3, s17 >= 0, s17 <= 2, z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z' >= 0
   insert#1(z, z') -{ 0 }-> insert#2(0, z', z0, z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z' >= 0
   insert#1(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   insert#1(z, z') -{ 0 }-> 1 + z' + 0 :|: z' >= 0, z = 0
   insert#2(z, z', z'', z3) -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0, z3 >= 0
   insert#2(z, z', z'', z3) -{ 0 }-> 1 + z' + (1 + z'' + z3) :|: z'' >= 0, z = 1, z' >= 0, z3 >= 0
   insert#2(z, z', z'', z3) -{ 0 }-> 1 + z'' + insert(z', z3) :|: z = 2, z'' >= 0, z' >= 0, z3 >= 0
   insertionsort(z) -{ 0 }-> insertionsort#1(z) :|: z >= 0
   insertionsort(z) -{ 0 }-> 0 :|: z >= 0
   insertionsort#1(z) -{ 0 }-> insert(z0, insertionsort#1(z1)) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   insertionsort#1(z) -{ 0 }-> insert(z0, 0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   insertionsort#1(z) -{ 0 }-> 0 :|: z = 0
   insertionsort#1(z) -{ 0 }-> 0 :|: z >= 0

Function symbols to be analyzed: {#LESS}, {flatten#1}, {insertionsort#1}, {INSERT#1,INSERT#2,INSERT}, {flatten}, {FLATTEN,FLATTEN#1}, {insertionsort}, {INSERTIONSORT,INSERTIONSORT#1}, {FLATTENSORT}
Previous analysis results are:
  APPEND#1: runtime: O(n^1) [4*z], size: O(1) [0]
  APPEND: runtime: O(n^1) [1 + 4*z], size: O(1) [1]
  #cklt: runtime: O(1) [0], size: O(1) [2]
  #compare: runtime: O(1) [0], size: O(1) [3]
  #COMPARE: runtime: O(1) [0], size: O(n^1) [z + z']
  append#1: runtime: O(1) [0], size: O(n^1) [z + z']
  append: runtime: O(1) [0], size: O(n^1) [z + z']
  #less: runtime: O(1) [0], size: O(1) [2]
  insert#2: runtime: O(1) [0], size: O(n^1) [2 + z' + z'' + z3]
  insert: runtime: O(1) [0], size: O(n^1) [1 + z + z']
  insert#1: runtime: O(1) [0], size: O(n^1) [1 + z + z']

----------------------------------------

(77) ResultPropagationProof (UPPER BOUND(ID))
Applied inner abstraction using the recently inferred runtime/size bounds where possible.
----------------------------------------

(78)
Obligation:
Complexity RNTS consisting of the following rules:

   #COMPARE(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   #COMPARE(z, z') -{ 0 }-> 1 + s19 :|: s19 >= 0, s19 <= z' - 1 + (z - 1), z' - 1 >= 0, z - 1 >= 0
   #COMPARE(z, z') -{ 0 }-> 1 + s20 :|: s20 >= 0, s20 <= z - 1 + (z' - 1), z' - 1 >= 0, z - 1 >= 0
   #LESS(z, z') -{ 1 }-> 1 + s18 :|: s18 >= 0, s18 <= z + z', z' >= 0, z >= 0
   #cklt(z) -{ 0 }-> 2 :|: z = 3
   #cklt(z) -{ 0 }-> 1 :|: z = 1
   #cklt(z) -{ 0 }-> 1 :|: z = 2
   #cklt(z) -{ 0 }-> 0 :|: z >= 0
   #compare(z, z') -{ 0 }-> s8 :|: s8 >= 0, s8 <= 3, z' - 1 >= 0, z - 1 >= 0
   #compare(z, z') -{ 0 }-> s9 :|: s9 >= 0, s9 <= 3, z' - 1 >= 0, z - 1 >= 0
   #compare(z, z') -{ 0 }-> 3 :|: z' - 1 >= 0, z = 0
   #compare(z, z') -{ 0 }-> 3 :|: z - 1 >= 0, z' = 0
   #compare(z, z') -{ 0 }-> 3 :|: z' - 1 >= 0, z - 1 >= 0
   #compare(z, z') -{ 0 }-> 2 :|: z' - 1 >= 0, z = 0
   #compare(z, z') -{ 0 }-> 2 :|: z - 1 >= 0, z' = 0
   #compare(z, z') -{ 0 }-> 2 :|: z' - 1 >= 0, z - 1 >= 0
   #compare(z, z') -{ 0 }-> 1 :|: z = 0, z' = 0
   #compare(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   #less(z, z') -{ 0 }-> s13 :|: s12 >= 0, s12 <= 3, s13 >= 0, s13 <= 2, z' - 1 >= 0, z - 1 >= 0
   #less(z, z') -{ 0 }-> s15 :|: s14 >= 0, s14 <= 3, s15 >= 0, s15 <= 2, z - 1 >= 0, z' - 1 >= 0
   #less(z, z') -{ 0 }-> 2 :|: z' - 1 >= 0, z = 0, 3 = 3
   #less(z, z') -{ 0 }-> 2 :|: z - 1 >= 0, z' = 0, 3 = 3
   #less(z, z') -{ 0 }-> 2 :|: z - 1 >= 0, z' - 1 >= 0, 3 = 3
   #less(z, z') -{ 0 }-> 1 :|: z = 0, z' = 0, 1 = 1
   #less(z, z') -{ 0 }-> 1 :|: z' - 1 >= 0, z = 0, 2 = 2
   #less(z, z') -{ 0 }-> 1 :|: z - 1 >= 0, z' = 0, 2 = 2
   #less(z, z') -{ 0 }-> 1 :|: z' - 1 >= 0, z - 1 >= 0, 2 = 2
   #less(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   #less(z, z') -{ 0 }-> 0 :|: z = 0, z' = 0, v0 >= 0, 1 = v0
   #less(z, z') -{ 0 }-> 0 :|: z' - 1 >= 0, z = 0, v0 >= 0, 2 = v0
   #less(z, z') -{ 0 }-> 0 :|: z' - 1 >= 0, z = 0, v0 >= 0, 3 = v0
   #less(z, z') -{ 0 }-> 0 :|: z - 1 >= 0, z' = 0, v0 >= 0, 3 = v0
   #less(z, z') -{ 0 }-> 0 :|: z - 1 >= 0, z' - 1 >= 0, v0 >= 0, 3 = v0
   #less(z, z') -{ 0 }-> 0 :|: z - 1 >= 0, z' = 0, v0 >= 0, 2 = v0
   #less(z, z') -{ 0 }-> 0 :|: z' - 1 >= 0, z - 1 >= 0, v0 >= 0, 2 = v0
   #less(z, z') -{ 0 }-> 0 :|: z' >= 0, z >= 0, v0 >= 0, 0 = v0
   APPEND(z, z') -{ 1 + 4*z }-> 1 + s :|: s >= 0, s <= 0, z' >= 0, z >= 0
   APPEND#1(z, z') -{ 2 + 4*z1 }-> 1 + s' :|: s' >= 0, s' <= 1, z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z' >= 0
   FLATTEN(z) -{ 1 }-> 1 + FLATTEN#1(z) :|: z >= 0
   FLATTEN#1(z) -{ 2 + 4*z0 }-> 1 + s22 + APPEND(flatten#1(z1), flatten#1(z2)) + FLATTEN(z1) :|: s21 >= 0, s21 <= 0 + 0, s22 >= 0, s22 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 2 + 4*z0 }-> 1 + s24 + APPEND(flatten#1(z1), 0) + FLATTEN(z1) :|: s23 >= 0, s23 <= 0 + 0, s24 >= 0, s24 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 2 + 4*z0 }-> 1 + s26 + APPEND(0, flatten#1(z2)) + FLATTEN(z1) :|: s25 >= 0, s25 <= 0 + 0, s26 >= 0, s26 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*z0 }-> 1 + s28 + s3 + FLATTEN(z1) :|: s27 >= 0, s27 <= 0 + 0, s28 >= 0, s28 <= 1, s3 >= 0, s3 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 2 + 4*z0 }-> 1 + s30 + APPEND(flatten#1(z1), flatten#1(z2)) + FLATTEN(z2) :|: s29 >= 0, s29 <= 0 + 0, s30 >= 0, s30 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 2 + 4*z0 }-> 1 + s32 + APPEND(flatten#1(z1), 0) + FLATTEN(z2) :|: s31 >= 0, s31 <= 0 + 0, s32 >= 0, s32 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 2 + 4*z0 }-> 1 + s34 + APPEND(0, flatten#1(z2)) + FLATTEN(z2) :|: s33 >= 0, s33 <= 0 + 0, s34 >= 0, s34 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*z0 }-> 1 + s36 + s7 + FLATTEN(z2) :|: s35 >= 0, s35 <= 0 + 0, s36 >= 0, s36 <= 1, s7 >= 0, s7 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 2 }-> 1 + APPEND(z0, append(flatten#1(z1), flatten#1(z2))) + s'' + FLATTEN(z1) :|: s'' >= 0, s'' <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 2 }-> 1 + APPEND(z0, append(flatten#1(z1), flatten#1(z2))) + s4 + FLATTEN(z2) :|: s4 >= 0, s4 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), flatten#1(z2))) + APPEND(flatten#1(z1), flatten#1(z2)) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), flatten#1(z2))) + APPEND(flatten#1(z1), flatten#1(z2)) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), flatten#1(z2))) + APPEND(flatten#1(z1), 0) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), flatten#1(z2))) + APPEND(flatten#1(z1), 0) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), flatten#1(z2))) + APPEND(0, flatten#1(z2)) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), flatten#1(z2))) + APPEND(0, flatten#1(z2)) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 2 }-> 1 + APPEND(z0, append(flatten#1(z1), 0)) + s1 + FLATTEN(z1) :|: s1 >= 0, s1 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 2 }-> 1 + APPEND(z0, append(flatten#1(z1), 0)) + s5 + FLATTEN(z2) :|: s5 >= 0, s5 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), 0)) + APPEND(flatten#1(z1), flatten#1(z2)) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), 0)) + APPEND(flatten#1(z1), flatten#1(z2)) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), 0)) + APPEND(flatten#1(z1), 0) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), 0)) + APPEND(flatten#1(z1), 0) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), 0)) + APPEND(0, flatten#1(z2)) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), 0)) + APPEND(0, flatten#1(z2)) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 2 }-> 1 + APPEND(z0, append(0, flatten#1(z2))) + s2 + FLATTEN(z1) :|: s2 >= 0, s2 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 2 }-> 1 + APPEND(z0, append(0, flatten#1(z2))) + s6 + FLATTEN(z2) :|: s6 >= 0, s6 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(0, flatten#1(z2))) + APPEND(flatten#1(z1), flatten#1(z2)) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(0, flatten#1(z2))) + APPEND(flatten#1(z1), flatten#1(z2)) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(0, flatten#1(z2))) + APPEND(flatten#1(z1), 0) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(0, flatten#1(z2))) + APPEND(flatten#1(z1), 0) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(0, flatten#1(z2))) + APPEND(0, flatten#1(z2)) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(0, flatten#1(z2))) + APPEND(0, flatten#1(z2)) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTENSORT(z) -{ 0 }-> 0 :|: z >= 0
   FLATTENSORT(z) -{ 0 }-> 1 + INSERTIONSORT(flatten#1(z)) :|: z >= 0
   FLATTENSORT(z) -{ 0 }-> 1 + INSERTIONSORT(0) :|: z >= 0
   INSERT(z, z') -{ 1 }-> 1 + INSERT#1(z', z) :|: z' >= 0, z >= 0
   INSERT#1(z, z') -{ 1 }-> 1 + INSERT#2(s11, z', z0, z1) + #LESS(z0, z') :|: s10 >= 0, s10 <= 3, s11 >= 0, s11 <= 2, z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z' >= 0
   INSERT#1(z, z') -{ 1 }-> 1 + INSERT#2(0, z', z0, z1) + #LESS(z0, z') :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z' >= 0
   INSERT#2(z, z', z'', z3) -{ 1 }-> 1 + INSERT(z', z3) :|: z = 2, z'' >= 0, z' >= 0, z3 >= 0
   INSERTIONSORT(z) -{ 1 }-> 1 + INSERTIONSORT#1(z) :|: z >= 0
   INSERTIONSORT#1(z) -{ 1 }-> 1 + INSERT(z0, insertionsort#1(z1)) + INSERTIONSORT(z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   INSERTIONSORT#1(z) -{ 1 }-> 1 + INSERT(z0, 0) + INSERTIONSORT(z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   append(z, z') -{ 0 }-> s37 :|: s37 >= 0, s37 <= z + z', z' >= 0, z >= 0
   append(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   append#1(z, z') -{ 0 }-> z' :|: z' >= 0, z = 0
   append#1(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   append#1(z, z') -{ 0 }-> 1 + z0 + s40 :|: s40 >= 0, s40 <= z1 + z', z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z' >= 0
   flatten(z) -{ 0 }-> flatten#1(z) :|: z >= 0
   flatten(z) -{ 0 }-> 0 :|: z >= 0
   flatten#1(z) -{ 0 }-> s39 :|: s38 >= 0, s38 <= 0 + 0, s39 >= 0, s39 <= z0 + s38, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   flatten#1(z) -{ 0 }-> append(z0, append(flatten#1(z1), flatten#1(z2))) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   flatten#1(z) -{ 0 }-> append(z0, append(flatten#1(z1), 0)) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   flatten#1(z) -{ 0 }-> append(z0, append(0, flatten#1(z2))) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   flatten#1(z) -{ 0 }-> 0 :|: z = 0
   flatten#1(z) -{ 0 }-> 0 :|: z >= 0
   insert(z, z') -{ 0 }-> s42 :|: s42 >= 0, s42 <= z' + z + 1, z' >= 0, z >= 0
   insert(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   insert#1(z, z') -{ 0 }-> s43 :|: s43 >= 0, s43 <= z' + z0 + z1 + 2, z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z' >= 0
   insert#1(z, z') -{ 0 }-> s45 :|: s45 >= 0, s45 <= z' + z0 + z1 + 2, s16 >= 0, s16 <= 3, s17 >= 0, s17 <= 2, z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z' >= 0
   insert#1(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   insert#1(z, z') -{ 0 }-> 1 + z' + 0 :|: z' >= 0, z = 0
   insert#2(z, z', z'', z3) -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0, z3 >= 0
   insert#2(z, z', z'', z3) -{ 0 }-> 1 + z' + (1 + z'' + z3) :|: z'' >= 0, z = 1, z' >= 0, z3 >= 0
   insert#2(z, z', z'', z3) -{ 0 }-> 1 + z'' + s44 :|: s44 >= 0, s44 <= z' + z3 + 1, z = 2, z'' >= 0, z' >= 0, z3 >= 0
   insertionsort(z) -{ 0 }-> insertionsort#1(z) :|: z >= 0
   insertionsort(z) -{ 0 }-> 0 :|: z >= 0
   insertionsort#1(z) -{ 0 }-> s41 :|: s41 >= 0, s41 <= z0 + 0 + 1, z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   insertionsort#1(z) -{ 0 }-> insert(z0, insertionsort#1(z1)) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   insertionsort#1(z) -{ 0 }-> 0 :|: z = 0
   insertionsort#1(z) -{ 0 }-> 0 :|: z >= 0

Function symbols to be analyzed: {#LESS}, {flatten#1}, {insertionsort#1}, {INSERT#1,INSERT#2,INSERT}, {flatten}, {FLATTEN,FLATTEN#1}, {insertionsort}, {INSERTIONSORT,INSERTIONSORT#1}, {FLATTENSORT}
Previous analysis results are:
  APPEND#1: runtime: O(n^1) [4*z], size: O(1) [0]
  APPEND: runtime: O(n^1) [1 + 4*z], size: O(1) [1]
  #cklt: runtime: O(1) [0], size: O(1) [2]
  #compare: runtime: O(1) [0], size: O(1) [3]
  #COMPARE: runtime: O(1) [0], size: O(n^1) [z + z']
  append#1: runtime: O(1) [0], size: O(n^1) [z + z']
  append: runtime: O(1) [0], size: O(n^1) [z + z']
  #less: runtime: O(1) [0], size: O(1) [2]
  insert#2: runtime: O(1) [0], size: O(n^1) [2 + z' + z'' + z3]
  insert: runtime: O(1) [0], size: O(n^1) [1 + z + z']
  insert#1: runtime: O(1) [0], size: O(n^1) [1 + z + z']

----------------------------------------

(79) IntTrsBoundProof (UPPER BOUND(ID))

Computed SIZE bound using CoFloCo for: #LESS
after applying outer abstraction to obtain an ITS,
resulting in: O(n^1) with polynomial bound: 1 + z + z'

----------------------------------------

(80)
Obligation:
Complexity RNTS consisting of the following rules:

   #COMPARE(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   #COMPARE(z, z') -{ 0 }-> 1 + s19 :|: s19 >= 0, s19 <= z' - 1 + (z - 1), z' - 1 >= 0, z - 1 >= 0
   #COMPARE(z, z') -{ 0 }-> 1 + s20 :|: s20 >= 0, s20 <= z - 1 + (z' - 1), z' - 1 >= 0, z - 1 >= 0
   #LESS(z, z') -{ 1 }-> 1 + s18 :|: s18 >= 0, s18 <= z + z', z' >= 0, z >= 0
   #cklt(z) -{ 0 }-> 2 :|: z = 3
   #cklt(z) -{ 0 }-> 1 :|: z = 1
   #cklt(z) -{ 0 }-> 1 :|: z = 2
   #cklt(z) -{ 0 }-> 0 :|: z >= 0
   #compare(z, z') -{ 0 }-> s8 :|: s8 >= 0, s8 <= 3, z' - 1 >= 0, z - 1 >= 0
   #compare(z, z') -{ 0 }-> s9 :|: s9 >= 0, s9 <= 3, z' - 1 >= 0, z - 1 >= 0
   #compare(z, z') -{ 0 }-> 3 :|: z' - 1 >= 0, z = 0
   #compare(z, z') -{ 0 }-> 3 :|: z - 1 >= 0, z' = 0
   #compare(z, z') -{ 0 }-> 3 :|: z' - 1 >= 0, z - 1 >= 0
   #compare(z, z') -{ 0 }-> 2 :|: z' - 1 >= 0, z = 0
   #compare(z, z') -{ 0 }-> 2 :|: z - 1 >= 0, z' = 0
   #compare(z, z') -{ 0 }-> 2 :|: z' - 1 >= 0, z - 1 >= 0
   #compare(z, z') -{ 0 }-> 1 :|: z = 0, z' = 0
   #compare(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   #less(z, z') -{ 0 }-> s13 :|: s12 >= 0, s12 <= 3, s13 >= 0, s13 <= 2, z' - 1 >= 0, z - 1 >= 0
   #less(z, z') -{ 0 }-> s15 :|: s14 >= 0, s14 <= 3, s15 >= 0, s15 <= 2, z - 1 >= 0, z' - 1 >= 0
   #less(z, z') -{ 0 }-> 2 :|: z' - 1 >= 0, z = 0, 3 = 3
   #less(z, z') -{ 0 }-> 2 :|: z - 1 >= 0, z' = 0, 3 = 3
   #less(z, z') -{ 0 }-> 2 :|: z - 1 >= 0, z' - 1 >= 0, 3 = 3
   #less(z, z') -{ 0 }-> 1 :|: z = 0, z' = 0, 1 = 1
   #less(z, z') -{ 0 }-> 1 :|: z' - 1 >= 0, z = 0, 2 = 2
   #less(z, z') -{ 0 }-> 1 :|: z - 1 >= 0, z' = 0, 2 = 2
   #less(z, z') -{ 0 }-> 1 :|: z' - 1 >= 0, z - 1 >= 0, 2 = 2
   #less(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   #less(z, z') -{ 0 }-> 0 :|: z = 0, z' = 0, v0 >= 0, 1 = v0
   #less(z, z') -{ 0 }-> 0 :|: z' - 1 >= 0, z = 0, v0 >= 0, 2 = v0
   #less(z, z') -{ 0 }-> 0 :|: z' - 1 >= 0, z = 0, v0 >= 0, 3 = v0
   #less(z, z') -{ 0 }-> 0 :|: z - 1 >= 0, z' = 0, v0 >= 0, 3 = v0
   #less(z, z') -{ 0 }-> 0 :|: z - 1 >= 0, z' - 1 >= 0, v0 >= 0, 3 = v0
   #less(z, z') -{ 0 }-> 0 :|: z - 1 >= 0, z' = 0, v0 >= 0, 2 = v0
   #less(z, z') -{ 0 }-> 0 :|: z' - 1 >= 0, z - 1 >= 0, v0 >= 0, 2 = v0
   #less(z, z') -{ 0 }-> 0 :|: z' >= 0, z >= 0, v0 >= 0, 0 = v0
   APPEND(z, z') -{ 1 + 4*z }-> 1 + s :|: s >= 0, s <= 0, z' >= 0, z >= 0
   APPEND#1(z, z') -{ 2 + 4*z1 }-> 1 + s' :|: s' >= 0, s' <= 1, z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z' >= 0
   FLATTEN(z) -{ 1 }-> 1 + FLATTEN#1(z) :|: z >= 0
   FLATTEN#1(z) -{ 2 + 4*z0 }-> 1 + s22 + APPEND(flatten#1(z1), flatten#1(z2)) + FLATTEN(z1) :|: s21 >= 0, s21 <= 0 + 0, s22 >= 0, s22 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 2 + 4*z0 }-> 1 + s24 + APPEND(flatten#1(z1), 0) + FLATTEN(z1) :|: s23 >= 0, s23 <= 0 + 0, s24 >= 0, s24 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 2 + 4*z0 }-> 1 + s26 + APPEND(0, flatten#1(z2)) + FLATTEN(z1) :|: s25 >= 0, s25 <= 0 + 0, s26 >= 0, s26 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*z0 }-> 1 + s28 + s3 + FLATTEN(z1) :|: s27 >= 0, s27 <= 0 + 0, s28 >= 0, s28 <= 1, s3 >= 0, s3 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 2 + 4*z0 }-> 1 + s30 + APPEND(flatten#1(z1), flatten#1(z2)) + FLATTEN(z2) :|: s29 >= 0, s29 <= 0 + 0, s30 >= 0, s30 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 2 + 4*z0 }-> 1 + s32 + APPEND(flatten#1(z1), 0) + FLATTEN(z2) :|: s31 >= 0, s31 <= 0 + 0, s32 >= 0, s32 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 2 + 4*z0 }-> 1 + s34 + APPEND(0, flatten#1(z2)) + FLATTEN(z2) :|: s33 >= 0, s33 <= 0 + 0, s34 >= 0, s34 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*z0 }-> 1 + s36 + s7 + FLATTEN(z2) :|: s35 >= 0, s35 <= 0 + 0, s36 >= 0, s36 <= 1, s7 >= 0, s7 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 2 }-> 1 + APPEND(z0, append(flatten#1(z1), flatten#1(z2))) + s'' + FLATTEN(z1) :|: s'' >= 0, s'' <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 2 }-> 1 + APPEND(z0, append(flatten#1(z1), flatten#1(z2))) + s4 + FLATTEN(z2) :|: s4 >= 0, s4 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), flatten#1(z2))) + APPEND(flatten#1(z1), flatten#1(z2)) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), flatten#1(z2))) + APPEND(flatten#1(z1), flatten#1(z2)) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), flatten#1(z2))) + APPEND(flatten#1(z1), 0) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), flatten#1(z2))) + APPEND(flatten#1(z1), 0) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), flatten#1(z2))) + APPEND(0, flatten#1(z2)) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), flatten#1(z2))) + APPEND(0, flatten#1(z2)) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 2 }-> 1 + APPEND(z0, append(flatten#1(z1), 0)) + s1 + FLATTEN(z1) :|: s1 >= 0, s1 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 2 }-> 1 + APPEND(z0, append(flatten#1(z1), 0)) + s5 + FLATTEN(z2) :|: s5 >= 0, s5 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), 0)) + APPEND(flatten#1(z1), flatten#1(z2)) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), 0)) + APPEND(flatten#1(z1), flatten#1(z2)) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), 0)) + APPEND(flatten#1(z1), 0) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), 0)) + APPEND(flatten#1(z1), 0) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), 0)) + APPEND(0, flatten#1(z2)) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), 0)) + APPEND(0, flatten#1(z2)) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 2 }-> 1 + APPEND(z0, append(0, flatten#1(z2))) + s2 + FLATTEN(z1) :|: s2 >= 0, s2 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 2 }-> 1 + APPEND(z0, append(0, flatten#1(z2))) + s6 + FLATTEN(z2) :|: s6 >= 0, s6 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(0, flatten#1(z2))) + APPEND(flatten#1(z1), flatten#1(z2)) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(0, flatten#1(z2))) + APPEND(flatten#1(z1), flatten#1(z2)) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(0, flatten#1(z2))) + APPEND(flatten#1(z1), 0) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(0, flatten#1(z2))) + APPEND(flatten#1(z1), 0) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(0, flatten#1(z2))) + APPEND(0, flatten#1(z2)) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(0, flatten#1(z2))) + APPEND(0, flatten#1(z2)) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTENSORT(z) -{ 0 }-> 0 :|: z >= 0
   FLATTENSORT(z) -{ 0 }-> 1 + INSERTIONSORT(flatten#1(z)) :|: z >= 0
   FLATTENSORT(z) -{ 0 }-> 1 + INSERTIONSORT(0) :|: z >= 0
   INSERT(z, z') -{ 1 }-> 1 + INSERT#1(z', z) :|: z' >= 0, z >= 0
   INSERT#1(z, z') -{ 1 }-> 1 + INSERT#2(s11, z', z0, z1) + #LESS(z0, z') :|: s10 >= 0, s10 <= 3, s11 >= 0, s11 <= 2, z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z' >= 0
   INSERT#1(z, z') -{ 1 }-> 1 + INSERT#2(0, z', z0, z1) + #LESS(z0, z') :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z' >= 0
   INSERT#2(z, z', z'', z3) -{ 1 }-> 1 + INSERT(z', z3) :|: z = 2, z'' >= 0, z' >= 0, z3 >= 0
   INSERTIONSORT(z) -{ 1 }-> 1 + INSERTIONSORT#1(z) :|: z >= 0
   INSERTIONSORT#1(z) -{ 1 }-> 1 + INSERT(z0, insertionsort#1(z1)) + INSERTIONSORT(z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   INSERTIONSORT#1(z) -{ 1 }-> 1 + INSERT(z0, 0) + INSERTIONSORT(z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   append(z, z') -{ 0 }-> s37 :|: s37 >= 0, s37 <= z + z', z' >= 0, z >= 0
   append(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   append#1(z, z') -{ 0 }-> z' :|: z' >= 0, z = 0
   append#1(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   append#1(z, z') -{ 0 }-> 1 + z0 + s40 :|: s40 >= 0, s40 <= z1 + z', z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z' >= 0
   flatten(z) -{ 0 }-> flatten#1(z) :|: z >= 0
   flatten(z) -{ 0 }-> 0 :|: z >= 0
   flatten#1(z) -{ 0 }-> s39 :|: s38 >= 0, s38 <= 0 + 0, s39 >= 0, s39 <= z0 + s38, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   flatten#1(z) -{ 0 }-> append(z0, append(flatten#1(z1), flatten#1(z2))) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   flatten#1(z) -{ 0 }-> append(z0, append(flatten#1(z1), 0)) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   flatten#1(z) -{ 0 }-> append(z0, append(0, flatten#1(z2))) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   flatten#1(z) -{ 0 }-> 0 :|: z = 0
   flatten#1(z) -{ 0 }-> 0 :|: z >= 0
   insert(z, z') -{ 0 }-> s42 :|: s42 >= 0, s42 <= z' + z + 1, z' >= 0, z >= 0
   insert(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   insert#1(z, z') -{ 0 }-> s43 :|: s43 >= 0, s43 <= z' + z0 + z1 + 2, z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z' >= 0
   insert#1(z, z') -{ 0 }-> s45 :|: s45 >= 0, s45 <= z' + z0 + z1 + 2, s16 >= 0, s16 <= 3, s17 >= 0, s17 <= 2, z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z' >= 0
   insert#1(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   insert#1(z, z') -{ 0 }-> 1 + z' + 0 :|: z' >= 0, z = 0
   insert#2(z, z', z'', z3) -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0, z3 >= 0
   insert#2(z, z', z'', z3) -{ 0 }-> 1 + z' + (1 + z'' + z3) :|: z'' >= 0, z = 1, z' >= 0, z3 >= 0
   insert#2(z, z', z'', z3) -{ 0 }-> 1 + z'' + s44 :|: s44 >= 0, s44 <= z' + z3 + 1, z = 2, z'' >= 0, z' >= 0, z3 >= 0
   insertionsort(z) -{ 0 }-> insertionsort#1(z) :|: z >= 0
   insertionsort(z) -{ 0 }-> 0 :|: z >= 0
   insertionsort#1(z) -{ 0 }-> s41 :|: s41 >= 0, s41 <= z0 + 0 + 1, z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   insertionsort#1(z) -{ 0 }-> insert(z0, insertionsort#1(z1)) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   insertionsort#1(z) -{ 0 }-> 0 :|: z = 0
   insertionsort#1(z) -{ 0 }-> 0 :|: z >= 0

Function symbols to be analyzed: {#LESS}, {flatten#1}, {insertionsort#1}, {INSERT#1,INSERT#2,INSERT}, {flatten}, {FLATTEN,FLATTEN#1}, {insertionsort}, {INSERTIONSORT,INSERTIONSORT#1}, {FLATTENSORT}
Previous analysis results are:
  APPEND#1: runtime: O(n^1) [4*z], size: O(1) [0]
  APPEND: runtime: O(n^1) [1 + 4*z], size: O(1) [1]
  #cklt: runtime: O(1) [0], size: O(1) [2]
  #compare: runtime: O(1) [0], size: O(1) [3]
  #COMPARE: runtime: O(1) [0], size: O(n^1) [z + z']
  append#1: runtime: O(1) [0], size: O(n^1) [z + z']
  append: runtime: O(1) [0], size: O(n^1) [z + z']
  #less: runtime: O(1) [0], size: O(1) [2]
  insert#2: runtime: O(1) [0], size: O(n^1) [2 + z' + z'' + z3]
  insert: runtime: O(1) [0], size: O(n^1) [1 + z + z']
  insert#1: runtime: O(1) [0], size: O(n^1) [1 + z + z']
  #LESS: runtime: ?, size: O(n^1) [1 + z + z']

----------------------------------------

(81) IntTrsBoundProof (UPPER BOUND(ID))

Computed RUNTIME bound using CoFloCo for: #LESS
after applying outer abstraction to obtain an ITS,
resulting in: O(1) with polynomial bound: 1

----------------------------------------

(82)
Obligation:
Complexity RNTS consisting of the following rules:

   #COMPARE(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   #COMPARE(z, z') -{ 0 }-> 1 + s19 :|: s19 >= 0, s19 <= z' - 1 + (z - 1), z' - 1 >= 0, z - 1 >= 0
   #COMPARE(z, z') -{ 0 }-> 1 + s20 :|: s20 >= 0, s20 <= z - 1 + (z' - 1), z' - 1 >= 0, z - 1 >= 0
   #LESS(z, z') -{ 1 }-> 1 + s18 :|: s18 >= 0, s18 <= z + z', z' >= 0, z >= 0
   #cklt(z) -{ 0 }-> 2 :|: z = 3
   #cklt(z) -{ 0 }-> 1 :|: z = 1
   #cklt(z) -{ 0 }-> 1 :|: z = 2
   #cklt(z) -{ 0 }-> 0 :|: z >= 0
   #compare(z, z') -{ 0 }-> s8 :|: s8 >= 0, s8 <= 3, z' - 1 >= 0, z - 1 >= 0
   #compare(z, z') -{ 0 }-> s9 :|: s9 >= 0, s9 <= 3, z' - 1 >= 0, z - 1 >= 0
   #compare(z, z') -{ 0 }-> 3 :|: z' - 1 >= 0, z = 0
   #compare(z, z') -{ 0 }-> 3 :|: z - 1 >= 0, z' = 0
   #compare(z, z') -{ 0 }-> 3 :|: z' - 1 >= 0, z - 1 >= 0
   #compare(z, z') -{ 0 }-> 2 :|: z' - 1 >= 0, z = 0
   #compare(z, z') -{ 0 }-> 2 :|: z - 1 >= 0, z' = 0
   #compare(z, z') -{ 0 }-> 2 :|: z' - 1 >= 0, z - 1 >= 0
   #compare(z, z') -{ 0 }-> 1 :|: z = 0, z' = 0
   #compare(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   #less(z, z') -{ 0 }-> s13 :|: s12 >= 0, s12 <= 3, s13 >= 0, s13 <= 2, z' - 1 >= 0, z - 1 >= 0
   #less(z, z') -{ 0 }-> s15 :|: s14 >= 0, s14 <= 3, s15 >= 0, s15 <= 2, z - 1 >= 0, z' - 1 >= 0
   #less(z, z') -{ 0 }-> 2 :|: z' - 1 >= 0, z = 0, 3 = 3
   #less(z, z') -{ 0 }-> 2 :|: z - 1 >= 0, z' = 0, 3 = 3
   #less(z, z') -{ 0 }-> 2 :|: z - 1 >= 0, z' - 1 >= 0, 3 = 3
   #less(z, z') -{ 0 }-> 1 :|: z = 0, z' = 0, 1 = 1
   #less(z, z') -{ 0 }-> 1 :|: z' - 1 >= 0, z = 0, 2 = 2
   #less(z, z') -{ 0 }-> 1 :|: z - 1 >= 0, z' = 0, 2 = 2
   #less(z, z') -{ 0 }-> 1 :|: z' - 1 >= 0, z - 1 >= 0, 2 = 2
   #less(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   #less(z, z') -{ 0 }-> 0 :|: z = 0, z' = 0, v0 >= 0, 1 = v0
   #less(z, z') -{ 0 }-> 0 :|: z' - 1 >= 0, z = 0, v0 >= 0, 2 = v0
   #less(z, z') -{ 0 }-> 0 :|: z' - 1 >= 0, z = 0, v0 >= 0, 3 = v0
   #less(z, z') -{ 0 }-> 0 :|: z - 1 >= 0, z' = 0, v0 >= 0, 3 = v0
   #less(z, z') -{ 0 }-> 0 :|: z - 1 >= 0, z' - 1 >= 0, v0 >= 0, 3 = v0
   #less(z, z') -{ 0 }-> 0 :|: z - 1 >= 0, z' = 0, v0 >= 0, 2 = v0
   #less(z, z') -{ 0 }-> 0 :|: z' - 1 >= 0, z - 1 >= 0, v0 >= 0, 2 = v0
   #less(z, z') -{ 0 }-> 0 :|: z' >= 0, z >= 0, v0 >= 0, 0 = v0
   APPEND(z, z') -{ 1 + 4*z }-> 1 + s :|: s >= 0, s <= 0, z' >= 0, z >= 0
   APPEND#1(z, z') -{ 2 + 4*z1 }-> 1 + s' :|: s' >= 0, s' <= 1, z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z' >= 0
   FLATTEN(z) -{ 1 }-> 1 + FLATTEN#1(z) :|: z >= 0
   FLATTEN#1(z) -{ 2 + 4*z0 }-> 1 + s22 + APPEND(flatten#1(z1), flatten#1(z2)) + FLATTEN(z1) :|: s21 >= 0, s21 <= 0 + 0, s22 >= 0, s22 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 2 + 4*z0 }-> 1 + s24 + APPEND(flatten#1(z1), 0) + FLATTEN(z1) :|: s23 >= 0, s23 <= 0 + 0, s24 >= 0, s24 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 2 + 4*z0 }-> 1 + s26 + APPEND(0, flatten#1(z2)) + FLATTEN(z1) :|: s25 >= 0, s25 <= 0 + 0, s26 >= 0, s26 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*z0 }-> 1 + s28 + s3 + FLATTEN(z1) :|: s27 >= 0, s27 <= 0 + 0, s28 >= 0, s28 <= 1, s3 >= 0, s3 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 2 + 4*z0 }-> 1 + s30 + APPEND(flatten#1(z1), flatten#1(z2)) + FLATTEN(z2) :|: s29 >= 0, s29 <= 0 + 0, s30 >= 0, s30 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 2 + 4*z0 }-> 1 + s32 + APPEND(flatten#1(z1), 0) + FLATTEN(z2) :|: s31 >= 0, s31 <= 0 + 0, s32 >= 0, s32 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 2 + 4*z0 }-> 1 + s34 + APPEND(0, flatten#1(z2)) + FLATTEN(z2) :|: s33 >= 0, s33 <= 0 + 0, s34 >= 0, s34 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*z0 }-> 1 + s36 + s7 + FLATTEN(z2) :|: s35 >= 0, s35 <= 0 + 0, s36 >= 0, s36 <= 1, s7 >= 0, s7 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 2 }-> 1 + APPEND(z0, append(flatten#1(z1), flatten#1(z2))) + s'' + FLATTEN(z1) :|: s'' >= 0, s'' <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 2 }-> 1 + APPEND(z0, append(flatten#1(z1), flatten#1(z2))) + s4 + FLATTEN(z2) :|: s4 >= 0, s4 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), flatten#1(z2))) + APPEND(flatten#1(z1), flatten#1(z2)) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), flatten#1(z2))) + APPEND(flatten#1(z1), flatten#1(z2)) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), flatten#1(z2))) + APPEND(flatten#1(z1), 0) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), flatten#1(z2))) + APPEND(flatten#1(z1), 0) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), flatten#1(z2))) + APPEND(0, flatten#1(z2)) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), flatten#1(z2))) + APPEND(0, flatten#1(z2)) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 2 }-> 1 + APPEND(z0, append(flatten#1(z1), 0)) + s1 + FLATTEN(z1) :|: s1 >= 0, s1 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 2 }-> 1 + APPEND(z0, append(flatten#1(z1), 0)) + s5 + FLATTEN(z2) :|: s5 >= 0, s5 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), 0)) + APPEND(flatten#1(z1), flatten#1(z2)) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), 0)) + APPEND(flatten#1(z1), flatten#1(z2)) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), 0)) + APPEND(flatten#1(z1), 0) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), 0)) + APPEND(flatten#1(z1), 0) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), 0)) + APPEND(0, flatten#1(z2)) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), 0)) + APPEND(0, flatten#1(z2)) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 2 }-> 1 + APPEND(z0, append(0, flatten#1(z2))) + s2 + FLATTEN(z1) :|: s2 >= 0, s2 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 2 }-> 1 + APPEND(z0, append(0, flatten#1(z2))) + s6 + FLATTEN(z2) :|: s6 >= 0, s6 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(0, flatten#1(z2))) + APPEND(flatten#1(z1), flatten#1(z2)) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(0, flatten#1(z2))) + APPEND(flatten#1(z1), flatten#1(z2)) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(0, flatten#1(z2))) + APPEND(flatten#1(z1), 0) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(0, flatten#1(z2))) + APPEND(flatten#1(z1), 0) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(0, flatten#1(z2))) + APPEND(0, flatten#1(z2)) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(0, flatten#1(z2))) + APPEND(0, flatten#1(z2)) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTENSORT(z) -{ 0 }-> 0 :|: z >= 0
   FLATTENSORT(z) -{ 0 }-> 1 + INSERTIONSORT(flatten#1(z)) :|: z >= 0
   FLATTENSORT(z) -{ 0 }-> 1 + INSERTIONSORT(0) :|: z >= 0
   INSERT(z, z') -{ 1 }-> 1 + INSERT#1(z', z) :|: z' >= 0, z >= 0
   INSERT#1(z, z') -{ 1 }-> 1 + INSERT#2(s11, z', z0, z1) + #LESS(z0, z') :|: s10 >= 0, s10 <= 3, s11 >= 0, s11 <= 2, z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z' >= 0
   INSERT#1(z, z') -{ 1 }-> 1 + INSERT#2(0, z', z0, z1) + #LESS(z0, z') :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z' >= 0
   INSERT#2(z, z', z'', z3) -{ 1 }-> 1 + INSERT(z', z3) :|: z = 2, z'' >= 0, z' >= 0, z3 >= 0
   INSERTIONSORT(z) -{ 1 }-> 1 + INSERTIONSORT#1(z) :|: z >= 0
   INSERTIONSORT#1(z) -{ 1 }-> 1 + INSERT(z0, insertionsort#1(z1)) + INSERTIONSORT(z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   INSERTIONSORT#1(z) -{ 1 }-> 1 + INSERT(z0, 0) + INSERTIONSORT(z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   append(z, z') -{ 0 }-> s37 :|: s37 >= 0, s37 <= z + z', z' >= 0, z >= 0
   append(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   append#1(z, z') -{ 0 }-> z' :|: z' >= 0, z = 0
   append#1(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   append#1(z, z') -{ 0 }-> 1 + z0 + s40 :|: s40 >= 0, s40 <= z1 + z', z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z' >= 0
   flatten(z) -{ 0 }-> flatten#1(z) :|: z >= 0
   flatten(z) -{ 0 }-> 0 :|: z >= 0
   flatten#1(z) -{ 0 }-> s39 :|: s38 >= 0, s38 <= 0 + 0, s39 >= 0, s39 <= z0 + s38, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   flatten#1(z) -{ 0 }-> append(z0, append(flatten#1(z1), flatten#1(z2))) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   flatten#1(z) -{ 0 }-> append(z0, append(flatten#1(z1), 0)) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   flatten#1(z) -{ 0 }-> append(z0, append(0, flatten#1(z2))) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   flatten#1(z) -{ 0 }-> 0 :|: z = 0
   flatten#1(z) -{ 0 }-> 0 :|: z >= 0
   insert(z, z') -{ 0 }-> s42 :|: s42 >= 0, s42 <= z' + z + 1, z' >= 0, z >= 0
   insert(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   insert#1(z, z') -{ 0 }-> s43 :|: s43 >= 0, s43 <= z' + z0 + z1 + 2, z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z' >= 0
   insert#1(z, z') -{ 0 }-> s45 :|: s45 >= 0, s45 <= z' + z0 + z1 + 2, s16 >= 0, s16 <= 3, s17 >= 0, s17 <= 2, z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z' >= 0
   insert#1(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   insert#1(z, z') -{ 0 }-> 1 + z' + 0 :|: z' >= 0, z = 0
   insert#2(z, z', z'', z3) -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0, z3 >= 0
   insert#2(z, z', z'', z3) -{ 0 }-> 1 + z' + (1 + z'' + z3) :|: z'' >= 0, z = 1, z' >= 0, z3 >= 0
   insert#2(z, z', z'', z3) -{ 0 }-> 1 + z'' + s44 :|: s44 >= 0, s44 <= z' + z3 + 1, z = 2, z'' >= 0, z' >= 0, z3 >= 0
   insertionsort(z) -{ 0 }-> insertionsort#1(z) :|: z >= 0
   insertionsort(z) -{ 0 }-> 0 :|: z >= 0
   insertionsort#1(z) -{ 0 }-> s41 :|: s41 >= 0, s41 <= z0 + 0 + 1, z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   insertionsort#1(z) -{ 0 }-> insert(z0, insertionsort#1(z1)) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   insertionsort#1(z) -{ 0 }-> 0 :|: z = 0
   insertionsort#1(z) -{ 0 }-> 0 :|: z >= 0

Function symbols to be analyzed: {flatten#1}, {insertionsort#1}, {INSERT#1,INSERT#2,INSERT}, {flatten}, {FLATTEN,FLATTEN#1}, {insertionsort}, {INSERTIONSORT,INSERTIONSORT#1}, {FLATTENSORT}
Previous analysis results are:
  APPEND#1: runtime: O(n^1) [4*z], size: O(1) [0]
  APPEND: runtime: O(n^1) [1 + 4*z], size: O(1) [1]
  #cklt: runtime: O(1) [0], size: O(1) [2]
  #compare: runtime: O(1) [0], size: O(1) [3]
  #COMPARE: runtime: O(1) [0], size: O(n^1) [z + z']
  append#1: runtime: O(1) [0], size: O(n^1) [z + z']
  append: runtime: O(1) [0], size: O(n^1) [z + z']
  #less: runtime: O(1) [0], size: O(1) [2]
  insert#2: runtime: O(1) [0], size: O(n^1) [2 + z' + z'' + z3]
  insert: runtime: O(1) [0], size: O(n^1) [1 + z + z']
  insert#1: runtime: O(1) [0], size: O(n^1) [1 + z + z']
  #LESS: runtime: O(1) [1], size: O(n^1) [1 + z + z']

----------------------------------------

(83) ResultPropagationProof (UPPER BOUND(ID))
Applied inner abstraction using the recently inferred runtime/size bounds where possible.
----------------------------------------

(84)
Obligation:
Complexity RNTS consisting of the following rules:

   #COMPARE(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   #COMPARE(z, z') -{ 0 }-> 1 + s19 :|: s19 >= 0, s19 <= z' - 1 + (z - 1), z' - 1 >= 0, z - 1 >= 0
   #COMPARE(z, z') -{ 0 }-> 1 + s20 :|: s20 >= 0, s20 <= z - 1 + (z' - 1), z' - 1 >= 0, z - 1 >= 0
   #LESS(z, z') -{ 1 }-> 1 + s18 :|: s18 >= 0, s18 <= z + z', z' >= 0, z >= 0
   #cklt(z) -{ 0 }-> 2 :|: z = 3
   #cklt(z) -{ 0 }-> 1 :|: z = 1
   #cklt(z) -{ 0 }-> 1 :|: z = 2
   #cklt(z) -{ 0 }-> 0 :|: z >= 0
   #compare(z, z') -{ 0 }-> s8 :|: s8 >= 0, s8 <= 3, z' - 1 >= 0, z - 1 >= 0
   #compare(z, z') -{ 0 }-> s9 :|: s9 >= 0, s9 <= 3, z' - 1 >= 0, z - 1 >= 0
   #compare(z, z') -{ 0 }-> 3 :|: z' - 1 >= 0, z = 0
   #compare(z, z') -{ 0 }-> 3 :|: z - 1 >= 0, z' = 0
   #compare(z, z') -{ 0 }-> 3 :|: z' - 1 >= 0, z - 1 >= 0
   #compare(z, z') -{ 0 }-> 2 :|: z' - 1 >= 0, z = 0
   #compare(z, z') -{ 0 }-> 2 :|: z - 1 >= 0, z' = 0
   #compare(z, z') -{ 0 }-> 2 :|: z' - 1 >= 0, z - 1 >= 0
   #compare(z, z') -{ 0 }-> 1 :|: z = 0, z' = 0
   #compare(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   #less(z, z') -{ 0 }-> s13 :|: s12 >= 0, s12 <= 3, s13 >= 0, s13 <= 2, z' - 1 >= 0, z - 1 >= 0
   #less(z, z') -{ 0 }-> s15 :|: s14 >= 0, s14 <= 3, s15 >= 0, s15 <= 2, z - 1 >= 0, z' - 1 >= 0
   #less(z, z') -{ 0 }-> 2 :|: z' - 1 >= 0, z = 0, 3 = 3
   #less(z, z') -{ 0 }-> 2 :|: z - 1 >= 0, z' = 0, 3 = 3
   #less(z, z') -{ 0 }-> 2 :|: z - 1 >= 0, z' - 1 >= 0, 3 = 3
   #less(z, z') -{ 0 }-> 1 :|: z = 0, z' = 0, 1 = 1
   #less(z, z') -{ 0 }-> 1 :|: z' - 1 >= 0, z = 0, 2 = 2
   #less(z, z') -{ 0 }-> 1 :|: z - 1 >= 0, z' = 0, 2 = 2
   #less(z, z') -{ 0 }-> 1 :|: z' - 1 >= 0, z - 1 >= 0, 2 = 2
   #less(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   #less(z, z') -{ 0 }-> 0 :|: z = 0, z' = 0, v0 >= 0, 1 = v0
   #less(z, z') -{ 0 }-> 0 :|: z' - 1 >= 0, z = 0, v0 >= 0, 2 = v0
   #less(z, z') -{ 0 }-> 0 :|: z' - 1 >= 0, z = 0, v0 >= 0, 3 = v0
   #less(z, z') -{ 0 }-> 0 :|: z - 1 >= 0, z' = 0, v0 >= 0, 3 = v0
   #less(z, z') -{ 0 }-> 0 :|: z - 1 >= 0, z' - 1 >= 0, v0 >= 0, 3 = v0
   #less(z, z') -{ 0 }-> 0 :|: z - 1 >= 0, z' = 0, v0 >= 0, 2 = v0
   #less(z, z') -{ 0 }-> 0 :|: z' - 1 >= 0, z - 1 >= 0, v0 >= 0, 2 = v0
   #less(z, z') -{ 0 }-> 0 :|: z' >= 0, z >= 0, v0 >= 0, 0 = v0
   APPEND(z, z') -{ 1 + 4*z }-> 1 + s :|: s >= 0, s <= 0, z' >= 0, z >= 0
   APPEND#1(z, z') -{ 2 + 4*z1 }-> 1 + s' :|: s' >= 0, s' <= 1, z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z' >= 0
   FLATTEN(z) -{ 1 }-> 1 + FLATTEN#1(z) :|: z >= 0
   FLATTEN#1(z) -{ 2 + 4*z0 }-> 1 + s22 + APPEND(flatten#1(z1), flatten#1(z2)) + FLATTEN(z1) :|: s21 >= 0, s21 <= 0 + 0, s22 >= 0, s22 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 2 + 4*z0 }-> 1 + s24 + APPEND(flatten#1(z1), 0) + FLATTEN(z1) :|: s23 >= 0, s23 <= 0 + 0, s24 >= 0, s24 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 2 + 4*z0 }-> 1 + s26 + APPEND(0, flatten#1(z2)) + FLATTEN(z1) :|: s25 >= 0, s25 <= 0 + 0, s26 >= 0, s26 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*z0 }-> 1 + s28 + s3 + FLATTEN(z1) :|: s27 >= 0, s27 <= 0 + 0, s28 >= 0, s28 <= 1, s3 >= 0, s3 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 2 + 4*z0 }-> 1 + s30 + APPEND(flatten#1(z1), flatten#1(z2)) + FLATTEN(z2) :|: s29 >= 0, s29 <= 0 + 0, s30 >= 0, s30 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 2 + 4*z0 }-> 1 + s32 + APPEND(flatten#1(z1), 0) + FLATTEN(z2) :|: s31 >= 0, s31 <= 0 + 0, s32 >= 0, s32 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 2 + 4*z0 }-> 1 + s34 + APPEND(0, flatten#1(z2)) + FLATTEN(z2) :|: s33 >= 0, s33 <= 0 + 0, s34 >= 0, s34 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*z0 }-> 1 + s36 + s7 + FLATTEN(z2) :|: s35 >= 0, s35 <= 0 + 0, s36 >= 0, s36 <= 1, s7 >= 0, s7 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 2 }-> 1 + APPEND(z0, append(flatten#1(z1), flatten#1(z2))) + s'' + FLATTEN(z1) :|: s'' >= 0, s'' <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 2 }-> 1 + APPEND(z0, append(flatten#1(z1), flatten#1(z2))) + s4 + FLATTEN(z2) :|: s4 >= 0, s4 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), flatten#1(z2))) + APPEND(flatten#1(z1), flatten#1(z2)) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), flatten#1(z2))) + APPEND(flatten#1(z1), flatten#1(z2)) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), flatten#1(z2))) + APPEND(flatten#1(z1), 0) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), flatten#1(z2))) + APPEND(flatten#1(z1), 0) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), flatten#1(z2))) + APPEND(0, flatten#1(z2)) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), flatten#1(z2))) + APPEND(0, flatten#1(z2)) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 2 }-> 1 + APPEND(z0, append(flatten#1(z1), 0)) + s1 + FLATTEN(z1) :|: s1 >= 0, s1 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 2 }-> 1 + APPEND(z0, append(flatten#1(z1), 0)) + s5 + FLATTEN(z2) :|: s5 >= 0, s5 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), 0)) + APPEND(flatten#1(z1), flatten#1(z2)) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), 0)) + APPEND(flatten#1(z1), flatten#1(z2)) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), 0)) + APPEND(flatten#1(z1), 0) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), 0)) + APPEND(flatten#1(z1), 0) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), 0)) + APPEND(0, flatten#1(z2)) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), 0)) + APPEND(0, flatten#1(z2)) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 2 }-> 1 + APPEND(z0, append(0, flatten#1(z2))) + s2 + FLATTEN(z1) :|: s2 >= 0, s2 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 2 }-> 1 + APPEND(z0, append(0, flatten#1(z2))) + s6 + FLATTEN(z2) :|: s6 >= 0, s6 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(0, flatten#1(z2))) + APPEND(flatten#1(z1), flatten#1(z2)) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(0, flatten#1(z2))) + APPEND(flatten#1(z1), flatten#1(z2)) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(0, flatten#1(z2))) + APPEND(flatten#1(z1), 0) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(0, flatten#1(z2))) + APPEND(flatten#1(z1), 0) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(0, flatten#1(z2))) + APPEND(0, flatten#1(z2)) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(0, flatten#1(z2))) + APPEND(0, flatten#1(z2)) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTENSORT(z) -{ 0 }-> 0 :|: z >= 0
   FLATTENSORT(z) -{ 0 }-> 1 + INSERTIONSORT(flatten#1(z)) :|: z >= 0
   FLATTENSORT(z) -{ 0 }-> 1 + INSERTIONSORT(0) :|: z >= 0
   INSERT(z, z') -{ 1 }-> 1 + INSERT#1(z', z) :|: z' >= 0, z >= 0
   INSERT#1(z, z') -{ 2 }-> 1 + INSERT#2(s11, z', z0, z1) + s47 :|: s47 >= 0, s47 <= z0 + z' + 1, s10 >= 0, s10 <= 3, s11 >= 0, s11 <= 2, z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z' >= 0
   INSERT#1(z, z') -{ 2 }-> 1 + INSERT#2(0, z', z0, z1) + s46 :|: s46 >= 0, s46 <= z0 + z' + 1, z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z' >= 0
   INSERT#2(z, z', z'', z3) -{ 1 }-> 1 + INSERT(z', z3) :|: z = 2, z'' >= 0, z' >= 0, z3 >= 0
   INSERTIONSORT(z) -{ 1 }-> 1 + INSERTIONSORT#1(z) :|: z >= 0
   INSERTIONSORT#1(z) -{ 1 }-> 1 + INSERT(z0, insertionsort#1(z1)) + INSERTIONSORT(z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   INSERTIONSORT#1(z) -{ 1 }-> 1 + INSERT(z0, 0) + INSERTIONSORT(z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   append(z, z') -{ 0 }-> s37 :|: s37 >= 0, s37 <= z + z', z' >= 0, z >= 0
   append(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   append#1(z, z') -{ 0 }-> z' :|: z' >= 0, z = 0
   append#1(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   append#1(z, z') -{ 0 }-> 1 + z0 + s40 :|: s40 >= 0, s40 <= z1 + z', z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z' >= 0
   flatten(z) -{ 0 }-> flatten#1(z) :|: z >= 0
   flatten(z) -{ 0 }-> 0 :|: z >= 0
   flatten#1(z) -{ 0 }-> s39 :|: s38 >= 0, s38 <= 0 + 0, s39 >= 0, s39 <= z0 + s38, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   flatten#1(z) -{ 0 }-> append(z0, append(flatten#1(z1), flatten#1(z2))) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   flatten#1(z) -{ 0 }-> append(z0, append(flatten#1(z1), 0)) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   flatten#1(z) -{ 0 }-> append(z0, append(0, flatten#1(z2))) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   flatten#1(z) -{ 0 }-> 0 :|: z = 0
   flatten#1(z) -{ 0 }-> 0 :|: z >= 0
   insert(z, z') -{ 0 }-> s42 :|: s42 >= 0, s42 <= z' + z + 1, z' >= 0, z >= 0
   insert(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   insert#1(z, z') -{ 0 }-> s43 :|: s43 >= 0, s43 <= z' + z0 + z1 + 2, z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z' >= 0
   insert#1(z, z') -{ 0 }-> s45 :|: s45 >= 0, s45 <= z' + z0 + z1 + 2, s16 >= 0, s16 <= 3, s17 >= 0, s17 <= 2, z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z' >= 0
   insert#1(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   insert#1(z, z') -{ 0 }-> 1 + z' + 0 :|: z' >= 0, z = 0
   insert#2(z, z', z'', z3) -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0, z3 >= 0
   insert#2(z, z', z'', z3) -{ 0 }-> 1 + z' + (1 + z'' + z3) :|: z'' >= 0, z = 1, z' >= 0, z3 >= 0
   insert#2(z, z', z'', z3) -{ 0 }-> 1 + z'' + s44 :|: s44 >= 0, s44 <= z' + z3 + 1, z = 2, z'' >= 0, z' >= 0, z3 >= 0
   insertionsort(z) -{ 0 }-> insertionsort#1(z) :|: z >= 0
   insertionsort(z) -{ 0 }-> 0 :|: z >= 0
   insertionsort#1(z) -{ 0 }-> s41 :|: s41 >= 0, s41 <= z0 + 0 + 1, z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   insertionsort#1(z) -{ 0 }-> insert(z0, insertionsort#1(z1)) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   insertionsort#1(z) -{ 0 }-> 0 :|: z = 0
   insertionsort#1(z) -{ 0 }-> 0 :|: z >= 0

Function symbols to be analyzed: {flatten#1}, {insertionsort#1}, {INSERT#1,INSERT#2,INSERT}, {flatten}, {FLATTEN,FLATTEN#1}, {insertionsort}, {INSERTIONSORT,INSERTIONSORT#1}, {FLATTENSORT}
Previous analysis results are:
  APPEND#1: runtime: O(n^1) [4*z], size: O(1) [0]
  APPEND: runtime: O(n^1) [1 + 4*z], size: O(1) [1]
  #cklt: runtime: O(1) [0], size: O(1) [2]
  #compare: runtime: O(1) [0], size: O(1) [3]
  #COMPARE: runtime: O(1) [0], size: O(n^1) [z + z']
  append#1: runtime: O(1) [0], size: O(n^1) [z + z']
  append: runtime: O(1) [0], size: O(n^1) [z + z']
  #less: runtime: O(1) [0], size: O(1) [2]
  insert#2: runtime: O(1) [0], size: O(n^1) [2 + z' + z'' + z3]
  insert: runtime: O(1) [0], size: O(n^1) [1 + z + z']
  insert#1: runtime: O(1) [0], size: O(n^1) [1 + z + z']
  #LESS: runtime: O(1) [1], size: O(n^1) [1 + z + z']

----------------------------------------

(85) IntTrsBoundProof (UPPER BOUND(ID))

Computed SIZE bound using CoFloCo for: flatten#1
after applying outer abstraction to obtain an ITS,
resulting in: O(n^1) with polynomial bound: 1 + z

----------------------------------------

(86)
Obligation:
Complexity RNTS consisting of the following rules:

   #COMPARE(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   #COMPARE(z, z') -{ 0 }-> 1 + s19 :|: s19 >= 0, s19 <= z' - 1 + (z - 1), z' - 1 >= 0, z - 1 >= 0
   #COMPARE(z, z') -{ 0 }-> 1 + s20 :|: s20 >= 0, s20 <= z - 1 + (z' - 1), z' - 1 >= 0, z - 1 >= 0
   #LESS(z, z') -{ 1 }-> 1 + s18 :|: s18 >= 0, s18 <= z + z', z' >= 0, z >= 0
   #cklt(z) -{ 0 }-> 2 :|: z = 3
   #cklt(z) -{ 0 }-> 1 :|: z = 1
   #cklt(z) -{ 0 }-> 1 :|: z = 2
   #cklt(z) -{ 0 }-> 0 :|: z >= 0
   #compare(z, z') -{ 0 }-> s8 :|: s8 >= 0, s8 <= 3, z' - 1 >= 0, z - 1 >= 0
   #compare(z, z') -{ 0 }-> s9 :|: s9 >= 0, s9 <= 3, z' - 1 >= 0, z - 1 >= 0
   #compare(z, z') -{ 0 }-> 3 :|: z' - 1 >= 0, z = 0
   #compare(z, z') -{ 0 }-> 3 :|: z - 1 >= 0, z' = 0
   #compare(z, z') -{ 0 }-> 3 :|: z' - 1 >= 0, z - 1 >= 0
   #compare(z, z') -{ 0 }-> 2 :|: z' - 1 >= 0, z = 0
   #compare(z, z') -{ 0 }-> 2 :|: z - 1 >= 0, z' = 0
   #compare(z, z') -{ 0 }-> 2 :|: z' - 1 >= 0, z - 1 >= 0
   #compare(z, z') -{ 0 }-> 1 :|: z = 0, z' = 0
   #compare(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   #less(z, z') -{ 0 }-> s13 :|: s12 >= 0, s12 <= 3, s13 >= 0, s13 <= 2, z' - 1 >= 0, z - 1 >= 0
   #less(z, z') -{ 0 }-> s15 :|: s14 >= 0, s14 <= 3, s15 >= 0, s15 <= 2, z - 1 >= 0, z' - 1 >= 0
   #less(z, z') -{ 0 }-> 2 :|: z' - 1 >= 0, z = 0, 3 = 3
   #less(z, z') -{ 0 }-> 2 :|: z - 1 >= 0, z' = 0, 3 = 3
   #less(z, z') -{ 0 }-> 2 :|: z - 1 >= 0, z' - 1 >= 0, 3 = 3
   #less(z, z') -{ 0 }-> 1 :|: z = 0, z' = 0, 1 = 1
   #less(z, z') -{ 0 }-> 1 :|: z' - 1 >= 0, z = 0, 2 = 2
   #less(z, z') -{ 0 }-> 1 :|: z - 1 >= 0, z' = 0, 2 = 2
   #less(z, z') -{ 0 }-> 1 :|: z' - 1 >= 0, z - 1 >= 0, 2 = 2
   #less(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   #less(z, z') -{ 0 }-> 0 :|: z = 0, z' = 0, v0 >= 0, 1 = v0
   #less(z, z') -{ 0 }-> 0 :|: z' - 1 >= 0, z = 0, v0 >= 0, 2 = v0
   #less(z, z') -{ 0 }-> 0 :|: z' - 1 >= 0, z = 0, v0 >= 0, 3 = v0
   #less(z, z') -{ 0 }-> 0 :|: z - 1 >= 0, z' = 0, v0 >= 0, 3 = v0
   #less(z, z') -{ 0 }-> 0 :|: z - 1 >= 0, z' - 1 >= 0, v0 >= 0, 3 = v0
   #less(z, z') -{ 0 }-> 0 :|: z - 1 >= 0, z' = 0, v0 >= 0, 2 = v0
   #less(z, z') -{ 0 }-> 0 :|: z' - 1 >= 0, z - 1 >= 0, v0 >= 0, 2 = v0
   #less(z, z') -{ 0 }-> 0 :|: z' >= 0, z >= 0, v0 >= 0, 0 = v0
   APPEND(z, z') -{ 1 + 4*z }-> 1 + s :|: s >= 0, s <= 0, z' >= 0, z >= 0
   APPEND#1(z, z') -{ 2 + 4*z1 }-> 1 + s' :|: s' >= 0, s' <= 1, z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z' >= 0
   FLATTEN(z) -{ 1 }-> 1 + FLATTEN#1(z) :|: z >= 0
   FLATTEN#1(z) -{ 2 + 4*z0 }-> 1 + s22 + APPEND(flatten#1(z1), flatten#1(z2)) + FLATTEN(z1) :|: s21 >= 0, s21 <= 0 + 0, s22 >= 0, s22 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 2 + 4*z0 }-> 1 + s24 + APPEND(flatten#1(z1), 0) + FLATTEN(z1) :|: s23 >= 0, s23 <= 0 + 0, s24 >= 0, s24 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 2 + 4*z0 }-> 1 + s26 + APPEND(0, flatten#1(z2)) + FLATTEN(z1) :|: s25 >= 0, s25 <= 0 + 0, s26 >= 0, s26 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*z0 }-> 1 + s28 + s3 + FLATTEN(z1) :|: s27 >= 0, s27 <= 0 + 0, s28 >= 0, s28 <= 1, s3 >= 0, s3 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 2 + 4*z0 }-> 1 + s30 + APPEND(flatten#1(z1), flatten#1(z2)) + FLATTEN(z2) :|: s29 >= 0, s29 <= 0 + 0, s30 >= 0, s30 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 2 + 4*z0 }-> 1 + s32 + APPEND(flatten#1(z1), 0) + FLATTEN(z2) :|: s31 >= 0, s31 <= 0 + 0, s32 >= 0, s32 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 2 + 4*z0 }-> 1 + s34 + APPEND(0, flatten#1(z2)) + FLATTEN(z2) :|: s33 >= 0, s33 <= 0 + 0, s34 >= 0, s34 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*z0 }-> 1 + s36 + s7 + FLATTEN(z2) :|: s35 >= 0, s35 <= 0 + 0, s36 >= 0, s36 <= 1, s7 >= 0, s7 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 2 }-> 1 + APPEND(z0, append(flatten#1(z1), flatten#1(z2))) + s'' + FLATTEN(z1) :|: s'' >= 0, s'' <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 2 }-> 1 + APPEND(z0, append(flatten#1(z1), flatten#1(z2))) + s4 + FLATTEN(z2) :|: s4 >= 0, s4 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), flatten#1(z2))) + APPEND(flatten#1(z1), flatten#1(z2)) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), flatten#1(z2))) + APPEND(flatten#1(z1), flatten#1(z2)) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), flatten#1(z2))) + APPEND(flatten#1(z1), 0) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), flatten#1(z2))) + APPEND(flatten#1(z1), 0) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), flatten#1(z2))) + APPEND(0, flatten#1(z2)) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), flatten#1(z2))) + APPEND(0, flatten#1(z2)) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 2 }-> 1 + APPEND(z0, append(flatten#1(z1), 0)) + s1 + FLATTEN(z1) :|: s1 >= 0, s1 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 2 }-> 1 + APPEND(z0, append(flatten#1(z1), 0)) + s5 + FLATTEN(z2) :|: s5 >= 0, s5 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), 0)) + APPEND(flatten#1(z1), flatten#1(z2)) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), 0)) + APPEND(flatten#1(z1), flatten#1(z2)) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), 0)) + APPEND(flatten#1(z1), 0) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), 0)) + APPEND(flatten#1(z1), 0) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), 0)) + APPEND(0, flatten#1(z2)) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), 0)) + APPEND(0, flatten#1(z2)) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 2 }-> 1 + APPEND(z0, append(0, flatten#1(z2))) + s2 + FLATTEN(z1) :|: s2 >= 0, s2 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 2 }-> 1 + APPEND(z0, append(0, flatten#1(z2))) + s6 + FLATTEN(z2) :|: s6 >= 0, s6 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(0, flatten#1(z2))) + APPEND(flatten#1(z1), flatten#1(z2)) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(0, flatten#1(z2))) + APPEND(flatten#1(z1), flatten#1(z2)) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(0, flatten#1(z2))) + APPEND(flatten#1(z1), 0) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(0, flatten#1(z2))) + APPEND(flatten#1(z1), 0) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(0, flatten#1(z2))) + APPEND(0, flatten#1(z2)) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(0, flatten#1(z2))) + APPEND(0, flatten#1(z2)) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTENSORT(z) -{ 0 }-> 0 :|: z >= 0
   FLATTENSORT(z) -{ 0 }-> 1 + INSERTIONSORT(flatten#1(z)) :|: z >= 0
   FLATTENSORT(z) -{ 0 }-> 1 + INSERTIONSORT(0) :|: z >= 0
   INSERT(z, z') -{ 1 }-> 1 + INSERT#1(z', z) :|: z' >= 0, z >= 0
   INSERT#1(z, z') -{ 2 }-> 1 + INSERT#2(s11, z', z0, z1) + s47 :|: s47 >= 0, s47 <= z0 + z' + 1, s10 >= 0, s10 <= 3, s11 >= 0, s11 <= 2, z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z' >= 0
   INSERT#1(z, z') -{ 2 }-> 1 + INSERT#2(0, z', z0, z1) + s46 :|: s46 >= 0, s46 <= z0 + z' + 1, z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z' >= 0
   INSERT#2(z, z', z'', z3) -{ 1 }-> 1 + INSERT(z', z3) :|: z = 2, z'' >= 0, z' >= 0, z3 >= 0
   INSERTIONSORT(z) -{ 1 }-> 1 + INSERTIONSORT#1(z) :|: z >= 0
   INSERTIONSORT#1(z) -{ 1 }-> 1 + INSERT(z0, insertionsort#1(z1)) + INSERTIONSORT(z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   INSERTIONSORT#1(z) -{ 1 }-> 1 + INSERT(z0, 0) + INSERTIONSORT(z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   append(z, z') -{ 0 }-> s37 :|: s37 >= 0, s37 <= z + z', z' >= 0, z >= 0
   append(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   append#1(z, z') -{ 0 }-> z' :|: z' >= 0, z = 0
   append#1(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   append#1(z, z') -{ 0 }-> 1 + z0 + s40 :|: s40 >= 0, s40 <= z1 + z', z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z' >= 0
   flatten(z) -{ 0 }-> flatten#1(z) :|: z >= 0
   flatten(z) -{ 0 }-> 0 :|: z >= 0
   flatten#1(z) -{ 0 }-> s39 :|: s38 >= 0, s38 <= 0 + 0, s39 >= 0, s39 <= z0 + s38, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   flatten#1(z) -{ 0 }-> append(z0, append(flatten#1(z1), flatten#1(z2))) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   flatten#1(z) -{ 0 }-> append(z0, append(flatten#1(z1), 0)) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   flatten#1(z) -{ 0 }-> append(z0, append(0, flatten#1(z2))) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   flatten#1(z) -{ 0 }-> 0 :|: z = 0
   flatten#1(z) -{ 0 }-> 0 :|: z >= 0
   insert(z, z') -{ 0 }-> s42 :|: s42 >= 0, s42 <= z' + z + 1, z' >= 0, z >= 0
   insert(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   insert#1(z, z') -{ 0 }-> s43 :|: s43 >= 0, s43 <= z' + z0 + z1 + 2, z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z' >= 0
   insert#1(z, z') -{ 0 }-> s45 :|: s45 >= 0, s45 <= z' + z0 + z1 + 2, s16 >= 0, s16 <= 3, s17 >= 0, s17 <= 2, z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z' >= 0
   insert#1(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   insert#1(z, z') -{ 0 }-> 1 + z' + 0 :|: z' >= 0, z = 0
   insert#2(z, z', z'', z3) -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0, z3 >= 0
   insert#2(z, z', z'', z3) -{ 0 }-> 1 + z' + (1 + z'' + z3) :|: z'' >= 0, z = 1, z' >= 0, z3 >= 0
   insert#2(z, z', z'', z3) -{ 0 }-> 1 + z'' + s44 :|: s44 >= 0, s44 <= z' + z3 + 1, z = 2, z'' >= 0, z' >= 0, z3 >= 0
   insertionsort(z) -{ 0 }-> insertionsort#1(z) :|: z >= 0
   insertionsort(z) -{ 0 }-> 0 :|: z >= 0
   insertionsort#1(z) -{ 0 }-> s41 :|: s41 >= 0, s41 <= z0 + 0 + 1, z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   insertionsort#1(z) -{ 0 }-> insert(z0, insertionsort#1(z1)) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   insertionsort#1(z) -{ 0 }-> 0 :|: z = 0
   insertionsort#1(z) -{ 0 }-> 0 :|: z >= 0

Function symbols to be analyzed: {flatten#1}, {insertionsort#1}, {INSERT#1,INSERT#2,INSERT}, {flatten}, {FLATTEN,FLATTEN#1}, {insertionsort}, {INSERTIONSORT,INSERTIONSORT#1}, {FLATTENSORT}
Previous analysis results are:
  APPEND#1: runtime: O(n^1) [4*z], size: O(1) [0]
  APPEND: runtime: O(n^1) [1 + 4*z], size: O(1) [1]
  #cklt: runtime: O(1) [0], size: O(1) [2]
  #compare: runtime: O(1) [0], size: O(1) [3]
  #COMPARE: runtime: O(1) [0], size: O(n^1) [z + z']
  append#1: runtime: O(1) [0], size: O(n^1) [z + z']
  append: runtime: O(1) [0], size: O(n^1) [z + z']
  #less: runtime: O(1) [0], size: O(1) [2]
  insert#2: runtime: O(1) [0], size: O(n^1) [2 + z' + z'' + z3]
  insert: runtime: O(1) [0], size: O(n^1) [1 + z + z']
  insert#1: runtime: O(1) [0], size: O(n^1) [1 + z + z']
  #LESS: runtime: O(1) [1], size: O(n^1) [1 + z + z']
  flatten#1: runtime: ?, size: O(n^1) [1 + z]

----------------------------------------

(87) IntTrsBoundProof (UPPER BOUND(ID))

Computed RUNTIME bound using CoFloCo for: flatten#1
after applying outer abstraction to obtain an ITS,
resulting in: O(1) with polynomial bound: 0

----------------------------------------

(88)
Obligation:
Complexity RNTS consisting of the following rules:

   #COMPARE(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   #COMPARE(z, z') -{ 0 }-> 1 + s19 :|: s19 >= 0, s19 <= z' - 1 + (z - 1), z' - 1 >= 0, z - 1 >= 0
   #COMPARE(z, z') -{ 0 }-> 1 + s20 :|: s20 >= 0, s20 <= z - 1 + (z' - 1), z' - 1 >= 0, z - 1 >= 0
   #LESS(z, z') -{ 1 }-> 1 + s18 :|: s18 >= 0, s18 <= z + z', z' >= 0, z >= 0
   #cklt(z) -{ 0 }-> 2 :|: z = 3
   #cklt(z) -{ 0 }-> 1 :|: z = 1
   #cklt(z) -{ 0 }-> 1 :|: z = 2
   #cklt(z) -{ 0 }-> 0 :|: z >= 0
   #compare(z, z') -{ 0 }-> s8 :|: s8 >= 0, s8 <= 3, z' - 1 >= 0, z - 1 >= 0
   #compare(z, z') -{ 0 }-> s9 :|: s9 >= 0, s9 <= 3, z' - 1 >= 0, z - 1 >= 0
   #compare(z, z') -{ 0 }-> 3 :|: z' - 1 >= 0, z = 0
   #compare(z, z') -{ 0 }-> 3 :|: z - 1 >= 0, z' = 0
   #compare(z, z') -{ 0 }-> 3 :|: z' - 1 >= 0, z - 1 >= 0
   #compare(z, z') -{ 0 }-> 2 :|: z' - 1 >= 0, z = 0
   #compare(z, z') -{ 0 }-> 2 :|: z - 1 >= 0, z' = 0
   #compare(z, z') -{ 0 }-> 2 :|: z' - 1 >= 0, z - 1 >= 0
   #compare(z, z') -{ 0 }-> 1 :|: z = 0, z' = 0
   #compare(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   #less(z, z') -{ 0 }-> s13 :|: s12 >= 0, s12 <= 3, s13 >= 0, s13 <= 2, z' - 1 >= 0, z - 1 >= 0
   #less(z, z') -{ 0 }-> s15 :|: s14 >= 0, s14 <= 3, s15 >= 0, s15 <= 2, z - 1 >= 0, z' - 1 >= 0
   #less(z, z') -{ 0 }-> 2 :|: z' - 1 >= 0, z = 0, 3 = 3
   #less(z, z') -{ 0 }-> 2 :|: z - 1 >= 0, z' = 0, 3 = 3
   #less(z, z') -{ 0 }-> 2 :|: z - 1 >= 0, z' - 1 >= 0, 3 = 3
   #less(z, z') -{ 0 }-> 1 :|: z = 0, z' = 0, 1 = 1
   #less(z, z') -{ 0 }-> 1 :|: z' - 1 >= 0, z = 0, 2 = 2
   #less(z, z') -{ 0 }-> 1 :|: z - 1 >= 0, z' = 0, 2 = 2
   #less(z, z') -{ 0 }-> 1 :|: z' - 1 >= 0, z - 1 >= 0, 2 = 2
   #less(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   #less(z, z') -{ 0 }-> 0 :|: z = 0, z' = 0, v0 >= 0, 1 = v0
   #less(z, z') -{ 0 }-> 0 :|: z' - 1 >= 0, z = 0, v0 >= 0, 2 = v0
   #less(z, z') -{ 0 }-> 0 :|: z' - 1 >= 0, z = 0, v0 >= 0, 3 = v0
   #less(z, z') -{ 0 }-> 0 :|: z - 1 >= 0, z' = 0, v0 >= 0, 3 = v0
   #less(z, z') -{ 0 }-> 0 :|: z - 1 >= 0, z' - 1 >= 0, v0 >= 0, 3 = v0
   #less(z, z') -{ 0 }-> 0 :|: z - 1 >= 0, z' = 0, v0 >= 0, 2 = v0
   #less(z, z') -{ 0 }-> 0 :|: z' - 1 >= 0, z - 1 >= 0, v0 >= 0, 2 = v0
   #less(z, z') -{ 0 }-> 0 :|: z' >= 0, z >= 0, v0 >= 0, 0 = v0
   APPEND(z, z') -{ 1 + 4*z }-> 1 + s :|: s >= 0, s <= 0, z' >= 0, z >= 0
   APPEND#1(z, z') -{ 2 + 4*z1 }-> 1 + s' :|: s' >= 0, s' <= 1, z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z' >= 0
   FLATTEN(z) -{ 1 }-> 1 + FLATTEN#1(z) :|: z >= 0
   FLATTEN#1(z) -{ 2 + 4*z0 }-> 1 + s22 + APPEND(flatten#1(z1), flatten#1(z2)) + FLATTEN(z1) :|: s21 >= 0, s21 <= 0 + 0, s22 >= 0, s22 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 2 + 4*z0 }-> 1 + s24 + APPEND(flatten#1(z1), 0) + FLATTEN(z1) :|: s23 >= 0, s23 <= 0 + 0, s24 >= 0, s24 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 2 + 4*z0 }-> 1 + s26 + APPEND(0, flatten#1(z2)) + FLATTEN(z1) :|: s25 >= 0, s25 <= 0 + 0, s26 >= 0, s26 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*z0 }-> 1 + s28 + s3 + FLATTEN(z1) :|: s27 >= 0, s27 <= 0 + 0, s28 >= 0, s28 <= 1, s3 >= 0, s3 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 2 + 4*z0 }-> 1 + s30 + APPEND(flatten#1(z1), flatten#1(z2)) + FLATTEN(z2) :|: s29 >= 0, s29 <= 0 + 0, s30 >= 0, s30 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 2 + 4*z0 }-> 1 + s32 + APPEND(flatten#1(z1), 0) + FLATTEN(z2) :|: s31 >= 0, s31 <= 0 + 0, s32 >= 0, s32 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 2 + 4*z0 }-> 1 + s34 + APPEND(0, flatten#1(z2)) + FLATTEN(z2) :|: s33 >= 0, s33 <= 0 + 0, s34 >= 0, s34 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*z0 }-> 1 + s36 + s7 + FLATTEN(z2) :|: s35 >= 0, s35 <= 0 + 0, s36 >= 0, s36 <= 1, s7 >= 0, s7 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 2 }-> 1 + APPEND(z0, append(flatten#1(z1), flatten#1(z2))) + s'' + FLATTEN(z1) :|: s'' >= 0, s'' <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 2 }-> 1 + APPEND(z0, append(flatten#1(z1), flatten#1(z2))) + s4 + FLATTEN(z2) :|: s4 >= 0, s4 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), flatten#1(z2))) + APPEND(flatten#1(z1), flatten#1(z2)) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), flatten#1(z2))) + APPEND(flatten#1(z1), flatten#1(z2)) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), flatten#1(z2))) + APPEND(flatten#1(z1), 0) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), flatten#1(z2))) + APPEND(flatten#1(z1), 0) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), flatten#1(z2))) + APPEND(0, flatten#1(z2)) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), flatten#1(z2))) + APPEND(0, flatten#1(z2)) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 2 }-> 1 + APPEND(z0, append(flatten#1(z1), 0)) + s1 + FLATTEN(z1) :|: s1 >= 0, s1 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 2 }-> 1 + APPEND(z0, append(flatten#1(z1), 0)) + s5 + FLATTEN(z2) :|: s5 >= 0, s5 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), 0)) + APPEND(flatten#1(z1), flatten#1(z2)) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), 0)) + APPEND(flatten#1(z1), flatten#1(z2)) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), 0)) + APPEND(flatten#1(z1), 0) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), 0)) + APPEND(flatten#1(z1), 0) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), 0)) + APPEND(0, flatten#1(z2)) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(flatten#1(z1), 0)) + APPEND(0, flatten#1(z2)) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 2 }-> 1 + APPEND(z0, append(0, flatten#1(z2))) + s2 + FLATTEN(z1) :|: s2 >= 0, s2 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 2 }-> 1 + APPEND(z0, append(0, flatten#1(z2))) + s6 + FLATTEN(z2) :|: s6 >= 0, s6 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(0, flatten#1(z2))) + APPEND(flatten#1(z1), flatten#1(z2)) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(0, flatten#1(z2))) + APPEND(flatten#1(z1), flatten#1(z2)) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(0, flatten#1(z2))) + APPEND(flatten#1(z1), 0) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(0, flatten#1(z2))) + APPEND(flatten#1(z1), 0) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(0, flatten#1(z2))) + APPEND(0, flatten#1(z2)) + FLATTEN(z1) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 1 }-> 1 + APPEND(z0, append(0, flatten#1(z2))) + APPEND(0, flatten#1(z2)) + FLATTEN(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTENSORT(z) -{ 0 }-> 0 :|: z >= 0
   FLATTENSORT(z) -{ 0 }-> 1 + INSERTIONSORT(flatten#1(z)) :|: z >= 0
   FLATTENSORT(z) -{ 0 }-> 1 + INSERTIONSORT(0) :|: z >= 0
   INSERT(z, z') -{ 1 }-> 1 + INSERT#1(z', z) :|: z' >= 0, z >= 0
   INSERT#1(z, z') -{ 2 }-> 1 + INSERT#2(s11, z', z0, z1) + s47 :|: s47 >= 0, s47 <= z0 + z' + 1, s10 >= 0, s10 <= 3, s11 >= 0, s11 <= 2, z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z' >= 0
   INSERT#1(z, z') -{ 2 }-> 1 + INSERT#2(0, z', z0, z1) + s46 :|: s46 >= 0, s46 <= z0 + z' + 1, z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z' >= 0
   INSERT#2(z, z', z'', z3) -{ 1 }-> 1 + INSERT(z', z3) :|: z = 2, z'' >= 0, z' >= 0, z3 >= 0
   INSERTIONSORT(z) -{ 1 }-> 1 + INSERTIONSORT#1(z) :|: z >= 0
   INSERTIONSORT#1(z) -{ 1 }-> 1 + INSERT(z0, insertionsort#1(z1)) + INSERTIONSORT(z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   INSERTIONSORT#1(z) -{ 1 }-> 1 + INSERT(z0, 0) + INSERTIONSORT(z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   append(z, z') -{ 0 }-> s37 :|: s37 >= 0, s37 <= z + z', z' >= 0, z >= 0
   append(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   append#1(z, z') -{ 0 }-> z' :|: z' >= 0, z = 0
   append#1(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   append#1(z, z') -{ 0 }-> 1 + z0 + s40 :|: s40 >= 0, s40 <= z1 + z', z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z' >= 0
   flatten(z) -{ 0 }-> flatten#1(z) :|: z >= 0
   flatten(z) -{ 0 }-> 0 :|: z >= 0
   flatten#1(z) -{ 0 }-> s39 :|: s38 >= 0, s38 <= 0 + 0, s39 >= 0, s39 <= z0 + s38, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   flatten#1(z) -{ 0 }-> append(z0, append(flatten#1(z1), flatten#1(z2))) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   flatten#1(z) -{ 0 }-> append(z0, append(flatten#1(z1), 0)) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   flatten#1(z) -{ 0 }-> append(z0, append(0, flatten#1(z2))) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   flatten#1(z) -{ 0 }-> 0 :|: z = 0
   flatten#1(z) -{ 0 }-> 0 :|: z >= 0
   insert(z, z') -{ 0 }-> s42 :|: s42 >= 0, s42 <= z' + z + 1, z' >= 0, z >= 0
   insert(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   insert#1(z, z') -{ 0 }-> s43 :|: s43 >= 0, s43 <= z' + z0 + z1 + 2, z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z' >= 0
   insert#1(z, z') -{ 0 }-> s45 :|: s45 >= 0, s45 <= z' + z0 + z1 + 2, s16 >= 0, s16 <= 3, s17 >= 0, s17 <= 2, z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z' >= 0
   insert#1(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   insert#1(z, z') -{ 0 }-> 1 + z' + 0 :|: z' >= 0, z = 0
   insert#2(z, z', z'', z3) -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0, z3 >= 0
   insert#2(z, z', z'', z3) -{ 0 }-> 1 + z' + (1 + z'' + z3) :|: z'' >= 0, z = 1, z' >= 0, z3 >= 0
   insert#2(z, z', z'', z3) -{ 0 }-> 1 + z'' + s44 :|: s44 >= 0, s44 <= z' + z3 + 1, z = 2, z'' >= 0, z' >= 0, z3 >= 0
   insertionsort(z) -{ 0 }-> insertionsort#1(z) :|: z >= 0
   insertionsort(z) -{ 0 }-> 0 :|: z >= 0
   insertionsort#1(z) -{ 0 }-> s41 :|: s41 >= 0, s41 <= z0 + 0 + 1, z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   insertionsort#1(z) -{ 0 }-> insert(z0, insertionsort#1(z1)) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   insertionsort#1(z) -{ 0 }-> 0 :|: z = 0
   insertionsort#1(z) -{ 0 }-> 0 :|: z >= 0

Function symbols to be analyzed: {insertionsort#1}, {INSERT#1,INSERT#2,INSERT}, {flatten}, {FLATTEN,FLATTEN#1}, {insertionsort}, {INSERTIONSORT,INSERTIONSORT#1}, {FLATTENSORT}
Previous analysis results are:
  APPEND#1: runtime: O(n^1) [4*z], size: O(1) [0]
  APPEND: runtime: O(n^1) [1 + 4*z], size: O(1) [1]
  #cklt: runtime: O(1) [0], size: O(1) [2]
  #compare: runtime: O(1) [0], size: O(1) [3]
  #COMPARE: runtime: O(1) [0], size: O(n^1) [z + z']
  append#1: runtime: O(1) [0], size: O(n^1) [z + z']
  append: runtime: O(1) [0], size: O(n^1) [z + z']
  #less: runtime: O(1) [0], size: O(1) [2]
  insert#2: runtime: O(1) [0], size: O(n^1) [2 + z' + z'' + z3]
  insert: runtime: O(1) [0], size: O(n^1) [1 + z + z']
  insert#1: runtime: O(1) [0], size: O(n^1) [1 + z + z']
  #LESS: runtime: O(1) [1], size: O(n^1) [1 + z + z']
  flatten#1: runtime: O(1) [0], size: O(n^1) [1 + z]

----------------------------------------

(89) ResultPropagationProof (UPPER BOUND(ID))
Applied inner abstraction using the recently inferred runtime/size bounds where possible.
----------------------------------------

(90)
Obligation:
Complexity RNTS consisting of the following rules:

