KILLED
proof of input_opzmNy4ifg.trs
# AProVE Commit ID: aff8ecad908e01718a4c36e68d2e55d5e0f16e15 fuhs 20220216 unpublished


The Runtime Complexity (parallel-innermost) of the given CpxTRS could be proven to be BOUNDS(1, INF).

(0) CpxTRS
(1) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms]
(2) CpxTRS
(3) RelTrsToTrsProof [UPPER BOUND(ID), 0 ms]
(4) CpxTRS
(5) RelTrsToWeightedTrsProof [UPPER BOUND(ID), 0 ms]
(6) CpxWeightedTrs
    (7) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms]
    (8) CpxTypedWeightedTrs
    (9) CompletionProof [UPPER BOUND(ID), 0 ms]
    (10) CpxTypedWeightedCompleteTrs
        (11) NarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
        (12) CpxTypedWeightedCompleteTrs
        (13) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 19 ms]
        (14) CpxRNTS
        (15) SimplificationProof [BOTH BOUNDS(ID, ID), 0 ms]
        (16) CpxRNTS
        (17) CpxRntsAnalysisOrderProof [BOTH BOUNDS(ID, ID), 3 ms]
        (18) CpxRNTS
        (19) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
        (20) CpxRNTS
        (21) IntTrsBoundProof [UPPER BOUND(ID), 393 ms]
        (22) CpxRNTS
        (23) IntTrsBoundProof [UPPER BOUND(ID), 135 ms]
        (24) CpxRNTS
        (25) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
        (26) CpxRNTS
        (27) IntTrsBoundProof [UPPER BOUND(ID), 520 ms]
        (28) CpxRNTS
        (29) IntTrsBoundProof [UPPER BOUND(ID), 98 ms]
        (30) CpxRNTS
        (31) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
        (32) CpxRNTS
        (33) IntTrsBoundProof [UPPER BOUND(ID), 184 ms]
        (34) CpxRNTS
        (35) IntTrsBoundProof [UPPER BOUND(ID), 84 ms]
        (36) CpxRNTS
        (37) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
        (38) CpxRNTS
        (39) IntTrsBoundProof [UPPER BOUND(ID), 141 ms]
        (40) CpxRNTS
        (41) IntTrsBoundProof [UPPER BOUND(ID), 85 ms]
        (42) CpxRNTS
        (43) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
        (44) CpxRNTS
        (45) IntTrsBoundProof [UPPER BOUND(ID), 255 ms]
        (46) CpxRNTS
        (47) IntTrsBoundProof [UPPER BOUND(ID), 148 ms]
        (48) CpxRNTS
        (49) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
        (50) CpxRNTS
        (51) IntTrsBoundProof [UPPER BOUND(ID), 4261 ms]
        (52) CpxRNTS
        (53) IntTrsBoundProof [UPPER BOUND(ID), 1286 ms]
        (54) CpxRNTS
        (55) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
        (56) CpxRNTS
        (57) IntTrsBoundProof [UPPER BOUND(ID), 179 ms]
        (58) CpxRNTS
        (59) IntTrsBoundProof [UPPER BOUND(ID), 73 ms]
        (60) CpxRNTS
        (61) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
        (62) CpxRNTS
        (63) IntTrsBoundProof [UPPER BOUND(ID), 141 ms]
        (64) CpxRNTS
        (65) IntTrsBoundProof [UPPER BOUND(ID), 3 ms]
        (66) CpxRNTS
        (67) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
        (68) CpxRNTS
        (69) IntTrsBoundProof [UPPER BOUND(ID), 11.9 s]
        (70) CpxRNTS
        (71) IntTrsBoundProof [UPPER BOUND(ID), 1840 ms]
        (72) CpxRNTS
    (73) CompletionProof [UPPER BOUND(ID), 0 ms]
    (74) CpxTypedWeightedCompleteTrs
        (75) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 25 ms]
        (76) CpxRNTS
(77) CpxTrsToCdtProof [UPPER BOUND(ID), 0 ms]
(78) CdtProblem
    (79) CdtLeafRemovalProof [ComplexityIfPolyImplication, 0 ms]
    (80) CdtProblem
    (81) CdtUsableRulesProof [BOTH BOUNDS(ID, ID), 0 ms]
    (82) CdtProblem
    (83) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (84) CdtProblem
    (85) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
    (86) CdtProblem
    (87) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (88) CdtProblem
    (89) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
    (90) CdtProblem
    (91) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (92) CdtProblem
    (93) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 13 ms]
    (94) CdtProblem
    (95) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
    (96) CdtProblem
    (97) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (98) CdtProblem
    (99) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (100) CdtProblem
    (101) CdtRewritingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (102) CdtProblem
    (103) CdtInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms]
    (104) CdtProblem
    (105) CdtInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms]
    (106) CdtProblem
    (107) CdtRewritingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (108) CdtProblem
    (109) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms]
    (110) CdtProblem
    (111) CdtRewritingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (112) CdtProblem
    (113) CdtInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms]
    (114) CdtProblem
    (115) CdtRewritingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (116) CdtProblem
    (117) CdtRewritingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (118) CdtProblem
    (119) CdtRewritingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (120) CdtProblem
    (121) CdtRewritingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (122) CdtProblem
    (123) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
    (124) CdtProblem
    (125) CdtRewritingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (126) CdtProblem
    (127) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
    (128) CdtProblem
    (129) CdtRewritingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (130) CdtProblem
    (131) CdtRewritingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (132) CdtProblem
    (133) CdtRewritingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (134) CdtProblem
    (135) CdtRewritingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (136) CdtProblem
    (137) CdtRewritingProof [BOTH BOUNDS(ID, ID), 5 ms]
    (138) CdtProblem
    (139) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
    (140) CdtProblem
    (141) CdtRewritingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (142) CdtProblem
    (143) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
    (144) CdtProblem
    (145) CdtRewritingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (146) CdtProblem
    (147) CdtInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms]
    (148) CdtProblem
    (149) CdtRewritingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (150) CdtProblem
    (151) CdtInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms]
    (152) CdtProblem
    (153) CdtRewritingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (154) CdtProblem
    (155) CdtInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms]
    (156) CdtProblem
    (157) CdtRewritingProof [BOTH BOUNDS(ID, ID), 1 ms]
    (158) CdtProblem
    (159) CdtInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms]
    (160) CdtProblem
    (161) CdtRewritingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (162) CdtProblem
    (163) CdtInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms]
    (164) CdtProblem
    (165) CdtRewritingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (166) CdtProblem
    (167) CdtRewritingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (168) CdtProblem
    (169) CdtRewritingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (170) CdtProblem
    (171) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms]
    (172) CdtProblem
    (173) CdtInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms]
    (174) CdtProblem
    (175) CdtInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms]
    (176) CdtProblem
    (177) CdtRewritingProof [BOTH BOUNDS(ID, ID), 7 ms]
    (178) CdtProblem
    (179) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms]
    (180) CdtProblem
    (181) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms]
    (182) CdtProblem
    (183) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms]
    (184) CdtProblem
    (185) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
    (186) CdtProblem
    (187) CdtRewritingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (188) CdtProblem
    (189) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
    (190) CdtProblem


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

(0)
Obligation:
The Runtime Complexity (parallel-innermost) of the given CpxTRS could be proven to be BOUNDS(1, INF).


The TRS R consists of the following rules:

   divide_ys#1(x2, x1) -> Cons(take#2(x1, x2), Cons(drop#2(x1, x2), Nil))
   cond_merge_ys_zs_2(True, Cons(x7, x8), Cons(x5, x6), x4, x3, x2, x1) -> Cons(x4, merge#2(x3, Cons(x5, x6)))
   cond_merge_ys_zs_2(False, Cons(x7, x8), Cons(x5, x6), x4, x3, x2, x1) -> Cons(x2, merge#2(Cons(x7, x8), x1))
   merge#2(Nil, x2) -> x2
   merge#2(Cons(x4, x2), Nil) -> Cons(x4, x2)
   merge#2(Cons(x8, x6), Cons(x4, x2)) -> cond_merge_ys_zs_2(leq#2(x8, x4), Cons(x8, x6), Cons(x4, x2), x8, x6, x4, x2)
   dc#1(map, divisible, mergesort_zs_3, divide, const_f, Nil) -> Nil
   dc#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x229, Nil)) -> Cons(x229, Nil)
   dc#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x51, Cons(x25, x33))) -> const_f#2(Cons(x51, Cons(x25, x33)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x51, Cons(x25, x33)), S(halve#1(length#1(x33))))))
   drop#2(0, x2) -> x2
   drop#2(S(0), Nil) -> bot[1]
   drop#2(S(x10), Cons(x56, x64)) -> drop#2(x10, x64)
   take#2(0, x2) -> Nil
   take#2(S(0), Nil) -> Cons(bot[0], Nil)
   take#2(S(x22), Cons(x56, x64)) -> Cons(x56, take#2(x22, x64))
   halve#1(0) -> 0
   halve#1(S(0)) -> S(0)
   halve#1(S(S(x14))) -> S(halve#1(x14))
   const_f#2(x3, Cons(x6, Cons(x4, x2))) -> merge#2(x6, x4)
   leq#2(0, x16) -> True
   leq#2(S(x20), 0) -> False
   leq#2(S(x4), S(x2)) -> leq#2(x4, x2)
   length#1(Nil) -> 0
   length#1(Cons(x6, x8)) -> S(length#1(x8))
   map#2(dc(x2, x4, x6, x8, x10), Nil) -> Nil
   map#2(dc(x6, x8, x10, x12, x14), Cons(x4, x2)) -> Cons(dc#1(x6, x8, x10, x12, x14, x4), map#2(dc(x6, x8, x10, x12, x14), x2))
   main(x113) -> dc#1(map, divisible, mergesort_zs_3, divide, const_f, x113)

S is empty.
Rewrite Strategy: PARALLEL_INNERMOST
----------------------------------------

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

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


The TRS R consists of the following rules:

   divide_ys#1(x2, x1) -> Cons(take#2(x1, x2), Cons(drop#2(x1, x2), Nil))
   cond_merge_ys_zs_2(True, Cons(x7, x8), Cons(x5, x6), x4, x3, x2, x1) -> Cons(x4, merge#2(x3, Cons(x5, x6)))
   cond_merge_ys_zs_2(False, Cons(x7, x8), Cons(x5, x6), x4, x3, x2, x1) -> Cons(x2, merge#2(Cons(x7, x8), x1))
   merge#2(Nil, x2) -> x2
   merge#2(Cons(x4, x2), Nil) -> Cons(x4, x2)
   merge#2(Cons(x8, x6), Cons(x4, x2)) -> cond_merge_ys_zs_2(leq#2(x8, x4), Cons(x8, x6), Cons(x4, x2), x8, x6, x4, x2)
   dc#1(map, divisible, mergesort_zs_3, divide, const_f, Nil) -> Nil
   dc#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x229, Nil)) -> Cons(x229, Nil)
   dc#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x51, Cons(x25, x33))) -> const_f#2(Cons(x51, Cons(x25, x33)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x51, Cons(x25, x33)), S(halve#1(length#1(x33))))))
   drop#2(0', x2) -> x2
   drop#2(S(0'), Nil) -> bot[1]
   drop#2(S(x10), Cons(x56, x64)) -> drop#2(x10, x64)
   take#2(0', x2) -> Nil
   take#2(S(0'), Nil) -> Cons(bot[0], Nil)
   take#2(S(x22), Cons(x56, x64)) -> Cons(x56, take#2(x22, x64))
   halve#1(0') -> 0'
   halve#1(S(0')) -> S(0')
   halve#1(S(S(x14))) -> S(halve#1(x14))
   const_f#2(x3, Cons(x6, Cons(x4, x2))) -> merge#2(x6, x4)
   leq#2(0', x16) -> True
   leq#2(S(x20), 0') -> False
   leq#2(S(x4), S(x2)) -> leq#2(x4, x2)
   length#1(Nil) -> 0'
   length#1(Cons(x6, x8)) -> S(length#1(x8))
   map#2(dc(x2, x4, x6, x8, x10), Nil) -> Nil
   map#2(dc(x6, x8, x10, x12, x14), Cons(x4, x2)) -> Cons(dc#1(x6, x8, x10, x12, x14, x4), map#2(dc(x6, x8, x10, x12, x14), x2))
   main(x113) -> dc#1(map, divisible, mergesort_zs_3, divide, const_f, x113)

S is empty.
Rewrite Strategy: PARALLEL_INNERMOST
----------------------------------------

(3) RelTrsToTrsProof (UPPER BOUND(ID))
transformed relative TRS to TRS
----------------------------------------

(4)
Obligation:
The Runtime Complexity (parallel-innermost) of the given CpxTRS could be proven to be BOUNDS(1, INF).


The TRS R consists of the following rules:

   divide_ys#1(x2, x1) -> Cons(take#2(x1, x2), Cons(drop#2(x1, x2), Nil))
   cond_merge_ys_zs_2(True, Cons(x7, x8), Cons(x5, x6), x4, x3, x2, x1) -> Cons(x4, merge#2(x3, Cons(x5, x6)))
   cond_merge_ys_zs_2(False, Cons(x7, x8), Cons(x5, x6), x4, x3, x2, x1) -> Cons(x2, merge#2(Cons(x7, x8), x1))
   merge#2(Nil, x2) -> x2
   merge#2(Cons(x4, x2), Nil) -> Cons(x4, x2)
   merge#2(Cons(x8, x6), Cons(x4, x2)) -> cond_merge_ys_zs_2(leq#2(x8, x4), Cons(x8, x6), Cons(x4, x2), x8, x6, x4, x2)
   dc#1(map, divisible, mergesort_zs_3, divide, const_f, Nil) -> Nil
   dc#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x229, Nil)) -> Cons(x229, Nil)
   dc#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x51, Cons(x25, x33))) -> const_f#2(Cons(x51, Cons(x25, x33)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x51, Cons(x25, x33)), S(halve#1(length#1(x33))))))
   drop#2(0, x2) -> x2
   drop#2(S(0), Nil) -> bot[1]
   drop#2(S(x10), Cons(x56, x64)) -> drop#2(x10, x64)
   take#2(0, x2) -> Nil
   take#2(S(0), Nil) -> Cons(bot[0], Nil)
   take#2(S(x22), Cons(x56, x64)) -> Cons(x56, take#2(x22, x64))
   halve#1(0) -> 0
   halve#1(S(0)) -> S(0)
   halve#1(S(S(x14))) -> S(halve#1(x14))
   const_f#2(x3, Cons(x6, Cons(x4, x2))) -> merge#2(x6, x4)
   leq#2(0, x16) -> True
   leq#2(S(x20), 0) -> False
   leq#2(S(x4), S(x2)) -> leq#2(x4, x2)
   length#1(Nil) -> 0
   length#1(Cons(x6, x8)) -> S(length#1(x8))
   map#2(dc(x2, x4, x6, x8, x10), Nil) -> Nil
   map#2(dc(x6, x8, x10, x12, x14), Cons(x4, x2)) -> Cons(dc#1(x6, x8, x10, x12, x14, x4), map#2(dc(x6, x8, x10, x12, x14), x2))
   main(x113) -> dc#1(map, divisible, mergesort_zs_3, divide, const_f, x113)

S is empty.
Rewrite Strategy: PARALLEL_INNERMOST
----------------------------------------

(5) RelTrsToWeightedTrsProof (UPPER BOUND(ID))
Transformed relative TRS to weighted TRS
----------------------------------------

(6)
Obligation:
The Runtime Complexity (innermost) of the given CpxWeightedTrs could be proven to be BOUNDS(1, INF).


The TRS R consists of the following rules:

   divide_ys#1(x2, x1) -> Cons(take#2(x1, x2), Cons(drop#2(x1, x2), Nil)) [1]
   cond_merge_ys_zs_2(True, Cons(x7, x8), Cons(x5, x6), x4, x3, x2, x1) -> Cons(x4, merge#2(x3, Cons(x5, x6))) [1]
   cond_merge_ys_zs_2(False, Cons(x7, x8), Cons(x5, x6), x4, x3, x2, x1) -> Cons(x2, merge#2(Cons(x7, x8), x1)) [1]
   merge#2(Nil, x2) -> x2 [1]
   merge#2(Cons(x4, x2), Nil) -> Cons(x4, x2) [1]
   merge#2(Cons(x8, x6), Cons(x4, x2)) -> cond_merge_ys_zs_2(leq#2(x8, x4), Cons(x8, x6), Cons(x4, x2), x8, x6, x4, x2) [1]
   dc#1(map, divisible, mergesort_zs_3, divide, const_f, Nil) -> Nil [1]
   dc#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x229, Nil)) -> Cons(x229, Nil) [1]
   dc#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x51, Cons(x25, x33))) -> const_f#2(Cons(x51, Cons(x25, x33)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x51, Cons(x25, x33)), S(halve#1(length#1(x33)))))) [1]
   drop#2(0, x2) -> x2 [1]
   drop#2(S(0), Nil) -> bot[1] [1]
   drop#2(S(x10), Cons(x56, x64)) -> drop#2(x10, x64) [1]
   take#2(0, x2) -> Nil [1]
   take#2(S(0), Nil) -> Cons(bot[0], Nil) [1]
   take#2(S(x22), Cons(x56, x64)) -> Cons(x56, take#2(x22, x64)) [1]
   halve#1(0) -> 0 [1]
   halve#1(S(0)) -> S(0) [1]
   halve#1(S(S(x14))) -> S(halve#1(x14)) [1]
   const_f#2(x3, Cons(x6, Cons(x4, x2))) -> merge#2(x6, x4) [1]
   leq#2(0, x16) -> True [1]
   leq#2(S(x20), 0) -> False [1]
   leq#2(S(x4), S(x2)) -> leq#2(x4, x2) [1]
   length#1(Nil) -> 0 [1]
   length#1(Cons(x6, x8)) -> S(length#1(x8)) [1]
   map#2(dc(x2, x4, x6, x8, x10), Nil) -> Nil [1]
   map#2(dc(x6, x8, x10, x12, x14), Cons(x4, x2)) -> Cons(dc#1(x6, x8, x10, x12, x14, x4), map#2(dc(x6, x8, x10, x12, x14), x2)) [1]
   main(x113) -> dc#1(map, divisible, mergesort_zs_3, divide, const_f, x113) [1]

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

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

(8)
Obligation:
Runtime Complexity Weighted TRS with Types.
The TRS R consists of the following rules:

   divide_ys#1(x2, x1) -> Cons(take#2(x1, x2), Cons(drop#2(x1, x2), Nil)) [1]
   cond_merge_ys_zs_2(True, Cons(x7, x8), Cons(x5, x6), x4, x3, x2, x1) -> Cons(x4, merge#2(x3, Cons(x5, x6))) [1]
   cond_merge_ys_zs_2(False, Cons(x7, x8), Cons(x5, x6), x4, x3, x2, x1) -> Cons(x2, merge#2(Cons(x7, x8), x1)) [1]
   merge#2(Nil, x2) -> x2 [1]
   merge#2(Cons(x4, x2), Nil) -> Cons(x4, x2) [1]
   merge#2(Cons(x8, x6), Cons(x4, x2)) -> cond_merge_ys_zs_2(leq#2(x8, x4), Cons(x8, x6), Cons(x4, x2), x8, x6, x4, x2) [1]
   dc#1(map, divisible, mergesort_zs_3, divide, const_f, Nil) -> Nil [1]
   dc#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x229, Nil)) -> Cons(x229, Nil) [1]
   dc#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x51, Cons(x25, x33))) -> const_f#2(Cons(x51, Cons(x25, x33)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x51, Cons(x25, x33)), S(halve#1(length#1(x33)))))) [1]
   drop#2(0, x2) -> x2 [1]
   drop#2(S(0), Nil) -> bot[1] [1]
   drop#2(S(x10), Cons(x56, x64)) -> drop#2(x10, x64) [1]
   take#2(0, x2) -> Nil [1]
   take#2(S(0), Nil) -> Cons(bot[0], Nil) [1]
   take#2(S(x22), Cons(x56, x64)) -> Cons(x56, take#2(x22, x64)) [1]
   halve#1(0) -> 0 [1]
   halve#1(S(0)) -> S(0) [1]
   halve#1(S(S(x14))) -> S(halve#1(x14)) [1]
   const_f#2(x3, Cons(x6, Cons(x4, x2))) -> merge#2(x6, x4) [1]
   leq#2(0, x16) -> True [1]
   leq#2(S(x20), 0) -> False [1]
   leq#2(S(x4), S(x2)) -> leq#2(x4, x2) [1]
   length#1(Nil) -> 0 [1]
   length#1(Cons(x6, x8)) -> S(length#1(x8)) [1]
   map#2(dc(x2, x4, x6, x8, x10), Nil) -> Nil [1]
   map#2(dc(x6, x8, x10, x12, x14), Cons(x4, x2)) -> Cons(dc#1(x6, x8, x10, x12, x14, x4), map#2(dc(x6, x8, x10, x12, x14), x2)) [1]
   main(x113) -> dc#1(map, divisible, mergesort_zs_3, divide, const_f, x113) [1]

The TRS has the following type information:
divide_ys#1 :: Nil:Cons:S:0:bot[1]:bot[0] -> Nil:Cons:S:0:bot[1]:bot[0] -> Nil:Cons:S:0:bot[1]:bot[0]
Cons :: Nil:Cons:S:0:bot[1]:bot[0] -> Nil:Cons:S:0:bot[1]:bot[0] -> Nil:Cons:S:0:bot[1]:bot[0]
take#2 :: Nil:Cons:S:0:bot[1]:bot[0] -> Nil:Cons:S:0:bot[1]:bot[0] -> Nil:Cons:S:0:bot[1]:bot[0]
drop#2 :: Nil:Cons:S:0:bot[1]:bot[0] -> Nil:Cons:S:0:bot[1]:bot[0] -> Nil:Cons:S:0:bot[1]:bot[0]
Nil :: Nil:Cons:S:0:bot[1]:bot[0]
cond_merge_ys_zs_2 :: True:False -> Nil:Cons:S:0:bot[1]:bot[0] -> Nil:Cons:S:0:bot[1]:bot[0] -> Nil:Cons:S:0:bot[1]:bot[0] -> Nil:Cons:S:0:bot[1]:bot[0] -> Nil:Cons:S:0:bot[1]:bot[0] -> Nil:Cons:S:0:bot[1]:bot[0] -> Nil:Cons:S:0:bot[1]:bot[0]
True :: True:False
merge#2 :: Nil:Cons:S:0:bot[1]:bot[0] -> Nil:Cons:S:0:bot[1]:bot[0] -> Nil:Cons:S:0:bot[1]:bot[0]
False :: True:False
leq#2 :: Nil:Cons:S:0:bot[1]:bot[0] -> Nil:Cons:S:0:bot[1]:bot[0] -> True:False
dc#1 :: map -> divisible -> mergesort_zs_3 -> divide -> const_f -> Nil:Cons:S:0:bot[1]:bot[0] -> Nil:Cons:S:0:bot[1]:bot[0]
map :: map
divisible :: divisible
mergesort_zs_3 :: mergesort_zs_3
divide :: divide
const_f :: const_f
const_f#2 :: Nil:Cons:S:0:bot[1]:bot[0] -> Nil:Cons:S:0:bot[1]:bot[0] -> Nil:Cons:S:0:bot[1]:bot[0]
map#2 :: dc -> Nil:Cons:S:0:bot[1]:bot[0] -> Nil:Cons:S:0:bot[1]:bot[0]
dc :: map -> divisible -> mergesort_zs_3 -> divide -> const_f -> dc
S :: Nil:Cons:S:0:bot[1]:bot[0] -> Nil:Cons:S:0:bot[1]:bot[0]
halve#1 :: Nil:Cons:S:0:bot[1]:bot[0] -> Nil:Cons:S:0:bot[1]:bot[0]
length#1 :: Nil:Cons:S:0:bot[1]:bot[0] -> Nil:Cons:S:0:bot[1]:bot[0]
0 :: Nil:Cons:S:0:bot[1]:bot[0]
bot[1] :: Nil:Cons:S:0:bot[1]:bot[0]
bot[0] :: Nil:Cons:S:0:bot[1]:bot[0]
main :: Nil:Cons:S:0:bot[1]:bot[0] -> Nil:Cons:S:0:bot[1]:bot[0]

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

(9) 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:

   main_1

(c) The following functions are completely defined:

   leq#2_2
   map#2_2
   divide_ys#1_2
   halve#1_1
   length#1_1
   dc#1_6
   take#2_2
   drop#2_2
   const_f#2_2
   merge#2_2
   cond_merge_ys_zs_2_7

Due to the following rules being added:

   leq#2(v0, v1) -> null_leq#2 [0]
   map#2(v0, v1) -> null_map#2 [0]
   halve#1(v0) -> null_halve#1 [0]
   length#1(v0) -> null_length#1 [0]
   dc#1(v0, v1, v2, v3, v4, v5) -> null_dc#1 [0]
   take#2(v0, v1) -> null_take#2 [0]
   drop#2(v0, v1) -> null_drop#2 [0]
   const_f#2(v0, v1) -> null_const_f#2 [0]
   merge#2(v0, v1) -> null_merge#2 [0]
   cond_merge_ys_zs_2(v0, v1, v2, v3, v4, v5, v6) -> null_cond_merge_ys_zs_2 [0]

And the following fresh constants:    null_leq#2, null_map#2, null_halve#1, null_length#1, null_dc#1, null_take#2, null_drop#2, null_const_f#2, null_merge#2, null_cond_merge_ys_zs_2, const

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

(10)
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:

   divide_ys#1(x2, x1) -> Cons(take#2(x1, x2), Cons(drop#2(x1, x2), Nil)) [1]
   cond_merge_ys_zs_2(True, Cons(x7, x8), Cons(x5, x6), x4, x3, x2, x1) -> Cons(x4, merge#2(x3, Cons(x5, x6))) [1]
   cond_merge_ys_zs_2(False, Cons(x7, x8), Cons(x5, x6), x4, x3, x2, x1) -> Cons(x2, merge#2(Cons(x7, x8), x1)) [1]
   merge#2(Nil, x2) -> x2 [1]
   merge#2(Cons(x4, x2), Nil) -> Cons(x4, x2) [1]
   merge#2(Cons(x8, x6), Cons(x4, x2)) -> cond_merge_ys_zs_2(leq#2(x8, x4), Cons(x8, x6), Cons(x4, x2), x8, x6, x4, x2) [1]
   dc#1(map, divisible, mergesort_zs_3, divide, const_f, Nil) -> Nil [1]
   dc#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x229, Nil)) -> Cons(x229, Nil) [1]
   dc#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x51, Cons(x25, x33))) -> const_f#2(Cons(x51, Cons(x25, x33)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x51, Cons(x25, x33)), S(halve#1(length#1(x33)))))) [1]
   drop#2(0, x2) -> x2 [1]
   drop#2(S(0), Nil) -> bot[1] [1]
   drop#2(S(x10), Cons(x56, x64)) -> drop#2(x10, x64) [1]
   take#2(0, x2) -> Nil [1]
   take#2(S(0), Nil) -> Cons(bot[0], Nil) [1]
   take#2(S(x22), Cons(x56, x64)) -> Cons(x56, take#2(x22, x64)) [1]
   halve#1(0) -> 0 [1]
   halve#1(S(0)) -> S(0) [1]
   halve#1(S(S(x14))) -> S(halve#1(x14)) [1]
   const_f#2(x3, Cons(x6, Cons(x4, x2))) -> merge#2(x6, x4) [1]
   leq#2(0, x16) -> True [1]
   leq#2(S(x20), 0) -> False [1]
   leq#2(S(x4), S(x2)) -> leq#2(x4, x2) [1]
   length#1(Nil) -> 0 [1]
   length#1(Cons(x6, x8)) -> S(length#1(x8)) [1]
   map#2(dc(x2, x4, x6, x8, x10), Nil) -> Nil [1]
   map#2(dc(x6, x8, x10, x12, x14), Cons(x4, x2)) -> Cons(dc#1(x6, x8, x10, x12, x14, x4), map#2(dc(x6, x8, x10, x12, x14), x2)) [1]
   main(x113) -> dc#1(map, divisible, mergesort_zs_3, divide, const_f, x113) [1]
   leq#2(v0, v1) -> null_leq#2 [0]
   map#2(v0, v1) -> null_map#2 [0]
   halve#1(v0) -> null_halve#1 [0]
   length#1(v0) -> null_length#1 [0]
   dc#1(v0, v1, v2, v3, v4, v5) -> null_dc#1 [0]
   take#2(v0, v1) -> null_take#2 [0]
   drop#2(v0, v1) -> null_drop#2 [0]
   const_f#2(v0, v1) -> null_const_f#2 [0]
   merge#2(v0, v1) -> null_merge#2 [0]
   cond_merge_ys_zs_2(v0, v1, v2, v3, v4, v5, v6) -> null_cond_merge_ys_zs_2 [0]

The TRS has the following type information:
divide_ys#1 :: Nil:Cons:S:0:bot[1]:bot[0]:null_map#2:null_halve#1:null_length#1:null_dc#1:null_take#2:null_drop#2:null_const_f#2:null_merge#2:null_cond_merge_ys_zs_2 -> Nil:Cons:S:0:bot[1]:bot[0]:null_map#2:null_halve#1:null_length#1:null_dc#1:null_take#2:null_drop#2:null_const_f#2:null_merge#2:null_cond_merge_ys_zs_2 -> Nil:Cons:S:0:bot[1]:bot[0]:null_map#2:null_halve#1:null_length#1:null_dc#1:null_take#2:null_drop#2:null_const_f#2:null_merge#2:null_cond_merge_ys_zs_2
Cons :: Nil:Cons:S:0:bot[1]:bot[0]:null_map#2:null_halve#1:null_length#1:null_dc#1:null_take#2:null_drop#2:null_const_f#2:null_merge#2:null_cond_merge_ys_zs_2 -> Nil:Cons:S:0:bot[1]:bot[0]:null_map#2:null_halve#1:null_length#1:null_dc#1:null_take#2:null_drop#2:null_const_f#2:null_merge#2:null_cond_merge_ys_zs_2 -> Nil:Cons:S:0:bot[1]:bot[0]:null_map#2:null_halve#1:null_length#1:null_dc#1:null_take#2:null_drop#2:null_const_f#2:null_merge#2:null_cond_merge_ys_zs_2
take#2 :: Nil:Cons:S:0:bot[1]:bot[0]:null_map#2:null_halve#1:null_length#1:null_dc#1:null_take#2:null_drop#2:null_const_f#2:null_merge#2:null_cond_merge_ys_zs_2 -> Nil:Cons:S:0:bot[1]:bot[0]:null_map#2:null_halve#1:null_length#1:null_dc#1:null_take#2:null_drop#2:null_const_f#2:null_merge#2:null_cond_merge_ys_zs_2 -> Nil:Cons:S:0:bot[1]:bot[0]:null_map#2:null_halve#1:null_length#1:null_dc#1:null_take#2:null_drop#2:null_const_f#2:null_merge#2:null_cond_merge_ys_zs_2
drop#2 :: Nil:Cons:S:0:bot[1]:bot[0]:null_map#2:null_halve#1:null_length#1:null_dc#1:null_take#2:null_drop#2:null_const_f#2:null_merge#2:null_cond_merge_ys_zs_2 -> Nil:Cons:S:0:bot[1]:bot[0]:null_map#2:null_halve#1:null_length#1:null_dc#1:null_take#2:null_drop#2:null_const_f#2:null_merge#2:null_cond_merge_ys_zs_2 -> Nil:Cons:S:0:bot[1]:bot[0]:null_map#2:null_halve#1:null_length#1:null_dc#1:null_take#2:null_drop#2:null_const_f#2:null_merge#2:null_cond_merge_ys_zs_2
Nil :: Nil:Cons:S:0:bot[1]:bot[0]:null_map#2:null_halve#1:null_length#1:null_dc#1:null_take#2:null_drop#2:null_const_f#2:null_merge#2:null_cond_merge_ys_zs_2
cond_merge_ys_zs_2 :: True:False:null_leq#2 -> Nil:Cons:S:0:bot[1]:bot[0]:null_map#2:null_halve#1:null_length#1:null_dc#1:null_take#2:null_drop#2:null_const_f#2:null_merge#2:null_cond_merge_ys_zs_2 -> Nil:Cons:S:0:bot[1]:bot[0]:null_map#2:null_halve#1:null_length#1:null_dc#1:null_take#2:null_drop#2:null_const_f#2:null_merge#2:null_cond_merge_ys_zs_2 -> Nil:Cons:S:0:bot[1]:bot[0]:null_map#2:null_halve#1:null_length#1:null_dc#1:null_take#2:null_drop#2:null_const_f#2:null_merge#2:null_cond_merge_ys_zs_2 -> Nil:Cons:S:0:bot[1]:bot[0]:null_map#2:null_halve#1:null_length#1:null_dc#1:null_take#2:null_drop#2:null_const_f#2:null_merge#2:null_cond_merge_ys_zs_2 -> Nil:Cons:S:0:bot[1]:bot[0]:null_map#2:null_halve#1:null_length#1:null_dc#1:null_take#2:null_drop#2:null_const_f#2:null_merge#2:null_cond_merge_ys_zs_2 -> Nil:Cons:S:0:bot[1]:bot[0]:null_map#2:null_halve#1:null_length#1:null_dc#1:null_take#2:null_drop#2:null_const_f#2:null_merge#2:null_cond_merge_ys_zs_2 -> Nil:Cons:S:0:bot[1]:bot[0]:null_map#2:null_halve#1:null_length#1:null_dc#1:null_take#2:null_drop#2:null_const_f#2:null_merge#2:null_cond_merge_ys_zs_2
True :: True:False:null_leq#2
merge#2 :: Nil:Cons:S:0:bot[1]:bot[0]:null_map#2:null_halve#1:null_length#1:null_dc#1:null_take#2:null_drop#2:null_const_f#2:null_merge#2:null_cond_merge_ys_zs_2 -> Nil:Cons:S:0:bot[1]:bot[0]:null_map#2:null_halve#1:null_length#1:null_dc#1:null_take#2:null_drop#2:null_const_f#2:null_merge#2:null_cond_merge_ys_zs_2 -> Nil:Cons:S:0:bot[1]:bot[0]:null_map#2:null_halve#1:null_length#1:null_dc#1:null_take#2:null_drop#2:null_const_f#2:null_merge#2:null_cond_merge_ys_zs_2
False :: True:False:null_leq#2
leq#2 :: Nil:Cons:S:0:bot[1]:bot[0]:null_map#2:null_halve#1:null_length#1:null_dc#1:null_take#2:null_drop#2:null_const_f#2:null_merge#2:null_cond_merge_ys_zs_2 -> Nil:Cons:S:0:bot[1]:bot[0]:null_map#2:null_halve#1:null_length#1:null_dc#1:null_take#2:null_drop#2:null_const_f#2:null_merge#2:null_cond_merge_ys_zs_2 -> True:False:null_leq#2
dc#1 :: map -> divisible -> mergesort_zs_3 -> divide -> const_f -> Nil:Cons:S:0:bot[1]:bot[0]:null_map#2:null_halve#1:null_length#1:null_dc#1:null_take#2:null_drop#2:null_const_f#2:null_merge#2:null_cond_merge_ys_zs_2 -> Nil:Cons:S:0:bot[1]:bot[0]:null_map#2:null_halve#1:null_length#1:null_dc#1:null_take#2:null_drop#2:null_const_f#2:null_merge#2:null_cond_merge_ys_zs_2
map :: map
divisible :: divisible
mergesort_zs_3 :: mergesort_zs_3
divide :: divide
const_f :: const_f
const_f#2 :: Nil:Cons:S:0:bot[1]:bot[0]:null_map#2:null_halve#1:null_length#1:null_dc#1:null_take#2:null_drop#2:null_const_f#2:null_merge#2:null_cond_merge_ys_zs_2 -> Nil:Cons:S:0:bot[1]:bot[0]:null_map#2:null_halve#1:null_length#1:null_dc#1:null_take#2:null_drop#2:null_const_f#2:null_merge#2:null_cond_merge_ys_zs_2 -> Nil:Cons:S:0:bot[1]:bot[0]:null_map#2:null_halve#1:null_length#1:null_dc#1:null_take#2:null_drop#2:null_const_f#2:null_merge#2:null_cond_merge_ys_zs_2
map#2 :: dc -> Nil:Cons:S:0:bot[1]:bot[0]:null_map#2:null_halve#1:null_length#1:null_dc#1:null_take#2:null_drop#2:null_const_f#2:null_merge#2:null_cond_merge_ys_zs_2 -> Nil:Cons:S:0:bot[1]:bot[0]:null_map#2:null_halve#1:null_length#1:null_dc#1:null_take#2:null_drop#2:null_const_f#2:null_merge#2:null_cond_merge_ys_zs_2
dc :: map -> divisible -> mergesort_zs_3 -> divide -> const_f -> dc
S :: Nil:Cons:S:0:bot[1]:bot[0]:null_map#2:null_halve#1:null_length#1:null_dc#1:null_take#2:null_drop#2:null_const_f#2:null_merge#2:null_cond_merge_ys_zs_2 -> Nil:Cons:S:0:bot[1]:bot[0]:null_map#2:null_halve#1:null_length#1:null_dc#1:null_take#2:null_drop#2:null_const_f#2:null_merge#2:null_cond_merge_ys_zs_2
halve#1 :: Nil:Cons:S:0:bot[1]:bot[0]:null_map#2:null_halve#1:null_length#1:null_dc#1:null_take#2:null_drop#2:null_const_f#2:null_merge#2:null_cond_merge_ys_zs_2 -> Nil:Cons:S:0:bot[1]:bot[0]:null_map#2:null_halve#1:null_length#1:null_dc#1:null_take#2:null_drop#2:null_const_f#2:null_merge#2:null_cond_merge_ys_zs_2
length#1 :: Nil:Cons:S:0:bot[1]:bot[0]:null_map#2:null_halve#1:null_length#1:null_dc#1:null_take#2:null_drop#2:null_const_f#2:null_merge#2:null_cond_merge_ys_zs_2 -> Nil:Cons:S:0:bot[1]:bot[0]:null_map#2:null_halve#1:null_length#1:null_dc#1:null_take#2:null_drop#2:null_const_f#2:null_merge#2:null_cond_merge_ys_zs_2
0 :: Nil:Cons:S:0:bot[1]:bot[0]:null_map#2:null_halve#1:null_length#1:null_dc#1:null_take#2:null_drop#2:null_const_f#2:null_merge#2:null_cond_merge_ys_zs_2
bot[1] :: Nil:Cons:S:0:bot[1]:bot[0]:null_map#2:null_halve#1:null_length#1:null_dc#1:null_take#2:null_drop#2:null_const_f#2:null_merge#2:null_cond_merge_ys_zs_2
bot[0] :: Nil:Cons:S:0:bot[1]:bot[0]:null_map#2:null_halve#1:null_length#1:null_dc#1:null_take#2:null_drop#2:null_const_f#2:null_merge#2:null_cond_merge_ys_zs_2
main :: Nil:Cons:S:0:bot[1]:bot[0]:null_map#2:null_halve#1:null_length#1:null_dc#1:null_take#2:null_drop#2:null_const_f#2:null_merge#2:null_cond_merge_ys_zs_2 -> Nil:Cons:S:0:bot[1]:bot[0]:null_map#2:null_halve#1:null_length#1:null_dc#1:null_take#2:null_drop#2:null_const_f#2:null_merge#2:null_cond_merge_ys_zs_2
null_leq#2 :: True:False:null_leq#2
null_map#2 :: Nil:Cons:S:0:bot[1]:bot[0]:null_map#2:null_halve#1:null_length#1:null_dc#1:null_take#2:null_drop#2:null_const_f#2:null_merge#2:null_cond_merge_ys_zs_2
null_halve#1 :: Nil:Cons:S:0:bot[1]:bot[0]:null_map#2:null_halve#1:null_length#1:null_dc#1:null_take#2:null_drop#2:null_const_f#2:null_merge#2:null_cond_merge_ys_zs_2
null_length#1 :: Nil:Cons:S:0:bot[1]:bot[0]:null_map#2:null_halve#1:null_length#1:null_dc#1:null_take#2:null_drop#2:null_const_f#2:null_merge#2:null_cond_merge_ys_zs_2
null_dc#1 :: Nil:Cons:S:0:bot[1]:bot[0]:null_map#2:null_halve#1:null_length#1:null_dc#1:null_take#2:null_drop#2:null_const_f#2:null_merge#2:null_cond_merge_ys_zs_2
null_take#2 :: Nil:Cons:S:0:bot[1]:bot[0]:null_map#2:null_halve#1:null_length#1:null_dc#1:null_take#2:null_drop#2:null_const_f#2:null_merge#2:null_cond_merge_ys_zs_2
null_drop#2 :: Nil:Cons:S:0:bot[1]:bot[0]:null_map#2:null_halve#1:null_length#1:null_dc#1:null_take#2:null_drop#2:null_const_f#2:null_merge#2:null_cond_merge_ys_zs_2
null_const_f#2 :: Nil:Cons:S:0:bot[1]:bot[0]:null_map#2:null_halve#1:null_length#1:null_dc#1:null_take#2:null_drop#2:null_const_f#2:null_merge#2:null_cond_merge_ys_zs_2
null_merge#2 :: Nil:Cons:S:0:bot[1]:bot[0]:null_map#2:null_halve#1:null_length#1:null_dc#1:null_take#2:null_drop#2:null_const_f#2:null_merge#2:null_cond_merge_ys_zs_2
null_cond_merge_ys_zs_2 :: Nil:Cons:S:0:bot[1]:bot[0]:null_map#2:null_halve#1:null_length#1:null_dc#1:null_take#2:null_drop#2:null_const_f#2:null_merge#2:null_cond_merge_ys_zs_2
const :: dc

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

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

(12)
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:

   divide_ys#1(x2, x1) -> Cons(take#2(x1, x2), Cons(drop#2(x1, x2), Nil)) [1]
   cond_merge_ys_zs_2(True, Cons(x7, x8), Cons(x5, x6), x4, x3, x2, x1) -> Cons(x4, merge#2(x3, Cons(x5, x6))) [1]
   cond_merge_ys_zs_2(False, Cons(x7, x8), Cons(x5, x6), x4, x3, x2, x1) -> Cons(x2, merge#2(Cons(x7, x8), x1)) [1]
   merge#2(Nil, x2) -> x2 [1]
   merge#2(Cons(x4, x2), Nil) -> Cons(x4, x2) [1]
   merge#2(Cons(0, x6), Cons(x4, x2)) -> cond_merge_ys_zs_2(True, Cons(0, x6), Cons(x4, x2), 0, x6, x4, x2) [2]
   merge#2(Cons(S(x20'), x6), Cons(0, x2)) -> cond_merge_ys_zs_2(False, Cons(S(x20'), x6), Cons(0, x2), S(x20'), x6, 0, x2) [2]
   merge#2(Cons(S(x4'), x6), Cons(S(x2'), x2)) -> cond_merge_ys_zs_2(leq#2(x4', x2'), Cons(S(x4'), x6), Cons(S(x2'), x2), S(x4'), x6, S(x2'), x2) [2]
   merge#2(Cons(x8, x6), Cons(x4, x2)) -> cond_merge_ys_zs_2(null_leq#2, Cons(x8, x6), Cons(x4, x2), x8, x6, x4, x2) [1]
   dc#1(map, divisible, mergesort_zs_3, divide, const_f, Nil) -> Nil [1]
   dc#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x229, Nil)) -> Cons(x229, Nil) [1]
   dc#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x51, Cons(x25, Nil))) -> const_f#2(Cons(x51, Cons(x25, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x51, Cons(x25, Nil)), S(halve#1(0))))) [2]
   dc#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x51, Cons(x25, Cons(x6', x8')))) -> const_f#2(Cons(x51, Cons(x25, Cons(x6', x8'))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x51, Cons(x25, Cons(x6', x8'))), S(halve#1(S(length#1(x8'))))))) [2]
   dc#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x51, Cons(x25, x33))) -> const_f#2(Cons(x51, Cons(x25, x33)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x51, Cons(x25, x33)), S(halve#1(null_length#1))))) [1]
   drop#2(0, x2) -> x2 [1]
   drop#2(S(0), Nil) -> bot[1] [1]
   drop#2(S(x10), Cons(x56, x64)) -> drop#2(x10, x64) [1]
   take#2(0, x2) -> Nil [1]
   take#2(S(0), Nil) -> Cons(bot[0], Nil) [1]
   take#2(S(x22), Cons(x56, x64)) -> Cons(x56, take#2(x22, x64)) [1]
   halve#1(0) -> 0 [1]
   halve#1(S(0)) -> S(0) [1]
   halve#1(S(S(x14))) -> S(halve#1(x14)) [1]
   const_f#2(x3, Cons(x6, Cons(x4, x2))) -> merge#2(x6, x4) [1]
   leq#2(0, x16) -> True [1]
   leq#2(S(x20), 0) -> False [1]
   leq#2(S(x4), S(x2)) -> leq#2(x4, x2) [1]
   length#1(Nil) -> 0 [1]
   length#1(Cons(x6, x8)) -> S(length#1(x8)) [1]
   map#2(dc(x2, x4, x6, x8, x10), Nil) -> Nil [1]
   map#2(dc(x6, x8, x10, x12, x14), Cons(x4, x2)) -> Cons(dc#1(x6, x8, x10, x12, x14, x4), map#2(dc(x6, x8, x10, x12, x14), x2)) [1]
   main(x113) -> dc#1(map, divisible, mergesort_zs_3, divide, const_f, x113) [1]
   leq#2(v0, v1) -> null_leq#2 [0]
   map#2(v0, v1) -> null_map#2 [0]
   halve#1(v0) -> null_halve#1 [0]
   length#1(v0) -> null_length#1 [0]
   dc#1(v0, v1, v2, v3, v4, v5) -> null_dc#1 [0]
   take#2(v0, v1) -> null_take#2 [0]
   drop#2(v0, v1) -> null_drop#2 [0]
   const_f#2(v0, v1) -> null_const_f#2 [0]
   merge#2(v0, v1) -> null_merge#2 [0]
   cond_merge_ys_zs_2(v0, v1, v2, v3, v4, v5, v6) -> null_cond_merge_ys_zs_2 [0]

The TRS has the following type information:
divide_ys#1 :: Nil:Cons:S:0:bot[1]:bot[0]:null_map#2:null_halve#1:null_length#1:null_dc#1:null_take#2:null_drop#2:null_const_f#2:null_merge#2:null_cond_merge_ys_zs_2 -> Nil:Cons:S:0:bot[1]:bot[0]:null_map#2:null_halve#1:null_length#1:null_dc#1:null_take#2:null_drop#2:null_const_f#2:null_merge#2:null_cond_merge_ys_zs_2 -> Nil:Cons:S:0:bot[1]:bot[0]:null_map#2:null_halve#1:null_length#1:null_dc#1:null_take#2:null_drop#2:null_const_f#2:null_merge#2:null_cond_merge_ys_zs_2
Cons :: Nil:Cons:S:0:bot[1]:bot[0]:null_map#2:null_halve#1:null_length#1:null_dc#1:null_take#2:null_drop#2:null_const_f#2:null_merge#2:null_cond_merge_ys_zs_2 -> Nil:Cons:S:0:bot[1]:bot[0]:null_map#2:null_halve#1:null_length#1:null_dc#1:null_take#2:null_drop#2:null_const_f#2:null_merge#2:null_cond_merge_ys_zs_2 -> Nil:Cons:S:0:bot[1]:bot[0]:null_map#2:null_halve#1:null_length#1:null_dc#1:null_take#2:null_drop#2:null_const_f#2:null_merge#2:null_cond_merge_ys_zs_2
take#2 :: Nil:Cons:S:0:bot[1]:bot[0]:null_map#2:null_halve#1:null_length#1:null_dc#1:null_take#2:null_drop#2:null_const_f#2:null_merge#2:null_cond_merge_ys_zs_2 -> Nil:Cons:S:0:bot[1]:bot[0]:null_map#2:null_halve#1:null_length#1:null_dc#1:null_take#2:null_drop#2:null_const_f#2:null_merge#2:null_cond_merge_ys_zs_2 -> Nil:Cons:S:0:bot[1]:bot[0]:null_map#2:null_halve#1:null_length#1:null_dc#1:null_take#2:null_drop#2:null_const_f#2:null_merge#2:null_cond_merge_ys_zs_2
drop#2 :: Nil:Cons:S:0:bot[1]:bot[0]:null_map#2:null_halve#1:null_length#1:null_dc#1:null_take#2:null_drop#2:null_const_f#2:null_merge#2:null_cond_merge_ys_zs_2 -> Nil:Cons:S:0:bot[1]:bot[0]:null_map#2:null_halve#1:null_length#1:null_dc#1:null_take#2:null_drop#2:null_const_f#2:null_merge#2:null_cond_merge_ys_zs_2 -> Nil:Cons:S:0:bot[1]:bot[0]:null_map#2:null_halve#1:null_length#1:null_dc#1:null_take#2:null_drop#2:null_const_f#2:null_merge#2:null_cond_merge_ys_zs_2
Nil :: Nil:Cons:S:0:bot[1]:bot[0]:null_map#2:null_halve#1:null_length#1:null_dc#1:null_take#2:null_drop#2:null_const_f#2:null_merge#2:null_cond_merge_ys_zs_2
cond_merge_ys_zs_2 :: True:False:null_leq#2 -> Nil:Cons:S:0:bot[1]:bot[0]:null_map#2:null_halve#1:null_length#1:null_dc#1:null_take#2:null_drop#2:null_const_f#2:null_merge#2:null_cond_merge_ys_zs_2 -> Nil:Cons:S:0:bot[1]:bot[0]:null_map#2:null_halve#1:null_length#1:null_dc#1:null_take#2:null_drop#2:null_const_f#2:null_merge#2:null_cond_merge_ys_zs_2 -> Nil:Cons:S:0:bot[1]:bot[0]:null_map#2:null_halve#1:null_length#1:null_dc#1:null_take#2:null_drop#2:null_const_f#2:null_merge#2:null_cond_merge_ys_zs_2 -> Nil:Cons:S:0:bot[1]:bot[0]:null_map#2:null_halve#1:null_length#1:null_dc#1:null_take#2:null_drop#2:null_const_f#2:null_merge#2:null_cond_merge_ys_zs_2 -> Nil:Cons:S:0:bot[1]:bot[0]:null_map#2:null_halve#1:null_length#1:null_dc#1:null_take#2:null_drop#2:null_const_f#2:null_merge#2:null_cond_merge_ys_zs_2 -> Nil:Cons:S:0:bot[1]:bot[0]:null_map#2:null_halve#1:null_length#1:null_dc#1:null_take#2:null_drop#2:null_const_f#2:null_merge#2:null_cond_merge_ys_zs_2 -> Nil:Cons:S:0:bot[1]:bot[0]:null_map#2:null_halve#1:null_length#1:null_dc#1:null_take#2:null_drop#2:null_const_f#2:null_merge#2:null_cond_merge_ys_zs_2
True :: True:False:null_leq#2
merge#2 :: Nil:Cons:S:0:bot[1]:bot[0]:null_map#2:null_halve#1:null_length#1:null_dc#1:null_take#2:null_drop#2:null_const_f#2:null_merge#2:null_cond_merge_ys_zs_2 -> Nil:Cons:S:0:bot[1]:bot[0]:null_map#2:null_halve#1:null_length#1:null_dc#1:null_take#2:null_drop#2:null_const_f#2:null_merge#2:null_cond_merge_ys_zs_2 -> Nil:Cons:S:0:bot[1]:bot[0]:null_map#2:null_halve#1:null_length#1:null_dc#1:null_take#2:null_drop#2:null_const_f#2:null_merge#2:null_cond_merge_ys_zs_2
False :: True:False:null_leq#2
leq#2 :: Nil:Cons:S:0:bot[1]:bot[0]:null_map#2:null_halve#1:null_length#1:null_dc#1:null_take#2:null_drop#2:null_const_f#2:null_merge#2:null_cond_merge_ys_zs_2 -> Nil:Cons:S:0:bot[1]:bot[0]:null_map#2:null_halve#1:null_length#1:null_dc#1:null_take#2:null_drop#2:null_const_f#2:null_merge#2:null_cond_merge_ys_zs_2 -> True:False:null_leq#2
dc#1 :: map -> divisible -> mergesort_zs_3 -> divide -> const_f -> Nil:Cons:S:0:bot[1]:bot[0]:null_map#2:null_halve#1:null_length#1:null_dc#1:null_take#2:null_drop#2:null_const_f#2:null_merge#2:null_cond_merge_ys_zs_2 -> Nil:Cons:S:0:bot[1]:bot[0]:null_map#2:null_halve#1:null_length#1:null_dc#1:null_take#2:null_drop#2:null_const_f#2:null_merge#2:null_cond_merge_ys_zs_2
map :: map
divisible :: divisible
mergesort_zs_3 :: mergesort_zs_3
divide :: divide
const_f :: const_f
const_f#2 :: Nil:Cons:S:0:bot[1]:bot[0]:null_map#2:null_halve#1:null_length#1:null_dc#1:null_take#2:null_drop#2:null_const_f#2:null_merge#2:null_cond_merge_ys_zs_2 -> Nil:Cons:S:0:bot[1]:bot[0]:null_map#2:null_halve#1:null_length#1:null_dc#1:null_take#2:null_drop#2:null_const_f#2:null_merge#2:null_cond_merge_ys_zs_2 -> Nil:Cons:S:0:bot[1]:bot[0]:null_map#2:null_halve#1:null_length#1:null_dc#1:null_take#2:null_drop#2:null_const_f#2:null_merge#2:null_cond_merge_ys_zs_2
map#2 :: dc -> Nil:Cons:S:0:bot[1]:bot[0]:null_map#2:null_halve#1:null_length#1:null_dc#1:null_take#2:null_drop#2:null_const_f#2:null_merge#2:null_cond_merge_ys_zs_2 -> Nil:Cons:S:0:bot[1]:bot[0]:null_map#2:null_halve#1:null_length#1:null_dc#1:null_take#2:null_drop#2:null_const_f#2:null_merge#2:null_cond_merge_ys_zs_2
dc :: map -> divisible -> mergesort_zs_3 -> divide -> const_f -> dc
S :: Nil:Cons:S:0:bot[1]:bot[0]:null_map#2:null_halve#1:null_length#1:null_dc#1:null_take#2:null_drop#2:null_const_f#2:null_merge#2:null_cond_merge_ys_zs_2 -> Nil:Cons:S:0:bot[1]:bot[0]:null_map#2:null_halve#1:null_length#1:null_dc#1:null_take#2:null_drop#2:null_const_f#2:null_merge#2:null_cond_merge_ys_zs_2
halve#1 :: Nil:Cons:S:0:bot[1]:bot[0]:null_map#2:null_halve#1:null_length#1:null_dc#1:null_take#2:null_drop#2:null_const_f#2:null_merge#2:null_cond_merge_ys_zs_2 -> Nil:Cons:S:0:bot[1]:bot[0]:null_map#2:null_halve#1:null_length#1:null_dc#1:null_take#2:null_drop#2:null_const_f#2:null_merge#2:null_cond_merge_ys_zs_2
length#1 :: Nil:Cons:S:0:bot[1]:bot[0]:null_map#2:null_halve#1:null_length#1:null_dc#1:null_take#2:null_drop#2:null_const_f#2:null_merge#2:null_cond_merge_ys_zs_2 -> Nil:Cons:S:0:bot[1]:bot[0]:null_map#2:null_halve#1:null_length#1:null_dc#1:null_take#2:null_drop#2:null_const_f#2:null_merge#2:null_cond_merge_ys_zs_2
0 :: Nil:Cons:S:0:bot[1]:bot[0]:null_map#2:null_halve#1:null_length#1:null_dc#1:null_take#2:null_drop#2:null_const_f#2:null_merge#2:null_cond_merge_ys_zs_2
bot[1] :: Nil:Cons:S:0:bot[1]:bot[0]:null_map#2:null_halve#1:null_length#1:null_dc#1:null_take#2:null_drop#2:null_const_f#2:null_merge#2:null_cond_merge_ys_zs_2
bot[0] :: Nil:Cons:S:0:bot[1]:bot[0]:null_map#2:null_halve#1:null_length#1:null_dc#1:null_take#2:null_drop#2:null_const_f#2:null_merge#2:null_cond_merge_ys_zs_2
main :: Nil:Cons:S:0:bot[1]:bot[0]:null_map#2:null_halve#1:null_length#1:null_dc#1:null_take#2:null_drop#2:null_const_f#2:null_merge#2:null_cond_merge_ys_zs_2 -> Nil:Cons:S:0:bot[1]:bot[0]:null_map#2:null_halve#1:null_length#1:null_dc#1:null_take#2:null_drop#2:null_const_f#2:null_merge#2:null_cond_merge_ys_zs_2
null_leq#2 :: True:False:null_leq#2
null_map#2 :: Nil:Cons:S:0:bot[1]:bot[0]:null_map#2:null_halve#1:null_length#1:null_dc#1:null_take#2:null_drop#2:null_const_f#2:null_merge#2:null_cond_merge_ys_zs_2
null_halve#1 :: Nil:Cons:S:0:bot[1]:bot[0]:null_map#2:null_halve#1:null_length#1:null_dc#1:null_take#2:null_drop#2:null_const_f#2:null_merge#2:null_cond_merge_ys_zs_2
null_length#1 :: Nil:Cons:S:0:bot[1]:bot[0]:null_map#2:null_halve#1:null_length#1:null_dc#1:null_take#2:null_drop#2:null_const_f#2:null_merge#2:null_cond_merge_ys_zs_2
null_dc#1 :: Nil:Cons:S:0:bot[1]:bot[0]:null_map#2:null_halve#1:null_length#1:null_dc#1:null_take#2:null_drop#2:null_const_f#2:null_merge#2:null_cond_merge_ys_zs_2
null_take#2 :: Nil:Cons:S:0:bot[1]:bot[0]:null_map#2:null_halve#1:null_length#1:null_dc#1:null_take#2:null_drop#2:null_const_f#2:null_merge#2:null_cond_merge_ys_zs_2
null_drop#2 :: Nil:Cons:S:0:bot[1]:bot[0]:null_map#2:null_halve#1:null_length#1:null_dc#1:null_take#2:null_drop#2:null_const_f#2:null_merge#2:null_cond_merge_ys_zs_2
null_const_f#2 :: Nil:Cons:S:0:bot[1]:bot[0]:null_map#2:null_halve#1:null_length#1:null_dc#1:null_take#2:null_drop#2:null_const_f#2:null_merge#2:null_cond_merge_ys_zs_2
null_merge#2 :: Nil:Cons:S:0:bot[1]:bot[0]:null_map#2:null_halve#1:null_length#1:null_dc#1:null_take#2:null_drop#2:null_const_f#2:null_merge#2:null_cond_merge_ys_zs_2
null_cond_merge_ys_zs_2 :: Nil:Cons:S:0:bot[1]:bot[0]:null_map#2:null_halve#1:null_length#1:null_dc#1:null_take#2:null_drop#2:null_const_f#2:null_merge#2:null_cond_merge_ys_zs_2
const :: dc

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

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

   Nil => 1
   True => 2
   False => 1
   map => 0
   divisible => 0
   mergesort_zs_3 => 0
   divide => 0
   const_f => 0
   0 => 0
   bot[1] => 3
   bot[0] => 2
   null_leq#2 => 0
   null_map#2 => 0
   null_halve#1 => 0
   null_length#1 => 0
   null_dc#1 => 0
   null_take#2 => 0
   null_drop#2 => 0
   null_const_f#2 => 0
   null_merge#2 => 0
   null_cond_merge_ys_zs_2 => 0
   const => 0

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

(14)
Obligation:
Complexity RNTS consisting of the following rules:

   cond_merge_ys_zs_2(z, z', z'', z1, z2, z3, z4) -{ 0 }-> 0 :|: z1 = v3, v0 >= 0, v6 >= 0, z'' = v2, v1 >= 0, v5 >= 0, z = v0, z' = v1, z2 = v4, v2 >= 0, v3 >= 0, z3 = v5, v4 >= 0, z4 = v6
   cond_merge_ys_zs_2(z, z', z'', z1, z2, z3, z4) -{ 1 }-> 1 + x2 + merge#2(1 + x7 + x8, x1) :|: x5 >= 0, x8 >= 0, z = 1, z' = 1 + x7 + x8, z'' = 1 + x5 + x6, x3 >= 0, x2 >= 0, z1 = x4, z2 = x3, z3 = x2, z4 = x1, x4 >= 0, x1 >= 0, x7 >= 0, x6 >= 0
   cond_merge_ys_zs_2(z, z', z'', z1, z2, z3, z4) -{ 1 }-> 1 + x4 + merge#2(x3, 1 + x5 + x6) :|: x5 >= 0, x8 >= 0, z' = 1 + x7 + x8, z'' = 1 + x5 + x6, x3 >= 0, x2 >= 0, z = 2, z1 = x4, z2 = x3, z3 = x2, z4 = x1, x4 >= 0, x1 >= 0, x7 >= 0, x6 >= 0
   const_f#2(z, z') -{ 1 }-> merge#2(x6, x4) :|: x4 >= 0, z' = 1 + x6 + (1 + x4 + x2), z = x3, x6 >= 0, x3 >= 0, x2 >= 0
   const_f#2(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1
   dc#1(z, z', z'', z1, z2, z3) -{ 1 }-> const_f#2(1 + x51 + (1 + x25 + x33), map#2(1 + 0 + 0 + 0 + 0 + 0, divide_ys#1(1 + x51 + (1 + x25 + x33), 1 + halve#1(0)))) :|: z'' = 0, z1 = 0, x33 >= 0, z3 = 1 + x51 + (1 + x25 + x33), z2 = 0, x51 >= 0, x25 >= 0, z = 0, z' = 0
   dc#1(z, z', z'', z1, z2, z3) -{ 2 }-> const_f#2(1 + x51 + (1 + x25 + 1), map#2(1 + 0 + 0 + 0 + 0 + 0, divide_ys#1(1 + x51 + (1 + x25 + 1), 1 + halve#1(0)))) :|: z'' = 0, z3 = 1 + x51 + (1 + x25 + 1), z1 = 0, z2 = 0, x51 >= 0, x25 >= 0, z = 0, z' = 0
   dc#1(z, z', z'', z1, z2, z3) -{ 2 }-> const_f#2(1 + x51 + (1 + x25 + (1 + x6' + x8')), map#2(1 + 0 + 0 + 0 + 0 + 0, divide_ys#1(1 + x51 + (1 + x25 + (1 + x6' + x8')), 1 + halve#1(1 + length#1(x8'))))) :|: z'' = 0, z1 = 0, z2 = 0, x51 >= 0, x25 >= 0, x6' >= 0, z3 = 1 + x51 + (1 + x25 + (1 + x6' + x8')), z = 0, x8' >= 0, z' = 0
   dc#1(z, z', z'', z1, z2, z3) -{ 1 }-> 1 :|: z'' = 0, z1 = 0, z2 = 0, z3 = 1, z = 0, z' = 0
   dc#1(z, z', z'', z1, z2, z3) -{ 0 }-> 0 :|: z1 = v3, z3 = v5, v0 >= 0, v4 >= 0, z'' = v2, v1 >= 0, v5 >= 0, z = v0, z' = v1, z2 = v4, v2 >= 0, v3 >= 0
   dc#1(z, z', z'', z1, z2, z3) -{ 1 }-> 1 + x229 + 1 :|: z'' = 0, z1 = 0, z2 = 0, x229 >= 0, z = 0, z' = 0, z3 = 1 + x229 + 1
   divide_ys#1(z, z') -{ 1 }-> 1 + take#2(x1, x2) + (1 + drop#2(x1, x2) + 1) :|: x1 >= 0, z = x2, z' = x1, x2 >= 0
   drop#2(z, z') -{ 1 }-> x2 :|: z' = x2, z = 0, x2 >= 0
   drop#2(z, z') -{ 1 }-> drop#2(x10, x64) :|: z' = 1 + x56 + x64, z = 1 + x10, x10 >= 0, x64 >= 0, x56 >= 0
   drop#2(z, z') -{ 1 }-> 3 :|: z = 1 + 0, z' = 1
   drop#2(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1
   halve#1(z) -{ 1 }-> 0 :|: z = 0
   halve#1(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0
   halve#1(z) -{ 1 }-> 1 + halve#1(x14) :|: z = 1 + (1 + x14), x14 >= 0
   halve#1(z) -{ 1 }-> 1 + 0 :|: z = 1 + 0
   length#1(z) -{ 1 }-> 0 :|: z = 1
   length#1(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0
   length#1(z) -{ 1 }-> 1 + length#1(x8) :|: x8 >= 0, x6 >= 0, z = 1 + x6 + x8
   leq#2(z, z') -{ 1 }-> leq#2(x4, x2) :|: x4 >= 0, z' = 1 + x2, z = 1 + x4, x2 >= 0
   leq#2(z, z') -{ 1 }-> 2 :|: z' = x16, z = 0, x16 >= 0
   leq#2(z, z') -{ 1 }-> 1 :|: x20 >= 0, z = 1 + x20, z' = 0
   leq#2(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1
   main(z) -{ 1 }-> dc#1(0, 0, 0, 0, 0, x113) :|: z = x113, x113 >= 0
   map#2(z, z') -{ 1 }-> 1 :|: x4 >= 0, x8 >= 0, x6 >= 0, z = 1 + x2 + x4 + x6 + x8 + x10, z' = 1, x10 >= 0, x2 >= 0
   map#2(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1
   map#2(z, z') -{ 1 }-> 1 + dc#1(x6, x8, x10, x12, x14, x4) + map#2(1 + x6 + x8 + x10 + x12 + x14, x2) :|: x4 >= 0, x8 >= 0, z' = 1 + x4 + x2, x6 >= 0, x12 >= 0, x14 >= 0, x10 >= 0, x2 >= 0, z = 1 + x6 + x8 + x10 + x12 + x14
   merge#2(z, z') -{ 1 }-> x2 :|: z' = x2, z = 1, x2 >= 0
   merge#2(z, z') -{ 2 }-> cond_merge_ys_zs_2(leq#2(x4', x2'), 1 + (1 + x4') + x6, 1 + (1 + x2') + x2, 1 + x4', x6, 1 + x2', x2) :|: x2' >= 0, z = 1 + (1 + x4') + x6, x6 >= 0, z' = 1 + (1 + x2') + x2, x4' >= 0, x2 >= 0
   merge#2(z, z') -{ 2 }-> cond_merge_ys_zs_2(2, 1 + 0 + x6, 1 + x4 + x2, 0, x6, x4, x2) :|: x4 >= 0, z' = 1 + x4 + x2, z = 1 + 0 + x6, x6 >= 0, x2 >= 0
   merge#2(z, z') -{ 2 }-> cond_merge_ys_zs_2(1, 1 + (1 + x20') + x6, 1 + 0 + x2, 1 + x20', x6, 0, x2) :|: z = 1 + (1 + x20') + x6, x6 >= 0, z' = 1 + 0 + x2, x20' >= 0, x2 >= 0
   merge#2(z, z') -{ 1 }-> cond_merge_ys_zs_2(0, 1 + x8 + x6, 1 + x4 + x2, x8, x6, x4, x2) :|: x4 >= 0, x8 >= 0, z' = 1 + x4 + x2, x6 >= 0, z = 1 + x8 + x6, x2 >= 0
   merge#2(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1
   merge#2(z, z') -{ 1 }-> 1 + x4 + x2 :|: x4 >= 0, z = 1 + x4 + x2, z' = 1, x2 >= 0
   take#2(z, z') -{ 1 }-> 1 :|: z' = x2, z = 0, x2 >= 0
   take#2(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1
   take#2(z, z') -{ 1 }-> 1 + x56 + take#2(x22, x64) :|: z' = 1 + x56 + x64, x22 >= 0, z = 1 + x22, x64 >= 0, x56 >= 0
   take#2(z, z') -{ 1 }-> 1 + 2 + 1 :|: z = 1 + 0, z' = 1


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

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

(16)
Obligation:
Complexity RNTS consisting of the following rules:

   cond_merge_ys_zs_2(z, z', z'', z1, z2, z3, z4) -{ 0 }-> 0 :|: z >= 0, z4 >= 0, z' >= 0, z3 >= 0, z'' >= 0, z1 >= 0, z2 >= 0
   cond_merge_ys_zs_2(z, z', z'', z1, z2, z3, z4) -{ 1 }-> 1 + z1 + merge#2(z2, 1 + x5 + x6) :|: x5 >= 0, x8 >= 0, z' = 1 + x7 + x8, z'' = 1 + x5 + x6, z2 >= 0, z3 >= 0, z = 2, z1 >= 0, z4 >= 0, x7 >= 0, x6 >= 0
   cond_merge_ys_zs_2(z, z', z'', z1, z2, z3, z4) -{ 1 }-> 1 + z3 + merge#2(1 + x7 + x8, z4) :|: x5 >= 0, x8 >= 0, z = 1, z' = 1 + x7 + x8, z'' = 1 + x5 + x6, z2 >= 0, z3 >= 0, z1 >= 0, z4 >= 0, x7 >= 0, x6 >= 0
   const_f#2(z, z') -{ 1 }-> merge#2(x6, x4) :|: x4 >= 0, z' = 1 + x6 + (1 + x4 + x2), x6 >= 0, z >= 0, x2 >= 0
   const_f#2(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   dc#1(z, z', z'', z1, z2, z3) -{ 1 }-> const_f#2(1 + x51 + (1 + x25 + x33), map#2(1 + 0 + 0 + 0 + 0 + 0, divide_ys#1(1 + x51 + (1 + x25 + x33), 1 + halve#1(0)))) :|: z'' = 0, z1 = 0, x33 >= 0, z3 = 1 + x51 + (1 + x25 + x33), z2 = 0, x51 >= 0, x25 >= 0, z = 0, z' = 0
   dc#1(z, z', z'', z1, z2, z3) -{ 2 }-> const_f#2(1 + x51 + (1 + x25 + 1), map#2(1 + 0 + 0 + 0 + 0 + 0, divide_ys#1(1 + x51 + (1 + x25 + 1), 1 + halve#1(0)))) :|: z'' = 0, z3 = 1 + x51 + (1 + x25 + 1), z1 = 0, z2 = 0, x51 >= 0, x25 >= 0, z = 0, z' = 0
   dc#1(z, z', z'', z1, z2, z3) -{ 2 }-> const_f#2(1 + x51 + (1 + x25 + (1 + x6' + x8')), map#2(1 + 0 + 0 + 0 + 0 + 0, divide_ys#1(1 + x51 + (1 + x25 + (1 + x6' + x8')), 1 + halve#1(1 + length#1(x8'))))) :|: z'' = 0, z1 = 0, z2 = 0, x51 >= 0, x25 >= 0, x6' >= 0, z3 = 1 + x51 + (1 + x25 + (1 + x6' + x8')), z = 0, x8' >= 0, z' = 0
   dc#1(z, z', z'', z1, z2, z3) -{ 1 }-> 1 :|: z'' = 0, z1 = 0, z2 = 0, z3 = 1, z = 0, z' = 0
   dc#1(z, z', z'', z1, z2, z3) -{ 0 }-> 0 :|: z >= 0, z2 >= 0, z' >= 0, z3 >= 0, z'' >= 0, z1 >= 0
   dc#1(z, z', z'', z1, z2, z3) -{ 1 }-> 1 + (z3 - 2) + 1 :|: z'' = 0, z1 = 0, z2 = 0, z3 - 2 >= 0, z = 0, z' = 0
   divide_ys#1(z, z') -{ 1 }-> 1 + take#2(z', z) + (1 + drop#2(z', z) + 1) :|: z' >= 0, z >= 0
   drop#2(z, z') -{ 1 }-> z' :|: z = 0, z' >= 0
   drop#2(z, z') -{ 1 }-> drop#2(z - 1, x64) :|: z' = 1 + x56 + x64, z - 1 >= 0, x64 >= 0, x56 >= 0
   drop#2(z, z') -{ 1 }-> 3 :|: z = 1 + 0, z' = 1
   drop#2(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   halve#1(z) -{ 1 }-> 0 :|: z = 0
   halve#1(z) -{ 0 }-> 0 :|: z >= 0
   halve#1(z) -{ 1 }-> 1 + halve#1(z - 2) :|: z - 2 >= 0
   halve#1(z) -{ 1 }-> 1 + 0 :|: z = 1 + 0
   length#1(z) -{ 1 }-> 0 :|: z = 1
   length#1(z) -{ 0 }-> 0 :|: z >= 0
   length#1(z) -{ 1 }-> 1 + length#1(x8) :|: x8 >= 0, x6 >= 0, z = 1 + x6 + x8
   leq#2(z, z') -{ 1 }-> leq#2(z - 1, z' - 1) :|: z - 1 >= 0, z' - 1 >= 0
   leq#2(z, z') -{ 1 }-> 2 :|: z = 0, z' >= 0
   leq#2(z, z') -{ 1 }-> 1 :|: z - 1 >= 0, z' = 0
   leq#2(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   main(z) -{ 1 }-> dc#1(0, 0, 0, 0, 0, z) :|: z >= 0
   map#2(z, z') -{ 1 }-> 1 :|: x4 >= 0, x8 >= 0, x6 >= 0, z = 1 + x2 + x4 + x6 + x8 + x10, z' = 1, x10 >= 0, x2 >= 0
   map#2(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   map#2(z, z') -{ 1 }-> 1 + dc#1(x6, x8, x10, x12, x14, x4) + map#2(1 + x6 + x8 + x10 + x12 + x14, x2) :|: x4 >= 0, x8 >= 0, z' = 1 + x4 + x2, x6 >= 0, x12 >= 0, x14 >= 0, x10 >= 0, x2 >= 0, z = 1 + x6 + x8 + x10 + x12 + x14
   merge#2(z, z') -{ 1 }-> z' :|: z = 1, z' >= 0
   merge#2(z, z') -{ 2 }-> cond_merge_ys_zs_2(leq#2(x4', x2'), 1 + (1 + x4') + x6, 1 + (1 + x2') + x2, 1 + x4', x6, 1 + x2', x2) :|: x2' >= 0, z = 1 + (1 + x4') + x6, x6 >= 0, z' = 1 + (1 + x2') + x2, x4' >= 0, x2 >= 0
   merge#2(z, z') -{ 2 }-> cond_merge_ys_zs_2(2, 1 + 0 + (z - 1), 1 + x4 + x2, 0, z - 1, x4, x2) :|: x4 >= 0, z' = 1 + x4 + x2, z - 1 >= 0, x2 >= 0
   merge#2(z, z') -{ 2 }-> cond_merge_ys_zs_2(1, 1 + (1 + x20') + x6, 1 + 0 + (z' - 1), 1 + x20', x6, 0, z' - 1) :|: z = 1 + (1 + x20') + x6, x6 >= 0, x20' >= 0, z' - 1 >= 0
   merge#2(z, z') -{ 1 }-> cond_merge_ys_zs_2(0, 1 + x8 + x6, 1 + x4 + x2, x8, x6, x4, x2) :|: x4 >= 0, x8 >= 0, z' = 1 + x4 + x2, x6 >= 0, z = 1 + x8 + x6, x2 >= 0
   merge#2(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   merge#2(z, z') -{ 1 }-> 1 + x4 + x2 :|: x4 >= 0, z = 1 + x4 + x2, z' = 1, x2 >= 0
   take#2(z, z') -{ 1 }-> 1 :|: z = 0, z' >= 0
   take#2(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   take#2(z, z') -{ 1 }-> 1 + x56 + take#2(z - 1, x64) :|: z' = 1 + x56 + x64, z - 1 >= 0, x64 >= 0, x56 >= 0
   take#2(z, z') -{ 1 }-> 1 + 2 + 1 :|: z = 1 + 0, z' = 1


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

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

   { leq#2 }
   { take#2 }
   { halve#1 }
   { length#1 }
   { drop#2 }
   { merge#2, cond_merge_ys_zs_2 }
   { divide_ys#1 }
   { const_f#2 }
   { dc#1, map#2 }
   { main }

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

(18)
Obligation:
Complexity RNTS consisting of the following rules:

   cond_merge_ys_zs_2(z, z', z'', z1, z2, z3, z4) -{ 0 }-> 0 :|: z >= 0, z4 >= 0, z' >= 0, z3 >= 0, z'' >= 0, z1 >= 0, z2 >= 0
   cond_merge_ys_zs_2(z, z', z'', z1, z2, z3, z4) -{ 1 }-> 1 + z1 + merge#2(z2, 1 + x5 + x6) :|: x5 >= 0, x8 >= 0, z' = 1 + x7 + x8, z'' = 1 + x5 + x6, z2 >= 0, z3 >= 0, z = 2, z1 >= 0, z4 >= 0, x7 >= 0, x6 >= 0
   cond_merge_ys_zs_2(z, z', z'', z1, z2, z3, z4) -{ 1 }-> 1 + z3 + merge#2(1 + x7 + x8, z4) :|: x5 >= 0, x8 >= 0, z = 1, z' = 1 + x7 + x8, z'' = 1 + x5 + x6, z2 >= 0, z3 >= 0, z1 >= 0, z4 >= 0, x7 >= 0, x6 >= 0
   const_f#2(z, z') -{ 1 }-> merge#2(x6, x4) :|: x4 >= 0, z' = 1 + x6 + (1 + x4 + x2), x6 >= 0, z >= 0, x2 >= 0
   const_f#2(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   dc#1(z, z', z'', z1, z2, z3) -{ 1 }-> const_f#2(1 + x51 + (1 + x25 + x33), map#2(1 + 0 + 0 + 0 + 0 + 0, divide_ys#1(1 + x51 + (1 + x25 + x33), 1 + halve#1(0)))) :|: z'' = 0, z1 = 0, x33 >= 0, z3 = 1 + x51 + (1 + x25 + x33), z2 = 0, x51 >= 0, x25 >= 0, z = 0, z' = 0
   dc#1(z, z', z'', z1, z2, z3) -{ 2 }-> const_f#2(1 + x51 + (1 + x25 + 1), map#2(1 + 0 + 0 + 0 + 0 + 0, divide_ys#1(1 + x51 + (1 + x25 + 1), 1 + halve#1(0)))) :|: z'' = 0, z3 = 1 + x51 + (1 + x25 + 1), z1 = 0, z2 = 0, x51 >= 0, x25 >= 0, z = 0, z' = 0
   dc#1(z, z', z'', z1, z2, z3) -{ 2 }-> const_f#2(1 + x51 + (1 + x25 + (1 + x6' + x8')), map#2(1 + 0 + 0 + 0 + 0 + 0, divide_ys#1(1 + x51 + (1 + x25 + (1 + x6' + x8')), 1 + halve#1(1 + length#1(x8'))))) :|: z'' = 0, z1 = 0, z2 = 0, x51 >= 0, x25 >= 0, x6' >= 0, z3 = 1 + x51 + (1 + x25 + (1 + x6' + x8')), z = 0, x8' >= 0, z' = 0
   dc#1(z, z', z'', z1, z2, z3) -{ 1 }-> 1 :|: z'' = 0, z1 = 0, z2 = 0, z3 = 1, z = 0, z' = 0
   dc#1(z, z', z'', z1, z2, z3) -{ 0 }-> 0 :|: z >= 0, z2 >= 0, z' >= 0, z3 >= 0, z'' >= 0, z1 >= 0
   dc#1(z, z', z'', z1, z2, z3) -{ 1 }-> 1 + (z3 - 2) + 1 :|: z'' = 0, z1 = 0, z2 = 0, z3 - 2 >= 0, z = 0, z' = 0
   divide_ys#1(z, z') -{ 1 }-> 1 + take#2(z', z) + (1 + drop#2(z', z) + 1) :|: z' >= 0, z >= 0
   drop#2(z, z') -{ 1 }-> z' :|: z = 0, z' >= 0
   drop#2(z, z') -{ 1 }-> drop#2(z - 1, x64) :|: z' = 1 + x56 + x64, z - 1 >= 0, x64 >= 0, x56 >= 0
   drop#2(z, z') -{ 1 }-> 3 :|: z = 1 + 0, z' = 1
   drop#2(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   halve#1(z) -{ 1 }-> 0 :|: z = 0
   halve#1(z) -{ 0 }-> 0 :|: z >= 0
   halve#1(z) -{ 1 }-> 1 + halve#1(z - 2) :|: z - 2 >= 0
   halve#1(z) -{ 1 }-> 1 + 0 :|: z = 1 + 0
   length#1(z) -{ 1 }-> 0 :|: z = 1
   length#1(z) -{ 0 }-> 0 :|: z >= 0
   length#1(z) -{ 1 }-> 1 + length#1(x8) :|: x8 >= 0, x6 >= 0, z = 1 + x6 + x8
   leq#2(z, z') -{ 1 }-> leq#2(z - 1, z' - 1) :|: z - 1 >= 0, z' - 1 >= 0
   leq#2(z, z') -{ 1 }-> 2 :|: z = 0, z' >= 0
   leq#2(z, z') -{ 1 }-> 1 :|: z - 1 >= 0, z' = 0
   leq#2(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   main(z) -{ 1 }-> dc#1(0, 0, 0, 0, 0, z) :|: z >= 0
   map#2(z, z') -{ 1 }-> 1 :|: x4 >= 0, x8 >= 0, x6 >= 0, z = 1 + x2 + x4 + x6 + x8 + x10, z' = 1, x10 >= 0, x2 >= 0
   map#2(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   map#2(z, z') -{ 1 }-> 1 + dc#1(x6, x8, x10, x12, x14, x4) + map#2(1 + x6 + x8 + x10 + x12 + x14, x2) :|: x4 >= 0, x8 >= 0, z' = 1 + x4 + x2, x6 >= 0, x12 >= 0, x14 >= 0, x10 >= 0, x2 >= 0, z = 1 + x6 + x8 + x10 + x12 + x14
   merge#2(z, z') -{ 1 }-> z' :|: z = 1, z' >= 0
   merge#2(z, z') -{ 2 }-> cond_merge_ys_zs_2(leq#2(x4', x2'), 1 + (1 + x4') + x6, 1 + (1 + x2') + x2, 1 + x4', x6, 1 + x2', x2) :|: x2' >= 0, z = 1 + (1 + x4') + x6, x6 >= 0, z' = 1 + (1 + x2') + x2, x4' >= 0, x2 >= 0
   merge#2(z, z') -{ 2 }-> cond_merge_ys_zs_2(2, 1 + 0 + (z - 1), 1 + x4 + x2, 0, z - 1, x4, x2) :|: x4 >= 0, z' = 1 + x4 + x2, z - 1 >= 0, x2 >= 0
   merge#2(z, z') -{ 2 }-> cond_merge_ys_zs_2(1, 1 + (1 + x20') + x6, 1 + 0 + (z' - 1), 1 + x20', x6, 0, z' - 1) :|: z = 1 + (1 + x20') + x6, x6 >= 0, x20' >= 0, z' - 1 >= 0
   merge#2(z, z') -{ 1 }-> cond_merge_ys_zs_2(0, 1 + x8 + x6, 1 + x4 + x2, x8, x6, x4, x2) :|: x4 >= 0, x8 >= 0, z' = 1 + x4 + x2, x6 >= 0, z = 1 + x8 + x6, x2 >= 0
   merge#2(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   merge#2(z, z') -{ 1 }-> 1 + x4 + x2 :|: x4 >= 0, z = 1 + x4 + x2, z' = 1, x2 >= 0
   take#2(z, z') -{ 1 }-> 1 :|: z = 0, z' >= 0
   take#2(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   take#2(z, z') -{ 1 }-> 1 + x56 + take#2(z - 1, x64) :|: z' = 1 + x56 + x64, z - 1 >= 0, x64 >= 0, x56 >= 0
   take#2(z, z') -{ 1 }-> 1 + 2 + 1 :|: z = 1 + 0, z' = 1

Function symbols to be analyzed: {leq#2}, {take#2}, {halve#1}, {length#1}, {drop#2}, {merge#2,cond_merge_ys_zs_2}, {divide_ys#1}, {const_f#2}, {dc#1,map#2}, {main}

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

(20)
Obligation:
Complexity RNTS consisting of the following rules:

   cond_merge_ys_zs_2(z, z', z'', z1, z2, z3, z4) -{ 0 }-> 0 :|: z >= 0, z4 >= 0, z' >= 0, z3 >= 0, z'' >= 0, z1 >= 0, z2 >= 0
   cond_merge_ys_zs_2(z, z', z'', z1, z2, z3, z4) -{ 1 }-> 1 + z1 + merge#2(z2, 1 + x5 + x6) :|: x5 >= 0, x8 >= 0, z' = 1 + x7 + x8, z'' = 1 + x5 + x6, z2 >= 0, z3 >= 0, z = 2, z1 >= 0, z4 >= 0, x7 >= 0, x6 >= 0
   cond_merge_ys_zs_2(z, z', z'', z1, z2, z3, z4) -{ 1 }-> 1 + z3 + merge#2(1 + x7 + x8, z4) :|: x5 >= 0, x8 >= 0, z = 1, z' = 1 + x7 + x8, z'' = 1 + x5 + x6, z2 >= 0, z3 >= 0, z1 >= 0, z4 >= 0, x7 >= 0, x6 >= 0
   const_f#2(z, z') -{ 1 }-> merge#2(x6, x4) :|: x4 >= 0, z' = 1 + x6 + (1 + x4 + x2), x6 >= 0, z >= 0, x2 >= 0
   const_f#2(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   dc#1(z, z', z'', z1, z2, z3) -{ 1 }-> const_f#2(1 + x51 + (1 + x25 + x33), map#2(1 + 0 + 0 + 0 + 0 + 0, divide_ys#1(1 + x51 + (1 + x25 + x33), 1 + halve#1(0)))) :|: z'' = 0, z1 = 0, x33 >= 0, z3 = 1 + x51 + (1 + x25 + x33), z2 = 0, x51 >= 0, x25 >= 0, z = 0, z' = 0
   dc#1(z, z', z'', z1, z2, z3) -{ 2 }-> const_f#2(1 + x51 + (1 + x25 + 1), map#2(1 + 0 + 0 + 0 + 0 + 0, divide_ys#1(1 + x51 + (1 + x25 + 1), 1 + halve#1(0)))) :|: z'' = 0, z3 = 1 + x51 + (1 + x25 + 1), z1 = 0, z2 = 0, x51 >= 0, x25 >= 0, z = 0, z' = 0
   dc#1(z, z', z'', z1, z2, z3) -{ 2 }-> const_f#2(1 + x51 + (1 + x25 + (1 + x6' + x8')), map#2(1 + 0 + 0 + 0 + 0 + 0, divide_ys#1(1 + x51 + (1 + x25 + (1 + x6' + x8')), 1 + halve#1(1 + length#1(x8'))))) :|: z'' = 0, z1 = 0, z2 = 0, x51 >= 0, x25 >= 0, x6' >= 0, z3 = 1 + x51 + (1 + x25 + (1 + x6' + x8')), z = 0, x8' >= 0, z' = 0
   dc#1(z, z', z'', z1, z2, z3) -{ 1 }-> 1 :|: z'' = 0, z1 = 0, z2 = 0, z3 = 1, z = 0, z' = 0
   dc#1(z, z', z'', z1, z2, z3) -{ 0 }-> 0 :|: z >= 0, z2 >= 0, z' >= 0, z3 >= 0, z'' >= 0, z1 >= 0
   dc#1(z, z', z'', z1, z2, z3) -{ 1 }-> 1 + (z3 - 2) + 1 :|: z'' = 0, z1 = 0, z2 = 0, z3 - 2 >= 0, z = 0, z' = 0
   divide_ys#1(z, z') -{ 1 }-> 1 + take#2(z', z) + (1 + drop#2(z', z) + 1) :|: z' >= 0, z >= 0
   drop#2(z, z') -{ 1 }-> z' :|: z = 0, z' >= 0
   drop#2(z, z') -{ 1 }-> drop#2(z - 1, x64) :|: z' = 1 + x56 + x64, z - 1 >= 0, x64 >= 0, x56 >= 0
   drop#2(z, z') -{ 1 }-> 3 :|: z = 1 + 0, z' = 1
   drop#2(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   halve#1(z) -{ 1 }-> 0 :|: z = 0
   halve#1(z) -{ 0 }-> 0 :|: z >= 0
   halve#1(z) -{ 1 }-> 1 + halve#1(z - 2) :|: z - 2 >= 0
   halve#1(z) -{ 1 }-> 1 + 0 :|: z = 1 + 0
   length#1(z) -{ 1 }-> 0 :|: z = 1
   length#1(z) -{ 0 }-> 0 :|: z >= 0
   length#1(z) -{ 1 }-> 1 + length#1(x8) :|: x8 >= 0, x6 >= 0, z = 1 + x6 + x8
   leq#2(z, z') -{ 1 }-> leq#2(z - 1, z' - 1) :|: z - 1 >= 0, z' - 1 >= 0
   leq#2(z, z') -{ 1 }-> 2 :|: z = 0, z' >= 0
   leq#2(z, z') -{ 1 }-> 1 :|: z - 1 >= 0, z' = 0
   leq#2(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   main(z) -{ 1 }-> dc#1(0, 0, 0, 0, 0, z) :|: z >= 0
   map#2(z, z') -{ 1 }-> 1 :|: x4 >= 0, x8 >= 0, x6 >= 0, z = 1 + x2 + x4 + x6 + x8 + x10, z' = 1, x10 >= 0, x2 >= 0
   map#2(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   map#2(z, z') -{ 1 }-> 1 + dc#1(x6, x8, x10, x12, x14, x4) + map#2(1 + x6 + x8 + x10 + x12 + x14, x2) :|: x4 >= 0, x8 >= 0, z' = 1 + x4 + x2, x6 >= 0, x12 >= 0, x14 >= 0, x10 >= 0, x2 >= 0, z = 1 + x6 + x8 + x10 + x12 + x14
   merge#2(z, z') -{ 1 }-> z' :|: z = 1, z' >= 0
   merge#2(z, z') -{ 2 }-> cond_merge_ys_zs_2(leq#2(x4', x2'), 1 + (1 + x4') + x6, 1 + (1 + x2') + x2, 1 + x4', x6, 1 + x2', x2) :|: x2' >= 0, z = 1 + (1 + x4') + x6, x6 >= 0, z' = 1 + (1 + x2') + x2, x4' >= 0, x2 >= 0
   merge#2(z, z') -{ 2 }-> cond_merge_ys_zs_2(2, 1 + 0 + (z - 1), 1 + x4 + x2, 0, z - 1, x4, x2) :|: x4 >= 0, z' = 1 + x4 + x2, z - 1 >= 0, x2 >= 0
   merge#2(z, z') -{ 2 }-> cond_merge_ys_zs_2(1, 1 + (1 + x20') + x6, 1 + 0 + (z' - 1), 1 + x20', x6, 0, z' - 1) :|: z = 1 + (1 + x20') + x6, x6 >= 0, x20' >= 0, z' - 1 >= 0
   merge#2(z, z') -{ 1 }-> cond_merge_ys_zs_2(0, 1 + x8 + x6, 1 + x4 + x2, x8, x6, x4, x2) :|: x4 >= 0, x8 >= 0, z' = 1 + x4 + x2, x6 >= 0, z = 1 + x8 + x6, x2 >= 0
   merge#2(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   merge#2(z, z') -{ 1 }-> 1 + x4 + x2 :|: x4 >= 0, z = 1 + x4 + x2, z' = 1, x2 >= 0
   take#2(z, z') -{ 1 }-> 1 :|: z = 0, z' >= 0
   take#2(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   take#2(z, z') -{ 1 }-> 1 + x56 + take#2(z - 1, x64) :|: z' = 1 + x56 + x64, z - 1 >= 0, x64 >= 0, x56 >= 0
   take#2(z, z') -{ 1 }-> 1 + 2 + 1 :|: z = 1 + 0, z' = 1

Function symbols to be analyzed: {leq#2}, {take#2}, {halve#1}, {length#1}, {drop#2}, {merge#2,cond_merge_ys_zs_2}, {divide_ys#1}, {const_f#2}, {dc#1,map#2}, {main}

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

(21) IntTrsBoundProof (UPPER BOUND(ID))

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

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

(22)
Obligation:
Complexity RNTS consisting of the following rules:

   cond_merge_ys_zs_2(z, z', z'', z1, z2, z3, z4) -{ 0 }-> 0 :|: z >= 0, z4 >= 0, z' >= 0, z3 >= 0, z'' >= 0, z1 >= 0, z2 >= 0
   cond_merge_ys_zs_2(z, z', z'', z1, z2, z3, z4) -{ 1 }-> 1 + z1 + merge#2(z2, 1 + x5 + x6) :|: x5 >= 0, x8 >= 0, z' = 1 + x7 + x8, z'' = 1 + x5 + x6, z2 >= 0, z3 >= 0, z = 2, z1 >= 0, z4 >= 0, x7 >= 0, x6 >= 0
   cond_merge_ys_zs_2(z, z', z'', z1, z2, z3, z4) -{ 1 }-> 1 + z3 + merge#2(1 + x7 + x8, z4) :|: x5 >= 0, x8 >= 0, z = 1, z' = 1 + x7 + x8, z'' = 1 + x5 + x6, z2 >= 0, z3 >= 0, z1 >= 0, z4 >= 0, x7 >= 0, x6 >= 0
   const_f#2(z, z') -{ 1 }-> merge#2(x6, x4) :|: x4 >= 0, z' = 1 + x6 + (1 + x4 + x2), x6 >= 0, z >= 0, x2 >= 0
   const_f#2(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   dc#1(z, z', z'', z1, z2, z3) -{ 1 }-> const_f#2(1 + x51 + (1 + x25 + x33), map#2(1 + 0 + 0 + 0 + 0 + 0, divide_ys#1(1 + x51 + (1 + x25 + x33), 1 + halve#1(0)))) :|: z'' = 0, z1 = 0, x33 >= 0, z3 = 1 + x51 + (1 + x25 + x33), z2 = 0, x51 >= 0, x25 >= 0, z = 0, z' = 0
   dc#1(z, z', z'', z1, z2, z3) -{ 2 }-> const_f#2(1 + x51 + (1 + x25 + 1), map#2(1 + 0 + 0 + 0 + 0 + 0, divide_ys#1(1 + x51 + (1 + x25 + 1), 1 + halve#1(0)))) :|: z'' = 0, z3 = 1 + x51 + (1 + x25 + 1), z1 = 0, z2 = 0, x51 >= 0, x25 >= 0, z = 0, z' = 0
   dc#1(z, z', z'', z1, z2, z3) -{ 2 }-> const_f#2(1 + x51 + (1 + x25 + (1 + x6' + x8')), map#2(1 + 0 + 0 + 0 + 0 + 0, divide_ys#1(1 + x51 + (1 + x25 + (1 + x6' + x8')), 1 + halve#1(1 + length#1(x8'))))) :|: z'' = 0, z1 = 0, z2 = 0, x51 >= 0, x25 >= 0, x6' >= 0, z3 = 1 + x51 + (1 + x25 + (1 + x6' + x8')), z = 0, x8' >= 0, z' = 0
   dc#1(z, z', z'', z1, z2, z3) -{ 1 }-> 1 :|: z'' = 0, z1 = 0, z2 = 0, z3 = 1, z = 0, z' = 0
   dc#1(z, z', z'', z1, z2, z3) -{ 0 }-> 0 :|: z >= 0, z2 >= 0, z' >= 0, z3 >= 0, z'' >= 0, z1 >= 0
   dc#1(z, z', z'', z1, z2, z3) -{ 1 }-> 1 + (z3 - 2) + 1 :|: z'' = 0, z1 = 0, z2 = 0, z3 - 2 >= 0, z = 0, z' = 0
   divide_ys#1(z, z') -{ 1 }-> 1 + take#2(z', z) + (1 + drop#2(z', z) + 1) :|: z' >= 0, z >= 0
   drop#2(z, z') -{ 1 }-> z' :|: z = 0, z' >= 0
   drop#2(z, z') -{ 1 }-> drop#2(z - 1, x64) :|: z' = 1 + x56 + x64, z - 1 >= 0, x64 >= 0, x56 >= 0
   drop#2(z, z') -{ 1 }-> 3 :|: z = 1 + 0, z' = 1
   drop#2(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   halve#1(z) -{ 1 }-> 0 :|: z = 0
   halve#1(z) -{ 0 }-> 0 :|: z >= 0
   halve#1(z) -{ 1 }-> 1 + halve#1(z - 2) :|: z - 2 >= 0
   halve#1(z) -{ 1 }-> 1 + 0 :|: z = 1 + 0
   length#1(z) -{ 1 }-> 0 :|: z = 1
   length#1(z) -{ 0 }-> 0 :|: z >= 0
   length#1(z) -{ 1 }-> 1 + length#1(x8) :|: x8 >= 0, x6 >= 0, z = 1 + x6 + x8
   leq#2(z, z') -{ 1 }-> leq#2(z - 1, z' - 1) :|: z - 1 >= 0, z' - 1 >= 0
   leq#2(z, z') -{ 1 }-> 2 :|: z = 0, z' >= 0
   leq#2(z, z') -{ 1 }-> 1 :|: z - 1 >= 0, z' = 0
   leq#2(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   main(z) -{ 1 }-> dc#1(0, 0, 0, 0, 0, z) :|: z >= 0
   map#2(z, z') -{ 1 }-> 1 :|: x4 >= 0, x8 >= 0, x6 >= 0, z = 1 + x2 + x4 + x6 + x8 + x10, z' = 1, x10 >= 0, x2 >= 0
   map#2(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   map#2(z, z') -{ 1 }-> 1 + dc#1(x6, x8, x10, x12, x14, x4) + map#2(1 + x6 + x8 + x10 + x12 + x14, x2) :|: x4 >= 0, x8 >= 0, z' = 1 + x4 + x2, x6 >= 0, x12 >= 0, x14 >= 0, x10 >= 0, x2 >= 0, z = 1 + x6 + x8 + x10 + x12 + x14
   merge#2(z, z') -{ 1 }-> z' :|: z = 1, z' >= 0
   merge#2(z, z') -{ 2 }-> cond_merge_ys_zs_2(leq#2(x4', x2'), 1 + (1 + x4') + x6, 1 + (1 + x2') + x2, 1 + x4', x6, 1 + x2', x2) :|: x2' >= 0, z = 1 + (1 + x4') + x6, x6 >= 0, z' = 1 + (1 + x2') + x2, x4' >= 0, x2 >= 0
   merge#2(z, z') -{ 2 }-> cond_merge_ys_zs_2(2, 1 + 0 + (z - 1), 1 + x4 + x2, 0, z - 1, x4, x2) :|: x4 >= 0, z' = 1 + x4 + x2, z - 1 >= 0, x2 >= 0
   merge#2(z, z') -{ 2 }-> cond_merge_ys_zs_2(1, 1 + (1 + x20') + x6, 1 + 0 + (z' - 1), 1 + x20', x6, 0, z' - 1) :|: z = 1 + (1 + x20') + x6, x6 >= 0, x20' >= 0, z' - 1 >= 0
   merge#2(z, z') -{ 1 }-> cond_merge_ys_zs_2(0, 1 + x8 + x6, 1 + x4 + x2, x8, x6, x4, x2) :|: x4 >= 0, x8 >= 0, z' = 1 + x4 + x2, x6 >= 0, z = 1 + x8 + x6, x2 >= 0
   merge#2(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   merge#2(z, z') -{ 1 }-> 1 + x4 + x2 :|: x4 >= 0, z = 1 + x4 + x2, z' = 1, x2 >= 0
   take#2(z, z') -{ 1 }-> 1 :|: z = 0, z' >= 0
   take#2(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   take#2(z, z') -{ 1 }-> 1 + x56 + take#2(z - 1, x64) :|: z' = 1 + x56 + x64, z - 1 >= 0, x64 >= 0, x56 >= 0
   take#2(z, z') -{ 1 }-> 1 + 2 + 1 :|: z = 1 + 0, z' = 1

Function symbols to be analyzed: {leq#2}, {take#2}, {halve#1}, {length#1}, {drop#2}, {merge#2,cond_merge_ys_zs_2}, {divide_ys#1}, {const_f#2}, {dc#1,map#2}, {main}
Previous analysis results are:
  leq#2: runtime: ?, size: O(1) [2]

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

(23) IntTrsBoundProof (UPPER BOUND(ID))

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

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

(24)
Obligation:
Complexity RNTS consisting of the following rules:

   cond_merge_ys_zs_2(z, z', z'', z1, z2, z3, z4) -{ 0 }-> 0 :|: z >= 0, z4 >= 0, z' >= 0, z3 >= 0, z'' >= 0, z1 >= 0, z2 >= 0
   cond_merge_ys_zs_2(z, z', z'', z1, z2, z3, z4) -{ 1 }-> 1 + z1 + merge#2(z2, 1 + x5 + x6) :|: x5 >= 0, x8 >= 0, z' = 1 + x7 + x8, z'' = 1 + x5 + x6, z2 >= 0, z3 >= 0, z = 2, z1 >= 0, z4 >= 0, x7 >= 0, x6 >= 0
   cond_merge_ys_zs_2(z, z', z'', z1, z2, z3, z4) -{ 1 }-> 1 + z3 + merge#2(1 + x7 + x8, z4) :|: x5 >= 0, x8 >= 0, z = 1, z' = 1 + x7 + x8, z'' = 1 + x5 + x6, z2 >= 0, z3 >= 0, z1 >= 0, z4 >= 0, x7 >= 0, x6 >= 0
   const_f#2(z, z') -{ 1 }-> merge#2(x6, x4) :|: x4 >= 0, z' = 1 + x6 + (1 + x4 + x2), x6 >= 0, z >= 0, x2 >= 0
   const_f#2(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   dc#1(z, z', z'', z1, z2, z3) -{ 1 }-> const_f#2(1 + x51 + (1 + x25 + x33), map#2(1 + 0 + 0 + 0 + 0 + 0, divide_ys#1(1 + x51 + (1 + x25 + x33), 1 + halve#1(0)))) :|: z'' = 0, z1 = 0, x33 >= 0, z3 = 1 + x51 + (1 + x25 + x33), z2 = 0, x51 >= 0, x25 >= 0, z = 0, z' = 0
   dc#1(z, z', z'', z1, z2, z3) -{ 2 }-> const_f#2(1 + x51 + (1 + x25 + 1), map#2(1 + 0 + 0 + 0 + 0 + 0, divide_ys#1(1 + x51 + (1 + x25 + 1), 1 + halve#1(0)))) :|: z'' = 0, z3 = 1 + x51 + (1 + x25 + 1), z1 = 0, z2 = 0, x51 >= 0, x25 >= 0, z = 0, z' = 0
   dc#1(z, z', z'', z1, z2, z3) -{ 2 }-> const_f#2(1 + x51 + (1 + x25 + (1 + x6' + x8')), map#2(1 + 0 + 0 + 0 + 0 + 0, divide_ys#1(1 + x51 + (1 + x25 + (1 + x6' + x8')), 1 + halve#1(1 + length#1(x8'))))) :|: z'' = 0, z1 = 0, z2 = 0, x51 >= 0, x25 >= 0, x6' >= 0, z3 = 1 + x51 + (1 + x25 + (1 + x6' + x8')), z = 0, x8' >= 0, z' = 0
   dc#1(z, z', z'', z1, z2, z3) -{ 1 }-> 1 :|: z'' = 0, z1 = 0, z2 = 0, z3 = 1, z = 0, z' = 0
   dc#1(z, z', z'', z1, z2, z3) -{ 0 }-> 0 :|: z >= 0, z2 >= 0, z' >= 0, z3 >= 0, z'' >= 0, z1 >= 0
   dc#1(z, z', z'', z1, z2, z3) -{ 1 }-> 1 + (z3 - 2) + 1 :|: z'' = 0, z1 = 0, z2 = 0, z3 - 2 >= 0, z = 0, z' = 0
   divide_ys#1(z, z') -{ 1 }-> 1 + take#2(z', z) + (1 + drop#2(z', z) + 1) :|: z' >= 0, z >= 0
   drop#2(z, z') -{ 1 }-> z' :|: z = 0, z' >= 0
   drop#2(z, z') -{ 1 }-> drop#2(z - 1, x64) :|: z' = 1 + x56 + x64, z - 1 >= 0, x64 >= 0, x56 >= 0
   drop#2(z, z') -{ 1 }-> 3 :|: z = 1 + 0, z' = 1
   drop#2(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   halve#1(z) -{ 1 }-> 0 :|: z = 0
   halve#1(z) -{ 0 }-> 0 :|: z >= 0
   halve#1(z) -{ 1 }-> 1 + halve#1(z - 2) :|: z - 2 >= 0
   halve#1(z) -{ 1 }-> 1 + 0 :|: z = 1 + 0
   length#1(z) -{ 1 }-> 0 :|: z = 1
   length#1(z) -{ 0 }-> 0 :|: z >= 0
   length#1(z) -{ 1 }-> 1 + length#1(x8) :|: x8 >= 0, x6 >= 0, z = 1 + x6 + x8
   leq#2(z, z') -{ 1 }-> leq#2(z - 1, z' - 1) :|: z - 1 >= 0, z' - 1 >= 0
   leq#2(z, z') -{ 1 }-> 2 :|: z = 0, z' >= 0
   leq#2(z, z') -{ 1 }-> 1 :|: z - 1 >= 0, z' = 0
   leq#2(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   main(z) -{ 1 }-> dc#1(0, 0, 0, 0, 0, z) :|: z >= 0
   map#2(z, z') -{ 1 }-> 1 :|: x4 >= 0, x8 >= 0, x6 >= 0, z = 1 + x2 + x4 + x6 + x8 + x10, z' = 1, x10 >= 0, x2 >= 0
   map#2(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   map#2(z, z') -{ 1 }-> 1 + dc#1(x6, x8, x10, x12, x14, x4) + map#2(1 + x6 + x8 + x10 + x12 + x14, x2) :|: x4 >= 0, x8 >= 0, z' = 1 + x4 + x2, x6 >= 0, x12 >= 0, x14 >= 0, x10 >= 0, x2 >= 0, z = 1 + x6 + x8 + x10 + x12 + x14
   merge#2(z, z') -{ 1 }-> z' :|: z = 1, z' >= 0
   merge#2(z, z') -{ 2 }-> cond_merge_ys_zs_2(leq#2(x4', x2'), 1 + (1 + x4') + x6, 1 + (1 + x2') + x2, 1 + x4', x6, 1 + x2', x2) :|: x2' >= 0, z = 1 + (1 + x4') + x6, x6 >= 0, z' = 1 + (1 + x2') + x2, x4' >= 0, x2 >= 0
   merge#2(z, z') -{ 2 }-> cond_merge_ys_zs_2(2, 1 + 0 + (z - 1), 1 + x4 + x2, 0, z - 1, x4, x2) :|: x4 >= 0, z' = 1 + x4 + x2, z - 1 >= 0, x2 >= 0
   merge#2(z, z') -{ 2 }-> cond_merge_ys_zs_2(1, 1 + (1 + x20') + x6, 1 + 0 + (z' - 1), 1 + x20', x6, 0, z' - 1) :|: z = 1 + (1 + x20') + x6, x6 >= 0, x20' >= 0, z' - 1 >= 0
   merge#2(z, z') -{ 1 }-> cond_merge_ys_zs_2(0, 1 + x8 + x6, 1 + x4 + x2, x8, x6, x4, x2) :|: x4 >= 0, x8 >= 0, z' = 1 + x4 + x2, x6 >= 0, z = 1 + x8 + x6, x2 >= 0
   merge#2(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   merge#2(z, z') -{ 1 }-> 1 + x4 + x2 :|: x4 >= 0, z = 1 + x4 + x2, z' = 1, x2 >= 0
   take#2(z, z') -{ 1 }-> 1 :|: z = 0, z' >= 0
   take#2(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   take#2(z, z') -{ 1 }-> 1 + x56 + take#2(z - 1, x64) :|: z' = 1 + x56 + x64, z - 1 >= 0, x64 >= 0, x56 >= 0
   take#2(z, z') -{ 1 }-> 1 + 2 + 1 :|: z = 1 + 0, z' = 1

Function symbols to be analyzed: {take#2}, {halve#1}, {length#1}, {drop#2}, {merge#2,cond_merge_ys_zs_2}, {divide_ys#1}, {const_f#2}, {dc#1,map#2}, {main}
Previous analysis results are:
  leq#2: runtime: O(n^1) [2 + z'], size: O(1) [2]