   #COMPARE(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   #COMPARE(z, z') -{ 0 }-> 1 + s19 :|: s19 >= 0, s19 <= z' - 1 + (z - 1), z' - 1 >= 0, z - 1 >= 0
   #COMPARE(z, z') -{ 0 }-> 1 + s20 :|: s20 >= 0, s20 <= z - 1 + (z' - 1), z' - 1 >= 0, z - 1 >= 0
   #LESS(z, z') -{ 1 }-> 1 + s18 :|: s18 >= 0, s18 <= z + z', z' >= 0, z >= 0
   #cklt(z) -{ 0 }-> 2 :|: z = 3
   #cklt(z) -{ 0 }-> 1 :|: z = 1
   #cklt(z) -{ 0 }-> 1 :|: z = 2
   #cklt(z) -{ 0 }-> 0 :|: z >= 0
   #compare(z, z') -{ 0 }-> s8 :|: s8 >= 0, s8 <= 3, z' - 1 >= 0, z - 1 >= 0
   #compare(z, z') -{ 0 }-> s9 :|: s9 >= 0, s9 <= 3, z' - 1 >= 0, z - 1 >= 0
   #compare(z, z') -{ 0 }-> 3 :|: z' - 1 >= 0, z = 0
   #compare(z, z') -{ 0 }-> 3 :|: z - 1 >= 0, z' = 0
   #compare(z, z') -{ 0 }-> 3 :|: z' - 1 >= 0, z - 1 >= 0
   #compare(z, z') -{ 0 }-> 2 :|: z' - 1 >= 0, z = 0
   #compare(z, z') -{ 0 }-> 2 :|: z - 1 >= 0, z' = 0
   #compare(z, z') -{ 0 }-> 2 :|: z' - 1 >= 0, z - 1 >= 0
   #compare(z, z') -{ 0 }-> 1 :|: z = 0, z' = 0
   #compare(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   #less(z, z') -{ 0 }-> s13 :|: s12 >= 0, s12 <= 3, s13 >= 0, s13 <= 2, z' - 1 >= 0, z - 1 >= 0
   #less(z, z') -{ 0 }-> s15 :|: s14 >= 0, s14 <= 3, s15 >= 0, s15 <= 2, z - 1 >= 0, z' - 1 >= 0
   #less(z, z') -{ 0 }-> 2 :|: z' - 1 >= 0, z = 0, 3 = 3
   #less(z, z') -{ 0 }-> 2 :|: z - 1 >= 0, z' = 0, 3 = 3
   #less(z, z') -{ 0 }-> 2 :|: z - 1 >= 0, z' - 1 >= 0, 3 = 3
   #less(z, z') -{ 0 }-> 1 :|: z = 0, z' = 0, 1 = 1
   #less(z, z') -{ 0 }-> 1 :|: z' - 1 >= 0, z = 0, 2 = 2
   #less(z, z') -{ 0 }-> 1 :|: z - 1 >= 0, z' = 0, 2 = 2
   #less(z, z') -{ 0 }-> 1 :|: z' - 1 >= 0, z - 1 >= 0, 2 = 2
   #less(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   #less(z, z') -{ 0 }-> 0 :|: z = 0, z' = 0, v0 >= 0, 1 = v0
   #less(z, z') -{ 0 }-> 0 :|: z' - 1 >= 0, z = 0, v0 >= 0, 2 = v0
   #less(z, z') -{ 0 }-> 0 :|: z' - 1 >= 0, z = 0, v0 >= 0, 3 = v0
   #less(z, z') -{ 0 }-> 0 :|: z - 1 >= 0, z' = 0, v0 >= 0, 3 = v0
   #less(z, z') -{ 0 }-> 0 :|: z - 1 >= 0, z' - 1 >= 0, v0 >= 0, 3 = v0
   #less(z, z') -{ 0 }-> 0 :|: z - 1 >= 0, z' = 0, v0 >= 0, 2 = v0
   #less(z, z') -{ 0 }-> 0 :|: z' - 1 >= 0, z - 1 >= 0, v0 >= 0, 2 = v0
   #less(z, z') -{ 0 }-> 0 :|: z' >= 0, z >= 0, v0 >= 0, 0 = v0
   APPEND(z, z') -{ 1 + 4*z }-> 1 + s :|: s >= 0, s <= 0, z' >= 0, z >= 0
   APPEND#1(z, z') -{ 2 + 4*z1 }-> 1 + s' :|: s' >= 0, s' <= 1, z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z' >= 0
   FLATTEN(z) -{ 1 }-> 1 + FLATTEN#1(z) :|: z >= 0
   FLATTEN#1(z) -{ 3 + 4*z0 }-> 1 + s103 + s105 + FLATTEN(z1) :|: s101 >= 0, s101 <= z2 + 1, s102 >= 0, s102 <= 0 + s101, s103 >= 0, s103 <= 1, s104 >= 0, s104 <= z2 + 1, s105 >= 0, s105 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*z0 }-> 1 + s108 + s2 + FLATTEN(z1) :|: s106 >= 0, s106 <= z2 + 1, s107 >= 0, s107 <= 0 + s106, s108 >= 0, s108 <= 1, s2 >= 0, s2 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*s120 + 4*z0 }-> 1 + s119 + s122 + FLATTEN(z2) :|: s116 >= 0, s116 <= z1 + 1, s117 >= 0, s117 <= z2 + 1, s118 >= 0, s118 <= s116 + s117, s119 >= 0, s119 <= 1, s120 >= 0, s120 <= z1 + 1, s121 >= 0, s121 <= z2 + 1, s122 >= 0, s122 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*s127 + 4*z0 }-> 1 + s126 + s128 + FLATTEN(z2) :|: s123 >= 0, s123 <= z1 + 1, s124 >= 0, s124 <= z2 + 1, s125 >= 0, s125 <= s123 + s124, s126 >= 0, s126 <= 1, s127 >= 0, s127 <= z1 + 1, s128 >= 0, s128 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*z0 }-> 1 + s132 + s134 + FLATTEN(z2) :|: s129 >= 0, s129 <= z1 + 1, s130 >= 0, s130 <= z2 + 1, s131 >= 0, s131 <= s129 + s130, s132 >= 0, s132 <= 1, s133 >= 0, s133 <= z2 + 1, s134 >= 0, s134 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*z0 }-> 1 + s138 + s4 + FLATTEN(z2) :|: s135 >= 0, s135 <= z1 + 1, s136 >= 0, s136 <= z2 + 1, s137 >= 0, s137 <= s135 + s136, s138 >= 0, s138 <= 1, s4 >= 0, s4 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*s142 + 4*z0 }-> 1 + s141 + s144 + FLATTEN(z2) :|: s139 >= 0, s139 <= z1 + 1, s140 >= 0, s140 <= s139 + 0, s141 >= 0, s141 <= 1, s142 >= 0, s142 <= z1 + 1, s143 >= 0, s143 <= z2 + 1, s144 >= 0, s144 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*s148 + 4*z0 }-> 1 + s147 + s149 + FLATTEN(z2) :|: s145 >= 0, s145 <= z1 + 1, s146 >= 0, s146 <= s145 + 0, s147 >= 0, s147 <= 1, s148 >= 0, s148 <= z1 + 1, s149 >= 0, s149 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*z0 }-> 1 + s152 + s154 + FLATTEN(z2) :|: s150 >= 0, s150 <= z1 + 1, s151 >= 0, s151 <= s150 + 0, s152 >= 0, s152 <= 1, s153 >= 0, s153 <= z2 + 1, s154 >= 0, s154 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*z0 }-> 1 + s157 + s5 + FLATTEN(z2) :|: s155 >= 0, s155 <= z1 + 1, s156 >= 0, s156 <= s155 + 0, s157 >= 0, s157 <= 1, s5 >= 0, s5 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*s161 + 4*z0 }-> 1 + s160 + s163 + FLATTEN(z2) :|: s158 >= 0, s158 <= z2 + 1, s159 >= 0, s159 <= 0 + s158, s160 >= 0, s160 <= 1, s161 >= 0, s161 <= z1 + 1, s162 >= 0, s162 <= z2 + 1, s163 >= 0, s163 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*s167 + 4*z0 }-> 1 + s166 + s168 + FLATTEN(z2) :|: s164 >= 0, s164 <= z2 + 1, s165 >= 0, s165 <= 0 + s164, s166 >= 0, s166 <= 1, s167 >= 0, s167 <= z1 + 1, s168 >= 0, s168 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*z0 }-> 1 + s171 + s173 + FLATTEN(z2) :|: s169 >= 0, s169 <= z2 + 1, s170 >= 0, s170 <= 0 + s169, s171 >= 0, s171 <= 1, s172 >= 0, s172 <= z2 + 1, s173 >= 0, s173 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*z0 }-> 1 + s176 + s6 + FLATTEN(z2) :|: s174 >= 0, s174 <= z2 + 1, s175 >= 0, s175 <= 0 + s174, s176 >= 0, s176 <= 1, s6 >= 0, s6 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*s109 + 4*z0 }-> 1 + s22 + s111 + FLATTEN(z1) :|: s109 >= 0, s109 <= z1 + 1, s110 >= 0, s110 <= z2 + 1, s111 >= 0, s111 <= 1, s21 >= 0, s21 <= 0 + 0, s22 >= 0, s22 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*s112 + 4*z0 }-> 1 + s24 + s113 + FLATTEN(z1) :|: s112 >= 0, s112 <= z1 + 1, s113 >= 0, s113 <= 1, s23 >= 0, s23 <= 0 + 0, s24 >= 0, s24 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*z0 }-> 1 + s26 + s115 + FLATTEN(z1) :|: s114 >= 0, s114 <= z2 + 1, s115 >= 0, s115 <= 1, s25 >= 0, s25 <= 0 + 0, s26 >= 0, s26 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*z0 }-> 1 + s28 + s3 + FLATTEN(z1) :|: s27 >= 0, s27 <= 0 + 0, s28 >= 0, s28 <= 1, s3 >= 0, s3 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*s177 + 4*z0 }-> 1 + s30 + s179 + FLATTEN(z2) :|: s177 >= 0, s177 <= z1 + 1, s178 >= 0, s178 <= z2 + 1, s179 >= 0, s179 <= 1, s29 >= 0, s29 <= 0 + 0, s30 >= 0, s30 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*s180 + 4*z0 }-> 1 + s32 + s181 + FLATTEN(z2) :|: s180 >= 0, s180 <= z1 + 1, s181 >= 0, s181 <= 1, s31 >= 0, s31 <= 0 + 0, s32 >= 0, s32 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*z0 }-> 1 + s34 + s183 + FLATTEN(z2) :|: s182 >= 0, s182 <= z2 + 1, s183 >= 0, s183 <= 1, s33 >= 0, s33 <= 0 + 0, s34 >= 0, s34 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*z0 }-> 1 + s36 + s7 + FLATTEN(z2) :|: s35 >= 0, s35 <= 0 + 0, s36 >= 0, s36 <= 1, s7 >= 0, s7 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*s52 + 4*z0 }-> 1 + s51 + s54 + FLATTEN(z1) :|: s48 >= 0, s48 <= z1 + 1, s49 >= 0, s49 <= z2 + 1, s50 >= 0, s50 <= s48 + s49, s51 >= 0, s51 <= 1, s52 >= 0, s52 <= z1 + 1, s53 >= 0, s53 <= z2 + 1, s54 >= 0, s54 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*s59 + 4*z0 }-> 1 + s58 + s60 + FLATTEN(z1) :|: s55 >= 0, s55 <= z1 + 1, s56 >= 0, s56 <= z2 + 1, s57 >= 0, s57 <= s55 + s56, s58 >= 0, s58 <= 1, s59 >= 0, s59 <= z1 + 1, s60 >= 0, s60 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*z0 }-> 1 + s64 + s66 + FLATTEN(z1) :|: s61 >= 0, s61 <= z1 + 1, s62 >= 0, s62 <= z2 + 1, s63 >= 0, s63 <= s61 + s62, s64 >= 0, s64 <= 1, s65 >= 0, s65 <= z2 + 1, s66 >= 0, s66 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*z0 }-> 1 + s70 + s'' + FLATTEN(z1) :|: s67 >= 0, s67 <= z1 + 1, s68 >= 0, s68 <= z2 + 1, s69 >= 0, s69 <= s67 + s68, s70 >= 0, s70 <= 1, s'' >= 0, s'' <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*s74 + 4*z0 }-> 1 + s73 + s76 + FLATTEN(z1) :|: s71 >= 0, s71 <= z1 + 1, s72 >= 0, s72 <= s71 + 0, s73 >= 0, s73 <= 1, s74 >= 0, s74 <= z1 + 1, s75 >= 0, s75 <= z2 + 1, s76 >= 0, s76 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*s80 + 4*z0 }-> 1 + s79 + s81 + FLATTEN(z1) :|: s77 >= 0, s77 <= z1 + 1, s78 >= 0, s78 <= s77 + 0, s79 >= 0, s79 <= 1, s80 >= 0, s80 <= z1 + 1, s81 >= 0, s81 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*z0 }-> 1 + s84 + s86 + FLATTEN(z1) :|: s82 >= 0, s82 <= z1 + 1, s83 >= 0, s83 <= s82 + 0, s84 >= 0, s84 <= 1, s85 >= 0, s85 <= z2 + 1, s86 >= 0, s86 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*z0 }-> 1 + s89 + s1 + FLATTEN(z1) :|: s87 >= 0, s87 <= z1 + 1, s88 >= 0, s88 <= s87 + 0, s89 >= 0, s89 <= 1, s1 >= 0, s1 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*s93 + 4*z0 }-> 1 + s92 + s95 + FLATTEN(z1) :|: s90 >= 0, s90 <= z2 + 1, s91 >= 0, s91 <= 0 + s90, s92 >= 0, s92 <= 1, s93 >= 0, s93 <= z1 + 1, s94 >= 0, s94 <= z2 + 1, s95 >= 0, s95 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*s99 + 4*z0 }-> 1 + s98 + s100 + FLATTEN(z1) :|: s96 >= 0, s96 <= z2 + 1, s97 >= 0, s97 <= 0 + s96, s98 >= 0, s98 <= 1, s99 >= 0, s99 <= z1 + 1, s100 >= 0, s100 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTENSORT(z) -{ 0 }-> 0 :|: z >= 0
   FLATTENSORT(z) -{ 0 }-> 1 + INSERTIONSORT(s184) :|: s184 >= 0, s184 <= z + 1, z >= 0
   FLATTENSORT(z) -{ 0 }-> 1 + INSERTIONSORT(0) :|: z >= 0
   INSERT(z, z') -{ 1 }-> 1 + INSERT#1(z', z) :|: z' >= 0, z >= 0
   INSERT#1(z, z') -{ 2 }-> 1 + INSERT#2(s11, z', z0, z1) + s47 :|: s47 >= 0, s47 <= z0 + z' + 1, s10 >= 0, s10 <= 3, s11 >= 0, s11 <= 2, z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z' >= 0
   INSERT#1(z, z') -{ 2 }-> 1 + INSERT#2(0, z', z0, z1) + s46 :|: s46 >= 0, s46 <= z0 + z' + 1, z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z' >= 0
   INSERT#2(z, z', z'', z3) -{ 1 }-> 1 + INSERT(z', z3) :|: z = 2, z'' >= 0, z' >= 0, z3 >= 0
   INSERTIONSORT(z) -{ 1 }-> 1 + INSERTIONSORT#1(z) :|: z >= 0
   INSERTIONSORT#1(z) -{ 1 }-> 1 + INSERT(z0, insertionsort#1(z1)) + INSERTIONSORT(z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   INSERTIONSORT#1(z) -{ 1 }-> 1 + INSERT(z0, 0) + INSERTIONSORT(z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   append(z, z') -{ 0 }-> s37 :|: s37 >= 0, s37 <= z + z', z' >= 0, z >= 0
   append(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   append#1(z, z') -{ 0 }-> z' :|: z' >= 0, z = 0
   append#1(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   append#1(z, z') -{ 0 }-> 1 + z0 + s40 :|: s40 >= 0, s40 <= z1 + z', z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z' >= 0
   flatten(z) -{ 0 }-> s185 :|: s185 >= 0, s185 <= z + 1, z >= 0
   flatten(z) -{ 0 }-> 0 :|: z >= 0
   flatten#1(z) -{ 0 }-> s189 :|: s186 >= 0, s186 <= z1 + 1, s187 >= 0, s187 <= z2 + 1, s188 >= 0, s188 <= s186 + s187, s189 >= 0, s189 <= z0 + s188, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   flatten#1(z) -{ 0 }-> s192 :|: s190 >= 0, s190 <= z1 + 1, s191 >= 0, s191 <= s190 + 0, s192 >= 0, s192 <= z0 + s191, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   flatten#1(z) -{ 0 }-> s195 :|: s193 >= 0, s193 <= z2 + 1, s194 >= 0, s194 <= 0 + s193, s195 >= 0, s195 <= z0 + s194, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   flatten#1(z) -{ 0 }-> s39 :|: s38 >= 0, s38 <= 0 + 0, s39 >= 0, s39 <= z0 + s38, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   flatten#1(z) -{ 0 }-> 0 :|: z = 0
   flatten#1(z) -{ 0 }-> 0 :|: z >= 0
   insert(z, z') -{ 0 }-> s42 :|: s42 >= 0, s42 <= z' + z + 1, z' >= 0, z >= 0
   insert(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   insert#1(z, z') -{ 0 }-> s43 :|: s43 >= 0, s43 <= z' + z0 + z1 + 2, z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z' >= 0
   insert#1(z, z') -{ 0 }-> s45 :|: s45 >= 0, s45 <= z' + z0 + z1 + 2, s16 >= 0, s16 <= 3, s17 >= 0, s17 <= 2, z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z' >= 0
   insert#1(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   insert#1(z, z') -{ 0 }-> 1 + z' + 0 :|: z' >= 0, z = 0
   insert#2(z, z', z'', z3) -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0, z3 >= 0
   insert#2(z, z', z'', z3) -{ 0 }-> 1 + z' + (1 + z'' + z3) :|: z'' >= 0, z = 1, z' >= 0, z3 >= 0
   insert#2(z, z', z'', z3) -{ 0 }-> 1 + z'' + s44 :|: s44 >= 0, s44 <= z' + z3 + 1, z = 2, z'' >= 0, z' >= 0, z3 >= 0
   insertionsort(z) -{ 0 }-> insertionsort#1(z) :|: z >= 0
   insertionsort(z) -{ 0 }-> 0 :|: z >= 0
   insertionsort#1(z) -{ 0 }-> s41 :|: s41 >= 0, s41 <= z0 + 0 + 1, z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   insertionsort#1(z) -{ 0 }-> insert(z0, insertionsort#1(z1)) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   insertionsort#1(z) -{ 0 }-> 0 :|: z = 0
   insertionsort#1(z) -{ 0 }-> 0 :|: z >= 0

Function symbols to be analyzed: {insertionsort#1}, {INSERT#1,INSERT#2,INSERT}, {flatten}, {FLATTEN,FLATTEN#1}, {insertionsort}, {INSERTIONSORT,INSERTIONSORT#1}, {FLATTENSORT}
Previous analysis results are:
  APPEND#1: runtime: O(n^1) [4*z], size: O(1) [0]
  APPEND: runtime: O(n^1) [1 + 4*z], size: O(1) [1]
  #cklt: runtime: O(1) [0], size: O(1) [2]
  #compare: runtime: O(1) [0], size: O(1) [3]
  #COMPARE: runtime: O(1) [0], size: O(n^1) [z + z']
  append#1: runtime: O(1) [0], size: O(n^1) [z + z']
  append: runtime: O(1) [0], size: O(n^1) [z + z']
  #less: runtime: O(1) [0], size: O(1) [2]
  insert#2: runtime: O(1) [0], size: O(n^1) [2 + z' + z'' + z3]
  insert: runtime: O(1) [0], size: O(n^1) [1 + z + z']
  insert#1: runtime: O(1) [0], size: O(n^1) [1 + z + z']
  #LESS: runtime: O(1) [1], size: O(n^1) [1 + z + z']
  flatten#1: runtime: O(1) [0], size: O(n^1) [1 + z]

----------------------------------------

(91) IntTrsBoundProof (UPPER BOUND(ID))

Computed SIZE bound using CoFloCo for: insertionsort#1
after applying outer abstraction to obtain an ITS,
resulting in: O(n^1) with polynomial bound: z

----------------------------------------

(92)
Obligation:
Complexity RNTS consisting of the following rules:

   #COMPARE(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   #COMPARE(z, z') -{ 0 }-> 1 + s19 :|: s19 >= 0, s19 <= z' - 1 + (z - 1), z' - 1 >= 0, z - 1 >= 0
   #COMPARE(z, z') -{ 0 }-> 1 + s20 :|: s20 >= 0, s20 <= z - 1 + (z' - 1), z' - 1 >= 0, z - 1 >= 0
   #LESS(z, z') -{ 1 }-> 1 + s18 :|: s18 >= 0, s18 <= z + z', z' >= 0, z >= 0
   #cklt(z) -{ 0 }-> 2 :|: z = 3
   #cklt(z) -{ 0 }-> 1 :|: z = 1
   #cklt(z) -{ 0 }-> 1 :|: z = 2
   #cklt(z) -{ 0 }-> 0 :|: z >= 0
   #compare(z, z') -{ 0 }-> s8 :|: s8 >= 0, s8 <= 3, z' - 1 >= 0, z - 1 >= 0
   #compare(z, z') -{ 0 }-> s9 :|: s9 >= 0, s9 <= 3, z' - 1 >= 0, z - 1 >= 0
   #compare(z, z') -{ 0 }-> 3 :|: z' - 1 >= 0, z = 0
   #compare(z, z') -{ 0 }-> 3 :|: z - 1 >= 0, z' = 0
   #compare(z, z') -{ 0 }-> 3 :|: z' - 1 >= 0, z - 1 >= 0
   #compare(z, z') -{ 0 }-> 2 :|: z' - 1 >= 0, z = 0
   #compare(z, z') -{ 0 }-> 2 :|: z - 1 >= 0, z' = 0
   #compare(z, z') -{ 0 }-> 2 :|: z' - 1 >= 0, z - 1 >= 0
   #compare(z, z') -{ 0 }-> 1 :|: z = 0, z' = 0
   #compare(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   #less(z, z') -{ 0 }-> s13 :|: s12 >= 0, s12 <= 3, s13 >= 0, s13 <= 2, z' - 1 >= 0, z - 1 >= 0
   #less(z, z') -{ 0 }-> s15 :|: s14 >= 0, s14 <= 3, s15 >= 0, s15 <= 2, z - 1 >= 0, z' - 1 >= 0
   #less(z, z') -{ 0 }-> 2 :|: z' - 1 >= 0, z = 0, 3 = 3
   #less(z, z') -{ 0 }-> 2 :|: z - 1 >= 0, z' = 0, 3 = 3
   #less(z, z') -{ 0 }-> 2 :|: z - 1 >= 0, z' - 1 >= 0, 3 = 3
   #less(z, z') -{ 0 }-> 1 :|: z = 0, z' = 0, 1 = 1
   #less(z, z') -{ 0 }-> 1 :|: z' - 1 >= 0, z = 0, 2 = 2
   #less(z, z') -{ 0 }-> 1 :|: z - 1 >= 0, z' = 0, 2 = 2
   #less(z, z') -{ 0 }-> 1 :|: z' - 1 >= 0, z - 1 >= 0, 2 = 2
   #less(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   #less(z, z') -{ 0 }-> 0 :|: z = 0, z' = 0, v0 >= 0, 1 = v0
   #less(z, z') -{ 0 }-> 0 :|: z' - 1 >= 0, z = 0, v0 >= 0, 2 = v0
   #less(z, z') -{ 0 }-> 0 :|: z' - 1 >= 0, z = 0, v0 >= 0, 3 = v0
   #less(z, z') -{ 0 }-> 0 :|: z - 1 >= 0, z' = 0, v0 >= 0, 3 = v0
   #less(z, z') -{ 0 }-> 0 :|: z - 1 >= 0, z' - 1 >= 0, v0 >= 0, 3 = v0
   #less(z, z') -{ 0 }-> 0 :|: z - 1 >= 0, z' = 0, v0 >= 0, 2 = v0
   #less(z, z') -{ 0 }-> 0 :|: z' - 1 >= 0, z - 1 >= 0, v0 >= 0, 2 = v0
   #less(z, z') -{ 0 }-> 0 :|: z' >= 0, z >= 0, v0 >= 0, 0 = v0
   APPEND(z, z') -{ 1 + 4*z }-> 1 + s :|: s >= 0, s <= 0, z' >= 0, z >= 0
   APPEND#1(z, z') -{ 2 + 4*z1 }-> 1 + s' :|: s' >= 0, s' <= 1, z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z' >= 0
   FLATTEN(z) -{ 1 }-> 1 + FLATTEN#1(z) :|: z >= 0
   FLATTEN#1(z) -{ 3 + 4*z0 }-> 1 + s103 + s105 + FLATTEN(z1) :|: s101 >= 0, s101 <= z2 + 1, s102 >= 0, s102 <= 0 + s101, s103 >= 0, s103 <= 1, s104 >= 0, s104 <= z2 + 1, s105 >= 0, s105 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*z0 }-> 1 + s108 + s2 + FLATTEN(z1) :|: s106 >= 0, s106 <= z2 + 1, s107 >= 0, s107 <= 0 + s106, s108 >= 0, s108 <= 1, s2 >= 0, s2 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*s120 + 4*z0 }-> 1 + s119 + s122 + FLATTEN(z2) :|: s116 >= 0, s116 <= z1 + 1, s117 >= 0, s117 <= z2 + 1, s118 >= 0, s118 <= s116 + s117, s119 >= 0, s119 <= 1, s120 >= 0, s120 <= z1 + 1, s121 >= 0, s121 <= z2 + 1, s122 >= 0, s122 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*s127 + 4*z0 }-> 1 + s126 + s128 + FLATTEN(z2) :|: s123 >= 0, s123 <= z1 + 1, s124 >= 0, s124 <= z2 + 1, s125 >= 0, s125 <= s123 + s124, s126 >= 0, s126 <= 1, s127 >= 0, s127 <= z1 + 1, s128 >= 0, s128 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*z0 }-> 1 + s132 + s134 + FLATTEN(z2) :|: s129 >= 0, s129 <= z1 + 1, s130 >= 0, s130 <= z2 + 1, s131 >= 0, s131 <= s129 + s130, s132 >= 0, s132 <= 1, s133 >= 0, s133 <= z2 + 1, s134 >= 0, s134 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*z0 }-> 1 + s138 + s4 + FLATTEN(z2) :|: s135 >= 0, s135 <= z1 + 1, s136 >= 0, s136 <= z2 + 1, s137 >= 0, s137 <= s135 + s136, s138 >= 0, s138 <= 1, s4 >= 0, s4 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*s142 + 4*z0 }-> 1 + s141 + s144 + FLATTEN(z2) :|: s139 >= 0, s139 <= z1 + 1, s140 >= 0, s140 <= s139 + 0, s141 >= 0, s141 <= 1, s142 >= 0, s142 <= z1 + 1, s143 >= 0, s143 <= z2 + 1, s144 >= 0, s144 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*s148 + 4*z0 }-> 1 + s147 + s149 + FLATTEN(z2) :|: s145 >= 0, s145 <= z1 + 1, s146 >= 0, s146 <= s145 + 0, s147 >= 0, s147 <= 1, s148 >= 0, s148 <= z1 + 1, s149 >= 0, s149 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*z0 }-> 1 + s152 + s154 + FLATTEN(z2) :|: s150 >= 0, s150 <= z1 + 1, s151 >= 0, s151 <= s150 + 0, s152 >= 0, s152 <= 1, s153 >= 0, s153 <= z2 + 1, s154 >= 0, s154 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*z0 }-> 1 + s157 + s5 + FLATTEN(z2) :|: s155 >= 0, s155 <= z1 + 1, s156 >= 0, s156 <= s155 + 0, s157 >= 0, s157 <= 1, s5 >= 0, s5 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*s161 + 4*z0 }-> 1 + s160 + s163 + FLATTEN(z2) :|: s158 >= 0, s158 <= z2 + 1, s159 >= 0, s159 <= 0 + s158, s160 >= 0, s160 <= 1, s161 >= 0, s161 <= z1 + 1, s162 >= 0, s162 <= z2 + 1, s163 >= 0, s163 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*s167 + 4*z0 }-> 1 + s166 + s168 + FLATTEN(z2) :|: s164 >= 0, s164 <= z2 + 1, s165 >= 0, s165 <= 0 + s164, s166 >= 0, s166 <= 1, s167 >= 0, s167 <= z1 + 1, s168 >= 0, s168 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*z0 }-> 1 + s171 + s173 + FLATTEN(z2) :|: s169 >= 0, s169 <= z2 + 1, s170 >= 0, s170 <= 0 + s169, s171 >= 0, s171 <= 1, s172 >= 0, s172 <= z2 + 1, s173 >= 0, s173 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*z0 }-> 1 + s176 + s6 + FLATTEN(z2) :|: s174 >= 0, s174 <= z2 + 1, s175 >= 0, s175 <= 0 + s174, s176 >= 0, s176 <= 1, s6 >= 0, s6 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*s109 + 4*z0 }-> 1 + s22 + s111 + FLATTEN(z1) :|: s109 >= 0, s109 <= z1 + 1, s110 >= 0, s110 <= z2 + 1, s111 >= 0, s111 <= 1, s21 >= 0, s21 <= 0 + 0, s22 >= 0, s22 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*s112 + 4*z0 }-> 1 + s24 + s113 + FLATTEN(z1) :|: s112 >= 0, s112 <= z1 + 1, s113 >= 0, s113 <= 1, s23 >= 0, s23 <= 0 + 0, s24 >= 0, s24 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*z0 }-> 1 + s26 + s115 + FLATTEN(z1) :|: s114 >= 0, s114 <= z2 + 1, s115 >= 0, s115 <= 1, s25 >= 0, s25 <= 0 + 0, s26 >= 0, s26 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*z0 }-> 1 + s28 + s3 + FLATTEN(z1) :|: s27 >= 0, s27 <= 0 + 0, s28 >= 0, s28 <= 1, s3 >= 0, s3 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*s177 + 4*z0 }-> 1 + s30 + s179 + FLATTEN(z2) :|: s177 >= 0, s177 <= z1 + 1, s178 >= 0, s178 <= z2 + 1, s179 >= 0, s179 <= 1, s29 >= 0, s29 <= 0 + 0, s30 >= 0, s30 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*s180 + 4*z0 }-> 1 + s32 + s181 + FLATTEN(z2) :|: s180 >= 0, s180 <= z1 + 1, s181 >= 0, s181 <= 1, s31 >= 0, s31 <= 0 + 0, s32 >= 0, s32 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*z0 }-> 1 + s34 + s183 + FLATTEN(z2) :|: s182 >= 0, s182 <= z2 + 1, s183 >= 0, s183 <= 1, s33 >= 0, s33 <= 0 + 0, s34 >= 0, s34 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*z0 }-> 1 + s36 + s7 + FLATTEN(z2) :|: s35 >= 0, s35 <= 0 + 0, s36 >= 0, s36 <= 1, s7 >= 0, s7 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*s52 + 4*z0 }-> 1 + s51 + s54 + FLATTEN(z1) :|: s48 >= 0, s48 <= z1 + 1, s49 >= 0, s49 <= z2 + 1, s50 >= 0, s50 <= s48 + s49, s51 >= 0, s51 <= 1, s52 >= 0, s52 <= z1 + 1, s53 >= 0, s53 <= z2 + 1, s54 >= 0, s54 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*s59 + 4*z0 }-> 1 + s58 + s60 + FLATTEN(z1) :|: s55 >= 0, s55 <= z1 + 1, s56 >= 0, s56 <= z2 + 1, s57 >= 0, s57 <= s55 + s56, s58 >= 0, s58 <= 1, s59 >= 0, s59 <= z1 + 1, s60 >= 0, s60 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*z0 }-> 1 + s64 + s66 + FLATTEN(z1) :|: s61 >= 0, s61 <= z1 + 1, s62 >= 0, s62 <= z2 + 1, s63 >= 0, s63 <= s61 + s62, s64 >= 0, s64 <= 1, s65 >= 0, s65 <= z2 + 1, s66 >= 0, s66 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*z0 }-> 1 + s70 + s'' + FLATTEN(z1) :|: s67 >= 0, s67 <= z1 + 1, s68 >= 0, s68 <= z2 + 1, s69 >= 0, s69 <= s67 + s68, s70 >= 0, s70 <= 1, s'' >= 0, s'' <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*s74 + 4*z0 }-> 1 + s73 + s76 + FLATTEN(z1) :|: s71 >= 0, s71 <= z1 + 1, s72 >= 0, s72 <= s71 + 0, s73 >= 0, s73 <= 1, s74 >= 0, s74 <= z1 + 1, s75 >= 0, s75 <= z2 + 1, s76 >= 0, s76 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*s80 + 4*z0 }-> 1 + s79 + s81 + FLATTEN(z1) :|: s77 >= 0, s77 <= z1 + 1, s78 >= 0, s78 <= s77 + 0, s79 >= 0, s79 <= 1, s80 >= 0, s80 <= z1 + 1, s81 >= 0, s81 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*z0 }-> 1 + s84 + s86 + FLATTEN(z1) :|: s82 >= 0, s82 <= z1 + 1, s83 >= 0, s83 <= s82 + 0, s84 >= 0, s84 <= 1, s85 >= 0, s85 <= z2 + 1, s86 >= 0, s86 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*z0 }-> 1 + s89 + s1 + FLATTEN(z1) :|: s87 >= 0, s87 <= z1 + 1, s88 >= 0, s88 <= s87 + 0, s89 >= 0, s89 <= 1, s1 >= 0, s1 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*s93 + 4*z0 }-> 1 + s92 + s95 + FLATTEN(z1) :|: s90 >= 0, s90 <= z2 + 1, s91 >= 0, s91 <= 0 + s90, s92 >= 0, s92 <= 1, s93 >= 0, s93 <= z1 + 1, s94 >= 0, s94 <= z2 + 1, s95 >= 0, s95 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*s99 + 4*z0 }-> 1 + s98 + s100 + FLATTEN(z1) :|: s96 >= 0, s96 <= z2 + 1, s97 >= 0, s97 <= 0 + s96, s98 >= 0, s98 <= 1, s99 >= 0, s99 <= z1 + 1, s100 >= 0, s100 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTENSORT(z) -{ 0 }-> 0 :|: z >= 0
   FLATTENSORT(z) -{ 0 }-> 1 + INSERTIONSORT(s184) :|: s184 >= 0, s184 <= z + 1, z >= 0
   FLATTENSORT(z) -{ 0 }-> 1 + INSERTIONSORT(0) :|: z >= 0
   INSERT(z, z') -{ 1 }-> 1 + INSERT#1(z', z) :|: z' >= 0, z >= 0
   INSERT#1(z, z') -{ 2 }-> 1 + INSERT#2(s11, z', z0, z1) + s47 :|: s47 >= 0, s47 <= z0 + z' + 1, s10 >= 0, s10 <= 3, s11 >= 0, s11 <= 2, z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z' >= 0
   INSERT#1(z, z') -{ 2 }-> 1 + INSERT#2(0, z', z0, z1) + s46 :|: s46 >= 0, s46 <= z0 + z' + 1, z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z' >= 0
   INSERT#2(z, z', z'', z3) -{ 1 }-> 1 + INSERT(z', z3) :|: z = 2, z'' >= 0, z' >= 0, z3 >= 0
   INSERTIONSORT(z) -{ 1 }-> 1 + INSERTIONSORT#1(z) :|: z >= 0
   INSERTIONSORT#1(z) -{ 1 }-> 1 + INSERT(z0, insertionsort#1(z1)) + INSERTIONSORT(z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   INSERTIONSORT#1(z) -{ 1 }-> 1 + INSERT(z0, 0) + INSERTIONSORT(z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   append(z, z') -{ 0 }-> s37 :|: s37 >= 0, s37 <= z + z', z' >= 0, z >= 0
   append(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   append#1(z, z') -{ 0 }-> z' :|: z' >= 0, z = 0
   append#1(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   append#1(z, z') -{ 0 }-> 1 + z0 + s40 :|: s40 >= 0, s40 <= z1 + z', z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z' >= 0
   flatten(z) -{ 0 }-> s185 :|: s185 >= 0, s185 <= z + 1, z >= 0
   flatten(z) -{ 0 }-> 0 :|: z >= 0
   flatten#1(z) -{ 0 }-> s189 :|: s186 >= 0, s186 <= z1 + 1, s187 >= 0, s187 <= z2 + 1, s188 >= 0, s188 <= s186 + s187, s189 >= 0, s189 <= z0 + s188, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   flatten#1(z) -{ 0 }-> s192 :|: s190 >= 0, s190 <= z1 + 1, s191 >= 0, s191 <= s190 + 0, s192 >= 0, s192 <= z0 + s191, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   flatten#1(z) -{ 0 }-> s195 :|: s193 >= 0, s193 <= z2 + 1, s194 >= 0, s194 <= 0 + s193, s195 >= 0, s195 <= z0 + s194, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   flatten#1(z) -{ 0 }-> s39 :|: s38 >= 0, s38 <= 0 + 0, s39 >= 0, s39 <= z0 + s38, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   flatten#1(z) -{ 0 }-> 0 :|: z = 0
   flatten#1(z) -{ 0 }-> 0 :|: z >= 0
   insert(z, z') -{ 0 }-> s42 :|: s42 >= 0, s42 <= z' + z + 1, z' >= 0, z >= 0
   insert(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   insert#1(z, z') -{ 0 }-> s43 :|: s43 >= 0, s43 <= z' + z0 + z1 + 2, z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z' >= 0
   insert#1(z, z') -{ 0 }-> s45 :|: s45 >= 0, s45 <= z' + z0 + z1 + 2, s16 >= 0, s16 <= 3, s17 >= 0, s17 <= 2, z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z' >= 0
   insert#1(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   insert#1(z, z') -{ 0 }-> 1 + z' + 0 :|: z' >= 0, z = 0
   insert#2(z, z', z'', z3) -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0, z3 >= 0
   insert#2(z, z', z'', z3) -{ 0 }-> 1 + z' + (1 + z'' + z3) :|: z'' >= 0, z = 1, z' >= 0, z3 >= 0
   insert#2(z, z', z'', z3) -{ 0 }-> 1 + z'' + s44 :|: s44 >= 0, s44 <= z' + z3 + 1, z = 2, z'' >= 0, z' >= 0, z3 >= 0
   insertionsort(z) -{ 0 }-> insertionsort#1(z) :|: z >= 0
   insertionsort(z) -{ 0 }-> 0 :|: z >= 0
   insertionsort#1(z) -{ 0 }-> s41 :|: s41 >= 0, s41 <= z0 + 0 + 1, z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   insertionsort#1(z) -{ 0 }-> insert(z0, insertionsort#1(z1)) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   insertionsort#1(z) -{ 0 }-> 0 :|: z = 0
   insertionsort#1(z) -{ 0 }-> 0 :|: z >= 0

Function symbols to be analyzed: {insertionsort#1}, {INSERT#1,INSERT#2,INSERT}, {flatten}, {FLATTEN,FLATTEN#1}, {insertionsort}, {INSERTIONSORT,INSERTIONSORT#1}, {FLATTENSORT}
Previous analysis results are:
  APPEND#1: runtime: O(n^1) [4*z], size: O(1) [0]
  APPEND: runtime: O(n^1) [1 + 4*z], size: O(1) [1]
  #cklt: runtime: O(1) [0], size: O(1) [2]
  #compare: runtime: O(1) [0], size: O(1) [3]
  #COMPARE: runtime: O(1) [0], size: O(n^1) [z + z']
  append#1: runtime: O(1) [0], size: O(n^1) [z + z']
  append: runtime: O(1) [0], size: O(n^1) [z + z']
  #less: runtime: O(1) [0], size: O(1) [2]
  insert#2: runtime: O(1) [0], size: O(n^1) [2 + z' + z'' + z3]
  insert: runtime: O(1) [0], size: O(n^1) [1 + z + z']
  insert#1: runtime: O(1) [0], size: O(n^1) [1 + z + z']
  #LESS: runtime: O(1) [1], size: O(n^1) [1 + z + z']
  flatten#1: runtime: O(1) [0], size: O(n^1) [1 + z]
  insertionsort#1: runtime: ?, size: O(n^1) [z]

----------------------------------------

(93) IntTrsBoundProof (UPPER BOUND(ID))

Computed RUNTIME bound using CoFloCo for: insertionsort#1
after applying outer abstraction to obtain an ITS,
resulting in: O(1) with polynomial bound: 0

----------------------------------------

(94)
Obligation:
Complexity RNTS consisting of the following rules:

   #COMPARE(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   #COMPARE(z, z') -{ 0 }-> 1 + s19 :|: s19 >= 0, s19 <= z' - 1 + (z - 1), z' - 1 >= 0, z - 1 >= 0
   #COMPARE(z, z') -{ 0 }-> 1 + s20 :|: s20 >= 0, s20 <= z - 1 + (z' - 1), z' - 1 >= 0, z - 1 >= 0
   #LESS(z, z') -{ 1 }-> 1 + s18 :|: s18 >= 0, s18 <= z + z', z' >= 0, z >= 0
   #cklt(z) -{ 0 }-> 2 :|: z = 3
   #cklt(z) -{ 0 }-> 1 :|: z = 1
   #cklt(z) -{ 0 }-> 1 :|: z = 2
   #cklt(z) -{ 0 }-> 0 :|: z >= 0
   #compare(z, z') -{ 0 }-> s8 :|: s8 >= 0, s8 <= 3, z' - 1 >= 0, z - 1 >= 0
   #compare(z, z') -{ 0 }-> s9 :|: s9 >= 0, s9 <= 3, z' - 1 >= 0, z - 1 >= 0
   #compare(z, z') -{ 0 }-> 3 :|: z' - 1 >= 0, z = 0
   #compare(z, z') -{ 0 }-> 3 :|: z - 1 >= 0, z' = 0
   #compare(z, z') -{ 0 }-> 3 :|: z' - 1 >= 0, z - 1 >= 0
   #compare(z, z') -{ 0 }-> 2 :|: z' - 1 >= 0, z = 0
   #compare(z, z') -{ 0 }-> 2 :|: z - 1 >= 0, z' = 0
   #compare(z, z') -{ 0 }-> 2 :|: z' - 1 >= 0, z - 1 >= 0
   #compare(z, z') -{ 0 }-> 1 :|: z = 0, z' = 0
   #compare(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   #less(z, z') -{ 0 }-> s13 :|: s12 >= 0, s12 <= 3, s13 >= 0, s13 <= 2, z' - 1 >= 0, z - 1 >= 0
   #less(z, z') -{ 0 }-> s15 :|: s14 >= 0, s14 <= 3, s15 >= 0, s15 <= 2, z - 1 >= 0, z' - 1 >= 0
   #less(z, z') -{ 0 }-> 2 :|: z' - 1 >= 0, z = 0, 3 = 3
   #less(z, z') -{ 0 }-> 2 :|: z - 1 >= 0, z' = 0, 3 = 3
   #less(z, z') -{ 0 }-> 2 :|: z - 1 >= 0, z' - 1 >= 0, 3 = 3
   #less(z, z') -{ 0 }-> 1 :|: z = 0, z' = 0, 1 = 1
   #less(z, z') -{ 0 }-> 1 :|: z' - 1 >= 0, z = 0, 2 = 2
   #less(z, z') -{ 0 }-> 1 :|: z - 1 >= 0, z' = 0, 2 = 2
   #less(z, z') -{ 0 }-> 1 :|: z' - 1 >= 0, z - 1 >= 0, 2 = 2
   #less(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   #less(z, z') -{ 0 }-> 0 :|: z = 0, z' = 0, v0 >= 0, 1 = v0
   #less(z, z') -{ 0 }-> 0 :|: z' - 1 >= 0, z = 0, v0 >= 0, 2 = v0
   #less(z, z') -{ 0 }-> 0 :|: z' - 1 >= 0, z = 0, v0 >= 0, 3 = v0
   #less(z, z') -{ 0 }-> 0 :|: z - 1 >= 0, z' = 0, v0 >= 0, 3 = v0
   #less(z, z') -{ 0 }-> 0 :|: z - 1 >= 0, z' - 1 >= 0, v0 >= 0, 3 = v0
   #less(z, z') -{ 0 }-> 0 :|: z - 1 >= 0, z' = 0, v0 >= 0, 2 = v0
   #less(z, z') -{ 0 }-> 0 :|: z' - 1 >= 0, z - 1 >= 0, v0 >= 0, 2 = v0
   #less(z, z') -{ 0 }-> 0 :|: z' >= 0, z >= 0, v0 >= 0, 0 = v0
   APPEND(z, z') -{ 1 + 4*z }-> 1 + s :|: s >= 0, s <= 0, z' >= 0, z >= 0
   APPEND#1(z, z') -{ 2 + 4*z1 }-> 1 + s' :|: s' >= 0, s' <= 1, z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z' >= 0
   FLATTEN(z) -{ 1 }-> 1 + FLATTEN#1(z) :|: z >= 0
   FLATTEN#1(z) -{ 3 + 4*z0 }-> 1 + s103 + s105 + FLATTEN(z1) :|: s101 >= 0, s101 <= z2 + 1, s102 >= 0, s102 <= 0 + s101, s103 >= 0, s103 <= 1, s104 >= 0, s104 <= z2 + 1, s105 >= 0, s105 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*z0 }-> 1 + s108 + s2 + FLATTEN(z1) :|: s106 >= 0, s106 <= z2 + 1, s107 >= 0, s107 <= 0 + s106, s108 >= 0, s108 <= 1, s2 >= 0, s2 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*s120 + 4*z0 }-> 1 + s119 + s122 + FLATTEN(z2) :|: s116 >= 0, s116 <= z1 + 1, s117 >= 0, s117 <= z2 + 1, s118 >= 0, s118 <= s116 + s117, s119 >= 0, s119 <= 1, s120 >= 0, s120 <= z1 + 1, s121 >= 0, s121 <= z2 + 1, s122 >= 0, s122 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*s127 + 4*z0 }-> 1 + s126 + s128 + FLATTEN(z2) :|: s123 >= 0, s123 <= z1 + 1, s124 >= 0, s124 <= z2 + 1, s125 >= 0, s125 <= s123 + s124, s126 >= 0, s126 <= 1, s127 >= 0, s127 <= z1 + 1, s128 >= 0, s128 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*z0 }-> 1 + s132 + s134 + FLATTEN(z2) :|: s129 >= 0, s129 <= z1 + 1, s130 >= 0, s130 <= z2 + 1, s131 >= 0, s131 <= s129 + s130, s132 >= 0, s132 <= 1, s133 >= 0, s133 <= z2 + 1, s134 >= 0, s134 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*z0 }-> 1 + s138 + s4 + FLATTEN(z2) :|: s135 >= 0, s135 <= z1 + 1, s136 >= 0, s136 <= z2 + 1, s137 >= 0, s137 <= s135 + s136, s138 >= 0, s138 <= 1, s4 >= 0, s4 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*s142 + 4*z0 }-> 1 + s141 + s144 + FLATTEN(z2) :|: s139 >= 0, s139 <= z1 + 1, s140 >= 0, s140 <= s139 + 0, s141 >= 0, s141 <= 1, s142 >= 0, s142 <= z1 + 1, s143 >= 0, s143 <= z2 + 1, s144 >= 0, s144 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*s148 + 4*z0 }-> 1 + s147 + s149 + FLATTEN(z2) :|: s145 >= 0, s145 <= z1 + 1, s146 >= 0, s146 <= s145 + 0, s147 >= 0, s147 <= 1, s148 >= 0, s148 <= z1 + 1, s149 >= 0, s149 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*z0 }-> 1 + s152 + s154 + FLATTEN(z2) :|: s150 >= 0, s150 <= z1 + 1, s151 >= 0, s151 <= s150 + 0, s152 >= 0, s152 <= 1, s153 >= 0, s153 <= z2 + 1, s154 >= 0, s154 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*z0 }-> 1 + s157 + s5 + FLATTEN(z2) :|: s155 >= 0, s155 <= z1 + 1, s156 >= 0, s156 <= s155 + 0, s157 >= 0, s157 <= 1, s5 >= 0, s5 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*s161 + 4*z0 }-> 1 + s160 + s163 + FLATTEN(z2) :|: s158 >= 0, s158 <= z2 + 1, s159 >= 0, s159 <= 0 + s158, s160 >= 0, s160 <= 1, s161 >= 0, s161 <= z1 + 1, s162 >= 0, s162 <= z2 + 1, s163 >= 0, s163 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*s167 + 4*z0 }-> 1 + s166 + s168 + FLATTEN(z2) :|: s164 >= 0, s164 <= z2 + 1, s165 >= 0, s165 <= 0 + s164, s166 >= 0, s166 <= 1, s167 >= 0, s167 <= z1 + 1, s168 >= 0, s168 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*z0 }-> 1 + s171 + s173 + FLATTEN(z2) :|: s169 >= 0, s169 <= z2 + 1, s170 >= 0, s170 <= 0 + s169, s171 >= 0, s171 <= 1, s172 >= 0, s172 <= z2 + 1, s173 >= 0, s173 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*z0 }-> 1 + s176 + s6 + FLATTEN(z2) :|: s174 >= 0, s174 <= z2 + 1, s175 >= 0, s175 <= 0 + s174, s176 >= 0, s176 <= 1, s6 >= 0, s6 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*s109 + 4*z0 }-> 1 + s22 + s111 + FLATTEN(z1) :|: s109 >= 0, s109 <= z1 + 1, s110 >= 0, s110 <= z2 + 1, s111 >= 0, s111 <= 1, s21 >= 0, s21 <= 0 + 0, s22 >= 0, s22 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*s112 + 4*z0 }-> 1 + s24 + s113 + FLATTEN(z1) :|: s112 >= 0, s112 <= z1 + 1, s113 >= 0, s113 <= 1, s23 >= 0, s23 <= 0 + 0, s24 >= 0, s24 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*z0 }-> 1 + s26 + s115 + FLATTEN(z1) :|: s114 >= 0, s114 <= z2 + 1, s115 >= 0, s115 <= 1, s25 >= 0, s25 <= 0 + 0, s26 >= 0, s26 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*z0 }-> 1 + s28 + s3 + FLATTEN(z1) :|: s27 >= 0, s27 <= 0 + 0, s28 >= 0, s28 <= 1, s3 >= 0, s3 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*s177 + 4*z0 }-> 1 + s30 + s179 + FLATTEN(z2) :|: s177 >= 0, s177 <= z1 + 1, s178 >= 0, s178 <= z2 + 1, s179 >= 0, s179 <= 1, s29 >= 0, s29 <= 0 + 0, s30 >= 0, s30 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*s180 + 4*z0 }-> 1 + s32 + s181 + FLATTEN(z2) :|: s180 >= 0, s180 <= z1 + 1, s181 >= 0, s181 <= 1, s31 >= 0, s31 <= 0 + 0, s32 >= 0, s32 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*z0 }-> 1 + s34 + s183 + FLATTEN(z2) :|: s182 >= 0, s182 <= z2 + 1, s183 >= 0, s183 <= 1, s33 >= 0, s33 <= 0 + 0, s34 >= 0, s34 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*z0 }-> 1 + s36 + s7 + FLATTEN(z2) :|: s35 >= 0, s35 <= 0 + 0, s36 >= 0, s36 <= 1, s7 >= 0, s7 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*s52 + 4*z0 }-> 1 + s51 + s54 + FLATTEN(z1) :|: s48 >= 0, s48 <= z1 + 1, s49 >= 0, s49 <= z2 + 1, s50 >= 0, s50 <= s48 + s49, s51 >= 0, s51 <= 1, s52 >= 0, s52 <= z1 + 1, s53 >= 0, s53 <= z2 + 1, s54 >= 0, s54 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*s59 + 4*z0 }-> 1 + s58 + s60 + FLATTEN(z1) :|: s55 >= 0, s55 <= z1 + 1, s56 >= 0, s56 <= z2 + 1, s57 >= 0, s57 <= s55 + s56, s58 >= 0, s58 <= 1, s59 >= 0, s59 <= z1 + 1, s60 >= 0, s60 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*z0 }-> 1 + s64 + s66 + FLATTEN(z1) :|: s61 >= 0, s61 <= z1 + 1, s62 >= 0, s62 <= z2 + 1, s63 >= 0, s63 <= s61 + s62, s64 >= 0, s64 <= 1, s65 >= 0, s65 <= z2 + 1, s66 >= 0, s66 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*z0 }-> 1 + s70 + s'' + FLATTEN(z1) :|: s67 >= 0, s67 <= z1 + 1, s68 >= 0, s68 <= z2 + 1, s69 >= 0, s69 <= s67 + s68, s70 >= 0, s70 <= 1, s'' >= 0, s'' <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*s74 + 4*z0 }-> 1 + s73 + s76 + FLATTEN(z1) :|: s71 >= 0, s71 <= z1 + 1, s72 >= 0, s72 <= s71 + 0, s73 >= 0, s73 <= 1, s74 >= 0, s74 <= z1 + 1, s75 >= 0, s75 <= z2 + 1, s76 >= 0, s76 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*s80 + 4*z0 }-> 1 + s79 + s81 + FLATTEN(z1) :|: s77 >= 0, s77 <= z1 + 1, s78 >= 0, s78 <= s77 + 0, s79 >= 0, s79 <= 1, s80 >= 0, s80 <= z1 + 1, s81 >= 0, s81 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*z0 }-> 1 + s84 + s86 + FLATTEN(z1) :|: s82 >= 0, s82 <= z1 + 1, s83 >= 0, s83 <= s82 + 0, s84 >= 0, s84 <= 1, s85 >= 0, s85 <= z2 + 1, s86 >= 0, s86 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*z0 }-> 1 + s89 + s1 + FLATTEN(z1) :|: s87 >= 0, s87 <= z1 + 1, s88 >= 0, s88 <= s87 + 0, s89 >= 0, s89 <= 1, s1 >= 0, s1 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*s93 + 4*z0 }-> 1 + s92 + s95 + FLATTEN(z1) :|: s90 >= 0, s90 <= z2 + 1, s91 >= 0, s91 <= 0 + s90, s92 >= 0, s92 <= 1, s93 >= 0, s93 <= z1 + 1, s94 >= 0, s94 <= z2 + 1, s95 >= 0, s95 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*s99 + 4*z0 }-> 1 + s98 + s100 + FLATTEN(z1) :|: s96 >= 0, s96 <= z2 + 1, s97 >= 0, s97 <= 0 + s96, s98 >= 0, s98 <= 1, s99 >= 0, s99 <= z1 + 1, s100 >= 0, s100 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTENSORT(z) -{ 0 }-> 0 :|: z >= 0
   FLATTENSORT(z) -{ 0 }-> 1 + INSERTIONSORT(s184) :|: s184 >= 0, s184 <= z + 1, z >= 0
   FLATTENSORT(z) -{ 0 }-> 1 + INSERTIONSORT(0) :|: z >= 0
   INSERT(z, z') -{ 1 }-> 1 + INSERT#1(z', z) :|: z' >= 0, z >= 0
   INSERT#1(z, z') -{ 2 }-> 1 + INSERT#2(s11, z', z0, z1) + s47 :|: s47 >= 0, s47 <= z0 + z' + 1, s10 >= 0, s10 <= 3, s11 >= 0, s11 <= 2, z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z' >= 0
   INSERT#1(z, z') -{ 2 }-> 1 + INSERT#2(0, z', z0, z1) + s46 :|: s46 >= 0, s46 <= z0 + z' + 1, z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z' >= 0
   INSERT#2(z, z', z'', z3) -{ 1 }-> 1 + INSERT(z', z3) :|: z = 2, z'' >= 0, z' >= 0, z3 >= 0
   INSERTIONSORT(z) -{ 1 }-> 1 + INSERTIONSORT#1(z) :|: z >= 0
   INSERTIONSORT#1(z) -{ 1 }-> 1 + INSERT(z0, insertionsort#1(z1)) + INSERTIONSORT(z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   INSERTIONSORT#1(z) -{ 1 }-> 1 + INSERT(z0, 0) + INSERTIONSORT(z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   append(z, z') -{ 0 }-> s37 :|: s37 >= 0, s37 <= z + z', z' >= 0, z >= 0
   append(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   append#1(z, z') -{ 0 }-> z' :|: z' >= 0, z = 0
   append#1(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   append#1(z, z') -{ 0 }-> 1 + z0 + s40 :|: s40 >= 0, s40 <= z1 + z', z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z' >= 0
   flatten(z) -{ 0 }-> s185 :|: s185 >= 0, s185 <= z + 1, z >= 0
   flatten(z) -{ 0 }-> 0 :|: z >= 0
   flatten#1(z) -{ 0 }-> s189 :|: s186 >= 0, s186 <= z1 + 1, s187 >= 0, s187 <= z2 + 1, s188 >= 0, s188 <= s186 + s187, s189 >= 0, s189 <= z0 + s188, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   flatten#1(z) -{ 0 }-> s192 :|: s190 >= 0, s190 <= z1 + 1, s191 >= 0, s191 <= s190 + 0, s192 >= 0, s192 <= z0 + s191, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   flatten#1(z) -{ 0 }-> s195 :|: s193 >= 0, s193 <= z2 + 1, s194 >= 0, s194 <= 0 + s193, s195 >= 0, s195 <= z0 + s194, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   flatten#1(z) -{ 0 }-> s39 :|: s38 >= 0, s38 <= 0 + 0, s39 >= 0, s39 <= z0 + s38, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   flatten#1(z) -{ 0 }-> 0 :|: z = 0
   flatten#1(z) -{ 0 }-> 0 :|: z >= 0
   insert(z, z') -{ 0 }-> s42 :|: s42 >= 0, s42 <= z' + z + 1, z' >= 0, z >= 0
   insert(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   insert#1(z, z') -{ 0 }-> s43 :|: s43 >= 0, s43 <= z' + z0 + z1 + 2, z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z' >= 0
   insert#1(z, z') -{ 0 }-> s45 :|: s45 >= 0, s45 <= z' + z0 + z1 + 2, s16 >= 0, s16 <= 3, s17 >= 0, s17 <= 2, z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z' >= 0
   insert#1(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   insert#1(z, z') -{ 0 }-> 1 + z' + 0 :|: z' >= 0, z = 0
   insert#2(z, z', z'', z3) -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0, z3 >= 0
   insert#2(z, z', z'', z3) -{ 0 }-> 1 + z' + (1 + z'' + z3) :|: z'' >= 0, z = 1, z' >= 0, z3 >= 0
   insert#2(z, z', z'', z3) -{ 0 }-> 1 + z'' + s44 :|: s44 >= 0, s44 <= z' + z3 + 1, z = 2, z'' >= 0, z' >= 0, z3 >= 0
   insertionsort(z) -{ 0 }-> insertionsort#1(z) :|: z >= 0
   insertionsort(z) -{ 0 }-> 0 :|: z >= 0
   insertionsort#1(z) -{ 0 }-> s41 :|: s41 >= 0, s41 <= z0 + 0 + 1, z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   insertionsort#1(z) -{ 0 }-> insert(z0, insertionsort#1(z1)) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   insertionsort#1(z) -{ 0 }-> 0 :|: z = 0
   insertionsort#1(z) -{ 0 }-> 0 :|: z >= 0

Function symbols to be analyzed: {INSERT#1,INSERT#2,INSERT}, {flatten}, {FLATTEN,FLATTEN#1}, {insertionsort}, {INSERTIONSORT,INSERTIONSORT#1}, {FLATTENSORT}
Previous analysis results are:
  APPEND#1: runtime: O(n^1) [4*z], size: O(1) [0]
  APPEND: runtime: O(n^1) [1 + 4*z], size: O(1) [1]
  #cklt: runtime: O(1) [0], size: O(1) [2]
  #compare: runtime: O(1) [0], size: O(1) [3]
  #COMPARE: runtime: O(1) [0], size: O(n^1) [z + z']
  append#1: runtime: O(1) [0], size: O(n^1) [z + z']
  append: runtime: O(1) [0], size: O(n^1) [z + z']
  #less: runtime: O(1) [0], size: O(1) [2]
  insert#2: runtime: O(1) [0], size: O(n^1) [2 + z' + z'' + z3]
  insert: runtime: O(1) [0], size: O(n^1) [1 + z + z']
  insert#1: runtime: O(1) [0], size: O(n^1) [1 + z + z']
  #LESS: runtime: O(1) [1], size: O(n^1) [1 + z + z']
  flatten#1: runtime: O(1) [0], size: O(n^1) [1 + z]
  insertionsort#1: runtime: O(1) [0], size: O(n^1) [z]

----------------------------------------

(95) ResultPropagationProof (UPPER BOUND(ID))
Applied inner abstraction using the recently inferred runtime/size bounds where possible.
----------------------------------------

(96)
Obligation:
Complexity RNTS consisting of the following rules:

   #COMPARE(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   #COMPARE(z, z') -{ 0 }-> 1 + s19 :|: s19 >= 0, s19 <= z' - 1 + (z - 1), z' - 1 >= 0, z - 1 >= 0
   #COMPARE(z, z') -{ 0 }-> 1 + s20 :|: s20 >= 0, s20 <= z - 1 + (z' - 1), z' - 1 >= 0, z - 1 >= 0
   #LESS(z, z') -{ 1 }-> 1 + s18 :|: s18 >= 0, s18 <= z + z', z' >= 0, z >= 0
   #cklt(z) -{ 0 }-> 2 :|: z = 3
   #cklt(z) -{ 0 }-> 1 :|: z = 1
   #cklt(z) -{ 0 }-> 1 :|: z = 2
   #cklt(z) -{ 0 }-> 0 :|: z >= 0
   #compare(z, z') -{ 0 }-> s8 :|: s8 >= 0, s8 <= 3, z' - 1 >= 0, z - 1 >= 0
   #compare(z, z') -{ 0 }-> s9 :|: s9 >= 0, s9 <= 3, z' - 1 >= 0, z - 1 >= 0
   #compare(z, z') -{ 0 }-> 3 :|: z' - 1 >= 0, z = 0
   #compare(z, z') -{ 0 }-> 3 :|: z - 1 >= 0, z' = 0
   #compare(z, z') -{ 0 }-> 3 :|: z' - 1 >= 0, z - 1 >= 0
   #compare(z, z') -{ 0 }-> 2 :|: z' - 1 >= 0, z = 0
   #compare(z, z') -{ 0 }-> 2 :|: z - 1 >= 0, z' = 0
   #compare(z, z') -{ 0 }-> 2 :|: z' - 1 >= 0, z - 1 >= 0
   #compare(z, z') -{ 0 }-> 1 :|: z = 0, z' = 0
   #compare(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   #less(z, z') -{ 0 }-> s13 :|: s12 >= 0, s12 <= 3, s13 >= 0, s13 <= 2, z' - 1 >= 0, z - 1 >= 0
   #less(z, z') -{ 0 }-> s15 :|: s14 >= 0, s14 <= 3, s15 >= 0, s15 <= 2, z - 1 >= 0, z' - 1 >= 0
   #less(z, z') -{ 0 }-> 2 :|: z' - 1 >= 0, z = 0, 3 = 3
   #less(z, z') -{ 0 }-> 2 :|: z - 1 >= 0, z' = 0, 3 = 3
   #less(z, z') -{ 0 }-> 2 :|: z - 1 >= 0, z' - 1 >= 0, 3 = 3
   #less(z, z') -{ 0 }-> 1 :|: z = 0, z' = 0, 1 = 1
   #less(z, z') -{ 0 }-> 1 :|: z' - 1 >= 0, z = 0, 2 = 2
   #less(z, z') -{ 0 }-> 1 :|: z - 1 >= 0, z' = 0, 2 = 2
   #less(z, z') -{ 0 }-> 1 :|: z' - 1 >= 0, z - 1 >= 0, 2 = 2
   #less(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   #less(z, z') -{ 0 }-> 0 :|: z = 0, z' = 0, v0 >= 0, 1 = v0
   #less(z, z') -{ 0 }-> 0 :|: z' - 1 >= 0, z = 0, v0 >= 0, 2 = v0
   #less(z, z') -{ 0 }-> 0 :|: z' - 1 >= 0, z = 0, v0 >= 0, 3 = v0
   #less(z, z') -{ 0 }-> 0 :|: z - 1 >= 0, z' = 0, v0 >= 0, 3 = v0
   #less(z, z') -{ 0 }-> 0 :|: z - 1 >= 0, z' - 1 >= 0, v0 >= 0, 3 = v0
   #less(z, z') -{ 0 }-> 0 :|: z - 1 >= 0, z' = 0, v0 >= 0, 2 = v0
   #less(z, z') -{ 0 }-> 0 :|: z' - 1 >= 0, z - 1 >= 0, v0 >= 0, 2 = v0
   #less(z, z') -{ 0 }-> 0 :|: z' >= 0, z >= 0, v0 >= 0, 0 = v0
   APPEND(z, z') -{ 1 + 4*z }-> 1 + s :|: s >= 0, s <= 0, z' >= 0, z >= 0
   APPEND#1(z, z') -{ 2 + 4*z1 }-> 1 + s' :|: s' >= 0, s' <= 1, z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z' >= 0
   FLATTEN(z) -{ 1 }-> 1 + FLATTEN#1(z) :|: z >= 0
   FLATTEN#1(z) -{ 3 + 4*z0 }-> 1 + s103 + s105 + FLATTEN(z1) :|: s101 >= 0, s101 <= z2 + 1, s102 >= 0, s102 <= 0 + s101, s103 >= 0, s103 <= 1, s104 >= 0, s104 <= z2 + 1, s105 >= 0, s105 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*z0 }-> 1 + s108 + s2 + FLATTEN(z1) :|: s106 >= 0, s106 <= z2 + 1, s107 >= 0, s107 <= 0 + s106, s108 >= 0, s108 <= 1, s2 >= 0, s2 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*s120 + 4*z0 }-> 1 + s119 + s122 + FLATTEN(z2) :|: s116 >= 0, s116 <= z1 + 1, s117 >= 0, s117 <= z2 + 1, s118 >= 0, s118 <= s116 + s117, s119 >= 0, s119 <= 1, s120 >= 0, s120 <= z1 + 1, s121 >= 0, s121 <= z2 + 1, s122 >= 0, s122 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*s127 + 4*z0 }-> 1 + s126 + s128 + FLATTEN(z2) :|: s123 >= 0, s123 <= z1 + 1, s124 >= 0, s124 <= z2 + 1, s125 >= 0, s125 <= s123 + s124, s126 >= 0, s126 <= 1, s127 >= 0, s127 <= z1 + 1, s128 >= 0, s128 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*z0 }-> 1 + s132 + s134 + FLATTEN(z2) :|: s129 >= 0, s129 <= z1 + 1, s130 >= 0, s130 <= z2 + 1, s131 >= 0, s131 <= s129 + s130, s132 >= 0, s132 <= 1, s133 >= 0, s133 <= z2 + 1, s134 >= 0, s134 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*z0 }-> 1 + s138 + s4 + FLATTEN(z2) :|: s135 >= 0, s135 <= z1 + 1, s136 >= 0, s136 <= z2 + 1, s137 >= 0, s137 <= s135 + s136, s138 >= 0, s138 <= 1, s4 >= 0, s4 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*s142 + 4*z0 }-> 1 + s141 + s144 + FLATTEN(z2) :|: s139 >= 0, s139 <= z1 + 1, s140 >= 0, s140 <= s139 + 0, s141 >= 0, s141 <= 1, s142 >= 0, s142 <= z1 + 1, s143 >= 0, s143 <= z2 + 1, s144 >= 0, s144 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*s148 + 4*z0 }-> 1 + s147 + s149 + FLATTEN(z2) :|: s145 >= 0, s145 <= z1 + 1, s146 >= 0, s146 <= s145 + 0, s147 >= 0, s147 <= 1, s148 >= 0, s148 <= z1 + 1, s149 >= 0, s149 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*z0 }-> 1 + s152 + s154 + FLATTEN(z2) :|: s150 >= 0, s150 <= z1 + 1, s151 >= 0, s151 <= s150 + 0, s152 >= 0, s152 <= 1, s153 >= 0, s153 <= z2 + 1, s154 >= 0, s154 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*z0 }-> 1 + s157 + s5 + FLATTEN(z2) :|: s155 >= 0, s155 <= z1 + 1, s156 >= 0, s156 <= s155 + 0, s157 >= 0, s157 <= 1, s5 >= 0, s5 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*s161 + 4*z0 }-> 1 + s160 + s163 + FLATTEN(z2) :|: s158 >= 0, s158 <= z2 + 1, s159 >= 0, s159 <= 0 + s158, s160 >= 0, s160 <= 1, s161 >= 0, s161 <= z1 + 1, s162 >= 0, s162 <= z2 + 1, s163 >= 0, s163 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*s167 + 4*z0 }-> 1 + s166 + s168 + FLATTEN(z2) :|: s164 >= 0, s164 <= z2 + 1, s165 >= 0, s165 <= 0 + s164, s166 >= 0, s166 <= 1, s167 >= 0, s167 <= z1 + 1, s168 >= 0, s168 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*z0 }-> 1 + s171 + s173 + FLATTEN(z2) :|: s169 >= 0, s169 <= z2 + 1, s170 >= 0, s170 <= 0 + s169, s171 >= 0, s171 <= 1, s172 >= 0, s172 <= z2 + 1, s173 >= 0, s173 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*z0 }-> 1 + s176 + s6 + FLATTEN(z2) :|: s174 >= 0, s174 <= z2 + 1, s175 >= 0, s175 <= 0 + s174, s176 >= 0, s176 <= 1, s6 >= 0, s6 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*s109 + 4*z0 }-> 1 + s22 + s111 + FLATTEN(z1) :|: s109 >= 0, s109 <= z1 + 1, s110 >= 0, s110 <= z2 + 1, s111 >= 0, s111 <= 1, s21 >= 0, s21 <= 0 + 0, s22 >= 0, s22 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*s112 + 4*z0 }-> 1 + s24 + s113 + FLATTEN(z1) :|: s112 >= 0, s112 <= z1 + 1, s113 >= 0, s113 <= 1, s23 >= 0, s23 <= 0 + 0, s24 >= 0, s24 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*z0 }-> 1 + s26 + s115 + FLATTEN(z1) :|: s114 >= 0, s114 <= z2 + 1, s115 >= 0, s115 <= 1, s25 >= 0, s25 <= 0 + 0, s26 >= 0, s26 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*z0 }-> 1 + s28 + s3 + FLATTEN(z1) :|: s27 >= 0, s27 <= 0 + 0, s28 >= 0, s28 <= 1, s3 >= 0, s3 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*s177 + 4*z0 }-> 1 + s30 + s179 + FLATTEN(z2) :|: s177 >= 0, s177 <= z1 + 1, s178 >= 0, s178 <= z2 + 1, s179 >= 0, s179 <= 1, s29 >= 0, s29 <= 0 + 0, s30 >= 0, s30 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*s180 + 4*z0 }-> 1 + s32 + s181 + FLATTEN(z2) :|: s180 >= 0, s180 <= z1 + 1, s181 >= 0, s181 <= 1, s31 >= 0, s31 <= 0 + 0, s32 >= 0, s32 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*z0 }-> 1 + s34 + s183 + FLATTEN(z2) :|: s182 >= 0, s182 <= z2 + 1, s183 >= 0, s183 <= 1, s33 >= 0, s33 <= 0 + 0, s34 >= 0, s34 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*z0 }-> 1 + s36 + s7 + FLATTEN(z2) :|: s35 >= 0, s35 <= 0 + 0, s36 >= 0, s36 <= 1, s7 >= 0, s7 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*s52 + 4*z0 }-> 1 + s51 + s54 + FLATTEN(z1) :|: s48 >= 0, s48 <= z1 + 1, s49 >= 0, s49 <= z2 + 1, s50 >= 0, s50 <= s48 + s49, s51 >= 0, s51 <= 1, s52 >= 0, s52 <= z1 + 1, s53 >= 0, s53 <= z2 + 1, s54 >= 0, s54 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*s59 + 4*z0 }-> 1 + s58 + s60 + FLATTEN(z1) :|: s55 >= 0, s55 <= z1 + 1, s56 >= 0, s56 <= z2 + 1, s57 >= 0, s57 <= s55 + s56, s58 >= 0, s58 <= 1, s59 >= 0, s59 <= z1 + 1, s60 >= 0, s60 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*z0 }-> 1 + s64 + s66 + FLATTEN(z1) :|: s61 >= 0, s61 <= z1 + 1, s62 >= 0, s62 <= z2 + 1, s63 >= 0, s63 <= s61 + s62, s64 >= 0, s64 <= 1, s65 >= 0, s65 <= z2 + 1, s66 >= 0, s66 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*z0 }-> 1 + s70 + s'' + FLATTEN(z1) :|: s67 >= 0, s67 <= z1 + 1, s68 >= 0, s68 <= z2 + 1, s69 >= 0, s69 <= s67 + s68, s70 >= 0, s70 <= 1, s'' >= 0, s'' <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*s74 + 4*z0 }-> 1 + s73 + s76 + FLATTEN(z1) :|: s71 >= 0, s71 <= z1 + 1, s72 >= 0, s72 <= s71 + 0, s73 >= 0, s73 <= 1, s74 >= 0, s74 <= z1 + 1, s75 >= 0, s75 <= z2 + 1, s76 >= 0, s76 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*s80 + 4*z0 }-> 1 + s79 + s81 + FLATTEN(z1) :|: s77 >= 0, s77 <= z1 + 1, s78 >= 0, s78 <= s77 + 0, s79 >= 0, s79 <= 1, s80 >= 0, s80 <= z1 + 1, s81 >= 0, s81 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*z0 }-> 1 + s84 + s86 + FLATTEN(z1) :|: s82 >= 0, s82 <= z1 + 1, s83 >= 0, s83 <= s82 + 0, s84 >= 0, s84 <= 1, s85 >= 0, s85 <= z2 + 1, s86 >= 0, s86 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*z0 }-> 1 + s89 + s1 + FLATTEN(z1) :|: s87 >= 0, s87 <= z1 + 1, s88 >= 0, s88 <= s87 + 0, s89 >= 0, s89 <= 1, s1 >= 0, s1 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*s93 + 4*z0 }-> 1 + s92 + s95 + FLATTEN(z1) :|: s90 >= 0, s90 <= z2 + 1, s91 >= 0, s91 <= 0 + s90, s92 >= 0, s92 <= 1, s93 >= 0, s93 <= z1 + 1, s94 >= 0, s94 <= z2 + 1, s95 >= 0, s95 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*s99 + 4*z0 }-> 1 + s98 + s100 + FLATTEN(z1) :|: s96 >= 0, s96 <= z2 + 1, s97 >= 0, s97 <= 0 + s96, s98 >= 0, s98 <= 1, s99 >= 0, s99 <= z1 + 1, s100 >= 0, s100 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTENSORT(z) -{ 0 }-> 0 :|: z >= 0
   FLATTENSORT(z) -{ 0 }-> 1 + INSERTIONSORT(s184) :|: s184 >= 0, s184 <= z + 1, z >= 0
   FLATTENSORT(z) -{ 0 }-> 1 + INSERTIONSORT(0) :|: z >= 0
   INSERT(z, z') -{ 1 }-> 1 + INSERT#1(z', z) :|: z' >= 0, z >= 0
   INSERT#1(z, z') -{ 2 }-> 1 + INSERT#2(s11, z', z0, z1) + s47 :|: s47 >= 0, s47 <= z0 + z' + 1, s10 >= 0, s10 <= 3, s11 >= 0, s11 <= 2, z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z' >= 0
   INSERT#1(z, z') -{ 2 }-> 1 + INSERT#2(0, z', z0, z1) + s46 :|: s46 >= 0, s46 <= z0 + z' + 1, z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z' >= 0
   INSERT#2(z, z', z'', z3) -{ 1 }-> 1 + INSERT(z', z3) :|: z = 2, z'' >= 0, z' >= 0, z3 >= 0
   INSERTIONSORT(z) -{ 1 }-> 1 + INSERTIONSORT#1(z) :|: z >= 0
   INSERTIONSORT#1(z) -{ 1 }-> 1 + INSERT(z0, s196) + INSERTIONSORT(z1) :|: s196 >= 0, s196 <= z1, z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   INSERTIONSORT#1(z) -{ 1 }-> 1 + INSERT(z0, 0) + INSERTIONSORT(z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   append(z, z') -{ 0 }-> s37 :|: s37 >= 0, s37 <= z + z', z' >= 0, z >= 0
   append(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   append#1(z, z') -{ 0 }-> z' :|: z' >= 0, z = 0
   append#1(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   append#1(z, z') -{ 0 }-> 1 + z0 + s40 :|: s40 >= 0, s40 <= z1 + z', z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z' >= 0
   flatten(z) -{ 0 }-> s185 :|: s185 >= 0, s185 <= z + 1, z >= 0
   flatten(z) -{ 0 }-> 0 :|: z >= 0
   flatten#1(z) -{ 0 }-> s189 :|: s186 >= 0, s186 <= z1 + 1, s187 >= 0, s187 <= z2 + 1, s188 >= 0, s188 <= s186 + s187, s189 >= 0, s189 <= z0 + s188, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   flatten#1(z) -{ 0 }-> s192 :|: s190 >= 0, s190 <= z1 + 1, s191 >= 0, s191 <= s190 + 0, s192 >= 0, s192 <= z0 + s191, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   flatten#1(z) -{ 0 }-> s195 :|: s193 >= 0, s193 <= z2 + 1, s194 >= 0, s194 <= 0 + s193, s195 >= 0, s195 <= z0 + s194, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   flatten#1(z) -{ 0 }-> s39 :|: s38 >= 0, s38 <= 0 + 0, s39 >= 0, s39 <= z0 + s38, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   flatten#1(z) -{ 0 }-> 0 :|: z = 0
   flatten#1(z) -{ 0 }-> 0 :|: z >= 0
   insert(z, z') -{ 0 }-> s42 :|: s42 >= 0, s42 <= z' + z + 1, z' >= 0, z >= 0
   insert(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   insert#1(z, z') -{ 0 }-> s43 :|: s43 >= 0, s43 <= z' + z0 + z1 + 2, z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z' >= 0
   insert#1(z, z') -{ 0 }-> s45 :|: s45 >= 0, s45 <= z' + z0 + z1 + 2, s16 >= 0, s16 <= 3, s17 >= 0, s17 <= 2, z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z' >= 0
   insert#1(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   insert#1(z, z') -{ 0 }-> 1 + z' + 0 :|: z' >= 0, z = 0
   insert#2(z, z', z'', z3) -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0, z3 >= 0
   insert#2(z, z', z'', z3) -{ 0 }-> 1 + z' + (1 + z'' + z3) :|: z'' >= 0, z = 1, z' >= 0, z3 >= 0
   insert#2(z, z', z'', z3) -{ 0 }-> 1 + z'' + s44 :|: s44 >= 0, s44 <= z' + z3 + 1, z = 2, z'' >= 0, z' >= 0, z3 >= 0
   insertionsort(z) -{ 0 }-> s197 :|: s197 >= 0, s197 <= z, z >= 0
   insertionsort(z) -{ 0 }-> 0 :|: z >= 0
   insertionsort#1(z) -{ 0 }-> s199 :|: s198 >= 0, s198 <= z1, s199 >= 0, s199 <= z0 + s198 + 1, z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   insertionsort#1(z) -{ 0 }-> s41 :|: s41 >= 0, s41 <= z0 + 0 + 1, z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   insertionsort#1(z) -{ 0 }-> 0 :|: z = 0
   insertionsort#1(z) -{ 0 }-> 0 :|: z >= 0

Function symbols to be analyzed: {INSERT#1,INSERT#2,INSERT}, {flatten}, {FLATTEN,FLATTEN#1}, {insertionsort}, {INSERTIONSORT,INSERTIONSORT#1}, {FLATTENSORT}
Previous analysis results are:
  APPEND#1: runtime: O(n^1) [4*z], size: O(1) [0]
  APPEND: runtime: O(n^1) [1 + 4*z], size: O(1) [1]
  #cklt: runtime: O(1) [0], size: O(1) [2]
  #compare: runtime: O(1) [0], size: O(1) [3]
  #COMPARE: runtime: O(1) [0], size: O(n^1) [z + z']
  append#1: runtime: O(1) [0], size: O(n^1) [z + z']
  append: runtime: O(1) [0], size: O(n^1) [z + z']
  #less: runtime: O(1) [0], size: O(1) [2]
  insert#2: runtime: O(1) [0], size: O(n^1) [2 + z' + z'' + z3]
  insert: runtime: O(1) [0], size: O(n^1) [1 + z + z']
  insert#1: runtime: O(1) [0], size: O(n^1) [1 + z + z']
  #LESS: runtime: O(1) [1], size: O(n^1) [1 + z + z']
  flatten#1: runtime: O(1) [0], size: O(n^1) [1 + z]
  insertionsort#1: runtime: O(1) [0], size: O(n^1) [z]

----------------------------------------

(97) IntTrsBoundProof (UPPER BOUND(ID))

Computed SIZE bound using CoFloCo for: INSERT#1
after applying outer abstraction to obtain an ITS,
resulting in: O(1) with polynomial bound: 0

Computed SIZE bound using CoFloCo for: INSERT#2
after applying outer abstraction to obtain an ITS,
resulting in: O(1) with polynomial bound: 2

Computed SIZE bound using CoFloCo for: INSERT
after applying outer abstraction to obtain an ITS,
resulting in: O(1) with polynomial bound: 1

----------------------------------------

(98)
Obligation:
Complexity RNTS consisting of the following rules:

   #COMPARE(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   #COMPARE(z, z') -{ 0 }-> 1 + s19 :|: s19 >= 0, s19 <= z' - 1 + (z - 1), z' - 1 >= 0, z - 1 >= 0
   #COMPARE(z, z') -{ 0 }-> 1 + s20 :|: s20 >= 0, s20 <= z - 1 + (z' - 1), z' - 1 >= 0, z - 1 >= 0
   #LESS(z, z') -{ 1 }-> 1 + s18 :|: s18 >= 0, s18 <= z + z', z' >= 0, z >= 0
   #cklt(z) -{ 0 }-> 2 :|: z = 3
   #cklt(z) -{ 0 }-> 1 :|: z = 1
   #cklt(z) -{ 0 }-> 1 :|: z = 2
   #cklt(z) -{ 0 }-> 0 :|: z >= 0
   #compare(z, z') -{ 0 }-> s8 :|: s8 >= 0, s8 <= 3, z' - 1 >= 0, z - 1 >= 0
   #compare(z, z') -{ 0 }-> s9 :|: s9 >= 0, s9 <= 3, z' - 1 >= 0, z - 1 >= 0
   #compare(z, z') -{ 0 }-> 3 :|: z' - 1 >= 0, z = 0
   #compare(z, z') -{ 0 }-> 3 :|: z - 1 >= 0, z' = 0
   #compare(z, z') -{ 0 }-> 3 :|: z' - 1 >= 0, z - 1 >= 0
   #compare(z, z') -{ 0 }-> 2 :|: z' - 1 >= 0, z = 0
   #compare(z, z') -{ 0 }-> 2 :|: z - 1 >= 0, z' = 0
   #compare(z, z') -{ 0 }-> 2 :|: z' - 1 >= 0, z - 1 >= 0
   #compare(z, z') -{ 0 }-> 1 :|: z = 0, z' = 0
   #compare(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   #less(z, z') -{ 0 }-> s13 :|: s12 >= 0, s12 <= 3, s13 >= 0, s13 <= 2, z' - 1 >= 0, z - 1 >= 0
   #less(z, z') -{ 0 }-> s15 :|: s14 >= 0, s14 <= 3, s15 >= 0, s15 <= 2, z - 1 >= 0, z' - 1 >= 0
   #less(z, z') -{ 0 }-> 2 :|: z' - 1 >= 0, z = 0, 3 = 3
   #less(z, z') -{ 0 }-> 2 :|: z - 1 >= 0, z' = 0, 3 = 3
   #less(z, z') -{ 0 }-> 2 :|: z - 1 >= 0, z' - 1 >= 0, 3 = 3
   #less(z, z') -{ 0 }-> 1 :|: z = 0, z' = 0, 1 = 1
   #less(z, z') -{ 0 }-> 1 :|: z' - 1 >= 0, z = 0, 2 = 2
   #less(z, z') -{ 0 }-> 1 :|: z - 1 >= 0, z' = 0, 2 = 2
   #less(z, z') -{ 0 }-> 1 :|: z' - 1 >= 0, z - 1 >= 0, 2 = 2
   #less(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   #less(z, z') -{ 0 }-> 0 :|: z = 0, z' = 0, v0 >= 0, 1 = v0
   #less(z, z') -{ 0 }-> 0 :|: z' - 1 >= 0, z = 0, v0 >= 0, 2 = v0
   #less(z, z') -{ 0 }-> 0 :|: z' - 1 >= 0, z = 0, v0 >= 0, 3 = v0
   #less(z, z') -{ 0 }-> 0 :|: z - 1 >= 0, z' = 0, v0 >= 0, 3 = v0
   #less(z, z') -{ 0 }-> 0 :|: z - 1 >= 0, z' - 1 >= 0, v0 >= 0, 3 = v0
   #less(z, z') -{ 0 }-> 0 :|: z - 1 >= 0, z' = 0, v0 >= 0, 2 = v0
   #less(z, z') -{ 0 }-> 0 :|: z' - 1 >= 0, z - 1 >= 0, v0 >= 0, 2 = v0
   #less(z, z') -{ 0 }-> 0 :|: z' >= 0, z >= 0, v0 >= 0, 0 = v0
   APPEND(z, z') -{ 1 + 4*z }-> 1 + s :|: s >= 0, s <= 0, z' >= 0, z >= 0
   APPEND#1(z, z') -{ 2 + 4*z1 }-> 1 + s' :|: s' >= 0, s' <= 1, z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z' >= 0
   FLATTEN(z) -{ 1 }-> 1 + FLATTEN#1(z) :|: z >= 0
   FLATTEN#1(z) -{ 3 + 4*z0 }-> 1 + s103 + s105 + FLATTEN(z1) :|: s101 >= 0, s101 <= z2 + 1, s102 >= 0, s102 <= 0 + s101, s103 >= 0, s103 <= 1, s104 >= 0, s104 <= z2 + 1, s105 >= 0, s105 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*z0 }-> 1 + s108 + s2 + FLATTEN(z1) :|: s106 >= 0, s106 <= z2 + 1, s107 >= 0, s107 <= 0 + s106, s108 >= 0, s108 <= 1, s2 >= 0, s2 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*s120 + 4*z0 }-> 1 + s119 + s122 + FLATTEN(z2) :|: s116 >= 0, s116 <= z1 + 1, s117 >= 0, s117 <= z2 + 1, s118 >= 0, s118 <= s116 + s117, s119 >= 0, s119 <= 1, s120 >= 0, s120 <= z1 + 1, s121 >= 0, s121 <= z2 + 1, s122 >= 0, s122 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*s127 + 4*z0 }-> 1 + s126 + s128 + FLATTEN(z2) :|: s123 >= 0, s123 <= z1 + 1, s124 >= 0, s124 <= z2 + 1, s125 >= 0, s125 <= s123 + s124, s126 >= 0, s126 <= 1, s127 >= 0, s127 <= z1 + 1, s128 >= 0, s128 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*z0 }-> 1 + s132 + s134 + FLATTEN(z2) :|: s129 >= 0, s129 <= z1 + 1, s130 >= 0, s130 <= z2 + 1, s131 >= 0, s131 <= s129 + s130, s132 >= 0, s132 <= 1, s133 >= 0, s133 <= z2 + 1, s134 >= 0, s134 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*z0 }-> 1 + s138 + s4 + FLATTEN(z2) :|: s135 >= 0, s135 <= z1 + 1, s136 >= 0, s136 <= z2 + 1, s137 >= 0, s137 <= s135 + s136, s138 >= 0, s138 <= 1, s4 >= 0, s4 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*s142 + 4*z0 }-> 1 + s141 + s144 + FLATTEN(z2) :|: s139 >= 0, s139 <= z1 + 1, s140 >= 0, s140 <= s139 + 0, s141 >= 0, s141 <= 1, s142 >= 0, s142 <= z1 + 1, s143 >= 0, s143 <= z2 + 1, s144 >= 0, s144 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*s148 + 4*z0 }-> 1 + s147 + s149 + FLATTEN(z2) :|: s145 >= 0, s145 <= z1 + 1, s146 >= 0, s146 <= s145 + 0, s147 >= 0, s147 <= 1, s148 >= 0, s148 <= z1 + 1, s149 >= 0, s149 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*z0 }-> 1 + s152 + s154 + FLATTEN(z2) :|: s150 >= 0, s150 <= z1 + 1, s151 >= 0, s151 <= s150 + 0, s152 >= 0, s152 <= 1, s153 >= 0, s153 <= z2 + 1, s154 >= 0, s154 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*z0 }-> 1 + s157 + s5 + FLATTEN(z2) :|: s155 >= 0, s155 <= z1 + 1, s156 >= 0, s156 <= s155 + 0, s157 >= 0, s157 <= 1, s5 >= 0, s5 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*s161 + 4*z0 }-> 1 + s160 + s163 + FLATTEN(z2) :|: s158 >= 0, s158 <= z2 + 1, s159 >= 0, s159 <= 0 + s158, s160 >= 0, s160 <= 1, s161 >= 0, s161 <= z1 + 1, s162 >= 0, s162 <= z2 + 1, s163 >= 0, s163 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*s167 + 4*z0 }-> 1 + s166 + s168 + FLATTEN(z2) :|: s164 >= 0, s164 <= z2 + 1, s165 >= 0, s165 <= 0 + s164, s166 >= 0, s166 <= 1, s167 >= 0, s167 <= z1 + 1, s168 >= 0, s168 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*z0 }-> 1 + s171 + s173 + FLATTEN(z2) :|: s169 >= 0, s169 <= z2 + 1, s170 >= 0, s170 <= 0 + s169, s171 >= 0, s171 <= 1, s172 >= 0, s172 <= z2 + 1, s173 >= 0, s173 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*z0 }-> 1 + s176 + s6 + FLATTEN(z2) :|: s174 >= 0, s174 <= z2 + 1, s175 >= 0, s175 <= 0 + s174, s176 >= 0, s176 <= 1, s6 >= 0, s6 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*s109 + 4*z0 }-> 1 + s22 + s111 + FLATTEN(z1) :|: s109 >= 0, s109 <= z1 + 1, s110 >= 0, s110 <= z2 + 1, s111 >= 0, s111 <= 1, s21 >= 0, s21 <= 0 + 0, s22 >= 0, s22 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*s112 + 4*z0 }-> 1 + s24 + s113 + FLATTEN(z1) :|: s112 >= 0, s112 <= z1 + 1, s113 >= 0, s113 <= 1, s23 >= 0, s23 <= 0 + 0, s24 >= 0, s24 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*z0 }-> 1 + s26 + s115 + FLATTEN(z1) :|: s114 >= 0, s114 <= z2 + 1, s115 >= 0, s115 <= 1, s25 >= 0, s25 <= 0 + 0, s26 >= 0, s26 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*z0 }-> 1 + s28 + s3 + FLATTEN(z1) :|: s27 >= 0, s27 <= 0 + 0, s28 >= 0, s28 <= 1, s3 >= 0, s3 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*s177 + 4*z0 }-> 1 + s30 + s179 + FLATTEN(z2) :|: s177 >= 0, s177 <= z1 + 1, s178 >= 0, s178 <= z2 + 1, s179 >= 0, s179 <= 1, s29 >= 0, s29 <= 0 + 0, s30 >= 0, s30 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*s180 + 4*z0 }-> 1 + s32 + s181 + FLATTEN(z2) :|: s180 >= 0, s180 <= z1 + 1, s181 >= 0, s181 <= 1, s31 >= 0, s31 <= 0 + 0, s32 >= 0, s32 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*z0 }-> 1 + s34 + s183 + FLATTEN(z2) :|: s182 >= 0, s182 <= z2 + 1, s183 >= 0, s183 <= 1, s33 >= 0, s33 <= 0 + 0, s34 >= 0, s34 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*z0 }-> 1 + s36 + s7 + FLATTEN(z2) :|: s35 >= 0, s35 <= 0 + 0, s36 >= 0, s36 <= 1, s7 >= 0, s7 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*s52 + 4*z0 }-> 1 + s51 + s54 + FLATTEN(z1) :|: s48 >= 0, s48 <= z1 + 1, s49 >= 0, s49 <= z2 + 1, s50 >= 0, s50 <= s48 + s49, s51 >= 0, s51 <= 1, s52 >= 0, s52 <= z1 + 1, s53 >= 0, s53 <= z2 + 1, s54 >= 0, s54 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*s59 + 4*z0 }-> 1 + s58 + s60 + FLATTEN(z1) :|: s55 >= 0, s55 <= z1 + 1, s56 >= 0, s56 <= z2 + 1, s57 >= 0, s57 <= s55 + s56, s58 >= 0, s58 <= 1, s59 >= 0, s59 <= z1 + 1, s60 >= 0, s60 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*z0 }-> 1 + s64 + s66 + FLATTEN(z1) :|: s61 >= 0, s61 <= z1 + 1, s62 >= 0, s62 <= z2 + 1, s63 >= 0, s63 <= s61 + s62, s64 >= 0, s64 <= 1, s65 >= 0, s65 <= z2 + 1, s66 >= 0, s66 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*z0 }-> 1 + s70 + s'' + FLATTEN(z1) :|: s67 >= 0, s67 <= z1 + 1, s68 >= 0, s68 <= z2 + 1, s69 >= 0, s69 <= s67 + s68, s70 >= 0, s70 <= 1, s'' >= 0, s'' <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*s74 + 4*z0 }-> 1 + s73 + s76 + FLATTEN(z1) :|: s71 >= 0, s71 <= z1 + 1, s72 >= 0, s72 <= s71 + 0, s73 >= 0, s73 <= 1, s74 >= 0, s74 <= z1 + 1, s75 >= 0, s75 <= z2 + 1, s76 >= 0, s76 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*s80 + 4*z0 }-> 1 + s79 + s81 + FLATTEN(z1) :|: s77 >= 0, s77 <= z1 + 1, s78 >= 0, s78 <= s77 + 0, s79 >= 0, s79 <= 1, s80 >= 0, s80 <= z1 + 1, s81 >= 0, s81 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*z0 }-> 1 + s84 + s86 + FLATTEN(z1) :|: s82 >= 0, s82 <= z1 + 1, s83 >= 0, s83 <= s82 + 0, s84 >= 0, s84 <= 1, s85 >= 0, s85 <= z2 + 1, s86 >= 0, s86 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*z0 }-> 1 + s89 + s1 + FLATTEN(z1) :|: s87 >= 0, s87 <= z1 + 1, s88 >= 0, s88 <= s87 + 0, s89 >= 0, s89 <= 1, s1 >= 0, s1 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*s93 + 4*z0 }-> 1 + s92 + s95 + FLATTEN(z1) :|: s90 >= 0, s90 <= z2 + 1, s91 >= 0, s91 <= 0 + s90, s92 >= 0, s92 <= 1, s93 >= 0, s93 <= z1 + 1, s94 >= 0, s94 <= z2 + 1, s95 >= 0, s95 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*s99 + 4*z0 }-> 1 + s98 + s100 + FLATTEN(z1) :|: s96 >= 0, s96 <= z2 + 1, s97 >= 0, s97 <= 0 + s96, s98 >= 0, s98 <= 1, s99 >= 0, s99 <= z1 + 1, s100 >= 0, s100 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTENSORT(z) -{ 0 }-> 0 :|: z >= 0
   FLATTENSORT(z) -{ 0 }-> 1 + INSERTIONSORT(s184) :|: s184 >= 0, s184 <= z + 1, z >= 0
   FLATTENSORT(z) -{ 0 }-> 1 + INSERTIONSORT(0) :|: z >= 0
   INSERT(z, z') -{ 1 }-> 1 + INSERT#1(z', z) :|: z' >= 0, z >= 0
   INSERT#1(z, z') -{ 2 }-> 1 + INSERT#2(s11, z', z0, z1) + s47 :|: s47 >= 0, s47 <= z0 + z' + 1, s10 >= 0, s10 <= 3, s11 >= 0, s11 <= 2, z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z' >= 0
   INSERT#1(z, z') -{ 2 }-> 1 + INSERT#2(0, z', z0, z1) + s46 :|: s46 >= 0, s46 <= z0 + z' + 1, z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z' >= 0
   INSERT#2(z, z', z'', z3) -{ 1 }-> 1 + INSERT(z', z3) :|: z = 2, z'' >= 0, z' >= 0, z3 >= 0
   INSERTIONSORT(z) -{ 1 }-> 1 + INSERTIONSORT#1(z) :|: z >= 0
   INSERTIONSORT#1(z) -{ 1 }-> 1 + INSERT(z0, s196) + INSERTIONSORT(z1) :|: s196 >= 0, s196 <= z1, z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   INSERTIONSORT#1(z) -{ 1 }-> 1 + INSERT(z0, 0) + INSERTIONSORT(z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   append(z, z') -{ 0 }-> s37 :|: s37 >= 0, s37 <= z + z', z' >= 0, z >= 0
   append(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   append#1(z, z') -{ 0 }-> z' :|: z' >= 0, z = 0
   append#1(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   append#1(z, z') -{ 0 }-> 1 + z0 + s40 :|: s40 >= 0, s40 <= z1 + z', z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z' >= 0
   flatten(z) -{ 0 }-> s185 :|: s185 >= 0, s185 <= z + 1, z >= 0
   flatten(z) -{ 0 }-> 0 :|: z >= 0
   flatten#1(z) -{ 0 }-> s189 :|: s186 >= 0, s186 <= z1 + 1, s187 >= 0, s187 <= z2 + 1, s188 >= 0, s188 <= s186 + s187, s189 >= 0, s189 <= z0 + s188, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   flatten#1(z) -{ 0 }-> s192 :|: s190 >= 0, s190 <= z1 + 1, s191 >= 0, s191 <= s190 + 0, s192 >= 0, s192 <= z0 + s191, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   flatten#1(z) -{ 0 }-> s195 :|: s193 >= 0, s193 <= z2 + 1, s194 >= 0, s194 <= 0 + s193, s195 >= 0, s195 <= z0 + s194, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   flatten#1(z) -{ 0 }-> s39 :|: s38 >= 0, s38 <= 0 + 0, s39 >= 0, s39 <= z0 + s38, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   flatten#1(z) -{ 0 }-> 0 :|: z = 0
   flatten#1(z) -{ 0 }-> 0 :|: z >= 0
   insert(z, z') -{ 0 }-> s42 :|: s42 >= 0, s42 <= z' + z + 1, z' >= 0, z >= 0
   insert(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   insert#1(z, z') -{ 0 }-> s43 :|: s43 >= 0, s43 <= z' + z0 + z1 + 2, z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z' >= 0
   insert#1(z, z') -{ 0 }-> s45 :|: s45 >= 0, s45 <= z' + z0 + z1 + 2, s16 >= 0, s16 <= 3, s17 >= 0, s17 <= 2, z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z' >= 0
   insert#1(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   insert#1(z, z') -{ 0 }-> 1 + z' + 0 :|: z' >= 0, z = 0
   insert#2(z, z', z'', z3) -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0, z3 >= 0
   insert#2(z, z', z'', z3) -{ 0 }-> 1 + z' + (1 + z'' + z3) :|: z'' >= 0, z = 1, z' >= 0, z3 >= 0
   insert#2(z, z', z'', z3) -{ 0 }-> 1 + z'' + s44 :|: s44 >= 0, s44 <= z' + z3 + 1, z = 2, z'' >= 0, z' >= 0, z3 >= 0
   insertionsort(z) -{ 0 }-> s197 :|: s197 >= 0, s197 <= z, z >= 0
   insertionsort(z) -{ 0 }-> 0 :|: z >= 0
   insertionsort#1(z) -{ 0 }-> s199 :|: s198 >= 0, s198 <= z1, s199 >= 0, s199 <= z0 + s198 + 1, z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   insertionsort#1(z) -{ 0 }-> s41 :|: s41 >= 0, s41 <= z0 + 0 + 1, z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   insertionsort#1(z) -{ 0 }-> 0 :|: z = 0
   insertionsort#1(z) -{ 0 }-> 0 :|: z >= 0

Function symbols to be analyzed: {INSERT#1,INSERT#2,INSERT}, {flatten}, {FLATTEN,FLATTEN#1}, {insertionsort}, {INSERTIONSORT,INSERTIONSORT#1}, {FLATTENSORT}
Previous analysis results are:
  APPEND#1: runtime: O(n^1) [4*z], size: O(1) [0]
  APPEND: runtime: O(n^1) [1 + 4*z], size: O(1) [1]
  #cklt: runtime: O(1) [0], size: O(1) [2]
  #compare: runtime: O(1) [0], size: O(1) [3]
  #COMPARE: runtime: O(1) [0], size: O(n^1) [z + z']
  append#1: runtime: O(1) [0], size: O(n^1) [z + z']
  append: runtime: O(1) [0], size: O(n^1) [z + z']
  #less: runtime: O(1) [0], size: O(1) [2]
  insert#2: runtime: O(1) [0], size: O(n^1) [2 + z' + z'' + z3]
  insert: runtime: O(1) [0], size: O(n^1) [1 + z + z']
  insert#1: runtime: O(1) [0], size: O(n^1) [1 + z + z']
  #LESS: runtime: O(1) [1], size: O(n^1) [1 + z + z']
  flatten#1: runtime: O(1) [0], size: O(n^1) [1 + z]
  insertionsort#1: runtime: O(1) [0], size: O(n^1) [z]
  INSERT#1: runtime: ?, size: O(1) [0]
  INSERT#2: runtime: ?, size: O(1) [2]
  INSERT: runtime: ?, size: O(1) [1]

----------------------------------------

(99) IntTrsBoundProof (UPPER BOUND(ID))

Computed RUNTIME bound using CoFloCo for: INSERT#1
after applying outer abstraction to obtain an ITS,
resulting in: O(n^1) with polynomial bound: 7 + 4*z

Computed RUNTIME bound using CoFloCo for: INSERT#2
after applying outer abstraction to obtain an ITS,
resulting in: O(n^1) with polynomial bound: 9 + 4*z3

Computed RUNTIME bound using CoFloCo for: INSERT
after applying outer abstraction to obtain an ITS,
resulting in: O(n^1) with polynomial bound: 8 + 4*z'

----------------------------------------

(100)
Obligation:
Complexity RNTS consisting of the following rules:

   #COMPARE(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   #COMPARE(z, z') -{ 0 }-> 1 + s19 :|: s19 >= 0, s19 <= z' - 1 + (z - 1), z' - 1 >= 0, z - 1 >= 0
   #COMPARE(z, z') -{ 0 }-> 1 + s20 :|: s20 >= 0, s20 <= z - 1 + (z' - 1), z' - 1 >= 0, z - 1 >= 0
   #LESS(z, z') -{ 1 }-> 1 + s18 :|: s18 >= 0, s18 <= z + z', z' >= 0, z >= 0
   #cklt(z) -{ 0 }-> 2 :|: z = 3
   #cklt(z) -{ 0 }-> 1 :|: z = 1
   #cklt(z) -{ 0 }-> 1 :|: z = 2
   #cklt(z) -{ 0 }-> 0 :|: z >= 0
   #compare(z, z') -{ 0 }-> s8 :|: s8 >= 0, s8 <= 3, z' - 1 >= 0, z - 1 >= 0
   #compare(z, z') -{ 0 }-> s9 :|: s9 >= 0, s9 <= 3, z' - 1 >= 0, z - 1 >= 0
   #compare(z, z') -{ 0 }-> 3 :|: z' - 1 >= 0, z = 0
   #compare(z, z') -{ 0 }-> 3 :|: z - 1 >= 0, z' = 0
   #compare(z, z') -{ 0 }-> 3 :|: z' - 1 >= 0, z - 1 >= 0
   #compare(z, z') -{ 0 }-> 2 :|: z' - 1 >= 0, z = 0
   #compare(z, z') -{ 0 }-> 2 :|: z - 1 >= 0, z' = 0
   #compare(z, z') -{ 0 }-> 2 :|: z' - 1 >= 0, z - 1 >= 0
   #compare(z, z') -{ 0 }-> 1 :|: z = 0, z' = 0
   #compare(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   #less(z, z') -{ 0 }-> s13 :|: s12 >= 0, s12 <= 3, s13 >= 0, s13 <= 2, z' - 1 >= 0, z - 1 >= 0
   #less(z, z') -{ 0 }-> s15 :|: s14 >= 0, s14 <= 3, s15 >= 0, s15 <= 2, z - 1 >= 0, z' - 1 >= 0
   #less(z, z') -{ 0 }-> 2 :|: z' - 1 >= 0, z = 0, 3 = 3
   #less(z, z') -{ 0 }-> 2 :|: z - 1 >= 0, z' = 0, 3 = 3
   #less(z, z') -{ 0 }-> 2 :|: z - 1 >= 0, z' - 1 >= 0, 3 = 3
   #less(z, z') -{ 0 }-> 1 :|: z = 0, z' = 0, 1 = 1
   #less(z, z') -{ 0 }-> 1 :|: z' - 1 >= 0, z = 0, 2 = 2
   #less(z, z') -{ 0 }-> 1 :|: z - 1 >= 0, z' = 0, 2 = 2
   #less(z, z') -{ 0 }-> 1 :|: z' - 1 >= 0, z - 1 >= 0, 2 = 2
   #less(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   #less(z, z') -{ 0 }-> 0 :|: z = 0, z' = 0, v0 >= 0, 1 = v0
   #less(z, z') -{ 0 }-> 0 :|: z' - 1 >= 0, z = 0, v0 >= 0, 2 = v0
   #less(z, z') -{ 0 }-> 0 :|: z' - 1 >= 0, z = 0, v0 >= 0, 3 = v0
   #less(z, z') -{ 0 }-> 0 :|: z - 1 >= 0, z' = 0, v0 >= 0, 3 = v0
   #less(z, z') -{ 0 }-> 0 :|: z - 1 >= 0, z' - 1 >= 0, v0 >= 0, 3 = v0
   #less(z, z') -{ 0 }-> 0 :|: z - 1 >= 0, z' = 0, v0 >= 0, 2 = v0
   #less(z, z') -{ 0 }-> 0 :|: z' - 1 >= 0, z - 1 >= 0, v0 >= 0, 2 = v0
   #less(z, z') -{ 0 }-> 0 :|: z' >= 0, z >= 0, v0 >= 0, 0 = v0
   APPEND(z, z') -{ 1 + 4*z }-> 1 + s :|: s >= 0, s <= 0, z' >= 0, z >= 0
   APPEND#1(z, z') -{ 2 + 4*z1 }-> 1 + s' :|: s' >= 0, s' <= 1, z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z' >= 0
   FLATTEN(z) -{ 1 }-> 1 + FLATTEN#1(z) :|: z >= 0
   FLATTEN#1(z) -{ 3 + 4*z0 }-> 1 + s103 + s105 + FLATTEN(z1) :|: s101 >= 0, s101 <= z2 + 1, s102 >= 0, s102 <= 0 + s101, s103 >= 0, s103 <= 1, s104 >= 0, s104 <= z2 + 1, s105 >= 0, s105 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*z0 }-> 1 + s108 + s2 + FLATTEN(z1) :|: s106 >= 0, s106 <= z2 + 1, s107 >= 0, s107 <= 0 + s106, s108 >= 0, s108 <= 1, s2 >= 0, s2 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*s120 + 4*z0 }-> 1 + s119 + s122 + FLATTEN(z2) :|: s116 >= 0, s116 <= z1 + 1, s117 >= 0, s117 <= z2 + 1, s118 >= 0, s118 <= s116 + s117, s119 >= 0, s119 <= 1, s120 >= 0, s120 <= z1 + 1, s121 >= 0, s121 <= z2 + 1, s122 >= 0, s122 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*s127 + 4*z0 }-> 1 + s126 + s128 + FLATTEN(z2) :|: s123 >= 0, s123 <= z1 + 1, s124 >= 0, s124 <= z2 + 1, s125 >= 0, s125 <= s123 + s124, s126 >= 0, s126 <= 1, s127 >= 0, s127 <= z1 + 1, s128 >= 0, s128 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*z0 }-> 1 + s132 + s134 + FLATTEN(z2) :|: s129 >= 0, s129 <= z1 + 1, s130 >= 0, s130 <= z2 + 1, s131 >= 0, s131 <= s129 + s130, s132 >= 0, s132 <= 1, s133 >= 0, s133 <= z2 + 1, s134 >= 0, s134 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*z0 }-> 1 + s138 + s4 + FLATTEN(z2) :|: s135 >= 0, s135 <= z1 + 1, s136 >= 0, s136 <= z2 + 1, s137 >= 0, s137 <= s135 + s136, s138 >= 0, s138 <= 1, s4 >= 0, s4 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*s142 + 4*z0 }-> 1 + s141 + s144 + FLATTEN(z2) :|: s139 >= 0, s139 <= z1 + 1, s140 >= 0, s140 <= s139 + 0, s141 >= 0, s141 <= 1, s142 >= 0, s142 <= z1 + 1, s143 >= 0, s143 <= z2 + 1, s144 >= 0, s144 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*s148 + 4*z0 }-> 1 + s147 + s149 + FLATTEN(z2) :|: s145 >= 0, s145 <= z1 + 1, s146 >= 0, s146 <= s145 + 0, s147 >= 0, s147 <= 1, s148 >= 0, s148 <= z1 + 1, s149 >= 0, s149 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*z0 }-> 1 + s152 + s154 + FLATTEN(z2) :|: s150 >= 0, s150 <= z1 + 1, s151 >= 0, s151 <= s150 + 0, s152 >= 0, s152 <= 1, s153 >= 0, s153 <= z2 + 1, s154 >= 0, s154 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*z0 }-> 1 + s157 + s5 + FLATTEN(z2) :|: s155 >= 0, s155 <= z1 + 1, s156 >= 0, s156 <= s155 + 0, s157 >= 0, s157 <= 1, s5 >= 0, s5 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*s161 + 4*z0 }-> 1 + s160 + s163 + FLATTEN(z2) :|: s158 >= 0, s158 <= z2 + 1, s159 >= 0, s159 <= 0 + s158, s160 >= 0, s160 <= 1, s161 >= 0, s161 <= z1 + 1, s162 >= 0, s162 <= z2 + 1, s163 >= 0, s163 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*s167 + 4*z0 }-> 1 + s166 + s168 + FLATTEN(z2) :|: s164 >= 0, s164 <= z2 + 1, s165 >= 0, s165 <= 0 + s164, s166 >= 0, s166 <= 1, s167 >= 0, s167 <= z1 + 1, s168 >= 0, s168 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*z0 }-> 1 + s171 + s173 + FLATTEN(z2) :|: s169 >= 0, s169 <= z2 + 1, s170 >= 0, s170 <= 0 + s169, s171 >= 0, s171 <= 1, s172 >= 0, s172 <= z2 + 1, s173 >= 0, s173 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*z0 }-> 1 + s176 + s6 + FLATTEN(z2) :|: s174 >= 0, s174 <= z2 + 1, s175 >= 0, s175 <= 0 + s174, s176 >= 0, s176 <= 1, s6 >= 0, s6 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*s109 + 4*z0 }-> 1 + s22 + s111 + FLATTEN(z1) :|: s109 >= 0, s109 <= z1 + 1, s110 >= 0, s110 <= z2 + 1, s111 >= 0, s111 <= 1, s21 >= 0, s21 <= 0 + 0, s22 >= 0, s22 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*s112 + 4*z0 }-> 1 + s24 + s113 + FLATTEN(z1) :|: s112 >= 0, s112 <= z1 + 1, s113 >= 0, s113 <= 1, s23 >= 0, s23 <= 0 + 0, s24 >= 0, s24 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*z0 }-> 1 + s26 + s115 + FLATTEN(z1) :|: s114 >= 0, s114 <= z2 + 1, s115 >= 0, s115 <= 1, s25 >= 0, s25 <= 0 + 0, s26 >= 0, s26 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*z0 }-> 1 + s28 + s3 + FLATTEN(z1) :|: s27 >= 0, s27 <= 0 + 0, s28 >= 0, s28 <= 1, s3 >= 0, s3 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*s177 + 4*z0 }-> 1 + s30 + s179 + FLATTEN(z2) :|: s177 >= 0, s177 <= z1 + 1, s178 >= 0, s178 <= z2 + 1, s179 >= 0, s179 <= 1, s29 >= 0, s29 <= 0 + 0, s30 >= 0, s30 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*s180 + 4*z0 }-> 1 + s32 + s181 + FLATTEN(z2) :|: s180 >= 0, s180 <= z1 + 1, s181 >= 0, s181 <= 1, s31 >= 0, s31 <= 0 + 0, s32 >= 0, s32 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*z0 }-> 1 + s34 + s183 + FLATTEN(z2) :|: s182 >= 0, s182 <= z2 + 1, s183 >= 0, s183 <= 1, s33 >= 0, s33 <= 0 + 0, s34 >= 0, s34 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*z0 }-> 1 + s36 + s7 + FLATTEN(z2) :|: s35 >= 0, s35 <= 0 + 0, s36 >= 0, s36 <= 1, s7 >= 0, s7 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*s52 + 4*z0 }-> 1 + s51 + s54 + FLATTEN(z1) :|: s48 >= 0, s48 <= z1 + 1, s49 >= 0, s49 <= z2 + 1, s50 >= 0, s50 <= s48 + s49, s51 >= 0, s51 <= 1, s52 >= 0, s52 <= z1 + 1, s53 >= 0, s53 <= z2 + 1, s54 >= 0, s54 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*s59 + 4*z0 }-> 1 + s58 + s60 + FLATTEN(z1) :|: s55 >= 0, s55 <= z1 + 1, s56 >= 0, s56 <= z2 + 1, s57 >= 0, s57 <= s55 + s56, s58 >= 0, s58 <= 1, s59 >= 0, s59 <= z1 + 1, s60 >= 0, s60 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*z0 }-> 1 + s64 + s66 + FLATTEN(z1) :|: s61 >= 0, s61 <= z1 + 1, s62 >= 0, s62 <= z2 + 1, s63 >= 0, s63 <= s61 + s62, s64 >= 0, s64 <= 1, s65 >= 0, s65 <= z2 + 1, s66 >= 0, s66 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*z0 }-> 1 + s70 + s'' + FLATTEN(z1) :|: s67 >= 0, s67 <= z1 + 1, s68 >= 0, s68 <= z2 + 1, s69 >= 0, s69 <= s67 + s68, s70 >= 0, s70 <= 1, s'' >= 0, s'' <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*s74 + 4*z0 }-> 1 + s73 + s76 + FLATTEN(z1) :|: s71 >= 0, s71 <= z1 + 1, s72 >= 0, s72 <= s71 + 0, s73 >= 0, s73 <= 1, s74 >= 0, s74 <= z1 + 1, s75 >= 0, s75 <= z2 + 1, s76 >= 0, s76 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*s80 + 4*z0 }-> 1 + s79 + s81 + FLATTEN(z1) :|: s77 >= 0, s77 <= z1 + 1, s78 >= 0, s78 <= s77 + 0, s79 >= 0, s79 <= 1, s80 >= 0, s80 <= z1 + 1, s81 >= 0, s81 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*z0 }-> 1 + s84 + s86 + FLATTEN(z1) :|: s82 >= 0, s82 <= z1 + 1, s83 >= 0, s83 <= s82 + 0, s84 >= 0, s84 <= 1, s85 >= 0, s85 <= z2 + 1, s86 >= 0, s86 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*z0 }-> 1 + s89 + s1 + FLATTEN(z1) :|: s87 >= 0, s87 <= z1 + 1, s88 >= 0, s88 <= s87 + 0, s89 >= 0, s89 <= 1, s1 >= 0, s1 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*s93 + 4*z0 }-> 1 + s92 + s95 + FLATTEN(z1) :|: s90 >= 0, s90 <= z2 + 1, s91 >= 0, s91 <= 0 + s90, s92 >= 0, s92 <= 1, s93 >= 0, s93 <= z1 + 1, s94 >= 0, s94 <= z2 + 1, s95 >= 0, s95 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*s99 + 4*z0 }-> 1 + s98 + s100 + FLATTEN(z1) :|: s96 >= 0, s96 <= z2 + 1, s97 >= 0, s97 <= 0 + s96, s98 >= 0, s98 <= 1, s99 >= 0, s99 <= z1 + 1, s100 >= 0, s100 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTENSORT(z) -{ 0 }-> 0 :|: z >= 0
   FLATTENSORT(z) -{ 0 }-> 1 + INSERTIONSORT(s184) :|: s184 >= 0, s184 <= z + 1, z >= 0
   FLATTENSORT(z) -{ 0 }-> 1 + INSERTIONSORT(0) :|: z >= 0
   INSERT(z, z') -{ 1 }-> 1 + INSERT#1(z', z) :|: z' >= 0, z >= 0
   INSERT#1(z, z') -{ 2 }-> 1 + INSERT#2(s11, z', z0, z1) + s47 :|: s47 >= 0, s47 <= z0 + z' + 1, s10 >= 0, s10 <= 3, s11 >= 0, s11 <= 2, z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z' >= 0
   INSERT#1(z, z') -{ 2 }-> 1 + INSERT#2(0, z', z0, z1) + s46 :|: s46 >= 0, s46 <= z0 + z' + 1, z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z' >= 0
   INSERT#2(z, z', z'', z3) -{ 1 }-> 1 + INSERT(z', z3) :|: z = 2, z'' >= 0, z' >= 0, z3 >= 0
   INSERTIONSORT(z) -{ 1 }-> 1 + INSERTIONSORT#1(z) :|: z >= 0
   INSERTIONSORT#1(z) -{ 1 }-> 1 + INSERT(z0, s196) + INSERTIONSORT(z1) :|: s196 >= 0, s196 <= z1, z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   INSERTIONSORT#1(z) -{ 1 }-> 1 + INSERT(z0, 0) + INSERTIONSORT(z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   append(z, z') -{ 0 }-> s37 :|: s37 >= 0, s37 <= z + z', z' >= 0, z >= 0
   append(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   append#1(z, z') -{ 0 }-> z' :|: z' >= 0, z = 0
   append#1(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   append#1(z, z') -{ 0 }-> 1 + z0 + s40 :|: s40 >= 0, s40 <= z1 + z', z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z' >= 0
   flatten(z) -{ 0 }-> s185 :|: s185 >= 0, s185 <= z + 1, z >= 0
   flatten(z) -{ 0 }-> 0 :|: z >= 0
   flatten#1(z) -{ 0 }-> s189 :|: s186 >= 0, s186 <= z1 + 1, s187 >= 0, s187 <= z2 + 1, s188 >= 0, s188 <= s186 + s187, s189 >= 0, s189 <= z0 + s188, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   flatten#1(z) -{ 0 }-> s192 :|: s190 >= 0, s190 <= z1 + 1, s191 >= 0, s191 <= s190 + 0, s192 >= 0, s192 <= z0 + s191, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   flatten#1(z) -{ 0 }-> s195 :|: s193 >= 0, s193 <= z2 + 1, s194 >= 0, s194 <= 0 + s193, s195 >= 0, s195 <= z0 + s194, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   flatten#1(z) -{ 0 }-> s39 :|: s38 >= 0, s38 <= 0 + 0, s39 >= 0, s39 <= z0 + s38, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   flatten#1(z) -{ 0 }-> 0 :|: z = 0
   flatten#1(z) -{ 0 }-> 0 :|: z >= 0
   insert(z, z') -{ 0 }-> s42 :|: s42 >= 0, s42 <= z' + z + 1, z' >= 0, z >= 0
   insert(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   insert#1(z, z') -{ 0 }-> s43 :|: s43 >= 0, s43 <= z' + z0 + z1 + 2, z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z' >= 0
   insert#1(z, z') -{ 0 }-> s45 :|: s45 >= 0, s45 <= z' + z0 + z1 + 2, s16 >= 0, s16 <= 3, s17 >= 0, s17 <= 2, z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z' >= 0
   insert#1(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   insert#1(z, z') -{ 0 }-> 1 + z' + 0 :|: z' >= 0, z = 0
   insert#2(z, z', z'', z3) -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0, z3 >= 0
   insert#2(z, z', z'', z3) -{ 0 }-> 1 + z' + (1 + z'' + z3) :|: z'' >= 0, z = 1, z' >= 0, z3 >= 0
   insert#2(z, z', z'', z3) -{ 0 }-> 1 + z'' + s44 :|: s44 >= 0, s44 <= z' + z3 + 1, z = 2, z'' >= 0, z' >= 0, z3 >= 0
   insertionsort(z) -{ 0 }-> s197 :|: s197 >= 0, s197 <= z, z >= 0
   insertionsort(z) -{ 0 }-> 0 :|: z >= 0
   insertionsort#1(z) -{ 0 }-> s199 :|: s198 >= 0, s198 <= z1, s199 >= 0, s199 <= z0 + s198 + 1, z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   insertionsort#1(z) -{ 0 }-> s41 :|: s41 >= 0, s41 <= z0 + 0 + 1, z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   insertionsort#1(z) -{ 0 }-> 0 :|: z = 0
   insertionsort#1(z) -{ 0 }-> 0 :|: z >= 0

Function symbols to be analyzed: {flatten}, {FLATTEN,FLATTEN#1}, {insertionsort}, {INSERTIONSORT,INSERTIONSORT#1}, {FLATTENSORT}
Previous analysis results are:
  APPEND#1: runtime: O(n^1) [4*z], size: O(1) [0]
  APPEND: runtime: O(n^1) [1 + 4*z], size: O(1) [1]
  #cklt: runtime: O(1) [0], size: O(1) [2]
  #compare: runtime: O(1) [0], size: O(1) [3]
  #COMPARE: runtime: O(1) [0], size: O(n^1) [z + z']
  append#1: runtime: O(1) [0], size: O(n^1) [z + z']
  append: runtime: O(1) [0], size: O(n^1) [z + z']
  #less: runtime: O(1) [0], size: O(1) [2]
  insert#2: runtime: O(1) [0], size: O(n^1) [2 + z' + z'' + z3]
  insert: runtime: O(1) [0], size: O(n^1) [1 + z + z']
  insert#1: runtime: O(1) [0], size: O(n^1) [1 + z + z']
  #LESS: runtime: O(1) [1], size: O(n^1) [1 + z + z']
  flatten#1: runtime: O(1) [0], size: O(n^1) [1 + z]
  insertionsort#1: runtime: O(1) [0], size: O(n^1) [z]
  INSERT#1: runtime: O(n^1) [7 + 4*z], size: O(1) [0]
  INSERT#2: runtime: O(n^1) [9 + 4*z3], size: O(1) [2]
  INSERT: runtime: O(n^1) [8 + 4*z'], size: O(1) [1]

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(101) ResultPropagationProof (UPPER BOUND(ID))
Applied inner abstraction using the recently inferred runtime/size bounds where possible.
----------------------------------------

(102)
Obligation:
Complexity RNTS consisting of the following rules:

   #COMPARE(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   #COMPARE(z, z') -{ 0 }-> 1 + s19 :|: s19 >= 0, s19 <= z' - 1 + (z - 1), z' - 1 >= 0, z - 1 >= 0
   #COMPARE(z, z') -{ 0 }-> 1 + s20 :|: s20 >= 0, s20 <= z - 1 + (z' - 1), z' - 1 >= 0, z - 1 >= 0
   #LESS(z, z') -{ 1 }-> 1 + s18 :|: s18 >= 0, s18 <= z + z', z' >= 0, z >= 0
   #cklt(z) -{ 0 }-> 2 :|: z = 3
   #cklt(z) -{ 0 }-> 1 :|: z = 1
   #cklt(z) -{ 0 }-> 1 :|: z = 2
   #cklt(z) -{ 0 }-> 0 :|: z >= 0
   #compare(z, z') -{ 0 }-> s8 :|: s8 >= 0, s8 <= 3, z' - 1 >= 0, z - 1 >= 0
   #compare(z, z') -{ 0 }-> s9 :|: s9 >= 0, s9 <= 3, z' - 1 >= 0, z - 1 >= 0
   #compare(z, z') -{ 0 }-> 3 :|: z' - 1 >= 0, z = 0
   #compare(z, z') -{ 0 }-> 3 :|: z - 1 >= 0, z' = 0
   #compare(z, z') -{ 0 }-> 3 :|: z' - 1 >= 0, z - 1 >= 0
   #compare(z, z') -{ 0 }-> 2 :|: z' - 1 >= 0, z = 0
   #compare(z, z') -{ 0 }-> 2 :|: z - 1 >= 0, z' = 0
   #compare(z, z') -{ 0 }-> 2 :|: z' - 1 >= 0, z - 1 >= 0
   #compare(z, z') -{ 0 }-> 1 :|: z = 0, z' = 0
   #compare(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   #less(z, z') -{ 0 }-> s13 :|: s12 >= 0, s12 <= 3, s13 >= 0, s13 <= 2, z' - 1 >= 0, z - 1 >= 0
   #less(z, z') -{ 0 }-> s15 :|: s14 >= 0, s14 <= 3, s15 >= 0, s15 <= 2, z - 1 >= 0, z' - 1 >= 0
   #less(z, z') -{ 0 }-> 2 :|: z' - 1 >= 0, z = 0, 3 = 3
   #less(z, z') -{ 0 }-> 2 :|: z - 1 >= 0, z' = 0, 3 = 3
   #less(z, z') -{ 0 }-> 2 :|: z - 1 >= 0, z' - 1 >= 0, 3 = 3
   #less(z, z') -{ 0 }-> 1 :|: z = 0, z' = 0, 1 = 1
   #less(z, z') -{ 0 }-> 1 :|: z' - 1 >= 0, z = 0, 2 = 2
   #less(z, z') -{ 0 }-> 1 :|: z - 1 >= 0, z' = 0, 2 = 2
   #less(z, z') -{ 0 }-> 1 :|: z' - 1 >= 0, z - 1 >= 0, 2 = 2
   #less(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   #less(z, z') -{ 0 }-> 0 :|: z = 0, z' = 0, v0 >= 0, 1 = v0
   #less(z, z') -{ 0 }-> 0 :|: z' - 1 >= 0, z = 0, v0 >= 0, 2 = v0
   #less(z, z') -{ 0 }-> 0 :|: z' - 1 >= 0, z = 0, v0 >= 0, 3 = v0
   #less(z, z') -{ 0 }-> 0 :|: z - 1 >= 0, z' = 0, v0 >= 0, 3 = v0
   #less(z, z') -{ 0 }-> 0 :|: z - 1 >= 0, z' - 1 >= 0, v0 >= 0, 3 = v0
   #less(z, z') -{ 0 }-> 0 :|: z - 1 >= 0, z' = 0, v0 >= 0, 2 = v0
   #less(z, z') -{ 0 }-> 0 :|: z' - 1 >= 0, z - 1 >= 0, v0 >= 0, 2 = v0
   #less(z, z') -{ 0 }-> 0 :|: z' >= 0, z >= 0, v0 >= 0, 0 = v0
   APPEND(z, z') -{ 1 + 4*z }-> 1 + s :|: s >= 0, s <= 0, z' >= 0, z >= 0
   APPEND#1(z, z') -{ 2 + 4*z1 }-> 1 + s' :|: s' >= 0, s' <= 1, z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z' >= 0
   FLATTEN(z) -{ 1 }-> 1 + FLATTEN#1(z) :|: z >= 0
   FLATTEN#1(z) -{ 3 + 4*z0 }-> 1 + s103 + s105 + FLATTEN(z1) :|: s101 >= 0, s101 <= z2 + 1, s102 >= 0, s102 <= 0 + s101, s103 >= 0, s103 <= 1, s104 >= 0, s104 <= z2 + 1, s105 >= 0, s105 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*z0 }-> 1 + s108 + s2 + FLATTEN(z1) :|: s106 >= 0, s106 <= z2 + 1, s107 >= 0, s107 <= 0 + s106, s108 >= 0, s108 <= 1, s2 >= 0, s2 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*s120 + 4*z0 }-> 1 + s119 + s122 + FLATTEN(z2) :|: s116 >= 0, s116 <= z1 + 1, s117 >= 0, s117 <= z2 + 1, s118 >= 0, s118 <= s116 + s117, s119 >= 0, s119 <= 1, s120 >= 0, s120 <= z1 + 1, s121 >= 0, s121 <= z2 + 1, s122 >= 0, s122 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*s127 + 4*z0 }-> 1 + s126 + s128 + FLATTEN(z2) :|: s123 >= 0, s123 <= z1 + 1, s124 >= 0, s124 <= z2 + 1, s125 >= 0, s125 <= s123 + s124, s126 >= 0, s126 <= 1, s127 >= 0, s127 <= z1 + 1, s128 >= 0, s128 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*z0 }-> 1 + s132 + s134 + FLATTEN(z2) :|: s129 >= 0, s129 <= z1 + 1, s130 >= 0, s130 <= z2 + 1, s131 >= 0, s131 <= s129 + s130, s132 >= 0, s132 <= 1, s133 >= 0, s133 <= z2 + 1, s134 >= 0, s134 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*z0 }-> 1 + s138 + s4 + FLATTEN(z2) :|: s135 >= 0, s135 <= z1 + 1, s136 >= 0, s136 <= z2 + 1, s137 >= 0, s137 <= s135 + s136, s138 >= 0, s138 <= 1, s4 >= 0, s4 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*s142 + 4*z0 }-> 1 + s141 + s144 + FLATTEN(z2) :|: s139 >= 0, s139 <= z1 + 1, s140 >= 0, s140 <= s139 + 0, s141 >= 0, s141 <= 1, s142 >= 0, s142 <= z1 + 1, s143 >= 0, s143 <= z2 + 1, s144 >= 0, s144 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*s148 + 4*z0 }-> 1 + s147 + s149 + FLATTEN(z2) :|: s145 >= 0, s145 <= z1 + 1, s146 >= 0, s146 <= s145 + 0, s147 >= 0, s147 <= 1, s148 >= 0, s148 <= z1 + 1, s149 >= 0, s149 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*z0 }-> 1 + s152 + s154 + FLATTEN(z2) :|: s150 >= 0, s150 <= z1 + 1, s151 >= 0, s151 <= s150 + 0, s152 >= 0, s152 <= 1, s153 >= 0, s153 <= z2 + 1, s154 >= 0, s154 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*z0 }-> 1 + s157 + s5 + FLATTEN(z2) :|: s155 >= 0, s155 <= z1 + 1, s156 >= 0, s156 <= s155 + 0, s157 >= 0, s157 <= 1, s5 >= 0, s5 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*s161 + 4*z0 }-> 1 + s160 + s163 + FLATTEN(z2) :|: s158 >= 0, s158 <= z2 + 1, s159 >= 0, s159 <= 0 + s158, s160 >= 0, s160 <= 1, s161 >= 0, s161 <= z1 + 1, s162 >= 0, s162 <= z2 + 1, s163 >= 0, s163 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*s167 + 4*z0 }-> 1 + s166 + s168 + FLATTEN(z2) :|: s164 >= 0, s164 <= z2 + 1, s165 >= 0, s165 <= 0 + s164, s166 >= 0, s166 <= 1, s167 >= 0, s167 <= z1 + 1, s168 >= 0, s168 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*z0 }-> 1 + s171 + s173 + FLATTEN(z2) :|: s169 >= 0, s169 <= z2 + 1, s170 >= 0, s170 <= 0 + s169, s171 >= 0, s171 <= 1, s172 >= 0, s172 <= z2 + 1, s173 >= 0, s173 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*z0 }-> 1 + s176 + s6 + FLATTEN(z2) :|: s174 >= 0, s174 <= z2 + 1, s175 >= 0, s175 <= 0 + s174, s176 >= 0, s176 <= 1, s6 >= 0, s6 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*s109 + 4*z0 }-> 1 + s22 + s111 + FLATTEN(z1) :|: s109 >= 0, s109 <= z1 + 1, s110 >= 0, s110 <= z2 + 1, s111 >= 0, s111 <= 1, s21 >= 0, s21 <= 0 + 0, s22 >= 0, s22 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*s112 + 4*z0 }-> 1 + s24 + s113 + FLATTEN(z1) :|: s112 >= 0, s112 <= z1 + 1, s113 >= 0, s113 <= 1, s23 >= 0, s23 <= 0 + 0, s24 >= 0, s24 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*z0 }-> 1 + s26 + s115 + FLATTEN(z1) :|: s114 >= 0, s114 <= z2 + 1, s115 >= 0, s115 <= 1, s25 >= 0, s25 <= 0 + 0, s26 >= 0, s26 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*z0 }-> 1 + s28 + s3 + FLATTEN(z1) :|: s27 >= 0, s27 <= 0 + 0, s28 >= 0, s28 <= 1, s3 >= 0, s3 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*s177 + 4*z0 }-> 1 + s30 + s179 + FLATTEN(z2) :|: s177 >= 0, s177 <= z1 + 1, s178 >= 0, s178 <= z2 + 1, s179 >= 0, s179 <= 1, s29 >= 0, s29 <= 0 + 0, s30 >= 0, s30 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*s180 + 4*z0 }-> 1 + s32 + s181 + FLATTEN(z2) :|: s180 >= 0, s180 <= z1 + 1, s181 >= 0, s181 <= 1, s31 >= 0, s31 <= 0 + 0, s32 >= 0, s32 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*z0 }-> 1 + s34 + s183 + FLATTEN(z2) :|: s182 >= 0, s182 <= z2 + 1, s183 >= 0, s183 <= 1, s33 >= 0, s33 <= 0 + 0, s34 >= 0, s34 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*z0 }-> 1 + s36 + s7 + FLATTEN(z2) :|: s35 >= 0, s35 <= 0 + 0, s36 >= 0, s36 <= 1, s7 >= 0, s7 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*s52 + 4*z0 }-> 1 + s51 + s54 + FLATTEN(z1) :|: s48 >= 0, s48 <= z1 + 1, s49 >= 0, s49 <= z2 + 1, s50 >= 0, s50 <= s48 + s49, s51 >= 0, s51 <= 1, s52 >= 0, s52 <= z1 + 1, s53 >= 0, s53 <= z2 + 1, s54 >= 0, s54 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*s59 + 4*z0 }-> 1 + s58 + s60 + FLATTEN(z1) :|: s55 >= 0, s55 <= z1 + 1, s56 >= 0, s56 <= z2 + 1, s57 >= 0, s57 <= s55 + s56, s58 >= 0, s58 <= 1, s59 >= 0, s59 <= z1 + 1, s60 >= 0, s60 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*z0 }-> 1 + s64 + s66 + FLATTEN(z1) :|: s61 >= 0, s61 <= z1 + 1, s62 >= 0, s62 <= z2 + 1, s63 >= 0, s63 <= s61 + s62, s64 >= 0, s64 <= 1, s65 >= 0, s65 <= z2 + 1, s66 >= 0, s66 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*z0 }-> 1 + s70 + s'' + FLATTEN(z1) :|: s67 >= 0, s67 <= z1 + 1, s68 >= 0, s68 <= z2 + 1, s69 >= 0, s69 <= s67 + s68, s70 >= 0, s70 <= 1, s'' >= 0, s'' <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*s74 + 4*z0 }-> 1 + s73 + s76 + FLATTEN(z1) :|: s71 >= 0, s71 <= z1 + 1, s72 >= 0, s72 <= s71 + 0, s73 >= 0, s73 <= 1, s74 >= 0, s74 <= z1 + 1, s75 >= 0, s75 <= z2 + 1, s76 >= 0, s76 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*s80 + 4*z0 }-> 1 + s79 + s81 + FLATTEN(z1) :|: s77 >= 0, s77 <= z1 + 1, s78 >= 0, s78 <= s77 + 0, s79 >= 0, s79 <= 1, s80 >= 0, s80 <= z1 + 1, s81 >= 0, s81 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*z0 }-> 1 + s84 + s86 + FLATTEN(z1) :|: s82 >= 0, s82 <= z1 + 1, s83 >= 0, s83 <= s82 + 0, s84 >= 0, s84 <= 1, s85 >= 0, s85 <= z2 + 1, s86 >= 0, s86 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*z0 }-> 1 + s89 + s1 + FLATTEN(z1) :|: s87 >= 0, s87 <= z1 + 1, s88 >= 0, s88 <= s87 + 0, s89 >= 0, s89 <= 1, s1 >= 0, s1 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*s93 + 4*z0 }-> 1 + s92 + s95 + FLATTEN(z1) :|: s90 >= 0, s90 <= z2 + 1, s91 >= 0, s91 <= 0 + s90, s92 >= 0, s92 <= 1, s93 >= 0, s93 <= z1 + 1, s94 >= 0, s94 <= z2 + 1, s95 >= 0, s95 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*s99 + 4*z0 }-> 1 + s98 + s100 + FLATTEN(z1) :|: s96 >= 0, s96 <= z2 + 1, s97 >= 0, s97 <= 0 + s96, s98 >= 0, s98 <= 1, s99 >= 0, s99 <= z1 + 1, s100 >= 0, s100 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTENSORT(z) -{ 0 }-> 0 :|: z >= 0
   FLATTENSORT(z) -{ 0 }-> 1 + INSERTIONSORT(s184) :|: s184 >= 0, s184 <= z + 1, z >= 0
   FLATTENSORT(z) -{ 0 }-> 1 + INSERTIONSORT(0) :|: z >= 0
   INSERT(z, z') -{ 8 + 4*z' }-> 1 + s200 :|: s200 >= 0, s200 <= 0, z' >= 0, z >= 0
   INSERT#1(z, z') -{ 11 + 4*z1 }-> 1 + s201 + s46 :|: s201 >= 0, s201 <= 2, s46 >= 0, s46 <= z0 + z' + 1, z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z' >= 0
   INSERT#1(z, z') -{ 11 + 4*z1 }-> 1 + s205 + s47 :|: s205 >= 0, s205 <= 2, s47 >= 0, s47 <= z0 + z' + 1, s10 >= 0, s10 <= 3, s11 >= 0, s11 <= 2, z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z' >= 0
   INSERT#2(z, z', z'', z3) -{ 9 + 4*z3 }-> 1 + s202 :|: s202 >= 0, s202 <= 1, z = 2, z'' >= 0, z' >= 0, z3 >= 0
   INSERTIONSORT(z) -{ 1 }-> 1 + INSERTIONSORT#1(z) :|: z >= 0
   INSERTIONSORT#1(z) -{ 9 + 4*s196 }-> 1 + s203 + INSERTIONSORT(z1) :|: s203 >= 0, s203 <= 1, s196 >= 0, s196 <= z1, z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   INSERTIONSORT#1(z) -{ 9 }-> 1 + s204 + INSERTIONSORT(z1) :|: s204 >= 0, s204 <= 1, z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   append(z, z') -{ 0 }-> s37 :|: s37 >= 0, s37 <= z + z', z' >= 0, z >= 0
   append(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   append#1(z, z') -{ 0 }-> z' :|: z' >= 0, z = 0
   append#1(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   append#1(z, z') -{ 0 }-> 1 + z0 + s40 :|: s40 >= 0, s40 <= z1 + z', z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z' >= 0
   flatten(z) -{ 0 }-> s185 :|: s185 >= 0, s185 <= z + 1, z >= 0
   flatten(z) -{ 0 }-> 0 :|: z >= 0
   flatten#1(z) -{ 0 }-> s189 :|: s186 >= 0, s186 <= z1 + 1, s187 >= 0, s187 <= z2 + 1, s188 >= 0, s188 <= s186 + s187, s189 >= 0, s189 <= z0 + s188, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   flatten#1(z) -{ 0 }-> s192 :|: s190 >= 0, s190 <= z1 + 1, s191 >= 0, s191 <= s190 + 0, s192 >= 0, s192 <= z0 + s191, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   flatten#1(z) -{ 0 }-> s195 :|: s193 >= 0, s193 <= z2 + 1, s194 >= 0, s194 <= 0 + s193, s195 >= 0, s195 <= z0 + s194, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   flatten#1(z) -{ 0 }-> s39 :|: s38 >= 0, s38 <= 0 + 0, s39 >= 0, s39 <= z0 + s38, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   flatten#1(z) -{ 0 }-> 0 :|: z = 0
   flatten#1(z) -{ 0 }-> 0 :|: z >= 0
   insert(z, z') -{ 0 }-> s42 :|: s42 >= 0, s42 <= z' + z + 1, z' >= 0, z >= 0
   insert(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   insert#1(z, z') -{ 0 }-> s43 :|: s43 >= 0, s43 <= z' + z0 + z1 + 2, z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z' >= 0
   insert#1(z, z') -{ 0 }-> s45 :|: s45 >= 0, s45 <= z' + z0 + z1 + 2, s16 >= 0, s16 <= 3, s17 >= 0, s17 <= 2, z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z' >= 0
   insert#1(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   insert#1(z, z') -{ 0 }-> 1 + z' + 0 :|: z' >= 0, z = 0
   insert#2(z, z', z'', z3) -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0, z3 >= 0
   insert#2(z, z', z'', z3) -{ 0 }-> 1 + z' + (1 + z'' + z3) :|: z'' >= 0, z = 1, z' >= 0, z3 >= 0
   insert#2(z, z', z'', z3) -{ 0 }-> 1 + z'' + s44 :|: s44 >= 0, s44 <= z' + z3 + 1, z = 2, z'' >= 0, z' >= 0, z3 >= 0
   insertionsort(z) -{ 0 }-> s197 :|: s197 >= 0, s197 <= z, z >= 0
   insertionsort(z) -{ 0 }-> 0 :|: z >= 0
   insertionsort#1(z) -{ 0 }-> s199 :|: s198 >= 0, s198 <= z1, s199 >= 0, s199 <= z0 + s198 + 1, z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   insertionsort#1(z) -{ 0 }-> s41 :|: s41 >= 0, s41 <= z0 + 0 + 1, z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   insertionsort#1(z) -{ 0 }-> 0 :|: z = 0
   insertionsort#1(z) -{ 0 }-> 0 :|: z >= 0

Function symbols to be analyzed: {flatten}, {FLATTEN,FLATTEN#1}, {insertionsort}, {INSERTIONSORT,INSERTIONSORT#1}, {FLATTENSORT}
Previous analysis results are:
  APPEND#1: runtime: O(n^1) [4*z], size: O(1) [0]
  APPEND: runtime: O(n^1) [1 + 4*z], size: O(1) [1]
  #cklt: runtime: O(1) [0], size: O(1) [2]
  #compare: runtime: O(1) [0], size: O(1) [3]
  #COMPARE: runtime: O(1) [0], size: O(n^1) [z + z']
  append#1: runtime: O(1) [0], size: O(n^1) [z + z']
  append: runtime: O(1) [0], size: O(n^1) [z + z']
  #less: runtime: O(1) [0], size: O(1) [2]
  insert#2: runtime: O(1) [0], size: O(n^1) [2 + z' + z'' + z3]
  insert: runtime: O(1) [0], size: O(n^1) [1 + z + z']
  insert#1: runtime: O(1) [0], size: O(n^1) [1 + z + z']
  #LESS: runtime: O(1) [1], size: O(n^1) [1 + z + z']
  flatten#1: runtime: O(1) [0], size: O(n^1) [1 + z]
  insertionsort#1: runtime: O(1) [0], size: O(n^1) [z]
  INSERT#1: runtime: O(n^1) [7 + 4*z], size: O(1) [0]
  INSERT#2: runtime: O(n^1) [9 + 4*z3], size: O(1) [2]
  INSERT: runtime: O(n^1) [8 + 4*z'], size: O(1) [1]

----------------------------------------

(103) IntTrsBoundProof (UPPER BOUND(ID))

Computed SIZE bound using CoFloCo for: flatten
after applying outer abstraction to obtain an ITS,
resulting in: O(n^1) with polynomial bound: 1 + z

----------------------------------------

(104)
Obligation:
Complexity RNTS consisting of the following rules:

   #COMPARE(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   #COMPARE(z, z') -{ 0 }-> 1 + s19 :|: s19 >= 0, s19 <= z' - 1 + (z - 1), z' - 1 >= 0, z - 1 >= 0
   #COMPARE(z, z') -{ 0 }-> 1 + s20 :|: s20 >= 0, s20 <= z - 1 + (z' - 1), z' - 1 >= 0, z - 1 >= 0
   #LESS(z, z') -{ 1 }-> 1 + s18 :|: s18 >= 0, s18 <= z + z', z' >= 0, z >= 0
   #cklt(z) -{ 0 }-> 2 :|: z = 3
   #cklt(z) -{ 0 }-> 1 :|: z = 1
   #cklt(z) -{ 0 }-> 1 :|: z = 2
   #cklt(z) -{ 0 }-> 0 :|: z >= 0
   #compare(z, z') -{ 0 }-> s8 :|: s8 >= 0, s8 <= 3, z' - 1 >= 0, z - 1 >= 0
   #compare(z, z') -{ 0 }-> s9 :|: s9 >= 0, s9 <= 3, z' - 1 >= 0, z - 1 >= 0
   #compare(z, z') -{ 0 }-> 3 :|: z' - 1 >= 0, z = 0
   #compare(z, z') -{ 0 }-> 3 :|: z - 1 >= 0, z' = 0
   #compare(z, z') -{ 0 }-> 3 :|: z' - 1 >= 0, z - 1 >= 0
   #compare(z, z') -{ 0 }-> 2 :|: z' - 1 >= 0, z = 0
   #compare(z, z') -{ 0 }-> 2 :|: z - 1 >= 0, z' = 0
   #compare(z, z') -{ 0 }-> 2 :|: z' - 1 >= 0, z - 1 >= 0
   #compare(z, z') -{ 0 }-> 1 :|: z = 0, z' = 0
   #compare(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   #less(z, z') -{ 0 }-> s13 :|: s12 >= 0, s12 <= 3, s13 >= 0, s13 <= 2, z' - 1 >= 0, z - 1 >= 0
   #less(z, z') -{ 0 }-> s15 :|: s14 >= 0, s14 <= 3, s15 >= 0, s15 <= 2, z - 1 >= 0, z' - 1 >= 0
   #less(z, z') -{ 0 }-> 2 :|: z' - 1 >= 0, z = 0, 3 = 3
   #less(z, z') -{ 0 }-> 2 :|: z - 1 >= 0, z' = 0, 3 = 3
   #less(z, z') -{ 0 }-> 2 :|: z - 1 >= 0, z' - 1 >= 0, 3 = 3
   #less(z, z') -{ 0 }-> 1 :|: z = 0, z' = 0, 1 = 1
   #less(z, z') -{ 0 }-> 1 :|: z' - 1 >= 0, z = 0, 2 = 2
   #less(z, z') -{ 0 }-> 1 :|: z - 1 >= 0, z' = 0, 2 = 2
   #less(z, z') -{ 0 }-> 1 :|: z' - 1 >= 0, z - 1 >= 0, 2 = 2
   #less(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   #less(z, z') -{ 0 }-> 0 :|: z = 0, z' = 0, v0 >= 0, 1 = v0
   #less(z, z') -{ 0 }-> 0 :|: z' - 1 >= 0, z = 0, v0 >= 0, 2 = v0
   #less(z, z') -{ 0 }-> 0 :|: z' - 1 >= 0, z = 0, v0 >= 0, 3 = v0
   #less(z, z') -{ 0 }-> 0 :|: z - 1 >= 0, z' = 0, v0 >= 0, 3 = v0
   #less(z, z') -{ 0 }-> 0 :|: z - 1 >= 0, z' - 1 >= 0, v0 >= 0, 3 = v0
   #less(z, z') -{ 0 }-> 0 :|: z - 1 >= 0, z' = 0, v0 >= 0, 2 = v0
   #less(z, z') -{ 0 }-> 0 :|: z' - 1 >= 0, z - 1 >= 0, v0 >= 0, 2 = v0
   #less(z, z') -{ 0 }-> 0 :|: z' >= 0, z >= 0, v0 >= 0, 0 = v0
   APPEND(z, z') -{ 1 + 4*z }-> 1 + s :|: s >= 0, s <= 0, z' >= 0, z >= 0
   APPEND#1(z, z') -{ 2 + 4*z1 }-> 1 + s' :|: s' >= 0, s' <= 1, z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z' >= 0
   FLATTEN(z) -{ 1 }-> 1 + FLATTEN#1(z) :|: z >= 0
   FLATTEN#1(z) -{ 3 + 4*z0 }-> 1 + s103 + s105 + FLATTEN(z1) :|: s101 >= 0, s101 <= z2 + 1, s102 >= 0, s102 <= 0 + s101, s103 >= 0, s103 <= 1, s104 >= 0, s104 <= z2 + 1, s105 >= 0, s105 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*z0 }-> 1 + s108 + s2 + FLATTEN(z1) :|: s106 >= 0, s106 <= z2 + 1, s107 >= 0, s107 <= 0 + s106, s108 >= 0, s108 <= 1, s2 >= 0, s2 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*s120 + 4*z0 }-> 1 + s119 + s122 + FLATTEN(z2) :|: s116 >= 0, s116 <= z1 + 1, s117 >= 0, s117 <= z2 + 1, s118 >= 0, s118 <= s116 + s117, s119 >= 0, s119 <= 1, s120 >= 0, s120 <= z1 + 1, s121 >= 0, s121 <= z2 + 1, s122 >= 0, s122 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*s127 + 4*z0 }-> 1 + s126 + s128 + FLATTEN(z2) :|: s123 >= 0, s123 <= z1 + 1, s124 >= 0, s124 <= z2 + 1, s125 >= 0, s125 <= s123 + s124, s126 >= 0, s126 <= 1, s127 >= 0, s127 <= z1 + 1, s128 >= 0, s128 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*z0 }-> 1 + s132 + s134 + FLATTEN(z2) :|: s129 >= 0, s129 <= z1 + 1, s130 >= 0, s130 <= z2 + 1, s131 >= 0, s131 <= s129 + s130, s132 >= 0, s132 <= 1, s133 >= 0, s133 <= z2 + 1, s134 >= 0, s134 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*z0 }-> 1 + s138 + s4 + FLATTEN(z2) :|: s135 >= 0, s135 <= z1 + 1, s136 >= 0, s136 <= z2 + 1, s137 >= 0, s137 <= s135 + s136, s138 >= 0, s138 <= 1, s4 >= 0, s4 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*s142 + 4*z0 }-> 1 + s141 + s144 + FLATTEN(z2) :|: s139 >= 0, s139 <= z1 + 1, s140 >= 0, s140 <= s139 + 0, s141 >= 0, s141 <= 1, s142 >= 0, s142 <= z1 + 1, s143 >= 0, s143 <= z2 + 1, s144 >= 0, s144 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*s148 + 4*z0 }-> 1 + s147 + s149 + FLATTEN(z2) :|: s145 >= 0, s145 <= z1 + 1, s146 >= 0, s146 <= s145 + 0, s147 >= 0, s147 <= 1, s148 >= 0, s148 <= z1 + 1, s149 >= 0, s149 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*z0 }-> 1 + s152 + s154 + FLATTEN(z2) :|: s150 >= 0, s150 <= z1 + 1, s151 >= 0, s151 <= s150 + 0, s152 >= 0, s152 <= 1, s153 >= 0, s153 <= z2 + 1, s154 >= 0, s154 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*z0 }-> 1 + s157 + s5 + FLATTEN(z2) :|: s155 >= 0, s155 <= z1 + 1, s156 >= 0, s156 <= s155 + 0, s157 >= 0, s157 <= 1, s5 >= 0, s5 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*s161 + 4*z0 }-> 1 + s160 + s163 + FLATTEN(z2) :|: s158 >= 0, s158 <= z2 + 1, s159 >= 0, s159 <= 0 + s158, s160 >= 0, s160 <= 1, s161 >= 0, s161 <= z1 + 1, s162 >= 0, s162 <= z2 + 1, s163 >= 0, s163 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*s167 + 4*z0 }-> 1 + s166 + s168 + FLATTEN(z2) :|: s164 >= 0, s164 <= z2 + 1, s165 >= 0, s165 <= 0 + s164, s166 >= 0, s166 <= 1, s167 >= 0, s167 <= z1 + 1, s168 >= 0, s168 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*z0 }-> 1 + s171 + s173 + FLATTEN(z2) :|: s169 >= 0, s169 <= z2 + 1, s170 >= 0, s170 <= 0 + s169, s171 >= 0, s171 <= 1, s172 >= 0, s172 <= z2 + 1, s173 >= 0, s173 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*z0 }-> 1 + s176 + s6 + FLATTEN(z2) :|: s174 >= 0, s174 <= z2 + 1, s175 >= 0, s175 <= 0 + s174, s176 >= 0, s176 <= 1, s6 >= 0, s6 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*s109 + 4*z0 }-> 1 + s22 + s111 + FLATTEN(z1) :|: s109 >= 0, s109 <= z1 + 1, s110 >= 0, s110 <= z2 + 1, s111 >= 0, s111 <= 1, s21 >= 0, s21 <= 0 + 0, s22 >= 0, s22 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*s112 + 4*z0 }-> 1 + s24 + s113 + FLATTEN(z1) :|: s112 >= 0, s112 <= z1 + 1, s113 >= 0, s113 <= 1, s23 >= 0, s23 <= 0 + 0, s24 >= 0, s24 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*z0 }-> 1 + s26 + s115 + FLATTEN(z1) :|: s114 >= 0, s114 <= z2 + 1, s115 >= 0, s115 <= 1, s25 >= 0, s25 <= 0 + 0, s26 >= 0, s26 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*z0 }-> 1 + s28 + s3 + FLATTEN(z1) :|: s27 >= 0, s27 <= 0 + 0, s28 >= 0, s28 <= 1, s3 >= 0, s3 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*s177 + 4*z0 }-> 1 + s30 + s179 + FLATTEN(z2) :|: s177 >= 0, s177 <= z1 + 1, s178 >= 0, s178 <= z2 + 1, s179 >= 0, s179 <= 1, s29 >= 0, s29 <= 0 + 0, s30 >= 0, s30 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*s180 + 4*z0 }-> 1 + s32 + s181 + FLATTEN(z2) :|: s180 >= 0, s180 <= z1 + 1, s181 >= 0, s181 <= 1, s31 >= 0, s31 <= 0 + 0, s32 >= 0, s32 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*z0 }-> 1 + s34 + s183 + FLATTEN(z2) :|: s182 >= 0, s182 <= z2 + 1, s183 >= 0, s183 <= 1, s33 >= 0, s33 <= 0 + 0, s34 >= 0, s34 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*z0 }-> 1 + s36 + s7 + FLATTEN(z2) :|: s35 >= 0, s35 <= 0 + 0, s36 >= 0, s36 <= 1, s7 >= 0, s7 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*s52 + 4*z0 }-> 1 + s51 + s54 + FLATTEN(z1) :|: s48 >= 0, s48 <= z1 + 1, s49 >= 0, s49 <= z2 + 1, s50 >= 0, s50 <= s48 + s49, s51 >= 0, s51 <= 1, s52 >= 0, s52 <= z1 + 1, s53 >= 0, s53 <= z2 + 1, s54 >= 0, s54 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*s59 + 4*z0 }-> 1 + s58 + s60 + FLATTEN(z1) :|: s55 >= 0, s55 <= z1 + 1, s56 >= 0, s56 <= z2 + 1, s57 >= 0, s57 <= s55 + s56, s58 >= 0, s58 <= 1, s59 >= 0, s59 <= z1 + 1, s60 >= 0, s60 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*z0 }-> 1 + s64 + s66 + FLATTEN(z1) :|: s61 >= 0, s61 <= z1 + 1, s62 >= 0, s62 <= z2 + 1, s63 >= 0, s63 <= s61 + s62, s64 >= 0, s64 <= 1, s65 >= 0, s65 <= z2 + 1, s66 >= 0, s66 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*z0 }-> 1 + s70 + s'' + FLATTEN(z1) :|: s67 >= 0, s67 <= z1 + 1, s68 >= 0, s68 <= z2 + 1, s69 >= 0, s69 <= s67 + s68, s70 >= 0, s70 <= 1, s'' >= 0, s'' <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*s74 + 4*z0 }-> 1 + s73 + s76 + FLATTEN(z1) :|: s71 >= 0, s71 <= z1 + 1, s72 >= 0, s72 <= s71 + 0, s73 >= 0, s73 <= 1, s74 >= 0, s74 <= z1 + 1, s75 >= 0, s75 <= z2 + 1, s76 >= 0, s76 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*s80 + 4*z0 }-> 1 + s79 + s81 + FLATTEN(z1) :|: s77 >= 0, s77 <= z1 + 1, s78 >= 0, s78 <= s77 + 0, s79 >= 0, s79 <= 1, s80 >= 0, s80 <= z1 + 1, s81 >= 0, s81 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*z0 }-> 1 + s84 + s86 + FLATTEN(z1) :|: s82 >= 0, s82 <= z1 + 1, s83 >= 0, s83 <= s82 + 0, s84 >= 0, s84 <= 1, s85 >= 0, s85 <= z2 + 1, s86 >= 0, s86 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*z0 }-> 1 + s89 + s1 + FLATTEN(z1) :|: s87 >= 0, s87 <= z1 + 1, s88 >= 0, s88 <= s87 + 0, s89 >= 0, s89 <= 1, s1 >= 0, s1 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*s93 + 4*z0 }-> 1 + s92 + s95 + FLATTEN(z1) :|: s90 >= 0, s90 <= z2 + 1, s91 >= 0, s91 <= 0 + s90, s92 >= 0, s92 <= 1, s93 >= 0, s93 <= z1 + 1, s94 >= 0, s94 <= z2 + 1, s95 >= 0, s95 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*s99 + 4*z0 }-> 1 + s98 + s100 + FLATTEN(z1) :|: s96 >= 0, s96 <= z2 + 1, s97 >= 0, s97 <= 0 + s96, s98 >= 0, s98 <= 1, s99 >= 0, s99 <= z1 + 1, s100 >= 0, s100 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTENSORT(z) -{ 0 }-> 0 :|: z >= 0
   FLATTENSORT(z) -{ 0 }-> 1 + INSERTIONSORT(s184) :|: s184 >= 0, s184 <= z + 1, z >= 0
   FLATTENSORT(z) -{ 0 }-> 1 + INSERTIONSORT(0) :|: z >= 0
   INSERT(z, z') -{ 8 + 4*z' }-> 1 + s200 :|: s200 >= 0, s200 <= 0, z' >= 0, z >= 0
   INSERT#1(z, z') -{ 11 + 4*z1 }-> 1 + s201 + s46 :|: s201 >= 0, s201 <= 2, s46 >= 0, s46 <= z0 + z' + 1, z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z' >= 0
   INSERT#1(z, z') -{ 11 + 4*z1 }-> 1 + s205 + s47 :|: s205 >= 0, s205 <= 2, s47 >= 0, s47 <= z0 + z' + 1, s10 >= 0, s10 <= 3, s11 >= 0, s11 <= 2, z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z' >= 0
   INSERT#2(z, z', z'', z3) -{ 9 + 4*z3 }-> 1 + s202 :|: s202 >= 0, s202 <= 1, z = 2, z'' >= 0, z' >= 0, z3 >= 0
   INSERTIONSORT(z) -{ 1 }-> 1 + INSERTIONSORT#1(z) :|: z >= 0
   INSERTIONSORT#1(z) -{ 9 + 4*s196 }-> 1 + s203 + INSERTIONSORT(z1) :|: s203 >= 0, s203 <= 1, s196 >= 0, s196 <= z1, z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   INSERTIONSORT#1(z) -{ 9 }-> 1 + s204 + INSERTIONSORT(z1) :|: s204 >= 0, s204 <= 1, z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   append(z, z') -{ 0 }-> s37 :|: s37 >= 0, s37 <= z + z', z' >= 0, z >= 0
   append(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   append#1(z, z') -{ 0 }-> z' :|: z' >= 0, z = 0
   append#1(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   append#1(z, z') -{ 0 }-> 1 + z0 + s40 :|: s40 >= 0, s40 <= z1 + z', z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z' >= 0
   flatten(z) -{ 0 }-> s185 :|: s185 >= 0, s185 <= z + 1, z >= 0
   flatten(z) -{ 0 }-> 0 :|: z >= 0
   flatten#1(z) -{ 0 }-> s189 :|: s186 >= 0, s186 <= z1 + 1, s187 >= 0, s187 <= z2 + 1, s188 >= 0, s188 <= s186 + s187, s189 >= 0, s189 <= z0 + s188, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   flatten#1(z) -{ 0 }-> s192 :|: s190 >= 0, s190 <= z1 + 1, s191 >= 0, s191 <= s190 + 0, s192 >= 0, s192 <= z0 + s191, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   flatten#1(z) -{ 0 }-> s195 :|: s193 >= 0, s193 <= z2 + 1, s194 >= 0, s194 <= 0 + s193, s195 >= 0, s195 <= z0 + s194, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   flatten#1(z) -{ 0 }-> s39 :|: s38 >= 0, s38 <= 0 + 0, s39 >= 0, s39 <= z0 + s38, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   flatten#1(z) -{ 0 }-> 0 :|: z = 0
   flatten#1(z) -{ 0 }-> 0 :|: z >= 0
   insert(z, z') -{ 0 }-> s42 :|: s42 >= 0, s42 <= z' + z + 1, z' >= 0, z >= 0
   insert(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   insert#1(z, z') -{ 0 }-> s43 :|: s43 >= 0, s43 <= z' + z0 + z1 + 2, z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z' >= 0
   insert#1(z, z') -{ 0 }-> s45 :|: s45 >= 0, s45 <= z' + z0 + z1 + 2, s16 >= 0, s16 <= 3, s17 >= 0, s17 <= 2, z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z' >= 0
   insert#1(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   insert#1(z, z') -{ 0 }-> 1 + z' + 0 :|: z' >= 0, z = 0
   insert#2(z, z', z'', z3) -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0, z3 >= 0
   insert#2(z, z', z'', z3) -{ 0 }-> 1 + z' + (1 + z'' + z3) :|: z'' >= 0, z = 1, z' >= 0, z3 >= 0
   insert#2(z, z', z'', z3) -{ 0 }-> 1 + z'' + s44 :|: s44 >= 0, s44 <= z' + z3 + 1, z = 2, z'' >= 0, z' >= 0, z3 >= 0
   insertionsort(z) -{ 0 }-> s197 :|: s197 >= 0, s197 <= z, z >= 0
   insertionsort(z) -{ 0 }-> 0 :|: z >= 0
   insertionsort#1(z) -{ 0 }-> s199 :|: s198 >= 0, s198 <= z1, s199 >= 0, s199 <= z0 + s198 + 1, z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   insertionsort#1(z) -{ 0 }-> s41 :|: s41 >= 0, s41 <= z0 + 0 + 1, z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   insertionsort#1(z) -{ 0 }-> 0 :|: z = 0
   insertionsort#1(z) -{ 0 }-> 0 :|: z >= 0

Function symbols to be analyzed: {flatten}, {FLATTEN,FLATTEN#1}, {insertionsort}, {INSERTIONSORT,INSERTIONSORT#1}, {FLATTENSORT}
Previous analysis results are:
  APPEND#1: runtime: O(n^1) [4*z], size: O(1) [0]
  APPEND: runtime: O(n^1) [1 + 4*z], size: O(1) [1]
  #cklt: runtime: O(1) [0], size: O(1) [2]
  #compare: runtime: O(1) [0], size: O(1) [3]
  #COMPARE: runtime: O(1) [0], size: O(n^1) [z + z']
  append#1: runtime: O(1) [0], size: O(n^1) [z + z']
  append: runtime: O(1) [0], size: O(n^1) [z + z']
  #less: runtime: O(1) [0], size: O(1) [2]
  insert#2: runtime: O(1) [0], size: O(n^1) [2 + z' + z'' + z3]
  insert: runtime: O(1) [0], size: O(n^1) [1 + z + z']
  insert#1: runtime: O(1) [0], size: O(n^1) [1 + z + z']
  #LESS: runtime: O(1) [1], size: O(n^1) [1 + z + z']
  flatten#1: runtime: O(1) [0], size: O(n^1) [1 + z]
  insertionsort#1: runtime: O(1) [0], size: O(n^1) [z]
  INSERT#1: runtime: O(n^1) [7 + 4*z], size: O(1) [0]
  INSERT#2: runtime: O(n^1) [9 + 4*z3], size: O(1) [2]
  INSERT: runtime: O(n^1) [8 + 4*z'], size: O(1) [1]
  flatten: runtime: ?, size: O(n^1) [1 + z]

----------------------------------------

(105) IntTrsBoundProof (UPPER BOUND(ID))

Computed RUNTIME bound using CoFloCo for: flatten
after applying outer abstraction to obtain an ITS,
resulting in: O(1) with polynomial bound: 0

----------------------------------------

(106)
Obligation:
Complexity RNTS consisting of the following rules:

   #COMPARE(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   #COMPARE(z, z') -{ 0 }-> 1 + s19 :|: s19 >= 0, s19 <= z' - 1 + (z - 1), z' - 1 >= 0, z - 1 >= 0
   #COMPARE(z, z') -{ 0 }-> 1 + s20 :|: s20 >= 0, s20 <= z - 1 + (z' - 1), z' - 1 >= 0, z - 1 >= 0
   #LESS(z, z') -{ 1 }-> 1 + s18 :|: s18 >= 0, s18 <= z + z', z' >= 0, z >= 0
   #cklt(z) -{ 0 }-> 2 :|: z = 3
   #cklt(z) -{ 0 }-> 1 :|: z = 1
   #cklt(z) -{ 0 }-> 1 :|: z = 2
   #cklt(z) -{ 0 }-> 0 :|: z >= 0
   #compare(z, z') -{ 0 }-> s8 :|: s8 >= 0, s8 <= 3, z' - 1 >= 0, z - 1 >= 0
   #compare(z, z') -{ 0 }-> s9 :|: s9 >= 0, s9 <= 3, z' - 1 >= 0, z - 1 >= 0
   #compare(z, z') -{ 0 }-> 3 :|: z' - 1 >= 0, z = 0
   #compare(z, z') -{ 0 }-> 3 :|: z - 1 >= 0, z' = 0
   #compare(z, z') -{ 0 }-> 3 :|: z' - 1 >= 0, z - 1 >= 0
   #compare(z, z') -{ 0 }-> 2 :|: z' - 1 >= 0, z = 0
   #compare(z, z') -{ 0 }-> 2 :|: z - 1 >= 0, z' = 0
   #compare(z, z') -{ 0 }-> 2 :|: z' - 1 >= 0, z - 1 >= 0
   #compare(z, z') -{ 0 }-> 1 :|: z = 0, z' = 0
   #compare(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   #less(z, z') -{ 0 }-> s13 :|: s12 >= 0, s12 <= 3, s13 >= 0, s13 <= 2, z' - 1 >= 0, z - 1 >= 0
   #less(z, z') -{ 0 }-> s15 :|: s14 >= 0, s14 <= 3, s15 >= 0, s15 <= 2, z - 1 >= 0, z' - 1 >= 0
   #less(z, z') -{ 0 }-> 2 :|: z' - 1 >= 0, z = 0, 3 = 3
   #less(z, z') -{ 0 }-> 2 :|: z - 1 >= 0, z' = 0, 3 = 3
   #less(z, z') -{ 0 }-> 2 :|: z - 1 >= 0, z' - 1 >= 0, 3 = 3
   #less(z, z') -{ 0 }-> 1 :|: z = 0, z' = 0, 1 = 1
   #less(z, z') -{ 0 }-> 1 :|: z' - 1 >= 0, z = 0, 2 = 2
   #less(z, z') -{ 0 }-> 1 :|: z - 1 >= 0, z' = 0, 2 = 2
   #less(z, z') -{ 0 }-> 1 :|: z' - 1 >= 0, z - 1 >= 0, 2 = 2
   #less(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   #less(z, z') -{ 0 }-> 0 :|: z = 0, z' = 0, v0 >= 0, 1 = v0
   #less(z, z') -{ 0 }-> 0 :|: z' - 1 >= 0, z = 0, v0 >= 0, 2 = v0
   #less(z, z') -{ 0 }-> 0 :|: z' - 1 >= 0, z = 0, v0 >= 0, 3 = v0
   #less(z, z') -{ 0 }-> 0 :|: z - 1 >= 0, z' = 0, v0 >= 0, 3 = v0
   #less(z, z') -{ 0 }-> 0 :|: z - 1 >= 0, z' - 1 >= 0, v0 >= 0, 3 = v0
   #less(z, z') -{ 0 }-> 0 :|: z - 1 >= 0, z' = 0, v0 >= 0, 2 = v0
   #less(z, z') -{ 0 }-> 0 :|: z' - 1 >= 0, z - 1 >= 0, v0 >= 0, 2 = v0
   #less(z, z') -{ 0 }-> 0 :|: z' >= 0, z >= 0, v0 >= 0, 0 = v0
   APPEND(z, z') -{ 1 + 4*z }-> 1 + s :|: s >= 0, s <= 0, z' >= 0, z >= 0
   APPEND#1(z, z') -{ 2 + 4*z1 }-> 1 + s' :|: s' >= 0, s' <= 1, z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z' >= 0
   FLATTEN(z) -{ 1 }-> 1 + FLATTEN#1(z) :|: z >= 0
   FLATTEN#1(z) -{ 3 + 4*z0 }-> 1 + s103 + s105 + FLATTEN(z1) :|: s101 >= 0, s101 <= z2 + 1, s102 >= 0, s102 <= 0 + s101, s103 >= 0, s103 <= 1, s104 >= 0, s104 <= z2 + 1, s105 >= 0, s105 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*z0 }-> 1 + s108 + s2 + FLATTEN(z1) :|: s106 >= 0, s106 <= z2 + 1, s107 >= 0, s107 <= 0 + s106, s108 >= 0, s108 <= 1, s2 >= 0, s2 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*s120 + 4*z0 }-> 1 + s119 + s122 + FLATTEN(z2) :|: s116 >= 0, s116 <= z1 + 1, s117 >= 0, s117 <= z2 + 1, s118 >= 0, s118 <= s116 + s117, s119 >= 0, s119 <= 1, s120 >= 0, s120 <= z1 + 1, s121 >= 0, s121 <= z2 + 1, s122 >= 0, s122 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*s127 + 4*z0 }-> 1 + s126 + s128 + FLATTEN(z2) :|: s123 >= 0, s123 <= z1 + 1, s124 >= 0, s124 <= z2 + 1, s125 >= 0, s125 <= s123 + s124, s126 >= 0, s126 <= 1, s127 >= 0, s127 <= z1 + 1, s128 >= 0, s128 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*z0 }-> 1 + s132 + s134 + FLATTEN(z2) :|: s129 >= 0, s129 <= z1 + 1, s130 >= 0, s130 <= z2 + 1, s131 >= 0, s131 <= s129 + s130, s132 >= 0, s132 <= 1, s133 >= 0, s133 <= z2 + 1, s134 >= 0, s134 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*z0 }-> 1 + s138 + s4 + FLATTEN(z2) :|: s135 >= 0, s135 <= z1 + 1, s136 >= 0, s136 <= z2 + 1, s137 >= 0, s137 <= s135 + s136, s138 >= 0, s138 <= 1, s4 >= 0, s4 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*s142 + 4*z0 }-> 1 + s141 + s144 + FLATTEN(z2) :|: s139 >= 0, s139 <= z1 + 1, s140 >= 0, s140 <= s139 + 0, s141 >= 0, s141 <= 1, s142 >= 0, s142 <= z1 + 1, s143 >= 0, s143 <= z2 + 1, s144 >= 0, s144 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*s148 + 4*z0 }-> 1 + s147 + s149 + FLATTEN(z2) :|: s145 >= 0, s145 <= z1 + 1, s146 >= 0, s146 <= s145 + 0, s147 >= 0, s147 <= 1, s148 >= 0, s148 <= z1 + 1, s149 >= 0, s149 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*z0 }-> 1 + s152 + s154 + FLATTEN(z2) :|: s150 >= 0, s150 <= z1 + 1, s151 >= 0, s151 <= s150 + 0, s152 >= 0, s152 <= 1, s153 >= 0, s153 <= z2 + 1, s154 >= 0, s154 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*z0 }-> 1 + s157 + s5 + FLATTEN(z2) :|: s155 >= 0, s155 <= z1 + 1, s156 >= 0, s156 <= s155 + 0, s157 >= 0, s157 <= 1, s5 >= 0, s5 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*s161 + 4*z0 }-> 1 + s160 + s163 + FLATTEN(z2) :|: s158 >= 0, s158 <= z2 + 1, s159 >= 0, s159 <= 0 + s158, s160 >= 0, s160 <= 1, s161 >= 0, s161 <= z1 + 1, s162 >= 0, s162 <= z2 + 1, s163 >= 0, s163 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*s167 + 4*z0 }-> 1 + s166 + s168 + FLATTEN(z2) :|: s164 >= 0, s164 <= z2 + 1, s165 >= 0, s165 <= 0 + s164, s166 >= 0, s166 <= 1, s167 >= 0, s167 <= z1 + 1, s168 >= 0, s168 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*z0 }-> 1 + s171 + s173 + FLATTEN(z2) :|: s169 >= 0, s169 <= z2 + 1, s170 >= 0, s170 <= 0 + s169, s171 >= 0, s171 <= 1, s172 >= 0, s172 <= z2 + 1, s173 >= 0, s173 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*z0 }-> 1 + s176 + s6 + FLATTEN(z2) :|: s174 >= 0, s174 <= z2 + 1, s175 >= 0, s175 <= 0 + s174, s176 >= 0, s176 <= 1, s6 >= 0, s6 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*s109 + 4*z0 }-> 1 + s22 + s111 + FLATTEN(z1) :|: s109 >= 0, s109 <= z1 + 1, s110 >= 0, s110 <= z2 + 1, s111 >= 0, s111 <= 1, s21 >= 0, s21 <= 0 + 0, s22 >= 0, s22 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*s112 + 4*z0 }-> 1 + s24 + s113 + FLATTEN(z1) :|: s112 >= 0, s112 <= z1 + 1, s113 >= 0, s113 <= 1, s23 >= 0, s23 <= 0 + 0, s24 >= 0, s24 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*z0 }-> 1 + s26 + s115 + FLATTEN(z1) :|: s114 >= 0, s114 <= z2 + 1, s115 >= 0, s115 <= 1, s25 >= 0, s25 <= 0 + 0, s26 >= 0, s26 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*z0 }-> 1 + s28 + s3 + FLATTEN(z1) :|: s27 >= 0, s27 <= 0 + 0, s28 >= 0, s28 <= 1, s3 >= 0, s3 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*s177 + 4*z0 }-> 1 + s30 + s179 + FLATTEN(z2) :|: s177 >= 0, s177 <= z1 + 1, s178 >= 0, s178 <= z2 + 1, s179 >= 0, s179 <= 1, s29 >= 0, s29 <= 0 + 0, s30 >= 0, s30 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*s180 + 4*z0 }-> 1 + s32 + s181 + FLATTEN(z2) :|: s180 >= 0, s180 <= z1 + 1, s181 >= 0, s181 <= 1, s31 >= 0, s31 <= 0 + 0, s32 >= 0, s32 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*z0 }-> 1 + s34 + s183 + FLATTEN(z2) :|: s182 >= 0, s182 <= z2 + 1, s183 >= 0, s183 <= 1, s33 >= 0, s33 <= 0 + 0, s34 >= 0, s34 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*z0 }-> 1 + s36 + s7 + FLATTEN(z2) :|: s35 >= 0, s35 <= 0 + 0, s36 >= 0, s36 <= 1, s7 >= 0, s7 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*s52 + 4*z0 }-> 1 + s51 + s54 + FLATTEN(z1) :|: s48 >= 0, s48 <= z1 + 1, s49 >= 0, s49 <= z2 + 1, s50 >= 0, s50 <= s48 + s49, s51 >= 0, s51 <= 1, s52 >= 0, s52 <= z1 + 1, s53 >= 0, s53 <= z2 + 1, s54 >= 0, s54 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*s59 + 4*z0 }-> 1 + s58 + s60 + FLATTEN(z1) :|: s55 >= 0, s55 <= z1 + 1, s56 >= 0, s56 <= z2 + 1, s57 >= 0, s57 <= s55 + s56, s58 >= 0, s58 <= 1, s59 >= 0, s59 <= z1 + 1, s60 >= 0, s60 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*z0 }-> 1 + s64 + s66 + FLATTEN(z1) :|: s61 >= 0, s61 <= z1 + 1, s62 >= 0, s62 <= z2 + 1, s63 >= 0, s63 <= s61 + s62, s64 >= 0, s64 <= 1, s65 >= 0, s65 <= z2 + 1, s66 >= 0, s66 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*z0 }-> 1 + s70 + s'' + FLATTEN(z1) :|: s67 >= 0, s67 <= z1 + 1, s68 >= 0, s68 <= z2 + 1, s69 >= 0, s69 <= s67 + s68, s70 >= 0, s70 <= 1, s'' >= 0, s'' <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*s74 + 4*z0 }-> 1 + s73 + s76 + FLATTEN(z1) :|: s71 >= 0, s71 <= z1 + 1, s72 >= 0, s72 <= s71 + 0, s73 >= 0, s73 <= 1, s74 >= 0, s74 <= z1 + 1, s75 >= 0, s75 <= z2 + 1, s76 >= 0, s76 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*s80 + 4*z0 }-> 1 + s79 + s81 + FLATTEN(z1) :|: s77 >= 0, s77 <= z1 + 1, s78 >= 0, s78 <= s77 + 0, s79 >= 0, s79 <= 1, s80 >= 0, s80 <= z1 + 1, s81 >= 0, s81 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*z0 }-> 1 + s84 + s86 + FLATTEN(z1) :|: s82 >= 0, s82 <= z1 + 1, s83 >= 0, s83 <= s82 + 0, s84 >= 0, s84 <= 1, s85 >= 0, s85 <= z2 + 1, s86 >= 0, s86 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*z0 }-> 1 + s89 + s1 + FLATTEN(z1) :|: s87 >= 0, s87 <= z1 + 1, s88 >= 0, s88 <= s87 + 0, s89 >= 0, s89 <= 1, s1 >= 0, s1 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*s93 + 4*z0 }-> 1 + s92 + s95 + FLATTEN(z1) :|: s90 >= 0, s90 <= z2 + 1, s91 >= 0, s91 <= 0 + s90, s92 >= 0, s92 <= 1, s93 >= 0, s93 <= z1 + 1, s94 >= 0, s94 <= z2 + 1, s95 >= 0, s95 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*s99 + 4*z0 }-> 1 + s98 + s100 + FLATTEN(z1) :|: s96 >= 0, s96 <= z2 + 1, s97 >= 0, s97 <= 0 + s96, s98 >= 0, s98 <= 1, s99 >= 0, s99 <= z1 + 1, s100 >= 0, s100 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTENSORT(z) -{ 0 }-> 0 :|: z >= 0
   FLATTENSORT(z) -{ 0 }-> 1 + INSERTIONSORT(s184) :|: s184 >= 0, s184 <= z + 1, z >= 0
   FLATTENSORT(z) -{ 0 }-> 1 + INSERTIONSORT(0) :|: z >= 0
   INSERT(z, z') -{ 8 + 4*z' }-> 1 + s200 :|: s200 >= 0, s200 <= 0, z' >= 0, z >= 0
   INSERT#1(z, z') -{ 11 + 4*z1 }-> 1 + s201 + s46 :|: s201 >= 0, s201 <= 2, s46 >= 0, s46 <= z0 + z' + 1, z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z' >= 0
   INSERT#1(z, z') -{ 11 + 4*z1 }-> 1 + s205 + s47 :|: s205 >= 0, s205 <= 2, s47 >= 0, s47 <= z0 + z' + 1, s10 >= 0, s10 <= 3, s11 >= 0, s11 <= 2, z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z' >= 0
   INSERT#2(z, z', z'', z3) -{ 9 + 4*z3 }-> 1 + s202 :|: s202 >= 0, s202 <= 1, z = 2, z'' >= 0, z' >= 0, z3 >= 0
   INSERTIONSORT(z) -{ 1 }-> 1 + INSERTIONSORT#1(z) :|: z >= 0
   INSERTIONSORT#1(z) -{ 9 + 4*s196 }-> 1 + s203 + INSERTIONSORT(z1) :|: s203 >= 0, s203 <= 1, s196 >= 0, s196 <= z1, z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   INSERTIONSORT#1(z) -{ 9 }-> 1 + s204 + INSERTIONSORT(z1) :|: s204 >= 0, s204 <= 1, z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   append(z, z') -{ 0 }-> s37 :|: s37 >= 0, s37 <= z + z', z' >= 0, z >= 0
   append(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   append#1(z, z') -{ 0 }-> z' :|: z' >= 0, z = 0
   append#1(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   append#1(z, z') -{ 0 }-> 1 + z0 + s40 :|: s40 >= 0, s40 <= z1 + z', z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z' >= 0
   flatten(z) -{ 0 }-> s185 :|: s185 >= 0, s185 <= z + 1, z >= 0
   flatten(z) -{ 0 }-> 0 :|: z >= 0
   flatten#1(z) -{ 0 }-> s189 :|: s186 >= 0, s186 <= z1 + 1, s187 >= 0, s187 <= z2 + 1, s188 >= 0, s188 <= s186 + s187, s189 >= 0, s189 <= z0 + s188, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   flatten#1(z) -{ 0 }-> s192 :|: s190 >= 0, s190 <= z1 + 1, s191 >= 0, s191 <= s190 + 0, s192 >= 0, s192 <= z0 + s191, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   flatten#1(z) -{ 0 }-> s195 :|: s193 >= 0, s193 <= z2 + 1, s194 >= 0, s194 <= 0 + s193, s195 >= 0, s195 <= z0 + s194, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   flatten#1(z) -{ 0 }-> s39 :|: s38 >= 0, s38 <= 0 + 0, s39 >= 0, s39 <= z0 + s38, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   flatten#1(z) -{ 0 }-> 0 :|: z = 0
   flatten#1(z) -{ 0 }-> 0 :|: z >= 0
   insert(z, z') -{ 0 }-> s42 :|: s42 >= 0, s42 <= z' + z + 1, z' >= 0, z >= 0
   insert(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   insert#1(z, z') -{ 0 }-> s43 :|: s43 >= 0, s43 <= z' + z0 + z1 + 2, z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z' >= 0
   insert#1(z, z') -{ 0 }-> s45 :|: s45 >= 0, s45 <= z' + z0 + z1 + 2, s16 >= 0, s16 <= 3, s17 >= 0, s17 <= 2, z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z' >= 0
   insert#1(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   insert#1(z, z') -{ 0 }-> 1 + z' + 0 :|: z' >= 0, z = 0
   insert#2(z, z', z'', z3) -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0, z3 >= 0
   insert#2(z, z', z'', z3) -{ 0 }-> 1 + z' + (1 + z'' + z3) :|: z'' >= 0, z = 1, z' >= 0, z3 >= 0
   insert#2(z, z', z'', z3) -{ 0 }-> 1 + z'' + s44 :|: s44 >= 0, s44 <= z' + z3 + 1, z = 2, z'' >= 0, z' >= 0, z3 >= 0
   insertionsort(z) -{ 0 }-> s197 :|: s197 >= 0, s197 <= z, z >= 0
   insertionsort(z) -{ 0 }-> 0 :|: z >= 0
   insertionsort#1(z) -{ 0 }-> s199 :|: s198 >= 0, s198 <= z1, s199 >= 0, s199 <= z0 + s198 + 1, z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   insertionsort#1(z) -{ 0 }-> s41 :|: s41 >= 0, s41 <= z0 + 0 + 1, z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   insertionsort#1(z) -{ 0 }-> 0 :|: z = 0
   insertionsort#1(z) -{ 0 }-> 0 :|: z >= 0