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

(26)
Obligation:
Complexity RNTS consisting of the following rules:

   cond_merge_ys_zs_2(z, z', z'', z1, z2, z3, z4) -{ 0 }-> 0 :|: z >= 0, z4 >= 0, z' >= 0, z3 >= 0, z'' >= 0, z1 >= 0, z2 >= 0
   cond_merge_ys_zs_2(z, z', z'', z1, z2, z3, z4) -{ 1 }-> 1 + z1 + merge#2(z2, 1 + x5 + x6) :|: x5 >= 0, x8 >= 0, z' = 1 + x7 + x8, z'' = 1 + x5 + x6, z2 >= 0, z3 >= 0, z = 2, z1 >= 0, z4 >= 0, x7 >= 0, x6 >= 0
   cond_merge_ys_zs_2(z, z', z'', z1, z2, z3, z4) -{ 1 }-> 1 + z3 + merge#2(1 + x7 + x8, z4) :|: x5 >= 0, x8 >= 0, z = 1, z' = 1 + x7 + x8, z'' = 1 + x5 + x6, z2 >= 0, z3 >= 0, z1 >= 0, z4 >= 0, x7 >= 0, x6 >= 0
   const_f#2(z, z') -{ 1 }-> merge#2(x6, x4) :|: x4 >= 0, z' = 1 + x6 + (1 + x4 + x2), x6 >= 0, z >= 0, x2 >= 0
   const_f#2(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   dc#1(z, z', z'', z1, z2, z3) -{ 1 }-> const_f#2(1 + x51 + (1 + x25 + x33), map#2(1 + 0 + 0 + 0 + 0 + 0, divide_ys#1(1 + x51 + (1 + x25 + x33), 1 + halve#1(0)))) :|: z'' = 0, z1 = 0, x33 >= 0, z3 = 1 + x51 + (1 + x25 + x33), z2 = 0, x51 >= 0, x25 >= 0, z = 0, z' = 0
   dc#1(z, z', z'', z1, z2, z3) -{ 2 }-> const_f#2(1 + x51 + (1 + x25 + 1), map#2(1 + 0 + 0 + 0 + 0 + 0, divide_ys#1(1 + x51 + (1 + x25 + 1), 1 + halve#1(0)))) :|: z'' = 0, z3 = 1 + x51 + (1 + x25 + 1), z1 = 0, z2 = 0, x51 >= 0, x25 >= 0, z = 0, z' = 0
   dc#1(z, z', z'', z1, z2, z3) -{ 2 }-> const_f#2(1 + x51 + (1 + x25 + (1 + x6' + x8')), map#2(1 + 0 + 0 + 0 + 0 + 0, divide_ys#1(1 + x51 + (1 + x25 + (1 + x6' + x8')), 1 + halve#1(1 + length#1(x8'))))) :|: z'' = 0, z1 = 0, z2 = 0, x51 >= 0, x25 >= 0, x6' >= 0, z3 = 1 + x51 + (1 + x25 + (1 + x6' + x8')), z = 0, x8' >= 0, z' = 0
   dc#1(z, z', z'', z1, z2, z3) -{ 1 }-> 1 :|: z'' = 0, z1 = 0, z2 = 0, z3 = 1, z = 0, z' = 0
   dc#1(z, z', z'', z1, z2, z3) -{ 0 }-> 0 :|: z >= 0, z2 >= 0, z' >= 0, z3 >= 0, z'' >= 0, z1 >= 0
   dc#1(z, z', z'', z1, z2, z3) -{ 1 }-> 1 + (z3 - 2) + 1 :|: z'' = 0, z1 = 0, z2 = 0, z3 - 2 >= 0, z = 0, z' = 0
   divide_ys#1(z, z') -{ 1 }-> 1 + take#2(z', z) + (1 + drop#2(z', z) + 1) :|: z' >= 0, z >= 0
   drop#2(z, z') -{ 1 }-> z' :|: z = 0, z' >= 0
   drop#2(z, z') -{ 1 }-> drop#2(z - 1, x64) :|: z' = 1 + x56 + x64, z - 1 >= 0, x64 >= 0, x56 >= 0
   drop#2(z, z') -{ 1 }-> 3 :|: z = 1 + 0, z' = 1
   drop#2(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   halve#1(z) -{ 1 }-> 0 :|: z = 0
   halve#1(z) -{ 0 }-> 0 :|: z >= 0
   halve#1(z) -{ 1 }-> 1 + halve#1(z - 2) :|: z - 2 >= 0
   halve#1(z) -{ 1 }-> 1 + 0 :|: z = 1 + 0
   length#1(z) -{ 1 }-> 0 :|: z = 1
   length#1(z) -{ 0 }-> 0 :|: z >= 0
   length#1(z) -{ 1 }-> 1 + length#1(x8) :|: x8 >= 0, x6 >= 0, z = 1 + x6 + x8
   leq#2(z, z') -{ 2 + z' }-> s' :|: s' >= 0, s' <= 2, z - 1 >= 0, z' - 1 >= 0
   leq#2(z, z') -{ 1 }-> 2 :|: z = 0, z' >= 0
   leq#2(z, z') -{ 1 }-> 1 :|: z - 1 >= 0, z' = 0
   leq#2(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   main(z) -{ 1 }-> dc#1(0, 0, 0, 0, 0, z) :|: z >= 0
   map#2(z, z') -{ 1 }-> 1 :|: x4 >= 0, x8 >= 0, x6 >= 0, z = 1 + x2 + x4 + x6 + x8 + x10, z' = 1, x10 >= 0, x2 >= 0
   map#2(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   map#2(z, z') -{ 1 }-> 1 + dc#1(x6, x8, x10, x12, x14, x4) + map#2(1 + x6 + x8 + x10 + x12 + x14, x2) :|: x4 >= 0, x8 >= 0, z' = 1 + x4 + x2, x6 >= 0, x12 >= 0, x14 >= 0, x10 >= 0, x2 >= 0, z = 1 + x6 + x8 + x10 + x12 + x14
   merge#2(z, z') -{ 1 }-> z' :|: z = 1, z' >= 0
   merge#2(z, z') -{ 4 + x2' }-> cond_merge_ys_zs_2(s, 1 + (1 + x4') + x6, 1 + (1 + x2') + x2, 1 + x4', x6, 1 + x2', x2) :|: s >= 0, s <= 2, x2' >= 0, z = 1 + (1 + x4') + x6, x6 >= 0, z' = 1 + (1 + x2') + x2, x4' >= 0, x2 >= 0
   merge#2(z, z') -{ 2 }-> cond_merge_ys_zs_2(2, 1 + 0 + (z - 1), 1 + x4 + x2, 0, z - 1, x4, x2) :|: x4 >= 0, z' = 1 + x4 + x2, z - 1 >= 0, x2 >= 0
   merge#2(z, z') -{ 2 }-> cond_merge_ys_zs_2(1, 1 + (1 + x20') + x6, 1 + 0 + (z' - 1), 1 + x20', x6, 0, z' - 1) :|: z = 1 + (1 + x20') + x6, x6 >= 0, x20' >= 0, z' - 1 >= 0
   merge#2(z, z') -{ 1 }-> cond_merge_ys_zs_2(0, 1 + x8 + x6, 1 + x4 + x2, x8, x6, x4, x2) :|: x4 >= 0, x8 >= 0, z' = 1 + x4 + x2, x6 >= 0, z = 1 + x8 + x6, x2 >= 0
   merge#2(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   merge#2(z, z') -{ 1 }-> 1 + x4 + x2 :|: x4 >= 0, z = 1 + x4 + x2, z' = 1, x2 >= 0
   take#2(z, z') -{ 1 }-> 1 :|: z = 0, z' >= 0
   take#2(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   take#2(z, z') -{ 1 }-> 1 + x56 + take#2(z - 1, x64) :|: z' = 1 + x56 + x64, z - 1 >= 0, x64 >= 0, x56 >= 0
   take#2(z, z') -{ 1 }-> 1 + 2 + 1 :|: z = 1 + 0, z' = 1

Function symbols to be analyzed: {take#2}, {halve#1}, {length#1}, {drop#2}, {merge#2,cond_merge_ys_zs_2}, {divide_ys#1}, {const_f#2}, {dc#1,map#2}, {main}
Previous analysis results are:
  leq#2: runtime: O(n^1) [2 + z'], size: O(1) [2]

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

(27) IntTrsBoundProof (UPPER BOUND(ID))

Computed SIZE bound using CoFloCo for: take#2
after applying outer abstraction to obtain an ITS,
resulting in: O(n^1) with polynomial bound: 4 + z'

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

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

   cond_merge_ys_zs_2(z, z', z'', z1, z2, z3, z4) -{ 0 }-> 0 :|: z >= 0, z4 >= 0, z' >= 0, z3 >= 0, z'' >= 0, z1 >= 0, z2 >= 0
   cond_merge_ys_zs_2(z, z', z'', z1, z2, z3, z4) -{ 1 }-> 1 + z1 + merge#2(z2, 1 + x5 + x6) :|: x5 >= 0, x8 >= 0, z' = 1 + x7 + x8, z'' = 1 + x5 + x6, z2 >= 0, z3 >= 0, z = 2, z1 >= 0, z4 >= 0, x7 >= 0, x6 >= 0
   cond_merge_ys_zs_2(z, z', z'', z1, z2, z3, z4) -{ 1 }-> 1 + z3 + merge#2(1 + x7 + x8, z4) :|: x5 >= 0, x8 >= 0, z = 1, z' = 1 + x7 + x8, z'' = 1 + x5 + x6, z2 >= 0, z3 >= 0, z1 >= 0, z4 >= 0, x7 >= 0, x6 >= 0
   const_f#2(z, z') -{ 1 }-> merge#2(x6, x4) :|: x4 >= 0, z' = 1 + x6 + (1 + x4 + x2), x6 >= 0, z >= 0, x2 >= 0
   const_f#2(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   dc#1(z, z', z'', z1, z2, z3) -{ 1 }-> const_f#2(1 + x51 + (1 + x25 + x33), map#2(1 + 0 + 0 + 0 + 0 + 0, divide_ys#1(1 + x51 + (1 + x25 + x33), 1 + halve#1(0)))) :|: z'' = 0, z1 = 0, x33 >= 0, z3 = 1 + x51 + (1 + x25 + x33), z2 = 0, x51 >= 0, x25 >= 0, z = 0, z' = 0
   dc#1(z, z', z'', z1, z2, z3) -{ 2 }-> const_f#2(1 + x51 + (1 + x25 + 1), map#2(1 + 0 + 0 + 0 + 0 + 0, divide_ys#1(1 + x51 + (1 + x25 + 1), 1 + halve#1(0)))) :|: z'' = 0, z3 = 1 + x51 + (1 + x25 + 1), z1 = 0, z2 = 0, x51 >= 0, x25 >= 0, z = 0, z' = 0
   dc#1(z, z', z'', z1, z2, z3) -{ 2 }-> const_f#2(1 + x51 + (1 + x25 + (1 + x6' + x8')), map#2(1 + 0 + 0 + 0 + 0 + 0, divide_ys#1(1 + x51 + (1 + x25 + (1 + x6' + x8')), 1 + halve#1(1 + length#1(x8'))))) :|: z'' = 0, z1 = 0, z2 = 0, x51 >= 0, x25 >= 0, x6' >= 0, z3 = 1 + x51 + (1 + x25 + (1 + x6' + x8')), z = 0, x8' >= 0, z' = 0
   dc#1(z, z', z'', z1, z2, z3) -{ 1 }-> 1 :|: z'' = 0, z1 = 0, z2 = 0, z3 = 1, z = 0, z' = 0
   dc#1(z, z', z'', z1, z2, z3) -{ 0 }-> 0 :|: z >= 0, z2 >= 0, z' >= 0, z3 >= 0, z'' >= 0, z1 >= 0
   dc#1(z, z', z'', z1, z2, z3) -{ 1 }-> 1 + (z3 - 2) + 1 :|: z'' = 0, z1 = 0, z2 = 0, z3 - 2 >= 0, z = 0, z' = 0
   divide_ys#1(z, z') -{ 1 }-> 1 + take#2(z', z) + (1 + drop#2(z', z) + 1) :|: z' >= 0, z >= 0
   drop#2(z, z') -{ 1 }-> z' :|: z = 0, z' >= 0
   drop#2(z, z') -{ 1 }-> drop#2(z - 1, x64) :|: z' = 1 + x56 + x64, z - 1 >= 0, x64 >= 0, x56 >= 0
   drop#2(z, z') -{ 1 }-> 3 :|: z = 1 + 0, z' = 1
   drop#2(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   halve#1(z) -{ 1 }-> 0 :|: z = 0
   halve#1(z) -{ 0 }-> 0 :|: z >= 0
   halve#1(z) -{ 1 }-> 1 + halve#1(z - 2) :|: z - 2 >= 0
   halve#1(z) -{ 1 }-> 1 + 0 :|: z = 1 + 0
   length#1(z) -{ 1 }-> 0 :|: z = 1
   length#1(z) -{ 0 }-> 0 :|: z >= 0
   length#1(z) -{ 1 }-> 1 + length#1(x8) :|: x8 >= 0, x6 >= 0, z = 1 + x6 + x8
   leq#2(z, z') -{ 2 + z' }-> s' :|: s' >= 0, s' <= 2, z - 1 >= 0, z' - 1 >= 0
   leq#2(z, z') -{ 1 }-> 2 :|: z = 0, z' >= 0
   leq#2(z, z') -{ 1 }-> 1 :|: z - 1 >= 0, z' = 0
   leq#2(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   main(z) -{ 1 }-> dc#1(0, 0, 0, 0, 0, z) :|: z >= 0
   map#2(z, z') -{ 1 }-> 1 :|: x4 >= 0, x8 >= 0, x6 >= 0, z = 1 + x2 + x4 + x6 + x8 + x10, z' = 1, x10 >= 0, x2 >= 0
   map#2(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   map#2(z, z') -{ 1 }-> 1 + dc#1(x6, x8, x10, x12, x14, x4) + map#2(1 + x6 + x8 + x10 + x12 + x14, x2) :|: x4 >= 0, x8 >= 0, z' = 1 + x4 + x2, x6 >= 0, x12 >= 0, x14 >= 0, x10 >= 0, x2 >= 0, z = 1 + x6 + x8 + x10 + x12 + x14
   merge#2(z, z') -{ 1 }-> z' :|: z = 1, z' >= 0
   merge#2(z, z') -{ 4 + x2' }-> cond_merge_ys_zs_2(s, 1 + (1 + x4') + x6, 1 + (1 + x2') + x2, 1 + x4', x6, 1 + x2', x2) :|: s >= 0, s <= 2, x2' >= 0, z = 1 + (1 + x4') + x6, x6 >= 0, z' = 1 + (1 + x2') + x2, x4' >= 0, x2 >= 0
   merge#2(z, z') -{ 2 }-> cond_merge_ys_zs_2(2, 1 + 0 + (z - 1), 1 + x4 + x2, 0, z - 1, x4, x2) :|: x4 >= 0, z' = 1 + x4 + x2, z - 1 >= 0, x2 >= 0
   merge#2(z, z') -{ 2 }-> cond_merge_ys_zs_2(1, 1 + (1 + x20') + x6, 1 + 0 + (z' - 1), 1 + x20', x6, 0, z' - 1) :|: z = 1 + (1 + x20') + x6, x6 >= 0, x20' >= 0, z' - 1 >= 0
   merge#2(z, z') -{ 1 }-> cond_merge_ys_zs_2(0, 1 + x8 + x6, 1 + x4 + x2, x8, x6, x4, x2) :|: x4 >= 0, x8 >= 0, z' = 1 + x4 + x2, x6 >= 0, z = 1 + x8 + x6, x2 >= 0
   merge#2(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   merge#2(z, z') -{ 1 }-> 1 + x4 + x2 :|: x4 >= 0, z = 1 + x4 + x2, z' = 1, x2 >= 0
   take#2(z, z') -{ 1 }-> 1 :|: z = 0, z' >= 0
   take#2(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   take#2(z, z') -{ 1 }-> 1 + x56 + take#2(z - 1, x64) :|: z' = 1 + x56 + x64, z - 1 >= 0, x64 >= 0, x56 >= 0
   take#2(z, z') -{ 1 }-> 1 + 2 + 1 :|: z = 1 + 0, z' = 1

Function symbols to be analyzed: {take#2}, {halve#1}, {length#1}, {drop#2}, {merge#2,cond_merge_ys_zs_2}, {divide_ys#1}, {const_f#2}, {dc#1,map#2}, {main}
Previous analysis results are:
  leq#2: runtime: O(n^1) [2 + z'], size: O(1) [2]
  take#2: runtime: ?, size: O(n^1) [4 + z']

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

(29) IntTrsBoundProof (UPPER BOUND(ID))

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

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

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

   cond_merge_ys_zs_2(z, z', z'', z1, z2, z3, z4) -{ 0 }-> 0 :|: z >= 0, z4 >= 0, z' >= 0, z3 >= 0, z'' >= 0, z1 >= 0, z2 >= 0
   cond_merge_ys_zs_2(z, z', z'', z1, z2, z3, z4) -{ 1 }-> 1 + z1 + merge#2(z2, 1 + x5 + x6) :|: x5 >= 0, x8 >= 0, z' = 1 + x7 + x8, z'' = 1 + x5 + x6, z2 >= 0, z3 >= 0, z = 2, z1 >= 0, z4 >= 0, x7 >= 0, x6 >= 0
   cond_merge_ys_zs_2(z, z', z'', z1, z2, z3, z4) -{ 1 }-> 1 + z3 + merge#2(1 + x7 + x8, z4) :|: x5 >= 0, x8 >= 0, z = 1, z' = 1 + x7 + x8, z'' = 1 + x5 + x6, z2 >= 0, z3 >= 0, z1 >= 0, z4 >= 0, x7 >= 0, x6 >= 0
   const_f#2(z, z') -{ 1 }-> merge#2(x6, x4) :|: x4 >= 0, z' = 1 + x6 + (1 + x4 + x2), x6 >= 0, z >= 0, x2 >= 0
   const_f#2(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   dc#1(z, z', z'', z1, z2, z3) -{ 1 }-> const_f#2(1 + x51 + (1 + x25 + x33), map#2(1 + 0 + 0 + 0 + 0 + 0, divide_ys#1(1 + x51 + (1 + x25 + x33), 1 + halve#1(0)))) :|: z'' = 0, z1 = 0, x33 >= 0, z3 = 1 + x51 + (1 + x25 + x33), z2 = 0, x51 >= 0, x25 >= 0, z = 0, z' = 0
   dc#1(z, z', z'', z1, z2, z3) -{ 2 }-> const_f#2(1 + x51 + (1 + x25 + 1), map#2(1 + 0 + 0 + 0 + 0 + 0, divide_ys#1(1 + x51 + (1 + x25 + 1), 1 + halve#1(0)))) :|: z'' = 0, z3 = 1 + x51 + (1 + x25 + 1), z1 = 0, z2 = 0, x51 >= 0, x25 >= 0, z = 0, z' = 0
   dc#1(z, z', z'', z1, z2, z3) -{ 2 }-> const_f#2(1 + x51 + (1 + x25 + (1 + x6' + x8')), map#2(1 + 0 + 0 + 0 + 0 + 0, divide_ys#1(1 + x51 + (1 + x25 + (1 + x6' + x8')), 1 + halve#1(1 + length#1(x8'))))) :|: z'' = 0, z1 = 0, z2 = 0, x51 >= 0, x25 >= 0, x6' >= 0, z3 = 1 + x51 + (1 + x25 + (1 + x6' + x8')), z = 0, x8' >= 0, z' = 0
   dc#1(z, z', z'', z1, z2, z3) -{ 1 }-> 1 :|: z'' = 0, z1 = 0, z2 = 0, z3 = 1, z = 0, z' = 0
   dc#1(z, z', z'', z1, z2, z3) -{ 0 }-> 0 :|: z >= 0, z2 >= 0, z' >= 0, z3 >= 0, z'' >= 0, z1 >= 0
   dc#1(z, z', z'', z1, z2, z3) -{ 1 }-> 1 + (z3 - 2) + 1 :|: z'' = 0, z1 = 0, z2 = 0, z3 - 2 >= 0, z = 0, z' = 0
   divide_ys#1(z, z') -{ 1 }-> 1 + take#2(z', z) + (1 + drop#2(z', z) + 1) :|: z' >= 0, z >= 0
   drop#2(z, z') -{ 1 }-> z' :|: z = 0, z' >= 0
   drop#2(z, z') -{ 1 }-> drop#2(z - 1, x64) :|: z' = 1 + x56 + x64, z - 1 >= 0, x64 >= 0, x56 >= 0
   drop#2(z, z') -{ 1 }-> 3 :|: z = 1 + 0, z' = 1
   drop#2(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   halve#1(z) -{ 1 }-> 0 :|: z = 0
   halve#1(z) -{ 0 }-> 0 :|: z >= 0
   halve#1(z) -{ 1 }-> 1 + halve#1(z - 2) :|: z - 2 >= 0
   halve#1(z) -{ 1 }-> 1 + 0 :|: z = 1 + 0
   length#1(z) -{ 1 }-> 0 :|: z = 1
   length#1(z) -{ 0 }-> 0 :|: z >= 0
   length#1(z) -{ 1 }-> 1 + length#1(x8) :|: x8 >= 0, x6 >= 0, z = 1 + x6 + x8
   leq#2(z, z') -{ 2 + z' }-> s' :|: s' >= 0, s' <= 2, z - 1 >= 0, z' - 1 >= 0
   leq#2(z, z') -{ 1 }-> 2 :|: z = 0, z' >= 0
   leq#2(z, z') -{ 1 }-> 1 :|: z - 1 >= 0, z' = 0
   leq#2(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   main(z) -{ 1 }-> dc#1(0, 0, 0, 0, 0, z) :|: z >= 0
   map#2(z, z') -{ 1 }-> 1 :|: x4 >= 0, x8 >= 0, x6 >= 0, z = 1 + x2 + x4 + x6 + x8 + x10, z' = 1, x10 >= 0, x2 >= 0
   map#2(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   map#2(z, z') -{ 1 }-> 1 + dc#1(x6, x8, x10, x12, x14, x4) + map#2(1 + x6 + x8 + x10 + x12 + x14, x2) :|: x4 >= 0, x8 >= 0, z' = 1 + x4 + x2, x6 >= 0, x12 >= 0, x14 >= 0, x10 >= 0, x2 >= 0, z = 1 + x6 + x8 + x10 + x12 + x14
   merge#2(z, z') -{ 1 }-> z' :|: z = 1, z' >= 0
   merge#2(z, z') -{ 4 + x2' }-> cond_merge_ys_zs_2(s, 1 + (1 + x4') + x6, 1 + (1 + x2') + x2, 1 + x4', x6, 1 + x2', x2) :|: s >= 0, s <= 2, x2' >= 0, z = 1 + (1 + x4') + x6, x6 >= 0, z' = 1 + (1 + x2') + x2, x4' >= 0, x2 >= 0
   merge#2(z, z') -{ 2 }-> cond_merge_ys_zs_2(2, 1 + 0 + (z - 1), 1 + x4 + x2, 0, z - 1, x4, x2) :|: x4 >= 0, z' = 1 + x4 + x2, z - 1 >= 0, x2 >= 0
   merge#2(z, z') -{ 2 }-> cond_merge_ys_zs_2(1, 1 + (1 + x20') + x6, 1 + 0 + (z' - 1), 1 + x20', x6, 0, z' - 1) :|: z = 1 + (1 + x20') + x6, x6 >= 0, x20' >= 0, z' - 1 >= 0
   merge#2(z, z') -{ 1 }-> cond_merge_ys_zs_2(0, 1 + x8 + x6, 1 + x4 + x2, x8, x6, x4, x2) :|: x4 >= 0, x8 >= 0, z' = 1 + x4 + x2, x6 >= 0, z = 1 + x8 + x6, x2 >= 0
   merge#2(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   merge#2(z, z') -{ 1 }-> 1 + x4 + x2 :|: x4 >= 0, z = 1 + x4 + x2, z' = 1, x2 >= 0
   take#2(z, z') -{ 1 }-> 1 :|: z = 0, z' >= 0
   take#2(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   take#2(z, z') -{ 1 }-> 1 + x56 + take#2(z - 1, x64) :|: z' = 1 + x56 + x64, z - 1 >= 0, x64 >= 0, x56 >= 0
   take#2(z, z') -{ 1 }-> 1 + 2 + 1 :|: z = 1 + 0, z' = 1

Function symbols to be analyzed: {halve#1}, {length#1}, {drop#2}, {merge#2,cond_merge_ys_zs_2}, {divide_ys#1}, {const_f#2}, {dc#1,map#2}, {main}
Previous analysis results are:
  leq#2: runtime: O(n^1) [2 + z'], size: O(1) [2]
  take#2: runtime: O(n^1) [2 + z'], size: O(n^1) [4 + z']

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

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

   cond_merge_ys_zs_2(z, z', z'', z1, z2, z3, z4) -{ 0 }-> 0 :|: z >= 0, z4 >= 0, z' >= 0, z3 >= 0, z'' >= 0, z1 >= 0, z2 >= 0
   cond_merge_ys_zs_2(z, z', z'', z1, z2, z3, z4) -{ 1 }-> 1 + z1 + merge#2(z2, 1 + x5 + x6) :|: x5 >= 0, x8 >= 0, z' = 1 + x7 + x8, z'' = 1 + x5 + x6, z2 >= 0, z3 >= 0, z = 2, z1 >= 0, z4 >= 0, x7 >= 0, x6 >= 0
   cond_merge_ys_zs_2(z, z', z'', z1, z2, z3, z4) -{ 1 }-> 1 + z3 + merge#2(1 + x7 + x8, z4) :|: x5 >= 0, x8 >= 0, z = 1, z' = 1 + x7 + x8, z'' = 1 + x5 + x6, z2 >= 0, z3 >= 0, z1 >= 0, z4 >= 0, x7 >= 0, x6 >= 0
   const_f#2(z, z') -{ 1 }-> merge#2(x6, x4) :|: x4 >= 0, z' = 1 + x6 + (1 + x4 + x2), x6 >= 0, z >= 0, x2 >= 0
   const_f#2(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   dc#1(z, z', z'', z1, z2, z3) -{ 1 }-> const_f#2(1 + x51 + (1 + x25 + x33), map#2(1 + 0 + 0 + 0 + 0 + 0, divide_ys#1(1 + x51 + (1 + x25 + x33), 1 + halve#1(0)))) :|: z'' = 0, z1 = 0, x33 >= 0, z3 = 1 + x51 + (1 + x25 + x33), z2 = 0, x51 >= 0, x25 >= 0, z = 0, z' = 0
   dc#1(z, z', z'', z1, z2, z3) -{ 2 }-> const_f#2(1 + x51 + (1 + x25 + 1), map#2(1 + 0 + 0 + 0 + 0 + 0, divide_ys#1(1 + x51 + (1 + x25 + 1), 1 + halve#1(0)))) :|: z'' = 0, z3 = 1 + x51 + (1 + x25 + 1), z1 = 0, z2 = 0, x51 >= 0, x25 >= 0, z = 0, z' = 0
   dc#1(z, z', z'', z1, z2, z3) -{ 2 }-> const_f#2(1 + x51 + (1 + x25 + (1 + x6' + x8')), map#2(1 + 0 + 0 + 0 + 0 + 0, divide_ys#1(1 + x51 + (1 + x25 + (1 + x6' + x8')), 1 + halve#1(1 + length#1(x8'))))) :|: z'' = 0, z1 = 0, z2 = 0, x51 >= 0, x25 >= 0, x6' >= 0, z3 = 1 + x51 + (1 + x25 + (1 + x6' + x8')), z = 0, x8' >= 0, z' = 0
   dc#1(z, z', z'', z1, z2, z3) -{ 1 }-> 1 :|: z'' = 0, z1 = 0, z2 = 0, z3 = 1, z = 0, z' = 0
   dc#1(z, z', z'', z1, z2, z3) -{ 0 }-> 0 :|: z >= 0, z2 >= 0, z' >= 0, z3 >= 0, z'' >= 0, z1 >= 0
   dc#1(z, z', z'', z1, z2, z3) -{ 1 }-> 1 + (z3 - 2) + 1 :|: z'' = 0, z1 = 0, z2 = 0, z3 - 2 >= 0, z = 0, z' = 0
   divide_ys#1(z, z') -{ 3 + z }-> 1 + s'' + (1 + drop#2(z', z) + 1) :|: s'' >= 0, s'' <= z + 4, z' >= 0, z >= 0
   drop#2(z, z') -{ 1 }-> z' :|: z = 0, z' >= 0
   drop#2(z, z') -{ 1 }-> drop#2(z - 1, x64) :|: z' = 1 + x56 + x64, z - 1 >= 0, x64 >= 0, x56 >= 0
   drop#2(z, z') -{ 1 }-> 3 :|: z = 1 + 0, z' = 1
   drop#2(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   halve#1(z) -{ 1 }-> 0 :|: z = 0
   halve#1(z) -{ 0 }-> 0 :|: z >= 0
   halve#1(z) -{ 1 }-> 1 + halve#1(z - 2) :|: z - 2 >= 0
   halve#1(z) -{ 1 }-> 1 + 0 :|: z = 1 + 0
   length#1(z) -{ 1 }-> 0 :|: z = 1
   length#1(z) -{ 0 }-> 0 :|: z >= 0
   length#1(z) -{ 1 }-> 1 + length#1(x8) :|: x8 >= 0, x6 >= 0, z = 1 + x6 + x8
   leq#2(z, z') -{ 2 + z' }-> s' :|: s' >= 0, s' <= 2, z - 1 >= 0, z' - 1 >= 0
   leq#2(z, z') -{ 1 }-> 2 :|: z = 0, z' >= 0
   leq#2(z, z') -{ 1 }-> 1 :|: z - 1 >= 0, z' = 0
   leq#2(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   main(z) -{ 1 }-> dc#1(0, 0, 0, 0, 0, z) :|: z >= 0
   map#2(z, z') -{ 1 }-> 1 :|: x4 >= 0, x8 >= 0, x6 >= 0, z = 1 + x2 + x4 + x6 + x8 + x10, z' = 1, x10 >= 0, x2 >= 0
   map#2(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   map#2(z, z') -{ 1 }-> 1 + dc#1(x6, x8, x10, x12, x14, x4) + map#2(1 + x6 + x8 + x10 + x12 + x14, x2) :|: x4 >= 0, x8 >= 0, z' = 1 + x4 + x2, x6 >= 0, x12 >= 0, x14 >= 0, x10 >= 0, x2 >= 0, z = 1 + x6 + x8 + x10 + x12 + x14
   merge#2(z, z') -{ 1 }-> z' :|: z = 1, z' >= 0
   merge#2(z, z') -{ 4 + x2' }-> cond_merge_ys_zs_2(s, 1 + (1 + x4') + x6, 1 + (1 + x2') + x2, 1 + x4', x6, 1 + x2', x2) :|: s >= 0, s <= 2, x2' >= 0, z = 1 + (1 + x4') + x6, x6 >= 0, z' = 1 + (1 + x2') + x2, x4' >= 0, x2 >= 0
   merge#2(z, z') -{ 2 }-> cond_merge_ys_zs_2(2, 1 + 0 + (z - 1), 1 + x4 + x2, 0, z - 1, x4, x2) :|: x4 >= 0, z' = 1 + x4 + x2, z - 1 >= 0, x2 >= 0
   merge#2(z, z') -{ 2 }-> cond_merge_ys_zs_2(1, 1 + (1 + x20') + x6, 1 + 0 + (z' - 1), 1 + x20', x6, 0, z' - 1) :|: z = 1 + (1 + x20') + x6, x6 >= 0, x20' >= 0, z' - 1 >= 0
   merge#2(z, z') -{ 1 }-> cond_merge_ys_zs_2(0, 1 + x8 + x6, 1 + x4 + x2, x8, x6, x4, x2) :|: x4 >= 0, x8 >= 0, z' = 1 + x4 + x2, x6 >= 0, z = 1 + x8 + x6, x2 >= 0
   merge#2(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   merge#2(z, z') -{ 1 }-> 1 + x4 + x2 :|: x4 >= 0, z = 1 + x4 + x2, z' = 1, x2 >= 0
   take#2(z, z') -{ 1 }-> 1 :|: z = 0, z' >= 0
   take#2(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   take#2(z, z') -{ 3 + x64 }-> 1 + x56 + s1 :|: s1 >= 0, s1 <= x64 + 4, z' = 1 + x56 + x64, z - 1 >= 0, x64 >= 0, x56 >= 0
   take#2(z, z') -{ 1 }-> 1 + 2 + 1 :|: z = 1 + 0, z' = 1

Function symbols to be analyzed: {halve#1}, {length#1}, {drop#2}, {merge#2,cond_merge_ys_zs_2}, {divide_ys#1}, {const_f#2}, {dc#1,map#2}, {main}
Previous analysis results are:
  leq#2: runtime: O(n^1) [2 + z'], size: O(1) [2]
  take#2: runtime: O(n^1) [2 + z'], size: O(n^1) [4 + z']

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

(33) IntTrsBoundProof (UPPER BOUND(ID))

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

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

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

   cond_merge_ys_zs_2(z, z', z'', z1, z2, z3, z4) -{ 0 }-> 0 :|: z >= 0, z4 >= 0, z' >= 0, z3 >= 0, z'' >= 0, z1 >= 0, z2 >= 0
   cond_merge_ys_zs_2(z, z', z'', z1, z2, z3, z4) -{ 1 }-> 1 + z1 + merge#2(z2, 1 + x5 + x6) :|: x5 >= 0, x8 >= 0, z' = 1 + x7 + x8, z'' = 1 + x5 + x6, z2 >= 0, z3 >= 0, z = 2, z1 >= 0, z4 >= 0, x7 >= 0, x6 >= 0
   cond_merge_ys_zs_2(z, z', z'', z1, z2, z3, z4) -{ 1 }-> 1 + z3 + merge#2(1 + x7 + x8, z4) :|: x5 >= 0, x8 >= 0, z = 1, z' = 1 + x7 + x8, z'' = 1 + x5 + x6, z2 >= 0, z3 >= 0, z1 >= 0, z4 >= 0, x7 >= 0, x6 >= 0
   const_f#2(z, z') -{ 1 }-> merge#2(x6, x4) :|: x4 >= 0, z' = 1 + x6 + (1 + x4 + x2), x6 >= 0, z >= 0, x2 >= 0
   const_f#2(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   dc#1(z, z', z'', z1, z2, z3) -{ 1 }-> const_f#2(1 + x51 + (1 + x25 + x33), map#2(1 + 0 + 0 + 0 + 0 + 0, divide_ys#1(1 + x51 + (1 + x25 + x33), 1 + halve#1(0)))) :|: z'' = 0, z1 = 0, x33 >= 0, z3 = 1 + x51 + (1 + x25 + x33), z2 = 0, x51 >= 0, x25 >= 0, z = 0, z' = 0
   dc#1(z, z', z'', z1, z2, z3) -{ 2 }-> const_f#2(1 + x51 + (1 + x25 + 1), map#2(1 + 0 + 0 + 0 + 0 + 0, divide_ys#1(1 + x51 + (1 + x25 + 1), 1 + halve#1(0)))) :|: z'' = 0, z3 = 1 + x51 + (1 + x25 + 1), z1 = 0, z2 = 0, x51 >= 0, x25 >= 0, z = 0, z' = 0
   dc#1(z, z', z'', z1, z2, z3) -{ 2 }-> const_f#2(1 + x51 + (1 + x25 + (1 + x6' + x8')), map#2(1 + 0 + 0 + 0 + 0 + 0, divide_ys#1(1 + x51 + (1 + x25 + (1 + x6' + x8')), 1 + halve#1(1 + length#1(x8'))))) :|: z'' = 0, z1 = 0, z2 = 0, x51 >= 0, x25 >= 0, x6' >= 0, z3 = 1 + x51 + (1 + x25 + (1 + x6' + x8')), z = 0, x8' >= 0, z' = 0
   dc#1(z, z', z'', z1, z2, z3) -{ 1 }-> 1 :|: z'' = 0, z1 = 0, z2 = 0, z3 = 1, z = 0, z' = 0
   dc#1(z, z', z'', z1, z2, z3) -{ 0 }-> 0 :|: z >= 0, z2 >= 0, z' >= 0, z3 >= 0, z'' >= 0, z1 >= 0
   dc#1(z, z', z'', z1, z2, z3) -{ 1 }-> 1 + (z3 - 2) + 1 :|: z'' = 0, z1 = 0, z2 = 0, z3 - 2 >= 0, z = 0, z' = 0
   divide_ys#1(z, z') -{ 3 + z }-> 1 + s'' + (1 + drop#2(z', z) + 1) :|: s'' >= 0, s'' <= z + 4, z' >= 0, z >= 0
   drop#2(z, z') -{ 1 }-> z' :|: z = 0, z' >= 0
   drop#2(z, z') -{ 1 }-> drop#2(z - 1, x64) :|: z' = 1 + x56 + x64, z - 1 >= 0, x64 >= 0, x56 >= 0
   drop#2(z, z') -{ 1 }-> 3 :|: z = 1 + 0, z' = 1
   drop#2(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   halve#1(z) -{ 1 }-> 0 :|: z = 0
   halve#1(z) -{ 0 }-> 0 :|: z >= 0
   halve#1(z) -{ 1 }-> 1 + halve#1(z - 2) :|: z - 2 >= 0
   halve#1(z) -{ 1 }-> 1 + 0 :|: z = 1 + 0
   length#1(z) -{ 1 }-> 0 :|: z = 1
   length#1(z) -{ 0 }-> 0 :|: z >= 0
   length#1(z) -{ 1 }-> 1 + length#1(x8) :|: x8 >= 0, x6 >= 0, z = 1 + x6 + x8
   leq#2(z, z') -{ 2 + z' }-> s' :|: s' >= 0, s' <= 2, z - 1 >= 0, z' - 1 >= 0
   leq#2(z, z') -{ 1 }-> 2 :|: z = 0, z' >= 0
   leq#2(z, z') -{ 1 }-> 1 :|: z - 1 >= 0, z' = 0
   leq#2(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   main(z) -{ 1 }-> dc#1(0, 0, 0, 0, 0, z) :|: z >= 0
   map#2(z, z') -{ 1 }-> 1 :|: x4 >= 0, x8 >= 0, x6 >= 0, z = 1 + x2 + x4 + x6 + x8 + x10, z' = 1, x10 >= 0, x2 >= 0
   map#2(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   map#2(z, z') -{ 1 }-> 1 + dc#1(x6, x8, x10, x12, x14, x4) + map#2(1 + x6 + x8 + x10 + x12 + x14, x2) :|: x4 >= 0, x8 >= 0, z' = 1 + x4 + x2, x6 >= 0, x12 >= 0, x14 >= 0, x10 >= 0, x2 >= 0, z = 1 + x6 + x8 + x10 + x12 + x14
   merge#2(z, z') -{ 1 }-> z' :|: z = 1, z' >= 0
   merge#2(z, z') -{ 4 + x2' }-> cond_merge_ys_zs_2(s, 1 + (1 + x4') + x6, 1 + (1 + x2') + x2, 1 + x4', x6, 1 + x2', x2) :|: s >= 0, s <= 2, x2' >= 0, z = 1 + (1 + x4') + x6, x6 >= 0, z' = 1 + (1 + x2') + x2, x4' >= 0, x2 >= 0
   merge#2(z, z') -{ 2 }-> cond_merge_ys_zs_2(2, 1 + 0 + (z - 1), 1 + x4 + x2, 0, z - 1, x4, x2) :|: x4 >= 0, z' = 1 + x4 + x2, z - 1 >= 0, x2 >= 0
   merge#2(z, z') -{ 2 }-> cond_merge_ys_zs_2(1, 1 + (1 + x20') + x6, 1 + 0 + (z' - 1), 1 + x20', x6, 0, z' - 1) :|: z = 1 + (1 + x20') + x6, x6 >= 0, x20' >= 0, z' - 1 >= 0
   merge#2(z, z') -{ 1 }-> cond_merge_ys_zs_2(0, 1 + x8 + x6, 1 + x4 + x2, x8, x6, x4, x2) :|: x4 >= 0, x8 >= 0, z' = 1 + x4 + x2, x6 >= 0, z = 1 + x8 + x6, x2 >= 0
   merge#2(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   merge#2(z, z') -{ 1 }-> 1 + x4 + x2 :|: x4 >= 0, z = 1 + x4 + x2, z' = 1, x2 >= 0
   take#2(z, z') -{ 1 }-> 1 :|: z = 0, z' >= 0
   take#2(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   take#2(z, z') -{ 3 + x64 }-> 1 + x56 + s1 :|: s1 >= 0, s1 <= x64 + 4, z' = 1 + x56 + x64, z - 1 >= 0, x64 >= 0, x56 >= 0
   take#2(z, z') -{ 1 }-> 1 + 2 + 1 :|: z = 1 + 0, z' = 1

Function symbols to be analyzed: {halve#1}, {length#1}, {drop#2}, {merge#2,cond_merge_ys_zs_2}, {divide_ys#1}, {const_f#2}, {dc#1,map#2}, {main}
Previous analysis results are:
  leq#2: runtime: O(n^1) [2 + z'], size: O(1) [2]
  take#2: runtime: O(n^1) [2 + z'], size: O(n^1) [4 + z']
  halve#1: runtime: ?, size: O(n^1) [1 + z]

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

(35) IntTrsBoundProof (UPPER BOUND(ID))

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

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

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

   cond_merge_ys_zs_2(z, z', z'', z1, z2, z3, z4) -{ 0 }-> 0 :|: z >= 0, z4 >= 0, z' >= 0, z3 >= 0, z'' >= 0, z1 >= 0, z2 >= 0
   cond_merge_ys_zs_2(z, z', z'', z1, z2, z3, z4) -{ 1 }-> 1 + z1 + merge#2(z2, 1 + x5 + x6) :|: x5 >= 0, x8 >= 0, z' = 1 + x7 + x8, z'' = 1 + x5 + x6, z2 >= 0, z3 >= 0, z = 2, z1 >= 0, z4 >= 0, x7 >= 0, x6 >= 0
   cond_merge_ys_zs_2(z, z', z'', z1, z2, z3, z4) -{ 1 }-> 1 + z3 + merge#2(1 + x7 + x8, z4) :|: x5 >= 0, x8 >= 0, z = 1, z' = 1 + x7 + x8, z'' = 1 + x5 + x6, z2 >= 0, z3 >= 0, z1 >= 0, z4 >= 0, x7 >= 0, x6 >= 0
   const_f#2(z, z') -{ 1 }-> merge#2(x6, x4) :|: x4 >= 0, z' = 1 + x6 + (1 + x4 + x2), x6 >= 0, z >= 0, x2 >= 0
   const_f#2(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   dc#1(z, z', z'', z1, z2, z3) -{ 1 }-> const_f#2(1 + x51 + (1 + x25 + x33), map#2(1 + 0 + 0 + 0 + 0 + 0, divide_ys#1(1 + x51 + (1 + x25 + x33), 1 + halve#1(0)))) :|: z'' = 0, z1 = 0, x33 >= 0, z3 = 1 + x51 + (1 + x25 + x33), z2 = 0, x51 >= 0, x25 >= 0, z = 0, z' = 0
   dc#1(z, z', z'', z1, z2, z3) -{ 2 }-> const_f#2(1 + x51 + (1 + x25 + 1), map#2(1 + 0 + 0 + 0 + 0 + 0, divide_ys#1(1 + x51 + (1 + x25 + 1), 1 + halve#1(0)))) :|: z'' = 0, z3 = 1 + x51 + (1 + x25 + 1), z1 = 0, z2 = 0, x51 >= 0, x25 >= 0, z = 0, z' = 0
   dc#1(z, z', z'', z1, z2, z3) -{ 2 }-> const_f#2(1 + x51 + (1 + x25 + (1 + x6' + x8')), map#2(1 + 0 + 0 + 0 + 0 + 0, divide_ys#1(1 + x51 + (1 + x25 + (1 + x6' + x8')), 1 + halve#1(1 + length#1(x8'))))) :|: z'' = 0, z1 = 0, z2 = 0, x51 >= 0, x25 >= 0, x6' >= 0, z3 = 1 + x51 + (1 + x25 + (1 + x6' + x8')), z = 0, x8' >= 0, z' = 0
   dc#1(z, z', z'', z1, z2, z3) -{ 1 }-> 1 :|: z'' = 0, z1 = 0, z2 = 0, z3 = 1, z = 0, z' = 0
   dc#1(z, z', z'', z1, z2, z3) -{ 0 }-> 0 :|: z >= 0, z2 >= 0, z' >= 0, z3 >= 0, z'' >= 0, z1 >= 0
   dc#1(z, z', z'', z1, z2, z3) -{ 1 }-> 1 + (z3 - 2) + 1 :|: z'' = 0, z1 = 0, z2 = 0, z3 - 2 >= 0, z = 0, z' = 0
   divide_ys#1(z, z') -{ 3 + z }-> 1 + s'' + (1 + drop#2(z', z) + 1) :|: s'' >= 0, s'' <= z + 4, z' >= 0, z >= 0
   drop#2(z, z') -{ 1 }-> z' :|: z = 0, z' >= 0
   drop#2(z, z') -{ 1 }-> drop#2(z - 1, x64) :|: z' = 1 + x56 + x64, z - 1 >= 0, x64 >= 0, x56 >= 0
   drop#2(z, z') -{ 1 }-> 3 :|: z = 1 + 0, z' = 1
   drop#2(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   halve#1(z) -{ 1 }-> 0 :|: z = 0
   halve#1(z) -{ 0 }-> 0 :|: z >= 0
   halve#1(z) -{ 1 }-> 1 + halve#1(z - 2) :|: z - 2 >= 0
   halve#1(z) -{ 1 }-> 1 + 0 :|: z = 1 + 0
   length#1(z) -{ 1 }-> 0 :|: z = 1
   length#1(z) -{ 0 }-> 0 :|: z >= 0
   length#1(z) -{ 1 }-> 1 + length#1(x8) :|: x8 >= 0, x6 >= 0, z = 1 + x6 + x8
   leq#2(z, z') -{ 2 + z' }-> s' :|: s' >= 0, s' <= 2, z - 1 >= 0, z' - 1 >= 0
   leq#2(z, z') -{ 1 }-> 2 :|: z = 0, z' >= 0
   leq#2(z, z') -{ 1 }-> 1 :|: z - 1 >= 0, z' = 0
   leq#2(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   main(z) -{ 1 }-> dc#1(0, 0, 0, 0, 0, z) :|: z >= 0
   map#2(z, z') -{ 1 }-> 1 :|: x4 >= 0, x8 >= 0, x6 >= 0, z = 1 + x2 + x4 + x6 + x8 + x10, z' = 1, x10 >= 0, x2 >= 0
   map#2(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   map#2(z, z') -{ 1 }-> 1 + dc#1(x6, x8, x10, x12, x14, x4) + map#2(1 + x6 + x8 + x10 + x12 + x14, x2) :|: x4 >= 0, x8 >= 0, z' = 1 + x4 + x2, x6 >= 0, x12 >= 0, x14 >= 0, x10 >= 0, x2 >= 0, z = 1 + x6 + x8 + x10 + x12 + x14
   merge#2(z, z') -{ 1 }-> z' :|: z = 1, z' >= 0
   merge#2(z, z') -{ 4 + x2' }-> cond_merge_ys_zs_2(s, 1 + (1 + x4') + x6, 1 + (1 + x2') + x2, 1 + x4', x6, 1 + x2', x2) :|: s >= 0, s <= 2, x2' >= 0, z = 1 + (1 + x4') + x6, x6 >= 0, z' = 1 + (1 + x2') + x2, x4' >= 0, x2 >= 0
   merge#2(z, z') -{ 2 }-> cond_merge_ys_zs_2(2, 1 + 0 + (z - 1), 1 + x4 + x2, 0, z - 1, x4, x2) :|: x4 >= 0, z' = 1 + x4 + x2, z - 1 >= 0, x2 >= 0
   merge#2(z, z') -{ 2 }-> cond_merge_ys_zs_2(1, 1 + (1 + x20') + x6, 1 + 0 + (z' - 1), 1 + x20', x6, 0, z' - 1) :|: z = 1 + (1 + x20') + x6, x6 >= 0, x20' >= 0, z' - 1 >= 0
   merge#2(z, z') -{ 1 }-> cond_merge_ys_zs_2(0, 1 + x8 + x6, 1 + x4 + x2, x8, x6, x4, x2) :|: x4 >= 0, x8 >= 0, z' = 1 + x4 + x2, x6 >= 0, z = 1 + x8 + x6, x2 >= 0
   merge#2(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   merge#2(z, z') -{ 1 }-> 1 + x4 + x2 :|: x4 >= 0, z = 1 + x4 + x2, z' = 1, x2 >= 0
   take#2(z, z') -{ 1 }-> 1 :|: z = 0, z' >= 0
   take#2(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   take#2(z, z') -{ 3 + x64 }-> 1 + x56 + s1 :|: s1 >= 0, s1 <= x64 + 4, z' = 1 + x56 + x64, z - 1 >= 0, x64 >= 0, x56 >= 0
   take#2(z, z') -{ 1 }-> 1 + 2 + 1 :|: z = 1 + 0, z' = 1

Function symbols to be analyzed: {length#1}, {drop#2}, {merge#2,cond_merge_ys_zs_2}, {divide_ys#1}, {const_f#2}, {dc#1,map#2}, {main}
Previous analysis results are:
  leq#2: runtime: O(n^1) [2 + z'], size: O(1) [2]
  take#2: runtime: O(n^1) [2 + z'], size: O(n^1) [4 + z']
  halve#1: runtime: O(n^1) [2 + z], size: O(n^1) [1 + z]

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

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

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

   cond_merge_ys_zs_2(z, z', z'', z1, z2, z3, z4) -{ 0 }-> 0 :|: z >= 0, z4 >= 0, z' >= 0, z3 >= 0, z'' >= 0, z1 >= 0, z2 >= 0
   cond_merge_ys_zs_2(z, z', z'', z1, z2, z3, z4) -{ 1 }-> 1 + z1 + merge#2(z2, 1 + x5 + x6) :|: x5 >= 0, x8 >= 0, z' = 1 + x7 + x8, z'' = 1 + x5 + x6, z2 >= 0, z3 >= 0, z = 2, z1 >= 0, z4 >= 0, x7 >= 0, x6 >= 0
   cond_merge_ys_zs_2(z, z', z'', z1, z2, z3, z4) -{ 1 }-> 1 + z3 + merge#2(1 + x7 + x8, z4) :|: x5 >= 0, x8 >= 0, z = 1, z' = 1 + x7 + x8, z'' = 1 + x5 + x6, z2 >= 0, z3 >= 0, z1 >= 0, z4 >= 0, x7 >= 0, x6 >= 0
   const_f#2(z, z') -{ 1 }-> merge#2(x6, x4) :|: x4 >= 0, z' = 1 + x6 + (1 + x4 + x2), x6 >= 0, z >= 0, x2 >= 0
   const_f#2(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   dc#1(z, z', z'', z1, z2, z3) -{ 3 }-> const_f#2(1 + x51 + (1 + x25 + x33), map#2(1 + 0 + 0 + 0 + 0 + 0, divide_ys#1(1 + x51 + (1 + x25 + x33), 1 + s3))) :|: s3 >= 0, s3 <= 0 + 1, z'' = 0, z1 = 0, x33 >= 0, z3 = 1 + x51 + (1 + x25 + x33), z2 = 0, x51 >= 0, x25 >= 0, z = 0, z' = 0
   dc#1(z, z', z'', z1, z2, z3) -{ 4 }-> const_f#2(1 + x51 + (1 + x25 + 1), map#2(1 + 0 + 0 + 0 + 0 + 0, divide_ys#1(1 + x51 + (1 + x25 + 1), 1 + s2))) :|: s2 >= 0, s2 <= 0 + 1, z'' = 0, z3 = 1 + x51 + (1 + x25 + 1), z1 = 0, z2 = 0, x51 >= 0, x25 >= 0, z = 0, z' = 0
   dc#1(z, z', z'', z1, z2, z3) -{ 2 }-> const_f#2(1 + x51 + (1 + x25 + (1 + x6' + x8')), map#2(1 + 0 + 0 + 0 + 0 + 0, divide_ys#1(1 + x51 + (1 + x25 + (1 + x6' + x8')), 1 + halve#1(1 + length#1(x8'))))) :|: z'' = 0, z1 = 0, z2 = 0, x51 >= 0, x25 >= 0, x6' >= 0, z3 = 1 + x51 + (1 + x25 + (1 + x6' + x8')), z = 0, x8' >= 0, z' = 0
   dc#1(z, z', z'', z1, z2, z3) -{ 1 }-> 1 :|: z'' = 0, z1 = 0, z2 = 0, z3 = 1, z = 0, z' = 0
   dc#1(z, z', z'', z1, z2, z3) -{ 0 }-> 0 :|: z >= 0, z2 >= 0, z' >= 0, z3 >= 0, z'' >= 0, z1 >= 0
   dc#1(z, z', z'', z1, z2, z3) -{ 1 }-> 1 + (z3 - 2) + 1 :|: z'' = 0, z1 = 0, z2 = 0, z3 - 2 >= 0, z = 0, z' = 0
   divide_ys#1(z, z') -{ 3 + z }-> 1 + s'' + (1 + drop#2(z', z) + 1) :|: s'' >= 0, s'' <= z + 4, z' >= 0, z >= 0
   drop#2(z, z') -{ 1 }-> z' :|: z = 0, z' >= 0
   drop#2(z, z') -{ 1 }-> drop#2(z - 1, x64) :|: z' = 1 + x56 + x64, z - 1 >= 0, x64 >= 0, x56 >= 0
   drop#2(z, z') -{ 1 }-> 3 :|: z = 1 + 0, z' = 1
   drop#2(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   halve#1(z) -{ 1 }-> 0 :|: z = 0
   halve#1(z) -{ 0 }-> 0 :|: z >= 0
   halve#1(z) -{ 1 + z }-> 1 + s4 :|: s4 >= 0, s4 <= z - 2 + 1, z - 2 >= 0
   halve#1(z) -{ 1 }-> 1 + 0 :|: z = 1 + 0
   length#1(z) -{ 1 }-> 0 :|: z = 1
   length#1(z) -{ 0 }-> 0 :|: z >= 0
   length#1(z) -{ 1 }-> 1 + length#1(x8) :|: x8 >= 0, x6 >= 0, z = 1 + x6 + x8
   leq#2(z, z') -{ 2 + z' }-> s' :|: s' >= 0, s' <= 2, z - 1 >= 0, z' - 1 >= 0
   leq#2(z, z') -{ 1 }-> 2 :|: z = 0, z' >= 0
   leq#2(z, z') -{ 1 }-> 1 :|: z - 1 >= 0, z' = 0
   leq#2(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   main(z) -{ 1 }-> dc#1(0, 0, 0, 0, 0, z) :|: z >= 0
   map#2(z, z') -{ 1 }-> 1 :|: x4 >= 0, x8 >= 0, x6 >= 0, z = 1 + x2 + x4 + x6 + x8 + x10, z' = 1, x10 >= 0, x2 >= 0
   map#2(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   map#2(z, z') -{ 1 }-> 1 + dc#1(x6, x8, x10, x12, x14, x4) + map#2(1 + x6 + x8 + x10 + x12 + x14, x2) :|: x4 >= 0, x8 >= 0, z' = 1 + x4 + x2, x6 >= 0, x12 >= 0, x14 >= 0, x10 >= 0, x2 >= 0, z = 1 + x6 + x8 + x10 + x12 + x14
   merge#2(z, z') -{ 1 }-> z' :|: z = 1, z' >= 0
   merge#2(z, z') -{ 4 + x2' }-> cond_merge_ys_zs_2(s, 1 + (1 + x4') + x6, 1 + (1 + x2') + x2, 1 + x4', x6, 1 + x2', x2) :|: s >= 0, s <= 2, x2' >= 0, z = 1 + (1 + x4') + x6, x6 >= 0, z' = 1 + (1 + x2') + x2, x4' >= 0, x2 >= 0
   merge#2(z, z') -{ 2 }-> cond_merge_ys_zs_2(2, 1 + 0 + (z - 1), 1 + x4 + x2, 0, z - 1, x4, x2) :|: x4 >= 0, z' = 1 + x4 + x2, z - 1 >= 0, x2 >= 0
   merge#2(z, z') -{ 2 }-> cond_merge_ys_zs_2(1, 1 + (1 + x20') + x6, 1 + 0 + (z' - 1), 1 + x20', x6, 0, z' - 1) :|: z = 1 + (1 + x20') + x6, x6 >= 0, x20' >= 0, z' - 1 >= 0
   merge#2(z, z') -{ 1 }-> cond_merge_ys_zs_2(0, 1 + x8 + x6, 1 + x4 + x2, x8, x6, x4, x2) :|: x4 >= 0, x8 >= 0, z' = 1 + x4 + x2, x6 >= 0, z = 1 + x8 + x6, x2 >= 0
   merge#2(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   merge#2(z, z') -{ 1 }-> 1 + x4 + x2 :|: x4 >= 0, z = 1 + x4 + x2, z' = 1, x2 >= 0
   take#2(z, z') -{ 1 }-> 1 :|: z = 0, z' >= 0
   take#2(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   take#2(z, z') -{ 3 + x64 }-> 1 + x56 + s1 :|: s1 >= 0, s1 <= x64 + 4, z' = 1 + x56 + x64, z - 1 >= 0, x64 >= 0, x56 >= 0
   take#2(z, z') -{ 1 }-> 1 + 2 + 1 :|: z = 1 + 0, z' = 1

Function symbols to be analyzed: {length#1}, {drop#2}, {merge#2,cond_merge_ys_zs_2}, {divide_ys#1}, {const_f#2}, {dc#1,map#2}, {main}
Previous analysis results are:
  leq#2: runtime: O(n^1) [2 + z'], size: O(1) [2]
  take#2: runtime: O(n^1) [2 + z'], size: O(n^1) [4 + z']
  halve#1: runtime: O(n^1) [2 + z], size: O(n^1) [1 + z]

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(39) IntTrsBoundProof (UPPER BOUND(ID))

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

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

   cond_merge_ys_zs_2(z, z', z'', z1, z2, z3, z4) -{ 0 }-> 0 :|: z >= 0, z4 >= 0, z' >= 0, z3 >= 0, z'' >= 0, z1 >= 0, z2 >= 0
   cond_merge_ys_zs_2(z, z', z'', z1, z2, z3, z4) -{ 1 }-> 1 + z1 + merge#2(z2, 1 + x5 + x6) :|: x5 >= 0, x8 >= 0, z' = 1 + x7 + x8, z'' = 1 + x5 + x6, z2 >= 0, z3 >= 0, z = 2, z1 >= 0, z4 >= 0, x7 >= 0, x6 >= 0
   cond_merge_ys_zs_2(z, z', z'', z1, z2, z3, z4) -{ 1 }-> 1 + z3 + merge#2(1 + x7 + x8, z4) :|: x5 >= 0, x8 >= 0, z = 1, z' = 1 + x7 + x8, z'' = 1 + x5 + x6, z2 >= 0, z3 >= 0, z1 >= 0, z4 >= 0, x7 >= 0, x6 >= 0
   const_f#2(z, z') -{ 1 }-> merge#2(x6, x4) :|: x4 >= 0, z' = 1 + x6 + (1 + x4 + x2), x6 >= 0, z >= 0, x2 >= 0
   const_f#2(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   dc#1(z, z', z'', z1, z2, z3) -{ 3 }-> const_f#2(1 + x51 + (1 + x25 + x33), map#2(1 + 0 + 0 + 0 + 0 + 0, divide_ys#1(1 + x51 + (1 + x25 + x33), 1 + s3))) :|: s3 >= 0, s3 <= 0 + 1, z'' = 0, z1 = 0, x33 >= 0, z3 = 1 + x51 + (1 + x25 + x33), z2 = 0, x51 >= 0, x25 >= 0, z = 0, z' = 0
   dc#1(z, z', z'', z1, z2, z3) -{ 4 }-> const_f#2(1 + x51 + (1 + x25 + 1), map#2(1 + 0 + 0 + 0 + 0 + 0, divide_ys#1(1 + x51 + (1 + x25 + 1), 1 + s2))) :|: s2 >= 0, s2 <= 0 + 1, z'' = 0, z3 = 1 + x51 + (1 + x25 + 1), z1 = 0, z2 = 0, x51 >= 0, x25 >= 0, z = 0, z' = 0
   dc#1(z, z', z'', z1, z2, z3) -{ 2 }-> const_f#2(1 + x51 + (1 + x25 + (1 + x6' + x8')), map#2(1 + 0 + 0 + 0 + 0 + 0, divide_ys#1(1 + x51 + (1 + x25 + (1 + x6' + x8')), 1 + halve#1(1 + length#1(x8'))))) :|: z'' = 0, z1 = 0, z2 = 0, x51 >= 0, x25 >= 0, x6' >= 0, z3 = 1 + x51 + (1 + x25 + (1 + x6' + x8')), z = 0, x8' >= 0, z' = 0
   dc#1(z, z', z'', z1, z2, z3) -{ 1 }-> 1 :|: z'' = 0, z1 = 0, z2 = 0, z3 = 1, z = 0, z' = 0
   dc#1(z, z', z'', z1, z2, z3) -{ 0 }-> 0 :|: z >= 0, z2 >= 0, z' >= 0, z3 >= 0, z'' >= 0, z1 >= 0
   dc#1(z, z', z'', z1, z2, z3) -{ 1 }-> 1 + (z3 - 2) + 1 :|: z'' = 0, z1 = 0, z2 = 0, z3 - 2 >= 0, z = 0, z' = 0
   divide_ys#1(z, z') -{ 3 + z }-> 1 + s'' + (1 + drop#2(z', z) + 1) :|: s'' >= 0, s'' <= z + 4, z' >= 0, z >= 0
   drop#2(z, z') -{ 1 }-> z' :|: z = 0, z' >= 0
   drop#2(z, z') -{ 1 }-> drop#2(z - 1, x64) :|: z' = 1 + x56 + x64, z - 1 >= 0, x64 >= 0, x56 >= 0
   drop#2(z, z') -{ 1 }-> 3 :|: z = 1 + 0, z' = 1
   drop#2(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   halve#1(z) -{ 1 }-> 0 :|: z = 0
   halve#1(z) -{ 0 }-> 0 :|: z >= 0
   halve#1(z) -{ 1 + z }-> 1 + s4 :|: s4 >= 0, s4 <= z - 2 + 1, z - 2 >= 0
   halve#1(z) -{ 1 }-> 1 + 0 :|: z = 1 + 0
   length#1(z) -{ 1 }-> 0 :|: z = 1
   length#1(z) -{ 0 }-> 0 :|: z >= 0
   length#1(z) -{ 1 }-> 1 + length#1(x8) :|: x8 >= 0, x6 >= 0, z = 1 + x6 + x8
   leq#2(z, z') -{ 2 + z' }-> s' :|: s' >= 0, s' <= 2, z - 1 >= 0, z' - 1 >= 0
   leq#2(z, z') -{ 1 }-> 2 :|: z = 0, z' >= 0
   leq#2(z, z') -{ 1 }-> 1 :|: z - 1 >= 0, z' = 0
   leq#2(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   main(z) -{ 1 }-> dc#1(0, 0, 0, 0, 0, z) :|: z >= 0
   map#2(z, z') -{ 1 }-> 1 :|: x4 >= 0, x8 >= 0, x6 >= 0, z = 1 + x2 + x4 + x6 + x8 + x10, z' = 1, x10 >= 0, x2 >= 0
   map#2(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   map#2(z, z') -{ 1 }-> 1 + dc#1(x6, x8, x10, x12, x14, x4) + map#2(1 + x6 + x8 + x10 + x12 + x14, x2) :|: x4 >= 0, x8 >= 0, z' = 1 + x4 + x2, x6 >= 0, x12 >= 0, x14 >= 0, x10 >= 0, x2 >= 0, z = 1 + x6 + x8 + x10 + x12 + x14
   merge#2(z, z') -{ 1 }-> z' :|: z = 1, z' >= 0
   merge#2(z, z') -{ 4 + x2' }-> cond_merge_ys_zs_2(s, 1 + (1 + x4') + x6, 1 + (1 + x2') + x2, 1 + x4', x6, 1 + x2', x2) :|: s >= 0, s <= 2, x2' >= 0, z = 1 + (1 + x4') + x6, x6 >= 0, z' = 1 + (1 + x2') + x2, x4' >= 0, x2 >= 0
   merge#2(z, z') -{ 2 }-> cond_merge_ys_zs_2(2, 1 + 0 + (z - 1), 1 + x4 + x2, 0, z - 1, x4, x2) :|: x4 >= 0, z' = 1 + x4 + x2, z - 1 >= 0, x2 >= 0
   merge#2(z, z') -{ 2 }-> cond_merge_ys_zs_2(1, 1 + (1 + x20') + x6, 1 + 0 + (z' - 1), 1 + x20', x6, 0, z' - 1) :|: z = 1 + (1 + x20') + x6, x6 >= 0, x20' >= 0, z' - 1 >= 0
   merge#2(z, z') -{ 1 }-> cond_merge_ys_zs_2(0, 1 + x8 + x6, 1 + x4 + x2, x8, x6, x4, x2) :|: x4 >= 0, x8 >= 0, z' = 1 + x4 + x2, x6 >= 0, z = 1 + x8 + x6, x2 >= 0
   merge#2(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   merge#2(z, z') -{ 1 }-> 1 + x4 + x2 :|: x4 >= 0, z = 1 + x4 + x2, z' = 1, x2 >= 0
   take#2(z, z') -{ 1 }-> 1 :|: z = 0, z' >= 0
   take#2(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   take#2(z, z') -{ 3 + x64 }-> 1 + x56 + s1 :|: s1 >= 0, s1 <= x64 + 4, z' = 1 + x56 + x64, z - 1 >= 0, x64 >= 0, x56 >= 0
   take#2(z, z') -{ 1 }-> 1 + 2 + 1 :|: z = 1 + 0, z' = 1

Function symbols to be analyzed: {length#1}, {drop#2}, {merge#2,cond_merge_ys_zs_2}, {divide_ys#1}, {const_f#2}, {dc#1,map#2}, {main}
Previous analysis results are:
  leq#2: runtime: O(n^1) [2 + z'], size: O(1) [2]
  take#2: runtime: O(n^1) [2 + z'], size: O(n^1) [4 + z']
  halve#1: runtime: O(n^1) [2 + z], size: O(n^1) [1 + z]
  length#1: runtime: ?, size: O(n^1) [z]

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(41) IntTrsBoundProof (UPPER BOUND(ID))

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

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

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

   cond_merge_ys_zs_2(z, z', z'', z1, z2, z3, z4) -{ 0 }-> 0 :|: z >= 0, z4 >= 0, z' >= 0, z3 >= 0, z'' >= 0, z1 >= 0, z2 >= 0
   cond_merge_ys_zs_2(z, z', z'', z1, z2, z3, z4) -{ 1 }-> 1 + z1 + merge#2(z2, 1 + x5 + x6) :|: x5 >= 0, x8 >= 0, z' = 1 + x7 + x8, z'' = 1 + x5 + x6, z2 >= 0, z3 >= 0, z = 2, z1 >= 0, z4 >= 0, x7 >= 0, x6 >= 0
   cond_merge_ys_zs_2(z, z', z'', z1, z2, z3, z4) -{ 1 }-> 1 + z3 + merge#2(1 + x7 + x8, z4) :|: x5 >= 0, x8 >= 0, z = 1, z' = 1 + x7 + x8, z'' = 1 + x5 + x6, z2 >= 0, z3 >= 0, z1 >= 0, z4 >= 0, x7 >= 0, x6 >= 0
   const_f#2(z, z') -{ 1 }-> merge#2(x6, x4) :|: x4 >= 0, z' = 1 + x6 + (1 + x4 + x2), x6 >= 0, z >= 0, x2 >= 0
   const_f#2(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   dc#1(z, z', z'', z1, z2, z3) -{ 3 }-> const_f#2(1 + x51 + (1 + x25 + x33), map#2(1 + 0 + 0 + 0 + 0 + 0, divide_ys#1(1 + x51 + (1 + x25 + x33), 1 + s3))) :|: s3 >= 0, s3 <= 0 + 1, z'' = 0, z1 = 0, x33 >= 0, z3 = 1 + x51 + (1 + x25 + x33), z2 = 0, x51 >= 0, x25 >= 0, z = 0, z' = 0
   dc#1(z, z', z'', z1, z2, z3) -{ 4 }-> const_f#2(1 + x51 + (1 + x25 + 1), map#2(1 + 0 + 0 + 0 + 0 + 0, divide_ys#1(1 + x51 + (1 + x25 + 1), 1 + s2))) :|: s2 >= 0, s2 <= 0 + 1, z'' = 0, z3 = 1 + x51 + (1 + x25 + 1), z1 = 0, z2 = 0, x51 >= 0, x25 >= 0, z = 0, z' = 0
   dc#1(z, z', z'', z1, z2, z3) -{ 2 }-> const_f#2(1 + x51 + (1 + x25 + (1 + x6' + x8')), map#2(1 + 0 + 0 + 0 + 0 + 0, divide_ys#1(1 + x51 + (1 + x25 + (1 + x6' + x8')), 1 + halve#1(1 + length#1(x8'))))) :|: z'' = 0, z1 = 0, z2 = 0, x51 >= 0, x25 >= 0, x6' >= 0, z3 = 1 + x51 + (1 + x25 + (1 + x6' + x8')), z = 0, x8' >= 0, z' = 0
   dc#1(z, z', z'', z1, z2, z3) -{ 1 }-> 1 :|: z'' = 0, z1 = 0, z2 = 0, z3 = 1, z = 0, z' = 0
   dc#1(z, z', z'', z1, z2, z3) -{ 0 }-> 0 :|: z >= 0, z2 >= 0, z' >= 0, z3 >= 0, z'' >= 0, z1 >= 0
   dc#1(z, z', z'', z1, z2, z3) -{ 1 }-> 1 + (z3 - 2) + 1 :|: z'' = 0, z1 = 0, z2 = 0, z3 - 2 >= 0, z = 0, z' = 0
   divide_ys#1(z, z') -{ 3 + z }-> 1 + s'' + (1 + drop#2(z', z) + 1) :|: s'' >= 0, s'' <= z + 4, z' >= 0, z >= 0
   drop#2(z, z') -{ 1 }-> z' :|: z = 0, z' >= 0
   drop#2(z, z') -{ 1 }-> drop#2(z - 1, x64) :|: z' = 1 + x56 + x64, z - 1 >= 0, x64 >= 0, x56 >= 0
   drop#2(z, z') -{ 1 }-> 3 :|: z = 1 + 0, z' = 1
   drop#2(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   halve#1(z) -{ 1 }-> 0 :|: z = 0
   halve#1(z) -{ 0 }-> 0 :|: z >= 0
   halve#1(z) -{ 1 + z }-> 1 + s4 :|: s4 >= 0, s4 <= z - 2 + 1, z - 2 >= 0
   halve#1(z) -{ 1 }-> 1 + 0 :|: z = 1 + 0
   length#1(z) -{ 1 }-> 0 :|: z = 1
   length#1(z) -{ 0 }-> 0 :|: z >= 0
   length#1(z) -{ 1 }-> 1 + length#1(x8) :|: x8 >= 0, x6 >= 0, z = 1 + x6 + x8
   leq#2(z, z') -{ 2 + z' }-> s' :|: s' >= 0, s' <= 2, z - 1 >= 0, z' - 1 >= 0
   leq#2(z, z') -{ 1 }-> 2 :|: z = 0, z' >= 0
   leq#2(z, z') -{ 1 }-> 1 :|: z - 1 >= 0, z' = 0
   leq#2(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   main(z) -{ 1 }-> dc#1(0, 0, 0, 0, 0, z) :|: z >= 0
   map#2(z, z') -{ 1 }-> 1 :|: x4 >= 0, x8 >= 0, x6 >= 0, z = 1 + x2 + x4 + x6 + x8 + x10, z' = 1, x10 >= 0, x2 >= 0
   map#2(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   map#2(z, z') -{ 1 }-> 1 + dc#1(x6, x8, x10, x12, x14, x4) + map#2(1 + x6 + x8 + x10 + x12 + x14, x2) :|: x4 >= 0, x8 >= 0, z' = 1 + x4 + x2, x6 >= 0, x12 >= 0, x14 >= 0, x10 >= 0, x2 >= 0, z = 1 + x6 + x8 + x10 + x12 + x14
   merge#2(z, z') -{ 1 }-> z' :|: z = 1, z' >= 0
   merge#2(z, z') -{ 4 + x2' }-> cond_merge_ys_zs_2(s, 1 + (1 + x4') + x6, 1 + (1 + x2') + x2, 1 + x4', x6, 1 + x2', x2) :|: s >= 0, s <= 2, x2' >= 0, z = 1 + (1 + x4') + x6, x6 >= 0, z' = 1 + (1 + x2') + x2, x4' >= 0, x2 >= 0
   merge#2(z, z') -{ 2 }-> cond_merge_ys_zs_2(2, 1 + 0 + (z - 1), 1 + x4 + x2, 0, z - 1, x4, x2) :|: x4 >= 0, z' = 1 + x4 + x2, z - 1 >= 0, x2 >= 0
   merge#2(z, z') -{ 2 }-> cond_merge_ys_zs_2(1, 1 + (1 + x20') + x6, 1 + 0 + (z' - 1), 1 + x20', x6, 0, z' - 1) :|: z = 1 + (1 + x20') + x6, x6 >= 0, x20' >= 0, z' - 1 >= 0
   merge#2(z, z') -{ 1 }-> cond_merge_ys_zs_2(0, 1 + x8 + x6, 1 + x4 + x2, x8, x6, x4, x2) :|: x4 >= 0, x8 >= 0, z' = 1 + x4 + x2, x6 >= 0, z = 1 + x8 + x6, x2 >= 0
   merge#2(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   merge#2(z, z') -{ 1 }-> 1 + x4 + x2 :|: x4 >= 0, z = 1 + x4 + x2, z' = 1, x2 >= 0
   take#2(z, z') -{ 1 }-> 1 :|: z = 0, z' >= 0
   take#2(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   take#2(z, z') -{ 3 + x64 }-> 1 + x56 + s1 :|: s1 >= 0, s1 <= x64 + 4, z' = 1 + x56 + x64, z - 1 >= 0, x64 >= 0, x56 >= 0
   take#2(z, z') -{ 1 }-> 1 + 2 + 1 :|: z = 1 + 0, z' = 1

Function symbols to be analyzed: {drop#2}, {merge#2,cond_merge_ys_zs_2}, {divide_ys#1}, {const_f#2}, {dc#1,map#2}, {main}
Previous analysis results are:
  leq#2: runtime: O(n^1) [2 + z'], size: O(1) [2]
  take#2: runtime: O(n^1) [2 + z'], size: O(n^1) [4 + z']
  halve#1: runtime: O(n^1) [2 + z], size: O(n^1) [1 + z]
  length#1: runtime: O(n^1) [1 + z], size: O(n^1) [z]

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

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

   cond_merge_ys_zs_2(z, z', z'', z1, z2, z3, z4) -{ 0 }-> 0 :|: z >= 0, z4 >= 0, z' >= 0, z3 >= 0, z'' >= 0, z1 >= 0, z2 >= 0
   cond_merge_ys_zs_2(z, z', z'', z1, z2, z3, z4) -{ 1 }-> 1 + z1 + merge#2(z2, 1 + x5 + x6) :|: x5 >= 0, x8 >= 0, z' = 1 + x7 + x8, z'' = 1 + x5 + x6, z2 >= 0, z3 >= 0, z = 2, z1 >= 0, z4 >= 0, x7 >= 0, x6 >= 0
   cond_merge_ys_zs_2(z, z', z'', z1, z2, z3, z4) -{ 1 }-> 1 + z3 + merge#2(1 + x7 + x8, z4) :|: x5 >= 0, x8 >= 0, z = 1, z' = 1 + x7 + x8, z'' = 1 + x5 + x6, z2 >= 0, z3 >= 0, z1 >= 0, z4 >= 0, x7 >= 0, x6 >= 0
   const_f#2(z, z') -{ 1 }-> merge#2(x6, x4) :|: x4 >= 0, z' = 1 + x6 + (1 + x4 + x2), x6 >= 0, z >= 0, x2 >= 0
   const_f#2(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   dc#1(z, z', z'', z1, z2, z3) -{ 3 }-> const_f#2(1 + x51 + (1 + x25 + x33), map#2(1 + 0 + 0 + 0 + 0 + 0, divide_ys#1(1 + x51 + (1 + x25 + x33), 1 + s3))) :|: s3 >= 0, s3 <= 0 + 1, z'' = 0, z1 = 0, x33 >= 0, z3 = 1 + x51 + (1 + x25 + x33), z2 = 0, x51 >= 0, x25 >= 0, z = 0, z' = 0
   dc#1(z, z', z'', z1, z2, z3) -{ 4 }-> const_f#2(1 + x51 + (1 + x25 + 1), map#2(1 + 0 + 0 + 0 + 0 + 0, divide_ys#1(1 + x51 + (1 + x25 + 1), 1 + s2))) :|: s2 >= 0, s2 <= 0 + 1, z'' = 0, z3 = 1 + x51 + (1 + x25 + 1), z1 = 0, z2 = 0, x51 >= 0, x25 >= 0, z = 0, z' = 0
   dc#1(z, z', z'', z1, z2, z3) -{ 6 + s5 + x8' }-> const_f#2(1 + x51 + (1 + x25 + (1 + x6' + x8')), map#2(1 + 0 + 0 + 0 + 0 + 0, divide_ys#1(1 + x51 + (1 + x25 + (1 + x6' + x8')), 1 + s6))) :|: s5 >= 0, s5 <= x8', s6 >= 0, s6 <= 1 + s5 + 1, z'' = 0, z1 = 0, z2 = 0, x51 >= 0, x25 >= 0, x6' >= 0, z3 = 1 + x51 + (1 + x25 + (1 + x6' + x8')), z = 0, x8' >= 0, z' = 0
   dc#1(z, z', z'', z1, z2, z3) -{ 1 }-> 1 :|: z'' = 0, z1 = 0, z2 = 0, z3 = 1, z = 0, z' = 0
   dc#1(z, z', z'', z1, z2, z3) -{ 0 }-> 0 :|: z >= 0, z2 >= 0, z' >= 0, z3 >= 0, z'' >= 0, z1 >= 0
   dc#1(z, z', z'', z1, z2, z3) -{ 1 }-> 1 + (z3 - 2) + 1 :|: z'' = 0, z1 = 0, z2 = 0, z3 - 2 >= 0, z = 0, z' = 0
   divide_ys#1(z, z') -{ 3 + z }-> 1 + s'' + (1 + drop#2(z', z) + 1) :|: s'' >= 0, s'' <= z + 4, z' >= 0, z >= 0
   drop#2(z, z') -{ 1 }-> z' :|: z = 0, z' >= 0
   drop#2(z, z') -{ 1 }-> drop#2(z - 1, x64) :|: z' = 1 + x56 + x64, z - 1 >= 0, x64 >= 0, x56 >= 0
   drop#2(z, z') -{ 1 }-> 3 :|: z = 1 + 0, z' = 1
   drop#2(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   halve#1(z) -{ 1 }-> 0 :|: z = 0
   halve#1(z) -{ 0 }-> 0 :|: z >= 0
   halve#1(z) -{ 1 + z }-> 1 + s4 :|: s4 >= 0, s4 <= z - 2 + 1, z - 2 >= 0
   halve#1(z) -{ 1 }-> 1 + 0 :|: z = 1 + 0
   length#1(z) -{ 1 }-> 0 :|: z = 1
   length#1(z) -{ 0 }-> 0 :|: z >= 0
   length#1(z) -{ 2 + x8 }-> 1 + s7 :|: s7 >= 0, s7 <= x8, x8 >= 0, x6 >= 0, z = 1 + x6 + x8
   leq#2(z, z') -{ 2 + z' }-> s' :|: s' >= 0, s' <= 2, z - 1 >= 0, z' - 1 >= 0
   leq#2(z, z') -{ 1 }-> 2 :|: z = 0, z' >= 0
   leq#2(z, z') -{ 1 }-> 1 :|: z - 1 >= 0, z' = 0
   leq#2(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   main(z) -{ 1 }-> dc#1(0, 0, 0, 0, 0, z) :|: z >= 0
   map#2(z, z') -{ 1 }-> 1 :|: x4 >= 0, x8 >= 0, x6 >= 0, z = 1 + x2 + x4 + x6 + x8 + x10, z' = 1, x10 >= 0, x2 >= 0
   map#2(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   map#2(z, z') -{ 1 }-> 1 + dc#1(x6, x8, x10, x12, x14, x4) + map#2(1 + x6 + x8 + x10 + x12 + x14, x2) :|: x4 >= 0, x8 >= 0, z' = 1 + x4 + x2, x6 >= 0, x12 >= 0, x14 >= 0, x10 >= 0, x2 >= 0, z = 1 + x6 + x8 + x10 + x12 + x14
   merge#2(z, z') -{ 1 }-> z' :|: z = 1, z' >= 0
   merge#2(z, z') -{ 4 + x2' }-> cond_merge_ys_zs_2(s, 1 + (1 + x4') + x6, 1 + (1 + x2') + x2, 1 + x4', x6, 1 + x2', x2) :|: s >= 0, s <= 2, x2' >= 0, z = 1 + (1 + x4') + x6, x6 >= 0, z' = 1 + (1 + x2') + x2, x4' >= 0, x2 >= 0
   merge#2(z, z') -{ 2 }-> cond_merge_ys_zs_2(2, 1 + 0 + (z - 1), 1 + x4 + x2, 0, z - 1, x4, x2) :|: x4 >= 0, z' = 1 + x4 + x2, z - 1 >= 0, x2 >= 0
   merge#2(z, z') -{ 2 }-> cond_merge_ys_zs_2(1, 1 + (1 + x20') + x6, 1 + 0 + (z' - 1), 1 + x20', x6, 0, z' - 1) :|: z = 1 + (1 + x20') + x6, x6 >= 0, x20' >= 0, z' - 1 >= 0
   merge#2(z, z') -{ 1 }-> cond_merge_ys_zs_2(0, 1 + x8 + x6, 1 + x4 + x2, x8, x6, x4, x2) :|: x4 >= 0, x8 >= 0, z' = 1 + x4 + x2, x6 >= 0, z = 1 + x8 + x6, x2 >= 0
   merge#2(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   merge#2(z, z') -{ 1 }-> 1 + x4 + x2 :|: x4 >= 0, z = 1 + x4 + x2, z' = 1, x2 >= 0
   take#2(z, z') -{ 1 }-> 1 :|: z = 0, z' >= 0
   take#2(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   take#2(z, z') -{ 3 + x64 }-> 1 + x56 + s1 :|: s1 >= 0, s1 <= x64 + 4, z' = 1 + x56 + x64, z - 1 >= 0, x64 >= 0, x56 >= 0
   take#2(z, z') -{ 1 }-> 1 + 2 + 1 :|: z = 1 + 0, z' = 1

Function symbols to be analyzed: {drop#2}, {merge#2,cond_merge_ys_zs_2}, {divide_ys#1}, {const_f#2}, {dc#1,map#2}, {main}
Previous analysis results are:
  leq#2: runtime: O(n^1) [2 + z'], size: O(1) [2]
  take#2: runtime: O(n^1) [2 + z'], size: O(n^1) [4 + z']
  halve#1: runtime: O(n^1) [2 + z], size: O(n^1) [1 + z]
  length#1: runtime: O(n^1) [1 + z], size: O(n^1) [z]

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

(45) IntTrsBoundProof (UPPER BOUND(ID))

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

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

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

   cond_merge_ys_zs_2(z, z', z'', z1, z2, z3, z4) -{ 0 }-> 0 :|: z >= 0, z4 >= 0, z' >= 0, z3 >= 0, z'' >= 0, z1 >= 0, z2 >= 0
   cond_merge_ys_zs_2(z, z', z'', z1, z2, z3, z4) -{ 1 }-> 1 + z1 + merge#2(z2, 1 + x5 + x6) :|: x5 >= 0, x8 >= 0, z' = 1 + x7 + x8, z'' = 1 + x5 + x6, z2 >= 0, z3 >= 0, z = 2, z1 >= 0, z4 >= 0, x7 >= 0, x6 >= 0
   cond_merge_ys_zs_2(z, z', z'', z1, z2, z3, z4) -{ 1 }-> 1 + z3 + merge#2(1 + x7 + x8, z4) :|: x5 >= 0, x8 >= 0, z = 1, z' = 1 + x7 + x8, z'' = 1 + x5 + x6, z2 >= 0, z3 >= 0, z1 >= 0, z4 >= 0, x7 >= 0, x6 >= 0
   const_f#2(z, z') -{ 1 }-> merge#2(x6, x4) :|: x4 >= 0, z' = 1 + x6 + (1 + x4 + x2), x6 >= 0, z >= 0, x2 >= 0
   const_f#2(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   dc#1(z, z', z'', z1, z2, z3) -{ 3 }-> const_f#2(1 + x51 + (1 + x25 + x33), map#2(1 + 0 + 0 + 0 + 0 + 0, divide_ys#1(1 + x51 + (1 + x25 + x33), 1 + s3))) :|: s3 >= 0, s3 <= 0 + 1, z'' = 0, z1 = 0, x33 >= 0, z3 = 1 + x51 + (1 + x25 + x33), z2 = 0, x51 >= 0, x25 >= 0, z = 0, z' = 0
   dc#1(z, z', z'', z1, z2, z3) -{ 4 }-> const_f#2(1 + x51 + (1 + x25 + 1), map#2(1 + 0 + 0 + 0 + 0 + 0, divide_ys#1(1 + x51 + (1 + x25 + 1), 1 + s2))) :|: s2 >= 0, s2 <= 0 + 1, z'' = 0, z3 = 1 + x51 + (1 + x25 + 1), z1 = 0, z2 = 0, x51 >= 0, x25 >= 0, z = 0, z' = 0
   dc#1(z, z', z'', z1, z2, z3) -{ 6 + s5 + x8' }-> const_f#2(1 + x51 + (1 + x25 + (1 + x6' + x8')), map#2(1 + 0 + 0 + 0 + 0 + 0, divide_ys#1(1 + x51 + (1 + x25 + (1 + x6' + x8')), 1 + s6))) :|: s5 >= 0, s5 <= x8', s6 >= 0, s6 <= 1 + s5 + 1, z'' = 0, z1 = 0, z2 = 0, x51 >= 0, x25 >= 0, x6' >= 0, z3 = 1 + x51 + (1 + x25 + (1 + x6' + x8')), z = 0, x8' >= 0, z' = 0
   dc#1(z, z', z'', z1, z2, z3) -{ 1 }-> 1 :|: z'' = 0, z1 = 0, z2 = 0, z3 = 1, z = 0, z' = 0
   dc#1(z, z', z'', z1, z2, z3) -{ 0 }-> 0 :|: z >= 0, z2 >= 0, z' >= 0, z3 >= 0, z'' >= 0, z1 >= 0
   dc#1(z, z', z'', z1, z2, z3) -{ 1 }-> 1 + (z3 - 2) + 1 :|: z'' = 0, z1 = 0, z2 = 0, z3 - 2 >= 0, z = 0, z' = 0
   divide_ys#1(z, z') -{ 3 + z }-> 1 + s'' + (1 + drop#2(z', z) + 1) :|: s'' >= 0, s'' <= z + 4, z' >= 0, z >= 0
   drop#2(z, z') -{ 1 }-> z' :|: z = 0, z' >= 0
   drop#2(z, z') -{ 1 }-> drop#2(z - 1, x64) :|: z' = 1 + x56 + x64, z - 1 >= 0, x64 >= 0, x56 >= 0
   drop#2(z, z') -{ 1 }-> 3 :|: z = 1 + 0, z' = 1
   drop#2(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   halve#1(z) -{ 1 }-> 0 :|: z = 0
   halve#1(z) -{ 0 }-> 0 :|: z >= 0
   halve#1(z) -{ 1 + z }-> 1 + s4 :|: s4 >= 0, s4 <= z - 2 + 1, z - 2 >= 0
   halve#1(z) -{ 1 }-> 1 + 0 :|: z = 1 + 0
   length#1(z) -{ 1 }-> 0 :|: z = 1
   length#1(z) -{ 0 }-> 0 :|: z >= 0
   length#1(z) -{ 2 + x8 }-> 1 + s7 :|: s7 >= 0, s7 <= x8, x8 >= 0, x6 >= 0, z = 1 + x6 + x8
   leq#2(z, z') -{ 2 + z' }-> s' :|: s' >= 0, s' <= 2, z - 1 >= 0, z' - 1 >= 0
   leq#2(z, z') -{ 1 }-> 2 :|: z = 0, z' >= 0
   leq#2(z, z') -{ 1 }-> 1 :|: z - 1 >= 0, z' = 0
   leq#2(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   main(z) -{ 1 }-> dc#1(0, 0, 0, 0, 0, z) :|: z >= 0
   map#2(z, z') -{ 1 }-> 1 :|: x4 >= 0, x8 >= 0, x6 >= 0, z = 1 + x2 + x4 + x6 + x8 + x10, z' = 1, x10 >= 0, x2 >= 0
   map#2(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   map#2(z, z') -{ 1 }-> 1 + dc#1(x6, x8, x10, x12, x14, x4) + map#2(1 + x6 + x8 + x10 + x12 + x14, x2) :|: x4 >= 0, x8 >= 0, z' = 1 + x4 + x2, x6 >= 0, x12 >= 0, x14 >= 0, x10 >= 0, x2 >= 0, z = 1 + x6 + x8 + x10 + x12 + x14
   merge#2(z, z') -{ 1 }-> z' :|: z = 1, z' >= 0
   merge#2(z, z') -{ 4 + x2' }-> cond_merge_ys_zs_2(s, 1 + (1 + x4') + x6, 1 + (1 + x2') + x2, 1 + x4', x6, 1 + x2', x2) :|: s >= 0, s <= 2, x2' >= 0, z = 1 + (1 + x4') + x6, x6 >= 0, z' = 1 + (1 + x2') + x2, x4' >= 0, x2 >= 0
   merge#2(z, z') -{ 2 }-> cond_merge_ys_zs_2(2, 1 + 0 + (z - 1), 1 + x4 + x2, 0, z - 1, x4, x2) :|: x4 >= 0, z' = 1 + x4 + x2, z - 1 >= 0, x2 >= 0
   merge#2(z, z') -{ 2 }-> cond_merge_ys_zs_2(1, 1 + (1 + x20') + x6, 1 + 0 + (z' - 1), 1 + x20', x6, 0, z' - 1) :|: z = 1 + (1 + x20') + x6, x6 >= 0, x20' >= 0, z' - 1 >= 0
   merge#2(z, z') -{ 1 }-> cond_merge_ys_zs_2(0, 1 + x8 + x6, 1 + x4 + x2, x8, x6, x4, x2) :|: x4 >= 0, x8 >= 0, z' = 1 + x4 + x2, x6 >= 0, z = 1 + x8 + x6, x2 >= 0
   merge#2(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   merge#2(z, z') -{ 1 }-> 1 + x4 + x2 :|: x4 >= 0, z = 1 + x4 + x2, z' = 1, x2 >= 0
   take#2(z, z') -{ 1 }-> 1 :|: z = 0, z' >= 0
   take#2(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   take#2(z, z') -{ 3 + x64 }-> 1 + x56 + s1 :|: s1 >= 0, s1 <= x64 + 4, z' = 1 + x56 + x64, z - 1 >= 0, x64 >= 0, x56 >= 0
   take#2(z, z') -{ 1 }-> 1 + 2 + 1 :|: z = 1 + 0, z' = 1

Function symbols to be analyzed: {drop#2}, {merge#2,cond_merge_ys_zs_2}, {divide_ys#1}, {const_f#2}, {dc#1,map#2}, {main}
Previous analysis results are:
  leq#2: runtime: O(n^1) [2 + z'], size: O(1) [2]
  take#2: runtime: O(n^1) [2 + z'], size: O(n^1) [4 + z']
  halve#1: runtime: O(n^1) [2 + z], size: O(n^1) [1 + z]
  length#1: runtime: O(n^1) [1 + z], size: O(n^1) [z]
  drop#2: runtime: ?, size: O(n^1) [2 + z']

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

(47) IntTrsBoundProof (UPPER BOUND(ID))

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

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

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

   cond_merge_ys_zs_2(z, z', z'', z1, z2, z3, z4) -{ 0 }-> 0 :|: z >= 0, z4 >= 0, z' >= 0, z3 >= 0, z'' >= 0, z1 >= 0, z2 >= 0
   cond_merge_ys_zs_2(z, z', z'', z1, z2, z3, z4) -{ 1 }-> 1 + z1 + merge#2(z2, 1 + x5 + x6) :|: x5 >= 0, x8 >= 0, z' = 1 + x7 + x8, z'' = 1 + x5 + x6, z2 >= 0, z3 >= 0, z = 2, z1 >= 0, z4 >= 0, x7 >= 0, x6 >= 0
   cond_merge_ys_zs_2(z, z', z'', z1, z2, z3, z4) -{ 1 }-> 1 + z3 + merge#2(1 + x7 + x8, z4) :|: x5 >= 0, x8 >= 0, z = 1, z' = 1 + x7 + x8, z'' = 1 + x5 + x6, z2 >= 0, z3 >= 0, z1 >= 0, z4 >= 0, x7 >= 0, x6 >= 0
   const_f#2(z, z') -{ 1 }-> merge#2(x6, x4) :|: x4 >= 0, z' = 1 + x6 + (1 + x4 + x2), x6 >= 0, z >= 0, x2 >= 0
   const_f#2(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   dc#1(z, z', z'', z1, z2, z3) -{ 3 }-> const_f#2(1 + x51 + (1 + x25 + x33), map#2(1 + 0 + 0 + 0 + 0 + 0, divide_ys#1(1 + x51 + (1 + x25 + x33), 1 + s3))) :|: s3 >= 0, s3 <= 0 + 1, z'' = 0, z1 = 0, x33 >= 0, z3 = 1 + x51 + (1 + x25 + x33), z2 = 0, x51 >= 0, x25 >= 0, z = 0, z' = 0
   dc#1(z, z', z'', z1, z2, z3) -{ 4 }-> const_f#2(1 + x51 + (1 + x25 + 1), map#2(1 + 0 + 0 + 0 + 0 + 0, divide_ys#1(1 + x51 + (1 + x25 + 1), 1 + s2))) :|: s2 >= 0, s2 <= 0 + 1, z'' = 0, z3 = 1 + x51 + (1 + x25 + 1), z1 = 0, z2 = 0, x51 >= 0, x25 >= 0, z = 0, z' = 0
   dc#1(z, z', z'', z1, z2, z3) -{ 6 + s5 + x8' }-> const_f#2(1 + x51 + (1 + x25 + (1 + x6' + x8')), map#2(1 + 0 + 0 + 0 + 0 + 0, divide_ys#1(1 + x51 + (1 + x25 + (1 + x6' + x8')), 1 + s6))) :|: s5 >= 0, s5 <= x8', s6 >= 0, s6 <= 1 + s5 + 1, z'' = 0, z1 = 0, z2 = 0, x51 >= 0, x25 >= 0, x6' >= 0, z3 = 1 + x51 + (1 + x25 + (1 + x6' + x8')), z = 0, x8' >= 0, z' = 0
   dc#1(z, z', z'', z1, z2, z3) -{ 1 }-> 1 :|: z'' = 0, z1 = 0, z2 = 0, z3 = 1, z = 0, z' = 0
   dc#1(z, z', z'', z1, z2, z3) -{ 0 }-> 0 :|: z >= 0, z2 >= 0, z' >= 0, z3 >= 0, z'' >= 0, z1 >= 0
   dc#1(z, z', z'', z1, z2, z3) -{ 1 }-> 1 + (z3 - 2) + 1 :|: z'' = 0, z1 = 0, z2 = 0, z3 - 2 >= 0, z = 0, z' = 0
   divide_ys#1(z, z') -{ 3 + z }-> 1 + s'' + (1 + drop#2(z', z) + 1) :|: s'' >= 0, s'' <= z + 4, z' >= 0, z >= 0
   drop#2(z, z') -{ 1 }-> z' :|: z = 0, z' >= 0
   drop#2(z, z') -{ 1 }-> drop#2(z - 1, x64) :|: z' = 1 + x56 + x64, z - 1 >= 0, x64 >= 0, x56 >= 0
   drop#2(z, z') -{ 1 }-> 3 :|: z = 1 + 0, z' = 1
   drop#2(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   halve#1(z) -{ 1 }-> 0 :|: z = 0
   halve#1(z) -{ 0 }-> 0 :|: z >= 0
   halve#1(z) -{ 1 + z }-> 1 + s4 :|: s4 >= 0, s4 <= z - 2 + 1, z - 2 >= 0
   halve#1(z) -{ 1 }-> 1 + 0 :|: z = 1 + 0
   length#1(z) -{ 1 }-> 0 :|: z = 1
   length#1(z) -{ 0 }-> 0 :|: z >= 0
   length#1(z) -{ 2 + x8 }-> 1 + s7 :|: s7 >= 0, s7 <= x8, x8 >= 0, x6 >= 0, z = 1 + x6 + x8
   leq#2(z, z') -{ 2 + z' }-> s' :|: s' >= 0, s' <= 2, z - 1 >= 0, z' - 1 >= 0
   leq#2(z, z') -{ 1 }-> 2 :|: z = 0, z' >= 0
   leq#2(z, z') -{ 1 }-> 1 :|: z - 1 >= 0, z' = 0
   leq#2(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   main(z) -{ 1 }-> dc#1(0, 0, 0, 0, 0, z) :|: z >= 0
   map#2(z, z') -{ 1 }-> 1 :|: x4 >= 0, x8 >= 0, x6 >= 0, z = 1 + x2 + x4 + x6 + x8 + x10, z' = 1, x10 >= 0, x2 >= 0
   map#2(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   map#2(z, z') -{ 1 }-> 1 + dc#1(x6, x8, x10, x12, x14, x4) + map#2(1 + x6 + x8 + x10 + x12 + x14, x2) :|: x4 >= 0, x8 >= 0, z' = 1 + x4 + x2, x6 >= 0, x12 >= 0, x14 >= 0, x10 >= 0, x2 >= 0, z = 1 + x6 + x8 + x10 + x12 + x14
   merge#2(z, z') -{ 1 }-> z' :|: z = 1, z' >= 0
   merge#2(z, z') -{ 4 + x2' }-> cond_merge_ys_zs_2(s, 1 + (1 + x4') + x6, 1 + (1 + x2') + x2, 1 + x4', x6, 1 + x2', x2) :|: s >= 0, s <= 2, x2' >= 0, z = 1 + (1 + x4') + x6, x6 >= 0, z' = 1 + (1 + x2') + x2, x4' >= 0, x2 >= 0
   merge#2(z, z') -{ 2 }-> cond_merge_ys_zs_2(2, 1 + 0 + (z - 1), 1 + x4 + x2, 0, z - 1, x4, x2) :|: x4 >= 0, z' = 1 + x4 + x2, z - 1 >= 0, x2 >= 0
   merge#2(z, z') -{ 2 }-> cond_merge_ys_zs_2(1, 1 + (1 + x20') + x6, 1 + 0 + (z' - 1), 1 + x20', x6, 0, z' - 1) :|: z = 1 + (1 + x20') + x6, x6 >= 0, x20' >= 0, z' - 1 >= 0
   merge#2(z, z') -{ 1 }-> cond_merge_ys_zs_2(0, 1 + x8 + x6, 1 + x4 + x2, x8, x6, x4, x2) :|: x4 >= 0, x8 >= 0, z' = 1 + x4 + x2, x6 >= 0, z = 1 + x8 + x6, x2 >= 0
   merge#2(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   merge#2(z, z') -{ 1 }-> 1 + x4 + x2 :|: x4 >= 0, z = 1 + x4 + x2, z' = 1, x2 >= 0
   take#2(z, z') -{ 1 }-> 1 :|: z = 0, z' >= 0
   take#2(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   take#2(z, z') -{ 3 + x64 }-> 1 + x56 + s1 :|: s1 >= 0, s1 <= x64 + 4, z' = 1 + x56 + x64, z - 1 >= 0, x64 >= 0, x56 >= 0
   take#2(z, z') -{ 1 }-> 1 + 2 + 1 :|: z = 1 + 0, z' = 1

Function symbols to be analyzed: {merge#2,cond_merge_ys_zs_2}, {divide_ys#1}, {const_f#2}, {dc#1,map#2}, {main}
Previous analysis results are:
  leq#2: runtime: O(n^1) [2 + z'], size: O(1) [2]
  take#2: runtime: O(n^1) [2 + z'], size: O(n^1) [4 + z']
  halve#1: runtime: O(n^1) [2 + z], size: O(n^1) [1 + z]
  length#1: runtime: O(n^1) [1 + z], size: O(n^1) [z]
  drop#2: runtime: O(n^1) [2 + z'], size: O(n^1) [2 + z']

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

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

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

   cond_merge_ys_zs_2(z, z', z'', z1, z2, z3, z4) -{ 0 }-> 0 :|: z >= 0, z4 >= 0, z' >= 0, z3 >= 0, z'' >= 0, z1 >= 0, z2 >= 0
   cond_merge_ys_zs_2(z, z', z'', z1, z2, z3, z4) -{ 1 }-> 1 + z1 + merge#2(z2, 1 + x5 + x6) :|: x5 >= 0, x8 >= 0, z' = 1 + x7 + x8, z'' = 1 + x5 + x6, z2 >= 0, z3 >= 0, z = 2, z1 >= 0, z4 >= 0, x7 >= 0, x6 >= 0
   cond_merge_ys_zs_2(z, z', z'', z1, z2, z3, z4) -{ 1 }-> 1 + z3 + merge#2(1 + x7 + x8, z4) :|: x5 >= 0, x8 >= 0, z = 1, z' = 1 + x7 + x8, z'' = 1 + x5 + x6, z2 >= 0, z3 >= 0, z1 >= 0, z4 >= 0, x7 >= 0, x6 >= 0
   const_f#2(z, z') -{ 1 }-> merge#2(x6, x4) :|: x4 >= 0, z' = 1 + x6 + (1 + x4 + x2), x6 >= 0, z >= 0, x2 >= 0
   const_f#2(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   dc#1(z, z', z'', z1, z2, z3) -{ 3 }-> const_f#2(1 + x51 + (1 + x25 + x33), map#2(1 + 0 + 0 + 0 + 0 + 0, divide_ys#1(1 + x51 + (1 + x25 + x33), 1 + s3))) :|: s3 >= 0, s3 <= 0 + 1, z'' = 0, z1 = 0, x33 >= 0, z3 = 1 + x51 + (1 + x25 + x33), z2 = 0, x51 >= 0, x25 >= 0, z = 0, z' = 0
   dc#1(z, z', z'', z1, z2, z3) -{ 4 }-> const_f#2(1 + x51 + (1 + x25 + 1), map#2(1 + 0 + 0 + 0 + 0 + 0, divide_ys#1(1 + x51 + (1 + x25 + 1), 1 + s2))) :|: s2 >= 0, s2 <= 0 + 1, z'' = 0, z3 = 1 + x51 + (1 + x25 + 1), z1 = 0, z2 = 0, x51 >= 0, x25 >= 0, z = 0, z' = 0
   dc#1(z, z', z'', z1, z2, z3) -{ 6 + s5 + x8' }-> const_f#2(1 + x51 + (1 + x25 + (1 + x6' + x8')), map#2(1 + 0 + 0 + 0 + 0 + 0, divide_ys#1(1 + x51 + (1 + x25 + (1 + x6' + x8')), 1 + s6))) :|: s5 >= 0, s5 <= x8', s6 >= 0, s6 <= 1 + s5 + 1, z'' = 0, z1 = 0, z2 = 0, x51 >= 0, x25 >= 0, x6' >= 0, z3 = 1 + x51 + (1 + x25 + (1 + x6' + x8')), z = 0, x8' >= 0, z' = 0
   dc#1(z, z', z'', z1, z2, z3) -{ 1 }-> 1 :|: z'' = 0, z1 = 0, z2 = 0, z3 = 1, z = 0, z' = 0
   dc#1(z, z', z'', z1, z2, z3) -{ 0 }-> 0 :|: z >= 0, z2 >= 0, z' >= 0, z3 >= 0, z'' >= 0, z1 >= 0
   dc#1(z, z', z'', z1, z2, z3) -{ 1 }-> 1 + (z3 - 2) + 1 :|: z'' = 0, z1 = 0, z2 = 0, z3 - 2 >= 0, z = 0, z' = 0
   divide_ys#1(z, z') -{ 5 + 2*z }-> 1 + s'' + (1 + s8 + 1) :|: s8 >= 0, s8 <= z + 2, s'' >= 0, s'' <= z + 4, z' >= 0, z >= 0
   drop#2(z, z') -{ 3 + x64 }-> s9 :|: s9 >= 0, s9 <= x64 + 2, z' = 1 + x56 + x64, z - 1 >= 0, x64 >= 0, x56 >= 0
   drop#2(z, z') -{ 1 }-> z' :|: z = 0, z' >= 0
   drop#2(z, z') -{ 1 }-> 3 :|: z = 1 + 0, z' = 1
   drop#2(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   halve#1(z) -{ 1 }-> 0 :|: z = 0
   halve#1(z) -{ 0 }-> 0 :|: z >= 0
   halve#1(z) -{ 1 + z }-> 1 + s4 :|: s4 >= 0, s4 <= z - 2 + 1, z - 2 >= 0
   halve#1(z) -{ 1 }-> 1 + 0 :|: z = 1 + 0
   length#1(z) -{ 1 }-> 0 :|: z = 1
   length#1(z) -{ 0 }-> 0 :|: z >= 0
   length#1(z) -{ 2 + x8 }-> 1 + s7 :|: s7 >= 0, s7 <= x8, x8 >= 0, x6 >= 0, z = 1 + x6 + x8
   leq#2(z, z') -{ 2 + z' }-> s' :|: s' >= 0, s' <= 2, z - 1 >= 0, z' - 1 >= 0
   leq#2(z, z') -{ 1 }-> 2 :|: z = 0, z' >= 0
   leq#2(z, z') -{ 1 }-> 1 :|: z - 1 >= 0, z' = 0
   leq#2(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   main(z) -{ 1 }-> dc#1(0, 0, 0, 0, 0, z) :|: z >= 0
   map#2(z, z') -{ 1 }-> 1 :|: x4 >= 0, x8 >= 0, x6 >= 0, z = 1 + x2 + x4 + x6 + x8 + x10, z' = 1, x10 >= 0, x2 >= 0
   map#2(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   map#2(z, z') -{ 1 }-> 1 + dc#1(x6, x8, x10, x12, x14, x4) + map#2(1 + x6 + x8 + x10 + x12 + x14, x2) :|: x4 >= 0, x8 >= 0, z' = 1 + x4 + x2, x6 >= 0, x12 >= 0, x14 >= 0, x10 >= 0, x2 >= 0, z = 1 + x6 + x8 + x10 + x12 + x14
   merge#2(z, z') -{ 1 }-> z' :|: z = 1, z' >= 0
   merge#2(z, z') -{ 4 + x2' }-> cond_merge_ys_zs_2(s, 1 + (1 + x4') + x6, 1 + (1 + x2') + x2, 1 + x4', x6, 1 + x2', x2) :|: s >= 0, s <= 2, x2' >= 0, z = 1 + (1 + x4') + x6, x6 >= 0, z' = 1 + (1 + x2') + x2, x4' >= 0, x2 >= 0
   merge#2(z, z') -{ 2 }-> cond_merge_ys_zs_2(2, 1 + 0 + (z - 1), 1 + x4 + x2, 0, z - 1, x4, x2) :|: x4 >= 0, z' = 1 + x4 + x2, z - 1 >= 0, x2 >= 0
   merge#2(z, z') -{ 2 }-> cond_merge_ys_zs_2(1, 1 + (1 + x20') + x6, 1 + 0 + (z' - 1), 1 + x20', x6, 0, z' - 1) :|: z = 1 + (1 + x20') + x6, x6 >= 0, x20' >= 0, z' - 1 >= 0
   merge#2(z, z') -{ 1 }-> cond_merge_ys_zs_2(0, 1 + x8 + x6, 1 + x4 + x2, x8, x6, x4, x2) :|: x4 >= 0, x8 >= 0, z' = 1 + x4 + x2, x6 >= 0, z = 1 + x8 + x6, x2 >= 0
   merge#2(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   merge#2(z, z') -{ 1 }-> 1 + x4 + x2 :|: x4 >= 0, z = 1 + x4 + x2, z' = 1, x2 >= 0
   take#2(z, z') -{ 1 }-> 1 :|: z = 0, z' >= 0
   take#2(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   take#2(z, z') -{ 3 + x64 }-> 1 + x56 + s1 :|: s1 >= 0, s1 <= x64 + 4, z' = 1 + x56 + x64, z - 1 >= 0, x64 >= 0, x56 >= 0
   take#2(z, z') -{ 1 }-> 1 + 2 + 1 :|: z = 1 + 0, z' = 1