Function symbols to be analyzed: {FLATTEN,FLATTEN#1}, {insertionsort}, {INSERTIONSORT,INSERTIONSORT#1}, {FLATTENSORT}
Previous analysis results are:
  APPEND#1: runtime: O(n^1) [4*z], size: O(1) [0]
  APPEND: runtime: O(n^1) [1 + 4*z], size: O(1) [1]
  #cklt: runtime: O(1) [0], size: O(1) [2]
  #compare: runtime: O(1) [0], size: O(1) [3]
  #COMPARE: runtime: O(1) [0], size: O(n^1) [z + z']
  append#1: runtime: O(1) [0], size: O(n^1) [z + z']
  append: runtime: O(1) [0], size: O(n^1) [z + z']
  #less: runtime: O(1) [0], size: O(1) [2]
  insert#2: runtime: O(1) [0], size: O(n^1) [2 + z' + z'' + z3]
  insert: runtime: O(1) [0], size: O(n^1) [1 + z + z']
  insert#1: runtime: O(1) [0], size: O(n^1) [1 + z + z']
  #LESS: runtime: O(1) [1], size: O(n^1) [1 + z + z']
  flatten#1: runtime: O(1) [0], size: O(n^1) [1 + z]
  insertionsort#1: runtime: O(1) [0], size: O(n^1) [z]
  INSERT#1: runtime: O(n^1) [7 + 4*z], size: O(1) [0]
  INSERT#2: runtime: O(n^1) [9 + 4*z3], size: O(1) [2]
  INSERT: runtime: O(n^1) [8 + 4*z'], size: O(1) [1]
  flatten: runtime: O(1) [0], size: O(n^1) [1 + z]

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(107) ResultPropagationProof (UPPER BOUND(ID))
Applied inner abstraction using the recently inferred runtime/size bounds where possible.
----------------------------------------

(108)
Obligation:
Complexity RNTS consisting of the following rules:

   #COMPARE(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   #COMPARE(z, z') -{ 0 }-> 1 + s19 :|: s19 >= 0, s19 <= z' - 1 + (z - 1), z' - 1 >= 0, z - 1 >= 0
   #COMPARE(z, z') -{ 0 }-> 1 + s20 :|: s20 >= 0, s20 <= z - 1 + (z' - 1), z' - 1 >= 0, z - 1 >= 0
   #LESS(z, z') -{ 1 }-> 1 + s18 :|: s18 >= 0, s18 <= z + z', z' >= 0, z >= 0
   #cklt(z) -{ 0 }-> 2 :|: z = 3
   #cklt(z) -{ 0 }-> 1 :|: z = 1
   #cklt(z) -{ 0 }-> 1 :|: z = 2
   #cklt(z) -{ 0 }-> 0 :|: z >= 0
   #compare(z, z') -{ 0 }-> s8 :|: s8 >= 0, s8 <= 3, z' - 1 >= 0, z - 1 >= 0
   #compare(z, z') -{ 0 }-> s9 :|: s9 >= 0, s9 <= 3, z' - 1 >= 0, z - 1 >= 0
   #compare(z, z') -{ 0 }-> 3 :|: z' - 1 >= 0, z = 0
   #compare(z, z') -{ 0 }-> 3 :|: z - 1 >= 0, z' = 0
   #compare(z, z') -{ 0 }-> 3 :|: z' - 1 >= 0, z - 1 >= 0
   #compare(z, z') -{ 0 }-> 2 :|: z' - 1 >= 0, z = 0
   #compare(z, z') -{ 0 }-> 2 :|: z - 1 >= 0, z' = 0
   #compare(z, z') -{ 0 }-> 2 :|: z' - 1 >= 0, z - 1 >= 0
   #compare(z, z') -{ 0 }-> 1 :|: z = 0, z' = 0
   #compare(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   #less(z, z') -{ 0 }-> s13 :|: s12 >= 0, s12 <= 3, s13 >= 0, s13 <= 2, z' - 1 >= 0, z - 1 >= 0
   #less(z, z') -{ 0 }-> s15 :|: s14 >= 0, s14 <= 3, s15 >= 0, s15 <= 2, z - 1 >= 0, z' - 1 >= 0
   #less(z, z') -{ 0 }-> 2 :|: z' - 1 >= 0, z = 0, 3 = 3
   #less(z, z') -{ 0 }-> 2 :|: z - 1 >= 0, z' = 0, 3 = 3
   #less(z, z') -{ 0 }-> 2 :|: z - 1 >= 0, z' - 1 >= 0, 3 = 3
   #less(z, z') -{ 0 }-> 1 :|: z = 0, z' = 0, 1 = 1
   #less(z, z') -{ 0 }-> 1 :|: z' - 1 >= 0, z = 0, 2 = 2
   #less(z, z') -{ 0 }-> 1 :|: z - 1 >= 0, z' = 0, 2 = 2
   #less(z, z') -{ 0 }-> 1 :|: z' - 1 >= 0, z - 1 >= 0, 2 = 2
   #less(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   #less(z, z') -{ 0 }-> 0 :|: z = 0, z' = 0, v0 >= 0, 1 = v0
   #less(z, z') -{ 0 }-> 0 :|: z' - 1 >= 0, z = 0, v0 >= 0, 2 = v0
   #less(z, z') -{ 0 }-> 0 :|: z' - 1 >= 0, z = 0, v0 >= 0, 3 = v0
   #less(z, z') -{ 0 }-> 0 :|: z - 1 >= 0, z' = 0, v0 >= 0, 3 = v0
   #less(z, z') -{ 0 }-> 0 :|: z - 1 >= 0, z' - 1 >= 0, v0 >= 0, 3 = v0
   #less(z, z') -{ 0 }-> 0 :|: z - 1 >= 0, z' = 0, v0 >= 0, 2 = v0
   #less(z, z') -{ 0 }-> 0 :|: z' - 1 >= 0, z - 1 >= 0, v0 >= 0, 2 = v0
   #less(z, z') -{ 0 }-> 0 :|: z' >= 0, z >= 0, v0 >= 0, 0 = v0
   APPEND(z, z') -{ 1 + 4*z }-> 1 + s :|: s >= 0, s <= 0, z' >= 0, z >= 0
   APPEND#1(z, z') -{ 2 + 4*z1 }-> 1 + s' :|: s' >= 0, s' <= 1, z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z' >= 0
   FLATTEN(z) -{ 1 }-> 1 + FLATTEN#1(z) :|: z >= 0
   FLATTEN#1(z) -{ 3 + 4*z0 }-> 1 + s103 + s105 + FLATTEN(z1) :|: s101 >= 0, s101 <= z2 + 1, s102 >= 0, s102 <= 0 + s101, s103 >= 0, s103 <= 1, s104 >= 0, s104 <= z2 + 1, s105 >= 0, s105 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*z0 }-> 1 + s108 + s2 + FLATTEN(z1) :|: s106 >= 0, s106 <= z2 + 1, s107 >= 0, s107 <= 0 + s106, s108 >= 0, s108 <= 1, s2 >= 0, s2 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*s120 + 4*z0 }-> 1 + s119 + s122 + FLATTEN(z2) :|: s116 >= 0, s116 <= z1 + 1, s117 >= 0, s117 <= z2 + 1, s118 >= 0, s118 <= s116 + s117, s119 >= 0, s119 <= 1, s120 >= 0, s120 <= z1 + 1, s121 >= 0, s121 <= z2 + 1, s122 >= 0, s122 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*s127 + 4*z0 }-> 1 + s126 + s128 + FLATTEN(z2) :|: s123 >= 0, s123 <= z1 + 1, s124 >= 0, s124 <= z2 + 1, s125 >= 0, s125 <= s123 + s124, s126 >= 0, s126 <= 1, s127 >= 0, s127 <= z1 + 1, s128 >= 0, s128 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*z0 }-> 1 + s132 + s134 + FLATTEN(z2) :|: s129 >= 0, s129 <= z1 + 1, s130 >= 0, s130 <= z2 + 1, s131 >= 0, s131 <= s129 + s130, s132 >= 0, s132 <= 1, s133 >= 0, s133 <= z2 + 1, s134 >= 0, s134 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*z0 }-> 1 + s138 + s4 + FLATTEN(z2) :|: s135 >= 0, s135 <= z1 + 1, s136 >= 0, s136 <= z2 + 1, s137 >= 0, s137 <= s135 + s136, s138 >= 0, s138 <= 1, s4 >= 0, s4 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*s142 + 4*z0 }-> 1 + s141 + s144 + FLATTEN(z2) :|: s139 >= 0, s139 <= z1 + 1, s140 >= 0, s140 <= s139 + 0, s141 >= 0, s141 <= 1, s142 >= 0, s142 <= z1 + 1, s143 >= 0, s143 <= z2 + 1, s144 >= 0, s144 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*s148 + 4*z0 }-> 1 + s147 + s149 + FLATTEN(z2) :|: s145 >= 0, s145 <= z1 + 1, s146 >= 0, s146 <= s145 + 0, s147 >= 0, s147 <= 1, s148 >= 0, s148 <= z1 + 1, s149 >= 0, s149 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*z0 }-> 1 + s152 + s154 + FLATTEN(z2) :|: s150 >= 0, s150 <= z1 + 1, s151 >= 0, s151 <= s150 + 0, s152 >= 0, s152 <= 1, s153 >= 0, s153 <= z2 + 1, s154 >= 0, s154 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*z0 }-> 1 + s157 + s5 + FLATTEN(z2) :|: s155 >= 0, s155 <= z1 + 1, s156 >= 0, s156 <= s155 + 0, s157 >= 0, s157 <= 1, s5 >= 0, s5 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*s161 + 4*z0 }-> 1 + s160 + s163 + FLATTEN(z2) :|: s158 >= 0, s158 <= z2 + 1, s159 >= 0, s159 <= 0 + s158, s160 >= 0, s160 <= 1, s161 >= 0, s161 <= z1 + 1, s162 >= 0, s162 <= z2 + 1, s163 >= 0, s163 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*s167 + 4*z0 }-> 1 + s166 + s168 + FLATTEN(z2) :|: s164 >= 0, s164 <= z2 + 1, s165 >= 0, s165 <= 0 + s164, s166 >= 0, s166 <= 1, s167 >= 0, s167 <= z1 + 1, s168 >= 0, s168 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*z0 }-> 1 + s171 + s173 + FLATTEN(z2) :|: s169 >= 0, s169 <= z2 + 1, s170 >= 0, s170 <= 0 + s169, s171 >= 0, s171 <= 1, s172 >= 0, s172 <= z2 + 1, s173 >= 0, s173 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*z0 }-> 1 + s176 + s6 + FLATTEN(z2) :|: s174 >= 0, s174 <= z2 + 1, s175 >= 0, s175 <= 0 + s174, s176 >= 0, s176 <= 1, s6 >= 0, s6 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*s109 + 4*z0 }-> 1 + s22 + s111 + FLATTEN(z1) :|: s109 >= 0, s109 <= z1 + 1, s110 >= 0, s110 <= z2 + 1, s111 >= 0, s111 <= 1, s21 >= 0, s21 <= 0 + 0, s22 >= 0, s22 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*s112 + 4*z0 }-> 1 + s24 + s113 + FLATTEN(z1) :|: s112 >= 0, s112 <= z1 + 1, s113 >= 0, s113 <= 1, s23 >= 0, s23 <= 0 + 0, s24 >= 0, s24 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*z0 }-> 1 + s26 + s115 + FLATTEN(z1) :|: s114 >= 0, s114 <= z2 + 1, s115 >= 0, s115 <= 1, s25 >= 0, s25 <= 0 + 0, s26 >= 0, s26 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*z0 }-> 1 + s28 + s3 + FLATTEN(z1) :|: s27 >= 0, s27 <= 0 + 0, s28 >= 0, s28 <= 1, s3 >= 0, s3 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*s177 + 4*z0 }-> 1 + s30 + s179 + FLATTEN(z2) :|: s177 >= 0, s177 <= z1 + 1, s178 >= 0, s178 <= z2 + 1, s179 >= 0, s179 <= 1, s29 >= 0, s29 <= 0 + 0, s30 >= 0, s30 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*s180 + 4*z0 }-> 1 + s32 + s181 + FLATTEN(z2) :|: s180 >= 0, s180 <= z1 + 1, s181 >= 0, s181 <= 1, s31 >= 0, s31 <= 0 + 0, s32 >= 0, s32 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*z0 }-> 1 + s34 + s183 + FLATTEN(z2) :|: s182 >= 0, s182 <= z2 + 1, s183 >= 0, s183 <= 1, s33 >= 0, s33 <= 0 + 0, s34 >= 0, s34 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*z0 }-> 1 + s36 + s7 + FLATTEN(z2) :|: s35 >= 0, s35 <= 0 + 0, s36 >= 0, s36 <= 1, s7 >= 0, s7 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*s52 + 4*z0 }-> 1 + s51 + s54 + FLATTEN(z1) :|: s48 >= 0, s48 <= z1 + 1, s49 >= 0, s49 <= z2 + 1, s50 >= 0, s50 <= s48 + s49, s51 >= 0, s51 <= 1, s52 >= 0, s52 <= z1 + 1, s53 >= 0, s53 <= z2 + 1, s54 >= 0, s54 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*s59 + 4*z0 }-> 1 + s58 + s60 + FLATTEN(z1) :|: s55 >= 0, s55 <= z1 + 1, s56 >= 0, s56 <= z2 + 1, s57 >= 0, s57 <= s55 + s56, s58 >= 0, s58 <= 1, s59 >= 0, s59 <= z1 + 1, s60 >= 0, s60 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*z0 }-> 1 + s64 + s66 + FLATTEN(z1) :|: s61 >= 0, s61 <= z1 + 1, s62 >= 0, s62 <= z2 + 1, s63 >= 0, s63 <= s61 + s62, s64 >= 0, s64 <= 1, s65 >= 0, s65 <= z2 + 1, s66 >= 0, s66 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*z0 }-> 1 + s70 + s'' + FLATTEN(z1) :|: s67 >= 0, s67 <= z1 + 1, s68 >= 0, s68 <= z2 + 1, s69 >= 0, s69 <= s67 + s68, s70 >= 0, s70 <= 1, s'' >= 0, s'' <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*s74 + 4*z0 }-> 1 + s73 + s76 + FLATTEN(z1) :|: s71 >= 0, s71 <= z1 + 1, s72 >= 0, s72 <= s71 + 0, s73 >= 0, s73 <= 1, s74 >= 0, s74 <= z1 + 1, s75 >= 0, s75 <= z2 + 1, s76 >= 0, s76 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*s80 + 4*z0 }-> 1 + s79 + s81 + FLATTEN(z1) :|: s77 >= 0, s77 <= z1 + 1, s78 >= 0, s78 <= s77 + 0, s79 >= 0, s79 <= 1, s80 >= 0, s80 <= z1 + 1, s81 >= 0, s81 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*z0 }-> 1 + s84 + s86 + FLATTEN(z1) :|: s82 >= 0, s82 <= z1 + 1, s83 >= 0, s83 <= s82 + 0, s84 >= 0, s84 <= 1, s85 >= 0, s85 <= z2 + 1, s86 >= 0, s86 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*z0 }-> 1 + s89 + s1 + FLATTEN(z1) :|: s87 >= 0, s87 <= z1 + 1, s88 >= 0, s88 <= s87 + 0, s89 >= 0, s89 <= 1, s1 >= 0, s1 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*s93 + 4*z0 }-> 1 + s92 + s95 + FLATTEN(z1) :|: s90 >= 0, s90 <= z2 + 1, s91 >= 0, s91 <= 0 + s90, s92 >= 0, s92 <= 1, s93 >= 0, s93 <= z1 + 1, s94 >= 0, s94 <= z2 + 1, s95 >= 0, s95 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*s99 + 4*z0 }-> 1 + s98 + s100 + FLATTEN(z1) :|: s96 >= 0, s96 <= z2 + 1, s97 >= 0, s97 <= 0 + s96, s98 >= 0, s98 <= 1, s99 >= 0, s99 <= z1 + 1, s100 >= 0, s100 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTENSORT(z) -{ 0 }-> 0 :|: z >= 0
   FLATTENSORT(z) -{ 0 }-> 1 + INSERTIONSORT(s184) :|: s184 >= 0, s184 <= z + 1, z >= 0
   FLATTENSORT(z) -{ 0 }-> 1 + INSERTIONSORT(0) :|: z >= 0
   INSERT(z, z') -{ 8 + 4*z' }-> 1 + s200 :|: s200 >= 0, s200 <= 0, z' >= 0, z >= 0
   INSERT#1(z, z') -{ 11 + 4*z1 }-> 1 + s201 + s46 :|: s201 >= 0, s201 <= 2, s46 >= 0, s46 <= z0 + z' + 1, z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z' >= 0
   INSERT#1(z, z') -{ 11 + 4*z1 }-> 1 + s205 + s47 :|: s205 >= 0, s205 <= 2, s47 >= 0, s47 <= z0 + z' + 1, s10 >= 0, s10 <= 3, s11 >= 0, s11 <= 2, z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z' >= 0
   INSERT#2(z, z', z'', z3) -{ 9 + 4*z3 }-> 1 + s202 :|: s202 >= 0, s202 <= 1, z = 2, z'' >= 0, z' >= 0, z3 >= 0
   INSERTIONSORT(z) -{ 1 }-> 1 + INSERTIONSORT#1(z) :|: z >= 0
   INSERTIONSORT#1(z) -{ 9 + 4*s196 }-> 1 + s203 + INSERTIONSORT(z1) :|: s203 >= 0, s203 <= 1, s196 >= 0, s196 <= z1, z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   INSERTIONSORT#1(z) -{ 9 }-> 1 + s204 + INSERTIONSORT(z1) :|: s204 >= 0, s204 <= 1, z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   append(z, z') -{ 0 }-> s37 :|: s37 >= 0, s37 <= z + z', z' >= 0, z >= 0
   append(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   append#1(z, z') -{ 0 }-> z' :|: z' >= 0, z = 0
   append#1(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   append#1(z, z') -{ 0 }-> 1 + z0 + s40 :|: s40 >= 0, s40 <= z1 + z', z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z' >= 0
   flatten(z) -{ 0 }-> s185 :|: s185 >= 0, s185 <= z + 1, z >= 0
   flatten(z) -{ 0 }-> 0 :|: z >= 0
   flatten#1(z) -{ 0 }-> s189 :|: s186 >= 0, s186 <= z1 + 1, s187 >= 0, s187 <= z2 + 1, s188 >= 0, s188 <= s186 + s187, s189 >= 0, s189 <= z0 + s188, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   flatten#1(z) -{ 0 }-> s192 :|: s190 >= 0, s190 <= z1 + 1, s191 >= 0, s191 <= s190 + 0, s192 >= 0, s192 <= z0 + s191, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   flatten#1(z) -{ 0 }-> s195 :|: s193 >= 0, s193 <= z2 + 1, s194 >= 0, s194 <= 0 + s193, s195 >= 0, s195 <= z0 + s194, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   flatten#1(z) -{ 0 }-> s39 :|: s38 >= 0, s38 <= 0 + 0, s39 >= 0, s39 <= z0 + s38, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   flatten#1(z) -{ 0 }-> 0 :|: z = 0
   flatten#1(z) -{ 0 }-> 0 :|: z >= 0
   insert(z, z') -{ 0 }-> s42 :|: s42 >= 0, s42 <= z' + z + 1, z' >= 0, z >= 0
   insert(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   insert#1(z, z') -{ 0 }-> s43 :|: s43 >= 0, s43 <= z' + z0 + z1 + 2, z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z' >= 0
   insert#1(z, z') -{ 0 }-> s45 :|: s45 >= 0, s45 <= z' + z0 + z1 + 2, s16 >= 0, s16 <= 3, s17 >= 0, s17 <= 2, z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z' >= 0
   insert#1(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   insert#1(z, z') -{ 0 }-> 1 + z' + 0 :|: z' >= 0, z = 0
   insert#2(z, z', z'', z3) -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0, z3 >= 0
   insert#2(z, z', z'', z3) -{ 0 }-> 1 + z' + (1 + z'' + z3) :|: z'' >= 0, z = 1, z' >= 0, z3 >= 0
   insert#2(z, z', z'', z3) -{ 0 }-> 1 + z'' + s44 :|: s44 >= 0, s44 <= z' + z3 + 1, z = 2, z'' >= 0, z' >= 0, z3 >= 0
   insertionsort(z) -{ 0 }-> s197 :|: s197 >= 0, s197 <= z, z >= 0
   insertionsort(z) -{ 0 }-> 0 :|: z >= 0
   insertionsort#1(z) -{ 0 }-> s199 :|: s198 >= 0, s198 <= z1, s199 >= 0, s199 <= z0 + s198 + 1, z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   insertionsort#1(z) -{ 0 }-> s41 :|: s41 >= 0, s41 <= z0 + 0 + 1, z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   insertionsort#1(z) -{ 0 }-> 0 :|: z = 0
   insertionsort#1(z) -{ 0 }-> 0 :|: z >= 0

Function symbols to be analyzed: {FLATTEN,FLATTEN#1}, {insertionsort}, {INSERTIONSORT,INSERTIONSORT#1}, {FLATTENSORT}
Previous analysis results are:
  APPEND#1: runtime: O(n^1) [4*z], size: O(1) [0]
  APPEND: runtime: O(n^1) [1 + 4*z], size: O(1) [1]
  #cklt: runtime: O(1) [0], size: O(1) [2]
  #compare: runtime: O(1) [0], size: O(1) [3]
  #COMPARE: runtime: O(1) [0], size: O(n^1) [z + z']
  append#1: runtime: O(1) [0], size: O(n^1) [z + z']
  append: runtime: O(1) [0], size: O(n^1) [z + z']
  #less: runtime: O(1) [0], size: O(1) [2]
  insert#2: runtime: O(1) [0], size: O(n^1) [2 + z' + z'' + z3]
  insert: runtime: O(1) [0], size: O(n^1) [1 + z + z']
  insert#1: runtime: O(1) [0], size: O(n^1) [1 + z + z']
  #LESS: runtime: O(1) [1], size: O(n^1) [1 + z + z']
  flatten#1: runtime: O(1) [0], size: O(n^1) [1 + z]
  insertionsort#1: runtime: O(1) [0], size: O(n^1) [z]
  INSERT#1: runtime: O(n^1) [7 + 4*z], size: O(1) [0]
  INSERT#2: runtime: O(n^1) [9 + 4*z3], size: O(1) [2]
  INSERT: runtime: O(n^1) [8 + 4*z'], size: O(1) [1]
  flatten: runtime: O(1) [0], size: O(n^1) [1 + z]

----------------------------------------

(109) IntTrsBoundProof (UPPER BOUND(ID))

Computed SIZE bound using CoFloCo for: FLATTEN
after applying outer abstraction to obtain an ITS,
resulting in: O(1) with polynomial bound: 0

Computed SIZE bound using CoFloCo for: FLATTEN#1
after applying outer abstraction to obtain an ITS,
resulting in: O(1) with polynomial bound: 3

----------------------------------------

(110)
Obligation:
Complexity RNTS consisting of the following rules:

   #COMPARE(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   #COMPARE(z, z') -{ 0 }-> 1 + s19 :|: s19 >= 0, s19 <= z' - 1 + (z - 1), z' - 1 >= 0, z - 1 >= 0
   #COMPARE(z, z') -{ 0 }-> 1 + s20 :|: s20 >= 0, s20 <= z - 1 + (z' - 1), z' - 1 >= 0, z - 1 >= 0
   #LESS(z, z') -{ 1 }-> 1 + s18 :|: s18 >= 0, s18 <= z + z', z' >= 0, z >= 0
   #cklt(z) -{ 0 }-> 2 :|: z = 3
   #cklt(z) -{ 0 }-> 1 :|: z = 1
   #cklt(z) -{ 0 }-> 1 :|: z = 2
   #cklt(z) -{ 0 }-> 0 :|: z >= 0
   #compare(z, z') -{ 0 }-> s8 :|: s8 >= 0, s8 <= 3, z' - 1 >= 0, z - 1 >= 0
   #compare(z, z') -{ 0 }-> s9 :|: s9 >= 0, s9 <= 3, z' - 1 >= 0, z - 1 >= 0
   #compare(z, z') -{ 0 }-> 3 :|: z' - 1 >= 0, z = 0
   #compare(z, z') -{ 0 }-> 3 :|: z - 1 >= 0, z' = 0
   #compare(z, z') -{ 0 }-> 3 :|: z' - 1 >= 0, z - 1 >= 0
   #compare(z, z') -{ 0 }-> 2 :|: z' - 1 >= 0, z = 0
   #compare(z, z') -{ 0 }-> 2 :|: z - 1 >= 0, z' = 0
   #compare(z, z') -{ 0 }-> 2 :|: z' - 1 >= 0, z - 1 >= 0
   #compare(z, z') -{ 0 }-> 1 :|: z = 0, z' = 0
   #compare(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   #less(z, z') -{ 0 }-> s13 :|: s12 >= 0, s12 <= 3, s13 >= 0, s13 <= 2, z' - 1 >= 0, z - 1 >= 0
   #less(z, z') -{ 0 }-> s15 :|: s14 >= 0, s14 <= 3, s15 >= 0, s15 <= 2, z - 1 >= 0, z' - 1 >= 0
   #less(z, z') -{ 0 }-> 2 :|: z' - 1 >= 0, z = 0, 3 = 3
   #less(z, z') -{ 0 }-> 2 :|: z - 1 >= 0, z' = 0, 3 = 3
   #less(z, z') -{ 0 }-> 2 :|: z - 1 >= 0, z' - 1 >= 0, 3 = 3
   #less(z, z') -{ 0 }-> 1 :|: z = 0, z' = 0, 1 = 1
   #less(z, z') -{ 0 }-> 1 :|: z' - 1 >= 0, z = 0, 2 = 2
   #less(z, z') -{ 0 }-> 1 :|: z - 1 >= 0, z' = 0, 2 = 2
   #less(z, z') -{ 0 }-> 1 :|: z' - 1 >= 0, z - 1 >= 0, 2 = 2
   #less(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   #less(z, z') -{ 0 }-> 0 :|: z = 0, z' = 0, v0 >= 0, 1 = v0
   #less(z, z') -{ 0 }-> 0 :|: z' - 1 >= 0, z = 0, v0 >= 0, 2 = v0
   #less(z, z') -{ 0 }-> 0 :|: z' - 1 >= 0, z = 0, v0 >= 0, 3 = v0
   #less(z, z') -{ 0 }-> 0 :|: z - 1 >= 0, z' = 0, v0 >= 0, 3 = v0
   #less(z, z') -{ 0 }-> 0 :|: z - 1 >= 0, z' - 1 >= 0, v0 >= 0, 3 = v0
   #less(z, z') -{ 0 }-> 0 :|: z - 1 >= 0, z' = 0, v0 >= 0, 2 = v0
   #less(z, z') -{ 0 }-> 0 :|: z' - 1 >= 0, z - 1 >= 0, v0 >= 0, 2 = v0
   #less(z, z') -{ 0 }-> 0 :|: z' >= 0, z >= 0, v0 >= 0, 0 = v0
   APPEND(z, z') -{ 1 + 4*z }-> 1 + s :|: s >= 0, s <= 0, z' >= 0, z >= 0
   APPEND#1(z, z') -{ 2 + 4*z1 }-> 1 + s' :|: s' >= 0, s' <= 1, z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z' >= 0
   FLATTEN(z) -{ 1 }-> 1 + FLATTEN#1(z) :|: z >= 0
   FLATTEN#1(z) -{ 3 + 4*z0 }-> 1 + s103 + s105 + FLATTEN(z1) :|: s101 >= 0, s101 <= z2 + 1, s102 >= 0, s102 <= 0 + s101, s103 >= 0, s103 <= 1, s104 >= 0, s104 <= z2 + 1, s105 >= 0, s105 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*z0 }-> 1 + s108 + s2 + FLATTEN(z1) :|: s106 >= 0, s106 <= z2 + 1, s107 >= 0, s107 <= 0 + s106, s108 >= 0, s108 <= 1, s2 >= 0, s2 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*s120 + 4*z0 }-> 1 + s119 + s122 + FLATTEN(z2) :|: s116 >= 0, s116 <= z1 + 1, s117 >= 0, s117 <= z2 + 1, s118 >= 0, s118 <= s116 + s117, s119 >= 0, s119 <= 1, s120 >= 0, s120 <= z1 + 1, s121 >= 0, s121 <= z2 + 1, s122 >= 0, s122 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*s127 + 4*z0 }-> 1 + s126 + s128 + FLATTEN(z2) :|: s123 >= 0, s123 <= z1 + 1, s124 >= 0, s124 <= z2 + 1, s125 >= 0, s125 <= s123 + s124, s126 >= 0, s126 <= 1, s127 >= 0, s127 <= z1 + 1, s128 >= 0, s128 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*z0 }-> 1 + s132 + s134 + FLATTEN(z2) :|: s129 >= 0, s129 <= z1 + 1, s130 >= 0, s130 <= z2 + 1, s131 >= 0, s131 <= s129 + s130, s132 >= 0, s132 <= 1, s133 >= 0, s133 <= z2 + 1, s134 >= 0, s134 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*z0 }-> 1 + s138 + s4 + FLATTEN(z2) :|: s135 >= 0, s135 <= z1 + 1, s136 >= 0, s136 <= z2 + 1, s137 >= 0, s137 <= s135 + s136, s138 >= 0, s138 <= 1, s4 >= 0, s4 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*s142 + 4*z0 }-> 1 + s141 + s144 + FLATTEN(z2) :|: s139 >= 0, s139 <= z1 + 1, s140 >= 0, s140 <= s139 + 0, s141 >= 0, s141 <= 1, s142 >= 0, s142 <= z1 + 1, s143 >= 0, s143 <= z2 + 1, s144 >= 0, s144 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*s148 + 4*z0 }-> 1 + s147 + s149 + FLATTEN(z2) :|: s145 >= 0, s145 <= z1 + 1, s146 >= 0, s146 <= s145 + 0, s147 >= 0, s147 <= 1, s148 >= 0, s148 <= z1 + 1, s149 >= 0, s149 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*z0 }-> 1 + s152 + s154 + FLATTEN(z2) :|: s150 >= 0, s150 <= z1 + 1, s151 >= 0, s151 <= s150 + 0, s152 >= 0, s152 <= 1, s153 >= 0, s153 <= z2 + 1, s154 >= 0, s154 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*z0 }-> 1 + s157 + s5 + FLATTEN(z2) :|: s155 >= 0, s155 <= z1 + 1, s156 >= 0, s156 <= s155 + 0, s157 >= 0, s157 <= 1, s5 >= 0, s5 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*s161 + 4*z0 }-> 1 + s160 + s163 + FLATTEN(z2) :|: s158 >= 0, s158 <= z2 + 1, s159 >= 0, s159 <= 0 + s158, s160 >= 0, s160 <= 1, s161 >= 0, s161 <= z1 + 1, s162 >= 0, s162 <= z2 + 1, s163 >= 0, s163 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*s167 + 4*z0 }-> 1 + s166 + s168 + FLATTEN(z2) :|: s164 >= 0, s164 <= z2 + 1, s165 >= 0, s165 <= 0 + s164, s166 >= 0, s166 <= 1, s167 >= 0, s167 <= z1 + 1, s168 >= 0, s168 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*z0 }-> 1 + s171 + s173 + FLATTEN(z2) :|: s169 >= 0, s169 <= z2 + 1, s170 >= 0, s170 <= 0 + s169, s171 >= 0, s171 <= 1, s172 >= 0, s172 <= z2 + 1, s173 >= 0, s173 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*z0 }-> 1 + s176 + s6 + FLATTEN(z2) :|: s174 >= 0, s174 <= z2 + 1, s175 >= 0, s175 <= 0 + s174, s176 >= 0, s176 <= 1, s6 >= 0, s6 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*s109 + 4*z0 }-> 1 + s22 + s111 + FLATTEN(z1) :|: s109 >= 0, s109 <= z1 + 1, s110 >= 0, s110 <= z2 + 1, s111 >= 0, s111 <= 1, s21 >= 0, s21 <= 0 + 0, s22 >= 0, s22 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*s112 + 4*z0 }-> 1 + s24 + s113 + FLATTEN(z1) :|: s112 >= 0, s112 <= z1 + 1, s113 >= 0, s113 <= 1, s23 >= 0, s23 <= 0 + 0, s24 >= 0, s24 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*z0 }-> 1 + s26 + s115 + FLATTEN(z1) :|: s114 >= 0, s114 <= z2 + 1, s115 >= 0, s115 <= 1, s25 >= 0, s25 <= 0 + 0, s26 >= 0, s26 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*z0 }-> 1 + s28 + s3 + FLATTEN(z1) :|: s27 >= 0, s27 <= 0 + 0, s28 >= 0, s28 <= 1, s3 >= 0, s3 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*s177 + 4*z0 }-> 1 + s30 + s179 + FLATTEN(z2) :|: s177 >= 0, s177 <= z1 + 1, s178 >= 0, s178 <= z2 + 1, s179 >= 0, s179 <= 1, s29 >= 0, s29 <= 0 + 0, s30 >= 0, s30 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*s180 + 4*z0 }-> 1 + s32 + s181 + FLATTEN(z2) :|: s180 >= 0, s180 <= z1 + 1, s181 >= 0, s181 <= 1, s31 >= 0, s31 <= 0 + 0, s32 >= 0, s32 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*z0 }-> 1 + s34 + s183 + FLATTEN(z2) :|: s182 >= 0, s182 <= z2 + 1, s183 >= 0, s183 <= 1, s33 >= 0, s33 <= 0 + 0, s34 >= 0, s34 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*z0 }-> 1 + s36 + s7 + FLATTEN(z2) :|: s35 >= 0, s35 <= 0 + 0, s36 >= 0, s36 <= 1, s7 >= 0, s7 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*s52 + 4*z0 }-> 1 + s51 + s54 + FLATTEN(z1) :|: s48 >= 0, s48 <= z1 + 1, s49 >= 0, s49 <= z2 + 1, s50 >= 0, s50 <= s48 + s49, s51 >= 0, s51 <= 1, s52 >= 0, s52 <= z1 + 1, s53 >= 0, s53 <= z2 + 1, s54 >= 0, s54 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*s59 + 4*z0 }-> 1 + s58 + s60 + FLATTEN(z1) :|: s55 >= 0, s55 <= z1 + 1, s56 >= 0, s56 <= z2 + 1, s57 >= 0, s57 <= s55 + s56, s58 >= 0, s58 <= 1, s59 >= 0, s59 <= z1 + 1, s60 >= 0, s60 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*z0 }-> 1 + s64 + s66 + FLATTEN(z1) :|: s61 >= 0, s61 <= z1 + 1, s62 >= 0, s62 <= z2 + 1, s63 >= 0, s63 <= s61 + s62, s64 >= 0, s64 <= 1, s65 >= 0, s65 <= z2 + 1, s66 >= 0, s66 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*z0 }-> 1 + s70 + s'' + FLATTEN(z1) :|: s67 >= 0, s67 <= z1 + 1, s68 >= 0, s68 <= z2 + 1, s69 >= 0, s69 <= s67 + s68, s70 >= 0, s70 <= 1, s'' >= 0, s'' <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*s74 + 4*z0 }-> 1 + s73 + s76 + FLATTEN(z1) :|: s71 >= 0, s71 <= z1 + 1, s72 >= 0, s72 <= s71 + 0, s73 >= 0, s73 <= 1, s74 >= 0, s74 <= z1 + 1, s75 >= 0, s75 <= z2 + 1, s76 >= 0, s76 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*s80 + 4*z0 }-> 1 + s79 + s81 + FLATTEN(z1) :|: s77 >= 0, s77 <= z1 + 1, s78 >= 0, s78 <= s77 + 0, s79 >= 0, s79 <= 1, s80 >= 0, s80 <= z1 + 1, s81 >= 0, s81 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*z0 }-> 1 + s84 + s86 + FLATTEN(z1) :|: s82 >= 0, s82 <= z1 + 1, s83 >= 0, s83 <= s82 + 0, s84 >= 0, s84 <= 1, s85 >= 0, s85 <= z2 + 1, s86 >= 0, s86 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*z0 }-> 1 + s89 + s1 + FLATTEN(z1) :|: s87 >= 0, s87 <= z1 + 1, s88 >= 0, s88 <= s87 + 0, s89 >= 0, s89 <= 1, s1 >= 0, s1 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*s93 + 4*z0 }-> 1 + s92 + s95 + FLATTEN(z1) :|: s90 >= 0, s90 <= z2 + 1, s91 >= 0, s91 <= 0 + s90, s92 >= 0, s92 <= 1, s93 >= 0, s93 <= z1 + 1, s94 >= 0, s94 <= z2 + 1, s95 >= 0, s95 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*s99 + 4*z0 }-> 1 + s98 + s100 + FLATTEN(z1) :|: s96 >= 0, s96 <= z2 + 1, s97 >= 0, s97 <= 0 + s96, s98 >= 0, s98 <= 1, s99 >= 0, s99 <= z1 + 1, s100 >= 0, s100 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTENSORT(z) -{ 0 }-> 0 :|: z >= 0
   FLATTENSORT(z) -{ 0 }-> 1 + INSERTIONSORT(s184) :|: s184 >= 0, s184 <= z + 1, z >= 0
   FLATTENSORT(z) -{ 0 }-> 1 + INSERTIONSORT(0) :|: z >= 0
   INSERT(z, z') -{ 8 + 4*z' }-> 1 + s200 :|: s200 >= 0, s200 <= 0, z' >= 0, z >= 0
   INSERT#1(z, z') -{ 11 + 4*z1 }-> 1 + s201 + s46 :|: s201 >= 0, s201 <= 2, s46 >= 0, s46 <= z0 + z' + 1, z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z' >= 0
   INSERT#1(z, z') -{ 11 + 4*z1 }-> 1 + s205 + s47 :|: s205 >= 0, s205 <= 2, s47 >= 0, s47 <= z0 + z' + 1, s10 >= 0, s10 <= 3, s11 >= 0, s11 <= 2, z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z' >= 0
   INSERT#2(z, z', z'', z3) -{ 9 + 4*z3 }-> 1 + s202 :|: s202 >= 0, s202 <= 1, z = 2, z'' >= 0, z' >= 0, z3 >= 0
   INSERTIONSORT(z) -{ 1 }-> 1 + INSERTIONSORT#1(z) :|: z >= 0
   INSERTIONSORT#1(z) -{ 9 + 4*s196 }-> 1 + s203 + INSERTIONSORT(z1) :|: s203 >= 0, s203 <= 1, s196 >= 0, s196 <= z1, z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   INSERTIONSORT#1(z) -{ 9 }-> 1 + s204 + INSERTIONSORT(z1) :|: s204 >= 0, s204 <= 1, z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   append(z, z') -{ 0 }-> s37 :|: s37 >= 0, s37 <= z + z', z' >= 0, z >= 0
   append(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   append#1(z, z') -{ 0 }-> z' :|: z' >= 0, z = 0
   append#1(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   append#1(z, z') -{ 0 }-> 1 + z0 + s40 :|: s40 >= 0, s40 <= z1 + z', z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z' >= 0
   flatten(z) -{ 0 }-> s185 :|: s185 >= 0, s185 <= z + 1, z >= 0
   flatten(z) -{ 0 }-> 0 :|: z >= 0
   flatten#1(z) -{ 0 }-> s189 :|: s186 >= 0, s186 <= z1 + 1, s187 >= 0, s187 <= z2 + 1, s188 >= 0, s188 <= s186 + s187, s189 >= 0, s189 <= z0 + s188, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   flatten#1(z) -{ 0 }-> s192 :|: s190 >= 0, s190 <= z1 + 1, s191 >= 0, s191 <= s190 + 0, s192 >= 0, s192 <= z0 + s191, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   flatten#1(z) -{ 0 }-> s195 :|: s193 >= 0, s193 <= z2 + 1, s194 >= 0, s194 <= 0 + s193, s195 >= 0, s195 <= z0 + s194, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   flatten#1(z) -{ 0 }-> s39 :|: s38 >= 0, s38 <= 0 + 0, s39 >= 0, s39 <= z0 + s38, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   flatten#1(z) -{ 0 }-> 0 :|: z = 0
   flatten#1(z) -{ 0 }-> 0 :|: z >= 0
   insert(z, z') -{ 0 }-> s42 :|: s42 >= 0, s42 <= z' + z + 1, z' >= 0, z >= 0
   insert(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   insert#1(z, z') -{ 0 }-> s43 :|: s43 >= 0, s43 <= z' + z0 + z1 + 2, z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z' >= 0
   insert#1(z, z') -{ 0 }-> s45 :|: s45 >= 0, s45 <= z' + z0 + z1 + 2, s16 >= 0, s16 <= 3, s17 >= 0, s17 <= 2, z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z' >= 0
   insert#1(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   insert#1(z, z') -{ 0 }-> 1 + z' + 0 :|: z' >= 0, z = 0
   insert#2(z, z', z'', z3) -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0, z3 >= 0
   insert#2(z, z', z'', z3) -{ 0 }-> 1 + z' + (1 + z'' + z3) :|: z'' >= 0, z = 1, z' >= 0, z3 >= 0
   insert#2(z, z', z'', z3) -{ 0 }-> 1 + z'' + s44 :|: s44 >= 0, s44 <= z' + z3 + 1, z = 2, z'' >= 0, z' >= 0, z3 >= 0
   insertionsort(z) -{ 0 }-> s197 :|: s197 >= 0, s197 <= z, z >= 0
   insertionsort(z) -{ 0 }-> 0 :|: z >= 0
   insertionsort#1(z) -{ 0 }-> s199 :|: s198 >= 0, s198 <= z1, s199 >= 0, s199 <= z0 + s198 + 1, z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   insertionsort#1(z) -{ 0 }-> s41 :|: s41 >= 0, s41 <= z0 + 0 + 1, z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   insertionsort#1(z) -{ 0 }-> 0 :|: z = 0
   insertionsort#1(z) -{ 0 }-> 0 :|: z >= 0

Function symbols to be analyzed: {FLATTEN,FLATTEN#1}, {insertionsort}, {INSERTIONSORT,INSERTIONSORT#1}, {FLATTENSORT}
Previous analysis results are:
  APPEND#1: runtime: O(n^1) [4*z], size: O(1) [0]
  APPEND: runtime: O(n^1) [1 + 4*z], size: O(1) [1]
  #cklt: runtime: O(1) [0], size: O(1) [2]
  #compare: runtime: O(1) [0], size: O(1) [3]
  #COMPARE: runtime: O(1) [0], size: O(n^1) [z + z']
  append#1: runtime: O(1) [0], size: O(n^1) [z + z']
  append: runtime: O(1) [0], size: O(n^1) [z + z']
  #less: runtime: O(1) [0], size: O(1) [2]
  insert#2: runtime: O(1) [0], size: O(n^1) [2 + z' + z'' + z3]
  insert: runtime: O(1) [0], size: O(n^1) [1 + z + z']
  insert#1: runtime: O(1) [0], size: O(n^1) [1 + z + z']
  #LESS: runtime: O(1) [1], size: O(n^1) [1 + z + z']
  flatten#1: runtime: O(1) [0], size: O(n^1) [1 + z]
  insertionsort#1: runtime: O(1) [0], size: O(n^1) [z]
  INSERT#1: runtime: O(n^1) [7 + 4*z], size: O(1) [0]
  INSERT#2: runtime: O(n^1) [9 + 4*z3], size: O(1) [2]
  INSERT: runtime: O(n^1) [8 + 4*z'], size: O(1) [1]
  flatten: runtime: O(1) [0], size: O(n^1) [1 + z]
  FLATTEN: runtime: ?, size: O(1) [0]
  FLATTEN#1: runtime: ?, size: O(1) [3]

----------------------------------------

(111) IntTrsBoundProof (UPPER BOUND(ID))

Computed RUNTIME bound using CoFloCo for: FLATTEN
after applying outer abstraction to obtain an ITS,
resulting in: O(n^2) with polynomial bound: 17 + 124*z + 4*z^2

Computed RUNTIME bound using KoAT for: FLATTEN#1
after applying outer abstraction to obtain an ITS,
resulting in: O(n^2) with polynomial bound: 704 + 4160*z + 128*z^2

----------------------------------------

(112)
Obligation:
Complexity RNTS consisting of the following rules:

   #COMPARE(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   #COMPARE(z, z') -{ 0 }-> 1 + s19 :|: s19 >= 0, s19 <= z' - 1 + (z - 1), z' - 1 >= 0, z - 1 >= 0
   #COMPARE(z, z') -{ 0 }-> 1 + s20 :|: s20 >= 0, s20 <= z - 1 + (z' - 1), z' - 1 >= 0, z - 1 >= 0
   #LESS(z, z') -{ 1 }-> 1 + s18 :|: s18 >= 0, s18 <= z + z', z' >= 0, z >= 0
   #cklt(z) -{ 0 }-> 2 :|: z = 3
   #cklt(z) -{ 0 }-> 1 :|: z = 1
   #cklt(z) -{ 0 }-> 1 :|: z = 2
   #cklt(z) -{ 0 }-> 0 :|: z >= 0
   #compare(z, z') -{ 0 }-> s8 :|: s8 >= 0, s8 <= 3, z' - 1 >= 0, z - 1 >= 0
   #compare(z, z') -{ 0 }-> s9 :|: s9 >= 0, s9 <= 3, z' - 1 >= 0, z - 1 >= 0
   #compare(z, z') -{ 0 }-> 3 :|: z' - 1 >= 0, z = 0
   #compare(z, z') -{ 0 }-> 3 :|: z - 1 >= 0, z' = 0
   #compare(z, z') -{ 0 }-> 3 :|: z' - 1 >= 0, z - 1 >= 0
   #compare(z, z') -{ 0 }-> 2 :|: z' - 1 >= 0, z = 0
   #compare(z, z') -{ 0 }-> 2 :|: z - 1 >= 0, z' = 0
   #compare(z, z') -{ 0 }-> 2 :|: z' - 1 >= 0, z - 1 >= 0
   #compare(z, z') -{ 0 }-> 1 :|: z = 0, z' = 0
   #compare(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   #less(z, z') -{ 0 }-> s13 :|: s12 >= 0, s12 <= 3, s13 >= 0, s13 <= 2, z' - 1 >= 0, z - 1 >= 0
   #less(z, z') -{ 0 }-> s15 :|: s14 >= 0, s14 <= 3, s15 >= 0, s15 <= 2, z - 1 >= 0, z' - 1 >= 0
   #less(z, z') -{ 0 }-> 2 :|: z' - 1 >= 0, z = 0, 3 = 3
   #less(z, z') -{ 0 }-> 2 :|: z - 1 >= 0, z' = 0, 3 = 3
   #less(z, z') -{ 0 }-> 2 :|: z - 1 >= 0, z' - 1 >= 0, 3 = 3
   #less(z, z') -{ 0 }-> 1 :|: z = 0, z' = 0, 1 = 1
   #less(z, z') -{ 0 }-> 1 :|: z' - 1 >= 0, z = 0, 2 = 2
   #less(z, z') -{ 0 }-> 1 :|: z - 1 >= 0, z' = 0, 2 = 2
   #less(z, z') -{ 0 }-> 1 :|: z' - 1 >= 0, z - 1 >= 0, 2 = 2
   #less(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   #less(z, z') -{ 0 }-> 0 :|: z = 0, z' = 0, v0 >= 0, 1 = v0
   #less(z, z') -{ 0 }-> 0 :|: z' - 1 >= 0, z = 0, v0 >= 0, 2 = v0
   #less(z, z') -{ 0 }-> 0 :|: z' - 1 >= 0, z = 0, v0 >= 0, 3 = v0
   #less(z, z') -{ 0 }-> 0 :|: z - 1 >= 0, z' = 0, v0 >= 0, 3 = v0
   #less(z, z') -{ 0 }-> 0 :|: z - 1 >= 0, z' - 1 >= 0, v0 >= 0, 3 = v0
   #less(z, z') -{ 0 }-> 0 :|: z - 1 >= 0, z' = 0, v0 >= 0, 2 = v0
   #less(z, z') -{ 0 }-> 0 :|: z' - 1 >= 0, z - 1 >= 0, v0 >= 0, 2 = v0
   #less(z, z') -{ 0 }-> 0 :|: z' >= 0, z >= 0, v0 >= 0, 0 = v0
   APPEND(z, z') -{ 1 + 4*z }-> 1 + s :|: s >= 0, s <= 0, z' >= 0, z >= 0
   APPEND#1(z, z') -{ 2 + 4*z1 }-> 1 + s' :|: s' >= 0, s' <= 1, z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z' >= 0
   FLATTEN(z) -{ 1 }-> 1 + FLATTEN#1(z) :|: z >= 0
   FLATTEN#1(z) -{ 3 + 4*z0 }-> 1 + s103 + s105 + FLATTEN(z1) :|: s101 >= 0, s101 <= z2 + 1, s102 >= 0, s102 <= 0 + s101, s103 >= 0, s103 <= 1, s104 >= 0, s104 <= z2 + 1, s105 >= 0, s105 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*z0 }-> 1 + s108 + s2 + FLATTEN(z1) :|: s106 >= 0, s106 <= z2 + 1, s107 >= 0, s107 <= 0 + s106, s108 >= 0, s108 <= 1, s2 >= 0, s2 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*s120 + 4*z0 }-> 1 + s119 + s122 + FLATTEN(z2) :|: s116 >= 0, s116 <= z1 + 1, s117 >= 0, s117 <= z2 + 1, s118 >= 0, s118 <= s116 + s117, s119 >= 0, s119 <= 1, s120 >= 0, s120 <= z1 + 1, s121 >= 0, s121 <= z2 + 1, s122 >= 0, s122 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*s127 + 4*z0 }-> 1 + s126 + s128 + FLATTEN(z2) :|: s123 >= 0, s123 <= z1 + 1, s124 >= 0, s124 <= z2 + 1, s125 >= 0, s125 <= s123 + s124, s126 >= 0, s126 <= 1, s127 >= 0, s127 <= z1 + 1, s128 >= 0, s128 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*z0 }-> 1 + s132 + s134 + FLATTEN(z2) :|: s129 >= 0, s129 <= z1 + 1, s130 >= 0, s130 <= z2 + 1, s131 >= 0, s131 <= s129 + s130, s132 >= 0, s132 <= 1, s133 >= 0, s133 <= z2 + 1, s134 >= 0, s134 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*z0 }-> 1 + s138 + s4 + FLATTEN(z2) :|: s135 >= 0, s135 <= z1 + 1, s136 >= 0, s136 <= z2 + 1, s137 >= 0, s137 <= s135 + s136, s138 >= 0, s138 <= 1, s4 >= 0, s4 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*s142 + 4*z0 }-> 1 + s141 + s144 + FLATTEN(z2) :|: s139 >= 0, s139 <= z1 + 1, s140 >= 0, s140 <= s139 + 0, s141 >= 0, s141 <= 1, s142 >= 0, s142 <= z1 + 1, s143 >= 0, s143 <= z2 + 1, s144 >= 0, s144 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*s148 + 4*z0 }-> 1 + s147 + s149 + FLATTEN(z2) :|: s145 >= 0, s145 <= z1 + 1, s146 >= 0, s146 <= s145 + 0, s147 >= 0, s147 <= 1, s148 >= 0, s148 <= z1 + 1, s149 >= 0, s149 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*z0 }-> 1 + s152 + s154 + FLATTEN(z2) :|: s150 >= 0, s150 <= z1 + 1, s151 >= 0, s151 <= s150 + 0, s152 >= 0, s152 <= 1, s153 >= 0, s153 <= z2 + 1, s154 >= 0, s154 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*z0 }-> 1 + s157 + s5 + FLATTEN(z2) :|: s155 >= 0, s155 <= z1 + 1, s156 >= 0, s156 <= s155 + 0, s157 >= 0, s157 <= 1, s5 >= 0, s5 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*s161 + 4*z0 }-> 1 + s160 + s163 + FLATTEN(z2) :|: s158 >= 0, s158 <= z2 + 1, s159 >= 0, s159 <= 0 + s158, s160 >= 0, s160 <= 1, s161 >= 0, s161 <= z1 + 1, s162 >= 0, s162 <= z2 + 1, s163 >= 0, s163 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*s167 + 4*z0 }-> 1 + s166 + s168 + FLATTEN(z2) :|: s164 >= 0, s164 <= z2 + 1, s165 >= 0, s165 <= 0 + s164, s166 >= 0, s166 <= 1, s167 >= 0, s167 <= z1 + 1, s168 >= 0, s168 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*z0 }-> 1 + s171 + s173 + FLATTEN(z2) :|: s169 >= 0, s169 <= z2 + 1, s170 >= 0, s170 <= 0 + s169, s171 >= 0, s171 <= 1, s172 >= 0, s172 <= z2 + 1, s173 >= 0, s173 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*z0 }-> 1 + s176 + s6 + FLATTEN(z2) :|: s174 >= 0, s174 <= z2 + 1, s175 >= 0, s175 <= 0 + s174, s176 >= 0, s176 <= 1, s6 >= 0, s6 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*s109 + 4*z0 }-> 1 + s22 + s111 + FLATTEN(z1) :|: s109 >= 0, s109 <= z1 + 1, s110 >= 0, s110 <= z2 + 1, s111 >= 0, s111 <= 1, s21 >= 0, s21 <= 0 + 0, s22 >= 0, s22 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*s112 + 4*z0 }-> 1 + s24 + s113 + FLATTEN(z1) :|: s112 >= 0, s112 <= z1 + 1, s113 >= 0, s113 <= 1, s23 >= 0, s23 <= 0 + 0, s24 >= 0, s24 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*z0 }-> 1 + s26 + s115 + FLATTEN(z1) :|: s114 >= 0, s114 <= z2 + 1, s115 >= 0, s115 <= 1, s25 >= 0, s25 <= 0 + 0, s26 >= 0, s26 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*z0 }-> 1 + s28 + s3 + FLATTEN(z1) :|: s27 >= 0, s27 <= 0 + 0, s28 >= 0, s28 <= 1, s3 >= 0, s3 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*s177 + 4*z0 }-> 1 + s30 + s179 + FLATTEN(z2) :|: s177 >= 0, s177 <= z1 + 1, s178 >= 0, s178 <= z2 + 1, s179 >= 0, s179 <= 1, s29 >= 0, s29 <= 0 + 0, s30 >= 0, s30 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*s180 + 4*z0 }-> 1 + s32 + s181 + FLATTEN(z2) :|: s180 >= 0, s180 <= z1 + 1, s181 >= 0, s181 <= 1, s31 >= 0, s31 <= 0 + 0, s32 >= 0, s32 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*z0 }-> 1 + s34 + s183 + FLATTEN(z2) :|: s182 >= 0, s182 <= z2 + 1, s183 >= 0, s183 <= 1, s33 >= 0, s33 <= 0 + 0, s34 >= 0, s34 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*z0 }-> 1 + s36 + s7 + FLATTEN(z2) :|: s35 >= 0, s35 <= 0 + 0, s36 >= 0, s36 <= 1, s7 >= 0, s7 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*s52 + 4*z0 }-> 1 + s51 + s54 + FLATTEN(z1) :|: s48 >= 0, s48 <= z1 + 1, s49 >= 0, s49 <= z2 + 1, s50 >= 0, s50 <= s48 + s49, s51 >= 0, s51 <= 1, s52 >= 0, s52 <= z1 + 1, s53 >= 0, s53 <= z2 + 1, s54 >= 0, s54 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*s59 + 4*z0 }-> 1 + s58 + s60 + FLATTEN(z1) :|: s55 >= 0, s55 <= z1 + 1, s56 >= 0, s56 <= z2 + 1, s57 >= 0, s57 <= s55 + s56, s58 >= 0, s58 <= 1, s59 >= 0, s59 <= z1 + 1, s60 >= 0, s60 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*z0 }-> 1 + s64 + s66 + FLATTEN(z1) :|: s61 >= 0, s61 <= z1 + 1, s62 >= 0, s62 <= z2 + 1, s63 >= 0, s63 <= s61 + s62, s64 >= 0, s64 <= 1, s65 >= 0, s65 <= z2 + 1, s66 >= 0, s66 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*z0 }-> 1 + s70 + s'' + FLATTEN(z1) :|: s67 >= 0, s67 <= z1 + 1, s68 >= 0, s68 <= z2 + 1, s69 >= 0, s69 <= s67 + s68, s70 >= 0, s70 <= 1, s'' >= 0, s'' <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*s74 + 4*z0 }-> 1 + s73 + s76 + FLATTEN(z1) :|: s71 >= 0, s71 <= z1 + 1, s72 >= 0, s72 <= s71 + 0, s73 >= 0, s73 <= 1, s74 >= 0, s74 <= z1 + 1, s75 >= 0, s75 <= z2 + 1, s76 >= 0, s76 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*s80 + 4*z0 }-> 1 + s79 + s81 + FLATTEN(z1) :|: s77 >= 0, s77 <= z1 + 1, s78 >= 0, s78 <= s77 + 0, s79 >= 0, s79 <= 1, s80 >= 0, s80 <= z1 + 1, s81 >= 0, s81 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*z0 }-> 1 + s84 + s86 + FLATTEN(z1) :|: s82 >= 0, s82 <= z1 + 1, s83 >= 0, s83 <= s82 + 0, s84 >= 0, s84 <= 1, s85 >= 0, s85 <= z2 + 1, s86 >= 0, s86 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*z0 }-> 1 + s89 + s1 + FLATTEN(z1) :|: s87 >= 0, s87 <= z1 + 1, s88 >= 0, s88 <= s87 + 0, s89 >= 0, s89 <= 1, s1 >= 0, s1 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*s93 + 4*z0 }-> 1 + s92 + s95 + FLATTEN(z1) :|: s90 >= 0, s90 <= z2 + 1, s91 >= 0, s91 <= 0 + s90, s92 >= 0, s92 <= 1, s93 >= 0, s93 <= z1 + 1, s94 >= 0, s94 <= z2 + 1, s95 >= 0, s95 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 3 + 4*s99 + 4*z0 }-> 1 + s98 + s100 + FLATTEN(z1) :|: s96 >= 0, s96 <= z2 + 1, s97 >= 0, s97 <= 0 + s96, s98 >= 0, s98 <= 1, s99 >= 0, s99 <= z1 + 1, s100 >= 0, s100 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTENSORT(z) -{ 0 }-> 0 :|: z >= 0
   FLATTENSORT(z) -{ 0 }-> 1 + INSERTIONSORT(s184) :|: s184 >= 0, s184 <= z + 1, z >= 0
   FLATTENSORT(z) -{ 0 }-> 1 + INSERTIONSORT(0) :|: z >= 0
   INSERT(z, z') -{ 8 + 4*z' }-> 1 + s200 :|: s200 >= 0, s200 <= 0, z' >= 0, z >= 0
   INSERT#1(z, z') -{ 11 + 4*z1 }-> 1 + s201 + s46 :|: s201 >= 0, s201 <= 2, s46 >= 0, s46 <= z0 + z' + 1, z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z' >= 0
   INSERT#1(z, z') -{ 11 + 4*z1 }-> 1 + s205 + s47 :|: s205 >= 0, s205 <= 2, s47 >= 0, s47 <= z0 + z' + 1, s10 >= 0, s10 <= 3, s11 >= 0, s11 <= 2, z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z' >= 0
   INSERT#2(z, z', z'', z3) -{ 9 + 4*z3 }-> 1 + s202 :|: s202 >= 0, s202 <= 1, z = 2, z'' >= 0, z' >= 0, z3 >= 0
   INSERTIONSORT(z) -{ 1 }-> 1 + INSERTIONSORT#1(z) :|: z >= 0
   INSERTIONSORT#1(z) -{ 9 + 4*s196 }-> 1 + s203 + INSERTIONSORT(z1) :|: s203 >= 0, s203 <= 1, s196 >= 0, s196 <= z1, z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   INSERTIONSORT#1(z) -{ 9 }-> 1 + s204 + INSERTIONSORT(z1) :|: s204 >= 0, s204 <= 1, z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   append(z, z') -{ 0 }-> s37 :|: s37 >= 0, s37 <= z + z', z' >= 0, z >= 0
   append(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   append#1(z, z') -{ 0 }-> z' :|: z' >= 0, z = 0
   append#1(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   append#1(z, z') -{ 0 }-> 1 + z0 + s40 :|: s40 >= 0, s40 <= z1 + z', z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z' >= 0
   flatten(z) -{ 0 }-> s185 :|: s185 >= 0, s185 <= z + 1, z >= 0
   flatten(z) -{ 0 }-> 0 :|: z >= 0
   flatten#1(z) -{ 0 }-> s189 :|: s186 >= 0, s186 <= z1 + 1, s187 >= 0, s187 <= z2 + 1, s188 >= 0, s188 <= s186 + s187, s189 >= 0, s189 <= z0 + s188, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   flatten#1(z) -{ 0 }-> s192 :|: s190 >= 0, s190 <= z1 + 1, s191 >= 0, s191 <= s190 + 0, s192 >= 0, s192 <= z0 + s191, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   flatten#1(z) -{ 0 }-> s195 :|: s193 >= 0, s193 <= z2 + 1, s194 >= 0, s194 <= 0 + s193, s195 >= 0, s195 <= z0 + s194, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   flatten#1(z) -{ 0 }-> s39 :|: s38 >= 0, s38 <= 0 + 0, s39 >= 0, s39 <= z0 + s38, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   flatten#1(z) -{ 0 }-> 0 :|: z = 0
   flatten#1(z) -{ 0 }-> 0 :|: z >= 0
   insert(z, z') -{ 0 }-> s42 :|: s42 >= 0, s42 <= z' + z + 1, z' >= 0, z >= 0
   insert(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   insert#1(z, z') -{ 0 }-> s43 :|: s43 >= 0, s43 <= z' + z0 + z1 + 2, z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z' >= 0
   insert#1(z, z') -{ 0 }-> s45 :|: s45 >= 0, s45 <= z' + z0 + z1 + 2, s16 >= 0, s16 <= 3, s17 >= 0, s17 <= 2, z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z' >= 0
   insert#1(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   insert#1(z, z') -{ 0 }-> 1 + z' + 0 :|: z' >= 0, z = 0
   insert#2(z, z', z'', z3) -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0, z3 >= 0
   insert#2(z, z', z'', z3) -{ 0 }-> 1 + z' + (1 + z'' + z3) :|: z'' >= 0, z = 1, z' >= 0, z3 >= 0
   insert#2(z, z', z'', z3) -{ 0 }-> 1 + z'' + s44 :|: s44 >= 0, s44 <= z' + z3 + 1, z = 2, z'' >= 0, z' >= 0, z3 >= 0
   insertionsort(z) -{ 0 }-> s197 :|: s197 >= 0, s197 <= z, z >= 0
   insertionsort(z) -{ 0 }-> 0 :|: z >= 0
   insertionsort#1(z) -{ 0 }-> s199 :|: s198 >= 0, s198 <= z1, s199 >= 0, s199 <= z0 + s198 + 1, z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   insertionsort#1(z) -{ 0 }-> s41 :|: s41 >= 0, s41 <= z0 + 0 + 1, z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   insertionsort#1(z) -{ 0 }-> 0 :|: z = 0
   insertionsort#1(z) -{ 0 }-> 0 :|: z >= 0

Function symbols to be analyzed: {insertionsort}, {INSERTIONSORT,INSERTIONSORT#1}, {FLATTENSORT}
Previous analysis results are:
  APPEND#1: runtime: O(n^1) [4*z], size: O(1) [0]
  APPEND: runtime: O(n^1) [1 + 4*z], size: O(1) [1]
  #cklt: runtime: O(1) [0], size: O(1) [2]
  #compare: runtime: O(1) [0], size: O(1) [3]
  #COMPARE: runtime: O(1) [0], size: O(n^1) [z + z']
  append#1: runtime: O(1) [0], size: O(n^1) [z + z']
  append: runtime: O(1) [0], size: O(n^1) [z + z']
  #less: runtime: O(1) [0], size: O(1) [2]
  insert#2: runtime: O(1) [0], size: O(n^1) [2 + z' + z'' + z3]
  insert: runtime: O(1) [0], size: O(n^1) [1 + z + z']
  insert#1: runtime: O(1) [0], size: O(n^1) [1 + z + z']
  #LESS: runtime: O(1) [1], size: O(n^1) [1 + z + z']
  flatten#1: runtime: O(1) [0], size: O(n^1) [1 + z]
  insertionsort#1: runtime: O(1) [0], size: O(n^1) [z]
  INSERT#1: runtime: O(n^1) [7 + 4*z], size: O(1) [0]
  INSERT#2: runtime: O(n^1) [9 + 4*z3], size: O(1) [2]
  INSERT: runtime: O(n^1) [8 + 4*z'], size: O(1) [1]
  flatten: runtime: O(1) [0], size: O(n^1) [1 + z]
  FLATTEN: runtime: O(n^2) [17 + 124*z + 4*z^2], size: O(1) [0]
  FLATTEN#1: runtime: O(n^2) [704 + 4160*z + 128*z^2], size: O(1) [3]

----------------------------------------

(113) ResultPropagationProof (UPPER BOUND(ID))
Applied inner abstraction using the recently inferred runtime/size bounds where possible.
----------------------------------------

(114)
Obligation:
Complexity RNTS consisting of the following rules:

   #COMPARE(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   #COMPARE(z, z') -{ 0 }-> 1 + s19 :|: s19 >= 0, s19 <= z' - 1 + (z - 1), z' - 1 >= 0, z - 1 >= 0
   #COMPARE(z, z') -{ 0 }-> 1 + s20 :|: s20 >= 0, s20 <= z - 1 + (z' - 1), z' - 1 >= 0, z - 1 >= 0
   #LESS(z, z') -{ 1 }-> 1 + s18 :|: s18 >= 0, s18 <= z + z', z' >= 0, z >= 0
   #cklt(z) -{ 0 }-> 2 :|: z = 3
   #cklt(z) -{ 0 }-> 1 :|: z = 1
   #cklt(z) -{ 0 }-> 1 :|: z = 2
   #cklt(z) -{ 0 }-> 0 :|: z >= 0
   #compare(z, z') -{ 0 }-> s8 :|: s8 >= 0, s8 <= 3, z' - 1 >= 0, z - 1 >= 0
   #compare(z, z') -{ 0 }-> s9 :|: s9 >= 0, s9 <= 3, z' - 1 >= 0, z - 1 >= 0
   #compare(z, z') -{ 0 }-> 3 :|: z' - 1 >= 0, z = 0
   #compare(z, z') -{ 0 }-> 3 :|: z - 1 >= 0, z' = 0
   #compare(z, z') -{ 0 }-> 3 :|: z' - 1 >= 0, z - 1 >= 0
   #compare(z, z') -{ 0 }-> 2 :|: z' - 1 >= 0, z = 0
   #compare(z, z') -{ 0 }-> 2 :|: z - 1 >= 0, z' = 0
   #compare(z, z') -{ 0 }-> 2 :|: z' - 1 >= 0, z - 1 >= 0
   #compare(z, z') -{ 0 }-> 1 :|: z = 0, z' = 0
   #compare(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   #less(z, z') -{ 0 }-> s13 :|: s12 >= 0, s12 <= 3, s13 >= 0, s13 <= 2, z' - 1 >= 0, z - 1 >= 0
   #less(z, z') -{ 0 }-> s15 :|: s14 >= 0, s14 <= 3, s15 >= 0, s15 <= 2, z - 1 >= 0, z' - 1 >= 0
   #less(z, z') -{ 0 }-> 2 :|: z' - 1 >= 0, z = 0, 3 = 3
   #less(z, z') -{ 0 }-> 2 :|: z - 1 >= 0, z' = 0, 3 = 3
   #less(z, z') -{ 0 }-> 2 :|: z - 1 >= 0, z' - 1 >= 0, 3 = 3
   #less(z, z') -{ 0 }-> 1 :|: z = 0, z' = 0, 1 = 1
   #less(z, z') -{ 0 }-> 1 :|: z' - 1 >= 0, z = 0, 2 = 2
   #less(z, z') -{ 0 }-> 1 :|: z - 1 >= 0, z' = 0, 2 = 2
   #less(z, z') -{ 0 }-> 1 :|: z' - 1 >= 0, z - 1 >= 0, 2 = 2
   #less(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   #less(z, z') -{ 0 }-> 0 :|: z = 0, z' = 0, v0 >= 0, 1 = v0
   #less(z, z') -{ 0 }-> 0 :|: z' - 1 >= 0, z = 0, v0 >= 0, 2 = v0
   #less(z, z') -{ 0 }-> 0 :|: z' - 1 >= 0, z = 0, v0 >= 0, 3 = v0
   #less(z, z') -{ 0 }-> 0 :|: z - 1 >= 0, z' = 0, v0 >= 0, 3 = v0
   #less(z, z') -{ 0 }-> 0 :|: z - 1 >= 0, z' - 1 >= 0, v0 >= 0, 3 = v0
   #less(z, z') -{ 0 }-> 0 :|: z - 1 >= 0, z' = 0, v0 >= 0, 2 = v0
   #less(z, z') -{ 0 }-> 0 :|: z' - 1 >= 0, z - 1 >= 0, v0 >= 0, 2 = v0
   #less(z, z') -{ 0 }-> 0 :|: z' >= 0, z >= 0, v0 >= 0, 0 = v0
   APPEND(z, z') -{ 1 + 4*z }-> 1 + s :|: s >= 0, s <= 0, z' >= 0, z >= 0
   APPEND#1(z, z') -{ 2 + 4*z1 }-> 1 + s' :|: s' >= 0, s' <= 1, z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z' >= 0
   FLATTEN(z) -{ 705 + 4160*z + 128*z^2 }-> 1 + s206 :|: s206 >= 0, s206 <= 3, z >= 0
   FLATTEN#1(z) -{ 20 + 4*z0 + 124*z1 + 4*z1^2 }-> 1 + s103 + s105 + s217 :|: s217 >= 0, s217 <= 0, s101 >= 0, s101 <= z2 + 1, s102 >= 0, s102 <= 0 + s101, s103 >= 0, s103 <= 1, s104 >= 0, s104 <= z2 + 1, s105 >= 0, s105 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 20 + 4*z0 + 124*z1 + 4*z1^2 }-> 1 + s108 + s2 + s218 :|: s218 >= 0, s218 <= 0, s106 >= 0, s106 <= z2 + 1, s107 >= 0, s107 <= 0 + s106, s108 >= 0, s108 <= 1, s2 >= 0, s2 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 20 + 4*s120 + 4*z0 + 124*z2 + 4*z2^2 }-> 1 + s119 + s122 + s223 :|: s223 >= 0, s223 <= 0, s116 >= 0, s116 <= z1 + 1, s117 >= 0, s117 <= z2 + 1, s118 >= 0, s118 <= s116 + s117, s119 >= 0, s119 <= 1, s120 >= 0, s120 <= z1 + 1, s121 >= 0, s121 <= z2 + 1, s122 >= 0, s122 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 20 + 4*s127 + 4*z0 + 124*z2 + 4*z2^2 }-> 1 + s126 + s128 + s224 :|: s224 >= 0, s224 <= 0, s123 >= 0, s123 <= z1 + 1, s124 >= 0, s124 <= z2 + 1, s125 >= 0, s125 <= s123 + s124, s126 >= 0, s126 <= 1, s127 >= 0, s127 <= z1 + 1, s128 >= 0, s128 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 20 + 4*z0 + 124*z2 + 4*z2^2 }-> 1 + s132 + s134 + s225 :|: s225 >= 0, s225 <= 0, s129 >= 0, s129 <= z1 + 1, s130 >= 0, s130 <= z2 + 1, s131 >= 0, s131 <= s129 + s130, s132 >= 0, s132 <= 1, s133 >= 0, s133 <= z2 + 1, s134 >= 0, s134 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 20 + 4*z0 + 124*z2 + 4*z2^2 }-> 1 + s138 + s4 + s226 :|: s226 >= 0, s226 <= 0, s135 >= 0, s135 <= z1 + 1, s136 >= 0, s136 <= z2 + 1, s137 >= 0, s137 <= s135 + s136, s138 >= 0, s138 <= 1, s4 >= 0, s4 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 20 + 4*s142 + 4*z0 + 124*z2 + 4*z2^2 }-> 1 + s141 + s144 + s227 :|: s227 >= 0, s227 <= 0, s139 >= 0, s139 <= z1 + 1, s140 >= 0, s140 <= s139 + 0, s141 >= 0, s141 <= 1, s142 >= 0, s142 <= z1 + 1, s143 >= 0, s143 <= z2 + 1, s144 >= 0, s144 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 20 + 4*s148 + 4*z0 + 124*z2 + 4*z2^2 }-> 1 + s147 + s149 + s228 :|: s228 >= 0, s228 <= 0, s145 >= 0, s145 <= z1 + 1, s146 >= 0, s146 <= s145 + 0, s147 >= 0, s147 <= 1, s148 >= 0, s148 <= z1 + 1, s149 >= 0, s149 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 20 + 4*z0 + 124*z2 + 4*z2^2 }-> 1 + s152 + s154 + s229 :|: s229 >= 0, s229 <= 0, s150 >= 0, s150 <= z1 + 1, s151 >= 0, s151 <= s150 + 0, s152 >= 0, s152 <= 1, s153 >= 0, s153 <= z2 + 1, s154 >= 0, s154 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 20 + 4*z0 + 124*z2 + 4*z2^2 }-> 1 + s157 + s5 + s230 :|: s230 >= 0, s230 <= 0, s155 >= 0, s155 <= z1 + 1, s156 >= 0, s156 <= s155 + 0, s157 >= 0, s157 <= 1, s5 >= 0, s5 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 20 + 4*s161 + 4*z0 + 124*z2 + 4*z2^2 }-> 1 + s160 + s163 + s231 :|: s231 >= 0, s231 <= 0, s158 >= 0, s158 <= z2 + 1, s159 >= 0, s159 <= 0 + s158, s160 >= 0, s160 <= 1, s161 >= 0, s161 <= z1 + 1, s162 >= 0, s162 <= z2 + 1, s163 >= 0, s163 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 20 + 4*s167 + 4*z0 + 124*z2 + 4*z2^2 }-> 1 + s166 + s168 + s232 :|: s232 >= 0, s232 <= 0, s164 >= 0, s164 <= z2 + 1, s165 >= 0, s165 <= 0 + s164, s166 >= 0, s166 <= 1, s167 >= 0, s167 <= z1 + 1, s168 >= 0, s168 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 20 + 4*z0 + 124*z2 + 4*z2^2 }-> 1 + s171 + s173 + s233 :|: s233 >= 0, s233 <= 0, s169 >= 0, s169 <= z2 + 1, s170 >= 0, s170 <= 0 + s169, s171 >= 0, s171 <= 1, s172 >= 0, s172 <= z2 + 1, s173 >= 0, s173 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 20 + 4*z0 + 124*z2 + 4*z2^2 }-> 1 + s176 + s6 + s234 :|: s234 >= 0, s234 <= 0, s174 >= 0, s174 <= z2 + 1, s175 >= 0, s175 <= 0 + s174, s176 >= 0, s176 <= 1, s6 >= 0, s6 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 20 + 4*s109 + 4*z0 + 124*z1 + 4*z1^2 }-> 1 + s22 + s111 + s219 :|: s219 >= 0, s219 <= 0, s109 >= 0, s109 <= z1 + 1, s110 >= 0, s110 <= z2 + 1, s111 >= 0, s111 <= 1, s21 >= 0, s21 <= 0 + 0, s22 >= 0, s22 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 20 + 4*s112 + 4*z0 + 124*z1 + 4*z1^2 }-> 1 + s24 + s113 + s220 :|: s220 >= 0, s220 <= 0, s112 >= 0, s112 <= z1 + 1, s113 >= 0, s113 <= 1, s23 >= 0, s23 <= 0 + 0, s24 >= 0, s24 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 20 + 4*z0 + 124*z1 + 4*z1^2 }-> 1 + s26 + s115 + s221 :|: s221 >= 0, s221 <= 0, s114 >= 0, s114 <= z2 + 1, s115 >= 0, s115 <= 1, s25 >= 0, s25 <= 0 + 0, s26 >= 0, s26 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 20 + 4*z0 + 124*z1 + 4*z1^2 }-> 1 + s28 + s3 + s222 :|: s222 >= 0, s222 <= 0, s27 >= 0, s27 <= 0 + 0, s28 >= 0, s28 <= 1, s3 >= 0, s3 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 20 + 4*s177 + 4*z0 + 124*z2 + 4*z2^2 }-> 1 + s30 + s179 + s235 :|: s235 >= 0, s235 <= 0, s177 >= 0, s177 <= z1 + 1, s178 >= 0, s178 <= z2 + 1, s179 >= 0, s179 <= 1, s29 >= 0, s29 <= 0 + 0, s30 >= 0, s30 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 20 + 4*s180 + 4*z0 + 124*z2 + 4*z2^2 }-> 1 + s32 + s181 + s236 :|: s236 >= 0, s236 <= 0, s180 >= 0, s180 <= z1 + 1, s181 >= 0, s181 <= 1, s31 >= 0, s31 <= 0 + 0, s32 >= 0, s32 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 20 + 4*z0 + 124*z2 + 4*z2^2 }-> 1 + s34 + s183 + s237 :|: s237 >= 0, s237 <= 0, s182 >= 0, s182 <= z2 + 1, s183 >= 0, s183 <= 1, s33 >= 0, s33 <= 0 + 0, s34 >= 0, s34 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 20 + 4*z0 + 124*z2 + 4*z2^2 }-> 1 + s36 + s7 + s238 :|: s238 >= 0, s238 <= 0, s35 >= 0, s35 <= 0 + 0, s36 >= 0, s36 <= 1, s7 >= 0, s7 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 20 + 4*s52 + 4*z0 + 124*z1 + 4*z1^2 }-> 1 + s51 + s54 + s207 :|: s207 >= 0, s207 <= 0, s48 >= 0, s48 <= z1 + 1, s49 >= 0, s49 <= z2 + 1, s50 >= 0, s50 <= s48 + s49, s51 >= 0, s51 <= 1, s52 >= 0, s52 <= z1 + 1, s53 >= 0, s53 <= z2 + 1, s54 >= 0, s54 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 20 + 4*s59 + 4*z0 + 124*z1 + 4*z1^2 }-> 1 + s58 + s60 + s208 :|: s208 >= 0, s208 <= 0, s55 >= 0, s55 <= z1 + 1, s56 >= 0, s56 <= z2 + 1, s57 >= 0, s57 <= s55 + s56, s58 >= 0, s58 <= 1, s59 >= 0, s59 <= z1 + 1, s60 >= 0, s60 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 20 + 4*z0 + 124*z1 + 4*z1^2 }-> 1 + s64 + s66 + s209 :|: s209 >= 0, s209 <= 0, s61 >= 0, s61 <= z1 + 1, s62 >= 0, s62 <= z2 + 1, s63 >= 0, s63 <= s61 + s62, s64 >= 0, s64 <= 1, s65 >= 0, s65 <= z2 + 1, s66 >= 0, s66 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 20 + 4*z0 + 124*z1 + 4*z1^2 }-> 1 + s70 + s'' + s210 :|: s210 >= 0, s210 <= 0, s67 >= 0, s67 <= z1 + 1, s68 >= 0, s68 <= z2 + 1, s69 >= 0, s69 <= s67 + s68, s70 >= 0, s70 <= 1, s'' >= 0, s'' <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 20 + 4*s74 + 4*z0 + 124*z1 + 4*z1^2 }-> 1 + s73 + s76 + s211 :|: s211 >= 0, s211 <= 0, s71 >= 0, s71 <= z1 + 1, s72 >= 0, s72 <= s71 + 0, s73 >= 0, s73 <= 1, s74 >= 0, s74 <= z1 + 1, s75 >= 0, s75 <= z2 + 1, s76 >= 0, s76 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 20 + 4*s80 + 4*z0 + 124*z1 + 4*z1^2 }-> 1 + s79 + s81 + s212 :|: s212 >= 0, s212 <= 0, s77 >= 0, s77 <= z1 + 1, s78 >= 0, s78 <= s77 + 0, s79 >= 0, s79 <= 1, s80 >= 0, s80 <= z1 + 1, s81 >= 0, s81 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 20 + 4*z0 + 124*z1 + 4*z1^2 }-> 1 + s84 + s86 + s213 :|: s213 >= 0, s213 <= 0, s82 >= 0, s82 <= z1 + 1, s83 >= 0, s83 <= s82 + 0, s84 >= 0, s84 <= 1, s85 >= 0, s85 <= z2 + 1, s86 >= 0, s86 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 20 + 4*z0 + 124*z1 + 4*z1^2 }-> 1 + s89 + s1 + s214 :|: s214 >= 0, s214 <= 0, s87 >= 0, s87 <= z1 + 1, s88 >= 0, s88 <= s87 + 0, s89 >= 0, s89 <= 1, s1 >= 0, s1 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 20 + 4*s93 + 4*z0 + 124*z1 + 4*z1^2 }-> 1 + s92 + s95 + s215 :|: s215 >= 0, s215 <= 0, s90 >= 0, s90 <= z2 + 1, s91 >= 0, s91 <= 0 + s90, s92 >= 0, s92 <= 1, s93 >= 0, s93 <= z1 + 1, s94 >= 0, s94 <= z2 + 1, s95 >= 0, s95 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 20 + 4*s99 + 4*z0 + 124*z1 + 4*z1^2 }-> 1 + s98 + s100 + s216 :|: s216 >= 0, s216 <= 0, s96 >= 0, s96 <= z2 + 1, s97 >= 0, s97 <= 0 + s96, s98 >= 0, s98 <= 1, s99 >= 0, s99 <= z1 + 1, s100 >= 0, s100 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTENSORT(z) -{ 0 }-> 0 :|: z >= 0
   FLATTENSORT(z) -{ 0 }-> 1 + INSERTIONSORT(s184) :|: s184 >= 0, s184 <= z + 1, z >= 0
   FLATTENSORT(z) -{ 0 }-> 1 + INSERTIONSORT(0) :|: z >= 0
   INSERT(z, z') -{ 8 + 4*z' }-> 1 + s200 :|: s200 >= 0, s200 <= 0, z' >= 0, z >= 0
   INSERT#1(z, z') -{ 11 + 4*z1 }-> 1 + s201 + s46 :|: s201 >= 0, s201 <= 2, s46 >= 0, s46 <= z0 + z' + 1, z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z' >= 0
   INSERT#1(z, z') -{ 11 + 4*z1 }-> 1 + s205 + s47 :|: s205 >= 0, s205 <= 2, s47 >= 0, s47 <= z0 + z' + 1, s10 >= 0, s10 <= 3, s11 >= 0, s11 <= 2, z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z' >= 0
   INSERT#2(z, z', z'', z3) -{ 9 + 4*z3 }-> 1 + s202 :|: s202 >= 0, s202 <= 1, z = 2, z'' >= 0, z' >= 0, z3 >= 0
   INSERTIONSORT(z) -{ 1 }-> 1 + INSERTIONSORT#1(z) :|: z >= 0
   INSERTIONSORT#1(z) -{ 9 + 4*s196 }-> 1 + s203 + INSERTIONSORT(z1) :|: s203 >= 0, s203 <= 1, s196 >= 0, s196 <= z1, z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   INSERTIONSORT#1(z) -{ 9 }-> 1 + s204 + INSERTIONSORT(z1) :|: s204 >= 0, s204 <= 1, z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   append(z, z') -{ 0 }-> s37 :|: s37 >= 0, s37 <= z + z', z' >= 0, z >= 0
   append(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   append#1(z, z') -{ 0 }-> z' :|: z' >= 0, z = 0
   append#1(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   append#1(z, z') -{ 0 }-> 1 + z0 + s40 :|: s40 >= 0, s40 <= z1 + z', z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z' >= 0
   flatten(z) -{ 0 }-> s185 :|: s185 >= 0, s185 <= z + 1, z >= 0
   flatten(z) -{ 0 }-> 0 :|: z >= 0
   flatten#1(z) -{ 0 }-> s189 :|: s186 >= 0, s186 <= z1 + 1, s187 >= 0, s187 <= z2 + 1, s188 >= 0, s188 <= s186 + s187, s189 >= 0, s189 <= z0 + s188, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   flatten#1(z) -{ 0 }-> s192 :|: s190 >= 0, s190 <= z1 + 1, s191 >= 0, s191 <= s190 + 0, s192 >= 0, s192 <= z0 + s191, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   flatten#1(z) -{ 0 }-> s195 :|: s193 >= 0, s193 <= z2 + 1, s194 >= 0, s194 <= 0 + s193, s195 >= 0, s195 <= z0 + s194, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   flatten#1(z) -{ 0 }-> s39 :|: s38 >= 0, s38 <= 0 + 0, s39 >= 0, s39 <= z0 + s38, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   flatten#1(z) -{ 0 }-> 0 :|: z = 0
   flatten#1(z) -{ 0 }-> 0 :|: z >= 0
   insert(z, z') -{ 0 }-> s42 :|: s42 >= 0, s42 <= z' + z + 1, z' >= 0, z >= 0
   insert(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   insert#1(z, z') -{ 0 }-> s43 :|: s43 >= 0, s43 <= z' + z0 + z1 + 2, z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z' >= 0
   insert#1(z, z') -{ 0 }-> s45 :|: s45 >= 0, s45 <= z' + z0 + z1 + 2, s16 >= 0, s16 <= 3, s17 >= 0, s17 <= 2, z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z' >= 0
   insert#1(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   insert#1(z, z') -{ 0 }-> 1 + z' + 0 :|: z' >= 0, z = 0
   insert#2(z, z', z'', z3) -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0, z3 >= 0
   insert#2(z, z', z'', z3) -{ 0 }-> 1 + z' + (1 + z'' + z3) :|: z'' >= 0, z = 1, z' >= 0, z3 >= 0
   insert#2(z, z', z'', z3) -{ 0 }-> 1 + z'' + s44 :|: s44 >= 0, s44 <= z' + z3 + 1, z = 2, z'' >= 0, z' >= 0, z3 >= 0
   insertionsort(z) -{ 0 }-> s197 :|: s197 >= 0, s197 <= z, z >= 0
   insertionsort(z) -{ 0 }-> 0 :|: z >= 0
   insertionsort#1(z) -{ 0 }-> s199 :|: s198 >= 0, s198 <= z1, s199 >= 0, s199 <= z0 + s198 + 1, z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   insertionsort#1(z) -{ 0 }-> s41 :|: s41 >= 0, s41 <= z0 + 0 + 1, z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   insertionsort#1(z) -{ 0 }-> 0 :|: z = 0
   insertionsort#1(z) -{ 0 }-> 0 :|: z >= 0

Function symbols to be analyzed: {insertionsort}, {INSERTIONSORT,INSERTIONSORT#1}, {FLATTENSORT}
Previous analysis results are:
  APPEND#1: runtime: O(n^1) [4*z], size: O(1) [0]
  APPEND: runtime: O(n^1) [1 + 4*z], size: O(1) [1]
  #cklt: runtime: O(1) [0], size: O(1) [2]
  #compare: runtime: O(1) [0], size: O(1) [3]
  #COMPARE: runtime: O(1) [0], size: O(n^1) [z + z']
  append#1: runtime: O(1) [0], size: O(n^1) [z + z']
  append: runtime: O(1) [0], size: O(n^1) [z + z']
  #less: runtime: O(1) [0], size: O(1) [2]
  insert#2: runtime: O(1) [0], size: O(n^1) [2 + z' + z'' + z3]
  insert: runtime: O(1) [0], size: O(n^1) [1 + z + z']
  insert#1: runtime: O(1) [0], size: O(n^1) [1 + z + z']
  #LESS: runtime: O(1) [1], size: O(n^1) [1 + z + z']
  flatten#1: runtime: O(1) [0], size: O(n^1) [1 + z]
  insertionsort#1: runtime: O(1) [0], size: O(n^1) [z]
  INSERT#1: runtime: O(n^1) [7 + 4*z], size: O(1) [0]
  INSERT#2: runtime: O(n^1) [9 + 4*z3], size: O(1) [2]
  INSERT: runtime: O(n^1) [8 + 4*z'], size: O(1) [1]
  flatten: runtime: O(1) [0], size: O(n^1) [1 + z]
  FLATTEN: runtime: O(n^2) [17 + 124*z + 4*z^2], size: O(1) [0]
  FLATTEN#1: runtime: O(n^2) [704 + 4160*z + 128*z^2], size: O(1) [3]

----------------------------------------

(115) IntTrsBoundProof (UPPER BOUND(ID))

Computed SIZE bound using CoFloCo for: insertionsort
after applying outer abstraction to obtain an ITS,
resulting in: O(n^1) with polynomial bound: z

----------------------------------------

(116)
Obligation:
Complexity RNTS consisting of the following rules:

   #COMPARE(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   #COMPARE(z, z') -{ 0 }-> 1 + s19 :|: s19 >= 0, s19 <= z' - 1 + (z - 1), z' - 1 >= 0, z - 1 >= 0
   #COMPARE(z, z') -{ 0 }-> 1 + s20 :|: s20 >= 0, s20 <= z - 1 + (z' - 1), z' - 1 >= 0, z - 1 >= 0
   #LESS(z, z') -{ 1 }-> 1 + s18 :|: s18 >= 0, s18 <= z + z', z' >= 0, z >= 0
   #cklt(z) -{ 0 }-> 2 :|: z = 3
   #cklt(z) -{ 0 }-> 1 :|: z = 1
   #cklt(z) -{ 0 }-> 1 :|: z = 2
   #cklt(z) -{ 0 }-> 0 :|: z >= 0
   #compare(z, z') -{ 0 }-> s8 :|: s8 >= 0, s8 <= 3, z' - 1 >= 0, z - 1 >= 0
   #compare(z, z') -{ 0 }-> s9 :|: s9 >= 0, s9 <= 3, z' - 1 >= 0, z - 1 >= 0
   #compare(z, z') -{ 0 }-> 3 :|: z' - 1 >= 0, z = 0
   #compare(z, z') -{ 0 }-> 3 :|: z - 1 >= 0, z' = 0
   #compare(z, z') -{ 0 }-> 3 :|: z' - 1 >= 0, z - 1 >= 0
   #compare(z, z') -{ 0 }-> 2 :|: z' - 1 >= 0, z = 0
   #compare(z, z') -{ 0 }-> 2 :|: z - 1 >= 0, z' = 0
   #compare(z, z') -{ 0 }-> 2 :|: z' - 1 >= 0, z - 1 >= 0
   #compare(z, z') -{ 0 }-> 1 :|: z = 0, z' = 0
   #compare(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   #less(z, z') -{ 0 }-> s13 :|: s12 >= 0, s12 <= 3, s13 >= 0, s13 <= 2, z' - 1 >= 0, z - 1 >= 0
   #less(z, z') -{ 0 }-> s15 :|: s14 >= 0, s14 <= 3, s15 >= 0, s15 <= 2, z - 1 >= 0, z' - 1 >= 0
   #less(z, z') -{ 0 }-> 2 :|: z' - 1 >= 0, z = 0, 3 = 3
   #less(z, z') -{ 0 }-> 2 :|: z - 1 >= 0, z' = 0, 3 = 3
   #less(z, z') -{ 0 }-> 2 :|: z - 1 >= 0, z' - 1 >= 0, 3 = 3
   #less(z, z') -{ 0 }-> 1 :|: z = 0, z' = 0, 1 = 1
   #less(z, z') -{ 0 }-> 1 :|: z' - 1 >= 0, z = 0, 2 = 2
   #less(z, z') -{ 0 }-> 1 :|: z - 1 >= 0, z' = 0, 2 = 2
   #less(z, z') -{ 0 }-> 1 :|: z' - 1 >= 0, z - 1 >= 0, 2 = 2
   #less(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   #less(z, z') -{ 0 }-> 0 :|: z = 0, z' = 0, v0 >= 0, 1 = v0
   #less(z, z') -{ 0 }-> 0 :|: z' - 1 >= 0, z = 0, v0 >= 0, 2 = v0
   #less(z, z') -{ 0 }-> 0 :|: z' - 1 >= 0, z = 0, v0 >= 0, 3 = v0
   #less(z, z') -{ 0 }-> 0 :|: z - 1 >= 0, z' = 0, v0 >= 0, 3 = v0
   #less(z, z') -{ 0 }-> 0 :|: z - 1 >= 0, z' - 1 >= 0, v0 >= 0, 3 = v0
   #less(z, z') -{ 0 }-> 0 :|: z - 1 >= 0, z' = 0, v0 >= 0, 2 = v0
   #less(z, z') -{ 0 }-> 0 :|: z' - 1 >= 0, z - 1 >= 0, v0 >= 0, 2 = v0
   #less(z, z') -{ 0 }-> 0 :|: z' >= 0, z >= 0, v0 >= 0, 0 = v0
   APPEND(z, z') -{ 1 + 4*z }-> 1 + s :|: s >= 0, s <= 0, z' >= 0, z >= 0
   APPEND#1(z, z') -{ 2 + 4*z1 }-> 1 + s' :|: s' >= 0, s' <= 1, z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z' >= 0
   FLATTEN(z) -{ 705 + 4160*z + 128*z^2 }-> 1 + s206 :|: s206 >= 0, s206 <= 3, z >= 0
   FLATTEN#1(z) -{ 20 + 4*z0 + 124*z1 + 4*z1^2 }-> 1 + s103 + s105 + s217 :|: s217 >= 0, s217 <= 0, s101 >= 0, s101 <= z2 + 1, s102 >= 0, s102 <= 0 + s101, s103 >= 0, s103 <= 1, s104 >= 0, s104 <= z2 + 1, s105 >= 0, s105 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 20 + 4*z0 + 124*z1 + 4*z1^2 }-> 1 + s108 + s2 + s218 :|: s218 >= 0, s218 <= 0, s106 >= 0, s106 <= z2 + 1, s107 >= 0, s107 <= 0 + s106, s108 >= 0, s108 <= 1, s2 >= 0, s2 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 20 + 4*s120 + 4*z0 + 124*z2 + 4*z2^2 }-> 1 + s119 + s122 + s223 :|: s223 >= 0, s223 <= 0, s116 >= 0, s116 <= z1 + 1, s117 >= 0, s117 <= z2 + 1, s118 >= 0, s118 <= s116 + s117, s119 >= 0, s119 <= 1, s120 >= 0, s120 <= z1 + 1, s121 >= 0, s121 <= z2 + 1, s122 >= 0, s122 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 20 + 4*s127 + 4*z0 + 124*z2 + 4*z2^2 }-> 1 + s126 + s128 + s224 :|: s224 >= 0, s224 <= 0, s123 >= 0, s123 <= z1 + 1, s124 >= 0, s124 <= z2 + 1, s125 >= 0, s125 <= s123 + s124, s126 >= 0, s126 <= 1, s127 >= 0, s127 <= z1 + 1, s128 >= 0, s128 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 20 + 4*z0 + 124*z2 + 4*z2^2 }-> 1 + s132 + s134 + s225 :|: s225 >= 0, s225 <= 0, s129 >= 0, s129 <= z1 + 1, s130 >= 0, s130 <= z2 + 1, s131 >= 0, s131 <= s129 + s130, s132 >= 0, s132 <= 1, s133 >= 0, s133 <= z2 + 1, s134 >= 0, s134 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 20 + 4*z0 + 124*z2 + 4*z2^2 }-> 1 + s138 + s4 + s226 :|: s226 >= 0, s226 <= 0, s135 >= 0, s135 <= z1 + 1, s136 >= 0, s136 <= z2 + 1, s137 >= 0, s137 <= s135 + s136, s138 >= 0, s138 <= 1, s4 >= 0, s4 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 20 + 4*s142 + 4*z0 + 124*z2 + 4*z2^2 }-> 1 + s141 + s144 + s227 :|: s227 >= 0, s227 <= 0, s139 >= 0, s139 <= z1 + 1, s140 >= 0, s140 <= s139 + 0, s141 >= 0, s141 <= 1, s142 >= 0, s142 <= z1 + 1, s143 >= 0, s143 <= z2 + 1, s144 >= 0, s144 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 20 + 4*s148 + 4*z0 + 124*z2 + 4*z2^2 }-> 1 + s147 + s149 + s228 :|: s228 >= 0, s228 <= 0, s145 >= 0, s145 <= z1 + 1, s146 >= 0, s146 <= s145 + 0, s147 >= 0, s147 <= 1, s148 >= 0, s148 <= z1 + 1, s149 >= 0, s149 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 20 + 4*z0 + 124*z2 + 4*z2^2 }-> 1 + s152 + s154 + s229 :|: s229 >= 0, s229 <= 0, s150 >= 0, s150 <= z1 + 1, s151 >= 0, s151 <= s150 + 0, s152 >= 0, s152 <= 1, s153 >= 0, s153 <= z2 + 1, s154 >= 0, s154 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 20 + 4*z0 + 124*z2 + 4*z2^2 }-> 1 + s157 + s5 + s230 :|: s230 >= 0, s230 <= 0, s155 >= 0, s155 <= z1 + 1, s156 >= 0, s156 <= s155 + 0, s157 >= 0, s157 <= 1, s5 >= 0, s5 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 20 + 4*s161 + 4*z0 + 124*z2 + 4*z2^2 }-> 1 + s160 + s163 + s231 :|: s231 >= 0, s231 <= 0, s158 >= 0, s158 <= z2 + 1, s159 >= 0, s159 <= 0 + s158, s160 >= 0, s160 <= 1, s161 >= 0, s161 <= z1 + 1, s162 >= 0, s162 <= z2 + 1, s163 >= 0, s163 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 20 + 4*s167 + 4*z0 + 124*z2 + 4*z2^2 }-> 1 + s166 + s168 + s232 :|: s232 >= 0, s232 <= 0, s164 >= 0, s164 <= z2 + 1, s165 >= 0, s165 <= 0 + s164, s166 >= 0, s166 <= 1, s167 >= 0, s167 <= z1 + 1, s168 >= 0, s168 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 20 + 4*z0 + 124*z2 + 4*z2^2 }-> 1 + s171 + s173 + s233 :|: s233 >= 0, s233 <= 0, s169 >= 0, s169 <= z2 + 1, s170 >= 0, s170 <= 0 + s169, s171 >= 0, s171 <= 1, s172 >= 0, s172 <= z2 + 1, s173 >= 0, s173 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 20 + 4*z0 + 124*z2 + 4*z2^2 }-> 1 + s176 + s6 + s234 :|: s234 >= 0, s234 <= 0, s174 >= 0, s174 <= z2 + 1, s175 >= 0, s175 <= 0 + s174, s176 >= 0, s176 <= 1, s6 >= 0, s6 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 20 + 4*s109 + 4*z0 + 124*z1 + 4*z1^2 }-> 1 + s22 + s111 + s219 :|: s219 >= 0, s219 <= 0, s109 >= 0, s109 <= z1 + 1, s110 >= 0, s110 <= z2 + 1, s111 >= 0, s111 <= 1, s21 >= 0, s21 <= 0 + 0, s22 >= 0, s22 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 20 + 4*s112 + 4*z0 + 124*z1 + 4*z1^2 }-> 1 + s24 + s113 + s220 :|: s220 >= 0, s220 <= 0, s112 >= 0, s112 <= z1 + 1, s113 >= 0, s113 <= 1, s23 >= 0, s23 <= 0 + 0, s24 >= 0, s24 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 20 + 4*z0 + 124*z1 + 4*z1^2 }-> 1 + s26 + s115 + s221 :|: s221 >= 0, s221 <= 0, s114 >= 0, s114 <= z2 + 1, s115 >= 0, s115 <= 1, s25 >= 0, s25 <= 0 + 0, s26 >= 0, s26 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 20 + 4*z0 + 124*z1 + 4*z1^2 }-> 1 + s28 + s3 + s222 :|: s222 >= 0, s222 <= 0, s27 >= 0, s27 <= 0 + 0, s28 >= 0, s28 <= 1, s3 >= 0, s3 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 20 + 4*s177 + 4*z0 + 124*z2 + 4*z2^2 }-> 1 + s30 + s179 + s235 :|: s235 >= 0, s235 <= 0, s177 >= 0, s177 <= z1 + 1, s178 >= 0, s178 <= z2 + 1, s179 >= 0, s179 <= 1, s29 >= 0, s29 <= 0 + 0, s30 >= 0, s30 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 20 + 4*s180 + 4*z0 + 124*z2 + 4*z2^2 }-> 1 + s32 + s181 + s236 :|: s236 >= 0, s236 <= 0, s180 >= 0, s180 <= z1 + 1, s181 >= 0, s181 <= 1, s31 >= 0, s31 <= 0 + 0, s32 >= 0, s32 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 20 + 4*z0 + 124*z2 + 4*z2^2 }-> 1 + s34 + s183 + s237 :|: s237 >= 0, s237 <= 0, s182 >= 0, s182 <= z2 + 1, s183 >= 0, s183 <= 1, s33 >= 0, s33 <= 0 + 0, s34 >= 0, s34 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 20 + 4*z0 + 124*z2 + 4*z2^2 }-> 1 + s36 + s7 + s238 :|: s238 >= 0, s238 <= 0, s35 >= 0, s35 <= 0 + 0, s36 >= 0, s36 <= 1, s7 >= 0, s7 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 20 + 4*s52 + 4*z0 + 124*z1 + 4*z1^2 }-> 1 + s51 + s54 + s207 :|: s207 >= 0, s207 <= 0, s48 >= 0, s48 <= z1 + 1, s49 >= 0, s49 <= z2 + 1, s50 >= 0, s50 <= s48 + s49, s51 >= 0, s51 <= 1, s52 >= 0, s52 <= z1 + 1, s53 >= 0, s53 <= z2 + 1, s54 >= 0, s54 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 20 + 4*s59 + 4*z0 + 124*z1 + 4*z1^2 }-> 1 + s58 + s60 + s208 :|: s208 >= 0, s208 <= 0, s55 >= 0, s55 <= z1 + 1, s56 >= 0, s56 <= z2 + 1, s57 >= 0, s57 <= s55 + s56, s58 >= 0, s58 <= 1, s59 >= 0, s59 <= z1 + 1, s60 >= 0, s60 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 20 + 4*z0 + 124*z1 + 4*z1^2 }-> 1 + s64 + s66 + s209 :|: s209 >= 0, s209 <= 0, s61 >= 0, s61 <= z1 + 1, s62 >= 0, s62 <= z2 + 1, s63 >= 0, s63 <= s61 + s62, s64 >= 0, s64 <= 1, s65 >= 0, s65 <= z2 + 1, s66 >= 0, s66 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 20 + 4*z0 + 124*z1 + 4*z1^2 }-> 1 + s70 + s'' + s210 :|: s210 >= 0, s210 <= 0, s67 >= 0, s67 <= z1 + 1, s68 >= 0, s68 <= z2 + 1, s69 >= 0, s69 <= s67 + s68, s70 >= 0, s70 <= 1, s'' >= 0, s'' <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 20 + 4*s74 + 4*z0 + 124*z1 + 4*z1^2 }-> 1 + s73 + s76 + s211 :|: s211 >= 0, s211 <= 0, s71 >= 0, s71 <= z1 + 1, s72 >= 0, s72 <= s71 + 0, s73 >= 0, s73 <= 1, s74 >= 0, s74 <= z1 + 1, s75 >= 0, s75 <= z2 + 1, s76 >= 0, s76 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 20 + 4*s80 + 4*z0 + 124*z1 + 4*z1^2 }-> 1 + s79 + s81 + s212 :|: s212 >= 0, s212 <= 0, s77 >= 0, s77 <= z1 + 1, s78 >= 0, s78 <= s77 + 0, s79 >= 0, s79 <= 1, s80 >= 0, s80 <= z1 + 1, s81 >= 0, s81 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 20 + 4*z0 + 124*z1 + 4*z1^2 }-> 1 + s84 + s86 + s213 :|: s213 >= 0, s213 <= 0, s82 >= 0, s82 <= z1 + 1, s83 >= 0, s83 <= s82 + 0, s84 >= 0, s84 <= 1, s85 >= 0, s85 <= z2 + 1, s86 >= 0, s86 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 20 + 4*z0 + 124*z1 + 4*z1^2 }-> 1 + s89 + s1 + s214 :|: s214 >= 0, s214 <= 0, s87 >= 0, s87 <= z1 + 1, s88 >= 0, s88 <= s87 + 0, s89 >= 0, s89 <= 1, s1 >= 0, s1 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 20 + 4*s93 + 4*z0 + 124*z1 + 4*z1^2 }-> 1 + s92 + s95 + s215 :|: s215 >= 0, s215 <= 0, s90 >= 0, s90 <= z2 + 1, s91 >= 0, s91 <= 0 + s90, s92 >= 0, s92 <= 1, s93 >= 0, s93 <= z1 + 1, s94 >= 0, s94 <= z2 + 1, s95 >= 0, s95 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 20 + 4*s99 + 4*z0 + 124*z1 + 4*z1^2 }-> 1 + s98 + s100 + s216 :|: s216 >= 0, s216 <= 0, s96 >= 0, s96 <= z2 + 1, s97 >= 0, s97 <= 0 + s96, s98 >= 0, s98 <= 1, s99 >= 0, s99 <= z1 + 1, s100 >= 0, s100 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTENSORT(z) -{ 0 }-> 0 :|: z >= 0
   FLATTENSORT(z) -{ 0 }-> 1 + INSERTIONSORT(s184) :|: s184 >= 0, s184 <= z + 1, z >= 0
   FLATTENSORT(z) -{ 0 }-> 1 + INSERTIONSORT(0) :|: z >= 0
   INSERT(z, z') -{ 8 + 4*z' }-> 1 + s200 :|: s200 >= 0, s200 <= 0, z' >= 0, z >= 0
   INSERT#1(z, z') -{ 11 + 4*z1 }-> 1 + s201 + s46 :|: s201 >= 0, s201 <= 2, s46 >= 0, s46 <= z0 + z' + 1, z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z' >= 0
   INSERT#1(z, z') -{ 11 + 4*z1 }-> 1 + s205 + s47 :|: s205 >= 0, s205 <= 2, s47 >= 0, s47 <= z0 + z' + 1, s10 >= 0, s10 <= 3, s11 >= 0, s11 <= 2, z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z' >= 0
   INSERT#2(z, z', z'', z3) -{ 9 + 4*z3 }-> 1 + s202 :|: s202 >= 0, s202 <= 1, z = 2, z'' >= 0, z' >= 0, z3 >= 0
   INSERTIONSORT(z) -{ 1 }-> 1 + INSERTIONSORT#1(z) :|: z >= 0
   INSERTIONSORT#1(z) -{ 9 + 4*s196 }-> 1 + s203 + INSERTIONSORT(z1) :|: s203 >= 0, s203 <= 1, s196 >= 0, s196 <= z1, z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   INSERTIONSORT#1(z) -{ 9 }-> 1 + s204 + INSERTIONSORT(z1) :|: s204 >= 0, s204 <= 1, z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   append(z, z') -{ 0 }-> s37 :|: s37 >= 0, s37 <= z + z', z' >= 0, z >= 0
   append(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   append#1(z, z') -{ 0 }-> z' :|: z' >= 0, z = 0
   append#1(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   append#1(z, z') -{ 0 }-> 1 + z0 + s40 :|: s40 >= 0, s40 <= z1 + z', z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z' >= 0
   flatten(z) -{ 0 }-> s185 :|: s185 >= 0, s185 <= z + 1, z >= 0
   flatten(z) -{ 0 }-> 0 :|: z >= 0
   flatten#1(z) -{ 0 }-> s189 :|: s186 >= 0, s186 <= z1 + 1, s187 >= 0, s187 <= z2 + 1, s188 >= 0, s188 <= s186 + s187, s189 >= 0, s189 <= z0 + s188, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   flatten#1(z) -{ 0 }-> s192 :|: s190 >= 0, s190 <= z1 + 1, s191 >= 0, s191 <= s190 + 0, s192 >= 0, s192 <= z0 + s191, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   flatten#1(z) -{ 0 }-> s195 :|: s193 >= 0, s193 <= z2 + 1, s194 >= 0, s194 <= 0 + s193, s195 >= 0, s195 <= z0 + s194, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   flatten#1(z) -{ 0 }-> s39 :|: s38 >= 0, s38 <= 0 + 0, s39 >= 0, s39 <= z0 + s38, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   flatten#1(z) -{ 0 }-> 0 :|: z = 0
   flatten#1(z) -{ 0 }-> 0 :|: z >= 0
   insert(z, z') -{ 0 }-> s42 :|: s42 >= 0, s42 <= z' + z + 1, z' >= 0, z >= 0
   insert(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   insert#1(z, z') -{ 0 }-> s43 :|: s43 >= 0, s43 <= z' + z0 + z1 + 2, z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z' >= 0
   insert#1(z, z') -{ 0 }-> s45 :|: s45 >= 0, s45 <= z' + z0 + z1 + 2, s16 >= 0, s16 <= 3, s17 >= 0, s17 <= 2, z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z' >= 0
   insert#1(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   insert#1(z, z') -{ 0 }-> 1 + z' + 0 :|: z' >= 0, z = 0
   insert#2(z, z', z'', z3) -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0, z3 >= 0
   insert#2(z, z', z'', z3) -{ 0 }-> 1 + z' + (1 + z'' + z3) :|: z'' >= 0, z = 1, z' >= 0, z3 >= 0
   insert#2(z, z', z'', z3) -{ 0 }-> 1 + z'' + s44 :|: s44 >= 0, s44 <= z' + z3 + 1, z = 2, z'' >= 0, z' >= 0, z3 >= 0
   insertionsort(z) -{ 0 }-> s197 :|: s197 >= 0, s197 <= z, z >= 0
   insertionsort(z) -{ 0 }-> 0 :|: z >= 0
   insertionsort#1(z) -{ 0 }-> s199 :|: s198 >= 0, s198 <= z1, s199 >= 0, s199 <= z0 + s198 + 1, z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   insertionsort#1(z) -{ 0 }-> s41 :|: s41 >= 0, s41 <= z0 + 0 + 1, z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   insertionsort#1(z) -{ 0 }-> 0 :|: z = 0
   insertionsort#1(z) -{ 0 }-> 0 :|: z >= 0

Function symbols to be analyzed: {insertionsort}, {INSERTIONSORT,INSERTIONSORT#1}, {FLATTENSORT}
Previous analysis results are:
  APPEND#1: runtime: O(n^1) [4*z], size: O(1) [0]
  APPEND: runtime: O(n^1) [1 + 4*z], size: O(1) [1]
  #cklt: runtime: O(1) [0], size: O(1) [2]
  #compare: runtime: O(1) [0], size: O(1) [3]
  #COMPARE: runtime: O(1) [0], size: O(n^1) [z + z']
  append#1: runtime: O(1) [0], size: O(n^1) [z + z']
  append: runtime: O(1) [0], size: O(n^1) [z + z']
  #less: runtime: O(1) [0], size: O(1) [2]
  insert#2: runtime: O(1) [0], size: O(n^1) [2 + z' + z'' + z3]
  insert: runtime: O(1) [0], size: O(n^1) [1 + z + z']
  insert#1: runtime: O(1) [0], size: O(n^1) [1 + z + z']
  #LESS: runtime: O(1) [1], size: O(n^1) [1 + z + z']
  flatten#1: runtime: O(1) [0], size: O(n^1) [1 + z]
  insertionsort#1: runtime: O(1) [0], size: O(n^1) [z]
  INSERT#1: runtime: O(n^1) [7 + 4*z], size: O(1) [0]
  INSERT#2: runtime: O(n^1) [9 + 4*z3], size: O(1) [2]
  INSERT: runtime: O(n^1) [8 + 4*z'], size: O(1) [1]
  flatten: runtime: O(1) [0], size: O(n^1) [1 + z]
  FLATTEN: runtime: O(n^2) [17 + 124*z + 4*z^2], size: O(1) [0]
  FLATTEN#1: runtime: O(n^2) [704 + 4160*z + 128*z^2], size: O(1) [3]
  insertionsort: runtime: ?, size: O(n^1) [z]

----------------------------------------

(117) IntTrsBoundProof (UPPER BOUND(ID))

Computed RUNTIME bound using CoFloCo for: insertionsort
after applying outer abstraction to obtain an ITS,
resulting in: O(1) with polynomial bound: 0

----------------------------------------

(118)
Obligation:
Complexity RNTS consisting of the following rules:

   #COMPARE(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   #COMPARE(z, z') -{ 0 }-> 1 + s19 :|: s19 >= 0, s19 <= z' - 1 + (z - 1), z' - 1 >= 0, z - 1 >= 0
   #COMPARE(z, z') -{ 0 }-> 1 + s20 :|: s20 >= 0, s20 <= z - 1 + (z' - 1), z' - 1 >= 0, z - 1 >= 0
   #LESS(z, z') -{ 1 }-> 1 + s18 :|: s18 >= 0, s18 <= z + z', z' >= 0, z >= 0
   #cklt(z) -{ 0 }-> 2 :|: z = 3
   #cklt(z) -{ 0 }-> 1 :|: z = 1
   #cklt(z) -{ 0 }-> 1 :|: z = 2
   #cklt(z) -{ 0 }-> 0 :|: z >= 0
   #compare(z, z') -{ 0 }-> s8 :|: s8 >= 0, s8 <= 3, z' - 1 >= 0, z - 1 >= 0
   #compare(z, z') -{ 0 }-> s9 :|: s9 >= 0, s9 <= 3, z' - 1 >= 0, z - 1 >= 0
   #compare(z, z') -{ 0 }-> 3 :|: z' - 1 >= 0, z = 0
   #compare(z, z') -{ 0 }-> 3 :|: z - 1 >= 0, z' = 0
   #compare(z, z') -{ 0 }-> 3 :|: z' - 1 >= 0, z - 1 >= 0
   #compare(z, z') -{ 0 }-> 2 :|: z' - 1 >= 0, z = 0
   #compare(z, z') -{ 0 }-> 2 :|: z - 1 >= 0, z' = 0
   #compare(z, z') -{ 0 }-> 2 :|: z' - 1 >= 0, z - 1 >= 0
   #compare(z, z') -{ 0 }-> 1 :|: z = 0, z' = 0
   #compare(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   #less(z, z') -{ 0 }-> s13 :|: s12 >= 0, s12 <= 3, s13 >= 0, s13 <= 2, z' - 1 >= 0, z - 1 >= 0
   #less(z, z') -{ 0 }-> s15 :|: s14 >= 0, s14 <= 3, s15 >= 0, s15 <= 2, z - 1 >= 0, z' - 1 >= 0
   #less(z, z') -{ 0 }-> 2 :|: z' - 1 >= 0, z = 0, 3 = 3
   #less(z, z') -{ 0 }-> 2 :|: z - 1 >= 0, z' = 0, 3 = 3
   #less(z, z') -{ 0 }-> 2 :|: z - 1 >= 0, z' - 1 >= 0, 3 = 3
   #less(z, z') -{ 0 }-> 1 :|: z = 0, z' = 0, 1 = 1
   #less(z, z') -{ 0 }-> 1 :|: z' - 1 >= 0, z = 0, 2 = 2
   #less(z, z') -{ 0 }-> 1 :|: z - 1 >= 0, z' = 0, 2 = 2
   #less(z, z') -{ 0 }-> 1 :|: z' - 1 >= 0, z - 1 >= 0, 2 = 2
   #less(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   #less(z, z') -{ 0 }-> 0 :|: z = 0, z' = 0, v0 >= 0, 1 = v0
   #less(z, z') -{ 0 }-> 0 :|: z' - 1 >= 0, z = 0, v0 >= 0, 2 = v0
   #less(z, z') -{ 0 }-> 0 :|: z' - 1 >= 0, z = 0, v0 >= 0, 3 = v0
   #less(z, z') -{ 0 }-> 0 :|: z - 1 >= 0, z' = 0, v0 >= 0, 3 = v0
   #less(z, z') -{ 0 }-> 0 :|: z - 1 >= 0, z' - 1 >= 0, v0 >= 0, 3 = v0
   #less(z, z') -{ 0 }-> 0 :|: z - 1 >= 0, z' = 0, v0 >= 0, 2 = v0
   #less(z, z') -{ 0 }-> 0 :|: z' - 1 >= 0, z - 1 >= 0, v0 >= 0, 2 = v0
   #less(z, z') -{ 0 }-> 0 :|: z' >= 0, z >= 0, v0 >= 0, 0 = v0
   APPEND(z, z') -{ 1 + 4*z }-> 1 + s :|: s >= 0, s <= 0, z' >= 0, z >= 0
   APPEND#1(z, z') -{ 2 + 4*z1 }-> 1 + s' :|: s' >= 0, s' <= 1, z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z' >= 0
   FLATTEN(z) -{ 705 + 4160*z + 128*z^2 }-> 1 + s206 :|: s206 >= 0, s206 <= 3, z >= 0
   FLATTEN#1(z) -{ 20 + 4*z0 + 124*z1 + 4*z1^2 }-> 1 + s103 + s105 + s217 :|: s217 >= 0, s217 <= 0, s101 >= 0, s101 <= z2 + 1, s102 >= 0, s102 <= 0 + s101, s103 >= 0, s103 <= 1, s104 >= 0, s104 <= z2 + 1, s105 >= 0, s105 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 20 + 4*z0 + 124*z1 + 4*z1^2 }-> 1 + s108 + s2 + s218 :|: s218 >= 0, s218 <= 0, s106 >= 0, s106 <= z2 + 1, s107 >= 0, s107 <= 0 + s106, s108 >= 0, s108 <= 1, s2 >= 0, s2 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 20 + 4*s120 + 4*z0 + 124*z2 + 4*z2^2 }-> 1 + s119 + s122 + s223 :|: s223 >= 0, s223 <= 0, s116 >= 0, s116 <= z1 + 1, s117 >= 0, s117 <= z2 + 1, s118 >= 0, s118 <= s116 + s117, s119 >= 0, s119 <= 1, s120 >= 0, s120 <= z1 + 1, s121 >= 0, s121 <= z2 + 1, s122 >= 0, s122 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 20 + 4*s127 + 4*z0 + 124*z2 + 4*z2^2 }-> 1 + s126 + s128 + s224 :|: s224 >= 0, s224 <= 0, s123 >= 0, s123 <= z1 + 1, s124 >= 0, s124 <= z2 + 1, s125 >= 0, s125 <= s123 + s124, s126 >= 0, s126 <= 1, s127 >= 0, s127 <= z1 + 1, s128 >= 0, s128 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 20 + 4*z0 + 124*z2 + 4*z2^2 }-> 1 + s132 + s134 + s225 :|: s225 >= 0, s225 <= 0, s129 >= 0, s129 <= z1 + 1, s130 >= 0, s130 <= z2 + 1, s131 >= 0, s131 <= s129 + s130, s132 >= 0, s132 <= 1, s133 >= 0, s133 <= z2 + 1, s134 >= 0, s134 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 20 + 4*z0 + 124*z2 + 4*z2^2 }-> 1 + s138 + s4 + s226 :|: s226 >= 0, s226 <= 0, s135 >= 0, s135 <= z1 + 1, s136 >= 0, s136 <= z2 + 1, s137 >= 0, s137 <= s135 + s136, s138 >= 0, s138 <= 1, s4 >= 0, s4 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 20 + 4*s142 + 4*z0 + 124*z2 + 4*z2^2 }-> 1 + s141 + s144 + s227 :|: s227 >= 0, s227 <= 0, s139 >= 0, s139 <= z1 + 1, s140 >= 0, s140 <= s139 + 0, s141 >= 0, s141 <= 1, s142 >= 0, s142 <= z1 + 1, s143 >= 0, s143 <= z2 + 1, s144 >= 0, s144 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 20 + 4*s148 + 4*z0 + 124*z2 + 4*z2^2 }-> 1 + s147 + s149 + s228 :|: s228 >= 0, s228 <= 0, s145 >= 0, s145 <= z1 + 1, s146 >= 0, s146 <= s145 + 0, s147 >= 0, s147 <= 1, s148 >= 0, s148 <= z1 + 1, s149 >= 0, s149 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 20 + 4*z0 + 124*z2 + 4*z2^2 }-> 1 + s152 + s154 + s229 :|: s229 >= 0, s229 <= 0, s150 >= 0, s150 <= z1 + 1, s151 >= 0, s151 <= s150 + 0, s152 >= 0, s152 <= 1, s153 >= 0, s153 <= z2 + 1, s154 >= 0, s154 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 20 + 4*z0 + 124*z2 + 4*z2^2 }-> 1 + s157 + s5 + s230 :|: s230 >= 0, s230 <= 0, s155 >= 0, s155 <= z1 + 1, s156 >= 0, s156 <= s155 + 0, s157 >= 0, s157 <= 1, s5 >= 0, s5 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 20 + 4*s161 + 4*z0 + 124*z2 + 4*z2^2 }-> 1 + s160 + s163 + s231 :|: s231 >= 0, s231 <= 0, s158 >= 0, s158 <= z2 + 1, s159 >= 0, s159 <= 0 + s158, s160 >= 0, s160 <= 1, s161 >= 0, s161 <= z1 + 1, s162 >= 0, s162 <= z2 + 1, s163 >= 0, s163 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 20 + 4*s167 + 4*z0 + 124*z2 + 4*z2^2 }-> 1 + s166 + s168 + s232 :|: s232 >= 0, s232 <= 0, s164 >= 0, s164 <= z2 + 1, s165 >= 0, s165 <= 0 + s164, s166 >= 0, s166 <= 1, s167 >= 0, s167 <= z1 + 1, s168 >= 0, s168 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 20 + 4*z0 + 124*z2 + 4*z2^2 }-> 1 + s171 + s173 + s233 :|: s233 >= 0, s233 <= 0, s169 >= 0, s169 <= z2 + 1, s170 >= 0, s170 <= 0 + s169, s171 >= 0, s171 <= 1, s172 >= 0, s172 <= z2 + 1, s173 >= 0, s173 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 20 + 4*z0 + 124*z2 + 4*z2^2 }-> 1 + s176 + s6 + s234 :|: s234 >= 0, s234 <= 0, s174 >= 0, s174 <= z2 + 1, s175 >= 0, s175 <= 0 + s174, s176 >= 0, s176 <= 1, s6 >= 0, s6 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 20 + 4*s109 + 4*z0 + 124*z1 + 4*z1^2 }-> 1 + s22 + s111 + s219 :|: s219 >= 0, s219 <= 0, s109 >= 0, s109 <= z1 + 1, s110 >= 0, s110 <= z2 + 1, s111 >= 0, s111 <= 1, s21 >= 0, s21 <= 0 + 0, s22 >= 0, s22 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 20 + 4*s112 + 4*z0 + 124*z1 + 4*z1^2 }-> 1 + s24 + s113 + s220 :|: s220 >= 0, s220 <= 0, s112 >= 0, s112 <= z1 + 1, s113 >= 0, s113 <= 1, s23 >= 0, s23 <= 0 + 0, s24 >= 0, s24 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 20 + 4*z0 + 124*z1 + 4*z1^2 }-> 1 + s26 + s115 + s221 :|: s221 >= 0, s221 <= 0, s114 >= 0, s114 <= z2 + 1, s115 >= 0, s115 <= 1, s25 >= 0, s25 <= 0 + 0, s26 >= 0, s26 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 20 + 4*z0 + 124*z1 + 4*z1^2 }-> 1 + s28 + s3 + s222 :|: s222 >= 0, s222 <= 0, s27 >= 0, s27 <= 0 + 0, s28 >= 0, s28 <= 1, s3 >= 0, s3 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 20 + 4*s177 + 4*z0 + 124*z2 + 4*z2^2 }-> 1 + s30 + s179 + s235 :|: s235 >= 0, s235 <= 0, s177 >= 0, s177 <= z1 + 1, s178 >= 0, s178 <= z2 + 1, s179 >= 0, s179 <= 1, s29 >= 0, s29 <= 0 + 0, s30 >= 0, s30 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 20 + 4*s180 + 4*z0 + 124*z2 + 4*z2^2 }-> 1 + s32 + s181 + s236 :|: s236 >= 0, s236 <= 0, s180 >= 0, s180 <= z1 + 1, s181 >= 0, s181 <= 1, s31 >= 0, s31 <= 0 + 0, s32 >= 0, s32 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 20 + 4*z0 + 124*z2 + 4*z2^2 }-> 1 + s34 + s183 + s237 :|: s237 >= 0, s237 <= 0, s182 >= 0, s182 <= z2 + 1, s183 >= 0, s183 <= 1, s33 >= 0, s33 <= 0 + 0, s34 >= 0, s34 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 20 + 4*z0 + 124*z2 + 4*z2^2 }-> 1 + s36 + s7 + s238 :|: s238 >= 0, s238 <= 0, s35 >= 0, s35 <= 0 + 0, s36 >= 0, s36 <= 1, s7 >= 0, s7 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 20 + 4*s52 + 4*z0 + 124*z1 + 4*z1^2 }-> 1 + s51 + s54 + s207 :|: s207 >= 0, s207 <= 0, s48 >= 0, s48 <= z1 + 1, s49 >= 0, s49 <= z2 + 1, s50 >= 0, s50 <= s48 + s49, s51 >= 0, s51 <= 1, s52 >= 0, s52 <= z1 + 1, s53 >= 0, s53 <= z2 + 1, s54 >= 0, s54 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 20 + 4*s59 + 4*z0 + 124*z1 + 4*z1^2 }-> 1 + s58 + s60 + s208 :|: s208 >= 0, s208 <= 0, s55 >= 0, s55 <= z1 + 1, s56 >= 0, s56 <= z2 + 1, s57 >= 0, s57 <= s55 + s56, s58 >= 0, s58 <= 1, s59 >= 0, s59 <= z1 + 1, s60 >= 0, s60 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 20 + 4*z0 + 124*z1 + 4*z1^2 }-> 1 + s64 + s66 + s209 :|: s209 >= 0, s209 <= 0, s61 >= 0, s61 <= z1 + 1, s62 >= 0, s62 <= z2 + 1, s63 >= 0, s63 <= s61 + s62, s64 >= 0, s64 <= 1, s65 >= 0, s65 <= z2 + 1, s66 >= 0, s66 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 20 + 4*z0 + 124*z1 + 4*z1^2 }-> 1 + s70 + s'' + s210 :|: s210 >= 0, s210 <= 0, s67 >= 0, s67 <= z1 + 1, s68 >= 0, s68 <= z2 + 1, s69 >= 0, s69 <= s67 + s68, s70 >= 0, s70 <= 1, s'' >= 0, s'' <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 20 + 4*s74 + 4*z0 + 124*z1 + 4*z1^2 }-> 1 + s73 + s76 + s211 :|: s211 >= 0, s211 <= 0, s71 >= 0, s71 <= z1 + 1, s72 >= 0, s72 <= s71 + 0, s73 >= 0, s73 <= 1, s74 >= 0, s74 <= z1 + 1, s75 >= 0, s75 <= z2 + 1, s76 >= 0, s76 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 20 + 4*s80 + 4*z0 + 124*z1 + 4*z1^2 }-> 1 + s79 + s81 + s212 :|: s212 >= 0, s212 <= 0, s77 >= 0, s77 <= z1 + 1, s78 >= 0, s78 <= s77 + 0, s79 >= 0, s79 <= 1, s80 >= 0, s80 <= z1 + 1, s81 >= 0, s81 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 20 + 4*z0 + 124*z1 + 4*z1^2 }-> 1 + s84 + s86 + s213 :|: s213 >= 0, s213 <= 0, s82 >= 0, s82 <= z1 + 1, s83 >= 0, s83 <= s82 + 0, s84 >= 0, s84 <= 1, s85 >= 0, s85 <= z2 + 1, s86 >= 0, s86 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 20 + 4*z0 + 124*z1 + 4*z1^2 }-> 1 + s89 + s1 + s214 :|: s214 >= 0, s214 <= 0, s87 >= 0, s87 <= z1 + 1, s88 >= 0, s88 <= s87 + 0, s89 >= 0, s89 <= 1, s1 >= 0, s1 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 20 + 4*s93 + 4*z0 + 124*z1 + 4*z1^2 }-> 1 + s92 + s95 + s215 :|: s215 >= 0, s215 <= 0, s90 >= 0, s90 <= z2 + 1, s91 >= 0, s91 <= 0 + s90, s92 >= 0, s92 <= 1, s93 >= 0, s93 <= z1 + 1, s94 >= 0, s94 <= z2 + 1, s95 >= 0, s95 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 20 + 4*s99 + 4*z0 + 124*z1 + 4*z1^2 }-> 1 + s98 + s100 + s216 :|: s216 >= 0, s216 <= 0, s96 >= 0, s96 <= z2 + 1, s97 >= 0, s97 <= 0 + s96, s98 >= 0, s98 <= 1, s99 >= 0, s99 <= z1 + 1, s100 >= 0, s100 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTENSORT(z) -{ 0 }-> 0 :|: z >= 0
   FLATTENSORT(z) -{ 0 }-> 1 + INSERTIONSORT(s184) :|: s184 >= 0, s184 <= z + 1, z >= 0
   FLATTENSORT(z) -{ 0 }-> 1 + INSERTIONSORT(0) :|: z >= 0
   INSERT(z, z') -{ 8 + 4*z' }-> 1 + s200 :|: s200 >= 0, s200 <= 0, z' >= 0, z >= 0
   INSERT#1(z, z') -{ 11 + 4*z1 }-> 1 + s201 + s46 :|: s201 >= 0, s201 <= 2, s46 >= 0, s46 <= z0 + z' + 1, z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z' >= 0
   INSERT#1(z, z') -{ 11 + 4*z1 }-> 1 + s205 + s47 :|: s205 >= 0, s205 <= 2, s47 >= 0, s47 <= z0 + z' + 1, s10 >= 0, s10 <= 3, s11 >= 0, s11 <= 2, z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z' >= 0
   INSERT#2(z, z', z'', z3) -{ 9 + 4*z3 }-> 1 + s202 :|: s202 >= 0, s202 <= 1, z = 2, z'' >= 0, z' >= 0, z3 >= 0
   INSERTIONSORT(z) -{ 1 }-> 1 + INSERTIONSORT#1(z) :|: z >= 0
   INSERTIONSORT#1(z) -{ 9 + 4*s196 }-> 1 + s203 + INSERTIONSORT(z1) :|: s203 >= 0, s203 <= 1, s196 >= 0, s196 <= z1, z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   INSERTIONSORT#1(z) -{ 9 }-> 1 + s204 + INSERTIONSORT(z1) :|: s204 >= 0, s204 <= 1, z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   append(z, z') -{ 0 }-> s37 :|: s37 >= 0, s37 <= z + z', z' >= 0, z >= 0
   append(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   append#1(z, z') -{ 0 }-> z' :|: z' >= 0, z = 0
   append#1(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   append#1(z, z') -{ 0 }-> 1 + z0 + s40 :|: s40 >= 0, s40 <= z1 + z', z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z' >= 0
   flatten(z) -{ 0 }-> s185 :|: s185 >= 0, s185 <= z + 1, z >= 0
   flatten(z) -{ 0 }-> 0 :|: z >= 0
   flatten#1(z) -{ 0 }-> s189 :|: s186 >= 0, s186 <= z1 + 1, s187 >= 0, s187 <= z2 + 1, s188 >= 0, s188 <= s186 + s187, s189 >= 0, s189 <= z0 + s188, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   flatten#1(z) -{ 0 }-> s192 :|: s190 >= 0, s190 <= z1 + 1, s191 >= 0, s191 <= s190 + 0, s192 >= 0, s192 <= z0 + s191, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   flatten#1(z) -{ 0 }-> s195 :|: s193 >= 0, s193 <= z2 + 1, s194 >= 0, s194 <= 0 + s193, s195 >= 0, s195 <= z0 + s194, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   flatten#1(z) -{ 0 }-> s39 :|: s38 >= 0, s38 <= 0 + 0, s39 >= 0, s39 <= z0 + s38, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   flatten#1(z) -{ 0 }-> 0 :|: z = 0
   flatten#1(z) -{ 0 }-> 0 :|: z >= 0
   insert(z, z') -{ 0 }-> s42 :|: s42 >= 0, s42 <= z' + z + 1, z' >= 0, z >= 0
   insert(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   insert#1(z, z') -{ 0 }-> s43 :|: s43 >= 0, s43 <= z' + z0 + z1 + 2, z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z' >= 0
   insert#1(z, z') -{ 0 }-> s45 :|: s45 >= 0, s45 <= z' + z0 + z1 + 2, s16 >= 0, s16 <= 3, s17 >= 0, s17 <= 2, z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z' >= 0
   insert#1(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   insert#1(z, z') -{ 0 }-> 1 + z' + 0 :|: z' >= 0, z = 0
   insert#2(z, z', z'', z3) -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0, z3 >= 0
   insert#2(z, z', z'', z3) -{ 0 }-> 1 + z' + (1 + z'' + z3) :|: z'' >= 0, z = 1, z' >= 0, z3 >= 0
   insert#2(z, z', z'', z3) -{ 0 }-> 1 + z'' + s44 :|: s44 >= 0, s44 <= z' + z3 + 1, z = 2, z'' >= 0, z' >= 0, z3 >= 0
   insertionsort(z) -{ 0 }-> s197 :|: s197 >= 0, s197 <= z, z >= 0
   insertionsort(z) -{ 0 }-> 0 :|: z >= 0
   insertionsort#1(z) -{ 0 }-> s199 :|: s198 >= 0, s198 <= z1, s199 >= 0, s199 <= z0 + s198 + 1, z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   insertionsort#1(z) -{ 0 }-> s41 :|: s41 >= 0, s41 <= z0 + 0 + 1, z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   insertionsort#1(z) -{ 0 }-> 0 :|: z = 0
   insertionsort#1(z) -{ 0 }-> 0 :|: z >= 0

Function symbols to be analyzed: {INSERTIONSORT,INSERTIONSORT#1}, {FLATTENSORT}
Previous analysis results are:
  APPEND#1: runtime: O(n^1) [4*z], size: O(1) [0]
  APPEND: runtime: O(n^1) [1 + 4*z], size: O(1) [1]
  #cklt: runtime: O(1) [0], size: O(1) [2]
  #compare: runtime: O(1) [0], size: O(1) [3]
  #COMPARE: runtime: O(1) [0], size: O(n^1) [z + z']
  append#1: runtime: O(1) [0], size: O(n^1) [z + z']
  append: runtime: O(1) [0], size: O(n^1) [z + z']
  #less: runtime: O(1) [0], size: O(1) [2]
  insert#2: runtime: O(1) [0], size: O(n^1) [2 + z' + z'' + z3]
  insert: runtime: O(1) [0], size: O(n^1) [1 + z + z']
  insert#1: runtime: O(1) [0], size: O(n^1) [1 + z + z']
  #LESS: runtime: O(1) [1], size: O(n^1) [1 + z + z']
  flatten#1: runtime: O(1) [0], size: O(n^1) [1 + z]
  insertionsort#1: runtime: O(1) [0], size: O(n^1) [z]
  INSERT#1: runtime: O(n^1) [7 + 4*z], size: O(1) [0]
  INSERT#2: runtime: O(n^1) [9 + 4*z3], size: O(1) [2]
  INSERT: runtime: O(n^1) [8 + 4*z'], size: O(1) [1]
  flatten: runtime: O(1) [0], size: O(n^1) [1 + z]
  FLATTEN: runtime: O(n^2) [17 + 124*z + 4*z^2], size: O(1) [0]
  FLATTEN#1: runtime: O(n^2) [704 + 4160*z + 128*z^2], size: O(1) [3]
  insertionsort: runtime: O(1) [0], size: O(n^1) [z]

----------------------------------------

(119) ResultPropagationProof (UPPER BOUND(ID))
Applied inner abstraction using the recently inferred runtime/size bounds where possible.
----------------------------------------

(120)
Obligation:
Complexity RNTS consisting of the following rules:

   #COMPARE(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   #COMPARE(z, z') -{ 0 }-> 1 + s19 :|: s19 >= 0, s19 <= z' - 1 + (z - 1), z' - 1 >= 0, z - 1 >= 0
   #COMPARE(z, z') -{ 0 }-> 1 + s20 :|: s20 >= 0, s20 <= z - 1 + (z' - 1), z' - 1 >= 0, z - 1 >= 0
   #LESS(z, z') -{ 1 }-> 1 + s18 :|: s18 >= 0, s18 <= z + z', z' >= 0, z >= 0
   #cklt(z) -{ 0 }-> 2 :|: z = 3
   #cklt(z) -{ 0 }-> 1 :|: z = 1
   #cklt(z) -{ 0 }-> 1 :|: z = 2
   #cklt(z) -{ 0 }-> 0 :|: z >= 0
   #compare(z, z') -{ 0 }-> s8 :|: s8 >= 0, s8 <= 3, z' - 1 >= 0, z - 1 >= 0
   #compare(z, z') -{ 0 }-> s9 :|: s9 >= 0, s9 <= 3, z' - 1 >= 0, z - 1 >= 0
   #compare(z, z') -{ 0 }-> 3 :|: z' - 1 >= 0, z = 0
   #compare(z, z') -{ 0 }-> 3 :|: z - 1 >= 0, z' = 0
   #compare(z, z') -{ 0 }-> 3 :|: z' - 1 >= 0, z - 1 >= 0
   #compare(z, z') -{ 0 }-> 2 :|: z' - 1 >= 0, z = 0
   #compare(z, z') -{ 0 }-> 2 :|: z - 1 >= 0, z' = 0
   #compare(z, z') -{ 0 }-> 2 :|: z' - 1 >= 0, z - 1 >= 0
   #compare(z, z') -{ 0 }-> 1 :|: z = 0, z' = 0
   #compare(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   #less(z, z') -{ 0 }-> s13 :|: s12 >= 0, s12 <= 3, s13 >= 0, s13 <= 2, z' - 1 >= 0, z - 1 >= 0
   #less(z, z') -{ 0 }-> s15 :|: s14 >= 0, s14 <= 3, s15 >= 0, s15 <= 2, z - 1 >= 0, z' - 1 >= 0
   #less(z, z') -{ 0 }-> 2 :|: z' - 1 >= 0, z = 0, 3 = 3
   #less(z, z') -{ 0 }-> 2 :|: z - 1 >= 0, z' = 0, 3 = 3
   #less(z, z') -{ 0 }-> 2 :|: z - 1 >= 0, z' - 1 >= 0, 3 = 3
   #less(z, z') -{ 0 }-> 1 :|: z = 0, z' = 0, 1 = 1
   #less(z, z') -{ 0 }-> 1 :|: z' - 1 >= 0, z = 0, 2 = 2
   #less(z, z') -{ 0 }-> 1 :|: z - 1 >= 0, z' = 0, 2 = 2
   #less(z, z') -{ 0 }-> 1 :|: z' - 1 >= 0, z - 1 >= 0, 2 = 2
   #less(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   #less(z, z') -{ 0 }-> 0 :|: z = 0, z' = 0, v0 >= 0, 1 = v0
   #less(z, z') -{ 0 }-> 0 :|: z' - 1 >= 0, z = 0, v0 >= 0, 2 = v0
   #less(z, z') -{ 0 }-> 0 :|: z' - 1 >= 0, z = 0, v0 >= 0, 3 = v0
   #less(z, z') -{ 0 }-> 0 :|: z - 1 >= 0, z' = 0, v0 >= 0, 3 = v0
   #less(z, z') -{ 0 }-> 0 :|: z - 1 >= 0, z' - 1 >= 0, v0 >= 0, 3 = v0
   #less(z, z') -{ 0 }-> 0 :|: z - 1 >= 0, z' = 0, v0 >= 0, 2 = v0
   #less(z, z') -{ 0 }-> 0 :|: z' - 1 >= 0, z - 1 >= 0, v0 >= 0, 2 = v0
   #less(z, z') -{ 0 }-> 0 :|: z' >= 0, z >= 0, v0 >= 0, 0 = v0
   APPEND(z, z') -{ 1 + 4*z }-> 1 + s :|: s >= 0, s <= 0, z' >= 0, z >= 0
   APPEND#1(z, z') -{ 2 + 4*z1 }-> 1 + s' :|: s' >= 0, s' <= 1, z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z' >= 0
   FLATTEN(z) -{ 705 + 4160*z + 128*z^2 }-> 1 + s206 :|: s206 >= 0, s206 <= 3, z >= 0
   FLATTEN#1(z) -{ 20 + 4*z0 + 124*z1 + 4*z1^2 }-> 1 + s103 + s105 + s217 :|: s217 >= 0, s217 <= 0, s101 >= 0, s101 <= z2 + 1, s102 >= 0, s102 <= 0 + s101, s103 >= 0, s103 <= 1, s104 >= 0, s104 <= z2 + 1, s105 >= 0, s105 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 20 + 4*z0 + 124*z1 + 4*z1^2 }-> 1 + s108 + s2 + s218 :|: s218 >= 0, s218 <= 0, s106 >= 0, s106 <= z2 + 1, s107 >= 0, s107 <= 0 + s106, s108 >= 0, s108 <= 1, s2 >= 0, s2 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 20 + 4*s120 + 4*z0 + 124*z2 + 4*z2^2 }-> 1 + s119 + s122 + s223 :|: s223 >= 0, s223 <= 0, s116 >= 0, s116 <= z1 + 1, s117 >= 0, s117 <= z2 + 1, s118 >= 0, s118 <= s116 + s117, s119 >= 0, s119 <= 1, s120 >= 0, s120 <= z1 + 1, s121 >= 0, s121 <= z2 + 1, s122 >= 0, s122 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 20 + 4*s127 + 4*z0 + 124*z2 + 4*z2^2 }-> 1 + s126 + s128 + s224 :|: s224 >= 0, s224 <= 0, s123 >= 0, s123 <= z1 + 1, s124 >= 0, s124 <= z2 + 1, s125 >= 0, s125 <= s123 + s124, s126 >= 0, s126 <= 1, s127 >= 0, s127 <= z1 + 1, s128 >= 0, s128 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 20 + 4*z0 + 124*z2 + 4*z2^2 }-> 1 + s132 + s134 + s225 :|: s225 >= 0, s225 <= 0, s129 >= 0, s129 <= z1 + 1, s130 >= 0, s130 <= z2 + 1, s131 >= 0, s131 <= s129 + s130, s132 >= 0, s132 <= 1, s133 >= 0, s133 <= z2 + 1, s134 >= 0, s134 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 20 + 4*z0 + 124*z2 + 4*z2^2 }-> 1 + s138 + s4 + s226 :|: s226 >= 0, s226 <= 0, s135 >= 0, s135 <= z1 + 1, s136 >= 0, s136 <= z2 + 1, s137 >= 0, s137 <= s135 + s136, s138 >= 0, s138 <= 1, s4 >= 0, s4 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 20 + 4*s142 + 4*z0 + 124*z2 + 4*z2^2 }-> 1 + s141 + s144 + s227 :|: s227 >= 0, s227 <= 0, s139 >= 0, s139 <= z1 + 1, s140 >= 0, s140 <= s139 + 0, s141 >= 0, s141 <= 1, s142 >= 0, s142 <= z1 + 1, s143 >= 0, s143 <= z2 + 1, s144 >= 0, s144 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 20 + 4*s148 + 4*z0 + 124*z2 + 4*z2^2 }-> 1 + s147 + s149 + s228 :|: s228 >= 0, s228 <= 0, s145 >= 0, s145 <= z1 + 1, s146 >= 0, s146 <= s145 + 0, s147 >= 0, s147 <= 1, s148 >= 0, s148 <= z1 + 1, s149 >= 0, s149 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 20 + 4*z0 + 124*z2 + 4*z2^2 }-> 1 + s152 + s154 + s229 :|: s229 >= 0, s229 <= 0, s150 >= 0, s150 <= z1 + 1, s151 >= 0, s151 <= s150 + 0, s152 >= 0, s152 <= 1, s153 >= 0, s153 <= z2 + 1, s154 >= 0, s154 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 20 + 4*z0 + 124*z2 + 4*z2^2 }-> 1 + s157 + s5 + s230 :|: s230 >= 0, s230 <= 0, s155 >= 0, s155 <= z1 + 1, s156 >= 0, s156 <= s155 + 0, s157 >= 0, s157 <= 1, s5 >= 0, s5 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 20 + 4*s161 + 4*z0 + 124*z2 + 4*z2^2 }-> 1 + s160 + s163 + s231 :|: s231 >= 0, s231 <= 0, s158 >= 0, s158 <= z2 + 1, s159 >= 0, s159 <= 0 + s158, s160 >= 0, s160 <= 1, s161 >= 0, s161 <= z1 + 1, s162 >= 0, s162 <= z2 + 1, s163 >= 0, s163 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 20 + 4*s167 + 4*z0 + 124*z2 + 4*z2^2 }-> 1 + s166 + s168 + s232 :|: s232 >= 0, s232 <= 0, s164 >= 0, s164 <= z2 + 1, s165 >= 0, s165 <= 0 + s164, s166 >= 0, s166 <= 1, s167 >= 0, s167 <= z1 + 1, s168 >= 0, s168 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 20 + 4*z0 + 124*z2 + 4*z2^2 }-> 1 + s171 + s173 + s233 :|: s233 >= 0, s233 <= 0, s169 >= 0, s169 <= z2 + 1, s170 >= 0, s170 <= 0 + s169, s171 >= 0, s171 <= 1, s172 >= 0, s172 <= z2 + 1, s173 >= 0, s173 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 20 + 4*z0 + 124*z2 + 4*z2^2 }-> 1 + s176 + s6 + s234 :|: s234 >= 0, s234 <= 0, s174 >= 0, s174 <= z2 + 1, s175 >= 0, s175 <= 0 + s174, s176 >= 0, s176 <= 1, s6 >= 0, s6 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 20 + 4*s109 + 4*z0 + 124*z1 + 4*z1^2 }-> 1 + s22 + s111 + s219 :|: s219 >= 0, s219 <= 0, s109 >= 0, s109 <= z1 + 1, s110 >= 0, s110 <= z2 + 1, s111 >= 0, s111 <= 1, s21 >= 0, s21 <= 0 + 0, s22 >= 0, s22 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 20 + 4*s112 + 4*z0 + 124*z1 + 4*z1^2 }-> 1 + s24 + s113 + s220 :|: s220 >= 0, s220 <= 0, s112 >= 0, s112 <= z1 + 1, s113 >= 0, s113 <= 1, s23 >= 0, s23 <= 0 + 0, s24 >= 0, s24 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 20 + 4*z0 + 124*z1 + 4*z1^2 }-> 1 + s26 + s115 + s221 :|: s221 >= 0, s221 <= 0, s114 >= 0, s114 <= z2 + 1, s115 >= 0, s115 <= 1, s25 >= 0, s25 <= 0 + 0, s26 >= 0, s26 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 20 + 4*z0 + 124*z1 + 4*z1^2 }-> 1 + s28 + s3 + s222 :|: s222 >= 0, s222 <= 0, s27 >= 0, s27 <= 0 + 0, s28 >= 0, s28 <= 1, s3 >= 0, s3 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 20 + 4*s177 + 4*z0 + 124*z2 + 4*z2^2 }-> 1 + s30 + s179 + s235 :|: s235 >= 0, s235 <= 0, s177 >= 0, s177 <= z1 + 1, s178 >= 0, s178 <= z2 + 1, s179 >= 0, s179 <= 1, s29 >= 0, s29 <= 0 + 0, s30 >= 0, s30 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 20 + 4*s180 + 4*z0 + 124*z2 + 4*z2^2 }-> 1 + s32 + s181 + s236 :|: s236 >= 0, s236 <= 0, s180 >= 0, s180 <= z1 + 1, s181 >= 0, s181 <= 1, s31 >= 0, s31 <= 0 + 0, s32 >= 0, s32 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 20 + 4*z0 + 124*z2 + 4*z2^2 }-> 1 + s34 + s183 + s237 :|: s237 >= 0, s237 <= 0, s182 >= 0, s182 <= z2 + 1, s183 >= 0, s183 <= 1, s33 >= 0, s33 <= 0 + 0, s34 >= 0, s34 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 20 + 4*z0 + 124*z2 + 4*z2^2 }-> 1 + s36 + s7 + s238 :|: s238 >= 0, s238 <= 0, s35 >= 0, s35 <= 0 + 0, s36 >= 0, s36 <= 1, s7 >= 0, s7 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 20 + 4*s52 + 4*z0 + 124*z1 + 4*z1^2 }-> 1 + s51 + s54 + s207 :|: s207 >= 0, s207 <= 0, s48 >= 0, s48 <= z1 + 1, s49 >= 0, s49 <= z2 + 1, s50 >= 0, s50 <= s48 + s49, s51 >= 0, s51 <= 1, s52 >= 0, s52 <= z1 + 1, s53 >= 0, s53 <= z2 + 1, s54 >= 0, s54 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 20 + 4*s59 + 4*z0 + 124*z1 + 4*z1^2 }-> 1 + s58 + s60 + s208 :|: s208 >= 0, s208 <= 0, s55 >= 0, s55 <= z1 + 1, s56 >= 0, s56 <= z2 + 1, s57 >= 0, s57 <= s55 + s56, s58 >= 0, s58 <= 1, s59 >= 0, s59 <= z1 + 1, s60 >= 0, s60 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 20 + 4*z0 + 124*z1 + 4*z1^2 }-> 1 + s64 + s66 + s209 :|: s209 >= 0, s209 <= 0, s61 >= 0, s61 <= z1 + 1, s62 >= 0, s62 <= z2 + 1, s63 >= 0, s63 <= s61 + s62, s64 >= 0, s64 <= 1, s65 >= 0, s65 <= z2 + 1, s66 >= 0, s66 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 20 + 4*z0 + 124*z1 + 4*z1^2 }-> 1 + s70 + s'' + s210 :|: s210 >= 0, s210 <= 0, s67 >= 0, s67 <= z1 + 1, s68 >= 0, s68 <= z2 + 1, s69 >= 0, s69 <= s67 + s68, s70 >= 0, s70 <= 1, s'' >= 0, s'' <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 20 + 4*s74 + 4*z0 + 124*z1 + 4*z1^2 }-> 1 + s73 + s76 + s211 :|: s211 >= 0, s211 <= 0, s71 >= 0, s71 <= z1 + 1, s72 >= 0, s72 <= s71 + 0, s73 >= 0, s73 <= 1, s74 >= 0, s74 <= z1 + 1, s75 >= 0, s75 <= z2 + 1, s76 >= 0, s76 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 20 + 4*s80 + 4*z0 + 124*z1 + 4*z1^2 }-> 1 + s79 + s81 + s212 :|: s212 >= 0, s212 <= 0, s77 >= 0, s77 <= z1 + 1, s78 >= 0, s78 <= s77 + 0, s79 >= 0, s79 <= 1, s80 >= 0, s80 <= z1 + 1, s81 >= 0, s81 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 20 + 4*z0 + 124*z1 + 4*z1^2 }-> 1 + s84 + s86 + s213 :|: s213 >= 0, s213 <= 0, s82 >= 0, s82 <= z1 + 1, s83 >= 0, s83 <= s82 + 0, s84 >= 0, s84 <= 1, s85 >= 0, s85 <= z2 + 1, s86 >= 0, s86 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 20 + 4*z0 + 124*z1 + 4*z1^2 }-> 1 + s89 + s1 + s214 :|: s214 >= 0, s214 <= 0, s87 >= 0, s87 <= z1 + 1, s88 >= 0, s88 <= s87 + 0, s89 >= 0, s89 <= 1, s1 >= 0, s1 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 20 + 4*s93 + 4*z0 + 124*z1 + 4*z1^2 }-> 1 + s92 + s95 + s215 :|: s215 >= 0, s215 <= 0, s90 >= 0, s90 <= z2 + 1, s91 >= 0, s91 <= 0 + s90, s92 >= 0, s92 <= 1, s93 >= 0, s93 <= z1 + 1, s94 >= 0, s94 <= z2 + 1, s95 >= 0, s95 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 20 + 4*s99 + 4*z0 + 124*z1 + 4*z1^2 }-> 1 + s98 + s100 + s216 :|: s216 >= 0, s216 <= 0, s96 >= 0, s96 <= z2 + 1, s97 >= 0, s97 <= 0 + s96, s98 >= 0, s98 <= 1, s99 >= 0, s99 <= z1 + 1, s100 >= 0, s100 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTENSORT(z) -{ 0 }-> 0 :|: z >= 0
   FLATTENSORT(z) -{ 0 }-> 1 + INSERTIONSORT(s184) :|: s184 >= 0, s184 <= z + 1, z >= 0
   FLATTENSORT(z) -{ 0 }-> 1 + INSERTIONSORT(0) :|: z >= 0
   INSERT(z, z') -{ 8 + 4*z' }-> 1 + s200 :|: s200 >= 0, s200 <= 0, z' >= 0, z >= 0
   INSERT#1(z, z') -{ 11 + 4*z1 }-> 1 + s201 + s46 :|: s201 >= 0, s201 <= 2, s46 >= 0, s46 <= z0 + z' + 1, z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z' >= 0
   INSERT#1(z, z') -{ 11 + 4*z1 }-> 1 + s205 + s47 :|: s205 >= 0, s205 <= 2, s47 >= 0, s47 <= z0 + z' + 1, s10 >= 0, s10 <= 3, s11 >= 0, s11 <= 2, z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z' >= 0
   INSERT#2(z, z', z'', z3) -{ 9 + 4*z3 }-> 1 + s202 :|: s202 >= 0, s202 <= 1, z = 2, z'' >= 0, z' >= 0, z3 >= 0
   INSERTIONSORT(z) -{ 1 }-> 1 + INSERTIONSORT#1(z) :|: z >= 0
   INSERTIONSORT#1(z) -{ 9 + 4*s196 }-> 1 + s203 + INSERTIONSORT(z1) :|: s203 >= 0, s203 <= 1, s196 >= 0, s196 <= z1, z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   INSERTIONSORT#1(z) -{ 9 }-> 1 + s204 + INSERTIONSORT(z1) :|: s204 >= 0, s204 <= 1, z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   append(z, z') -{ 0 }-> s37 :|: s37 >= 0, s37 <= z + z', z' >= 0, z >= 0
   append(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   append#1(z, z') -{ 0 }-> z' :|: z' >= 0, z = 0
   append#1(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   append#1(z, z') -{ 0 }-> 1 + z0 + s40 :|: s40 >= 0, s40 <= z1 + z', z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z' >= 0
   flatten(z) -{ 0 }-> s185 :|: s185 >= 0, s185 <= z + 1, z >= 0
   flatten(z) -{ 0 }-> 0 :|: z >= 0
   flatten#1(z) -{ 0 }-> s189 :|: s186 >= 0, s186 <= z1 + 1, s187 >= 0, s187 <= z2 + 1, s188 >= 0, s188 <= s186 + s187, s189 >= 0, s189 <= z0 + s188, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   flatten#1(z) -{ 0 }-> s192 :|: s190 >= 0, s190 <= z1 + 1, s191 >= 0, s191 <= s190 + 0, s192 >= 0, s192 <= z0 + s191, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   flatten#1(z) -{ 0 }-> s195 :|: s193 >= 0, s193 <= z2 + 1, s194 >= 0, s194 <= 0 + s193, s195 >= 0, s195 <= z0 + s194, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   flatten#1(z) -{ 0 }-> s39 :|: s38 >= 0, s38 <= 0 + 0, s39 >= 0, s39 <= z0 + s38, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   flatten#1(z) -{ 0 }-> 0 :|: z = 0
   flatten#1(z) -{ 0 }-> 0 :|: z >= 0
   insert(z, z') -{ 0 }-> s42 :|: s42 >= 0, s42 <= z' + z + 1, z' >= 0, z >= 0
   insert(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   insert#1(z, z') -{ 0 }-> s43 :|: s43 >= 0, s43 <= z' + z0 + z1 + 2, z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z' >= 0
   insert#1(z, z') -{ 0 }-> s45 :|: s45 >= 0, s45 <= z' + z0 + z1 + 2, s16 >= 0, s16 <= 3, s17 >= 0, s17 <= 2, z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z' >= 0
   insert#1(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   insert#1(z, z') -{ 0 }-> 1 + z' + 0 :|: z' >= 0, z = 0
   insert#2(z, z', z'', z3) -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0, z3 >= 0
   insert#2(z, z', z'', z3) -{ 0 }-> 1 + z' + (1 + z'' + z3) :|: z'' >= 0, z = 1, z' >= 0, z3 >= 0
   insert#2(z, z', z'', z3) -{ 0 }-> 1 + z'' + s44 :|: s44 >= 0, s44 <= z' + z3 + 1, z = 2, z'' >= 0, z' >= 0, z3 >= 0
   insertionsort(z) -{ 0 }-> s197 :|: s197 >= 0, s197 <= z, z >= 0
   insertionsort(z) -{ 0 }-> 0 :|: z >= 0
   insertionsort#1(z) -{ 0 }-> s199 :|: s198 >= 0, s198 <= z1, s199 >= 0, s199 <= z0 + s198 + 1, z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   insertionsort#1(z) -{ 0 }-> s41 :|: s41 >= 0, s41 <= z0 + 0 + 1, z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   insertionsort#1(z) -{ 0 }-> 0 :|: z = 0
   insertionsort#1(z) -{ 0 }-> 0 :|: z >= 0

Function symbols to be analyzed: {INSERTIONSORT,INSERTIONSORT#1}, {FLATTENSORT}
Previous analysis results are:
  APPEND#1: runtime: O(n^1) [4*z], size: O(1) [0]
  APPEND: runtime: O(n^1) [1 + 4*z], size: O(1) [1]
  #cklt: runtime: O(1) [0], size: O(1) [2]
  #compare: runtime: O(1) [0], size: O(1) [3]
  #COMPARE: runtime: O(1) [0], size: O(n^1) [z + z']
  append#1: runtime: O(1) [0], size: O(n^1) [z + z']
  append: runtime: O(1) [0], size: O(n^1) [z + z']
  #less: runtime: O(1) [0], size: O(1) [2]
  insert#2: runtime: O(1) [0], size: O(n^1) [2 + z' + z'' + z3]
  insert: runtime: O(1) [0], size: O(n^1) [1 + z + z']
  insert#1: runtime: O(1) [0], size: O(n^1) [1 + z + z']
  #LESS: runtime: O(1) [1], size: O(n^1) [1 + z + z']
  flatten#1: runtime: O(1) [0], size: O(n^1) [1 + z]
  insertionsort#1: runtime: O(1) [0], size: O(n^1) [z]
  INSERT#1: runtime: O(n^1) [7 + 4*z], size: O(1) [0]
  INSERT#2: runtime: O(n^1) [9 + 4*z3], size: O(1) [2]
  INSERT: runtime: O(n^1) [8 + 4*z'], size: O(1) [1]
  flatten: runtime: O(1) [0], size: O(n^1) [1 + z]
  FLATTEN: runtime: O(n^2) [17 + 124*z + 4*z^2], size: O(1) [0]
  FLATTEN#1: runtime: O(n^2) [704 + 4160*z + 128*z^2], size: O(1) [3]
  insertionsort: runtime: O(1) [0], size: O(n^1) [z]

----------------------------------------

(121) IntTrsBoundProof (UPPER BOUND(ID))

Computed SIZE bound using CoFloCo for: INSERTIONSORT
after applying outer abstraction to obtain an ITS,
resulting in: O(1) with polynomial bound: 0

Computed SIZE bound using CoFloCo for: INSERTIONSORT#1
after applying outer abstraction to obtain an ITS,
resulting in: O(1) with polynomial bound: 2

----------------------------------------

(122)
Obligation:
Complexity RNTS consisting of the following rules:

   #COMPARE(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   #COMPARE(z, z') -{ 0 }-> 1 + s19 :|: s19 >= 0, s19 <= z' - 1 + (z - 1), z' - 1 >= 0, z - 1 >= 0
   #COMPARE(z, z') -{ 0 }-> 1 + s20 :|: s20 >= 0, s20 <= z - 1 + (z' - 1), z' - 1 >= 0, z - 1 >= 0
   #LESS(z, z') -{ 1 }-> 1 + s18 :|: s18 >= 0, s18 <= z + z', z' >= 0, z >= 0
   #cklt(z) -{ 0 }-> 2 :|: z = 3
   #cklt(z) -{ 0 }-> 1 :|: z = 1
   #cklt(z) -{ 0 }-> 1 :|: z = 2
   #cklt(z) -{ 0 }-> 0 :|: z >= 0
   #compare(z, z') -{ 0 }-> s8 :|: s8 >= 0, s8 <= 3, z' - 1 >= 0, z - 1 >= 0
   #compare(z, z') -{ 0 }-> s9 :|: s9 >= 0, s9 <= 3, z' - 1 >= 0, z - 1 >= 0
   #compare(z, z') -{ 0 }-> 3 :|: z' - 1 >= 0, z = 0
   #compare(z, z') -{ 0 }-> 3 :|: z - 1 >= 0, z' = 0
   #compare(z, z') -{ 0 }-> 3 :|: z' - 1 >= 0, z - 1 >= 0
   #compare(z, z') -{ 0 }-> 2 :|: z' - 1 >= 0, z = 0
   #compare(z, z') -{ 0 }-> 2 :|: z - 1 >= 0, z' = 0
   #compare(z, z') -{ 0 }-> 2 :|: z' - 1 >= 0, z - 1 >= 0
   #compare(z, z') -{ 0 }-> 1 :|: z = 0, z' = 0
   #compare(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   #less(z, z') -{ 0 }-> s13 :|: s12 >= 0, s12 <= 3, s13 >= 0, s13 <= 2, z' - 1 >= 0, z - 1 >= 0
   #less(z, z') -{ 0 }-> s15 :|: s14 >= 0, s14 <= 3, s15 >= 0, s15 <= 2, z - 1 >= 0, z' - 1 >= 0
   #less(z, z') -{ 0 }-> 2 :|: z' - 1 >= 0, z = 0, 3 = 3
   #less(z, z') -{ 0 }-> 2 :|: z - 1 >= 0, z' = 0, 3 = 3
   #less(z, z') -{ 0 }-> 2 :|: z - 1 >= 0, z' - 1 >= 0, 3 = 3
   #less(z, z') -{ 0 }-> 1 :|: z = 0, z' = 0, 1 = 1
   #less(z, z') -{ 0 }-> 1 :|: z' - 1 >= 0, z = 0, 2 = 2
   #less(z, z') -{ 0 }-> 1 :|: z - 1 >= 0, z' = 0, 2 = 2
   #less(z, z') -{ 0 }-> 1 :|: z' - 1 >= 0, z - 1 >= 0, 2 = 2
   #less(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   #less(z, z') -{ 0 }-> 0 :|: z = 0, z' = 0, v0 >= 0, 1 = v0
   #less(z, z') -{ 0 }-> 0 :|: z' - 1 >= 0, z = 0, v0 >= 0, 2 = v0
   #less(z, z') -{ 0 }-> 0 :|: z' - 1 >= 0, z = 0, v0 >= 0, 3 = v0
   #less(z, z') -{ 0 }-> 0 :|: z - 1 >= 0, z' = 0, v0 >= 0, 3 = v0
   #less(z, z') -{ 0 }-> 0 :|: z - 1 >= 0, z' - 1 >= 0, v0 >= 0, 3 = v0
   #less(z, z') -{ 0 }-> 0 :|: z - 1 >= 0, z' = 0, v0 >= 0, 2 = v0
   #less(z, z') -{ 0 }-> 0 :|: z' - 1 >= 0, z - 1 >= 0, v0 >= 0, 2 = v0
   #less(z, z') -{ 0 }-> 0 :|: z' >= 0, z >= 0, v0 >= 0, 0 = v0
   APPEND(z, z') -{ 1 + 4*z }-> 1 + s :|: s >= 0, s <= 0, z' >= 0, z >= 0
   APPEND#1(z, z') -{ 2 + 4*z1 }-> 1 + s' :|: s' >= 0, s' <= 1, z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z' >= 0
   FLATTEN(z) -{ 705 + 4160*z + 128*z^2 }-> 1 + s206 :|: s206 >= 0, s206 <= 3, z >= 0
   FLATTEN#1(z) -{ 20 + 4*z0 + 124*z1 + 4*z1^2 }-> 1 + s103 + s105 + s217 :|: s217 >= 0, s217 <= 0, s101 >= 0, s101 <= z2 + 1, s102 >= 0, s102 <= 0 + s101, s103 >= 0, s103 <= 1, s104 >= 0, s104 <= z2 + 1, s105 >= 0, s105 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 20 + 4*z0 + 124*z1 + 4*z1^2 }-> 1 + s108 + s2 + s218 :|: s218 >= 0, s218 <= 0, s106 >= 0, s106 <= z2 + 1, s107 >= 0, s107 <= 0 + s106, s108 >= 0, s108 <= 1, s2 >= 0, s2 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 20 + 4*s120 + 4*z0 + 124*z2 + 4*z2^2 }-> 1 + s119 + s122 + s223 :|: s223 >= 0, s223 <= 0, s116 >= 0, s116 <= z1 + 1, s117 >= 0, s117 <= z2 + 1, s118 >= 0, s118 <= s116 + s117, s119 >= 0, s119 <= 1, s120 >= 0, s120 <= z1 + 1, s121 >= 0, s121 <= z2 + 1, s122 >= 0, s122 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 20 + 4*s127 + 4*z0 + 124*z2 + 4*z2^2 }-> 1 + s126 + s128 + s224 :|: s224 >= 0, s224 <= 0, s123 >= 0, s123 <= z1 + 1, s124 >= 0, s124 <= z2 + 1, s125 >= 0, s125 <= s123 + s124, s126 >= 0, s126 <= 1, s127 >= 0, s127 <= z1 + 1, s128 >= 0, s128 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 20 + 4*z0 + 124*z2 + 4*z2^2 }-> 1 + s132 + s134 + s225 :|: s225 >= 0, s225 <= 0, s129 >= 0, s129 <= z1 + 1, s130 >= 0, s130 <= z2 + 1, s131 >= 0, s131 <= s129 + s130, s132 >= 0, s132 <= 1, s133 >= 0, s133 <= z2 + 1, s134 >= 0, s134 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 20 + 4*z0 + 124*z2 + 4*z2^2 }-> 1 + s138 + s4 + s226 :|: s226 >= 0, s226 <= 0, s135 >= 0, s135 <= z1 + 1, s136 >= 0, s136 <= z2 + 1, s137 >= 0, s137 <= s135 + s136, s138 >= 0, s138 <= 1, s4 >= 0, s4 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 20 + 4*s142 + 4*z0 + 124*z2 + 4*z2^2 }-> 1 + s141 + s144 + s227 :|: s227 >= 0, s227 <= 0, s139 >= 0, s139 <= z1 + 1, s140 >= 0, s140 <= s139 + 0, s141 >= 0, s141 <= 1, s142 >= 0, s142 <= z1 + 1, s143 >= 0, s143 <= z2 + 1, s144 >= 0, s144 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 20 + 4*s148 + 4*z0 + 124*z2 + 4*z2^2 }-> 1 + s147 + s149 + s228 :|: s228 >= 0, s228 <= 0, s145 >= 0, s145 <= z1 + 1, s146 >= 0, s146 <= s145 + 0, s147 >= 0, s147 <= 1, s148 >= 0, s148 <= z1 + 1, s149 >= 0, s149 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 20 + 4*z0 + 124*z2 + 4*z2^2 }-> 1 + s152 + s154 + s229 :|: s229 >= 0, s229 <= 0, s150 >= 0, s150 <= z1 + 1, s151 >= 0, s151 <= s150 + 0, s152 >= 0, s152 <= 1, s153 >= 0, s153 <= z2 + 1, s154 >= 0, s154 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 20 + 4*z0 + 124*z2 + 4*z2^2 }-> 1 + s157 + s5 + s230 :|: s230 >= 0, s230 <= 0, s155 >= 0, s155 <= z1 + 1, s156 >= 0, s156 <= s155 + 0, s157 >= 0, s157 <= 1, s5 >= 0, s5 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 20 + 4*s161 + 4*z0 + 124*z2 + 4*z2^2 }-> 1 + s160 + s163 + s231 :|: s231 >= 0, s231 <= 0, s158 >= 0, s158 <= z2 + 1, s159 >= 0, s159 <= 0 + s158, s160 >= 0, s160 <= 1, s161 >= 0, s161 <= z1 + 1, s162 >= 0, s162 <= z2 + 1, s163 >= 0, s163 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 20 + 4*s167 + 4*z0 + 124*z2 + 4*z2^2 }-> 1 + s166 + s168 + s232 :|: s232 >= 0, s232 <= 0, s164 >= 0, s164 <= z2 + 1, s165 >= 0, s165 <= 0 + s164, s166 >= 0, s166 <= 1, s167 >= 0, s167 <= z1 + 1, s168 >= 0, s168 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 20 + 4*z0 + 124*z2 + 4*z2^2 }-> 1 + s171 + s173 + s233 :|: s233 >= 0, s233 <= 0, s169 >= 0, s169 <= z2 + 1, s170 >= 0, s170 <= 0 + s169, s171 >= 0, s171 <= 1, s172 >= 0, s172 <= z2 + 1, s173 >= 0, s173 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 20 + 4*z0 + 124*z2 + 4*z2^2 }-> 1 + s176 + s6 + s234 :|: s234 >= 0, s234 <= 0, s174 >= 0, s174 <= z2 + 1, s175 >= 0, s175 <= 0 + s174, s176 >= 0, s176 <= 1, s6 >= 0, s6 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 20 + 4*s109 + 4*z0 + 124*z1 + 4*z1^2 }-> 1 + s22 + s111 + s219 :|: s219 >= 0, s219 <= 0, s109 >= 0, s109 <= z1 + 1, s110 >= 0, s110 <= z2 + 1, s111 >= 0, s111 <= 1, s21 >= 0, s21 <= 0 + 0, s22 >= 0, s22 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 20 + 4*s112 + 4*z0 + 124*z1 + 4*z1^2 }-> 1 + s24 + s113 + s220 :|: s220 >= 0, s220 <= 0, s112 >= 0, s112 <= z1 + 1, s113 >= 0, s113 <= 1, s23 >= 0, s23 <= 0 + 0, s24 >= 0, s24 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 20 + 4*z0 + 124*z1 + 4*z1^2 }-> 1 + s26 + s115 + s221 :|: s221 >= 0, s221 <= 0, s114 >= 0, s114 <= z2 + 1, s115 >= 0, s115 <= 1, s25 >= 0, s25 <= 0 + 0, s26 >= 0, s26 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 20 + 4*z0 + 124*z1 + 4*z1^2 }-> 1 + s28 + s3 + s222 :|: s222 >= 0, s222 <= 0, s27 >= 0, s27 <= 0 + 0, s28 >= 0, s28 <= 1, s3 >= 0, s3 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 20 + 4*s177 + 4*z0 + 124*z2 + 4*z2^2 }-> 1 + s30 + s179 + s235 :|: s235 >= 0, s235 <= 0, s177 >= 0, s177 <= z1 + 1, s178 >= 0, s178 <= z2 + 1, s179 >= 0, s179 <= 1, s29 >= 0, s29 <= 0 + 0, s30 >= 0, s30 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 20 + 4*s180 + 4*z0 + 124*z2 + 4*z2^2 }-> 1 + s32 + s181 + s236 :|: s236 >= 0, s236 <= 0, s180 >= 0, s180 <= z1 + 1, s181 >= 0, s181 <= 1, s31 >= 0, s31 <= 0 + 0, s32 >= 0, s32 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 20 + 4*z0 + 124*z2 + 4*z2^2 }-> 1 + s34 + s183 + s237 :|: s237 >= 0, s237 <= 0, s182 >= 0, s182 <= z2 + 1, s183 >= 0, s183 <= 1, s33 >= 0, s33 <= 0 + 0, s34 >= 0, s34 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 20 + 4*z0 + 124*z2 + 4*z2^2 }-> 1 + s36 + s7 + s238 :|: s238 >= 0, s238 <= 0, s35 >= 0, s35 <= 0 + 0, s36 >= 0, s36 <= 1, s7 >= 0, s7 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 20 + 4*s52 + 4*z0 + 124*z1 + 4*z1^2 }-> 1 + s51 + s54 + s207 :|: s207 >= 0, s207 <= 0, s48 >= 0, s48 <= z1 + 1, s49 >= 0, s49 <= z2 + 1, s50 >= 0, s50 <= s48 + s49, s51 >= 0, s51 <= 1, s52 >= 0, s52 <= z1 + 1, s53 >= 0, s53 <= z2 + 1, s54 >= 0, s54 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 20 + 4*s59 + 4*z0 + 124*z1 + 4*z1^2 }-> 1 + s58 + s60 + s208 :|: s208 >= 0, s208 <= 0, s55 >= 0, s55 <= z1 + 1, s56 >= 0, s56 <= z2 + 1, s57 >= 0, s57 <= s55 + s56, s58 >= 0, s58 <= 1, s59 >= 0, s59 <= z1 + 1, s60 >= 0, s60 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 20 + 4*z0 + 124*z1 + 4*z1^2 }-> 1 + s64 + s66 + s209 :|: s209 >= 0, s209 <= 0, s61 >= 0, s61 <= z1 + 1, s62 >= 0, s62 <= z2 + 1, s63 >= 0, s63 <= s61 + s62, s64 >= 0, s64 <= 1, s65 >= 0, s65 <= z2 + 1, s66 >= 0, s66 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 20 + 4*z0 + 124*z1 + 4*z1^2 }-> 1 + s70 + s'' + s210 :|: s210 >= 0, s210 <= 0, s67 >= 0, s67 <= z1 + 1, s68 >= 0, s68 <= z2 + 1, s69 >= 0, s69 <= s67 + s68, s70 >= 0, s70 <= 1, s'' >= 0, s'' <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 20 + 4*s74 + 4*z0 + 124*z1 + 4*z1^2 }-> 1 + s73 + s76 + s211 :|: s211 >= 0, s211 <= 0, s71 >= 0, s71 <= z1 + 1, s72 >= 0, s72 <= s71 + 0, s73 >= 0, s73 <= 1, s74 >= 0, s74 <= z1 + 1, s75 >= 0, s75 <= z2 + 1, s76 >= 0, s76 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 20 + 4*s80 + 4*z0 + 124*z1 + 4*z1^2 }-> 1 + s79 + s81 + s212 :|: s212 >= 0, s212 <= 0, s77 >= 0, s77 <= z1 + 1, s78 >= 0, s78 <= s77 + 0, s79 >= 0, s79 <= 1, s80 >= 0, s80 <= z1 + 1, s81 >= 0, s81 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 20 + 4*z0 + 124*z1 + 4*z1^2 }-> 1 + s84 + s86 + s213 :|: s213 >= 0, s213 <= 0, s82 >= 0, s82 <= z1 + 1, s83 >= 0, s83 <= s82 + 0, s84 >= 0, s84 <= 1, s85 >= 0, s85 <= z2 + 1, s86 >= 0, s86 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 20 + 4*z0 + 124*z1 + 4*z1^2 }-> 1 + s89 + s1 + s214 :|: s214 >= 0, s214 <= 0, s87 >= 0, s87 <= z1 + 1, s88 >= 0, s88 <= s87 + 0, s89 >= 0, s89 <= 1, s1 >= 0, s1 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 20 + 4*s93 + 4*z0 + 124*z1 + 4*z1^2 }-> 1 + s92 + s95 + s215 :|: s215 >= 0, s215 <= 0, s90 >= 0, s90 <= z2 + 1, s91 >= 0, s91 <= 0 + s90, s92 >= 0, s92 <= 1, s93 >= 0, s93 <= z1 + 1, s94 >= 0, s94 <= z2 + 1, s95 >= 0, s95 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 20 + 4*s99 + 4*z0 + 124*z1 + 4*z1^2 }-> 1 + s98 + s100 + s216 :|: s216 >= 0, s216 <= 0, s96 >= 0, s96 <= z2 + 1, s97 >= 0, s97 <= 0 + s96, s98 >= 0, s98 <= 1, s99 >= 0, s99 <= z1 + 1, s100 >= 0, s100 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTENSORT(z) -{ 0 }-> 0 :|: z >= 0
   FLATTENSORT(z) -{ 0 }-> 1 + INSERTIONSORT(s184) :|: s184 >= 0, s184 <= z + 1, z >= 0
   FLATTENSORT(z) -{ 0 }-> 1 + INSERTIONSORT(0) :|: z >= 0
   INSERT(z, z') -{ 8 + 4*z' }-> 1 + s200 :|: s200 >= 0, s200 <= 0, z' >= 0, z >= 0
   INSERT#1(z, z') -{ 11 + 4*z1 }-> 1 + s201 + s46 :|: s201 >= 0, s201 <= 2, s46 >= 0, s46 <= z0 + z' + 1, z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z' >= 0
   INSERT#1(z, z') -{ 11 + 4*z1 }-> 1 + s205 + s47 :|: s205 >= 0, s205 <= 2, s47 >= 0, s47 <= z0 + z' + 1, s10 >= 0, s10 <= 3, s11 >= 0, s11 <= 2, z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z' >= 0
   INSERT#2(z, z', z'', z3) -{ 9 + 4*z3 }-> 1 + s202 :|: s202 >= 0, s202 <= 1, z = 2, z'' >= 0, z' >= 0, z3 >= 0
   INSERTIONSORT(z) -{ 1 }-> 1 + INSERTIONSORT#1(z) :|: z >= 0
   INSERTIONSORT#1(z) -{ 9 + 4*s196 }-> 1 + s203 + INSERTIONSORT(z1) :|: s203 >= 0, s203 <= 1, s196 >= 0, s196 <= z1, z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   INSERTIONSORT#1(z) -{ 9 }-> 1 + s204 + INSERTIONSORT(z1) :|: s204 >= 0, s204 <= 1, z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   append(z, z') -{ 0 }-> s37 :|: s37 >= 0, s37 <= z + z', z' >= 0, z >= 0
   append(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   append#1(z, z') -{ 0 }-> z' :|: z' >= 0, z = 0
   append#1(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   append#1(z, z') -{ 0 }-> 1 + z0 + s40 :|: s40 >= 0, s40 <= z1 + z', z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z' >= 0
   flatten(z) -{ 0 }-> s185 :|: s185 >= 0, s185 <= z + 1, z >= 0
   flatten(z) -{ 0 }-> 0 :|: z >= 0
   flatten#1(z) -{ 0 }-> s189 :|: s186 >= 0, s186 <= z1 + 1, s187 >= 0, s187 <= z2 + 1, s188 >= 0, s188 <= s186 + s187, s189 >= 0, s189 <= z0 + s188, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   flatten#1(z) -{ 0 }-> s192 :|: s190 >= 0, s190 <= z1 + 1, s191 >= 0, s191 <= s190 + 0, s192 >= 0, s192 <= z0 + s191, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   flatten#1(z) -{ 0 }-> s195 :|: s193 >= 0, s193 <= z2 + 1, s194 >= 0, s194 <= 0 + s193, s195 >= 0, s195 <= z0 + s194, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   flatten#1(z) -{ 0 }-> s39 :|: s38 >= 0, s38 <= 0 + 0, s39 >= 0, s39 <= z0 + s38, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   flatten#1(z) -{ 0 }-> 0 :|: z = 0
   flatten#1(z) -{ 0 }-> 0 :|: z >= 0
   insert(z, z') -{ 0 }-> s42 :|: s42 >= 0, s42 <= z' + z + 1, z' >= 0, z >= 0
   insert(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   insert#1(z, z') -{ 0 }-> s43 :|: s43 >= 0, s43 <= z' + z0 + z1 + 2, z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z' >= 0
   insert#1(z, z') -{ 0 }-> s45 :|: s45 >= 0, s45 <= z' + z0 + z1 + 2, s16 >= 0, s16 <= 3, s17 >= 0, s17 <= 2, z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z' >= 0
   insert#1(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   insert#1(z, z') -{ 0 }-> 1 + z' + 0 :|: z' >= 0, z = 0
   insert#2(z, z', z'', z3) -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0, z3 >= 0
   insert#2(z, z', z'', z3) -{ 0 }-> 1 + z' + (1 + z'' + z3) :|: z'' >= 0, z = 1, z' >= 0, z3 >= 0
   insert#2(z, z', z'', z3) -{ 0 }-> 1 + z'' + s44 :|: s44 >= 0, s44 <= z' + z3 + 1, z = 2, z'' >= 0, z' >= 0, z3 >= 0
   insertionsort(z) -{ 0 }-> s197 :|: s197 >= 0, s197 <= z, z >= 0
   insertionsort(z) -{ 0 }-> 0 :|: z >= 0
   insertionsort#1(z) -{ 0 }-> s199 :|: s198 >= 0, s198 <= z1, s199 >= 0, s199 <= z0 + s198 + 1, z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   insertionsort#1(z) -{ 0 }-> s41 :|: s41 >= 0, s41 <= z0 + 0 + 1, z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   insertionsort#1(z) -{ 0 }-> 0 :|: z = 0
   insertionsort#1(z) -{ 0 }-> 0 :|: z >= 0