Function symbols to be analyzed: {merge#2,cond_merge_ys_zs_2}, {divide_ys#1}, {const_f#2}, {dc#1,map#2}, {main}
Previous analysis results are:
  leq#2: runtime: O(n^1) [2 + z'], size: O(1) [2]
  take#2: runtime: O(n^1) [2 + z'], size: O(n^1) [4 + z']
  halve#1: runtime: O(n^1) [2 + z], size: O(n^1) [1 + z]
  length#1: runtime: O(n^1) [1 + z], size: O(n^1) [z]
  drop#2: runtime: O(n^1) [2 + z'], size: O(n^1) [2 + z']

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

(51) IntTrsBoundProof (UPPER BOUND(ID))

Computed SIZE bound using CoFloCo for: merge#2
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: cond_merge_ys_zs_2
after applying outer abstraction to obtain an ITS,
resulting in: O(n^1) with polynomial bound: 2 + z' + z'' + z1 + z2 + z3 + z4

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

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

   cond_merge_ys_zs_2(z, z', z'', z1, z2, z3, z4) -{ 0 }-> 0 :|: z >= 0, z4 >= 0, z' >= 0, z3 >= 0, z'' >= 0, z1 >= 0, z2 >= 0
   cond_merge_ys_zs_2(z, z', z'', z1, z2, z3, z4) -{ 1 }-> 1 + z1 + merge#2(z2, 1 + x5 + x6) :|: x5 >= 0, x8 >= 0, z' = 1 + x7 + x8, z'' = 1 + x5 + x6, z2 >= 0, z3 >= 0, z = 2, z1 >= 0, z4 >= 0, x7 >= 0, x6 >= 0
   cond_merge_ys_zs_2(z, z', z'', z1, z2, z3, z4) -{ 1 }-> 1 + z3 + merge#2(1 + x7 + x8, z4) :|: x5 >= 0, x8 >= 0, z = 1, z' = 1 + x7 + x8, z'' = 1 + x5 + x6, z2 >= 0, z3 >= 0, z1 >= 0, z4 >= 0, x7 >= 0, x6 >= 0
   const_f#2(z, z') -{ 1 }-> merge#2(x6, x4) :|: x4 >= 0, z' = 1 + x6 + (1 + x4 + x2), x6 >= 0, z >= 0, x2 >= 0
   const_f#2(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   dc#1(z, z', z'', z1, z2, z3) -{ 3 }-> const_f#2(1 + x51 + (1 + x25 + x33), map#2(1 + 0 + 0 + 0 + 0 + 0, divide_ys#1(1 + x51 + (1 + x25 + x33), 1 + s3))) :|: s3 >= 0, s3 <= 0 + 1, z'' = 0, z1 = 0, x33 >= 0, z3 = 1 + x51 + (1 + x25 + x33), z2 = 0, x51 >= 0, x25 >= 0, z = 0, z' = 0
   dc#1(z, z', z'', z1, z2, z3) -{ 4 }-> const_f#2(1 + x51 + (1 + x25 + 1), map#2(1 + 0 + 0 + 0 + 0 + 0, divide_ys#1(1 + x51 + (1 + x25 + 1), 1 + s2))) :|: s2 >= 0, s2 <= 0 + 1, z'' = 0, z3 = 1 + x51 + (1 + x25 + 1), z1 = 0, z2 = 0, x51 >= 0, x25 >= 0, z = 0, z' = 0
   dc#1(z, z', z'', z1, z2, z3) -{ 6 + s5 + x8' }-> const_f#2(1 + x51 + (1 + x25 + (1 + x6' + x8')), map#2(1 + 0 + 0 + 0 + 0 + 0, divide_ys#1(1 + x51 + (1 + x25 + (1 + x6' + x8')), 1 + s6))) :|: s5 >= 0, s5 <= x8', s6 >= 0, s6 <= 1 + s5 + 1, z'' = 0, z1 = 0, z2 = 0, x51 >= 0, x25 >= 0, x6' >= 0, z3 = 1 + x51 + (1 + x25 + (1 + x6' + x8')), z = 0, x8' >= 0, z' = 0
   dc#1(z, z', z'', z1, z2, z3) -{ 1 }-> 1 :|: z'' = 0, z1 = 0, z2 = 0, z3 = 1, z = 0, z' = 0
   dc#1(z, z', z'', z1, z2, z3) -{ 0 }-> 0 :|: z >= 0, z2 >= 0, z' >= 0, z3 >= 0, z'' >= 0, z1 >= 0
   dc#1(z, z', z'', z1, z2, z3) -{ 1 }-> 1 + (z3 - 2) + 1 :|: z'' = 0, z1 = 0, z2 = 0, z3 - 2 >= 0, z = 0, z' = 0
   divide_ys#1(z, z') -{ 5 + 2*z }-> 1 + s'' + (1 + s8 + 1) :|: s8 >= 0, s8 <= z + 2, s'' >= 0, s'' <= z + 4, z' >= 0, z >= 0
   drop#2(z, z') -{ 3 + x64 }-> s9 :|: s9 >= 0, s9 <= x64 + 2, z' = 1 + x56 + x64, z - 1 >= 0, x64 >= 0, x56 >= 0
   drop#2(z, z') -{ 1 }-> z' :|: z = 0, z' >= 0
   drop#2(z, z') -{ 1 }-> 3 :|: z = 1 + 0, z' = 1
   drop#2(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   halve#1(z) -{ 1 }-> 0 :|: z = 0
   halve#1(z) -{ 0 }-> 0 :|: z >= 0
   halve#1(z) -{ 1 + z }-> 1 + s4 :|: s4 >= 0, s4 <= z - 2 + 1, z - 2 >= 0
   halve#1(z) -{ 1 }-> 1 + 0 :|: z = 1 + 0
   length#1(z) -{ 1 }-> 0 :|: z = 1
   length#1(z) -{ 0 }-> 0 :|: z >= 0
   length#1(z) -{ 2 + x8 }-> 1 + s7 :|: s7 >= 0, s7 <= x8, x8 >= 0, x6 >= 0, z = 1 + x6 + x8
   leq#2(z, z') -{ 2 + z' }-> s' :|: s' >= 0, s' <= 2, z - 1 >= 0, z' - 1 >= 0
   leq#2(z, z') -{ 1 }-> 2 :|: z = 0, z' >= 0
   leq#2(z, z') -{ 1 }-> 1 :|: z - 1 >= 0, z' = 0
   leq#2(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   main(z) -{ 1 }-> dc#1(0, 0, 0, 0, 0, z) :|: z >= 0
   map#2(z, z') -{ 1 }-> 1 :|: x4 >= 0, x8 >= 0, x6 >= 0, z = 1 + x2 + x4 + x6 + x8 + x10, z' = 1, x10 >= 0, x2 >= 0
   map#2(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   map#2(z, z') -{ 1 }-> 1 + dc#1(x6, x8, x10, x12, x14, x4) + map#2(1 + x6 + x8 + x10 + x12 + x14, x2) :|: x4 >= 0, x8 >= 0, z' = 1 + x4 + x2, x6 >= 0, x12 >= 0, x14 >= 0, x10 >= 0, x2 >= 0, z = 1 + x6 + x8 + x10 + x12 + x14
   merge#2(z, z') -{ 1 }-> z' :|: z = 1, z' >= 0
   merge#2(z, z') -{ 4 + x2' }-> cond_merge_ys_zs_2(s, 1 + (1 + x4') + x6, 1 + (1 + x2') + x2, 1 + x4', x6, 1 + x2', x2) :|: s >= 0, s <= 2, x2' >= 0, z = 1 + (1 + x4') + x6, x6 >= 0, z' = 1 + (1 + x2') + x2, x4' >= 0, x2 >= 0
   merge#2(z, z') -{ 2 }-> cond_merge_ys_zs_2(2, 1 + 0 + (z - 1), 1 + x4 + x2, 0, z - 1, x4, x2) :|: x4 >= 0, z' = 1 + x4 + x2, z - 1 >= 0, x2 >= 0
   merge#2(z, z') -{ 2 }-> cond_merge_ys_zs_2(1, 1 + (1 + x20') + x6, 1 + 0 + (z' - 1), 1 + x20', x6, 0, z' - 1) :|: z = 1 + (1 + x20') + x6, x6 >= 0, x20' >= 0, z' - 1 >= 0
   merge#2(z, z') -{ 1 }-> cond_merge_ys_zs_2(0, 1 + x8 + x6, 1 + x4 + x2, x8, x6, x4, x2) :|: x4 >= 0, x8 >= 0, z' = 1 + x4 + x2, x6 >= 0, z = 1 + x8 + x6, x2 >= 0
   merge#2(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   merge#2(z, z') -{ 1 }-> 1 + x4 + x2 :|: x4 >= 0, z = 1 + x4 + x2, z' = 1, x2 >= 0
   take#2(z, z') -{ 1 }-> 1 :|: z = 0, z' >= 0
   take#2(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   take#2(z, z') -{ 3 + x64 }-> 1 + x56 + s1 :|: s1 >= 0, s1 <= x64 + 4, z' = 1 + x56 + x64, z - 1 >= 0, x64 >= 0, x56 >= 0
   take#2(z, z') -{ 1 }-> 1 + 2 + 1 :|: z = 1 + 0, z' = 1

Function symbols to be analyzed: {merge#2,cond_merge_ys_zs_2}, {divide_ys#1}, {const_f#2}, {dc#1,map#2}, {main}
Previous analysis results are:
  leq#2: runtime: O(n^1) [2 + z'], size: O(1) [2]
  take#2: runtime: O(n^1) [2 + z'], size: O(n^1) [4 + z']
  halve#1: runtime: O(n^1) [2 + z], size: O(n^1) [1 + z]
  length#1: runtime: O(n^1) [1 + z], size: O(n^1) [z]
  drop#2: runtime: O(n^1) [2 + z'], size: O(n^1) [2 + z']
  merge#2: runtime: ?, size: O(n^1) [1 + z + z']
  cond_merge_ys_zs_2: runtime: ?, size: O(n^1) [2 + z' + z'' + z1 + z2 + z3 + z4]

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

(53) IntTrsBoundProof (UPPER BOUND(ID))

Computed RUNTIME bound using CoFloCo for: merge#2
after applying outer abstraction to obtain an ITS,
resulting in: O(n^2) with polynomial bound: 11 + 5*z + z*z' + 12*z' + 2*z'^2

Computed RUNTIME bound using KoAT for: cond_merge_ys_zs_2
after applying outer abstraction to obtain an ITS,
resulting in: O(n^2) with polynomial bound: 43 + 10*z' + 2*z'*z4 + 32*z'' + 2*z''*z2 + 8*z''^2 + 6*z2 + 13*z4 + 2*z4^2

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

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

   cond_merge_ys_zs_2(z, z', z'', z1, z2, z3, z4) -{ 0 }-> 0 :|: z >= 0, z4 >= 0, z' >= 0, z3 >= 0, z'' >= 0, z1 >= 0, z2 >= 0
   cond_merge_ys_zs_2(z, z', z'', z1, z2, z3, z4) -{ 1 }-> 1 + z1 + merge#2(z2, 1 + x5 + x6) :|: x5 >= 0, x8 >= 0, z' = 1 + x7 + x8, z'' = 1 + x5 + x6, z2 >= 0, z3 >= 0, z = 2, z1 >= 0, z4 >= 0, x7 >= 0, x6 >= 0
   cond_merge_ys_zs_2(z, z', z'', z1, z2, z3, z4) -{ 1 }-> 1 + z3 + merge#2(1 + x7 + x8, z4) :|: x5 >= 0, x8 >= 0, z = 1, z' = 1 + x7 + x8, z'' = 1 + x5 + x6, z2 >= 0, z3 >= 0, z1 >= 0, z4 >= 0, x7 >= 0, x6 >= 0
   const_f#2(z, z') -{ 1 }-> merge#2(x6, x4) :|: x4 >= 0, z' = 1 + x6 + (1 + x4 + x2), x6 >= 0, z >= 0, x2 >= 0
   const_f#2(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   dc#1(z, z', z'', z1, z2, z3) -{ 3 }-> const_f#2(1 + x51 + (1 + x25 + x33), map#2(1 + 0 + 0 + 0 + 0 + 0, divide_ys#1(1 + x51 + (1 + x25 + x33), 1 + s3))) :|: s3 >= 0, s3 <= 0 + 1, z'' = 0, z1 = 0, x33 >= 0, z3 = 1 + x51 + (1 + x25 + x33), z2 = 0, x51 >= 0, x25 >= 0, z = 0, z' = 0
   dc#1(z, z', z'', z1, z2, z3) -{ 4 }-> const_f#2(1 + x51 + (1 + x25 + 1), map#2(1 + 0 + 0 + 0 + 0 + 0, divide_ys#1(1 + x51 + (1 + x25 + 1), 1 + s2))) :|: s2 >= 0, s2 <= 0 + 1, z'' = 0, z3 = 1 + x51 + (1 + x25 + 1), z1 = 0, z2 = 0, x51 >= 0, x25 >= 0, z = 0, z' = 0
   dc#1(z, z', z'', z1, z2, z3) -{ 6 + s5 + x8' }-> const_f#2(1 + x51 + (1 + x25 + (1 + x6' + x8')), map#2(1 + 0 + 0 + 0 + 0 + 0, divide_ys#1(1 + x51 + (1 + x25 + (1 + x6' + x8')), 1 + s6))) :|: s5 >= 0, s5 <= x8', s6 >= 0, s6 <= 1 + s5 + 1, z'' = 0, z1 = 0, z2 = 0, x51 >= 0, x25 >= 0, x6' >= 0, z3 = 1 + x51 + (1 + x25 + (1 + x6' + x8')), z = 0, x8' >= 0, z' = 0
   dc#1(z, z', z'', z1, z2, z3) -{ 1 }-> 1 :|: z'' = 0, z1 = 0, z2 = 0, z3 = 1, z = 0, z' = 0
   dc#1(z, z', z'', z1, z2, z3) -{ 0 }-> 0 :|: z >= 0, z2 >= 0, z' >= 0, z3 >= 0, z'' >= 0, z1 >= 0
   dc#1(z, z', z'', z1, z2, z3) -{ 1 }-> 1 + (z3 - 2) + 1 :|: z'' = 0, z1 = 0, z2 = 0, z3 - 2 >= 0, z = 0, z' = 0
   divide_ys#1(z, z') -{ 5 + 2*z }-> 1 + s'' + (1 + s8 + 1) :|: s8 >= 0, s8 <= z + 2, s'' >= 0, s'' <= z + 4, z' >= 0, z >= 0
   drop#2(z, z') -{ 3 + x64 }-> s9 :|: s9 >= 0, s9 <= x64 + 2, z' = 1 + x56 + x64, z - 1 >= 0, x64 >= 0, x56 >= 0
   drop#2(z, z') -{ 1 }-> z' :|: z = 0, z' >= 0
   drop#2(z, z') -{ 1 }-> 3 :|: z = 1 + 0, z' = 1
   drop#2(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   halve#1(z) -{ 1 }-> 0 :|: z = 0
   halve#1(z) -{ 0 }-> 0 :|: z >= 0
   halve#1(z) -{ 1 + z }-> 1 + s4 :|: s4 >= 0, s4 <= z - 2 + 1, z - 2 >= 0
   halve#1(z) -{ 1 }-> 1 + 0 :|: z = 1 + 0
   length#1(z) -{ 1 }-> 0 :|: z = 1
   length#1(z) -{ 0 }-> 0 :|: z >= 0
   length#1(z) -{ 2 + x8 }-> 1 + s7 :|: s7 >= 0, s7 <= x8, x8 >= 0, x6 >= 0, z = 1 + x6 + x8
   leq#2(z, z') -{ 2 + z' }-> s' :|: s' >= 0, s' <= 2, z - 1 >= 0, z' - 1 >= 0
   leq#2(z, z') -{ 1 }-> 2 :|: z = 0, z' >= 0
   leq#2(z, z') -{ 1 }-> 1 :|: z - 1 >= 0, z' = 0
   leq#2(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   main(z) -{ 1 }-> dc#1(0, 0, 0, 0, 0, z) :|: z >= 0
   map#2(z, z') -{ 1 }-> 1 :|: x4 >= 0, x8 >= 0, x6 >= 0, z = 1 + x2 + x4 + x6 + x8 + x10, z' = 1, x10 >= 0, x2 >= 0
   map#2(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   map#2(z, z') -{ 1 }-> 1 + dc#1(x6, x8, x10, x12, x14, x4) + map#2(1 + x6 + x8 + x10 + x12 + x14, x2) :|: x4 >= 0, x8 >= 0, z' = 1 + x4 + x2, x6 >= 0, x12 >= 0, x14 >= 0, x10 >= 0, x2 >= 0, z = 1 + x6 + x8 + x10 + x12 + x14
   merge#2(z, z') -{ 1 }-> z' :|: z = 1, z' >= 0
   merge#2(z, z') -{ 4 + x2' }-> cond_merge_ys_zs_2(s, 1 + (1 + x4') + x6, 1 + (1 + x2') + x2, 1 + x4', x6, 1 + x2', x2) :|: s >= 0, s <= 2, x2' >= 0, z = 1 + (1 + x4') + x6, x6 >= 0, z' = 1 + (1 + x2') + x2, x4' >= 0, x2 >= 0
   merge#2(z, z') -{ 2 }-> cond_merge_ys_zs_2(2, 1 + 0 + (z - 1), 1 + x4 + x2, 0, z - 1, x4, x2) :|: x4 >= 0, z' = 1 + x4 + x2, z - 1 >= 0, x2 >= 0
   merge#2(z, z') -{ 2 }-> cond_merge_ys_zs_2(1, 1 + (1 + x20') + x6, 1 + 0 + (z' - 1), 1 + x20', x6, 0, z' - 1) :|: z = 1 + (1 + x20') + x6, x6 >= 0, x20' >= 0, z' - 1 >= 0
   merge#2(z, z') -{ 1 }-> cond_merge_ys_zs_2(0, 1 + x8 + x6, 1 + x4 + x2, x8, x6, x4, x2) :|: x4 >= 0, x8 >= 0, z' = 1 + x4 + x2, x6 >= 0, z = 1 + x8 + x6, x2 >= 0
   merge#2(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   merge#2(z, z') -{ 1 }-> 1 + x4 + x2 :|: x4 >= 0, z = 1 + x4 + x2, z' = 1, x2 >= 0
   take#2(z, z') -{ 1 }-> 1 :|: z = 0, z' >= 0
   take#2(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   take#2(z, z') -{ 3 + x64 }-> 1 + x56 + s1 :|: s1 >= 0, s1 <= x64 + 4, z' = 1 + x56 + x64, z - 1 >= 0, x64 >= 0, x56 >= 0
   take#2(z, z') -{ 1 }-> 1 + 2 + 1 :|: z = 1 + 0, z' = 1

Function symbols to be analyzed: {divide_ys#1}, {const_f#2}, {dc#1,map#2}, {main}
Previous analysis results are:
  leq#2: runtime: O(n^1) [2 + z'], size: O(1) [2]
  take#2: runtime: O(n^1) [2 + z'], size: O(n^1) [4 + z']
  halve#1: runtime: O(n^1) [2 + z], size: O(n^1) [1 + z]
  length#1: runtime: O(n^1) [1 + z], size: O(n^1) [z]
  drop#2: runtime: O(n^1) [2 + z'], size: O(n^1) [2 + z']
  merge#2: runtime: O(n^2) [11 + 5*z + z*z' + 12*z' + 2*z'^2], size: O(n^1) [1 + z + z']
  cond_merge_ys_zs_2: runtime: O(n^2) [43 + 10*z' + 2*z'*z4 + 32*z'' + 2*z''*z2 + 8*z''^2 + 6*z2 + 13*z4 + 2*z4^2], size: O(n^1) [2 + z' + z'' + z1 + z2 + z3 + z4]

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

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

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

   cond_merge_ys_zs_2(z, z', z'', z1, z2, z3, z4) -{ 0 }-> 0 :|: z >= 0, z4 >= 0, z' >= 0, z3 >= 0, z'' >= 0, z1 >= 0, z2 >= 0
   cond_merge_ys_zs_2(z, z', z'', z1, z2, z3, z4) -{ 26 + 16*x5 + 4*x5*x6 + x5*z2 + 2*x5^2 + 16*x6 + x6*z2 + 2*x6^2 + 6*z2 }-> 1 + z1 + s10 :|: s10 >= 0, s10 <= 1 + x5 + x6 + z2 + 1, x5 >= 0, x8 >= 0, z' = 1 + x7 + x8, z'' = 1 + x5 + x6, z2 >= 0, z3 >= 0, z = 2, z1 >= 0, z4 >= 0, x7 >= 0, x6 >= 0
   cond_merge_ys_zs_2(z, z', z'', z1, z2, z3, z4) -{ 17 + 5*x7 + x7*z4 + 5*x8 + x8*z4 + 13*z4 + 2*z4^2 }-> 1 + z3 + s11 :|: s11 >= 0, s11 <= z4 + (1 + x7 + x8) + 1, x5 >= 0, x8 >= 0, z = 1, z' = 1 + x7 + x8, z'' = 1 + x5 + x6, z2 >= 0, z3 >= 0, z1 >= 0, z4 >= 0, x7 >= 0, x6 >= 0
   const_f#2(z, z') -{ 12 + 12*x4 + x4*x6 + 2*x4^2 + 5*x6 }-> s16 :|: s16 >= 0, s16 <= x4 + x6 + 1, x4 >= 0, z' = 1 + x6 + (1 + x4 + x2), x6 >= 0, z >= 0, x2 >= 0
   const_f#2(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   dc#1(z, z', z'', z1, z2, z3) -{ 3 }-> const_f#2(1 + x51 + (1 + x25 + x33), map#2(1 + 0 + 0 + 0 + 0 + 0, divide_ys#1(1 + x51 + (1 + x25 + x33), 1 + s3))) :|: s3 >= 0, s3 <= 0 + 1, z'' = 0, z1 = 0, x33 >= 0, z3 = 1 + x51 + (1 + x25 + x33), z2 = 0, x51 >= 0, x25 >= 0, z = 0, z' = 0
   dc#1(z, z', z'', z1, z2, z3) -{ 4 }-> const_f#2(1 + x51 + (1 + x25 + 1), map#2(1 + 0 + 0 + 0 + 0 + 0, divide_ys#1(1 + x51 + (1 + x25 + 1), 1 + s2))) :|: s2 >= 0, s2 <= 0 + 1, z'' = 0, z3 = 1 + x51 + (1 + x25 + 1), z1 = 0, z2 = 0, x51 >= 0, x25 >= 0, z = 0, z' = 0
   dc#1(z, z', z'', z1, z2, z3) -{ 6 + s5 + x8' }-> const_f#2(1 + x51 + (1 + x25 + (1 + x6' + x8')), map#2(1 + 0 + 0 + 0 + 0 + 0, divide_ys#1(1 + x51 + (1 + x25 + (1 + x6' + x8')), 1 + s6))) :|: s5 >= 0, s5 <= x8', s6 >= 0, s6 <= 1 + s5 + 1, z'' = 0, z1 = 0, z2 = 0, x51 >= 0, x25 >= 0, x6' >= 0, z3 = 1 + x51 + (1 + x25 + (1 + x6' + x8')), z = 0, x8' >= 0, z' = 0
   dc#1(z, z', z'', z1, z2, z3) -{ 1 }-> 1 :|: z'' = 0, z1 = 0, z2 = 0, z3 = 1, z = 0, z' = 0
   dc#1(z, z', z'', z1, z2, z3) -{ 0 }-> 0 :|: z >= 0, z2 >= 0, z' >= 0, z3 >= 0, z'' >= 0, z1 >= 0
   dc#1(z, z', z'', z1, z2, z3) -{ 1 }-> 1 + (z3 - 2) + 1 :|: z'' = 0, z1 = 0, z2 = 0, z3 - 2 >= 0, z = 0, z' = 0
   divide_ys#1(z, z') -{ 5 + 2*z }-> 1 + s'' + (1 + s8 + 1) :|: s8 >= 0, s8 <= z + 2, s'' >= 0, s'' <= z + 4, z' >= 0, z >= 0
   drop#2(z, z') -{ 3 + x64 }-> s9 :|: s9 >= 0, s9 <= x64 + 2, z' = 1 + x56 + x64, z - 1 >= 0, x64 >= 0, x56 >= 0
   drop#2(z, z') -{ 1 }-> z' :|: z = 0, z' >= 0
   drop#2(z, z') -{ 1 }-> 3 :|: z = 1 + 0, z' = 1
   drop#2(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   halve#1(z) -{ 1 }-> 0 :|: z = 0
   halve#1(z) -{ 0 }-> 0 :|: z >= 0
   halve#1(z) -{ 1 + z }-> 1 + s4 :|: s4 >= 0, s4 <= z - 2 + 1, z - 2 >= 0
   halve#1(z) -{ 1 }-> 1 + 0 :|: z = 1 + 0
   length#1(z) -{ 1 }-> 0 :|: z = 1
   length#1(z) -{ 0 }-> 0 :|: z >= 0
   length#1(z) -{ 2 + x8 }-> 1 + s7 :|: s7 >= 0, s7 <= x8, x8 >= 0, x6 >= 0, z = 1 + x6 + x8
   leq#2(z, z') -{ 2 + z' }-> s' :|: s' >= 0, s' <= 2, z - 1 >= 0, z' - 1 >= 0
   leq#2(z, z') -{ 1 }-> 2 :|: z = 0, z' >= 0
   leq#2(z, z') -{ 1 }-> 1 :|: z - 1 >= 0, z' = 0
   leq#2(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   main(z) -{ 1 }-> dc#1(0, 0, 0, 0, 0, z) :|: z >= 0
   map#2(z, z') -{ 1 }-> 1 :|: x4 >= 0, x8 >= 0, x6 >= 0, z = 1 + x2 + x4 + x6 + x8 + x10, z' = 1, x10 >= 0, x2 >= 0
   map#2(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   map#2(z, z') -{ 1 }-> 1 + dc#1(x6, x8, x10, x12, x14, x4) + map#2(1 + x6 + x8 + x10 + x12 + x14, x2) :|: x4 >= 0, x8 >= 0, z' = 1 + x4 + x2, x6 >= 0, x12 >= 0, x14 >= 0, x10 >= 0, x2 >= 0, z = 1 + x6 + x8 + x10 + x12 + x14
   merge#2(z, z') -{ 77 + 59*x2 + 16*x2*x4 + 4*x2*z + 10*x2^2 + 46*x4 + 2*x4*z + 8*x4^2 + 18*z }-> s12 :|: s12 >= 0, s12 <= 1 + x4 + x2 + 0 + (z - 1) + 2 + (1 + 0 + (z - 1)) + x4 + x2, x4 >= 0, z' = 1 + x4 + x2, z - 1 >= 0, x2 >= 0
   merge#2(z, z') -{ 50 + 8*x20' + 2*x20'*z' + 14*x6 + 4*x6*z' + 45*z' + 10*z'^2 }-> s13 :|: s13 >= 0, s13 <= 1 + 0 + (z' - 1) + (1 + x20') + x6 + 2 + (1 + (1 + x20') + x6) + 0 + (z' - 1), z = 1 + (1 + x20') + x6, x6 >= 0, x20' >= 0, z' - 1 >= 0
   merge#2(z, z') -{ 163 + 81*x2 + 16*x2*x2' + 2*x2*x4' + 4*x2*x6 + 10*x2^2 + 65*x2' + 2*x2'*x6 + 8*x2'^2 + 10*x4' + 20*x6 }-> s14 :|: s14 >= 0, s14 <= 1 + (1 + x2') + x2 + (1 + x4') + x6 + 2 + (1 + (1 + x4') + x6) + (1 + x2') + x2, s >= 0, s <= 2, x2' >= 0, z = 1 + (1 + x4') + x6, x6 >= 0, z' = 1 + (1 + x2') + x2, x4' >= 0, x2 >= 0
   merge#2(z, z') -{ 94 + 63*x2 + 16*x2*x4 + 4*x2*x6 + 2*x2*x8 + 10*x2^2 + 48*x4 + 2*x4*x6 + 8*x4^2 + 18*x6 + 10*x8 }-> s15 :|: s15 >= 0, s15 <= 1 + x4 + x2 + x8 + x6 + 2 + (1 + x8 + x6) + x4 + x2, x4 >= 0, x8 >= 0, z' = 1 + x4 + x2, x6 >= 0, z = 1 + x8 + x6, x2 >= 0
   merge#2(z, z') -{ 1 }-> z' :|: z = 1, z' >= 0
   merge#2(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   merge#2(z, z') -{ 1 }-> 1 + x4 + x2 :|: x4 >= 0, z = 1 + x4 + x2, z' = 1, x2 >= 0
   take#2(z, z') -{ 1 }-> 1 :|: z = 0, z' >= 0
   take#2(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   take#2(z, z') -{ 3 + x64 }-> 1 + x56 + s1 :|: s1 >= 0, s1 <= x64 + 4, z' = 1 + x56 + x64, z - 1 >= 0, x64 >= 0, x56 >= 0
   take#2(z, z') -{ 1 }-> 1 + 2 + 1 :|: z = 1 + 0, z' = 1

Function symbols to be analyzed: {divide_ys#1}, {const_f#2}, {dc#1,map#2}, {main}
Previous analysis results are:
  leq#2: runtime: O(n^1) [2 + z'], size: O(1) [2]
  take#2: runtime: O(n^1) [2 + z'], size: O(n^1) [4 + z']
  halve#1: runtime: O(n^1) [2 + z], size: O(n^1) [1 + z]
  length#1: runtime: O(n^1) [1 + z], size: O(n^1) [z]
  drop#2: runtime: O(n^1) [2 + z'], size: O(n^1) [2 + z']
  merge#2: runtime: O(n^2) [11 + 5*z + z*z' + 12*z' + 2*z'^2], size: O(n^1) [1 + z + z']
  cond_merge_ys_zs_2: runtime: O(n^2) [43 + 10*z' + 2*z'*z4 + 32*z'' + 2*z''*z2 + 8*z''^2 + 6*z2 + 13*z4 + 2*z4^2], size: O(n^1) [2 + z' + z'' + z1 + z2 + z3 + z4]

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

(57) IntTrsBoundProof (UPPER BOUND(ID))

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

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

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

   cond_merge_ys_zs_2(z, z', z'', z1, z2, z3, z4) -{ 0 }-> 0 :|: z >= 0, z4 >= 0, z' >= 0, z3 >= 0, z'' >= 0, z1 >= 0, z2 >= 0
   cond_merge_ys_zs_2(z, z', z'', z1, z2, z3, z4) -{ 26 + 16*x5 + 4*x5*x6 + x5*z2 + 2*x5^2 + 16*x6 + x6*z2 + 2*x6^2 + 6*z2 }-> 1 + z1 + s10 :|: s10 >= 0, s10 <= 1 + x5 + x6 + z2 + 1, x5 >= 0, x8 >= 0, z' = 1 + x7 + x8, z'' = 1 + x5 + x6, z2 >= 0, z3 >= 0, z = 2, z1 >= 0, z4 >= 0, x7 >= 0, x6 >= 0
   cond_merge_ys_zs_2(z, z', z'', z1, z2, z3, z4) -{ 17 + 5*x7 + x7*z4 + 5*x8 + x8*z4 + 13*z4 + 2*z4^2 }-> 1 + z3 + s11 :|: s11 >= 0, s11 <= z4 + (1 + x7 + x8) + 1, x5 >= 0, x8 >= 0, z = 1, z' = 1 + x7 + x8, z'' = 1 + x5 + x6, z2 >= 0, z3 >= 0, z1 >= 0, z4 >= 0, x7 >= 0, x6 >= 0
   const_f#2(z, z') -{ 12 + 12*x4 + x4*x6 + 2*x4^2 + 5*x6 }-> s16 :|: s16 >= 0, s16 <= x4 + x6 + 1, x4 >= 0, z' = 1 + x6 + (1 + x4 + x2), x6 >= 0, z >= 0, x2 >= 0
   const_f#2(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   dc#1(z, z', z'', z1, z2, z3) -{ 3 }-> const_f#2(1 + x51 + (1 + x25 + x33), map#2(1 + 0 + 0 + 0 + 0 + 0, divide_ys#1(1 + x51 + (1 + x25 + x33), 1 + s3))) :|: s3 >= 0, s3 <= 0 + 1, z'' = 0, z1 = 0, x33 >= 0, z3 = 1 + x51 + (1 + x25 + x33), z2 = 0, x51 >= 0, x25 >= 0, z = 0, z' = 0
   dc#1(z, z', z'', z1, z2, z3) -{ 4 }-> const_f#2(1 + x51 + (1 + x25 + 1), map#2(1 + 0 + 0 + 0 + 0 + 0, divide_ys#1(1 + x51 + (1 + x25 + 1), 1 + s2))) :|: s2 >= 0, s2 <= 0 + 1, z'' = 0, z3 = 1 + x51 + (1 + x25 + 1), z1 = 0, z2 = 0, x51 >= 0, x25 >= 0, z = 0, z' = 0
   dc#1(z, z', z'', z1, z2, z3) -{ 6 + s5 + x8' }-> const_f#2(1 + x51 + (1 + x25 + (1 + x6' + x8')), map#2(1 + 0 + 0 + 0 + 0 + 0, divide_ys#1(1 + x51 + (1 + x25 + (1 + x6' + x8')), 1 + s6))) :|: s5 >= 0, s5 <= x8', s6 >= 0, s6 <= 1 + s5 + 1, z'' = 0, z1 = 0, z2 = 0, x51 >= 0, x25 >= 0, x6' >= 0, z3 = 1 + x51 + (1 + x25 + (1 + x6' + x8')), z = 0, x8' >= 0, z' = 0
   dc#1(z, z', z'', z1, z2, z3) -{ 1 }-> 1 :|: z'' = 0, z1 = 0, z2 = 0, z3 = 1, z = 0, z' = 0
   dc#1(z, z', z'', z1, z2, z3) -{ 0 }-> 0 :|: z >= 0, z2 >= 0, z' >= 0, z3 >= 0, z'' >= 0, z1 >= 0
   dc#1(z, z', z'', z1, z2, z3) -{ 1 }-> 1 + (z3 - 2) + 1 :|: z'' = 0, z1 = 0, z2 = 0, z3 - 2 >= 0, z = 0, z' = 0
   divide_ys#1(z, z') -{ 5 + 2*z }-> 1 + s'' + (1 + s8 + 1) :|: s8 >= 0, s8 <= z + 2, s'' >= 0, s'' <= z + 4, z' >= 0, z >= 0
   drop#2(z, z') -{ 3 + x64 }-> s9 :|: s9 >= 0, s9 <= x64 + 2, z' = 1 + x56 + x64, z - 1 >= 0, x64 >= 0, x56 >= 0
   drop#2(z, z') -{ 1 }-> z' :|: z = 0, z' >= 0
   drop#2(z, z') -{ 1 }-> 3 :|: z = 1 + 0, z' = 1
   drop#2(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   halve#1(z) -{ 1 }-> 0 :|: z = 0
   halve#1(z) -{ 0 }-> 0 :|: z >= 0
   halve#1(z) -{ 1 + z }-> 1 + s4 :|: s4 >= 0, s4 <= z - 2 + 1, z - 2 >= 0
   halve#1(z) -{ 1 }-> 1 + 0 :|: z = 1 + 0
   length#1(z) -{ 1 }-> 0 :|: z = 1
   length#1(z) -{ 0 }-> 0 :|: z >= 0
   length#1(z) -{ 2 + x8 }-> 1 + s7 :|: s7 >= 0, s7 <= x8, x8 >= 0, x6 >= 0, z = 1 + x6 + x8
   leq#2(z, z') -{ 2 + z' }-> s' :|: s' >= 0, s' <= 2, z - 1 >= 0, z' - 1 >= 0
   leq#2(z, z') -{ 1 }-> 2 :|: z = 0, z' >= 0
   leq#2(z, z') -{ 1 }-> 1 :|: z - 1 >= 0, z' = 0
   leq#2(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   main(z) -{ 1 }-> dc#1(0, 0, 0, 0, 0, z) :|: z >= 0
   map#2(z, z') -{ 1 }-> 1 :|: x4 >= 0, x8 >= 0, x6 >= 0, z = 1 + x2 + x4 + x6 + x8 + x10, z' = 1, x10 >= 0, x2 >= 0
   map#2(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   map#2(z, z') -{ 1 }-> 1 + dc#1(x6, x8, x10, x12, x14, x4) + map#2(1 + x6 + x8 + x10 + x12 + x14, x2) :|: x4 >= 0, x8 >= 0, z' = 1 + x4 + x2, x6 >= 0, x12 >= 0, x14 >= 0, x10 >= 0, x2 >= 0, z = 1 + x6 + x8 + x10 + x12 + x14
   merge#2(z, z') -{ 77 + 59*x2 + 16*x2*x4 + 4*x2*z + 10*x2^2 + 46*x4 + 2*x4*z + 8*x4^2 + 18*z }-> s12 :|: s12 >= 0, s12 <= 1 + x4 + x2 + 0 + (z - 1) + 2 + (1 + 0 + (z - 1)) + x4 + x2, x4 >= 0, z' = 1 + x4 + x2, z - 1 >= 0, x2 >= 0
   merge#2(z, z') -{ 50 + 8*x20' + 2*x20'*z' + 14*x6 + 4*x6*z' + 45*z' + 10*z'^2 }-> s13 :|: s13 >= 0, s13 <= 1 + 0 + (z' - 1) + (1 + x20') + x6 + 2 + (1 + (1 + x20') + x6) + 0 + (z' - 1), z = 1 + (1 + x20') + x6, x6 >= 0, x20' >= 0, z' - 1 >= 0
   merge#2(z, z') -{ 163 + 81*x2 + 16*x2*x2' + 2*x2*x4' + 4*x2*x6 + 10*x2^2 + 65*x2' + 2*x2'*x6 + 8*x2'^2 + 10*x4' + 20*x6 }-> s14 :|: s14 >= 0, s14 <= 1 + (1 + x2') + x2 + (1 + x4') + x6 + 2 + (1 + (1 + x4') + x6) + (1 + x2') + x2, s >= 0, s <= 2, x2' >= 0, z = 1 + (1 + x4') + x6, x6 >= 0, z' = 1 + (1 + x2') + x2, x4' >= 0, x2 >= 0
   merge#2(z, z') -{ 94 + 63*x2 + 16*x2*x4 + 4*x2*x6 + 2*x2*x8 + 10*x2^2 + 48*x4 + 2*x4*x6 + 8*x4^2 + 18*x6 + 10*x8 }-> s15 :|: s15 >= 0, s15 <= 1 + x4 + x2 + x8 + x6 + 2 + (1 + x8 + x6) + x4 + x2, x4 >= 0, x8 >= 0, z' = 1 + x4 + x2, x6 >= 0, z = 1 + x8 + x6, x2 >= 0
   merge#2(z, z') -{ 1 }-> z' :|: z = 1, z' >= 0
   merge#2(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   merge#2(z, z') -{ 1 }-> 1 + x4 + x2 :|: x4 >= 0, z = 1 + x4 + x2, z' = 1, x2 >= 0
   take#2(z, z') -{ 1 }-> 1 :|: z = 0, z' >= 0
   take#2(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   take#2(z, z') -{ 3 + x64 }-> 1 + x56 + s1 :|: s1 >= 0, s1 <= x64 + 4, z' = 1 + x56 + x64, z - 1 >= 0, x64 >= 0, x56 >= 0
   take#2(z, z') -{ 1 }-> 1 + 2 + 1 :|: z = 1 + 0, z' = 1

Function symbols to be analyzed: {divide_ys#1}, {const_f#2}, {dc#1,map#2}, {main}
Previous analysis results are:
  leq#2: runtime: O(n^1) [2 + z'], size: O(1) [2]
  take#2: runtime: O(n^1) [2 + z'], size: O(n^1) [4 + z']
  halve#1: runtime: O(n^1) [2 + z], size: O(n^1) [1 + z]
  length#1: runtime: O(n^1) [1 + z], size: O(n^1) [z]
  drop#2: runtime: O(n^1) [2 + z'], size: O(n^1) [2 + z']
  merge#2: runtime: O(n^2) [11 + 5*z + z*z' + 12*z' + 2*z'^2], size: O(n^1) [1 + z + z']
  cond_merge_ys_zs_2: runtime: O(n^2) [43 + 10*z' + 2*z'*z4 + 32*z'' + 2*z''*z2 + 8*z''^2 + 6*z2 + 13*z4 + 2*z4^2], size: O(n^1) [2 + z' + z'' + z1 + z2 + z3 + z4]
  divide_ys#1: runtime: ?, size: O(n^1) [9 + 2*z]

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

(59) IntTrsBoundProof (UPPER BOUND(ID))

Computed RUNTIME bound using CoFloCo for: divide_ys#1
after applying outer abstraction to obtain an ITS,
resulting in: O(n^1) with polynomial bound: 5 + 2*z

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

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

   cond_merge_ys_zs_2(z, z', z'', z1, z2, z3, z4) -{ 0 }-> 0 :|: z >= 0, z4 >= 0, z' >= 0, z3 >= 0, z'' >= 0, z1 >= 0, z2 >= 0
   cond_merge_ys_zs_2(z, z', z'', z1, z2, z3, z4) -{ 26 + 16*x5 + 4*x5*x6 + x5*z2 + 2*x5^2 + 16*x6 + x6*z2 + 2*x6^2 + 6*z2 }-> 1 + z1 + s10 :|: s10 >= 0, s10 <= 1 + x5 + x6 + z2 + 1, x5 >= 0, x8 >= 0, z' = 1 + x7 + x8, z'' = 1 + x5 + x6, z2 >= 0, z3 >= 0, z = 2, z1 >= 0, z4 >= 0, x7 >= 0, x6 >= 0
   cond_merge_ys_zs_2(z, z', z'', z1, z2, z3, z4) -{ 17 + 5*x7 + x7*z4 + 5*x8 + x8*z4 + 13*z4 + 2*z4^2 }-> 1 + z3 + s11 :|: s11 >= 0, s11 <= z4 + (1 + x7 + x8) + 1, x5 >= 0, x8 >= 0, z = 1, z' = 1 + x7 + x8, z'' = 1 + x5 + x6, z2 >= 0, z3 >= 0, z1 >= 0, z4 >= 0, x7 >= 0, x6 >= 0
   const_f#2(z, z') -{ 12 + 12*x4 + x4*x6 + 2*x4^2 + 5*x6 }-> s16 :|: s16 >= 0, s16 <= x4 + x6 + 1, x4 >= 0, z' = 1 + x6 + (1 + x4 + x2), x6 >= 0, z >= 0, x2 >= 0
   const_f#2(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   dc#1(z, z', z'', z1, z2, z3) -{ 3 }-> const_f#2(1 + x51 + (1 + x25 + x33), map#2(1 + 0 + 0 + 0 + 0 + 0, divide_ys#1(1 + x51 + (1 + x25 + x33), 1 + s3))) :|: s3 >= 0, s3 <= 0 + 1, z'' = 0, z1 = 0, x33 >= 0, z3 = 1 + x51 + (1 + x25 + x33), z2 = 0, x51 >= 0, x25 >= 0, z = 0, z' = 0
   dc#1(z, z', z'', z1, z2, z3) -{ 4 }-> const_f#2(1 + x51 + (1 + x25 + 1), map#2(1 + 0 + 0 + 0 + 0 + 0, divide_ys#1(1 + x51 + (1 + x25 + 1), 1 + s2))) :|: s2 >= 0, s2 <= 0 + 1, z'' = 0, z3 = 1 + x51 + (1 + x25 + 1), z1 = 0, z2 = 0, x51 >= 0, x25 >= 0, z = 0, z' = 0
   dc#1(z, z', z'', z1, z2, z3) -{ 6 + s5 + x8' }-> const_f#2(1 + x51 + (1 + x25 + (1 + x6' + x8')), map#2(1 + 0 + 0 + 0 + 0 + 0, divide_ys#1(1 + x51 + (1 + x25 + (1 + x6' + x8')), 1 + s6))) :|: s5 >= 0, s5 <= x8', s6 >= 0, s6 <= 1 + s5 + 1, z'' = 0, z1 = 0, z2 = 0, x51 >= 0, x25 >= 0, x6' >= 0, z3 = 1 + x51 + (1 + x25 + (1 + x6' + x8')), z = 0, x8' >= 0, z' = 0
   dc#1(z, z', z'', z1, z2, z3) -{ 1 }-> 1 :|: z'' = 0, z1 = 0, z2 = 0, z3 = 1, z = 0, z' = 0
   dc#1(z, z', z'', z1, z2, z3) -{ 0 }-> 0 :|: z >= 0, z2 >= 0, z' >= 0, z3 >= 0, z'' >= 0, z1 >= 0
   dc#1(z, z', z'', z1, z2, z3) -{ 1 }-> 1 + (z3 - 2) + 1 :|: z'' = 0, z1 = 0, z2 = 0, z3 - 2 >= 0, z = 0, z' = 0
   divide_ys#1(z, z') -{ 5 + 2*z }-> 1 + s'' + (1 + s8 + 1) :|: s8 >= 0, s8 <= z + 2, s'' >= 0, s'' <= z + 4, z' >= 0, z >= 0
   drop#2(z, z') -{ 3 + x64 }-> s9 :|: s9 >= 0, s9 <= x64 + 2, z' = 1 + x56 + x64, z - 1 >= 0, x64 >= 0, x56 >= 0
   drop#2(z, z') -{ 1 }-> z' :|: z = 0, z' >= 0
   drop#2(z, z') -{ 1 }-> 3 :|: z = 1 + 0, z' = 1
   drop#2(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   halve#1(z) -{ 1 }-> 0 :|: z = 0
   halve#1(z) -{ 0 }-> 0 :|: z >= 0
   halve#1(z) -{ 1 + z }-> 1 + s4 :|: s4 >= 0, s4 <= z - 2 + 1, z - 2 >= 0
   halve#1(z) -{ 1 }-> 1 + 0 :|: z = 1 + 0
   length#1(z) -{ 1 }-> 0 :|: z = 1
   length#1(z) -{ 0 }-> 0 :|: z >= 0
   length#1(z) -{ 2 + x8 }-> 1 + s7 :|: s7 >= 0, s7 <= x8, x8 >= 0, x6 >= 0, z = 1 + x6 + x8
   leq#2(z, z') -{ 2 + z' }-> s' :|: s' >= 0, s' <= 2, z - 1 >= 0, z' - 1 >= 0
   leq#2(z, z') -{ 1 }-> 2 :|: z = 0, z' >= 0
   leq#2(z, z') -{ 1 }-> 1 :|: z - 1 >= 0, z' = 0
   leq#2(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   main(z) -{ 1 }-> dc#1(0, 0, 0, 0, 0, z) :|: z >= 0
   map#2(z, z') -{ 1 }-> 1 :|: x4 >= 0, x8 >= 0, x6 >= 0, z = 1 + x2 + x4 + x6 + x8 + x10, z' = 1, x10 >= 0, x2 >= 0
   map#2(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   map#2(z, z') -{ 1 }-> 1 + dc#1(x6, x8, x10, x12, x14, x4) + map#2(1 + x6 + x8 + x10 + x12 + x14, x2) :|: x4 >= 0, x8 >= 0, z' = 1 + x4 + x2, x6 >= 0, x12 >= 0, x14 >= 0, x10 >= 0, x2 >= 0, z = 1 + x6 + x8 + x10 + x12 + x14
   merge#2(z, z') -{ 77 + 59*x2 + 16*x2*x4 + 4*x2*z + 10*x2^2 + 46*x4 + 2*x4*z + 8*x4^2 + 18*z }-> s12 :|: s12 >= 0, s12 <= 1 + x4 + x2 + 0 + (z - 1) + 2 + (1 + 0 + (z - 1)) + x4 + x2, x4 >= 0, z' = 1 + x4 + x2, z - 1 >= 0, x2 >= 0
   merge#2(z, z') -{ 50 + 8*x20' + 2*x20'*z' + 14*x6 + 4*x6*z' + 45*z' + 10*z'^2 }-> s13 :|: s13 >= 0, s13 <= 1 + 0 + (z' - 1) + (1 + x20') + x6 + 2 + (1 + (1 + x20') + x6) + 0 + (z' - 1), z = 1 + (1 + x20') + x6, x6 >= 0, x20' >= 0, z' - 1 >= 0
   merge#2(z, z') -{ 163 + 81*x2 + 16*x2*x2' + 2*x2*x4' + 4*x2*x6 + 10*x2^2 + 65*x2' + 2*x2'*x6 + 8*x2'^2 + 10*x4' + 20*x6 }-> s14 :|: s14 >= 0, s14 <= 1 + (1 + x2') + x2 + (1 + x4') + x6 + 2 + (1 + (1 + x4') + x6) + (1 + x2') + x2, s >= 0, s <= 2, x2' >= 0, z = 1 + (1 + x4') + x6, x6 >= 0, z' = 1 + (1 + x2') + x2, x4' >= 0, x2 >= 0
   merge#2(z, z') -{ 94 + 63*x2 + 16*x2*x4 + 4*x2*x6 + 2*x2*x8 + 10*x2^2 + 48*x4 + 2*x4*x6 + 8*x4^2 + 18*x6 + 10*x8 }-> s15 :|: s15 >= 0, s15 <= 1 + x4 + x2 + x8 + x6 + 2 + (1 + x8 + x6) + x4 + x2, x4 >= 0, x8 >= 0, z' = 1 + x4 + x2, x6 >= 0, z = 1 + x8 + x6, x2 >= 0
   merge#2(z, z') -{ 1 }-> z' :|: z = 1, z' >= 0
   merge#2(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   merge#2(z, z') -{ 1 }-> 1 + x4 + x2 :|: x4 >= 0, z = 1 + x4 + x2, z' = 1, x2 >= 0
   take#2(z, z') -{ 1 }-> 1 :|: z = 0, z' >= 0
   take#2(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   take#2(z, z') -{ 3 + x64 }-> 1 + x56 + s1 :|: s1 >= 0, s1 <= x64 + 4, z' = 1 + x56 + x64, z - 1 >= 0, x64 >= 0, x56 >= 0
   take#2(z, z') -{ 1 }-> 1 + 2 + 1 :|: z = 1 + 0, z' = 1

Function symbols to be analyzed: {const_f#2}, {dc#1,map#2}, {main}
Previous analysis results are:
  leq#2: runtime: O(n^1) [2 + z'], size: O(1) [2]
  take#2: runtime: O(n^1) [2 + z'], size: O(n^1) [4 + z']
  halve#1: runtime: O(n^1) [2 + z], size: O(n^1) [1 + z]
  length#1: runtime: O(n^1) [1 + z], size: O(n^1) [z]
  drop#2: runtime: O(n^1) [2 + z'], size: O(n^1) [2 + z']
  merge#2: runtime: O(n^2) [11 + 5*z + z*z' + 12*z' + 2*z'^2], size: O(n^1) [1 + z + z']
  cond_merge_ys_zs_2: runtime: O(n^2) [43 + 10*z' + 2*z'*z4 + 32*z'' + 2*z''*z2 + 8*z''^2 + 6*z2 + 13*z4 + 2*z4^2], size: O(n^1) [2 + z' + z'' + z1 + z2 + z3 + z4]
  divide_ys#1: runtime: O(n^1) [5 + 2*z], size: O(n^1) [9 + 2*z]

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

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

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

   cond_merge_ys_zs_2(z, z', z'', z1, z2, z3, z4) -{ 0 }-> 0 :|: z >= 0, z4 >= 0, z' >= 0, z3 >= 0, z'' >= 0, z1 >= 0, z2 >= 0
   cond_merge_ys_zs_2(z, z', z'', z1, z2, z3, z4) -{ 26 + 16*x5 + 4*x5*x6 + x5*z2 + 2*x5^2 + 16*x6 + x6*z2 + 2*x6^2 + 6*z2 }-> 1 + z1 + s10 :|: s10 >= 0, s10 <= 1 + x5 + x6 + z2 + 1, x5 >= 0, x8 >= 0, z' = 1 + x7 + x8, z'' = 1 + x5 + x6, z2 >= 0, z3 >= 0, z = 2, z1 >= 0, z4 >= 0, x7 >= 0, x6 >= 0
   cond_merge_ys_zs_2(z, z', z'', z1, z2, z3, z4) -{ 17 + 5*x7 + x7*z4 + 5*x8 + x8*z4 + 13*z4 + 2*z4^2 }-> 1 + z3 + s11 :|: s11 >= 0, s11 <= z4 + (1 + x7 + x8) + 1, x5 >= 0, x8 >= 0, z = 1, z' = 1 + x7 + x8, z'' = 1 + x5 + x6, z2 >= 0, z3 >= 0, z1 >= 0, z4 >= 0, x7 >= 0, x6 >= 0
   const_f#2(z, z') -{ 12 + 12*x4 + x4*x6 + 2*x4^2 + 5*x6 }-> s16 :|: s16 >= 0, s16 <= x4 + x6 + 1, x4 >= 0, z' = 1 + x6 + (1 + x4 + x2), x6 >= 0, z >= 0, x2 >= 0
   const_f#2(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   dc#1(z, z', z'', z1, z2, z3) -{ 12 + 2*x25 + 2*x33 + 2*x51 }-> const_f#2(1 + x51 + (1 + x25 + x33), map#2(1 + 0 + 0 + 0 + 0 + 0, s19)) :|: s19 >= 0, s19 <= 2 * (1 + x51 + (1 + x25 + x33)) + 9, s3 >= 0, s3 <= 0 + 1, z'' = 0, z1 = 0, x33 >= 0, z3 = 1 + x51 + (1 + x25 + x33), z2 = 0, x51 >= 0, x25 >= 0, z = 0, z' = 0
   dc#1(z, z', z'', z1, z2, z3) -{ 15 + 2*x25 + 2*x51 }-> const_f#2(1 + x51 + (1 + x25 + 1), map#2(1 + 0 + 0 + 0 + 0 + 0, s17)) :|: s17 >= 0, s17 <= 2 * (1 + x51 + (1 + x25 + 1)) + 9, s2 >= 0, s2 <= 0 + 1, z'' = 0, z3 = 1 + x51 + (1 + x25 + 1), z1 = 0, z2 = 0, x51 >= 0, x25 >= 0, z = 0, z' = 0
   dc#1(z, z', z'', z1, z2, z3) -{ 17 + s5 + 2*x25 + 2*x51 + 2*x6' + 3*x8' }-> const_f#2(1 + x51 + (1 + x25 + (1 + x6' + x8')), map#2(1 + 0 + 0 + 0 + 0 + 0, s18)) :|: s18 >= 0, s18 <= 2 * (1 + x51 + (1 + x25 + (1 + x6' + x8'))) + 9, s5 >= 0, s5 <= x8', s6 >= 0, s6 <= 1 + s5 + 1, z'' = 0, z1 = 0, z2 = 0, x51 >= 0, x25 >= 0, x6' >= 0, z3 = 1 + x51 + (1 + x25 + (1 + x6' + x8')), z = 0, x8' >= 0, z' = 0
   dc#1(z, z', z'', z1, z2, z3) -{ 1 }-> 1 :|: z'' = 0, z1 = 0, z2 = 0, z3 = 1, z = 0, z' = 0
   dc#1(z, z', z'', z1, z2, z3) -{ 0 }-> 0 :|: z >= 0, z2 >= 0, z' >= 0, z3 >= 0, z'' >= 0, z1 >= 0
   dc#1(z, z', z'', z1, z2, z3) -{ 1 }-> 1 + (z3 - 2) + 1 :|: z'' = 0, z1 = 0, z2 = 0, z3 - 2 >= 0, z = 0, z' = 0
   divide_ys#1(z, z') -{ 5 + 2*z }-> 1 + s'' + (1 + s8 + 1) :|: s8 >= 0, s8 <= z + 2, s'' >= 0, s'' <= z + 4, z' >= 0, z >= 0
   drop#2(z, z') -{ 3 + x64 }-> s9 :|: s9 >= 0, s9 <= x64 + 2, z' = 1 + x56 + x64, z - 1 >= 0, x64 >= 0, x56 >= 0
   drop#2(z, z') -{ 1 }-> z' :|: z = 0, z' >= 0
   drop#2(z, z') -{ 1 }-> 3 :|: z = 1 + 0, z' = 1
   drop#2(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   halve#1(z) -{ 1 }-> 0 :|: z = 0
   halve#1(z) -{ 0 }-> 0 :|: z >= 0
   halve#1(z) -{ 1 + z }-> 1 + s4 :|: s4 >= 0, s4 <= z - 2 + 1, z - 2 >= 0
   halve#1(z) -{ 1 }-> 1 + 0 :|: z = 1 + 0
   length#1(z) -{ 1 }-> 0 :|: z = 1
   length#1(z) -{ 0 }-> 0 :|: z >= 0
   length#1(z) -{ 2 + x8 }-> 1 + s7 :|: s7 >= 0, s7 <= x8, x8 >= 0, x6 >= 0, z = 1 + x6 + x8
   leq#2(z, z') -{ 2 + z' }-> s' :|: s' >= 0, s' <= 2, z - 1 >= 0, z' - 1 >= 0
   leq#2(z, z') -{ 1 }-> 2 :|: z = 0, z' >= 0
   leq#2(z, z') -{ 1 }-> 1 :|: z - 1 >= 0, z' = 0
   leq#2(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   main(z) -{ 1 }-> dc#1(0, 0, 0, 0, 0, z) :|: z >= 0
   map#2(z, z') -{ 1 }-> 1 :|: x4 >= 0, x8 >= 0, x6 >= 0, z = 1 + x2 + x4 + x6 + x8 + x10, z' = 1, x10 >= 0, x2 >= 0
   map#2(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   map#2(z, z') -{ 1 }-> 1 + dc#1(x6, x8, x10, x12, x14, x4) + map#2(1 + x6 + x8 + x10 + x12 + x14, x2) :|: x4 >= 0, x8 >= 0, z' = 1 + x4 + x2, x6 >= 0, x12 >= 0, x14 >= 0, x10 >= 0, x2 >= 0, z = 1 + x6 + x8 + x10 + x12 + x14
   merge#2(z, z') -{ 77 + 59*x2 + 16*x2*x4 + 4*x2*z + 10*x2^2 + 46*x4 + 2*x4*z + 8*x4^2 + 18*z }-> s12 :|: s12 >= 0, s12 <= 1 + x4 + x2 + 0 + (z - 1) + 2 + (1 + 0 + (z - 1)) + x4 + x2, x4 >= 0, z' = 1 + x4 + x2, z - 1 >= 0, x2 >= 0
   merge#2(z, z') -{ 50 + 8*x20' + 2*x20'*z' + 14*x6 + 4*x6*z' + 45*z' + 10*z'^2 }-> s13 :|: s13 >= 0, s13 <= 1 + 0 + (z' - 1) + (1 + x20') + x6 + 2 + (1 + (1 + x20') + x6) + 0 + (z' - 1), z = 1 + (1 + x20') + x6, x6 >= 0, x20' >= 0, z' - 1 >= 0
   merge#2(z, z') -{ 163 + 81*x2 + 16*x2*x2' + 2*x2*x4' + 4*x2*x6 + 10*x2^2 + 65*x2' + 2*x2'*x6 + 8*x2'^2 + 10*x4' + 20*x6 }-> s14 :|: s14 >= 0, s14 <= 1 + (1 + x2') + x2 + (1 + x4') + x6 + 2 + (1 + (1 + x4') + x6) + (1 + x2') + x2, s >= 0, s <= 2, x2' >= 0, z = 1 + (1 + x4') + x6, x6 >= 0, z' = 1 + (1 + x2') + x2, x4' >= 0, x2 >= 0
   merge#2(z, z') -{ 94 + 63*x2 + 16*x2*x4 + 4*x2*x6 + 2*x2*x8 + 10*x2^2 + 48*x4 + 2*x4*x6 + 8*x4^2 + 18*x6 + 10*x8 }-> s15 :|: s15 >= 0, s15 <= 1 + x4 + x2 + x8 + x6 + 2 + (1 + x8 + x6) + x4 + x2, x4 >= 0, x8 >= 0, z' = 1 + x4 + x2, x6 >= 0, z = 1 + x8 + x6, x2 >= 0
   merge#2(z, z') -{ 1 }-> z' :|: z = 1, z' >= 0
   merge#2(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   merge#2(z, z') -{ 1 }-> 1 + x4 + x2 :|: x4 >= 0, z = 1 + x4 + x2, z' = 1, x2 >= 0
   take#2(z, z') -{ 1 }-> 1 :|: z = 0, z' >= 0
   take#2(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   take#2(z, z') -{ 3 + x64 }-> 1 + x56 + s1 :|: s1 >= 0, s1 <= x64 + 4, z' = 1 + x56 + x64, z - 1 >= 0, x64 >= 0, x56 >= 0
   take#2(z, z') -{ 1 }-> 1 + 2 + 1 :|: z = 1 + 0, z' = 1

Function symbols to be analyzed: {const_f#2}, {dc#1,map#2}, {main}
Previous analysis results are:
  leq#2: runtime: O(n^1) [2 + z'], size: O(1) [2]
  take#2: runtime: O(n^1) [2 + z'], size: O(n^1) [4 + z']
  halve#1: runtime: O(n^1) [2 + z], size: O(n^1) [1 + z]
  length#1: runtime: O(n^1) [1 + z], size: O(n^1) [z]
  drop#2: runtime: O(n^1) [2 + z'], size: O(n^1) [2 + z']
  merge#2: runtime: O(n^2) [11 + 5*z + z*z' + 12*z' + 2*z'^2], size: O(n^1) [1 + z + z']
  cond_merge_ys_zs_2: runtime: O(n^2) [43 + 10*z' + 2*z'*z4 + 32*z'' + 2*z''*z2 + 8*z''^2 + 6*z2 + 13*z4 + 2*z4^2], size: O(n^1) [2 + z' + z'' + z1 + z2 + z3 + z4]
  divide_ys#1: runtime: O(n^1) [5 + 2*z], size: O(n^1) [9 + 2*z]

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

(63) IntTrsBoundProof (UPPER BOUND(ID))

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

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

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

   cond_merge_ys_zs_2(z, z', z'', z1, z2, z3, z4) -{ 0 }-> 0 :|: z >= 0, z4 >= 0, z' >= 0, z3 >= 0, z'' >= 0, z1 >= 0, z2 >= 0
   cond_merge_ys_zs_2(z, z', z'', z1, z2, z3, z4) -{ 26 + 16*x5 + 4*x5*x6 + x5*z2 + 2*x5^2 + 16*x6 + x6*z2 + 2*x6^2 + 6*z2 }-> 1 + z1 + s10 :|: s10 >= 0, s10 <= 1 + x5 + x6 + z2 + 1, x5 >= 0, x8 >= 0, z' = 1 + x7 + x8, z'' = 1 + x5 + x6, z2 >= 0, z3 >= 0, z = 2, z1 >= 0, z4 >= 0, x7 >= 0, x6 >= 0
   cond_merge_ys_zs_2(z, z', z'', z1, z2, z3, z4) -{ 17 + 5*x7 + x7*z4 + 5*x8 + x8*z4 + 13*z4 + 2*z4^2 }-> 1 + z3 + s11 :|: s11 >= 0, s11 <= z4 + (1 + x7 + x8) + 1, x5 >= 0, x8 >= 0, z = 1, z' = 1 + x7 + x8, z'' = 1 + x5 + x6, z2 >= 0, z3 >= 0, z1 >= 0, z4 >= 0, x7 >= 0, x6 >= 0
   const_f#2(z, z') -{ 12 + 12*x4 + x4*x6 + 2*x4^2 + 5*x6 }-> s16 :|: s16 >= 0, s16 <= x4 + x6 + 1, x4 >= 0, z' = 1 + x6 + (1 + x4 + x2), x6 >= 0, z >= 0, x2 >= 0
   const_f#2(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   dc#1(z, z', z'', z1, z2, z3) -{ 12 + 2*x25 + 2*x33 + 2*x51 }-> const_f#2(1 + x51 + (1 + x25 + x33), map#2(1 + 0 + 0 + 0 + 0 + 0, s19)) :|: s19 >= 0, s19 <= 2 * (1 + x51 + (1 + x25 + x33)) + 9, s3 >= 0, s3 <= 0 + 1, z'' = 0, z1 = 0, x33 >= 0, z3 = 1 + x51 + (1 + x25 + x33), z2 = 0, x51 >= 0, x25 >= 0, z = 0, z' = 0
   dc#1(z, z', z'', z1, z2, z3) -{ 15 + 2*x25 + 2*x51 }-> const_f#2(1 + x51 + (1 + x25 + 1), map#2(1 + 0 + 0 + 0 + 0 + 0, s17)) :|: s17 >= 0, s17 <= 2 * (1 + x51 + (1 + x25 + 1)) + 9, s2 >= 0, s2 <= 0 + 1, z'' = 0, z3 = 1 + x51 + (1 + x25 + 1), z1 = 0, z2 = 0, x51 >= 0, x25 >= 0, z = 0, z' = 0
   dc#1(z, z', z'', z1, z2, z3) -{ 17 + s5 + 2*x25 + 2*x51 + 2*x6' + 3*x8' }-> const_f#2(1 + x51 + (1 + x25 + (1 + x6' + x8')), map#2(1 + 0 + 0 + 0 + 0 + 0, s18)) :|: s18 >= 0, s18 <= 2 * (1 + x51 + (1 + x25 + (1 + x6' + x8'))) + 9, s5 >= 0, s5 <= x8', s6 >= 0, s6 <= 1 + s5 + 1, z'' = 0, z1 = 0, z2 = 0, x51 >= 0, x25 >= 0, x6' >= 0, z3 = 1 + x51 + (1 + x25 + (1 + x6' + x8')), z = 0, x8' >= 0, z' = 0
   dc#1(z, z', z'', z1, z2, z3) -{ 1 }-> 1 :|: z'' = 0, z1 = 0, z2 = 0, z3 = 1, z = 0, z' = 0
   dc#1(z, z', z'', z1, z2, z3) -{ 0 }-> 0 :|: z >= 0, z2 >= 0, z' >= 0, z3 >= 0, z'' >= 0, z1 >= 0
   dc#1(z, z', z'', z1, z2, z3) -{ 1 }-> 1 + (z3 - 2) + 1 :|: z'' = 0, z1 = 0, z2 = 0, z3 - 2 >= 0, z = 0, z' = 0
   divide_ys#1(z, z') -{ 5 + 2*z }-> 1 + s'' + (1 + s8 + 1) :|: s8 >= 0, s8 <= z + 2, s'' >= 0, s'' <= z + 4, z' >= 0, z >= 0
   drop#2(z, z') -{ 3 + x64 }-> s9 :|: s9 >= 0, s9 <= x64 + 2, z' = 1 + x56 + x64, z - 1 >= 0, x64 >= 0, x56 >= 0
   drop#2(z, z') -{ 1 }-> z' :|: z = 0, z' >= 0
   drop#2(z, z') -{ 1 }-> 3 :|: z = 1 + 0, z' = 1
   drop#2(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   halve#1(z) -{ 1 }-> 0 :|: z = 0
   halve#1(z) -{ 0 }-> 0 :|: z >= 0
   halve#1(z) -{ 1 + z }-> 1 + s4 :|: s4 >= 0, s4 <= z - 2 + 1, z - 2 >= 0
   halve#1(z) -{ 1 }-> 1 + 0 :|: z = 1 + 0
   length#1(z) -{ 1 }-> 0 :|: z = 1
   length#1(z) -{ 0 }-> 0 :|: z >= 0
   length#1(z) -{ 2 + x8 }-> 1 + s7 :|: s7 >= 0, s7 <= x8, x8 >= 0, x6 >= 0, z = 1 + x6 + x8
   leq#2(z, z') -{ 2 + z' }-> s' :|: s' >= 0, s' <= 2, z - 1 >= 0, z' - 1 >= 0
   leq#2(z, z') -{ 1 }-> 2 :|: z = 0, z' >= 0
   leq#2(z, z') -{ 1 }-> 1 :|: z - 1 >= 0, z' = 0
   leq#2(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   main(z) -{ 1 }-> dc#1(0, 0, 0, 0, 0, z) :|: z >= 0
   map#2(z, z') -{ 1 }-> 1 :|: x4 >= 0, x8 >= 0, x6 >= 0, z = 1 + x2 + x4 + x6 + x8 + x10, z' = 1, x10 >= 0, x2 >= 0
   map#2(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   map#2(z, z') -{ 1 }-> 1 + dc#1(x6, x8, x10, x12, x14, x4) + map#2(1 + x6 + x8 + x10 + x12 + x14, x2) :|: x4 >= 0, x8 >= 0, z' = 1 + x4 + x2, x6 >= 0, x12 >= 0, x14 >= 0, x10 >= 0, x2 >= 0, z = 1 + x6 + x8 + x10 + x12 + x14
   merge#2(z, z') -{ 77 + 59*x2 + 16*x2*x4 + 4*x2*z + 10*x2^2 + 46*x4 + 2*x4*z + 8*x4^2 + 18*z }-> s12 :|: s12 >= 0, s12 <= 1 + x4 + x2 + 0 + (z - 1) + 2 + (1 + 0 + (z - 1)) + x4 + x2, x4 >= 0, z' = 1 + x4 + x2, z - 1 >= 0, x2 >= 0
   merge#2(z, z') -{ 50 + 8*x20' + 2*x20'*z' + 14*x6 + 4*x6*z' + 45*z' + 10*z'^2 }-> s13 :|: s13 >= 0, s13 <= 1 + 0 + (z' - 1) + (1 + x20') + x6 + 2 + (1 + (1 + x20') + x6) + 0 + (z' - 1), z = 1 + (1 + x20') + x6, x6 >= 0, x20' >= 0, z' - 1 >= 0
   merge#2(z, z') -{ 163 + 81*x2 + 16*x2*x2' + 2*x2*x4' + 4*x2*x6 + 10*x2^2 + 65*x2' + 2*x2'*x6 + 8*x2'^2 + 10*x4' + 20*x6 }-> s14 :|: s14 >= 0, s14 <= 1 + (1 + x2') + x2 + (1 + x4') + x6 + 2 + (1 + (1 + x4') + x6) + (1 + x2') + x2, s >= 0, s <= 2, x2' >= 0, z = 1 + (1 + x4') + x6, x6 >= 0, z' = 1 + (1 + x2') + x2, x4' >= 0, x2 >= 0
   merge#2(z, z') -{ 94 + 63*x2 + 16*x2*x4 + 4*x2*x6 + 2*x2*x8 + 10*x2^2 + 48*x4 + 2*x4*x6 + 8*x4^2 + 18*x6 + 10*x8 }-> s15 :|: s15 >= 0, s15 <= 1 + x4 + x2 + x8 + x6 + 2 + (1 + x8 + x6) + x4 + x2, x4 >= 0, x8 >= 0, z' = 1 + x4 + x2, x6 >= 0, z = 1 + x8 + x6, x2 >= 0
   merge#2(z, z') -{ 1 }-> z' :|: z = 1, z' >= 0
   merge#2(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   merge#2(z, z') -{ 1 }-> 1 + x4 + x2 :|: x4 >= 0, z = 1 + x4 + x2, z' = 1, x2 >= 0
   take#2(z, z') -{ 1 }-> 1 :|: z = 0, z' >= 0
   take#2(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   take#2(z, z') -{ 3 + x64 }-> 1 + x56 + s1 :|: s1 >= 0, s1 <= x64 + 4, z' = 1 + x56 + x64, z - 1 >= 0, x64 >= 0, x56 >= 0
   take#2(z, z') -{ 1 }-> 1 + 2 + 1 :|: z = 1 + 0, z' = 1

Function symbols to be analyzed: {const_f#2}, {dc#1,map#2}, {main}
Previous analysis results are:
  leq#2: runtime: O(n^1) [2 + z'], size: O(1) [2]
  take#2: runtime: O(n^1) [2 + z'], size: O(n^1) [4 + z']
  halve#1: runtime: O(n^1) [2 + z], size: O(n^1) [1 + z]
  length#1: runtime: O(n^1) [1 + z], size: O(n^1) [z]
  drop#2: runtime: O(n^1) [2 + z'], size: O(n^1) [2 + z']
  merge#2: runtime: O(n^2) [11 + 5*z + z*z' + 12*z' + 2*z'^2], size: O(n^1) [1 + z + z']
  cond_merge_ys_zs_2: runtime: O(n^2) [43 + 10*z' + 2*z'*z4 + 32*z'' + 2*z''*z2 + 8*z''^2 + 6*z2 + 13*z4 + 2*z4^2], size: O(n^1) [2 + z' + z'' + z1 + z2 + z3 + z4]
  divide_ys#1: runtime: O(n^1) [5 + 2*z], size: O(n^1) [9 + 2*z]
  const_f#2: runtime: ?, size: O(n^1) [z']

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

(65) IntTrsBoundProof (UPPER BOUND(ID))

Computed RUNTIME bound using KoAT for: const_f#2
after applying outer abstraction to obtain an ITS,
resulting in: O(n^2) with polynomial bound: 12 + 17*z' + 3*z'^2

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

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

   cond_merge_ys_zs_2(z, z', z'', z1, z2, z3, z4) -{ 0 }-> 0 :|: z >= 0, z4 >= 0, z' >= 0, z3 >= 0, z'' >= 0, z1 >= 0, z2 >= 0
   cond_merge_ys_zs_2(z, z', z'', z1, z2, z3, z4) -{ 26 + 16*x5 + 4*x5*x6 + x5*z2 + 2*x5^2 + 16*x6 + x6*z2 + 2*x6^2 + 6*z2 }-> 1 + z1 + s10 :|: s10 >= 0, s10 <= 1 + x5 + x6 + z2 + 1, x5 >= 0, x8 >= 0, z' = 1 + x7 + x8, z'' = 1 + x5 + x6, z2 >= 0, z3 >= 0, z = 2, z1 >= 0, z4 >= 0, x7 >= 0, x6 >= 0
   cond_merge_ys_zs_2(z, z', z'', z1, z2, z3, z4) -{ 17 + 5*x7 + x7*z4 + 5*x8 + x8*z4 + 13*z4 + 2*z4^2 }-> 1 + z3 + s11 :|: s11 >= 0, s11 <= z4 + (1 + x7 + x8) + 1, x5 >= 0, x8 >= 0, z = 1, z' = 1 + x7 + x8, z'' = 1 + x5 + x6, z2 >= 0, z3 >= 0, z1 >= 0, z4 >= 0, x7 >= 0, x6 >= 0
   const_f#2(z, z') -{ 12 + 12*x4 + x4*x6 + 2*x4^2 + 5*x6 }-> s16 :|: s16 >= 0, s16 <= x4 + x6 + 1, x4 >= 0, z' = 1 + x6 + (1 + x4 + x2), x6 >= 0, z >= 0, x2 >= 0
   const_f#2(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   dc#1(z, z', z'', z1, z2, z3) -{ 12 + 2*x25 + 2*x33 + 2*x51 }-> const_f#2(1 + x51 + (1 + x25 + x33), map#2(1 + 0 + 0 + 0 + 0 + 0, s19)) :|: s19 >= 0, s19 <= 2 * (1 + x51 + (1 + x25 + x33)) + 9, s3 >= 0, s3 <= 0 + 1, z'' = 0, z1 = 0, x33 >= 0, z3 = 1 + x51 + (1 + x25 + x33), z2 = 0, x51 >= 0, x25 >= 0, z = 0, z' = 0
   dc#1(z, z', z'', z1, z2, z3) -{ 15 + 2*x25 + 2*x51 }-> const_f#2(1 + x51 + (1 + x25 + 1), map#2(1 + 0 + 0 + 0 + 0 + 0, s17)) :|: s17 >= 0, s17 <= 2 * (1 + x51 + (1 + x25 + 1)) + 9, s2 >= 0, s2 <= 0 + 1, z'' = 0, z3 = 1 + x51 + (1 + x25 + 1), z1 = 0, z2 = 0, x51 >= 0, x25 >= 0, z = 0, z' = 0
   dc#1(z, z', z'', z1, z2, z3) -{ 17 + s5 + 2*x25 + 2*x51 + 2*x6' + 3*x8' }-> const_f#2(1 + x51 + (1 + x25 + (1 + x6' + x8')), map#2(1 + 0 + 0 + 0 + 0 + 0, s18)) :|: s18 >= 0, s18 <= 2 * (1 + x51 + (1 + x25 + (1 + x6' + x8'))) + 9, s5 >= 0, s5 <= x8', s6 >= 0, s6 <= 1 + s5 + 1, z'' = 0, z1 = 0, z2 = 0, x51 >= 0, x25 >= 0, x6' >= 0, z3 = 1 + x51 + (1 + x25 + (1 + x6' + x8')), z = 0, x8' >= 0, z' = 0
   dc#1(z, z', z'', z1, z2, z3) -{ 1 }-> 1 :|: z'' = 0, z1 = 0, z2 = 0, z3 = 1, z = 0, z' = 0
   dc#1(z, z', z'', z1, z2, z3) -{ 0 }-> 0 :|: z >= 0, z2 >= 0, z' >= 0, z3 >= 0, z'' >= 0, z1 >= 0
   dc#1(z, z', z'', z1, z2, z3) -{ 1 }-> 1 + (z3 - 2) + 1 :|: z'' = 0, z1 = 0, z2 = 0, z3 - 2 >= 0, z = 0, z' = 0
   divide_ys#1(z, z') -{ 5 + 2*z }-> 1 + s'' + (1 + s8 + 1) :|: s8 >= 0, s8 <= z + 2, s'' >= 0, s'' <= z + 4, z' >= 0, z >= 0
   drop#2(z, z') -{ 3 + x64 }-> s9 :|: s9 >= 0, s9 <= x64 + 2, z' = 1 + x56 + x64, z - 1 >= 0, x64 >= 0, x56 >= 0
   drop#2(z, z') -{ 1 }-> z' :|: z = 0, z' >= 0
   drop#2(z, z') -{ 1 }-> 3 :|: z = 1 + 0, z' = 1
   drop#2(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   halve#1(z) -{ 1 }-> 0 :|: z = 0
   halve#1(z) -{ 0 }-> 0 :|: z >= 0
   halve#1(z) -{ 1 + z }-> 1 + s4 :|: s4 >= 0, s4 <= z - 2 + 1, z - 2 >= 0
   halve#1(z) -{ 1 }-> 1 + 0 :|: z = 1 + 0
   length#1(z) -{ 1 }-> 0 :|: z = 1
   length#1(z) -{ 0 }-> 0 :|: z >= 0
   length#1(z) -{ 2 + x8 }-> 1 + s7 :|: s7 >= 0, s7 <= x8, x8 >= 0, x6 >= 0, z = 1 + x6 + x8
   leq#2(z, z') -{ 2 + z' }-> s' :|: s' >= 0, s' <= 2, z - 1 >= 0, z' - 1 >= 0
   leq#2(z, z') -{ 1 }-> 2 :|: z = 0, z' >= 0
   leq#2(z, z') -{ 1 }-> 1 :|: z - 1 >= 0, z' = 0
   leq#2(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   main(z) -{ 1 }-> dc#1(0, 0, 0, 0, 0, z) :|: z >= 0
   map#2(z, z') -{ 1 }-> 1 :|: x4 >= 0, x8 >= 0, x6 >= 0, z = 1 + x2 + x4 + x6 + x8 + x10, z' = 1, x10 >= 0, x2 >= 0
   map#2(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   map#2(z, z') -{ 1 }-> 1 + dc#1(x6, x8, x10, x12, x14, x4) + map#2(1 + x6 + x8 + x10 + x12 + x14, x2) :|: x4 >= 0, x8 >= 0, z' = 1 + x4 + x2, x6 >= 0, x12 >= 0, x14 >= 0, x10 >= 0, x2 >= 0, z = 1 + x6 + x8 + x10 + x12 + x14
   merge#2(z, z') -{ 77 + 59*x2 + 16*x2*x4 + 4*x2*z + 10*x2^2 + 46*x4 + 2*x4*z + 8*x4^2 + 18*z }-> s12 :|: s12 >= 0, s12 <= 1 + x4 + x2 + 0 + (z - 1) + 2 + (1 + 0 + (z - 1)) + x4 + x2, x4 >= 0, z' = 1 + x4 + x2, z - 1 >= 0, x2 >= 0
   merge#2(z, z') -{ 50 + 8*x20' + 2*x20'*z' + 14*x6 + 4*x6*z' + 45*z' + 10*z'^2 }-> s13 :|: s13 >= 0, s13 <= 1 + 0 + (z' - 1) + (1 + x20') + x6 + 2 + (1 + (1 + x20') + x6) + 0 + (z' - 1), z = 1 + (1 + x20') + x6, x6 >= 0, x20' >= 0, z' - 1 >= 0
   merge#2(z, z') -{ 163 + 81*x2 + 16*x2*x2' + 2*x2*x4' + 4*x2*x6 + 10*x2^2 + 65*x2' + 2*x2'*x6 + 8*x2'^2 + 10*x4' + 20*x6 }-> s14 :|: s14 >= 0, s14 <= 1 + (1 + x2') + x2 + (1 + x4') + x6 + 2 + (1 + (1 + x4') + x6) + (1 + x2') + x2, s >= 0, s <= 2, x2' >= 0, z = 1 + (1 + x4') + x6, x6 >= 0, z' = 1 + (1 + x2') + x2, x4' >= 0, x2 >= 0
   merge#2(z, z') -{ 94 + 63*x2 + 16*x2*x4 + 4*x2*x6 + 2*x2*x8 + 10*x2^2 + 48*x4 + 2*x4*x6 + 8*x4^2 + 18*x6 + 10*x8 }-> s15 :|: s15 >= 0, s15 <= 1 + x4 + x2 + x8 + x6 + 2 + (1 + x8 + x6) + x4 + x2, x4 >= 0, x8 >= 0, z' = 1 + x4 + x2, x6 >= 0, z = 1 + x8 + x6, x2 >= 0
   merge#2(z, z') -{ 1 }-> z' :|: z = 1, z' >= 0
   merge#2(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   merge#2(z, z') -{ 1 }-> 1 + x4 + x2 :|: x4 >= 0, z = 1 + x4 + x2, z' = 1, x2 >= 0
   take#2(z, z') -{ 1 }-> 1 :|: z = 0, z' >= 0
   take#2(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   take#2(z, z') -{ 3 + x64 }-> 1 + x56 + s1 :|: s1 >= 0, s1 <= x64 + 4, z' = 1 + x56 + x64, z - 1 >= 0, x64 >= 0, x56 >= 0
   take#2(z, z') -{ 1 }-> 1 + 2 + 1 :|: z = 1 + 0, z' = 1

Function symbols to be analyzed: {dc#1,map#2}, {main}
Previous analysis results are:
  leq#2: runtime: O(n^1) [2 + z'], size: O(1) [2]
  take#2: runtime: O(n^1) [2 + z'], size: O(n^1) [4 + z']
  halve#1: runtime: O(n^1) [2 + z], size: O(n^1) [1 + z]
  length#1: runtime: O(n^1) [1 + z], size: O(n^1) [z]
  drop#2: runtime: O(n^1) [2 + z'], size: O(n^1) [2 + z']
  merge#2: runtime: O(n^2) [11 + 5*z + z*z' + 12*z' + 2*z'^2], size: O(n^1) [1 + z + z']
  cond_merge_ys_zs_2: runtime: O(n^2) [43 + 10*z' + 2*z'*z4 + 32*z'' + 2*z''*z2 + 8*z''^2 + 6*z2 + 13*z4 + 2*z4^2], size: O(n^1) [2 + z' + z'' + z1 + z2 + z3 + z4]
  divide_ys#1: runtime: O(n^1) [5 + 2*z], size: O(n^1) [9 + 2*z]
  const_f#2: runtime: O(n^2) [12 + 17*z' + 3*z'^2], size: O(n^1) [z']

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

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

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

   cond_merge_ys_zs_2(z, z', z'', z1, z2, z3, z4) -{ 0 }-> 0 :|: z >= 0, z4 >= 0, z' >= 0, z3 >= 0, z'' >= 0, z1 >= 0, z2 >= 0
   cond_merge_ys_zs_2(z, z', z'', z1, z2, z3, z4) -{ 26 + 16*x5 + 4*x5*x6 + x5*z2 + 2*x5^2 + 16*x6 + x6*z2 + 2*x6^2 + 6*z2 }-> 1 + z1 + s10 :|: s10 >= 0, s10 <= 1 + x5 + x6 + z2 + 1, x5 >= 0, x8 >= 0, z' = 1 + x7 + x8, z'' = 1 + x5 + x6, z2 >= 0, z3 >= 0, z = 2, z1 >= 0, z4 >= 0, x7 >= 0, x6 >= 0
   cond_merge_ys_zs_2(z, z', z'', z1, z2, z3, z4) -{ 17 + 5*x7 + x7*z4 + 5*x8 + x8*z4 + 13*z4 + 2*z4^2 }-> 1 + z3 + s11 :|: s11 >= 0, s11 <= z4 + (1 + x7 + x8) + 1, x5 >= 0, x8 >= 0, z = 1, z' = 1 + x7 + x8, z'' = 1 + x5 + x6, z2 >= 0, z3 >= 0, z1 >= 0, z4 >= 0, x7 >= 0, x6 >= 0
   const_f#2(z, z') -{ 12 + 12*x4 + x4*x6 + 2*x4^2 + 5*x6 }-> s16 :|: s16 >= 0, s16 <= x4 + x6 + 1, x4 >= 0, z' = 1 + x6 + (1 + x4 + x2), x6 >= 0, z >= 0, x2 >= 0
   const_f#2(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   dc#1(z, z', z'', z1, z2, z3) -{ 12 + 2*x25 + 2*x33 + 2*x51 }-> const_f#2(1 + x51 + (1 + x25 + x33), map#2(1 + 0 + 0 + 0 + 0 + 0, s19)) :|: s19 >= 0, s19 <= 2 * (1 + x51 + (1 + x25 + x33)) + 9, s3 >= 0, s3 <= 0 + 1, z'' = 0, z1 = 0, x33 >= 0, z3 = 1 + x51 + (1 + x25 + x33), z2 = 0, x51 >= 0, x25 >= 0, z = 0, z' = 0
   dc#1(z, z', z'', z1, z2, z3) -{ 15 + 2*x25 + 2*x51 }-> const_f#2(1 + x51 + (1 + x25 + 1), map#2(1 + 0 + 0 + 0 + 0 + 0, s17)) :|: s17 >= 0, s17 <= 2 * (1 + x51 + (1 + x25 + 1)) + 9, s2 >= 0, s2 <= 0 + 1, z'' = 0, z3 = 1 + x51 + (1 + x25 + 1), z1 = 0, z2 = 0, x51 >= 0, x25 >= 0, z = 0, z' = 0
   dc#1(z, z', z'', z1, z2, z3) -{ 17 + s5 + 2*x25 + 2*x51 + 2*x6' + 3*x8' }-> const_f#2(1 + x51 + (1 + x25 + (1 + x6' + x8')), map#2(1 + 0 + 0 + 0 + 0 + 0, s18)) :|: s18 >= 0, s18 <= 2 * (1 + x51 + (1 + x25 + (1 + x6' + x8'))) + 9, s5 >= 0, s5 <= x8', s6 >= 0, s6 <= 1 + s5 + 1, z'' = 0, z1 = 0, z2 = 0, x51 >= 0, x25 >= 0, x6' >= 0, z3 = 1 + x51 + (1 + x25 + (1 + x6' + x8')), z = 0, x8' >= 0, z' = 0
   dc#1(z, z', z'', z1, z2, z3) -{ 1 }-> 1 :|: z'' = 0, z1 = 0, z2 = 0, z3 = 1, z = 0, z' = 0
   dc#1(z, z', z'', z1, z2, z3) -{ 0 }-> 0 :|: z >= 0, z2 >= 0, z' >= 0, z3 >= 0, z'' >= 0, z1 >= 0
   dc#1(z, z', z'', z1, z2, z3) -{ 1 }-> 1 + (z3 - 2) + 1 :|: z'' = 0, z1 = 0, z2 = 0, z3 - 2 >= 0, z = 0, z' = 0
   divide_ys#1(z, z') -{ 5 + 2*z }-> 1 + s'' + (1 + s8 + 1) :|: s8 >= 0, s8 <= z + 2, s'' >= 0, s'' <= z + 4, z' >= 0, z >= 0
   drop#2(z, z') -{ 3 + x64 }-> s9 :|: s9 >= 0, s9 <= x64 + 2, z' = 1 + x56 + x64, z - 1 >= 0, x64 >= 0, x56 >= 0
   drop#2(z, z') -{ 1 }-> z' :|: z = 0, z' >= 0
   drop#2(z, z') -{ 1 }-> 3 :|: z = 1 + 0, z' = 1
   drop#2(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   halve#1(z) -{ 1 }-> 0 :|: z = 0
   halve#1(z) -{ 0 }-> 0 :|: z >= 0
   halve#1(z) -{ 1 + z }-> 1 + s4 :|: s4 >= 0, s4 <= z - 2 + 1, z - 2 >= 0
   halve#1(z) -{ 1 }-> 1 + 0 :|: z = 1 + 0
   length#1(z) -{ 1 }-> 0 :|: z = 1
   length#1(z) -{ 0 }-> 0 :|: z >= 0
   length#1(z) -{ 2 + x8 }-> 1 + s7 :|: s7 >= 0, s7 <= x8, x8 >= 0, x6 >= 0, z = 1 + x6 + x8
   leq#2(z, z') -{ 2 + z' }-> s' :|: s' >= 0, s' <= 2, z - 1 >= 0, z' - 1 >= 0
   leq#2(z, z') -{ 1 }-> 2 :|: z = 0, z' >= 0
   leq#2(z, z') -{ 1 }-> 1 :|: z - 1 >= 0, z' = 0
   leq#2(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   main(z) -{ 1 }-> dc#1(0, 0, 0, 0, 0, z) :|: z >= 0
   map#2(z, z') -{ 1 }-> 1 :|: x4 >= 0, x8 >= 0, x6 >= 0, z = 1 + x2 + x4 + x6 + x8 + x10, z' = 1, x10 >= 0, x2 >= 0
   map#2(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   map#2(z, z') -{ 1 }-> 1 + dc#1(x6, x8, x10, x12, x14, x4) + map#2(1 + x6 + x8 + x10 + x12 + x14, x2) :|: x4 >= 0, x8 >= 0, z' = 1 + x4 + x2, x6 >= 0, x12 >= 0, x14 >= 0, x10 >= 0, x2 >= 0, z = 1 + x6 + x8 + x10 + x12 + x14
   merge#2(z, z') -{ 77 + 59*x2 + 16*x2*x4 + 4*x2*z + 10*x2^2 + 46*x4 + 2*x4*z + 8*x4^2 + 18*z }-> s12 :|: s12 >= 0, s12 <= 1 + x4 + x2 + 0 + (z - 1) + 2 + (1 + 0 + (z - 1)) + x4 + x2, x4 >= 0, z' = 1 + x4 + x2, z - 1 >= 0, x2 >= 0
   merge#2(z, z') -{ 50 + 8*x20' + 2*x20'*z' + 14*x6 + 4*x6*z' + 45*z' + 10*z'^2 }-> s13 :|: s13 >= 0, s13 <= 1 + 0 + (z' - 1) + (1 + x20') + x6 + 2 + (1 + (1 + x20') + x6) + 0 + (z' - 1), z = 1 + (1 + x20') + x6, x6 >= 0, x20' >= 0, z' - 1 >= 0
   merge#2(z, z') -{ 163 + 81*x2 + 16*x2*x2' + 2*x2*x4' + 4*x2*x6 + 10*x2^2 + 65*x2' + 2*x2'*x6 + 8*x2'^2 + 10*x4' + 20*x6 }-> s14 :|: s14 >= 0, s14 <= 1 + (1 + x2') + x2 + (1 + x4') + x6 + 2 + (1 + (1 + x4') + x6) + (1 + x2') + x2, s >= 0, s <= 2, x2' >= 0, z = 1 + (1 + x4') + x6, x6 >= 0, z' = 1 + (1 + x2') + x2, x4' >= 0, x2 >= 0
   merge#2(z, z') -{ 94 + 63*x2 + 16*x2*x4 + 4*x2*x6 + 2*x2*x8 + 10*x2^2 + 48*x4 + 2*x4*x6 + 8*x4^2 + 18*x6 + 10*x8 }-> s15 :|: s15 >= 0, s15 <= 1 + x4 + x2 + x8 + x6 + 2 + (1 + x8 + x6) + x4 + x2, x4 >= 0, x8 >= 0, z' = 1 + x4 + x2, x6 >= 0, z = 1 + x8 + x6, x2 >= 0
   merge#2(z, z') -{ 1 }-> z' :|: z = 1, z' >= 0
   merge#2(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   merge#2(z, z') -{ 1 }-> 1 + x4 + x2 :|: x4 >= 0, z = 1 + x4 + x2, z' = 1, x2 >= 0
   take#2(z, z') -{ 1 }-> 1 :|: z = 0, z' >= 0
   take#2(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   take#2(z, z') -{ 3 + x64 }-> 1 + x56 + s1 :|: s1 >= 0, s1 <= x64 + 4, z' = 1 + x56 + x64, z - 1 >= 0, x64 >= 0, x56 >= 0
   take#2(z, z') -{ 1 }-> 1 + 2 + 1 :|: z = 1 + 0, z' = 1

Function symbols to be analyzed: {dc#1,map#2}, {main}
Previous analysis results are:
  leq#2: runtime: O(n^1) [2 + z'], size: O(1) [2]
  take#2: runtime: O(n^1) [2 + z'], size: O(n^1) [4 + z']
  halve#1: runtime: O(n^1) [2 + z], size: O(n^1) [1 + z]
  length#1: runtime: O(n^1) [1 + z], size: O(n^1) [z]
  drop#2: runtime: O(n^1) [2 + z'], size: O(n^1) [2 + z']
  merge#2: runtime: O(n^2) [11 + 5*z + z*z' + 12*z' + 2*z'^2], size: O(n^1) [1 + z + z']
  cond_merge_ys_zs_2: runtime: O(n^2) [43 + 10*z' + 2*z'*z4 + 32*z'' + 2*z''*z2 + 8*z''^2 + 6*z2 + 13*z4 + 2*z4^2], size: O(n^1) [2 + z' + z'' + z1 + z2 + z3 + z4]
  divide_ys#1: runtime: O(n^1) [5 + 2*z], size: O(n^1) [9 + 2*z]
  const_f#2: runtime: O(n^2) [12 + 17*z' + 3*z'^2], size: O(n^1) [z']

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

(69) IntTrsBoundProof (UPPER BOUND(ID))

Computed SIZE bound using CoFloCo for: dc#1
after applying outer abstraction to obtain an ITS,
resulting in: INF with polynomial bound: ?

Computed SIZE bound using CoFloCo for: map#2
after applying outer abstraction to obtain an ITS,
resulting in: INF with polynomial bound: ?

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

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

   cond_merge_ys_zs_2(z, z', z'', z1, z2, z3, z4) -{ 0 }-> 0 :|: z >= 0, z4 >= 0, z' >= 0, z3 >= 0, z'' >= 0, z1 >= 0, z2 >= 0
   cond_merge_ys_zs_2(z, z', z'', z1, z2, z3, z4) -{ 26 + 16*x5 + 4*x5*x6 + x5*z2 + 2*x5^2 + 16*x6 + x6*z2 + 2*x6^2 + 6*z2 }-> 1 + z1 + s10 :|: s10 >= 0, s10 <= 1 + x5 + x6 + z2 + 1, x5 >= 0, x8 >= 0, z' = 1 + x7 + x8, z'' = 1 + x5 + x6, z2 >= 0, z3 >= 0, z = 2, z1 >= 0, z4 >= 0, x7 >= 0, x6 >= 0
   cond_merge_ys_zs_2(z, z', z'', z1, z2, z3, z4) -{ 17 + 5*x7 + x7*z4 + 5*x8 + x8*z4 + 13*z4 + 2*z4^2 }-> 1 + z3 + s11 :|: s11 >= 0, s11 <= z4 + (1 + x7 + x8) + 1, x5 >= 0, x8 >= 0, z = 1, z' = 1 + x7 + x8, z'' = 1 + x5 + x6, z2 >= 0, z3 >= 0, z1 >= 0, z4 >= 0, x7 >= 0, x6 >= 0
   const_f#2(z, z') -{ 12 + 12*x4 + x4*x6 + 2*x4^2 + 5*x6 }-> s16 :|: s16 >= 0, s16 <= x4 + x6 + 1, x4 >= 0, z' = 1 + x6 + (1 + x4 + x2), x6 >= 0, z >= 0, x2 >= 0
   const_f#2(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   dc#1(z, z', z'', z1, z2, z3) -{ 12 + 2*x25 + 2*x33 + 2*x51 }-> const_f#2(1 + x51 + (1 + x25 + x33), map#2(1 + 0 + 0 + 0 + 0 + 0, s19)) :|: s19 >= 0, s19 <= 2 * (1 + x51 + (1 + x25 + x33)) + 9, s3 >= 0, s3 <= 0 + 1, z'' = 0, z1 = 0, x33 >= 0, z3 = 1 + x51 + (1 + x25 + x33), z2 = 0, x51 >= 0, x25 >= 0, z = 0, z' = 0
   dc#1(z, z', z'', z1, z2, z3) -{ 15 + 2*x25 + 2*x51 }-> const_f#2(1 + x51 + (1 + x25 + 1), map#2(1 + 0 + 0 + 0 + 0 + 0, s17)) :|: s17 >= 0, s17 <= 2 * (1 + x51 + (1 + x25 + 1)) + 9, s2 >= 0, s2 <= 0 + 1, z'' = 0, z3 = 1 + x51 + (1 + x25 + 1), z1 = 0, z2 = 0, x51 >= 0, x25 >= 0, z = 0, z' = 0
   dc#1(z, z', z'', z1, z2, z3) -{ 17 + s5 + 2*x25 + 2*x51 + 2*x6' + 3*x8' }-> const_f#2(1 + x51 + (1 + x25 + (1 + x6' + x8')), map#2(1 + 0 + 0 + 0 + 0 + 0, s18)) :|: s18 >= 0, s18 <= 2 * (1 + x51 + (1 + x25 + (1 + x6' + x8'))) + 9, s5 >= 0, s5 <= x8', s6 >= 0, s6 <= 1 + s5 + 1, z'' = 0, z1 = 0, z2 = 0, x51 >= 0, x25 >= 0, x6' >= 0, z3 = 1 + x51 + (1 + x25 + (1 + x6' + x8')), z = 0, x8' >= 0, z' = 0
   dc#1(z, z', z'', z1, z2, z3) -{ 1 }-> 1 :|: z'' = 0, z1 = 0, z2 = 0, z3 = 1, z = 0, z' = 0
   dc#1(z, z', z'', z1, z2, z3) -{ 0 }-> 0 :|: z >= 0, z2 >= 0, z' >= 0, z3 >= 0, z'' >= 0, z1 >= 0
   dc#1(z, z', z'', z1, z2, z3) -{ 1 }-> 1 + (z3 - 2) + 1 :|: z'' = 0, z1 = 0, z2 = 0, z3 - 2 >= 0, z = 0, z' = 0
   divide_ys#1(z, z') -{ 5 + 2*z }-> 1 + s'' + (1 + s8 + 1) :|: s8 >= 0, s8 <= z + 2, s'' >= 0, s'' <= z + 4, z' >= 0, z >= 0
   drop#2(z, z') -{ 3 + x64 }-> s9 :|: s9 >= 0, s9 <= x64 + 2, z' = 1 + x56 + x64, z - 1 >= 0, x64 >= 0, x56 >= 0
   drop#2(z, z') -{ 1 }-> z' :|: z = 0, z' >= 0
   drop#2(z, z') -{ 1 }-> 3 :|: z = 1 + 0, z' = 1
   drop#2(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   halve#1(z) -{ 1 }-> 0 :|: z = 0
   halve#1(z) -{ 0 }-> 0 :|: z >= 0
   halve#1(z) -{ 1 + z }-> 1 + s4 :|: s4 >= 0, s4 <= z - 2 + 1, z - 2 >= 0
   halve#1(z) -{ 1 }-> 1 + 0 :|: z = 1 + 0
   length#1(z) -{ 1 }-> 0 :|: z = 1
   length#1(z) -{ 0 }-> 0 :|: z >= 0
   length#1(z) -{ 2 + x8 }-> 1 + s7 :|: s7 >= 0, s7 <= x8, x8 >= 0, x6 >= 0, z = 1 + x6 + x8
   leq#2(z, z') -{ 2 + z' }-> s' :|: s' >= 0, s' <= 2, z - 1 >= 0, z' - 1 >= 0
   leq#2(z, z') -{ 1 }-> 2 :|: z = 0, z' >= 0
   leq#2(z, z') -{ 1 }-> 1 :|: z - 1 >= 0, z' = 0
   leq#2(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   main(z) -{ 1 }-> dc#1(0, 0, 0, 0, 0, z) :|: z >= 0
   map#2(z, z') -{ 1 }-> 1 :|: x4 >= 0, x8 >= 0, x6 >= 0, z = 1 + x2 + x4 + x6 + x8 + x10, z' = 1, x10 >= 0, x2 >= 0
   map#2(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   map#2(z, z') -{ 1 }-> 1 + dc#1(x6, x8, x10, x12, x14, x4) + map#2(1 + x6 + x8 + x10 + x12 + x14, x2) :|: x4 >= 0, x8 >= 0, z' = 1 + x4 + x2, x6 >= 0, x12 >= 0, x14 >= 0, x10 >= 0, x2 >= 0, z = 1 + x6 + x8 + x10 + x12 + x14
   merge#2(z, z') -{ 77 + 59*x2 + 16*x2*x4 + 4*x2*z + 10*x2^2 + 46*x4 + 2*x4*z + 8*x4^2 + 18*z }-> s12 :|: s12 >= 0, s12 <= 1 + x4 + x2 + 0 + (z - 1) + 2 + (1 + 0 + (z - 1)) + x4 + x2, x4 >= 0, z' = 1 + x4 + x2, z - 1 >= 0, x2 >= 0
   merge#2(z, z') -{ 50 + 8*x20' + 2*x20'*z' + 14*x6 + 4*x6*z' + 45*z' + 10*z'^2 }-> s13 :|: s13 >= 0, s13 <= 1 + 0 + (z' - 1) + (1 + x20') + x6 + 2 + (1 + (1 + x20') + x6) + 0 + (z' - 1), z = 1 + (1 + x20') + x6, x6 >= 0, x20' >= 0, z' - 1 >= 0
   merge#2(z, z') -{ 163 + 81*x2 + 16*x2*x2' + 2*x2*x4' + 4*x2*x6 + 10*x2^2 + 65*x2' + 2*x2'*x6 + 8*x2'^2 + 10*x4' + 20*x6 }-> s14 :|: s14 >= 0, s14 <= 1 + (1 + x2') + x2 + (1 + x4') + x6 + 2 + (1 + (1 + x4') + x6) + (1 + x2') + x2, s >= 0, s <= 2, x2' >= 0, z = 1 + (1 + x4') + x6, x6 >= 0, z' = 1 + (1 + x2') + x2, x4' >= 0, x2 >= 0
   merge#2(z, z') -{ 94 + 63*x2 + 16*x2*x4 + 4*x2*x6 + 2*x2*x8 + 10*x2^2 + 48*x4 + 2*x4*x6 + 8*x4^2 + 18*x6 + 10*x8 }-> s15 :|: s15 >= 0, s15 <= 1 + x4 + x2 + x8 + x6 + 2 + (1 + x8 + x6) + x4 + x2, x4 >= 0, x8 >= 0, z' = 1 + x4 + x2, x6 >= 0, z = 1 + x8 + x6, x2 >= 0
   merge#2(z, z') -{ 1 }-> z' :|: z = 1, z' >= 0
   merge#2(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   merge#2(z, z') -{ 1 }-> 1 + x4 + x2 :|: x4 >= 0, z = 1 + x4 + x2, z' = 1, x2 >= 0
   take#2(z, z') -{ 1 }-> 1 :|: z = 0, z' >= 0
   take#2(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   take#2(z, z') -{ 3 + x64 }-> 1 + x56 + s1 :|: s1 >= 0, s1 <= x64 + 4, z' = 1 + x56 + x64, z - 1 >= 0, x64 >= 0, x56 >= 0
   take#2(z, z') -{ 1 }-> 1 + 2 + 1 :|: z = 1 + 0, z' = 1

Function symbols to be analyzed: {dc#1,map#2}, {main}
Previous analysis results are:
  leq#2: runtime: O(n^1) [2 + z'], size: O(1) [2]
  take#2: runtime: O(n^1) [2 + z'], size: O(n^1) [4 + z']
  halve#1: runtime: O(n^1) [2 + z], size: O(n^1) [1 + z]
  length#1: runtime: O(n^1) [1 + z], size: O(n^1) [z]
  drop#2: runtime: O(n^1) [2 + z'], size: O(n^1) [2 + z']
  merge#2: runtime: O(n^2) [11 + 5*z + z*z' + 12*z' + 2*z'^2], size: O(n^1) [1 + z + z']
  cond_merge_ys_zs_2: runtime: O(n^2) [43 + 10*z' + 2*z'*z4 + 32*z'' + 2*z''*z2 + 8*z''^2 + 6*z2 + 13*z4 + 2*z4^2], size: O(n^1) [2 + z' + z'' + z1 + z2 + z3 + z4]
  divide_ys#1: runtime: O(n^1) [5 + 2*z], size: O(n^1) [9 + 2*z]
  const_f#2: runtime: O(n^2) [12 + 17*z' + 3*z'^2], size: O(n^1) [z']
  dc#1: runtime: ?, size: INF
  map#2: runtime: ?, size: INF

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

(71) IntTrsBoundProof (UPPER BOUND(ID))

Computed RUNTIME bound using CoFloCo for: dc#1
after applying outer abstraction to obtain an ITS,
resulting in: INF with polynomial bound: ?