Function symbols to be analyzed: {INSERTIONSORT,INSERTIONSORT#1}, {FLATTENSORT}
Previous analysis results are:
  APPEND#1: runtime: O(n^1) [4*z], size: O(1) [0]
  APPEND: runtime: O(n^1) [1 + 4*z], size: O(1) [1]
  #cklt: runtime: O(1) [0], size: O(1) [2]
  #compare: runtime: O(1) [0], size: O(1) [3]
  #COMPARE: runtime: O(1) [0], size: O(n^1) [z + z']
  append#1: runtime: O(1) [0], size: O(n^1) [z + z']
  append: runtime: O(1) [0], size: O(n^1) [z + z']
  #less: runtime: O(1) [0], size: O(1) [2]
  insert#2: runtime: O(1) [0], size: O(n^1) [2 + z' + z'' + z3]
  insert: runtime: O(1) [0], size: O(n^1) [1 + z + z']
  insert#1: runtime: O(1) [0], size: O(n^1) [1 + z + z']
  #LESS: runtime: O(1) [1], size: O(n^1) [1 + z + z']
  flatten#1: runtime: O(1) [0], size: O(n^1) [1 + z]
  insertionsort#1: runtime: O(1) [0], size: O(n^1) [z]
  INSERT#1: runtime: O(n^1) [7 + 4*z], size: O(1) [0]
  INSERT#2: runtime: O(n^1) [9 + 4*z3], size: O(1) [2]
  INSERT: runtime: O(n^1) [8 + 4*z'], size: O(1) [1]
  flatten: runtime: O(1) [0], size: O(n^1) [1 + z]
  FLATTEN: runtime: O(n^2) [17 + 124*z + 4*z^2], size: O(1) [0]
  FLATTEN#1: runtime: O(n^2) [704 + 4160*z + 128*z^2], size: O(1) [3]
  insertionsort: runtime: O(1) [0], size: O(n^1) [z]
  INSERTIONSORT: runtime: ?, size: O(1) [0]
  INSERTIONSORT#1: runtime: ?, size: O(1) [2]

----------------------------------------

(123) IntTrsBoundProof (UPPER BOUND(ID))

Computed RUNTIME bound using CoFloCo for: INSERTIONSORT
after applying outer abstraction to obtain an ITS,
resulting in: O(n^2) with polynomial bound: 1 + 10*z + 4*z^2

Computed RUNTIME bound using KoAT for: INSERTIONSORT#1
after applying outer abstraction to obtain an ITS,
resulting in: O(n^2) with polynomial bound: 20 + 24*z + 8*z^2

----------------------------------------

(124)
Obligation:
Complexity RNTS consisting of the following rules:

   #COMPARE(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   #COMPARE(z, z') -{ 0 }-> 1 + s19 :|: s19 >= 0, s19 <= z' - 1 + (z - 1), z' - 1 >= 0, z - 1 >= 0
   #COMPARE(z, z') -{ 0 }-> 1 + s20 :|: s20 >= 0, s20 <= z - 1 + (z' - 1), z' - 1 >= 0, z - 1 >= 0
   #LESS(z, z') -{ 1 }-> 1 + s18 :|: s18 >= 0, s18 <= z + z', z' >= 0, z >= 0
   #cklt(z) -{ 0 }-> 2 :|: z = 3
   #cklt(z) -{ 0 }-> 1 :|: z = 1
   #cklt(z) -{ 0 }-> 1 :|: z = 2
   #cklt(z) -{ 0 }-> 0 :|: z >= 0
   #compare(z, z') -{ 0 }-> s8 :|: s8 >= 0, s8 <= 3, z' - 1 >= 0, z - 1 >= 0
   #compare(z, z') -{ 0 }-> s9 :|: s9 >= 0, s9 <= 3, z' - 1 >= 0, z - 1 >= 0
   #compare(z, z') -{ 0 }-> 3 :|: z' - 1 >= 0, z = 0
   #compare(z, z') -{ 0 }-> 3 :|: z - 1 >= 0, z' = 0
   #compare(z, z') -{ 0 }-> 3 :|: z' - 1 >= 0, z - 1 >= 0
   #compare(z, z') -{ 0 }-> 2 :|: z' - 1 >= 0, z = 0
   #compare(z, z') -{ 0 }-> 2 :|: z - 1 >= 0, z' = 0
   #compare(z, z') -{ 0 }-> 2 :|: z' - 1 >= 0, z - 1 >= 0
   #compare(z, z') -{ 0 }-> 1 :|: z = 0, z' = 0
   #compare(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   #less(z, z') -{ 0 }-> s13 :|: s12 >= 0, s12 <= 3, s13 >= 0, s13 <= 2, z' - 1 >= 0, z - 1 >= 0
   #less(z, z') -{ 0 }-> s15 :|: s14 >= 0, s14 <= 3, s15 >= 0, s15 <= 2, z - 1 >= 0, z' - 1 >= 0
   #less(z, z') -{ 0 }-> 2 :|: z' - 1 >= 0, z = 0, 3 = 3
   #less(z, z') -{ 0 }-> 2 :|: z - 1 >= 0, z' = 0, 3 = 3
   #less(z, z') -{ 0 }-> 2 :|: z - 1 >= 0, z' - 1 >= 0, 3 = 3
   #less(z, z') -{ 0 }-> 1 :|: z = 0, z' = 0, 1 = 1
   #less(z, z') -{ 0 }-> 1 :|: z' - 1 >= 0, z = 0, 2 = 2
   #less(z, z') -{ 0 }-> 1 :|: z - 1 >= 0, z' = 0, 2 = 2
   #less(z, z') -{ 0 }-> 1 :|: z' - 1 >= 0, z - 1 >= 0, 2 = 2
   #less(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   #less(z, z') -{ 0 }-> 0 :|: z = 0, z' = 0, v0 >= 0, 1 = v0
   #less(z, z') -{ 0 }-> 0 :|: z' - 1 >= 0, z = 0, v0 >= 0, 2 = v0
   #less(z, z') -{ 0 }-> 0 :|: z' - 1 >= 0, z = 0, v0 >= 0, 3 = v0
   #less(z, z') -{ 0 }-> 0 :|: z - 1 >= 0, z' = 0, v0 >= 0, 3 = v0
   #less(z, z') -{ 0 }-> 0 :|: z - 1 >= 0, z' - 1 >= 0, v0 >= 0, 3 = v0
   #less(z, z') -{ 0 }-> 0 :|: z - 1 >= 0, z' = 0, v0 >= 0, 2 = v0
   #less(z, z') -{ 0 }-> 0 :|: z' - 1 >= 0, z - 1 >= 0, v0 >= 0, 2 = v0
   #less(z, z') -{ 0 }-> 0 :|: z' >= 0, z >= 0, v0 >= 0, 0 = v0
   APPEND(z, z') -{ 1 + 4*z }-> 1 + s :|: s >= 0, s <= 0, z' >= 0, z >= 0
   APPEND#1(z, z') -{ 2 + 4*z1 }-> 1 + s' :|: s' >= 0, s' <= 1, z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z' >= 0
   FLATTEN(z) -{ 705 + 4160*z + 128*z^2 }-> 1 + s206 :|: s206 >= 0, s206 <= 3, z >= 0
   FLATTEN#1(z) -{ 20 + 4*z0 + 124*z1 + 4*z1^2 }-> 1 + s103 + s105 + s217 :|: s217 >= 0, s217 <= 0, s101 >= 0, s101 <= z2 + 1, s102 >= 0, s102 <= 0 + s101, s103 >= 0, s103 <= 1, s104 >= 0, s104 <= z2 + 1, s105 >= 0, s105 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 20 + 4*z0 + 124*z1 + 4*z1^2 }-> 1 + s108 + s2 + s218 :|: s218 >= 0, s218 <= 0, s106 >= 0, s106 <= z2 + 1, s107 >= 0, s107 <= 0 + s106, s108 >= 0, s108 <= 1, s2 >= 0, s2 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 20 + 4*s120 + 4*z0 + 124*z2 + 4*z2^2 }-> 1 + s119 + s122 + s223 :|: s223 >= 0, s223 <= 0, s116 >= 0, s116 <= z1 + 1, s117 >= 0, s117 <= z2 + 1, s118 >= 0, s118 <= s116 + s117, s119 >= 0, s119 <= 1, s120 >= 0, s120 <= z1 + 1, s121 >= 0, s121 <= z2 + 1, s122 >= 0, s122 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 20 + 4*s127 + 4*z0 + 124*z2 + 4*z2^2 }-> 1 + s126 + s128 + s224 :|: s224 >= 0, s224 <= 0, s123 >= 0, s123 <= z1 + 1, s124 >= 0, s124 <= z2 + 1, s125 >= 0, s125 <= s123 + s124, s126 >= 0, s126 <= 1, s127 >= 0, s127 <= z1 + 1, s128 >= 0, s128 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 20 + 4*z0 + 124*z2 + 4*z2^2 }-> 1 + s132 + s134 + s225 :|: s225 >= 0, s225 <= 0, s129 >= 0, s129 <= z1 + 1, s130 >= 0, s130 <= z2 + 1, s131 >= 0, s131 <= s129 + s130, s132 >= 0, s132 <= 1, s133 >= 0, s133 <= z2 + 1, s134 >= 0, s134 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 20 + 4*z0 + 124*z2 + 4*z2^2 }-> 1 + s138 + s4 + s226 :|: s226 >= 0, s226 <= 0, s135 >= 0, s135 <= z1 + 1, s136 >= 0, s136 <= z2 + 1, s137 >= 0, s137 <= s135 + s136, s138 >= 0, s138 <= 1, s4 >= 0, s4 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 20 + 4*s142 + 4*z0 + 124*z2 + 4*z2^2 }-> 1 + s141 + s144 + s227 :|: s227 >= 0, s227 <= 0, s139 >= 0, s139 <= z1 + 1, s140 >= 0, s140 <= s139 + 0, s141 >= 0, s141 <= 1, s142 >= 0, s142 <= z1 + 1, s143 >= 0, s143 <= z2 + 1, s144 >= 0, s144 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 20 + 4*s148 + 4*z0 + 124*z2 + 4*z2^2 }-> 1 + s147 + s149 + s228 :|: s228 >= 0, s228 <= 0, s145 >= 0, s145 <= z1 + 1, s146 >= 0, s146 <= s145 + 0, s147 >= 0, s147 <= 1, s148 >= 0, s148 <= z1 + 1, s149 >= 0, s149 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 20 + 4*z0 + 124*z2 + 4*z2^2 }-> 1 + s152 + s154 + s229 :|: s229 >= 0, s229 <= 0, s150 >= 0, s150 <= z1 + 1, s151 >= 0, s151 <= s150 + 0, s152 >= 0, s152 <= 1, s153 >= 0, s153 <= z2 + 1, s154 >= 0, s154 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 20 + 4*z0 + 124*z2 + 4*z2^2 }-> 1 + s157 + s5 + s230 :|: s230 >= 0, s230 <= 0, s155 >= 0, s155 <= z1 + 1, s156 >= 0, s156 <= s155 + 0, s157 >= 0, s157 <= 1, s5 >= 0, s5 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 20 + 4*s161 + 4*z0 + 124*z2 + 4*z2^2 }-> 1 + s160 + s163 + s231 :|: s231 >= 0, s231 <= 0, s158 >= 0, s158 <= z2 + 1, s159 >= 0, s159 <= 0 + s158, s160 >= 0, s160 <= 1, s161 >= 0, s161 <= z1 + 1, s162 >= 0, s162 <= z2 + 1, s163 >= 0, s163 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 20 + 4*s167 + 4*z0 + 124*z2 + 4*z2^2 }-> 1 + s166 + s168 + s232 :|: s232 >= 0, s232 <= 0, s164 >= 0, s164 <= z2 + 1, s165 >= 0, s165 <= 0 + s164, s166 >= 0, s166 <= 1, s167 >= 0, s167 <= z1 + 1, s168 >= 0, s168 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 20 + 4*z0 + 124*z2 + 4*z2^2 }-> 1 + s171 + s173 + s233 :|: s233 >= 0, s233 <= 0, s169 >= 0, s169 <= z2 + 1, s170 >= 0, s170 <= 0 + s169, s171 >= 0, s171 <= 1, s172 >= 0, s172 <= z2 + 1, s173 >= 0, s173 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 20 + 4*z0 + 124*z2 + 4*z2^2 }-> 1 + s176 + s6 + s234 :|: s234 >= 0, s234 <= 0, s174 >= 0, s174 <= z2 + 1, s175 >= 0, s175 <= 0 + s174, s176 >= 0, s176 <= 1, s6 >= 0, s6 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 20 + 4*s109 + 4*z0 + 124*z1 + 4*z1^2 }-> 1 + s22 + s111 + s219 :|: s219 >= 0, s219 <= 0, s109 >= 0, s109 <= z1 + 1, s110 >= 0, s110 <= z2 + 1, s111 >= 0, s111 <= 1, s21 >= 0, s21 <= 0 + 0, s22 >= 0, s22 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 20 + 4*s112 + 4*z0 + 124*z1 + 4*z1^2 }-> 1 + s24 + s113 + s220 :|: s220 >= 0, s220 <= 0, s112 >= 0, s112 <= z1 + 1, s113 >= 0, s113 <= 1, s23 >= 0, s23 <= 0 + 0, s24 >= 0, s24 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 20 + 4*z0 + 124*z1 + 4*z1^2 }-> 1 + s26 + s115 + s221 :|: s221 >= 0, s221 <= 0, s114 >= 0, s114 <= z2 + 1, s115 >= 0, s115 <= 1, s25 >= 0, s25 <= 0 + 0, s26 >= 0, s26 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 20 + 4*z0 + 124*z1 + 4*z1^2 }-> 1 + s28 + s3 + s222 :|: s222 >= 0, s222 <= 0, s27 >= 0, s27 <= 0 + 0, s28 >= 0, s28 <= 1, s3 >= 0, s3 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 20 + 4*s177 + 4*z0 + 124*z2 + 4*z2^2 }-> 1 + s30 + s179 + s235 :|: s235 >= 0, s235 <= 0, s177 >= 0, s177 <= z1 + 1, s178 >= 0, s178 <= z2 + 1, s179 >= 0, s179 <= 1, s29 >= 0, s29 <= 0 + 0, s30 >= 0, s30 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 20 + 4*s180 + 4*z0 + 124*z2 + 4*z2^2 }-> 1 + s32 + s181 + s236 :|: s236 >= 0, s236 <= 0, s180 >= 0, s180 <= z1 + 1, s181 >= 0, s181 <= 1, s31 >= 0, s31 <= 0 + 0, s32 >= 0, s32 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 20 + 4*z0 + 124*z2 + 4*z2^2 }-> 1 + s34 + s183 + s237 :|: s237 >= 0, s237 <= 0, s182 >= 0, s182 <= z2 + 1, s183 >= 0, s183 <= 1, s33 >= 0, s33 <= 0 + 0, s34 >= 0, s34 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 20 + 4*z0 + 124*z2 + 4*z2^2 }-> 1 + s36 + s7 + s238 :|: s238 >= 0, s238 <= 0, s35 >= 0, s35 <= 0 + 0, s36 >= 0, s36 <= 1, s7 >= 0, s7 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 20 + 4*s52 + 4*z0 + 124*z1 + 4*z1^2 }-> 1 + s51 + s54 + s207 :|: s207 >= 0, s207 <= 0, s48 >= 0, s48 <= z1 + 1, s49 >= 0, s49 <= z2 + 1, s50 >= 0, s50 <= s48 + s49, s51 >= 0, s51 <= 1, s52 >= 0, s52 <= z1 + 1, s53 >= 0, s53 <= z2 + 1, s54 >= 0, s54 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 20 + 4*s59 + 4*z0 + 124*z1 + 4*z1^2 }-> 1 + s58 + s60 + s208 :|: s208 >= 0, s208 <= 0, s55 >= 0, s55 <= z1 + 1, s56 >= 0, s56 <= z2 + 1, s57 >= 0, s57 <= s55 + s56, s58 >= 0, s58 <= 1, s59 >= 0, s59 <= z1 + 1, s60 >= 0, s60 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 20 + 4*z0 + 124*z1 + 4*z1^2 }-> 1 + s64 + s66 + s209 :|: s209 >= 0, s209 <= 0, s61 >= 0, s61 <= z1 + 1, s62 >= 0, s62 <= z2 + 1, s63 >= 0, s63 <= s61 + s62, s64 >= 0, s64 <= 1, s65 >= 0, s65 <= z2 + 1, s66 >= 0, s66 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 20 + 4*z0 + 124*z1 + 4*z1^2 }-> 1 + s70 + s'' + s210 :|: s210 >= 0, s210 <= 0, s67 >= 0, s67 <= z1 + 1, s68 >= 0, s68 <= z2 + 1, s69 >= 0, s69 <= s67 + s68, s70 >= 0, s70 <= 1, s'' >= 0, s'' <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 20 + 4*s74 + 4*z0 + 124*z1 + 4*z1^2 }-> 1 + s73 + s76 + s211 :|: s211 >= 0, s211 <= 0, s71 >= 0, s71 <= z1 + 1, s72 >= 0, s72 <= s71 + 0, s73 >= 0, s73 <= 1, s74 >= 0, s74 <= z1 + 1, s75 >= 0, s75 <= z2 + 1, s76 >= 0, s76 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 20 + 4*s80 + 4*z0 + 124*z1 + 4*z1^2 }-> 1 + s79 + s81 + s212 :|: s212 >= 0, s212 <= 0, s77 >= 0, s77 <= z1 + 1, s78 >= 0, s78 <= s77 + 0, s79 >= 0, s79 <= 1, s80 >= 0, s80 <= z1 + 1, s81 >= 0, s81 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 20 + 4*z0 + 124*z1 + 4*z1^2 }-> 1 + s84 + s86 + s213 :|: s213 >= 0, s213 <= 0, s82 >= 0, s82 <= z1 + 1, s83 >= 0, s83 <= s82 + 0, s84 >= 0, s84 <= 1, s85 >= 0, s85 <= z2 + 1, s86 >= 0, s86 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 20 + 4*z0 + 124*z1 + 4*z1^2 }-> 1 + s89 + s1 + s214 :|: s214 >= 0, s214 <= 0, s87 >= 0, s87 <= z1 + 1, s88 >= 0, s88 <= s87 + 0, s89 >= 0, s89 <= 1, s1 >= 0, s1 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 20 + 4*s93 + 4*z0 + 124*z1 + 4*z1^2 }-> 1 + s92 + s95 + s215 :|: s215 >= 0, s215 <= 0, s90 >= 0, s90 <= z2 + 1, s91 >= 0, s91 <= 0 + s90, s92 >= 0, s92 <= 1, s93 >= 0, s93 <= z1 + 1, s94 >= 0, s94 <= z2 + 1, s95 >= 0, s95 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 20 + 4*s99 + 4*z0 + 124*z1 + 4*z1^2 }-> 1 + s98 + s100 + s216 :|: s216 >= 0, s216 <= 0, s96 >= 0, s96 <= z2 + 1, s97 >= 0, s97 <= 0 + s96, s98 >= 0, s98 <= 1, s99 >= 0, s99 <= z1 + 1, s100 >= 0, s100 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTENSORT(z) -{ 0 }-> 0 :|: z >= 0
   FLATTENSORT(z) -{ 0 }-> 1 + INSERTIONSORT(s184) :|: s184 >= 0, s184 <= z + 1, z >= 0
   FLATTENSORT(z) -{ 0 }-> 1 + INSERTIONSORT(0) :|: z >= 0
   INSERT(z, z') -{ 8 + 4*z' }-> 1 + s200 :|: s200 >= 0, s200 <= 0, z' >= 0, z >= 0
   INSERT#1(z, z') -{ 11 + 4*z1 }-> 1 + s201 + s46 :|: s201 >= 0, s201 <= 2, s46 >= 0, s46 <= z0 + z' + 1, z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z' >= 0
   INSERT#1(z, z') -{ 11 + 4*z1 }-> 1 + s205 + s47 :|: s205 >= 0, s205 <= 2, s47 >= 0, s47 <= z0 + z' + 1, s10 >= 0, s10 <= 3, s11 >= 0, s11 <= 2, z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z' >= 0
   INSERT#2(z, z', z'', z3) -{ 9 + 4*z3 }-> 1 + s202 :|: s202 >= 0, s202 <= 1, z = 2, z'' >= 0, z' >= 0, z3 >= 0
   INSERTIONSORT(z) -{ 1 }-> 1 + INSERTIONSORT#1(z) :|: z >= 0
   INSERTIONSORT#1(z) -{ 9 + 4*s196 }-> 1 + s203 + INSERTIONSORT(z1) :|: s203 >= 0, s203 <= 1, s196 >= 0, s196 <= z1, z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   INSERTIONSORT#1(z) -{ 9 }-> 1 + s204 + INSERTIONSORT(z1) :|: s204 >= 0, s204 <= 1, z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   append(z, z') -{ 0 }-> s37 :|: s37 >= 0, s37 <= z + z', z' >= 0, z >= 0
   append(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   append#1(z, z') -{ 0 }-> z' :|: z' >= 0, z = 0
   append#1(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   append#1(z, z') -{ 0 }-> 1 + z0 + s40 :|: s40 >= 0, s40 <= z1 + z', z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z' >= 0
   flatten(z) -{ 0 }-> s185 :|: s185 >= 0, s185 <= z + 1, z >= 0
   flatten(z) -{ 0 }-> 0 :|: z >= 0
   flatten#1(z) -{ 0 }-> s189 :|: s186 >= 0, s186 <= z1 + 1, s187 >= 0, s187 <= z2 + 1, s188 >= 0, s188 <= s186 + s187, s189 >= 0, s189 <= z0 + s188, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   flatten#1(z) -{ 0 }-> s192 :|: s190 >= 0, s190 <= z1 + 1, s191 >= 0, s191 <= s190 + 0, s192 >= 0, s192 <= z0 + s191, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   flatten#1(z) -{ 0 }-> s195 :|: s193 >= 0, s193 <= z2 + 1, s194 >= 0, s194 <= 0 + s193, s195 >= 0, s195 <= z0 + s194, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   flatten#1(z) -{ 0 }-> s39 :|: s38 >= 0, s38 <= 0 + 0, s39 >= 0, s39 <= z0 + s38, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   flatten#1(z) -{ 0 }-> 0 :|: z = 0
   flatten#1(z) -{ 0 }-> 0 :|: z >= 0
   insert(z, z') -{ 0 }-> s42 :|: s42 >= 0, s42 <= z' + z + 1, z' >= 0, z >= 0
   insert(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   insert#1(z, z') -{ 0 }-> s43 :|: s43 >= 0, s43 <= z' + z0 + z1 + 2, z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z' >= 0
   insert#1(z, z') -{ 0 }-> s45 :|: s45 >= 0, s45 <= z' + z0 + z1 + 2, s16 >= 0, s16 <= 3, s17 >= 0, s17 <= 2, z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z' >= 0
   insert#1(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   insert#1(z, z') -{ 0 }-> 1 + z' + 0 :|: z' >= 0, z = 0
   insert#2(z, z', z'', z3) -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0, z3 >= 0
   insert#2(z, z', z'', z3) -{ 0 }-> 1 + z' + (1 + z'' + z3) :|: z'' >= 0, z = 1, z' >= 0, z3 >= 0
   insert#2(z, z', z'', z3) -{ 0 }-> 1 + z'' + s44 :|: s44 >= 0, s44 <= z' + z3 + 1, z = 2, z'' >= 0, z' >= 0, z3 >= 0
   insertionsort(z) -{ 0 }-> s197 :|: s197 >= 0, s197 <= z, z >= 0
   insertionsort(z) -{ 0 }-> 0 :|: z >= 0
   insertionsort#1(z) -{ 0 }-> s199 :|: s198 >= 0, s198 <= z1, s199 >= 0, s199 <= z0 + s198 + 1, z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   insertionsort#1(z) -{ 0 }-> s41 :|: s41 >= 0, s41 <= z0 + 0 + 1, z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   insertionsort#1(z) -{ 0 }-> 0 :|: z = 0
   insertionsort#1(z) -{ 0 }-> 0 :|: z >= 0

Function symbols to be analyzed: {FLATTENSORT}
Previous analysis results are:
  APPEND#1: runtime: O(n^1) [4*z], size: O(1) [0]
  APPEND: runtime: O(n^1) [1 + 4*z], size: O(1) [1]
  #cklt: runtime: O(1) [0], size: O(1) [2]
  #compare: runtime: O(1) [0], size: O(1) [3]
  #COMPARE: runtime: O(1) [0], size: O(n^1) [z + z']
  append#1: runtime: O(1) [0], size: O(n^1) [z + z']
  append: runtime: O(1) [0], size: O(n^1) [z + z']
  #less: runtime: O(1) [0], size: O(1) [2]
  insert#2: runtime: O(1) [0], size: O(n^1) [2 + z' + z'' + z3]
  insert: runtime: O(1) [0], size: O(n^1) [1 + z + z']
  insert#1: runtime: O(1) [0], size: O(n^1) [1 + z + z']
  #LESS: runtime: O(1) [1], size: O(n^1) [1 + z + z']
  flatten#1: runtime: O(1) [0], size: O(n^1) [1 + z]
  insertionsort#1: runtime: O(1) [0], size: O(n^1) [z]
  INSERT#1: runtime: O(n^1) [7 + 4*z], size: O(1) [0]
  INSERT#2: runtime: O(n^1) [9 + 4*z3], size: O(1) [2]
  INSERT: runtime: O(n^1) [8 + 4*z'], size: O(1) [1]
  flatten: runtime: O(1) [0], size: O(n^1) [1 + z]
  FLATTEN: runtime: O(n^2) [17 + 124*z + 4*z^2], size: O(1) [0]
  FLATTEN#1: runtime: O(n^2) [704 + 4160*z + 128*z^2], size: O(1) [3]
  insertionsort: runtime: O(1) [0], size: O(n^1) [z]
  INSERTIONSORT: runtime: O(n^2) [1 + 10*z + 4*z^2], size: O(1) [0]
  INSERTIONSORT#1: runtime: O(n^2) [20 + 24*z + 8*z^2], size: O(1) [2]

----------------------------------------

(125) ResultPropagationProof (UPPER BOUND(ID))
Applied inner abstraction using the recently inferred runtime/size bounds where possible.
----------------------------------------

(126)
Obligation:
Complexity RNTS consisting of the following rules:

   #COMPARE(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   #COMPARE(z, z') -{ 0 }-> 1 + s19 :|: s19 >= 0, s19 <= z' - 1 + (z - 1), z' - 1 >= 0, z - 1 >= 0
   #COMPARE(z, z') -{ 0 }-> 1 + s20 :|: s20 >= 0, s20 <= z - 1 + (z' - 1), z' - 1 >= 0, z - 1 >= 0
   #LESS(z, z') -{ 1 }-> 1 + s18 :|: s18 >= 0, s18 <= z + z', z' >= 0, z >= 0
   #cklt(z) -{ 0 }-> 2 :|: z = 3
   #cklt(z) -{ 0 }-> 1 :|: z = 1
   #cklt(z) -{ 0 }-> 1 :|: z = 2
   #cklt(z) -{ 0 }-> 0 :|: z >= 0
   #compare(z, z') -{ 0 }-> s8 :|: s8 >= 0, s8 <= 3, z' - 1 >= 0, z - 1 >= 0
   #compare(z, z') -{ 0 }-> s9 :|: s9 >= 0, s9 <= 3, z' - 1 >= 0, z - 1 >= 0
   #compare(z, z') -{ 0 }-> 3 :|: z' - 1 >= 0, z = 0
   #compare(z, z') -{ 0 }-> 3 :|: z - 1 >= 0, z' = 0
   #compare(z, z') -{ 0 }-> 3 :|: z' - 1 >= 0, z - 1 >= 0
   #compare(z, z') -{ 0 }-> 2 :|: z' - 1 >= 0, z = 0
   #compare(z, z') -{ 0 }-> 2 :|: z - 1 >= 0, z' = 0
   #compare(z, z') -{ 0 }-> 2 :|: z' - 1 >= 0, z - 1 >= 0
   #compare(z, z') -{ 0 }-> 1 :|: z = 0, z' = 0
   #compare(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   #less(z, z') -{ 0 }-> s13 :|: s12 >= 0, s12 <= 3, s13 >= 0, s13 <= 2, z' - 1 >= 0, z - 1 >= 0
   #less(z, z') -{ 0 }-> s15 :|: s14 >= 0, s14 <= 3, s15 >= 0, s15 <= 2, z - 1 >= 0, z' - 1 >= 0
   #less(z, z') -{ 0 }-> 2 :|: z' - 1 >= 0, z = 0, 3 = 3
   #less(z, z') -{ 0 }-> 2 :|: z - 1 >= 0, z' = 0, 3 = 3
   #less(z, z') -{ 0 }-> 2 :|: z - 1 >= 0, z' - 1 >= 0, 3 = 3
   #less(z, z') -{ 0 }-> 1 :|: z = 0, z' = 0, 1 = 1
   #less(z, z') -{ 0 }-> 1 :|: z' - 1 >= 0, z = 0, 2 = 2
   #less(z, z') -{ 0 }-> 1 :|: z - 1 >= 0, z' = 0, 2 = 2
   #less(z, z') -{ 0 }-> 1 :|: z' - 1 >= 0, z - 1 >= 0, 2 = 2
   #less(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   #less(z, z') -{ 0 }-> 0 :|: z = 0, z' = 0, v0 >= 0, 1 = v0
   #less(z, z') -{ 0 }-> 0 :|: z' - 1 >= 0, z = 0, v0 >= 0, 2 = v0
   #less(z, z') -{ 0 }-> 0 :|: z' - 1 >= 0, z = 0, v0 >= 0, 3 = v0
   #less(z, z') -{ 0 }-> 0 :|: z - 1 >= 0, z' = 0, v0 >= 0, 3 = v0
   #less(z, z') -{ 0 }-> 0 :|: z - 1 >= 0, z' - 1 >= 0, v0 >= 0, 3 = v0
   #less(z, z') -{ 0 }-> 0 :|: z - 1 >= 0, z' = 0, v0 >= 0, 2 = v0
   #less(z, z') -{ 0 }-> 0 :|: z' - 1 >= 0, z - 1 >= 0, v0 >= 0, 2 = v0
   #less(z, z') -{ 0 }-> 0 :|: z' >= 0, z >= 0, v0 >= 0, 0 = v0
   APPEND(z, z') -{ 1 + 4*z }-> 1 + s :|: s >= 0, s <= 0, z' >= 0, z >= 0
   APPEND#1(z, z') -{ 2 + 4*z1 }-> 1 + s' :|: s' >= 0, s' <= 1, z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z' >= 0
   FLATTEN(z) -{ 705 + 4160*z + 128*z^2 }-> 1 + s206 :|: s206 >= 0, s206 <= 3, z >= 0
   FLATTEN#1(z) -{ 20 + 4*z0 + 124*z1 + 4*z1^2 }-> 1 + s103 + s105 + s217 :|: s217 >= 0, s217 <= 0, s101 >= 0, s101 <= z2 + 1, s102 >= 0, s102 <= 0 + s101, s103 >= 0, s103 <= 1, s104 >= 0, s104 <= z2 + 1, s105 >= 0, s105 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 20 + 4*z0 + 124*z1 + 4*z1^2 }-> 1 + s108 + s2 + s218 :|: s218 >= 0, s218 <= 0, s106 >= 0, s106 <= z2 + 1, s107 >= 0, s107 <= 0 + s106, s108 >= 0, s108 <= 1, s2 >= 0, s2 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 20 + 4*s120 + 4*z0 + 124*z2 + 4*z2^2 }-> 1 + s119 + s122 + s223 :|: s223 >= 0, s223 <= 0, s116 >= 0, s116 <= z1 + 1, s117 >= 0, s117 <= z2 + 1, s118 >= 0, s118 <= s116 + s117, s119 >= 0, s119 <= 1, s120 >= 0, s120 <= z1 + 1, s121 >= 0, s121 <= z2 + 1, s122 >= 0, s122 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 20 + 4*s127 + 4*z0 + 124*z2 + 4*z2^2 }-> 1 + s126 + s128 + s224 :|: s224 >= 0, s224 <= 0, s123 >= 0, s123 <= z1 + 1, s124 >= 0, s124 <= z2 + 1, s125 >= 0, s125 <= s123 + s124, s126 >= 0, s126 <= 1, s127 >= 0, s127 <= z1 + 1, s128 >= 0, s128 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 20 + 4*z0 + 124*z2 + 4*z2^2 }-> 1 + s132 + s134 + s225 :|: s225 >= 0, s225 <= 0, s129 >= 0, s129 <= z1 + 1, s130 >= 0, s130 <= z2 + 1, s131 >= 0, s131 <= s129 + s130, s132 >= 0, s132 <= 1, s133 >= 0, s133 <= z2 + 1, s134 >= 0, s134 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 20 + 4*z0 + 124*z2 + 4*z2^2 }-> 1 + s138 + s4 + s226 :|: s226 >= 0, s226 <= 0, s135 >= 0, s135 <= z1 + 1, s136 >= 0, s136 <= z2 + 1, s137 >= 0, s137 <= s135 + s136, s138 >= 0, s138 <= 1, s4 >= 0, s4 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 20 + 4*s142 + 4*z0 + 124*z2 + 4*z2^2 }-> 1 + s141 + s144 + s227 :|: s227 >= 0, s227 <= 0, s139 >= 0, s139 <= z1 + 1, s140 >= 0, s140 <= s139 + 0, s141 >= 0, s141 <= 1, s142 >= 0, s142 <= z1 + 1, s143 >= 0, s143 <= z2 + 1, s144 >= 0, s144 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 20 + 4*s148 + 4*z0 + 124*z2 + 4*z2^2 }-> 1 + s147 + s149 + s228 :|: s228 >= 0, s228 <= 0, s145 >= 0, s145 <= z1 + 1, s146 >= 0, s146 <= s145 + 0, s147 >= 0, s147 <= 1, s148 >= 0, s148 <= z1 + 1, s149 >= 0, s149 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 20 + 4*z0 + 124*z2 + 4*z2^2 }-> 1 + s152 + s154 + s229 :|: s229 >= 0, s229 <= 0, s150 >= 0, s150 <= z1 + 1, s151 >= 0, s151 <= s150 + 0, s152 >= 0, s152 <= 1, s153 >= 0, s153 <= z2 + 1, s154 >= 0, s154 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 20 + 4*z0 + 124*z2 + 4*z2^2 }-> 1 + s157 + s5 + s230 :|: s230 >= 0, s230 <= 0, s155 >= 0, s155 <= z1 + 1, s156 >= 0, s156 <= s155 + 0, s157 >= 0, s157 <= 1, s5 >= 0, s5 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 20 + 4*s161 + 4*z0 + 124*z2 + 4*z2^2 }-> 1 + s160 + s163 + s231 :|: s231 >= 0, s231 <= 0, s158 >= 0, s158 <= z2 + 1, s159 >= 0, s159 <= 0 + s158, s160 >= 0, s160 <= 1, s161 >= 0, s161 <= z1 + 1, s162 >= 0, s162 <= z2 + 1, s163 >= 0, s163 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 20 + 4*s167 + 4*z0 + 124*z2 + 4*z2^2 }-> 1 + s166 + s168 + s232 :|: s232 >= 0, s232 <= 0, s164 >= 0, s164 <= z2 + 1, s165 >= 0, s165 <= 0 + s164, s166 >= 0, s166 <= 1, s167 >= 0, s167 <= z1 + 1, s168 >= 0, s168 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 20 + 4*z0 + 124*z2 + 4*z2^2 }-> 1 + s171 + s173 + s233 :|: s233 >= 0, s233 <= 0, s169 >= 0, s169 <= z2 + 1, s170 >= 0, s170 <= 0 + s169, s171 >= 0, s171 <= 1, s172 >= 0, s172 <= z2 + 1, s173 >= 0, s173 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 20 + 4*z0 + 124*z2 + 4*z2^2 }-> 1 + s176 + s6 + s234 :|: s234 >= 0, s234 <= 0, s174 >= 0, s174 <= z2 + 1, s175 >= 0, s175 <= 0 + s174, s176 >= 0, s176 <= 1, s6 >= 0, s6 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 20 + 4*s109 + 4*z0 + 124*z1 + 4*z1^2 }-> 1 + s22 + s111 + s219 :|: s219 >= 0, s219 <= 0, s109 >= 0, s109 <= z1 + 1, s110 >= 0, s110 <= z2 + 1, s111 >= 0, s111 <= 1, s21 >= 0, s21 <= 0 + 0, s22 >= 0, s22 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 20 + 4*s112 + 4*z0 + 124*z1 + 4*z1^2 }-> 1 + s24 + s113 + s220 :|: s220 >= 0, s220 <= 0, s112 >= 0, s112 <= z1 + 1, s113 >= 0, s113 <= 1, s23 >= 0, s23 <= 0 + 0, s24 >= 0, s24 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 20 + 4*z0 + 124*z1 + 4*z1^2 }-> 1 + s26 + s115 + s221 :|: s221 >= 0, s221 <= 0, s114 >= 0, s114 <= z2 + 1, s115 >= 0, s115 <= 1, s25 >= 0, s25 <= 0 + 0, s26 >= 0, s26 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 20 + 4*z0 + 124*z1 + 4*z1^2 }-> 1 + s28 + s3 + s222 :|: s222 >= 0, s222 <= 0, s27 >= 0, s27 <= 0 + 0, s28 >= 0, s28 <= 1, s3 >= 0, s3 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 20 + 4*s177 + 4*z0 + 124*z2 + 4*z2^2 }-> 1 + s30 + s179 + s235 :|: s235 >= 0, s235 <= 0, s177 >= 0, s177 <= z1 + 1, s178 >= 0, s178 <= z2 + 1, s179 >= 0, s179 <= 1, s29 >= 0, s29 <= 0 + 0, s30 >= 0, s30 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 20 + 4*s180 + 4*z0 + 124*z2 + 4*z2^2 }-> 1 + s32 + s181 + s236 :|: s236 >= 0, s236 <= 0, s180 >= 0, s180 <= z1 + 1, s181 >= 0, s181 <= 1, s31 >= 0, s31 <= 0 + 0, s32 >= 0, s32 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 20 + 4*z0 + 124*z2 + 4*z2^2 }-> 1 + s34 + s183 + s237 :|: s237 >= 0, s237 <= 0, s182 >= 0, s182 <= z2 + 1, s183 >= 0, s183 <= 1, s33 >= 0, s33 <= 0 + 0, s34 >= 0, s34 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 20 + 4*z0 + 124*z2 + 4*z2^2 }-> 1 + s36 + s7 + s238 :|: s238 >= 0, s238 <= 0, s35 >= 0, s35 <= 0 + 0, s36 >= 0, s36 <= 1, s7 >= 0, s7 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 20 + 4*s52 + 4*z0 + 124*z1 + 4*z1^2 }-> 1 + s51 + s54 + s207 :|: s207 >= 0, s207 <= 0, s48 >= 0, s48 <= z1 + 1, s49 >= 0, s49 <= z2 + 1, s50 >= 0, s50 <= s48 + s49, s51 >= 0, s51 <= 1, s52 >= 0, s52 <= z1 + 1, s53 >= 0, s53 <= z2 + 1, s54 >= 0, s54 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 20 + 4*s59 + 4*z0 + 124*z1 + 4*z1^2 }-> 1 + s58 + s60 + s208 :|: s208 >= 0, s208 <= 0, s55 >= 0, s55 <= z1 + 1, s56 >= 0, s56 <= z2 + 1, s57 >= 0, s57 <= s55 + s56, s58 >= 0, s58 <= 1, s59 >= 0, s59 <= z1 + 1, s60 >= 0, s60 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 20 + 4*z0 + 124*z1 + 4*z1^2 }-> 1 + s64 + s66 + s209 :|: s209 >= 0, s209 <= 0, s61 >= 0, s61 <= z1 + 1, s62 >= 0, s62 <= z2 + 1, s63 >= 0, s63 <= s61 + s62, s64 >= 0, s64 <= 1, s65 >= 0, s65 <= z2 + 1, s66 >= 0, s66 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 20 + 4*z0 + 124*z1 + 4*z1^2 }-> 1 + s70 + s'' + s210 :|: s210 >= 0, s210 <= 0, s67 >= 0, s67 <= z1 + 1, s68 >= 0, s68 <= z2 + 1, s69 >= 0, s69 <= s67 + s68, s70 >= 0, s70 <= 1, s'' >= 0, s'' <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 20 + 4*s74 + 4*z0 + 124*z1 + 4*z1^2 }-> 1 + s73 + s76 + s211 :|: s211 >= 0, s211 <= 0, s71 >= 0, s71 <= z1 + 1, s72 >= 0, s72 <= s71 + 0, s73 >= 0, s73 <= 1, s74 >= 0, s74 <= z1 + 1, s75 >= 0, s75 <= z2 + 1, s76 >= 0, s76 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 20 + 4*s80 + 4*z0 + 124*z1 + 4*z1^2 }-> 1 + s79 + s81 + s212 :|: s212 >= 0, s212 <= 0, s77 >= 0, s77 <= z1 + 1, s78 >= 0, s78 <= s77 + 0, s79 >= 0, s79 <= 1, s80 >= 0, s80 <= z1 + 1, s81 >= 0, s81 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 20 + 4*z0 + 124*z1 + 4*z1^2 }-> 1 + s84 + s86 + s213 :|: s213 >= 0, s213 <= 0, s82 >= 0, s82 <= z1 + 1, s83 >= 0, s83 <= s82 + 0, s84 >= 0, s84 <= 1, s85 >= 0, s85 <= z2 + 1, s86 >= 0, s86 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 20 + 4*z0 + 124*z1 + 4*z1^2 }-> 1 + s89 + s1 + s214 :|: s214 >= 0, s214 <= 0, s87 >= 0, s87 <= z1 + 1, s88 >= 0, s88 <= s87 + 0, s89 >= 0, s89 <= 1, s1 >= 0, s1 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 20 + 4*s93 + 4*z0 + 124*z1 + 4*z1^2 }-> 1 + s92 + s95 + s215 :|: s215 >= 0, s215 <= 0, s90 >= 0, s90 <= z2 + 1, s91 >= 0, s91 <= 0 + s90, s92 >= 0, s92 <= 1, s93 >= 0, s93 <= z1 + 1, s94 >= 0, s94 <= z2 + 1, s95 >= 0, s95 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 20 + 4*s99 + 4*z0 + 124*z1 + 4*z1^2 }-> 1 + s98 + s100 + s216 :|: s216 >= 0, s216 <= 0, s96 >= 0, s96 <= z2 + 1, s97 >= 0, s97 <= 0 + s96, s98 >= 0, s98 <= 1, s99 >= 0, s99 <= z1 + 1, s100 >= 0, s100 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTENSORT(z) -{ 0 }-> 0 :|: z >= 0
   FLATTENSORT(z) -{ 1 + 10*s184 + 4*s184^2 }-> 1 + s242 :|: s242 >= 0, s242 <= 0, s184 >= 0, s184 <= z + 1, z >= 0
   FLATTENSORT(z) -{ 1 }-> 1 + s243 :|: s243 >= 0, s243 <= 0, z >= 0
   INSERT(z, z') -{ 8 + 4*z' }-> 1 + s200 :|: s200 >= 0, s200 <= 0, z' >= 0, z >= 0
   INSERT#1(z, z') -{ 11 + 4*z1 }-> 1 + s201 + s46 :|: s201 >= 0, s201 <= 2, s46 >= 0, s46 <= z0 + z' + 1, z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z' >= 0
   INSERT#1(z, z') -{ 11 + 4*z1 }-> 1 + s205 + s47 :|: s205 >= 0, s205 <= 2, s47 >= 0, s47 <= z0 + z' + 1, s10 >= 0, s10 <= 3, s11 >= 0, s11 <= 2, z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z' >= 0
   INSERT#2(z, z', z'', z3) -{ 9 + 4*z3 }-> 1 + s202 :|: s202 >= 0, s202 <= 1, z = 2, z'' >= 0, z' >= 0, z3 >= 0
   INSERTIONSORT(z) -{ 21 + 24*z + 8*z^2 }-> 1 + s239 :|: s239 >= 0, s239 <= 2, z >= 0
   INSERTIONSORT#1(z) -{ 10 + 4*s196 + 10*z1 + 4*z1^2 }-> 1 + s203 + s240 :|: s240 >= 0, s240 <= 0, s203 >= 0, s203 <= 1, s196 >= 0, s196 <= z1, z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   INSERTIONSORT#1(z) -{ 10 + 10*z1 + 4*z1^2 }-> 1 + s204 + s241 :|: s241 >= 0, s241 <= 0, s204 >= 0, s204 <= 1, z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   append(z, z') -{ 0 }-> s37 :|: s37 >= 0, s37 <= z + z', z' >= 0, z >= 0
   append(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   append#1(z, z') -{ 0 }-> z' :|: z' >= 0, z = 0
   append#1(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   append#1(z, z') -{ 0 }-> 1 + z0 + s40 :|: s40 >= 0, s40 <= z1 + z', z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z' >= 0
   flatten(z) -{ 0 }-> s185 :|: s185 >= 0, s185 <= z + 1, z >= 0
   flatten(z) -{ 0 }-> 0 :|: z >= 0
   flatten#1(z) -{ 0 }-> s189 :|: s186 >= 0, s186 <= z1 + 1, s187 >= 0, s187 <= z2 + 1, s188 >= 0, s188 <= s186 + s187, s189 >= 0, s189 <= z0 + s188, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   flatten#1(z) -{ 0 }-> s192 :|: s190 >= 0, s190 <= z1 + 1, s191 >= 0, s191 <= s190 + 0, s192 >= 0, s192 <= z0 + s191, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   flatten#1(z) -{ 0 }-> s195 :|: s193 >= 0, s193 <= z2 + 1, s194 >= 0, s194 <= 0 + s193, s195 >= 0, s195 <= z0 + s194, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   flatten#1(z) -{ 0 }-> s39 :|: s38 >= 0, s38 <= 0 + 0, s39 >= 0, s39 <= z0 + s38, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   flatten#1(z) -{ 0 }-> 0 :|: z = 0
   flatten#1(z) -{ 0 }-> 0 :|: z >= 0
   insert(z, z') -{ 0 }-> s42 :|: s42 >= 0, s42 <= z' + z + 1, z' >= 0, z >= 0
   insert(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   insert#1(z, z') -{ 0 }-> s43 :|: s43 >= 0, s43 <= z' + z0 + z1 + 2, z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z' >= 0
   insert#1(z, z') -{ 0 }-> s45 :|: s45 >= 0, s45 <= z' + z0 + z1 + 2, s16 >= 0, s16 <= 3, s17 >= 0, s17 <= 2, z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z' >= 0
   insert#1(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   insert#1(z, z') -{ 0 }-> 1 + z' + 0 :|: z' >= 0, z = 0
   insert#2(z, z', z'', z3) -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0, z3 >= 0
   insert#2(z, z', z'', z3) -{ 0 }-> 1 + z' + (1 + z'' + z3) :|: z'' >= 0, z = 1, z' >= 0, z3 >= 0
   insert#2(z, z', z'', z3) -{ 0 }-> 1 + z'' + s44 :|: s44 >= 0, s44 <= z' + z3 + 1, z = 2, z'' >= 0, z' >= 0, z3 >= 0
   insertionsort(z) -{ 0 }-> s197 :|: s197 >= 0, s197 <= z, z >= 0
   insertionsort(z) -{ 0 }-> 0 :|: z >= 0
   insertionsort#1(z) -{ 0 }-> s199 :|: s198 >= 0, s198 <= z1, s199 >= 0, s199 <= z0 + s198 + 1, z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   insertionsort#1(z) -{ 0 }-> s41 :|: s41 >= 0, s41 <= z0 + 0 + 1, z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   insertionsort#1(z) -{ 0 }-> 0 :|: z = 0
   insertionsort#1(z) -{ 0 }-> 0 :|: z >= 0

Function symbols to be analyzed: {FLATTENSORT}
Previous analysis results are:
  APPEND#1: runtime: O(n^1) [4*z], size: O(1) [0]
  APPEND: runtime: O(n^1) [1 + 4*z], size: O(1) [1]
  #cklt: runtime: O(1) [0], size: O(1) [2]
  #compare: runtime: O(1) [0], size: O(1) [3]
  #COMPARE: runtime: O(1) [0], size: O(n^1) [z + z']
  append#1: runtime: O(1) [0], size: O(n^1) [z + z']
  append: runtime: O(1) [0], size: O(n^1) [z + z']
  #less: runtime: O(1) [0], size: O(1) [2]
  insert#2: runtime: O(1) [0], size: O(n^1) [2 + z' + z'' + z3]
  insert: runtime: O(1) [0], size: O(n^1) [1 + z + z']
  insert#1: runtime: O(1) [0], size: O(n^1) [1 + z + z']
  #LESS: runtime: O(1) [1], size: O(n^1) [1 + z + z']
  flatten#1: runtime: O(1) [0], size: O(n^1) [1 + z]
  insertionsort#1: runtime: O(1) [0], size: O(n^1) [z]
  INSERT#1: runtime: O(n^1) [7 + 4*z], size: O(1) [0]
  INSERT#2: runtime: O(n^1) [9 + 4*z3], size: O(1) [2]
  INSERT: runtime: O(n^1) [8 + 4*z'], size: O(1) [1]
  flatten: runtime: O(1) [0], size: O(n^1) [1 + z]
  FLATTEN: runtime: O(n^2) [17 + 124*z + 4*z^2], size: O(1) [0]
  FLATTEN#1: runtime: O(n^2) [704 + 4160*z + 128*z^2], size: O(1) [3]
  insertionsort: runtime: O(1) [0], size: O(n^1) [z]
  INSERTIONSORT: runtime: O(n^2) [1 + 10*z + 4*z^2], size: O(1) [0]
  INSERTIONSORT#1: runtime: O(n^2) [20 + 24*z + 8*z^2], size: O(1) [2]

----------------------------------------

(127) IntTrsBoundProof (UPPER BOUND(ID))

Computed SIZE bound using CoFloCo for: FLATTENSORT
after applying outer abstraction to obtain an ITS,
resulting in: O(1) with polynomial bound: 1

----------------------------------------

(128)
Obligation:
Complexity RNTS consisting of the following rules:

   #COMPARE(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   #COMPARE(z, z') -{ 0 }-> 1 + s19 :|: s19 >= 0, s19 <= z' - 1 + (z - 1), z' - 1 >= 0, z - 1 >= 0
   #COMPARE(z, z') -{ 0 }-> 1 + s20 :|: s20 >= 0, s20 <= z - 1 + (z' - 1), z' - 1 >= 0, z - 1 >= 0
   #LESS(z, z') -{ 1 }-> 1 + s18 :|: s18 >= 0, s18 <= z + z', z' >= 0, z >= 0
   #cklt(z) -{ 0 }-> 2 :|: z = 3
   #cklt(z) -{ 0 }-> 1 :|: z = 1
   #cklt(z) -{ 0 }-> 1 :|: z = 2
   #cklt(z) -{ 0 }-> 0 :|: z >= 0
   #compare(z, z') -{ 0 }-> s8 :|: s8 >= 0, s8 <= 3, z' - 1 >= 0, z - 1 >= 0
   #compare(z, z') -{ 0 }-> s9 :|: s9 >= 0, s9 <= 3, z' - 1 >= 0, z - 1 >= 0
   #compare(z, z') -{ 0 }-> 3 :|: z' - 1 >= 0, z = 0
   #compare(z, z') -{ 0 }-> 3 :|: z - 1 >= 0, z' = 0
   #compare(z, z') -{ 0 }-> 3 :|: z' - 1 >= 0, z - 1 >= 0
   #compare(z, z') -{ 0 }-> 2 :|: z' - 1 >= 0, z = 0
   #compare(z, z') -{ 0 }-> 2 :|: z - 1 >= 0, z' = 0
   #compare(z, z') -{ 0 }-> 2 :|: z' - 1 >= 0, z - 1 >= 0
   #compare(z, z') -{ 0 }-> 1 :|: z = 0, z' = 0
   #compare(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   #less(z, z') -{ 0 }-> s13 :|: s12 >= 0, s12 <= 3, s13 >= 0, s13 <= 2, z' - 1 >= 0, z - 1 >= 0
   #less(z, z') -{ 0 }-> s15 :|: s14 >= 0, s14 <= 3, s15 >= 0, s15 <= 2, z - 1 >= 0, z' - 1 >= 0
   #less(z, z') -{ 0 }-> 2 :|: z' - 1 >= 0, z = 0, 3 = 3
   #less(z, z') -{ 0 }-> 2 :|: z - 1 >= 0, z' = 0, 3 = 3
   #less(z, z') -{ 0 }-> 2 :|: z - 1 >= 0, z' - 1 >= 0, 3 = 3
   #less(z, z') -{ 0 }-> 1 :|: z = 0, z' = 0, 1 = 1
   #less(z, z') -{ 0 }-> 1 :|: z' - 1 >= 0, z = 0, 2 = 2
   #less(z, z') -{ 0 }-> 1 :|: z - 1 >= 0, z' = 0, 2 = 2
   #less(z, z') -{ 0 }-> 1 :|: z' - 1 >= 0, z - 1 >= 0, 2 = 2
   #less(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   #less(z, z') -{ 0 }-> 0 :|: z = 0, z' = 0, v0 >= 0, 1 = v0
   #less(z, z') -{ 0 }-> 0 :|: z' - 1 >= 0, z = 0, v0 >= 0, 2 = v0
   #less(z, z') -{ 0 }-> 0 :|: z' - 1 >= 0, z = 0, v0 >= 0, 3 = v0
   #less(z, z') -{ 0 }-> 0 :|: z - 1 >= 0, z' = 0, v0 >= 0, 3 = v0
   #less(z, z') -{ 0 }-> 0 :|: z - 1 >= 0, z' - 1 >= 0, v0 >= 0, 3 = v0
   #less(z, z') -{ 0 }-> 0 :|: z - 1 >= 0, z' = 0, v0 >= 0, 2 = v0
   #less(z, z') -{ 0 }-> 0 :|: z' - 1 >= 0, z - 1 >= 0, v0 >= 0, 2 = v0
   #less(z, z') -{ 0 }-> 0 :|: z' >= 0, z >= 0, v0 >= 0, 0 = v0
   APPEND(z, z') -{ 1 + 4*z }-> 1 + s :|: s >= 0, s <= 0, z' >= 0, z >= 0
   APPEND#1(z, z') -{ 2 + 4*z1 }-> 1 + s' :|: s' >= 0, s' <= 1, z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z' >= 0
   FLATTEN(z) -{ 705 + 4160*z + 128*z^2 }-> 1 + s206 :|: s206 >= 0, s206 <= 3, z >= 0
   FLATTEN#1(z) -{ 20 + 4*z0 + 124*z1 + 4*z1^2 }-> 1 + s103 + s105 + s217 :|: s217 >= 0, s217 <= 0, s101 >= 0, s101 <= z2 + 1, s102 >= 0, s102 <= 0 + s101, s103 >= 0, s103 <= 1, s104 >= 0, s104 <= z2 + 1, s105 >= 0, s105 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 20 + 4*z0 + 124*z1 + 4*z1^2 }-> 1 + s108 + s2 + s218 :|: s218 >= 0, s218 <= 0, s106 >= 0, s106 <= z2 + 1, s107 >= 0, s107 <= 0 + s106, s108 >= 0, s108 <= 1, s2 >= 0, s2 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 20 + 4*s120 + 4*z0 + 124*z2 + 4*z2^2 }-> 1 + s119 + s122 + s223 :|: s223 >= 0, s223 <= 0, s116 >= 0, s116 <= z1 + 1, s117 >= 0, s117 <= z2 + 1, s118 >= 0, s118 <= s116 + s117, s119 >= 0, s119 <= 1, s120 >= 0, s120 <= z1 + 1, s121 >= 0, s121 <= z2 + 1, s122 >= 0, s122 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 20 + 4*s127 + 4*z0 + 124*z2 + 4*z2^2 }-> 1 + s126 + s128 + s224 :|: s224 >= 0, s224 <= 0, s123 >= 0, s123 <= z1 + 1, s124 >= 0, s124 <= z2 + 1, s125 >= 0, s125 <= s123 + s124, s126 >= 0, s126 <= 1, s127 >= 0, s127 <= z1 + 1, s128 >= 0, s128 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 20 + 4*z0 + 124*z2 + 4*z2^2 }-> 1 + s132 + s134 + s225 :|: s225 >= 0, s225 <= 0, s129 >= 0, s129 <= z1 + 1, s130 >= 0, s130 <= z2 + 1, s131 >= 0, s131 <= s129 + s130, s132 >= 0, s132 <= 1, s133 >= 0, s133 <= z2 + 1, s134 >= 0, s134 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 20 + 4*z0 + 124*z2 + 4*z2^2 }-> 1 + s138 + s4 + s226 :|: s226 >= 0, s226 <= 0, s135 >= 0, s135 <= z1 + 1, s136 >= 0, s136 <= z2 + 1, s137 >= 0, s137 <= s135 + s136, s138 >= 0, s138 <= 1, s4 >= 0, s4 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 20 + 4*s142 + 4*z0 + 124*z2 + 4*z2^2 }-> 1 + s141 + s144 + s227 :|: s227 >= 0, s227 <= 0, s139 >= 0, s139 <= z1 + 1, s140 >= 0, s140 <= s139 + 0, s141 >= 0, s141 <= 1, s142 >= 0, s142 <= z1 + 1, s143 >= 0, s143 <= z2 + 1, s144 >= 0, s144 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 20 + 4*s148 + 4*z0 + 124*z2 + 4*z2^2 }-> 1 + s147 + s149 + s228 :|: s228 >= 0, s228 <= 0, s145 >= 0, s145 <= z1 + 1, s146 >= 0, s146 <= s145 + 0, s147 >= 0, s147 <= 1, s148 >= 0, s148 <= z1 + 1, s149 >= 0, s149 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 20 + 4*z0 + 124*z2 + 4*z2^2 }-> 1 + s152 + s154 + s229 :|: s229 >= 0, s229 <= 0, s150 >= 0, s150 <= z1 + 1, s151 >= 0, s151 <= s150 + 0, s152 >= 0, s152 <= 1, s153 >= 0, s153 <= z2 + 1, s154 >= 0, s154 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 20 + 4*z0 + 124*z2 + 4*z2^2 }-> 1 + s157 + s5 + s230 :|: s230 >= 0, s230 <= 0, s155 >= 0, s155 <= z1 + 1, s156 >= 0, s156 <= s155 + 0, s157 >= 0, s157 <= 1, s5 >= 0, s5 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 20 + 4*s161 + 4*z0 + 124*z2 + 4*z2^2 }-> 1 + s160 + s163 + s231 :|: s231 >= 0, s231 <= 0, s158 >= 0, s158 <= z2 + 1, s159 >= 0, s159 <= 0 + s158, s160 >= 0, s160 <= 1, s161 >= 0, s161 <= z1 + 1, s162 >= 0, s162 <= z2 + 1, s163 >= 0, s163 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 20 + 4*s167 + 4*z0 + 124*z2 + 4*z2^2 }-> 1 + s166 + s168 + s232 :|: s232 >= 0, s232 <= 0, s164 >= 0, s164 <= z2 + 1, s165 >= 0, s165 <= 0 + s164, s166 >= 0, s166 <= 1, s167 >= 0, s167 <= z1 + 1, s168 >= 0, s168 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 20 + 4*z0 + 124*z2 + 4*z2^2 }-> 1 + s171 + s173 + s233 :|: s233 >= 0, s233 <= 0, s169 >= 0, s169 <= z2 + 1, s170 >= 0, s170 <= 0 + s169, s171 >= 0, s171 <= 1, s172 >= 0, s172 <= z2 + 1, s173 >= 0, s173 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 20 + 4*z0 + 124*z2 + 4*z2^2 }-> 1 + s176 + s6 + s234 :|: s234 >= 0, s234 <= 0, s174 >= 0, s174 <= z2 + 1, s175 >= 0, s175 <= 0 + s174, s176 >= 0, s176 <= 1, s6 >= 0, s6 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 20 + 4*s109 + 4*z0 + 124*z1 + 4*z1^2 }-> 1 + s22 + s111 + s219 :|: s219 >= 0, s219 <= 0, s109 >= 0, s109 <= z1 + 1, s110 >= 0, s110 <= z2 + 1, s111 >= 0, s111 <= 1, s21 >= 0, s21 <= 0 + 0, s22 >= 0, s22 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 20 + 4*s112 + 4*z0 + 124*z1 + 4*z1^2 }-> 1 + s24 + s113 + s220 :|: s220 >= 0, s220 <= 0, s112 >= 0, s112 <= z1 + 1, s113 >= 0, s113 <= 1, s23 >= 0, s23 <= 0 + 0, s24 >= 0, s24 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 20 + 4*z0 + 124*z1 + 4*z1^2 }-> 1 + s26 + s115 + s221 :|: s221 >= 0, s221 <= 0, s114 >= 0, s114 <= z2 + 1, s115 >= 0, s115 <= 1, s25 >= 0, s25 <= 0 + 0, s26 >= 0, s26 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 20 + 4*z0 + 124*z1 + 4*z1^2 }-> 1 + s28 + s3 + s222 :|: s222 >= 0, s222 <= 0, s27 >= 0, s27 <= 0 + 0, s28 >= 0, s28 <= 1, s3 >= 0, s3 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 20 + 4*s177 + 4*z0 + 124*z2 + 4*z2^2 }-> 1 + s30 + s179 + s235 :|: s235 >= 0, s235 <= 0, s177 >= 0, s177 <= z1 + 1, s178 >= 0, s178 <= z2 + 1, s179 >= 0, s179 <= 1, s29 >= 0, s29 <= 0 + 0, s30 >= 0, s30 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 20 + 4*s180 + 4*z0 + 124*z2 + 4*z2^2 }-> 1 + s32 + s181 + s236 :|: s236 >= 0, s236 <= 0, s180 >= 0, s180 <= z1 + 1, s181 >= 0, s181 <= 1, s31 >= 0, s31 <= 0 + 0, s32 >= 0, s32 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 20 + 4*z0 + 124*z2 + 4*z2^2 }-> 1 + s34 + s183 + s237 :|: s237 >= 0, s237 <= 0, s182 >= 0, s182 <= z2 + 1, s183 >= 0, s183 <= 1, s33 >= 0, s33 <= 0 + 0, s34 >= 0, s34 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 20 + 4*z0 + 124*z2 + 4*z2^2 }-> 1 + s36 + s7 + s238 :|: s238 >= 0, s238 <= 0, s35 >= 0, s35 <= 0 + 0, s36 >= 0, s36 <= 1, s7 >= 0, s7 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 20 + 4*s52 + 4*z0 + 124*z1 + 4*z1^2 }-> 1 + s51 + s54 + s207 :|: s207 >= 0, s207 <= 0, s48 >= 0, s48 <= z1 + 1, s49 >= 0, s49 <= z2 + 1, s50 >= 0, s50 <= s48 + s49, s51 >= 0, s51 <= 1, s52 >= 0, s52 <= z1 + 1, s53 >= 0, s53 <= z2 + 1, s54 >= 0, s54 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 20 + 4*s59 + 4*z0 + 124*z1 + 4*z1^2 }-> 1 + s58 + s60 + s208 :|: s208 >= 0, s208 <= 0, s55 >= 0, s55 <= z1 + 1, s56 >= 0, s56 <= z2 + 1, s57 >= 0, s57 <= s55 + s56, s58 >= 0, s58 <= 1, s59 >= 0, s59 <= z1 + 1, s60 >= 0, s60 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 20 + 4*z0 + 124*z1 + 4*z1^2 }-> 1 + s64 + s66 + s209 :|: s209 >= 0, s209 <= 0, s61 >= 0, s61 <= z1 + 1, s62 >= 0, s62 <= z2 + 1, s63 >= 0, s63 <= s61 + s62, s64 >= 0, s64 <= 1, s65 >= 0, s65 <= z2 + 1, s66 >= 0, s66 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 20 + 4*z0 + 124*z1 + 4*z1^2 }-> 1 + s70 + s'' + s210 :|: s210 >= 0, s210 <= 0, s67 >= 0, s67 <= z1 + 1, s68 >= 0, s68 <= z2 + 1, s69 >= 0, s69 <= s67 + s68, s70 >= 0, s70 <= 1, s'' >= 0, s'' <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 20 + 4*s74 + 4*z0 + 124*z1 + 4*z1^2 }-> 1 + s73 + s76 + s211 :|: s211 >= 0, s211 <= 0, s71 >= 0, s71 <= z1 + 1, s72 >= 0, s72 <= s71 + 0, s73 >= 0, s73 <= 1, s74 >= 0, s74 <= z1 + 1, s75 >= 0, s75 <= z2 + 1, s76 >= 0, s76 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 20 + 4*s80 + 4*z0 + 124*z1 + 4*z1^2 }-> 1 + s79 + s81 + s212 :|: s212 >= 0, s212 <= 0, s77 >= 0, s77 <= z1 + 1, s78 >= 0, s78 <= s77 + 0, s79 >= 0, s79 <= 1, s80 >= 0, s80 <= z1 + 1, s81 >= 0, s81 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 20 + 4*z0 + 124*z1 + 4*z1^2 }-> 1 + s84 + s86 + s213 :|: s213 >= 0, s213 <= 0, s82 >= 0, s82 <= z1 + 1, s83 >= 0, s83 <= s82 + 0, s84 >= 0, s84 <= 1, s85 >= 0, s85 <= z2 + 1, s86 >= 0, s86 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 20 + 4*z0 + 124*z1 + 4*z1^2 }-> 1 + s89 + s1 + s214 :|: s214 >= 0, s214 <= 0, s87 >= 0, s87 <= z1 + 1, s88 >= 0, s88 <= s87 + 0, s89 >= 0, s89 <= 1, s1 >= 0, s1 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 20 + 4*s93 + 4*z0 + 124*z1 + 4*z1^2 }-> 1 + s92 + s95 + s215 :|: s215 >= 0, s215 <= 0, s90 >= 0, s90 <= z2 + 1, s91 >= 0, s91 <= 0 + s90, s92 >= 0, s92 <= 1, s93 >= 0, s93 <= z1 + 1, s94 >= 0, s94 <= z2 + 1, s95 >= 0, s95 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 20 + 4*s99 + 4*z0 + 124*z1 + 4*z1^2 }-> 1 + s98 + s100 + s216 :|: s216 >= 0, s216 <= 0, s96 >= 0, s96 <= z2 + 1, s97 >= 0, s97 <= 0 + s96, s98 >= 0, s98 <= 1, s99 >= 0, s99 <= z1 + 1, s100 >= 0, s100 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTENSORT(z) -{ 0 }-> 0 :|: z >= 0
   FLATTENSORT(z) -{ 1 + 10*s184 + 4*s184^2 }-> 1 + s242 :|: s242 >= 0, s242 <= 0, s184 >= 0, s184 <= z + 1, z >= 0
   FLATTENSORT(z) -{ 1 }-> 1 + s243 :|: s243 >= 0, s243 <= 0, z >= 0
   INSERT(z, z') -{ 8 + 4*z' }-> 1 + s200 :|: s200 >= 0, s200 <= 0, z' >= 0, z >= 0
   INSERT#1(z, z') -{ 11 + 4*z1 }-> 1 + s201 + s46 :|: s201 >= 0, s201 <= 2, s46 >= 0, s46 <= z0 + z' + 1, z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z' >= 0
   INSERT#1(z, z') -{ 11 + 4*z1 }-> 1 + s205 + s47 :|: s205 >= 0, s205 <= 2, s47 >= 0, s47 <= z0 + z' + 1, s10 >= 0, s10 <= 3, s11 >= 0, s11 <= 2, z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z' >= 0
   INSERT#2(z, z', z'', z3) -{ 9 + 4*z3 }-> 1 + s202 :|: s202 >= 0, s202 <= 1, z = 2, z'' >= 0, z' >= 0, z3 >= 0
   INSERTIONSORT(z) -{ 21 + 24*z + 8*z^2 }-> 1 + s239 :|: s239 >= 0, s239 <= 2, z >= 0
   INSERTIONSORT#1(z) -{ 10 + 4*s196 + 10*z1 + 4*z1^2 }-> 1 + s203 + s240 :|: s240 >= 0, s240 <= 0, s203 >= 0, s203 <= 1, s196 >= 0, s196 <= z1, z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   INSERTIONSORT#1(z) -{ 10 + 10*z1 + 4*z1^2 }-> 1 + s204 + s241 :|: s241 >= 0, s241 <= 0, s204 >= 0, s204 <= 1, z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   append(z, z') -{ 0 }-> s37 :|: s37 >= 0, s37 <= z + z', z' >= 0, z >= 0
   append(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   append#1(z, z') -{ 0 }-> z' :|: z' >= 0, z = 0
   append#1(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   append#1(z, z') -{ 0 }-> 1 + z0 + s40 :|: s40 >= 0, s40 <= z1 + z', z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z' >= 0
   flatten(z) -{ 0 }-> s185 :|: s185 >= 0, s185 <= z + 1, z >= 0
   flatten(z) -{ 0 }-> 0 :|: z >= 0
   flatten#1(z) -{ 0 }-> s189 :|: s186 >= 0, s186 <= z1 + 1, s187 >= 0, s187 <= z2 + 1, s188 >= 0, s188 <= s186 + s187, s189 >= 0, s189 <= z0 + s188, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   flatten#1(z) -{ 0 }-> s192 :|: s190 >= 0, s190 <= z1 + 1, s191 >= 0, s191 <= s190 + 0, s192 >= 0, s192 <= z0 + s191, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   flatten#1(z) -{ 0 }-> s195 :|: s193 >= 0, s193 <= z2 + 1, s194 >= 0, s194 <= 0 + s193, s195 >= 0, s195 <= z0 + s194, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   flatten#1(z) -{ 0 }-> s39 :|: s38 >= 0, s38 <= 0 + 0, s39 >= 0, s39 <= z0 + s38, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   flatten#1(z) -{ 0 }-> 0 :|: z = 0
   flatten#1(z) -{ 0 }-> 0 :|: z >= 0
   insert(z, z') -{ 0 }-> s42 :|: s42 >= 0, s42 <= z' + z + 1, z' >= 0, z >= 0
   insert(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   insert#1(z, z') -{ 0 }-> s43 :|: s43 >= 0, s43 <= z' + z0 + z1 + 2, z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z' >= 0
   insert#1(z, z') -{ 0 }-> s45 :|: s45 >= 0, s45 <= z' + z0 + z1 + 2, s16 >= 0, s16 <= 3, s17 >= 0, s17 <= 2, z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z' >= 0
   insert#1(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   insert#1(z, z') -{ 0 }-> 1 + z' + 0 :|: z' >= 0, z = 0
   insert#2(z, z', z'', z3) -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0, z3 >= 0
   insert#2(z, z', z'', z3) -{ 0 }-> 1 + z' + (1 + z'' + z3) :|: z'' >= 0, z = 1, z' >= 0, z3 >= 0
   insert#2(z, z', z'', z3) -{ 0 }-> 1 + z'' + s44 :|: s44 >= 0, s44 <= z' + z3 + 1, z = 2, z'' >= 0, z' >= 0, z3 >= 0
   insertionsort(z) -{ 0 }-> s197 :|: s197 >= 0, s197 <= z, z >= 0
   insertionsort(z) -{ 0 }-> 0 :|: z >= 0
   insertionsort#1(z) -{ 0 }-> s199 :|: s198 >= 0, s198 <= z1, s199 >= 0, s199 <= z0 + s198 + 1, z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   insertionsort#1(z) -{ 0 }-> s41 :|: s41 >= 0, s41 <= z0 + 0 + 1, z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   insertionsort#1(z) -{ 0 }-> 0 :|: z = 0
   insertionsort#1(z) -{ 0 }-> 0 :|: z >= 0

Function symbols to be analyzed: {FLATTENSORT}
Previous analysis results are:
  APPEND#1: runtime: O(n^1) [4*z], size: O(1) [0]
  APPEND: runtime: O(n^1) [1 + 4*z], size: O(1) [1]
  #cklt: runtime: O(1) [0], size: O(1) [2]
  #compare: runtime: O(1) [0], size: O(1) [3]
  #COMPARE: runtime: O(1) [0], size: O(n^1) [z + z']
  append#1: runtime: O(1) [0], size: O(n^1) [z + z']
  append: runtime: O(1) [0], size: O(n^1) [z + z']
  #less: runtime: O(1) [0], size: O(1) [2]
  insert#2: runtime: O(1) [0], size: O(n^1) [2 + z' + z'' + z3]
  insert: runtime: O(1) [0], size: O(n^1) [1 + z + z']
  insert#1: runtime: O(1) [0], size: O(n^1) [1 + z + z']
  #LESS: runtime: O(1) [1], size: O(n^1) [1 + z + z']
  flatten#1: runtime: O(1) [0], size: O(n^1) [1 + z]
  insertionsort#1: runtime: O(1) [0], size: O(n^1) [z]
  INSERT#1: runtime: O(n^1) [7 + 4*z], size: O(1) [0]
  INSERT#2: runtime: O(n^1) [9 + 4*z3], size: O(1) [2]
  INSERT: runtime: O(n^1) [8 + 4*z'], size: O(1) [1]
  flatten: runtime: O(1) [0], size: O(n^1) [1 + z]
  FLATTEN: runtime: O(n^2) [17 + 124*z + 4*z^2], size: O(1) [0]
  FLATTEN#1: runtime: O(n^2) [704 + 4160*z + 128*z^2], size: O(1) [3]
  insertionsort: runtime: O(1) [0], size: O(n^1) [z]
  INSERTIONSORT: runtime: O(n^2) [1 + 10*z + 4*z^2], size: O(1) [0]
  INSERTIONSORT#1: runtime: O(n^2) [20 + 24*z + 8*z^2], size: O(1) [2]
  FLATTENSORT: runtime: ?, size: O(1) [1]

----------------------------------------

(129) IntTrsBoundProof (UPPER BOUND(ID))

Computed RUNTIME bound using KoAT for: FLATTENSORT
after applying outer abstraction to obtain an ITS,
resulting in: O(n^2) with polynomial bound: 16 + 18*z + 4*z^2

----------------------------------------

(130)
Obligation:
Complexity RNTS consisting of the following rules:

   #COMPARE(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   #COMPARE(z, z') -{ 0 }-> 1 + s19 :|: s19 >= 0, s19 <= z' - 1 + (z - 1), z' - 1 >= 0, z - 1 >= 0
   #COMPARE(z, z') -{ 0 }-> 1 + s20 :|: s20 >= 0, s20 <= z - 1 + (z' - 1), z' - 1 >= 0, z - 1 >= 0
   #LESS(z, z') -{ 1 }-> 1 + s18 :|: s18 >= 0, s18 <= z + z', z' >= 0, z >= 0
   #cklt(z) -{ 0 }-> 2 :|: z = 3
   #cklt(z) -{ 0 }-> 1 :|: z = 1
   #cklt(z) -{ 0 }-> 1 :|: z = 2
   #cklt(z) -{ 0 }-> 0 :|: z >= 0
   #compare(z, z') -{ 0 }-> s8 :|: s8 >= 0, s8 <= 3, z' - 1 >= 0, z - 1 >= 0
   #compare(z, z') -{ 0 }-> s9 :|: s9 >= 0, s9 <= 3, z' - 1 >= 0, z - 1 >= 0
   #compare(z, z') -{ 0 }-> 3 :|: z' - 1 >= 0, z = 0
   #compare(z, z') -{ 0 }-> 3 :|: z - 1 >= 0, z' = 0
   #compare(z, z') -{ 0 }-> 3 :|: z' - 1 >= 0, z - 1 >= 0
   #compare(z, z') -{ 0 }-> 2 :|: z' - 1 >= 0, z = 0
   #compare(z, z') -{ 0 }-> 2 :|: z - 1 >= 0, z' = 0
   #compare(z, z') -{ 0 }-> 2 :|: z' - 1 >= 0, z - 1 >= 0
   #compare(z, z') -{ 0 }-> 1 :|: z = 0, z' = 0
   #compare(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   #less(z, z') -{ 0 }-> s13 :|: s12 >= 0, s12 <= 3, s13 >= 0, s13 <= 2, z' - 1 >= 0, z - 1 >= 0
   #less(z, z') -{ 0 }-> s15 :|: s14 >= 0, s14 <= 3, s15 >= 0, s15 <= 2, z - 1 >= 0, z' - 1 >= 0
   #less(z, z') -{ 0 }-> 2 :|: z' - 1 >= 0, z = 0, 3 = 3
   #less(z, z') -{ 0 }-> 2 :|: z - 1 >= 0, z' = 0, 3 = 3
   #less(z, z') -{ 0 }-> 2 :|: z - 1 >= 0, z' - 1 >= 0, 3 = 3
   #less(z, z') -{ 0 }-> 1 :|: z = 0, z' = 0, 1 = 1
   #less(z, z') -{ 0 }-> 1 :|: z' - 1 >= 0, z = 0, 2 = 2
   #less(z, z') -{ 0 }-> 1 :|: z - 1 >= 0, z' = 0, 2 = 2
   #less(z, z') -{ 0 }-> 1 :|: z' - 1 >= 0, z - 1 >= 0, 2 = 2
   #less(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   #less(z, z') -{ 0 }-> 0 :|: z = 0, z' = 0, v0 >= 0, 1 = v0
   #less(z, z') -{ 0 }-> 0 :|: z' - 1 >= 0, z = 0, v0 >= 0, 2 = v0
   #less(z, z') -{ 0 }-> 0 :|: z' - 1 >= 0, z = 0, v0 >= 0, 3 = v0
   #less(z, z') -{ 0 }-> 0 :|: z - 1 >= 0, z' = 0, v0 >= 0, 3 = v0
   #less(z, z') -{ 0 }-> 0 :|: z - 1 >= 0, z' - 1 >= 0, v0 >= 0, 3 = v0
   #less(z, z') -{ 0 }-> 0 :|: z - 1 >= 0, z' = 0, v0 >= 0, 2 = v0
   #less(z, z') -{ 0 }-> 0 :|: z' - 1 >= 0, z - 1 >= 0, v0 >= 0, 2 = v0
   #less(z, z') -{ 0 }-> 0 :|: z' >= 0, z >= 0, v0 >= 0, 0 = v0
   APPEND(z, z') -{ 1 + 4*z }-> 1 + s :|: s >= 0, s <= 0, z' >= 0, z >= 0
   APPEND#1(z, z') -{ 2 + 4*z1 }-> 1 + s' :|: s' >= 0, s' <= 1, z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z' >= 0
   FLATTEN(z) -{ 705 + 4160*z + 128*z^2 }-> 1 + s206 :|: s206 >= 0, s206 <= 3, z >= 0
   FLATTEN#1(z) -{ 20 + 4*z0 + 124*z1 + 4*z1^2 }-> 1 + s103 + s105 + s217 :|: s217 >= 0, s217 <= 0, s101 >= 0, s101 <= z2 + 1, s102 >= 0, s102 <= 0 + s101, s103 >= 0, s103 <= 1, s104 >= 0, s104 <= z2 + 1, s105 >= 0, s105 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 20 + 4*z0 + 124*z1 + 4*z1^2 }-> 1 + s108 + s2 + s218 :|: s218 >= 0, s218 <= 0, s106 >= 0, s106 <= z2 + 1, s107 >= 0, s107 <= 0 + s106, s108 >= 0, s108 <= 1, s2 >= 0, s2 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 20 + 4*s120 + 4*z0 + 124*z2 + 4*z2^2 }-> 1 + s119 + s122 + s223 :|: s223 >= 0, s223 <= 0, s116 >= 0, s116 <= z1 + 1, s117 >= 0, s117 <= z2 + 1, s118 >= 0, s118 <= s116 + s117, s119 >= 0, s119 <= 1, s120 >= 0, s120 <= z1 + 1, s121 >= 0, s121 <= z2 + 1, s122 >= 0, s122 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 20 + 4*s127 + 4*z0 + 124*z2 + 4*z2^2 }-> 1 + s126 + s128 + s224 :|: s224 >= 0, s224 <= 0, s123 >= 0, s123 <= z1 + 1, s124 >= 0, s124 <= z2 + 1, s125 >= 0, s125 <= s123 + s124, s126 >= 0, s126 <= 1, s127 >= 0, s127 <= z1 + 1, s128 >= 0, s128 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 20 + 4*z0 + 124*z2 + 4*z2^2 }-> 1 + s132 + s134 + s225 :|: s225 >= 0, s225 <= 0, s129 >= 0, s129 <= z1 + 1, s130 >= 0, s130 <= z2 + 1, s131 >= 0, s131 <= s129 + s130, s132 >= 0, s132 <= 1, s133 >= 0, s133 <= z2 + 1, s134 >= 0, s134 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 20 + 4*z0 + 124*z2 + 4*z2^2 }-> 1 + s138 + s4 + s226 :|: s226 >= 0, s226 <= 0, s135 >= 0, s135 <= z1 + 1, s136 >= 0, s136 <= z2 + 1, s137 >= 0, s137 <= s135 + s136, s138 >= 0, s138 <= 1, s4 >= 0, s4 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 20 + 4*s142 + 4*z0 + 124*z2 + 4*z2^2 }-> 1 + s141 + s144 + s227 :|: s227 >= 0, s227 <= 0, s139 >= 0, s139 <= z1 + 1, s140 >= 0, s140 <= s139 + 0, s141 >= 0, s141 <= 1, s142 >= 0, s142 <= z1 + 1, s143 >= 0, s143 <= z2 + 1, s144 >= 0, s144 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 20 + 4*s148 + 4*z0 + 124*z2 + 4*z2^2 }-> 1 + s147 + s149 + s228 :|: s228 >= 0, s228 <= 0, s145 >= 0, s145 <= z1 + 1, s146 >= 0, s146 <= s145 + 0, s147 >= 0, s147 <= 1, s148 >= 0, s148 <= z1 + 1, s149 >= 0, s149 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 20 + 4*z0 + 124*z2 + 4*z2^2 }-> 1 + s152 + s154 + s229 :|: s229 >= 0, s229 <= 0, s150 >= 0, s150 <= z1 + 1, s151 >= 0, s151 <= s150 + 0, s152 >= 0, s152 <= 1, s153 >= 0, s153 <= z2 + 1, s154 >= 0, s154 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 20 + 4*z0 + 124*z2 + 4*z2^2 }-> 1 + s157 + s5 + s230 :|: s230 >= 0, s230 <= 0, s155 >= 0, s155 <= z1 + 1, s156 >= 0, s156 <= s155 + 0, s157 >= 0, s157 <= 1, s5 >= 0, s5 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 20 + 4*s161 + 4*z0 + 124*z2 + 4*z2^2 }-> 1 + s160 + s163 + s231 :|: s231 >= 0, s231 <= 0, s158 >= 0, s158 <= z2 + 1, s159 >= 0, s159 <= 0 + s158, s160 >= 0, s160 <= 1, s161 >= 0, s161 <= z1 + 1, s162 >= 0, s162 <= z2 + 1, s163 >= 0, s163 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 20 + 4*s167 + 4*z0 + 124*z2 + 4*z2^2 }-> 1 + s166 + s168 + s232 :|: s232 >= 0, s232 <= 0, s164 >= 0, s164 <= z2 + 1, s165 >= 0, s165 <= 0 + s164, s166 >= 0, s166 <= 1, s167 >= 0, s167 <= z1 + 1, s168 >= 0, s168 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 20 + 4*z0 + 124*z2 + 4*z2^2 }-> 1 + s171 + s173 + s233 :|: s233 >= 0, s233 <= 0, s169 >= 0, s169 <= z2 + 1, s170 >= 0, s170 <= 0 + s169, s171 >= 0, s171 <= 1, s172 >= 0, s172 <= z2 + 1, s173 >= 0, s173 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 20 + 4*z0 + 124*z2 + 4*z2^2 }-> 1 + s176 + s6 + s234 :|: s234 >= 0, s234 <= 0, s174 >= 0, s174 <= z2 + 1, s175 >= 0, s175 <= 0 + s174, s176 >= 0, s176 <= 1, s6 >= 0, s6 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 20 + 4*s109 + 4*z0 + 124*z1 + 4*z1^2 }-> 1 + s22 + s111 + s219 :|: s219 >= 0, s219 <= 0, s109 >= 0, s109 <= z1 + 1, s110 >= 0, s110 <= z2 + 1, s111 >= 0, s111 <= 1, s21 >= 0, s21 <= 0 + 0, s22 >= 0, s22 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 20 + 4*s112 + 4*z0 + 124*z1 + 4*z1^2 }-> 1 + s24 + s113 + s220 :|: s220 >= 0, s220 <= 0, s112 >= 0, s112 <= z1 + 1, s113 >= 0, s113 <= 1, s23 >= 0, s23 <= 0 + 0, s24 >= 0, s24 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 20 + 4*z0 + 124*z1 + 4*z1^2 }-> 1 + s26 + s115 + s221 :|: s221 >= 0, s221 <= 0, s114 >= 0, s114 <= z2 + 1, s115 >= 0, s115 <= 1, s25 >= 0, s25 <= 0 + 0, s26 >= 0, s26 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 20 + 4*z0 + 124*z1 + 4*z1^2 }-> 1 + s28 + s3 + s222 :|: s222 >= 0, s222 <= 0, s27 >= 0, s27 <= 0 + 0, s28 >= 0, s28 <= 1, s3 >= 0, s3 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 20 + 4*s177 + 4*z0 + 124*z2 + 4*z2^2 }-> 1 + s30 + s179 + s235 :|: s235 >= 0, s235 <= 0, s177 >= 0, s177 <= z1 + 1, s178 >= 0, s178 <= z2 + 1, s179 >= 0, s179 <= 1, s29 >= 0, s29 <= 0 + 0, s30 >= 0, s30 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 20 + 4*s180 + 4*z0 + 124*z2 + 4*z2^2 }-> 1 + s32 + s181 + s236 :|: s236 >= 0, s236 <= 0, s180 >= 0, s180 <= z1 + 1, s181 >= 0, s181 <= 1, s31 >= 0, s31 <= 0 + 0, s32 >= 0, s32 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 20 + 4*z0 + 124*z2 + 4*z2^2 }-> 1 + s34 + s183 + s237 :|: s237 >= 0, s237 <= 0, s182 >= 0, s182 <= z2 + 1, s183 >= 0, s183 <= 1, s33 >= 0, s33 <= 0 + 0, s34 >= 0, s34 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 20 + 4*z0 + 124*z2 + 4*z2^2 }-> 1 + s36 + s7 + s238 :|: s238 >= 0, s238 <= 0, s35 >= 0, s35 <= 0 + 0, s36 >= 0, s36 <= 1, s7 >= 0, s7 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 20 + 4*s52 + 4*z0 + 124*z1 + 4*z1^2 }-> 1 + s51 + s54 + s207 :|: s207 >= 0, s207 <= 0, s48 >= 0, s48 <= z1 + 1, s49 >= 0, s49 <= z2 + 1, s50 >= 0, s50 <= s48 + s49, s51 >= 0, s51 <= 1, s52 >= 0, s52 <= z1 + 1, s53 >= 0, s53 <= z2 + 1, s54 >= 0, s54 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 20 + 4*s59 + 4*z0 + 124*z1 + 4*z1^2 }-> 1 + s58 + s60 + s208 :|: s208 >= 0, s208 <= 0, s55 >= 0, s55 <= z1 + 1, s56 >= 0, s56 <= z2 + 1, s57 >= 0, s57 <= s55 + s56, s58 >= 0, s58 <= 1, s59 >= 0, s59 <= z1 + 1, s60 >= 0, s60 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 20 + 4*z0 + 124*z1 + 4*z1^2 }-> 1 + s64 + s66 + s209 :|: s209 >= 0, s209 <= 0, s61 >= 0, s61 <= z1 + 1, s62 >= 0, s62 <= z2 + 1, s63 >= 0, s63 <= s61 + s62, s64 >= 0, s64 <= 1, s65 >= 0, s65 <= z2 + 1, s66 >= 0, s66 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 20 + 4*z0 + 124*z1 + 4*z1^2 }-> 1 + s70 + s'' + s210 :|: s210 >= 0, s210 <= 0, s67 >= 0, s67 <= z1 + 1, s68 >= 0, s68 <= z2 + 1, s69 >= 0, s69 <= s67 + s68, s70 >= 0, s70 <= 1, s'' >= 0, s'' <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 20 + 4*s74 + 4*z0 + 124*z1 + 4*z1^2 }-> 1 + s73 + s76 + s211 :|: s211 >= 0, s211 <= 0, s71 >= 0, s71 <= z1 + 1, s72 >= 0, s72 <= s71 + 0, s73 >= 0, s73 <= 1, s74 >= 0, s74 <= z1 + 1, s75 >= 0, s75 <= z2 + 1, s76 >= 0, s76 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 20 + 4*s80 + 4*z0 + 124*z1 + 4*z1^2 }-> 1 + s79 + s81 + s212 :|: s212 >= 0, s212 <= 0, s77 >= 0, s77 <= z1 + 1, s78 >= 0, s78 <= s77 + 0, s79 >= 0, s79 <= 1, s80 >= 0, s80 <= z1 + 1, s81 >= 0, s81 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 20 + 4*z0 + 124*z1 + 4*z1^2 }-> 1 + s84 + s86 + s213 :|: s213 >= 0, s213 <= 0, s82 >= 0, s82 <= z1 + 1, s83 >= 0, s83 <= s82 + 0, s84 >= 0, s84 <= 1, s85 >= 0, s85 <= z2 + 1, s86 >= 0, s86 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 20 + 4*z0 + 124*z1 + 4*z1^2 }-> 1 + s89 + s1 + s214 :|: s214 >= 0, s214 <= 0, s87 >= 0, s87 <= z1 + 1, s88 >= 0, s88 <= s87 + 0, s89 >= 0, s89 <= 1, s1 >= 0, s1 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 20 + 4*s93 + 4*z0 + 124*z1 + 4*z1^2 }-> 1 + s92 + s95 + s215 :|: s215 >= 0, s215 <= 0, s90 >= 0, s90 <= z2 + 1, s91 >= 0, s91 <= 0 + s90, s92 >= 0, s92 <= 1, s93 >= 0, s93 <= z1 + 1, s94 >= 0, s94 <= z2 + 1, s95 >= 0, s95 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTEN#1(z) -{ 20 + 4*s99 + 4*z0 + 124*z1 + 4*z1^2 }-> 1 + s98 + s100 + s216 :|: s216 >= 0, s216 <= 0, s96 >= 0, s96 <= z2 + 1, s97 >= 0, s97 <= 0 + s96, s98 >= 0, s98 <= 1, s99 >= 0, s99 <= z1 + 1, s100 >= 0, s100 <= 1, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   FLATTENSORT(z) -{ 0 }-> 0 :|: z >= 0
   FLATTENSORT(z) -{ 1 + 10*s184 + 4*s184^2 }-> 1 + s242 :|: s242 >= 0, s242 <= 0, s184 >= 0, s184 <= z + 1, z >= 0
   FLATTENSORT(z) -{ 1 }-> 1 + s243 :|: s243 >= 0, s243 <= 0, z >= 0
   INSERT(z, z') -{ 8 + 4*z' }-> 1 + s200 :|: s200 >= 0, s200 <= 0, z' >= 0, z >= 0
   INSERT#1(z, z') -{ 11 + 4*z1 }-> 1 + s201 + s46 :|: s201 >= 0, s201 <= 2, s46 >= 0, s46 <= z0 + z' + 1, z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z' >= 0
   INSERT#1(z, z') -{ 11 + 4*z1 }-> 1 + s205 + s47 :|: s205 >= 0, s205 <= 2, s47 >= 0, s47 <= z0 + z' + 1, s10 >= 0, s10 <= 3, s11 >= 0, s11 <= 2, z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z' >= 0
   INSERT#2(z, z', z'', z3) -{ 9 + 4*z3 }-> 1 + s202 :|: s202 >= 0, s202 <= 1, z = 2, z'' >= 0, z' >= 0, z3 >= 0
   INSERTIONSORT(z) -{ 21 + 24*z + 8*z^2 }-> 1 + s239 :|: s239 >= 0, s239 <= 2, z >= 0
   INSERTIONSORT#1(z) -{ 10 + 4*s196 + 10*z1 + 4*z1^2 }-> 1 + s203 + s240 :|: s240 >= 0, s240 <= 0, s203 >= 0, s203 <= 1, s196 >= 0, s196 <= z1, z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   INSERTIONSORT#1(z) -{ 10 + 10*z1 + 4*z1^2 }-> 1 + s204 + s241 :|: s241 >= 0, s241 <= 0, s204 >= 0, s204 <= 1, z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   append(z, z') -{ 0 }-> s37 :|: s37 >= 0, s37 <= z + z', z' >= 0, z >= 0
   append(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   append#1(z, z') -{ 0 }-> z' :|: z' >= 0, z = 0
   append#1(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   append#1(z, z') -{ 0 }-> 1 + z0 + s40 :|: s40 >= 0, s40 <= z1 + z', z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z' >= 0
   flatten(z) -{ 0 }-> s185 :|: s185 >= 0, s185 <= z + 1, z >= 0
   flatten(z) -{ 0 }-> 0 :|: z >= 0
   flatten#1(z) -{ 0 }-> s189 :|: s186 >= 0, s186 <= z1 + 1, s187 >= 0, s187 <= z2 + 1, s188 >= 0, s188 <= s186 + s187, s189 >= 0, s189 <= z0 + s188, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   flatten#1(z) -{ 0 }-> s192 :|: s190 >= 0, s190 <= z1 + 1, s191 >= 0, s191 <= s190 + 0, s192 >= 0, s192 <= z0 + s191, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   flatten#1(z) -{ 0 }-> s195 :|: s193 >= 0, s193 <= z2 + 1, s194 >= 0, s194 <= 0 + s193, s195 >= 0, s195 <= z0 + s194, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   flatten#1(z) -{ 0 }-> s39 :|: s38 >= 0, s38 <= 0 + 0, s39 >= 0, s39 <= z0 + s38, z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   flatten#1(z) -{ 0 }-> 0 :|: z = 0
   flatten#1(z) -{ 0 }-> 0 :|: z >= 0
   insert(z, z') -{ 0 }-> s42 :|: s42 >= 0, s42 <= z' + z + 1, z' >= 0, z >= 0
   insert(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   insert#1(z, z') -{ 0 }-> s43 :|: s43 >= 0, s43 <= z' + z0 + z1 + 2, z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z' >= 0
   insert#1(z, z') -{ 0 }-> s45 :|: s45 >= 0, s45 <= z' + z0 + z1 + 2, s16 >= 0, s16 <= 3, s17 >= 0, s17 <= 2, z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z' >= 0
   insert#1(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   insert#1(z, z') -{ 0 }-> 1 + z' + 0 :|: z' >= 0, z = 0
   insert#2(z, z', z'', z3) -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0, z3 >= 0
   insert#2(z, z', z'', z3) -{ 0 }-> 1 + z' + (1 + z'' + z3) :|: z'' >= 0, z = 1, z' >= 0, z3 >= 0
   insert#2(z, z', z'', z3) -{ 0 }-> 1 + z'' + s44 :|: s44 >= 0, s44 <= z' + z3 + 1, z = 2, z'' >= 0, z' >= 0, z3 >= 0
   insertionsort(z) -{ 0 }-> s197 :|: s197 >= 0, s197 <= z, z >= 0
   insertionsort(z) -{ 0 }-> 0 :|: z >= 0
   insertionsort#1(z) -{ 0 }-> s199 :|: s198 >= 0, s198 <= z1, s199 >= 0, s199 <= z0 + s198 + 1, z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   insertionsort#1(z) -{ 0 }-> s41 :|: s41 >= 0, s41 <= z0 + 0 + 1, z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   insertionsort#1(z) -{ 0 }-> 0 :|: z = 0
   insertionsort#1(z) -{ 0 }-> 0 :|: z >= 0