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

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

   cond_merge_ys_zs_2(z, z', z'', z1, z2, z3, z4) -{ 0 }-> 0 :|: z >= 0, z4 >= 0, z' >= 0, z3 >= 0, z'' >= 0, z1 >= 0, z2 >= 0
   cond_merge_ys_zs_2(z, z', z'', z1, z2, z3, z4) -{ 26 + 16*x5 + 4*x5*x6 + x5*z2 + 2*x5^2 + 16*x6 + x6*z2 + 2*x6^2 + 6*z2 }-> 1 + z1 + s10 :|: s10 >= 0, s10 <= 1 + x5 + x6 + z2 + 1, x5 >= 0, x8 >= 0, z' = 1 + x7 + x8, z'' = 1 + x5 + x6, z2 >= 0, z3 >= 0, z = 2, z1 >= 0, z4 >= 0, x7 >= 0, x6 >= 0
   cond_merge_ys_zs_2(z, z', z'', z1, z2, z3, z4) -{ 17 + 5*x7 + x7*z4 + 5*x8 + x8*z4 + 13*z4 + 2*z4^2 }-> 1 + z3 + s11 :|: s11 >= 0, s11 <= z4 + (1 + x7 + x8) + 1, x5 >= 0, x8 >= 0, z = 1, z' = 1 + x7 + x8, z'' = 1 + x5 + x6, z2 >= 0, z3 >= 0, z1 >= 0, z4 >= 0, x7 >= 0, x6 >= 0
   const_f#2(z, z') -{ 12 + 12*x4 + x4*x6 + 2*x4^2 + 5*x6 }-> s16 :|: s16 >= 0, s16 <= x4 + x6 + 1, x4 >= 0, z' = 1 + x6 + (1 + x4 + x2), x6 >= 0, z >= 0, x2 >= 0
   const_f#2(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   dc#1(z, z', z'', z1, z2, z3) -{ 12 + 2*x25 + 2*x33 + 2*x51 }-> const_f#2(1 + x51 + (1 + x25 + x33), map#2(1 + 0 + 0 + 0 + 0 + 0, s19)) :|: s19 >= 0, s19 <= 2 * (1 + x51 + (1 + x25 + x33)) + 9, s3 >= 0, s3 <= 0 + 1, z'' = 0, z1 = 0, x33 >= 0, z3 = 1 + x51 + (1 + x25 + x33), z2 = 0, x51 >= 0, x25 >= 0, z = 0, z' = 0
   dc#1(z, z', z'', z1, z2, z3) -{ 15 + 2*x25 + 2*x51 }-> const_f#2(1 + x51 + (1 + x25 + 1), map#2(1 + 0 + 0 + 0 + 0 + 0, s17)) :|: s17 >= 0, s17 <= 2 * (1 + x51 + (1 + x25 + 1)) + 9, s2 >= 0, s2 <= 0 + 1, z'' = 0, z3 = 1 + x51 + (1 + x25 + 1), z1 = 0, z2 = 0, x51 >= 0, x25 >= 0, z = 0, z' = 0
   dc#1(z, z', z'', z1, z2, z3) -{ 17 + s5 + 2*x25 + 2*x51 + 2*x6' + 3*x8' }-> const_f#2(1 + x51 + (1 + x25 + (1 + x6' + x8')), map#2(1 + 0 + 0 + 0 + 0 + 0, s18)) :|: s18 >= 0, s18 <= 2 * (1 + x51 + (1 + x25 + (1 + x6' + x8'))) + 9, s5 >= 0, s5 <= x8', s6 >= 0, s6 <= 1 + s5 + 1, z'' = 0, z1 = 0, z2 = 0, x51 >= 0, x25 >= 0, x6' >= 0, z3 = 1 + x51 + (1 + x25 + (1 + x6' + x8')), z = 0, x8' >= 0, z' = 0
   dc#1(z, z', z'', z1, z2, z3) -{ 1 }-> 1 :|: z'' = 0, z1 = 0, z2 = 0, z3 = 1, z = 0, z' = 0
   dc#1(z, z', z'', z1, z2, z3) -{ 0 }-> 0 :|: z >= 0, z2 >= 0, z' >= 0, z3 >= 0, z'' >= 0, z1 >= 0
   dc#1(z, z', z'', z1, z2, z3) -{ 1 }-> 1 + (z3 - 2) + 1 :|: z'' = 0, z1 = 0, z2 = 0, z3 - 2 >= 0, z = 0, z' = 0
   divide_ys#1(z, z') -{ 5 + 2*z }-> 1 + s'' + (1 + s8 + 1) :|: s8 >= 0, s8 <= z + 2, s'' >= 0, s'' <= z + 4, z' >= 0, z >= 0
   drop#2(z, z') -{ 3 + x64 }-> s9 :|: s9 >= 0, s9 <= x64 + 2, z' = 1 + x56 + x64, z - 1 >= 0, x64 >= 0, x56 >= 0
   drop#2(z, z') -{ 1 }-> z' :|: z = 0, z' >= 0
   drop#2(z, z') -{ 1 }-> 3 :|: z = 1 + 0, z' = 1
   drop#2(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   halve#1(z) -{ 1 }-> 0 :|: z = 0
   halve#1(z) -{ 0 }-> 0 :|: z >= 0
   halve#1(z) -{ 1 + z }-> 1 + s4 :|: s4 >= 0, s4 <= z - 2 + 1, z - 2 >= 0
   halve#1(z) -{ 1 }-> 1 + 0 :|: z = 1 + 0
   length#1(z) -{ 1 }-> 0 :|: z = 1
   length#1(z) -{ 0 }-> 0 :|: z >= 0
   length#1(z) -{ 2 + x8 }-> 1 + s7 :|: s7 >= 0, s7 <= x8, x8 >= 0, x6 >= 0, z = 1 + x6 + x8
   leq#2(z, z') -{ 2 + z' }-> s' :|: s' >= 0, s' <= 2, z - 1 >= 0, z' - 1 >= 0
   leq#2(z, z') -{ 1 }-> 2 :|: z = 0, z' >= 0
   leq#2(z, z') -{ 1 }-> 1 :|: z - 1 >= 0, z' = 0
   leq#2(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   main(z) -{ 1 }-> dc#1(0, 0, 0, 0, 0, z) :|: z >= 0
   map#2(z, z') -{ 1 }-> 1 :|: x4 >= 0, x8 >= 0, x6 >= 0, z = 1 + x2 + x4 + x6 + x8 + x10, z' = 1, x10 >= 0, x2 >= 0
   map#2(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   map#2(z, z') -{ 1 }-> 1 + dc#1(x6, x8, x10, x12, x14, x4) + map#2(1 + x6 + x8 + x10 + x12 + x14, x2) :|: x4 >= 0, x8 >= 0, z' = 1 + x4 + x2, x6 >= 0, x12 >= 0, x14 >= 0, x10 >= 0, x2 >= 0, z = 1 + x6 + x8 + x10 + x12 + x14
   merge#2(z, z') -{ 77 + 59*x2 + 16*x2*x4 + 4*x2*z + 10*x2^2 + 46*x4 + 2*x4*z + 8*x4^2 + 18*z }-> s12 :|: s12 >= 0, s12 <= 1 + x4 + x2 + 0 + (z - 1) + 2 + (1 + 0 + (z - 1)) + x4 + x2, x4 >= 0, z' = 1 + x4 + x2, z - 1 >= 0, x2 >= 0
   merge#2(z, z') -{ 50 + 8*x20' + 2*x20'*z' + 14*x6 + 4*x6*z' + 45*z' + 10*z'^2 }-> s13 :|: s13 >= 0, s13 <= 1 + 0 + (z' - 1) + (1 + x20') + x6 + 2 + (1 + (1 + x20') + x6) + 0 + (z' - 1), z = 1 + (1 + x20') + x6, x6 >= 0, x20' >= 0, z' - 1 >= 0
   merge#2(z, z') -{ 163 + 81*x2 + 16*x2*x2' + 2*x2*x4' + 4*x2*x6 + 10*x2^2 + 65*x2' + 2*x2'*x6 + 8*x2'^2 + 10*x4' + 20*x6 }-> s14 :|: s14 >= 0, s14 <= 1 + (1 + x2') + x2 + (1 + x4') + x6 + 2 + (1 + (1 + x4') + x6) + (1 + x2') + x2, s >= 0, s <= 2, x2' >= 0, z = 1 + (1 + x4') + x6, x6 >= 0, z' = 1 + (1 + x2') + x2, x4' >= 0, x2 >= 0
   merge#2(z, z') -{ 94 + 63*x2 + 16*x2*x4 + 4*x2*x6 + 2*x2*x8 + 10*x2^2 + 48*x4 + 2*x4*x6 + 8*x4^2 + 18*x6 + 10*x8 }-> s15 :|: s15 >= 0, s15 <= 1 + x4 + x2 + x8 + x6 + 2 + (1 + x8 + x6) + x4 + x2, x4 >= 0, x8 >= 0, z' = 1 + x4 + x2, x6 >= 0, z = 1 + x8 + x6, x2 >= 0
   merge#2(z, z') -{ 1 }-> z' :|: z = 1, z' >= 0
   merge#2(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   merge#2(z, z') -{ 1 }-> 1 + x4 + x2 :|: x4 >= 0, z = 1 + x4 + x2, z' = 1, x2 >= 0
   take#2(z, z') -{ 1 }-> 1 :|: z = 0, z' >= 0
   take#2(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   take#2(z, z') -{ 3 + x64 }-> 1 + x56 + s1 :|: s1 >= 0, s1 <= x64 + 4, z' = 1 + x56 + x64, z - 1 >= 0, x64 >= 0, x56 >= 0
   take#2(z, z') -{ 1 }-> 1 + 2 + 1 :|: z = 1 + 0, z' = 1

Function symbols to be analyzed: {dc#1,map#2}, {main}
Previous analysis results are:
  leq#2: runtime: O(n^1) [2 + z'], size: O(1) [2]
  take#2: runtime: O(n^1) [2 + z'], size: O(n^1) [4 + z']
  halve#1: runtime: O(n^1) [2 + z], size: O(n^1) [1 + z]
  length#1: runtime: O(n^1) [1 + z], size: O(n^1) [z]
  drop#2: runtime: O(n^1) [2 + z'], size: O(n^1) [2 + z']
  merge#2: runtime: O(n^2) [11 + 5*z + z*z' + 12*z' + 2*z'^2], size: O(n^1) [1 + z + z']
  cond_merge_ys_zs_2: runtime: O(n^2) [43 + 10*z' + 2*z'*z4 + 32*z'' + 2*z''*z2 + 8*z''^2 + 6*z2 + 13*z4 + 2*z4^2], size: O(n^1) [2 + z' + z'' + z1 + z2 + z3 + z4]
  divide_ys#1: runtime: O(n^1) [5 + 2*z], size: O(n^1) [9 + 2*z]
  const_f#2: runtime: O(n^2) [12 + 17*z' + 3*z'^2], size: O(n^1) [z']
  dc#1: runtime: INF, size: INF
  map#2: runtime: ?, size: INF

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

(73) CompletionProof (UPPER BOUND(ID))
The TRS is a completely defined constructor system, as every type has a constant constructor and the following rules were added:

   cond_merge_ys_zs_2(v0, v1, v2, v3, v4, v5, v6) -> null_cond_merge_ys_zs_2 [0]
   merge#2(v0, v1) -> null_merge#2 [0]
   dc#1(v0, v1, v2, v3, v4, v5) -> null_dc#1 [0]
   drop#2(v0, v1) -> null_drop#2 [0]
   take#2(v0, v1) -> null_take#2 [0]
   halve#1(v0) -> null_halve#1 [0]
   const_f#2(v0, v1) -> null_const_f#2 [0]
   leq#2(v0, v1) -> null_leq#2 [0]
   length#1(v0) -> null_length#1 [0]
   map#2(v0, v1) -> null_map#2 [0]

And the following fresh constants:    null_cond_merge_ys_zs_2, null_merge#2, null_dc#1, null_drop#2, null_take#2, null_halve#1, null_const_f#2, null_leq#2, null_length#1, null_map#2, const

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

(74)
Obligation:
Runtime Complexity Weighted TRS where all functions are completely defined. The underlying TRS is:

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

   divide_ys#1(x2, x1) -> Cons(take#2(x1, x2), Cons(drop#2(x1, x2), Nil)) [1]
   cond_merge_ys_zs_2(True, Cons(x7, x8), Cons(x5, x6), x4, x3, x2, x1) -> Cons(x4, merge#2(x3, Cons(x5, x6))) [1]
   cond_merge_ys_zs_2(False, Cons(x7, x8), Cons(x5, x6), x4, x3, x2, x1) -> Cons(x2, merge#2(Cons(x7, x8), x1)) [1]
   merge#2(Nil, x2) -> x2 [1]
   merge#2(Cons(x4, x2), Nil) -> Cons(x4, x2) [1]
   merge#2(Cons(x8, x6), Cons(x4, x2)) -> cond_merge_ys_zs_2(leq#2(x8, x4), Cons(x8, x6), Cons(x4, x2), x8, x6, x4, x2) [1]
   dc#1(map, divisible, mergesort_zs_3, divide, const_f, Nil) -> Nil [1]
   dc#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x229, Nil)) -> Cons(x229, Nil) [1]
   dc#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x51, Cons(x25, x33))) -> const_f#2(Cons(x51, Cons(x25, x33)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x51, Cons(x25, x33)), S(halve#1(length#1(x33)))))) [1]
   drop#2(0, x2) -> x2 [1]
   drop#2(S(0), Nil) -> bot[1] [1]
   drop#2(S(x10), Cons(x56, x64)) -> drop#2(x10, x64) [1]
   take#2(0, x2) -> Nil [1]
   take#2(S(0), Nil) -> Cons(bot[0], Nil) [1]
   take#2(S(x22), Cons(x56, x64)) -> Cons(x56, take#2(x22, x64)) [1]
   halve#1(0) -> 0 [1]
   halve#1(S(0)) -> S(0) [1]
   halve#1(S(S(x14))) -> S(halve#1(x14)) [1]
   const_f#2(x3, Cons(x6, Cons(x4, x2))) -> merge#2(x6, x4) [1]
   leq#2(0, x16) -> True [1]
   leq#2(S(x20), 0) -> False [1]
   leq#2(S(x4), S(x2)) -> leq#2(x4, x2) [1]
   length#1(Nil) -> 0 [1]
   length#1(Cons(x6, x8)) -> S(length#1(x8)) [1]
   map#2(dc(x2, x4, x6, x8, x10), Nil) -> Nil [1]
   map#2(dc(x6, x8, x10, x12, x14), Cons(x4, x2)) -> Cons(dc#1(x6, x8, x10, x12, x14, x4), map#2(dc(x6, x8, x10, x12, x14), x2)) [1]
   main(x113) -> dc#1(map, divisible, mergesort_zs_3, divide, const_f, x113) [1]
   cond_merge_ys_zs_2(v0, v1, v2, v3, v4, v5, v6) -> null_cond_merge_ys_zs_2 [0]
   merge#2(v0, v1) -> null_merge#2 [0]
   dc#1(v0, v1, v2, v3, v4, v5) -> null_dc#1 [0]
   drop#2(v0, v1) -> null_drop#2 [0]
   take#2(v0, v1) -> null_take#2 [0]
   halve#1(v0) -> null_halve#1 [0]
   const_f#2(v0, v1) -> null_const_f#2 [0]
   leq#2(v0, v1) -> null_leq#2 [0]
   length#1(v0) -> null_length#1 [0]
   map#2(v0, v1) -> null_map#2 [0]

The TRS has the following type information:
divide_ys#1 :: Nil:Cons:S:0:bot[1]:bot[0]:null_cond_merge_ys_zs_2:null_merge#2:null_dc#1:null_drop#2:null_take#2:null_halve#1:null_const_f#2:null_length#1:null_map#2 -> Nil:Cons:S:0:bot[1]:bot[0]:null_cond_merge_ys_zs_2:null_merge#2:null_dc#1:null_drop#2:null_take#2:null_halve#1:null_const_f#2:null_length#1:null_map#2 -> Nil:Cons:S:0:bot[1]:bot[0]:null_cond_merge_ys_zs_2:null_merge#2:null_dc#1:null_drop#2:null_take#2:null_halve#1:null_const_f#2:null_length#1:null_map#2
Cons :: Nil:Cons:S:0:bot[1]:bot[0]:null_cond_merge_ys_zs_2:null_merge#2:null_dc#1:null_drop#2:null_take#2:null_halve#1:null_const_f#2:null_length#1:null_map#2 -> Nil:Cons:S:0:bot[1]:bot[0]:null_cond_merge_ys_zs_2:null_merge#2:null_dc#1:null_drop#2:null_take#2:null_halve#1:null_const_f#2:null_length#1:null_map#2 -> Nil:Cons:S:0:bot[1]:bot[0]:null_cond_merge_ys_zs_2:null_merge#2:null_dc#1:null_drop#2:null_take#2:null_halve#1:null_const_f#2:null_length#1:null_map#2
take#2 :: Nil:Cons:S:0:bot[1]:bot[0]:null_cond_merge_ys_zs_2:null_merge#2:null_dc#1:null_drop#2:null_take#2:null_halve#1:null_const_f#2:null_length#1:null_map#2 -> Nil:Cons:S:0:bot[1]:bot[0]:null_cond_merge_ys_zs_2:null_merge#2:null_dc#1:null_drop#2:null_take#2:null_halve#1:null_const_f#2:null_length#1:null_map#2 -> Nil:Cons:S:0:bot[1]:bot[0]:null_cond_merge_ys_zs_2:null_merge#2:null_dc#1:null_drop#2:null_take#2:null_halve#1:null_const_f#2:null_length#1:null_map#2
drop#2 :: Nil:Cons:S:0:bot[1]:bot[0]:null_cond_merge_ys_zs_2:null_merge#2:null_dc#1:null_drop#2:null_take#2:null_halve#1:null_const_f#2:null_length#1:null_map#2 -> Nil:Cons:S:0:bot[1]:bot[0]:null_cond_merge_ys_zs_2:null_merge#2:null_dc#1:null_drop#2:null_take#2:null_halve#1:null_const_f#2:null_length#1:null_map#2 -> Nil:Cons:S:0:bot[1]:bot[0]:null_cond_merge_ys_zs_2:null_merge#2:null_dc#1:null_drop#2:null_take#2:null_halve#1:null_const_f#2:null_length#1:null_map#2
Nil :: Nil:Cons:S:0:bot[1]:bot[0]:null_cond_merge_ys_zs_2:null_merge#2:null_dc#1:null_drop#2:null_take#2:null_halve#1:null_const_f#2:null_length#1:null_map#2
cond_merge_ys_zs_2 :: True:False:null_leq#2 -> Nil:Cons:S:0:bot[1]:bot[0]:null_cond_merge_ys_zs_2:null_merge#2:null_dc#1:null_drop#2:null_take#2:null_halve#1:null_const_f#2:null_length#1:null_map#2 -> Nil:Cons:S:0:bot[1]:bot[0]:null_cond_merge_ys_zs_2:null_merge#2:null_dc#1:null_drop#2:null_take#2:null_halve#1:null_const_f#2:null_length#1:null_map#2 -> Nil:Cons:S:0:bot[1]:bot[0]:null_cond_merge_ys_zs_2:null_merge#2:null_dc#1:null_drop#2:null_take#2:null_halve#1:null_const_f#2:null_length#1:null_map#2 -> Nil:Cons:S:0:bot[1]:bot[0]:null_cond_merge_ys_zs_2:null_merge#2:null_dc#1:null_drop#2:null_take#2:null_halve#1:null_const_f#2:null_length#1:null_map#2 -> Nil:Cons:S:0:bot[1]:bot[0]:null_cond_merge_ys_zs_2:null_merge#2:null_dc#1:null_drop#2:null_take#2:null_halve#1:null_const_f#2:null_length#1:null_map#2 -> Nil:Cons:S:0:bot[1]:bot[0]:null_cond_merge_ys_zs_2:null_merge#2:null_dc#1:null_drop#2:null_take#2:null_halve#1:null_const_f#2:null_length#1:null_map#2 -> Nil:Cons:S:0:bot[1]:bot[0]:null_cond_merge_ys_zs_2:null_merge#2:null_dc#1:null_drop#2:null_take#2:null_halve#1:null_const_f#2:null_length#1:null_map#2
True :: True:False:null_leq#2
merge#2 :: Nil:Cons:S:0:bot[1]:bot[0]:null_cond_merge_ys_zs_2:null_merge#2:null_dc#1:null_drop#2:null_take#2:null_halve#1:null_const_f#2:null_length#1:null_map#2 -> Nil:Cons:S:0:bot[1]:bot[0]:null_cond_merge_ys_zs_2:null_merge#2:null_dc#1:null_drop#2:null_take#2:null_halve#1:null_const_f#2:null_length#1:null_map#2 -> Nil:Cons:S:0:bot[1]:bot[0]:null_cond_merge_ys_zs_2:null_merge#2:null_dc#1:null_drop#2:null_take#2:null_halve#1:null_const_f#2:null_length#1:null_map#2
False :: True:False:null_leq#2
leq#2 :: Nil:Cons:S:0:bot[1]:bot[0]:null_cond_merge_ys_zs_2:null_merge#2:null_dc#1:null_drop#2:null_take#2:null_halve#1:null_const_f#2:null_length#1:null_map#2 -> Nil:Cons:S:0:bot[1]:bot[0]:null_cond_merge_ys_zs_2:null_merge#2:null_dc#1:null_drop#2:null_take#2:null_halve#1:null_const_f#2:null_length#1:null_map#2 -> True:False:null_leq#2
dc#1 :: map -> divisible -> mergesort_zs_3 -> divide -> const_f -> Nil:Cons:S:0:bot[1]:bot[0]:null_cond_merge_ys_zs_2:null_merge#2:null_dc#1:null_drop#2:null_take#2:null_halve#1:null_const_f#2:null_length#1:null_map#2 -> Nil:Cons:S:0:bot[1]:bot[0]:null_cond_merge_ys_zs_2:null_merge#2:null_dc#1:null_drop#2:null_take#2:null_halve#1:null_const_f#2:null_length#1:null_map#2
map :: map
divisible :: divisible
mergesort_zs_3 :: mergesort_zs_3
divide :: divide
const_f :: const_f
const_f#2 :: Nil:Cons:S:0:bot[1]:bot[0]:null_cond_merge_ys_zs_2:null_merge#2:null_dc#1:null_drop#2:null_take#2:null_halve#1:null_const_f#2:null_length#1:null_map#2 -> Nil:Cons:S:0:bot[1]:bot[0]:null_cond_merge_ys_zs_2:null_merge#2:null_dc#1:null_drop#2:null_take#2:null_halve#1:null_const_f#2:null_length#1:null_map#2 -> Nil:Cons:S:0:bot[1]:bot[0]:null_cond_merge_ys_zs_2:null_merge#2:null_dc#1:null_drop#2:null_take#2:null_halve#1:null_const_f#2:null_length#1:null_map#2
map#2 :: dc -> Nil:Cons:S:0:bot[1]:bot[0]:null_cond_merge_ys_zs_2:null_merge#2:null_dc#1:null_drop#2:null_take#2:null_halve#1:null_const_f#2:null_length#1:null_map#2 -> Nil:Cons:S:0:bot[1]:bot[0]:null_cond_merge_ys_zs_2:null_merge#2:null_dc#1:null_drop#2:null_take#2:null_halve#1:null_const_f#2:null_length#1:null_map#2
dc :: map -> divisible -> mergesort_zs_3 -> divide -> const_f -> dc
S :: Nil:Cons:S:0:bot[1]:bot[0]:null_cond_merge_ys_zs_2:null_merge#2:null_dc#1:null_drop#2:null_take#2:null_halve#1:null_const_f#2:null_length#1:null_map#2 -> Nil:Cons:S:0:bot[1]:bot[0]:null_cond_merge_ys_zs_2:null_merge#2:null_dc#1:null_drop#2:null_take#2:null_halve#1:null_const_f#2:null_length#1:null_map#2
halve#1 :: Nil:Cons:S:0:bot[1]:bot[0]:null_cond_merge_ys_zs_2:null_merge#2:null_dc#1:null_drop#2:null_take#2:null_halve#1:null_const_f#2:null_length#1:null_map#2 -> Nil:Cons:S:0:bot[1]:bot[0]:null_cond_merge_ys_zs_2:null_merge#2:null_dc#1:null_drop#2:null_take#2:null_halve#1:null_const_f#2:null_length#1:null_map#2
length#1 :: Nil:Cons:S:0:bot[1]:bot[0]:null_cond_merge_ys_zs_2:null_merge#2:null_dc#1:null_drop#2:null_take#2:null_halve#1:null_const_f#2:null_length#1:null_map#2 -> Nil:Cons:S:0:bot[1]:bot[0]:null_cond_merge_ys_zs_2:null_merge#2:null_dc#1:null_drop#2:null_take#2:null_halve#1:null_const_f#2:null_length#1:null_map#2
0 :: Nil:Cons:S:0:bot[1]:bot[0]:null_cond_merge_ys_zs_2:null_merge#2:null_dc#1:null_drop#2:null_take#2:null_halve#1:null_const_f#2:null_length#1:null_map#2
bot[1] :: Nil:Cons:S:0:bot[1]:bot[0]:null_cond_merge_ys_zs_2:null_merge#2:null_dc#1:null_drop#2:null_take#2:null_halve#1:null_const_f#2:null_length#1:null_map#2
bot[0] :: Nil:Cons:S:0:bot[1]:bot[0]:null_cond_merge_ys_zs_2:null_merge#2:null_dc#1:null_drop#2:null_take#2:null_halve#1:null_const_f#2:null_length#1:null_map#2
main :: Nil:Cons:S:0:bot[1]:bot[0]:null_cond_merge_ys_zs_2:null_merge#2:null_dc#1:null_drop#2:null_take#2:null_halve#1:null_const_f#2:null_length#1:null_map#2 -> Nil:Cons:S:0:bot[1]:bot[0]:null_cond_merge_ys_zs_2:null_merge#2:null_dc#1:null_drop#2:null_take#2:null_halve#1:null_const_f#2:null_length#1:null_map#2
null_cond_merge_ys_zs_2 :: Nil:Cons:S:0:bot[1]:bot[0]:null_cond_merge_ys_zs_2:null_merge#2:null_dc#1:null_drop#2:null_take#2:null_halve#1:null_const_f#2:null_length#1:null_map#2
null_merge#2 :: Nil:Cons:S:0:bot[1]:bot[0]:null_cond_merge_ys_zs_2:null_merge#2:null_dc#1:null_drop#2:null_take#2:null_halve#1:null_const_f#2:null_length#1:null_map#2
null_dc#1 :: Nil:Cons:S:0:bot[1]:bot[0]:null_cond_merge_ys_zs_2:null_merge#2:null_dc#1:null_drop#2:null_take#2:null_halve#1:null_const_f#2:null_length#1:null_map#2
null_drop#2 :: Nil:Cons:S:0:bot[1]:bot[0]:null_cond_merge_ys_zs_2:null_merge#2:null_dc#1:null_drop#2:null_take#2:null_halve#1:null_const_f#2:null_length#1:null_map#2
null_take#2 :: Nil:Cons:S:0:bot[1]:bot[0]:null_cond_merge_ys_zs_2:null_merge#2:null_dc#1:null_drop#2:null_take#2:null_halve#1:null_const_f#2:null_length#1:null_map#2
null_halve#1 :: Nil:Cons:S:0:bot[1]:bot[0]:null_cond_merge_ys_zs_2:null_merge#2:null_dc#1:null_drop#2:null_take#2:null_halve#1:null_const_f#2:null_length#1:null_map#2
null_const_f#2 :: Nil:Cons:S:0:bot[1]:bot[0]:null_cond_merge_ys_zs_2:null_merge#2:null_dc#1:null_drop#2:null_take#2:null_halve#1:null_const_f#2:null_length#1:null_map#2
null_leq#2 :: True:False:null_leq#2
null_length#1 :: Nil:Cons:S:0:bot[1]:bot[0]:null_cond_merge_ys_zs_2:null_merge#2:null_dc#1:null_drop#2:null_take#2:null_halve#1:null_const_f#2:null_length#1:null_map#2
null_map#2 :: Nil:Cons:S:0:bot[1]:bot[0]:null_cond_merge_ys_zs_2:null_merge#2:null_dc#1:null_drop#2:null_take#2:null_halve#1:null_const_f#2:null_length#1:null_map#2
const :: dc

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

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

   Nil => 1
   True => 2
   False => 1
   map => 0
   divisible => 0
   mergesort_zs_3 => 0
   divide => 0
   const_f => 0
   0 => 0
   bot[1] => 3
   bot[0] => 2
   null_cond_merge_ys_zs_2 => 0
   null_merge#2 => 0
   null_dc#1 => 0
   null_drop#2 => 0
   null_take#2 => 0
   null_halve#1 => 0
   null_const_f#2 => 0
   null_leq#2 => 0
   null_length#1 => 0
   null_map#2 => 0
   const => 0

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

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

   cond_merge_ys_zs_2(z, z', z'', z1, z2, z3, z4) -{ 0 }-> 0 :|: z1 = v3, v0 >= 0, v6 >= 0, z'' = v2, v1 >= 0, v5 >= 0, z = v0, z' = v1, z2 = v4, v2 >= 0, v3 >= 0, z3 = v5, v4 >= 0, z4 = v6
   cond_merge_ys_zs_2(z, z', z'', z1, z2, z3, z4) -{ 1 }-> 1 + x2 + merge#2(1 + x7 + x8, x1) :|: x5 >= 0, x8 >= 0, z = 1, z' = 1 + x7 + x8, z'' = 1 + x5 + x6, x3 >= 0, x2 >= 0, z1 = x4, z2 = x3, z3 = x2, z4 = x1, x4 >= 0, x1 >= 0, x7 >= 0, x6 >= 0
   cond_merge_ys_zs_2(z, z', z'', z1, z2, z3, z4) -{ 1 }-> 1 + x4 + merge#2(x3, 1 + x5 + x6) :|: x5 >= 0, x8 >= 0, z' = 1 + x7 + x8, z'' = 1 + x5 + x6, x3 >= 0, x2 >= 0, z = 2, z1 = x4, z2 = x3, z3 = x2, z4 = x1, x4 >= 0, x1 >= 0, x7 >= 0, x6 >= 0
   const_f#2(z, z') -{ 1 }-> merge#2(x6, x4) :|: x4 >= 0, z' = 1 + x6 + (1 + x4 + x2), z = x3, x6 >= 0, x3 >= 0, x2 >= 0
   const_f#2(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1
   dc#1(z, z', z'', z1, z2, z3) -{ 1 }-> const_f#2(1 + x51 + (1 + x25 + x33), map#2(1 + 0 + 0 + 0 + 0 + 0, divide_ys#1(1 + x51 + (1 + x25 + x33), 1 + halve#1(length#1(x33))))) :|: z'' = 0, z1 = 0, x33 >= 0, z3 = 1 + x51 + (1 + x25 + x33), z2 = 0, x51 >= 0, x25 >= 0, z = 0, z' = 0
   dc#1(z, z', z'', z1, z2, z3) -{ 1 }-> 1 :|: z'' = 0, z1 = 0, z2 = 0, z3 = 1, z = 0, z' = 0
   dc#1(z, z', z'', z1, z2, z3) -{ 0 }-> 0 :|: z1 = v3, z3 = v5, v0 >= 0, v4 >= 0, z'' = v2, v1 >= 0, v5 >= 0, z = v0, z' = v1, z2 = v4, v2 >= 0, v3 >= 0
   dc#1(z, z', z'', z1, z2, z3) -{ 1 }-> 1 + x229 + 1 :|: z'' = 0, z1 = 0, z2 = 0, x229 >= 0, z = 0, z' = 0, z3 = 1 + x229 + 1
   divide_ys#1(z, z') -{ 1 }-> 1 + take#2(x1, x2) + (1 + drop#2(x1, x2) + 1) :|: x1 >= 0, z = x2, z' = x1, x2 >= 0
   drop#2(z, z') -{ 1 }-> x2 :|: z' = x2, z = 0, x2 >= 0
   drop#2(z, z') -{ 1 }-> drop#2(x10, x64) :|: z' = 1 + x56 + x64, z = 1 + x10, x10 >= 0, x64 >= 0, x56 >= 0
   drop#2(z, z') -{ 1 }-> 3 :|: z = 1 + 0, z' = 1
   drop#2(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1
   halve#1(z) -{ 1 }-> 0 :|: z = 0
   halve#1(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0
   halve#1(z) -{ 1 }-> 1 + halve#1(x14) :|: z = 1 + (1 + x14), x14 >= 0
   halve#1(z) -{ 1 }-> 1 + 0 :|: z = 1 + 0
   length#1(z) -{ 1 }-> 0 :|: z = 1
   length#1(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0
   length#1(z) -{ 1 }-> 1 + length#1(x8) :|: x8 >= 0, x6 >= 0, z = 1 + x6 + x8
   leq#2(z, z') -{ 1 }-> leq#2(x4, x2) :|: x4 >= 0, z' = 1 + x2, z = 1 + x4, x2 >= 0
   leq#2(z, z') -{ 1 }-> 2 :|: z' = x16, z = 0, x16 >= 0
   leq#2(z, z') -{ 1 }-> 1 :|: x20 >= 0, z = 1 + x20, z' = 0
   leq#2(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1
   main(z) -{ 1 }-> dc#1(0, 0, 0, 0, 0, x113) :|: z = x113, x113 >= 0
   map#2(z, z') -{ 1 }-> 1 :|: x4 >= 0, x8 >= 0, x6 >= 0, z = 1 + x2 + x4 + x6 + x8 + x10, z' = 1, x10 >= 0, x2 >= 0
   map#2(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1
   map#2(z, z') -{ 1 }-> 1 + dc#1(x6, x8, x10, x12, x14, x4) + map#2(1 + x6 + x8 + x10 + x12 + x14, x2) :|: x4 >= 0, x8 >= 0, z' = 1 + x4 + x2, x6 >= 0, x12 >= 0, x14 >= 0, x10 >= 0, x2 >= 0, z = 1 + x6 + x8 + x10 + x12 + x14
   merge#2(z, z') -{ 1 }-> x2 :|: z' = x2, z = 1, x2 >= 0
   merge#2(z, z') -{ 1 }-> cond_merge_ys_zs_2(leq#2(x8, x4), 1 + x8 + x6, 1 + x4 + x2, x8, x6, x4, x2) :|: x4 >= 0, x8 >= 0, z' = 1 + x4 + x2, x6 >= 0, z = 1 + x8 + x6, x2 >= 0
   merge#2(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1
   merge#2(z, z') -{ 1 }-> 1 + x4 + x2 :|: x4 >= 0, z = 1 + x4 + x2, z' = 1, x2 >= 0
   take#2(z, z') -{ 1 }-> 1 :|: z' = x2, z = 0, x2 >= 0
   take#2(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1
   take#2(z, z') -{ 1 }-> 1 + x56 + take#2(x22, x64) :|: z' = 1 + x56 + x64, x22 >= 0, z = 1 + x22, x64 >= 0, x56 >= 0
   take#2(z, z') -{ 1 }-> 1 + 2 + 1 :|: z = 1 + 0, z' = 1

Only complete derivations are relevant for the runtime complexity.

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

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

(78)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   divide_ys#1(z0, z1) -> Cons(take#2(z1, z0), Cons(drop#2(z1, z0), Nil))
   cond_merge_ys_zs_2(True, Cons(z0, z1), Cons(z2, z3), z4, z5, z6, z7) -> Cons(z4, merge#2(z5, Cons(z2, z3)))
   cond_merge_ys_zs_2(False, Cons(z0, z1), Cons(z2, z3), z4, z5, z6, z7) -> Cons(z6, merge#2(Cons(z0, z1), z7))
   merge#2(Nil, z0) -> z0
   merge#2(Cons(z0, z1), Nil) -> Cons(z0, z1)
   merge#2(Cons(z0, z1), Cons(z2, z3)) -> cond_merge_ys_zs_2(leq#2(z0, z2), Cons(z0, z1), Cons(z2, z3), z0, z1, z2, z3)
   dc#1(map, divisible, mergesort_zs_3, divide, const_f, Nil) -> Nil
   dc#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Nil)) -> Cons(z0, Nil)
   dc#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> const_f#2(Cons(z0, Cons(z1, z2)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2))))))
   drop#2(0, z0) -> z0
   drop#2(S(0), Nil) -> bot[1]
   drop#2(S(z0), Cons(z1, z2)) -> drop#2(z0, z2)
   take#2(0, z0) -> Nil
   take#2(S(0), Nil) -> Cons(bot[0], Nil)
   take#2(S(z0), Cons(z1, z2)) -> Cons(z1, take#2(z0, z2))
   halve#1(0) -> 0
   halve#1(S(0)) -> S(0)
   halve#1(S(S(z0))) -> S(halve#1(z0))
   const_f#2(z0, Cons(z1, Cons(z2, z3))) -> merge#2(z1, z2)
   leq#2(0, z0) -> True
   leq#2(S(z0), 0) -> False
   leq#2(S(z0), S(z1)) -> leq#2(z0, z1)
   length#1(Nil) -> 0
   length#1(Cons(z0, z1)) -> S(length#1(z1))
   map#2(dc(z0, z1, z2, z3, z4), Nil) -> Nil
   map#2(dc(z0, z1, z2, z3, z4), Cons(z5, z6)) -> Cons(dc#1(z0, z1, z2, z3, z4, z5), map#2(dc(z0, z1, z2, z3, z4), z6))
   main(z0) -> dc#1(map, divisible, mergesort_zs_3, divide, const_f, z0)
Tuples:
   DIVIDE_YS#1(z0, z1) -> c(TAKE#2(z1, z0))
   DIVIDE_YS#1(z0, z1) -> c1(DROP#2(z1, z0))
   COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(z2, z3), z4, z5, z6, z7) -> c2(MERGE#2(z5, Cons(z2, z3)))
   COND_MERGE_YS_ZS_2(False, Cons(z0, z1), Cons(z2, z3), z4, z5, z6, z7) -> c3(MERGE#2(Cons(z0, z1), z7))
   MERGE#2(Nil, z0) -> c4
   MERGE#2(Cons(z0, z1), Nil) -> c5
   MERGE#2(Cons(z0, z1), Cons(z2, z3)) -> c6(COND_MERGE_YS_ZS_2(leq#2(z0, z2), Cons(z0, z1), Cons(z2, z3), z0, z1, z2, z3), LEQ#2(z0, z2))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Nil) -> c7
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Nil)) -> c8
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> c9(CONST_F#2(Cons(z0, Cons(z1, z2)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2)))))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2))))), DIVIDE_YS#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2)))), HALVE#1(length#1(z2)), LENGTH#1(z2))
   DROP#2(0, z0) -> c10
   DROP#2(S(0), Nil) -> c11
   DROP#2(S(z0), Cons(z1, z2)) -> c12(DROP#2(z0, z2))
   TAKE#2(0, z0) -> c13
   TAKE#2(S(0), Nil) -> c14
   TAKE#2(S(z0), Cons(z1, z2)) -> c15(TAKE#2(z0, z2))
   HALVE#1(0) -> c16
   HALVE#1(S(0)) -> c17
   HALVE#1(S(S(z0))) -> c18(HALVE#1(z0))
   CONST_F#2(z0, Cons(z1, Cons(z2, z3))) -> c19(MERGE#2(z1, z2))
   LEQ#2(0, z0) -> c20
   LEQ#2(S(z0), 0) -> c21
   LEQ#2(S(z0), S(z1)) -> c22(LEQ#2(z0, z1))
   LENGTH#1(Nil) -> c23
   LENGTH#1(Cons(z0, z1)) -> c24(LENGTH#1(z1))
   MAP#2(dc(z0, z1, z2, z3, z4), Nil) -> c25
   MAP#2(dc(z0, z1, z2, z3, z4), Cons(z5, z6)) -> c26(DC#1(z0, z1, z2, z3, z4, z5))
   MAP#2(dc(z0, z1, z2, z3, z4), Cons(z5, z6)) -> c27(MAP#2(dc(z0, z1, z2, z3, z4), z6))
   MAIN(z0) -> c28(DC#1(map, divisible, mergesort_zs_3, divide, const_f, z0))
S tuples:
   DIVIDE_YS#1(z0, z1) -> c(TAKE#2(z1, z0))
   DIVIDE_YS#1(z0, z1) -> c1(DROP#2(z1, z0))
   COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(z2, z3), z4, z5, z6, z7) -> c2(MERGE#2(z5, Cons(z2, z3)))
   COND_MERGE_YS_ZS_2(False, Cons(z0, z1), Cons(z2, z3), z4, z5, z6, z7) -> c3(MERGE#2(Cons(z0, z1), z7))
   MERGE#2(Nil, z0) -> c4
   MERGE#2(Cons(z0, z1), Nil) -> c5
   MERGE#2(Cons(z0, z1), Cons(z2, z3)) -> c6(COND_MERGE_YS_ZS_2(leq#2(z0, z2), Cons(z0, z1), Cons(z2, z3), z0, z1, z2, z3), LEQ#2(z0, z2))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Nil) -> c7
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Nil)) -> c8
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> c9(CONST_F#2(Cons(z0, Cons(z1, z2)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2)))))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2))))), DIVIDE_YS#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2)))), HALVE#1(length#1(z2)), LENGTH#1(z2))
   DROP#2(0, z0) -> c10
   DROP#2(S(0), Nil) -> c11
   DROP#2(S(z0), Cons(z1, z2)) -> c12(DROP#2(z0, z2))
   TAKE#2(0, z0) -> c13
   TAKE#2(S(0), Nil) -> c14
   TAKE#2(S(z0), Cons(z1, z2)) -> c15(TAKE#2(z0, z2))
   HALVE#1(0) -> c16
   HALVE#1(S(0)) -> c17
   HALVE#1(S(S(z0))) -> c18(HALVE#1(z0))
   CONST_F#2(z0, Cons(z1, Cons(z2, z3))) -> c19(MERGE#2(z1, z2))
   LEQ#2(0, z0) -> c20
   LEQ#2(S(z0), 0) -> c21
   LEQ#2(S(z0), S(z1)) -> c22(LEQ#2(z0, z1))
   LENGTH#1(Nil) -> c23
   LENGTH#1(Cons(z0, z1)) -> c24(LENGTH#1(z1))
   MAP#2(dc(z0, z1, z2, z3, z4), Nil) -> c25
   MAP#2(dc(z0, z1, z2, z3, z4), Cons(z5, z6)) -> c26(DC#1(z0, z1, z2, z3, z4, z5))
   MAP#2(dc(z0, z1, z2, z3, z4), Cons(z5, z6)) -> c27(MAP#2(dc(z0, z1, z2, z3, z4), z6))
   MAIN(z0) -> c28(DC#1(map, divisible, mergesort_zs_3, divide, const_f, z0))
K tuples:none
Defined Rule Symbols:   divide_ys#1_2, cond_merge_ys_zs_2_7, merge#2_2, dc#1_6, drop#2_2, take#2_2, halve#1_1, const_f#2_2, leq#2_2, length#1_1, map#2_2, main_1

Defined Pair Symbols:   DIVIDE_YS#1_2, COND_MERGE_YS_ZS_2_7, MERGE#2_2, DC#1_6, DROP#2_2, TAKE#2_2, HALVE#1_1, CONST_F#2_2, LEQ#2_2, LENGTH#1_1, MAP#2_2, MAIN_1

Compound Symbols:   c_1, c1_1, c2_1, c3_1, c4, c5, c6_2, c7, c8, c9_5, c10, c11, c12_1, c13, c14, c15_1, c16, c17, c18_1, c19_1, c20, c21, c22_1, c23, c24_1, c25, c26_1, c27_1, c28_1


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

(79) CdtLeafRemovalProof (ComplexityIfPolyImplication)
Removed 1 leading nodes:
   MAIN(z0) -> c28(DC#1(map, divisible, mergesort_zs_3, divide, const_f, z0))
Removed 14 trailing nodes:
   MAP#2(dc(z0, z1, z2, z3, z4), Nil) -> c25
   MERGE#2(Cons(z0, z1), Nil) -> c5
   LEQ#2(S(z0), 0) -> c21
   TAKE#2(0, z0) -> c13
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Nil)) -> c8
   LENGTH#1(Nil) -> c23
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Nil) -> c7
   TAKE#2(S(0), Nil) -> c14
   HALVE#1(0) -> c16
   HALVE#1(S(0)) -> c17
   MERGE#2(Nil, z0) -> c4
   LEQ#2(0, z0) -> c20
   DROP#2(S(0), Nil) -> c11
   DROP#2(0, z0) -> c10

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

(80)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   divide_ys#1(z0, z1) -> Cons(take#2(z1, z0), Cons(drop#2(z1, z0), Nil))
   cond_merge_ys_zs_2(True, Cons(z0, z1), Cons(z2, z3), z4, z5, z6, z7) -> Cons(z4, merge#2(z5, Cons(z2, z3)))
   cond_merge_ys_zs_2(False, Cons(z0, z1), Cons(z2, z3), z4, z5, z6, z7) -> Cons(z6, merge#2(Cons(z0, z1), z7))
   merge#2(Nil, z0) -> z0
   merge#2(Cons(z0, z1), Nil) -> Cons(z0, z1)
   merge#2(Cons(z0, z1), Cons(z2, z3)) -> cond_merge_ys_zs_2(leq#2(z0, z2), Cons(z0, z1), Cons(z2, z3), z0, z1, z2, z3)
   dc#1(map, divisible, mergesort_zs_3, divide, const_f, Nil) -> Nil
   dc#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Nil)) -> Cons(z0, Nil)
   dc#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> const_f#2(Cons(z0, Cons(z1, z2)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2))))))
   drop#2(0, z0) -> z0
   drop#2(S(0), Nil) -> bot[1]
   drop#2(S(z0), Cons(z1, z2)) -> drop#2(z0, z2)
   take#2(0, z0) -> Nil
   take#2(S(0), Nil) -> Cons(bot[0], Nil)
   take#2(S(z0), Cons(z1, z2)) -> Cons(z1, take#2(z0, z2))
   halve#1(0) -> 0
   halve#1(S(0)) -> S(0)
   halve#1(S(S(z0))) -> S(halve#1(z0))
   const_f#2(z0, Cons(z1, Cons(z2, z3))) -> merge#2(z1, z2)
   leq#2(0, z0) -> True
   leq#2(S(z0), 0) -> False
   leq#2(S(z0), S(z1)) -> leq#2(z0, z1)
   length#1(Nil) -> 0
   length#1(Cons(z0, z1)) -> S(length#1(z1))
   map#2(dc(z0, z1, z2, z3, z4), Nil) -> Nil
   map#2(dc(z0, z1, z2, z3, z4), Cons(z5, z6)) -> Cons(dc#1(z0, z1, z2, z3, z4, z5), map#2(dc(z0, z1, z2, z3, z4), z6))
   main(z0) -> dc#1(map, divisible, mergesort_zs_3, divide, const_f, z0)
Tuples:
   DIVIDE_YS#1(z0, z1) -> c(TAKE#2(z1, z0))
   DIVIDE_YS#1(z0, z1) -> c1(DROP#2(z1, z0))
   COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(z2, z3), z4, z5, z6, z7) -> c2(MERGE#2(z5, Cons(z2, z3)))
   COND_MERGE_YS_ZS_2(False, Cons(z0, z1), Cons(z2, z3), z4, z5, z6, z7) -> c3(MERGE#2(Cons(z0, z1), z7))
   MERGE#2(Cons(z0, z1), Cons(z2, z3)) -> c6(COND_MERGE_YS_ZS_2(leq#2(z0, z2), Cons(z0, z1), Cons(z2, z3), z0, z1, z2, z3), LEQ#2(z0, z2))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> c9(CONST_F#2(Cons(z0, Cons(z1, z2)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2)))))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2))))), DIVIDE_YS#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2)))), HALVE#1(length#1(z2)), LENGTH#1(z2))
   DROP#2(S(z0), Cons(z1, z2)) -> c12(DROP#2(z0, z2))
   TAKE#2(S(z0), Cons(z1, z2)) -> c15(TAKE#2(z0, z2))
   HALVE#1(S(S(z0))) -> c18(HALVE#1(z0))
   CONST_F#2(z0, Cons(z1, Cons(z2, z3))) -> c19(MERGE#2(z1, z2))
   LEQ#2(S(z0), S(z1)) -> c22(LEQ#2(z0, z1))
   LENGTH#1(Cons(z0, z1)) -> c24(LENGTH#1(z1))
   MAP#2(dc(z0, z1, z2, z3, z4), Cons(z5, z6)) -> c26(DC#1(z0, z1, z2, z3, z4, z5))
   MAP#2(dc(z0, z1, z2, z3, z4), Cons(z5, z6)) -> c27(MAP#2(dc(z0, z1, z2, z3, z4), z6))
S tuples:
   DIVIDE_YS#1(z0, z1) -> c(TAKE#2(z1, z0))
   DIVIDE_YS#1(z0, z1) -> c1(DROP#2(z1, z0))
   COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(z2, z3), z4, z5, z6, z7) -> c2(MERGE#2(z5, Cons(z2, z3)))
   COND_MERGE_YS_ZS_2(False, Cons(z0, z1), Cons(z2, z3), z4, z5, z6, z7) -> c3(MERGE#2(Cons(z0, z1), z7))
   MERGE#2(Cons(z0, z1), Cons(z2, z3)) -> c6(COND_MERGE_YS_ZS_2(leq#2(z0, z2), Cons(z0, z1), Cons(z2, z3), z0, z1, z2, z3), LEQ#2(z0, z2))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> c9(CONST_F#2(Cons(z0, Cons(z1, z2)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2)))))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2))))), DIVIDE_YS#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2)))), HALVE#1(length#1(z2)), LENGTH#1(z2))
   DROP#2(S(z0), Cons(z1, z2)) -> c12(DROP#2(z0, z2))
   TAKE#2(S(z0), Cons(z1, z2)) -> c15(TAKE#2(z0, z2))
   HALVE#1(S(S(z0))) -> c18(HALVE#1(z0))
   CONST_F#2(z0, Cons(z1, Cons(z2, z3))) -> c19(MERGE#2(z1, z2))
   LEQ#2(S(z0), S(z1)) -> c22(LEQ#2(z0, z1))
   LENGTH#1(Cons(z0, z1)) -> c24(LENGTH#1(z1))
   MAP#2(dc(z0, z1, z2, z3, z4), Cons(z5, z6)) -> c26(DC#1(z0, z1, z2, z3, z4, z5))
   MAP#2(dc(z0, z1, z2, z3, z4), Cons(z5, z6)) -> c27(MAP#2(dc(z0, z1, z2, z3, z4), z6))
K tuples:none
Defined Rule Symbols:   divide_ys#1_2, cond_merge_ys_zs_2_7, merge#2_2, dc#1_6, drop#2_2, take#2_2, halve#1_1, const_f#2_2, leq#2_2, length#1_1, map#2_2, main_1

Defined Pair Symbols:   DIVIDE_YS#1_2, COND_MERGE_YS_ZS_2_7, MERGE#2_2, DC#1_6, DROP#2_2, TAKE#2_2, HALVE#1_1, CONST_F#2_2, LEQ#2_2, LENGTH#1_1, MAP#2_2

Compound Symbols:   c_1, c1_1, c2_1, c3_1, c6_2, c9_5, c12_1, c15_1, c18_1, c19_1, c22_1, c24_1, c26_1, c27_1


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

(81) CdtUsableRulesProof (BOTH BOUNDS(ID, ID))
The following rules are not usable and were removed:
   main(z0) -> dc#1(map, divisible, mergesort_zs_3, divide, const_f, z0)

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

(82)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   leq#2(0, z0) -> True
   leq#2(S(z0), 0) -> False
   leq#2(S(z0), S(z1)) -> leq#2(z0, z1)
   map#2(dc(z0, z1, z2, z3, z4), Nil) -> Nil
   map#2(dc(z0, z1, z2, z3, z4), Cons(z5, z6)) -> Cons(dc#1(z0, z1, z2, z3, z4, z5), map#2(dc(z0, z1, z2, z3, z4), z6))
   divide_ys#1(z0, z1) -> Cons(take#2(z1, z0), Cons(drop#2(z1, z0), Nil))
   halve#1(0) -> 0
   halve#1(S(0)) -> S(0)
   halve#1(S(S(z0))) -> S(halve#1(z0))
   length#1(Nil) -> 0
   length#1(Cons(z0, z1)) -> S(length#1(z1))
   take#2(0, z0) -> Nil
   take#2(S(0), Nil) -> Cons(bot[0], Nil)
   take#2(S(z0), Cons(z1, z2)) -> Cons(z1, take#2(z0, z2))
   drop#2(0, z0) -> z0
   drop#2(S(0), Nil) -> bot[1]
   drop#2(S(z0), Cons(z1, z2)) -> drop#2(z0, z2)
   dc#1(map, divisible, mergesort_zs_3, divide, const_f, Nil) -> Nil
   dc#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Nil)) -> Cons(z0, Nil)
   dc#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> const_f#2(Cons(z0, Cons(z1, z2)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2))))))
   const_f#2(z0, Cons(z1, Cons(z2, z3))) -> merge#2(z1, z2)
   merge#2(Nil, z0) -> z0
   merge#2(Cons(z0, z1), Nil) -> Cons(z0, z1)
   merge#2(Cons(z0, z1), Cons(z2, z3)) -> cond_merge_ys_zs_2(leq#2(z0, z2), Cons(z0, z1), Cons(z2, z3), z0, z1, z2, z3)
   cond_merge_ys_zs_2(True, Cons(z0, z1), Cons(z2, z3), z4, z5, z6, z7) -> Cons(z4, merge#2(z5, Cons(z2, z3)))
   cond_merge_ys_zs_2(False, Cons(z0, z1), Cons(z2, z3), z4, z5, z6, z7) -> Cons(z6, merge#2(Cons(z0, z1), z7))
Tuples:
   DIVIDE_YS#1(z0, z1) -> c(TAKE#2(z1, z0))
   DIVIDE_YS#1(z0, z1) -> c1(DROP#2(z1, z0))
   COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(z2, z3), z4, z5, z6, z7) -> c2(MERGE#2(z5, Cons(z2, z3)))
   COND_MERGE_YS_ZS_2(False, Cons(z0, z1), Cons(z2, z3), z4, z5, z6, z7) -> c3(MERGE#2(Cons(z0, z1), z7))
   MERGE#2(Cons(z0, z1), Cons(z2, z3)) -> c6(COND_MERGE_YS_ZS_2(leq#2(z0, z2), Cons(z0, z1), Cons(z2, z3), z0, z1, z2, z3), LEQ#2(z0, z2))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> c9(CONST_F#2(Cons(z0, Cons(z1, z2)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2)))))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2))))), DIVIDE_YS#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2)))), HALVE#1(length#1(z2)), LENGTH#1(z2))
   DROP#2(S(z0), Cons(z1, z2)) -> c12(DROP#2(z0, z2))
   TAKE#2(S(z0), Cons(z1, z2)) -> c15(TAKE#2(z0, z2))
   HALVE#1(S(S(z0))) -> c18(HALVE#1(z0))
   CONST_F#2(z0, Cons(z1, Cons(z2, z3))) -> c19(MERGE#2(z1, z2))
   LEQ#2(S(z0), S(z1)) -> c22(LEQ#2(z0, z1))
   LENGTH#1(Cons(z0, z1)) -> c24(LENGTH#1(z1))
   MAP#2(dc(z0, z1, z2, z3, z4), Cons(z5, z6)) -> c26(DC#1(z0, z1, z2, z3, z4, z5))
   MAP#2(dc(z0, z1, z2, z3, z4), Cons(z5, z6)) -> c27(MAP#2(dc(z0, z1, z2, z3, z4), z6))
S tuples:
   DIVIDE_YS#1(z0, z1) -> c(TAKE#2(z1, z0))
   DIVIDE_YS#1(z0, z1) -> c1(DROP#2(z1, z0))
   COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(z2, z3), z4, z5, z6, z7) -> c2(MERGE#2(z5, Cons(z2, z3)))
   COND_MERGE_YS_ZS_2(False, Cons(z0, z1), Cons(z2, z3), z4, z5, z6, z7) -> c3(MERGE#2(Cons(z0, z1), z7))
   MERGE#2(Cons(z0, z1), Cons(z2, z3)) -> c6(COND_MERGE_YS_ZS_2(leq#2(z0, z2), Cons(z0, z1), Cons(z2, z3), z0, z1, z2, z3), LEQ#2(z0, z2))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> c9(CONST_F#2(Cons(z0, Cons(z1, z2)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2)))))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2))))), DIVIDE_YS#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2)))), HALVE#1(length#1(z2)), LENGTH#1(z2))
   DROP#2(S(z0), Cons(z1, z2)) -> c12(DROP#2(z0, z2))
   TAKE#2(S(z0), Cons(z1, z2)) -> c15(TAKE#2(z0, z2))
   HALVE#1(S(S(z0))) -> c18(HALVE#1(z0))
   CONST_F#2(z0, Cons(z1, Cons(z2, z3))) -> c19(MERGE#2(z1, z2))
   LEQ#2(S(z0), S(z1)) -> c22(LEQ#2(z0, z1))
   LENGTH#1(Cons(z0, z1)) -> c24(LENGTH#1(z1))
   MAP#2(dc(z0, z1, z2, z3, z4), Cons(z5, z6)) -> c26(DC#1(z0, z1, z2, z3, z4, z5))
   MAP#2(dc(z0, z1, z2, z3, z4), Cons(z5, z6)) -> c27(MAP#2(dc(z0, z1, z2, z3, z4), z6))
K tuples:none
Defined Rule Symbols:   leq#2_2, map#2_2, divide_ys#1_2, halve#1_1, length#1_1, take#2_2, drop#2_2, dc#1_6, const_f#2_2, merge#2_2, cond_merge_ys_zs_2_7

Defined Pair Symbols:   DIVIDE_YS#1_2, COND_MERGE_YS_ZS_2_7, MERGE#2_2, DC#1_6, DROP#2_2, TAKE#2_2, HALVE#1_1, CONST_F#2_2, LEQ#2_2, LENGTH#1_1, MAP#2_2

Compound Symbols:   c_1, c1_1, c2_1, c3_1, c6_2, c9_5, c12_1, c15_1, c18_1, c19_1, c22_1, c24_1, c26_1, c27_1


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

(83) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace MERGE#2(Cons(z0, z1), Cons(z2, z3)) -> c6(COND_MERGE_YS_ZS_2(leq#2(z0, z2), Cons(z0, z1), Cons(z2, z3), z0, z1, z2, z3), LEQ#2(z0, z2)) by 
   MERGE#2(Cons(0, x1), Cons(z0, x3)) -> c6(COND_MERGE_YS_ZS_2(True, Cons(0, x1), Cons(z0, x3), 0, x1, z0, x3), LEQ#2(0, z0))
   MERGE#2(Cons(S(z0), x1), Cons(0, x3)) -> c6(COND_MERGE_YS_ZS_2(False, Cons(S(z0), x1), Cons(0, x3), S(z0), x1, 0, x3), LEQ#2(S(z0), 0))
   MERGE#2(Cons(S(z0), x1), Cons(S(z1), x3)) -> c6(COND_MERGE_YS_ZS_2(leq#2(z0, z1), Cons(S(z0), x1), Cons(S(z1), x3), S(z0), x1, S(z1), x3), LEQ#2(S(z0), S(z1)))

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

(84)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   leq#2(0, z0) -> True
   leq#2(S(z0), 0) -> False
   leq#2(S(z0), S(z1)) -> leq#2(z0, z1)
   map#2(dc(z0, z1, z2, z3, z4), Nil) -> Nil
   map#2(dc(z0, z1, z2, z3, z4), Cons(z5, z6)) -> Cons(dc#1(z0, z1, z2, z3, z4, z5), map#2(dc(z0, z1, z2, z3, z4), z6))
   divide_ys#1(z0, z1) -> Cons(take#2(z1, z0), Cons(drop#2(z1, z0), Nil))
   halve#1(0) -> 0
   halve#1(S(0)) -> S(0)
   halve#1(S(S(z0))) -> S(halve#1(z0))
   length#1(Nil) -> 0
   length#1(Cons(z0, z1)) -> S(length#1(z1))
   take#2(0, z0) -> Nil
   take#2(S(0), Nil) -> Cons(bot[0], Nil)
   take#2(S(z0), Cons(z1, z2)) -> Cons(z1, take#2(z0, z2))
   drop#2(0, z0) -> z0
   drop#2(S(0), Nil) -> bot[1]
   drop#2(S(z0), Cons(z1, z2)) -> drop#2(z0, z2)
   dc#1(map, divisible, mergesort_zs_3, divide, const_f, Nil) -> Nil
   dc#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Nil)) -> Cons(z0, Nil)
   dc#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> const_f#2(Cons(z0, Cons(z1, z2)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2))))))
   const_f#2(z0, Cons(z1, Cons(z2, z3))) -> merge#2(z1, z2)
   merge#2(Nil, z0) -> z0
   merge#2(Cons(z0, z1), Nil) -> Cons(z0, z1)
   merge#2(Cons(z0, z1), Cons(z2, z3)) -> cond_merge_ys_zs_2(leq#2(z0, z2), Cons(z0, z1), Cons(z2, z3), z0, z1, z2, z3)
   cond_merge_ys_zs_2(True, Cons(z0, z1), Cons(z2, z3), z4, z5, z6, z7) -> Cons(z4, merge#2(z5, Cons(z2, z3)))
   cond_merge_ys_zs_2(False, Cons(z0, z1), Cons(z2, z3), z4, z5, z6, z7) -> Cons(z6, merge#2(Cons(z0, z1), z7))
Tuples:
   DIVIDE_YS#1(z0, z1) -> c(TAKE#2(z1, z0))
   DIVIDE_YS#1(z0, z1) -> c1(DROP#2(z1, z0))
   COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(z2, z3), z4, z5, z6, z7) -> c2(MERGE#2(z5, Cons(z2, z3)))
   COND_MERGE_YS_ZS_2(False, Cons(z0, z1), Cons(z2, z3), z4, z5, z6, z7) -> c3(MERGE#2(Cons(z0, z1), z7))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> c9(CONST_F#2(Cons(z0, Cons(z1, z2)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2)))))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2))))), DIVIDE_YS#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2)))), HALVE#1(length#1(z2)), LENGTH#1(z2))
   DROP#2(S(z0), Cons(z1, z2)) -> c12(DROP#2(z0, z2))
   TAKE#2(S(z0), Cons(z1, z2)) -> c15(TAKE#2(z0, z2))
   HALVE#1(S(S(z0))) -> c18(HALVE#1(z0))
   CONST_F#2(z0, Cons(z1, Cons(z2, z3))) -> c19(MERGE#2(z1, z2))
   LEQ#2(S(z0), S(z1)) -> c22(LEQ#2(z0, z1))
   LENGTH#1(Cons(z0, z1)) -> c24(LENGTH#1(z1))
   MAP#2(dc(z0, z1, z2, z3, z4), Cons(z5, z6)) -> c26(DC#1(z0, z1, z2, z3, z4, z5))
   MAP#2(dc(z0, z1, z2, z3, z4), Cons(z5, z6)) -> c27(MAP#2(dc(z0, z1, z2, z3, z4), z6))
   MERGE#2(Cons(0, x1), Cons(z0, x3)) -> c6(COND_MERGE_YS_ZS_2(True, Cons(0, x1), Cons(z0, x3), 0, x1, z0, x3), LEQ#2(0, z0))
   MERGE#2(Cons(S(z0), x1), Cons(0, x3)) -> c6(COND_MERGE_YS_ZS_2(False, Cons(S(z0), x1), Cons(0, x3), S(z0), x1, 0, x3), LEQ#2(S(z0), 0))
   MERGE#2(Cons(S(z0), x1), Cons(S(z1), x3)) -> c6(COND_MERGE_YS_ZS_2(leq#2(z0, z1), Cons(S(z0), x1), Cons(S(z1), x3), S(z0), x1, S(z1), x3), LEQ#2(S(z0), S(z1)))
S tuples:
   DIVIDE_YS#1(z0, z1) -> c(TAKE#2(z1, z0))
   DIVIDE_YS#1(z0, z1) -> c1(DROP#2(z1, z0))
   COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(z2, z3), z4, z5, z6, z7) -> c2(MERGE#2(z5, Cons(z2, z3)))
   COND_MERGE_YS_ZS_2(False, Cons(z0, z1), Cons(z2, z3), z4, z5, z6, z7) -> c3(MERGE#2(Cons(z0, z1), z7))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> c9(CONST_F#2(Cons(z0, Cons(z1, z2)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2)))))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2))))), DIVIDE_YS#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2)))), HALVE#1(length#1(z2)), LENGTH#1(z2))
   DROP#2(S(z0), Cons(z1, z2)) -> c12(DROP#2(z0, z2))
   TAKE#2(S(z0), Cons(z1, z2)) -> c15(TAKE#2(z0, z2))
   HALVE#1(S(S(z0))) -> c18(HALVE#1(z0))
   CONST_F#2(z0, Cons(z1, Cons(z2, z3))) -> c19(MERGE#2(z1, z2))
   LEQ#2(S(z0), S(z1)) -> c22(LEQ#2(z0, z1))
   LENGTH#1(Cons(z0, z1)) -> c24(LENGTH#1(z1))
   MAP#2(dc(z0, z1, z2, z3, z4), Cons(z5, z6)) -> c26(DC#1(z0, z1, z2, z3, z4, z5))
   MAP#2(dc(z0, z1, z2, z3, z4), Cons(z5, z6)) -> c27(MAP#2(dc(z0, z1, z2, z3, z4), z6))
   MERGE#2(Cons(0, x1), Cons(z0, x3)) -> c6(COND_MERGE_YS_ZS_2(True, Cons(0, x1), Cons(z0, x3), 0, x1, z0, x3), LEQ#2(0, z0))
   MERGE#2(Cons(S(z0), x1), Cons(0, x3)) -> c6(COND_MERGE_YS_ZS_2(False, Cons(S(z0), x1), Cons(0, x3), S(z0), x1, 0, x3), LEQ#2(S(z0), 0))
   MERGE#2(Cons(S(z0), x1), Cons(S(z1), x3)) -> c6(COND_MERGE_YS_ZS_2(leq#2(z0, z1), Cons(S(z0), x1), Cons(S(z1), x3), S(z0), x1, S(z1), x3), LEQ#2(S(z0), S(z1)))
K tuples:none
Defined Rule Symbols:   leq#2_2, map#2_2, divide_ys#1_2, halve#1_1, length#1_1, take#2_2, drop#2_2, dc#1_6, const_f#2_2, merge#2_2, cond_merge_ys_zs_2_7

Defined Pair Symbols:   DIVIDE_YS#1_2, COND_MERGE_YS_ZS_2_7, DC#1_6, DROP#2_2, TAKE#2_2, HALVE#1_1, CONST_F#2_2, LEQ#2_2, LENGTH#1_1, MAP#2_2, MERGE#2_2

Compound Symbols:   c_1, c1_1, c2_1, c3_1, c9_5, c12_1, c15_1, c18_1, c19_1, c22_1, c24_1, c26_1, c27_1, c6_2


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

(85) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID))
Removed 2 trailing tuple parts
----------------------------------------

(86)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   leq#2(0, z0) -> True
   leq#2(S(z0), 0) -> False
   leq#2(S(z0), S(z1)) -> leq#2(z0, z1)
   map#2(dc(z0, z1, z2, z3, z4), Nil) -> Nil
   map#2(dc(z0, z1, z2, z3, z4), Cons(z5, z6)) -> Cons(dc#1(z0, z1, z2, z3, z4, z5), map#2(dc(z0, z1, z2, z3, z4), z6))
   divide_ys#1(z0, z1) -> Cons(take#2(z1, z0), Cons(drop#2(z1, z0), Nil))
   halve#1(0) -> 0
   halve#1(S(0)) -> S(0)
   halve#1(S(S(z0))) -> S(halve#1(z0))
   length#1(Nil) -> 0
   length#1(Cons(z0, z1)) -> S(length#1(z1))
   take#2(0, z0) -> Nil
   take#2(S(0), Nil) -> Cons(bot[0], Nil)
   take#2(S(z0), Cons(z1, z2)) -> Cons(z1, take#2(z0, z2))
   drop#2(0, z0) -> z0
   drop#2(S(0), Nil) -> bot[1]
   drop#2(S(z0), Cons(z1, z2)) -> drop#2(z0, z2)
   dc#1(map, divisible, mergesort_zs_3, divide, const_f, Nil) -> Nil
   dc#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Nil)) -> Cons(z0, Nil)
   dc#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> const_f#2(Cons(z0, Cons(z1, z2)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2))))))
   const_f#2(z0, Cons(z1, Cons(z2, z3))) -> merge#2(z1, z2)
   merge#2(Nil, z0) -> z0
   merge#2(Cons(z0, z1), Nil) -> Cons(z0, z1)
   merge#2(Cons(z0, z1), Cons(z2, z3)) -> cond_merge_ys_zs_2(leq#2(z0, z2), Cons(z0, z1), Cons(z2, z3), z0, z1, z2, z3)
   cond_merge_ys_zs_2(True, Cons(z0, z1), Cons(z2, z3), z4, z5, z6, z7) -> Cons(z4, merge#2(z5, Cons(z2, z3)))
   cond_merge_ys_zs_2(False, Cons(z0, z1), Cons(z2, z3), z4, z5, z6, z7) -> Cons(z6, merge#2(Cons(z0, z1), z7))
Tuples:
   DIVIDE_YS#1(z0, z1) -> c(TAKE#2(z1, z0))
   DIVIDE_YS#1(z0, z1) -> c1(DROP#2(z1, z0))
   COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(z2, z3), z4, z5, z6, z7) -> c2(MERGE#2(z5, Cons(z2, z3)))
   COND_MERGE_YS_ZS_2(False, Cons(z0, z1), Cons(z2, z3), z4, z5, z6, z7) -> c3(MERGE#2(Cons(z0, z1), z7))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> c9(CONST_F#2(Cons(z0, Cons(z1, z2)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2)))))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2))))), DIVIDE_YS#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2)))), HALVE#1(length#1(z2)), LENGTH#1(z2))
   DROP#2(S(z0), Cons(z1, z2)) -> c12(DROP#2(z0, z2))
   TAKE#2(S(z0), Cons(z1, z2)) -> c15(TAKE#2(z0, z2))
   HALVE#1(S(S(z0))) -> c18(HALVE#1(z0))
   CONST_F#2(z0, Cons(z1, Cons(z2, z3))) -> c19(MERGE#2(z1, z2))
   LEQ#2(S(z0), S(z1)) -> c22(LEQ#2(z0, z1))
   LENGTH#1(Cons(z0, z1)) -> c24(LENGTH#1(z1))
   MAP#2(dc(z0, z1, z2, z3, z4), Cons(z5, z6)) -> c26(DC#1(z0, z1, z2, z3, z4, z5))
   MAP#2(dc(z0, z1, z2, z3, z4), Cons(z5, z6)) -> c27(MAP#2(dc(z0, z1, z2, z3, z4), z6))
   MERGE#2(Cons(S(z0), x1), Cons(S(z1), x3)) -> c6(COND_MERGE_YS_ZS_2(leq#2(z0, z1), Cons(S(z0), x1), Cons(S(z1), x3), S(z0), x1, S(z1), x3), LEQ#2(S(z0), S(z1)))
   MERGE#2(Cons(0, x1), Cons(z0, x3)) -> c6(COND_MERGE_YS_ZS_2(True, Cons(0, x1), Cons(z0, x3), 0, x1, z0, x3))
   MERGE#2(Cons(S(z0), x1), Cons(0, x3)) -> c6(COND_MERGE_YS_ZS_2(False, Cons(S(z0), x1), Cons(0, x3), S(z0), x1, 0, x3))
S tuples:
   DIVIDE_YS#1(z0, z1) -> c(TAKE#2(z1, z0))
   DIVIDE_YS#1(z0, z1) -> c1(DROP#2(z1, z0))
   COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(z2, z3), z4, z5, z6, z7) -> c2(MERGE#2(z5, Cons(z2, z3)))
   COND_MERGE_YS_ZS_2(False, Cons(z0, z1), Cons(z2, z3), z4, z5, z6, z7) -> c3(MERGE#2(Cons(z0, z1), z7))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> c9(CONST_F#2(Cons(z0, Cons(z1, z2)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2)))))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2))))), DIVIDE_YS#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2)))), HALVE#1(length#1(z2)), LENGTH#1(z2))
   DROP#2(S(z0), Cons(z1, z2)) -> c12(DROP#2(z0, z2))
   TAKE#2(S(z0), Cons(z1, z2)) -> c15(TAKE#2(z0, z2))
   HALVE#1(S(S(z0))) -> c18(HALVE#1(z0))
   CONST_F#2(z0, Cons(z1, Cons(z2, z3))) -> c19(MERGE#2(z1, z2))
   LEQ#2(S(z0), S(z1)) -> c22(LEQ#2(z0, z1))
   LENGTH#1(Cons(z0, z1)) -> c24(LENGTH#1(z1))
   MAP#2(dc(z0, z1, z2, z3, z4), Cons(z5, z6)) -> c26(DC#1(z0, z1, z2, z3, z4, z5))
   MAP#2(dc(z0, z1, z2, z3, z4), Cons(z5, z6)) -> c27(MAP#2(dc(z0, z1, z2, z3, z4), z6))
   MERGE#2(Cons(S(z0), x1), Cons(S(z1), x3)) -> c6(COND_MERGE_YS_ZS_2(leq#2(z0, z1), Cons(S(z0), x1), Cons(S(z1), x3), S(z0), x1, S(z1), x3), LEQ#2(S(z0), S(z1)))
   MERGE#2(Cons(0, x1), Cons(z0, x3)) -> c6(COND_MERGE_YS_ZS_2(True, Cons(0, x1), Cons(z0, x3), 0, x1, z0, x3))
   MERGE#2(Cons(S(z0), x1), Cons(0, x3)) -> c6(COND_MERGE_YS_ZS_2(False, Cons(S(z0), x1), Cons(0, x3), S(z0), x1, 0, x3))
K tuples:none
Defined Rule Symbols:   leq#2_2, map#2_2, divide_ys#1_2, halve#1_1, length#1_1, take#2_2, drop#2_2, dc#1_6, const_f#2_2, merge#2_2, cond_merge_ys_zs_2_7

Defined Pair Symbols:   DIVIDE_YS#1_2, COND_MERGE_YS_ZS_2_7, DC#1_6, DROP#2_2, TAKE#2_2, HALVE#1_1, CONST_F#2_2, LEQ#2_2, LENGTH#1_1, MAP#2_2, MERGE#2_2

Compound Symbols:   c_1, c1_1, c2_1, c3_1, c9_5, c12_1, c15_1, c18_1, c19_1, c22_1, c24_1, c26_1, c27_1, c6_2, c6_1


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

(87) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> c9(CONST_F#2(Cons(z0, Cons(z1, z2)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2)))))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2))))), DIVIDE_YS#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2)))), HALVE#1(length#1(z2)), LENGTH#1(z2)) by 
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, x2))) -> c9(CONST_F#2(Cons(x0, Cons(x1, x2)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(x2))), Cons(x0, Cons(x1, x2))), Cons(drop#2(S(halve#1(length#1(x2))), Cons(x0, Cons(x1, x2))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, x2)), S(halve#1(length#1(x2))))), DIVIDE_YS#1(Cons(x0, Cons(x1, x2)), S(halve#1(length#1(x2)))), HALVE#1(length#1(x2)), LENGTH#1(x2))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Nil))) -> c9(CONST_F#2(Cons(x0, Cons(x1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Nil)), S(halve#1(0))))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Nil)), S(halve#1(length#1(Nil)))), HALVE#1(length#1(Nil)), LENGTH#1(Nil))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Cons(z0, z1)))) -> c9(CONST_F#2(Cons(x0, Cons(x1, Cons(z0, z1))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Cons(z0, z1))), S(halve#1(S(length#1(z1))))))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Cons(z0, z1))), S(halve#1(length#1(Cons(z0, z1)))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(z0, z1))), S(halve#1(length#1(Cons(z0, z1))))), HALVE#1(length#1(Cons(z0, z1))), LENGTH#1(Cons(z0, z1)))

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

(88)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   leq#2(0, z0) -> True
   leq#2(S(z0), 0) -> False
   leq#2(S(z0), S(z1)) -> leq#2(z0, z1)
   map#2(dc(z0, z1, z2, z3, z4), Nil) -> Nil
   map#2(dc(z0, z1, z2, z3, z4), Cons(z5, z6)) -> Cons(dc#1(z0, z1, z2, z3, z4, z5), map#2(dc(z0, z1, z2, z3, z4), z6))
   divide_ys#1(z0, z1) -> Cons(take#2(z1, z0), Cons(drop#2(z1, z0), Nil))
   halve#1(0) -> 0
   halve#1(S(0)) -> S(0)
   halve#1(S(S(z0))) -> S(halve#1(z0))
   length#1(Nil) -> 0
   length#1(Cons(z0, z1)) -> S(length#1(z1))
   take#2(0, z0) -> Nil
   take#2(S(0), Nil) -> Cons(bot[0], Nil)
   take#2(S(z0), Cons(z1, z2)) -> Cons(z1, take#2(z0, z2))
   drop#2(0, z0) -> z0
   drop#2(S(0), Nil) -> bot[1]
   drop#2(S(z0), Cons(z1, z2)) -> drop#2(z0, z2)
   dc#1(map, divisible, mergesort_zs_3, divide, const_f, Nil) -> Nil
   dc#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Nil)) -> Cons(z0, Nil)
   dc#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> const_f#2(Cons(z0, Cons(z1, z2)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2))))))
   const_f#2(z0, Cons(z1, Cons(z2, z3))) -> merge#2(z1, z2)
   merge#2(Nil, z0) -> z0
   merge#2(Cons(z0, z1), Nil) -> Cons(z0, z1)
   merge#2(Cons(z0, z1), Cons(z2, z3)) -> cond_merge_ys_zs_2(leq#2(z0, z2), Cons(z0, z1), Cons(z2, z3), z0, z1, z2, z3)
   cond_merge_ys_zs_2(True, Cons(z0, z1), Cons(z2, z3), z4, z5, z6, z7) -> Cons(z4, merge#2(z5, Cons(z2, z3)))
   cond_merge_ys_zs_2(False, Cons(z0, z1), Cons(z2, z3), z4, z5, z6, z7) -> Cons(z6, merge#2(Cons(z0, z1), z7))
Tuples:
   DIVIDE_YS#1(z0, z1) -> c(TAKE#2(z1, z0))
   DIVIDE_YS#1(z0, z1) -> c1(DROP#2(z1, z0))
   COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(z2, z3), z4, z5, z6, z7) -> c2(MERGE#2(z5, Cons(z2, z3)))
   COND_MERGE_YS_ZS_2(False, Cons(z0, z1), Cons(z2, z3), z4, z5, z6, z7) -> c3(MERGE#2(Cons(z0, z1), z7))
   DROP#2(S(z0), Cons(z1, z2)) -> c12(DROP#2(z0, z2))
   TAKE#2(S(z0), Cons(z1, z2)) -> c15(TAKE#2(z0, z2))
   HALVE#1(S(S(z0))) -> c18(HALVE#1(z0))
   CONST_F#2(z0, Cons(z1, Cons(z2, z3))) -> c19(MERGE#2(z1, z2))
   LEQ#2(S(z0), S(z1)) -> c22(LEQ#2(z0, z1))
   LENGTH#1(Cons(z0, z1)) -> c24(LENGTH#1(z1))
   MAP#2(dc(z0, z1, z2, z3, z4), Cons(z5, z6)) -> c26(DC#1(z0, z1, z2, z3, z4, z5))
   MAP#2(dc(z0, z1, z2, z3, z4), Cons(z5, z6)) -> c27(MAP#2(dc(z0, z1, z2, z3, z4), z6))
   MERGE#2(Cons(S(z0), x1), Cons(S(z1), x3)) -> c6(COND_MERGE_YS_ZS_2(leq#2(z0, z1), Cons(S(z0), x1), Cons(S(z1), x3), S(z0), x1, S(z1), x3), LEQ#2(S(z0), S(z1)))
   MERGE#2(Cons(0, x1), Cons(z0, x3)) -> c6(COND_MERGE_YS_ZS_2(True, Cons(0, x1), Cons(z0, x3), 0, x1, z0, x3))
   MERGE#2(Cons(S(z0), x1), Cons(0, x3)) -> c6(COND_MERGE_YS_ZS_2(False, Cons(S(z0), x1), Cons(0, x3), S(z0), x1, 0, x3))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, x2))) -> c9(CONST_F#2(Cons(x0, Cons(x1, x2)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(x2))), Cons(x0, Cons(x1, x2))), Cons(drop#2(S(halve#1(length#1(x2))), Cons(x0, Cons(x1, x2))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, x2)), S(halve#1(length#1(x2))))), DIVIDE_YS#1(Cons(x0, Cons(x1, x2)), S(halve#1(length#1(x2)))), HALVE#1(length#1(x2)), LENGTH#1(x2))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Nil))) -> c9(CONST_F#2(Cons(x0, Cons(x1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Nil)), S(halve#1(0))))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Nil)), S(halve#1(length#1(Nil)))), HALVE#1(length#1(Nil)), LENGTH#1(Nil))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Cons(z0, z1)))) -> c9(CONST_F#2(Cons(x0, Cons(x1, Cons(z0, z1))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Cons(z0, z1))), S(halve#1(S(length#1(z1))))))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Cons(z0, z1))), S(halve#1(length#1(Cons(z0, z1)))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(z0, z1))), S(halve#1(length#1(Cons(z0, z1))))), HALVE#1(length#1(Cons(z0, z1))), LENGTH#1(Cons(z0, z1)))
S tuples:
   DIVIDE_YS#1(z0, z1) -> c(TAKE#2(z1, z0))
   DIVIDE_YS#1(z0, z1) -> c1(DROP#2(z1, z0))
   COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(z2, z3), z4, z5, z6, z7) -> c2(MERGE#2(z5, Cons(z2, z3)))
   COND_MERGE_YS_ZS_2(False, Cons(z0, z1), Cons(z2, z3), z4, z5, z6, z7) -> c3(MERGE#2(Cons(z0, z1), z7))
   DROP#2(S(z0), Cons(z1, z2)) -> c12(DROP#2(z0, z2))
   TAKE#2(S(z0), Cons(z1, z2)) -> c15(TAKE#2(z0, z2))
   HALVE#1(S(S(z0))) -> c18(HALVE#1(z0))
   CONST_F#2(z0, Cons(z1, Cons(z2, z3))) -> c19(MERGE#2(z1, z2))
   LEQ#2(S(z0), S(z1)) -> c22(LEQ#2(z0, z1))
   LENGTH#1(Cons(z0, z1)) -> c24(LENGTH#1(z1))
   MAP#2(dc(z0, z1, z2, z3, z4), Cons(z5, z6)) -> c26(DC#1(z0, z1, z2, z3, z4, z5))
   MAP#2(dc(z0, z1, z2, z3, z4), Cons(z5, z6)) -> c27(MAP#2(dc(z0, z1, z2, z3, z4), z6))
   MERGE#2(Cons(S(z0), x1), Cons(S(z1), x3)) -> c6(COND_MERGE_YS_ZS_2(leq#2(z0, z1), Cons(S(z0), x1), Cons(S(z1), x3), S(z0), x1, S(z1), x3), LEQ#2(S(z0), S(z1)))
   MERGE#2(Cons(0, x1), Cons(z0, x3)) -> c6(COND_MERGE_YS_ZS_2(True, Cons(0, x1), Cons(z0, x3), 0, x1, z0, x3))
   MERGE#2(Cons(S(z0), x1), Cons(0, x3)) -> c6(COND_MERGE_YS_ZS_2(False, Cons(S(z0), x1), Cons(0, x3), S(z0), x1, 0, x3))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, x2))) -> c9(CONST_F#2(Cons(x0, Cons(x1, x2)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(x2))), Cons(x0, Cons(x1, x2))), Cons(drop#2(S(halve#1(length#1(x2))), Cons(x0, Cons(x1, x2))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, x2)), S(halve#1(length#1(x2))))), DIVIDE_YS#1(Cons(x0, Cons(x1, x2)), S(halve#1(length#1(x2)))), HALVE#1(length#1(x2)), LENGTH#1(x2))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Nil))) -> c9(CONST_F#2(Cons(x0, Cons(x1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Nil)), S(halve#1(0))))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Nil)), S(halve#1(length#1(Nil)))), HALVE#1(length#1(Nil)), LENGTH#1(Nil))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Cons(z0, z1)))) -> c9(CONST_F#2(Cons(x0, Cons(x1, Cons(z0, z1))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Cons(z0, z1))), S(halve#1(S(length#1(z1))))))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Cons(z0, z1))), S(halve#1(length#1(Cons(z0, z1)))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(z0, z1))), S(halve#1(length#1(Cons(z0, z1))))), HALVE#1(length#1(Cons(z0, z1))), LENGTH#1(Cons(z0, z1)))
K tuples:none
Defined Rule Symbols:   leq#2_2, map#2_2, divide_ys#1_2, halve#1_1, length#1_1, take#2_2, drop#2_2, dc#1_6, const_f#2_2, merge#2_2, cond_merge_ys_zs_2_7

Defined Pair Symbols:   DIVIDE_YS#1_2, COND_MERGE_YS_ZS_2_7, DROP#2_2, TAKE#2_2, HALVE#1_1, CONST_F#2_2, LEQ#2_2, LENGTH#1_1, MAP#2_2, MERGE#2_2, DC#1_6

Compound Symbols:   c_1, c1_1, c2_1, c3_1, c12_1, c15_1, c18_1, c19_1, c22_1, c24_1, c26_1, c27_1, c6_2, c6_1, c9_5


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

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

(90)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   leq#2(0, z0) -> True
   leq#2(S(z0), 0) -> False
   leq#2(S(z0), S(z1)) -> leq#2(z0, z1)
   map#2(dc(z0, z1, z2, z3, z4), Nil) -> Nil
   map#2(dc(z0, z1, z2, z3, z4), Cons(z5, z6)) -> Cons(dc#1(z0, z1, z2, z3, z4, z5), map#2(dc(z0, z1, z2, z3, z4), z6))
   divide_ys#1(z0, z1) -> Cons(take#2(z1, z0), Cons(drop#2(z1, z0), Nil))
   halve#1(0) -> 0
   halve#1(S(0)) -> S(0)
   halve#1(S(S(z0))) -> S(halve#1(z0))
   length#1(Nil) -> 0
   length#1(Cons(z0, z1)) -> S(length#1(z1))
   take#2(0, z0) -> Nil
   take#2(S(0), Nil) -> Cons(bot[0], Nil)
   take#2(S(z0), Cons(z1, z2)) -> Cons(z1, take#2(z0, z2))
   drop#2(0, z0) -> z0
   drop#2(S(0), Nil) -> bot[1]
   drop#2(S(z0), Cons(z1, z2)) -> drop#2(z0, z2)
   dc#1(map, divisible, mergesort_zs_3, divide, const_f, Nil) -> Nil
   dc#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Nil)) -> Cons(z0, Nil)
   dc#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> const_f#2(Cons(z0, Cons(z1, z2)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2))))))
   const_f#2(z0, Cons(z1, Cons(z2, z3))) -> merge#2(z1, z2)
   merge#2(Nil, z0) -> z0
   merge#2(Cons(z0, z1), Nil) -> Cons(z0, z1)
   merge#2(Cons(z0, z1), Cons(z2, z3)) -> cond_merge_ys_zs_2(leq#2(z0, z2), Cons(z0, z1), Cons(z2, z3), z0, z1, z2, z3)
   cond_merge_ys_zs_2(True, Cons(z0, z1), Cons(z2, z3), z4, z5, z6, z7) -> Cons(z4, merge#2(z5, Cons(z2, z3)))
   cond_merge_ys_zs_2(False, Cons(z0, z1), Cons(z2, z3), z4, z5, z6, z7) -> Cons(z6, merge#2(Cons(z0, z1), z7))
Tuples:
   DIVIDE_YS#1(z0, z1) -> c(TAKE#2(z1, z0))
   DIVIDE_YS#1(z0, z1) -> c1(DROP#2(z1, z0))
   COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(z2, z3), z4, z5, z6, z7) -> c2(MERGE#2(z5, Cons(z2, z3)))
   COND_MERGE_YS_ZS_2(False, Cons(z0, z1), Cons(z2, z3), z4, z5, z6, z7) -> c3(MERGE#2(Cons(z0, z1), z7))
   DROP#2(S(z0), Cons(z1, z2)) -> c12(DROP#2(z0, z2))
   TAKE#2(S(z0), Cons(z1, z2)) -> c15(TAKE#2(z0, z2))
   HALVE#1(S(S(z0))) -> c18(HALVE#1(z0))
   CONST_F#2(z0, Cons(z1, Cons(z2, z3))) -> c19(MERGE#2(z1, z2))
   LEQ#2(S(z0), S(z1)) -> c22(LEQ#2(z0, z1))
   LENGTH#1(Cons(z0, z1)) -> c24(LENGTH#1(z1))
   MAP#2(dc(z0, z1, z2, z3, z4), Cons(z5, z6)) -> c26(DC#1(z0, z1, z2, z3, z4, z5))
   MAP#2(dc(z0, z1, z2, z3, z4), Cons(z5, z6)) -> c27(MAP#2(dc(z0, z1, z2, z3, z4), z6))
   MERGE#2(Cons(S(z0), x1), Cons(S(z1), x3)) -> c6(COND_MERGE_YS_ZS_2(leq#2(z0, z1), Cons(S(z0), x1), Cons(S(z1), x3), S(z0), x1, S(z1), x3), LEQ#2(S(z0), S(z1)))
   MERGE#2(Cons(0, x1), Cons(z0, x3)) -> c6(COND_MERGE_YS_ZS_2(True, Cons(0, x1), Cons(z0, x3), 0, x1, z0, x3))
   MERGE#2(Cons(S(z0), x1), Cons(0, x3)) -> c6(COND_MERGE_YS_ZS_2(False, Cons(S(z0), x1), Cons(0, x3), S(z0), x1, 0, x3))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, x2))) -> c9(CONST_F#2(Cons(x0, Cons(x1, x2)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(x2))), Cons(x0, Cons(x1, x2))), Cons(drop#2(S(halve#1(length#1(x2))), Cons(x0, Cons(x1, x2))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, x2)), S(halve#1(length#1(x2))))), DIVIDE_YS#1(Cons(x0, Cons(x1, x2)), S(halve#1(length#1(x2)))), HALVE#1(length#1(x2)), LENGTH#1(x2))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Cons(z0, z1)))) -> c9(CONST_F#2(Cons(x0, Cons(x1, Cons(z0, z1))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Cons(z0, z1))), S(halve#1(S(length#1(z1))))))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Cons(z0, z1))), S(halve#1(length#1(Cons(z0, z1)))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(z0, z1))), S(halve#1(length#1(Cons(z0, z1))))), HALVE#1(length#1(Cons(z0, z1))), LENGTH#1(Cons(z0, z1)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Nil))) -> c9(CONST_F#2(Cons(x0, Cons(x1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Nil)), S(halve#1(0))))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Nil)), S(halve#1(length#1(Nil)))), HALVE#1(length#1(Nil)))
S tuples:
   DIVIDE_YS#1(z0, z1) -> c(TAKE#2(z1, z0))
   DIVIDE_YS#1(z0, z1) -> c1(DROP#2(z1, z0))
   COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(z2, z3), z4, z5, z6, z7) -> c2(MERGE#2(z5, Cons(z2, z3)))
   COND_MERGE_YS_ZS_2(False, Cons(z0, z1), Cons(z2, z3), z4, z5, z6, z7) -> c3(MERGE#2(Cons(z0, z1), z7))
   DROP#2(S(z0), Cons(z1, z2)) -> c12(DROP#2(z0, z2))
   TAKE#2(S(z0), Cons(z1, z2)) -> c15(TAKE#2(z0, z2))
   HALVE#1(S(S(z0))) -> c18(HALVE#1(z0))
   CONST_F#2(z0, Cons(z1, Cons(z2, z3))) -> c19(MERGE#2(z1, z2))
   LEQ#2(S(z0), S(z1)) -> c22(LEQ#2(z0, z1))
   LENGTH#1(Cons(z0, z1)) -> c24(LENGTH#1(z1))
   MAP#2(dc(z0, z1, z2, z3, z4), Cons(z5, z6)) -> c26(DC#1(z0, z1, z2, z3, z4, z5))
   MAP#2(dc(z0, z1, z2, z3, z4), Cons(z5, z6)) -> c27(MAP#2(dc(z0, z1, z2, z3, z4), z6))
   MERGE#2(Cons(S(z0), x1), Cons(S(z1), x3)) -> c6(COND_MERGE_YS_ZS_2(leq#2(z0, z1), Cons(S(z0), x1), Cons(S(z1), x3), S(z0), x1, S(z1), x3), LEQ#2(S(z0), S(z1)))
   MERGE#2(Cons(0, x1), Cons(z0, x3)) -> c6(COND_MERGE_YS_ZS_2(True, Cons(0, x1), Cons(z0, x3), 0, x1, z0, x3))
   MERGE#2(Cons(S(z0), x1), Cons(0, x3)) -> c6(COND_MERGE_YS_ZS_2(False, Cons(S(z0), x1), Cons(0, x3), S(z0), x1, 0, x3))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, x2))) -> c9(CONST_F#2(Cons(x0, Cons(x1, x2)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(x2))), Cons(x0, Cons(x1, x2))), Cons(drop#2(S(halve#1(length#1(x2))), Cons(x0, Cons(x1, x2))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, x2)), S(halve#1(length#1(x2))))), DIVIDE_YS#1(Cons(x0, Cons(x1, x2)), S(halve#1(length#1(x2)))), HALVE#1(length#1(x2)), LENGTH#1(x2))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Cons(z0, z1)))) -> c9(CONST_F#2(Cons(x0, Cons(x1, Cons(z0, z1))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Cons(z0, z1))), S(halve#1(S(length#1(z1))))))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Cons(z0, z1))), S(halve#1(length#1(Cons(z0, z1)))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(z0, z1))), S(halve#1(length#1(Cons(z0, z1))))), HALVE#1(length#1(Cons(z0, z1))), LENGTH#1(Cons(z0, z1)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Nil))) -> c9(CONST_F#2(Cons(x0, Cons(x1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Nil)), S(halve#1(0))))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Nil)), S(halve#1(length#1(Nil)))), HALVE#1(length#1(Nil)))
K tuples:none
Defined Rule Symbols:   leq#2_2, map#2_2, divide_ys#1_2, halve#1_1, length#1_1, take#2_2, drop#2_2, dc#1_6, const_f#2_2, merge#2_2, cond_merge_ys_zs_2_7

Defined Pair Symbols:   DIVIDE_YS#1_2, COND_MERGE_YS_ZS_2_7, DROP#2_2, TAKE#2_2, HALVE#1_1, CONST_F#2_2, LEQ#2_2, LENGTH#1_1, MAP#2_2, MERGE#2_2, DC#1_6

Compound Symbols:   c_1, c1_1, c2_1, c3_1, c12_1, c15_1, c18_1, c19_1, c22_1, c24_1, c26_1, c27_1, c6_2, c6_1, c9_5, c9_4


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

(91) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace MERGE#2(Cons(S(z0), x1), Cons(S(z1), x3)) -> c6(COND_MERGE_YS_ZS_2(leq#2(z0, z1), Cons(S(z0), x1), Cons(S(z1), x3), S(z0), x1, S(z1), x3), LEQ#2(S(z0), S(z1))) by 
   MERGE#2(Cons(S(0), x1), Cons(S(z0), x3)) -> c6(COND_MERGE_YS_ZS_2(True, Cons(S(0), x1), Cons(S(z0), x3), S(0), x1, S(z0), x3), LEQ#2(S(0), S(z0)))
   MERGE#2(Cons(S(S(z0)), x1), Cons(S(0), x3)) -> c6(COND_MERGE_YS_ZS_2(False, Cons(S(S(z0)), x1), Cons(S(0), x3), S(S(z0)), x1, S(0), x3), LEQ#2(S(S(z0)), S(0)))
   MERGE#2(Cons(S(S(z0)), x1), Cons(S(S(z1)), x3)) -> c6(COND_MERGE_YS_ZS_2(leq#2(z0, z1), Cons(S(S(z0)), x1), Cons(S(S(z1)), x3), S(S(z0)), x1, S(S(z1)), x3), LEQ#2(S(S(z0)), S(S(z1))))
   MERGE#2(Cons(S(x0), x1), Cons(S(x2), x3)) -> c6(LEQ#2(S(x0), S(x2)))

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

(92)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   leq#2(0, z0) -> True
   leq#2(S(z0), 0) -> False
   leq#2(S(z0), S(z1)) -> leq#2(z0, z1)
   map#2(dc(z0, z1, z2, z3, z4), Nil) -> Nil
   map#2(dc(z0, z1, z2, z3, z4), Cons(z5, z6)) -> Cons(dc#1(z0, z1, z2, z3, z4, z5), map#2(dc(z0, z1, z2, z3, z4), z6))
   divide_ys#1(z0, z1) -> Cons(take#2(z1, z0), Cons(drop#2(z1, z0), Nil))
   halve#1(0) -> 0
   halve#1(S(0)) -> S(0)
   halve#1(S(S(z0))) -> S(halve#1(z0))
   length#1(Nil) -> 0
   length#1(Cons(z0, z1)) -> S(length#1(z1))
   take#2(0, z0) -> Nil
   take#2(S(0), Nil) -> Cons(bot[0], Nil)
   take#2(S(z0), Cons(z1, z2)) -> Cons(z1, take#2(z0, z2))
   drop#2(0, z0) -> z0
   drop#2(S(0), Nil) -> bot[1]
   drop#2(S(z0), Cons(z1, z2)) -> drop#2(z0, z2)
   dc#1(map, divisible, mergesort_zs_3, divide, const_f, Nil) -> Nil
   dc#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Nil)) -> Cons(z0, Nil)
   dc#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> const_f#2(Cons(z0, Cons(z1, z2)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2))))))
   const_f#2(z0, Cons(z1, Cons(z2, z3))) -> merge#2(z1, z2)
   merge#2(Nil, z0) -> z0
   merge#2(Cons(z0, z1), Nil) -> Cons(z0, z1)
   merge#2(Cons(z0, z1), Cons(z2, z3)) -> cond_merge_ys_zs_2(leq#2(z0, z2), Cons(z0, z1), Cons(z2, z3), z0, z1, z2, z3)
   cond_merge_ys_zs_2(True, Cons(z0, z1), Cons(z2, z3), z4, z5, z6, z7) -> Cons(z4, merge#2(z5, Cons(z2, z3)))
   cond_merge_ys_zs_2(False, Cons(z0, z1), Cons(z2, z3), z4, z5, z6, z7) -> Cons(z6, merge#2(Cons(z0, z1), z7))
Tuples:
   DIVIDE_YS#1(z0, z1) -> c(TAKE#2(z1, z0))
   DIVIDE_YS#1(z0, z1) -> c1(DROP#2(z1, z0))
   COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(z2, z3), z4, z5, z6, z7) -> c2(MERGE#2(z5, Cons(z2, z3)))
   COND_MERGE_YS_ZS_2(False, Cons(z0, z1), Cons(z2, z3), z4, z5, z6, z7) -> c3(MERGE#2(Cons(z0, z1), z7))
   DROP#2(S(z0), Cons(z1, z2)) -> c12(DROP#2(z0, z2))
   TAKE#2(S(z0), Cons(z1, z2)) -> c15(TAKE#2(z0, z2))
   HALVE#1(S(S(z0))) -> c18(HALVE#1(z0))
   CONST_F#2(z0, Cons(z1, Cons(z2, z3))) -> c19(MERGE#2(z1, z2))
   LEQ#2(S(z0), S(z1)) -> c22(LEQ#2(z0, z1))
   LENGTH#1(Cons(z0, z1)) -> c24(LENGTH#1(z1))
   MAP#2(dc(z0, z1, z2, z3, z4), Cons(z5, z6)) -> c26(DC#1(z0, z1, z2, z3, z4, z5))
   MAP#2(dc(z0, z1, z2, z3, z4), Cons(z5, z6)) -> c27(MAP#2(dc(z0, z1, z2, z3, z4), z6))
   MERGE#2(Cons(0, x1), Cons(z0, x3)) -> c6(COND_MERGE_YS_ZS_2(True, Cons(0, x1), Cons(z0, x3), 0, x1, z0, x3))
   MERGE#2(Cons(S(z0), x1), Cons(0, x3)) -> c6(COND_MERGE_YS_ZS_2(False, Cons(S(z0), x1), Cons(0, x3), S(z0), x1, 0, x3))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, x2))) -> c9(CONST_F#2(Cons(x0, Cons(x1, x2)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(x2))), Cons(x0, Cons(x1, x2))), Cons(drop#2(S(halve#1(length#1(x2))), Cons(x0, Cons(x1, x2))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, x2)), S(halve#1(length#1(x2))))), DIVIDE_YS#1(Cons(x0, Cons(x1, x2)), S(halve#1(length#1(x2)))), HALVE#1(length#1(x2)), LENGTH#1(x2))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Cons(z0, z1)))) -> c9(CONST_F#2(Cons(x0, Cons(x1, Cons(z0, z1))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Cons(z0, z1))), S(halve#1(S(length#1(z1))))))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Cons(z0, z1))), S(halve#1(length#1(Cons(z0, z1)))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(z0, z1))), S(halve#1(length#1(Cons(z0, z1))))), HALVE#1(length#1(Cons(z0, z1))), LENGTH#1(Cons(z0, z1)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Nil))) -> c9(CONST_F#2(Cons(x0, Cons(x1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Nil)), S(halve#1(0))))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Nil)), S(halve#1(length#1(Nil)))), HALVE#1(length#1(Nil)))
   MERGE#2(Cons(S(0), x1), Cons(S(z0), x3)) -> c6(COND_MERGE_YS_ZS_2(True, Cons(S(0), x1), Cons(S(z0), x3), S(0), x1, S(z0), x3), LEQ#2(S(0), S(z0)))
   MERGE#2(Cons(S(S(z0)), x1), Cons(S(0), x3)) -> c6(COND_MERGE_YS_ZS_2(False, Cons(S(S(z0)), x1), Cons(S(0), x3), S(S(z0)), x1, S(0), x3), LEQ#2(S(S(z0)), S(0)))
   MERGE#2(Cons(S(S(z0)), x1), Cons(S(S(z1)), x3)) -> c6(COND_MERGE_YS_ZS_2(leq#2(z0, z1), Cons(S(S(z0)), x1), Cons(S(S(z1)), x3), S(S(z0)), x1, S(S(z1)), x3), LEQ#2(S(S(z0)), S(S(z1))))
   MERGE#2(Cons(S(x0), x1), Cons(S(x2), x3)) -> c6(LEQ#2(S(x0), S(x2)))
S tuples:
   DIVIDE_YS#1(z0, z1) -> c(TAKE#2(z1, z0))
   DIVIDE_YS#1(z0, z1) -> c1(DROP#2(z1, z0))
   COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(z2, z3), z4, z5, z6, z7) -> c2(MERGE#2(z5, Cons(z2, z3)))
   COND_MERGE_YS_ZS_2(False, Cons(z0, z1), Cons(z2, z3), z4, z5, z6, z7) -> c3(MERGE#2(Cons(z0, z1), z7))
   DROP#2(S(z0), Cons(z1, z2)) -> c12(DROP#2(z0, z2))
   TAKE#2(S(z0), Cons(z1, z2)) -> c15(TAKE#2(z0, z2))
   HALVE#1(S(S(z0))) -> c18(HALVE#1(z0))
   CONST_F#2(z0, Cons(z1, Cons(z2, z3))) -> c19(MERGE#2(z1, z2))
   LEQ#2(S(z0), S(z1)) -> c22(LEQ#2(z0, z1))
   LENGTH#1(Cons(z0, z1)) -> c24(LENGTH#1(z1))
   MAP#2(dc(z0, z1, z2, z3, z4), Cons(z5, z6)) -> c26(DC#1(z0, z1, z2, z3, z4, z5))
   MAP#2(dc(z0, z1, z2, z3, z4), Cons(z5, z6)) -> c27(MAP#2(dc(z0, z1, z2, z3, z4), z6))
   MERGE#2(Cons(0, x1), Cons(z0, x3)) -> c6(COND_MERGE_YS_ZS_2(True, Cons(0, x1), Cons(z0, x3), 0, x1, z0, x3))
   MERGE#2(Cons(S(z0), x1), Cons(0, x3)) -> c6(COND_MERGE_YS_ZS_2(False, Cons(S(z0), x1), Cons(0, x3), S(z0), x1, 0, x3))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, x2))) -> c9(CONST_F#2(Cons(x0, Cons(x1, x2)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(x2))), Cons(x0, Cons(x1, x2))), Cons(drop#2(S(halve#1(length#1(x2))), Cons(x0, Cons(x1, x2))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, x2)), S(halve#1(length#1(x2))))), DIVIDE_YS#1(Cons(x0, Cons(x1, x2)), S(halve#1(length#1(x2)))), HALVE#1(length#1(x2)), LENGTH#1(x2))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Cons(z0, z1)))) -> c9(CONST_F#2(Cons(x0, Cons(x1, Cons(z0, z1))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Cons(z0, z1))), S(halve#1(S(length#1(z1))))))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Cons(z0, z1))), S(halve#1(length#1(Cons(z0, z1)))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(z0, z1))), S(halve#1(length#1(Cons(z0, z1))))), HALVE#1(length#1(Cons(z0, z1))), LENGTH#1(Cons(z0, z1)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Nil))) -> c9(CONST_F#2(Cons(x0, Cons(x1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Nil)), S(halve#1(0))))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Nil)), S(halve#1(length#1(Nil)))), HALVE#1(length#1(Nil)))
   MERGE#2(Cons(S(0), x1), Cons(S(z0), x3)) -> c6(COND_MERGE_YS_ZS_2(True, Cons(S(0), x1), Cons(S(z0), x3), S(0), x1, S(z0), x3), LEQ#2(S(0), S(z0)))
   MERGE#2(Cons(S(S(z0)), x1), Cons(S(0), x3)) -> c6(COND_MERGE_YS_ZS_2(False, Cons(S(S(z0)), x1), Cons(S(0), x3), S(S(z0)), x1, S(0), x3), LEQ#2(S(S(z0)), S(0)))
   MERGE#2(Cons(S(S(z0)), x1), Cons(S(S(z1)), x3)) -> c6(COND_MERGE_YS_ZS_2(leq#2(z0, z1), Cons(S(S(z0)), x1), Cons(S(S(z1)), x3), S(S(z0)), x1, S(S(z1)), x3), LEQ#2(S(S(z0)), S(S(z1))))
   MERGE#2(Cons(S(x0), x1), Cons(S(x2), x3)) -> c6(LEQ#2(S(x0), S(x2)))
K tuples:none
Defined Rule Symbols:   leq#2_2, map#2_2, divide_ys#1_2, halve#1_1, length#1_1, take#2_2, drop#2_2, dc#1_6, const_f#2_2, merge#2_2, cond_merge_ys_zs_2_7

Defined Pair Symbols:   DIVIDE_YS#1_2, COND_MERGE_YS_ZS_2_7, DROP#2_2, TAKE#2_2, HALVE#1_1, CONST_F#2_2, LEQ#2_2, LENGTH#1_1, MAP#2_2, MERGE#2_2, DC#1_6

Compound Symbols:   c_1, c1_1, c2_1, c3_1, c12_1, c15_1, c18_1, c19_1, c22_1, c24_1, c26_1, c27_1, c6_1, c9_5, c9_4, c6_2


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(93) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, x2))) -> c9(CONST_F#2(Cons(x0, Cons(x1, x2)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(x2))), Cons(x0, Cons(x1, x2))), Cons(drop#2(S(halve#1(length#1(x2))), Cons(x0, Cons(x1, x2))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, x2)), S(halve#1(length#1(x2))))), DIVIDE_YS#1(Cons(x0, Cons(x1, x2)), S(halve#1(length#1(x2)))), HALVE#1(length#1(x2)), LENGTH#1(x2)) by 
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, x2))) -> c9(CONST_F#2(Cons(x0, Cons(x1, x2)), Cons(dc#1(map, divisible, mergesort_zs_3, divide, const_f, take#2(S(halve#1(length#1(x2))), Cons(x0, Cons(x1, x2)))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(drop#2(S(halve#1(length#1(x2))), Cons(x0, Cons(x1, x2))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, x2)), S(halve#1(length#1(x2))))), DIVIDE_YS#1(Cons(x0, Cons(x1, x2)), S(halve#1(length#1(x2)))), HALVE#1(length#1(x2)), LENGTH#1(x2))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z1, Cons(x1, x2))) -> c9(CONST_F#2(Cons(z1, Cons(x1, x2)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(x2))), Cons(z1, Cons(x1, x2))), Cons(drop#2(halve#1(length#1(x2)), Cons(x1, x2)), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z1, Cons(x1, x2)), S(halve#1(length#1(x2))))), DIVIDE_YS#1(Cons(z1, Cons(x1, x2)), S(halve#1(length#1(x2)))), HALVE#1(length#1(x2)), LENGTH#1(x2))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Nil))) -> c9(CONST_F#2(Cons(x0, Cons(x1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(Nil))), Cons(x0, Cons(x1, Nil))), Cons(drop#2(S(halve#1(0)), Cons(x0, Cons(x1, Nil))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Nil)), S(halve#1(length#1(Nil)))), HALVE#1(length#1(Nil)), LENGTH#1(Nil))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Cons(z0, z1)))) -> c9(CONST_F#2(Cons(x0, Cons(x1, Cons(z0, z1))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(Cons(z0, z1)))), Cons(x0, Cons(x1, Cons(z0, z1)))), Cons(drop#2(S(halve#1(S(length#1(z1)))), Cons(x0, Cons(x1, Cons(z0, z1)))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Cons(z0, z1))), S(halve#1(length#1(Cons(z0, z1)))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(z0, z1))), S(halve#1(length#1(Cons(z0, z1))))), HALVE#1(length#1(Cons(z0, z1))), LENGTH#1(Cons(z0, z1)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z1, Cons(x1, x2))) -> c9(CONST_F#2(Cons(z1, Cons(x1, x2)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(Cons(z1, take#2(halve#1(length#1(x2)), Cons(x1, x2))), Cons(drop#2(S(halve#1(length#1(x2))), Cons(z1, Cons(x1, x2))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z1, Cons(x1, x2)), S(halve#1(length#1(x2))))), DIVIDE_YS#1(Cons(z1, Cons(x1, x2)), S(halve#1(length#1(x2)))), HALVE#1(length#1(x2)), LENGTH#1(x2))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Nil))) -> c9(CONST_F#2(Cons(x0, Cons(x1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(0)), Cons(x0, Cons(x1, Nil))), Cons(drop#2(S(halve#1(length#1(Nil))), Cons(x0, Cons(x1, Nil))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Nil)), S(halve#1(length#1(Nil)))), HALVE#1(length#1(Nil)), LENGTH#1(Nil))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Cons(z0, z1)))) -> c9(CONST_F#2(Cons(x0, Cons(x1, Cons(z0, z1))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(S(length#1(z1)))), Cons(x0, Cons(x1, Cons(z0, z1)))), Cons(drop#2(S(halve#1(length#1(Cons(z0, z1)))), Cons(x0, Cons(x1, Cons(z0, z1)))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Cons(z0, z1))), S(halve#1(length#1(Cons(z0, z1)))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(z0, z1))), S(halve#1(length#1(Cons(z0, z1))))), HALVE#1(length#1(Cons(z0, z1))), LENGTH#1(Cons(z0, z1)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, x2))) -> c9(MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, x2)), S(halve#1(length#1(x2))))), DIVIDE_YS#1(Cons(x0, Cons(x1, x2)), S(halve#1(length#1(x2)))))

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

(94)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   leq#2(0, z0) -> True
   leq#2(S(z0), 0) -> False
   leq#2(S(z0), S(z1)) -> leq#2(z0, z1)
   map#2(dc(z0, z1, z2, z3, z4), Nil) -> Nil
   map#2(dc(z0, z1, z2, z3, z4), Cons(z5, z6)) -> Cons(dc#1(z0, z1, z2, z3, z4, z5), map#2(dc(z0, z1, z2, z3, z4), z6))
   divide_ys#1(z0, z1) -> Cons(take#2(z1, z0), Cons(drop#2(z1, z0), Nil))
   halve#1(0) -> 0
   halve#1(S(0)) -> S(0)
   halve#1(S(S(z0))) -> S(halve#1(z0))
   length#1(Nil) -> 0
   length#1(Cons(z0, z1)) -> S(length#1(z1))
   take#2(0, z0) -> Nil
   take#2(S(0), Nil) -> Cons(bot[0], Nil)
   take#2(S(z0), Cons(z1, z2)) -> Cons(z1, take#2(z0, z2))
   drop#2(0, z0) -> z0
   drop#2(S(0), Nil) -> bot[1]
   drop#2(S(z0), Cons(z1, z2)) -> drop#2(z0, z2)
   dc#1(map, divisible, mergesort_zs_3, divide, const_f, Nil) -> Nil
   dc#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Nil)) -> Cons(z0, Nil)
   dc#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> const_f#2(Cons(z0, Cons(z1, z2)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2))))))
   const_f#2(z0, Cons(z1, Cons(z2, z3))) -> merge#2(z1, z2)
   merge#2(Nil, z0) -> z0
   merge#2(Cons(z0, z1), Nil) -> Cons(z0, z1)
   merge#2(Cons(z0, z1), Cons(z2, z3)) -> cond_merge_ys_zs_2(leq#2(z0, z2), Cons(z0, z1), Cons(z2, z3), z0, z1, z2, z3)
   cond_merge_ys_zs_2(True, Cons(z0, z1), Cons(z2, z3), z4, z5, z6, z7) -> Cons(z4, merge#2(z5, Cons(z2, z3)))
   cond_merge_ys_zs_2(False, Cons(z0, z1), Cons(z2, z3), z4, z5, z6, z7) -> Cons(z6, merge#2(Cons(z0, z1), z7))
Tuples:
   DIVIDE_YS#1(z0, z1) -> c(TAKE#2(z1, z0))
   DIVIDE_YS#1(z0, z1) -> c1(DROP#2(z1, z0))
   COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(z2, z3), z4, z5, z6, z7) -> c2(MERGE#2(z5, Cons(z2, z3)))
   COND_MERGE_YS_ZS_2(False, Cons(z0, z1), Cons(z2, z3), z4, z5, z6, z7) -> c3(MERGE#2(Cons(z0, z1), z7))
   DROP#2(S(z0), Cons(z1, z2)) -> c12(DROP#2(z0, z2))
   TAKE#2(S(z0), Cons(z1, z2)) -> c15(TAKE#2(z0, z2))
   HALVE#1(S(S(z0))) -> c18(HALVE#1(z0))
   CONST_F#2(z0, Cons(z1, Cons(z2, z3))) -> c19(MERGE#2(z1, z2))
   LEQ#2(S(z0), S(z1)) -> c22(LEQ#2(z0, z1))
   LENGTH#1(Cons(z0, z1)) -> c24(LENGTH#1(z1))
   MAP#2(dc(z0, z1, z2, z3, z4), Cons(z5, z6)) -> c26(DC#1(z0, z1, z2, z3, z4, z5))
   MAP#2(dc(z0, z1, z2, z3, z4), Cons(z5, z6)) -> c27(MAP#2(dc(z0, z1, z2, z3, z4), z6))
   MERGE#2(Cons(0, x1), Cons(z0, x3)) -> c6(COND_MERGE_YS_ZS_2(True, Cons(0, x1), Cons(z0, x3), 0, x1, z0, x3))
   MERGE#2(Cons(S(z0), x1), Cons(0, x3)) -> c6(COND_MERGE_YS_ZS_2(False, Cons(S(z0), x1), Cons(0, x3), S(z0), x1, 0, x3))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Cons(z0, z1)))) -> c9(CONST_F#2(Cons(x0, Cons(x1, Cons(z0, z1))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Cons(z0, z1))), S(halve#1(S(length#1(z1))))))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Cons(z0, z1))), S(halve#1(length#1(Cons(z0, z1)))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(z0, z1))), S(halve#1(length#1(Cons(z0, z1))))), HALVE#1(length#1(Cons(z0, z1))), LENGTH#1(Cons(z0, z1)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Nil))) -> c9(CONST_F#2(Cons(x0, Cons(x1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Nil)), S(halve#1(0))))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Nil)), S(halve#1(length#1(Nil)))), HALVE#1(length#1(Nil)))
   MERGE#2(Cons(S(0), x1), Cons(S(z0), x3)) -> c6(COND_MERGE_YS_ZS_2(True, Cons(S(0), x1), Cons(S(z0), x3), S(0), x1, S(z0), x3), LEQ#2(S(0), S(z0)))
   MERGE#2(Cons(S(S(z0)), x1), Cons(S(0), x3)) -> c6(COND_MERGE_YS_ZS_2(False, Cons(S(S(z0)), x1), Cons(S(0), x3), S(S(z0)), x1, S(0), x3), LEQ#2(S(S(z0)), S(0)))
   MERGE#2(Cons(S(S(z0)), x1), Cons(S(S(z1)), x3)) -> c6(COND_MERGE_YS_ZS_2(leq#2(z0, z1), Cons(S(S(z0)), x1), Cons(S(S(z1)), x3), S(S(z0)), x1, S(S(z1)), x3), LEQ#2(S(S(z0)), S(S(z1))))
   MERGE#2(Cons(S(x0), x1), Cons(S(x2), x3)) -> c6(LEQ#2(S(x0), S(x2)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, x2))) -> c9(CONST_F#2(Cons(x0, Cons(x1, x2)), Cons(dc#1(map, divisible, mergesort_zs_3, divide, const_f, take#2(S(halve#1(length#1(x2))), Cons(x0, Cons(x1, x2)))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(drop#2(S(halve#1(length#1(x2))), Cons(x0, Cons(x1, x2))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, x2)), S(halve#1(length#1(x2))))), DIVIDE_YS#1(Cons(x0, Cons(x1, x2)), S(halve#1(length#1(x2)))), HALVE#1(length#1(x2)), LENGTH#1(x2))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z1, Cons(x1, x2))) -> c9(CONST_F#2(Cons(z1, Cons(x1, x2)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(x2))), Cons(z1, Cons(x1, x2))), Cons(drop#2(halve#1(length#1(x2)), Cons(x1, x2)), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z1, Cons(x1, x2)), S(halve#1(length#1(x2))))), DIVIDE_YS#1(Cons(z1, Cons(x1, x2)), S(halve#1(length#1(x2)))), HALVE#1(length#1(x2)), LENGTH#1(x2))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Nil))) -> c9(CONST_F#2(Cons(x0, Cons(x1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(Nil))), Cons(x0, Cons(x1, Nil))), Cons(drop#2(S(halve#1(0)), Cons(x0, Cons(x1, Nil))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Nil)), S(halve#1(length#1(Nil)))), HALVE#1(length#1(Nil)), LENGTH#1(Nil))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Cons(z0, z1)))) -> c9(CONST_F#2(Cons(x0, Cons(x1, Cons(z0, z1))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(Cons(z0, z1)))), Cons(x0, Cons(x1, Cons(z0, z1)))), Cons(drop#2(S(halve#1(S(length#1(z1)))), Cons(x0, Cons(x1, Cons(z0, z1)))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Cons(z0, z1))), S(halve#1(length#1(Cons(z0, z1)))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(z0, z1))), S(halve#1(length#1(Cons(z0, z1))))), HALVE#1(length#1(Cons(z0, z1))), LENGTH#1(Cons(z0, z1)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z1, Cons(x1, x2))) -> c9(CONST_F#2(Cons(z1, Cons(x1, x2)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(Cons(z1, take#2(halve#1(length#1(x2)), Cons(x1, x2))), Cons(drop#2(S(halve#1(length#1(x2))), Cons(z1, Cons(x1, x2))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z1, Cons(x1, x2)), S(halve#1(length#1(x2))))), DIVIDE_YS#1(Cons(z1, Cons(x1, x2)), S(halve#1(length#1(x2)))), HALVE#1(length#1(x2)), LENGTH#1(x2))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Nil))) -> c9(CONST_F#2(Cons(x0, Cons(x1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(0)), Cons(x0, Cons(x1, Nil))), Cons(drop#2(S(halve#1(length#1(Nil))), Cons(x0, Cons(x1, Nil))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Nil)), S(halve#1(length#1(Nil)))), HALVE#1(length#1(Nil)), LENGTH#1(Nil))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Cons(z0, z1)))) -> c9(CONST_F#2(Cons(x0, Cons(x1, Cons(z0, z1))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(S(length#1(z1)))), Cons(x0, Cons(x1, Cons(z0, z1)))), Cons(drop#2(S(halve#1(length#1(Cons(z0, z1)))), Cons(x0, Cons(x1, Cons(z0, z1)))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Cons(z0, z1))), S(halve#1(length#1(Cons(z0, z1)))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(z0, z1))), S(halve#1(length#1(Cons(z0, z1))))), HALVE#1(length#1(Cons(z0, z1))), LENGTH#1(Cons(z0, z1)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, x2))) -> c9(MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, x2)), S(halve#1(length#1(x2))))), DIVIDE_YS#1(Cons(x0, Cons(x1, x2)), S(halve#1(length#1(x2)))))
S tuples:
   DIVIDE_YS#1(z0, z1) -> c(TAKE#2(z1, z0))
   DIVIDE_YS#1(z0, z1) -> c1(DROP#2(z1, z0))
   COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(z2, z3), z4, z5, z6, z7) -> c2(MERGE#2(z5, Cons(z2, z3)))
   COND_MERGE_YS_ZS_2(False, Cons(z0, z1), Cons(z2, z3), z4, z5, z6, z7) -> c3(MERGE#2(Cons(z0, z1), z7))
   DROP#2(S(z0), Cons(z1, z2)) -> c12(DROP#2(z0, z2))
   TAKE#2(S(z0), Cons(z1, z2)) -> c15(TAKE#2(z0, z2))
   HALVE#1(S(S(z0))) -> c18(HALVE#1(z0))
   CONST_F#2(z0, Cons(z1, Cons(z2, z3))) -> c19(MERGE#2(z1, z2))
   LEQ#2(S(z0), S(z1)) -> c22(LEQ#2(z0, z1))
   LENGTH#1(Cons(z0, z1)) -> c24(LENGTH#1(z1))
   MAP#2(dc(z0, z1, z2, z3, z4), Cons(z5, z6)) -> c26(DC#1(z0, z1, z2, z3, z4, z5))
   MAP#2(dc(z0, z1, z2, z3, z4), Cons(z5, z6)) -> c27(MAP#2(dc(z0, z1, z2, z3, z4), z6))
   MERGE#2(Cons(0, x1), Cons(z0, x3)) -> c6(COND_MERGE_YS_ZS_2(True, Cons(0, x1), Cons(z0, x3), 0, x1, z0, x3))
   MERGE#2(Cons(S(z0), x1), Cons(0, x3)) -> c6(COND_MERGE_YS_ZS_2(False, Cons(S(z0), x1), Cons(0, x3), S(z0), x1, 0, x3))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Cons(z0, z1)))) -> c9(CONST_F#2(Cons(x0, Cons(x1, Cons(z0, z1))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Cons(z0, z1))), S(halve#1(S(length#1(z1))))))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Cons(z0, z1))), S(halve#1(length#1(Cons(z0, z1)))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(z0, z1))), S(halve#1(length#1(Cons(z0, z1))))), HALVE#1(length#1(Cons(z0, z1))), LENGTH#1(Cons(z0, z1)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Nil))) -> c9(CONST_F#2(Cons(x0, Cons(x1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Nil)), S(halve#1(0))))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Nil)), S(halve#1(length#1(Nil)))), HALVE#1(length#1(Nil)))
   MERGE#2(Cons(S(0), x1), Cons(S(z0), x3)) -> c6(COND_MERGE_YS_ZS_2(True, Cons(S(0), x1), Cons(S(z0), x3), S(0), x1, S(z0), x3), LEQ#2(S(0), S(z0)))
   MERGE#2(Cons(S(S(z0)), x1), Cons(S(0), x3)) -> c6(COND_MERGE_YS_ZS_2(False, Cons(S(S(z0)), x1), Cons(S(0), x3), S(S(z0)), x1, S(0), x3), LEQ#2(S(S(z0)), S(0)))
   MERGE#2(Cons(S(S(z0)), x1), Cons(S(S(z1)), x3)) -> c6(COND_MERGE_YS_ZS_2(leq#2(z0, z1), Cons(S(S(z0)), x1), Cons(S(S(z1)), x3), S(S(z0)), x1, S(S(z1)), x3), LEQ#2(S(S(z0)), S(S(z1))))
   MERGE#2(Cons(S(x0), x1), Cons(S(x2), x3)) -> c6(LEQ#2(S(x0), S(x2)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, x2))) -> c9(CONST_F#2(Cons(x0, Cons(x1, x2)), Cons(dc#1(map, divisible, mergesort_zs_3, divide, const_f, take#2(S(halve#1(length#1(x2))), Cons(x0, Cons(x1, x2)))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(drop#2(S(halve#1(length#1(x2))), Cons(x0, Cons(x1, x2))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, x2)), S(halve#1(length#1(x2))))), DIVIDE_YS#1(Cons(x0, Cons(x1, x2)), S(halve#1(length#1(x2)))), HALVE#1(length#1(x2)), LENGTH#1(x2))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z1, Cons(x1, x2))) -> c9(CONST_F#2(Cons(z1, Cons(x1, x2)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(x2))), Cons(z1, Cons(x1, x2))), Cons(drop#2(halve#1(length#1(x2)), Cons(x1, x2)), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z1, Cons(x1, x2)), S(halve#1(length#1(x2))))), DIVIDE_YS#1(Cons(z1, Cons(x1, x2)), S(halve#1(length#1(x2)))), HALVE#1(length#1(x2)), LENGTH#1(x2))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Nil))) -> c9(CONST_F#2(Cons(x0, Cons(x1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(Nil))), Cons(x0, Cons(x1, Nil))), Cons(drop#2(S(halve#1(0)), Cons(x0, Cons(x1, Nil))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Nil)), S(halve#1(length#1(Nil)))), HALVE#1(length#1(Nil)), LENGTH#1(Nil))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Cons(z0, z1)))) -> c9(CONST_F#2(Cons(x0, Cons(x1, Cons(z0, z1))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(Cons(z0, z1)))), Cons(x0, Cons(x1, Cons(z0, z1)))), Cons(drop#2(S(halve#1(S(length#1(z1)))), Cons(x0, Cons(x1, Cons(z0, z1)))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Cons(z0, z1))), S(halve#1(length#1(Cons(z0, z1)))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(z0, z1))), S(halve#1(length#1(Cons(z0, z1))))), HALVE#1(length#1(Cons(z0, z1))), LENGTH#1(Cons(z0, z1)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z1, Cons(x1, x2))) -> c9(CONST_F#2(Cons(z1, Cons(x1, x2)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(Cons(z1, take#2(halve#1(length#1(x2)), Cons(x1, x2))), Cons(drop#2(S(halve#1(length#1(x2))), Cons(z1, Cons(x1, x2))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z1, Cons(x1, x2)), S(halve#1(length#1(x2))))), DIVIDE_YS#1(Cons(z1, Cons(x1, x2)), S(halve#1(length#1(x2)))), HALVE#1(length#1(x2)), LENGTH#1(x2))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Nil))) -> c9(CONST_F#2(Cons(x0, Cons(x1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(0)), Cons(x0, Cons(x1, Nil))), Cons(drop#2(S(halve#1(length#1(Nil))), Cons(x0, Cons(x1, Nil))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Nil)), S(halve#1(length#1(Nil)))), HALVE#1(length#1(Nil)), LENGTH#1(Nil))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Cons(z0, z1)))) -> c9(CONST_F#2(Cons(x0, Cons(x1, Cons(z0, z1))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(S(length#1(z1)))), Cons(x0, Cons(x1, Cons(z0, z1)))), Cons(drop#2(S(halve#1(length#1(Cons(z0, z1)))), Cons(x0, Cons(x1, Cons(z0, z1)))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Cons(z0, z1))), S(halve#1(length#1(Cons(z0, z1)))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(z0, z1))), S(halve#1(length#1(Cons(z0, z1))))), HALVE#1(length#1(Cons(z0, z1))), LENGTH#1(Cons(z0, z1)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, x2))) -> c9(MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, x2)), S(halve#1(length#1(x2))))), DIVIDE_YS#1(Cons(x0, Cons(x1, x2)), S(halve#1(length#1(x2)))))
K tuples:none
Defined Rule Symbols:   leq#2_2, map#2_2, divide_ys#1_2, halve#1_1, length#1_1, take#2_2, drop#2_2, dc#1_6, const_f#2_2, merge#2_2, cond_merge_ys_zs_2_7

Defined Pair Symbols:   DIVIDE_YS#1_2, COND_MERGE_YS_ZS_2_7, DROP#2_2, TAKE#2_2, HALVE#1_1, CONST_F#2_2, LEQ#2_2, LENGTH#1_1, MAP#2_2, MERGE#2_2, DC#1_6

Compound Symbols:   c_1, c1_1, c2_1, c3_1, c12_1, c15_1, c18_1, c19_1, c22_1, c24_1, c26_1, c27_1, c6_1, c9_5, c9_4, c6_2, c9_2


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

(95) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID))
Removed 2 trailing tuple parts
----------------------------------------

(96)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   leq#2(0, z0) -> True
   leq#2(S(z0), 0) -> False
   leq#2(S(z0), S(z1)) -> leq#2(z0, z1)
   map#2(dc(z0, z1, z2, z3, z4), Nil) -> Nil
   map#2(dc(z0, z1, z2, z3, z4), Cons(z5, z6)) -> Cons(dc#1(z0, z1, z2, z3, z4, z5), map#2(dc(z0, z1, z2, z3, z4), z6))
   divide_ys#1(z0, z1) -> Cons(take#2(z1, z0), Cons(drop#2(z1, z0), Nil))
   halve#1(0) -> 0
   halve#1(S(0)) -> S(0)
   halve#1(S(S(z0))) -> S(halve#1(z0))
   length#1(Nil) -> 0
   length#1(Cons(z0, z1)) -> S(length#1(z1))
   take#2(0, z0) -> Nil
   take#2(S(0), Nil) -> Cons(bot[0], Nil)
   take#2(S(z0), Cons(z1, z2)) -> Cons(z1, take#2(z0, z2))
   drop#2(0, z0) -> z0
   drop#2(S(0), Nil) -> bot[1]
   drop#2(S(z0), Cons(z1, z2)) -> drop#2(z0, z2)
   dc#1(map, divisible, mergesort_zs_3, divide, const_f, Nil) -> Nil
   dc#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Nil)) -> Cons(z0, Nil)
   dc#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> const_f#2(Cons(z0, Cons(z1, z2)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2))))))
   const_f#2(z0, Cons(z1, Cons(z2, z3))) -> merge#2(z1, z2)
   merge#2(Nil, z0) -> z0
   merge#2(Cons(z0, z1), Nil) -> Cons(z0, z1)
   merge#2(Cons(z0, z1), Cons(z2, z3)) -> cond_merge_ys_zs_2(leq#2(z0, z2), Cons(z0, z1), Cons(z2, z3), z0, z1, z2, z3)
   cond_merge_ys_zs_2(True, Cons(z0, z1), Cons(z2, z3), z4, z5, z6, z7) -> Cons(z4, merge#2(z5, Cons(z2, z3)))
   cond_merge_ys_zs_2(False, Cons(z0, z1), Cons(z2, z3), z4, z5, z6, z7) -> Cons(z6, merge#2(Cons(z0, z1), z7))
Tuples:
   DIVIDE_YS#1(z0, z1) -> c(TAKE#2(z1, z0))
   DIVIDE_YS#1(z0, z1) -> c1(DROP#2(z1, z0))
   COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(z2, z3), z4, z5, z6, z7) -> c2(MERGE#2(z5, Cons(z2, z3)))
   COND_MERGE_YS_ZS_2(False, Cons(z0, z1), Cons(z2, z3), z4, z5, z6, z7) -> c3(MERGE#2(Cons(z0, z1), z7))
   DROP#2(S(z0), Cons(z1, z2)) -> c12(DROP#2(z0, z2))
   TAKE#2(S(z0), Cons(z1, z2)) -> c15(TAKE#2(z0, z2))
   HALVE#1(S(S(z0))) -> c18(HALVE#1(z0))
   CONST_F#2(z0, Cons(z1, Cons(z2, z3))) -> c19(MERGE#2(z1, z2))
   LEQ#2(S(z0), S(z1)) -> c22(LEQ#2(z0, z1))
   LENGTH#1(Cons(z0, z1)) -> c24(LENGTH#1(z1))
   MAP#2(dc(z0, z1, z2, z3, z4), Cons(z5, z6)) -> c26(DC#1(z0, z1, z2, z3, z4, z5))
   MAP#2(dc(z0, z1, z2, z3, z4), Cons(z5, z6)) -> c27(MAP#2(dc(z0, z1, z2, z3, z4), z6))
   MERGE#2(Cons(0, x1), Cons(z0, x3)) -> c6(COND_MERGE_YS_ZS_2(True, Cons(0, x1), Cons(z0, x3), 0, x1, z0, x3))
   MERGE#2(Cons(S(z0), x1), Cons(0, x3)) -> c6(COND_MERGE_YS_ZS_2(False, Cons(S(z0), x1), Cons(0, x3), S(z0), x1, 0, x3))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Cons(z0, z1)))) -> c9(CONST_F#2(Cons(x0, Cons(x1, Cons(z0, z1))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Cons(z0, z1))), S(halve#1(S(length#1(z1))))))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Cons(z0, z1))), S(halve#1(length#1(Cons(z0, z1)))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(z0, z1))), S(halve#1(length#1(Cons(z0, z1))))), HALVE#1(length#1(Cons(z0, z1))), LENGTH#1(Cons(z0, z1)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Nil))) -> c9(CONST_F#2(Cons(x0, Cons(x1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Nil)), S(halve#1(0))))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Nil)), S(halve#1(length#1(Nil)))), HALVE#1(length#1(Nil)))
   MERGE#2(Cons(S(0), x1), Cons(S(z0), x3)) -> c6(COND_MERGE_YS_ZS_2(True, Cons(S(0), x1), Cons(S(z0), x3), S(0), x1, S(z0), x3), LEQ#2(S(0), S(z0)))
   MERGE#2(Cons(S(S(z0)), x1), Cons(S(0), x3)) -> c6(COND_MERGE_YS_ZS_2(False, Cons(S(S(z0)), x1), Cons(S(0), x3), S(S(z0)), x1, S(0), x3), LEQ#2(S(S(z0)), S(0)))
   MERGE#2(Cons(S(S(z0)), x1), Cons(S(S(z1)), x3)) -> c6(COND_MERGE_YS_ZS_2(leq#2(z0, z1), Cons(S(S(z0)), x1), Cons(S(S(z1)), x3), S(S(z0)), x1, S(S(z1)), x3), LEQ#2(S(S(z0)), S(S(z1))))
   MERGE#2(Cons(S(x0), x1), Cons(S(x2), x3)) -> c6(LEQ#2(S(x0), S(x2)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, x2))) -> c9(CONST_F#2(Cons(x0, Cons(x1, x2)), Cons(dc#1(map, divisible, mergesort_zs_3, divide, const_f, take#2(S(halve#1(length#1(x2))), Cons(x0, Cons(x1, x2)))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(drop#2(S(halve#1(length#1(x2))), Cons(x0, Cons(x1, x2))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, x2)), S(halve#1(length#1(x2))))), DIVIDE_YS#1(Cons(x0, Cons(x1, x2)), S(halve#1(length#1(x2)))), HALVE#1(length#1(x2)), LENGTH#1(x2))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z1, Cons(x1, x2))) -> c9(CONST_F#2(Cons(z1, Cons(x1, x2)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(x2))), Cons(z1, Cons(x1, x2))), Cons(drop#2(halve#1(length#1(x2)), Cons(x1, x2)), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z1, Cons(x1, x2)), S(halve#1(length#1(x2))))), DIVIDE_YS#1(Cons(z1, Cons(x1, x2)), S(halve#1(length#1(x2)))), HALVE#1(length#1(x2)), LENGTH#1(x2))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Cons(z0, z1)))) -> c9(CONST_F#2(Cons(x0, Cons(x1, Cons(z0, z1))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(Cons(z0, z1)))), Cons(x0, Cons(x1, Cons(z0, z1)))), Cons(drop#2(S(halve#1(S(length#1(z1)))), Cons(x0, Cons(x1, Cons(z0, z1)))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Cons(z0, z1))), S(halve#1(length#1(Cons(z0, z1)))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(z0, z1))), S(halve#1(length#1(Cons(z0, z1))))), HALVE#1(length#1(Cons(z0, z1))), LENGTH#1(Cons(z0, z1)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z1, Cons(x1, x2))) -> c9(CONST_F#2(Cons(z1, Cons(x1, x2)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(Cons(z1, take#2(halve#1(length#1(x2)), Cons(x1, x2))), Cons(drop#2(S(halve#1(length#1(x2))), Cons(z1, Cons(x1, x2))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z1, Cons(x1, x2)), S(halve#1(length#1(x2))))), DIVIDE_YS#1(Cons(z1, Cons(x1, x2)), S(halve#1(length#1(x2)))), HALVE#1(length#1(x2)), LENGTH#1(x2))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Cons(z0, z1)))) -> c9(CONST_F#2(Cons(x0, Cons(x1, Cons(z0, z1))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(S(length#1(z1)))), Cons(x0, Cons(x1, Cons(z0, z1)))), Cons(drop#2(S(halve#1(length#1(Cons(z0, z1)))), Cons(x0, Cons(x1, Cons(z0, z1)))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Cons(z0, z1))), S(halve#1(length#1(Cons(z0, z1)))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(z0, z1))), S(halve#1(length#1(Cons(z0, z1))))), HALVE#1(length#1(Cons(z0, z1))), LENGTH#1(Cons(z0, z1)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, x2))) -> c9(MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, x2)), S(halve#1(length#1(x2))))), DIVIDE_YS#1(Cons(x0, Cons(x1, x2)), S(halve#1(length#1(x2)))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Nil))) -> c9(CONST_F#2(Cons(x0, Cons(x1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(Nil))), Cons(x0, Cons(x1, Nil))), Cons(drop#2(S(halve#1(0)), Cons(x0, Cons(x1, Nil))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Nil)), S(halve#1(length#1(Nil)))), HALVE#1(length#1(Nil)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Nil))) -> c9(CONST_F#2(Cons(x0, Cons(x1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(0)), Cons(x0, Cons(x1, Nil))), Cons(drop#2(S(halve#1(length#1(Nil))), Cons(x0, Cons(x1, Nil))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Nil)), S(halve#1(length#1(Nil)))), HALVE#1(length#1(Nil)))
S tuples:
   DIVIDE_YS#1(z0, z1) -> c(TAKE#2(z1, z0))
   DIVIDE_YS#1(z0, z1) -> c1(DROP#2(z1, z0))
   COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(z2, z3), z4, z5, z6, z7) -> c2(MERGE#2(z5, Cons(z2, z3)))
   COND_MERGE_YS_ZS_2(False, Cons(z0, z1), Cons(z2, z3), z4, z5, z6, z7) -> c3(MERGE#2(Cons(z0, z1), z7))
   DROP#2(S(z0), Cons(z1, z2)) -> c12(DROP#2(z0, z2))
   TAKE#2(S(z0), Cons(z1, z2)) -> c15(TAKE#2(z0, z2))
   HALVE#1(S(S(z0))) -> c18(HALVE#1(z0))
   CONST_F#2(z0, Cons(z1, Cons(z2, z3))) -> c19(MERGE#2(z1, z2))
   LEQ#2(S(z0), S(z1)) -> c22(LEQ#2(z0, z1))
   LENGTH#1(Cons(z0, z1)) -> c24(LENGTH#1(z1))
   MAP#2(dc(z0, z1, z2, z3, z4), Cons(z5, z6)) -> c26(DC#1(z0, z1, z2, z3, z4, z5))
   MAP#2(dc(z0, z1, z2, z3, z4), Cons(z5, z6)) -> c27(MAP#2(dc(z0, z1, z2, z3, z4), z6))
   MERGE#2(Cons(0, x1), Cons(z0, x3)) -> c6(COND_MERGE_YS_ZS_2(True, Cons(0, x1), Cons(z0, x3), 0, x1, z0, x3))
   MERGE#2(Cons(S(z0), x1), Cons(0, x3)) -> c6(COND_MERGE_YS_ZS_2(False, Cons(S(z0), x1), Cons(0, x3), S(z0), x1, 0, x3))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Cons(z0, z1)))) -> c9(CONST_F#2(Cons(x0, Cons(x1, Cons(z0, z1))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Cons(z0, z1))), S(halve#1(S(length#1(z1))))))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Cons(z0, z1))), S(halve#1(length#1(Cons(z0, z1)))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(z0, z1))), S(halve#1(length#1(Cons(z0, z1))))), HALVE#1(length#1(Cons(z0, z1))), LENGTH#1(Cons(z0, z1)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Nil))) -> c9(CONST_F#2(Cons(x0, Cons(x1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Nil)), S(halve#1(0))))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Nil)), S(halve#1(length#1(Nil)))), HALVE#1(length#1(Nil)))
   MERGE#2(Cons(S(0), x1), Cons(S(z0), x3)) -> c6(COND_MERGE_YS_ZS_2(True, Cons(S(0), x1), Cons(S(z0), x3), S(0), x1, S(z0), x3), LEQ#2(S(0), S(z0)))
   MERGE#2(Cons(S(S(z0)), x1), Cons(S(0), x3)) -> c6(COND_MERGE_YS_ZS_2(False, Cons(S(S(z0)), x1), Cons(S(0), x3), S(S(z0)), x1, S(0), x3), LEQ#2(S(S(z0)), S(0)))
   MERGE#2(Cons(S(S(z0)), x1), Cons(S(S(z1)), x3)) -> c6(COND_MERGE_YS_ZS_2(leq#2(z0, z1), Cons(S(S(z0)), x1), Cons(S(S(z1)), x3), S(S(z0)), x1, S(S(z1)), x3), LEQ#2(S(S(z0)), S(S(z1))))
   MERGE#2(Cons(S(x0), x1), Cons(S(x2), x3)) -> c6(LEQ#2(S(x0), S(x2)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, x2))) -> c9(CONST_F#2(Cons(x0, Cons(x1, x2)), Cons(dc#1(map, divisible, mergesort_zs_3, divide, const_f, take#2(S(halve#1(length#1(x2))), Cons(x0, Cons(x1, x2)))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(drop#2(S(halve#1(length#1(x2))), Cons(x0, Cons(x1, x2))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, x2)), S(halve#1(length#1(x2))))), DIVIDE_YS#1(Cons(x0, Cons(x1, x2)), S(halve#1(length#1(x2)))), HALVE#1(length#1(x2)), LENGTH#1(x2))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z1, Cons(x1, x2))) -> c9(CONST_F#2(Cons(z1, Cons(x1, x2)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(x2))), Cons(z1, Cons(x1, x2))), Cons(drop#2(halve#1(length#1(x2)), Cons(x1, x2)), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z1, Cons(x1, x2)), S(halve#1(length#1(x2))))), DIVIDE_YS#1(Cons(z1, Cons(x1, x2)), S(halve#1(length#1(x2)))), HALVE#1(length#1(x2)), LENGTH#1(x2))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Cons(z0, z1)))) -> c9(CONST_F#2(Cons(x0, Cons(x1, Cons(z0, z1))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(Cons(z0, z1)))), Cons(x0, Cons(x1, Cons(z0, z1)))), Cons(drop#2(S(halve#1(S(length#1(z1)))), Cons(x0, Cons(x1, Cons(z0, z1)))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Cons(z0, z1))), S(halve#1(length#1(Cons(z0, z1)))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(z0, z1))), S(halve#1(length#1(Cons(z0, z1))))), HALVE#1(length#1(Cons(z0, z1))), LENGTH#1(Cons(z0, z1)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z1, Cons(x1, x2))) -> c9(CONST_F#2(Cons(z1, Cons(x1, x2)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(Cons(z1, take#2(halve#1(length#1(x2)), Cons(x1, x2))), Cons(drop#2(S(halve#1(length#1(x2))), Cons(z1, Cons(x1, x2))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z1, Cons(x1, x2)), S(halve#1(length#1(x2))))), DIVIDE_YS#1(Cons(z1, Cons(x1, x2)), S(halve#1(length#1(x2)))), HALVE#1(length#1(x2)), LENGTH#1(x2))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Cons(z0, z1)))) -> c9(CONST_F#2(Cons(x0, Cons(x1, Cons(z0, z1))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(S(length#1(z1)))), Cons(x0, Cons(x1, Cons(z0, z1)))), Cons(drop#2(S(halve#1(length#1(Cons(z0, z1)))), Cons(x0, Cons(x1, Cons(z0, z1)))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Cons(z0, z1))), S(halve#1(length#1(Cons(z0, z1)))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(z0, z1))), S(halve#1(length#1(Cons(z0, z1))))), HALVE#1(length#1(Cons(z0, z1))), LENGTH#1(Cons(z0, z1)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, x2))) -> c9(MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, x2)), S(halve#1(length#1(x2))))), DIVIDE_YS#1(Cons(x0, Cons(x1, x2)), S(halve#1(length#1(x2)))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Nil))) -> c9(CONST_F#2(Cons(x0, Cons(x1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(Nil))), Cons(x0, Cons(x1, Nil))), Cons(drop#2(S(halve#1(0)), Cons(x0, Cons(x1, Nil))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Nil)), S(halve#1(length#1(Nil)))), HALVE#1(length#1(Nil)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Nil))) -> c9(CONST_F#2(Cons(x0, Cons(x1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(0)), Cons(x0, Cons(x1, Nil))), Cons(drop#2(S(halve#1(length#1(Nil))), Cons(x0, Cons(x1, Nil))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Nil)), S(halve#1(length#1(Nil)))), HALVE#1(length#1(Nil)))
K tuples:none
Defined Rule Symbols:   leq#2_2, map#2_2, divide_ys#1_2, halve#1_1, length#1_1, take#2_2, drop#2_2, dc#1_6, const_f#2_2, merge#2_2, cond_merge_ys_zs_2_7

Defined Pair Symbols:   DIVIDE_YS#1_2, COND_MERGE_YS_ZS_2_7, DROP#2_2, TAKE#2_2, HALVE#1_1, CONST_F#2_2, LEQ#2_2, LENGTH#1_1, MAP#2_2, MERGE#2_2, DC#1_6

Compound Symbols:   c_1, c1_1, c2_1, c3_1, c12_1, c15_1, c18_1, c19_1, c22_1, c24_1, c26_1, c27_1, c6_1, c9_5, c9_4, c6_2, c9_2


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(97) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Cons(z0, z1)))) -> c9(CONST_F#2(Cons(x0, Cons(x1, Cons(z0, z1))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Cons(z0, z1))), S(halve#1(S(length#1(z1))))))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Cons(z0, z1))), S(halve#1(length#1(Cons(z0, z1)))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(z0, z1))), S(halve#1(length#1(Cons(z0, z1))))), HALVE#1(length#1(Cons(z0, z1))), LENGTH#1(Cons(z0, z1))) by 
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Cons(x2, x3)))) -> c9(CONST_F#2(Cons(x0, Cons(x1, Cons(x2, x3))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(S(length#1(x3)))), Cons(x0, Cons(x1, Cons(x2, x3)))), Cons(drop#2(S(halve#1(S(length#1(x3)))), Cons(x0, Cons(x1, Cons(x2, x3)))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Cons(x2, x3))), S(halve#1(length#1(Cons(x2, x3)))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, x3))), S(halve#1(length#1(Cons(x2, x3))))), HALVE#1(length#1(Cons(x2, x3))), LENGTH#1(Cons(x2, x3)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Cons(x2, Nil)))) -> c9(CONST_F#2(Cons(x0, Cons(x1, Cons(x2, Nil))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Cons(x2, Nil))), S(halve#1(S(0)))))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Cons(x2, Nil))), S(halve#1(length#1(Cons(x2, Nil)))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Nil))), S(halve#1(length#1(Cons(x2, Nil))))), HALVE#1(length#1(Cons(x2, Nil))), LENGTH#1(Cons(x2, Nil)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Cons(x2, Cons(z0, z1))))) -> c9(CONST_F#2(Cons(x0, Cons(x1, Cons(x2, Cons(z0, z1)))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Cons(x2, Cons(z0, z1)))), S(halve#1(S(S(length#1(z1)))))))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Cons(x2, Cons(z0, z1)))), S(halve#1(length#1(Cons(x2, Cons(z0, z1))))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Cons(z0, z1)))), S(halve#1(length#1(Cons(x2, Cons(z0, z1)))))), HALVE#1(length#1(Cons(x2, Cons(z0, z1)))), LENGTH#1(Cons(x2, Cons(z0, z1))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Cons(x2, x3)))) -> c9(MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Cons(x2, x3))), S(halve#1(length#1(Cons(x2, x3)))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, x3))), S(halve#1(length#1(Cons(x2, x3))))), HALVE#1(length#1(Cons(x2, x3))), LENGTH#1(Cons(x2, x3)))

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

(98)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   leq#2(0, z0) -> True
   leq#2(S(z0), 0) -> False
   leq#2(S(z0), S(z1)) -> leq#2(z0, z1)
   map#2(dc(z0, z1, z2, z3, z4), Nil) -> Nil
   map#2(dc(z0, z1, z2, z3, z4), Cons(z5, z6)) -> Cons(dc#1(z0, z1, z2, z3, z4, z5), map#2(dc(z0, z1, z2, z3, z4), z6))
   divide_ys#1(z0, z1) -> Cons(take#2(z1, z0), Cons(drop#2(z1, z0), Nil))
   halve#1(0) -> 0
   halve#1(S(0)) -> S(0)
   halve#1(S(S(z0))) -> S(halve#1(z0))
   length#1(Nil) -> 0
   length#1(Cons(z0, z1)) -> S(length#1(z1))
   take#2(0, z0) -> Nil
   take#2(S(0), Nil) -> Cons(bot[0], Nil)
   take#2(S(z0), Cons(z1, z2)) -> Cons(z1, take#2(z0, z2))
   drop#2(0, z0) -> z0
   drop#2(S(0), Nil) -> bot[1]
   drop#2(S(z0), Cons(z1, z2)) -> drop#2(z0, z2)
   dc#1(map, divisible, mergesort_zs_3, divide, const_f, Nil) -> Nil
   dc#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Nil)) -> Cons(z0, Nil)
   dc#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> const_f#2(Cons(z0, Cons(z1, z2)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2))))))
   const_f#2(z0, Cons(z1, Cons(z2, z3))) -> merge#2(z1, z2)
   merge#2(Nil, z0) -> z0
   merge#2(Cons(z0, z1), Nil) -> Cons(z0, z1)
   merge#2(Cons(z0, z1), Cons(z2, z3)) -> cond_merge_ys_zs_2(leq#2(z0, z2), Cons(z0, z1), Cons(z2, z3), z0, z1, z2, z3)
   cond_merge_ys_zs_2(True, Cons(z0, z1), Cons(z2, z3), z4, z5, z6, z7) -> Cons(z4, merge#2(z5, Cons(z2, z3)))
   cond_merge_ys_zs_2(False, Cons(z0, z1), Cons(z2, z3), z4, z5, z6, z7) -> Cons(z6, merge#2(Cons(z0, z1), z7))
Tuples:
   DIVIDE_YS#1(z0, z1) -> c(TAKE#2(z1, z0))
   DIVIDE_YS#1(z0, z1) -> c1(DROP#2(z1, z0))
   COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(z2, z3), z4, z5, z6, z7) -> c2(MERGE#2(z5, Cons(z2, z3)))
   COND_MERGE_YS_ZS_2(False, Cons(z0, z1), Cons(z2, z3), z4, z5, z6, z7) -> c3(MERGE#2(Cons(z0, z1), z7))
   DROP#2(S(z0), Cons(z1, z2)) -> c12(DROP#2(z0, z2))
   TAKE#2(S(z0), Cons(z1, z2)) -> c15(TAKE#2(z0, z2))
   HALVE#1(S(S(z0))) -> c18(HALVE#1(z0))
   CONST_F#2(z0, Cons(z1, Cons(z2, z3))) -> c19(MERGE#2(z1, z2))
   LEQ#2(S(z0), S(z1)) -> c22(LEQ#2(z0, z1))
   LENGTH#1(Cons(z0, z1)) -> c24(LENGTH#1(z1))
   MAP#2(dc(z0, z1, z2, z3, z4), Cons(z5, z6)) -> c26(DC#1(z0, z1, z2, z3, z4, z5))
   MAP#2(dc(z0, z1, z2, z3, z4), Cons(z5, z6)) -> c27(MAP#2(dc(z0, z1, z2, z3, z4), z6))
   MERGE#2(Cons(0, x1), Cons(z0, x3)) -> c6(COND_MERGE_YS_ZS_2(True, Cons(0, x1), Cons(z0, x3), 0, x1, z0, x3))
   MERGE#2(Cons(S(z0), x1), Cons(0, x3)) -> c6(COND_MERGE_YS_ZS_2(False, Cons(S(z0), x1), Cons(0, x3), S(z0), x1, 0, x3))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Nil))) -> c9(CONST_F#2(Cons(x0, Cons(x1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Nil)), S(halve#1(0))))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Nil)), S(halve#1(length#1(Nil)))), HALVE#1(length#1(Nil)))
   MERGE#2(Cons(S(0), x1), Cons(S(z0), x3)) -> c6(COND_MERGE_YS_ZS_2(True, Cons(S(0), x1), Cons(S(z0), x3), S(0), x1, S(z0), x3), LEQ#2(S(0), S(z0)))
   MERGE#2(Cons(S(S(z0)), x1), Cons(S(0), x3)) -> c6(COND_MERGE_YS_ZS_2(False, Cons(S(S(z0)), x1), Cons(S(0), x3), S(S(z0)), x1, S(0), x3), LEQ#2(S(S(z0)), S(0)))
   MERGE#2(Cons(S(S(z0)), x1), Cons(S(S(z1)), x3)) -> c6(COND_MERGE_YS_ZS_2(leq#2(z0, z1), Cons(S(S(z0)), x1), Cons(S(S(z1)), x3), S(S(z0)), x1, S(S(z1)), x3), LEQ#2(S(S(z0)), S(S(z1))))
   MERGE#2(Cons(S(x0), x1), Cons(S(x2), x3)) -> c6(LEQ#2(S(x0), S(x2)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, x2))) -> c9(CONST_F#2(Cons(x0, Cons(x1, x2)), Cons(dc#1(map, divisible, mergesort_zs_3, divide, const_f, take#2(S(halve#1(length#1(x2))), Cons(x0, Cons(x1, x2)))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(drop#2(S(halve#1(length#1(x2))), Cons(x0, Cons(x1, x2))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, x2)), S(halve#1(length#1(x2))))), DIVIDE_YS#1(Cons(x0, Cons(x1, x2)), S(halve#1(length#1(x2)))), HALVE#1(length#1(x2)), LENGTH#1(x2))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z1, Cons(x1, x2))) -> c9(CONST_F#2(Cons(z1, Cons(x1, x2)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(x2))), Cons(z1, Cons(x1, x2))), Cons(drop#2(halve#1(length#1(x2)), Cons(x1, x2)), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z1, Cons(x1, x2)), S(halve#1(length#1(x2))))), DIVIDE_YS#1(Cons(z1, Cons(x1, x2)), S(halve#1(length#1(x2)))), HALVE#1(length#1(x2)), LENGTH#1(x2))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Cons(z0, z1)))) -> c9(CONST_F#2(Cons(x0, Cons(x1, Cons(z0, z1))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(Cons(z0, z1)))), Cons(x0, Cons(x1, Cons(z0, z1)))), Cons(drop#2(S(halve#1(S(length#1(z1)))), Cons(x0, Cons(x1, Cons(z0, z1)))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Cons(z0, z1))), S(halve#1(length#1(Cons(z0, z1)))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(z0, z1))), S(halve#1(length#1(Cons(z0, z1))))), HALVE#1(length#1(Cons(z0, z1))), LENGTH#1(Cons(z0, z1)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z1, Cons(x1, x2))) -> c9(CONST_F#2(Cons(z1, Cons(x1, x2)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(Cons(z1, take#2(halve#1(length#1(x2)), Cons(x1, x2))), Cons(drop#2(S(halve#1(length#1(x2))), Cons(z1, Cons(x1, x2))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z1, Cons(x1, x2)), S(halve#1(length#1(x2))))), DIVIDE_YS#1(Cons(z1, Cons(x1, x2)), S(halve#1(length#1(x2)))), HALVE#1(length#1(x2)), LENGTH#1(x2))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Cons(z0, z1)))) -> c9(CONST_F#2(Cons(x0, Cons(x1, Cons(z0, z1))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(S(length#1(z1)))), Cons(x0, Cons(x1, Cons(z0, z1)))), Cons(drop#2(S(halve#1(length#1(Cons(z0, z1)))), Cons(x0, Cons(x1, Cons(z0, z1)))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Cons(z0, z1))), S(halve#1(length#1(Cons(z0, z1)))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(z0, z1))), S(halve#1(length#1(Cons(z0, z1))))), HALVE#1(length#1(Cons(z0, z1))), LENGTH#1(Cons(z0, z1)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, x2))) -> c9(MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, x2)), S(halve#1(length#1(x2))))), DIVIDE_YS#1(Cons(x0, Cons(x1, x2)), S(halve#1(length#1(x2)))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Nil))) -> c9(CONST_F#2(Cons(x0, Cons(x1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(Nil))), Cons(x0, Cons(x1, Nil))), Cons(drop#2(S(halve#1(0)), Cons(x0, Cons(x1, Nil))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Nil)), S(halve#1(length#1(Nil)))), HALVE#1(length#1(Nil)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Nil))) -> c9(CONST_F#2(Cons(x0, Cons(x1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(0)), Cons(x0, Cons(x1, Nil))), Cons(drop#2(S(halve#1(length#1(Nil))), Cons(x0, Cons(x1, Nil))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Nil)), S(halve#1(length#1(Nil)))), HALVE#1(length#1(Nil)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Cons(x2, x3)))) -> c9(CONST_F#2(Cons(x0, Cons(x1, Cons(x2, x3))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(S(length#1(x3)))), Cons(x0, Cons(x1, Cons(x2, x3)))), Cons(drop#2(S(halve#1(S(length#1(x3)))), Cons(x0, Cons(x1, Cons(x2, x3)))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Cons(x2, x3))), S(halve#1(length#1(Cons(x2, x3)))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, x3))), S(halve#1(length#1(Cons(x2, x3))))), HALVE#1(length#1(Cons(x2, x3))), LENGTH#1(Cons(x2, x3)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Cons(x2, Nil)))) -> c9(CONST_F#2(Cons(x0, Cons(x1, Cons(x2, Nil))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Cons(x2, Nil))), S(halve#1(S(0)))))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Cons(x2, Nil))), S(halve#1(length#1(Cons(x2, Nil)))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Nil))), S(halve#1(length#1(Cons(x2, Nil))))), HALVE#1(length#1(Cons(x2, Nil))), LENGTH#1(Cons(x2, Nil)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Cons(x2, Cons(z0, z1))))) -> c9(CONST_F#2(Cons(x0, Cons(x1, Cons(x2, Cons(z0, z1)))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Cons(x2, Cons(z0, z1)))), S(halve#1(S(S(length#1(z1)))))))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Cons(x2, Cons(z0, z1)))), S(halve#1(length#1(Cons(x2, Cons(z0, z1))))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Cons(z0, z1)))), S(halve#1(length#1(Cons(x2, Cons(z0, z1)))))), HALVE#1(length#1(Cons(x2, Cons(z0, z1)))), LENGTH#1(Cons(x2, Cons(z0, z1))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Cons(x2, x3)))) -> c9(MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Cons(x2, x3))), S(halve#1(length#1(Cons(x2, x3)))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, x3))), S(halve#1(length#1(Cons(x2, x3))))), HALVE#1(length#1(Cons(x2, x3))), LENGTH#1(Cons(x2, x3)))
S tuples:
   DIVIDE_YS#1(z0, z1) -> c(TAKE#2(z1, z0))
   DIVIDE_YS#1(z0, z1) -> c1(DROP#2(z1, z0))
   COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(z2, z3), z4, z5, z6, z7) -> c2(MERGE#2(z5, Cons(z2, z3)))
   COND_MERGE_YS_ZS_2(False, Cons(z0, z1), Cons(z2, z3), z4, z5, z6, z7) -> c3(MERGE#2(Cons(z0, z1), z7))
   DROP#2(S(z0), Cons(z1, z2)) -> c12(DROP#2(z0, z2))
   TAKE#2(S(z0), Cons(z1, z2)) -> c15(TAKE#2(z0, z2))
   HALVE#1(S(S(z0))) -> c18(HALVE#1(z0))
   CONST_F#2(z0, Cons(z1, Cons(z2, z3))) -> c19(MERGE#2(z1, z2))
   LEQ#2(S(z0), S(z1)) -> c22(LEQ#2(z0, z1))
   LENGTH#1(Cons(z0, z1)) -> c24(LENGTH#1(z1))
   MAP#2(dc(z0, z1, z2, z3, z4), Cons(z5, z6)) -> c26(DC#1(z0, z1, z2, z3, z4, z5))
   MAP#2(dc(z0, z1, z2, z3, z4), Cons(z5, z6)) -> c27(MAP#2(dc(z0, z1, z2, z3, z4), z6))
   MERGE#2(Cons(0, x1), Cons(z0, x3)) -> c6(COND_MERGE_YS_ZS_2(True, Cons(0, x1), Cons(z0, x3), 0, x1, z0, x3))
   MERGE#2(Cons(S(z0), x1), Cons(0, x3)) -> c6(COND_MERGE_YS_ZS_2(False, Cons(S(z0), x1), Cons(0, x3), S(z0), x1, 0, x3))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Nil))) -> c9(CONST_F#2(Cons(x0, Cons(x1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Nil)), S(halve#1(0))))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Nil)), S(halve#1(length#1(Nil)))), HALVE#1(length#1(Nil)))
   MERGE#2(Cons(S(0), x1), Cons(S(z0), x3)) -> c6(COND_MERGE_YS_ZS_2(True, Cons(S(0), x1), Cons(S(z0), x3), S(0), x1, S(z0), x3), LEQ#2(S(0), S(z0)))
   MERGE#2(Cons(S(S(z0)), x1), Cons(S(0), x3)) -> c6(COND_MERGE_YS_ZS_2(False, Cons(S(S(z0)), x1), Cons(S(0), x3), S(S(z0)), x1, S(0), x3), LEQ#2(S(S(z0)), S(0)))
   MERGE#2(Cons(S(S(z0)), x1), Cons(S(S(z1)), x3)) -> c6(COND_MERGE_YS_ZS_2(leq#2(z0, z1), Cons(S(S(z0)), x1), Cons(S(S(z1)), x3), S(S(z0)), x1, S(S(z1)), x3), LEQ#2(S(S(z0)), S(S(z1))))
   MERGE#2(Cons(S(x0), x1), Cons(S(x2), x3)) -> c6(LEQ#2(S(x0), S(x2)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, x2))) -> c9(CONST_F#2(Cons(x0, Cons(x1, x2)), Cons(dc#1(map, divisible, mergesort_zs_3, divide, const_f, take#2(S(halve#1(length#1(x2))), Cons(x0, Cons(x1, x2)))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(drop#2(S(halve#1(length#1(x2))), Cons(x0, Cons(x1, x2))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, x2)), S(halve#1(length#1(x2))))), DIVIDE_YS#1(Cons(x0, Cons(x1, x2)), S(halve#1(length#1(x2)))), HALVE#1(length#1(x2)), LENGTH#1(x2))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z1, Cons(x1, x2))) -> c9(CONST_F#2(Cons(z1, Cons(x1, x2)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(x2))), Cons(z1, Cons(x1, x2))), Cons(drop#2(halve#1(length#1(x2)), Cons(x1, x2)), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z1, Cons(x1, x2)), S(halve#1(length#1(x2))))), DIVIDE_YS#1(Cons(z1, Cons(x1, x2)), S(halve#1(length#1(x2)))), HALVE#1(length#1(x2)), LENGTH#1(x2))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Cons(z0, z1)))) -> c9(CONST_F#2(Cons(x0, Cons(x1, Cons(z0, z1))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(Cons(z0, z1)))), Cons(x0, Cons(x1, Cons(z0, z1)))), Cons(drop#2(S(halve#1(S(length#1(z1)))), Cons(x0, Cons(x1, Cons(z0, z1)))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Cons(z0, z1))), S(halve#1(length#1(Cons(z0, z1)))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(z0, z1))), S(halve#1(length#1(Cons(z0, z1))))), HALVE#1(length#1(Cons(z0, z1))), LENGTH#1(Cons(z0, z1)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z1, Cons(x1, x2))) -> c9(CONST_F#2(Cons(z1, Cons(x1, x2)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(Cons(z1, take#2(halve#1(length#1(x2)), Cons(x1, x2))), Cons(drop#2(S(halve#1(length#1(x2))), Cons(z1, Cons(x1, x2))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z1, Cons(x1, x2)), S(halve#1(length#1(x2))))), DIVIDE_YS#1(Cons(z1, Cons(x1, x2)), S(halve#1(length#1(x2)))), HALVE#1(length#1(x2)), LENGTH#1(x2))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Cons(z0, z1)))) -> c9(CONST_F#2(Cons(x0, Cons(x1, Cons(z0, z1))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(S(length#1(z1)))), Cons(x0, Cons(x1, Cons(z0, z1)))), Cons(drop#2(S(halve#1(length#1(Cons(z0, z1)))), Cons(x0, Cons(x1, Cons(z0, z1)))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Cons(z0, z1))), S(halve#1(length#1(Cons(z0, z1)))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(z0, z1))), S(halve#1(length#1(Cons(z0, z1))))), HALVE#1(length#1(Cons(z0, z1))), LENGTH#1(Cons(z0, z1)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, x2))) -> c9(MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, x2)), S(halve#1(length#1(x2))))), DIVIDE_YS#1(Cons(x0, Cons(x1, x2)), S(halve#1(length#1(x2)))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Nil))) -> c9(CONST_F#2(Cons(x0, Cons(x1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(Nil))), Cons(x0, Cons(x1, Nil))), Cons(drop#2(S(halve#1(0)), Cons(x0, Cons(x1, Nil))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Nil)), S(halve#1(length#1(Nil)))), HALVE#1(length#1(Nil)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Nil))) -> c9(CONST_F#2(Cons(x0, Cons(x1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(0)), Cons(x0, Cons(x1, Nil))), Cons(drop#2(S(halve#1(length#1(Nil))), Cons(x0, Cons(x1, Nil))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Nil)), S(halve#1(length#1(Nil)))), HALVE#1(length#1(Nil)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Cons(x2, x3)))) -> c9(CONST_F#2(Cons(x0, Cons(x1, Cons(x2, x3))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(S(length#1(x3)))), Cons(x0, Cons(x1, Cons(x2, x3)))), Cons(drop#2(S(halve#1(S(length#1(x3)))), Cons(x0, Cons(x1, Cons(x2, x3)))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Cons(x2, x3))), S(halve#1(length#1(Cons(x2, x3)))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, x3))), S(halve#1(length#1(Cons(x2, x3))))), HALVE#1(length#1(Cons(x2, x3))), LENGTH#1(Cons(x2, x3)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Cons(x2, Nil)))) -> c9(CONST_F#2(Cons(x0, Cons(x1, Cons(x2, Nil))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Cons(x2, Nil))), S(halve#1(S(0)))))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Cons(x2, Nil))), S(halve#1(length#1(Cons(x2, Nil)))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Nil))), S(halve#1(length#1(Cons(x2, Nil))))), HALVE#1(length#1(Cons(x2, Nil))), LENGTH#1(Cons(x2, Nil)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Cons(x2, Cons(z0, z1))))) -> c9(CONST_F#2(Cons(x0, Cons(x1, Cons(x2, Cons(z0, z1)))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Cons(x2, Cons(z0, z1)))), S(halve#1(S(S(length#1(z1)))))))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Cons(x2, Cons(z0, z1)))), S(halve#1(length#1(Cons(x2, Cons(z0, z1))))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Cons(z0, z1)))), S(halve#1(length#1(Cons(x2, Cons(z0, z1)))))), HALVE#1(length#1(Cons(x2, Cons(z0, z1)))), LENGTH#1(Cons(x2, Cons(z0, z1))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Cons(x2, x3)))) -> c9(MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Cons(x2, x3))), S(halve#1(length#1(Cons(x2, x3)))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, x3))), S(halve#1(length#1(Cons(x2, x3))))), HALVE#1(length#1(Cons(x2, x3))), LENGTH#1(Cons(x2, x3)))
K tuples:none
Defined Rule Symbols:   leq#2_2, map#2_2, divide_ys#1_2, halve#1_1, length#1_1, take#2_2, drop#2_2, dc#1_6, const_f#2_2, merge#2_2, cond_merge_ys_zs_2_7

Defined Pair Symbols:   DIVIDE_YS#1_2, COND_MERGE_YS_ZS_2_7, DROP#2_2, TAKE#2_2, HALVE#1_1, CONST_F#2_2, LEQ#2_2, LENGTH#1_1, MAP#2_2, MERGE#2_2, DC#1_6

Compound Symbols:   c_1, c1_1, c2_1, c3_1, c12_1, c15_1, c18_1, c19_1, c22_1, c24_1, c26_1, c27_1, c6_1, c9_4, c6_2, c9_5, c9_2


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

(99) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Nil))) -> c9(CONST_F#2(Cons(x0, Cons(x1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Nil)), S(halve#1(0))))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Nil)), S(halve#1(length#1(Nil)))), HALVE#1(length#1(Nil))) by 
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Nil))) -> c9(CONST_F#2(Cons(x0, Cons(x1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(0)), Cons(x0, Cons(x1, Nil))), Cons(drop#2(S(halve#1(0)), Cons(x0, Cons(x1, Nil))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Nil)), S(halve#1(length#1(Nil)))), HALVE#1(length#1(Nil)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Nil))) -> c9(CONST_F#2(Cons(x0, Cons(x1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Nil)), S(0)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Nil)), S(halve#1(length#1(Nil)))), HALVE#1(length#1(Nil)))

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

(100)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   leq#2(0, z0) -> True
   leq#2(S(z0), 0) -> False
   leq#2(S(z0), S(z1)) -> leq#2(z0, z1)
   map#2(dc(z0, z1, z2, z3, z4), Nil) -> Nil
   map#2(dc(z0, z1, z2, z3, z4), Cons(z5, z6)) -> Cons(dc#1(z0, z1, z2, z3, z4, z5), map#2(dc(z0, z1, z2, z3, z4), z6))
   divide_ys#1(z0, z1) -> Cons(take#2(z1, z0), Cons(drop#2(z1, z0), Nil))
   halve#1(0) -> 0
   halve#1(S(0)) -> S(0)
   halve#1(S(S(z0))) -> S(halve#1(z0))
   length#1(Nil) -> 0
   length#1(Cons(z0, z1)) -> S(length#1(z1))
   take#2(0, z0) -> Nil
   take#2(S(0), Nil) -> Cons(bot[0], Nil)
   take#2(S(z0), Cons(z1, z2)) -> Cons(z1, take#2(z0, z2))
   drop#2(0, z0) -> z0
   drop#2(S(0), Nil) -> bot[1]
   drop#2(S(z0), Cons(z1, z2)) -> drop#2(z0, z2)
   dc#1(map, divisible, mergesort_zs_3, divide, const_f, Nil) -> Nil
   dc#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Nil)) -> Cons(z0, Nil)
   dc#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> const_f#2(Cons(z0, Cons(z1, z2)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2))))))
   const_f#2(z0, Cons(z1, Cons(z2, z3))) -> merge#2(z1, z2)
   merge#2(Nil, z0) -> z0
   merge#2(Cons(z0, z1), Nil) -> Cons(z0, z1)
   merge#2(Cons(z0, z1), Cons(z2, z3)) -> cond_merge_ys_zs_2(leq#2(z0, z2), Cons(z0, z1), Cons(z2, z3), z0, z1, z2, z3)
   cond_merge_ys_zs_2(True, Cons(z0, z1), Cons(z2, z3), z4, z5, z6, z7) -> Cons(z4, merge#2(z5, Cons(z2, z3)))
   cond_merge_ys_zs_2(False, Cons(z0, z1), Cons(z2, z3), z4, z5, z6, z7) -> Cons(z6, merge#2(Cons(z0, z1), z7))
Tuples:
   DIVIDE_YS#1(z0, z1) -> c(TAKE#2(z1, z0))
   DIVIDE_YS#1(z0, z1) -> c1(DROP#2(z1, z0))
   COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(z2, z3), z4, z5, z6, z7) -> c2(MERGE#2(z5, Cons(z2, z3)))
   COND_MERGE_YS_ZS_2(False, Cons(z0, z1), Cons(z2, z3), z4, z5, z6, z7) -> c3(MERGE#2(Cons(z0, z1), z7))
   DROP#2(S(z0), Cons(z1, z2)) -> c12(DROP#2(z0, z2))
   TAKE#2(S(z0), Cons(z1, z2)) -> c15(TAKE#2(z0, z2))
   HALVE#1(S(S(z0))) -> c18(HALVE#1(z0))
   CONST_F#2(z0, Cons(z1, Cons(z2, z3))) -> c19(MERGE#2(z1, z2))
   LEQ#2(S(z0), S(z1)) -> c22(LEQ#2(z0, z1))
   LENGTH#1(Cons(z0, z1)) -> c24(LENGTH#1(z1))
   MAP#2(dc(z0, z1, z2, z3, z4), Cons(z5, z6)) -> c26(DC#1(z0, z1, z2, z3, z4, z5))
   MAP#2(dc(z0, z1, z2, z3, z4), Cons(z5, z6)) -> c27(MAP#2(dc(z0, z1, z2, z3, z4), z6))
   MERGE#2(Cons(0, x1), Cons(z0, x3)) -> c6(COND_MERGE_YS_ZS_2(True, Cons(0, x1), Cons(z0, x3), 0, x1, z0, x3))
   MERGE#2(Cons(S(z0), x1), Cons(0, x3)) -> c6(COND_MERGE_YS_ZS_2(False, Cons(S(z0), x1), Cons(0, x3), S(z0), x1, 0, x3))
   MERGE#2(Cons(S(0), x1), Cons(S(z0), x3)) -> c6(COND_MERGE_YS_ZS_2(True, Cons(S(0), x1), Cons(S(z0), x3), S(0), x1, S(z0), x3), LEQ#2(S(0), S(z0)))
   MERGE#2(Cons(S(S(z0)), x1), Cons(S(0), x3)) -> c6(COND_MERGE_YS_ZS_2(False, Cons(S(S(z0)), x1), Cons(S(0), x3), S(S(z0)), x1, S(0), x3), LEQ#2(S(S(z0)), S(0)))
   MERGE#2(Cons(S(S(z0)), x1), Cons(S(S(z1)), x3)) -> c6(COND_MERGE_YS_ZS_2(leq#2(z0, z1), Cons(S(S(z0)), x1), Cons(S(S(z1)), x3), S(S(z0)), x1, S(S(z1)), x3), LEQ#2(S(S(z0)), S(S(z1))))
   MERGE#2(Cons(S(x0), x1), Cons(S(x2), x3)) -> c6(LEQ#2(S(x0), S(x2)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, x2))) -> c9(CONST_F#2(Cons(x0, Cons(x1, x2)), Cons(dc#1(map, divisible, mergesort_zs_3, divide, const_f, take#2(S(halve#1(length#1(x2))), Cons(x0, Cons(x1, x2)))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(drop#2(S(halve#1(length#1(x2))), Cons(x0, Cons(x1, x2))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, x2)), S(halve#1(length#1(x2))))), DIVIDE_YS#1(Cons(x0, Cons(x1, x2)), S(halve#1(length#1(x2)))), HALVE#1(length#1(x2)), LENGTH#1(x2))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z1, Cons(x1, x2))) -> c9(CONST_F#2(Cons(z1, Cons(x1, x2)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(x2))), Cons(z1, Cons(x1, x2))), Cons(drop#2(halve#1(length#1(x2)), Cons(x1, x2)), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z1, Cons(x1, x2)), S(halve#1(length#1(x2))))), DIVIDE_YS#1(Cons(z1, Cons(x1, x2)), S(halve#1(length#1(x2)))), HALVE#1(length#1(x2)), LENGTH#1(x2))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Cons(z0, z1)))) -> c9(CONST_F#2(Cons(x0, Cons(x1, Cons(z0, z1))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(Cons(z0, z1)))), Cons(x0, Cons(x1, Cons(z0, z1)))), Cons(drop#2(S(halve#1(S(length#1(z1)))), Cons(x0, Cons(x1, Cons(z0, z1)))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Cons(z0, z1))), S(halve#1(length#1(Cons(z0, z1)))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(z0, z1))), S(halve#1(length#1(Cons(z0, z1))))), HALVE#1(length#1(Cons(z0, z1))), LENGTH#1(Cons(z0, z1)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z1, Cons(x1, x2))) -> c9(CONST_F#2(Cons(z1, Cons(x1, x2)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(Cons(z1, take#2(halve#1(length#1(x2)), Cons(x1, x2))), Cons(drop#2(S(halve#1(length#1(x2))), Cons(z1, Cons(x1, x2))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z1, Cons(x1, x2)), S(halve#1(length#1(x2))))), DIVIDE_YS#1(Cons(z1, Cons(x1, x2)), S(halve#1(length#1(x2)))), HALVE#1(length#1(x2)), LENGTH#1(x2))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Cons(z0, z1)))) -> c9(CONST_F#2(Cons(x0, Cons(x1, Cons(z0, z1))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(S(length#1(z1)))), Cons(x0, Cons(x1, Cons(z0, z1)))), Cons(drop#2(S(halve#1(length#1(Cons(z0, z1)))), Cons(x0, Cons(x1, Cons(z0, z1)))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Cons(z0, z1))), S(halve#1(length#1(Cons(z0, z1)))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(z0, z1))), S(halve#1(length#1(Cons(z0, z1))))), HALVE#1(length#1(Cons(z0, z1))), LENGTH#1(Cons(z0, z1)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, x2))) -> c9(MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, x2)), S(halve#1(length#1(x2))))), DIVIDE_YS#1(Cons(x0, Cons(x1, x2)), S(halve#1(length#1(x2)))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Nil))) -> c9(CONST_F#2(Cons(x0, Cons(x1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(Nil))), Cons(x0, Cons(x1, Nil))), Cons(drop#2(S(halve#1(0)), Cons(x0, Cons(x1, Nil))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Nil)), S(halve#1(length#1(Nil)))), HALVE#1(length#1(Nil)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Nil))) -> c9(CONST_F#2(Cons(x0, Cons(x1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(0)), Cons(x0, Cons(x1, Nil))), Cons(drop#2(S(halve#1(length#1(Nil))), Cons(x0, Cons(x1, Nil))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Nil)), S(halve#1(length#1(Nil)))), HALVE#1(length#1(Nil)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Cons(x2, x3)))) -> c9(CONST_F#2(Cons(x0, Cons(x1, Cons(x2, x3))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(S(length#1(x3)))), Cons(x0, Cons(x1, Cons(x2, x3)))), Cons(drop#2(S(halve#1(S(length#1(x3)))), Cons(x0, Cons(x1, Cons(x2, x3)))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Cons(x2, x3))), S(halve#1(length#1(Cons(x2, x3)))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, x3))), S(halve#1(length#1(Cons(x2, x3))))), HALVE#1(length#1(Cons(x2, x3))), LENGTH#1(Cons(x2, x3)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Cons(x2, Nil)))) -> c9(CONST_F#2(Cons(x0, Cons(x1, Cons(x2, Nil))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Cons(x2, Nil))), S(halve#1(S(0)))))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Cons(x2, Nil))), S(halve#1(length#1(Cons(x2, Nil)))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Nil))), S(halve#1(length#1(Cons(x2, Nil))))), HALVE#1(length#1(Cons(x2, Nil))), LENGTH#1(Cons(x2, Nil)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Cons(x2, Cons(z0, z1))))) -> c9(CONST_F#2(Cons(x0, Cons(x1, Cons(x2, Cons(z0, z1)))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Cons(x2, Cons(z0, z1)))), S(halve#1(S(S(length#1(z1)))))))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Cons(x2, Cons(z0, z1)))), S(halve#1(length#1(Cons(x2, Cons(z0, z1))))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Cons(z0, z1)))), S(halve#1(length#1(Cons(x2, Cons(z0, z1)))))), HALVE#1(length#1(Cons(x2, Cons(z0, z1)))), LENGTH#1(Cons(x2, Cons(z0, z1))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Cons(x2, x3)))) -> c9(MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Cons(x2, x3))), S(halve#1(length#1(Cons(x2, x3)))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, x3))), S(halve#1(length#1(Cons(x2, x3))))), HALVE#1(length#1(Cons(x2, x3))), LENGTH#1(Cons(x2, x3)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Nil))) -> c9(CONST_F#2(Cons(x0, Cons(x1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(0)), Cons(x0, Cons(x1, Nil))), Cons(drop#2(S(halve#1(0)), Cons(x0, Cons(x1, Nil))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Nil)), S(halve#1(length#1(Nil)))), HALVE#1(length#1(Nil)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Nil))) -> c9(CONST_F#2(Cons(x0, Cons(x1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Nil)), S(0)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Nil)), S(halve#1(length#1(Nil)))), HALVE#1(length#1(Nil)))
S tuples:
   DIVIDE_YS#1(z0, z1) -> c(TAKE#2(z1, z0))
   DIVIDE_YS#1(z0, z1) -> c1(DROP#2(z1, z0))
   COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(z2, z3), z4, z5, z6, z7) -> c2(MERGE#2(z5, Cons(z2, z3)))
   COND_MERGE_YS_ZS_2(False, Cons(z0, z1), Cons(z2, z3), z4, z5, z6, z7) -> c3(MERGE#2(Cons(z0, z1), z7))
   DROP#2(S(z0), Cons(z1, z2)) -> c12(DROP#2(z0, z2))
   TAKE#2(S(z0), Cons(z1, z2)) -> c15(TAKE#2(z0, z2))
   HALVE#1(S(S(z0))) -> c18(HALVE#1(z0))
   CONST_F#2(z0, Cons(z1, Cons(z2, z3))) -> c19(MERGE#2(z1, z2))
   LEQ#2(S(z0), S(z1)) -> c22(LEQ#2(z0, z1))
   LENGTH#1(Cons(z0, z1)) -> c24(LENGTH#1(z1))
   MAP#2(dc(z0, z1, z2, z3, z4), Cons(z5, z6)) -> c26(DC#1(z0, z1, z2, z3, z4, z5))
   MAP#2(dc(z0, z1, z2, z3, z4), Cons(z5, z6)) -> c27(MAP#2(dc(z0, z1, z2, z3, z4), z6))
   MERGE#2(Cons(0, x1), Cons(z0, x3)) -> c6(COND_MERGE_YS_ZS_2(True, Cons(0, x1), Cons(z0, x3), 0, x1, z0, x3))
   MERGE#2(Cons(S(z0), x1), Cons(0, x3)) -> c6(COND_MERGE_YS_ZS_2(False, Cons(S(z0), x1), Cons(0, x3), S(z0), x1, 0, x3))
   MERGE#2(Cons(S(0), x1), Cons(S(z0), x3)) -> c6(COND_MERGE_YS_ZS_2(True, Cons(S(0), x1), Cons(S(z0), x3), S(0), x1, S(z0), x3), LEQ#2(S(0), S(z0)))
   MERGE#2(Cons(S(S(z0)), x1), Cons(S(0), x3)) -> c6(COND_MERGE_YS_ZS_2(False, Cons(S(S(z0)), x1), Cons(S(0), x3), S(S(z0)), x1, S(0), x3), LEQ#2(S(S(z0)), S(0)))
   MERGE#2(Cons(S(S(z0)), x1), Cons(S(S(z1)), x3)) -> c6(COND_MERGE_YS_ZS_2(leq#2(z0, z1), Cons(S(S(z0)), x1), Cons(S(S(z1)), x3), S(S(z0)), x1, S(S(z1)), x3), LEQ#2(S(S(z0)), S(S(z1))))
   MERGE#2(Cons(S(x0), x1), Cons(S(x2), x3)) -> c6(LEQ#2(S(x0), S(x2)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, x2))) -> c9(CONST_F#2(Cons(x0, Cons(x1, x2)), Cons(dc#1(map, divisible, mergesort_zs_3, divide, const_f, take#2(S(halve#1(length#1(x2))), Cons(x0, Cons(x1, x2)))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(drop#2(S(halve#1(length#1(x2))), Cons(x0, Cons(x1, x2))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, x2)), S(halve#1(length#1(x2))))), DIVIDE_YS#1(Cons(x0, Cons(x1, x2)), S(halve#1(length#1(x2)))), HALVE#1(length#1(x2)), LENGTH#1(x2))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z1, Cons(x1, x2))) -> c9(CONST_F#2(Cons(z1, Cons(x1, x2)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(x2))), Cons(z1, Cons(x1, x2))), Cons(drop#2(halve#1(length#1(x2)), Cons(x1, x2)), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z1, Cons(x1, x2)), S(halve#1(length#1(x2))))), DIVIDE_YS#1(Cons(z1, Cons(x1, x2)), S(halve#1(length#1(x2)))), HALVE#1(length#1(x2)), LENGTH#1(x2))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Cons(z0, z1)))) -> c9(CONST_F#2(Cons(x0, Cons(x1, Cons(z0, z1))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(Cons(z0, z1)))), Cons(x0, Cons(x1, Cons(z0, z1)))), Cons(drop#2(S(halve#1(S(length#1(z1)))), Cons(x0, Cons(x1, Cons(z0, z1)))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Cons(z0, z1))), S(halve#1(length#1(Cons(z0, z1)))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(z0, z1))), S(halve#1(length#1(Cons(z0, z1))))), HALVE#1(length#1(Cons(z0, z1))), LENGTH#1(Cons(z0, z1)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z1, Cons(x1, x2))) -> c9(CONST_F#2(Cons(z1, Cons(x1, x2)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(Cons(z1, take#2(halve#1(length#1(x2)), Cons(x1, x2))), Cons(drop#2(S(halve#1(length#1(x2))), Cons(z1, Cons(x1, x2))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z1, Cons(x1, x2)), S(halve#1(length#1(x2))))), DIVIDE_YS#1(Cons(z1, Cons(x1, x2)), S(halve#1(length#1(x2)))), HALVE#1(length#1(x2)), LENGTH#1(x2))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Cons(z0, z1)))) -> c9(CONST_F#2(Cons(x0, Cons(x1, Cons(z0, z1))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(S(length#1(z1)))), Cons(x0, Cons(x1, Cons(z0, z1)))), Cons(drop#2(S(halve#1(length#1(Cons(z0, z1)))), Cons(x0, Cons(x1, Cons(z0, z1)))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Cons(z0, z1))), S(halve#1(length#1(Cons(z0, z1)))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(z0, z1))), S(halve#1(length#1(Cons(z0, z1))))), HALVE#1(length#1(Cons(z0, z1))), LENGTH#1(Cons(z0, z1)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, x2))) -> c9(MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, x2)), S(halve#1(length#1(x2))))), DIVIDE_YS#1(Cons(x0, Cons(x1, x2)), S(halve#1(length#1(x2)))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Nil))) -> c9(CONST_F#2(Cons(x0, Cons(x1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(Nil))), Cons(x0, Cons(x1, Nil))), Cons(drop#2(S(halve#1(0)), Cons(x0, Cons(x1, Nil))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Nil)), S(halve#1(length#1(Nil)))), HALVE#1(length#1(Nil)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Nil))) -> c9(CONST_F#2(Cons(x0, Cons(x1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(0)), Cons(x0, Cons(x1, Nil))), Cons(drop#2(S(halve#1(length#1(Nil))), Cons(x0, Cons(x1, Nil))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Nil)), S(halve#1(length#1(Nil)))), HALVE#1(length#1(Nil)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Cons(x2, x3)))) -> c9(CONST_F#2(Cons(x0, Cons(x1, Cons(x2, x3))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(S(length#1(x3)))), Cons(x0, Cons(x1, Cons(x2, x3)))), Cons(drop#2(S(halve#1(S(length#1(x3)))), Cons(x0, Cons(x1, Cons(x2, x3)))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Cons(x2, x3))), S(halve#1(length#1(Cons(x2, x3)))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, x3))), S(halve#1(length#1(Cons(x2, x3))))), HALVE#1(length#1(Cons(x2, x3))), LENGTH#1(Cons(x2, x3)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Cons(x2, Nil)))) -> c9(CONST_F#2(Cons(x0, Cons(x1, Cons(x2, Nil))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Cons(x2, Nil))), S(halve#1(S(0)))))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Cons(x2, Nil))), S(halve#1(length#1(Cons(x2, Nil)))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Nil))), S(halve#1(length#1(Cons(x2, Nil))))), HALVE#1(length#1(Cons(x2, Nil))), LENGTH#1(Cons(x2, Nil)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Cons(x2, Cons(z0, z1))))) -> c9(CONST_F#2(Cons(x0, Cons(x1, Cons(x2, Cons(z0, z1)))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Cons(x2, Cons(z0, z1)))), S(halve#1(S(S(length#1(z1)))))))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Cons(x2, Cons(z0, z1)))), S(halve#1(length#1(Cons(x2, Cons(z0, z1))))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Cons(z0, z1)))), S(halve#1(length#1(Cons(x2, Cons(z0, z1)))))), HALVE#1(length#1(Cons(x2, Cons(z0, z1)))), LENGTH#1(Cons(x2, Cons(z0, z1))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Cons(x2, x3)))) -> c9(MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Cons(x2, x3))), S(halve#1(length#1(Cons(x2, x3)))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, x3))), S(halve#1(length#1(Cons(x2, x3))))), HALVE#1(length#1(Cons(x2, x3))), LENGTH#1(Cons(x2, x3)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Nil))) -> c9(CONST_F#2(Cons(x0, Cons(x1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(0)), Cons(x0, Cons(x1, Nil))), Cons(drop#2(S(halve#1(0)), Cons(x0, Cons(x1, Nil))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Nil)), S(halve#1(length#1(Nil)))), HALVE#1(length#1(Nil)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Nil))) -> c9(CONST_F#2(Cons(x0, Cons(x1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Nil)), S(0)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Nil)), S(halve#1(length#1(Nil)))), HALVE#1(length#1(Nil)))
K tuples:none
Defined Rule Symbols:   leq#2_2, map#2_2, divide_ys#1_2, halve#1_1, length#1_1, take#2_2, drop#2_2, dc#1_6, const_f#2_2, merge#2_2, cond_merge_ys_zs_2_7

Defined Pair Symbols:   DIVIDE_YS#1_2, COND_MERGE_YS_ZS_2_7, DROP#2_2, TAKE#2_2, HALVE#1_1, CONST_F#2_2, LEQ#2_2, LENGTH#1_1, MAP#2_2, MERGE#2_2, DC#1_6

Compound Symbols:   c_1, c1_1, c2_1, c3_1, c12_1, c15_1, c18_1, c19_1, c22_1, c24_1, c26_1, c27_1, c6_1, c6_2, c9_5, c9_2, c9_4


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(101) CdtRewritingProof (BOTH BOUNDS(ID, ID))
Used rewriting to replace DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, x2))) -> c9(CONST_F#2(Cons(x0, Cons(x1, x2)), Cons(dc#1(map, divisible, mergesort_zs_3, divide, const_f, take#2(S(halve#1(length#1(x2))), Cons(x0, Cons(x1, x2)))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(drop#2(S(halve#1(length#1(x2))), Cons(x0, Cons(x1, x2))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, x2)), S(halve#1(length#1(x2))))), DIVIDE_YS#1(Cons(x0, Cons(x1, x2)), S(halve#1(length#1(x2)))), HALVE#1(length#1(x2)), LENGTH#1(x2)) by DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> c9(CONST_F#2(Cons(z0, Cons(z1, z2)), Cons(dc#1(map, divisible, mergesort_zs_3, divide, const_f, take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2)))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(drop#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Nil))), DIVIDE_YS#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2)))), HALVE#1(length#1(z2)), LENGTH#1(z2))
----------------------------------------

(102)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   leq#2(0, z0) -> True
   leq#2(S(z0), 0) -> False
   leq#2(S(z0), S(z1)) -> leq#2(z0, z1)
   map#2(dc(z0, z1, z2, z3, z4), Nil) -> Nil
   map#2(dc(z0, z1, z2, z3, z4), Cons(z5, z6)) -> Cons(dc#1(z0, z1, z2, z3, z4, z5), map#2(dc(z0, z1, z2, z3, z4), z6))
   divide_ys#1(z0, z1) -> Cons(take#2(z1, z0), Cons(drop#2(z1, z0), Nil))
   halve#1(0) -> 0
   halve#1(S(0)) -> S(0)
   halve#1(S(S(z0))) -> S(halve#1(z0))
   length#1(Nil) -> 0
   length#1(Cons(z0, z1)) -> S(length#1(z1))
   take#2(0, z0) -> Nil
   take#2(S(0), Nil) -> Cons(bot[0], Nil)
   take#2(S(z0), Cons(z1, z2)) -> Cons(z1, take#2(z0, z2))
   drop#2(0, z0) -> z0
   drop#2(S(0), Nil) -> bot[1]
   drop#2(S(z0), Cons(z1, z2)) -> drop#2(z0, z2)
   dc#1(map, divisible, mergesort_zs_3, divide, const_f, Nil) -> Nil
   dc#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Nil)) -> Cons(z0, Nil)
   dc#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> const_f#2(Cons(z0, Cons(z1, z2)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2))))))
   const_f#2(z0, Cons(z1, Cons(z2, z3))) -> merge#2(z1, z2)
   merge#2(Nil, z0) -> z0
   merge#2(Cons(z0, z1), Nil) -> Cons(z0, z1)
   merge#2(Cons(z0, z1), Cons(z2, z3)) -> cond_merge_ys_zs_2(leq#2(z0, z2), Cons(z0, z1), Cons(z2, z3), z0, z1, z2, z3)
   cond_merge_ys_zs_2(True, Cons(z0, z1), Cons(z2, z3), z4, z5, z6, z7) -> Cons(z4, merge#2(z5, Cons(z2, z3)))
   cond_merge_ys_zs_2(False, Cons(z0, z1), Cons(z2, z3), z4, z5, z6, z7) -> Cons(z6, merge#2(Cons(z0, z1), z7))
Tuples:
   DIVIDE_YS#1(z0, z1) -> c(TAKE#2(z1, z0))
   DIVIDE_YS#1(z0, z1) -> c1(DROP#2(z1, z0))
   COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(z2, z3), z4, z5, z6, z7) -> c2(MERGE#2(z5, Cons(z2, z3)))
   COND_MERGE_YS_ZS_2(False, Cons(z0, z1), Cons(z2, z3), z4, z5, z6, z7) -> c3(MERGE#2(Cons(z0, z1), z7))
   DROP#2(S(z0), Cons(z1, z2)) -> c12(DROP#2(z0, z2))
   TAKE#2(S(z0), Cons(z1, z2)) -> c15(TAKE#2(z0, z2))
   HALVE#1(S(S(z0))) -> c18(HALVE#1(z0))
   CONST_F#2(z0, Cons(z1, Cons(z2, z3))) -> c19(MERGE#2(z1, z2))
   LEQ#2(S(z0), S(z1)) -> c22(LEQ#2(z0, z1))
   LENGTH#1(Cons(z0, z1)) -> c24(LENGTH#1(z1))
   MAP#2(dc(z0, z1, z2, z3, z4), Cons(z5, z6)) -> c26(DC#1(z0, z1, z2, z3, z4, z5))
   MAP#2(dc(z0, z1, z2, z3, z4), Cons(z5, z6)) -> c27(MAP#2(dc(z0, z1, z2, z3, z4), z6))
   MERGE#2(Cons(0, x1), Cons(z0, x3)) -> c6(COND_MERGE_YS_ZS_2(True, Cons(0, x1), Cons(z0, x3), 0, x1, z0, x3))
   MERGE#2(Cons(S(z0), x1), Cons(0, x3)) -> c6(COND_MERGE_YS_ZS_2(False, Cons(S(z0), x1), Cons(0, x3), S(z0), x1, 0, x3))
   MERGE#2(Cons(S(0), x1), Cons(S(z0), x3)) -> c6(COND_MERGE_YS_ZS_2(True, Cons(S(0), x1), Cons(S(z0), x3), S(0), x1, S(z0), x3), LEQ#2(S(0), S(z0)))
   MERGE#2(Cons(S(S(z0)), x1), Cons(S(0), x3)) -> c6(COND_MERGE_YS_ZS_2(False, Cons(S(S(z0)), x1), Cons(S(0), x3), S(S(z0)), x1, S(0), x3), LEQ#2(S(S(z0)), S(0)))
   MERGE#2(Cons(S(S(z0)), x1), Cons(S(S(z1)), x3)) -> c6(COND_MERGE_YS_ZS_2(leq#2(z0, z1), Cons(S(S(z0)), x1), Cons(S(S(z1)), x3), S(S(z0)), x1, S(S(z1)), x3), LEQ#2(S(S(z0)), S(S(z1))))
   MERGE#2(Cons(S(x0), x1), Cons(S(x2), x3)) -> c6(LEQ#2(S(x0), S(x2)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z1, Cons(x1, x2))) -> c9(CONST_F#2(Cons(z1, Cons(x1, x2)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(x2))), Cons(z1, Cons(x1, x2))), Cons(drop#2(halve#1(length#1(x2)), Cons(x1, x2)), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z1, Cons(x1, x2)), S(halve#1(length#1(x2))))), DIVIDE_YS#1(Cons(z1, Cons(x1, x2)), S(halve#1(length#1(x2)))), HALVE#1(length#1(x2)), LENGTH#1(x2))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Cons(z0, z1)))) -> c9(CONST_F#2(Cons(x0, Cons(x1, Cons(z0, z1))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(Cons(z0, z1)))), Cons(x0, Cons(x1, Cons(z0, z1)))), Cons(drop#2(S(halve#1(S(length#1(z1)))), Cons(x0, Cons(x1, Cons(z0, z1)))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Cons(z0, z1))), S(halve#1(length#1(Cons(z0, z1)))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(z0, z1))), S(halve#1(length#1(Cons(z0, z1))))), HALVE#1(length#1(Cons(z0, z1))), LENGTH#1(Cons(z0, z1)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z1, Cons(x1, x2))) -> c9(CONST_F#2(Cons(z1, Cons(x1, x2)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(Cons(z1, take#2(halve#1(length#1(x2)), Cons(x1, x2))), Cons(drop#2(S(halve#1(length#1(x2))), Cons(z1, Cons(x1, x2))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z1, Cons(x1, x2)), S(halve#1(length#1(x2))))), DIVIDE_YS#1(Cons(z1, Cons(x1, x2)), S(halve#1(length#1(x2)))), HALVE#1(length#1(x2)), LENGTH#1(x2))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Cons(z0, z1)))) -> c9(CONST_F#2(Cons(x0, Cons(x1, Cons(z0, z1))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(S(length#1(z1)))), Cons(x0, Cons(x1, Cons(z0, z1)))), Cons(drop#2(S(halve#1(length#1(Cons(z0, z1)))), Cons(x0, Cons(x1, Cons(z0, z1)))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Cons(z0, z1))), S(halve#1(length#1(Cons(z0, z1)))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(z0, z1))), S(halve#1(length#1(Cons(z0, z1))))), HALVE#1(length#1(Cons(z0, z1))), LENGTH#1(Cons(z0, z1)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, x2))) -> c9(MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, x2)), S(halve#1(length#1(x2))))), DIVIDE_YS#1(Cons(x0, Cons(x1, x2)), S(halve#1(length#1(x2)))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Nil))) -> c9(CONST_F#2(Cons(x0, Cons(x1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(Nil))), Cons(x0, Cons(x1, Nil))), Cons(drop#2(S(halve#1(0)), Cons(x0, Cons(x1, Nil))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Nil)), S(halve#1(length#1(Nil)))), HALVE#1(length#1(Nil)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Nil))) -> c9(CONST_F#2(Cons(x0, Cons(x1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(0)), Cons(x0, Cons(x1, Nil))), Cons(drop#2(S(halve#1(length#1(Nil))), Cons(x0, Cons(x1, Nil))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Nil)), S(halve#1(length#1(Nil)))), HALVE#1(length#1(Nil)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Cons(x2, x3)))) -> c9(CONST_F#2(Cons(x0, Cons(x1, Cons(x2, x3))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(S(length#1(x3)))), Cons(x0, Cons(x1, Cons(x2, x3)))), Cons(drop#2(S(halve#1(S(length#1(x3)))), Cons(x0, Cons(x1, Cons(x2, x3)))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Cons(x2, x3))), S(halve#1(length#1(Cons(x2, x3)))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, x3))), S(halve#1(length#1(Cons(x2, x3))))), HALVE#1(length#1(Cons(x2, x3))), LENGTH#1(Cons(x2, x3)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Cons(x2, Nil)))) -> c9(CONST_F#2(Cons(x0, Cons(x1, Cons(x2, Nil))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Cons(x2, Nil))), S(halve#1(S(0)))))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Cons(x2, Nil))), S(halve#1(length#1(Cons(x2, Nil)))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Nil))), S(halve#1(length#1(Cons(x2, Nil))))), HALVE#1(length#1(Cons(x2, Nil))), LENGTH#1(Cons(x2, Nil)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Cons(x2, Cons(z0, z1))))) -> c9(CONST_F#2(Cons(x0, Cons(x1, Cons(x2, Cons(z0, z1)))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Cons(x2, Cons(z0, z1)))), S(halve#1(S(S(length#1(z1)))))))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Cons(x2, Cons(z0, z1)))), S(halve#1(length#1(Cons(x2, Cons(z0, z1))))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Cons(z0, z1)))), S(halve#1(length#1(Cons(x2, Cons(z0, z1)))))), HALVE#1(length#1(Cons(x2, Cons(z0, z1)))), LENGTH#1(Cons(x2, Cons(z0, z1))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Cons(x2, x3)))) -> c9(MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Cons(x2, x3))), S(halve#1(length#1(Cons(x2, x3)))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, x3))), S(halve#1(length#1(Cons(x2, x3))))), HALVE#1(length#1(Cons(x2, x3))), LENGTH#1(Cons(x2, x3)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Nil))) -> c9(CONST_F#2(Cons(x0, Cons(x1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(0)), Cons(x0, Cons(x1, Nil))), Cons(drop#2(S(halve#1(0)), Cons(x0, Cons(x1, Nil))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Nil)), S(halve#1(length#1(Nil)))), HALVE#1(length#1(Nil)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Nil))) -> c9(CONST_F#2(Cons(x0, Cons(x1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Nil)), S(0)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Nil)), S(halve#1(length#1(Nil)))), HALVE#1(length#1(Nil)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> c9(CONST_F#2(Cons(z0, Cons(z1, z2)), Cons(dc#1(map, divisible, mergesort_zs_3, divide, const_f, take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2)))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(drop#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Nil))), DIVIDE_YS#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2)))), HALVE#1(length#1(z2)), LENGTH#1(z2))
S tuples:
   DIVIDE_YS#1(z0, z1) -> c(TAKE#2(z1, z0))
   DIVIDE_YS#1(z0, z1) -> c1(DROP#2(z1, z0))
   COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(z2, z3), z4, z5, z6, z7) -> c2(MERGE#2(z5, Cons(z2, z3)))
   COND_MERGE_YS_ZS_2(False, Cons(z0, z1), Cons(z2, z3), z4, z5, z6, z7) -> c3(MERGE#2(Cons(z0, z1), z7))
   DROP#2(S(z0), Cons(z1, z2)) -> c12(DROP#2(z0, z2))
   TAKE#2(S(z0), Cons(z1, z2)) -> c15(TAKE#2(z0, z2))
   HALVE#1(S(S(z0))) -> c18(HALVE#1(z0))
   CONST_F#2(z0, Cons(z1, Cons(z2, z3))) -> c19(MERGE#2(z1, z2))
   LEQ#2(S(z0), S(z1)) -> c22(LEQ#2(z0, z1))
   LENGTH#1(Cons(z0, z1)) -> c24(LENGTH#1(z1))
   MAP#2(dc(z0, z1, z2, z3, z4), Cons(z5, z6)) -> c26(DC#1(z0, z1, z2, z3, z4, z5))
   MAP#2(dc(z0, z1, z2, z3, z4), Cons(z5, z6)) -> c27(MAP#2(dc(z0, z1, z2, z3, z4), z6))
   MERGE#2(Cons(0, x1), Cons(z0, x3)) -> c6(COND_MERGE_YS_ZS_2(True, Cons(0, x1), Cons(z0, x3), 0, x1, z0, x3))
   MERGE#2(Cons(S(z0), x1), Cons(0, x3)) -> c6(COND_MERGE_YS_ZS_2(False, Cons(S(z0), x1), Cons(0, x3), S(z0), x1, 0, x3))
   MERGE#2(Cons(S(0), x1), Cons(S(z0), x3)) -> c6(COND_MERGE_YS_ZS_2(True, Cons(S(0), x1), Cons(S(z0), x3), S(0), x1, S(z0), x3), LEQ#2(S(0), S(z0)))
   MERGE#2(Cons(S(S(z0)), x1), Cons(S(0), x3)) -> c6(COND_MERGE_YS_ZS_2(False, Cons(S(S(z0)), x1), Cons(S(0), x3), S(S(z0)), x1, S(0), x3), LEQ#2(S(S(z0)), S(0)))
   MERGE#2(Cons(S(S(z0)), x1), Cons(S(S(z1)), x3)) -> c6(COND_MERGE_YS_ZS_2(leq#2(z0, z1), Cons(S(S(z0)), x1), Cons(S(S(z1)), x3), S(S(z0)), x1, S(S(z1)), x3), LEQ#2(S(S(z0)), S(S(z1))))
   MERGE#2(Cons(S(x0), x1), Cons(S(x2), x3)) -> c6(LEQ#2(S(x0), S(x2)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z1, Cons(x1, x2))) -> c9(CONST_F#2(Cons(z1, Cons(x1, x2)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(x2))), Cons(z1, Cons(x1, x2))), Cons(drop#2(halve#1(length#1(x2)), Cons(x1, x2)), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z1, Cons(x1, x2)), S(halve#1(length#1(x2))))), DIVIDE_YS#1(Cons(z1, Cons(x1, x2)), S(halve#1(length#1(x2)))), HALVE#1(length#1(x2)), LENGTH#1(x2))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Cons(z0, z1)))) -> c9(CONST_F#2(Cons(x0, Cons(x1, Cons(z0, z1))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(Cons(z0, z1)))), Cons(x0, Cons(x1, Cons(z0, z1)))), Cons(drop#2(S(halve#1(S(length#1(z1)))), Cons(x0, Cons(x1, Cons(z0, z1)))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Cons(z0, z1))), S(halve#1(length#1(Cons(z0, z1)))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(z0, z1))), S(halve#1(length#1(Cons(z0, z1))))), HALVE#1(length#1(Cons(z0, z1))), LENGTH#1(Cons(z0, z1)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z1, Cons(x1, x2))) -> c9(CONST_F#2(Cons(z1, Cons(x1, x2)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(Cons(z1, take#2(halve#1(length#1(x2)), Cons(x1, x2))), Cons(drop#2(S(halve#1(length#1(x2))), Cons(z1, Cons(x1, x2))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z1, Cons(x1, x2)), S(halve#1(length#1(x2))))), DIVIDE_YS#1(Cons(z1, Cons(x1, x2)), S(halve#1(length#1(x2)))), HALVE#1(length#1(x2)), LENGTH#1(x2))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Cons(z0, z1)))) -> c9(CONST_F#2(Cons(x0, Cons(x1, Cons(z0, z1))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(S(length#1(z1)))), Cons(x0, Cons(x1, Cons(z0, z1)))), Cons(drop#2(S(halve#1(length#1(Cons(z0, z1)))), Cons(x0, Cons(x1, Cons(z0, z1)))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Cons(z0, z1))), S(halve#1(length#1(Cons(z0, z1)))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(z0, z1))), S(halve#1(length#1(Cons(z0, z1))))), HALVE#1(length#1(Cons(z0, z1))), LENGTH#1(Cons(z0, z1)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, x2))) -> c9(MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, x2)), S(halve#1(length#1(x2))))), DIVIDE_YS#1(Cons(x0, Cons(x1, x2)), S(halve#1(length#1(x2)))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Nil))) -> c9(CONST_F#2(Cons(x0, Cons(x1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(Nil))), Cons(x0, Cons(x1, Nil))), Cons(drop#2(S(halve#1(0)), Cons(x0, Cons(x1, Nil))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Nil)), S(halve#1(length#1(Nil)))), HALVE#1(length#1(Nil)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Nil))) -> c9(CONST_F#2(Cons(x0, Cons(x1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(0)), Cons(x0, Cons(x1, Nil))), Cons(drop#2(S(halve#1(length#1(Nil))), Cons(x0, Cons(x1, Nil))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Nil)), S(halve#1(length#1(Nil)))), HALVE#1(length#1(Nil)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Cons(x2, x3)))) -> c9(CONST_F#2(Cons(x0, Cons(x1, Cons(x2, x3))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(S(length#1(x3)))), Cons(x0, Cons(x1, Cons(x2, x3)))), Cons(drop#2(S(halve#1(S(length#1(x3)))), Cons(x0, Cons(x1, Cons(x2, x3)))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Cons(x2, x3))), S(halve#1(length#1(Cons(x2, x3)))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, x3))), S(halve#1(length#1(Cons(x2, x3))))), HALVE#1(length#1(Cons(x2, x3))), LENGTH#1(Cons(x2, x3)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Cons(x2, Nil)))) -> c9(CONST_F#2(Cons(x0, Cons(x1, Cons(x2, Nil))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Cons(x2, Nil))), S(halve#1(S(0)))))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Cons(x2, Nil))), S(halve#1(length#1(Cons(x2, Nil)))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Nil))), S(halve#1(length#1(Cons(x2, Nil))))), HALVE#1(length#1(Cons(x2, Nil))), LENGTH#1(Cons(x2, Nil)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Cons(x2, Cons(z0, z1))))) -> c9(CONST_F#2(Cons(x0, Cons(x1, Cons(x2, Cons(z0, z1)))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Cons(x2, Cons(z0, z1)))), S(halve#1(S(S(length#1(z1)))))))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Cons(x2, Cons(z0, z1)))), S(halve#1(length#1(Cons(x2, Cons(z0, z1))))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Cons(z0, z1)))), S(halve#1(length#1(Cons(x2, Cons(z0, z1)))))), HALVE#1(length#1(Cons(x2, Cons(z0, z1)))), LENGTH#1(Cons(x2, Cons(z0, z1))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Cons(x2, x3)))) -> c9(MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Cons(x2, x3))), S(halve#1(length#1(Cons(x2, x3)))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, x3))), S(halve#1(length#1(Cons(x2, x3))))), HALVE#1(length#1(Cons(x2, x3))), LENGTH#1(Cons(x2, x3)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Nil))) -> c9(CONST_F#2(Cons(x0, Cons(x1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(0)), Cons(x0, Cons(x1, Nil))), Cons(drop#2(S(halve#1(0)), Cons(x0, Cons(x1, Nil))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Nil)), S(halve#1(length#1(Nil)))), HALVE#1(length#1(Nil)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Nil))) -> c9(CONST_F#2(Cons(x0, Cons(x1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Nil)), S(0)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Nil)), S(halve#1(length#1(Nil)))), HALVE#1(length#1(Nil)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> c9(CONST_F#2(Cons(z0, Cons(z1, z2)), Cons(dc#1(map, divisible, mergesort_zs_3, divide, const_f, take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2)))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(drop#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Nil))), DIVIDE_YS#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2)))), HALVE#1(length#1(z2)), LENGTH#1(z2))
K tuples:none
Defined Rule Symbols:   leq#2_2, map#2_2, divide_ys#1_2, halve#1_1, length#1_1, take#2_2, drop#2_2, dc#1_6, const_f#2_2, merge#2_2, cond_merge_ys_zs_2_7

Defined Pair Symbols:   DIVIDE_YS#1_2, COND_MERGE_YS_ZS_2_7, DROP#2_2, TAKE#2_2, HALVE#1_1, CONST_F#2_2, LEQ#2_2, LENGTH#1_1, MAP#2_2, MERGE#2_2, DC#1_6

Compound Symbols:   c_1, c1_1, c2_1, c3_1, c12_1, c15_1, c18_1, c19_1, c22_1, c24_1, c26_1, c27_1, c6_1, c6_2, c9_5, c9_2, c9_4


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(103) CdtInstantiationProof (BOTH BOUNDS(ID, ID))
Use instantiation to replace DIVIDE_YS#1(z0, z1) -> c(TAKE#2(z1, z0)) by 
   DIVIDE_YS#1(Cons(x0, Cons(x1, x2)), S(y11)) -> c(TAKE#2(S(y11), Cons(x0, Cons(x1, x2))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, x3))), S(y11)) -> c(TAKE#2(S(y11), Cons(x0, Cons(x1, Cons(x2, x3)))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Nil)), S(y10)) -> c(TAKE#2(S(y10), Cons(x0, Cons(x1, Nil))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Nil))), S(y7)) -> c(TAKE#2(S(y7), Cons(x0, Cons(x1, Cons(x2, Nil)))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4)))), S(y8)) -> c(TAKE#2(S(y8), Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4))))))