Function symbols to be analyzed: 
Previous analysis results are:
  APPEND#1: runtime: O(n^1) [4*z], size: O(1) [0]
  APPEND: runtime: O(n^1) [1 + 4*z], size: O(1) [1]
  #cklt: runtime: O(1) [0], size: O(1) [2]
  #compare: runtime: O(1) [0], size: O(1) [3]
  #COMPARE: runtime: O(1) [0], size: O(n^1) [z + z']
  append#1: runtime: O(1) [0], size: O(n^1) [z + z']
  append: runtime: O(1) [0], size: O(n^1) [z + z']
  #less: runtime: O(1) [0], size: O(1) [2]
  insert#2: runtime: O(1) [0], size: O(n^1) [2 + z' + z'' + z3]
  insert: runtime: O(1) [0], size: O(n^1) [1 + z + z']
  insert#1: runtime: O(1) [0], size: O(n^1) [1 + z + z']
  #LESS: runtime: O(1) [1], size: O(n^1) [1 + z + z']
  flatten#1: runtime: O(1) [0], size: O(n^1) [1 + z]
  insertionsort#1: runtime: O(1) [0], size: O(n^1) [z]
  INSERT#1: runtime: O(n^1) [7 + 4*z], size: O(1) [0]
  INSERT#2: runtime: O(n^1) [9 + 4*z3], size: O(1) [2]
  INSERT: runtime: O(n^1) [8 + 4*z'], size: O(1) [1]
  flatten: runtime: O(1) [0], size: O(n^1) [1 + z]
  FLATTEN: runtime: O(n^2) [17 + 124*z + 4*z^2], size: O(1) [0]
  FLATTEN#1: runtime: O(n^2) [704 + 4160*z + 128*z^2], size: O(1) [3]
  insertionsort: runtime: O(1) [0], size: O(n^1) [z]
  INSERTIONSORT: runtime: O(n^2) [1 + 10*z + 4*z^2], size: O(1) [0]
  INSERTIONSORT#1: runtime: O(n^2) [20 + 24*z + 8*z^2], size: O(1) [2]
  FLATTENSORT: runtime: O(n^2) [16 + 18*z + 4*z^2], size: O(1) [1]

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(131) FinalProof (FINISHED)
Computed overall runtime complexity
----------------------------------------

(132)
BOUNDS(1, n^2)

----------------------------------------

(133) CpxTrsToCdtProof (BOTH BOUNDS(ID, ID))
Converted Cpx (relative) TRS with rewrite strategy PARALLEL_INNERMOST to CDT
----------------------------------------

(134)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   #cklt(#EQ) -> #false
   #cklt(#GT) -> #false
   #cklt(#LT) -> #true
   #compare(#0, #0) -> #EQ
   #compare(#0, #neg(z0)) -> #GT
   #compare(#0, #pos(z0)) -> #LT
   #compare(#0, #s(z0)) -> #LT
   #compare(#neg(z0), #0) -> #LT
   #compare(#neg(z0), #neg(z1)) -> #compare(z1, z0)
   #compare(#neg(z0), #pos(z1)) -> #LT
   #compare(#pos(z0), #0) -> #GT
   #compare(#pos(z0), #neg(z1)) -> #GT
   #compare(#pos(z0), #pos(z1)) -> #compare(z0, z1)
   #compare(#s(z0), #0) -> #GT
   #compare(#s(z0), #s(z1)) -> #compare(z0, z1)
   #less(z0, z1) -> #cklt(#compare(z0, z1))
   append(z0, z1) -> append#1(z0, z1)
   append#1(::(z0, z1), z2) -> ::(z0, append(z1, z2))
   append#1(nil, z0) -> z0
   flatten(z0) -> flatten#1(z0)
   flatten#1(leaf) -> nil
   flatten#1(node(z0, z1, z2)) -> append(z0, append(flatten(z1), flatten(z2)))
   flattensort(z0) -> insertionsort(flatten(z0))
   insert(z0, z1) -> insert#1(z1, z0)
   insert#1(::(z0, z1), z2) -> insert#2(#less(z0, z2), z2, z0, z1)
   insert#1(nil, z0) -> ::(z0, nil)
   insert#2(#false, z0, z1, z2) -> ::(z0, ::(z1, z2))
   insert#2(#true, z0, z1, z2) -> ::(z1, insert(z0, z2))
   insertionsort(z0) -> insertionsort#1(z0)
   insertionsort#1(::(z0, z1)) -> insert(z0, insertionsort(z1))
   insertionsort#1(nil) -> nil
Tuples:
   #CKLT(#EQ) -> c
   #CKLT(#GT) -> c1
   #CKLT(#LT) -> c2
   #COMPARE(#0, #0) -> c3
   #COMPARE(#0, #neg(z0)) -> c4
   #COMPARE(#0, #pos(z0)) -> c5
   #COMPARE(#0, #s(z0)) -> c6
   #COMPARE(#neg(z0), #0) -> c7
   #COMPARE(#neg(z0), #neg(z1)) -> c8(#COMPARE(z1, z0))
   #COMPARE(#neg(z0), #pos(z1)) -> c9
   #COMPARE(#pos(z0), #0) -> c10
   #COMPARE(#pos(z0), #neg(z1)) -> c11
   #COMPARE(#pos(z0), #pos(z1)) -> c12(#COMPARE(z0, z1))
   #COMPARE(#s(z0), #0) -> c13
   #COMPARE(#s(z0), #s(z1)) -> c14(#COMPARE(z0, z1))
   #LESS(z0, z1) -> c15(#CKLT(#compare(z0, z1)), #COMPARE(z0, z1))
   APPEND(z0, z1) -> c16(APPEND#1(z0, z1))
   APPEND#1(::(z0, z1), z2) -> c17(APPEND(z1, z2))
   APPEND#1(nil, z0) -> c18
   FLATTEN(z0) -> c19(FLATTEN#1(z0))
   FLATTEN#1(leaf) -> c20
   FLATTEN#1(node(z0, z1, z2)) -> c21(APPEND(z0, append(flatten(z1), flatten(z2))), APPEND(flatten(z1), flatten(z2)), FLATTEN(z1))
   FLATTEN#1(node(z0, z1, z2)) -> c22(APPEND(z0, append(flatten(z1), flatten(z2))), APPEND(flatten(z1), flatten(z2)), FLATTEN(z2))
   FLATTENSORT(z0) -> c23(INSERTIONSORT(flatten(z0)), FLATTEN(z0))
   INSERT(z0, z1) -> c24(INSERT#1(z1, z0))
   INSERT#1(::(z0, z1), z2) -> c25(INSERT#2(#less(z0, z2), z2, z0, z1), #LESS(z0, z2))
   INSERT#1(nil, z0) -> c26
   INSERT#2(#false, z0, z1, z2) -> c27
   INSERT#2(#true, z0, z1, z2) -> c28(INSERT(z0, z2))
   INSERTIONSORT(z0) -> c29(INSERTIONSORT#1(z0))
   INSERTIONSORT#1(::(z0, z1)) -> c30(INSERT(z0, insertionsort(z1)), INSERTIONSORT(z1))
   INSERTIONSORT#1(nil) -> c31
S tuples:
   #LESS(z0, z1) -> c15(#CKLT(#compare(z0, z1)), #COMPARE(z0, z1))
   APPEND(z0, z1) -> c16(APPEND#1(z0, z1))
   APPEND#1(::(z0, z1), z2) -> c17(APPEND(z1, z2))
   APPEND#1(nil, z0) -> c18
   FLATTEN(z0) -> c19(FLATTEN#1(z0))
   FLATTEN#1(leaf) -> c20
   FLATTEN#1(node(z0, z1, z2)) -> c21(APPEND(z0, append(flatten(z1), flatten(z2))), APPEND(flatten(z1), flatten(z2)), FLATTEN(z1))
   FLATTEN#1(node(z0, z1, z2)) -> c22(APPEND(z0, append(flatten(z1), flatten(z2))), APPEND(flatten(z1), flatten(z2)), FLATTEN(z2))
   FLATTENSORT(z0) -> c23(INSERTIONSORT(flatten(z0)), FLATTEN(z0))
   INSERT(z0, z1) -> c24(INSERT#1(z1, z0))
   INSERT#1(::(z0, z1), z2) -> c25(INSERT#2(#less(z0, z2), z2, z0, z1), #LESS(z0, z2))
   INSERT#1(nil, z0) -> c26
   INSERT#2(#false, z0, z1, z2) -> c27
   INSERT#2(#true, z0, z1, z2) -> c28(INSERT(z0, z2))
   INSERTIONSORT(z0) -> c29(INSERTIONSORT#1(z0))
   INSERTIONSORT#1(::(z0, z1)) -> c30(INSERT(z0, insertionsort(z1)), INSERTIONSORT(z1))
   INSERTIONSORT#1(nil) -> c31
K tuples:none
Defined Rule Symbols:   #less_2, append_2, append#1_2, flatten_1, flatten#1_1, flattensort_1, insert_2, insert#1_2, insert#2_4, insertionsort_1, insertionsort#1_1, #cklt_1, #compare_2

Defined Pair Symbols:   #CKLT_1, #COMPARE_2, #LESS_2, APPEND_2, APPEND#1_2, FLATTEN_1, FLATTEN#1_1, FLATTENSORT_1, INSERT_2, INSERT#1_2, INSERT#2_4, INSERTIONSORT_1, INSERTIONSORT#1_1

Compound Symbols:   c, c1, c2, c3, c4, c5, c6, c7, c8_1, c9, c10, c11, c12_1, c13, c14_1, c15_2, c16_1, c17_1, c18, c19_1, c20, c21_3, c22_3, c23_2, c24_1, c25_2, c26, c27, c28_1, c29_1, c30_2, c31


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(135) CdtToCpxRelTrsProof (BOTH BOUNDS(ID, ID))
Converted S to standard rules, and D \ S as well as R to relative rules.
----------------------------------------

(136)
Obligation:
The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(n^1, INF).


The TRS R consists of the following rules:

   #LESS(z0, z1) -> c15(#CKLT(#compare(z0, z1)), #COMPARE(z0, z1))
   APPEND(z0, z1) -> c16(APPEND#1(z0, z1))
   APPEND#1(::(z0, z1), z2) -> c17(APPEND(z1, z2))
   APPEND#1(nil, z0) -> c18
   FLATTEN(z0) -> c19(FLATTEN#1(z0))
   FLATTEN#1(leaf) -> c20
   FLATTEN#1(node(z0, z1, z2)) -> c21(APPEND(z0, append(flatten(z1), flatten(z2))), APPEND(flatten(z1), flatten(z2)), FLATTEN(z1))
   FLATTEN#1(node(z0, z1, z2)) -> c22(APPEND(z0, append(flatten(z1), flatten(z2))), APPEND(flatten(z1), flatten(z2)), FLATTEN(z2))
   FLATTENSORT(z0) -> c23(INSERTIONSORT(flatten(z0)), FLATTEN(z0))
   INSERT(z0, z1) -> c24(INSERT#1(z1, z0))
   INSERT#1(::(z0, z1), z2) -> c25(INSERT#2(#less(z0, z2), z2, z0, z1), #LESS(z0, z2))
   INSERT#1(nil, z0) -> c26
   INSERT#2(#false, z0, z1, z2) -> c27
   INSERT#2(#true, z0, z1, z2) -> c28(INSERT(z0, z2))
   INSERTIONSORT(z0) -> c29(INSERTIONSORT#1(z0))
   INSERTIONSORT#1(::(z0, z1)) -> c30(INSERT(z0, insertionsort(z1)), INSERTIONSORT(z1))
   INSERTIONSORT#1(nil) -> c31

The (relative) TRS S consists of the following rules:

   #CKLT(#EQ) -> c
   #CKLT(#GT) -> c1
   #CKLT(#LT) -> c2
   #COMPARE(#0, #0) -> c3
   #COMPARE(#0, #neg(z0)) -> c4
   #COMPARE(#0, #pos(z0)) -> c5
   #COMPARE(#0, #s(z0)) -> c6
   #COMPARE(#neg(z0), #0) -> c7
   #COMPARE(#neg(z0), #neg(z1)) -> c8(#COMPARE(z1, z0))
   #COMPARE(#neg(z0), #pos(z1)) -> c9
   #COMPARE(#pos(z0), #0) -> c10
   #COMPARE(#pos(z0), #neg(z1)) -> c11
   #COMPARE(#pos(z0), #pos(z1)) -> c12(#COMPARE(z0, z1))
   #COMPARE(#s(z0), #0) -> c13
   #COMPARE(#s(z0), #s(z1)) -> c14(#COMPARE(z0, z1))
   #cklt(#EQ) -> #false
   #cklt(#GT) -> #false
   #cklt(#LT) -> #true
   #compare(#0, #0) -> #EQ
   #compare(#0, #neg(z0)) -> #GT
   #compare(#0, #pos(z0)) -> #LT
   #compare(#0, #s(z0)) -> #LT
   #compare(#neg(z0), #0) -> #LT
   #compare(#neg(z0), #neg(z1)) -> #compare(z1, z0)
   #compare(#neg(z0), #pos(z1)) -> #LT
   #compare(#pos(z0), #0) -> #GT
   #compare(#pos(z0), #neg(z1)) -> #GT
   #compare(#pos(z0), #pos(z1)) -> #compare(z0, z1)
   #compare(#s(z0), #0) -> #GT
   #compare(#s(z0), #s(z1)) -> #compare(z0, z1)
   #less(z0, z1) -> #cklt(#compare(z0, z1))
   append(z0, z1) -> append#1(z0, z1)
   append#1(::(z0, z1), z2) -> ::(z0, append(z1, z2))
   append#1(nil, z0) -> z0
   flatten(z0) -> flatten#1(z0)
   flatten#1(leaf) -> nil
   flatten#1(node(z0, z1, z2)) -> append(z0, append(flatten(z1), flatten(z2)))
   flattensort(z0) -> insertionsort(flatten(z0))
   insert(z0, z1) -> insert#1(z1, z0)
   insert#1(::(z0, z1), z2) -> insert#2(#less(z0, z2), z2, z0, z1)
   insert#1(nil, z0) -> ::(z0, nil)
   insert#2(#false, z0, z1, z2) -> ::(z0, ::(z1, z2))
   insert#2(#true, z0, z1, z2) -> ::(z1, insert(z0, z2))
   insertionsort(z0) -> insertionsort#1(z0)
   insertionsort#1(::(z0, z1)) -> insert(z0, insertionsort(z1))
   insertionsort#1(nil) -> nil

Rewrite Strategy: INNERMOST
----------------------------------------

(137) RenamingProof (BOTH BOUNDS(ID, ID))
Renamed function symbols to avoid clashes with predefined symbol.
----------------------------------------

(138)
Obligation:
The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(n^1, INF).


The TRS R consists of the following rules:

   #LESS(z0, z1) -> c15(#CKLT(#compare(z0, z1)), #COMPARE(z0, z1))
   APPEND(z0, z1) -> c16(APPEND#1(z0, z1))
   APPEND#1(::(z0, z1), z2) -> c17(APPEND(z1, z2))
   APPEND#1(nil, z0) -> c18
   FLATTEN(z0) -> c19(FLATTEN#1(z0))
   FLATTEN#1(leaf) -> c20
   FLATTEN#1(node(z0, z1, z2)) -> c21(APPEND(z0, append(flatten(z1), flatten(z2))), APPEND(flatten(z1), flatten(z2)), FLATTEN(z1))
   FLATTEN#1(node(z0, z1, z2)) -> c22(APPEND(z0, append(flatten(z1), flatten(z2))), APPEND(flatten(z1), flatten(z2)), FLATTEN(z2))
   FLATTENSORT(z0) -> c23(INSERTIONSORT(flatten(z0)), FLATTEN(z0))
   INSERT(z0, z1) -> c24(INSERT#1(z1, z0))
   INSERT#1(::(z0, z1), z2) -> c25(INSERT#2(#less(z0, z2), z2, z0, z1), #LESS(z0, z2))
   INSERT#1(nil, z0) -> c26
   INSERT#2(#false, z0, z1, z2) -> c27
   INSERT#2(#true, z0, z1, z2) -> c28(INSERT(z0, z2))
   INSERTIONSORT(z0) -> c29(INSERTIONSORT#1(z0))
   INSERTIONSORT#1(::(z0, z1)) -> c30(INSERT(z0, insertionsort(z1)), INSERTIONSORT(z1))
   INSERTIONSORT#1(nil) -> c31

The (relative) TRS S consists of the following rules:

   #CKLT(#EQ) -> c
   #CKLT(#GT) -> c1
   #CKLT(#LT) -> c2
   #COMPARE(#0, #0) -> c3
   #COMPARE(#0, #neg(z0)) -> c4
   #COMPARE(#0, #pos(z0)) -> c5
   #COMPARE(#0, #s(z0)) -> c6
   #COMPARE(#neg(z0), #0) -> c7
   #COMPARE(#neg(z0), #neg(z1)) -> c8(#COMPARE(z1, z0))
   #COMPARE(#neg(z0), #pos(z1)) -> c9
   #COMPARE(#pos(z0), #0) -> c10
   #COMPARE(#pos(z0), #neg(z1)) -> c11
   #COMPARE(#pos(z0), #pos(z1)) -> c12(#COMPARE(z0, z1))
   #COMPARE(#s(z0), #0) -> c13
   #COMPARE(#s(z0), #s(z1)) -> c14(#COMPARE(z0, z1))
   #cklt(#EQ) -> #false
   #cklt(#GT) -> #false
   #cklt(#LT) -> #true
   #compare(#0, #0) -> #EQ
   #compare(#0, #neg(z0)) -> #GT
   #compare(#0, #pos(z0)) -> #LT
   #compare(#0, #s(z0)) -> #LT
   #compare(#neg(z0), #0) -> #LT
   #compare(#neg(z0), #neg(z1)) -> #compare(z1, z0)
   #compare(#neg(z0), #pos(z1)) -> #LT
   #compare(#pos(z0), #0) -> #GT
   #compare(#pos(z0), #neg(z1)) -> #GT
   #compare(#pos(z0), #pos(z1)) -> #compare(z0, z1)
   #compare(#s(z0), #0) -> #GT
   #compare(#s(z0), #s(z1)) -> #compare(z0, z1)
   #less(z0, z1) -> #cklt(#compare(z0, z1))
   append(z0, z1) -> append#1(z0, z1)
   append#1(::(z0, z1), z2) -> ::(z0, append(z1, z2))
   append#1(nil, z0) -> z0
   flatten(z0) -> flatten#1(z0)
   flatten#1(leaf) -> nil
   flatten#1(node(z0, z1, z2)) -> append(z0, append(flatten(z1), flatten(z2)))
   flattensort(z0) -> insertionsort(flatten(z0))
   insert(z0, z1) -> insert#1(z1, z0)
   insert#1(::(z0, z1), z2) -> insert#2(#less(z0, z2), z2, z0, z1)
   insert#1(nil, z0) -> ::(z0, nil)
   insert#2(#false, z0, z1, z2) -> ::(z0, ::(z1, z2))
   insert#2(#true, z0, z1, z2) -> ::(z1, insert(z0, z2))
   insertionsort(z0) -> insertionsort#1(z0)
   insertionsort#1(::(z0, z1)) -> insert(z0, insertionsort(z1))
   insertionsort#1(nil) -> nil

Rewrite Strategy: INNERMOST
----------------------------------------

(139) TypeInferenceProof (BOTH BOUNDS(ID, ID))
Inferred types.
----------------------------------------

(140)
Obligation:
Innermost TRS:
Rules:
#LESS(z0, z1) -> c15(#CKLT(#compare(z0, z1)), #COMPARE(z0, z1))
APPEND(z0, z1) -> c16(APPEND#1(z0, z1))
APPEND#1(::(z0, z1), z2) -> c17(APPEND(z1, z2))
APPEND#1(nil, z0) -> c18
FLATTEN(z0) -> c19(FLATTEN#1(z0))
FLATTEN#1(leaf) -> c20
FLATTEN#1(node(z0, z1, z2)) -> c21(APPEND(z0, append(flatten(z1), flatten(z2))), APPEND(flatten(z1), flatten(z2)), FLATTEN(z1))
FLATTEN#1(node(z0, z1, z2)) -> c22(APPEND(z0, append(flatten(z1), flatten(z2))), APPEND(flatten(z1), flatten(z2)), FLATTEN(z2))
FLATTENSORT(z0) -> c23(INSERTIONSORT(flatten(z0)), FLATTEN(z0))
INSERT(z0, z1) -> c24(INSERT#1(z1, z0))
INSERT#1(::(z0, z1), z2) -> c25(INSERT#2(#less(z0, z2), z2, z0, z1), #LESS(z0, z2))
INSERT#1(nil, z0) -> c26
INSERT#2(#false, z0, z1, z2) -> c27
INSERT#2(#true, z0, z1, z2) -> c28(INSERT(z0, z2))
INSERTIONSORT(z0) -> c29(INSERTIONSORT#1(z0))
INSERTIONSORT#1(::(z0, z1)) -> c30(INSERT(z0, insertionsort(z1)), INSERTIONSORT(z1))
INSERTIONSORT#1(nil) -> c31
#CKLT(#EQ) -> c
#CKLT(#GT) -> c1
#CKLT(#LT) -> c2
#COMPARE(#0, #0) -> c3
#COMPARE(#0, #neg(z0)) -> c4
#COMPARE(#0, #pos(z0)) -> c5
#COMPARE(#0, #s(z0)) -> c6
#COMPARE(#neg(z0), #0) -> c7
#COMPARE(#neg(z0), #neg(z1)) -> c8(#COMPARE(z1, z0))
#COMPARE(#neg(z0), #pos(z1)) -> c9
#COMPARE(#pos(z0), #0) -> c10
#COMPARE(#pos(z0), #neg(z1)) -> c11
#COMPARE(#pos(z0), #pos(z1)) -> c12(#COMPARE(z0, z1))
#COMPARE(#s(z0), #0) -> c13
#COMPARE(#s(z0), #s(z1)) -> c14(#COMPARE(z0, z1))
#cklt(#EQ) -> #false
#cklt(#GT) -> #false
#cklt(#LT) -> #true
#compare(#0, #0) -> #EQ
#compare(#0, #neg(z0)) -> #GT
#compare(#0, #pos(z0)) -> #LT
#compare(#0, #s(z0)) -> #LT
#compare(#neg(z0), #0) -> #LT
#compare(#neg(z0), #neg(z1)) -> #compare(z1, z0)
#compare(#neg(z0), #pos(z1)) -> #LT
#compare(#pos(z0), #0) -> #GT
#compare(#pos(z0), #neg(z1)) -> #GT
#compare(#pos(z0), #pos(z1)) -> #compare(z0, z1)
#compare(#s(z0), #0) -> #GT
#compare(#s(z0), #s(z1)) -> #compare(z0, z1)
#less(z0, z1) -> #cklt(#compare(z0, z1))
append(z0, z1) -> append#1(z0, z1)
append#1(::(z0, z1), z2) -> ::(z0, append(z1, z2))
append#1(nil, z0) -> z0
flatten(z0) -> flatten#1(z0)
flatten#1(leaf) -> nil
flatten#1(node(z0, z1, z2)) -> append(z0, append(flatten(z1), flatten(z2)))
flattensort(z0) -> insertionsort(flatten(z0))
insert(z0, z1) -> insert#1(z1, z0)
insert#1(::(z0, z1), z2) -> insert#2(#less(z0, z2), z2, z0, z1)
insert#1(nil, z0) -> ::(z0, nil)
insert#2(#false, z0, z1, z2) -> ::(z0, ::(z1, z2))
insert#2(#true, z0, z1, z2) -> ::(z1, insert(z0, z2))
insertionsort(z0) -> insertionsort#1(z0)
insertionsort#1(::(z0, z1)) -> insert(z0, insertionsort(z1))
insertionsort#1(nil) -> nil

Types:
#LESS :: #0:#neg:#pos:#s -> #0:#neg:#pos:#s -> c15
c15 :: c:c1:c2 -> c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c14 -> c15
#CKLT :: #EQ:#GT:#LT -> c:c1:c2
#compare :: #0:#neg:#pos:#s -> #0:#neg:#pos:#s -> #EQ:#GT:#LT
#COMPARE :: #0:#neg:#pos:#s -> #0:#neg:#pos:#s -> c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c14
APPEND :: :::nil -> :::nil -> c16
c16 :: c17:c18 -> c16
APPEND#1 :: :::nil -> :::nil -> c17:c18
:: :: #0:#neg:#pos:#s -> :::nil -> :::nil
c17 :: c16 -> c17:c18
nil :: :::nil
c18 :: c17:c18
FLATTEN :: leaf:node -> c19
c19 :: c20:c21:c22 -> c19
FLATTEN#1 :: leaf:node -> c20:c21:c22
leaf :: leaf:node
c20 :: c20:c21:c22
node :: :::nil -> leaf:node -> leaf:node -> leaf:node
c21 :: c16 -> c16 -> c19 -> c20:c21:c22
append :: :::nil -> :::nil -> :::nil
flatten :: leaf:node -> :::nil
c22 :: c16 -> c16 -> c19 -> c20:c21:c22
FLATTENSORT :: leaf:node -> c23
c23 :: c29 -> c19 -> c23
INSERTIONSORT :: :::nil -> c29
INSERT :: #0:#neg:#pos:#s -> :::nil -> c24
c24 :: c25:c26 -> c24
INSERT#1 :: :::nil -> #0:#neg:#pos:#s -> c25:c26
c25 :: c27:c28 -> c15 -> c25:c26
INSERT#2 :: #false:#true -> #0:#neg:#pos:#s -> #0:#neg:#pos:#s -> :::nil -> c27:c28
#less :: #0:#neg:#pos:#s -> #0:#neg:#pos:#s -> #false:#true
c26 :: c25:c26
#false :: #false:#true
c27 :: c27:c28
#true :: #false:#true
c28 :: c24 -> c27:c28
c29 :: c30:c31 -> c29
INSERTIONSORT#1 :: :::nil -> c30:c31
c30 :: c24 -> c29 -> c30:c31
insertionsort :: :::nil -> :::nil
c31 :: c30:c31
#EQ :: #EQ:#GT:#LT
c :: c:c1:c2
#GT :: #EQ:#GT:#LT
c1 :: c:c1:c2
#LT :: #EQ:#GT:#LT
c2 :: c:c1:c2
#0 :: #0:#neg:#pos:#s
c3 :: c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c14
#neg :: #0:#neg:#pos:#s -> #0:#neg:#pos:#s
c4 :: c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c14
#pos :: #0:#neg:#pos:#s -> #0:#neg:#pos:#s
c5 :: c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c14
#s :: #0:#neg:#pos:#s -> #0:#neg:#pos:#s
c6 :: c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c14
c7 :: c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c14
c8 :: c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c14 -> c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c14
c9 :: c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c14
c10 :: c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c14
c11 :: c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c14
c12 :: c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c14 -> c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c14
c13 :: c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c14
c14 :: c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c14 -> c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c14
#cklt :: #EQ:#GT:#LT -> #false:#true
append#1 :: :::nil -> :::nil -> :::nil
flatten#1 :: leaf:node -> :::nil
flattensort :: leaf:node -> :::nil
insert :: #0:#neg:#pos:#s -> :::nil -> :::nil
insert#1 :: :::nil -> #0:#neg:#pos:#s -> :::nil
insert#2 :: #false:#true -> #0:#neg:#pos:#s -> #0:#neg:#pos:#s -> :::nil -> :::nil
insertionsort#1 :: :::nil -> :::nil
hole_c151_32 :: c15
hole_#0:#neg:#pos:#s2_32 :: #0:#neg:#pos:#s
hole_c:c1:c23_32 :: c:c1:c2
hole_c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c144_32 :: c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c14
hole_#EQ:#GT:#LT5_32 :: #EQ:#GT:#LT
hole_c166_32 :: c16
hole_:::nil7_32 :: :::nil
hole_c17:c188_32 :: c17:c18
hole_c199_32 :: c19
hole_leaf:node10_32 :: leaf:node
hole_c20:c21:c2211_32 :: c20:c21:c22
hole_c2312_32 :: c23
hole_c2913_32 :: c29
hole_c2414_32 :: c24
hole_c25:c2615_32 :: c25:c26
hole_c27:c2816_32 :: c27:c28
hole_#false:#true17_32 :: #false:#true
hole_c30:c3118_32 :: c30:c31
gen_#0:#neg:#pos:#s19_32 :: Nat -> #0:#neg:#pos:#s
gen_c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c1420_32 :: Nat -> c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c14
gen_:::nil21_32 :: Nat -> :::nil
gen_leaf:node22_32 :: Nat -> leaf:node

----------------------------------------

(141) OrderProof (LOWER BOUND(ID))
Heuristically decided to analyse the following defined symbols:
#compare, #COMPARE, APPEND, APPEND#1, FLATTEN, FLATTEN#1, append, flatten, INSERTIONSORT, INSERT, INSERT#1, INSERTIONSORT#1, insertionsort, append#1, flatten#1, insert, insert#1, insertionsort#1

They will be analysed ascendingly in the following order:
APPEND = APPEND#1
APPEND < FLATTEN#1
FLATTEN = FLATTEN#1
append < FLATTEN#1
flatten < FLATTEN#1
append = append#1
append < flatten#1
flatten = flatten#1
INSERTIONSORT = INSERTIONSORT#1
INSERT = INSERT#1
INSERT < INSERTIONSORT#1
insertionsort < INSERTIONSORT#1
insertionsort = insertionsort#1
insert = insert#1
insert < insertionsort#1

----------------------------------------

(142)
Obligation:
Innermost TRS:
Rules:
#LESS(z0, z1) -> c15(#CKLT(#compare(z0, z1)), #COMPARE(z0, z1))
APPEND(z0, z1) -> c16(APPEND#1(z0, z1))
APPEND#1(::(z0, z1), z2) -> c17(APPEND(z1, z2))
APPEND#1(nil, z0) -> c18
FLATTEN(z0) -> c19(FLATTEN#1(z0))
FLATTEN#1(leaf) -> c20
FLATTEN#1(node(z0, z1, z2)) -> c21(APPEND(z0, append(flatten(z1), flatten(z2))), APPEND(flatten(z1), flatten(z2)), FLATTEN(z1))
FLATTEN#1(node(z0, z1, z2)) -> c22(APPEND(z0, append(flatten(z1), flatten(z2))), APPEND(flatten(z1), flatten(z2)), FLATTEN(z2))
FLATTENSORT(z0) -> c23(INSERTIONSORT(flatten(z0)), FLATTEN(z0))
INSERT(z0, z1) -> c24(INSERT#1(z1, z0))
INSERT#1(::(z0, z1), z2) -> c25(INSERT#2(#less(z0, z2), z2, z0, z1), #LESS(z0, z2))
INSERT#1(nil, z0) -> c26
INSERT#2(#false, z0, z1, z2) -> c27
INSERT#2(#true, z0, z1, z2) -> c28(INSERT(z0, z2))
INSERTIONSORT(z0) -> c29(INSERTIONSORT#1(z0))
INSERTIONSORT#1(::(z0, z1)) -> c30(INSERT(z0, insertionsort(z1)), INSERTIONSORT(z1))
INSERTIONSORT#1(nil) -> c31
#CKLT(#EQ) -> c
#CKLT(#GT) -> c1
#CKLT(#LT) -> c2
#COMPARE(#0, #0) -> c3
#COMPARE(#0, #neg(z0)) -> c4
#COMPARE(#0, #pos(z0)) -> c5
#COMPARE(#0, #s(z0)) -> c6
#COMPARE(#neg(z0), #0) -> c7
#COMPARE(#neg(z0), #neg(z1)) -> c8(#COMPARE(z1, z0))
#COMPARE(#neg(z0), #pos(z1)) -> c9
#COMPARE(#pos(z0), #0) -> c10
#COMPARE(#pos(z0), #neg(z1)) -> c11
#COMPARE(#pos(z0), #pos(z1)) -> c12(#COMPARE(z0, z1))
#COMPARE(#s(z0), #0) -> c13
#COMPARE(#s(z0), #s(z1)) -> c14(#COMPARE(z0, z1))
#cklt(#EQ) -> #false
#cklt(#GT) -> #false
#cklt(#LT) -> #true
#compare(#0, #0) -> #EQ
#compare(#0, #neg(z0)) -> #GT
#compare(#0, #pos(z0)) -> #LT
#compare(#0, #s(z0)) -> #LT
#compare(#neg(z0), #0) -> #LT
#compare(#neg(z0), #neg(z1)) -> #compare(z1, z0)
#compare(#neg(z0), #pos(z1)) -> #LT
#compare(#pos(z0), #0) -> #GT
#compare(#pos(z0), #neg(z1)) -> #GT
#compare(#pos(z0), #pos(z1)) -> #compare(z0, z1)
#compare(#s(z0), #0) -> #GT
#compare(#s(z0), #s(z1)) -> #compare(z0, z1)
#less(z0, z1) -> #cklt(#compare(z0, z1))
append(z0, z1) -> append#1(z0, z1)
append#1(::(z0, z1), z2) -> ::(z0, append(z1, z2))
append#1(nil, z0) -> z0
flatten(z0) -> flatten#1(z0)
flatten#1(leaf) -> nil
flatten#1(node(z0, z1, z2)) -> append(z0, append(flatten(z1), flatten(z2)))
flattensort(z0) -> insertionsort(flatten(z0))
insert(z0, z1) -> insert#1(z1, z0)
insert#1(::(z0, z1), z2) -> insert#2(#less(z0, z2), z2, z0, z1)
insert#1(nil, z0) -> ::(z0, nil)
insert#2(#false, z0, z1, z2) -> ::(z0, ::(z1, z2))
insert#2(#true, z0, z1, z2) -> ::(z1, insert(z0, z2))
insertionsort(z0) -> insertionsort#1(z0)
insertionsort#1(::(z0, z1)) -> insert(z0, insertionsort(z1))
insertionsort#1(nil) -> nil

Types:
#LESS :: #0:#neg:#pos:#s -> #0:#neg:#pos:#s -> c15
c15 :: c:c1:c2 -> c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c14 -> c15
#CKLT :: #EQ:#GT:#LT -> c:c1:c2
#compare :: #0:#neg:#pos:#s -> #0:#neg:#pos:#s -> #EQ:#GT:#LT
#COMPARE :: #0:#neg:#pos:#s -> #0:#neg:#pos:#s -> c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c14
APPEND :: :::nil -> :::nil -> c16
c16 :: c17:c18 -> c16
APPEND#1 :: :::nil -> :::nil -> c17:c18
:: :: #0:#neg:#pos:#s -> :::nil -> :::nil
c17 :: c16 -> c17:c18
nil :: :::nil
c18 :: c17:c18
FLATTEN :: leaf:node -> c19
c19 :: c20:c21:c22 -> c19
FLATTEN#1 :: leaf:node -> c20:c21:c22
leaf :: leaf:node
c20 :: c20:c21:c22
node :: :::nil -> leaf:node -> leaf:node -> leaf:node
c21 :: c16 -> c16 -> c19 -> c20:c21:c22
append :: :::nil -> :::nil -> :::nil
flatten :: leaf:node -> :::nil
c22 :: c16 -> c16 -> c19 -> c20:c21:c22
FLATTENSORT :: leaf:node -> c23
c23 :: c29 -> c19 -> c23
INSERTIONSORT :: :::nil -> c29
INSERT :: #0:#neg:#pos:#s -> :::nil -> c24
c24 :: c25:c26 -> c24
INSERT#1 :: :::nil -> #0:#neg:#pos:#s -> c25:c26
c25 :: c27:c28 -> c15 -> c25:c26
INSERT#2 :: #false:#true -> #0:#neg:#pos:#s -> #0:#neg:#pos:#s -> :::nil -> c27:c28
#less :: #0:#neg:#pos:#s -> #0:#neg:#pos:#s -> #false:#true
c26 :: c25:c26
#false :: #false:#true
c27 :: c27:c28
#true :: #false:#true
c28 :: c24 -> c27:c28
c29 :: c30:c31 -> c29
INSERTIONSORT#1 :: :::nil -> c30:c31
c30 :: c24 -> c29 -> c30:c31
insertionsort :: :::nil -> :::nil
c31 :: c30:c31
#EQ :: #EQ:#GT:#LT
c :: c:c1:c2
#GT :: #EQ:#GT:#LT
c1 :: c:c1:c2
#LT :: #EQ:#GT:#LT
c2 :: c:c1:c2
#0 :: #0:#neg:#pos:#s
c3 :: c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c14
#neg :: #0:#neg:#pos:#s -> #0:#neg:#pos:#s
c4 :: c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c14
#pos :: #0:#neg:#pos:#s -> #0:#neg:#pos:#s
c5 :: c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c14
#s :: #0:#neg:#pos:#s -> #0:#neg:#pos:#s
c6 :: c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c14
c7 :: c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c14
c8 :: c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c14 -> c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c14
c9 :: c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c14
c10 :: c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c14
c11 :: c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c14
c12 :: c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c14 -> c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c14
c13 :: c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c14
c14 :: c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c14 -> c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c14
#cklt :: #EQ:#GT:#LT -> #false:#true
append#1 :: :::nil -> :::nil -> :::nil
flatten#1 :: leaf:node -> :::nil
flattensort :: leaf:node -> :::nil
insert :: #0:#neg:#pos:#s -> :::nil -> :::nil
insert#1 :: :::nil -> #0:#neg:#pos:#s -> :::nil
insert#2 :: #false:#true -> #0:#neg:#pos:#s -> #0:#neg:#pos:#s -> :::nil -> :::nil
insertionsort#1 :: :::nil -> :::nil
hole_c151_32 :: c15
hole_#0:#neg:#pos:#s2_32 :: #0:#neg:#pos:#s
hole_c:c1:c23_32 :: c:c1:c2
hole_c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c144_32 :: c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c14
hole_#EQ:#GT:#LT5_32 :: #EQ:#GT:#LT
hole_c166_32 :: c16
hole_:::nil7_32 :: :::nil
hole_c17:c188_32 :: c17:c18
hole_c199_32 :: c19
hole_leaf:node10_32 :: leaf:node
hole_c20:c21:c2211_32 :: c20:c21:c22
hole_c2312_32 :: c23
hole_c2913_32 :: c29
hole_c2414_32 :: c24
hole_c25:c2615_32 :: c25:c26
hole_c27:c2816_32 :: c27:c28
hole_#false:#true17_32 :: #false:#true
hole_c30:c3118_32 :: c30:c31
gen_#0:#neg:#pos:#s19_32 :: Nat -> #0:#neg:#pos:#s
gen_c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c1420_32 :: Nat -> c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c14
gen_:::nil21_32 :: Nat -> :::nil
gen_leaf:node22_32 :: Nat -> leaf:node


Generator Equations:
gen_#0:#neg:#pos:#s19_32(0) <=> #0
gen_#0:#neg:#pos:#s19_32(+(x, 1)) <=> #neg(gen_#0:#neg:#pos:#s19_32(x))
gen_c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c1420_32(0) <=> c3
gen_c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c1420_32(+(x, 1)) <=> c8(gen_c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c1420_32(x))
gen_:::nil21_32(0) <=> nil
gen_:::nil21_32(+(x, 1)) <=> ::(#0, gen_:::nil21_32(x))
gen_leaf:node22_32(0) <=> leaf
gen_leaf:node22_32(+(x, 1)) <=> node(nil, leaf, gen_leaf:node22_32(x))


The following defined symbols remain to be analysed:
#compare, #COMPARE, APPEND, APPEND#1, FLATTEN, FLATTEN#1, append, flatten, INSERTIONSORT, INSERT, INSERT#1, INSERTIONSORT#1, insertionsort, append#1, flatten#1, insert, insert#1, insertionsort#1

They will be analysed ascendingly in the following order:
APPEND = APPEND#1
APPEND < FLATTEN#1
FLATTEN = FLATTEN#1
append < FLATTEN#1
flatten < FLATTEN#1
append = append#1
append < flatten#1
flatten = flatten#1
INSERTIONSORT = INSERTIONSORT#1
INSERT = INSERT#1
INSERT < INSERTIONSORT#1
insertionsort < INSERTIONSORT#1
insertionsort = insertionsort#1
insert = insert#1
insert < insertionsort#1

----------------------------------------

(143) RewriteLemmaProof (LOWER BOUND(ID))
Proved the following rewrite lemma:
#compare(gen_#0:#neg:#pos:#s19_32(n24_32), gen_#0:#neg:#pos:#s19_32(n24_32)) -> #EQ, rt in Omega(0)

Induction Base:
#compare(gen_#0:#neg:#pos:#s19_32(0), gen_#0:#neg:#pos:#s19_32(0)) ->_R^Omega(0)
#EQ

Induction Step:
#compare(gen_#0:#neg:#pos:#s19_32(+(n24_32, 1)), gen_#0:#neg:#pos:#s19_32(+(n24_32, 1))) ->_R^Omega(0)
#compare(gen_#0:#neg:#pos:#s19_32(n24_32), gen_#0:#neg:#pos:#s19_32(n24_32)) ->_IH
#EQ

We have rt in Omega(1) and sz in O(n). Thus, we have irc_R in Omega(n^0).
----------------------------------------

(144)
Obligation:
Innermost TRS:
Rules:
#LESS(z0, z1) -> c15(#CKLT(#compare(z0, z1)), #COMPARE(z0, z1))
APPEND(z0, z1) -> c16(APPEND#1(z0, z1))
APPEND#1(::(z0, z1), z2) -> c17(APPEND(z1, z2))
APPEND#1(nil, z0) -> c18
FLATTEN(z0) -> c19(FLATTEN#1(z0))
FLATTEN#1(leaf) -> c20
FLATTEN#1(node(z0, z1, z2)) -> c21(APPEND(z0, append(flatten(z1), flatten(z2))), APPEND(flatten(z1), flatten(z2)), FLATTEN(z1))
FLATTEN#1(node(z0, z1, z2)) -> c22(APPEND(z0, append(flatten(z1), flatten(z2))), APPEND(flatten(z1), flatten(z2)), FLATTEN(z2))
FLATTENSORT(z0) -> c23(INSERTIONSORT(flatten(z0)), FLATTEN(z0))
INSERT(z0, z1) -> c24(INSERT#1(z1, z0))
INSERT#1(::(z0, z1), z2) -> c25(INSERT#2(#less(z0, z2), z2, z0, z1), #LESS(z0, z2))
INSERT#1(nil, z0) -> c26
INSERT#2(#false, z0, z1, z2) -> c27
INSERT#2(#true, z0, z1, z2) -> c28(INSERT(z0, z2))
INSERTIONSORT(z0) -> c29(INSERTIONSORT#1(z0))
INSERTIONSORT#1(::(z0, z1)) -> c30(INSERT(z0, insertionsort(z1)), INSERTIONSORT(z1))
INSERTIONSORT#1(nil) -> c31
#CKLT(#EQ) -> c
#CKLT(#GT) -> c1
#CKLT(#LT) -> c2
#COMPARE(#0, #0) -> c3
#COMPARE(#0, #neg(z0)) -> c4
#COMPARE(#0, #pos(z0)) -> c5
#COMPARE(#0, #s(z0)) -> c6
#COMPARE(#neg(z0), #0) -> c7
#COMPARE(#neg(z0), #neg(z1)) -> c8(#COMPARE(z1, z0))
#COMPARE(#neg(z0), #pos(z1)) -> c9
#COMPARE(#pos(z0), #0) -> c10
#COMPARE(#pos(z0), #neg(z1)) -> c11
#COMPARE(#pos(z0), #pos(z1)) -> c12(#COMPARE(z0, z1))
#COMPARE(#s(z0), #0) -> c13
#COMPARE(#s(z0), #s(z1)) -> c14(#COMPARE(z0, z1))
#cklt(#EQ) -> #false
#cklt(#GT) -> #false
#cklt(#LT) -> #true
#compare(#0, #0) -> #EQ
#compare(#0, #neg(z0)) -> #GT
#compare(#0, #pos(z0)) -> #LT
#compare(#0, #s(z0)) -> #LT
#compare(#neg(z0), #0) -> #LT
#compare(#neg(z0), #neg(z1)) -> #compare(z1, z0)
#compare(#neg(z0), #pos(z1)) -> #LT
#compare(#pos(z0), #0) -> #GT
#compare(#pos(z0), #neg(z1)) -> #GT
#compare(#pos(z0), #pos(z1)) -> #compare(z0, z1)
#compare(#s(z0), #0) -> #GT
#compare(#s(z0), #s(z1)) -> #compare(z0, z1)
#less(z0, z1) -> #cklt(#compare(z0, z1))
append(z0, z1) -> append#1(z0, z1)
append#1(::(z0, z1), z2) -> ::(z0, append(z1, z2))
append#1(nil, z0) -> z0
flatten(z0) -> flatten#1(z0)
flatten#1(leaf) -> nil
flatten#1(node(z0, z1, z2)) -> append(z0, append(flatten(z1), flatten(z2)))
flattensort(z0) -> insertionsort(flatten(z0))
insert(z0, z1) -> insert#1(z1, z0)
insert#1(::(z0, z1), z2) -> insert#2(#less(z0, z2), z2, z0, z1)
insert#1(nil, z0) -> ::(z0, nil)
insert#2(#false, z0, z1, z2) -> ::(z0, ::(z1, z2))
insert#2(#true, z0, z1, z2) -> ::(z1, insert(z0, z2))
insertionsort(z0) -> insertionsort#1(z0)
insertionsort#1(::(z0, z1)) -> insert(z0, insertionsort(z1))
insertionsort#1(nil) -> nil

Types:
#LESS :: #0:#neg:#pos:#s -> #0:#neg:#pos:#s -> c15
c15 :: c:c1:c2 -> c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c14 -> c15
#CKLT :: #EQ:#GT:#LT -> c:c1:c2
#compare :: #0:#neg:#pos:#s -> #0:#neg:#pos:#s -> #EQ:#GT:#LT
#COMPARE :: #0:#neg:#pos:#s -> #0:#neg:#pos:#s -> c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c14
APPEND :: :::nil -> :::nil -> c16
c16 :: c17:c18 -> c16
APPEND#1 :: :::nil -> :::nil -> c17:c18
:: :: #0:#neg:#pos:#s -> :::nil -> :::nil
c17 :: c16 -> c17:c18
nil :: :::nil
c18 :: c17:c18
FLATTEN :: leaf:node -> c19
c19 :: c20:c21:c22 -> c19
FLATTEN#1 :: leaf:node -> c20:c21:c22
leaf :: leaf:node
c20 :: c20:c21:c22
node :: :::nil -> leaf:node -> leaf:node -> leaf:node
c21 :: c16 -> c16 -> c19 -> c20:c21:c22
append :: :::nil -> :::nil -> :::nil
flatten :: leaf:node -> :::nil
c22 :: c16 -> c16 -> c19 -> c20:c21:c22
FLATTENSORT :: leaf:node -> c23
c23 :: c29 -> c19 -> c23
INSERTIONSORT :: :::nil -> c29
INSERT :: #0:#neg:#pos:#s -> :::nil -> c24
c24 :: c25:c26 -> c24
INSERT#1 :: :::nil -> #0:#neg:#pos:#s -> c25:c26
c25 :: c27:c28 -> c15 -> c25:c26
INSERT#2 :: #false:#true -> #0:#neg:#pos:#s -> #0:#neg:#pos:#s -> :::nil -> c27:c28
#less :: #0:#neg:#pos:#s -> #0:#neg:#pos:#s -> #false:#true
c26 :: c25:c26
#false :: #false:#true
c27 :: c27:c28
#true :: #false:#true
c28 :: c24 -> c27:c28
c29 :: c30:c31 -> c29
INSERTIONSORT#1 :: :::nil -> c30:c31
c30 :: c24 -> c29 -> c30:c31
insertionsort :: :::nil -> :::nil
c31 :: c30:c31
#EQ :: #EQ:#GT:#LT
c :: c:c1:c2
#GT :: #EQ:#GT:#LT
c1 :: c:c1:c2
#LT :: #EQ:#GT:#LT
c2 :: c:c1:c2
#0 :: #0:#neg:#pos:#s
c3 :: c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c14
#neg :: #0:#neg:#pos:#s -> #0:#neg:#pos:#s
c4 :: c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c14
#pos :: #0:#neg:#pos:#s -> #0:#neg:#pos:#s
c5 :: c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c14
#s :: #0:#neg:#pos:#s -> #0:#neg:#pos:#s
c6 :: c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c14
c7 :: c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c14
c8 :: c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c14 -> c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c14
c9 :: c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c14
c10 :: c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c14
c11 :: c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c14
c12 :: c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c14 -> c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c14
c13 :: c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c14
c14 :: c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c14 -> c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c14
#cklt :: #EQ:#GT:#LT -> #false:#true
append#1 :: :::nil -> :::nil -> :::nil
flatten#1 :: leaf:node -> :::nil
flattensort :: leaf:node -> :::nil
insert :: #0:#neg:#pos:#s -> :::nil -> :::nil
insert#1 :: :::nil -> #0:#neg:#pos:#s -> :::nil
insert#2 :: #false:#true -> #0:#neg:#pos:#s -> #0:#neg:#pos:#s -> :::nil -> :::nil
insertionsort#1 :: :::nil -> :::nil
hole_c151_32 :: c15
hole_#0:#neg:#pos:#s2_32 :: #0:#neg:#pos:#s
hole_c:c1:c23_32 :: c:c1:c2
hole_c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c144_32 :: c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c14
hole_#EQ:#GT:#LT5_32 :: #EQ:#GT:#LT
hole_c166_32 :: c16
hole_:::nil7_32 :: :::nil
hole_c17:c188_32 :: c17:c18
hole_c199_32 :: c19
hole_leaf:node10_32 :: leaf:node
hole_c20:c21:c2211_32 :: c20:c21:c22
hole_c2312_32 :: c23
hole_c2913_32 :: c29
hole_c2414_32 :: c24
hole_c25:c2615_32 :: c25:c26
hole_c27:c2816_32 :: c27:c28
hole_#false:#true17_32 :: #false:#true
hole_c30:c3118_32 :: c30:c31
gen_#0:#neg:#pos:#s19_32 :: Nat -> #0:#neg:#pos:#s
gen_c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c1420_32 :: Nat -> c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c14
gen_:::nil21_32 :: Nat -> :::nil
gen_leaf:node22_32 :: Nat -> leaf:node


Lemmas:
#compare(gen_#0:#neg:#pos:#s19_32(n24_32), gen_#0:#neg:#pos:#s19_32(n24_32)) -> #EQ, rt in Omega(0)


Generator Equations:
gen_#0:#neg:#pos:#s19_32(0) <=> #0
gen_#0:#neg:#pos:#s19_32(+(x, 1)) <=> #neg(gen_#0:#neg:#pos:#s19_32(x))
gen_c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c1420_32(0) <=> c3
gen_c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c1420_32(+(x, 1)) <=> c8(gen_c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c1420_32(x))
gen_:::nil21_32(0) <=> nil
gen_:::nil21_32(+(x, 1)) <=> ::(#0, gen_:::nil21_32(x))
gen_leaf:node22_32(0) <=> leaf
gen_leaf:node22_32(+(x, 1)) <=> node(nil, leaf, gen_leaf:node22_32(x))


The following defined symbols remain to be analysed:
#COMPARE, APPEND, APPEND#1, FLATTEN, FLATTEN#1, append, flatten, INSERTIONSORT, INSERT, INSERT#1, INSERTIONSORT#1, insertionsort, append#1, flatten#1, insert, insert#1, insertionsort#1

They will be analysed ascendingly in the following order:
APPEND = APPEND#1
APPEND < FLATTEN#1
FLATTEN = FLATTEN#1
append < FLATTEN#1
flatten < FLATTEN#1
append = append#1
append < flatten#1
flatten = flatten#1
INSERTIONSORT = INSERTIONSORT#1
INSERT = INSERT#1
INSERT < INSERTIONSORT#1
insertionsort < INSERTIONSORT#1
insertionsort = insertionsort#1
insert = insert#1
insert < insertionsort#1

----------------------------------------

(145) RewriteLemmaProof (LOWER BOUND(ID))
Proved the following rewrite lemma:
#COMPARE(gen_#0:#neg:#pos:#s19_32(n318895_32), gen_#0:#neg:#pos:#s19_32(n318895_32)) -> gen_c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c1420_32(n318895_32), rt in Omega(0)

Induction Base:
#COMPARE(gen_#0:#neg:#pos:#s19_32(0), gen_#0:#neg:#pos:#s19_32(0)) ->_R^Omega(0)
c3

Induction Step:
#COMPARE(gen_#0:#neg:#pos:#s19_32(+(n318895_32, 1)), gen_#0:#neg:#pos:#s19_32(+(n318895_32, 1))) ->_R^Omega(0)
c8(#COMPARE(gen_#0:#neg:#pos:#s19_32(n318895_32), gen_#0:#neg:#pos:#s19_32(n318895_32))) ->_IH
c8(gen_c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c1420_32(c318896_32))

We have rt in Omega(1) and sz in O(n). Thus, we have irc_R in Omega(n^0).
----------------------------------------

(146)
Obligation:
Innermost TRS:
Rules:
#LESS(z0, z1) -> c15(#CKLT(#compare(z0, z1)), #COMPARE(z0, z1))
APPEND(z0, z1) -> c16(APPEND#1(z0, z1))
APPEND#1(::(z0, z1), z2) -> c17(APPEND(z1, z2))
APPEND#1(nil, z0) -> c18
FLATTEN(z0) -> c19(FLATTEN#1(z0))
FLATTEN#1(leaf) -> c20
FLATTEN#1(node(z0, z1, z2)) -> c21(APPEND(z0, append(flatten(z1), flatten(z2))), APPEND(flatten(z1), flatten(z2)), FLATTEN(z1))
FLATTEN#1(node(z0, z1, z2)) -> c22(APPEND(z0, append(flatten(z1), flatten(z2))), APPEND(flatten(z1), flatten(z2)), FLATTEN(z2))
FLATTENSORT(z0) -> c23(INSERTIONSORT(flatten(z0)), FLATTEN(z0))
INSERT(z0, z1) -> c24(INSERT#1(z1, z0))
INSERT#1(::(z0, z1), z2) -> c25(INSERT#2(#less(z0, z2), z2, z0, z1), #LESS(z0, z2))
INSERT#1(nil, z0) -> c26
INSERT#2(#false, z0, z1, z2) -> c27
INSERT#2(#true, z0, z1, z2) -> c28(INSERT(z0, z2))
INSERTIONSORT(z0) -> c29(INSERTIONSORT#1(z0))
INSERTIONSORT#1(::(z0, z1)) -> c30(INSERT(z0, insertionsort(z1)), INSERTIONSORT(z1))
INSERTIONSORT#1(nil) -> c31
#CKLT(#EQ) -> c
#CKLT(#GT) -> c1
#CKLT(#LT) -> c2
#COMPARE(#0, #0) -> c3
#COMPARE(#0, #neg(z0)) -> c4
#COMPARE(#0, #pos(z0)) -> c5
#COMPARE(#0, #s(z0)) -> c6
#COMPARE(#neg(z0), #0) -> c7
#COMPARE(#neg(z0), #neg(z1)) -> c8(#COMPARE(z1, z0))
#COMPARE(#neg(z0), #pos(z1)) -> c9
#COMPARE(#pos(z0), #0) -> c10
#COMPARE(#pos(z0), #neg(z1)) -> c11
#COMPARE(#pos(z0), #pos(z1)) -> c12(#COMPARE(z0, z1))
#COMPARE(#s(z0), #0) -> c13
#COMPARE(#s(z0), #s(z1)) -> c14(#COMPARE(z0, z1))
#cklt(#EQ) -> #false
#cklt(#GT) -> #false
#cklt(#LT) -> #true
#compare(#0, #0) -> #EQ
#compare(#0, #neg(z0)) -> #GT
#compare(#0, #pos(z0)) -> #LT
#compare(#0, #s(z0)) -> #LT
#compare(#neg(z0), #0) -> #LT
#compare(#neg(z0), #neg(z1)) -> #compare(z1, z0)
#compare(#neg(z0), #pos(z1)) -> #LT
#compare(#pos(z0), #0) -> #GT
#compare(#pos(z0), #neg(z1)) -> #GT
#compare(#pos(z0), #pos(z1)) -> #compare(z0, z1)
#compare(#s(z0), #0) -> #GT
#compare(#s(z0), #s(z1)) -> #compare(z0, z1)
#less(z0, z1) -> #cklt(#compare(z0, z1))
append(z0, z1) -> append#1(z0, z1)
append#1(::(z0, z1), z2) -> ::(z0, append(z1, z2))
append#1(nil, z0) -> z0
flatten(z0) -> flatten#1(z0)
flatten#1(leaf) -> nil
flatten#1(node(z0, z1, z2)) -> append(z0, append(flatten(z1), flatten(z2)))
flattensort(z0) -> insertionsort(flatten(z0))
insert(z0, z1) -> insert#1(z1, z0)
insert#1(::(z0, z1), z2) -> insert#2(#less(z0, z2), z2, z0, z1)
insert#1(nil, z0) -> ::(z0, nil)
insert#2(#false, z0, z1, z2) -> ::(z0, ::(z1, z2))
insert#2(#true, z0, z1, z2) -> ::(z1, insert(z0, z2))
insertionsort(z0) -> insertionsort#1(z0)
insertionsort#1(::(z0, z1)) -> insert(z0, insertionsort(z1))
insertionsort#1(nil) -> nil

Types:
#LESS :: #0:#neg:#pos:#s -> #0:#neg:#pos:#s -> c15
c15 :: c:c1:c2 -> c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c14 -> c15
#CKLT :: #EQ:#GT:#LT -> c:c1:c2
#compare :: #0:#neg:#pos:#s -> #0:#neg:#pos:#s -> #EQ:#GT:#LT
#COMPARE :: #0:#neg:#pos:#s -> #0:#neg:#pos:#s -> c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c14
APPEND :: :::nil -> :::nil -> c16
c16 :: c17:c18 -> c16
APPEND#1 :: :::nil -> :::nil -> c17:c18
:: :: #0:#neg:#pos:#s -> :::nil -> :::nil
c17 :: c16 -> c17:c18
nil :: :::nil
c18 :: c17:c18
FLATTEN :: leaf:node -> c19
c19 :: c20:c21:c22 -> c19
FLATTEN#1 :: leaf:node -> c20:c21:c22
leaf :: leaf:node
c20 :: c20:c21:c22
node :: :::nil -> leaf:node -> leaf:node -> leaf:node
c21 :: c16 -> c16 -> c19 -> c20:c21:c22
append :: :::nil -> :::nil -> :::nil
flatten :: leaf:node -> :::nil
c22 :: c16 -> c16 -> c19 -> c20:c21:c22
FLATTENSORT :: leaf:node -> c23
c23 :: c29 -> c19 -> c23
INSERTIONSORT :: :::nil -> c29
INSERT :: #0:#neg:#pos:#s -> :::nil -> c24
c24 :: c25:c26 -> c24
INSERT#1 :: :::nil -> #0:#neg:#pos:#s -> c25:c26
c25 :: c27:c28 -> c15 -> c25:c26
INSERT#2 :: #false:#true -> #0:#neg:#pos:#s -> #0:#neg:#pos:#s -> :::nil -> c27:c28
#less :: #0:#neg:#pos:#s -> #0:#neg:#pos:#s -> #false:#true
c26 :: c25:c26
#false :: #false:#true
c27 :: c27:c28
#true :: #false:#true
c28 :: c24 -> c27:c28
c29 :: c30:c31 -> c29
INSERTIONSORT#1 :: :::nil -> c30:c31
c30 :: c24 -> c29 -> c30:c31
insertionsort :: :::nil -> :::nil
c31 :: c30:c31
#EQ :: #EQ:#GT:#LT
c :: c:c1:c2
#GT :: #EQ:#GT:#LT
c1 :: c:c1:c2
#LT :: #EQ:#GT:#LT
c2 :: c:c1:c2
#0 :: #0:#neg:#pos:#s
c3 :: c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c14
#neg :: #0:#neg:#pos:#s -> #0:#neg:#pos:#s
c4 :: c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c14
#pos :: #0:#neg:#pos:#s -> #0:#neg:#pos:#s
c5 :: c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c14
#s :: #0:#neg:#pos:#s -> #0:#neg:#pos:#s
c6 :: c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c14
c7 :: c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c14
c8 :: c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c14 -> c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c14
c9 :: c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c14
c10 :: c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c14
c11 :: c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c14
c12 :: c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c14 -> c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c14
c13 :: c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c14
c14 :: c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c14 -> c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c14
#cklt :: #EQ:#GT:#LT -> #false:#true
append#1 :: :::nil -> :::nil -> :::nil
flatten#1 :: leaf:node -> :::nil
flattensort :: leaf:node -> :::nil
insert :: #0:#neg:#pos:#s -> :::nil -> :::nil
insert#1 :: :::nil -> #0:#neg:#pos:#s -> :::nil
insert#2 :: #false:#true -> #0:#neg:#pos:#s -> #0:#neg:#pos:#s -> :::nil -> :::nil
insertionsort#1 :: :::nil -> :::nil
hole_c151_32 :: c15
hole_#0:#neg:#pos:#s2_32 :: #0:#neg:#pos:#s
hole_c:c1:c23_32 :: c:c1:c2
hole_c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c144_32 :: c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c14
hole_#EQ:#GT:#LT5_32 :: #EQ:#GT:#LT
hole_c166_32 :: c16
hole_:::nil7_32 :: :::nil
hole_c17:c188_32 :: c17:c18
hole_c199_32 :: c19
hole_leaf:node10_32 :: leaf:node
hole_c20:c21:c2211_32 :: c20:c21:c22
hole_c2312_32 :: c23
hole_c2913_32 :: c29
hole_c2414_32 :: c24
hole_c25:c2615_32 :: c25:c26
hole_c27:c2816_32 :: c27:c28
hole_#false:#true17_32 :: #false:#true
hole_c30:c3118_32 :: c30:c31
gen_#0:#neg:#pos:#s19_32 :: Nat -> #0:#neg:#pos:#s
gen_c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c1420_32 :: Nat -> c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c14
gen_:::nil21_32 :: Nat -> :::nil
gen_leaf:node22_32 :: Nat -> leaf:node


Lemmas:
#compare(gen_#0:#neg:#pos:#s19_32(n24_32), gen_#0:#neg:#pos:#s19_32(n24_32)) -> #EQ, rt in Omega(0)
#COMPARE(gen_#0:#neg:#pos:#s19_32(n318895_32), gen_#0:#neg:#pos:#s19_32(n318895_32)) -> gen_c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c1420_32(n318895_32), rt in Omega(0)


Generator Equations:
gen_#0:#neg:#pos:#s19_32(0) <=> #0
gen_#0:#neg:#pos:#s19_32(+(x, 1)) <=> #neg(gen_#0:#neg:#pos:#s19_32(x))
gen_c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c1420_32(0) <=> c3
gen_c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c1420_32(+(x, 1)) <=> c8(gen_c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c1420_32(x))
gen_:::nil21_32(0) <=> nil
gen_:::nil21_32(+(x, 1)) <=> ::(#0, gen_:::nil21_32(x))
gen_leaf:node22_32(0) <=> leaf
gen_leaf:node22_32(+(x, 1)) <=> node(nil, leaf, gen_leaf:node22_32(x))


The following defined symbols remain to be analysed:
insert#1, APPEND, APPEND#1, FLATTEN, FLATTEN#1, append, flatten, INSERTIONSORT, INSERT, INSERT#1, INSERTIONSORT#1, insertionsort, append#1, flatten#1, insert, insertionsort#1

They will be analysed ascendingly in the following order:
APPEND = APPEND#1
APPEND < FLATTEN#1
FLATTEN = FLATTEN#1
append < FLATTEN#1
flatten < FLATTEN#1
append = append#1
append < flatten#1
flatten = flatten#1
INSERTIONSORT = INSERTIONSORT#1
INSERT = INSERT#1
INSERT < INSERTIONSORT#1
insertionsort < INSERTIONSORT#1
insertionsort = insertionsort#1
insert = insert#1
insert < insertionsort#1

----------------------------------------

(147) RewriteLemmaProof (LOWER BOUND(ID))
Proved the following rewrite lemma:
insertionsort#1(gen_:::nil21_32(n638834_32)) -> *23_32, rt in Omega(0)

Induction Base:
insertionsort#1(gen_:::nil21_32(0))

Induction Step:
insertionsort#1(gen_:::nil21_32(+(n638834_32, 1))) ->_R^Omega(0)
insert(#0, insertionsort(gen_:::nil21_32(n638834_32))) ->_R^Omega(0)
insert(#0, insertionsort#1(gen_:::nil21_32(n638834_32))) ->_IH
insert(#0, *23_32)

We have rt in Omega(1) and sz in O(n). Thus, we have irc_R in Omega(n^0).
----------------------------------------

(148)
Obligation:
Innermost TRS:
Rules:
#LESS(z0, z1) -> c15(#CKLT(#compare(z0, z1)), #COMPARE(z0, z1))
APPEND(z0, z1) -> c16(APPEND#1(z0, z1))
APPEND#1(::(z0, z1), z2) -> c17(APPEND(z1, z2))
APPEND#1(nil, z0) -> c18
FLATTEN(z0) -> c19(FLATTEN#1(z0))
FLATTEN#1(leaf) -> c20
FLATTEN#1(node(z0, z1, z2)) -> c21(APPEND(z0, append(flatten(z1), flatten(z2))), APPEND(flatten(z1), flatten(z2)), FLATTEN(z1))
FLATTEN#1(node(z0, z1, z2)) -> c22(APPEND(z0, append(flatten(z1), flatten(z2))), APPEND(flatten(z1), flatten(z2)), FLATTEN(z2))
FLATTENSORT(z0) -> c23(INSERTIONSORT(flatten(z0)), FLATTEN(z0))
INSERT(z0, z1) -> c24(INSERT#1(z1, z0))
INSERT#1(::(z0, z1), z2) -> c25(INSERT#2(#less(z0, z2), z2, z0, z1), #LESS(z0, z2))
INSERT#1(nil, z0) -> c26
INSERT#2(#false, z0, z1, z2) -> c27
INSERT#2(#true, z0, z1, z2) -> c28(INSERT(z0, z2))
INSERTIONSORT(z0) -> c29(INSERTIONSORT#1(z0))
INSERTIONSORT#1(::(z0, z1)) -> c30(INSERT(z0, insertionsort(z1)), INSERTIONSORT(z1))
INSERTIONSORT#1(nil) -> c31
#CKLT(#EQ) -> c
#CKLT(#GT) -> c1
#CKLT(#LT) -> c2
#COMPARE(#0, #0) -> c3
#COMPARE(#0, #neg(z0)) -> c4
#COMPARE(#0, #pos(z0)) -> c5
#COMPARE(#0, #s(z0)) -> c6
#COMPARE(#neg(z0), #0) -> c7
#COMPARE(#neg(z0), #neg(z1)) -> c8(#COMPARE(z1, z0))
#COMPARE(#neg(z0), #pos(z1)) -> c9
#COMPARE(#pos(z0), #0) -> c10
#COMPARE(#pos(z0), #neg(z1)) -> c11
#COMPARE(#pos(z0), #pos(z1)) -> c12(#COMPARE(z0, z1))
#COMPARE(#s(z0), #0) -> c13
#COMPARE(#s(z0), #s(z1)) -> c14(#COMPARE(z0, z1))
#cklt(#EQ) -> #false
#cklt(#GT) -> #false
#cklt(#LT) -> #true
#compare(#0, #0) -> #EQ
#compare(#0, #neg(z0)) -> #GT
#compare(#0, #pos(z0)) -> #LT
#compare(#0, #s(z0)) -> #LT
#compare(#neg(z0), #0) -> #LT
#compare(#neg(z0), #neg(z1)) -> #compare(z1, z0)
#compare(#neg(z0), #pos(z1)) -> #LT
#compare(#pos(z0), #0) -> #GT
#compare(#pos(z0), #neg(z1)) -> #GT
#compare(#pos(z0), #pos(z1)) -> #compare(z0, z1)
#compare(#s(z0), #0) -> #GT
#compare(#s(z0), #s(z1)) -> #compare(z0, z1)
#less(z0, z1) -> #cklt(#compare(z0, z1))
append(z0, z1) -> append#1(z0, z1)
append#1(::(z0, z1), z2) -> ::(z0, append(z1, z2))
append#1(nil, z0) -> z0
flatten(z0) -> flatten#1(z0)
flatten#1(leaf) -> nil
flatten#1(node(z0, z1, z2)) -> append(z0, append(flatten(z1), flatten(z2)))
flattensort(z0) -> insertionsort(flatten(z0))
insert(z0, z1) -> insert#1(z1, z0)
insert#1(::(z0, z1), z2) -> insert#2(#less(z0, z2), z2, z0, z1)
insert#1(nil, z0) -> ::(z0, nil)
insert#2(#false, z0, z1, z2) -> ::(z0, ::(z1, z2))
insert#2(#true, z0, z1, z2) -> ::(z1, insert(z0, z2))
insertionsort(z0) -> insertionsort#1(z0)
insertionsort#1(::(z0, z1)) -> insert(z0, insertionsort(z1))
insertionsort#1(nil) -> nil

Types:
#LESS :: #0:#neg:#pos:#s -> #0:#neg:#pos:#s -> c15
c15 :: c:c1:c2 -> c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c14 -> c15
#CKLT :: #EQ:#GT:#LT -> c:c1:c2
#compare :: #0:#neg:#pos:#s -> #0:#neg:#pos:#s -> #EQ:#GT:#LT
#COMPARE :: #0:#neg:#pos:#s -> #0:#neg:#pos:#s -> c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c14
APPEND :: :::nil -> :::nil -> c16
c16 :: c17:c18 -> c16
APPEND#1 :: :::nil -> :::nil -> c17:c18
:: :: #0:#neg:#pos:#s -> :::nil -> :::nil
c17 :: c16 -> c17:c18
nil :: :::nil
c18 :: c17:c18
FLATTEN :: leaf:node -> c19
c19 :: c20:c21:c22 -> c19
FLATTEN#1 :: leaf:node -> c20:c21:c22
leaf :: leaf:node
c20 :: c20:c21:c22
node :: :::nil -> leaf:node -> leaf:node -> leaf:node
c21 :: c16 -> c16 -> c19 -> c20:c21:c22
append :: :::nil -> :::nil -> :::nil
flatten :: leaf:node -> :::nil
c22 :: c16 -> c16 -> c19 -> c20:c21:c22
FLATTENSORT :: leaf:node -> c23
c23 :: c29 -> c19 -> c23
INSERTIONSORT :: :::nil -> c29
INSERT :: #0:#neg:#pos:#s -> :::nil -> c24
c24 :: c25:c26 -> c24
INSERT#1 :: :::nil -> #0:#neg:#pos:#s -> c25:c26
c25 :: c27:c28 -> c15 -> c25:c26
INSERT#2 :: #false:#true -> #0:#neg:#pos:#s -> #0:#neg:#pos:#s -> :::nil -> c27:c28
#less :: #0:#neg:#pos:#s -> #0:#neg:#pos:#s -> #false:#true
c26 :: c25:c26
#false :: #false:#true
c27 :: c27:c28
#true :: #false:#true
c28 :: c24 -> c27:c28
c29 :: c30:c31 -> c29
INSERTIONSORT#1 :: :::nil -> c30:c31
c30 :: c24 -> c29 -> c30:c31
insertionsort :: :::nil -> :::nil
c31 :: c30:c31
#EQ :: #EQ:#GT:#LT
c :: c:c1:c2
#GT :: #EQ:#GT:#LT
c1 :: c:c1:c2
#LT :: #EQ:#GT:#LT
c2 :: c:c1:c2
#0 :: #0:#neg:#pos:#s
c3 :: c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c14
#neg :: #0:#neg:#pos:#s -> #0:#neg:#pos:#s
c4 :: c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c14
#pos :: #0:#neg:#pos:#s -> #0:#neg:#pos:#s
c5 :: c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c14
#s :: #0:#neg:#pos:#s -> #0:#neg:#pos:#s
c6 :: c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c14
c7 :: c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c14
c8 :: c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c14 -> c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c14
c9 :: c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c14
c10 :: c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c14
c11 :: c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c14
c12 :: c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c14 -> c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c14
c13 :: c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c14
c14 :: c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c14 -> c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c14
#cklt :: #EQ:#GT:#LT -> #false:#true
append#1 :: :::nil -> :::nil -> :::nil
flatten#1 :: leaf:node -> :::nil
flattensort :: leaf:node -> :::nil
insert :: #0:#neg:#pos:#s -> :::nil -> :::nil
insert#1 :: :::nil -> #0:#neg:#pos:#s -> :::nil
insert#2 :: #false:#true -> #0:#neg:#pos:#s -> #0:#neg:#pos:#s -> :::nil -> :::nil
insertionsort#1 :: :::nil -> :::nil
hole_c151_32 :: c15
hole_#0:#neg:#pos:#s2_32 :: #0:#neg:#pos:#s
hole_c:c1:c23_32 :: c:c1:c2
hole_c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c144_32 :: c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c14
hole_#EQ:#GT:#LT5_32 :: #EQ:#GT:#LT
hole_c166_32 :: c16
hole_:::nil7_32 :: :::nil
hole_c17:c188_32 :: c17:c18
hole_c199_32 :: c19
hole_leaf:node10_32 :: leaf:node
hole_c20:c21:c2211_32 :: c20:c21:c22
hole_c2312_32 :: c23
hole_c2913_32 :: c29
hole_c2414_32 :: c24
hole_c25:c2615_32 :: c25:c26
hole_c27:c2816_32 :: c27:c28
hole_#false:#true17_32 :: #false:#true
hole_c30:c3118_32 :: c30:c31
gen_#0:#neg:#pos:#s19_32 :: Nat -> #0:#neg:#pos:#s
gen_c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c1420_32 :: Nat -> c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c14
gen_:::nil21_32 :: Nat -> :::nil
gen_leaf:node22_32 :: Nat -> leaf:node


Lemmas:
#compare(gen_#0:#neg:#pos:#s19_32(n24_32), gen_#0:#neg:#pos:#s19_32(n24_32)) -> #EQ, rt in Omega(0)
#COMPARE(gen_#0:#neg:#pos:#s19_32(n318895_32), gen_#0:#neg:#pos:#s19_32(n318895_32)) -> gen_c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c1420_32(n318895_32), rt in Omega(0)
insertionsort#1(gen_:::nil21_32(n638834_32)) -> *23_32, rt in Omega(0)


Generator Equations:
gen_#0:#neg:#pos:#s19_32(0) <=> #0
gen_#0:#neg:#pos:#s19_32(+(x, 1)) <=> #neg(gen_#0:#neg:#pos:#s19_32(x))
gen_c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c1420_32(0) <=> c3
gen_c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c1420_32(+(x, 1)) <=> c8(gen_c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c1420_32(x))
gen_:::nil21_32(0) <=> nil
gen_:::nil21_32(+(x, 1)) <=> ::(#0, gen_:::nil21_32(x))
gen_leaf:node22_32(0) <=> leaf
gen_leaf:node22_32(+(x, 1)) <=> node(nil, leaf, gen_leaf:node22_32(x))


The following defined symbols remain to be analysed:
insertionsort, APPEND, APPEND#1, FLATTEN, FLATTEN#1, append, flatten, INSERTIONSORT, INSERT, INSERT#1, INSERTIONSORT#1, append#1, flatten#1

They will be analysed ascendingly in the following order:
APPEND = APPEND#1
APPEND < FLATTEN#1
FLATTEN = FLATTEN#1
append < FLATTEN#1
flatten < FLATTEN#1
append = append#1
append < flatten#1
flatten = flatten#1
INSERTIONSORT = INSERTIONSORT#1
INSERT = INSERT#1
INSERT < INSERTIONSORT#1
insertionsort < INSERTIONSORT#1
insertionsort = insertionsort#1

----------------------------------------

(149) RewriteLemmaProof (LOWER BOUND(ID))
Proved the following rewrite lemma:
insertionsort(gen_:::nil21_32(n643249_32)) -> *23_32, rt in Omega(0)

Induction Base:
insertionsort(gen_:::nil21_32(0))

Induction Step:
insertionsort(gen_:::nil21_32(+(n643249_32, 1))) ->_R^Omega(0)
insertionsort#1(gen_:::nil21_32(+(n643249_32, 1))) ->_R^Omega(0)
insert(#0, insertionsort(gen_:::nil21_32(n643249_32))) ->_IH
insert(#0, *23_32)

We have rt in Omega(1) and sz in O(n). Thus, we have irc_R in Omega(n^0).
----------------------------------------

(150)
Obligation:
Innermost TRS:
Rules:
#LESS(z0, z1) -> c15(#CKLT(#compare(z0, z1)), #COMPARE(z0, z1))
APPEND(z0, z1) -> c16(APPEND#1(z0, z1))
APPEND#1(::(z0, z1), z2) -> c17(APPEND(z1, z2))
APPEND#1(nil, z0) -> c18
FLATTEN(z0) -> c19(FLATTEN#1(z0))
FLATTEN#1(leaf) -> c20
FLATTEN#1(node(z0, z1, z2)) -> c21(APPEND(z0, append(flatten(z1), flatten(z2))), APPEND(flatten(z1), flatten(z2)), FLATTEN(z1))
FLATTEN#1(node(z0, z1, z2)) -> c22(APPEND(z0, append(flatten(z1), flatten(z2))), APPEND(flatten(z1), flatten(z2)), FLATTEN(z2))
FLATTENSORT(z0) -> c23(INSERTIONSORT(flatten(z0)), FLATTEN(z0))
INSERT(z0, z1) -> c24(INSERT#1(z1, z0))
INSERT#1(::(z0, z1), z2) -> c25(INSERT#2(#less(z0, z2), z2, z0, z1), #LESS(z0, z2))
INSERT#1(nil, z0) -> c26
INSERT#2(#false, z0, z1, z2) -> c27
INSERT#2(#true, z0, z1, z2) -> c28(INSERT(z0, z2))
INSERTIONSORT(z0) -> c29(INSERTIONSORT#1(z0))
INSERTIONSORT#1(::(z0, z1)) -> c30(INSERT(z0, insertionsort(z1)), INSERTIONSORT(z1))
INSERTIONSORT#1(nil) -> c31
#CKLT(#EQ) -> c
#CKLT(#GT) -> c1
#CKLT(#LT) -> c2
#COMPARE(#0, #0) -> c3
#COMPARE(#0, #neg(z0)) -> c4
#COMPARE(#0, #pos(z0)) -> c5
#COMPARE(#0, #s(z0)) -> c6
#COMPARE(#neg(z0), #0) -> c7
#COMPARE(#neg(z0), #neg(z1)) -> c8(#COMPARE(z1, z0))
#COMPARE(#neg(z0), #pos(z1)) -> c9
#COMPARE(#pos(z0), #0) -> c10
#COMPARE(#pos(z0), #neg(z1)) -> c11
#COMPARE(#pos(z0), #pos(z1)) -> c12(#COMPARE(z0, z1))
#COMPARE(#s(z0), #0) -> c13
#COMPARE(#s(z0), #s(z1)) -> c14(#COMPARE(z0, z1))
#cklt(#EQ) -> #false
#cklt(#GT) -> #false
#cklt(#LT) -> #true
#compare(#0, #0) -> #EQ
#compare(#0, #neg(z0)) -> #GT
#compare(#0, #pos(z0)) -> #LT
#compare(#0, #s(z0)) -> #LT
#compare(#neg(z0), #0) -> #LT
#compare(#neg(z0), #neg(z1)) -> #compare(z1, z0)
#compare(#neg(z0), #pos(z1)) -> #LT
#compare(#pos(z0), #0) -> #GT
#compare(#pos(z0), #neg(z1)) -> #GT
#compare(#pos(z0), #pos(z1)) -> #compare(z0, z1)
#compare(#s(z0), #0) -> #GT
#compare(#s(z0), #s(z1)) -> #compare(z0, z1)
#less(z0, z1) -> #cklt(#compare(z0, z1))
append(z0, z1) -> append#1(z0, z1)
append#1(::(z0, z1), z2) -> ::(z0, append(z1, z2))
append#1(nil, z0) -> z0
flatten(z0) -> flatten#1(z0)
flatten#1(leaf) -> nil
flatten#1(node(z0, z1, z2)) -> append(z0, append(flatten(z1), flatten(z2)))
flattensort(z0) -> insertionsort(flatten(z0))
insert(z0, z1) -> insert#1(z1, z0)
insert#1(::(z0, z1), z2) -> insert#2(#less(z0, z2), z2, z0, z1)
insert#1(nil, z0) -> ::(z0, nil)
insert#2(#false, z0, z1, z2) -> ::(z0, ::(z1, z2))
insert#2(#true, z0, z1, z2) -> ::(z1, insert(z0, z2))
insertionsort(z0) -> insertionsort#1(z0)
insertionsort#1(::(z0, z1)) -> insert(z0, insertionsort(z1))
insertionsort#1(nil) -> nil