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

(104)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   leq#2(0, z0) -> True
   leq#2(S(z0), 0) -> False
   leq#2(S(z0), S(z1)) -> leq#2(z0, z1)
   map#2(dc(z0, z1, z2, z3, z4), Nil) -> Nil
   map#2(dc(z0, z1, z2, z3, z4), Cons(z5, z6)) -> Cons(dc#1(z0, z1, z2, z3, z4, z5), map#2(dc(z0, z1, z2, z3, z4), z6))
   divide_ys#1(z0, z1) -> Cons(take#2(z1, z0), Cons(drop#2(z1, z0), Nil))
   halve#1(0) -> 0
   halve#1(S(0)) -> S(0)
   halve#1(S(S(z0))) -> S(halve#1(z0))
   length#1(Nil) -> 0
   length#1(Cons(z0, z1)) -> S(length#1(z1))
   take#2(0, z0) -> Nil
   take#2(S(0), Nil) -> Cons(bot[0], Nil)
   take#2(S(z0), Cons(z1, z2)) -> Cons(z1, take#2(z0, z2))
   drop#2(0, z0) -> z0
   drop#2(S(0), Nil) -> bot[1]
   drop#2(S(z0), Cons(z1, z2)) -> drop#2(z0, z2)
   dc#1(map, divisible, mergesort_zs_3, divide, const_f, Nil) -> Nil
   dc#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Nil)) -> Cons(z0, Nil)
   dc#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> const_f#2(Cons(z0, Cons(z1, z2)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2))))))
   const_f#2(z0, Cons(z1, Cons(z2, z3))) -> merge#2(z1, z2)
   merge#2(Nil, z0) -> z0
   merge#2(Cons(z0, z1), Nil) -> Cons(z0, z1)
   merge#2(Cons(z0, z1), Cons(z2, z3)) -> cond_merge_ys_zs_2(leq#2(z0, z2), Cons(z0, z1), Cons(z2, z3), z0, z1, z2, z3)
   cond_merge_ys_zs_2(True, Cons(z0, z1), Cons(z2, z3), z4, z5, z6, z7) -> Cons(z4, merge#2(z5, Cons(z2, z3)))
   cond_merge_ys_zs_2(False, Cons(z0, z1), Cons(z2, z3), z4, z5, z6, z7) -> Cons(z6, merge#2(Cons(z0, z1), z7))
Tuples:
   DIVIDE_YS#1(z0, z1) -> c1(DROP#2(z1, z0))
   COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(z2, z3), z4, z5, z6, z7) -> c2(MERGE#2(z5, Cons(z2, z3)))
   COND_MERGE_YS_ZS_2(False, Cons(z0, z1), Cons(z2, z3), z4, z5, z6, z7) -> c3(MERGE#2(Cons(z0, z1), z7))
   DROP#2(S(z0), Cons(z1, z2)) -> c12(DROP#2(z0, z2))
   TAKE#2(S(z0), Cons(z1, z2)) -> c15(TAKE#2(z0, z2))
   HALVE#1(S(S(z0))) -> c18(HALVE#1(z0))
   CONST_F#2(z0, Cons(z1, Cons(z2, z3))) -> c19(MERGE#2(z1, z2))
   LEQ#2(S(z0), S(z1)) -> c22(LEQ#2(z0, z1))
   LENGTH#1(Cons(z0, z1)) -> c24(LENGTH#1(z1))
   MAP#2(dc(z0, z1, z2, z3, z4), Cons(z5, z6)) -> c26(DC#1(z0, z1, z2, z3, z4, z5))
   MAP#2(dc(z0, z1, z2, z3, z4), Cons(z5, z6)) -> c27(MAP#2(dc(z0, z1, z2, z3, z4), z6))
   MERGE#2(Cons(0, x1), Cons(z0, x3)) -> c6(COND_MERGE_YS_ZS_2(True, Cons(0, x1), Cons(z0, x3), 0, x1, z0, x3))
   MERGE#2(Cons(S(z0), x1), Cons(0, x3)) -> c6(COND_MERGE_YS_ZS_2(False, Cons(S(z0), x1), Cons(0, x3), S(z0), x1, 0, x3))
   MERGE#2(Cons(S(0), x1), Cons(S(z0), x3)) -> c6(COND_MERGE_YS_ZS_2(True, Cons(S(0), x1), Cons(S(z0), x3), S(0), x1, S(z0), x3), LEQ#2(S(0), S(z0)))
   MERGE#2(Cons(S(S(z0)), x1), Cons(S(0), x3)) -> c6(COND_MERGE_YS_ZS_2(False, Cons(S(S(z0)), x1), Cons(S(0), x3), S(S(z0)), x1, S(0), x3), LEQ#2(S(S(z0)), S(0)))
   MERGE#2(Cons(S(S(z0)), x1), Cons(S(S(z1)), x3)) -> c6(COND_MERGE_YS_ZS_2(leq#2(z0, z1), Cons(S(S(z0)), x1), Cons(S(S(z1)), x3), S(S(z0)), x1, S(S(z1)), x3), LEQ#2(S(S(z0)), S(S(z1))))
   MERGE#2(Cons(S(x0), x1), Cons(S(x2), x3)) -> c6(LEQ#2(S(x0), S(x2)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z1, Cons(x1, x2))) -> c9(CONST_F#2(Cons(z1, Cons(x1, x2)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(x2))), Cons(z1, Cons(x1, x2))), Cons(drop#2(halve#1(length#1(x2)), Cons(x1, x2)), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z1, Cons(x1, x2)), S(halve#1(length#1(x2))))), DIVIDE_YS#1(Cons(z1, Cons(x1, x2)), S(halve#1(length#1(x2)))), HALVE#1(length#1(x2)), LENGTH#1(x2))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Cons(z0, z1)))) -> c9(CONST_F#2(Cons(x0, Cons(x1, Cons(z0, z1))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(Cons(z0, z1)))), Cons(x0, Cons(x1, Cons(z0, z1)))), Cons(drop#2(S(halve#1(S(length#1(z1)))), Cons(x0, Cons(x1, Cons(z0, z1)))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Cons(z0, z1))), S(halve#1(length#1(Cons(z0, z1)))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(z0, z1))), S(halve#1(length#1(Cons(z0, z1))))), HALVE#1(length#1(Cons(z0, z1))), LENGTH#1(Cons(z0, z1)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z1, Cons(x1, x2))) -> c9(CONST_F#2(Cons(z1, Cons(x1, x2)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(Cons(z1, take#2(halve#1(length#1(x2)), Cons(x1, x2))), Cons(drop#2(S(halve#1(length#1(x2))), Cons(z1, Cons(x1, x2))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z1, Cons(x1, x2)), S(halve#1(length#1(x2))))), DIVIDE_YS#1(Cons(z1, Cons(x1, x2)), S(halve#1(length#1(x2)))), HALVE#1(length#1(x2)), LENGTH#1(x2))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Cons(z0, z1)))) -> c9(CONST_F#2(Cons(x0, Cons(x1, Cons(z0, z1))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(S(length#1(z1)))), Cons(x0, Cons(x1, Cons(z0, z1)))), Cons(drop#2(S(halve#1(length#1(Cons(z0, z1)))), Cons(x0, Cons(x1, Cons(z0, z1)))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Cons(z0, z1))), S(halve#1(length#1(Cons(z0, z1)))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(z0, z1))), S(halve#1(length#1(Cons(z0, z1))))), HALVE#1(length#1(Cons(z0, z1))), LENGTH#1(Cons(z0, z1)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, x2))) -> c9(MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, x2)), S(halve#1(length#1(x2))))), DIVIDE_YS#1(Cons(x0, Cons(x1, x2)), S(halve#1(length#1(x2)))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Nil))) -> c9(CONST_F#2(Cons(x0, Cons(x1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(Nil))), Cons(x0, Cons(x1, Nil))), Cons(drop#2(S(halve#1(0)), Cons(x0, Cons(x1, Nil))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Nil)), S(halve#1(length#1(Nil)))), HALVE#1(length#1(Nil)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Nil))) -> c9(CONST_F#2(Cons(x0, Cons(x1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(0)), Cons(x0, Cons(x1, Nil))), Cons(drop#2(S(halve#1(length#1(Nil))), Cons(x0, Cons(x1, Nil))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Nil)), S(halve#1(length#1(Nil)))), HALVE#1(length#1(Nil)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Cons(x2, x3)))) -> c9(CONST_F#2(Cons(x0, Cons(x1, Cons(x2, x3))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(S(length#1(x3)))), Cons(x0, Cons(x1, Cons(x2, x3)))), Cons(drop#2(S(halve#1(S(length#1(x3)))), Cons(x0, Cons(x1, Cons(x2, x3)))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Cons(x2, x3))), S(halve#1(length#1(Cons(x2, x3)))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, x3))), S(halve#1(length#1(Cons(x2, x3))))), HALVE#1(length#1(Cons(x2, x3))), LENGTH#1(Cons(x2, x3)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Cons(x2, Nil)))) -> c9(CONST_F#2(Cons(x0, Cons(x1, Cons(x2, Nil))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Cons(x2, Nil))), S(halve#1(S(0)))))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Cons(x2, Nil))), S(halve#1(length#1(Cons(x2, Nil)))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Nil))), S(halve#1(length#1(Cons(x2, Nil))))), HALVE#1(length#1(Cons(x2, Nil))), LENGTH#1(Cons(x2, Nil)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Cons(x2, Cons(z0, z1))))) -> c9(CONST_F#2(Cons(x0, Cons(x1, Cons(x2, Cons(z0, z1)))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Cons(x2, Cons(z0, z1)))), S(halve#1(S(S(length#1(z1)))))))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Cons(x2, Cons(z0, z1)))), S(halve#1(length#1(Cons(x2, Cons(z0, z1))))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Cons(z0, z1)))), S(halve#1(length#1(Cons(x2, Cons(z0, z1)))))), HALVE#1(length#1(Cons(x2, Cons(z0, z1)))), LENGTH#1(Cons(x2, Cons(z0, z1))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Cons(x2, x3)))) -> c9(MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Cons(x2, x3))), S(halve#1(length#1(Cons(x2, x3)))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, x3))), S(halve#1(length#1(Cons(x2, x3))))), HALVE#1(length#1(Cons(x2, x3))), LENGTH#1(Cons(x2, x3)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Nil))) -> c9(CONST_F#2(Cons(x0, Cons(x1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(0)), Cons(x0, Cons(x1, Nil))), Cons(drop#2(S(halve#1(0)), Cons(x0, Cons(x1, Nil))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Nil)), S(halve#1(length#1(Nil)))), HALVE#1(length#1(Nil)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Nil))) -> c9(CONST_F#2(Cons(x0, Cons(x1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Nil)), S(0)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Nil)), S(halve#1(length#1(Nil)))), HALVE#1(length#1(Nil)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> c9(CONST_F#2(Cons(z0, Cons(z1, z2)), Cons(dc#1(map, divisible, mergesort_zs_3, divide, const_f, take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2)))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(drop#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Nil))), DIVIDE_YS#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2)))), HALVE#1(length#1(z2)), LENGTH#1(z2))
   DIVIDE_YS#1(Cons(x0, Cons(x1, x2)), S(y11)) -> c(TAKE#2(S(y11), Cons(x0, Cons(x1, x2))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, x3))), S(y11)) -> c(TAKE#2(S(y11), Cons(x0, Cons(x1, Cons(x2, x3)))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Nil)), S(y10)) -> c(TAKE#2(S(y10), Cons(x0, Cons(x1, Nil))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Nil))), S(y7)) -> c(TAKE#2(S(y7), Cons(x0, Cons(x1, Cons(x2, Nil)))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4)))), S(y8)) -> c(TAKE#2(S(y8), Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4))))))
S tuples:
   DIVIDE_YS#1(z0, z1) -> c1(DROP#2(z1, z0))
   COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(z2, z3), z4, z5, z6, z7) -> c2(MERGE#2(z5, Cons(z2, z3)))
   COND_MERGE_YS_ZS_2(False, Cons(z0, z1), Cons(z2, z3), z4, z5, z6, z7) -> c3(MERGE#2(Cons(z0, z1), z7))
   DROP#2(S(z0), Cons(z1, z2)) -> c12(DROP#2(z0, z2))
   TAKE#2(S(z0), Cons(z1, z2)) -> c15(TAKE#2(z0, z2))
   HALVE#1(S(S(z0))) -> c18(HALVE#1(z0))
   CONST_F#2(z0, Cons(z1, Cons(z2, z3))) -> c19(MERGE#2(z1, z2))
   LEQ#2(S(z0), S(z1)) -> c22(LEQ#2(z0, z1))
   LENGTH#1(Cons(z0, z1)) -> c24(LENGTH#1(z1))
   MAP#2(dc(z0, z1, z2, z3, z4), Cons(z5, z6)) -> c26(DC#1(z0, z1, z2, z3, z4, z5))
   MAP#2(dc(z0, z1, z2, z3, z4), Cons(z5, z6)) -> c27(MAP#2(dc(z0, z1, z2, z3, z4), z6))
   MERGE#2(Cons(0, x1), Cons(z0, x3)) -> c6(COND_MERGE_YS_ZS_2(True, Cons(0, x1), Cons(z0, x3), 0, x1, z0, x3))
   MERGE#2(Cons(S(z0), x1), Cons(0, x3)) -> c6(COND_MERGE_YS_ZS_2(False, Cons(S(z0), x1), Cons(0, x3), S(z0), x1, 0, x3))
   MERGE#2(Cons(S(0), x1), Cons(S(z0), x3)) -> c6(COND_MERGE_YS_ZS_2(True, Cons(S(0), x1), Cons(S(z0), x3), S(0), x1, S(z0), x3), LEQ#2(S(0), S(z0)))
   MERGE#2(Cons(S(S(z0)), x1), Cons(S(0), x3)) -> c6(COND_MERGE_YS_ZS_2(False, Cons(S(S(z0)), x1), Cons(S(0), x3), S(S(z0)), x1, S(0), x3), LEQ#2(S(S(z0)), S(0)))
   MERGE#2(Cons(S(S(z0)), x1), Cons(S(S(z1)), x3)) -> c6(COND_MERGE_YS_ZS_2(leq#2(z0, z1), Cons(S(S(z0)), x1), Cons(S(S(z1)), x3), S(S(z0)), x1, S(S(z1)), x3), LEQ#2(S(S(z0)), S(S(z1))))
   MERGE#2(Cons(S(x0), x1), Cons(S(x2), x3)) -> c6(LEQ#2(S(x0), S(x2)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z1, Cons(x1, x2))) -> c9(CONST_F#2(Cons(z1, Cons(x1, x2)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(x2))), Cons(z1, Cons(x1, x2))), Cons(drop#2(halve#1(length#1(x2)), Cons(x1, x2)), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z1, Cons(x1, x2)), S(halve#1(length#1(x2))))), DIVIDE_YS#1(Cons(z1, Cons(x1, x2)), S(halve#1(length#1(x2)))), HALVE#1(length#1(x2)), LENGTH#1(x2))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Cons(z0, z1)))) -> c9(CONST_F#2(Cons(x0, Cons(x1, Cons(z0, z1))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(Cons(z0, z1)))), Cons(x0, Cons(x1, Cons(z0, z1)))), Cons(drop#2(S(halve#1(S(length#1(z1)))), Cons(x0, Cons(x1, Cons(z0, z1)))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Cons(z0, z1))), S(halve#1(length#1(Cons(z0, z1)))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(z0, z1))), S(halve#1(length#1(Cons(z0, z1))))), HALVE#1(length#1(Cons(z0, z1))), LENGTH#1(Cons(z0, z1)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z1, Cons(x1, x2))) -> c9(CONST_F#2(Cons(z1, Cons(x1, x2)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(Cons(z1, take#2(halve#1(length#1(x2)), Cons(x1, x2))), Cons(drop#2(S(halve#1(length#1(x2))), Cons(z1, Cons(x1, x2))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z1, Cons(x1, x2)), S(halve#1(length#1(x2))))), DIVIDE_YS#1(Cons(z1, Cons(x1, x2)), S(halve#1(length#1(x2)))), HALVE#1(length#1(x2)), LENGTH#1(x2))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Cons(z0, z1)))) -> c9(CONST_F#2(Cons(x0, Cons(x1, Cons(z0, z1))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(S(length#1(z1)))), Cons(x0, Cons(x1, Cons(z0, z1)))), Cons(drop#2(S(halve#1(length#1(Cons(z0, z1)))), Cons(x0, Cons(x1, Cons(z0, z1)))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Cons(z0, z1))), S(halve#1(length#1(Cons(z0, z1)))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(z0, z1))), S(halve#1(length#1(Cons(z0, z1))))), HALVE#1(length#1(Cons(z0, z1))), LENGTH#1(Cons(z0, z1)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, x2))) -> c9(MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, x2)), S(halve#1(length#1(x2))))), DIVIDE_YS#1(Cons(x0, Cons(x1, x2)), S(halve#1(length#1(x2)))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Nil))) -> c9(CONST_F#2(Cons(x0, Cons(x1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(Nil))), Cons(x0, Cons(x1, Nil))), Cons(drop#2(S(halve#1(0)), Cons(x0, Cons(x1, Nil))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Nil)), S(halve#1(length#1(Nil)))), HALVE#1(length#1(Nil)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Nil))) -> c9(CONST_F#2(Cons(x0, Cons(x1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(0)), Cons(x0, Cons(x1, Nil))), Cons(drop#2(S(halve#1(length#1(Nil))), Cons(x0, Cons(x1, Nil))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Nil)), S(halve#1(length#1(Nil)))), HALVE#1(length#1(Nil)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Cons(x2, x3)))) -> c9(CONST_F#2(Cons(x0, Cons(x1, Cons(x2, x3))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(S(length#1(x3)))), Cons(x0, Cons(x1, Cons(x2, x3)))), Cons(drop#2(S(halve#1(S(length#1(x3)))), Cons(x0, Cons(x1, Cons(x2, x3)))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Cons(x2, x3))), S(halve#1(length#1(Cons(x2, x3)))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, x3))), S(halve#1(length#1(Cons(x2, x3))))), HALVE#1(length#1(Cons(x2, x3))), LENGTH#1(Cons(x2, x3)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Cons(x2, Nil)))) -> c9(CONST_F#2(Cons(x0, Cons(x1, Cons(x2, Nil))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Cons(x2, Nil))), S(halve#1(S(0)))))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Cons(x2, Nil))), S(halve#1(length#1(Cons(x2, Nil)))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Nil))), S(halve#1(length#1(Cons(x2, Nil))))), HALVE#1(length#1(Cons(x2, Nil))), LENGTH#1(Cons(x2, Nil)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Cons(x2, Cons(z0, z1))))) -> c9(CONST_F#2(Cons(x0, Cons(x1, Cons(x2, Cons(z0, z1)))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Cons(x2, Cons(z0, z1)))), S(halve#1(S(S(length#1(z1)))))))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Cons(x2, Cons(z0, z1)))), S(halve#1(length#1(Cons(x2, Cons(z0, z1))))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Cons(z0, z1)))), S(halve#1(length#1(Cons(x2, Cons(z0, z1)))))), HALVE#1(length#1(Cons(x2, Cons(z0, z1)))), LENGTH#1(Cons(x2, Cons(z0, z1))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Cons(x2, x3)))) -> c9(MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Cons(x2, x3))), S(halve#1(length#1(Cons(x2, x3)))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, x3))), S(halve#1(length#1(Cons(x2, x3))))), HALVE#1(length#1(Cons(x2, x3))), LENGTH#1(Cons(x2, x3)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Nil))) -> c9(CONST_F#2(Cons(x0, Cons(x1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(0)), Cons(x0, Cons(x1, Nil))), Cons(drop#2(S(halve#1(0)), Cons(x0, Cons(x1, Nil))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Nil)), S(halve#1(length#1(Nil)))), HALVE#1(length#1(Nil)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Nil))) -> c9(CONST_F#2(Cons(x0, Cons(x1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Nil)), S(0)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Nil)), S(halve#1(length#1(Nil)))), HALVE#1(length#1(Nil)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> c9(CONST_F#2(Cons(z0, Cons(z1, z2)), Cons(dc#1(map, divisible, mergesort_zs_3, divide, const_f, take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2)))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(drop#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Nil))), DIVIDE_YS#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2)))), HALVE#1(length#1(z2)), LENGTH#1(z2))
   DIVIDE_YS#1(Cons(x0, Cons(x1, x2)), S(y11)) -> c(TAKE#2(S(y11), Cons(x0, Cons(x1, x2))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, x3))), S(y11)) -> c(TAKE#2(S(y11), Cons(x0, Cons(x1, Cons(x2, x3)))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Nil)), S(y10)) -> c(TAKE#2(S(y10), Cons(x0, Cons(x1, Nil))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Nil))), S(y7)) -> c(TAKE#2(S(y7), Cons(x0, Cons(x1, Cons(x2, Nil)))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4)))), S(y8)) -> c(TAKE#2(S(y8), Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4))))))
K tuples:none
Defined Rule Symbols:   leq#2_2, map#2_2, divide_ys#1_2, halve#1_1, length#1_1, take#2_2, drop#2_2, dc#1_6, const_f#2_2, merge#2_2, cond_merge_ys_zs_2_7

Defined Pair Symbols:   DIVIDE_YS#1_2, COND_MERGE_YS_ZS_2_7, DROP#2_2, TAKE#2_2, HALVE#1_1, CONST_F#2_2, LEQ#2_2, LENGTH#1_1, MAP#2_2, MERGE#2_2, DC#1_6

Compound Symbols:   c1_1, c2_1, c3_1, c12_1, c15_1, c18_1, c19_1, c22_1, c24_1, c26_1, c27_1, c6_1, c6_2, c9_5, c9_2, c9_4, c_1


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(105) CdtInstantiationProof (BOTH BOUNDS(ID, ID))
Use instantiation to replace DIVIDE_YS#1(z0, z1) -> c1(DROP#2(z1, z0)) by 
   DIVIDE_YS#1(Cons(x0, Cons(x1, x2)), S(y11)) -> c1(DROP#2(S(y11), Cons(x0, Cons(x1, x2))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, x3))), S(y11)) -> c1(DROP#2(S(y11), Cons(x0, Cons(x1, Cons(x2, x3)))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Nil)), S(y10)) -> c1(DROP#2(S(y10), Cons(x0, Cons(x1, Nil))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Nil))), S(y7)) -> c1(DROP#2(S(y7), Cons(x0, Cons(x1, Cons(x2, Nil)))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4)))), S(y8)) -> c1(DROP#2(S(y8), Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4))))))

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(106)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   leq#2(0, z0) -> True
   leq#2(S(z0), 0) -> False
   leq#2(S(z0), S(z1)) -> leq#2(z0, z1)
   map#2(dc(z0, z1, z2, z3, z4), Nil) -> Nil
   map#2(dc(z0, z1, z2, z3, z4), Cons(z5, z6)) -> Cons(dc#1(z0, z1, z2, z3, z4, z5), map#2(dc(z0, z1, z2, z3, z4), z6))
   divide_ys#1(z0, z1) -> Cons(take#2(z1, z0), Cons(drop#2(z1, z0), Nil))
   halve#1(0) -> 0
   halve#1(S(0)) -> S(0)
   halve#1(S(S(z0))) -> S(halve#1(z0))
   length#1(Nil) -> 0
   length#1(Cons(z0, z1)) -> S(length#1(z1))
   take#2(0, z0) -> Nil
   take#2(S(0), Nil) -> Cons(bot[0], Nil)
   take#2(S(z0), Cons(z1, z2)) -> Cons(z1, take#2(z0, z2))
   drop#2(0, z0) -> z0
   drop#2(S(0), Nil) -> bot[1]
   drop#2(S(z0), Cons(z1, z2)) -> drop#2(z0, z2)
   dc#1(map, divisible, mergesort_zs_3, divide, const_f, Nil) -> Nil
   dc#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Nil)) -> Cons(z0, Nil)
   dc#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> const_f#2(Cons(z0, Cons(z1, z2)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2))))))
   const_f#2(z0, Cons(z1, Cons(z2, z3))) -> merge#2(z1, z2)
   merge#2(Nil, z0) -> z0
   merge#2(Cons(z0, z1), Nil) -> Cons(z0, z1)
   merge#2(Cons(z0, z1), Cons(z2, z3)) -> cond_merge_ys_zs_2(leq#2(z0, z2), Cons(z0, z1), Cons(z2, z3), z0, z1, z2, z3)
   cond_merge_ys_zs_2(True, Cons(z0, z1), Cons(z2, z3), z4, z5, z6, z7) -> Cons(z4, merge#2(z5, Cons(z2, z3)))
   cond_merge_ys_zs_2(False, Cons(z0, z1), Cons(z2, z3), z4, z5, z6, z7) -> Cons(z6, merge#2(Cons(z0, z1), z7))
Tuples:
   COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(z2, z3), z4, z5, z6, z7) -> c2(MERGE#2(z5, Cons(z2, z3)))
   COND_MERGE_YS_ZS_2(False, Cons(z0, z1), Cons(z2, z3), z4, z5, z6, z7) -> c3(MERGE#2(Cons(z0, z1), z7))
   DROP#2(S(z0), Cons(z1, z2)) -> c12(DROP#2(z0, z2))
   TAKE#2(S(z0), Cons(z1, z2)) -> c15(TAKE#2(z0, z2))
   HALVE#1(S(S(z0))) -> c18(HALVE#1(z0))
   CONST_F#2(z0, Cons(z1, Cons(z2, z3))) -> c19(MERGE#2(z1, z2))
   LEQ#2(S(z0), S(z1)) -> c22(LEQ#2(z0, z1))
   LENGTH#1(Cons(z0, z1)) -> c24(LENGTH#1(z1))
   MAP#2(dc(z0, z1, z2, z3, z4), Cons(z5, z6)) -> c26(DC#1(z0, z1, z2, z3, z4, z5))
   MAP#2(dc(z0, z1, z2, z3, z4), Cons(z5, z6)) -> c27(MAP#2(dc(z0, z1, z2, z3, z4), z6))
   MERGE#2(Cons(0, x1), Cons(z0, x3)) -> c6(COND_MERGE_YS_ZS_2(True, Cons(0, x1), Cons(z0, x3), 0, x1, z0, x3))
   MERGE#2(Cons(S(z0), x1), Cons(0, x3)) -> c6(COND_MERGE_YS_ZS_2(False, Cons(S(z0), x1), Cons(0, x3), S(z0), x1, 0, x3))
   MERGE#2(Cons(S(0), x1), Cons(S(z0), x3)) -> c6(COND_MERGE_YS_ZS_2(True, Cons(S(0), x1), Cons(S(z0), x3), S(0), x1, S(z0), x3), LEQ#2(S(0), S(z0)))
   MERGE#2(Cons(S(S(z0)), x1), Cons(S(0), x3)) -> c6(COND_MERGE_YS_ZS_2(False, Cons(S(S(z0)), x1), Cons(S(0), x3), S(S(z0)), x1, S(0), x3), LEQ#2(S(S(z0)), S(0)))
   MERGE#2(Cons(S(S(z0)), x1), Cons(S(S(z1)), x3)) -> c6(COND_MERGE_YS_ZS_2(leq#2(z0, z1), Cons(S(S(z0)), x1), Cons(S(S(z1)), x3), S(S(z0)), x1, S(S(z1)), x3), LEQ#2(S(S(z0)), S(S(z1))))
   MERGE#2(Cons(S(x0), x1), Cons(S(x2), x3)) -> c6(LEQ#2(S(x0), S(x2)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z1, Cons(x1, x2))) -> c9(CONST_F#2(Cons(z1, Cons(x1, x2)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(x2))), Cons(z1, Cons(x1, x2))), Cons(drop#2(halve#1(length#1(x2)), Cons(x1, x2)), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z1, Cons(x1, x2)), S(halve#1(length#1(x2))))), DIVIDE_YS#1(Cons(z1, Cons(x1, x2)), S(halve#1(length#1(x2)))), HALVE#1(length#1(x2)), LENGTH#1(x2))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Cons(z0, z1)))) -> c9(CONST_F#2(Cons(x0, Cons(x1, Cons(z0, z1))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(Cons(z0, z1)))), Cons(x0, Cons(x1, Cons(z0, z1)))), Cons(drop#2(S(halve#1(S(length#1(z1)))), Cons(x0, Cons(x1, Cons(z0, z1)))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Cons(z0, z1))), S(halve#1(length#1(Cons(z0, z1)))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(z0, z1))), S(halve#1(length#1(Cons(z0, z1))))), HALVE#1(length#1(Cons(z0, z1))), LENGTH#1(Cons(z0, z1)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z1, Cons(x1, x2))) -> c9(CONST_F#2(Cons(z1, Cons(x1, x2)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(Cons(z1, take#2(halve#1(length#1(x2)), Cons(x1, x2))), Cons(drop#2(S(halve#1(length#1(x2))), Cons(z1, Cons(x1, x2))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z1, Cons(x1, x2)), S(halve#1(length#1(x2))))), DIVIDE_YS#1(Cons(z1, Cons(x1, x2)), S(halve#1(length#1(x2)))), HALVE#1(length#1(x2)), LENGTH#1(x2))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Cons(z0, z1)))) -> c9(CONST_F#2(Cons(x0, Cons(x1, Cons(z0, z1))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(S(length#1(z1)))), Cons(x0, Cons(x1, Cons(z0, z1)))), Cons(drop#2(S(halve#1(length#1(Cons(z0, z1)))), Cons(x0, Cons(x1, Cons(z0, z1)))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Cons(z0, z1))), S(halve#1(length#1(Cons(z0, z1)))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(z0, z1))), S(halve#1(length#1(Cons(z0, z1))))), HALVE#1(length#1(Cons(z0, z1))), LENGTH#1(Cons(z0, z1)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, x2))) -> c9(MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, x2)), S(halve#1(length#1(x2))))), DIVIDE_YS#1(Cons(x0, Cons(x1, x2)), S(halve#1(length#1(x2)))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Nil))) -> c9(CONST_F#2(Cons(x0, Cons(x1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(Nil))), Cons(x0, Cons(x1, Nil))), Cons(drop#2(S(halve#1(0)), Cons(x0, Cons(x1, Nil))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Nil)), S(halve#1(length#1(Nil)))), HALVE#1(length#1(Nil)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Nil))) -> c9(CONST_F#2(Cons(x0, Cons(x1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(0)), Cons(x0, Cons(x1, Nil))), Cons(drop#2(S(halve#1(length#1(Nil))), Cons(x0, Cons(x1, Nil))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Nil)), S(halve#1(length#1(Nil)))), HALVE#1(length#1(Nil)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Cons(x2, x3)))) -> c9(CONST_F#2(Cons(x0, Cons(x1, Cons(x2, x3))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(S(length#1(x3)))), Cons(x0, Cons(x1, Cons(x2, x3)))), Cons(drop#2(S(halve#1(S(length#1(x3)))), Cons(x0, Cons(x1, Cons(x2, x3)))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Cons(x2, x3))), S(halve#1(length#1(Cons(x2, x3)))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, x3))), S(halve#1(length#1(Cons(x2, x3))))), HALVE#1(length#1(Cons(x2, x3))), LENGTH#1(Cons(x2, x3)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Cons(x2, Nil)))) -> c9(CONST_F#2(Cons(x0, Cons(x1, Cons(x2, Nil))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Cons(x2, Nil))), S(halve#1(S(0)))))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Cons(x2, Nil))), S(halve#1(length#1(Cons(x2, Nil)))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Nil))), S(halve#1(length#1(Cons(x2, Nil))))), HALVE#1(length#1(Cons(x2, Nil))), LENGTH#1(Cons(x2, Nil)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Cons(x2, Cons(z0, z1))))) -> c9(CONST_F#2(Cons(x0, Cons(x1, Cons(x2, Cons(z0, z1)))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Cons(x2, Cons(z0, z1)))), S(halve#1(S(S(length#1(z1)))))))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Cons(x2, Cons(z0, z1)))), S(halve#1(length#1(Cons(x2, Cons(z0, z1))))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Cons(z0, z1)))), S(halve#1(length#1(Cons(x2, Cons(z0, z1)))))), HALVE#1(length#1(Cons(x2, Cons(z0, z1)))), LENGTH#1(Cons(x2, Cons(z0, z1))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Cons(x2, x3)))) -> c9(MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Cons(x2, x3))), S(halve#1(length#1(Cons(x2, x3)))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, x3))), S(halve#1(length#1(Cons(x2, x3))))), HALVE#1(length#1(Cons(x2, x3))), LENGTH#1(Cons(x2, x3)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Nil))) -> c9(CONST_F#2(Cons(x0, Cons(x1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(0)), Cons(x0, Cons(x1, Nil))), Cons(drop#2(S(halve#1(0)), Cons(x0, Cons(x1, Nil))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Nil)), S(halve#1(length#1(Nil)))), HALVE#1(length#1(Nil)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Nil))) -> c9(CONST_F#2(Cons(x0, Cons(x1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Nil)), S(0)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Nil)), S(halve#1(length#1(Nil)))), HALVE#1(length#1(Nil)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> c9(CONST_F#2(Cons(z0, Cons(z1, z2)), Cons(dc#1(map, divisible, mergesort_zs_3, divide, const_f, take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2)))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(drop#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Nil))), DIVIDE_YS#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2)))), HALVE#1(length#1(z2)), LENGTH#1(z2))
   DIVIDE_YS#1(Cons(x0, Cons(x1, x2)), S(y11)) -> c(TAKE#2(S(y11), Cons(x0, Cons(x1, x2))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, x3))), S(y11)) -> c(TAKE#2(S(y11), Cons(x0, Cons(x1, Cons(x2, x3)))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Nil)), S(y10)) -> c(TAKE#2(S(y10), Cons(x0, Cons(x1, Nil))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Nil))), S(y7)) -> c(TAKE#2(S(y7), Cons(x0, Cons(x1, Cons(x2, Nil)))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4)))), S(y8)) -> c(TAKE#2(S(y8), Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4))))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, x2)), S(y11)) -> c1(DROP#2(S(y11), Cons(x0, Cons(x1, x2))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, x3))), S(y11)) -> c1(DROP#2(S(y11), Cons(x0, Cons(x1, Cons(x2, x3)))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Nil)), S(y10)) -> c1(DROP#2(S(y10), Cons(x0, Cons(x1, Nil))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Nil))), S(y7)) -> c1(DROP#2(S(y7), Cons(x0, Cons(x1, Cons(x2, Nil)))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4)))), S(y8)) -> c1(DROP#2(S(y8), Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4))))))
S tuples:
   COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(z2, z3), z4, z5, z6, z7) -> c2(MERGE#2(z5, Cons(z2, z3)))
   COND_MERGE_YS_ZS_2(False, Cons(z0, z1), Cons(z2, z3), z4, z5, z6, z7) -> c3(MERGE#2(Cons(z0, z1), z7))
   DROP#2(S(z0), Cons(z1, z2)) -> c12(DROP#2(z0, z2))
   TAKE#2(S(z0), Cons(z1, z2)) -> c15(TAKE#2(z0, z2))
   HALVE#1(S(S(z0))) -> c18(HALVE#1(z0))
   CONST_F#2(z0, Cons(z1, Cons(z2, z3))) -> c19(MERGE#2(z1, z2))
   LEQ#2(S(z0), S(z1)) -> c22(LEQ#2(z0, z1))
   LENGTH#1(Cons(z0, z1)) -> c24(LENGTH#1(z1))
   MAP#2(dc(z0, z1, z2, z3, z4), Cons(z5, z6)) -> c26(DC#1(z0, z1, z2, z3, z4, z5))
   MAP#2(dc(z0, z1, z2, z3, z4), Cons(z5, z6)) -> c27(MAP#2(dc(z0, z1, z2, z3, z4), z6))
   MERGE#2(Cons(0, x1), Cons(z0, x3)) -> c6(COND_MERGE_YS_ZS_2(True, Cons(0, x1), Cons(z0, x3), 0, x1, z0, x3))
   MERGE#2(Cons(S(z0), x1), Cons(0, x3)) -> c6(COND_MERGE_YS_ZS_2(False, Cons(S(z0), x1), Cons(0, x3), S(z0), x1, 0, x3))
   MERGE#2(Cons(S(0), x1), Cons(S(z0), x3)) -> c6(COND_MERGE_YS_ZS_2(True, Cons(S(0), x1), Cons(S(z0), x3), S(0), x1, S(z0), x3), LEQ#2(S(0), S(z0)))
   MERGE#2(Cons(S(S(z0)), x1), Cons(S(0), x3)) -> c6(COND_MERGE_YS_ZS_2(False, Cons(S(S(z0)), x1), Cons(S(0), x3), S(S(z0)), x1, S(0), x3), LEQ#2(S(S(z0)), S(0)))
   MERGE#2(Cons(S(S(z0)), x1), Cons(S(S(z1)), x3)) -> c6(COND_MERGE_YS_ZS_2(leq#2(z0, z1), Cons(S(S(z0)), x1), Cons(S(S(z1)), x3), S(S(z0)), x1, S(S(z1)), x3), LEQ#2(S(S(z0)), S(S(z1))))
   MERGE#2(Cons(S(x0), x1), Cons(S(x2), x3)) -> c6(LEQ#2(S(x0), S(x2)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z1, Cons(x1, x2))) -> c9(CONST_F#2(Cons(z1, Cons(x1, x2)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(x2))), Cons(z1, Cons(x1, x2))), Cons(drop#2(halve#1(length#1(x2)), Cons(x1, x2)), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z1, Cons(x1, x2)), S(halve#1(length#1(x2))))), DIVIDE_YS#1(Cons(z1, Cons(x1, x2)), S(halve#1(length#1(x2)))), HALVE#1(length#1(x2)), LENGTH#1(x2))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Cons(z0, z1)))) -> c9(CONST_F#2(Cons(x0, Cons(x1, Cons(z0, z1))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(Cons(z0, z1)))), Cons(x0, Cons(x1, Cons(z0, z1)))), Cons(drop#2(S(halve#1(S(length#1(z1)))), Cons(x0, Cons(x1, Cons(z0, z1)))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Cons(z0, z1))), S(halve#1(length#1(Cons(z0, z1)))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(z0, z1))), S(halve#1(length#1(Cons(z0, z1))))), HALVE#1(length#1(Cons(z0, z1))), LENGTH#1(Cons(z0, z1)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z1, Cons(x1, x2))) -> c9(CONST_F#2(Cons(z1, Cons(x1, x2)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(Cons(z1, take#2(halve#1(length#1(x2)), Cons(x1, x2))), Cons(drop#2(S(halve#1(length#1(x2))), Cons(z1, Cons(x1, x2))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z1, Cons(x1, x2)), S(halve#1(length#1(x2))))), DIVIDE_YS#1(Cons(z1, Cons(x1, x2)), S(halve#1(length#1(x2)))), HALVE#1(length#1(x2)), LENGTH#1(x2))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Cons(z0, z1)))) -> c9(CONST_F#2(Cons(x0, Cons(x1, Cons(z0, z1))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(S(length#1(z1)))), Cons(x0, Cons(x1, Cons(z0, z1)))), Cons(drop#2(S(halve#1(length#1(Cons(z0, z1)))), Cons(x0, Cons(x1, Cons(z0, z1)))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Cons(z0, z1))), S(halve#1(length#1(Cons(z0, z1)))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(z0, z1))), S(halve#1(length#1(Cons(z0, z1))))), HALVE#1(length#1(Cons(z0, z1))), LENGTH#1(Cons(z0, z1)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, x2))) -> c9(MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, x2)), S(halve#1(length#1(x2))))), DIVIDE_YS#1(Cons(x0, Cons(x1, x2)), S(halve#1(length#1(x2)))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Nil))) -> c9(CONST_F#2(Cons(x0, Cons(x1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(Nil))), Cons(x0, Cons(x1, Nil))), Cons(drop#2(S(halve#1(0)), Cons(x0, Cons(x1, Nil))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Nil)), S(halve#1(length#1(Nil)))), HALVE#1(length#1(Nil)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Nil))) -> c9(CONST_F#2(Cons(x0, Cons(x1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(0)), Cons(x0, Cons(x1, Nil))), Cons(drop#2(S(halve#1(length#1(Nil))), Cons(x0, Cons(x1, Nil))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Nil)), S(halve#1(length#1(Nil)))), HALVE#1(length#1(Nil)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Cons(x2, x3)))) -> c9(CONST_F#2(Cons(x0, Cons(x1, Cons(x2, x3))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(S(length#1(x3)))), Cons(x0, Cons(x1, Cons(x2, x3)))), Cons(drop#2(S(halve#1(S(length#1(x3)))), Cons(x0, Cons(x1, Cons(x2, x3)))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Cons(x2, x3))), S(halve#1(length#1(Cons(x2, x3)))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, x3))), S(halve#1(length#1(Cons(x2, x3))))), HALVE#1(length#1(Cons(x2, x3))), LENGTH#1(Cons(x2, x3)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Cons(x2, Nil)))) -> c9(CONST_F#2(Cons(x0, Cons(x1, Cons(x2, Nil))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Cons(x2, Nil))), S(halve#1(S(0)))))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Cons(x2, Nil))), S(halve#1(length#1(Cons(x2, Nil)))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Nil))), S(halve#1(length#1(Cons(x2, Nil))))), HALVE#1(length#1(Cons(x2, Nil))), LENGTH#1(Cons(x2, Nil)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Cons(x2, Cons(z0, z1))))) -> c9(CONST_F#2(Cons(x0, Cons(x1, Cons(x2, Cons(z0, z1)))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Cons(x2, Cons(z0, z1)))), S(halve#1(S(S(length#1(z1)))))))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Cons(x2, Cons(z0, z1)))), S(halve#1(length#1(Cons(x2, Cons(z0, z1))))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Cons(z0, z1)))), S(halve#1(length#1(Cons(x2, Cons(z0, z1)))))), HALVE#1(length#1(Cons(x2, Cons(z0, z1)))), LENGTH#1(Cons(x2, Cons(z0, z1))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Cons(x2, x3)))) -> c9(MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Cons(x2, x3))), S(halve#1(length#1(Cons(x2, x3)))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, x3))), S(halve#1(length#1(Cons(x2, x3))))), HALVE#1(length#1(Cons(x2, x3))), LENGTH#1(Cons(x2, x3)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Nil))) -> c9(CONST_F#2(Cons(x0, Cons(x1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(0)), Cons(x0, Cons(x1, Nil))), Cons(drop#2(S(halve#1(0)), Cons(x0, Cons(x1, Nil))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Nil)), S(halve#1(length#1(Nil)))), HALVE#1(length#1(Nil)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Nil))) -> c9(CONST_F#2(Cons(x0, Cons(x1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Nil)), S(0)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Nil)), S(halve#1(length#1(Nil)))), HALVE#1(length#1(Nil)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> c9(CONST_F#2(Cons(z0, Cons(z1, z2)), Cons(dc#1(map, divisible, mergesort_zs_3, divide, const_f, take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2)))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(drop#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Nil))), DIVIDE_YS#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2)))), HALVE#1(length#1(z2)), LENGTH#1(z2))
   DIVIDE_YS#1(Cons(x0, Cons(x1, x2)), S(y11)) -> c(TAKE#2(S(y11), Cons(x0, Cons(x1, x2))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, x3))), S(y11)) -> c(TAKE#2(S(y11), Cons(x0, Cons(x1, Cons(x2, x3)))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Nil)), S(y10)) -> c(TAKE#2(S(y10), Cons(x0, Cons(x1, Nil))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Nil))), S(y7)) -> c(TAKE#2(S(y7), Cons(x0, Cons(x1, Cons(x2, Nil)))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4)))), S(y8)) -> c(TAKE#2(S(y8), Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4))))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, x2)), S(y11)) -> c1(DROP#2(S(y11), Cons(x0, Cons(x1, x2))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, x3))), S(y11)) -> c1(DROP#2(S(y11), Cons(x0, Cons(x1, Cons(x2, x3)))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Nil)), S(y10)) -> c1(DROP#2(S(y10), Cons(x0, Cons(x1, Nil))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Nil))), S(y7)) -> c1(DROP#2(S(y7), Cons(x0, Cons(x1, Cons(x2, Nil)))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4)))), S(y8)) -> c1(DROP#2(S(y8), Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4))))))
K tuples:none
Defined Rule Symbols:   leq#2_2, map#2_2, divide_ys#1_2, halve#1_1, length#1_1, take#2_2, drop#2_2, dc#1_6, const_f#2_2, merge#2_2, cond_merge_ys_zs_2_7

Defined Pair Symbols:   COND_MERGE_YS_ZS_2_7, DROP#2_2, TAKE#2_2, HALVE#1_1, CONST_F#2_2, LEQ#2_2, LENGTH#1_1, MAP#2_2, MERGE#2_2, DC#1_6, DIVIDE_YS#1_2

Compound Symbols:   c2_1, c3_1, c12_1, c15_1, c18_1, c19_1, c22_1, c24_1, c26_1, c27_1, c6_1, c6_2, c9_5, c9_2, c9_4, c_1, c1_1


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

(107) CdtRewritingProof (BOTH BOUNDS(ID, ID))
Used rewriting to replace DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z1, Cons(x1, x2))) -> c9(CONST_F#2(Cons(z1, Cons(x1, x2)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(x2))), Cons(z1, Cons(x1, x2))), Cons(drop#2(halve#1(length#1(x2)), Cons(x1, x2)), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z1, Cons(x1, x2)), S(halve#1(length#1(x2))))), DIVIDE_YS#1(Cons(z1, Cons(x1, x2)), S(halve#1(length#1(x2)))), HALVE#1(length#1(x2)), LENGTH#1(x2)) by DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> c9(CONST_F#2(Cons(z0, Cons(z1, z2)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(halve#1(length#1(z2)), Cons(z1, z2)), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Nil))), DIVIDE_YS#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2)))), HALVE#1(length#1(z2)), LENGTH#1(z2))
----------------------------------------

(108)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   leq#2(0, z0) -> True
   leq#2(S(z0), 0) -> False
   leq#2(S(z0), S(z1)) -> leq#2(z0, z1)
   map#2(dc(z0, z1, z2, z3, z4), Nil) -> Nil
   map#2(dc(z0, z1, z2, z3, z4), Cons(z5, z6)) -> Cons(dc#1(z0, z1, z2, z3, z4, z5), map#2(dc(z0, z1, z2, z3, z4), z6))
   divide_ys#1(z0, z1) -> Cons(take#2(z1, z0), Cons(drop#2(z1, z0), Nil))
   halve#1(0) -> 0
   halve#1(S(0)) -> S(0)
   halve#1(S(S(z0))) -> S(halve#1(z0))
   length#1(Nil) -> 0
   length#1(Cons(z0, z1)) -> S(length#1(z1))
   take#2(0, z0) -> Nil
   take#2(S(0), Nil) -> Cons(bot[0], Nil)
   take#2(S(z0), Cons(z1, z2)) -> Cons(z1, take#2(z0, z2))
   drop#2(0, z0) -> z0
   drop#2(S(0), Nil) -> bot[1]
   drop#2(S(z0), Cons(z1, z2)) -> drop#2(z0, z2)
   dc#1(map, divisible, mergesort_zs_3, divide, const_f, Nil) -> Nil
   dc#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Nil)) -> Cons(z0, Nil)
   dc#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> const_f#2(Cons(z0, Cons(z1, z2)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2))))))
   const_f#2(z0, Cons(z1, Cons(z2, z3))) -> merge#2(z1, z2)
   merge#2(Nil, z0) -> z0
   merge#2(Cons(z0, z1), Nil) -> Cons(z0, z1)
   merge#2(Cons(z0, z1), Cons(z2, z3)) -> cond_merge_ys_zs_2(leq#2(z0, z2), Cons(z0, z1), Cons(z2, z3), z0, z1, z2, z3)
   cond_merge_ys_zs_2(True, Cons(z0, z1), Cons(z2, z3), z4, z5, z6, z7) -> Cons(z4, merge#2(z5, Cons(z2, z3)))
   cond_merge_ys_zs_2(False, Cons(z0, z1), Cons(z2, z3), z4, z5, z6, z7) -> Cons(z6, merge#2(Cons(z0, z1), z7))
Tuples:
   COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(z2, z3), z4, z5, z6, z7) -> c2(MERGE#2(z5, Cons(z2, z3)))
   COND_MERGE_YS_ZS_2(False, Cons(z0, z1), Cons(z2, z3), z4, z5, z6, z7) -> c3(MERGE#2(Cons(z0, z1), z7))
   DROP#2(S(z0), Cons(z1, z2)) -> c12(DROP#2(z0, z2))
   TAKE#2(S(z0), Cons(z1, z2)) -> c15(TAKE#2(z0, z2))
   HALVE#1(S(S(z0))) -> c18(HALVE#1(z0))
   CONST_F#2(z0, Cons(z1, Cons(z2, z3))) -> c19(MERGE#2(z1, z2))
   LEQ#2(S(z0), S(z1)) -> c22(LEQ#2(z0, z1))
   LENGTH#1(Cons(z0, z1)) -> c24(LENGTH#1(z1))
   MAP#2(dc(z0, z1, z2, z3, z4), Cons(z5, z6)) -> c26(DC#1(z0, z1, z2, z3, z4, z5))
   MAP#2(dc(z0, z1, z2, z3, z4), Cons(z5, z6)) -> c27(MAP#2(dc(z0, z1, z2, z3, z4), z6))
   MERGE#2(Cons(0, x1), Cons(z0, x3)) -> c6(COND_MERGE_YS_ZS_2(True, Cons(0, x1), Cons(z0, x3), 0, x1, z0, x3))
   MERGE#2(Cons(S(z0), x1), Cons(0, x3)) -> c6(COND_MERGE_YS_ZS_2(False, Cons(S(z0), x1), Cons(0, x3), S(z0), x1, 0, x3))
   MERGE#2(Cons(S(0), x1), Cons(S(z0), x3)) -> c6(COND_MERGE_YS_ZS_2(True, Cons(S(0), x1), Cons(S(z0), x3), S(0), x1, S(z0), x3), LEQ#2(S(0), S(z0)))
   MERGE#2(Cons(S(S(z0)), x1), Cons(S(0), x3)) -> c6(COND_MERGE_YS_ZS_2(False, Cons(S(S(z0)), x1), Cons(S(0), x3), S(S(z0)), x1, S(0), x3), LEQ#2(S(S(z0)), S(0)))
   MERGE#2(Cons(S(S(z0)), x1), Cons(S(S(z1)), x3)) -> c6(COND_MERGE_YS_ZS_2(leq#2(z0, z1), Cons(S(S(z0)), x1), Cons(S(S(z1)), x3), S(S(z0)), x1, S(S(z1)), x3), LEQ#2(S(S(z0)), S(S(z1))))
   MERGE#2(Cons(S(x0), x1), Cons(S(x2), x3)) -> c6(LEQ#2(S(x0), S(x2)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Cons(z0, z1)))) -> c9(CONST_F#2(Cons(x0, Cons(x1, Cons(z0, z1))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(Cons(z0, z1)))), Cons(x0, Cons(x1, Cons(z0, z1)))), Cons(drop#2(S(halve#1(S(length#1(z1)))), Cons(x0, Cons(x1, Cons(z0, z1)))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Cons(z0, z1))), S(halve#1(length#1(Cons(z0, z1)))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(z0, z1))), S(halve#1(length#1(Cons(z0, z1))))), HALVE#1(length#1(Cons(z0, z1))), LENGTH#1(Cons(z0, z1)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z1, Cons(x1, x2))) -> c9(CONST_F#2(Cons(z1, Cons(x1, x2)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(Cons(z1, take#2(halve#1(length#1(x2)), Cons(x1, x2))), Cons(drop#2(S(halve#1(length#1(x2))), Cons(z1, Cons(x1, x2))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z1, Cons(x1, x2)), S(halve#1(length#1(x2))))), DIVIDE_YS#1(Cons(z1, Cons(x1, x2)), S(halve#1(length#1(x2)))), HALVE#1(length#1(x2)), LENGTH#1(x2))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Cons(z0, z1)))) -> c9(CONST_F#2(Cons(x0, Cons(x1, Cons(z0, z1))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(S(length#1(z1)))), Cons(x0, Cons(x1, Cons(z0, z1)))), Cons(drop#2(S(halve#1(length#1(Cons(z0, z1)))), Cons(x0, Cons(x1, Cons(z0, z1)))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Cons(z0, z1))), S(halve#1(length#1(Cons(z0, z1)))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(z0, z1))), S(halve#1(length#1(Cons(z0, z1))))), HALVE#1(length#1(Cons(z0, z1))), LENGTH#1(Cons(z0, z1)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, x2))) -> c9(MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, x2)), S(halve#1(length#1(x2))))), DIVIDE_YS#1(Cons(x0, Cons(x1, x2)), S(halve#1(length#1(x2)))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Nil))) -> c9(CONST_F#2(Cons(x0, Cons(x1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(Nil))), Cons(x0, Cons(x1, Nil))), Cons(drop#2(S(halve#1(0)), Cons(x0, Cons(x1, Nil))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Nil)), S(halve#1(length#1(Nil)))), HALVE#1(length#1(Nil)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Nil))) -> c9(CONST_F#2(Cons(x0, Cons(x1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(0)), Cons(x0, Cons(x1, Nil))), Cons(drop#2(S(halve#1(length#1(Nil))), Cons(x0, Cons(x1, Nil))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Nil)), S(halve#1(length#1(Nil)))), HALVE#1(length#1(Nil)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Cons(x2, x3)))) -> c9(CONST_F#2(Cons(x0, Cons(x1, Cons(x2, x3))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(S(length#1(x3)))), Cons(x0, Cons(x1, Cons(x2, x3)))), Cons(drop#2(S(halve#1(S(length#1(x3)))), Cons(x0, Cons(x1, Cons(x2, x3)))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Cons(x2, x3))), S(halve#1(length#1(Cons(x2, x3)))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, x3))), S(halve#1(length#1(Cons(x2, x3))))), HALVE#1(length#1(Cons(x2, x3))), LENGTH#1(Cons(x2, x3)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Cons(x2, Nil)))) -> c9(CONST_F#2(Cons(x0, Cons(x1, Cons(x2, Nil))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Cons(x2, Nil))), S(halve#1(S(0)))))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Cons(x2, Nil))), S(halve#1(length#1(Cons(x2, Nil)))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Nil))), S(halve#1(length#1(Cons(x2, Nil))))), HALVE#1(length#1(Cons(x2, Nil))), LENGTH#1(Cons(x2, Nil)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Cons(x2, Cons(z0, z1))))) -> c9(CONST_F#2(Cons(x0, Cons(x1, Cons(x2, Cons(z0, z1)))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Cons(x2, Cons(z0, z1)))), S(halve#1(S(S(length#1(z1)))))))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Cons(x2, Cons(z0, z1)))), S(halve#1(length#1(Cons(x2, Cons(z0, z1))))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Cons(z0, z1)))), S(halve#1(length#1(Cons(x2, Cons(z0, z1)))))), HALVE#1(length#1(Cons(x2, Cons(z0, z1)))), LENGTH#1(Cons(x2, Cons(z0, z1))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Cons(x2, x3)))) -> c9(MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Cons(x2, x3))), S(halve#1(length#1(Cons(x2, x3)))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, x3))), S(halve#1(length#1(Cons(x2, x3))))), HALVE#1(length#1(Cons(x2, x3))), LENGTH#1(Cons(x2, x3)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Nil))) -> c9(CONST_F#2(Cons(x0, Cons(x1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(0)), Cons(x0, Cons(x1, Nil))), Cons(drop#2(S(halve#1(0)), Cons(x0, Cons(x1, Nil))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Nil)), S(halve#1(length#1(Nil)))), HALVE#1(length#1(Nil)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Nil))) -> c9(CONST_F#2(Cons(x0, Cons(x1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Nil)), S(0)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Nil)), S(halve#1(length#1(Nil)))), HALVE#1(length#1(Nil)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> c9(CONST_F#2(Cons(z0, Cons(z1, z2)), Cons(dc#1(map, divisible, mergesort_zs_3, divide, const_f, take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2)))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(drop#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Nil))), DIVIDE_YS#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2)))), HALVE#1(length#1(z2)), LENGTH#1(z2))
   DIVIDE_YS#1(Cons(x0, Cons(x1, x2)), S(y11)) -> c(TAKE#2(S(y11), Cons(x0, Cons(x1, x2))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, x3))), S(y11)) -> c(TAKE#2(S(y11), Cons(x0, Cons(x1, Cons(x2, x3)))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Nil)), S(y10)) -> c(TAKE#2(S(y10), Cons(x0, Cons(x1, Nil))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Nil))), S(y7)) -> c(TAKE#2(S(y7), Cons(x0, Cons(x1, Cons(x2, Nil)))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4)))), S(y8)) -> c(TAKE#2(S(y8), Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4))))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, x2)), S(y11)) -> c1(DROP#2(S(y11), Cons(x0, Cons(x1, x2))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, x3))), S(y11)) -> c1(DROP#2(S(y11), Cons(x0, Cons(x1, Cons(x2, x3)))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Nil)), S(y10)) -> c1(DROP#2(S(y10), Cons(x0, Cons(x1, Nil))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Nil))), S(y7)) -> c1(DROP#2(S(y7), Cons(x0, Cons(x1, Cons(x2, Nil)))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4)))), S(y8)) -> c1(DROP#2(S(y8), Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4))))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> c9(CONST_F#2(Cons(z0, Cons(z1, z2)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(halve#1(length#1(z2)), Cons(z1, z2)), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Nil))), DIVIDE_YS#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2)))), HALVE#1(length#1(z2)), LENGTH#1(z2))
S tuples:
   COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(z2, z3), z4, z5, z6, z7) -> c2(MERGE#2(z5, Cons(z2, z3)))
   COND_MERGE_YS_ZS_2(False, Cons(z0, z1), Cons(z2, z3), z4, z5, z6, z7) -> c3(MERGE#2(Cons(z0, z1), z7))
   DROP#2(S(z0), Cons(z1, z2)) -> c12(DROP#2(z0, z2))
   TAKE#2(S(z0), Cons(z1, z2)) -> c15(TAKE#2(z0, z2))
   HALVE#1(S(S(z0))) -> c18(HALVE#1(z0))
   CONST_F#2(z0, Cons(z1, Cons(z2, z3))) -> c19(MERGE#2(z1, z2))
   LEQ#2(S(z0), S(z1)) -> c22(LEQ#2(z0, z1))
   LENGTH#1(Cons(z0, z1)) -> c24(LENGTH#1(z1))
   MAP#2(dc(z0, z1, z2, z3, z4), Cons(z5, z6)) -> c26(DC#1(z0, z1, z2, z3, z4, z5))
   MAP#2(dc(z0, z1, z2, z3, z4), Cons(z5, z6)) -> c27(MAP#2(dc(z0, z1, z2, z3, z4), z6))
   MERGE#2(Cons(0, x1), Cons(z0, x3)) -> c6(COND_MERGE_YS_ZS_2(True, Cons(0, x1), Cons(z0, x3), 0, x1, z0, x3))
   MERGE#2(Cons(S(z0), x1), Cons(0, x3)) -> c6(COND_MERGE_YS_ZS_2(False, Cons(S(z0), x1), Cons(0, x3), S(z0), x1, 0, x3))
   MERGE#2(Cons(S(0), x1), Cons(S(z0), x3)) -> c6(COND_MERGE_YS_ZS_2(True, Cons(S(0), x1), Cons(S(z0), x3), S(0), x1, S(z0), x3), LEQ#2(S(0), S(z0)))
   MERGE#2(Cons(S(S(z0)), x1), Cons(S(0), x3)) -> c6(COND_MERGE_YS_ZS_2(False, Cons(S(S(z0)), x1), Cons(S(0), x3), S(S(z0)), x1, S(0), x3), LEQ#2(S(S(z0)), S(0)))
   MERGE#2(Cons(S(S(z0)), x1), Cons(S(S(z1)), x3)) -> c6(COND_MERGE_YS_ZS_2(leq#2(z0, z1), Cons(S(S(z0)), x1), Cons(S(S(z1)), x3), S(S(z0)), x1, S(S(z1)), x3), LEQ#2(S(S(z0)), S(S(z1))))
   MERGE#2(Cons(S(x0), x1), Cons(S(x2), x3)) -> c6(LEQ#2(S(x0), S(x2)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Cons(z0, z1)))) -> c9(CONST_F#2(Cons(x0, Cons(x1, Cons(z0, z1))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(Cons(z0, z1)))), Cons(x0, Cons(x1, Cons(z0, z1)))), Cons(drop#2(S(halve#1(S(length#1(z1)))), Cons(x0, Cons(x1, Cons(z0, z1)))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Cons(z0, z1))), S(halve#1(length#1(Cons(z0, z1)))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(z0, z1))), S(halve#1(length#1(Cons(z0, z1))))), HALVE#1(length#1(Cons(z0, z1))), LENGTH#1(Cons(z0, z1)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z1, Cons(x1, x2))) -> c9(CONST_F#2(Cons(z1, Cons(x1, x2)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(Cons(z1, take#2(halve#1(length#1(x2)), Cons(x1, x2))), Cons(drop#2(S(halve#1(length#1(x2))), Cons(z1, Cons(x1, x2))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z1, Cons(x1, x2)), S(halve#1(length#1(x2))))), DIVIDE_YS#1(Cons(z1, Cons(x1, x2)), S(halve#1(length#1(x2)))), HALVE#1(length#1(x2)), LENGTH#1(x2))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Cons(z0, z1)))) -> c9(CONST_F#2(Cons(x0, Cons(x1, Cons(z0, z1))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(S(length#1(z1)))), Cons(x0, Cons(x1, Cons(z0, z1)))), Cons(drop#2(S(halve#1(length#1(Cons(z0, z1)))), Cons(x0, Cons(x1, Cons(z0, z1)))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Cons(z0, z1))), S(halve#1(length#1(Cons(z0, z1)))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(z0, z1))), S(halve#1(length#1(Cons(z0, z1))))), HALVE#1(length#1(Cons(z0, z1))), LENGTH#1(Cons(z0, z1)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, x2))) -> c9(MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, x2)), S(halve#1(length#1(x2))))), DIVIDE_YS#1(Cons(x0, Cons(x1, x2)), S(halve#1(length#1(x2)))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Nil))) -> c9(CONST_F#2(Cons(x0, Cons(x1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(Nil))), Cons(x0, Cons(x1, Nil))), Cons(drop#2(S(halve#1(0)), Cons(x0, Cons(x1, Nil))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Nil)), S(halve#1(length#1(Nil)))), HALVE#1(length#1(Nil)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Nil))) -> c9(CONST_F#2(Cons(x0, Cons(x1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(0)), Cons(x0, Cons(x1, Nil))), Cons(drop#2(S(halve#1(length#1(Nil))), Cons(x0, Cons(x1, Nil))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Nil)), S(halve#1(length#1(Nil)))), HALVE#1(length#1(Nil)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Cons(x2, x3)))) -> c9(CONST_F#2(Cons(x0, Cons(x1, Cons(x2, x3))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(S(length#1(x3)))), Cons(x0, Cons(x1, Cons(x2, x3)))), Cons(drop#2(S(halve#1(S(length#1(x3)))), Cons(x0, Cons(x1, Cons(x2, x3)))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Cons(x2, x3))), S(halve#1(length#1(Cons(x2, x3)))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, x3))), S(halve#1(length#1(Cons(x2, x3))))), HALVE#1(length#1(Cons(x2, x3))), LENGTH#1(Cons(x2, x3)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Cons(x2, Nil)))) -> c9(CONST_F#2(Cons(x0, Cons(x1, Cons(x2, Nil))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Cons(x2, Nil))), S(halve#1(S(0)))))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Cons(x2, Nil))), S(halve#1(length#1(Cons(x2, Nil)))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Nil))), S(halve#1(length#1(Cons(x2, Nil))))), HALVE#1(length#1(Cons(x2, Nil))), LENGTH#1(Cons(x2, Nil)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Cons(x2, Cons(z0, z1))))) -> c9(CONST_F#2(Cons(x0, Cons(x1, Cons(x2, Cons(z0, z1)))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Cons(x2, Cons(z0, z1)))), S(halve#1(S(S(length#1(z1)))))))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Cons(x2, Cons(z0, z1)))), S(halve#1(length#1(Cons(x2, Cons(z0, z1))))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Cons(z0, z1)))), S(halve#1(length#1(Cons(x2, Cons(z0, z1)))))), HALVE#1(length#1(Cons(x2, Cons(z0, z1)))), LENGTH#1(Cons(x2, Cons(z0, z1))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Cons(x2, x3)))) -> c9(MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Cons(x2, x3))), S(halve#1(length#1(Cons(x2, x3)))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, x3))), S(halve#1(length#1(Cons(x2, x3))))), HALVE#1(length#1(Cons(x2, x3))), LENGTH#1(Cons(x2, x3)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Nil))) -> c9(CONST_F#2(Cons(x0, Cons(x1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(0)), Cons(x0, Cons(x1, Nil))), Cons(drop#2(S(halve#1(0)), Cons(x0, Cons(x1, Nil))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Nil)), S(halve#1(length#1(Nil)))), HALVE#1(length#1(Nil)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Nil))) -> c9(CONST_F#2(Cons(x0, Cons(x1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Nil)), S(0)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Nil)), S(halve#1(length#1(Nil)))), HALVE#1(length#1(Nil)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> c9(CONST_F#2(Cons(z0, Cons(z1, z2)), Cons(dc#1(map, divisible, mergesort_zs_3, divide, const_f, take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2)))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(drop#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Nil))), DIVIDE_YS#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2)))), HALVE#1(length#1(z2)), LENGTH#1(z2))
   DIVIDE_YS#1(Cons(x0, Cons(x1, x2)), S(y11)) -> c(TAKE#2(S(y11), Cons(x0, Cons(x1, x2))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, x3))), S(y11)) -> c(TAKE#2(S(y11), Cons(x0, Cons(x1, Cons(x2, x3)))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Nil)), S(y10)) -> c(TAKE#2(S(y10), Cons(x0, Cons(x1, Nil))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Nil))), S(y7)) -> c(TAKE#2(S(y7), Cons(x0, Cons(x1, Cons(x2, Nil)))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4)))), S(y8)) -> c(TAKE#2(S(y8), Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4))))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, x2)), S(y11)) -> c1(DROP#2(S(y11), Cons(x0, Cons(x1, x2))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, x3))), S(y11)) -> c1(DROP#2(S(y11), Cons(x0, Cons(x1, Cons(x2, x3)))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Nil)), S(y10)) -> c1(DROP#2(S(y10), Cons(x0, Cons(x1, Nil))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Nil))), S(y7)) -> c1(DROP#2(S(y7), Cons(x0, Cons(x1, Cons(x2, Nil)))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4)))), S(y8)) -> c1(DROP#2(S(y8), Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4))))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> c9(CONST_F#2(Cons(z0, Cons(z1, z2)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(halve#1(length#1(z2)), Cons(z1, z2)), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Nil))), DIVIDE_YS#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2)))), HALVE#1(length#1(z2)), LENGTH#1(z2))
K tuples:none
Defined Rule Symbols:   leq#2_2, map#2_2, divide_ys#1_2, halve#1_1, length#1_1, take#2_2, drop#2_2, dc#1_6, const_f#2_2, merge#2_2, cond_merge_ys_zs_2_7

Defined Pair Symbols:   COND_MERGE_YS_ZS_2_7, DROP#2_2, TAKE#2_2, HALVE#1_1, CONST_F#2_2, LEQ#2_2, LENGTH#1_1, MAP#2_2, MERGE#2_2, DC#1_6, DIVIDE_YS#1_2

Compound Symbols:   c2_1, c3_1, c12_1, c15_1, c18_1, c19_1, c22_1, c24_1, c26_1, c27_1, c6_1, c6_2, c9_5, c9_2, c9_4, c_1, c1_1


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(109) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID))
Use forward instantiation to replace COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(z2, z3), z4, z5, z6, z7) -> c2(MERGE#2(z5, Cons(z2, z3))) by 
   COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(z2, z3), z4, Cons(0, y0), z6, z7) -> c2(MERGE#2(Cons(0, y0), Cons(z2, z3)))
   COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(0, z3), z4, Cons(S(y0), y1), z6, z7) -> c2(MERGE#2(Cons(S(y0), y1), Cons(0, z3)))
   COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(S(y1), z3), z4, Cons(S(0), y0), z6, z7) -> c2(MERGE#2(Cons(S(0), y0), Cons(S(y1), z3)))
   COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(S(0), z3), z4, Cons(S(S(y0)), y1), z6, z7) -> c2(MERGE#2(Cons(S(S(y0)), y1), Cons(S(0), z3)))
   COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(S(S(y2)), z3), z4, Cons(S(S(y0)), y1), z6, z7) -> c2(MERGE#2(Cons(S(S(y0)), y1), Cons(S(S(y2)), z3)))
   COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(S(y2), z3), z4, Cons(S(y0), y1), z6, z7) -> c2(MERGE#2(Cons(S(y0), y1), Cons(S(y2), z3)))

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

(110)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   leq#2(0, z0) -> True
   leq#2(S(z0), 0) -> False
   leq#2(S(z0), S(z1)) -> leq#2(z0, z1)
   map#2(dc(z0, z1, z2, z3, z4), Nil) -> Nil
   map#2(dc(z0, z1, z2, z3, z4), Cons(z5, z6)) -> Cons(dc#1(z0, z1, z2, z3, z4, z5), map#2(dc(z0, z1, z2, z3, z4), z6))
   divide_ys#1(z0, z1) -> Cons(take#2(z1, z0), Cons(drop#2(z1, z0), Nil))
   halve#1(0) -> 0
   halve#1(S(0)) -> S(0)
   halve#1(S(S(z0))) -> S(halve#1(z0))
   length#1(Nil) -> 0
   length#1(Cons(z0, z1)) -> S(length#1(z1))
   take#2(0, z0) -> Nil
   take#2(S(0), Nil) -> Cons(bot[0], Nil)
   take#2(S(z0), Cons(z1, z2)) -> Cons(z1, take#2(z0, z2))
   drop#2(0, z0) -> z0
   drop#2(S(0), Nil) -> bot[1]
   drop#2(S(z0), Cons(z1, z2)) -> drop#2(z0, z2)
   dc#1(map, divisible, mergesort_zs_3, divide, const_f, Nil) -> Nil
   dc#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Nil)) -> Cons(z0, Nil)
   dc#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> const_f#2(Cons(z0, Cons(z1, z2)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2))))))
   const_f#2(z0, Cons(z1, Cons(z2, z3))) -> merge#2(z1, z2)
   merge#2(Nil, z0) -> z0
   merge#2(Cons(z0, z1), Nil) -> Cons(z0, z1)
   merge#2(Cons(z0, z1), Cons(z2, z3)) -> cond_merge_ys_zs_2(leq#2(z0, z2), Cons(z0, z1), Cons(z2, z3), z0, z1, z2, z3)
   cond_merge_ys_zs_2(True, Cons(z0, z1), Cons(z2, z3), z4, z5, z6, z7) -> Cons(z4, merge#2(z5, Cons(z2, z3)))
   cond_merge_ys_zs_2(False, Cons(z0, z1), Cons(z2, z3), z4, z5, z6, z7) -> Cons(z6, merge#2(Cons(z0, z1), z7))
Tuples:
   COND_MERGE_YS_ZS_2(False, Cons(z0, z1), Cons(z2, z3), z4, z5, z6, z7) -> c3(MERGE#2(Cons(z0, z1), z7))
   DROP#2(S(z0), Cons(z1, z2)) -> c12(DROP#2(z0, z2))
   TAKE#2(S(z0), Cons(z1, z2)) -> c15(TAKE#2(z0, z2))
   HALVE#1(S(S(z0))) -> c18(HALVE#1(z0))
   CONST_F#2(z0, Cons(z1, Cons(z2, z3))) -> c19(MERGE#2(z1, z2))
   LEQ#2(S(z0), S(z1)) -> c22(LEQ#2(z0, z1))
   LENGTH#1(Cons(z0, z1)) -> c24(LENGTH#1(z1))
   MAP#2(dc(z0, z1, z2, z3, z4), Cons(z5, z6)) -> c26(DC#1(z0, z1, z2, z3, z4, z5))
   MAP#2(dc(z0, z1, z2, z3, z4), Cons(z5, z6)) -> c27(MAP#2(dc(z0, z1, z2, z3, z4), z6))
   MERGE#2(Cons(0, x1), Cons(z0, x3)) -> c6(COND_MERGE_YS_ZS_2(True, Cons(0, x1), Cons(z0, x3), 0, x1, z0, x3))
   MERGE#2(Cons(S(z0), x1), Cons(0, x3)) -> c6(COND_MERGE_YS_ZS_2(False, Cons(S(z0), x1), Cons(0, x3), S(z0), x1, 0, x3))
   MERGE#2(Cons(S(0), x1), Cons(S(z0), x3)) -> c6(COND_MERGE_YS_ZS_2(True, Cons(S(0), x1), Cons(S(z0), x3), S(0), x1, S(z0), x3), LEQ#2(S(0), S(z0)))
   MERGE#2(Cons(S(S(z0)), x1), Cons(S(0), x3)) -> c6(COND_MERGE_YS_ZS_2(False, Cons(S(S(z0)), x1), Cons(S(0), x3), S(S(z0)), x1, S(0), x3), LEQ#2(S(S(z0)), S(0)))
   MERGE#2(Cons(S(S(z0)), x1), Cons(S(S(z1)), x3)) -> c6(COND_MERGE_YS_ZS_2(leq#2(z0, z1), Cons(S(S(z0)), x1), Cons(S(S(z1)), x3), S(S(z0)), x1, S(S(z1)), x3), LEQ#2(S(S(z0)), S(S(z1))))
   MERGE#2(Cons(S(x0), x1), Cons(S(x2), x3)) -> c6(LEQ#2(S(x0), S(x2)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Cons(z0, z1)))) -> c9(CONST_F#2(Cons(x0, Cons(x1, Cons(z0, z1))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(Cons(z0, z1)))), Cons(x0, Cons(x1, Cons(z0, z1)))), Cons(drop#2(S(halve#1(S(length#1(z1)))), Cons(x0, Cons(x1, Cons(z0, z1)))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Cons(z0, z1))), S(halve#1(length#1(Cons(z0, z1)))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(z0, z1))), S(halve#1(length#1(Cons(z0, z1))))), HALVE#1(length#1(Cons(z0, z1))), LENGTH#1(Cons(z0, z1)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z1, Cons(x1, x2))) -> c9(CONST_F#2(Cons(z1, Cons(x1, x2)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(Cons(z1, take#2(halve#1(length#1(x2)), Cons(x1, x2))), Cons(drop#2(S(halve#1(length#1(x2))), Cons(z1, Cons(x1, x2))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z1, Cons(x1, x2)), S(halve#1(length#1(x2))))), DIVIDE_YS#1(Cons(z1, Cons(x1, x2)), S(halve#1(length#1(x2)))), HALVE#1(length#1(x2)), LENGTH#1(x2))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Cons(z0, z1)))) -> c9(CONST_F#2(Cons(x0, Cons(x1, Cons(z0, z1))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(S(length#1(z1)))), Cons(x0, Cons(x1, Cons(z0, z1)))), Cons(drop#2(S(halve#1(length#1(Cons(z0, z1)))), Cons(x0, Cons(x1, Cons(z0, z1)))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Cons(z0, z1))), S(halve#1(length#1(Cons(z0, z1)))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(z0, z1))), S(halve#1(length#1(Cons(z0, z1))))), HALVE#1(length#1(Cons(z0, z1))), LENGTH#1(Cons(z0, z1)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, x2))) -> c9(MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, x2)), S(halve#1(length#1(x2))))), DIVIDE_YS#1(Cons(x0, Cons(x1, x2)), S(halve#1(length#1(x2)))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Nil))) -> c9(CONST_F#2(Cons(x0, Cons(x1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(Nil))), Cons(x0, Cons(x1, Nil))), Cons(drop#2(S(halve#1(0)), Cons(x0, Cons(x1, Nil))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Nil)), S(halve#1(length#1(Nil)))), HALVE#1(length#1(Nil)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Nil))) -> c9(CONST_F#2(Cons(x0, Cons(x1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(0)), Cons(x0, Cons(x1, Nil))), Cons(drop#2(S(halve#1(length#1(Nil))), Cons(x0, Cons(x1, Nil))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Nil)), S(halve#1(length#1(Nil)))), HALVE#1(length#1(Nil)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Cons(x2, x3)))) -> c9(CONST_F#2(Cons(x0, Cons(x1, Cons(x2, x3))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(S(length#1(x3)))), Cons(x0, Cons(x1, Cons(x2, x3)))), Cons(drop#2(S(halve#1(S(length#1(x3)))), Cons(x0, Cons(x1, Cons(x2, x3)))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Cons(x2, x3))), S(halve#1(length#1(Cons(x2, x3)))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, x3))), S(halve#1(length#1(Cons(x2, x3))))), HALVE#1(length#1(Cons(x2, x3))), LENGTH#1(Cons(x2, x3)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Cons(x2, Nil)))) -> c9(CONST_F#2(Cons(x0, Cons(x1, Cons(x2, Nil))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Cons(x2, Nil))), S(halve#1(S(0)))))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Cons(x2, Nil))), S(halve#1(length#1(Cons(x2, Nil)))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Nil))), S(halve#1(length#1(Cons(x2, Nil))))), HALVE#1(length#1(Cons(x2, Nil))), LENGTH#1(Cons(x2, Nil)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Cons(x2, Cons(z0, z1))))) -> c9(CONST_F#2(Cons(x0, Cons(x1, Cons(x2, Cons(z0, z1)))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Cons(x2, Cons(z0, z1)))), S(halve#1(S(S(length#1(z1)))))))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Cons(x2, Cons(z0, z1)))), S(halve#1(length#1(Cons(x2, Cons(z0, z1))))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Cons(z0, z1)))), S(halve#1(length#1(Cons(x2, Cons(z0, z1)))))), HALVE#1(length#1(Cons(x2, Cons(z0, z1)))), LENGTH#1(Cons(x2, Cons(z0, z1))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Cons(x2, x3)))) -> c9(MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Cons(x2, x3))), S(halve#1(length#1(Cons(x2, x3)))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, x3))), S(halve#1(length#1(Cons(x2, x3))))), HALVE#1(length#1(Cons(x2, x3))), LENGTH#1(Cons(x2, x3)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Nil))) -> c9(CONST_F#2(Cons(x0, Cons(x1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(0)), Cons(x0, Cons(x1, Nil))), Cons(drop#2(S(halve#1(0)), Cons(x0, Cons(x1, Nil))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Nil)), S(halve#1(length#1(Nil)))), HALVE#1(length#1(Nil)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Nil))) -> c9(CONST_F#2(Cons(x0, Cons(x1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Nil)), S(0)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Nil)), S(halve#1(length#1(Nil)))), HALVE#1(length#1(Nil)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> c9(CONST_F#2(Cons(z0, Cons(z1, z2)), Cons(dc#1(map, divisible, mergesort_zs_3, divide, const_f, take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2)))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(drop#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Nil))), DIVIDE_YS#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2)))), HALVE#1(length#1(z2)), LENGTH#1(z2))
   DIVIDE_YS#1(Cons(x0, Cons(x1, x2)), S(y11)) -> c(TAKE#2(S(y11), Cons(x0, Cons(x1, x2))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, x3))), S(y11)) -> c(TAKE#2(S(y11), Cons(x0, Cons(x1, Cons(x2, x3)))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Nil)), S(y10)) -> c(TAKE#2(S(y10), Cons(x0, Cons(x1, Nil))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Nil))), S(y7)) -> c(TAKE#2(S(y7), Cons(x0, Cons(x1, Cons(x2, Nil)))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4)))), S(y8)) -> c(TAKE#2(S(y8), Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4))))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, x2)), S(y11)) -> c1(DROP#2(S(y11), Cons(x0, Cons(x1, x2))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, x3))), S(y11)) -> c1(DROP#2(S(y11), Cons(x0, Cons(x1, Cons(x2, x3)))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Nil)), S(y10)) -> c1(DROP#2(S(y10), Cons(x0, Cons(x1, Nil))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Nil))), S(y7)) -> c1(DROP#2(S(y7), Cons(x0, Cons(x1, Cons(x2, Nil)))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4)))), S(y8)) -> c1(DROP#2(S(y8), Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4))))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> c9(CONST_F#2(Cons(z0, Cons(z1, z2)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(halve#1(length#1(z2)), Cons(z1, z2)), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Nil))), DIVIDE_YS#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2)))), HALVE#1(length#1(z2)), LENGTH#1(z2))
   COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(z2, z3), z4, Cons(0, y0), z6, z7) -> c2(MERGE#2(Cons(0, y0), Cons(z2, z3)))
   COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(0, z3), z4, Cons(S(y0), y1), z6, z7) -> c2(MERGE#2(Cons(S(y0), y1), Cons(0, z3)))
   COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(S(y1), z3), z4, Cons(S(0), y0), z6, z7) -> c2(MERGE#2(Cons(S(0), y0), Cons(S(y1), z3)))
   COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(S(0), z3), z4, Cons(S(S(y0)), y1), z6, z7) -> c2(MERGE#2(Cons(S(S(y0)), y1), Cons(S(0), z3)))
   COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(S(S(y2)), z3), z4, Cons(S(S(y0)), y1), z6, z7) -> c2(MERGE#2(Cons(S(S(y0)), y1), Cons(S(S(y2)), z3)))
   COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(S(y2), z3), z4, Cons(S(y0), y1), z6, z7) -> c2(MERGE#2(Cons(S(y0), y1), Cons(S(y2), z3)))
S tuples:
   COND_MERGE_YS_ZS_2(False, Cons(z0, z1), Cons(z2, z3), z4, z5, z6, z7) -> c3(MERGE#2(Cons(z0, z1), z7))
   DROP#2(S(z0), Cons(z1, z2)) -> c12(DROP#2(z0, z2))
   TAKE#2(S(z0), Cons(z1, z2)) -> c15(TAKE#2(z0, z2))
   HALVE#1(S(S(z0))) -> c18(HALVE#1(z0))
   CONST_F#2(z0, Cons(z1, Cons(z2, z3))) -> c19(MERGE#2(z1, z2))
   LEQ#2(S(z0), S(z1)) -> c22(LEQ#2(z0, z1))
   LENGTH#1(Cons(z0, z1)) -> c24(LENGTH#1(z1))
   MAP#2(dc(z0, z1, z2, z3, z4), Cons(z5, z6)) -> c26(DC#1(z0, z1, z2, z3, z4, z5))
   MAP#2(dc(z0, z1, z2, z3, z4), Cons(z5, z6)) -> c27(MAP#2(dc(z0, z1, z2, z3, z4), z6))
   MERGE#2(Cons(0, x1), Cons(z0, x3)) -> c6(COND_MERGE_YS_ZS_2(True, Cons(0, x1), Cons(z0, x3), 0, x1, z0, x3))
   MERGE#2(Cons(S(z0), x1), Cons(0, x3)) -> c6(COND_MERGE_YS_ZS_2(False, Cons(S(z0), x1), Cons(0, x3), S(z0), x1, 0, x3))
   MERGE#2(Cons(S(0), x1), Cons(S(z0), x3)) -> c6(COND_MERGE_YS_ZS_2(True, Cons(S(0), x1), Cons(S(z0), x3), S(0), x1, S(z0), x3), LEQ#2(S(0), S(z0)))
   MERGE#2(Cons(S(S(z0)), x1), Cons(S(0), x3)) -> c6(COND_MERGE_YS_ZS_2(False, Cons(S(S(z0)), x1), Cons(S(0), x3), S(S(z0)), x1, S(0), x3), LEQ#2(S(S(z0)), S(0)))
   MERGE#2(Cons(S(S(z0)), x1), Cons(S(S(z1)), x3)) -> c6(COND_MERGE_YS_ZS_2(leq#2(z0, z1), Cons(S(S(z0)), x1), Cons(S(S(z1)), x3), S(S(z0)), x1, S(S(z1)), x3), LEQ#2(S(S(z0)), S(S(z1))))
   MERGE#2(Cons(S(x0), x1), Cons(S(x2), x3)) -> c6(LEQ#2(S(x0), S(x2)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Cons(z0, z1)))) -> c9(CONST_F#2(Cons(x0, Cons(x1, Cons(z0, z1))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(Cons(z0, z1)))), Cons(x0, Cons(x1, Cons(z0, z1)))), Cons(drop#2(S(halve#1(S(length#1(z1)))), Cons(x0, Cons(x1, Cons(z0, z1)))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Cons(z0, z1))), S(halve#1(length#1(Cons(z0, z1)))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(z0, z1))), S(halve#1(length#1(Cons(z0, z1))))), HALVE#1(length#1(Cons(z0, z1))), LENGTH#1(Cons(z0, z1)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z1, Cons(x1, x2))) -> c9(CONST_F#2(Cons(z1, Cons(x1, x2)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(Cons(z1, take#2(halve#1(length#1(x2)), Cons(x1, x2))), Cons(drop#2(S(halve#1(length#1(x2))), Cons(z1, Cons(x1, x2))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z1, Cons(x1, x2)), S(halve#1(length#1(x2))))), DIVIDE_YS#1(Cons(z1, Cons(x1, x2)), S(halve#1(length#1(x2)))), HALVE#1(length#1(x2)), LENGTH#1(x2))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Cons(z0, z1)))) -> c9(CONST_F#2(Cons(x0, Cons(x1, Cons(z0, z1))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(S(length#1(z1)))), Cons(x0, Cons(x1, Cons(z0, z1)))), Cons(drop#2(S(halve#1(length#1(Cons(z0, z1)))), Cons(x0, Cons(x1, Cons(z0, z1)))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Cons(z0, z1))), S(halve#1(length#1(Cons(z0, z1)))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(z0, z1))), S(halve#1(length#1(Cons(z0, z1))))), HALVE#1(length#1(Cons(z0, z1))), LENGTH#1(Cons(z0, z1)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, x2))) -> c9(MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, x2)), S(halve#1(length#1(x2))))), DIVIDE_YS#1(Cons(x0, Cons(x1, x2)), S(halve#1(length#1(x2)))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Nil))) -> c9(CONST_F#2(Cons(x0, Cons(x1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(Nil))), Cons(x0, Cons(x1, Nil))), Cons(drop#2(S(halve#1(0)), Cons(x0, Cons(x1, Nil))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Nil)), S(halve#1(length#1(Nil)))), HALVE#1(length#1(Nil)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Nil))) -> c9(CONST_F#2(Cons(x0, Cons(x1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(0)), Cons(x0, Cons(x1, Nil))), Cons(drop#2(S(halve#1(length#1(Nil))), Cons(x0, Cons(x1, Nil))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Nil)), S(halve#1(length#1(Nil)))), HALVE#1(length#1(Nil)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Cons(x2, x3)))) -> c9(CONST_F#2(Cons(x0, Cons(x1, Cons(x2, x3))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(S(length#1(x3)))), Cons(x0, Cons(x1, Cons(x2, x3)))), Cons(drop#2(S(halve#1(S(length#1(x3)))), Cons(x0, Cons(x1, Cons(x2, x3)))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Cons(x2, x3))), S(halve#1(length#1(Cons(x2, x3)))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, x3))), S(halve#1(length#1(Cons(x2, x3))))), HALVE#1(length#1(Cons(x2, x3))), LENGTH#1(Cons(x2, x3)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Cons(x2, Nil)))) -> c9(CONST_F#2(Cons(x0, Cons(x1, Cons(x2, Nil))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Cons(x2, Nil))), S(halve#1(S(0)))))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Cons(x2, Nil))), S(halve#1(length#1(Cons(x2, Nil)))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Nil))), S(halve#1(length#1(Cons(x2, Nil))))), HALVE#1(length#1(Cons(x2, Nil))), LENGTH#1(Cons(x2, Nil)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Cons(x2, Cons(z0, z1))))) -> c9(CONST_F#2(Cons(x0, Cons(x1, Cons(x2, Cons(z0, z1)))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Cons(x2, Cons(z0, z1)))), S(halve#1(S(S(length#1(z1)))))))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Cons(x2, Cons(z0, z1)))), S(halve#1(length#1(Cons(x2, Cons(z0, z1))))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Cons(z0, z1)))), S(halve#1(length#1(Cons(x2, Cons(z0, z1)))))), HALVE#1(length#1(Cons(x2, Cons(z0, z1)))), LENGTH#1(Cons(x2, Cons(z0, z1))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Cons(x2, x3)))) -> c9(MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Cons(x2, x3))), S(halve#1(length#1(Cons(x2, x3)))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, x3))), S(halve#1(length#1(Cons(x2, x3))))), HALVE#1(length#1(Cons(x2, x3))), LENGTH#1(Cons(x2, x3)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Nil))) -> c9(CONST_F#2(Cons(x0, Cons(x1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(0)), Cons(x0, Cons(x1, Nil))), Cons(drop#2(S(halve#1(0)), Cons(x0, Cons(x1, Nil))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Nil)), S(halve#1(length#1(Nil)))), HALVE#1(length#1(Nil)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Nil))) -> c9(CONST_F#2(Cons(x0, Cons(x1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Nil)), S(0)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Nil)), S(halve#1(length#1(Nil)))), HALVE#1(length#1(Nil)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> c9(CONST_F#2(Cons(z0, Cons(z1, z2)), Cons(dc#1(map, divisible, mergesort_zs_3, divide, const_f, take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2)))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(drop#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Nil))), DIVIDE_YS#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2)))), HALVE#1(length#1(z2)), LENGTH#1(z2))
   DIVIDE_YS#1(Cons(x0, Cons(x1, x2)), S(y11)) -> c(TAKE#2(S(y11), Cons(x0, Cons(x1, x2))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, x3))), S(y11)) -> c(TAKE#2(S(y11), Cons(x0, Cons(x1, Cons(x2, x3)))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Nil)), S(y10)) -> c(TAKE#2(S(y10), Cons(x0, Cons(x1, Nil))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Nil))), S(y7)) -> c(TAKE#2(S(y7), Cons(x0, Cons(x1, Cons(x2, Nil)))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4)))), S(y8)) -> c(TAKE#2(S(y8), Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4))))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, x2)), S(y11)) -> c1(DROP#2(S(y11), Cons(x0, Cons(x1, x2))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, x3))), S(y11)) -> c1(DROP#2(S(y11), Cons(x0, Cons(x1, Cons(x2, x3)))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Nil)), S(y10)) -> c1(DROP#2(S(y10), Cons(x0, Cons(x1, Nil))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Nil))), S(y7)) -> c1(DROP#2(S(y7), Cons(x0, Cons(x1, Cons(x2, Nil)))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4)))), S(y8)) -> c1(DROP#2(S(y8), Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4))))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> c9(CONST_F#2(Cons(z0, Cons(z1, z2)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(halve#1(length#1(z2)), Cons(z1, z2)), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Nil))), DIVIDE_YS#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2)))), HALVE#1(length#1(z2)), LENGTH#1(z2))
   COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(z2, z3), z4, Cons(0, y0), z6, z7) -> c2(MERGE#2(Cons(0, y0), Cons(z2, z3)))
   COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(0, z3), z4, Cons(S(y0), y1), z6, z7) -> c2(MERGE#2(Cons(S(y0), y1), Cons(0, z3)))
   COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(S(y1), z3), z4, Cons(S(0), y0), z6, z7) -> c2(MERGE#2(Cons(S(0), y0), Cons(S(y1), z3)))
   COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(S(0), z3), z4, Cons(S(S(y0)), y1), z6, z7) -> c2(MERGE#2(Cons(S(S(y0)), y1), Cons(S(0), z3)))
   COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(S(S(y2)), z3), z4, Cons(S(S(y0)), y1), z6, z7) -> c2(MERGE#2(Cons(S(S(y0)), y1), Cons(S(S(y2)), z3)))
   COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(S(y2), z3), z4, Cons(S(y0), y1), z6, z7) -> c2(MERGE#2(Cons(S(y0), y1), Cons(S(y2), z3)))
K tuples:none
Defined Rule Symbols:   leq#2_2, map#2_2, divide_ys#1_2, halve#1_1, length#1_1, take#2_2, drop#2_2, dc#1_6, const_f#2_2, merge#2_2, cond_merge_ys_zs_2_7

Defined Pair Symbols:   COND_MERGE_YS_ZS_2_7, DROP#2_2, TAKE#2_2, HALVE#1_1, CONST_F#2_2, LEQ#2_2, LENGTH#1_1, MAP#2_2, MERGE#2_2, DC#1_6, DIVIDE_YS#1_2

Compound Symbols:   c3_1, c12_1, c15_1, c18_1, c19_1, c22_1, c24_1, c26_1, c27_1, c6_1, c6_2, c9_5, c9_2, c9_4, c_1, c1_1, c2_1


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

(111) CdtRewritingProof (BOTH BOUNDS(ID, ID))
Used rewriting to replace DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Cons(z0, z1)))) -> c9(CONST_F#2(Cons(x0, Cons(x1, Cons(z0, z1))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(Cons(z0, z1)))), Cons(x0, Cons(x1, Cons(z0, z1)))), Cons(drop#2(S(halve#1(S(length#1(z1)))), Cons(x0, Cons(x1, Cons(z0, z1)))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Cons(z0, z1))), S(halve#1(length#1(Cons(z0, z1)))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(z0, z1))), S(halve#1(length#1(Cons(z0, z1))))), HALVE#1(length#1(Cons(z0, z1))), LENGTH#1(Cons(z0, z1))) by DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, z3)))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Cons(z2, z3))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(Cons(z2, z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Cons(drop#2(S(halve#1(S(length#1(z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3)))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3))))), HALVE#1(S(length#1(z3))), LENGTH#1(Cons(z2, z3)))
----------------------------------------

(112)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   leq#2(0, z0) -> True
   leq#2(S(z0), 0) -> False
   leq#2(S(z0), S(z1)) -> leq#2(z0, z1)
   map#2(dc(z0, z1, z2, z3, z4), Nil) -> Nil
   map#2(dc(z0, z1, z2, z3, z4), Cons(z5, z6)) -> Cons(dc#1(z0, z1, z2, z3, z4, z5), map#2(dc(z0, z1, z2, z3, z4), z6))
   divide_ys#1(z0, z1) -> Cons(take#2(z1, z0), Cons(drop#2(z1, z0), Nil))
   halve#1(0) -> 0
   halve#1(S(0)) -> S(0)
   halve#1(S(S(z0))) -> S(halve#1(z0))
   length#1(Nil) -> 0
   length#1(Cons(z0, z1)) -> S(length#1(z1))
   take#2(0, z0) -> Nil
   take#2(S(0), Nil) -> Cons(bot[0], Nil)
   take#2(S(z0), Cons(z1, z2)) -> Cons(z1, take#2(z0, z2))
   drop#2(0, z0) -> z0
   drop#2(S(0), Nil) -> bot[1]
   drop#2(S(z0), Cons(z1, z2)) -> drop#2(z0, z2)
   dc#1(map, divisible, mergesort_zs_3, divide, const_f, Nil) -> Nil
   dc#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Nil)) -> Cons(z0, Nil)
   dc#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> const_f#2(Cons(z0, Cons(z1, z2)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2))))))
   const_f#2(z0, Cons(z1, Cons(z2, z3))) -> merge#2(z1, z2)
   merge#2(Nil, z0) -> z0
   merge#2(Cons(z0, z1), Nil) -> Cons(z0, z1)
   merge#2(Cons(z0, z1), Cons(z2, z3)) -> cond_merge_ys_zs_2(leq#2(z0, z2), Cons(z0, z1), Cons(z2, z3), z0, z1, z2, z3)
   cond_merge_ys_zs_2(True, Cons(z0, z1), Cons(z2, z3), z4, z5, z6, z7) -> Cons(z4, merge#2(z5, Cons(z2, z3)))
   cond_merge_ys_zs_2(False, Cons(z0, z1), Cons(z2, z3), z4, z5, z6, z7) -> Cons(z6, merge#2(Cons(z0, z1), z7))
Tuples:
   COND_MERGE_YS_ZS_2(False, Cons(z0, z1), Cons(z2, z3), z4, z5, z6, z7) -> c3(MERGE#2(Cons(z0, z1), z7))
   DROP#2(S(z0), Cons(z1, z2)) -> c12(DROP#2(z0, z2))
   TAKE#2(S(z0), Cons(z1, z2)) -> c15(TAKE#2(z0, z2))
   HALVE#1(S(S(z0))) -> c18(HALVE#1(z0))
   CONST_F#2(z0, Cons(z1, Cons(z2, z3))) -> c19(MERGE#2(z1, z2))
   LEQ#2(S(z0), S(z1)) -> c22(LEQ#2(z0, z1))
   LENGTH#1(Cons(z0, z1)) -> c24(LENGTH#1(z1))
   MAP#2(dc(z0, z1, z2, z3, z4), Cons(z5, z6)) -> c26(DC#1(z0, z1, z2, z3, z4, z5))
   MAP#2(dc(z0, z1, z2, z3, z4), Cons(z5, z6)) -> c27(MAP#2(dc(z0, z1, z2, z3, z4), z6))
   MERGE#2(Cons(0, x1), Cons(z0, x3)) -> c6(COND_MERGE_YS_ZS_2(True, Cons(0, x1), Cons(z0, x3), 0, x1, z0, x3))
   MERGE#2(Cons(S(z0), x1), Cons(0, x3)) -> c6(COND_MERGE_YS_ZS_2(False, Cons(S(z0), x1), Cons(0, x3), S(z0), x1, 0, x3))
   MERGE#2(Cons(S(0), x1), Cons(S(z0), x3)) -> c6(COND_MERGE_YS_ZS_2(True, Cons(S(0), x1), Cons(S(z0), x3), S(0), x1, S(z0), x3), LEQ#2(S(0), S(z0)))
   MERGE#2(Cons(S(S(z0)), x1), Cons(S(0), x3)) -> c6(COND_MERGE_YS_ZS_2(False, Cons(S(S(z0)), x1), Cons(S(0), x3), S(S(z0)), x1, S(0), x3), LEQ#2(S(S(z0)), S(0)))
   MERGE#2(Cons(S(S(z0)), x1), Cons(S(S(z1)), x3)) -> c6(COND_MERGE_YS_ZS_2(leq#2(z0, z1), Cons(S(S(z0)), x1), Cons(S(S(z1)), x3), S(S(z0)), x1, S(S(z1)), x3), LEQ#2(S(S(z0)), S(S(z1))))
   MERGE#2(Cons(S(x0), x1), Cons(S(x2), x3)) -> c6(LEQ#2(S(x0), S(x2)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z1, Cons(x1, x2))) -> c9(CONST_F#2(Cons(z1, Cons(x1, x2)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(Cons(z1, take#2(halve#1(length#1(x2)), Cons(x1, x2))), Cons(drop#2(S(halve#1(length#1(x2))), Cons(z1, Cons(x1, x2))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z1, Cons(x1, x2)), S(halve#1(length#1(x2))))), DIVIDE_YS#1(Cons(z1, Cons(x1, x2)), S(halve#1(length#1(x2)))), HALVE#1(length#1(x2)), LENGTH#1(x2))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Cons(z0, z1)))) -> c9(CONST_F#2(Cons(x0, Cons(x1, Cons(z0, z1))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(S(length#1(z1)))), Cons(x0, Cons(x1, Cons(z0, z1)))), Cons(drop#2(S(halve#1(length#1(Cons(z0, z1)))), Cons(x0, Cons(x1, Cons(z0, z1)))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Cons(z0, z1))), S(halve#1(length#1(Cons(z0, z1)))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(z0, z1))), S(halve#1(length#1(Cons(z0, z1))))), HALVE#1(length#1(Cons(z0, z1))), LENGTH#1(Cons(z0, z1)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, x2))) -> c9(MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, x2)), S(halve#1(length#1(x2))))), DIVIDE_YS#1(Cons(x0, Cons(x1, x2)), S(halve#1(length#1(x2)))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Nil))) -> c9(CONST_F#2(Cons(x0, Cons(x1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(Nil))), Cons(x0, Cons(x1, Nil))), Cons(drop#2(S(halve#1(0)), Cons(x0, Cons(x1, Nil))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Nil)), S(halve#1(length#1(Nil)))), HALVE#1(length#1(Nil)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Nil))) -> c9(CONST_F#2(Cons(x0, Cons(x1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(0)), Cons(x0, Cons(x1, Nil))), Cons(drop#2(S(halve#1(length#1(Nil))), Cons(x0, Cons(x1, Nil))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Nil)), S(halve#1(length#1(Nil)))), HALVE#1(length#1(Nil)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Cons(x2, x3)))) -> c9(CONST_F#2(Cons(x0, Cons(x1, Cons(x2, x3))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(S(length#1(x3)))), Cons(x0, Cons(x1, Cons(x2, x3)))), Cons(drop#2(S(halve#1(S(length#1(x3)))), Cons(x0, Cons(x1, Cons(x2, x3)))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Cons(x2, x3))), S(halve#1(length#1(Cons(x2, x3)))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, x3))), S(halve#1(length#1(Cons(x2, x3))))), HALVE#1(length#1(Cons(x2, x3))), LENGTH#1(Cons(x2, x3)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Cons(x2, Nil)))) -> c9(CONST_F#2(Cons(x0, Cons(x1, Cons(x2, Nil))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Cons(x2, Nil))), S(halve#1(S(0)))))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Cons(x2, Nil))), S(halve#1(length#1(Cons(x2, Nil)))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Nil))), S(halve#1(length#1(Cons(x2, Nil))))), HALVE#1(length#1(Cons(x2, Nil))), LENGTH#1(Cons(x2, Nil)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Cons(x2, Cons(z0, z1))))) -> c9(CONST_F#2(Cons(x0, Cons(x1, Cons(x2, Cons(z0, z1)))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Cons(x2, Cons(z0, z1)))), S(halve#1(S(S(length#1(z1)))))))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Cons(x2, Cons(z0, z1)))), S(halve#1(length#1(Cons(x2, Cons(z0, z1))))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Cons(z0, z1)))), S(halve#1(length#1(Cons(x2, Cons(z0, z1)))))), HALVE#1(length#1(Cons(x2, Cons(z0, z1)))), LENGTH#1(Cons(x2, Cons(z0, z1))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Cons(x2, x3)))) -> c9(MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Cons(x2, x3))), S(halve#1(length#1(Cons(x2, x3)))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, x3))), S(halve#1(length#1(Cons(x2, x3))))), HALVE#1(length#1(Cons(x2, x3))), LENGTH#1(Cons(x2, x3)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Nil))) -> c9(CONST_F#2(Cons(x0, Cons(x1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(0)), Cons(x0, Cons(x1, Nil))), Cons(drop#2(S(halve#1(0)), Cons(x0, Cons(x1, Nil))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Nil)), S(halve#1(length#1(Nil)))), HALVE#1(length#1(Nil)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Nil))) -> c9(CONST_F#2(Cons(x0, Cons(x1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Nil)), S(0)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Nil)), S(halve#1(length#1(Nil)))), HALVE#1(length#1(Nil)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> c9(CONST_F#2(Cons(z0, Cons(z1, z2)), Cons(dc#1(map, divisible, mergesort_zs_3, divide, const_f, take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2)))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(drop#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Nil))), DIVIDE_YS#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2)))), HALVE#1(length#1(z2)), LENGTH#1(z2))
   DIVIDE_YS#1(Cons(x0, Cons(x1, x2)), S(y11)) -> c(TAKE#2(S(y11), Cons(x0, Cons(x1, x2))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, x3))), S(y11)) -> c(TAKE#2(S(y11), Cons(x0, Cons(x1, Cons(x2, x3)))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Nil)), S(y10)) -> c(TAKE#2(S(y10), Cons(x0, Cons(x1, Nil))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Nil))), S(y7)) -> c(TAKE#2(S(y7), Cons(x0, Cons(x1, Cons(x2, Nil)))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4)))), S(y8)) -> c(TAKE#2(S(y8), Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4))))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, x2)), S(y11)) -> c1(DROP#2(S(y11), Cons(x0, Cons(x1, x2))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, x3))), S(y11)) -> c1(DROP#2(S(y11), Cons(x0, Cons(x1, Cons(x2, x3)))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Nil)), S(y10)) -> c1(DROP#2(S(y10), Cons(x0, Cons(x1, Nil))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Nil))), S(y7)) -> c1(DROP#2(S(y7), Cons(x0, Cons(x1, Cons(x2, Nil)))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4)))), S(y8)) -> c1(DROP#2(S(y8), Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4))))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> c9(CONST_F#2(Cons(z0, Cons(z1, z2)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(halve#1(length#1(z2)), Cons(z1, z2)), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Nil))), DIVIDE_YS#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2)))), HALVE#1(length#1(z2)), LENGTH#1(z2))
   COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(z2, z3), z4, Cons(0, y0), z6, z7) -> c2(MERGE#2(Cons(0, y0), Cons(z2, z3)))
   COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(0, z3), z4, Cons(S(y0), y1), z6, z7) -> c2(MERGE#2(Cons(S(y0), y1), Cons(0, z3)))
   COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(S(y1), z3), z4, Cons(S(0), y0), z6, z7) -> c2(MERGE#2(Cons(S(0), y0), Cons(S(y1), z3)))
   COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(S(0), z3), z4, Cons(S(S(y0)), y1), z6, z7) -> c2(MERGE#2(Cons(S(S(y0)), y1), Cons(S(0), z3)))
   COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(S(S(y2)), z3), z4, Cons(S(S(y0)), y1), z6, z7) -> c2(MERGE#2(Cons(S(S(y0)), y1), Cons(S(S(y2)), z3)))
   COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(S(y2), z3), z4, Cons(S(y0), y1), z6, z7) -> c2(MERGE#2(Cons(S(y0), y1), Cons(S(y2), z3)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, z3)))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Cons(z2, z3))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(Cons(z2, z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Cons(drop#2(S(halve#1(S(length#1(z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3)))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3))))), HALVE#1(S(length#1(z3))), LENGTH#1(Cons(z2, z3)))
S tuples:
   COND_MERGE_YS_ZS_2(False, Cons(z0, z1), Cons(z2, z3), z4, z5, z6, z7) -> c3(MERGE#2(Cons(z0, z1), z7))
   DROP#2(S(z0), Cons(z1, z2)) -> c12(DROP#2(z0, z2))
   TAKE#2(S(z0), Cons(z1, z2)) -> c15(TAKE#2(z0, z2))
   HALVE#1(S(S(z0))) -> c18(HALVE#1(z0))
   CONST_F#2(z0, Cons(z1, Cons(z2, z3))) -> c19(MERGE#2(z1, z2))
   LEQ#2(S(z0), S(z1)) -> c22(LEQ#2(z0, z1))
   LENGTH#1(Cons(z0, z1)) -> c24(LENGTH#1(z1))
   MAP#2(dc(z0, z1, z2, z3, z4), Cons(z5, z6)) -> c26(DC#1(z0, z1, z2, z3, z4, z5))
   MAP#2(dc(z0, z1, z2, z3, z4), Cons(z5, z6)) -> c27(MAP#2(dc(z0, z1, z2, z3, z4), z6))
   MERGE#2(Cons(0, x1), Cons(z0, x3)) -> c6(COND_MERGE_YS_ZS_2(True, Cons(0, x1), Cons(z0, x3), 0, x1, z0, x3))
   MERGE#2(Cons(S(z0), x1), Cons(0, x3)) -> c6(COND_MERGE_YS_ZS_2(False, Cons(S(z0), x1), Cons(0, x3), S(z0), x1, 0, x3))
   MERGE#2(Cons(S(0), x1), Cons(S(z0), x3)) -> c6(COND_MERGE_YS_ZS_2(True, Cons(S(0), x1), Cons(S(z0), x3), S(0), x1, S(z0), x3), LEQ#2(S(0), S(z0)))
   MERGE#2(Cons(S(S(z0)), x1), Cons(S(0), x3)) -> c6(COND_MERGE_YS_ZS_2(False, Cons(S(S(z0)), x1), Cons(S(0), x3), S(S(z0)), x1, S(0), x3), LEQ#2(S(S(z0)), S(0)))
   MERGE#2(Cons(S(S(z0)), x1), Cons(S(S(z1)), x3)) -> c6(COND_MERGE_YS_ZS_2(leq#2(z0, z1), Cons(S(S(z0)), x1), Cons(S(S(z1)), x3), S(S(z0)), x1, S(S(z1)), x3), LEQ#2(S(S(z0)), S(S(z1))))
   MERGE#2(Cons(S(x0), x1), Cons(S(x2), x3)) -> c6(LEQ#2(S(x0), S(x2)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z1, Cons(x1, x2))) -> c9(CONST_F#2(Cons(z1, Cons(x1, x2)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(Cons(z1, take#2(halve#1(length#1(x2)), Cons(x1, x2))), Cons(drop#2(S(halve#1(length#1(x2))), Cons(z1, Cons(x1, x2))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z1, Cons(x1, x2)), S(halve#1(length#1(x2))))), DIVIDE_YS#1(Cons(z1, Cons(x1, x2)), S(halve#1(length#1(x2)))), HALVE#1(length#1(x2)), LENGTH#1(x2))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Cons(z0, z1)))) -> c9(CONST_F#2(Cons(x0, Cons(x1, Cons(z0, z1))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(S(length#1(z1)))), Cons(x0, Cons(x1, Cons(z0, z1)))), Cons(drop#2(S(halve#1(length#1(Cons(z0, z1)))), Cons(x0, Cons(x1, Cons(z0, z1)))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Cons(z0, z1))), S(halve#1(length#1(Cons(z0, z1)))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(z0, z1))), S(halve#1(length#1(Cons(z0, z1))))), HALVE#1(length#1(Cons(z0, z1))), LENGTH#1(Cons(z0, z1)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, x2))) -> c9(MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, x2)), S(halve#1(length#1(x2))))), DIVIDE_YS#1(Cons(x0, Cons(x1, x2)), S(halve#1(length#1(x2)))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Nil))) -> c9(CONST_F#2(Cons(x0, Cons(x1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(Nil))), Cons(x0, Cons(x1, Nil))), Cons(drop#2(S(halve#1(0)), Cons(x0, Cons(x1, Nil))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Nil)), S(halve#1(length#1(Nil)))), HALVE#1(length#1(Nil)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Nil))) -> c9(CONST_F#2(Cons(x0, Cons(x1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(0)), Cons(x0, Cons(x1, Nil))), Cons(drop#2(S(halve#1(length#1(Nil))), Cons(x0, Cons(x1, Nil))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Nil)), S(halve#1(length#1(Nil)))), HALVE#1(length#1(Nil)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Cons(x2, x3)))) -> c9(CONST_F#2(Cons(x0, Cons(x1, Cons(x2, x3))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(S(length#1(x3)))), Cons(x0, Cons(x1, Cons(x2, x3)))), Cons(drop#2(S(halve#1(S(length#1(x3)))), Cons(x0, Cons(x1, Cons(x2, x3)))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Cons(x2, x3))), S(halve#1(length#1(Cons(x2, x3)))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, x3))), S(halve#1(length#1(Cons(x2, x3))))), HALVE#1(length#1(Cons(x2, x3))), LENGTH#1(Cons(x2, x3)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Cons(x2, Nil)))) -> c9(CONST_F#2(Cons(x0, Cons(x1, Cons(x2, Nil))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Cons(x2, Nil))), S(halve#1(S(0)))))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Cons(x2, Nil))), S(halve#1(length#1(Cons(x2, Nil)))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Nil))), S(halve#1(length#1(Cons(x2, Nil))))), HALVE#1(length#1(Cons(x2, Nil))), LENGTH#1(Cons(x2, Nil)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Cons(x2, Cons(z0, z1))))) -> c9(CONST_F#2(Cons(x0, Cons(x1, Cons(x2, Cons(z0, z1)))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Cons(x2, Cons(z0, z1)))), S(halve#1(S(S(length#1(z1)))))))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Cons(x2, Cons(z0, z1)))), S(halve#1(length#1(Cons(x2, Cons(z0, z1))))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Cons(z0, z1)))), S(halve#1(length#1(Cons(x2, Cons(z0, z1)))))), HALVE#1(length#1(Cons(x2, Cons(z0, z1)))), LENGTH#1(Cons(x2, Cons(z0, z1))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Cons(x2, x3)))) -> c9(MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Cons(x2, x3))), S(halve#1(length#1(Cons(x2, x3)))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, x3))), S(halve#1(length#1(Cons(x2, x3))))), HALVE#1(length#1(Cons(x2, x3))), LENGTH#1(Cons(x2, x3)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Nil))) -> c9(CONST_F#2(Cons(x0, Cons(x1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(0)), Cons(x0, Cons(x1, Nil))), Cons(drop#2(S(halve#1(0)), Cons(x0, Cons(x1, Nil))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Nil)), S(halve#1(length#1(Nil)))), HALVE#1(length#1(Nil)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Nil))) -> c9(CONST_F#2(Cons(x0, Cons(x1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Nil)), S(0)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Nil)), S(halve#1(length#1(Nil)))), HALVE#1(length#1(Nil)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> c9(CONST_F#2(Cons(z0, Cons(z1, z2)), Cons(dc#1(map, divisible, mergesort_zs_3, divide, const_f, take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2)))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(drop#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Nil))), DIVIDE_YS#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2)))), HALVE#1(length#1(z2)), LENGTH#1(z2))
   DIVIDE_YS#1(Cons(x0, Cons(x1, x2)), S(y11)) -> c(TAKE#2(S(y11), Cons(x0, Cons(x1, x2))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, x3))), S(y11)) -> c(TAKE#2(S(y11), Cons(x0, Cons(x1, Cons(x2, x3)))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Nil)), S(y10)) -> c(TAKE#2(S(y10), Cons(x0, Cons(x1, Nil))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Nil))), S(y7)) -> c(TAKE#2(S(y7), Cons(x0, Cons(x1, Cons(x2, Nil)))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4)))), S(y8)) -> c(TAKE#2(S(y8), Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4))))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, x2)), S(y11)) -> c1(DROP#2(S(y11), Cons(x0, Cons(x1, x2))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, x3))), S(y11)) -> c1(DROP#2(S(y11), Cons(x0, Cons(x1, Cons(x2, x3)))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Nil)), S(y10)) -> c1(DROP#2(S(y10), Cons(x0, Cons(x1, Nil))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Nil))), S(y7)) -> c1(DROP#2(S(y7), Cons(x0, Cons(x1, Cons(x2, Nil)))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4)))), S(y8)) -> c1(DROP#2(S(y8), Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4))))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> c9(CONST_F#2(Cons(z0, Cons(z1, z2)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(halve#1(length#1(z2)), Cons(z1, z2)), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Nil))), DIVIDE_YS#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2)))), HALVE#1(length#1(z2)), LENGTH#1(z2))
   COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(z2, z3), z4, Cons(0, y0), z6, z7) -> c2(MERGE#2(Cons(0, y0), Cons(z2, z3)))
   COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(0, z3), z4, Cons(S(y0), y1), z6, z7) -> c2(MERGE#2(Cons(S(y0), y1), Cons(0, z3)))
   COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(S(y1), z3), z4, Cons(S(0), y0), z6, z7) -> c2(MERGE#2(Cons(S(0), y0), Cons(S(y1), z3)))
   COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(S(0), z3), z4, Cons(S(S(y0)), y1), z6, z7) -> c2(MERGE#2(Cons(S(S(y0)), y1), Cons(S(0), z3)))
   COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(S(S(y2)), z3), z4, Cons(S(S(y0)), y1), z6, z7) -> c2(MERGE#2(Cons(S(S(y0)), y1), Cons(S(S(y2)), z3)))
   COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(S(y2), z3), z4, Cons(S(y0), y1), z6, z7) -> c2(MERGE#2(Cons(S(y0), y1), Cons(S(y2), z3)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, z3)))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Cons(z2, z3))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(Cons(z2, z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Cons(drop#2(S(halve#1(S(length#1(z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3)))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3))))), HALVE#1(S(length#1(z3))), LENGTH#1(Cons(z2, z3)))
K tuples:none
Defined Rule Symbols:   leq#2_2, map#2_2, divide_ys#1_2, halve#1_1, length#1_1, take#2_2, drop#2_2, dc#1_6, const_f#2_2, merge#2_2, cond_merge_ys_zs_2_7

Defined Pair Symbols:   COND_MERGE_YS_ZS_2_7, DROP#2_2, TAKE#2_2, HALVE#1_1, CONST_F#2_2, LEQ#2_2, LENGTH#1_1, MAP#2_2, MERGE#2_2, DC#1_6, DIVIDE_YS#1_2

Compound Symbols:   c3_1, c12_1, c15_1, c18_1, c19_1, c22_1, c24_1, c26_1, c27_1, c6_1, c6_2, c9_5, c9_2, c9_4, c_1, c1_1, c2_1


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

(113) CdtInstantiationProof (BOTH BOUNDS(ID, ID))
Use instantiation to replace COND_MERGE_YS_ZS_2(False, Cons(z0, z1), Cons(z2, z3), z4, z5, z6, z7) -> c3(MERGE#2(Cons(z0, z1), z7)) by 
   COND_MERGE_YS_ZS_2(False, Cons(S(x0), x1), Cons(0, x2), S(x0), x1, 0, x2) -> c3(MERGE#2(Cons(S(x0), x1), x2))
   COND_MERGE_YS_ZS_2(False, Cons(S(S(x0)), x1), Cons(S(0), x2), S(S(x0)), x1, S(0), x2) -> c3(MERGE#2(Cons(S(S(x0)), x1), x2))
   COND_MERGE_YS_ZS_2(False, Cons(S(S(x0)), x1), Cons(S(S(x2)), x3), S(S(x0)), x1, S(S(x2)), x3) -> c3(MERGE#2(Cons(S(S(x0)), x1), x3))

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

(114)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   leq#2(0, z0) -> True
   leq#2(S(z0), 0) -> False
   leq#2(S(z0), S(z1)) -> leq#2(z0, z1)
   map#2(dc(z0, z1, z2, z3, z4), Nil) -> Nil
   map#2(dc(z0, z1, z2, z3, z4), Cons(z5, z6)) -> Cons(dc#1(z0, z1, z2, z3, z4, z5), map#2(dc(z0, z1, z2, z3, z4), z6))
   divide_ys#1(z0, z1) -> Cons(take#2(z1, z0), Cons(drop#2(z1, z0), Nil))
   halve#1(0) -> 0
   halve#1(S(0)) -> S(0)
   halve#1(S(S(z0))) -> S(halve#1(z0))
   length#1(Nil) -> 0
   length#1(Cons(z0, z1)) -> S(length#1(z1))
   take#2(0, z0) -> Nil
   take#2(S(0), Nil) -> Cons(bot[0], Nil)
   take#2(S(z0), Cons(z1, z2)) -> Cons(z1, take#2(z0, z2))
   drop#2(0, z0) -> z0
   drop#2(S(0), Nil) -> bot[1]
   drop#2(S(z0), Cons(z1, z2)) -> drop#2(z0, z2)
   dc#1(map, divisible, mergesort_zs_3, divide, const_f, Nil) -> Nil
   dc#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Nil)) -> Cons(z0, Nil)
   dc#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> const_f#2(Cons(z0, Cons(z1, z2)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2))))))
   const_f#2(z0, Cons(z1, Cons(z2, z3))) -> merge#2(z1, z2)
   merge#2(Nil, z0) -> z0
   merge#2(Cons(z0, z1), Nil) -> Cons(z0, z1)
   merge#2(Cons(z0, z1), Cons(z2, z3)) -> cond_merge_ys_zs_2(leq#2(z0, z2), Cons(z0, z1), Cons(z2, z3), z0, z1, z2, z3)
   cond_merge_ys_zs_2(True, Cons(z0, z1), Cons(z2, z3), z4, z5, z6, z7) -> Cons(z4, merge#2(z5, Cons(z2, z3)))
   cond_merge_ys_zs_2(False, Cons(z0, z1), Cons(z2, z3), z4, z5, z6, z7) -> Cons(z6, merge#2(Cons(z0, z1), z7))
Tuples:
   DROP#2(S(z0), Cons(z1, z2)) -> c12(DROP#2(z0, z2))
   TAKE#2(S(z0), Cons(z1, z2)) -> c15(TAKE#2(z0, z2))
   HALVE#1(S(S(z0))) -> c18(HALVE#1(z0))
   CONST_F#2(z0, Cons(z1, Cons(z2, z3))) -> c19(MERGE#2(z1, z2))
   LEQ#2(S(z0), S(z1)) -> c22(LEQ#2(z0, z1))
   LENGTH#1(Cons(z0, z1)) -> c24(LENGTH#1(z1))
   MAP#2(dc(z0, z1, z2, z3, z4), Cons(z5, z6)) -> c26(DC#1(z0, z1, z2, z3, z4, z5))
   MAP#2(dc(z0, z1, z2, z3, z4), Cons(z5, z6)) -> c27(MAP#2(dc(z0, z1, z2, z3, z4), z6))
   MERGE#2(Cons(0, x1), Cons(z0, x3)) -> c6(COND_MERGE_YS_ZS_2(True, Cons(0, x1), Cons(z0, x3), 0, x1, z0, x3))
   MERGE#2(Cons(S(z0), x1), Cons(0, x3)) -> c6(COND_MERGE_YS_ZS_2(False, Cons(S(z0), x1), Cons(0, x3), S(z0), x1, 0, x3))
   MERGE#2(Cons(S(0), x1), Cons(S(z0), x3)) -> c6(COND_MERGE_YS_ZS_2(True, Cons(S(0), x1), Cons(S(z0), x3), S(0), x1, S(z0), x3), LEQ#2(S(0), S(z0)))
   MERGE#2(Cons(S(S(z0)), x1), Cons(S(0), x3)) -> c6(COND_MERGE_YS_ZS_2(False, Cons(S(S(z0)), x1), Cons(S(0), x3), S(S(z0)), x1, S(0), x3), LEQ#2(S(S(z0)), S(0)))
   MERGE#2(Cons(S(S(z0)), x1), Cons(S(S(z1)), x3)) -> c6(COND_MERGE_YS_ZS_2(leq#2(z0, z1), Cons(S(S(z0)), x1), Cons(S(S(z1)), x3), S(S(z0)), x1, S(S(z1)), x3), LEQ#2(S(S(z0)), S(S(z1))))
   MERGE#2(Cons(S(x0), x1), Cons(S(x2), x3)) -> c6(LEQ#2(S(x0), S(x2)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z1, Cons(x1, x2))) -> c9(CONST_F#2(Cons(z1, Cons(x1, x2)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(Cons(z1, take#2(halve#1(length#1(x2)), Cons(x1, x2))), Cons(drop#2(S(halve#1(length#1(x2))), Cons(z1, Cons(x1, x2))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z1, Cons(x1, x2)), S(halve#1(length#1(x2))))), DIVIDE_YS#1(Cons(z1, Cons(x1, x2)), S(halve#1(length#1(x2)))), HALVE#1(length#1(x2)), LENGTH#1(x2))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Cons(z0, z1)))) -> c9(CONST_F#2(Cons(x0, Cons(x1, Cons(z0, z1))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(S(length#1(z1)))), Cons(x0, Cons(x1, Cons(z0, z1)))), Cons(drop#2(S(halve#1(length#1(Cons(z0, z1)))), Cons(x0, Cons(x1, Cons(z0, z1)))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Cons(z0, z1))), S(halve#1(length#1(Cons(z0, z1)))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(z0, z1))), S(halve#1(length#1(Cons(z0, z1))))), HALVE#1(length#1(Cons(z0, z1))), LENGTH#1(Cons(z0, z1)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, x2))) -> c9(MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, x2)), S(halve#1(length#1(x2))))), DIVIDE_YS#1(Cons(x0, Cons(x1, x2)), S(halve#1(length#1(x2)))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Nil))) -> c9(CONST_F#2(Cons(x0, Cons(x1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(Nil))), Cons(x0, Cons(x1, Nil))), Cons(drop#2(S(halve#1(0)), Cons(x0, Cons(x1, Nil))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Nil)), S(halve#1(length#1(Nil)))), HALVE#1(length#1(Nil)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Nil))) -> c9(CONST_F#2(Cons(x0, Cons(x1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(0)), Cons(x0, Cons(x1, Nil))), Cons(drop#2(S(halve#1(length#1(Nil))), Cons(x0, Cons(x1, Nil))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Nil)), S(halve#1(length#1(Nil)))), HALVE#1(length#1(Nil)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Cons(x2, x3)))) -> c9(CONST_F#2(Cons(x0, Cons(x1, Cons(x2, x3))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(S(length#1(x3)))), Cons(x0, Cons(x1, Cons(x2, x3)))), Cons(drop#2(S(halve#1(S(length#1(x3)))), Cons(x0, Cons(x1, Cons(x2, x3)))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Cons(x2, x3))), S(halve#1(length#1(Cons(x2, x3)))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, x3))), S(halve#1(length#1(Cons(x2, x3))))), HALVE#1(length#1(Cons(x2, x3))), LENGTH#1(Cons(x2, x3)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Cons(x2, Nil)))) -> c9(CONST_F#2(Cons(x0, Cons(x1, Cons(x2, Nil))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Cons(x2, Nil))), S(halve#1(S(0)))))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Cons(x2, Nil))), S(halve#1(length#1(Cons(x2, Nil)))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Nil))), S(halve#1(length#1(Cons(x2, Nil))))), HALVE#1(length#1(Cons(x2, Nil))), LENGTH#1(Cons(x2, Nil)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Cons(x2, Cons(z0, z1))))) -> c9(CONST_F#2(Cons(x0, Cons(x1, Cons(x2, Cons(z0, z1)))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Cons(x2, Cons(z0, z1)))), S(halve#1(S(S(length#1(z1)))))))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Cons(x2, Cons(z0, z1)))), S(halve#1(length#1(Cons(x2, Cons(z0, z1))))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Cons(z0, z1)))), S(halve#1(length#1(Cons(x2, Cons(z0, z1)))))), HALVE#1(length#1(Cons(x2, Cons(z0, z1)))), LENGTH#1(Cons(x2, Cons(z0, z1))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Cons(x2, x3)))) -> c9(MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Cons(x2, x3))), S(halve#1(length#1(Cons(x2, x3)))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, x3))), S(halve#1(length#1(Cons(x2, x3))))), HALVE#1(length#1(Cons(x2, x3))), LENGTH#1(Cons(x2, x3)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Nil))) -> c9(CONST_F#2(Cons(x0, Cons(x1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(0)), Cons(x0, Cons(x1, Nil))), Cons(drop#2(S(halve#1(0)), Cons(x0, Cons(x1, Nil))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Nil)), S(halve#1(length#1(Nil)))), HALVE#1(length#1(Nil)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Nil))) -> c9(CONST_F#2(Cons(x0, Cons(x1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Nil)), S(0)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Nil)), S(halve#1(length#1(Nil)))), HALVE#1(length#1(Nil)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> c9(CONST_F#2(Cons(z0, Cons(z1, z2)), Cons(dc#1(map, divisible, mergesort_zs_3, divide, const_f, take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2)))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(drop#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Nil))), DIVIDE_YS#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2)))), HALVE#1(length#1(z2)), LENGTH#1(z2))
   DIVIDE_YS#1(Cons(x0, Cons(x1, x2)), S(y11)) -> c(TAKE#2(S(y11), Cons(x0, Cons(x1, x2))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, x3))), S(y11)) -> c(TAKE#2(S(y11), Cons(x0, Cons(x1, Cons(x2, x3)))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Nil)), S(y10)) -> c(TAKE#2(S(y10), Cons(x0, Cons(x1, Nil))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Nil))), S(y7)) -> c(TAKE#2(S(y7), Cons(x0, Cons(x1, Cons(x2, Nil)))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4)))), S(y8)) -> c(TAKE#2(S(y8), Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4))))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, x2)), S(y11)) -> c1(DROP#2(S(y11), Cons(x0, Cons(x1, x2))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, x3))), S(y11)) -> c1(DROP#2(S(y11), Cons(x0, Cons(x1, Cons(x2, x3)))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Nil)), S(y10)) -> c1(DROP#2(S(y10), Cons(x0, Cons(x1, Nil))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Nil))), S(y7)) -> c1(DROP#2(S(y7), Cons(x0, Cons(x1, Cons(x2, Nil)))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4)))), S(y8)) -> c1(DROP#2(S(y8), Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4))))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> c9(CONST_F#2(Cons(z0, Cons(z1, z2)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(halve#1(length#1(z2)), Cons(z1, z2)), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Nil))), DIVIDE_YS#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2)))), HALVE#1(length#1(z2)), LENGTH#1(z2))
   COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(z2, z3), z4, Cons(0, y0), z6, z7) -> c2(MERGE#2(Cons(0, y0), Cons(z2, z3)))
   COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(0, z3), z4, Cons(S(y0), y1), z6, z7) -> c2(MERGE#2(Cons(S(y0), y1), Cons(0, z3)))
   COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(S(y1), z3), z4, Cons(S(0), y0), z6, z7) -> c2(MERGE#2(Cons(S(0), y0), Cons(S(y1), z3)))
   COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(S(0), z3), z4, Cons(S(S(y0)), y1), z6, z7) -> c2(MERGE#2(Cons(S(S(y0)), y1), Cons(S(0), z3)))
   COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(S(S(y2)), z3), z4, Cons(S(S(y0)), y1), z6, z7) -> c2(MERGE#2(Cons(S(S(y0)), y1), Cons(S(S(y2)), z3)))
   COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(S(y2), z3), z4, Cons(S(y0), y1), z6, z7) -> c2(MERGE#2(Cons(S(y0), y1), Cons(S(y2), z3)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, z3)))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Cons(z2, z3))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(Cons(z2, z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Cons(drop#2(S(halve#1(S(length#1(z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3)))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3))))), HALVE#1(S(length#1(z3))), LENGTH#1(Cons(z2, z3)))
   COND_MERGE_YS_ZS_2(False, Cons(S(x0), x1), Cons(0, x2), S(x0), x1, 0, x2) -> c3(MERGE#2(Cons(S(x0), x1), x2))
   COND_MERGE_YS_ZS_2(False, Cons(S(S(x0)), x1), Cons(S(0), x2), S(S(x0)), x1, S(0), x2) -> c3(MERGE#2(Cons(S(S(x0)), x1), x2))
   COND_MERGE_YS_ZS_2(False, Cons(S(S(x0)), x1), Cons(S(S(x2)), x3), S(S(x0)), x1, S(S(x2)), x3) -> c3(MERGE#2(Cons(S(S(x0)), x1), x3))
S tuples:
   DROP#2(S(z0), Cons(z1, z2)) -> c12(DROP#2(z0, z2))
   TAKE#2(S(z0), Cons(z1, z2)) -> c15(TAKE#2(z0, z2))
   HALVE#1(S(S(z0))) -> c18(HALVE#1(z0))
   CONST_F#2(z0, Cons(z1, Cons(z2, z3))) -> c19(MERGE#2(z1, z2))
   LEQ#2(S(z0), S(z1)) -> c22(LEQ#2(z0, z1))
   LENGTH#1(Cons(z0, z1)) -> c24(LENGTH#1(z1))
   MAP#2(dc(z0, z1, z2, z3, z4), Cons(z5, z6)) -> c26(DC#1(z0, z1, z2, z3, z4, z5))
   MAP#2(dc(z0, z1, z2, z3, z4), Cons(z5, z6)) -> c27(MAP#2(dc(z0, z1, z2, z3, z4), z6))
   MERGE#2(Cons(0, x1), Cons(z0, x3)) -> c6(COND_MERGE_YS_ZS_2(True, Cons(0, x1), Cons(z0, x3), 0, x1, z0, x3))
   MERGE#2(Cons(S(z0), x1), Cons(0, x3)) -> c6(COND_MERGE_YS_ZS_2(False, Cons(S(z0), x1), Cons(0, x3), S(z0), x1, 0, x3))
   MERGE#2(Cons(S(0), x1), Cons(S(z0), x3)) -> c6(COND_MERGE_YS_ZS_2(True, Cons(S(0), x1), Cons(S(z0), x3), S(0), x1, S(z0), x3), LEQ#2(S(0), S(z0)))
   MERGE#2(Cons(S(S(z0)), x1), Cons(S(0), x3)) -> c6(COND_MERGE_YS_ZS_2(False, Cons(S(S(z0)), x1), Cons(S(0), x3), S(S(z0)), x1, S(0), x3), LEQ#2(S(S(z0)), S(0)))
   MERGE#2(Cons(S(S(z0)), x1), Cons(S(S(z1)), x3)) -> c6(COND_MERGE_YS_ZS_2(leq#2(z0, z1), Cons(S(S(z0)), x1), Cons(S(S(z1)), x3), S(S(z0)), x1, S(S(z1)), x3), LEQ#2(S(S(z0)), S(S(z1))))
   MERGE#2(Cons(S(x0), x1), Cons(S(x2), x3)) -> c6(LEQ#2(S(x0), S(x2)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z1, Cons(x1, x2))) -> c9(CONST_F#2(Cons(z1, Cons(x1, x2)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(Cons(z1, take#2(halve#1(length#1(x2)), Cons(x1, x2))), Cons(drop#2(S(halve#1(length#1(x2))), Cons(z1, Cons(x1, x2))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z1, Cons(x1, x2)), S(halve#1(length#1(x2))))), DIVIDE_YS#1(Cons(z1, Cons(x1, x2)), S(halve#1(length#1(x2)))), HALVE#1(length#1(x2)), LENGTH#1(x2))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Cons(z0, z1)))) -> c9(CONST_F#2(Cons(x0, Cons(x1, Cons(z0, z1))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(S(length#1(z1)))), Cons(x0, Cons(x1, Cons(z0, z1)))), Cons(drop#2(S(halve#1(length#1(Cons(z0, z1)))), Cons(x0, Cons(x1, Cons(z0, z1)))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Cons(z0, z1))), S(halve#1(length#1(Cons(z0, z1)))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(z0, z1))), S(halve#1(length#1(Cons(z0, z1))))), HALVE#1(length#1(Cons(z0, z1))), LENGTH#1(Cons(z0, z1)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, x2))) -> c9(MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, x2)), S(halve#1(length#1(x2))))), DIVIDE_YS#1(Cons(x0, Cons(x1, x2)), S(halve#1(length#1(x2)))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Nil))) -> c9(CONST_F#2(Cons(x0, Cons(x1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(Nil))), Cons(x0, Cons(x1, Nil))), Cons(drop#2(S(halve#1(0)), Cons(x0, Cons(x1, Nil))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Nil)), S(halve#1(length#1(Nil)))), HALVE#1(length#1(Nil)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Nil))) -> c9(CONST_F#2(Cons(x0, Cons(x1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(0)), Cons(x0, Cons(x1, Nil))), Cons(drop#2(S(halve#1(length#1(Nil))), Cons(x0, Cons(x1, Nil))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Nil)), S(halve#1(length#1(Nil)))), HALVE#1(length#1(Nil)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Cons(x2, x3)))) -> c9(CONST_F#2(Cons(x0, Cons(x1, Cons(x2, x3))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(S(length#1(x3)))), Cons(x0, Cons(x1, Cons(x2, x3)))), Cons(drop#2(S(halve#1(S(length#1(x3)))), Cons(x0, Cons(x1, Cons(x2, x3)))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Cons(x2, x3))), S(halve#1(length#1(Cons(x2, x3)))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, x3))), S(halve#1(length#1(Cons(x2, x3))))), HALVE#1(length#1(Cons(x2, x3))), LENGTH#1(Cons(x2, x3)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Cons(x2, Nil)))) -> c9(CONST_F#2(Cons(x0, Cons(x1, Cons(x2, Nil))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Cons(x2, Nil))), S(halve#1(S(0)))))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Cons(x2, Nil))), S(halve#1(length#1(Cons(x2, Nil)))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Nil))), S(halve#1(length#1(Cons(x2, Nil))))), HALVE#1(length#1(Cons(x2, Nil))), LENGTH#1(Cons(x2, Nil)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Cons(x2, Cons(z0, z1))))) -> c9(CONST_F#2(Cons(x0, Cons(x1, Cons(x2, Cons(z0, z1)))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Cons(x2, Cons(z0, z1)))), S(halve#1(S(S(length#1(z1)))))))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Cons(x2, Cons(z0, z1)))), S(halve#1(length#1(Cons(x2, Cons(z0, z1))))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Cons(z0, z1)))), S(halve#1(length#1(Cons(x2, Cons(z0, z1)))))), HALVE#1(length#1(Cons(x2, Cons(z0, z1)))), LENGTH#1(Cons(x2, Cons(z0, z1))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Cons(x2, x3)))) -> c9(MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Cons(x2, x3))), S(halve#1(length#1(Cons(x2, x3)))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, x3))), S(halve#1(length#1(Cons(x2, x3))))), HALVE#1(length#1(Cons(x2, x3))), LENGTH#1(Cons(x2, x3)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Nil))) -> c9(CONST_F#2(Cons(x0, Cons(x1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(0)), Cons(x0, Cons(x1, Nil))), Cons(drop#2(S(halve#1(0)), Cons(x0, Cons(x1, Nil))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Nil)), S(halve#1(length#1(Nil)))), HALVE#1(length#1(Nil)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Nil))) -> c9(CONST_F#2(Cons(x0, Cons(x1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Nil)), S(0)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Nil)), S(halve#1(length#1(Nil)))), HALVE#1(length#1(Nil)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> c9(CONST_F#2(Cons(z0, Cons(z1, z2)), Cons(dc#1(map, divisible, mergesort_zs_3, divide, const_f, take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2)))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(drop#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Nil))), DIVIDE_YS#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2)))), HALVE#1(length#1(z2)), LENGTH#1(z2))
   DIVIDE_YS#1(Cons(x0, Cons(x1, x2)), S(y11)) -> c(TAKE#2(S(y11), Cons(x0, Cons(x1, x2))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, x3))), S(y11)) -> c(TAKE#2(S(y11), Cons(x0, Cons(x1, Cons(x2, x3)))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Nil)), S(y10)) -> c(TAKE#2(S(y10), Cons(x0, Cons(x1, Nil))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Nil))), S(y7)) -> c(TAKE#2(S(y7), Cons(x0, Cons(x1, Cons(x2, Nil)))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4)))), S(y8)) -> c(TAKE#2(S(y8), Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4))))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, x2)), S(y11)) -> c1(DROP#2(S(y11), Cons(x0, Cons(x1, x2))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, x3))), S(y11)) -> c1(DROP#2(S(y11), Cons(x0, Cons(x1, Cons(x2, x3)))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Nil)), S(y10)) -> c1(DROP#2(S(y10), Cons(x0, Cons(x1, Nil))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Nil))), S(y7)) -> c1(DROP#2(S(y7), Cons(x0, Cons(x1, Cons(x2, Nil)))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4)))), S(y8)) -> c1(DROP#2(S(y8), Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4))))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> c9(CONST_F#2(Cons(z0, Cons(z1, z2)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(halve#1(length#1(z2)), Cons(z1, z2)), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Nil))), DIVIDE_YS#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2)))), HALVE#1(length#1(z2)), LENGTH#1(z2))
   COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(z2, z3), z4, Cons(0, y0), z6, z7) -> c2(MERGE#2(Cons(0, y0), Cons(z2, z3)))
   COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(0, z3), z4, Cons(S(y0), y1), z6, z7) -> c2(MERGE#2(Cons(S(y0), y1), Cons(0, z3)))
   COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(S(y1), z3), z4, Cons(S(0), y0), z6, z7) -> c2(MERGE#2(Cons(S(0), y0), Cons(S(y1), z3)))
   COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(S(0), z3), z4, Cons(S(S(y0)), y1), z6, z7) -> c2(MERGE#2(Cons(S(S(y0)), y1), Cons(S(0), z3)))
   COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(S(S(y2)), z3), z4, Cons(S(S(y0)), y1), z6, z7) -> c2(MERGE#2(Cons(S(S(y0)), y1), Cons(S(S(y2)), z3)))
   COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(S(y2), z3), z4, Cons(S(y0), y1), z6, z7) -> c2(MERGE#2(Cons(S(y0), y1), Cons(S(y2), z3)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, z3)))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Cons(z2, z3))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(Cons(z2, z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Cons(drop#2(S(halve#1(S(length#1(z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3)))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3))))), HALVE#1(S(length#1(z3))), LENGTH#1(Cons(z2, z3)))
   COND_MERGE_YS_ZS_2(False, Cons(S(x0), x1), Cons(0, x2), S(x0), x1, 0, x2) -> c3(MERGE#2(Cons(S(x0), x1), x2))
   COND_MERGE_YS_ZS_2(False, Cons(S(S(x0)), x1), Cons(S(0), x2), S(S(x0)), x1, S(0), x2) -> c3(MERGE#2(Cons(S(S(x0)), x1), x2))
   COND_MERGE_YS_ZS_2(False, Cons(S(S(x0)), x1), Cons(S(S(x2)), x3), S(S(x0)), x1, S(S(x2)), x3) -> c3(MERGE#2(Cons(S(S(x0)), x1), x3))
K tuples:none
Defined Rule Symbols:   leq#2_2, map#2_2, divide_ys#1_2, halve#1_1, length#1_1, take#2_2, drop#2_2, dc#1_6, const_f#2_2, merge#2_2, cond_merge_ys_zs_2_7

Defined Pair Symbols:   DROP#2_2, TAKE#2_2, HALVE#1_1, CONST_F#2_2, LEQ#2_2, LENGTH#1_1, MAP#2_2, MERGE#2_2, DC#1_6, DIVIDE_YS#1_2, COND_MERGE_YS_ZS_2_7

Compound Symbols:   c12_1, c15_1, c18_1, c19_1, c22_1, c24_1, c26_1, c27_1, c6_1, c6_2, c9_5, c9_2, c9_4, c_1, c1_1, c2_1, c3_1


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(115) CdtRewritingProof (BOTH BOUNDS(ID, ID))
Used rewriting to replace DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z1, Cons(x1, x2))) -> c9(CONST_F#2(Cons(z1, Cons(x1, x2)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(Cons(z1, take#2(halve#1(length#1(x2)), Cons(x1, x2))), Cons(drop#2(S(halve#1(length#1(x2))), Cons(z1, Cons(x1, x2))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z1, Cons(x1, x2)), S(halve#1(length#1(x2))))), DIVIDE_YS#1(Cons(z1, Cons(x1, x2)), S(halve#1(length#1(x2)))), HALVE#1(length#1(x2)), LENGTH#1(x2)) by DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> c9(CONST_F#2(Cons(z0, Cons(z1, z2)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(Cons(z0, take#2(halve#1(length#1(z2)), Cons(z1, z2))), Cons(drop#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Nil))), DIVIDE_YS#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2)))), HALVE#1(length#1(z2)), LENGTH#1(z2))
----------------------------------------

(116)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   leq#2(0, z0) -> True
   leq#2(S(z0), 0) -> False
   leq#2(S(z0), S(z1)) -> leq#2(z0, z1)
   map#2(dc(z0, z1, z2, z3, z4), Nil) -> Nil
   map#2(dc(z0, z1, z2, z3, z4), Cons(z5, z6)) -> Cons(dc#1(z0, z1, z2, z3, z4, z5), map#2(dc(z0, z1, z2, z3, z4), z6))
   divide_ys#1(z0, z1) -> Cons(take#2(z1, z0), Cons(drop#2(z1, z0), Nil))
   halve#1(0) -> 0
   halve#1(S(0)) -> S(0)
   halve#1(S(S(z0))) -> S(halve#1(z0))
   length#1(Nil) -> 0
   length#1(Cons(z0, z1)) -> S(length#1(z1))
   take#2(0, z0) -> Nil
   take#2(S(0), Nil) -> Cons(bot[0], Nil)
   take#2(S(z0), Cons(z1, z2)) -> Cons(z1, take#2(z0, z2))
   drop#2(0, z0) -> z0
   drop#2(S(0), Nil) -> bot[1]
   drop#2(S(z0), Cons(z1, z2)) -> drop#2(z0, z2)
   dc#1(map, divisible, mergesort_zs_3, divide, const_f, Nil) -> Nil
   dc#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Nil)) -> Cons(z0, Nil)
   dc#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> const_f#2(Cons(z0, Cons(z1, z2)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2))))))
   const_f#2(z0, Cons(z1, Cons(z2, z3))) -> merge#2(z1, z2)
   merge#2(Nil, z0) -> z0
   merge#2(Cons(z0, z1), Nil) -> Cons(z0, z1)
   merge#2(Cons(z0, z1), Cons(z2, z3)) -> cond_merge_ys_zs_2(leq#2(z0, z2), Cons(z0, z1), Cons(z2, z3), z0, z1, z2, z3)
   cond_merge_ys_zs_2(True, Cons(z0, z1), Cons(z2, z3), z4, z5, z6, z7) -> Cons(z4, merge#2(z5, Cons(z2, z3)))
   cond_merge_ys_zs_2(False, Cons(z0, z1), Cons(z2, z3), z4, z5, z6, z7) -> Cons(z6, merge#2(Cons(z0, z1), z7))
Tuples:
   DROP#2(S(z0), Cons(z1, z2)) -> c12(DROP#2(z0, z2))
   TAKE#2(S(z0), Cons(z1, z2)) -> c15(TAKE#2(z0, z2))
   HALVE#1(S(S(z0))) -> c18(HALVE#1(z0))
   CONST_F#2(z0, Cons(z1, Cons(z2, z3))) -> c19(MERGE#2(z1, z2))
   LEQ#2(S(z0), S(z1)) -> c22(LEQ#2(z0, z1))
   LENGTH#1(Cons(z0, z1)) -> c24(LENGTH#1(z1))
   MAP#2(dc(z0, z1, z2, z3, z4), Cons(z5, z6)) -> c26(DC#1(z0, z1, z2, z3, z4, z5))
   MAP#2(dc(z0, z1, z2, z3, z4), Cons(z5, z6)) -> c27(MAP#2(dc(z0, z1, z2, z3, z4), z6))
   MERGE#2(Cons(0, x1), Cons(z0, x3)) -> c6(COND_MERGE_YS_ZS_2(True, Cons(0, x1), Cons(z0, x3), 0, x1, z0, x3))
   MERGE#2(Cons(S(z0), x1), Cons(0, x3)) -> c6(COND_MERGE_YS_ZS_2(False, Cons(S(z0), x1), Cons(0, x3), S(z0), x1, 0, x3))
   MERGE#2(Cons(S(0), x1), Cons(S(z0), x3)) -> c6(COND_MERGE_YS_ZS_2(True, Cons(S(0), x1), Cons(S(z0), x3), S(0), x1, S(z0), x3), LEQ#2(S(0), S(z0)))
   MERGE#2(Cons(S(S(z0)), x1), Cons(S(0), x3)) -> c6(COND_MERGE_YS_ZS_2(False, Cons(S(S(z0)), x1), Cons(S(0), x3), S(S(z0)), x1, S(0), x3), LEQ#2(S(S(z0)), S(0)))
   MERGE#2(Cons(S(S(z0)), x1), Cons(S(S(z1)), x3)) -> c6(COND_MERGE_YS_ZS_2(leq#2(z0, z1), Cons(S(S(z0)), x1), Cons(S(S(z1)), x3), S(S(z0)), x1, S(S(z1)), x3), LEQ#2(S(S(z0)), S(S(z1))))
   MERGE#2(Cons(S(x0), x1), Cons(S(x2), x3)) -> c6(LEQ#2(S(x0), S(x2)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Cons(z0, z1)))) -> c9(CONST_F#2(Cons(x0, Cons(x1, Cons(z0, z1))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(S(length#1(z1)))), Cons(x0, Cons(x1, Cons(z0, z1)))), Cons(drop#2(S(halve#1(length#1(Cons(z0, z1)))), Cons(x0, Cons(x1, Cons(z0, z1)))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Cons(z0, z1))), S(halve#1(length#1(Cons(z0, z1)))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(z0, z1))), S(halve#1(length#1(Cons(z0, z1))))), HALVE#1(length#1(Cons(z0, z1))), LENGTH#1(Cons(z0, z1)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, x2))) -> c9(MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, x2)), S(halve#1(length#1(x2))))), DIVIDE_YS#1(Cons(x0, Cons(x1, x2)), S(halve#1(length#1(x2)))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Nil))) -> c9(CONST_F#2(Cons(x0, Cons(x1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(Nil))), Cons(x0, Cons(x1, Nil))), Cons(drop#2(S(halve#1(0)), Cons(x0, Cons(x1, Nil))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Nil)), S(halve#1(length#1(Nil)))), HALVE#1(length#1(Nil)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Nil))) -> c9(CONST_F#2(Cons(x0, Cons(x1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(0)), Cons(x0, Cons(x1, Nil))), Cons(drop#2(S(halve#1(length#1(Nil))), Cons(x0, Cons(x1, Nil))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Nil)), S(halve#1(length#1(Nil)))), HALVE#1(length#1(Nil)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Cons(x2, x3)))) -> c9(CONST_F#2(Cons(x0, Cons(x1, Cons(x2, x3))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(S(length#1(x3)))), Cons(x0, Cons(x1, Cons(x2, x3)))), Cons(drop#2(S(halve#1(S(length#1(x3)))), Cons(x0, Cons(x1, Cons(x2, x3)))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Cons(x2, x3))), S(halve#1(length#1(Cons(x2, x3)))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, x3))), S(halve#1(length#1(Cons(x2, x3))))), HALVE#1(length#1(Cons(x2, x3))), LENGTH#1(Cons(x2, x3)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Cons(x2, Nil)))) -> c9(CONST_F#2(Cons(x0, Cons(x1, Cons(x2, Nil))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Cons(x2, Nil))), S(halve#1(S(0)))))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Cons(x2, Nil))), S(halve#1(length#1(Cons(x2, Nil)))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Nil))), S(halve#1(length#1(Cons(x2, Nil))))), HALVE#1(length#1(Cons(x2, Nil))), LENGTH#1(Cons(x2, Nil)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Cons(x2, Cons(z0, z1))))) -> c9(CONST_F#2(Cons(x0, Cons(x1, Cons(x2, Cons(z0, z1)))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Cons(x2, Cons(z0, z1)))), S(halve#1(S(S(length#1(z1)))))))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Cons(x2, Cons(z0, z1)))), S(halve#1(length#1(Cons(x2, Cons(z0, z1))))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Cons(z0, z1)))), S(halve#1(length#1(Cons(x2, Cons(z0, z1)))))), HALVE#1(length#1(Cons(x2, Cons(z0, z1)))), LENGTH#1(Cons(x2, Cons(z0, z1))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Cons(x2, x3)))) -> c9(MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Cons(x2, x3))), S(halve#1(length#1(Cons(x2, x3)))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, x3))), S(halve#1(length#1(Cons(x2, x3))))), HALVE#1(length#1(Cons(x2, x3))), LENGTH#1(Cons(x2, x3)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Nil))) -> c9(CONST_F#2(Cons(x0, Cons(x1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(0)), Cons(x0, Cons(x1, Nil))), Cons(drop#2(S(halve#1(0)), Cons(x0, Cons(x1, Nil))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Nil)), S(halve#1(length#1(Nil)))), HALVE#1(length#1(Nil)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Nil))) -> c9(CONST_F#2(Cons(x0, Cons(x1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Nil)), S(0)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Nil)), S(halve#1(length#1(Nil)))), HALVE#1(length#1(Nil)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> c9(CONST_F#2(Cons(z0, Cons(z1, z2)), Cons(dc#1(map, divisible, mergesort_zs_3, divide, const_f, take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2)))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(drop#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Nil))), DIVIDE_YS#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2)))), HALVE#1(length#1(z2)), LENGTH#1(z2))
   DIVIDE_YS#1(Cons(x0, Cons(x1, x2)), S(y11)) -> c(TAKE#2(S(y11), Cons(x0, Cons(x1, x2))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, x3))), S(y11)) -> c(TAKE#2(S(y11), Cons(x0, Cons(x1, Cons(x2, x3)))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Nil)), S(y10)) -> c(TAKE#2(S(y10), Cons(x0, Cons(x1, Nil))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Nil))), S(y7)) -> c(TAKE#2(S(y7), Cons(x0, Cons(x1, Cons(x2, Nil)))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4)))), S(y8)) -> c(TAKE#2(S(y8), Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4))))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, x2)), S(y11)) -> c1(DROP#2(S(y11), Cons(x0, Cons(x1, x2))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, x3))), S(y11)) -> c1(DROP#2(S(y11), Cons(x0, Cons(x1, Cons(x2, x3)))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Nil)), S(y10)) -> c1(DROP#2(S(y10), Cons(x0, Cons(x1, Nil))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Nil))), S(y7)) -> c1(DROP#2(S(y7), Cons(x0, Cons(x1, Cons(x2, Nil)))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4)))), S(y8)) -> c1(DROP#2(S(y8), Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4))))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> c9(CONST_F#2(Cons(z0, Cons(z1, z2)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(halve#1(length#1(z2)), Cons(z1, z2)), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Nil))), DIVIDE_YS#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2)))), HALVE#1(length#1(z2)), LENGTH#1(z2))
   COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(z2, z3), z4, Cons(0, y0), z6, z7) -> c2(MERGE#2(Cons(0, y0), Cons(z2, z3)))
   COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(0, z3), z4, Cons(S(y0), y1), z6, z7) -> c2(MERGE#2(Cons(S(y0), y1), Cons(0, z3)))
   COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(S(y1), z3), z4, Cons(S(0), y0), z6, z7) -> c2(MERGE#2(Cons(S(0), y0), Cons(S(y1), z3)))
   COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(S(0), z3), z4, Cons(S(S(y0)), y1), z6, z7) -> c2(MERGE#2(Cons(S(S(y0)), y1), Cons(S(0), z3)))
   COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(S(S(y2)), z3), z4, Cons(S(S(y0)), y1), z6, z7) -> c2(MERGE#2(Cons(S(S(y0)), y1), Cons(S(S(y2)), z3)))
   COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(S(y2), z3), z4, Cons(S(y0), y1), z6, z7) -> c2(MERGE#2(Cons(S(y0), y1), Cons(S(y2), z3)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, z3)))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Cons(z2, z3))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(Cons(z2, z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Cons(drop#2(S(halve#1(S(length#1(z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3)))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3))))), HALVE#1(S(length#1(z3))), LENGTH#1(Cons(z2, z3)))
   COND_MERGE_YS_ZS_2(False, Cons(S(x0), x1), Cons(0, x2), S(x0), x1, 0, x2) -> c3(MERGE#2(Cons(S(x0), x1), x2))
   COND_MERGE_YS_ZS_2(False, Cons(S(S(x0)), x1), Cons(S(0), x2), S(S(x0)), x1, S(0), x2) -> c3(MERGE#2(Cons(S(S(x0)), x1), x2))
   COND_MERGE_YS_ZS_2(False, Cons(S(S(x0)), x1), Cons(S(S(x2)), x3), S(S(x0)), x1, S(S(x2)), x3) -> c3(MERGE#2(Cons(S(S(x0)), x1), x3))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> c9(CONST_F#2(Cons(z0, Cons(z1, z2)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(Cons(z0, take#2(halve#1(length#1(z2)), Cons(z1, z2))), Cons(drop#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Nil))), DIVIDE_YS#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2)))), HALVE#1(length#1(z2)), LENGTH#1(z2))
S tuples:
   DROP#2(S(z0), Cons(z1, z2)) -> c12(DROP#2(z0, z2))
   TAKE#2(S(z0), Cons(z1, z2)) -> c15(TAKE#2(z0, z2))
   HALVE#1(S(S(z0))) -> c18(HALVE#1(z0))
   CONST_F#2(z0, Cons(z1, Cons(z2, z3))) -> c19(MERGE#2(z1, z2))
   LEQ#2(S(z0), S(z1)) -> c22(LEQ#2(z0, z1))
   LENGTH#1(Cons(z0, z1)) -> c24(LENGTH#1(z1))
   MAP#2(dc(z0, z1, z2, z3, z4), Cons(z5, z6)) -> c26(DC#1(z0, z1, z2, z3, z4, z5))
   MAP#2(dc(z0, z1, z2, z3, z4), Cons(z5, z6)) -> c27(MAP#2(dc(z0, z1, z2, z3, z4), z6))
   MERGE#2(Cons(0, x1), Cons(z0, x3)) -> c6(COND_MERGE_YS_ZS_2(True, Cons(0, x1), Cons(z0, x3), 0, x1, z0, x3))
   MERGE#2(Cons(S(z0), x1), Cons(0, x3)) -> c6(COND_MERGE_YS_ZS_2(False, Cons(S(z0), x1), Cons(0, x3), S(z0), x1, 0, x3))
   MERGE#2(Cons(S(0), x1), Cons(S(z0), x3)) -> c6(COND_MERGE_YS_ZS_2(True, Cons(S(0), x1), Cons(S(z0), x3), S(0), x1, S(z0), x3), LEQ#2(S(0), S(z0)))
   MERGE#2(Cons(S(S(z0)), x1), Cons(S(0), x3)) -> c6(COND_MERGE_YS_ZS_2(False, Cons(S(S(z0)), x1), Cons(S(0), x3), S(S(z0)), x1, S(0), x3), LEQ#2(S(S(z0)), S(0)))
   MERGE#2(Cons(S(S(z0)), x1), Cons(S(S(z1)), x3)) -> c6(COND_MERGE_YS_ZS_2(leq#2(z0, z1), Cons(S(S(z0)), x1), Cons(S(S(z1)), x3), S(S(z0)), x1, S(S(z1)), x3), LEQ#2(S(S(z0)), S(S(z1))))
   MERGE#2(Cons(S(x0), x1), Cons(S(x2), x3)) -> c6(LEQ#2(S(x0), S(x2)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Cons(z0, z1)))) -> c9(CONST_F#2(Cons(x0, Cons(x1, Cons(z0, z1))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(S(length#1(z1)))), Cons(x0, Cons(x1, Cons(z0, z1)))), Cons(drop#2(S(halve#1(length#1(Cons(z0, z1)))), Cons(x0, Cons(x1, Cons(z0, z1)))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Cons(z0, z1))), S(halve#1(length#1(Cons(z0, z1)))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(z0, z1))), S(halve#1(length#1(Cons(z0, z1))))), HALVE#1(length#1(Cons(z0, z1))), LENGTH#1(Cons(z0, z1)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, x2))) -> c9(MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, x2)), S(halve#1(length#1(x2))))), DIVIDE_YS#1(Cons(x0, Cons(x1, x2)), S(halve#1(length#1(x2)))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Nil))) -> c9(CONST_F#2(Cons(x0, Cons(x1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(Nil))), Cons(x0, Cons(x1, Nil))), Cons(drop#2(S(halve#1(0)), Cons(x0, Cons(x1, Nil))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Nil)), S(halve#1(length#1(Nil)))), HALVE#1(length#1(Nil)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Nil))) -> c9(CONST_F#2(Cons(x0, Cons(x1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(0)), Cons(x0, Cons(x1, Nil))), Cons(drop#2(S(halve#1(length#1(Nil))), Cons(x0, Cons(x1, Nil))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Nil)), S(halve#1(length#1(Nil)))), HALVE#1(length#1(Nil)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Cons(x2, x3)))) -> c9(CONST_F#2(Cons(x0, Cons(x1, Cons(x2, x3))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(S(length#1(x3)))), Cons(x0, Cons(x1, Cons(x2, x3)))), Cons(drop#2(S(halve#1(S(length#1(x3)))), Cons(x0, Cons(x1, Cons(x2, x3)))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Cons(x2, x3))), S(halve#1(length#1(Cons(x2, x3)))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, x3))), S(halve#1(length#1(Cons(x2, x3))))), HALVE#1(length#1(Cons(x2, x3))), LENGTH#1(Cons(x2, x3)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Cons(x2, Nil)))) -> c9(CONST_F#2(Cons(x0, Cons(x1, Cons(x2, Nil))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Cons(x2, Nil))), S(halve#1(S(0)))))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Cons(x2, Nil))), S(halve#1(length#1(Cons(x2, Nil)))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Nil))), S(halve#1(length#1(Cons(x2, Nil))))), HALVE#1(length#1(Cons(x2, Nil))), LENGTH#1(Cons(x2, Nil)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Cons(x2, Cons(z0, z1))))) -> c9(CONST_F#2(Cons(x0, Cons(x1, Cons(x2, Cons(z0, z1)))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Cons(x2, Cons(z0, z1)))), S(halve#1(S(S(length#1(z1)))))))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Cons(x2, Cons(z0, z1)))), S(halve#1(length#1(Cons(x2, Cons(z0, z1))))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Cons(z0, z1)))), S(halve#1(length#1(Cons(x2, Cons(z0, z1)))))), HALVE#1(length#1(Cons(x2, Cons(z0, z1)))), LENGTH#1(Cons(x2, Cons(z0, z1))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Cons(x2, x3)))) -> c9(MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Cons(x2, x3))), S(halve#1(length#1(Cons(x2, x3)))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, x3))), S(halve#1(length#1(Cons(x2, x3))))), HALVE#1(length#1(Cons(x2, x3))), LENGTH#1(Cons(x2, x3)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Nil))) -> c9(CONST_F#2(Cons(x0, Cons(x1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(0)), Cons(x0, Cons(x1, Nil))), Cons(drop#2(S(halve#1(0)), Cons(x0, Cons(x1, Nil))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Nil)), S(halve#1(length#1(Nil)))), HALVE#1(length#1(Nil)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Nil))) -> c9(CONST_F#2(Cons(x0, Cons(x1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Nil)), S(0)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Nil)), S(halve#1(length#1(Nil)))), HALVE#1(length#1(Nil)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> c9(CONST_F#2(Cons(z0, Cons(z1, z2)), Cons(dc#1(map, divisible, mergesort_zs_3, divide, const_f, take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2)))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(drop#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Nil))), DIVIDE_YS#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2)))), HALVE#1(length#1(z2)), LENGTH#1(z2))
   DIVIDE_YS#1(Cons(x0, Cons(x1, x2)), S(y11)) -> c(TAKE#2(S(y11), Cons(x0, Cons(x1, x2))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, x3))), S(y11)) -> c(TAKE#2(S(y11), Cons(x0, Cons(x1, Cons(x2, x3)))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Nil)), S(y10)) -> c(TAKE#2(S(y10), Cons(x0, Cons(x1, Nil))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Nil))), S(y7)) -> c(TAKE#2(S(y7), Cons(x0, Cons(x1, Cons(x2, Nil)))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4)))), S(y8)) -> c(TAKE#2(S(y8), Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4))))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, x2)), S(y11)) -> c1(DROP#2(S(y11), Cons(x0, Cons(x1, x2))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, x3))), S(y11)) -> c1(DROP#2(S(y11), Cons(x0, Cons(x1, Cons(x2, x3)))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Nil)), S(y10)) -> c1(DROP#2(S(y10), Cons(x0, Cons(x1, Nil))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Nil))), S(y7)) -> c1(DROP#2(S(y7), Cons(x0, Cons(x1, Cons(x2, Nil)))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4)))), S(y8)) -> c1(DROP#2(S(y8), Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4))))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> c9(CONST_F#2(Cons(z0, Cons(z1, z2)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(halve#1(length#1(z2)), Cons(z1, z2)), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Nil))), DIVIDE_YS#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2)))), HALVE#1(length#1(z2)), LENGTH#1(z2))
   COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(z2, z3), z4, Cons(0, y0), z6, z7) -> c2(MERGE#2(Cons(0, y0), Cons(z2, z3)))
   COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(0, z3), z4, Cons(S(y0), y1), z6, z7) -> c2(MERGE#2(Cons(S(y0), y1), Cons(0, z3)))
   COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(S(y1), z3), z4, Cons(S(0), y0), z6, z7) -> c2(MERGE#2(Cons(S(0), y0), Cons(S(y1), z3)))
   COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(S(0), z3), z4, Cons(S(S(y0)), y1), z6, z7) -> c2(MERGE#2(Cons(S(S(y0)), y1), Cons(S(0), z3)))
   COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(S(S(y2)), z3), z4, Cons(S(S(y0)), y1), z6, z7) -> c2(MERGE#2(Cons(S(S(y0)), y1), Cons(S(S(y2)), z3)))
   COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(S(y2), z3), z4, Cons(S(y0), y1), z6, z7) -> c2(MERGE#2(Cons(S(y0), y1), Cons(S(y2), z3)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, z3)))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Cons(z2, z3))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(Cons(z2, z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Cons(drop#2(S(halve#1(S(length#1(z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3)))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3))))), HALVE#1(S(length#1(z3))), LENGTH#1(Cons(z2, z3)))
   COND_MERGE_YS_ZS_2(False, Cons(S(x0), x1), Cons(0, x2), S(x0), x1, 0, x2) -> c3(MERGE#2(Cons(S(x0), x1), x2))
   COND_MERGE_YS_ZS_2(False, Cons(S(S(x0)), x1), Cons(S(0), x2), S(S(x0)), x1, S(0), x2) -> c3(MERGE#2(Cons(S(S(x0)), x1), x2))
   COND_MERGE_YS_ZS_2(False, Cons(S(S(x0)), x1), Cons(S(S(x2)), x3), S(S(x0)), x1, S(S(x2)), x3) -> c3(MERGE#2(Cons(S(S(x0)), x1), x3))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> c9(CONST_F#2(Cons(z0, Cons(z1, z2)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(Cons(z0, take#2(halve#1(length#1(z2)), Cons(z1, z2))), Cons(drop#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Nil))), DIVIDE_YS#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2)))), HALVE#1(length#1(z2)), LENGTH#1(z2))
K tuples:none
Defined Rule Symbols:   leq#2_2, map#2_2, divide_ys#1_2, halve#1_1, length#1_1, take#2_2, drop#2_2, dc#1_6, const_f#2_2, merge#2_2, cond_merge_ys_zs_2_7

Defined Pair Symbols:   DROP#2_2, TAKE#2_2, HALVE#1_1, CONST_F#2_2, LEQ#2_2, LENGTH#1_1, MAP#2_2, MERGE#2_2, DC#1_6, DIVIDE_YS#1_2, COND_MERGE_YS_ZS_2_7

Compound Symbols:   c12_1, c15_1, c18_1, c19_1, c22_1, c24_1, c26_1, c27_1, c6_1, c6_2, c9_5, c9_2, c9_4, c_1, c1_1, c2_1, c3_1


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

(117) CdtRewritingProof (BOTH BOUNDS(ID, ID))
Used rewriting to replace DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Cons(z0, z1)))) -> c9(CONST_F#2(Cons(x0, Cons(x1, Cons(z0, z1))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(S(length#1(z1)))), Cons(x0, Cons(x1, Cons(z0, z1)))), Cons(drop#2(S(halve#1(length#1(Cons(z0, z1)))), Cons(x0, Cons(x1, Cons(z0, z1)))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Cons(z0, z1))), S(halve#1(length#1(Cons(z0, z1)))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(z0, z1))), S(halve#1(length#1(Cons(z0, z1))))), HALVE#1(length#1(Cons(z0, z1))), LENGTH#1(Cons(z0, z1))) by DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, z3)))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Cons(z2, z3))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(S(length#1(z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Cons(drop#2(S(halve#1(length#1(Cons(z2, z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3)))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3))))), HALVE#1(S(length#1(z3))), LENGTH#1(Cons(z2, z3)))
----------------------------------------

(118)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   leq#2(0, z0) -> True
   leq#2(S(z0), 0) -> False
   leq#2(S(z0), S(z1)) -> leq#2(z0, z1)
   map#2(dc(z0, z1, z2, z3, z4), Nil) -> Nil
   map#2(dc(z0, z1, z2, z3, z4), Cons(z5, z6)) -> Cons(dc#1(z0, z1, z2, z3, z4, z5), map#2(dc(z0, z1, z2, z3, z4), z6))
   divide_ys#1(z0, z1) -> Cons(take#2(z1, z0), Cons(drop#2(z1, z0), Nil))
   halve#1(0) -> 0
   halve#1(S(0)) -> S(0)
   halve#1(S(S(z0))) -> S(halve#1(z0))
   length#1(Nil) -> 0
   length#1(Cons(z0, z1)) -> S(length#1(z1))
   take#2(0, z0) -> Nil
   take#2(S(0), Nil) -> Cons(bot[0], Nil)
   take#2(S(z0), Cons(z1, z2)) -> Cons(z1, take#2(z0, z2))
   drop#2(0, z0) -> z0
   drop#2(S(0), Nil) -> bot[1]
   drop#2(S(z0), Cons(z1, z2)) -> drop#2(z0, z2)
   dc#1(map, divisible, mergesort_zs_3, divide, const_f, Nil) -> Nil
   dc#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Nil)) -> Cons(z0, Nil)
   dc#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> const_f#2(Cons(z0, Cons(z1, z2)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2))))))
   const_f#2(z0, Cons(z1, Cons(z2, z3))) -> merge#2(z1, z2)
   merge#2(Nil, z0) -> z0
   merge#2(Cons(z0, z1), Nil) -> Cons(z0, z1)
   merge#2(Cons(z0, z1), Cons(z2, z3)) -> cond_merge_ys_zs_2(leq#2(z0, z2), Cons(z0, z1), Cons(z2, z3), z0, z1, z2, z3)
   cond_merge_ys_zs_2(True, Cons(z0, z1), Cons(z2, z3), z4, z5, z6, z7) -> Cons(z4, merge#2(z5, Cons(z2, z3)))
   cond_merge_ys_zs_2(False, Cons(z0, z1), Cons(z2, z3), z4, z5, z6, z7) -> Cons(z6, merge#2(Cons(z0, z1), z7))
Tuples:
   DROP#2(S(z0), Cons(z1, z2)) -> c12(DROP#2(z0, z2))
   TAKE#2(S(z0), Cons(z1, z2)) -> c15(TAKE#2(z0, z2))
   HALVE#1(S(S(z0))) -> c18(HALVE#1(z0))
   CONST_F#2(z0, Cons(z1, Cons(z2, z3))) -> c19(MERGE#2(z1, z2))
   LEQ#2(S(z0), S(z1)) -> c22(LEQ#2(z0, z1))
   LENGTH#1(Cons(z0, z1)) -> c24(LENGTH#1(z1))
   MAP#2(dc(z0, z1, z2, z3, z4), Cons(z5, z6)) -> c26(DC#1(z0, z1, z2, z3, z4, z5))
   MAP#2(dc(z0, z1, z2, z3, z4), Cons(z5, z6)) -> c27(MAP#2(dc(z0, z1, z2, z3, z4), z6))
   MERGE#2(Cons(0, x1), Cons(z0, x3)) -> c6(COND_MERGE_YS_ZS_2(True, Cons(0, x1), Cons(z0, x3), 0, x1, z0, x3))
   MERGE#2(Cons(S(z0), x1), Cons(0, x3)) -> c6(COND_MERGE_YS_ZS_2(False, Cons(S(z0), x1), Cons(0, x3), S(z0), x1, 0, x3))
   MERGE#2(Cons(S(0), x1), Cons(S(z0), x3)) -> c6(COND_MERGE_YS_ZS_2(True, Cons(S(0), x1), Cons(S(z0), x3), S(0), x1, S(z0), x3), LEQ#2(S(0), S(z0)))
   MERGE#2(Cons(S(S(z0)), x1), Cons(S(0), x3)) -> c6(COND_MERGE_YS_ZS_2(False, Cons(S(S(z0)), x1), Cons(S(0), x3), S(S(z0)), x1, S(0), x3), LEQ#2(S(S(z0)), S(0)))
   MERGE#2(Cons(S(S(z0)), x1), Cons(S(S(z1)), x3)) -> c6(COND_MERGE_YS_ZS_2(leq#2(z0, z1), Cons(S(S(z0)), x1), Cons(S(S(z1)), x3), S(S(z0)), x1, S(S(z1)), x3), LEQ#2(S(S(z0)), S(S(z1))))
   MERGE#2(Cons(S(x0), x1), Cons(S(x2), x3)) -> c6(LEQ#2(S(x0), S(x2)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, x2))) -> c9(MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, x2)), S(halve#1(length#1(x2))))), DIVIDE_YS#1(Cons(x0, Cons(x1, x2)), S(halve#1(length#1(x2)))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Nil))) -> c9(CONST_F#2(Cons(x0, Cons(x1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(Nil))), Cons(x0, Cons(x1, Nil))), Cons(drop#2(S(halve#1(0)), Cons(x0, Cons(x1, Nil))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Nil)), S(halve#1(length#1(Nil)))), HALVE#1(length#1(Nil)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Nil))) -> c9(CONST_F#2(Cons(x0, Cons(x1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(0)), Cons(x0, Cons(x1, Nil))), Cons(drop#2(S(halve#1(length#1(Nil))), Cons(x0, Cons(x1, Nil))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Nil)), S(halve#1(length#1(Nil)))), HALVE#1(length#1(Nil)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Cons(x2, x3)))) -> c9(CONST_F#2(Cons(x0, Cons(x1, Cons(x2, x3))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(S(length#1(x3)))), Cons(x0, Cons(x1, Cons(x2, x3)))), Cons(drop#2(S(halve#1(S(length#1(x3)))), Cons(x0, Cons(x1, Cons(x2, x3)))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Cons(x2, x3))), S(halve#1(length#1(Cons(x2, x3)))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, x3))), S(halve#1(length#1(Cons(x2, x3))))), HALVE#1(length#1(Cons(x2, x3))), LENGTH#1(Cons(x2, x3)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Cons(x2, Nil)))) -> c9(CONST_F#2(Cons(x0, Cons(x1, Cons(x2, Nil))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Cons(x2, Nil))), S(halve#1(S(0)))))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Cons(x2, Nil))), S(halve#1(length#1(Cons(x2, Nil)))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Nil))), S(halve#1(length#1(Cons(x2, Nil))))), HALVE#1(length#1(Cons(x2, Nil))), LENGTH#1(Cons(x2, Nil)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Cons(x2, Cons(z0, z1))))) -> c9(CONST_F#2(Cons(x0, Cons(x1, Cons(x2, Cons(z0, z1)))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Cons(x2, Cons(z0, z1)))), S(halve#1(S(S(length#1(z1)))))))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Cons(x2, Cons(z0, z1)))), S(halve#1(length#1(Cons(x2, Cons(z0, z1))))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Cons(z0, z1)))), S(halve#1(length#1(Cons(x2, Cons(z0, z1)))))), HALVE#1(length#1(Cons(x2, Cons(z0, z1)))), LENGTH#1(Cons(x2, Cons(z0, z1))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Cons(x2, x3)))) -> c9(MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Cons(x2, x3))), S(halve#1(length#1(Cons(x2, x3)))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, x3))), S(halve#1(length#1(Cons(x2, x3))))), HALVE#1(length#1(Cons(x2, x3))), LENGTH#1(Cons(x2, x3)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Nil))) -> c9(CONST_F#2(Cons(x0, Cons(x1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(0)), Cons(x0, Cons(x1, Nil))), Cons(drop#2(S(halve#1(0)), Cons(x0, Cons(x1, Nil))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Nil)), S(halve#1(length#1(Nil)))), HALVE#1(length#1(Nil)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Nil))) -> c9(CONST_F#2(Cons(x0, Cons(x1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Nil)), S(0)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Nil)), S(halve#1(length#1(Nil)))), HALVE#1(length#1(Nil)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> c9(CONST_F#2(Cons(z0, Cons(z1, z2)), Cons(dc#1(map, divisible, mergesort_zs_3, divide, const_f, take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2)))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(drop#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Nil))), DIVIDE_YS#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2)))), HALVE#1(length#1(z2)), LENGTH#1(z2))
   DIVIDE_YS#1(Cons(x0, Cons(x1, x2)), S(y11)) -> c(TAKE#2(S(y11), Cons(x0, Cons(x1, x2))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, x3))), S(y11)) -> c(TAKE#2(S(y11), Cons(x0, Cons(x1, Cons(x2, x3)))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Nil)), S(y10)) -> c(TAKE#2(S(y10), Cons(x0, Cons(x1, Nil))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Nil))), S(y7)) -> c(TAKE#2(S(y7), Cons(x0, Cons(x1, Cons(x2, Nil)))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4)))), S(y8)) -> c(TAKE#2(S(y8), Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4))))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, x2)), S(y11)) -> c1(DROP#2(S(y11), Cons(x0, Cons(x1, x2))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, x3))), S(y11)) -> c1(DROP#2(S(y11), Cons(x0, Cons(x1, Cons(x2, x3)))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Nil)), S(y10)) -> c1(DROP#2(S(y10), Cons(x0, Cons(x1, Nil))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Nil))), S(y7)) -> c1(DROP#2(S(y7), Cons(x0, Cons(x1, Cons(x2, Nil)))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4)))), S(y8)) -> c1(DROP#2(S(y8), Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4))))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> c9(CONST_F#2(Cons(z0, Cons(z1, z2)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(halve#1(length#1(z2)), Cons(z1, z2)), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Nil))), DIVIDE_YS#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2)))), HALVE#1(length#1(z2)), LENGTH#1(z2))
   COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(z2, z3), z4, Cons(0, y0), z6, z7) -> c2(MERGE#2(Cons(0, y0), Cons(z2, z3)))
   COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(0, z3), z4, Cons(S(y0), y1), z6, z7) -> c2(MERGE#2(Cons(S(y0), y1), Cons(0, z3)))
   COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(S(y1), z3), z4, Cons(S(0), y0), z6, z7) -> c2(MERGE#2(Cons(S(0), y0), Cons(S(y1), z3)))
   COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(S(0), z3), z4, Cons(S(S(y0)), y1), z6, z7) -> c2(MERGE#2(Cons(S(S(y0)), y1), Cons(S(0), z3)))
   COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(S(S(y2)), z3), z4, Cons(S(S(y0)), y1), z6, z7) -> c2(MERGE#2(Cons(S(S(y0)), y1), Cons(S(S(y2)), z3)))
   COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(S(y2), z3), z4, Cons(S(y0), y1), z6, z7) -> c2(MERGE#2(Cons(S(y0), y1), Cons(S(y2), z3)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, z3)))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Cons(z2, z3))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(Cons(z2, z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Cons(drop#2(S(halve#1(S(length#1(z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3)))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3))))), HALVE#1(S(length#1(z3))), LENGTH#1(Cons(z2, z3)))
   COND_MERGE_YS_ZS_2(False, Cons(S(x0), x1), Cons(0, x2), S(x0), x1, 0, x2) -> c3(MERGE#2(Cons(S(x0), x1), x2))
   COND_MERGE_YS_ZS_2(False, Cons(S(S(x0)), x1), Cons(S(0), x2), S(S(x0)), x1, S(0), x2) -> c3(MERGE#2(Cons(S(S(x0)), x1), x2))
   COND_MERGE_YS_ZS_2(False, Cons(S(S(x0)), x1), Cons(S(S(x2)), x3), S(S(x0)), x1, S(S(x2)), x3) -> c3(MERGE#2(Cons(S(S(x0)), x1), x3))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> c9(CONST_F#2(Cons(z0, Cons(z1, z2)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(Cons(z0, take#2(halve#1(length#1(z2)), Cons(z1, z2))), Cons(drop#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Nil))), DIVIDE_YS#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2)))), HALVE#1(length#1(z2)), LENGTH#1(z2))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, z3)))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Cons(z2, z3))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(S(length#1(z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Cons(drop#2(S(halve#1(length#1(Cons(z2, z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3)))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3))))), HALVE#1(S(length#1(z3))), LENGTH#1(Cons(z2, z3)))
S tuples:
   DROP#2(S(z0), Cons(z1, z2)) -> c12(DROP#2(z0, z2))
   TAKE#2(S(z0), Cons(z1, z2)) -> c15(TAKE#2(z0, z2))
   HALVE#1(S(S(z0))) -> c18(HALVE#1(z0))
   CONST_F#2(z0, Cons(z1, Cons(z2, z3))) -> c19(MERGE#2(z1, z2))
   LEQ#2(S(z0), S(z1)) -> c22(LEQ#2(z0, z1))
   LENGTH#1(Cons(z0, z1)) -> c24(LENGTH#1(z1))
   MAP#2(dc(z0, z1, z2, z3, z4), Cons(z5, z6)) -> c26(DC#1(z0, z1, z2, z3, z4, z5))
   MAP#2(dc(z0, z1, z2, z3, z4), Cons(z5, z6)) -> c27(MAP#2(dc(z0, z1, z2, z3, z4), z6))
   MERGE#2(Cons(0, x1), Cons(z0, x3)) -> c6(COND_MERGE_YS_ZS_2(True, Cons(0, x1), Cons(z0, x3), 0, x1, z0, x3))
   MERGE#2(Cons(S(z0), x1), Cons(0, x3)) -> c6(COND_MERGE_YS_ZS_2(False, Cons(S(z0), x1), Cons(0, x3), S(z0), x1, 0, x3))
   MERGE#2(Cons(S(0), x1), Cons(S(z0), x3)) -> c6(COND_MERGE_YS_ZS_2(True, Cons(S(0), x1), Cons(S(z0), x3), S(0), x1, S(z0), x3), LEQ#2(S(0), S(z0)))
   MERGE#2(Cons(S(S(z0)), x1), Cons(S(0), x3)) -> c6(COND_MERGE_YS_ZS_2(False, Cons(S(S(z0)), x1), Cons(S(0), x3), S(S(z0)), x1, S(0), x3), LEQ#2(S(S(z0)), S(0)))
   MERGE#2(Cons(S(S(z0)), x1), Cons(S(S(z1)), x3)) -> c6(COND_MERGE_YS_ZS_2(leq#2(z0, z1), Cons(S(S(z0)), x1), Cons(S(S(z1)), x3), S(S(z0)), x1, S(S(z1)), x3), LEQ#2(S(S(z0)), S(S(z1))))
   MERGE#2(Cons(S(x0), x1), Cons(S(x2), x3)) -> c6(LEQ#2(S(x0), S(x2)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, x2))) -> c9(MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, x2)), S(halve#1(length#1(x2))))), DIVIDE_YS#1(Cons(x0, Cons(x1, x2)), S(halve#1(length#1(x2)))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Nil))) -> c9(CONST_F#2(Cons(x0, Cons(x1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(Nil))), Cons(x0, Cons(x1, Nil))), Cons(drop#2(S(halve#1(0)), Cons(x0, Cons(x1, Nil))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Nil)), S(halve#1(length#1(Nil)))), HALVE#1(length#1(Nil)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Nil))) -> c9(CONST_F#2(Cons(x0, Cons(x1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(0)), Cons(x0, Cons(x1, Nil))), Cons(drop#2(S(halve#1(length#1(Nil))), Cons(x0, Cons(x1, Nil))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Nil)), S(halve#1(length#1(Nil)))), HALVE#1(length#1(Nil)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Cons(x2, x3)))) -> c9(CONST_F#2(Cons(x0, Cons(x1, Cons(x2, x3))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(S(length#1(x3)))), Cons(x0, Cons(x1, Cons(x2, x3)))), Cons(drop#2(S(halve#1(S(length#1(x3)))), Cons(x0, Cons(x1, Cons(x2, x3)))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Cons(x2, x3))), S(halve#1(length#1(Cons(x2, x3)))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, x3))), S(halve#1(length#1(Cons(x2, x3))))), HALVE#1(length#1(Cons(x2, x3))), LENGTH#1(Cons(x2, x3)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Cons(x2, Nil)))) -> c9(CONST_F#2(Cons(x0, Cons(x1, Cons(x2, Nil))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Cons(x2, Nil))), S(halve#1(S(0)))))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Cons(x2, Nil))), S(halve#1(length#1(Cons(x2, Nil)))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Nil))), S(halve#1(length#1(Cons(x2, Nil))))), HALVE#1(length#1(Cons(x2, Nil))), LENGTH#1(Cons(x2, Nil)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Cons(x2, Cons(z0, z1))))) -> c9(CONST_F#2(Cons(x0, Cons(x1, Cons(x2, Cons(z0, z1)))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Cons(x2, Cons(z0, z1)))), S(halve#1(S(S(length#1(z1)))))))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Cons(x2, Cons(z0, z1)))), S(halve#1(length#1(Cons(x2, Cons(z0, z1))))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Cons(z0, z1)))), S(halve#1(length#1(Cons(x2, Cons(z0, z1)))))), HALVE#1(length#1(Cons(x2, Cons(z0, z1)))), LENGTH#1(Cons(x2, Cons(z0, z1))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Cons(x2, x3)))) -> c9(MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Cons(x2, x3))), S(halve#1(length#1(Cons(x2, x3)))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, x3))), S(halve#1(length#1(Cons(x2, x3))))), HALVE#1(length#1(Cons(x2, x3))), LENGTH#1(Cons(x2, x3)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Nil))) -> c9(CONST_F#2(Cons(x0, Cons(x1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(0)), Cons(x0, Cons(x1, Nil))), Cons(drop#2(S(halve#1(0)), Cons(x0, Cons(x1, Nil))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Nil)), S(halve#1(length#1(Nil)))), HALVE#1(length#1(Nil)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Nil))) -> c9(CONST_F#2(Cons(x0, Cons(x1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Nil)), S(0)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Nil)), S(halve#1(length#1(Nil)))), HALVE#1(length#1(Nil)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> c9(CONST_F#2(Cons(z0, Cons(z1, z2)), Cons(dc#1(map, divisible, mergesort_zs_3, divide, const_f, take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2)))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(drop#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Nil))), DIVIDE_YS#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2)))), HALVE#1(length#1(z2)), LENGTH#1(z2))
   DIVIDE_YS#1(Cons(x0, Cons(x1, x2)), S(y11)) -> c(TAKE#2(S(y11), Cons(x0, Cons(x1, x2))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, x3))), S(y11)) -> c(TAKE#2(S(y11), Cons(x0, Cons(x1, Cons(x2, x3)))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Nil)), S(y10)) -> c(TAKE#2(S(y10), Cons(x0, Cons(x1, Nil))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Nil))), S(y7)) -> c(TAKE#2(S(y7), Cons(x0, Cons(x1, Cons(x2, Nil)))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4)))), S(y8)) -> c(TAKE#2(S(y8), Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4))))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, x2)), S(y11)) -> c1(DROP#2(S(y11), Cons(x0, Cons(x1, x2))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, x3))), S(y11)) -> c1(DROP#2(S(y11), Cons(x0, Cons(x1, Cons(x2, x3)))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Nil)), S(y10)) -> c1(DROP#2(S(y10), Cons(x0, Cons(x1, Nil))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Nil))), S(y7)) -> c1(DROP#2(S(y7), Cons(x0, Cons(x1, Cons(x2, Nil)))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4)))), S(y8)) -> c1(DROP#2(S(y8), Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4))))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> c9(CONST_F#2(Cons(z0, Cons(z1, z2)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(halve#1(length#1(z2)), Cons(z1, z2)), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Nil))), DIVIDE_YS#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2)))), HALVE#1(length#1(z2)), LENGTH#1(z2))
   COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(z2, z3), z4, Cons(0, y0), z6, z7) -> c2(MERGE#2(Cons(0, y0), Cons(z2, z3)))
   COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(0, z3), z4, Cons(S(y0), y1), z6, z7) -> c2(MERGE#2(Cons(S(y0), y1), Cons(0, z3)))
   COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(S(y1), z3), z4, Cons(S(0), y0), z6, z7) -> c2(MERGE#2(Cons(S(0), y0), Cons(S(y1), z3)))
   COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(S(0), z3), z4, Cons(S(S(y0)), y1), z6, z7) -> c2(MERGE#2(Cons(S(S(y0)), y1), Cons(S(0), z3)))
   COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(S(S(y2)), z3), z4, Cons(S(S(y0)), y1), z6, z7) -> c2(MERGE#2(Cons(S(S(y0)), y1), Cons(S(S(y2)), z3)))
   COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(S(y2), z3), z4, Cons(S(y0), y1), z6, z7) -> c2(MERGE#2(Cons(S(y0), y1), Cons(S(y2), z3)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, z3)))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Cons(z2, z3))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(Cons(z2, z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Cons(drop#2(S(halve#1(S(length#1(z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3)))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3))))), HALVE#1(S(length#1(z3))), LENGTH#1(Cons(z2, z3)))
   COND_MERGE_YS_ZS_2(False, Cons(S(x0), x1), Cons(0, x2), S(x0), x1, 0, x2) -> c3(MERGE#2(Cons(S(x0), x1), x2))
   COND_MERGE_YS_ZS_2(False, Cons(S(S(x0)), x1), Cons(S(0), x2), S(S(x0)), x1, S(0), x2) -> c3(MERGE#2(Cons(S(S(x0)), x1), x2))
   COND_MERGE_YS_ZS_2(False, Cons(S(S(x0)), x1), Cons(S(S(x2)), x3), S(S(x0)), x1, S(S(x2)), x3) -> c3(MERGE#2(Cons(S(S(x0)), x1), x3))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> c9(CONST_F#2(Cons(z0, Cons(z1, z2)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(Cons(z0, take#2(halve#1(length#1(z2)), Cons(z1, z2))), Cons(drop#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Nil))), DIVIDE_YS#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2)))), HALVE#1(length#1(z2)), LENGTH#1(z2))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, z3)))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Cons(z2, z3))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(S(length#1(z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Cons(drop#2(S(halve#1(length#1(Cons(z2, z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3)))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3))))), HALVE#1(S(length#1(z3))), LENGTH#1(Cons(z2, z3)))
K tuples:none
Defined Rule Symbols:   leq#2_2, map#2_2, divide_ys#1_2, halve#1_1, length#1_1, take#2_2, drop#2_2, dc#1_6, const_f#2_2, merge#2_2, cond_merge_ys_zs_2_7

Defined Pair Symbols:   DROP#2_2, TAKE#2_2, HALVE#1_1, CONST_F#2_2, LEQ#2_2, LENGTH#1_1, MAP#2_2, MERGE#2_2, DC#1_6, DIVIDE_YS#1_2, COND_MERGE_YS_ZS_2_7

Compound Symbols:   c12_1, c15_1, c18_1, c19_1, c22_1, c24_1, c26_1, c27_1, c6_1, c6_2, c9_2, c9_4, c9_5, c_1, c1_1, c2_1, c3_1


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

(119) CdtRewritingProof (BOTH BOUNDS(ID, ID))
Used rewriting to replace DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, x2))) -> c9(MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, x2)), S(halve#1(length#1(x2))))), DIVIDE_YS#1(Cons(x0, Cons(x1, x2)), S(halve#1(length#1(x2))))) by DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> c9(MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Nil))), DIVIDE_YS#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2)))))
----------------------------------------

(120)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   leq#2(0, z0) -> True
   leq#2(S(z0), 0) -> False
   leq#2(S(z0), S(z1)) -> leq#2(z0, z1)
   map#2(dc(z0, z1, z2, z3, z4), Nil) -> Nil
   map#2(dc(z0, z1, z2, z3, z4), Cons(z5, z6)) -> Cons(dc#1(z0, z1, z2, z3, z4, z5), map#2(dc(z0, z1, z2, z3, z4), z6))
   divide_ys#1(z0, z1) -> Cons(take#2(z1, z0), Cons(drop#2(z1, z0), Nil))
   halve#1(0) -> 0
   halve#1(S(0)) -> S(0)
   halve#1(S(S(z0))) -> S(halve#1(z0))
   length#1(Nil) -> 0
   length#1(Cons(z0, z1)) -> S(length#1(z1))
   take#2(0, z0) -> Nil
   take#2(S(0), Nil) -> Cons(bot[0], Nil)
   take#2(S(z0), Cons(z1, z2)) -> Cons(z1, take#2(z0, z2))
   drop#2(0, z0) -> z0
   drop#2(S(0), Nil) -> bot[1]
   drop#2(S(z0), Cons(z1, z2)) -> drop#2(z0, z2)
   dc#1(map, divisible, mergesort_zs_3, divide, const_f, Nil) -> Nil
   dc#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Nil)) -> Cons(z0, Nil)
   dc#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> const_f#2(Cons(z0, Cons(z1, z2)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2))))))
   const_f#2(z0, Cons(z1, Cons(z2, z3))) -> merge#2(z1, z2)
   merge#2(Nil, z0) -> z0
   merge#2(Cons(z0, z1), Nil) -> Cons(z0, z1)
   merge#2(Cons(z0, z1), Cons(z2, z3)) -> cond_merge_ys_zs_2(leq#2(z0, z2), Cons(z0, z1), Cons(z2, z3), z0, z1, z2, z3)
   cond_merge_ys_zs_2(True, Cons(z0, z1), Cons(z2, z3), z4, z5, z6, z7) -> Cons(z4, merge#2(z5, Cons(z2, z3)))
   cond_merge_ys_zs_2(False, Cons(z0, z1), Cons(z2, z3), z4, z5, z6, z7) -> Cons(z6, merge#2(Cons(z0, z1), z7))
Tuples:
   DROP#2(S(z0), Cons(z1, z2)) -> c12(DROP#2(z0, z2))
   TAKE#2(S(z0), Cons(z1, z2)) -> c15(TAKE#2(z0, z2))
   HALVE#1(S(S(z0))) -> c18(HALVE#1(z0))
   CONST_F#2(z0, Cons(z1, Cons(z2, z3))) -> c19(MERGE#2(z1, z2))
   LEQ#2(S(z0), S(z1)) -> c22(LEQ#2(z0, z1))
   LENGTH#1(Cons(z0, z1)) -> c24(LENGTH#1(z1))
   MAP#2(dc(z0, z1, z2, z3, z4), Cons(z5, z6)) -> c26(DC#1(z0, z1, z2, z3, z4, z5))
   MAP#2(dc(z0, z1, z2, z3, z4), Cons(z5, z6)) -> c27(MAP#2(dc(z0, z1, z2, z3, z4), z6))
   MERGE#2(Cons(0, x1), Cons(z0, x3)) -> c6(COND_MERGE_YS_ZS_2(True, Cons(0, x1), Cons(z0, x3), 0, x1, z0, x3))
   MERGE#2(Cons(S(z0), x1), Cons(0, x3)) -> c6(COND_MERGE_YS_ZS_2(False, Cons(S(z0), x1), Cons(0, x3), S(z0), x1, 0, x3))
   MERGE#2(Cons(S(0), x1), Cons(S(z0), x3)) -> c6(COND_MERGE_YS_ZS_2(True, Cons(S(0), x1), Cons(S(z0), x3), S(0), x1, S(z0), x3), LEQ#2(S(0), S(z0)))
   MERGE#2(Cons(S(S(z0)), x1), Cons(S(0), x3)) -> c6(COND_MERGE_YS_ZS_2(False, Cons(S(S(z0)), x1), Cons(S(0), x3), S(S(z0)), x1, S(0), x3), LEQ#2(S(S(z0)), S(0)))
   MERGE#2(Cons(S(S(z0)), x1), Cons(S(S(z1)), x3)) -> c6(COND_MERGE_YS_ZS_2(leq#2(z0, z1), Cons(S(S(z0)), x1), Cons(S(S(z1)), x3), S(S(z0)), x1, S(S(z1)), x3), LEQ#2(S(S(z0)), S(S(z1))))
   MERGE#2(Cons(S(x0), x1), Cons(S(x2), x3)) -> c6(LEQ#2(S(x0), S(x2)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Nil))) -> c9(CONST_F#2(Cons(x0, Cons(x1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(Nil))), Cons(x0, Cons(x1, Nil))), Cons(drop#2(S(halve#1(0)), Cons(x0, Cons(x1, Nil))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Nil)), S(halve#1(length#1(Nil)))), HALVE#1(length#1(Nil)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Nil))) -> c9(CONST_F#2(Cons(x0, Cons(x1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(0)), Cons(x0, Cons(x1, Nil))), Cons(drop#2(S(halve#1(length#1(Nil))), Cons(x0, Cons(x1, Nil))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Nil)), S(halve#1(length#1(Nil)))), HALVE#1(length#1(Nil)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Cons(x2, x3)))) -> c9(CONST_F#2(Cons(x0, Cons(x1, Cons(x2, x3))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(S(length#1(x3)))), Cons(x0, Cons(x1, Cons(x2, x3)))), Cons(drop#2(S(halve#1(S(length#1(x3)))), Cons(x0, Cons(x1, Cons(x2, x3)))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Cons(x2, x3))), S(halve#1(length#1(Cons(x2, x3)))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, x3))), S(halve#1(length#1(Cons(x2, x3))))), HALVE#1(length#1(Cons(x2, x3))), LENGTH#1(Cons(x2, x3)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Cons(x2, Nil)))) -> c9(CONST_F#2(Cons(x0, Cons(x1, Cons(x2, Nil))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Cons(x2, Nil))), S(halve#1(S(0)))))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Cons(x2, Nil))), S(halve#1(length#1(Cons(x2, Nil)))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Nil))), S(halve#1(length#1(Cons(x2, Nil))))), HALVE#1(length#1(Cons(x2, Nil))), LENGTH#1(Cons(x2, Nil)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Cons(x2, Cons(z0, z1))))) -> c9(CONST_F#2(Cons(x0, Cons(x1, Cons(x2, Cons(z0, z1)))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Cons(x2, Cons(z0, z1)))), S(halve#1(S(S(length#1(z1)))))))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Cons(x2, Cons(z0, z1)))), S(halve#1(length#1(Cons(x2, Cons(z0, z1))))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Cons(z0, z1)))), S(halve#1(length#1(Cons(x2, Cons(z0, z1)))))), HALVE#1(length#1(Cons(x2, Cons(z0, z1)))), LENGTH#1(Cons(x2, Cons(z0, z1))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Cons(x2, x3)))) -> c9(MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Cons(x2, x3))), S(halve#1(length#1(Cons(x2, x3)))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, x3))), S(halve#1(length#1(Cons(x2, x3))))), HALVE#1(length#1(Cons(x2, x3))), LENGTH#1(Cons(x2, x3)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Nil))) -> c9(CONST_F#2(Cons(x0, Cons(x1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(0)), Cons(x0, Cons(x1, Nil))), Cons(drop#2(S(halve#1(0)), Cons(x0, Cons(x1, Nil))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Nil)), S(halve#1(length#1(Nil)))), HALVE#1(length#1(Nil)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Nil))) -> c9(CONST_F#2(Cons(x0, Cons(x1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Nil)), S(0)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Nil)), S(halve#1(length#1(Nil)))), HALVE#1(length#1(Nil)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> c9(CONST_F#2(Cons(z0, Cons(z1, z2)), Cons(dc#1(map, divisible, mergesort_zs_3, divide, const_f, take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2)))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(drop#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Nil))), DIVIDE_YS#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2)))), HALVE#1(length#1(z2)), LENGTH#1(z2))
   DIVIDE_YS#1(Cons(x0, Cons(x1, x2)), S(y11)) -> c(TAKE#2(S(y11), Cons(x0, Cons(x1, x2))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, x3))), S(y11)) -> c(TAKE#2(S(y11), Cons(x0, Cons(x1, Cons(x2, x3)))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Nil)), S(y10)) -> c(TAKE#2(S(y10), Cons(x0, Cons(x1, Nil))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Nil))), S(y7)) -> c(TAKE#2(S(y7), Cons(x0, Cons(x1, Cons(x2, Nil)))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4)))), S(y8)) -> c(TAKE#2(S(y8), Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4))))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, x2)), S(y11)) -> c1(DROP#2(S(y11), Cons(x0, Cons(x1, x2))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, x3))), S(y11)) -> c1(DROP#2(S(y11), Cons(x0, Cons(x1, Cons(x2, x3)))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Nil)), S(y10)) -> c1(DROP#2(S(y10), Cons(x0, Cons(x1, Nil))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Nil))), S(y7)) -> c1(DROP#2(S(y7), Cons(x0, Cons(x1, Cons(x2, Nil)))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4)))), S(y8)) -> c1(DROP#2(S(y8), Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4))))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> c9(CONST_F#2(Cons(z0, Cons(z1, z2)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(halve#1(length#1(z2)), Cons(z1, z2)), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Nil))), DIVIDE_YS#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2)))), HALVE#1(length#1(z2)), LENGTH#1(z2))
   COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(z2, z3), z4, Cons(0, y0), z6, z7) -> c2(MERGE#2(Cons(0, y0), Cons(z2, z3)))
   COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(0, z3), z4, Cons(S(y0), y1), z6, z7) -> c2(MERGE#2(Cons(S(y0), y1), Cons(0, z3)))
   COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(S(y1), z3), z4, Cons(S(0), y0), z6, z7) -> c2(MERGE#2(Cons(S(0), y0), Cons(S(y1), z3)))
   COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(S(0), z3), z4, Cons(S(S(y0)), y1), z6, z7) -> c2(MERGE#2(Cons(S(S(y0)), y1), Cons(S(0), z3)))
   COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(S(S(y2)), z3), z4, Cons(S(S(y0)), y1), z6, z7) -> c2(MERGE#2(Cons(S(S(y0)), y1), Cons(S(S(y2)), z3)))
   COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(S(y2), z3), z4, Cons(S(y0), y1), z6, z7) -> c2(MERGE#2(Cons(S(y0), y1), Cons(S(y2), z3)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, z3)))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Cons(z2, z3))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(Cons(z2, z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Cons(drop#2(S(halve#1(S(length#1(z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3)))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3))))), HALVE#1(S(length#1(z3))), LENGTH#1(Cons(z2, z3)))
   COND_MERGE_YS_ZS_2(False, Cons(S(x0), x1), Cons(0, x2), S(x0), x1, 0, x2) -> c3(MERGE#2(Cons(S(x0), x1), x2))
   COND_MERGE_YS_ZS_2(False, Cons(S(S(x0)), x1), Cons(S(0), x2), S(S(x0)), x1, S(0), x2) -> c3(MERGE#2(Cons(S(S(x0)), x1), x2))
   COND_MERGE_YS_ZS_2(False, Cons(S(S(x0)), x1), Cons(S(S(x2)), x3), S(S(x0)), x1, S(S(x2)), x3) -> c3(MERGE#2(Cons(S(S(x0)), x1), x3))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> c9(CONST_F#2(Cons(z0, Cons(z1, z2)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(Cons(z0, take#2(halve#1(length#1(z2)), Cons(z1, z2))), Cons(drop#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Nil))), DIVIDE_YS#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2)))), HALVE#1(length#1(z2)), LENGTH#1(z2))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, z3)))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Cons(z2, z3))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(S(length#1(z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Cons(drop#2(S(halve#1(length#1(Cons(z2, z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3)))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3))))), HALVE#1(S(length#1(z3))), LENGTH#1(Cons(z2, z3)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> c9(MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Nil))), DIVIDE_YS#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2)))))
S tuples:
   DROP#2(S(z0), Cons(z1, z2)) -> c12(DROP#2(z0, z2))
   TAKE#2(S(z0), Cons(z1, z2)) -> c15(TAKE#2(z0, z2))
   HALVE#1(S(S(z0))) -> c18(HALVE#1(z0))
   CONST_F#2(z0, Cons(z1, Cons(z2, z3))) -> c19(MERGE#2(z1, z2))
   LEQ#2(S(z0), S(z1)) -> c22(LEQ#2(z0, z1))
   LENGTH#1(Cons(z0, z1)) -> c24(LENGTH#1(z1))
   MAP#2(dc(z0, z1, z2, z3, z4), Cons(z5, z6)) -> c26(DC#1(z0, z1, z2, z3, z4, z5))
   MAP#2(dc(z0, z1, z2, z3, z4), Cons(z5, z6)) -> c27(MAP#2(dc(z0, z1, z2, z3, z4), z6))
   MERGE#2(Cons(0, x1), Cons(z0, x3)) -> c6(COND_MERGE_YS_ZS_2(True, Cons(0, x1), Cons(z0, x3), 0, x1, z0, x3))
   MERGE#2(Cons(S(z0), x1), Cons(0, x3)) -> c6(COND_MERGE_YS_ZS_2(False, Cons(S(z0), x1), Cons(0, x3), S(z0), x1, 0, x3))
   MERGE#2(Cons(S(0), x1), Cons(S(z0), x3)) -> c6(COND_MERGE_YS_ZS_2(True, Cons(S(0), x1), Cons(S(z0), x3), S(0), x1, S(z0), x3), LEQ#2(S(0), S(z0)))
   MERGE#2(Cons(S(S(z0)), x1), Cons(S(0), x3)) -> c6(COND_MERGE_YS_ZS_2(False, Cons(S(S(z0)), x1), Cons(S(0), x3), S(S(z0)), x1, S(0), x3), LEQ#2(S(S(z0)), S(0)))
   MERGE#2(Cons(S(S(z0)), x1), Cons(S(S(z1)), x3)) -> c6(COND_MERGE_YS_ZS_2(leq#2(z0, z1), Cons(S(S(z0)), x1), Cons(S(S(z1)), x3), S(S(z0)), x1, S(S(z1)), x3), LEQ#2(S(S(z0)), S(S(z1))))
   MERGE#2(Cons(S(x0), x1), Cons(S(x2), x3)) -> c6(LEQ#2(S(x0), S(x2)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Nil))) -> c9(CONST_F#2(Cons(x0, Cons(x1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(Nil))), Cons(x0, Cons(x1, Nil))), Cons(drop#2(S(halve#1(0)), Cons(x0, Cons(x1, Nil))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Nil)), S(halve#1(length#1(Nil)))), HALVE#1(length#1(Nil)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Nil))) -> c9(CONST_F#2(Cons(x0, Cons(x1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(0)), Cons(x0, Cons(x1, Nil))), Cons(drop#2(S(halve#1(length#1(Nil))), Cons(x0, Cons(x1, Nil))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Nil)), S(halve#1(length#1(Nil)))), HALVE#1(length#1(Nil)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Cons(x2, x3)))) -> c9(CONST_F#2(Cons(x0, Cons(x1, Cons(x2, x3))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(S(length#1(x3)))), Cons(x0, Cons(x1, Cons(x2, x3)))), Cons(drop#2(S(halve#1(S(length#1(x3)))), Cons(x0, Cons(x1, Cons(x2, x3)))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Cons(x2, x3))), S(halve#1(length#1(Cons(x2, x3)))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, x3))), S(halve#1(length#1(Cons(x2, x3))))), HALVE#1(length#1(Cons(x2, x3))), LENGTH#1(Cons(x2, x3)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Cons(x2, Nil)))) -> c9(CONST_F#2(Cons(x0, Cons(x1, Cons(x2, Nil))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Cons(x2, Nil))), S(halve#1(S(0)))))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Cons(x2, Nil))), S(halve#1(length#1(Cons(x2, Nil)))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Nil))), S(halve#1(length#1(Cons(x2, Nil))))), HALVE#1(length#1(Cons(x2, Nil))), LENGTH#1(Cons(x2, Nil)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Cons(x2, Cons(z0, z1))))) -> c9(CONST_F#2(Cons(x0, Cons(x1, Cons(x2, Cons(z0, z1)))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Cons(x2, Cons(z0, z1)))), S(halve#1(S(S(length#1(z1)))))))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Cons(x2, Cons(z0, z1)))), S(halve#1(length#1(Cons(x2, Cons(z0, z1))))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Cons(z0, z1)))), S(halve#1(length#1(Cons(x2, Cons(z0, z1)))))), HALVE#1(length#1(Cons(x2, Cons(z0, z1)))), LENGTH#1(Cons(x2, Cons(z0, z1))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Cons(x2, x3)))) -> c9(MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Cons(x2, x3))), S(halve#1(length#1(Cons(x2, x3)))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, x3))), S(halve#1(length#1(Cons(x2, x3))))), HALVE#1(length#1(Cons(x2, x3))), LENGTH#1(Cons(x2, x3)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Nil))) -> c9(CONST_F#2(Cons(x0, Cons(x1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(0)), Cons(x0, Cons(x1, Nil))), Cons(drop#2(S(halve#1(0)), Cons(x0, Cons(x1, Nil))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Nil)), S(halve#1(length#1(Nil)))), HALVE#1(length#1(Nil)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Nil))) -> c9(CONST_F#2(Cons(x0, Cons(x1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Nil)), S(0)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Nil)), S(halve#1(length#1(Nil)))), HALVE#1(length#1(Nil)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> c9(CONST_F#2(Cons(z0, Cons(z1, z2)), Cons(dc#1(map, divisible, mergesort_zs_3, divide, const_f, take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2)))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(drop#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Nil))), DIVIDE_YS#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2)))), HALVE#1(length#1(z2)), LENGTH#1(z2))
   DIVIDE_YS#1(Cons(x0, Cons(x1, x2)), S(y11)) -> c(TAKE#2(S(y11), Cons(x0, Cons(x1, x2))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, x3))), S(y11)) -> c(TAKE#2(S(y11), Cons(x0, Cons(x1, Cons(x2, x3)))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Nil)), S(y10)) -> c(TAKE#2(S(y10), Cons(x0, Cons(x1, Nil))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Nil))), S(y7)) -> c(TAKE#2(S(y7), Cons(x0, Cons(x1, Cons(x2, Nil)))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4)))), S(y8)) -> c(TAKE#2(S(y8), Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4))))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, x2)), S(y11)) -> c1(DROP#2(S(y11), Cons(x0, Cons(x1, x2))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, x3))), S(y11)) -> c1(DROP#2(S(y11), Cons(x0, Cons(x1, Cons(x2, x3)))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Nil)), S(y10)) -> c1(DROP#2(S(y10), Cons(x0, Cons(x1, Nil))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Nil))), S(y7)) -> c1(DROP#2(S(y7), Cons(x0, Cons(x1, Cons(x2, Nil)))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4)))), S(y8)) -> c1(DROP#2(S(y8), Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4))))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> c9(CONST_F#2(Cons(z0, Cons(z1, z2)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(halve#1(length#1(z2)), Cons(z1, z2)), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Nil))), DIVIDE_YS#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2)))), HALVE#1(length#1(z2)), LENGTH#1(z2))
   COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(z2, z3), z4, Cons(0, y0), z6, z7) -> c2(MERGE#2(Cons(0, y0), Cons(z2, z3)))
   COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(0, z3), z4, Cons(S(y0), y1), z6, z7) -> c2(MERGE#2(Cons(S(y0), y1), Cons(0, z3)))
   COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(S(y1), z3), z4, Cons(S(0), y0), z6, z7) -> c2(MERGE#2(Cons(S(0), y0), Cons(S(y1), z3)))
   COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(S(0), z3), z4, Cons(S(S(y0)), y1), z6, z7) -> c2(MERGE#2(Cons(S(S(y0)), y1), Cons(S(0), z3)))
   COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(S(S(y2)), z3), z4, Cons(S(S(y0)), y1), z6, z7) -> c2(MERGE#2(Cons(S(S(y0)), y1), Cons(S(S(y2)), z3)))
   COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(S(y2), z3), z4, Cons(S(y0), y1), z6, z7) -> c2(MERGE#2(Cons(S(y0), y1), Cons(S(y2), z3)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, z3)))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Cons(z2, z3))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(Cons(z2, z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Cons(drop#2(S(halve#1(S(length#1(z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3)))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3))))), HALVE#1(S(length#1(z3))), LENGTH#1(Cons(z2, z3)))
   COND_MERGE_YS_ZS_2(False, Cons(S(x0), x1), Cons(0, x2), S(x0), x1, 0, x2) -> c3(MERGE#2(Cons(S(x0), x1), x2))
   COND_MERGE_YS_ZS_2(False, Cons(S(S(x0)), x1), Cons(S(0), x2), S(S(x0)), x1, S(0), x2) -> c3(MERGE#2(Cons(S(S(x0)), x1), x2))
   COND_MERGE_YS_ZS_2(False, Cons(S(S(x0)), x1), Cons(S(S(x2)), x3), S(S(x0)), x1, S(S(x2)), x3) -> c3(MERGE#2(Cons(S(S(x0)), x1), x3))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> c9(CONST_F#2(Cons(z0, Cons(z1, z2)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(Cons(z0, take#2(halve#1(length#1(z2)), Cons(z1, z2))), Cons(drop#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Nil))), DIVIDE_YS#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2)))), HALVE#1(length#1(z2)), LENGTH#1(z2))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, z3)))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Cons(z2, z3))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(S(length#1(z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Cons(drop#2(S(halve#1(length#1(Cons(z2, z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3)))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3))))), HALVE#1(S(length#1(z3))), LENGTH#1(Cons(z2, z3)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> c9(MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Nil))), DIVIDE_YS#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2)))))
K tuples:none
Defined Rule Symbols:   leq#2_2, map#2_2, divide_ys#1_2, halve#1_1, length#1_1, take#2_2, drop#2_2, dc#1_6, const_f#2_2, merge#2_2, cond_merge_ys_zs_2_7

Defined Pair Symbols:   DROP#2_2, TAKE#2_2, HALVE#1_1, CONST_F#2_2, LEQ#2_2, LENGTH#1_1, MAP#2_2, MERGE#2_2, DC#1_6, DIVIDE_YS#1_2, COND_MERGE_YS_ZS_2_7

Compound Symbols:   c12_1, c15_1, c18_1, c19_1, c22_1, c24_1, c26_1, c27_1, c6_1, c6_2, c9_4, c9_5, c_1, c1_1, c2_1, c3_1, c9_2


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(121) CdtRewritingProof (BOTH BOUNDS(ID, ID))
Used rewriting to replace DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Nil))) -> c9(CONST_F#2(Cons(x0, Cons(x1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(Nil))), Cons(x0, Cons(x1, Nil))), Cons(drop#2(S(halve#1(0)), Cons(x0, Cons(x1, Nil))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Nil)), S(halve#1(length#1(Nil)))), HALVE#1(length#1(Nil))) by DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Nil))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(Nil))), Cons(z0, Cons(z1, Nil))), Cons(drop#2(S(halve#1(0)), Cons(z0, Cons(z1, Nil))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil)))), HALVE#1(0))
----------------------------------------