Types:
#LESS :: #0:#neg:#pos:#s -> #0:#neg:#pos:#s -> c15
c15 :: c:c1:c2 -> c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c14 -> c15
#CKLT :: #EQ:#GT:#LT -> c:c1:c2
#compare :: #0:#neg:#pos:#s -> #0:#neg:#pos:#s -> #EQ:#GT:#LT
#COMPARE :: #0:#neg:#pos:#s -> #0:#neg:#pos:#s -> c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c14
APPEND :: :::nil -> :::nil -> c16
c16 :: c17:c18 -> c16
APPEND#1 :: :::nil -> :::nil -> c17:c18
:: :: #0:#neg:#pos:#s -> :::nil -> :::nil
c17 :: c16 -> c17:c18
nil :: :::nil
c18 :: c17:c18
FLATTEN :: leaf:node -> c19
c19 :: c20:c21:c22 -> c19
FLATTEN#1 :: leaf:node -> c20:c21:c22
leaf :: leaf:node
c20 :: c20:c21:c22
node :: :::nil -> leaf:node -> leaf:node -> leaf:node
c21 :: c16 -> c16 -> c19 -> c20:c21:c22
append :: :::nil -> :::nil -> :::nil
flatten :: leaf:node -> :::nil
c22 :: c16 -> c16 -> c19 -> c20:c21:c22
FLATTENSORT :: leaf:node -> c23
c23 :: c29 -> c19 -> c23
INSERTIONSORT :: :::nil -> c29
INSERT :: #0:#neg:#pos:#s -> :::nil -> c24
c24 :: c25:c26 -> c24
INSERT#1 :: :::nil -> #0:#neg:#pos:#s -> c25:c26
c25 :: c27:c28 -> c15 -> c25:c26
INSERT#2 :: #false:#true -> #0:#neg:#pos:#s -> #0:#neg:#pos:#s -> :::nil -> c27:c28
#less :: #0:#neg:#pos:#s -> #0:#neg:#pos:#s -> #false:#true
c26 :: c25:c26
#false :: #false:#true
c27 :: c27:c28
#true :: #false:#true
c28 :: c24 -> c27:c28
c29 :: c30:c31 -> c29
INSERTIONSORT#1 :: :::nil -> c30:c31
c30 :: c24 -> c29 -> c30:c31
insertionsort :: :::nil -> :::nil
c31 :: c30:c31
#EQ :: #EQ:#GT:#LT
c :: c:c1:c2
#GT :: #EQ:#GT:#LT
c1 :: c:c1:c2
#LT :: #EQ:#GT:#LT
c2 :: c:c1:c2
#0 :: #0:#neg:#pos:#s
c3 :: c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c14
#neg :: #0:#neg:#pos:#s -> #0:#neg:#pos:#s
c4 :: c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c14
#pos :: #0:#neg:#pos:#s -> #0:#neg:#pos:#s
c5 :: c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c14
#s :: #0:#neg:#pos:#s -> #0:#neg:#pos:#s
c6 :: c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c14
c7 :: c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c14
c8 :: c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c14 -> c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c14
c9 :: c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c14
c10 :: c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c14
c11 :: c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c14
c12 :: c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c14 -> c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c14
c13 :: c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c14
c14 :: c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c14 -> c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c14
#cklt :: #EQ:#GT:#LT -> #false:#true
append#1 :: :::nil -> :::nil -> :::nil
flatten#1 :: leaf:node -> :::nil
flattensort :: leaf:node -> :::nil
insert :: #0:#neg:#pos:#s -> :::nil -> :::nil
insert#1 :: :::nil -> #0:#neg:#pos:#s -> :::nil
insert#2 :: #false:#true -> #0:#neg:#pos:#s -> #0:#neg:#pos:#s -> :::nil -> :::nil
insertionsort#1 :: :::nil -> :::nil
hole_c151_32 :: c15
hole_#0:#neg:#pos:#s2_32 :: #0:#neg:#pos:#s
hole_c:c1:c23_32 :: c:c1:c2
hole_c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c144_32 :: c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c14
hole_#EQ:#GT:#LT5_32 :: #EQ:#GT:#LT
hole_c166_32 :: c16
hole_:::nil7_32 :: :::nil
hole_c17:c188_32 :: c17:c18
hole_c199_32 :: c19
hole_leaf:node10_32 :: leaf:node
hole_c20:c21:c2211_32 :: c20:c21:c22
hole_c2312_32 :: c23
hole_c2913_32 :: c29
hole_c2414_32 :: c24
hole_c25:c2615_32 :: c25:c26
hole_c27:c2816_32 :: c27:c28
hole_#false:#true17_32 :: #false:#true
hole_c30:c3118_32 :: c30:c31
gen_#0:#neg:#pos:#s19_32 :: Nat -> #0:#neg:#pos:#s
gen_c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c1420_32 :: Nat -> c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c14
gen_:::nil21_32 :: Nat -> :::nil
gen_leaf:node22_32 :: Nat -> leaf:node


Lemmas:
#compare(gen_#0:#neg:#pos:#s19_32(n24_32), gen_#0:#neg:#pos:#s19_32(n24_32)) -> #EQ, rt in Omega(0)
#COMPARE(gen_#0:#neg:#pos:#s19_32(n318895_32), gen_#0:#neg:#pos:#s19_32(n318895_32)) -> gen_c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c1420_32(n318895_32), rt in Omega(0)
insertionsort#1(gen_:::nil21_32(n638834_32)) -> *23_32, rt in Omega(0)
insertionsort(gen_:::nil21_32(n643249_32)) -> *23_32, rt in Omega(0)


Generator Equations:
gen_#0:#neg:#pos:#s19_32(0) <=> #0
gen_#0:#neg:#pos:#s19_32(+(x, 1)) <=> #neg(gen_#0:#neg:#pos:#s19_32(x))
gen_c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c1420_32(0) <=> c3
gen_c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c1420_32(+(x, 1)) <=> c8(gen_c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c1420_32(x))
gen_:::nil21_32(0) <=> nil
gen_:::nil21_32(+(x, 1)) <=> ::(#0, gen_:::nil21_32(x))
gen_leaf:node22_32(0) <=> leaf
gen_leaf:node22_32(+(x, 1)) <=> node(nil, leaf, gen_leaf:node22_32(x))


The following defined symbols remain to be analysed:
insertionsort#1, APPEND, APPEND#1, FLATTEN, FLATTEN#1, append, flatten, INSERTIONSORT, INSERT, INSERT#1, INSERTIONSORT#1, append#1, flatten#1

They will be analysed ascendingly in the following order:
APPEND = APPEND#1
APPEND < FLATTEN#1
FLATTEN = FLATTEN#1
append < FLATTEN#1
flatten < FLATTEN#1
append = append#1
append < flatten#1
flatten = flatten#1
INSERTIONSORT = INSERTIONSORT#1
INSERT = INSERT#1
INSERT < INSERTIONSORT#1
insertionsort < INSERTIONSORT#1
insertionsort = insertionsort#1

----------------------------------------

(151) RewriteLemmaProof (LOWER BOUND(ID))
Proved the following rewrite lemma:
insertionsort#1(gen_:::nil21_32(n653302_32)) -> *23_32, rt in Omega(0)

Induction Base:
insertionsort#1(gen_:::nil21_32(0))

Induction Step:
insertionsort#1(gen_:::nil21_32(+(n653302_32, 1))) ->_R^Omega(0)
insert(#0, insertionsort(gen_:::nil21_32(n653302_32))) ->_R^Omega(0)
insert(#0, insertionsort#1(gen_:::nil21_32(n653302_32))) ->_IH
insert(#0, *23_32)

We have rt in Omega(1) and sz in O(n). Thus, we have irc_R in Omega(n^0).
----------------------------------------

(152)
Obligation:
Innermost TRS:
Rules:
#LESS(z0, z1) -> c15(#CKLT(#compare(z0, z1)), #COMPARE(z0, z1))
APPEND(z0, z1) -> c16(APPEND#1(z0, z1))
APPEND#1(::(z0, z1), z2) -> c17(APPEND(z1, z2))
APPEND#1(nil, z0) -> c18
FLATTEN(z0) -> c19(FLATTEN#1(z0))
FLATTEN#1(leaf) -> c20
FLATTEN#1(node(z0, z1, z2)) -> c21(APPEND(z0, append(flatten(z1), flatten(z2))), APPEND(flatten(z1), flatten(z2)), FLATTEN(z1))
FLATTEN#1(node(z0, z1, z2)) -> c22(APPEND(z0, append(flatten(z1), flatten(z2))), APPEND(flatten(z1), flatten(z2)), FLATTEN(z2))
FLATTENSORT(z0) -> c23(INSERTIONSORT(flatten(z0)), FLATTEN(z0))
INSERT(z0, z1) -> c24(INSERT#1(z1, z0))
INSERT#1(::(z0, z1), z2) -> c25(INSERT#2(#less(z0, z2), z2, z0, z1), #LESS(z0, z2))
INSERT#1(nil, z0) -> c26
INSERT#2(#false, z0, z1, z2) -> c27
INSERT#2(#true, z0, z1, z2) -> c28(INSERT(z0, z2))
INSERTIONSORT(z0) -> c29(INSERTIONSORT#1(z0))
INSERTIONSORT#1(::(z0, z1)) -> c30(INSERT(z0, insertionsort(z1)), INSERTIONSORT(z1))
INSERTIONSORT#1(nil) -> c31
#CKLT(#EQ) -> c
#CKLT(#GT) -> c1
#CKLT(#LT) -> c2
#COMPARE(#0, #0) -> c3
#COMPARE(#0, #neg(z0)) -> c4
#COMPARE(#0, #pos(z0)) -> c5
#COMPARE(#0, #s(z0)) -> c6
#COMPARE(#neg(z0), #0) -> c7
#COMPARE(#neg(z0), #neg(z1)) -> c8(#COMPARE(z1, z0))
#COMPARE(#neg(z0), #pos(z1)) -> c9
#COMPARE(#pos(z0), #0) -> c10
#COMPARE(#pos(z0), #neg(z1)) -> c11
#COMPARE(#pos(z0), #pos(z1)) -> c12(#COMPARE(z0, z1))
#COMPARE(#s(z0), #0) -> c13
#COMPARE(#s(z0), #s(z1)) -> c14(#COMPARE(z0, z1))
#cklt(#EQ) -> #false
#cklt(#GT) -> #false
#cklt(#LT) -> #true
#compare(#0, #0) -> #EQ
#compare(#0, #neg(z0)) -> #GT
#compare(#0, #pos(z0)) -> #LT
#compare(#0, #s(z0)) -> #LT
#compare(#neg(z0), #0) -> #LT
#compare(#neg(z0), #neg(z1)) -> #compare(z1, z0)
#compare(#neg(z0), #pos(z1)) -> #LT
#compare(#pos(z0), #0) -> #GT
#compare(#pos(z0), #neg(z1)) -> #GT
#compare(#pos(z0), #pos(z1)) -> #compare(z0, z1)
#compare(#s(z0), #0) -> #GT
#compare(#s(z0), #s(z1)) -> #compare(z0, z1)
#less(z0, z1) -> #cklt(#compare(z0, z1))
append(z0, z1) -> append#1(z0, z1)
append#1(::(z0, z1), z2) -> ::(z0, append(z1, z2))
append#1(nil, z0) -> z0
flatten(z0) -> flatten#1(z0)
flatten#1(leaf) -> nil
flatten#1(node(z0, z1, z2)) -> append(z0, append(flatten(z1), flatten(z2)))
flattensort(z0) -> insertionsort(flatten(z0))
insert(z0, z1) -> insert#1(z1, z0)
insert#1(::(z0, z1), z2) -> insert#2(#less(z0, z2), z2, z0, z1)
insert#1(nil, z0) -> ::(z0, nil)
insert#2(#false, z0, z1, z2) -> ::(z0, ::(z1, z2))
insert#2(#true, z0, z1, z2) -> ::(z1, insert(z0, z2))
insertionsort(z0) -> insertionsort#1(z0)
insertionsort#1(::(z0, z1)) -> insert(z0, insertionsort(z1))
insertionsort#1(nil) -> nil

Types:
#LESS :: #0:#neg:#pos:#s -> #0:#neg:#pos:#s -> c15
c15 :: c:c1:c2 -> c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c14 -> c15
#CKLT :: #EQ:#GT:#LT -> c:c1:c2
#compare :: #0:#neg:#pos:#s -> #0:#neg:#pos:#s -> #EQ:#GT:#LT
#COMPARE :: #0:#neg:#pos:#s -> #0:#neg:#pos:#s -> c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c14
APPEND :: :::nil -> :::nil -> c16
c16 :: c17:c18 -> c16
APPEND#1 :: :::nil -> :::nil -> c17:c18
:: :: #0:#neg:#pos:#s -> :::nil -> :::nil
c17 :: c16 -> c17:c18
nil :: :::nil
c18 :: c17:c18
FLATTEN :: leaf:node -> c19
c19 :: c20:c21:c22 -> c19
FLATTEN#1 :: leaf:node -> c20:c21:c22
leaf :: leaf:node
c20 :: c20:c21:c22
node :: :::nil -> leaf:node -> leaf:node -> leaf:node
c21 :: c16 -> c16 -> c19 -> c20:c21:c22
append :: :::nil -> :::nil -> :::nil
flatten :: leaf:node -> :::nil
c22 :: c16 -> c16 -> c19 -> c20:c21:c22
FLATTENSORT :: leaf:node -> c23
c23 :: c29 -> c19 -> c23
INSERTIONSORT :: :::nil -> c29
INSERT :: #0:#neg:#pos:#s -> :::nil -> c24
c24 :: c25:c26 -> c24
INSERT#1 :: :::nil -> #0:#neg:#pos:#s -> c25:c26
c25 :: c27:c28 -> c15 -> c25:c26
INSERT#2 :: #false:#true -> #0:#neg:#pos:#s -> #0:#neg:#pos:#s -> :::nil -> c27:c28
#less :: #0:#neg:#pos:#s -> #0:#neg:#pos:#s -> #false:#true
c26 :: c25:c26
#false :: #false:#true
c27 :: c27:c28
#true :: #false:#true
c28 :: c24 -> c27:c28
c29 :: c30:c31 -> c29
INSERTIONSORT#1 :: :::nil -> c30:c31
c30 :: c24 -> c29 -> c30:c31
insertionsort :: :::nil -> :::nil
c31 :: c30:c31
#EQ :: #EQ:#GT:#LT
c :: c:c1:c2
#GT :: #EQ:#GT:#LT
c1 :: c:c1:c2
#LT :: #EQ:#GT:#LT
c2 :: c:c1:c2
#0 :: #0:#neg:#pos:#s
c3 :: c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c14
#neg :: #0:#neg:#pos:#s -> #0:#neg:#pos:#s
c4 :: c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c14
#pos :: #0:#neg:#pos:#s -> #0:#neg:#pos:#s
c5 :: c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c14
#s :: #0:#neg:#pos:#s -> #0:#neg:#pos:#s
c6 :: c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c14
c7 :: c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c14
c8 :: c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c14 -> c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c14
c9 :: c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c14
c10 :: c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c14
c11 :: c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c14
c12 :: c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c14 -> c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c14
c13 :: c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c14
c14 :: c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c14 -> c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c14
#cklt :: #EQ:#GT:#LT -> #false:#true
append#1 :: :::nil -> :::nil -> :::nil
flatten#1 :: leaf:node -> :::nil
flattensort :: leaf:node -> :::nil
insert :: #0:#neg:#pos:#s -> :::nil -> :::nil
insert#1 :: :::nil -> #0:#neg:#pos:#s -> :::nil
insert#2 :: #false:#true -> #0:#neg:#pos:#s -> #0:#neg:#pos:#s -> :::nil -> :::nil
insertionsort#1 :: :::nil -> :::nil
hole_c151_32 :: c15
hole_#0:#neg:#pos:#s2_32 :: #0:#neg:#pos:#s
hole_c:c1:c23_32 :: c:c1:c2
hole_c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c144_32 :: c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c14
hole_#EQ:#GT:#LT5_32 :: #EQ:#GT:#LT
hole_c166_32 :: c16
hole_:::nil7_32 :: :::nil
hole_c17:c188_32 :: c17:c18
hole_c199_32 :: c19
hole_leaf:node10_32 :: leaf:node
hole_c20:c21:c2211_32 :: c20:c21:c22
hole_c2312_32 :: c23
hole_c2913_32 :: c29
hole_c2414_32 :: c24
hole_c25:c2615_32 :: c25:c26
hole_c27:c2816_32 :: c27:c28
hole_#false:#true17_32 :: #false:#true
hole_c30:c3118_32 :: c30:c31
gen_#0:#neg:#pos:#s19_32 :: Nat -> #0:#neg:#pos:#s
gen_c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c1420_32 :: Nat -> c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c14
gen_:::nil21_32 :: Nat -> :::nil
gen_leaf:node22_32 :: Nat -> leaf:node


Lemmas:
#compare(gen_#0:#neg:#pos:#s19_32(n24_32), gen_#0:#neg:#pos:#s19_32(n24_32)) -> #EQ, rt in Omega(0)
#COMPARE(gen_#0:#neg:#pos:#s19_32(n318895_32), gen_#0:#neg:#pos:#s19_32(n318895_32)) -> gen_c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c1420_32(n318895_32), rt in Omega(0)
insertionsort#1(gen_:::nil21_32(n653302_32)) -> *23_32, rt in Omega(0)
insertionsort(gen_:::nil21_32(n643249_32)) -> *23_32, rt in Omega(0)


Generator Equations:
gen_#0:#neg:#pos:#s19_32(0) <=> #0
gen_#0:#neg:#pos:#s19_32(+(x, 1)) <=> #neg(gen_#0:#neg:#pos:#s19_32(x))
gen_c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c1420_32(0) <=> c3
gen_c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c1420_32(+(x, 1)) <=> c8(gen_c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c1420_32(x))
gen_:::nil21_32(0) <=> nil
gen_:::nil21_32(+(x, 1)) <=> ::(#0, gen_:::nil21_32(x))
gen_leaf:node22_32(0) <=> leaf
gen_leaf:node22_32(+(x, 1)) <=> node(nil, leaf, gen_leaf:node22_32(x))


The following defined symbols remain to be analysed:
INSERT#1, APPEND, APPEND#1, FLATTEN, FLATTEN#1, append, flatten, INSERTIONSORT, INSERT, INSERTIONSORT#1, append#1, flatten#1

They will be analysed ascendingly in the following order:
APPEND = APPEND#1
APPEND < FLATTEN#1
FLATTEN = FLATTEN#1
append < FLATTEN#1
flatten < FLATTEN#1
append = append#1
append < flatten#1
flatten = flatten#1
INSERTIONSORT = INSERTIONSORT#1
INSERT = INSERT#1
INSERT < INSERTIONSORT#1

----------------------------------------

(153) RewriteLemmaProof (LOWER BOUND(ID))
Proved the following rewrite lemma:
append#1(gen_:::nil21_32(n696814_32), gen_:::nil21_32(b)) -> gen_:::nil21_32(+(n696814_32, b)), rt in Omega(0)

Induction Base:
append#1(gen_:::nil21_32(0), gen_:::nil21_32(b)) ->_R^Omega(0)
gen_:::nil21_32(b)

Induction Step:
append#1(gen_:::nil21_32(+(n696814_32, 1)), gen_:::nil21_32(b)) ->_R^Omega(0)
::(#0, append(gen_:::nil21_32(n696814_32), gen_:::nil21_32(b))) ->_R^Omega(0)
::(#0, append#1(gen_:::nil21_32(n696814_32), gen_:::nil21_32(b))) ->_IH
::(#0, gen_:::nil21_32(+(b, c696815_32)))

We have rt in Omega(1) and sz in O(n). Thus, we have irc_R in Omega(n^0).
----------------------------------------

(154)
Obligation:
Innermost TRS:
Rules:
#LESS(z0, z1) -> c15(#CKLT(#compare(z0, z1)), #COMPARE(z0, z1))
APPEND(z0, z1) -> c16(APPEND#1(z0, z1))
APPEND#1(::(z0, z1), z2) -> c17(APPEND(z1, z2))
APPEND#1(nil, z0) -> c18
FLATTEN(z0) -> c19(FLATTEN#1(z0))
FLATTEN#1(leaf) -> c20
FLATTEN#1(node(z0, z1, z2)) -> c21(APPEND(z0, append(flatten(z1), flatten(z2))), APPEND(flatten(z1), flatten(z2)), FLATTEN(z1))
FLATTEN#1(node(z0, z1, z2)) -> c22(APPEND(z0, append(flatten(z1), flatten(z2))), APPEND(flatten(z1), flatten(z2)), FLATTEN(z2))
FLATTENSORT(z0) -> c23(INSERTIONSORT(flatten(z0)), FLATTEN(z0))
INSERT(z0, z1) -> c24(INSERT#1(z1, z0))
INSERT#1(::(z0, z1), z2) -> c25(INSERT#2(#less(z0, z2), z2, z0, z1), #LESS(z0, z2))
INSERT#1(nil, z0) -> c26
INSERT#2(#false, z0, z1, z2) -> c27
INSERT#2(#true, z0, z1, z2) -> c28(INSERT(z0, z2))
INSERTIONSORT(z0) -> c29(INSERTIONSORT#1(z0))
INSERTIONSORT#1(::(z0, z1)) -> c30(INSERT(z0, insertionsort(z1)), INSERTIONSORT(z1))
INSERTIONSORT#1(nil) -> c31
#CKLT(#EQ) -> c
#CKLT(#GT) -> c1
#CKLT(#LT) -> c2
#COMPARE(#0, #0) -> c3
#COMPARE(#0, #neg(z0)) -> c4
#COMPARE(#0, #pos(z0)) -> c5
#COMPARE(#0, #s(z0)) -> c6
#COMPARE(#neg(z0), #0) -> c7
#COMPARE(#neg(z0), #neg(z1)) -> c8(#COMPARE(z1, z0))
#COMPARE(#neg(z0), #pos(z1)) -> c9
#COMPARE(#pos(z0), #0) -> c10
#COMPARE(#pos(z0), #neg(z1)) -> c11
#COMPARE(#pos(z0), #pos(z1)) -> c12(#COMPARE(z0, z1))
#COMPARE(#s(z0), #0) -> c13
#COMPARE(#s(z0), #s(z1)) -> c14(#COMPARE(z0, z1))
#cklt(#EQ) -> #false
#cklt(#GT) -> #false
#cklt(#LT) -> #true
#compare(#0, #0) -> #EQ
#compare(#0, #neg(z0)) -> #GT
#compare(#0, #pos(z0)) -> #LT
#compare(#0, #s(z0)) -> #LT
#compare(#neg(z0), #0) -> #LT
#compare(#neg(z0), #neg(z1)) -> #compare(z1, z0)
#compare(#neg(z0), #pos(z1)) -> #LT
#compare(#pos(z0), #0) -> #GT
#compare(#pos(z0), #neg(z1)) -> #GT
#compare(#pos(z0), #pos(z1)) -> #compare(z0, z1)
#compare(#s(z0), #0) -> #GT
#compare(#s(z0), #s(z1)) -> #compare(z0, z1)
#less(z0, z1) -> #cklt(#compare(z0, z1))
append(z0, z1) -> append#1(z0, z1)
append#1(::(z0, z1), z2) -> ::(z0, append(z1, z2))
append#1(nil, z0) -> z0
flatten(z0) -> flatten#1(z0)
flatten#1(leaf) -> nil
flatten#1(node(z0, z1, z2)) -> append(z0, append(flatten(z1), flatten(z2)))
flattensort(z0) -> insertionsort(flatten(z0))
insert(z0, z1) -> insert#1(z1, z0)
insert#1(::(z0, z1), z2) -> insert#2(#less(z0, z2), z2, z0, z1)
insert#1(nil, z0) -> ::(z0, nil)
insert#2(#false, z0, z1, z2) -> ::(z0, ::(z1, z2))
insert#2(#true, z0, z1, z2) -> ::(z1, insert(z0, z2))
insertionsort(z0) -> insertionsort#1(z0)
insertionsort#1(::(z0, z1)) -> insert(z0, insertionsort(z1))
insertionsort#1(nil) -> nil

Types:
#LESS :: #0:#neg:#pos:#s -> #0:#neg:#pos:#s -> c15
c15 :: c:c1:c2 -> c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c14 -> c15
#CKLT :: #EQ:#GT:#LT -> c:c1:c2
#compare :: #0:#neg:#pos:#s -> #0:#neg:#pos:#s -> #EQ:#GT:#LT
#COMPARE :: #0:#neg:#pos:#s -> #0:#neg:#pos:#s -> c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c14
APPEND :: :::nil -> :::nil -> c16
c16 :: c17:c18 -> c16
APPEND#1 :: :::nil -> :::nil -> c17:c18
:: :: #0:#neg:#pos:#s -> :::nil -> :::nil
c17 :: c16 -> c17:c18
nil :: :::nil
c18 :: c17:c18
FLATTEN :: leaf:node -> c19
c19 :: c20:c21:c22 -> c19
FLATTEN#1 :: leaf:node -> c20:c21:c22
leaf :: leaf:node
c20 :: c20:c21:c22
node :: :::nil -> leaf:node -> leaf:node -> leaf:node
c21 :: c16 -> c16 -> c19 -> c20:c21:c22
append :: :::nil -> :::nil -> :::nil
flatten :: leaf:node -> :::nil
c22 :: c16 -> c16 -> c19 -> c20:c21:c22
FLATTENSORT :: leaf:node -> c23
c23 :: c29 -> c19 -> c23
INSERTIONSORT :: :::nil -> c29
INSERT :: #0:#neg:#pos:#s -> :::nil -> c24
c24 :: c25:c26 -> c24
INSERT#1 :: :::nil -> #0:#neg:#pos:#s -> c25:c26
c25 :: c27:c28 -> c15 -> c25:c26
INSERT#2 :: #false:#true -> #0:#neg:#pos:#s -> #0:#neg:#pos:#s -> :::nil -> c27:c28
#less :: #0:#neg:#pos:#s -> #0:#neg:#pos:#s -> #false:#true
c26 :: c25:c26
#false :: #false:#true
c27 :: c27:c28
#true :: #false:#true
c28 :: c24 -> c27:c28
c29 :: c30:c31 -> c29
INSERTIONSORT#1 :: :::nil -> c30:c31
c30 :: c24 -> c29 -> c30:c31
insertionsort :: :::nil -> :::nil
c31 :: c30:c31
#EQ :: #EQ:#GT:#LT
c :: c:c1:c2
#GT :: #EQ:#GT:#LT
c1 :: c:c1:c2
#LT :: #EQ:#GT:#LT
c2 :: c:c1:c2
#0 :: #0:#neg:#pos:#s
c3 :: c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c14
#neg :: #0:#neg:#pos:#s -> #0:#neg:#pos:#s
c4 :: c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c14
#pos :: #0:#neg:#pos:#s -> #0:#neg:#pos:#s
c5 :: c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c14
#s :: #0:#neg:#pos:#s -> #0:#neg:#pos:#s
c6 :: c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c14
c7 :: c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c14
c8 :: c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c14 -> c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c14
c9 :: c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c14
c10 :: c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c14
c11 :: c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c14
c12 :: c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c14 -> c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c14
c13 :: c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c14
c14 :: c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c14 -> c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c14
#cklt :: #EQ:#GT:#LT -> #false:#true
append#1 :: :::nil -> :::nil -> :::nil
flatten#1 :: leaf:node -> :::nil
flattensort :: leaf:node -> :::nil
insert :: #0:#neg:#pos:#s -> :::nil -> :::nil
insert#1 :: :::nil -> #0:#neg:#pos:#s -> :::nil
insert#2 :: #false:#true -> #0:#neg:#pos:#s -> #0:#neg:#pos:#s -> :::nil -> :::nil
insertionsort#1 :: :::nil -> :::nil
hole_c151_32 :: c15
hole_#0:#neg:#pos:#s2_32 :: #0:#neg:#pos:#s
hole_c:c1:c23_32 :: c:c1:c2
hole_c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c144_32 :: c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c14
hole_#EQ:#GT:#LT5_32 :: #EQ:#GT:#LT
hole_c166_32 :: c16
hole_:::nil7_32 :: :::nil
hole_c17:c188_32 :: c17:c18
hole_c199_32 :: c19
hole_leaf:node10_32 :: leaf:node
hole_c20:c21:c2211_32 :: c20:c21:c22
hole_c2312_32 :: c23
hole_c2913_32 :: c29
hole_c2414_32 :: c24
hole_c25:c2615_32 :: c25:c26
hole_c27:c2816_32 :: c27:c28
hole_#false:#true17_32 :: #false:#true
hole_c30:c3118_32 :: c30:c31
gen_#0:#neg:#pos:#s19_32 :: Nat -> #0:#neg:#pos:#s
gen_c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c1420_32 :: Nat -> c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c14
gen_:::nil21_32 :: Nat -> :::nil
gen_leaf:node22_32 :: Nat -> leaf:node


Lemmas:
#compare(gen_#0:#neg:#pos:#s19_32(n24_32), gen_#0:#neg:#pos:#s19_32(n24_32)) -> #EQ, rt in Omega(0)
#COMPARE(gen_#0:#neg:#pos:#s19_32(n318895_32), gen_#0:#neg:#pos:#s19_32(n318895_32)) -> gen_c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c1420_32(n318895_32), rt in Omega(0)
insertionsort#1(gen_:::nil21_32(n653302_32)) -> *23_32, rt in Omega(0)
insertionsort(gen_:::nil21_32(n643249_32)) -> *23_32, rt in Omega(0)
append#1(gen_:::nil21_32(n696814_32), gen_:::nil21_32(b)) -> gen_:::nil21_32(+(n696814_32, b)), rt in Omega(0)


Generator Equations:
gen_#0:#neg:#pos:#s19_32(0) <=> #0
gen_#0:#neg:#pos:#s19_32(+(x, 1)) <=> #neg(gen_#0:#neg:#pos:#s19_32(x))
gen_c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c1420_32(0) <=> c3
gen_c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c1420_32(+(x, 1)) <=> c8(gen_c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c1420_32(x))
gen_:::nil21_32(0) <=> nil
gen_:::nil21_32(+(x, 1)) <=> ::(#0, gen_:::nil21_32(x))
gen_leaf:node22_32(0) <=> leaf
gen_leaf:node22_32(+(x, 1)) <=> node(nil, leaf, gen_leaf:node22_32(x))


The following defined symbols remain to be analysed:
append, APPEND, APPEND#1, FLATTEN, FLATTEN#1, flatten, flatten#1

They will be analysed ascendingly in the following order:
APPEND = APPEND#1
APPEND < FLATTEN#1
FLATTEN = FLATTEN#1
append < FLATTEN#1
flatten < FLATTEN#1
append = append#1
append < flatten#1
flatten = flatten#1

----------------------------------------

(155) RewriteLemmaProof (LOWER BOUND(ID))
Proved the following rewrite lemma:
flatten#1(gen_leaf:node22_32(n699295_32)) -> gen_:::nil21_32(0), rt in Omega(0)

Induction Base:
flatten#1(gen_leaf:node22_32(0)) ->_R^Omega(0)
nil

Induction Step:
flatten#1(gen_leaf:node22_32(+(n699295_32, 1))) ->_R^Omega(0)
append(nil, append(flatten(leaf), flatten(gen_leaf:node22_32(n699295_32)))) ->_R^Omega(0)
append(nil, append(flatten#1(leaf), flatten(gen_leaf:node22_32(n699295_32)))) ->_R^Omega(0)
append(nil, append(nil, flatten(gen_leaf:node22_32(n699295_32)))) ->_R^Omega(0)
append(nil, append(nil, flatten#1(gen_leaf:node22_32(n699295_32)))) ->_IH
append(nil, append(nil, gen_:::nil21_32(0))) ->_R^Omega(0)
append(nil, append#1(nil, gen_:::nil21_32(0))) ->_L^Omega(0)
append(nil, gen_:::nil21_32(+(0, 0))) ->_R^Omega(0)
append#1(nil, gen_:::nil21_32(0)) ->_L^Omega(0)
gen_:::nil21_32(+(0, 0))

We have rt in Omega(1) and sz in O(n). Thus, we have irc_R in Omega(n^0).
----------------------------------------

(156)
Obligation:
Innermost TRS:
Rules:
#LESS(z0, z1) -> c15(#CKLT(#compare(z0, z1)), #COMPARE(z0, z1))
APPEND(z0, z1) -> c16(APPEND#1(z0, z1))
APPEND#1(::(z0, z1), z2) -> c17(APPEND(z1, z2))
APPEND#1(nil, z0) -> c18
FLATTEN(z0) -> c19(FLATTEN#1(z0))
FLATTEN#1(leaf) -> c20
FLATTEN#1(node(z0, z1, z2)) -> c21(APPEND(z0, append(flatten(z1), flatten(z2))), APPEND(flatten(z1), flatten(z2)), FLATTEN(z1))
FLATTEN#1(node(z0, z1, z2)) -> c22(APPEND(z0, append(flatten(z1), flatten(z2))), APPEND(flatten(z1), flatten(z2)), FLATTEN(z2))
FLATTENSORT(z0) -> c23(INSERTIONSORT(flatten(z0)), FLATTEN(z0))
INSERT(z0, z1) -> c24(INSERT#1(z1, z0))
INSERT#1(::(z0, z1), z2) -> c25(INSERT#2(#less(z0, z2), z2, z0, z1), #LESS(z0, z2))
INSERT#1(nil, z0) -> c26
INSERT#2(#false, z0, z1, z2) -> c27
INSERT#2(#true, z0, z1, z2) -> c28(INSERT(z0, z2))
INSERTIONSORT(z0) -> c29(INSERTIONSORT#1(z0))
INSERTIONSORT#1(::(z0, z1)) -> c30(INSERT(z0, insertionsort(z1)), INSERTIONSORT(z1))
INSERTIONSORT#1(nil) -> c31
#CKLT(#EQ) -> c
#CKLT(#GT) -> c1
#CKLT(#LT) -> c2
#COMPARE(#0, #0) -> c3
#COMPARE(#0, #neg(z0)) -> c4
#COMPARE(#0, #pos(z0)) -> c5
#COMPARE(#0, #s(z0)) -> c6
#COMPARE(#neg(z0), #0) -> c7
#COMPARE(#neg(z0), #neg(z1)) -> c8(#COMPARE(z1, z0))
#COMPARE(#neg(z0), #pos(z1)) -> c9
#COMPARE(#pos(z0), #0) -> c10
#COMPARE(#pos(z0), #neg(z1)) -> c11
#COMPARE(#pos(z0), #pos(z1)) -> c12(#COMPARE(z0, z1))
#COMPARE(#s(z0), #0) -> c13
#COMPARE(#s(z0), #s(z1)) -> c14(#COMPARE(z0, z1))
#cklt(#EQ) -> #false
#cklt(#GT) -> #false
#cklt(#LT) -> #true
#compare(#0, #0) -> #EQ
#compare(#0, #neg(z0)) -> #GT
#compare(#0, #pos(z0)) -> #LT
#compare(#0, #s(z0)) -> #LT
#compare(#neg(z0), #0) -> #LT
#compare(#neg(z0), #neg(z1)) -> #compare(z1, z0)
#compare(#neg(z0), #pos(z1)) -> #LT
#compare(#pos(z0), #0) -> #GT
#compare(#pos(z0), #neg(z1)) -> #GT
#compare(#pos(z0), #pos(z1)) -> #compare(z0, z1)
#compare(#s(z0), #0) -> #GT
#compare(#s(z0), #s(z1)) -> #compare(z0, z1)
#less(z0, z1) -> #cklt(#compare(z0, z1))
append(z0, z1) -> append#1(z0, z1)
append#1(::(z0, z1), z2) -> ::(z0, append(z1, z2))
append#1(nil, z0) -> z0
flatten(z0) -> flatten#1(z0)
flatten#1(leaf) -> nil
flatten#1(node(z0, z1, z2)) -> append(z0, append(flatten(z1), flatten(z2)))
flattensort(z0) -> insertionsort(flatten(z0))
insert(z0, z1) -> insert#1(z1, z0)
insert#1(::(z0, z1), z2) -> insert#2(#less(z0, z2), z2, z0, z1)
insert#1(nil, z0) -> ::(z0, nil)
insert#2(#false, z0, z1, z2) -> ::(z0, ::(z1, z2))
insert#2(#true, z0, z1, z2) -> ::(z1, insert(z0, z2))
insertionsort(z0) -> insertionsort#1(z0)
insertionsort#1(::(z0, z1)) -> insert(z0, insertionsort(z1))
insertionsort#1(nil) -> nil

Types:
#LESS :: #0:#neg:#pos:#s -> #0:#neg:#pos:#s -> c15
c15 :: c:c1:c2 -> c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c14 -> c15
#CKLT :: #EQ:#GT:#LT -> c:c1:c2
#compare :: #0:#neg:#pos:#s -> #0:#neg:#pos:#s -> #EQ:#GT:#LT
#COMPARE :: #0:#neg:#pos:#s -> #0:#neg:#pos:#s -> c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c14
APPEND :: :::nil -> :::nil -> c16
c16 :: c17:c18 -> c16
APPEND#1 :: :::nil -> :::nil -> c17:c18
:: :: #0:#neg:#pos:#s -> :::nil -> :::nil
c17 :: c16 -> c17:c18
nil :: :::nil
c18 :: c17:c18
FLATTEN :: leaf:node -> c19
c19 :: c20:c21:c22 -> c19
FLATTEN#1 :: leaf:node -> c20:c21:c22
leaf :: leaf:node
c20 :: c20:c21:c22
node :: :::nil -> leaf:node -> leaf:node -> leaf:node
c21 :: c16 -> c16 -> c19 -> c20:c21:c22
append :: :::nil -> :::nil -> :::nil
flatten :: leaf:node -> :::nil
c22 :: c16 -> c16 -> c19 -> c20:c21:c22
FLATTENSORT :: leaf:node -> c23
c23 :: c29 -> c19 -> c23
INSERTIONSORT :: :::nil -> c29
INSERT :: #0:#neg:#pos:#s -> :::nil -> c24
c24 :: c25:c26 -> c24
INSERT#1 :: :::nil -> #0:#neg:#pos:#s -> c25:c26
c25 :: c27:c28 -> c15 -> c25:c26
INSERT#2 :: #false:#true -> #0:#neg:#pos:#s -> #0:#neg:#pos:#s -> :::nil -> c27:c28
#less :: #0:#neg:#pos:#s -> #0:#neg:#pos:#s -> #false:#true
c26 :: c25:c26
#false :: #false:#true
c27 :: c27:c28
#true :: #false:#true
c28 :: c24 -> c27:c28
c29 :: c30:c31 -> c29
INSERTIONSORT#1 :: :::nil -> c30:c31
c30 :: c24 -> c29 -> c30:c31
insertionsort :: :::nil -> :::nil
c31 :: c30:c31
#EQ :: #EQ:#GT:#LT
c :: c:c1:c2
#GT :: #EQ:#GT:#LT
c1 :: c:c1:c2
#LT :: #EQ:#GT:#LT
c2 :: c:c1:c2
#0 :: #0:#neg:#pos:#s
c3 :: c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c14
#neg :: #0:#neg:#pos:#s -> #0:#neg:#pos:#s
c4 :: c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c14
#pos :: #0:#neg:#pos:#s -> #0:#neg:#pos:#s
c5 :: c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c14
#s :: #0:#neg:#pos:#s -> #0:#neg:#pos:#s
c6 :: c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c14
c7 :: c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c14
c8 :: c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c14 -> c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c14
c9 :: c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c14
c10 :: c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c14
c11 :: c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c14
c12 :: c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c14 -> c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c14
c13 :: c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c14
c14 :: c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c14 -> c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c14
#cklt :: #EQ:#GT:#LT -> #false:#true
append#1 :: :::nil -> :::nil -> :::nil
flatten#1 :: leaf:node -> :::nil
flattensort :: leaf:node -> :::nil
insert :: #0:#neg:#pos:#s -> :::nil -> :::nil
insert#1 :: :::nil -> #0:#neg:#pos:#s -> :::nil
insert#2 :: #false:#true -> #0:#neg:#pos:#s -> #0:#neg:#pos:#s -> :::nil -> :::nil
insertionsort#1 :: :::nil -> :::nil
hole_c151_32 :: c15
hole_#0:#neg:#pos:#s2_32 :: #0:#neg:#pos:#s
hole_c:c1:c23_32 :: c:c1:c2
hole_c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c144_32 :: c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c14
hole_#EQ:#GT:#LT5_32 :: #EQ:#GT:#LT
hole_c166_32 :: c16
hole_:::nil7_32 :: :::nil
hole_c17:c188_32 :: c17:c18
hole_c199_32 :: c19
hole_leaf:node10_32 :: leaf:node
hole_c20:c21:c2211_32 :: c20:c21:c22
hole_c2312_32 :: c23
hole_c2913_32 :: c29
hole_c2414_32 :: c24
hole_c25:c2615_32 :: c25:c26
hole_c27:c2816_32 :: c27:c28
hole_#false:#true17_32 :: #false:#true
hole_c30:c3118_32 :: c30:c31
gen_#0:#neg:#pos:#s19_32 :: Nat -> #0:#neg:#pos:#s
gen_c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c1420_32 :: Nat -> c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c14
gen_:::nil21_32 :: Nat -> :::nil
gen_leaf:node22_32 :: Nat -> leaf:node


Lemmas:
#compare(gen_#0:#neg:#pos:#s19_32(n24_32), gen_#0:#neg:#pos:#s19_32(n24_32)) -> #EQ, rt in Omega(0)
#COMPARE(gen_#0:#neg:#pos:#s19_32(n318895_32), gen_#0:#neg:#pos:#s19_32(n318895_32)) -> gen_c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c1420_32(n318895_32), rt in Omega(0)
insertionsort#1(gen_:::nil21_32(n653302_32)) -> *23_32, rt in Omega(0)
insertionsort(gen_:::nil21_32(n643249_32)) -> *23_32, rt in Omega(0)
append#1(gen_:::nil21_32(n696814_32), gen_:::nil21_32(b)) -> gen_:::nil21_32(+(n696814_32, b)), rt in Omega(0)
flatten#1(gen_leaf:node22_32(n699295_32)) -> gen_:::nil21_32(0), rt in Omega(0)


Generator Equations:
gen_#0:#neg:#pos:#s19_32(0) <=> #0
gen_#0:#neg:#pos:#s19_32(+(x, 1)) <=> #neg(gen_#0:#neg:#pos:#s19_32(x))
gen_c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c1420_32(0) <=> c3
gen_c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c1420_32(+(x, 1)) <=> c8(gen_c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c1420_32(x))
gen_:::nil21_32(0) <=> nil
gen_:::nil21_32(+(x, 1)) <=> ::(#0, gen_:::nil21_32(x))
gen_leaf:node22_32(0) <=> leaf
gen_leaf:node22_32(+(x, 1)) <=> node(nil, leaf, gen_leaf:node22_32(x))


The following defined symbols remain to be analysed:
flatten, APPEND, APPEND#1, FLATTEN, FLATTEN#1

They will be analysed ascendingly in the following order:
APPEND = APPEND#1
APPEND < FLATTEN#1
FLATTEN = FLATTEN#1
flatten < FLATTEN#1
flatten = flatten#1

----------------------------------------

(157) RewriteLemmaProof (LOWER BOUND(ID))
Proved the following rewrite lemma:
APPEND#1(gen_:::nil21_32(+(1, n702424_32)), gen_:::nil21_32(b)) -> *23_32, rt in Omega(n702424_32)

Induction Base:
APPEND#1(gen_:::nil21_32(+(1, 0)), gen_:::nil21_32(b))

Induction Step:
APPEND#1(gen_:::nil21_32(+(1, +(n702424_32, 1))), gen_:::nil21_32(b)) ->_R^Omega(1)
c17(APPEND(gen_:::nil21_32(+(1, n702424_32)), gen_:::nil21_32(b))) ->_R^Omega(1)
c17(c16(APPEND#1(gen_:::nil21_32(+(1, n702424_32)), gen_:::nil21_32(b)))) ->_IH
c17(c16(*23_32))

We have rt in Omega(n^1) and sz in O(n). Thus, we have irc_R in Omega(n).
----------------------------------------

(158)
Complex Obligation (BEST)

----------------------------------------

(159)
Obligation:
Proved the lower bound n^1 for the following obligation:

Innermost TRS:
Rules:
#LESS(z0, z1) -> c15(#CKLT(#compare(z0, z1)), #COMPARE(z0, z1))
APPEND(z0, z1) -> c16(APPEND#1(z0, z1))
APPEND#1(::(z0, z1), z2) -> c17(APPEND(z1, z2))
APPEND#1(nil, z0) -> c18
FLATTEN(z0) -> c19(FLATTEN#1(z0))
FLATTEN#1(leaf) -> c20
FLATTEN#1(node(z0, z1, z2)) -> c21(APPEND(z0, append(flatten(z1), flatten(z2))), APPEND(flatten(z1), flatten(z2)), FLATTEN(z1))
FLATTEN#1(node(z0, z1, z2)) -> c22(APPEND(z0, append(flatten(z1), flatten(z2))), APPEND(flatten(z1), flatten(z2)), FLATTEN(z2))
FLATTENSORT(z0) -> c23(INSERTIONSORT(flatten(z0)), FLATTEN(z0))
INSERT(z0, z1) -> c24(INSERT#1(z1, z0))
INSERT#1(::(z0, z1), z2) -> c25(INSERT#2(#less(z0, z2), z2, z0, z1), #LESS(z0, z2))
INSERT#1(nil, z0) -> c26
INSERT#2(#false, z0, z1, z2) -> c27
INSERT#2(#true, z0, z1, z2) -> c28(INSERT(z0, z2))
INSERTIONSORT(z0) -> c29(INSERTIONSORT#1(z0))
INSERTIONSORT#1(::(z0, z1)) -> c30(INSERT(z0, insertionsort(z1)), INSERTIONSORT(z1))
INSERTIONSORT#1(nil) -> c31
#CKLT(#EQ) -> c
#CKLT(#GT) -> c1
#CKLT(#LT) -> c2
#COMPARE(#0, #0) -> c3
#COMPARE(#0, #neg(z0)) -> c4
#COMPARE(#0, #pos(z0)) -> c5
#COMPARE(#0, #s(z0)) -> c6
#COMPARE(#neg(z0), #0) -> c7
#COMPARE(#neg(z0), #neg(z1)) -> c8(#COMPARE(z1, z0))
#COMPARE(#neg(z0), #pos(z1)) -> c9
#COMPARE(#pos(z0), #0) -> c10
#COMPARE(#pos(z0), #neg(z1)) -> c11
#COMPARE(#pos(z0), #pos(z1)) -> c12(#COMPARE(z0, z1))
#COMPARE(#s(z0), #0) -> c13
#COMPARE(#s(z0), #s(z1)) -> c14(#COMPARE(z0, z1))
#cklt(#EQ) -> #false
#cklt(#GT) -> #false
#cklt(#LT) -> #true
#compare(#0, #0) -> #EQ
#compare(#0, #neg(z0)) -> #GT
#compare(#0, #pos(z0)) -> #LT
#compare(#0, #s(z0)) -> #LT
#compare(#neg(z0), #0) -> #LT
#compare(#neg(z0), #neg(z1)) -> #compare(z1, z0)
#compare(#neg(z0), #pos(z1)) -> #LT
#compare(#pos(z0), #0) -> #GT
#compare(#pos(z0), #neg(z1)) -> #GT
#compare(#pos(z0), #pos(z1)) -> #compare(z0, z1)
#compare(#s(z0), #0) -> #GT
#compare(#s(z0), #s(z1)) -> #compare(z0, z1)
#less(z0, z1) -> #cklt(#compare(z0, z1))
append(z0, z1) -> append#1(z0, z1)
append#1(::(z0, z1), z2) -> ::(z0, append(z1, z2))
append#1(nil, z0) -> z0
flatten(z0) -> flatten#1(z0)
flatten#1(leaf) -> nil
flatten#1(node(z0, z1, z2)) -> append(z0, append(flatten(z1), flatten(z2)))
flattensort(z0) -> insertionsort(flatten(z0))
insert(z0, z1) -> insert#1(z1, z0)
insert#1(::(z0, z1), z2) -> insert#2(#less(z0, z2), z2, z0, z1)
insert#1(nil, z0) -> ::(z0, nil)
insert#2(#false, z0, z1, z2) -> ::(z0, ::(z1, z2))
insert#2(#true, z0, z1, z2) -> ::(z1, insert(z0, z2))
insertionsort(z0) -> insertionsort#1(z0)
insertionsort#1(::(z0, z1)) -> insert(z0, insertionsort(z1))
insertionsort#1(nil) -> nil

Types:
#LESS :: #0:#neg:#pos:#s -> #0:#neg:#pos:#s -> c15
c15 :: c:c1:c2 -> c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c14 -> c15
#CKLT :: #EQ:#GT:#LT -> c:c1:c2
#compare :: #0:#neg:#pos:#s -> #0:#neg:#pos:#s -> #EQ:#GT:#LT
#COMPARE :: #0:#neg:#pos:#s -> #0:#neg:#pos:#s -> c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c14
APPEND :: :::nil -> :::nil -> c16
c16 :: c17:c18 -> c16
APPEND#1 :: :::nil -> :::nil -> c17:c18
:: :: #0:#neg:#pos:#s -> :::nil -> :::nil
c17 :: c16 -> c17:c18
nil :: :::nil
c18 :: c17:c18
FLATTEN :: leaf:node -> c19
c19 :: c20:c21:c22 -> c19
FLATTEN#1 :: leaf:node -> c20:c21:c22
leaf :: leaf:node
c20 :: c20:c21:c22
node :: :::nil -> leaf:node -> leaf:node -> leaf:node
c21 :: c16 -> c16 -> c19 -> c20:c21:c22
append :: :::nil -> :::nil -> :::nil
flatten :: leaf:node -> :::nil
c22 :: c16 -> c16 -> c19 -> c20:c21:c22
FLATTENSORT :: leaf:node -> c23
c23 :: c29 -> c19 -> c23
INSERTIONSORT :: :::nil -> c29
INSERT :: #0:#neg:#pos:#s -> :::nil -> c24
c24 :: c25:c26 -> c24
INSERT#1 :: :::nil -> #0:#neg:#pos:#s -> c25:c26
c25 :: c27:c28 -> c15 -> c25:c26
INSERT#2 :: #false:#true -> #0:#neg:#pos:#s -> #0:#neg:#pos:#s -> :::nil -> c27:c28
#less :: #0:#neg:#pos:#s -> #0:#neg:#pos:#s -> #false:#true
c26 :: c25:c26
#false :: #false:#true
c27 :: c27:c28
#true :: #false:#true
c28 :: c24 -> c27:c28
c29 :: c30:c31 -> c29
INSERTIONSORT#1 :: :::nil -> c30:c31
c30 :: c24 -> c29 -> c30:c31
insertionsort :: :::nil -> :::nil
c31 :: c30:c31
#EQ :: #EQ:#GT:#LT
c :: c:c1:c2
#GT :: #EQ:#GT:#LT
c1 :: c:c1:c2
#LT :: #EQ:#GT:#LT
c2 :: c:c1:c2
#0 :: #0:#neg:#pos:#s
c3 :: c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c14
#neg :: #0:#neg:#pos:#s -> #0:#neg:#pos:#s
c4 :: c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c14
#pos :: #0:#neg:#pos:#s -> #0:#neg:#pos:#s
c5 :: c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c14
#s :: #0:#neg:#pos:#s -> #0:#neg:#pos:#s
c6 :: c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c14
c7 :: c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c14
c8 :: c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c14 -> c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c14
c9 :: c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c14
c10 :: c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c14
c11 :: c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c14
c12 :: c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c14 -> c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c14
c13 :: c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c14
c14 :: c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c14 -> c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c14
#cklt :: #EQ:#GT:#LT -> #false:#true
append#1 :: :::nil -> :::nil -> :::nil
flatten#1 :: leaf:node -> :::nil
flattensort :: leaf:node -> :::nil
insert :: #0:#neg:#pos:#s -> :::nil -> :::nil
insert#1 :: :::nil -> #0:#neg:#pos:#s -> :::nil
insert#2 :: #false:#true -> #0:#neg:#pos:#s -> #0:#neg:#pos:#s -> :::nil -> :::nil
insertionsort#1 :: :::nil -> :::nil
hole_c151_32 :: c15
hole_#0:#neg:#pos:#s2_32 :: #0:#neg:#pos:#s
hole_c:c1:c23_32 :: c:c1:c2
hole_c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c144_32 :: c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c14
hole_#EQ:#GT:#LT5_32 :: #EQ:#GT:#LT
hole_c166_32 :: c16
hole_:::nil7_32 :: :::nil
hole_c17:c188_32 :: c17:c18
hole_c199_32 :: c19
hole_leaf:node10_32 :: leaf:node
hole_c20:c21:c2211_32 :: c20:c21:c22
hole_c2312_32 :: c23
hole_c2913_32 :: c29
hole_c2414_32 :: c24
hole_c25:c2615_32 :: c25:c26
hole_c27:c2816_32 :: c27:c28
hole_#false:#true17_32 :: #false:#true
hole_c30:c3118_32 :: c30:c31
gen_#0:#neg:#pos:#s19_32 :: Nat -> #0:#neg:#pos:#s
gen_c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c1420_32 :: Nat -> c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c14
gen_:::nil21_32 :: Nat -> :::nil
gen_leaf:node22_32 :: Nat -> leaf:node


Lemmas:
#compare(gen_#0:#neg:#pos:#s19_32(n24_32), gen_#0:#neg:#pos:#s19_32(n24_32)) -> #EQ, rt in Omega(0)
#COMPARE(gen_#0:#neg:#pos:#s19_32(n318895_32), gen_#0:#neg:#pos:#s19_32(n318895_32)) -> gen_c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c1420_32(n318895_32), rt in Omega(0)
insertionsort#1(gen_:::nil21_32(n653302_32)) -> *23_32, rt in Omega(0)
insertionsort(gen_:::nil21_32(n643249_32)) -> *23_32, rt in Omega(0)
append#1(gen_:::nil21_32(n696814_32), gen_:::nil21_32(b)) -> gen_:::nil21_32(+(n696814_32, b)), rt in Omega(0)
flatten#1(gen_leaf:node22_32(n699295_32)) -> gen_:::nil21_32(0), rt in Omega(0)


Generator Equations:
gen_#0:#neg:#pos:#s19_32(0) <=> #0
gen_#0:#neg:#pos:#s19_32(+(x, 1)) <=> #neg(gen_#0:#neg:#pos:#s19_32(x))
gen_c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c1420_32(0) <=> c3
gen_c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c1420_32(+(x, 1)) <=> c8(gen_c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c1420_32(x))
gen_:::nil21_32(0) <=> nil
gen_:::nil21_32(+(x, 1)) <=> ::(#0, gen_:::nil21_32(x))
gen_leaf:node22_32(0) <=> leaf
gen_leaf:node22_32(+(x, 1)) <=> node(nil, leaf, gen_leaf:node22_32(x))


The following defined symbols remain to be analysed:
APPEND#1, APPEND, FLATTEN, FLATTEN#1

They will be analysed ascendingly in the following order:
APPEND = APPEND#1
APPEND < FLATTEN#1
FLATTEN = FLATTEN#1

----------------------------------------

(160) LowerBoundPropagationProof (FINISHED)
Propagated lower bound.
----------------------------------------

(161)
BOUNDS(n^1, INF)

----------------------------------------

(162)
Obligation:
Innermost TRS:
Rules:
#LESS(z0, z1) -> c15(#CKLT(#compare(z0, z1)), #COMPARE(z0, z1))
APPEND(z0, z1) -> c16(APPEND#1(z0, z1))
APPEND#1(::(z0, z1), z2) -> c17(APPEND(z1, z2))
APPEND#1(nil, z0) -> c18
FLATTEN(z0) -> c19(FLATTEN#1(z0))
FLATTEN#1(leaf) -> c20
FLATTEN#1(node(z0, z1, z2)) -> c21(APPEND(z0, append(flatten(z1), flatten(z2))), APPEND(flatten(z1), flatten(z2)), FLATTEN(z1))
FLATTEN#1(node(z0, z1, z2)) -> c22(APPEND(z0, append(flatten(z1), flatten(z2))), APPEND(flatten(z1), flatten(z2)), FLATTEN(z2))
FLATTENSORT(z0) -> c23(INSERTIONSORT(flatten(z0)), FLATTEN(z0))
INSERT(z0, z1) -> c24(INSERT#1(z1, z0))
INSERT#1(::(z0, z1), z2) -> c25(INSERT#2(#less(z0, z2), z2, z0, z1), #LESS(z0, z2))
INSERT#1(nil, z0) -> c26
INSERT#2(#false, z0, z1, z2) -> c27
INSERT#2(#true, z0, z1, z2) -> c28(INSERT(z0, z2))
INSERTIONSORT(z0) -> c29(INSERTIONSORT#1(z0))
INSERTIONSORT#1(::(z0, z1)) -> c30(INSERT(z0, insertionsort(z1)), INSERTIONSORT(z1))
INSERTIONSORT#1(nil) -> c31
#CKLT(#EQ) -> c
#CKLT(#GT) -> c1
#CKLT(#LT) -> c2
#COMPARE(#0, #0) -> c3
#COMPARE(#0, #neg(z0)) -> c4
#COMPARE(#0, #pos(z0)) -> c5
#COMPARE(#0, #s(z0)) -> c6
#COMPARE(#neg(z0), #0) -> c7
#COMPARE(#neg(z0), #neg(z1)) -> c8(#COMPARE(z1, z0))
#COMPARE(#neg(z0), #pos(z1)) -> c9
#COMPARE(#pos(z0), #0) -> c10
#COMPARE(#pos(z0), #neg(z1)) -> c11
#COMPARE(#pos(z0), #pos(z1)) -> c12(#COMPARE(z0, z1))
#COMPARE(#s(z0), #0) -> c13
#COMPARE(#s(z0), #s(z1)) -> c14(#COMPARE(z0, z1))
#cklt(#EQ) -> #false
#cklt(#GT) -> #false
#cklt(#LT) -> #true
#compare(#0, #0) -> #EQ
#compare(#0, #neg(z0)) -> #GT
#compare(#0, #pos(z0)) -> #LT
#compare(#0, #s(z0)) -> #LT
#compare(#neg(z0), #0) -> #LT
#compare(#neg(z0), #neg(z1)) -> #compare(z1, z0)
#compare(#neg(z0), #pos(z1)) -> #LT
#compare(#pos(z0), #0) -> #GT
#compare(#pos(z0), #neg(z1)) -> #GT
#compare(#pos(z0), #pos(z1)) -> #compare(z0, z1)
#compare(#s(z0), #0) -> #GT
#compare(#s(z0), #s(z1)) -> #compare(z0, z1)
#less(z0, z1) -> #cklt(#compare(z0, z1))
append(z0, z1) -> append#1(z0, z1)
append#1(::(z0, z1), z2) -> ::(z0, append(z1, z2))
append#1(nil, z0) -> z0
flatten(z0) -> flatten#1(z0)
flatten#1(leaf) -> nil
flatten#1(node(z0, z1, z2)) -> append(z0, append(flatten(z1), flatten(z2)))
flattensort(z0) -> insertionsort(flatten(z0))
insert(z0, z1) -> insert#1(z1, z0)
insert#1(::(z0, z1), z2) -> insert#2(#less(z0, z2), z2, z0, z1)
insert#1(nil, z0) -> ::(z0, nil)
insert#2(#false, z0, z1, z2) -> ::(z0, ::(z1, z2))
insert#2(#true, z0, z1, z2) -> ::(z1, insert(z0, z2))
insertionsort(z0) -> insertionsort#1(z0)
insertionsort#1(::(z0, z1)) -> insert(z0, insertionsort(z1))
insertionsort#1(nil) -> nil

Types:
#LESS :: #0:#neg:#pos:#s -> #0:#neg:#pos:#s -> c15
c15 :: c:c1:c2 -> c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c14 -> c15
#CKLT :: #EQ:#GT:#LT -> c:c1:c2
#compare :: #0:#neg:#pos:#s -> #0:#neg:#pos:#s -> #EQ:#GT:#LT
#COMPARE :: #0:#neg:#pos:#s -> #0:#neg:#pos:#s -> c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c14
APPEND :: :::nil -> :::nil -> c16
c16 :: c17:c18 -> c16
APPEND#1 :: :::nil -> :::nil -> c17:c18
:: :: #0:#neg:#pos:#s -> :::nil -> :::nil
c17 :: c16 -> c17:c18
nil :: :::nil
c18 :: c17:c18
FLATTEN :: leaf:node -> c19
c19 :: c20:c21:c22 -> c19
FLATTEN#1 :: leaf:node -> c20:c21:c22
leaf :: leaf:node
c20 :: c20:c21:c22
node :: :::nil -> leaf:node -> leaf:node -> leaf:node
c21 :: c16 -> c16 -> c19 -> c20:c21:c22
append :: :::nil -> :::nil -> :::nil
flatten :: leaf:node -> :::nil
c22 :: c16 -> c16 -> c19 -> c20:c21:c22
FLATTENSORT :: leaf:node -> c23
c23 :: c29 -> c19 -> c23
INSERTIONSORT :: :::nil -> c29
INSERT :: #0:#neg:#pos:#s -> :::nil -> c24
c24 :: c25:c26 -> c24
INSERT#1 :: :::nil -> #0:#neg:#pos:#s -> c25:c26
c25 :: c27:c28 -> c15 -> c25:c26
INSERT#2 :: #false:#true -> #0:#neg:#pos:#s -> #0:#neg:#pos:#s -> :::nil -> c27:c28
#less :: #0:#neg:#pos:#s -> #0:#neg:#pos:#s -> #false:#true
c26 :: c25:c26
#false :: #false:#true
c27 :: c27:c28
#true :: #false:#true
c28 :: c24 -> c27:c28
c29 :: c30:c31 -> c29
INSERTIONSORT#1 :: :::nil -> c30:c31
c30 :: c24 -> c29 -> c30:c31
insertionsort :: :::nil -> :::nil
c31 :: c30:c31
#EQ :: #EQ:#GT:#LT
c :: c:c1:c2
#GT :: #EQ:#GT:#LT
c1 :: c:c1:c2
#LT :: #EQ:#GT:#LT
c2 :: c:c1:c2
#0 :: #0:#neg:#pos:#s
c3 :: c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c14
#neg :: #0:#neg:#pos:#s -> #0:#neg:#pos:#s
c4 :: c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c14
#pos :: #0:#neg:#pos:#s -> #0:#neg:#pos:#s
c5 :: c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c14
#s :: #0:#neg:#pos:#s -> #0:#neg:#pos:#s
c6 :: c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c14
c7 :: c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c14
c8 :: c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c14 -> c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c14
c9 :: c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c14
c10 :: c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c14
c11 :: c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c14
c12 :: c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c14 -> c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c14
c13 :: c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c14
c14 :: c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c14 -> c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c14
#cklt :: #EQ:#GT:#LT -> #false:#true
append#1 :: :::nil -> :::nil -> :::nil
flatten#1 :: leaf:node -> :::nil
flattensort :: leaf:node -> :::nil
insert :: #0:#neg:#pos:#s -> :::nil -> :::nil
insert#1 :: :::nil -> #0:#neg:#pos:#s -> :::nil
insert#2 :: #false:#true -> #0:#neg:#pos:#s -> #0:#neg:#pos:#s -> :::nil -> :::nil
insertionsort#1 :: :::nil -> :::nil
hole_c151_32 :: c15
hole_#0:#neg:#pos:#s2_32 :: #0:#neg:#pos:#s
hole_c:c1:c23_32 :: c:c1:c2
hole_c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c144_32 :: c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c14
hole_#EQ:#GT:#LT5_32 :: #EQ:#GT:#LT
hole_c166_32 :: c16
hole_:::nil7_32 :: :::nil
hole_c17:c188_32 :: c17:c18
hole_c199_32 :: c19
hole_leaf:node10_32 :: leaf:node
hole_c20:c21:c2211_32 :: c20:c21:c22
hole_c2312_32 :: c23
hole_c2913_32 :: c29
hole_c2414_32 :: c24
hole_c25:c2615_32 :: c25:c26
hole_c27:c2816_32 :: c27:c28
hole_#false:#true17_32 :: #false:#true
hole_c30:c3118_32 :: c30:c31
gen_#0:#neg:#pos:#s19_32 :: Nat -> #0:#neg:#pos:#s
gen_c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c1420_32 :: Nat -> c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c14
gen_:::nil21_32 :: Nat -> :::nil
gen_leaf:node22_32 :: Nat -> leaf:node


Lemmas:
#compare(gen_#0:#neg:#pos:#s19_32(n24_32), gen_#0:#neg:#pos:#s19_32(n24_32)) -> #EQ, rt in Omega(0)
#COMPARE(gen_#0:#neg:#pos:#s19_32(n318895_32), gen_#0:#neg:#pos:#s19_32(n318895_32)) -> gen_c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c1420_32(n318895_32), rt in Omega(0)
insertionsort#1(gen_:::nil21_32(n653302_32)) -> *23_32, rt in Omega(0)
insertionsort(gen_:::nil21_32(n643249_32)) -> *23_32, rt in Omega(0)
append#1(gen_:::nil21_32(n696814_32), gen_:::nil21_32(b)) -> gen_:::nil21_32(+(n696814_32, b)), rt in Omega(0)
flatten#1(gen_leaf:node22_32(n699295_32)) -> gen_:::nil21_32(0), rt in Omega(0)
APPEND#1(gen_:::nil21_32(+(1, n702424_32)), gen_:::nil21_32(b)) -> *23_32, rt in Omega(n702424_32)


Generator Equations:
gen_#0:#neg:#pos:#s19_32(0) <=> #0
gen_#0:#neg:#pos:#s19_32(+(x, 1)) <=> #neg(gen_#0:#neg:#pos:#s19_32(x))
gen_c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c1420_32(0) <=> c3
gen_c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c1420_32(+(x, 1)) <=> c8(gen_c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c1420_32(x))
gen_:::nil21_32(0) <=> nil
gen_:::nil21_32(+(x, 1)) <=> ::(#0, gen_:::nil21_32(x))
gen_leaf:node22_32(0) <=> leaf
gen_leaf:node22_32(+(x, 1)) <=> node(nil, leaf, gen_leaf:node22_32(x))


The following defined symbols remain to be analysed:
APPEND, FLATTEN, FLATTEN#1

They will be analysed ascendingly in the following order:
APPEND = APPEND#1
APPEND < FLATTEN#1
FLATTEN = FLATTEN#1

----------------------------------------

(163) RewriteLemmaProof (LOWER BOUND(ID))
Proved the following rewrite lemma:
APPEND(gen_:::nil21_32(n706215_32), gen_:::nil21_32(b)) -> *23_32, rt in Omega(n706215_32)

Induction Base:
APPEND(gen_:::nil21_32(0), gen_:::nil21_32(b))

Induction Step:
APPEND(gen_:::nil21_32(+(n706215_32, 1)), gen_:::nil21_32(b)) ->_R^Omega(1)
c16(APPEND#1(gen_:::nil21_32(+(n706215_32, 1)), gen_:::nil21_32(b))) ->_R^Omega(1)
c16(c17(APPEND(gen_:::nil21_32(n706215_32), gen_:::nil21_32(b)))) ->_IH
c16(c17(*23_32))

We have rt in Omega(n^1) and sz in O(n). Thus, we have irc_R in Omega(n).
----------------------------------------

(164)
Obligation:
Innermost TRS:
Rules:
#LESS(z0, z1) -> c15(#CKLT(#compare(z0, z1)), #COMPARE(z0, z1))
APPEND(z0, z1) -> c16(APPEND#1(z0, z1))
APPEND#1(::(z0, z1), z2) -> c17(APPEND(z1, z2))
APPEND#1(nil, z0) -> c18
FLATTEN(z0) -> c19(FLATTEN#1(z0))
FLATTEN#1(leaf) -> c20
FLATTEN#1(node(z0, z1, z2)) -> c21(APPEND(z0, append(flatten(z1), flatten(z2))), APPEND(flatten(z1), flatten(z2)), FLATTEN(z1))
FLATTEN#1(node(z0, z1, z2)) -> c22(APPEND(z0, append(flatten(z1), flatten(z2))), APPEND(flatten(z1), flatten(z2)), FLATTEN(z2))
FLATTENSORT(z0) -> c23(INSERTIONSORT(flatten(z0)), FLATTEN(z0))
INSERT(z0, z1) -> c24(INSERT#1(z1, z0))
INSERT#1(::(z0, z1), z2) -> c25(INSERT#2(#less(z0, z2), z2, z0, z1), #LESS(z0, z2))
INSERT#1(nil, z0) -> c26
INSERT#2(#false, z0, z1, z2) -> c27
INSERT#2(#true, z0, z1, z2) -> c28(INSERT(z0, z2))
INSERTIONSORT(z0) -> c29(INSERTIONSORT#1(z0))
INSERTIONSORT#1(::(z0, z1)) -> c30(INSERT(z0, insertionsort(z1)), INSERTIONSORT(z1))
INSERTIONSORT#1(nil) -> c31
#CKLT(#EQ) -> c
#CKLT(#GT) -> c1
#CKLT(#LT) -> c2
#COMPARE(#0, #0) -> c3
#COMPARE(#0, #neg(z0)) -> c4
#COMPARE(#0, #pos(z0)) -> c5
#COMPARE(#0, #s(z0)) -> c6
#COMPARE(#neg(z0), #0) -> c7
#COMPARE(#neg(z0), #neg(z1)) -> c8(#COMPARE(z1, z0))
#COMPARE(#neg(z0), #pos(z1)) -> c9
#COMPARE(#pos(z0), #0) -> c10
#COMPARE(#pos(z0), #neg(z1)) -> c11
#COMPARE(#pos(z0), #pos(z1)) -> c12(#COMPARE(z0, z1))
#COMPARE(#s(z0), #0) -> c13
#COMPARE(#s(z0), #s(z1)) -> c14(#COMPARE(z0, z1))
#cklt(#EQ) -> #false
#cklt(#GT) -> #false
#cklt(#LT) -> #true
#compare(#0, #0) -> #EQ
#compare(#0, #neg(z0)) -> #GT
#compare(#0, #pos(z0)) -> #LT
#compare(#0, #s(z0)) -> #LT
#compare(#neg(z0), #0) -> #LT
#compare(#neg(z0), #neg(z1)) -> #compare(z1, z0)
#compare(#neg(z0), #pos(z1)) -> #LT
#compare(#pos(z0), #0) -> #GT
#compare(#pos(z0), #neg(z1)) -> #GT
#compare(#pos(z0), #pos(z1)) -> #compare(z0, z1)
#compare(#s(z0), #0) -> #GT
#compare(#s(z0), #s(z1)) -> #compare(z0, z1)
#less(z0, z1) -> #cklt(#compare(z0, z1))
append(z0, z1) -> append#1(z0, z1)
append#1(::(z0, z1), z2) -> ::(z0, append(z1, z2))
append#1(nil, z0) -> z0
flatten(z0) -> flatten#1(z0)
flatten#1(leaf) -> nil
flatten#1(node(z0, z1, z2)) -> append(z0, append(flatten(z1), flatten(z2)))
flattensort(z0) -> insertionsort(flatten(z0))
insert(z0, z1) -> insert#1(z1, z0)
insert#1(::(z0, z1), z2) -> insert#2(#less(z0, z2), z2, z0, z1)
insert#1(nil, z0) -> ::(z0, nil)
insert#2(#false, z0, z1, z2) -> ::(z0, ::(z1, z2))
insert#2(#true, z0, z1, z2) -> ::(z1, insert(z0, z2))
insertionsort(z0) -> insertionsort#1(z0)
insertionsort#1(::(z0, z1)) -> insert(z0, insertionsort(z1))
insertionsort#1(nil) -> nil

Types:
#LESS :: #0:#neg:#pos:#s -> #0:#neg:#pos:#s -> c15
c15 :: c:c1:c2 -> c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c14 -> c15
#CKLT :: #EQ:#GT:#LT -> c:c1:c2
#compare :: #0:#neg:#pos:#s -> #0:#neg:#pos:#s -> #EQ:#GT:#LT
#COMPARE :: #0:#neg:#pos:#s -> #0:#neg:#pos:#s -> c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c14
APPEND :: :::nil -> :::nil -> c16
c16 :: c17:c18 -> c16
APPEND#1 :: :::nil -> :::nil -> c17:c18
:: :: #0:#neg:#pos:#s -> :::nil -> :::nil
c17 :: c16 -> c17:c18
nil :: :::nil
c18 :: c17:c18
FLATTEN :: leaf:node -> c19
c19 :: c20:c21:c22 -> c19
FLATTEN#1 :: leaf:node -> c20:c21:c22
leaf :: leaf:node
c20 :: c20:c21:c22
node :: :::nil -> leaf:node -> leaf:node -> leaf:node
c21 :: c16 -> c16 -> c19 -> c20:c21:c22
append :: :::nil -> :::nil -> :::nil
flatten :: leaf:node -> :::nil
c22 :: c16 -> c16 -> c19 -> c20:c21:c22
FLATTENSORT :: leaf:node -> c23
c23 :: c29 -> c19 -> c23
INSERTIONSORT :: :::nil -> c29
INSERT :: #0:#neg:#pos:#s -> :::nil -> c24
c24 :: c25:c26 -> c24
INSERT#1 :: :::nil -> #0:#neg:#pos:#s -> c25:c26
c25 :: c27:c28 -> c15 -> c25:c26
INSERT#2 :: #false:#true -> #0:#neg:#pos:#s -> #0:#neg:#pos:#s -> :::nil -> c27:c28
#less :: #0:#neg:#pos:#s -> #0:#neg:#pos:#s -> #false:#true
c26 :: c25:c26
#false :: #false:#true
c27 :: c27:c28
#true :: #false:#true
c28 :: c24 -> c27:c28
c29 :: c30:c31 -> c29
INSERTIONSORT#1 :: :::nil -> c30:c31
c30 :: c24 -> c29 -> c30:c31
insertionsort :: :::nil -> :::nil
c31 :: c30:c31
#EQ :: #EQ:#GT:#LT
c :: c:c1:c2
#GT :: #EQ:#GT:#LT
c1 :: c:c1:c2
#LT :: #EQ:#GT:#LT
c2 :: c:c1:c2
#0 :: #0:#neg:#pos:#s
c3 :: c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c14
#neg :: #0:#neg:#pos:#s -> #0:#neg:#pos:#s
c4 :: c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c14
#pos :: #0:#neg:#pos:#s -> #0:#neg:#pos:#s
c5 :: c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c14
#s :: #0:#neg:#pos:#s -> #0:#neg:#pos:#s
c6 :: c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c14
c7 :: c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c14
c8 :: c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c14 -> c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c14
c9 :: c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c14
c10 :: c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c14
c11 :: c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c14
c12 :: c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c14 -> c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c14
c13 :: c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c14
c14 :: c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c14 -> c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c14
#cklt :: #EQ:#GT:#LT -> #false:#true
append#1 :: :::nil -> :::nil -> :::nil
flatten#1 :: leaf:node -> :::nil
flattensort :: leaf:node -> :::nil
insert :: #0:#neg:#pos:#s -> :::nil -> :::nil
insert#1 :: :::nil -> #0:#neg:#pos:#s -> :::nil
insert#2 :: #false:#true -> #0:#neg:#pos:#s -> #0:#neg:#pos:#s -> :::nil -> :::nil
insertionsort#1 :: :::nil -> :::nil
hole_c151_32 :: c15
hole_#0:#neg:#pos:#s2_32 :: #0:#neg:#pos:#s
hole_c:c1:c23_32 :: c:c1:c2
hole_c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c144_32 :: c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c14
hole_#EQ:#GT:#LT5_32 :: #EQ:#GT:#LT
hole_c166_32 :: c16
hole_:::nil7_32 :: :::nil
hole_c17:c188_32 :: c17:c18
hole_c199_32 :: c19
hole_leaf:node10_32 :: leaf:node
hole_c20:c21:c2211_32 :: c20:c21:c22
hole_c2312_32 :: c23
hole_c2913_32 :: c29
hole_c2414_32 :: c24
hole_c25:c2615_32 :: c25:c26
hole_c27:c2816_32 :: c27:c28
hole_#false:#true17_32 :: #false:#true
hole_c30:c3118_32 :: c30:c31
gen_#0:#neg:#pos:#s19_32 :: Nat -> #0:#neg:#pos:#s
gen_c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c1420_32 :: Nat -> c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c14
gen_:::nil21_32 :: Nat -> :::nil
gen_leaf:node22_32 :: Nat -> leaf:node


Lemmas:
#compare(gen_#0:#neg:#pos:#s19_32(n24_32), gen_#0:#neg:#pos:#s19_32(n24_32)) -> #EQ, rt in Omega(0)
#COMPARE(gen_#0:#neg:#pos:#s19_32(n318895_32), gen_#0:#neg:#pos:#s19_32(n318895_32)) -> gen_c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c1420_32(n318895_32), rt in Omega(0)
insertionsort#1(gen_:::nil21_32(n653302_32)) -> *23_32, rt in Omega(0)
insertionsort(gen_:::nil21_32(n643249_32)) -> *23_32, rt in Omega(0)
append#1(gen_:::nil21_32(n696814_32), gen_:::nil21_32(b)) -> gen_:::nil21_32(+(n696814_32, b)), rt in Omega(0)
flatten#1(gen_leaf:node22_32(n699295_32)) -> gen_:::nil21_32(0), rt in Omega(0)
APPEND#1(gen_:::nil21_32(+(1, n702424_32)), gen_:::nil21_32(b)) -> *23_32, rt in Omega(n702424_32)
APPEND(gen_:::nil21_32(n706215_32), gen_:::nil21_32(b)) -> *23_32, rt in Omega(n706215_32)


Generator Equations:
gen_#0:#neg:#pos:#s19_32(0) <=> #0
gen_#0:#neg:#pos:#s19_32(+(x, 1)) <=> #neg(gen_#0:#neg:#pos:#s19_32(x))
gen_c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c1420_32(0) <=> c3
gen_c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c1420_32(+(x, 1)) <=> c8(gen_c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c1420_32(x))
gen_:::nil21_32(0) <=> nil
gen_:::nil21_32(+(x, 1)) <=> ::(#0, gen_:::nil21_32(x))
gen_leaf:node22_32(0) <=> leaf
gen_leaf:node22_32(+(x, 1)) <=> node(nil, leaf, gen_leaf:node22_32(x))


The following defined symbols remain to be analysed:
APPEND#1, FLATTEN, FLATTEN#1

They will be analysed ascendingly in the following order:
APPEND = APPEND#1
APPEND < FLATTEN#1
FLATTEN = FLATTEN#1

----------------------------------------

(165) RewriteLemmaProof (LOWER BOUND(ID))
Proved the following rewrite lemma:
APPEND#1(gen_:::nil21_32(+(1, n711179_32)), gen_:::nil21_32(b)) -> *23_32, rt in Omega(n711179_32)

Induction Base:
APPEND#1(gen_:::nil21_32(+(1, 0)), gen_:::nil21_32(b))

Induction Step:
APPEND#1(gen_:::nil21_32(+(1, +(n711179_32, 1))), gen_:::nil21_32(b)) ->_R^Omega(1)
c17(APPEND(gen_:::nil21_32(+(1, n711179_32)), gen_:::nil21_32(b))) ->_R^Omega(1)
c17(c16(APPEND#1(gen_:::nil21_32(+(1, n711179_32)), gen_:::nil21_32(b)))) ->_IH
c17(c16(*23_32))

We have rt in Omega(n^1) and sz in O(n). Thus, we have irc_R in Omega(n).
----------------------------------------

(166)
Obligation:
Innermost TRS:
Rules:
#LESS(z0, z1) -> c15(#CKLT(#compare(z0, z1)), #COMPARE(z0, z1))
APPEND(z0, z1) -> c16(APPEND#1(z0, z1))
APPEND#1(::(z0, z1), z2) -> c17(APPEND(z1, z2))
APPEND#1(nil, z0) -> c18
FLATTEN(z0) -> c19(FLATTEN#1(z0))
FLATTEN#1(leaf) -> c20
FLATTEN#1(node(z0, z1, z2)) -> c21(APPEND(z0, append(flatten(z1), flatten(z2))), APPEND(flatten(z1), flatten(z2)), FLATTEN(z1))
FLATTEN#1(node(z0, z1, z2)) -> c22(APPEND(z0, append(flatten(z1), flatten(z2))), APPEND(flatten(z1), flatten(z2)), FLATTEN(z2))
FLATTENSORT(z0) -> c23(INSERTIONSORT(flatten(z0)), FLATTEN(z0))
INSERT(z0, z1) -> c24(INSERT#1(z1, z0))
INSERT#1(::(z0, z1), z2) -> c25(INSERT#2(#less(z0, z2), z2, z0, z1), #LESS(z0, z2))
INSERT#1(nil, z0) -> c26
INSERT#2(#false, z0, z1, z2) -> c27
INSERT#2(#true, z0, z1, z2) -> c28(INSERT(z0, z2))
INSERTIONSORT(z0) -> c29(INSERTIONSORT#1(z0))
INSERTIONSORT#1(::(z0, z1)) -> c30(INSERT(z0, insertionsort(z1)), INSERTIONSORT(z1))
INSERTIONSORT#1(nil) -> c31
#CKLT(#EQ) -> c
#CKLT(#GT) -> c1
#CKLT(#LT) -> c2
#COMPARE(#0, #0) -> c3
#COMPARE(#0, #neg(z0)) -> c4
#COMPARE(#0, #pos(z0)) -> c5
#COMPARE(#0, #s(z0)) -> c6
#COMPARE(#neg(z0), #0) -> c7
#COMPARE(#neg(z0), #neg(z1)) -> c8(#COMPARE(z1, z0))
#COMPARE(#neg(z0), #pos(z1)) -> c9
#COMPARE(#pos(z0), #0) -> c10
#COMPARE(#pos(z0), #neg(z1)) -> c11
#COMPARE(#pos(z0), #pos(z1)) -> c12(#COMPARE(z0, z1))
#COMPARE(#s(z0), #0) -> c13
#COMPARE(#s(z0), #s(z1)) -> c14(#COMPARE(z0, z1))
#cklt(#EQ) -> #false
#cklt(#GT) -> #false
#cklt(#LT) -> #true
#compare(#0, #0) -> #EQ
#compare(#0, #neg(z0)) -> #GT
#compare(#0, #pos(z0)) -> #LT
#compare(#0, #s(z0)) -> #LT
#compare(#neg(z0), #0) -> #LT
#compare(#neg(z0), #neg(z1)) -> #compare(z1, z0)
#compare(#neg(z0), #pos(z1)) -> #LT
#compare(#pos(z0), #0) -> #GT
#compare(#pos(z0), #neg(z1)) -> #GT
#compare(#pos(z0), #pos(z1)) -> #compare(z0, z1)
#compare(#s(z0), #0) -> #GT
#compare(#s(z0), #s(z1)) -> #compare(z0, z1)
#less(z0, z1) -> #cklt(#compare(z0, z1))
append(z0, z1) -> append#1(z0, z1)
append#1(::(z0, z1), z2) -> ::(z0, append(z1, z2))
append#1(nil, z0) -> z0
flatten(z0) -> flatten#1(z0)
flatten#1(leaf) -> nil
flatten#1(node(z0, z1, z2)) -> append(z0, append(flatten(z1), flatten(z2)))
flattensort(z0) -> insertionsort(flatten(z0))
insert(z0, z1) -> insert#1(z1, z0)
insert#1(::(z0, z1), z2) -> insert#2(#less(z0, z2), z2, z0, z1)
insert#1(nil, z0) -> ::(z0, nil)
insert#2(#false, z0, z1, z2) -> ::(z0, ::(z1, z2))
insert#2(#true, z0, z1, z2) -> ::(z1, insert(z0, z2))
insertionsort(z0) -> insertionsort#1(z0)
insertionsort#1(::(z0, z1)) -> insert(z0, insertionsort(z1))
insertionsort#1(nil) -> nil

Types:
#LESS :: #0:#neg:#pos:#s -> #0:#neg:#pos:#s -> c15
c15 :: c:c1:c2 -> c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c14 -> c15
#CKLT :: #EQ:#GT:#LT -> c:c1:c2
#compare :: #0:#neg:#pos:#s -> #0:#neg:#pos:#s -> #EQ:#GT:#LT
#COMPARE :: #0:#neg:#pos:#s -> #0:#neg:#pos:#s -> c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c14
APPEND :: :::nil -> :::nil -> c16
c16 :: c17:c18 -> c16
APPEND#1 :: :::nil -> :::nil -> c17:c18
:: :: #0:#neg:#pos:#s -> :::nil -> :::nil
c17 :: c16 -> c17:c18
nil :: :::nil
c18 :: c17:c18
FLATTEN :: leaf:node -> c19
c19 :: c20:c21:c22 -> c19
FLATTEN#1 :: leaf:node -> c20:c21:c22
leaf :: leaf:node
c20 :: c20:c21:c22
node :: :::nil -> leaf:node -> leaf:node -> leaf:node
c21 :: c16 -> c16 -> c19 -> c20:c21:c22
append :: :::nil -> :::nil -> :::nil
flatten :: leaf:node -> :::nil
c22 :: c16 -> c16 -> c19 -> c20:c21:c22
FLATTENSORT :: leaf:node -> c23
c23 :: c29 -> c19 -> c23
INSERTIONSORT :: :::nil -> c29
INSERT :: #0:#neg:#pos:#s -> :::nil -> c24
c24 :: c25:c26 -> c24
INSERT#1 :: :::nil -> #0:#neg:#pos:#s -> c25:c26
c25 :: c27:c28 -> c15 -> c25:c26
INSERT#2 :: #false:#true -> #0:#neg:#pos:#s -> #0:#neg:#pos:#s -> :::nil -> c27:c28
#less :: #0:#neg:#pos:#s -> #0:#neg:#pos:#s -> #false:#true
c26 :: c25:c26
#false :: #false:#true
c27 :: c27:c28
#true :: #false:#true
c28 :: c24 -> c27:c28
c29 :: c30:c31 -> c29
INSERTIONSORT#1 :: :::nil -> c30:c31
c30 :: c24 -> c29 -> c30:c31
insertionsort :: :::nil -> :::nil
c31 :: c30:c31
#EQ :: #EQ:#GT:#LT
c :: c:c1:c2
#GT :: #EQ:#GT:#LT
c1 :: c:c1:c2
#LT :: #EQ:#GT:#LT
c2 :: c:c1:c2
#0 :: #0:#neg:#pos:#s
c3 :: c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c14
#neg :: #0:#neg:#pos:#s -> #0:#neg:#pos:#s
c4 :: c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c14
#pos :: #0:#neg:#pos:#s -> #0:#neg:#pos:#s
c5 :: c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c14
#s :: #0:#neg:#pos:#s -> #0:#neg:#pos:#s
c6 :: c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c14
c7 :: c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c14
c8 :: c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c14 -> c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c14
c9 :: c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c14
c10 :: c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c14
c11 :: c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c14
c12 :: c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c14 -> c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c14
c13 :: c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c14
c14 :: c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c14 -> c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c14
#cklt :: #EQ:#GT:#LT -> #false:#true
append#1 :: :::nil -> :::nil -> :::nil
flatten#1 :: leaf:node -> :::nil
flattensort :: leaf:node -> :::nil
insert :: #0:#neg:#pos:#s -> :::nil -> :::nil
insert#1 :: :::nil -> #0:#neg:#pos:#s -> :::nil
insert#2 :: #false:#true -> #0:#neg:#pos:#s -> #0:#neg:#pos:#s -> :::nil -> :::nil
insertionsort#1 :: :::nil -> :::nil
hole_c151_32 :: c15
hole_#0:#neg:#pos:#s2_32 :: #0:#neg:#pos:#s
hole_c:c1:c23_32 :: c:c1:c2
hole_c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c144_32 :: c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c14
hole_#EQ:#GT:#LT5_32 :: #EQ:#GT:#LT
hole_c166_32 :: c16
hole_:::nil7_32 :: :::nil
hole_c17:c188_32 :: c17:c18
hole_c199_32 :: c19
hole_leaf:node10_32 :: leaf:node
hole_c20:c21:c2211_32 :: c20:c21:c22
hole_c2312_32 :: c23
hole_c2913_32 :: c29
hole_c2414_32 :: c24
hole_c25:c2615_32 :: c25:c26
hole_c27:c2816_32 :: c27:c28
hole_#false:#true17_32 :: #false:#true
hole_c30:c3118_32 :: c30:c31
gen_#0:#neg:#pos:#s19_32 :: Nat -> #0:#neg:#pos:#s
gen_c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c1420_32 :: Nat -> c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c14
gen_:::nil21_32 :: Nat -> :::nil
gen_leaf:node22_32 :: Nat -> leaf:node


Lemmas:
#compare(gen_#0:#neg:#pos:#s19_32(n24_32), gen_#0:#neg:#pos:#s19_32(n24_32)) -> #EQ, rt in Omega(0)
#COMPARE(gen_#0:#neg:#pos:#s19_32(n318895_32), gen_#0:#neg:#pos:#s19_32(n318895_32)) -> gen_c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c1420_32(n318895_32), rt in Omega(0)
insertionsort#1(gen_:::nil21_32(n653302_32)) -> *23_32, rt in Omega(0)
insertionsort(gen_:::nil21_32(n643249_32)) -> *23_32, rt in Omega(0)
append#1(gen_:::nil21_32(n696814_32), gen_:::nil21_32(b)) -> gen_:::nil21_32(+(n696814_32, b)), rt in Omega(0)
flatten#1(gen_leaf:node22_32(n699295_32)) -> gen_:::nil21_32(0), rt in Omega(0)
APPEND#1(gen_:::nil21_32(+(1, n711179_32)), gen_:::nil21_32(b)) -> *23_32, rt in Omega(n711179_32)
APPEND(gen_:::nil21_32(n706215_32), gen_:::nil21_32(b)) -> *23_32, rt in Omega(n706215_32)


Generator Equations:
gen_#0:#neg:#pos:#s19_32(0) <=> #0
gen_#0:#neg:#pos:#s19_32(+(x, 1)) <=> #neg(gen_#0:#neg:#pos:#s19_32(x))
gen_c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c1420_32(0) <=> c3
gen_c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c1420_32(+(x, 1)) <=> c8(gen_c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c1420_32(x))
gen_:::nil21_32(0) <=> nil
gen_:::nil21_32(+(x, 1)) <=> ::(#0, gen_:::nil21_32(x))
gen_leaf:node22_32(0) <=> leaf
gen_leaf:node22_32(+(x, 1)) <=> node(nil, leaf, gen_leaf:node22_32(x))


The following defined symbols remain to be analysed:
FLATTEN#1, FLATTEN

They will be analysed ascendingly in the following order:
FLATTEN = FLATTEN#1