(122)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   leq#2(0, z0) -> True
   leq#2(S(z0), 0) -> False
   leq#2(S(z0), S(z1)) -> leq#2(z0, z1)
   map#2(dc(z0, z1, z2, z3, z4), Nil) -> Nil
   map#2(dc(z0, z1, z2, z3, z4), Cons(z5, z6)) -> Cons(dc#1(z0, z1, z2, z3, z4, z5), map#2(dc(z0, z1, z2, z3, z4), z6))
   divide_ys#1(z0, z1) -> Cons(take#2(z1, z0), Cons(drop#2(z1, z0), Nil))
   halve#1(0) -> 0
   halve#1(S(0)) -> S(0)
   halve#1(S(S(z0))) -> S(halve#1(z0))
   length#1(Nil) -> 0
   length#1(Cons(z0, z1)) -> S(length#1(z1))
   take#2(0, z0) -> Nil
   take#2(S(0), Nil) -> Cons(bot[0], Nil)
   take#2(S(z0), Cons(z1, z2)) -> Cons(z1, take#2(z0, z2))
   drop#2(0, z0) -> z0
   drop#2(S(0), Nil) -> bot[1]
   drop#2(S(z0), Cons(z1, z2)) -> drop#2(z0, z2)
   dc#1(map, divisible, mergesort_zs_3, divide, const_f, Nil) -> Nil
   dc#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Nil)) -> Cons(z0, Nil)
   dc#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> const_f#2(Cons(z0, Cons(z1, z2)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2))))))
   const_f#2(z0, Cons(z1, Cons(z2, z3))) -> merge#2(z1, z2)
   merge#2(Nil, z0) -> z0
   merge#2(Cons(z0, z1), Nil) -> Cons(z0, z1)
   merge#2(Cons(z0, z1), Cons(z2, z3)) -> cond_merge_ys_zs_2(leq#2(z0, z2), Cons(z0, z1), Cons(z2, z3), z0, z1, z2, z3)
   cond_merge_ys_zs_2(True, Cons(z0, z1), Cons(z2, z3), z4, z5, z6, z7) -> Cons(z4, merge#2(z5, Cons(z2, z3)))
   cond_merge_ys_zs_2(False, Cons(z0, z1), Cons(z2, z3), z4, z5, z6, z7) -> Cons(z6, merge#2(Cons(z0, z1), z7))
Tuples:
   DROP#2(S(z0), Cons(z1, z2)) -> c12(DROP#2(z0, z2))
   TAKE#2(S(z0), Cons(z1, z2)) -> c15(TAKE#2(z0, z2))
   HALVE#1(S(S(z0))) -> c18(HALVE#1(z0))
   CONST_F#2(z0, Cons(z1, Cons(z2, z3))) -> c19(MERGE#2(z1, z2))
   LEQ#2(S(z0), S(z1)) -> c22(LEQ#2(z0, z1))
   LENGTH#1(Cons(z0, z1)) -> c24(LENGTH#1(z1))
   MAP#2(dc(z0, z1, z2, z3, z4), Cons(z5, z6)) -> c26(DC#1(z0, z1, z2, z3, z4, z5))
   MAP#2(dc(z0, z1, z2, z3, z4), Cons(z5, z6)) -> c27(MAP#2(dc(z0, z1, z2, z3, z4), z6))
   MERGE#2(Cons(0, x1), Cons(z0, x3)) -> c6(COND_MERGE_YS_ZS_2(True, Cons(0, x1), Cons(z0, x3), 0, x1, z0, x3))
   MERGE#2(Cons(S(z0), x1), Cons(0, x3)) -> c6(COND_MERGE_YS_ZS_2(False, Cons(S(z0), x1), Cons(0, x3), S(z0), x1, 0, x3))
   MERGE#2(Cons(S(0), x1), Cons(S(z0), x3)) -> c6(COND_MERGE_YS_ZS_2(True, Cons(S(0), x1), Cons(S(z0), x3), S(0), x1, S(z0), x3), LEQ#2(S(0), S(z0)))
   MERGE#2(Cons(S(S(z0)), x1), Cons(S(0), x3)) -> c6(COND_MERGE_YS_ZS_2(False, Cons(S(S(z0)), x1), Cons(S(0), x3), S(S(z0)), x1, S(0), x3), LEQ#2(S(S(z0)), S(0)))
   MERGE#2(Cons(S(S(z0)), x1), Cons(S(S(z1)), x3)) -> c6(COND_MERGE_YS_ZS_2(leq#2(z0, z1), Cons(S(S(z0)), x1), Cons(S(S(z1)), x3), S(S(z0)), x1, S(S(z1)), x3), LEQ#2(S(S(z0)), S(S(z1))))
   MERGE#2(Cons(S(x0), x1), Cons(S(x2), x3)) -> c6(LEQ#2(S(x0), S(x2)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Nil))) -> c9(CONST_F#2(Cons(x0, Cons(x1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(0)), Cons(x0, Cons(x1, Nil))), Cons(drop#2(S(halve#1(length#1(Nil))), Cons(x0, Cons(x1, Nil))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Nil)), S(halve#1(length#1(Nil)))), HALVE#1(length#1(Nil)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Cons(x2, x3)))) -> c9(CONST_F#2(Cons(x0, Cons(x1, Cons(x2, x3))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(S(length#1(x3)))), Cons(x0, Cons(x1, Cons(x2, x3)))), Cons(drop#2(S(halve#1(S(length#1(x3)))), Cons(x0, Cons(x1, Cons(x2, x3)))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Cons(x2, x3))), S(halve#1(length#1(Cons(x2, x3)))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, x3))), S(halve#1(length#1(Cons(x2, x3))))), HALVE#1(length#1(Cons(x2, x3))), LENGTH#1(Cons(x2, x3)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Cons(x2, Nil)))) -> c9(CONST_F#2(Cons(x0, Cons(x1, Cons(x2, Nil))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Cons(x2, Nil))), S(halve#1(S(0)))))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Cons(x2, Nil))), S(halve#1(length#1(Cons(x2, Nil)))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Nil))), S(halve#1(length#1(Cons(x2, Nil))))), HALVE#1(length#1(Cons(x2, Nil))), LENGTH#1(Cons(x2, Nil)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Cons(x2, Cons(z0, z1))))) -> c9(CONST_F#2(Cons(x0, Cons(x1, Cons(x2, Cons(z0, z1)))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Cons(x2, Cons(z0, z1)))), S(halve#1(S(S(length#1(z1)))))))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Cons(x2, Cons(z0, z1)))), S(halve#1(length#1(Cons(x2, Cons(z0, z1))))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Cons(z0, z1)))), S(halve#1(length#1(Cons(x2, Cons(z0, z1)))))), HALVE#1(length#1(Cons(x2, Cons(z0, z1)))), LENGTH#1(Cons(x2, Cons(z0, z1))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Cons(x2, x3)))) -> c9(MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Cons(x2, x3))), S(halve#1(length#1(Cons(x2, x3)))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, x3))), S(halve#1(length#1(Cons(x2, x3))))), HALVE#1(length#1(Cons(x2, x3))), LENGTH#1(Cons(x2, x3)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Nil))) -> c9(CONST_F#2(Cons(x0, Cons(x1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(0)), Cons(x0, Cons(x1, Nil))), Cons(drop#2(S(halve#1(0)), Cons(x0, Cons(x1, Nil))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Nil)), S(halve#1(length#1(Nil)))), HALVE#1(length#1(Nil)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Nil))) -> c9(CONST_F#2(Cons(x0, Cons(x1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Nil)), S(0)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Nil)), S(halve#1(length#1(Nil)))), HALVE#1(length#1(Nil)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> c9(CONST_F#2(Cons(z0, Cons(z1, z2)), Cons(dc#1(map, divisible, mergesort_zs_3, divide, const_f, take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2)))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(drop#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Nil))), DIVIDE_YS#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2)))), HALVE#1(length#1(z2)), LENGTH#1(z2))
   DIVIDE_YS#1(Cons(x0, Cons(x1, x2)), S(y11)) -> c(TAKE#2(S(y11), Cons(x0, Cons(x1, x2))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, x3))), S(y11)) -> c(TAKE#2(S(y11), Cons(x0, Cons(x1, Cons(x2, x3)))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Nil)), S(y10)) -> c(TAKE#2(S(y10), Cons(x0, Cons(x1, Nil))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Nil))), S(y7)) -> c(TAKE#2(S(y7), Cons(x0, Cons(x1, Cons(x2, Nil)))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4)))), S(y8)) -> c(TAKE#2(S(y8), Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4))))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, x2)), S(y11)) -> c1(DROP#2(S(y11), Cons(x0, Cons(x1, x2))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, x3))), S(y11)) -> c1(DROP#2(S(y11), Cons(x0, Cons(x1, Cons(x2, x3)))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Nil)), S(y10)) -> c1(DROP#2(S(y10), Cons(x0, Cons(x1, Nil))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Nil))), S(y7)) -> c1(DROP#2(S(y7), Cons(x0, Cons(x1, Cons(x2, Nil)))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4)))), S(y8)) -> c1(DROP#2(S(y8), Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4))))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> c9(CONST_F#2(Cons(z0, Cons(z1, z2)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(halve#1(length#1(z2)), Cons(z1, z2)), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Nil))), DIVIDE_YS#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2)))), HALVE#1(length#1(z2)), LENGTH#1(z2))
   COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(z2, z3), z4, Cons(0, y0), z6, z7) -> c2(MERGE#2(Cons(0, y0), Cons(z2, z3)))
   COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(0, z3), z4, Cons(S(y0), y1), z6, z7) -> c2(MERGE#2(Cons(S(y0), y1), Cons(0, z3)))
   COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(S(y1), z3), z4, Cons(S(0), y0), z6, z7) -> c2(MERGE#2(Cons(S(0), y0), Cons(S(y1), z3)))
   COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(S(0), z3), z4, Cons(S(S(y0)), y1), z6, z7) -> c2(MERGE#2(Cons(S(S(y0)), y1), Cons(S(0), z3)))
   COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(S(S(y2)), z3), z4, Cons(S(S(y0)), y1), z6, z7) -> c2(MERGE#2(Cons(S(S(y0)), y1), Cons(S(S(y2)), z3)))
   COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(S(y2), z3), z4, Cons(S(y0), y1), z6, z7) -> c2(MERGE#2(Cons(S(y0), y1), Cons(S(y2), z3)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, z3)))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Cons(z2, z3))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(Cons(z2, z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Cons(drop#2(S(halve#1(S(length#1(z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3)))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3))))), HALVE#1(S(length#1(z3))), LENGTH#1(Cons(z2, z3)))
   COND_MERGE_YS_ZS_2(False, Cons(S(x0), x1), Cons(0, x2), S(x0), x1, 0, x2) -> c3(MERGE#2(Cons(S(x0), x1), x2))
   COND_MERGE_YS_ZS_2(False, Cons(S(S(x0)), x1), Cons(S(0), x2), S(S(x0)), x1, S(0), x2) -> c3(MERGE#2(Cons(S(S(x0)), x1), x2))
   COND_MERGE_YS_ZS_2(False, Cons(S(S(x0)), x1), Cons(S(S(x2)), x3), S(S(x0)), x1, S(S(x2)), x3) -> c3(MERGE#2(Cons(S(S(x0)), x1), x3))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> c9(CONST_F#2(Cons(z0, Cons(z1, z2)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(Cons(z0, take#2(halve#1(length#1(z2)), Cons(z1, z2))), Cons(drop#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Nil))), DIVIDE_YS#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2)))), HALVE#1(length#1(z2)), LENGTH#1(z2))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, z3)))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Cons(z2, z3))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(S(length#1(z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Cons(drop#2(S(halve#1(length#1(Cons(z2, z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3)))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3))))), HALVE#1(S(length#1(z3))), LENGTH#1(Cons(z2, z3)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> c9(MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Nil))), DIVIDE_YS#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2)))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Nil))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(Nil))), Cons(z0, Cons(z1, Nil))), Cons(drop#2(S(halve#1(0)), Cons(z0, Cons(z1, Nil))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil)))), HALVE#1(0))
S tuples:
   DROP#2(S(z0), Cons(z1, z2)) -> c12(DROP#2(z0, z2))
   TAKE#2(S(z0), Cons(z1, z2)) -> c15(TAKE#2(z0, z2))
   HALVE#1(S(S(z0))) -> c18(HALVE#1(z0))
   CONST_F#2(z0, Cons(z1, Cons(z2, z3))) -> c19(MERGE#2(z1, z2))
   LEQ#2(S(z0), S(z1)) -> c22(LEQ#2(z0, z1))
   LENGTH#1(Cons(z0, z1)) -> c24(LENGTH#1(z1))
   MAP#2(dc(z0, z1, z2, z3, z4), Cons(z5, z6)) -> c26(DC#1(z0, z1, z2, z3, z4, z5))
   MAP#2(dc(z0, z1, z2, z3, z4), Cons(z5, z6)) -> c27(MAP#2(dc(z0, z1, z2, z3, z4), z6))
   MERGE#2(Cons(0, x1), Cons(z0, x3)) -> c6(COND_MERGE_YS_ZS_2(True, Cons(0, x1), Cons(z0, x3), 0, x1, z0, x3))
   MERGE#2(Cons(S(z0), x1), Cons(0, x3)) -> c6(COND_MERGE_YS_ZS_2(False, Cons(S(z0), x1), Cons(0, x3), S(z0), x1, 0, x3))
   MERGE#2(Cons(S(0), x1), Cons(S(z0), x3)) -> c6(COND_MERGE_YS_ZS_2(True, Cons(S(0), x1), Cons(S(z0), x3), S(0), x1, S(z0), x3), LEQ#2(S(0), S(z0)))
   MERGE#2(Cons(S(S(z0)), x1), Cons(S(0), x3)) -> c6(COND_MERGE_YS_ZS_2(False, Cons(S(S(z0)), x1), Cons(S(0), x3), S(S(z0)), x1, S(0), x3), LEQ#2(S(S(z0)), S(0)))
   MERGE#2(Cons(S(S(z0)), x1), Cons(S(S(z1)), x3)) -> c6(COND_MERGE_YS_ZS_2(leq#2(z0, z1), Cons(S(S(z0)), x1), Cons(S(S(z1)), x3), S(S(z0)), x1, S(S(z1)), x3), LEQ#2(S(S(z0)), S(S(z1))))
   MERGE#2(Cons(S(x0), x1), Cons(S(x2), x3)) -> c6(LEQ#2(S(x0), S(x2)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Nil))) -> c9(CONST_F#2(Cons(x0, Cons(x1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(0)), Cons(x0, Cons(x1, Nil))), Cons(drop#2(S(halve#1(length#1(Nil))), Cons(x0, Cons(x1, Nil))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Nil)), S(halve#1(length#1(Nil)))), HALVE#1(length#1(Nil)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Cons(x2, x3)))) -> c9(CONST_F#2(Cons(x0, Cons(x1, Cons(x2, x3))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(S(length#1(x3)))), Cons(x0, Cons(x1, Cons(x2, x3)))), Cons(drop#2(S(halve#1(S(length#1(x3)))), Cons(x0, Cons(x1, Cons(x2, x3)))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Cons(x2, x3))), S(halve#1(length#1(Cons(x2, x3)))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, x3))), S(halve#1(length#1(Cons(x2, x3))))), HALVE#1(length#1(Cons(x2, x3))), LENGTH#1(Cons(x2, x3)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Cons(x2, Nil)))) -> c9(CONST_F#2(Cons(x0, Cons(x1, Cons(x2, Nil))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Cons(x2, Nil))), S(halve#1(S(0)))))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Cons(x2, Nil))), S(halve#1(length#1(Cons(x2, Nil)))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Nil))), S(halve#1(length#1(Cons(x2, Nil))))), HALVE#1(length#1(Cons(x2, Nil))), LENGTH#1(Cons(x2, Nil)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Cons(x2, Cons(z0, z1))))) -> c9(CONST_F#2(Cons(x0, Cons(x1, Cons(x2, Cons(z0, z1)))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Cons(x2, Cons(z0, z1)))), S(halve#1(S(S(length#1(z1)))))))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Cons(x2, Cons(z0, z1)))), S(halve#1(length#1(Cons(x2, Cons(z0, z1))))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Cons(z0, z1)))), S(halve#1(length#1(Cons(x2, Cons(z0, z1)))))), HALVE#1(length#1(Cons(x2, Cons(z0, z1)))), LENGTH#1(Cons(x2, Cons(z0, z1))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Cons(x2, x3)))) -> c9(MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Cons(x2, x3))), S(halve#1(length#1(Cons(x2, x3)))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, x3))), S(halve#1(length#1(Cons(x2, x3))))), HALVE#1(length#1(Cons(x2, x3))), LENGTH#1(Cons(x2, x3)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Nil))) -> c9(CONST_F#2(Cons(x0, Cons(x1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(0)), Cons(x0, Cons(x1, Nil))), Cons(drop#2(S(halve#1(0)), Cons(x0, Cons(x1, Nil))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Nil)), S(halve#1(length#1(Nil)))), HALVE#1(length#1(Nil)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Nil))) -> c9(CONST_F#2(Cons(x0, Cons(x1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Nil)), S(0)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Nil)), S(halve#1(length#1(Nil)))), HALVE#1(length#1(Nil)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> c9(CONST_F#2(Cons(z0, Cons(z1, z2)), Cons(dc#1(map, divisible, mergesort_zs_3, divide, const_f, take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2)))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(drop#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Nil))), DIVIDE_YS#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2)))), HALVE#1(length#1(z2)), LENGTH#1(z2))
   DIVIDE_YS#1(Cons(x0, Cons(x1, x2)), S(y11)) -> c(TAKE#2(S(y11), Cons(x0, Cons(x1, x2))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, x3))), S(y11)) -> c(TAKE#2(S(y11), Cons(x0, Cons(x1, Cons(x2, x3)))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Nil)), S(y10)) -> c(TAKE#2(S(y10), Cons(x0, Cons(x1, Nil))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Nil))), S(y7)) -> c(TAKE#2(S(y7), Cons(x0, Cons(x1, Cons(x2, Nil)))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4)))), S(y8)) -> c(TAKE#2(S(y8), Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4))))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, x2)), S(y11)) -> c1(DROP#2(S(y11), Cons(x0, Cons(x1, x2))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, x3))), S(y11)) -> c1(DROP#2(S(y11), Cons(x0, Cons(x1, Cons(x2, x3)))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Nil)), S(y10)) -> c1(DROP#2(S(y10), Cons(x0, Cons(x1, Nil))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Nil))), S(y7)) -> c1(DROP#2(S(y7), Cons(x0, Cons(x1, Cons(x2, Nil)))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4)))), S(y8)) -> c1(DROP#2(S(y8), Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4))))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> c9(CONST_F#2(Cons(z0, Cons(z1, z2)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(halve#1(length#1(z2)), Cons(z1, z2)), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Nil))), DIVIDE_YS#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2)))), HALVE#1(length#1(z2)), LENGTH#1(z2))
   COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(z2, z3), z4, Cons(0, y0), z6, z7) -> c2(MERGE#2(Cons(0, y0), Cons(z2, z3)))
   COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(0, z3), z4, Cons(S(y0), y1), z6, z7) -> c2(MERGE#2(Cons(S(y0), y1), Cons(0, z3)))
   COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(S(y1), z3), z4, Cons(S(0), y0), z6, z7) -> c2(MERGE#2(Cons(S(0), y0), Cons(S(y1), z3)))
   COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(S(0), z3), z4, Cons(S(S(y0)), y1), z6, z7) -> c2(MERGE#2(Cons(S(S(y0)), y1), Cons(S(0), z3)))
   COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(S(S(y2)), z3), z4, Cons(S(S(y0)), y1), z6, z7) -> c2(MERGE#2(Cons(S(S(y0)), y1), Cons(S(S(y2)), z3)))
   COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(S(y2), z3), z4, Cons(S(y0), y1), z6, z7) -> c2(MERGE#2(Cons(S(y0), y1), Cons(S(y2), z3)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, z3)))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Cons(z2, z3))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(Cons(z2, z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Cons(drop#2(S(halve#1(S(length#1(z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3)))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3))))), HALVE#1(S(length#1(z3))), LENGTH#1(Cons(z2, z3)))
   COND_MERGE_YS_ZS_2(False, Cons(S(x0), x1), Cons(0, x2), S(x0), x1, 0, x2) -> c3(MERGE#2(Cons(S(x0), x1), x2))
   COND_MERGE_YS_ZS_2(False, Cons(S(S(x0)), x1), Cons(S(0), x2), S(S(x0)), x1, S(0), x2) -> c3(MERGE#2(Cons(S(S(x0)), x1), x2))
   COND_MERGE_YS_ZS_2(False, Cons(S(S(x0)), x1), Cons(S(S(x2)), x3), S(S(x0)), x1, S(S(x2)), x3) -> c3(MERGE#2(Cons(S(S(x0)), x1), x3))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> c9(CONST_F#2(Cons(z0, Cons(z1, z2)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(Cons(z0, take#2(halve#1(length#1(z2)), Cons(z1, z2))), Cons(drop#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Nil))), DIVIDE_YS#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2)))), HALVE#1(length#1(z2)), LENGTH#1(z2))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, z3)))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Cons(z2, z3))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(S(length#1(z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Cons(drop#2(S(halve#1(length#1(Cons(z2, z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3)))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3))))), HALVE#1(S(length#1(z3))), LENGTH#1(Cons(z2, z3)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> c9(MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Nil))), DIVIDE_YS#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2)))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Nil))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(Nil))), Cons(z0, Cons(z1, Nil))), Cons(drop#2(S(halve#1(0)), Cons(z0, Cons(z1, Nil))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil)))), HALVE#1(0))
K tuples:none
Defined Rule Symbols:   leq#2_2, map#2_2, divide_ys#1_2, halve#1_1, length#1_1, take#2_2, drop#2_2, dc#1_6, const_f#2_2, merge#2_2, cond_merge_ys_zs_2_7

Defined Pair Symbols:   DROP#2_2, TAKE#2_2, HALVE#1_1, CONST_F#2_2, LEQ#2_2, LENGTH#1_1, MAP#2_2, MERGE#2_2, DC#1_6, DIVIDE_YS#1_2, COND_MERGE_YS_ZS_2_7

Compound Symbols:   c12_1, c15_1, c18_1, c19_1, c22_1, c24_1, c26_1, c27_1, c6_1, c6_2, c9_4, c9_5, c_1, c1_1, c2_1, c3_1, c9_2


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

(124)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   leq#2(0, z0) -> True
   leq#2(S(z0), 0) -> False
   leq#2(S(z0), S(z1)) -> leq#2(z0, z1)
   map#2(dc(z0, z1, z2, z3, z4), Nil) -> Nil
   map#2(dc(z0, z1, z2, z3, z4), Cons(z5, z6)) -> Cons(dc#1(z0, z1, z2, z3, z4, z5), map#2(dc(z0, z1, z2, z3, z4), z6))
   divide_ys#1(z0, z1) -> Cons(take#2(z1, z0), Cons(drop#2(z1, z0), Nil))
   halve#1(0) -> 0
   halve#1(S(0)) -> S(0)
   halve#1(S(S(z0))) -> S(halve#1(z0))
   length#1(Nil) -> 0
   length#1(Cons(z0, z1)) -> S(length#1(z1))
   take#2(0, z0) -> Nil
   take#2(S(0), Nil) -> Cons(bot[0], Nil)
   take#2(S(z0), Cons(z1, z2)) -> Cons(z1, take#2(z0, z2))
   drop#2(0, z0) -> z0
   drop#2(S(0), Nil) -> bot[1]
   drop#2(S(z0), Cons(z1, z2)) -> drop#2(z0, z2)
   dc#1(map, divisible, mergesort_zs_3, divide, const_f, Nil) -> Nil
   dc#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Nil)) -> Cons(z0, Nil)
   dc#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> const_f#2(Cons(z0, Cons(z1, z2)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2))))))
   const_f#2(z0, Cons(z1, Cons(z2, z3))) -> merge#2(z1, z2)
   merge#2(Nil, z0) -> z0
   merge#2(Cons(z0, z1), Nil) -> Cons(z0, z1)
   merge#2(Cons(z0, z1), Cons(z2, z3)) -> cond_merge_ys_zs_2(leq#2(z0, z2), Cons(z0, z1), Cons(z2, z3), z0, z1, z2, z3)
   cond_merge_ys_zs_2(True, Cons(z0, z1), Cons(z2, z3), z4, z5, z6, z7) -> Cons(z4, merge#2(z5, Cons(z2, z3)))
   cond_merge_ys_zs_2(False, Cons(z0, z1), Cons(z2, z3), z4, z5, z6, z7) -> Cons(z6, merge#2(Cons(z0, z1), z7))
Tuples:
   DROP#2(S(z0), Cons(z1, z2)) -> c12(DROP#2(z0, z2))
   TAKE#2(S(z0), Cons(z1, z2)) -> c15(TAKE#2(z0, z2))
   HALVE#1(S(S(z0))) -> c18(HALVE#1(z0))
   CONST_F#2(z0, Cons(z1, Cons(z2, z3))) -> c19(MERGE#2(z1, z2))
   LEQ#2(S(z0), S(z1)) -> c22(LEQ#2(z0, z1))
   LENGTH#1(Cons(z0, z1)) -> c24(LENGTH#1(z1))
   MAP#2(dc(z0, z1, z2, z3, z4), Cons(z5, z6)) -> c26(DC#1(z0, z1, z2, z3, z4, z5))
   MAP#2(dc(z0, z1, z2, z3, z4), Cons(z5, z6)) -> c27(MAP#2(dc(z0, z1, z2, z3, z4), z6))
   MERGE#2(Cons(0, x1), Cons(z0, x3)) -> c6(COND_MERGE_YS_ZS_2(True, Cons(0, x1), Cons(z0, x3), 0, x1, z0, x3))
   MERGE#2(Cons(S(z0), x1), Cons(0, x3)) -> c6(COND_MERGE_YS_ZS_2(False, Cons(S(z0), x1), Cons(0, x3), S(z0), x1, 0, x3))
   MERGE#2(Cons(S(0), x1), Cons(S(z0), x3)) -> c6(COND_MERGE_YS_ZS_2(True, Cons(S(0), x1), Cons(S(z0), x3), S(0), x1, S(z0), x3), LEQ#2(S(0), S(z0)))
   MERGE#2(Cons(S(S(z0)), x1), Cons(S(0), x3)) -> c6(COND_MERGE_YS_ZS_2(False, Cons(S(S(z0)), x1), Cons(S(0), x3), S(S(z0)), x1, S(0), x3), LEQ#2(S(S(z0)), S(0)))
   MERGE#2(Cons(S(S(z0)), x1), Cons(S(S(z1)), x3)) -> c6(COND_MERGE_YS_ZS_2(leq#2(z0, z1), Cons(S(S(z0)), x1), Cons(S(S(z1)), x3), S(S(z0)), x1, S(S(z1)), x3), LEQ#2(S(S(z0)), S(S(z1))))
   MERGE#2(Cons(S(x0), x1), Cons(S(x2), x3)) -> c6(LEQ#2(S(x0), S(x2)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Nil))) -> c9(CONST_F#2(Cons(x0, Cons(x1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(0)), Cons(x0, Cons(x1, Nil))), Cons(drop#2(S(halve#1(length#1(Nil))), Cons(x0, Cons(x1, Nil))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Nil)), S(halve#1(length#1(Nil)))), HALVE#1(length#1(Nil)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Cons(x2, x3)))) -> c9(CONST_F#2(Cons(x0, Cons(x1, Cons(x2, x3))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(S(length#1(x3)))), Cons(x0, Cons(x1, Cons(x2, x3)))), Cons(drop#2(S(halve#1(S(length#1(x3)))), Cons(x0, Cons(x1, Cons(x2, x3)))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Cons(x2, x3))), S(halve#1(length#1(Cons(x2, x3)))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, x3))), S(halve#1(length#1(Cons(x2, x3))))), HALVE#1(length#1(Cons(x2, x3))), LENGTH#1(Cons(x2, x3)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Cons(x2, Nil)))) -> c9(CONST_F#2(Cons(x0, Cons(x1, Cons(x2, Nil))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Cons(x2, Nil))), S(halve#1(S(0)))))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Cons(x2, Nil))), S(halve#1(length#1(Cons(x2, Nil)))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Nil))), S(halve#1(length#1(Cons(x2, Nil))))), HALVE#1(length#1(Cons(x2, Nil))), LENGTH#1(Cons(x2, Nil)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Cons(x2, Cons(z0, z1))))) -> c9(CONST_F#2(Cons(x0, Cons(x1, Cons(x2, Cons(z0, z1)))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Cons(x2, Cons(z0, z1)))), S(halve#1(S(S(length#1(z1)))))))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Cons(x2, Cons(z0, z1)))), S(halve#1(length#1(Cons(x2, Cons(z0, z1))))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Cons(z0, z1)))), S(halve#1(length#1(Cons(x2, Cons(z0, z1)))))), HALVE#1(length#1(Cons(x2, Cons(z0, z1)))), LENGTH#1(Cons(x2, Cons(z0, z1))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Cons(x2, x3)))) -> c9(MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Cons(x2, x3))), S(halve#1(length#1(Cons(x2, x3)))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, x3))), S(halve#1(length#1(Cons(x2, x3))))), HALVE#1(length#1(Cons(x2, x3))), LENGTH#1(Cons(x2, x3)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Nil))) -> c9(CONST_F#2(Cons(x0, Cons(x1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(0)), Cons(x0, Cons(x1, Nil))), Cons(drop#2(S(halve#1(0)), Cons(x0, Cons(x1, Nil))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Nil)), S(halve#1(length#1(Nil)))), HALVE#1(length#1(Nil)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Nil))) -> c9(CONST_F#2(Cons(x0, Cons(x1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Nil)), S(0)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Nil)), S(halve#1(length#1(Nil)))), HALVE#1(length#1(Nil)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> c9(CONST_F#2(Cons(z0, Cons(z1, z2)), Cons(dc#1(map, divisible, mergesort_zs_3, divide, const_f, take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2)))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(drop#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Nil))), DIVIDE_YS#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2)))), HALVE#1(length#1(z2)), LENGTH#1(z2))
   DIVIDE_YS#1(Cons(x0, Cons(x1, x2)), S(y11)) -> c(TAKE#2(S(y11), Cons(x0, Cons(x1, x2))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, x3))), S(y11)) -> c(TAKE#2(S(y11), Cons(x0, Cons(x1, Cons(x2, x3)))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Nil)), S(y10)) -> c(TAKE#2(S(y10), Cons(x0, Cons(x1, Nil))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Nil))), S(y7)) -> c(TAKE#2(S(y7), Cons(x0, Cons(x1, Cons(x2, Nil)))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4)))), S(y8)) -> c(TAKE#2(S(y8), Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4))))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, x2)), S(y11)) -> c1(DROP#2(S(y11), Cons(x0, Cons(x1, x2))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, x3))), S(y11)) -> c1(DROP#2(S(y11), Cons(x0, Cons(x1, Cons(x2, x3)))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Nil)), S(y10)) -> c1(DROP#2(S(y10), Cons(x0, Cons(x1, Nil))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Nil))), S(y7)) -> c1(DROP#2(S(y7), Cons(x0, Cons(x1, Cons(x2, Nil)))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4)))), S(y8)) -> c1(DROP#2(S(y8), Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4))))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> c9(CONST_F#2(Cons(z0, Cons(z1, z2)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(halve#1(length#1(z2)), Cons(z1, z2)), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Nil))), DIVIDE_YS#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2)))), HALVE#1(length#1(z2)), LENGTH#1(z2))
   COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(z2, z3), z4, Cons(0, y0), z6, z7) -> c2(MERGE#2(Cons(0, y0), Cons(z2, z3)))
   COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(0, z3), z4, Cons(S(y0), y1), z6, z7) -> c2(MERGE#2(Cons(S(y0), y1), Cons(0, z3)))
   COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(S(y1), z3), z4, Cons(S(0), y0), z6, z7) -> c2(MERGE#2(Cons(S(0), y0), Cons(S(y1), z3)))
   COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(S(0), z3), z4, Cons(S(S(y0)), y1), z6, z7) -> c2(MERGE#2(Cons(S(S(y0)), y1), Cons(S(0), z3)))
   COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(S(S(y2)), z3), z4, Cons(S(S(y0)), y1), z6, z7) -> c2(MERGE#2(Cons(S(S(y0)), y1), Cons(S(S(y2)), z3)))
   COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(S(y2), z3), z4, Cons(S(y0), y1), z6, z7) -> c2(MERGE#2(Cons(S(y0), y1), Cons(S(y2), z3)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, z3)))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Cons(z2, z3))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(Cons(z2, z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Cons(drop#2(S(halve#1(S(length#1(z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3)))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3))))), HALVE#1(S(length#1(z3))), LENGTH#1(Cons(z2, z3)))
   COND_MERGE_YS_ZS_2(False, Cons(S(x0), x1), Cons(0, x2), S(x0), x1, 0, x2) -> c3(MERGE#2(Cons(S(x0), x1), x2))
   COND_MERGE_YS_ZS_2(False, Cons(S(S(x0)), x1), Cons(S(0), x2), S(S(x0)), x1, S(0), x2) -> c3(MERGE#2(Cons(S(S(x0)), x1), x2))
   COND_MERGE_YS_ZS_2(False, Cons(S(S(x0)), x1), Cons(S(S(x2)), x3), S(S(x0)), x1, S(S(x2)), x3) -> c3(MERGE#2(Cons(S(S(x0)), x1), x3))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> c9(CONST_F#2(Cons(z0, Cons(z1, z2)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(Cons(z0, take#2(halve#1(length#1(z2)), Cons(z1, z2))), Cons(drop#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Nil))), DIVIDE_YS#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2)))), HALVE#1(length#1(z2)), LENGTH#1(z2))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, z3)))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Cons(z2, z3))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(S(length#1(z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Cons(drop#2(S(halve#1(length#1(Cons(z2, z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3)))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3))))), HALVE#1(S(length#1(z3))), LENGTH#1(Cons(z2, z3)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> c9(MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Nil))), DIVIDE_YS#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2)))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Nil))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(Nil))), Cons(z0, Cons(z1, Nil))), Cons(drop#2(S(halve#1(0)), Cons(z0, Cons(z1, Nil))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil)))))
S tuples:
   DROP#2(S(z0), Cons(z1, z2)) -> c12(DROP#2(z0, z2))
   TAKE#2(S(z0), Cons(z1, z2)) -> c15(TAKE#2(z0, z2))
   HALVE#1(S(S(z0))) -> c18(HALVE#1(z0))
   CONST_F#2(z0, Cons(z1, Cons(z2, z3))) -> c19(MERGE#2(z1, z2))
   LEQ#2(S(z0), S(z1)) -> c22(LEQ#2(z0, z1))
   LENGTH#1(Cons(z0, z1)) -> c24(LENGTH#1(z1))
   MAP#2(dc(z0, z1, z2, z3, z4), Cons(z5, z6)) -> c26(DC#1(z0, z1, z2, z3, z4, z5))
   MAP#2(dc(z0, z1, z2, z3, z4), Cons(z5, z6)) -> c27(MAP#2(dc(z0, z1, z2, z3, z4), z6))
   MERGE#2(Cons(0, x1), Cons(z0, x3)) -> c6(COND_MERGE_YS_ZS_2(True, Cons(0, x1), Cons(z0, x3), 0, x1, z0, x3))
   MERGE#2(Cons(S(z0), x1), Cons(0, x3)) -> c6(COND_MERGE_YS_ZS_2(False, Cons(S(z0), x1), Cons(0, x3), S(z0), x1, 0, x3))
   MERGE#2(Cons(S(0), x1), Cons(S(z0), x3)) -> c6(COND_MERGE_YS_ZS_2(True, Cons(S(0), x1), Cons(S(z0), x3), S(0), x1, S(z0), x3), LEQ#2(S(0), S(z0)))
   MERGE#2(Cons(S(S(z0)), x1), Cons(S(0), x3)) -> c6(COND_MERGE_YS_ZS_2(False, Cons(S(S(z0)), x1), Cons(S(0), x3), S(S(z0)), x1, S(0), x3), LEQ#2(S(S(z0)), S(0)))
   MERGE#2(Cons(S(S(z0)), x1), Cons(S(S(z1)), x3)) -> c6(COND_MERGE_YS_ZS_2(leq#2(z0, z1), Cons(S(S(z0)), x1), Cons(S(S(z1)), x3), S(S(z0)), x1, S(S(z1)), x3), LEQ#2(S(S(z0)), S(S(z1))))
   MERGE#2(Cons(S(x0), x1), Cons(S(x2), x3)) -> c6(LEQ#2(S(x0), S(x2)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Nil))) -> c9(CONST_F#2(Cons(x0, Cons(x1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(0)), Cons(x0, Cons(x1, Nil))), Cons(drop#2(S(halve#1(length#1(Nil))), Cons(x0, Cons(x1, Nil))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Nil)), S(halve#1(length#1(Nil)))), HALVE#1(length#1(Nil)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Cons(x2, x3)))) -> c9(CONST_F#2(Cons(x0, Cons(x1, Cons(x2, x3))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(S(length#1(x3)))), Cons(x0, Cons(x1, Cons(x2, x3)))), Cons(drop#2(S(halve#1(S(length#1(x3)))), Cons(x0, Cons(x1, Cons(x2, x3)))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Cons(x2, x3))), S(halve#1(length#1(Cons(x2, x3)))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, x3))), S(halve#1(length#1(Cons(x2, x3))))), HALVE#1(length#1(Cons(x2, x3))), LENGTH#1(Cons(x2, x3)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Cons(x2, Nil)))) -> c9(CONST_F#2(Cons(x0, Cons(x1, Cons(x2, Nil))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Cons(x2, Nil))), S(halve#1(S(0)))))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Cons(x2, Nil))), S(halve#1(length#1(Cons(x2, Nil)))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Nil))), S(halve#1(length#1(Cons(x2, Nil))))), HALVE#1(length#1(Cons(x2, Nil))), LENGTH#1(Cons(x2, Nil)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Cons(x2, Cons(z0, z1))))) -> c9(CONST_F#2(Cons(x0, Cons(x1, Cons(x2, Cons(z0, z1)))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Cons(x2, Cons(z0, z1)))), S(halve#1(S(S(length#1(z1)))))))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Cons(x2, Cons(z0, z1)))), S(halve#1(length#1(Cons(x2, Cons(z0, z1))))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Cons(z0, z1)))), S(halve#1(length#1(Cons(x2, Cons(z0, z1)))))), HALVE#1(length#1(Cons(x2, Cons(z0, z1)))), LENGTH#1(Cons(x2, Cons(z0, z1))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Cons(x2, x3)))) -> c9(MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Cons(x2, x3))), S(halve#1(length#1(Cons(x2, x3)))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, x3))), S(halve#1(length#1(Cons(x2, x3))))), HALVE#1(length#1(Cons(x2, x3))), LENGTH#1(Cons(x2, x3)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Nil))) -> c9(CONST_F#2(Cons(x0, Cons(x1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(0)), Cons(x0, Cons(x1, Nil))), Cons(drop#2(S(halve#1(0)), Cons(x0, Cons(x1, Nil))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Nil)), S(halve#1(length#1(Nil)))), HALVE#1(length#1(Nil)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Nil))) -> c9(CONST_F#2(Cons(x0, Cons(x1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Nil)), S(0)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Nil)), S(halve#1(length#1(Nil)))), HALVE#1(length#1(Nil)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> c9(CONST_F#2(Cons(z0, Cons(z1, z2)), Cons(dc#1(map, divisible, mergesort_zs_3, divide, const_f, take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2)))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(drop#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Nil))), DIVIDE_YS#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2)))), HALVE#1(length#1(z2)), LENGTH#1(z2))
   DIVIDE_YS#1(Cons(x0, Cons(x1, x2)), S(y11)) -> c(TAKE#2(S(y11), Cons(x0, Cons(x1, x2))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, x3))), S(y11)) -> c(TAKE#2(S(y11), Cons(x0, Cons(x1, Cons(x2, x3)))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Nil)), S(y10)) -> c(TAKE#2(S(y10), Cons(x0, Cons(x1, Nil))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Nil))), S(y7)) -> c(TAKE#2(S(y7), Cons(x0, Cons(x1, Cons(x2, Nil)))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4)))), S(y8)) -> c(TAKE#2(S(y8), Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4))))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, x2)), S(y11)) -> c1(DROP#2(S(y11), Cons(x0, Cons(x1, x2))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, x3))), S(y11)) -> c1(DROP#2(S(y11), Cons(x0, Cons(x1, Cons(x2, x3)))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Nil)), S(y10)) -> c1(DROP#2(S(y10), Cons(x0, Cons(x1, Nil))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Nil))), S(y7)) -> c1(DROP#2(S(y7), Cons(x0, Cons(x1, Cons(x2, Nil)))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4)))), S(y8)) -> c1(DROP#2(S(y8), Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4))))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> c9(CONST_F#2(Cons(z0, Cons(z1, z2)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(halve#1(length#1(z2)), Cons(z1, z2)), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Nil))), DIVIDE_YS#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2)))), HALVE#1(length#1(z2)), LENGTH#1(z2))
   COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(z2, z3), z4, Cons(0, y0), z6, z7) -> c2(MERGE#2(Cons(0, y0), Cons(z2, z3)))
   COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(0, z3), z4, Cons(S(y0), y1), z6, z7) -> c2(MERGE#2(Cons(S(y0), y1), Cons(0, z3)))
   COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(S(y1), z3), z4, Cons(S(0), y0), z6, z7) -> c2(MERGE#2(Cons(S(0), y0), Cons(S(y1), z3)))
   COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(S(0), z3), z4, Cons(S(S(y0)), y1), z6, z7) -> c2(MERGE#2(Cons(S(S(y0)), y1), Cons(S(0), z3)))
   COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(S(S(y2)), z3), z4, Cons(S(S(y0)), y1), z6, z7) -> c2(MERGE#2(Cons(S(S(y0)), y1), Cons(S(S(y2)), z3)))
   COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(S(y2), z3), z4, Cons(S(y0), y1), z6, z7) -> c2(MERGE#2(Cons(S(y0), y1), Cons(S(y2), z3)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, z3)))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Cons(z2, z3))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(Cons(z2, z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Cons(drop#2(S(halve#1(S(length#1(z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3)))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3))))), HALVE#1(S(length#1(z3))), LENGTH#1(Cons(z2, z3)))
   COND_MERGE_YS_ZS_2(False, Cons(S(x0), x1), Cons(0, x2), S(x0), x1, 0, x2) -> c3(MERGE#2(Cons(S(x0), x1), x2))
   COND_MERGE_YS_ZS_2(False, Cons(S(S(x0)), x1), Cons(S(0), x2), S(S(x0)), x1, S(0), x2) -> c3(MERGE#2(Cons(S(S(x0)), x1), x2))
   COND_MERGE_YS_ZS_2(False, Cons(S(S(x0)), x1), Cons(S(S(x2)), x3), S(S(x0)), x1, S(S(x2)), x3) -> c3(MERGE#2(Cons(S(S(x0)), x1), x3))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> c9(CONST_F#2(Cons(z0, Cons(z1, z2)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(Cons(z0, take#2(halve#1(length#1(z2)), Cons(z1, z2))), Cons(drop#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Nil))), DIVIDE_YS#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2)))), HALVE#1(length#1(z2)), LENGTH#1(z2))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, z3)))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Cons(z2, z3))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(S(length#1(z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Cons(drop#2(S(halve#1(length#1(Cons(z2, z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3)))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3))))), HALVE#1(S(length#1(z3))), LENGTH#1(Cons(z2, z3)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> c9(MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Nil))), DIVIDE_YS#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2)))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Nil))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(Nil))), Cons(z0, Cons(z1, Nil))), Cons(drop#2(S(halve#1(0)), Cons(z0, Cons(z1, Nil))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil)))))
K tuples:none
Defined Rule Symbols:   leq#2_2, map#2_2, divide_ys#1_2, halve#1_1, length#1_1, take#2_2, drop#2_2, dc#1_6, const_f#2_2, merge#2_2, cond_merge_ys_zs_2_7

Defined Pair Symbols:   DROP#2_2, TAKE#2_2, HALVE#1_1, CONST_F#2_2, LEQ#2_2, LENGTH#1_1, MAP#2_2, MERGE#2_2, DC#1_6, DIVIDE_YS#1_2, COND_MERGE_YS_ZS_2_7

Compound Symbols:   c12_1, c15_1, c18_1, c19_1, c22_1, c24_1, c26_1, c27_1, c6_1, c6_2, c9_4, c9_5, c_1, c1_1, c2_1, c3_1, c9_2, c9_3


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

(125) CdtRewritingProof (BOTH BOUNDS(ID, ID))
Used rewriting to replace DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Nil))) -> c9(CONST_F#2(Cons(x0, Cons(x1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(0)), Cons(x0, Cons(x1, Nil))), Cons(drop#2(S(halve#1(length#1(Nil))), Cons(x0, Cons(x1, Nil))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Nil)), S(halve#1(length#1(Nil)))), HALVE#1(length#1(Nil))) by DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Nil))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(0)), Cons(z0, Cons(z1, Nil))), Cons(drop#2(S(halve#1(length#1(Nil))), Cons(z0, Cons(z1, Nil))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil)))), HALVE#1(0))
----------------------------------------

(126)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   leq#2(0, z0) -> True
   leq#2(S(z0), 0) -> False
   leq#2(S(z0), S(z1)) -> leq#2(z0, z1)
   map#2(dc(z0, z1, z2, z3, z4), Nil) -> Nil
   map#2(dc(z0, z1, z2, z3, z4), Cons(z5, z6)) -> Cons(dc#1(z0, z1, z2, z3, z4, z5), map#2(dc(z0, z1, z2, z3, z4), z6))
   divide_ys#1(z0, z1) -> Cons(take#2(z1, z0), Cons(drop#2(z1, z0), Nil))
   halve#1(0) -> 0
   halve#1(S(0)) -> S(0)
   halve#1(S(S(z0))) -> S(halve#1(z0))
   length#1(Nil) -> 0
   length#1(Cons(z0, z1)) -> S(length#1(z1))
   take#2(0, z0) -> Nil
   take#2(S(0), Nil) -> Cons(bot[0], Nil)
   take#2(S(z0), Cons(z1, z2)) -> Cons(z1, take#2(z0, z2))
   drop#2(0, z0) -> z0
   drop#2(S(0), Nil) -> bot[1]
   drop#2(S(z0), Cons(z1, z2)) -> drop#2(z0, z2)
   dc#1(map, divisible, mergesort_zs_3, divide, const_f, Nil) -> Nil
   dc#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Nil)) -> Cons(z0, Nil)
   dc#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> const_f#2(Cons(z0, Cons(z1, z2)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2))))))
   const_f#2(z0, Cons(z1, Cons(z2, z3))) -> merge#2(z1, z2)
   merge#2(Nil, z0) -> z0
   merge#2(Cons(z0, z1), Nil) -> Cons(z0, z1)
   merge#2(Cons(z0, z1), Cons(z2, z3)) -> cond_merge_ys_zs_2(leq#2(z0, z2), Cons(z0, z1), Cons(z2, z3), z0, z1, z2, z3)
   cond_merge_ys_zs_2(True, Cons(z0, z1), Cons(z2, z3), z4, z5, z6, z7) -> Cons(z4, merge#2(z5, Cons(z2, z3)))
   cond_merge_ys_zs_2(False, Cons(z0, z1), Cons(z2, z3), z4, z5, z6, z7) -> Cons(z6, merge#2(Cons(z0, z1), z7))
Tuples:
   DROP#2(S(z0), Cons(z1, z2)) -> c12(DROP#2(z0, z2))
   TAKE#2(S(z0), Cons(z1, z2)) -> c15(TAKE#2(z0, z2))
   HALVE#1(S(S(z0))) -> c18(HALVE#1(z0))
   CONST_F#2(z0, Cons(z1, Cons(z2, z3))) -> c19(MERGE#2(z1, z2))
   LEQ#2(S(z0), S(z1)) -> c22(LEQ#2(z0, z1))
   LENGTH#1(Cons(z0, z1)) -> c24(LENGTH#1(z1))
   MAP#2(dc(z0, z1, z2, z3, z4), Cons(z5, z6)) -> c26(DC#1(z0, z1, z2, z3, z4, z5))
   MAP#2(dc(z0, z1, z2, z3, z4), Cons(z5, z6)) -> c27(MAP#2(dc(z0, z1, z2, z3, z4), z6))
   MERGE#2(Cons(0, x1), Cons(z0, x3)) -> c6(COND_MERGE_YS_ZS_2(True, Cons(0, x1), Cons(z0, x3), 0, x1, z0, x3))
   MERGE#2(Cons(S(z0), x1), Cons(0, x3)) -> c6(COND_MERGE_YS_ZS_2(False, Cons(S(z0), x1), Cons(0, x3), S(z0), x1, 0, x3))
   MERGE#2(Cons(S(0), x1), Cons(S(z0), x3)) -> c6(COND_MERGE_YS_ZS_2(True, Cons(S(0), x1), Cons(S(z0), x3), S(0), x1, S(z0), x3), LEQ#2(S(0), S(z0)))
   MERGE#2(Cons(S(S(z0)), x1), Cons(S(0), x3)) -> c6(COND_MERGE_YS_ZS_2(False, Cons(S(S(z0)), x1), Cons(S(0), x3), S(S(z0)), x1, S(0), x3), LEQ#2(S(S(z0)), S(0)))
   MERGE#2(Cons(S(S(z0)), x1), Cons(S(S(z1)), x3)) -> c6(COND_MERGE_YS_ZS_2(leq#2(z0, z1), Cons(S(S(z0)), x1), Cons(S(S(z1)), x3), S(S(z0)), x1, S(S(z1)), x3), LEQ#2(S(S(z0)), S(S(z1))))
   MERGE#2(Cons(S(x0), x1), Cons(S(x2), x3)) -> c6(LEQ#2(S(x0), S(x2)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Cons(x2, x3)))) -> c9(CONST_F#2(Cons(x0, Cons(x1, Cons(x2, x3))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(S(length#1(x3)))), Cons(x0, Cons(x1, Cons(x2, x3)))), Cons(drop#2(S(halve#1(S(length#1(x3)))), Cons(x0, Cons(x1, Cons(x2, x3)))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Cons(x2, x3))), S(halve#1(length#1(Cons(x2, x3)))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, x3))), S(halve#1(length#1(Cons(x2, x3))))), HALVE#1(length#1(Cons(x2, x3))), LENGTH#1(Cons(x2, x3)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Cons(x2, Nil)))) -> c9(CONST_F#2(Cons(x0, Cons(x1, Cons(x2, Nil))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Cons(x2, Nil))), S(halve#1(S(0)))))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Cons(x2, Nil))), S(halve#1(length#1(Cons(x2, Nil)))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Nil))), S(halve#1(length#1(Cons(x2, Nil))))), HALVE#1(length#1(Cons(x2, Nil))), LENGTH#1(Cons(x2, Nil)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Cons(x2, Cons(z0, z1))))) -> c9(CONST_F#2(Cons(x0, Cons(x1, Cons(x2, Cons(z0, z1)))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Cons(x2, Cons(z0, z1)))), S(halve#1(S(S(length#1(z1)))))))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Cons(x2, Cons(z0, z1)))), S(halve#1(length#1(Cons(x2, Cons(z0, z1))))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Cons(z0, z1)))), S(halve#1(length#1(Cons(x2, Cons(z0, z1)))))), HALVE#1(length#1(Cons(x2, Cons(z0, z1)))), LENGTH#1(Cons(x2, Cons(z0, z1))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Cons(x2, x3)))) -> c9(MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Cons(x2, x3))), S(halve#1(length#1(Cons(x2, x3)))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, x3))), S(halve#1(length#1(Cons(x2, x3))))), HALVE#1(length#1(Cons(x2, x3))), LENGTH#1(Cons(x2, x3)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Nil))) -> c9(CONST_F#2(Cons(x0, Cons(x1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(0)), Cons(x0, Cons(x1, Nil))), Cons(drop#2(S(halve#1(0)), Cons(x0, Cons(x1, Nil))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Nil)), S(halve#1(length#1(Nil)))), HALVE#1(length#1(Nil)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Nil))) -> c9(CONST_F#2(Cons(x0, Cons(x1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Nil)), S(0)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Nil)), S(halve#1(length#1(Nil)))), HALVE#1(length#1(Nil)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> c9(CONST_F#2(Cons(z0, Cons(z1, z2)), Cons(dc#1(map, divisible, mergesort_zs_3, divide, const_f, take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2)))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(drop#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Nil))), DIVIDE_YS#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2)))), HALVE#1(length#1(z2)), LENGTH#1(z2))
   DIVIDE_YS#1(Cons(x0, Cons(x1, x2)), S(y11)) -> c(TAKE#2(S(y11), Cons(x0, Cons(x1, x2))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, x3))), S(y11)) -> c(TAKE#2(S(y11), Cons(x0, Cons(x1, Cons(x2, x3)))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Nil)), S(y10)) -> c(TAKE#2(S(y10), Cons(x0, Cons(x1, Nil))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Nil))), S(y7)) -> c(TAKE#2(S(y7), Cons(x0, Cons(x1, Cons(x2, Nil)))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4)))), S(y8)) -> c(TAKE#2(S(y8), Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4))))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, x2)), S(y11)) -> c1(DROP#2(S(y11), Cons(x0, Cons(x1, x2))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, x3))), S(y11)) -> c1(DROP#2(S(y11), Cons(x0, Cons(x1, Cons(x2, x3)))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Nil)), S(y10)) -> c1(DROP#2(S(y10), Cons(x0, Cons(x1, Nil))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Nil))), S(y7)) -> c1(DROP#2(S(y7), Cons(x0, Cons(x1, Cons(x2, Nil)))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4)))), S(y8)) -> c1(DROP#2(S(y8), Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4))))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> c9(CONST_F#2(Cons(z0, Cons(z1, z2)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(halve#1(length#1(z2)), Cons(z1, z2)), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Nil))), DIVIDE_YS#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2)))), HALVE#1(length#1(z2)), LENGTH#1(z2))
   COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(z2, z3), z4, Cons(0, y0), z6, z7) -> c2(MERGE#2(Cons(0, y0), Cons(z2, z3)))
   COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(0, z3), z4, Cons(S(y0), y1), z6, z7) -> c2(MERGE#2(Cons(S(y0), y1), Cons(0, z3)))
   COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(S(y1), z3), z4, Cons(S(0), y0), z6, z7) -> c2(MERGE#2(Cons(S(0), y0), Cons(S(y1), z3)))
   COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(S(0), z3), z4, Cons(S(S(y0)), y1), z6, z7) -> c2(MERGE#2(Cons(S(S(y0)), y1), Cons(S(0), z3)))
   COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(S(S(y2)), z3), z4, Cons(S(S(y0)), y1), z6, z7) -> c2(MERGE#2(Cons(S(S(y0)), y1), Cons(S(S(y2)), z3)))
   COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(S(y2), z3), z4, Cons(S(y0), y1), z6, z7) -> c2(MERGE#2(Cons(S(y0), y1), Cons(S(y2), z3)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, z3)))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Cons(z2, z3))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(Cons(z2, z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Cons(drop#2(S(halve#1(S(length#1(z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3)))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3))))), HALVE#1(S(length#1(z3))), LENGTH#1(Cons(z2, z3)))
   COND_MERGE_YS_ZS_2(False, Cons(S(x0), x1), Cons(0, x2), S(x0), x1, 0, x2) -> c3(MERGE#2(Cons(S(x0), x1), x2))
   COND_MERGE_YS_ZS_2(False, Cons(S(S(x0)), x1), Cons(S(0), x2), S(S(x0)), x1, S(0), x2) -> c3(MERGE#2(Cons(S(S(x0)), x1), x2))
   COND_MERGE_YS_ZS_2(False, Cons(S(S(x0)), x1), Cons(S(S(x2)), x3), S(S(x0)), x1, S(S(x2)), x3) -> c3(MERGE#2(Cons(S(S(x0)), x1), x3))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> c9(CONST_F#2(Cons(z0, Cons(z1, z2)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(Cons(z0, take#2(halve#1(length#1(z2)), Cons(z1, z2))), Cons(drop#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Nil))), DIVIDE_YS#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2)))), HALVE#1(length#1(z2)), LENGTH#1(z2))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, z3)))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Cons(z2, z3))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(S(length#1(z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Cons(drop#2(S(halve#1(length#1(Cons(z2, z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3)))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3))))), HALVE#1(S(length#1(z3))), LENGTH#1(Cons(z2, z3)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> c9(MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Nil))), DIVIDE_YS#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2)))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Nil))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(Nil))), Cons(z0, Cons(z1, Nil))), Cons(drop#2(S(halve#1(0)), Cons(z0, Cons(z1, Nil))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil)))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Nil))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(0)), Cons(z0, Cons(z1, Nil))), Cons(drop#2(S(halve#1(length#1(Nil))), Cons(z0, Cons(z1, Nil))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil)))), HALVE#1(0))
S tuples:
   DROP#2(S(z0), Cons(z1, z2)) -> c12(DROP#2(z0, z2))
   TAKE#2(S(z0), Cons(z1, z2)) -> c15(TAKE#2(z0, z2))
   HALVE#1(S(S(z0))) -> c18(HALVE#1(z0))
   CONST_F#2(z0, Cons(z1, Cons(z2, z3))) -> c19(MERGE#2(z1, z2))
   LEQ#2(S(z0), S(z1)) -> c22(LEQ#2(z0, z1))
   LENGTH#1(Cons(z0, z1)) -> c24(LENGTH#1(z1))
   MAP#2(dc(z0, z1, z2, z3, z4), Cons(z5, z6)) -> c26(DC#1(z0, z1, z2, z3, z4, z5))
   MAP#2(dc(z0, z1, z2, z3, z4), Cons(z5, z6)) -> c27(MAP#2(dc(z0, z1, z2, z3, z4), z6))
   MERGE#2(Cons(0, x1), Cons(z0, x3)) -> c6(COND_MERGE_YS_ZS_2(True, Cons(0, x1), Cons(z0, x3), 0, x1, z0, x3))
   MERGE#2(Cons(S(z0), x1), Cons(0, x3)) -> c6(COND_MERGE_YS_ZS_2(False, Cons(S(z0), x1), Cons(0, x3), S(z0), x1, 0, x3))
   MERGE#2(Cons(S(0), x1), Cons(S(z0), x3)) -> c6(COND_MERGE_YS_ZS_2(True, Cons(S(0), x1), Cons(S(z0), x3), S(0), x1, S(z0), x3), LEQ#2(S(0), S(z0)))
   MERGE#2(Cons(S(S(z0)), x1), Cons(S(0), x3)) -> c6(COND_MERGE_YS_ZS_2(False, Cons(S(S(z0)), x1), Cons(S(0), x3), S(S(z0)), x1, S(0), x3), LEQ#2(S(S(z0)), S(0)))
   MERGE#2(Cons(S(S(z0)), x1), Cons(S(S(z1)), x3)) -> c6(COND_MERGE_YS_ZS_2(leq#2(z0, z1), Cons(S(S(z0)), x1), Cons(S(S(z1)), x3), S(S(z0)), x1, S(S(z1)), x3), LEQ#2(S(S(z0)), S(S(z1))))
   MERGE#2(Cons(S(x0), x1), Cons(S(x2), x3)) -> c6(LEQ#2(S(x0), S(x2)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Cons(x2, x3)))) -> c9(CONST_F#2(Cons(x0, Cons(x1, Cons(x2, x3))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(S(length#1(x3)))), Cons(x0, Cons(x1, Cons(x2, x3)))), Cons(drop#2(S(halve#1(S(length#1(x3)))), Cons(x0, Cons(x1, Cons(x2, x3)))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Cons(x2, x3))), S(halve#1(length#1(Cons(x2, x3)))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, x3))), S(halve#1(length#1(Cons(x2, x3))))), HALVE#1(length#1(Cons(x2, x3))), LENGTH#1(Cons(x2, x3)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Cons(x2, Nil)))) -> c9(CONST_F#2(Cons(x0, Cons(x1, Cons(x2, Nil))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Cons(x2, Nil))), S(halve#1(S(0)))))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Cons(x2, Nil))), S(halve#1(length#1(Cons(x2, Nil)))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Nil))), S(halve#1(length#1(Cons(x2, Nil))))), HALVE#1(length#1(Cons(x2, Nil))), LENGTH#1(Cons(x2, Nil)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Cons(x2, Cons(z0, z1))))) -> c9(CONST_F#2(Cons(x0, Cons(x1, Cons(x2, Cons(z0, z1)))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Cons(x2, Cons(z0, z1)))), S(halve#1(S(S(length#1(z1)))))))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Cons(x2, Cons(z0, z1)))), S(halve#1(length#1(Cons(x2, Cons(z0, z1))))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Cons(z0, z1)))), S(halve#1(length#1(Cons(x2, Cons(z0, z1)))))), HALVE#1(length#1(Cons(x2, Cons(z0, z1)))), LENGTH#1(Cons(x2, Cons(z0, z1))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Cons(x2, x3)))) -> c9(MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Cons(x2, x3))), S(halve#1(length#1(Cons(x2, x3)))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, x3))), S(halve#1(length#1(Cons(x2, x3))))), HALVE#1(length#1(Cons(x2, x3))), LENGTH#1(Cons(x2, x3)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Nil))) -> c9(CONST_F#2(Cons(x0, Cons(x1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(0)), Cons(x0, Cons(x1, Nil))), Cons(drop#2(S(halve#1(0)), Cons(x0, Cons(x1, Nil))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Nil)), S(halve#1(length#1(Nil)))), HALVE#1(length#1(Nil)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Nil))) -> c9(CONST_F#2(Cons(x0, Cons(x1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Nil)), S(0)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Nil)), S(halve#1(length#1(Nil)))), HALVE#1(length#1(Nil)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> c9(CONST_F#2(Cons(z0, Cons(z1, z2)), Cons(dc#1(map, divisible, mergesort_zs_3, divide, const_f, take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2)))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(drop#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Nil))), DIVIDE_YS#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2)))), HALVE#1(length#1(z2)), LENGTH#1(z2))
   DIVIDE_YS#1(Cons(x0, Cons(x1, x2)), S(y11)) -> c(TAKE#2(S(y11), Cons(x0, Cons(x1, x2))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, x3))), S(y11)) -> c(TAKE#2(S(y11), Cons(x0, Cons(x1, Cons(x2, x3)))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Nil)), S(y10)) -> c(TAKE#2(S(y10), Cons(x0, Cons(x1, Nil))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Nil))), S(y7)) -> c(TAKE#2(S(y7), Cons(x0, Cons(x1, Cons(x2, Nil)))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4)))), S(y8)) -> c(TAKE#2(S(y8), Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4))))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, x2)), S(y11)) -> c1(DROP#2(S(y11), Cons(x0, Cons(x1, x2))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, x3))), S(y11)) -> c1(DROP#2(S(y11), Cons(x0, Cons(x1, Cons(x2, x3)))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Nil)), S(y10)) -> c1(DROP#2(S(y10), Cons(x0, Cons(x1, Nil))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Nil))), S(y7)) -> c1(DROP#2(S(y7), Cons(x0, Cons(x1, Cons(x2, Nil)))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4)))), S(y8)) -> c1(DROP#2(S(y8), Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4))))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> c9(CONST_F#2(Cons(z0, Cons(z1, z2)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(halve#1(length#1(z2)), Cons(z1, z2)), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Nil))), DIVIDE_YS#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2)))), HALVE#1(length#1(z2)), LENGTH#1(z2))
   COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(z2, z3), z4, Cons(0, y0), z6, z7) -> c2(MERGE#2(Cons(0, y0), Cons(z2, z3)))
   COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(0, z3), z4, Cons(S(y0), y1), z6, z7) -> c2(MERGE#2(Cons(S(y0), y1), Cons(0, z3)))
   COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(S(y1), z3), z4, Cons(S(0), y0), z6, z7) -> c2(MERGE#2(Cons(S(0), y0), Cons(S(y1), z3)))
   COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(S(0), z3), z4, Cons(S(S(y0)), y1), z6, z7) -> c2(MERGE#2(Cons(S(S(y0)), y1), Cons(S(0), z3)))
   COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(S(S(y2)), z3), z4, Cons(S(S(y0)), y1), z6, z7) -> c2(MERGE#2(Cons(S(S(y0)), y1), Cons(S(S(y2)), z3)))
   COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(S(y2), z3), z4, Cons(S(y0), y1), z6, z7) -> c2(MERGE#2(Cons(S(y0), y1), Cons(S(y2), z3)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, z3)))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Cons(z2, z3))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(Cons(z2, z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Cons(drop#2(S(halve#1(S(length#1(z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3)))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3))))), HALVE#1(S(length#1(z3))), LENGTH#1(Cons(z2, z3)))
   COND_MERGE_YS_ZS_2(False, Cons(S(x0), x1), Cons(0, x2), S(x0), x1, 0, x2) -> c3(MERGE#2(Cons(S(x0), x1), x2))
   COND_MERGE_YS_ZS_2(False, Cons(S(S(x0)), x1), Cons(S(0), x2), S(S(x0)), x1, S(0), x2) -> c3(MERGE#2(Cons(S(S(x0)), x1), x2))
   COND_MERGE_YS_ZS_2(False, Cons(S(S(x0)), x1), Cons(S(S(x2)), x3), S(S(x0)), x1, S(S(x2)), x3) -> c3(MERGE#2(Cons(S(S(x0)), x1), x3))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> c9(CONST_F#2(Cons(z0, Cons(z1, z2)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(Cons(z0, take#2(halve#1(length#1(z2)), Cons(z1, z2))), Cons(drop#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Nil))), DIVIDE_YS#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2)))), HALVE#1(length#1(z2)), LENGTH#1(z2))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, z3)))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Cons(z2, z3))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(S(length#1(z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Cons(drop#2(S(halve#1(length#1(Cons(z2, z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3)))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3))))), HALVE#1(S(length#1(z3))), LENGTH#1(Cons(z2, z3)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> c9(MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Nil))), DIVIDE_YS#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2)))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Nil))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(Nil))), Cons(z0, Cons(z1, Nil))), Cons(drop#2(S(halve#1(0)), Cons(z0, Cons(z1, Nil))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil)))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Nil))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(0)), Cons(z0, Cons(z1, Nil))), Cons(drop#2(S(halve#1(length#1(Nil))), Cons(z0, Cons(z1, Nil))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil)))), HALVE#1(0))
K tuples:none
Defined Rule Symbols:   leq#2_2, map#2_2, divide_ys#1_2, halve#1_1, length#1_1, take#2_2, drop#2_2, dc#1_6, const_f#2_2, merge#2_2, cond_merge_ys_zs_2_7

Defined Pair Symbols:   DROP#2_2, TAKE#2_2, HALVE#1_1, CONST_F#2_2, LEQ#2_2, LENGTH#1_1, MAP#2_2, MERGE#2_2, DC#1_6, DIVIDE_YS#1_2, COND_MERGE_YS_ZS_2_7

Compound Symbols:   c12_1, c15_1, c18_1, c19_1, c22_1, c24_1, c26_1, c27_1, c6_1, c6_2, c9_5, c9_4, c_1, c1_1, c2_1, c3_1, c9_2, c9_3


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

(128)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   leq#2(0, z0) -> True
   leq#2(S(z0), 0) -> False
   leq#2(S(z0), S(z1)) -> leq#2(z0, z1)
   map#2(dc(z0, z1, z2, z3, z4), Nil) -> Nil
   map#2(dc(z0, z1, z2, z3, z4), Cons(z5, z6)) -> Cons(dc#1(z0, z1, z2, z3, z4, z5), map#2(dc(z0, z1, z2, z3, z4), z6))
   divide_ys#1(z0, z1) -> Cons(take#2(z1, z0), Cons(drop#2(z1, z0), Nil))
   halve#1(0) -> 0
   halve#1(S(0)) -> S(0)
   halve#1(S(S(z0))) -> S(halve#1(z0))
   length#1(Nil) -> 0
   length#1(Cons(z0, z1)) -> S(length#1(z1))
   take#2(0, z0) -> Nil
   take#2(S(0), Nil) -> Cons(bot[0], Nil)
   take#2(S(z0), Cons(z1, z2)) -> Cons(z1, take#2(z0, z2))
   drop#2(0, z0) -> z0
   drop#2(S(0), Nil) -> bot[1]
   drop#2(S(z0), Cons(z1, z2)) -> drop#2(z0, z2)
   dc#1(map, divisible, mergesort_zs_3, divide, const_f, Nil) -> Nil
   dc#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Nil)) -> Cons(z0, Nil)
   dc#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> const_f#2(Cons(z0, Cons(z1, z2)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2))))))
   const_f#2(z0, Cons(z1, Cons(z2, z3))) -> merge#2(z1, z2)
   merge#2(Nil, z0) -> z0
   merge#2(Cons(z0, z1), Nil) -> Cons(z0, z1)
   merge#2(Cons(z0, z1), Cons(z2, z3)) -> cond_merge_ys_zs_2(leq#2(z0, z2), Cons(z0, z1), Cons(z2, z3), z0, z1, z2, z3)
   cond_merge_ys_zs_2(True, Cons(z0, z1), Cons(z2, z3), z4, z5, z6, z7) -> Cons(z4, merge#2(z5, Cons(z2, z3)))
   cond_merge_ys_zs_2(False, Cons(z0, z1), Cons(z2, z3), z4, z5, z6, z7) -> Cons(z6, merge#2(Cons(z0, z1), z7))
Tuples:
   DROP#2(S(z0), Cons(z1, z2)) -> c12(DROP#2(z0, z2))
   TAKE#2(S(z0), Cons(z1, z2)) -> c15(TAKE#2(z0, z2))
   HALVE#1(S(S(z0))) -> c18(HALVE#1(z0))
   CONST_F#2(z0, Cons(z1, Cons(z2, z3))) -> c19(MERGE#2(z1, z2))
   LEQ#2(S(z0), S(z1)) -> c22(LEQ#2(z0, z1))
   LENGTH#1(Cons(z0, z1)) -> c24(LENGTH#1(z1))
   MAP#2(dc(z0, z1, z2, z3, z4), Cons(z5, z6)) -> c26(DC#1(z0, z1, z2, z3, z4, z5))
   MAP#2(dc(z0, z1, z2, z3, z4), Cons(z5, z6)) -> c27(MAP#2(dc(z0, z1, z2, z3, z4), z6))
   MERGE#2(Cons(0, x1), Cons(z0, x3)) -> c6(COND_MERGE_YS_ZS_2(True, Cons(0, x1), Cons(z0, x3), 0, x1, z0, x3))
   MERGE#2(Cons(S(z0), x1), Cons(0, x3)) -> c6(COND_MERGE_YS_ZS_2(False, Cons(S(z0), x1), Cons(0, x3), S(z0), x1, 0, x3))
   MERGE#2(Cons(S(0), x1), Cons(S(z0), x3)) -> c6(COND_MERGE_YS_ZS_2(True, Cons(S(0), x1), Cons(S(z0), x3), S(0), x1, S(z0), x3), LEQ#2(S(0), S(z0)))
   MERGE#2(Cons(S(S(z0)), x1), Cons(S(0), x3)) -> c6(COND_MERGE_YS_ZS_2(False, Cons(S(S(z0)), x1), Cons(S(0), x3), S(S(z0)), x1, S(0), x3), LEQ#2(S(S(z0)), S(0)))
   MERGE#2(Cons(S(S(z0)), x1), Cons(S(S(z1)), x3)) -> c6(COND_MERGE_YS_ZS_2(leq#2(z0, z1), Cons(S(S(z0)), x1), Cons(S(S(z1)), x3), S(S(z0)), x1, S(S(z1)), x3), LEQ#2(S(S(z0)), S(S(z1))))
   MERGE#2(Cons(S(x0), x1), Cons(S(x2), x3)) -> c6(LEQ#2(S(x0), S(x2)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Cons(x2, x3)))) -> c9(CONST_F#2(Cons(x0, Cons(x1, Cons(x2, x3))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(S(length#1(x3)))), Cons(x0, Cons(x1, Cons(x2, x3)))), Cons(drop#2(S(halve#1(S(length#1(x3)))), Cons(x0, Cons(x1, Cons(x2, x3)))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Cons(x2, x3))), S(halve#1(length#1(Cons(x2, x3)))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, x3))), S(halve#1(length#1(Cons(x2, x3))))), HALVE#1(length#1(Cons(x2, x3))), LENGTH#1(Cons(x2, x3)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Cons(x2, Nil)))) -> c9(CONST_F#2(Cons(x0, Cons(x1, Cons(x2, Nil))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Cons(x2, Nil))), S(halve#1(S(0)))))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Cons(x2, Nil))), S(halve#1(length#1(Cons(x2, Nil)))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Nil))), S(halve#1(length#1(Cons(x2, Nil))))), HALVE#1(length#1(Cons(x2, Nil))), LENGTH#1(Cons(x2, Nil)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Cons(x2, Cons(z0, z1))))) -> c9(CONST_F#2(Cons(x0, Cons(x1, Cons(x2, Cons(z0, z1)))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Cons(x2, Cons(z0, z1)))), S(halve#1(S(S(length#1(z1)))))))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Cons(x2, Cons(z0, z1)))), S(halve#1(length#1(Cons(x2, Cons(z0, z1))))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Cons(z0, z1)))), S(halve#1(length#1(Cons(x2, Cons(z0, z1)))))), HALVE#1(length#1(Cons(x2, Cons(z0, z1)))), LENGTH#1(Cons(x2, Cons(z0, z1))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Cons(x2, x3)))) -> c9(MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Cons(x2, x3))), S(halve#1(length#1(Cons(x2, x3)))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, x3))), S(halve#1(length#1(Cons(x2, x3))))), HALVE#1(length#1(Cons(x2, x3))), LENGTH#1(Cons(x2, x3)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Nil))) -> c9(CONST_F#2(Cons(x0, Cons(x1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(0)), Cons(x0, Cons(x1, Nil))), Cons(drop#2(S(halve#1(0)), Cons(x0, Cons(x1, Nil))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Nil)), S(halve#1(length#1(Nil)))), HALVE#1(length#1(Nil)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Nil))) -> c9(CONST_F#2(Cons(x0, Cons(x1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Nil)), S(0)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Nil)), S(halve#1(length#1(Nil)))), HALVE#1(length#1(Nil)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> c9(CONST_F#2(Cons(z0, Cons(z1, z2)), Cons(dc#1(map, divisible, mergesort_zs_3, divide, const_f, take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2)))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(drop#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Nil))), DIVIDE_YS#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2)))), HALVE#1(length#1(z2)), LENGTH#1(z2))
   DIVIDE_YS#1(Cons(x0, Cons(x1, x2)), S(y11)) -> c(TAKE#2(S(y11), Cons(x0, Cons(x1, x2))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, x3))), S(y11)) -> c(TAKE#2(S(y11), Cons(x0, Cons(x1, Cons(x2, x3)))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Nil)), S(y10)) -> c(TAKE#2(S(y10), Cons(x0, Cons(x1, Nil))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Nil))), S(y7)) -> c(TAKE#2(S(y7), Cons(x0, Cons(x1, Cons(x2, Nil)))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4)))), S(y8)) -> c(TAKE#2(S(y8), Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4))))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, x2)), S(y11)) -> c1(DROP#2(S(y11), Cons(x0, Cons(x1, x2))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, x3))), S(y11)) -> c1(DROP#2(S(y11), Cons(x0, Cons(x1, Cons(x2, x3)))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Nil)), S(y10)) -> c1(DROP#2(S(y10), Cons(x0, Cons(x1, Nil))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Nil))), S(y7)) -> c1(DROP#2(S(y7), Cons(x0, Cons(x1, Cons(x2, Nil)))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4)))), S(y8)) -> c1(DROP#2(S(y8), Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4))))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> c9(CONST_F#2(Cons(z0, Cons(z1, z2)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(halve#1(length#1(z2)), Cons(z1, z2)), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Nil))), DIVIDE_YS#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2)))), HALVE#1(length#1(z2)), LENGTH#1(z2))
   COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(z2, z3), z4, Cons(0, y0), z6, z7) -> c2(MERGE#2(Cons(0, y0), Cons(z2, z3)))
   COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(0, z3), z4, Cons(S(y0), y1), z6, z7) -> c2(MERGE#2(Cons(S(y0), y1), Cons(0, z3)))
   COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(S(y1), z3), z4, Cons(S(0), y0), z6, z7) -> c2(MERGE#2(Cons(S(0), y0), Cons(S(y1), z3)))
   COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(S(0), z3), z4, Cons(S(S(y0)), y1), z6, z7) -> c2(MERGE#2(Cons(S(S(y0)), y1), Cons(S(0), z3)))
   COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(S(S(y2)), z3), z4, Cons(S(S(y0)), y1), z6, z7) -> c2(MERGE#2(Cons(S(S(y0)), y1), Cons(S(S(y2)), z3)))
   COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(S(y2), z3), z4, Cons(S(y0), y1), z6, z7) -> c2(MERGE#2(Cons(S(y0), y1), Cons(S(y2), z3)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, z3)))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Cons(z2, z3))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(Cons(z2, z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Cons(drop#2(S(halve#1(S(length#1(z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3)))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3))))), HALVE#1(S(length#1(z3))), LENGTH#1(Cons(z2, z3)))
   COND_MERGE_YS_ZS_2(False, Cons(S(x0), x1), Cons(0, x2), S(x0), x1, 0, x2) -> c3(MERGE#2(Cons(S(x0), x1), x2))
   COND_MERGE_YS_ZS_2(False, Cons(S(S(x0)), x1), Cons(S(0), x2), S(S(x0)), x1, S(0), x2) -> c3(MERGE#2(Cons(S(S(x0)), x1), x2))
   COND_MERGE_YS_ZS_2(False, Cons(S(S(x0)), x1), Cons(S(S(x2)), x3), S(S(x0)), x1, S(S(x2)), x3) -> c3(MERGE#2(Cons(S(S(x0)), x1), x3))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> c9(CONST_F#2(Cons(z0, Cons(z1, z2)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(Cons(z0, take#2(halve#1(length#1(z2)), Cons(z1, z2))), Cons(drop#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Nil))), DIVIDE_YS#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2)))), HALVE#1(length#1(z2)), LENGTH#1(z2))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, z3)))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Cons(z2, z3))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(S(length#1(z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Cons(drop#2(S(halve#1(length#1(Cons(z2, z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3)))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3))))), HALVE#1(S(length#1(z3))), LENGTH#1(Cons(z2, z3)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> c9(MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Nil))), DIVIDE_YS#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2)))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Nil))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(Nil))), Cons(z0, Cons(z1, Nil))), Cons(drop#2(S(halve#1(0)), Cons(z0, Cons(z1, Nil))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil)))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Nil))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(0)), Cons(z0, Cons(z1, Nil))), Cons(drop#2(S(halve#1(length#1(Nil))), Cons(z0, Cons(z1, Nil))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil)))))
S tuples:
   DROP#2(S(z0), Cons(z1, z2)) -> c12(DROP#2(z0, z2))
   TAKE#2(S(z0), Cons(z1, z2)) -> c15(TAKE#2(z0, z2))
   HALVE#1(S(S(z0))) -> c18(HALVE#1(z0))
   CONST_F#2(z0, Cons(z1, Cons(z2, z3))) -> c19(MERGE#2(z1, z2))
   LEQ#2(S(z0), S(z1)) -> c22(LEQ#2(z0, z1))
   LENGTH#1(Cons(z0, z1)) -> c24(LENGTH#1(z1))
   MAP#2(dc(z0, z1, z2, z3, z4), Cons(z5, z6)) -> c26(DC#1(z0, z1, z2, z3, z4, z5))
   MAP#2(dc(z0, z1, z2, z3, z4), Cons(z5, z6)) -> c27(MAP#2(dc(z0, z1, z2, z3, z4), z6))
   MERGE#2(Cons(0, x1), Cons(z0, x3)) -> c6(COND_MERGE_YS_ZS_2(True, Cons(0, x1), Cons(z0, x3), 0, x1, z0, x3))
   MERGE#2(Cons(S(z0), x1), Cons(0, x3)) -> c6(COND_MERGE_YS_ZS_2(False, Cons(S(z0), x1), Cons(0, x3), S(z0), x1, 0, x3))
   MERGE#2(Cons(S(0), x1), Cons(S(z0), x3)) -> c6(COND_MERGE_YS_ZS_2(True, Cons(S(0), x1), Cons(S(z0), x3), S(0), x1, S(z0), x3), LEQ#2(S(0), S(z0)))
   MERGE#2(Cons(S(S(z0)), x1), Cons(S(0), x3)) -> c6(COND_MERGE_YS_ZS_2(False, Cons(S(S(z0)), x1), Cons(S(0), x3), S(S(z0)), x1, S(0), x3), LEQ#2(S(S(z0)), S(0)))
   MERGE#2(Cons(S(S(z0)), x1), Cons(S(S(z1)), x3)) -> c6(COND_MERGE_YS_ZS_2(leq#2(z0, z1), Cons(S(S(z0)), x1), Cons(S(S(z1)), x3), S(S(z0)), x1, S(S(z1)), x3), LEQ#2(S(S(z0)), S(S(z1))))
   MERGE#2(Cons(S(x0), x1), Cons(S(x2), x3)) -> c6(LEQ#2(S(x0), S(x2)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Cons(x2, x3)))) -> c9(CONST_F#2(Cons(x0, Cons(x1, Cons(x2, x3))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(S(length#1(x3)))), Cons(x0, Cons(x1, Cons(x2, x3)))), Cons(drop#2(S(halve#1(S(length#1(x3)))), Cons(x0, Cons(x1, Cons(x2, x3)))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Cons(x2, x3))), S(halve#1(length#1(Cons(x2, x3)))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, x3))), S(halve#1(length#1(Cons(x2, x3))))), HALVE#1(length#1(Cons(x2, x3))), LENGTH#1(Cons(x2, x3)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Cons(x2, Nil)))) -> c9(CONST_F#2(Cons(x0, Cons(x1, Cons(x2, Nil))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Cons(x2, Nil))), S(halve#1(S(0)))))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Cons(x2, Nil))), S(halve#1(length#1(Cons(x2, Nil)))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Nil))), S(halve#1(length#1(Cons(x2, Nil))))), HALVE#1(length#1(Cons(x2, Nil))), LENGTH#1(Cons(x2, Nil)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Cons(x2, Cons(z0, z1))))) -> c9(CONST_F#2(Cons(x0, Cons(x1, Cons(x2, Cons(z0, z1)))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Cons(x2, Cons(z0, z1)))), S(halve#1(S(S(length#1(z1)))))))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Cons(x2, Cons(z0, z1)))), S(halve#1(length#1(Cons(x2, Cons(z0, z1))))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Cons(z0, z1)))), S(halve#1(length#1(Cons(x2, Cons(z0, z1)))))), HALVE#1(length#1(Cons(x2, Cons(z0, z1)))), LENGTH#1(Cons(x2, Cons(z0, z1))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Cons(x2, x3)))) -> c9(MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Cons(x2, x3))), S(halve#1(length#1(Cons(x2, x3)))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, x3))), S(halve#1(length#1(Cons(x2, x3))))), HALVE#1(length#1(Cons(x2, x3))), LENGTH#1(Cons(x2, x3)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Nil))) -> c9(CONST_F#2(Cons(x0, Cons(x1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(0)), Cons(x0, Cons(x1, Nil))), Cons(drop#2(S(halve#1(0)), Cons(x0, Cons(x1, Nil))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Nil)), S(halve#1(length#1(Nil)))), HALVE#1(length#1(Nil)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Nil))) -> c9(CONST_F#2(Cons(x0, Cons(x1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Nil)), S(0)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Nil)), S(halve#1(length#1(Nil)))), HALVE#1(length#1(Nil)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> c9(CONST_F#2(Cons(z0, Cons(z1, z2)), Cons(dc#1(map, divisible, mergesort_zs_3, divide, const_f, take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2)))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(drop#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Nil))), DIVIDE_YS#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2)))), HALVE#1(length#1(z2)), LENGTH#1(z2))
   DIVIDE_YS#1(Cons(x0, Cons(x1, x2)), S(y11)) -> c(TAKE#2(S(y11), Cons(x0, Cons(x1, x2))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, x3))), S(y11)) -> c(TAKE#2(S(y11), Cons(x0, Cons(x1, Cons(x2, x3)))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Nil)), S(y10)) -> c(TAKE#2(S(y10), Cons(x0, Cons(x1, Nil))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Nil))), S(y7)) -> c(TAKE#2(S(y7), Cons(x0, Cons(x1, Cons(x2, Nil)))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4)))), S(y8)) -> c(TAKE#2(S(y8), Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4))))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, x2)), S(y11)) -> c1(DROP#2(S(y11), Cons(x0, Cons(x1, x2))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, x3))), S(y11)) -> c1(DROP#2(S(y11), Cons(x0, Cons(x1, Cons(x2, x3)))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Nil)), S(y10)) -> c1(DROP#2(S(y10), Cons(x0, Cons(x1, Nil))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Nil))), S(y7)) -> c1(DROP#2(S(y7), Cons(x0, Cons(x1, Cons(x2, Nil)))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4)))), S(y8)) -> c1(DROP#2(S(y8), Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4))))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> c9(CONST_F#2(Cons(z0, Cons(z1, z2)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(halve#1(length#1(z2)), Cons(z1, z2)), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Nil))), DIVIDE_YS#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2)))), HALVE#1(length#1(z2)), LENGTH#1(z2))
   COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(z2, z3), z4, Cons(0, y0), z6, z7) -> c2(MERGE#2(Cons(0, y0), Cons(z2, z3)))
   COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(0, z3), z4, Cons(S(y0), y1), z6, z7) -> c2(MERGE#2(Cons(S(y0), y1), Cons(0, z3)))
   COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(S(y1), z3), z4, Cons(S(0), y0), z6, z7) -> c2(MERGE#2(Cons(S(0), y0), Cons(S(y1), z3)))
   COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(S(0), z3), z4, Cons(S(S(y0)), y1), z6, z7) -> c2(MERGE#2(Cons(S(S(y0)), y1), Cons(S(0), z3)))
   COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(S(S(y2)), z3), z4, Cons(S(S(y0)), y1), z6, z7) -> c2(MERGE#2(Cons(S(S(y0)), y1), Cons(S(S(y2)), z3)))
   COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(S(y2), z3), z4, Cons(S(y0), y1), z6, z7) -> c2(MERGE#2(Cons(S(y0), y1), Cons(S(y2), z3)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, z3)))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Cons(z2, z3))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(Cons(z2, z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Cons(drop#2(S(halve#1(S(length#1(z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3)))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3))))), HALVE#1(S(length#1(z3))), LENGTH#1(Cons(z2, z3)))
   COND_MERGE_YS_ZS_2(False, Cons(S(x0), x1), Cons(0, x2), S(x0), x1, 0, x2) -> c3(MERGE#2(Cons(S(x0), x1), x2))
   COND_MERGE_YS_ZS_2(False, Cons(S(S(x0)), x1), Cons(S(0), x2), S(S(x0)), x1, S(0), x2) -> c3(MERGE#2(Cons(S(S(x0)), x1), x2))
   COND_MERGE_YS_ZS_2(False, Cons(S(S(x0)), x1), Cons(S(S(x2)), x3), S(S(x0)), x1, S(S(x2)), x3) -> c3(MERGE#2(Cons(S(S(x0)), x1), x3))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> c9(CONST_F#2(Cons(z0, Cons(z1, z2)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(Cons(z0, take#2(halve#1(length#1(z2)), Cons(z1, z2))), Cons(drop#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Nil))), DIVIDE_YS#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2)))), HALVE#1(length#1(z2)), LENGTH#1(z2))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, z3)))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Cons(z2, z3))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(S(length#1(z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Cons(drop#2(S(halve#1(length#1(Cons(z2, z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3)))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3))))), HALVE#1(S(length#1(z3))), LENGTH#1(Cons(z2, z3)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> c9(MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Nil))), DIVIDE_YS#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2)))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Nil))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(Nil))), Cons(z0, Cons(z1, Nil))), Cons(drop#2(S(halve#1(0)), Cons(z0, Cons(z1, Nil))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil)))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Nil))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(0)), Cons(z0, Cons(z1, Nil))), Cons(drop#2(S(halve#1(length#1(Nil))), Cons(z0, Cons(z1, Nil))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil)))))
K tuples:none
Defined Rule Symbols:   leq#2_2, map#2_2, divide_ys#1_2, halve#1_1, length#1_1, take#2_2, drop#2_2, dc#1_6, const_f#2_2, merge#2_2, cond_merge_ys_zs_2_7

Defined Pair Symbols:   DROP#2_2, TAKE#2_2, HALVE#1_1, CONST_F#2_2, LEQ#2_2, LENGTH#1_1, MAP#2_2, MERGE#2_2, DC#1_6, DIVIDE_YS#1_2, COND_MERGE_YS_ZS_2_7

Compound Symbols:   c12_1, c15_1, c18_1, c19_1, c22_1, c24_1, c26_1, c27_1, c6_1, c6_2, c9_5, c9_4, c_1, c1_1, c2_1, c3_1, c9_2, c9_3


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(129) CdtRewritingProof (BOTH BOUNDS(ID, ID))
Used rewriting to replace DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Cons(x2, x3)))) -> c9(CONST_F#2(Cons(x0, Cons(x1, Cons(x2, x3))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(S(length#1(x3)))), Cons(x0, Cons(x1, Cons(x2, x3)))), Cons(drop#2(S(halve#1(S(length#1(x3)))), Cons(x0, Cons(x1, Cons(x2, x3)))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Cons(x2, x3))), S(halve#1(length#1(Cons(x2, x3)))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, x3))), S(halve#1(length#1(Cons(x2, x3))))), HALVE#1(length#1(Cons(x2, x3))), LENGTH#1(Cons(x2, x3))) by DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, z3)))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Cons(z2, z3))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(S(length#1(z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Cons(drop#2(S(halve#1(S(length#1(z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3)))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3))))), HALVE#1(S(length#1(z3))), LENGTH#1(Cons(z2, z3)))
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(130)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   leq#2(0, z0) -> True
   leq#2(S(z0), 0) -> False
   leq#2(S(z0), S(z1)) -> leq#2(z0, z1)
   map#2(dc(z0, z1, z2, z3, z4), Nil) -> Nil
   map#2(dc(z0, z1, z2, z3, z4), Cons(z5, z6)) -> Cons(dc#1(z0, z1, z2, z3, z4, z5), map#2(dc(z0, z1, z2, z3, z4), z6))
   divide_ys#1(z0, z1) -> Cons(take#2(z1, z0), Cons(drop#2(z1, z0), Nil))
   halve#1(0) -> 0
   halve#1(S(0)) -> S(0)
   halve#1(S(S(z0))) -> S(halve#1(z0))
   length#1(Nil) -> 0
   length#1(Cons(z0, z1)) -> S(length#1(z1))
   take#2(0, z0) -> Nil
   take#2(S(0), Nil) -> Cons(bot[0], Nil)
   take#2(S(z0), Cons(z1, z2)) -> Cons(z1, take#2(z0, z2))
   drop#2(0, z0) -> z0
   drop#2(S(0), Nil) -> bot[1]
   drop#2(S(z0), Cons(z1, z2)) -> drop#2(z0, z2)
   dc#1(map, divisible, mergesort_zs_3, divide, const_f, Nil) -> Nil
   dc#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Nil)) -> Cons(z0, Nil)
   dc#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> const_f#2(Cons(z0, Cons(z1, z2)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2))))))
   const_f#2(z0, Cons(z1, Cons(z2, z3))) -> merge#2(z1, z2)
   merge#2(Nil, z0) -> z0
   merge#2(Cons(z0, z1), Nil) -> Cons(z0, z1)
   merge#2(Cons(z0, z1), Cons(z2, z3)) -> cond_merge_ys_zs_2(leq#2(z0, z2), Cons(z0, z1), Cons(z2, z3), z0, z1, z2, z3)
   cond_merge_ys_zs_2(True, Cons(z0, z1), Cons(z2, z3), z4, z5, z6, z7) -> Cons(z4, merge#2(z5, Cons(z2, z3)))
   cond_merge_ys_zs_2(False, Cons(z0, z1), Cons(z2, z3), z4, z5, z6, z7) -> Cons(z6, merge#2(Cons(z0, z1), z7))
Tuples:
   DROP#2(S(z0), Cons(z1, z2)) -> c12(DROP#2(z0, z2))
   TAKE#2(S(z0), Cons(z1, z2)) -> c15(TAKE#2(z0, z2))
   HALVE#1(S(S(z0))) -> c18(HALVE#1(z0))
   CONST_F#2(z0, Cons(z1, Cons(z2, z3))) -> c19(MERGE#2(z1, z2))
   LEQ#2(S(z0), S(z1)) -> c22(LEQ#2(z0, z1))
   LENGTH#1(Cons(z0, z1)) -> c24(LENGTH#1(z1))
   MAP#2(dc(z0, z1, z2, z3, z4), Cons(z5, z6)) -> c26(DC#1(z0, z1, z2, z3, z4, z5))
   MAP#2(dc(z0, z1, z2, z3, z4), Cons(z5, z6)) -> c27(MAP#2(dc(z0, z1, z2, z3, z4), z6))
   MERGE#2(Cons(0, x1), Cons(z0, x3)) -> c6(COND_MERGE_YS_ZS_2(True, Cons(0, x1), Cons(z0, x3), 0, x1, z0, x3))
   MERGE#2(Cons(S(z0), x1), Cons(0, x3)) -> c6(COND_MERGE_YS_ZS_2(False, Cons(S(z0), x1), Cons(0, x3), S(z0), x1, 0, x3))
   MERGE#2(Cons(S(0), x1), Cons(S(z0), x3)) -> c6(COND_MERGE_YS_ZS_2(True, Cons(S(0), x1), Cons(S(z0), x3), S(0), x1, S(z0), x3), LEQ#2(S(0), S(z0)))
   MERGE#2(Cons(S(S(z0)), x1), Cons(S(0), x3)) -> c6(COND_MERGE_YS_ZS_2(False, Cons(S(S(z0)), x1), Cons(S(0), x3), S(S(z0)), x1, S(0), x3), LEQ#2(S(S(z0)), S(0)))
   MERGE#2(Cons(S(S(z0)), x1), Cons(S(S(z1)), x3)) -> c6(COND_MERGE_YS_ZS_2(leq#2(z0, z1), Cons(S(S(z0)), x1), Cons(S(S(z1)), x3), S(S(z0)), x1, S(S(z1)), x3), LEQ#2(S(S(z0)), S(S(z1))))
   MERGE#2(Cons(S(x0), x1), Cons(S(x2), x3)) -> c6(LEQ#2(S(x0), S(x2)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Cons(x2, Nil)))) -> c9(CONST_F#2(Cons(x0, Cons(x1, Cons(x2, Nil))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Cons(x2, Nil))), S(halve#1(S(0)))))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Cons(x2, Nil))), S(halve#1(length#1(Cons(x2, Nil)))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Nil))), S(halve#1(length#1(Cons(x2, Nil))))), HALVE#1(length#1(Cons(x2, Nil))), LENGTH#1(Cons(x2, Nil)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Cons(x2, Cons(z0, z1))))) -> c9(CONST_F#2(Cons(x0, Cons(x1, Cons(x2, Cons(z0, z1)))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Cons(x2, Cons(z0, z1)))), S(halve#1(S(S(length#1(z1)))))))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Cons(x2, Cons(z0, z1)))), S(halve#1(length#1(Cons(x2, Cons(z0, z1))))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Cons(z0, z1)))), S(halve#1(length#1(Cons(x2, Cons(z0, z1)))))), HALVE#1(length#1(Cons(x2, Cons(z0, z1)))), LENGTH#1(Cons(x2, Cons(z0, z1))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Cons(x2, x3)))) -> c9(MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Cons(x2, x3))), S(halve#1(length#1(Cons(x2, x3)))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, x3))), S(halve#1(length#1(Cons(x2, x3))))), HALVE#1(length#1(Cons(x2, x3))), LENGTH#1(Cons(x2, x3)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Nil))) -> c9(CONST_F#2(Cons(x0, Cons(x1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(0)), Cons(x0, Cons(x1, Nil))), Cons(drop#2(S(halve#1(0)), Cons(x0, Cons(x1, Nil))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Nil)), S(halve#1(length#1(Nil)))), HALVE#1(length#1(Nil)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Nil))) -> c9(CONST_F#2(Cons(x0, Cons(x1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Nil)), S(0)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Nil)), S(halve#1(length#1(Nil)))), HALVE#1(length#1(Nil)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> c9(CONST_F#2(Cons(z0, Cons(z1, z2)), Cons(dc#1(map, divisible, mergesort_zs_3, divide, const_f, take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2)))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(drop#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Nil))), DIVIDE_YS#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2)))), HALVE#1(length#1(z2)), LENGTH#1(z2))
   DIVIDE_YS#1(Cons(x0, Cons(x1, x2)), S(y11)) -> c(TAKE#2(S(y11), Cons(x0, Cons(x1, x2))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, x3))), S(y11)) -> c(TAKE#2(S(y11), Cons(x0, Cons(x1, Cons(x2, x3)))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Nil)), S(y10)) -> c(TAKE#2(S(y10), Cons(x0, Cons(x1, Nil))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Nil))), S(y7)) -> c(TAKE#2(S(y7), Cons(x0, Cons(x1, Cons(x2, Nil)))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4)))), S(y8)) -> c(TAKE#2(S(y8), Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4))))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, x2)), S(y11)) -> c1(DROP#2(S(y11), Cons(x0, Cons(x1, x2))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, x3))), S(y11)) -> c1(DROP#2(S(y11), Cons(x0, Cons(x1, Cons(x2, x3)))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Nil)), S(y10)) -> c1(DROP#2(S(y10), Cons(x0, Cons(x1, Nil))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Nil))), S(y7)) -> c1(DROP#2(S(y7), Cons(x0, Cons(x1, Cons(x2, Nil)))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4)))), S(y8)) -> c1(DROP#2(S(y8), Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4))))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> c9(CONST_F#2(Cons(z0, Cons(z1, z2)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(halve#1(length#1(z2)), Cons(z1, z2)), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Nil))), DIVIDE_YS#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2)))), HALVE#1(length#1(z2)), LENGTH#1(z2))
   COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(z2, z3), z4, Cons(0, y0), z6, z7) -> c2(MERGE#2(Cons(0, y0), Cons(z2, z3)))
   COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(0, z3), z4, Cons(S(y0), y1), z6, z7) -> c2(MERGE#2(Cons(S(y0), y1), Cons(0, z3)))
   COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(S(y1), z3), z4, Cons(S(0), y0), z6, z7) -> c2(MERGE#2(Cons(S(0), y0), Cons(S(y1), z3)))
   COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(S(0), z3), z4, Cons(S(S(y0)), y1), z6, z7) -> c2(MERGE#2(Cons(S(S(y0)), y1), Cons(S(0), z3)))
   COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(S(S(y2)), z3), z4, Cons(S(S(y0)), y1), z6, z7) -> c2(MERGE#2(Cons(S(S(y0)), y1), Cons(S(S(y2)), z3)))
   COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(S(y2), z3), z4, Cons(S(y0), y1), z6, z7) -> c2(MERGE#2(Cons(S(y0), y1), Cons(S(y2), z3)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, z3)))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Cons(z2, z3))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(Cons(z2, z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Cons(drop#2(S(halve#1(S(length#1(z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3)))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3))))), HALVE#1(S(length#1(z3))), LENGTH#1(Cons(z2, z3)))
   COND_MERGE_YS_ZS_2(False, Cons(S(x0), x1), Cons(0, x2), S(x0), x1, 0, x2) -> c3(MERGE#2(Cons(S(x0), x1), x2))
   COND_MERGE_YS_ZS_2(False, Cons(S(S(x0)), x1), Cons(S(0), x2), S(S(x0)), x1, S(0), x2) -> c3(MERGE#2(Cons(S(S(x0)), x1), x2))
   COND_MERGE_YS_ZS_2(False, Cons(S(S(x0)), x1), Cons(S(S(x2)), x3), S(S(x0)), x1, S(S(x2)), x3) -> c3(MERGE#2(Cons(S(S(x0)), x1), x3))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> c9(CONST_F#2(Cons(z0, Cons(z1, z2)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(Cons(z0, take#2(halve#1(length#1(z2)), Cons(z1, z2))), Cons(drop#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Nil))), DIVIDE_YS#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2)))), HALVE#1(length#1(z2)), LENGTH#1(z2))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, z3)))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Cons(z2, z3))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(S(length#1(z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Cons(drop#2(S(halve#1(length#1(Cons(z2, z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3)))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3))))), HALVE#1(S(length#1(z3))), LENGTH#1(Cons(z2, z3)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> c9(MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Nil))), DIVIDE_YS#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2)))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Nil))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(Nil))), Cons(z0, Cons(z1, Nil))), Cons(drop#2(S(halve#1(0)), Cons(z0, Cons(z1, Nil))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil)))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Nil))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(0)), Cons(z0, Cons(z1, Nil))), Cons(drop#2(S(halve#1(length#1(Nil))), Cons(z0, Cons(z1, Nil))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil)))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, z3)))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Cons(z2, z3))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(S(length#1(z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Cons(drop#2(S(halve#1(S(length#1(z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3)))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3))))), HALVE#1(S(length#1(z3))), LENGTH#1(Cons(z2, z3)))
S tuples:
   DROP#2(S(z0), Cons(z1, z2)) -> c12(DROP#2(z0, z2))
   TAKE#2(S(z0), Cons(z1, z2)) -> c15(TAKE#2(z0, z2))
   HALVE#1(S(S(z0))) -> c18(HALVE#1(z0))
   CONST_F#2(z0, Cons(z1, Cons(z2, z3))) -> c19(MERGE#2(z1, z2))
   LEQ#2(S(z0), S(z1)) -> c22(LEQ#2(z0, z1))
   LENGTH#1(Cons(z0, z1)) -> c24(LENGTH#1(z1))
   MAP#2(dc(z0, z1, z2, z3, z4), Cons(z5, z6)) -> c26(DC#1(z0, z1, z2, z3, z4, z5))
   MAP#2(dc(z0, z1, z2, z3, z4), Cons(z5, z6)) -> c27(MAP#2(dc(z0, z1, z2, z3, z4), z6))
   MERGE#2(Cons(0, x1), Cons(z0, x3)) -> c6(COND_MERGE_YS_ZS_2(True, Cons(0, x1), Cons(z0, x3), 0, x1, z0, x3))
   MERGE#2(Cons(S(z0), x1), Cons(0, x3)) -> c6(COND_MERGE_YS_ZS_2(False, Cons(S(z0), x1), Cons(0, x3), S(z0), x1, 0, x3))
   MERGE#2(Cons(S(0), x1), Cons(S(z0), x3)) -> c6(COND_MERGE_YS_ZS_2(True, Cons(S(0), x1), Cons(S(z0), x3), S(0), x1, S(z0), x3), LEQ#2(S(0), S(z0)))
   MERGE#2(Cons(S(S(z0)), x1), Cons(S(0), x3)) -> c6(COND_MERGE_YS_ZS_2(False, Cons(S(S(z0)), x1), Cons(S(0), x3), S(S(z0)), x1, S(0), x3), LEQ#2(S(S(z0)), S(0)))
   MERGE#2(Cons(S(S(z0)), x1), Cons(S(S(z1)), x3)) -> c6(COND_MERGE_YS_ZS_2(leq#2(z0, z1), Cons(S(S(z0)), x1), Cons(S(S(z1)), x3), S(S(z0)), x1, S(S(z1)), x3), LEQ#2(S(S(z0)), S(S(z1))))
   MERGE#2(Cons(S(x0), x1), Cons(S(x2), x3)) -> c6(LEQ#2(S(x0), S(x2)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Cons(x2, Nil)))) -> c9(CONST_F#2(Cons(x0, Cons(x1, Cons(x2, Nil))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Cons(x2, Nil))), S(halve#1(S(0)))))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Cons(x2, Nil))), S(halve#1(length#1(Cons(x2, Nil)))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Nil))), S(halve#1(length#1(Cons(x2, Nil))))), HALVE#1(length#1(Cons(x2, Nil))), LENGTH#1(Cons(x2, Nil)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Cons(x2, Cons(z0, z1))))) -> c9(CONST_F#2(Cons(x0, Cons(x1, Cons(x2, Cons(z0, z1)))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Cons(x2, Cons(z0, z1)))), S(halve#1(S(S(length#1(z1)))))))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Cons(x2, Cons(z0, z1)))), S(halve#1(length#1(Cons(x2, Cons(z0, z1))))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Cons(z0, z1)))), S(halve#1(length#1(Cons(x2, Cons(z0, z1)))))), HALVE#1(length#1(Cons(x2, Cons(z0, z1)))), LENGTH#1(Cons(x2, Cons(z0, z1))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Cons(x2, x3)))) -> c9(MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Cons(x2, x3))), S(halve#1(length#1(Cons(x2, x3)))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, x3))), S(halve#1(length#1(Cons(x2, x3))))), HALVE#1(length#1(Cons(x2, x3))), LENGTH#1(Cons(x2, x3)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Nil))) -> c9(CONST_F#2(Cons(x0, Cons(x1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(0)), Cons(x0, Cons(x1, Nil))), Cons(drop#2(S(halve#1(0)), Cons(x0, Cons(x1, Nil))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Nil)), S(halve#1(length#1(Nil)))), HALVE#1(length#1(Nil)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Nil))) -> c9(CONST_F#2(Cons(x0, Cons(x1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Nil)), S(0)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Nil)), S(halve#1(length#1(Nil)))), HALVE#1(length#1(Nil)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> c9(CONST_F#2(Cons(z0, Cons(z1, z2)), Cons(dc#1(map, divisible, mergesort_zs_3, divide, const_f, take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2)))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(drop#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Nil))), DIVIDE_YS#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2)))), HALVE#1(length#1(z2)), LENGTH#1(z2))
   DIVIDE_YS#1(Cons(x0, Cons(x1, x2)), S(y11)) -> c(TAKE#2(S(y11), Cons(x0, Cons(x1, x2))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, x3))), S(y11)) -> c(TAKE#2(S(y11), Cons(x0, Cons(x1, Cons(x2, x3)))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Nil)), S(y10)) -> c(TAKE#2(S(y10), Cons(x0, Cons(x1, Nil))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Nil))), S(y7)) -> c(TAKE#2(S(y7), Cons(x0, Cons(x1, Cons(x2, Nil)))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4)))), S(y8)) -> c(TAKE#2(S(y8), Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4))))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, x2)), S(y11)) -> c1(DROP#2(S(y11), Cons(x0, Cons(x1, x2))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, x3))), S(y11)) -> c1(DROP#2(S(y11), Cons(x0, Cons(x1, Cons(x2, x3)))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Nil)), S(y10)) -> c1(DROP#2(S(y10), Cons(x0, Cons(x1, Nil))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Nil))), S(y7)) -> c1(DROP#2(S(y7), Cons(x0, Cons(x1, Cons(x2, Nil)))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4)))), S(y8)) -> c1(DROP#2(S(y8), Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4))))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> c9(CONST_F#2(Cons(z0, Cons(z1, z2)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(halve#1(length#1(z2)), Cons(z1, z2)), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Nil))), DIVIDE_YS#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2)))), HALVE#1(length#1(z2)), LENGTH#1(z2))
   COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(z2, z3), z4, Cons(0, y0), z6, z7) -> c2(MERGE#2(Cons(0, y0), Cons(z2, z3)))
   COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(0, z3), z4, Cons(S(y0), y1), z6, z7) -> c2(MERGE#2(Cons(S(y0), y1), Cons(0, z3)))
   COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(S(y1), z3), z4, Cons(S(0), y0), z6, z7) -> c2(MERGE#2(Cons(S(0), y0), Cons(S(y1), z3)))
   COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(S(0), z3), z4, Cons(S(S(y0)), y1), z6, z7) -> c2(MERGE#2(Cons(S(S(y0)), y1), Cons(S(0), z3)))
   COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(S(S(y2)), z3), z4, Cons(S(S(y0)), y1), z6, z7) -> c2(MERGE#2(Cons(S(S(y0)), y1), Cons(S(S(y2)), z3)))
   COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(S(y2), z3), z4, Cons(S(y0), y1), z6, z7) -> c2(MERGE#2(Cons(S(y0), y1), Cons(S(y2), z3)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, z3)))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Cons(z2, z3))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(Cons(z2, z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Cons(drop#2(S(halve#1(S(length#1(z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3)))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3))))), HALVE#1(S(length#1(z3))), LENGTH#1(Cons(z2, z3)))
   COND_MERGE_YS_ZS_2(False, Cons(S(x0), x1), Cons(0, x2), S(x0), x1, 0, x2) -> c3(MERGE#2(Cons(S(x0), x1), x2))
   COND_MERGE_YS_ZS_2(False, Cons(S(S(x0)), x1), Cons(S(0), x2), S(S(x0)), x1, S(0), x2) -> c3(MERGE#2(Cons(S(S(x0)), x1), x2))
   COND_MERGE_YS_ZS_2(False, Cons(S(S(x0)), x1), Cons(S(S(x2)), x3), S(S(x0)), x1, S(S(x2)), x3) -> c3(MERGE#2(Cons(S(S(x0)), x1), x3))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> c9(CONST_F#2(Cons(z0, Cons(z1, z2)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(Cons(z0, take#2(halve#1(length#1(z2)), Cons(z1, z2))), Cons(drop#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Nil))), DIVIDE_YS#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2)))), HALVE#1(length#1(z2)), LENGTH#1(z2))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, z3)))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Cons(z2, z3))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(S(length#1(z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Cons(drop#2(S(halve#1(length#1(Cons(z2, z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3)))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3))))), HALVE#1(S(length#1(z3))), LENGTH#1(Cons(z2, z3)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> c9(MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Nil))), DIVIDE_YS#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2)))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Nil))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(Nil))), Cons(z0, Cons(z1, Nil))), Cons(drop#2(S(halve#1(0)), Cons(z0, Cons(z1, Nil))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil)))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Nil))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(0)), Cons(z0, Cons(z1, Nil))), Cons(drop#2(S(halve#1(length#1(Nil))), Cons(z0, Cons(z1, Nil))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil)))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, z3)))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Cons(z2, z3))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(S(length#1(z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Cons(drop#2(S(halve#1(S(length#1(z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3)))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3))))), HALVE#1(S(length#1(z3))), LENGTH#1(Cons(z2, z3)))
K tuples:none
Defined Rule Symbols:   leq#2_2, map#2_2, divide_ys#1_2, halve#1_1, length#1_1, take#2_2, drop#2_2, dc#1_6, const_f#2_2, merge#2_2, cond_merge_ys_zs_2_7

Defined Pair Symbols:   DROP#2_2, TAKE#2_2, HALVE#1_1, CONST_F#2_2, LEQ#2_2, LENGTH#1_1, MAP#2_2, MERGE#2_2, DC#1_6, DIVIDE_YS#1_2, COND_MERGE_YS_ZS_2_7

Compound Symbols:   c12_1, c15_1, c18_1, c19_1, c22_1, c24_1, c26_1, c27_1, c6_1, c6_2, c9_5, c9_4, c_1, c1_1, c2_1, c3_1, c9_2, c9_3


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

(131) CdtRewritingProof (BOTH BOUNDS(ID, ID))
Used rewriting to replace DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Cons(x2, Nil)))) -> c9(CONST_F#2(Cons(x0, Cons(x1, Cons(x2, Nil))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Cons(x2, Nil))), S(halve#1(S(0)))))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Cons(x2, Nil))), S(halve#1(length#1(Cons(x2, Nil)))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Nil))), S(halve#1(length#1(Cons(x2, Nil))))), HALVE#1(length#1(Cons(x2, Nil))), LENGTH#1(Cons(x2, Nil))) by DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, Nil)))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Cons(z2, Nil))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, Nil))), S(halve#1(S(0)))))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, Nil))), S(halve#1(length#1(Cons(z2, Nil)))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, Nil))), S(halve#1(length#1(Cons(z2, Nil))))), HALVE#1(S(length#1(Nil))), LENGTH#1(Cons(z2, Nil)))
----------------------------------------

(132)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   leq#2(0, z0) -> True
   leq#2(S(z0), 0) -> False
   leq#2(S(z0), S(z1)) -> leq#2(z0, z1)
   map#2(dc(z0, z1, z2, z3, z4), Nil) -> Nil
   map#2(dc(z0, z1, z2, z3, z4), Cons(z5, z6)) -> Cons(dc#1(z0, z1, z2, z3, z4, z5), map#2(dc(z0, z1, z2, z3, z4), z6))
   divide_ys#1(z0, z1) -> Cons(take#2(z1, z0), Cons(drop#2(z1, z0), Nil))
   halve#1(0) -> 0
   halve#1(S(0)) -> S(0)
   halve#1(S(S(z0))) -> S(halve#1(z0))
   length#1(Nil) -> 0
   length#1(Cons(z0, z1)) -> S(length#1(z1))
   take#2(0, z0) -> Nil
   take#2(S(0), Nil) -> Cons(bot[0], Nil)
   take#2(S(z0), Cons(z1, z2)) -> Cons(z1, take#2(z0, z2))
   drop#2(0, z0) -> z0
   drop#2(S(0), Nil) -> bot[1]
   drop#2(S(z0), Cons(z1, z2)) -> drop#2(z0, z2)
   dc#1(map, divisible, mergesort_zs_3, divide, const_f, Nil) -> Nil
   dc#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Nil)) -> Cons(z0, Nil)
   dc#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> const_f#2(Cons(z0, Cons(z1, z2)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2))))))
   const_f#2(z0, Cons(z1, Cons(z2, z3))) -> merge#2(z1, z2)
   merge#2(Nil, z0) -> z0
   merge#2(Cons(z0, z1), Nil) -> Cons(z0, z1)
   merge#2(Cons(z0, z1), Cons(z2, z3)) -> cond_merge_ys_zs_2(leq#2(z0, z2), Cons(z0, z1), Cons(z2, z3), z0, z1, z2, z3)
   cond_merge_ys_zs_2(True, Cons(z0, z1), Cons(z2, z3), z4, z5, z6, z7) -> Cons(z4, merge#2(z5, Cons(z2, z3)))
   cond_merge_ys_zs_2(False, Cons(z0, z1), Cons(z2, z3), z4, z5, z6, z7) -> Cons(z6, merge#2(Cons(z0, z1), z7))
Tuples:
   DROP#2(S(z0), Cons(z1, z2)) -> c12(DROP#2(z0, z2))
   TAKE#2(S(z0), Cons(z1, z2)) -> c15(TAKE#2(z0, z2))
   HALVE#1(S(S(z0))) -> c18(HALVE#1(z0))
   CONST_F#2(z0, Cons(z1, Cons(z2, z3))) -> c19(MERGE#2(z1, z2))
   LEQ#2(S(z0), S(z1)) -> c22(LEQ#2(z0, z1))
   LENGTH#1(Cons(z0, z1)) -> c24(LENGTH#1(z1))
   MAP#2(dc(z0, z1, z2, z3, z4), Cons(z5, z6)) -> c26(DC#1(z0, z1, z2, z3, z4, z5))
   MAP#2(dc(z0, z1, z2, z3, z4), Cons(z5, z6)) -> c27(MAP#2(dc(z0, z1, z2, z3, z4), z6))
   MERGE#2(Cons(0, x1), Cons(z0, x3)) -> c6(COND_MERGE_YS_ZS_2(True, Cons(0, x1), Cons(z0, x3), 0, x1, z0, x3))
   MERGE#2(Cons(S(z0), x1), Cons(0, x3)) -> c6(COND_MERGE_YS_ZS_2(False, Cons(S(z0), x1), Cons(0, x3), S(z0), x1, 0, x3))
   MERGE#2(Cons(S(0), x1), Cons(S(z0), x3)) -> c6(COND_MERGE_YS_ZS_2(True, Cons(S(0), x1), Cons(S(z0), x3), S(0), x1, S(z0), x3), LEQ#2(S(0), S(z0)))
   MERGE#2(Cons(S(S(z0)), x1), Cons(S(0), x3)) -> c6(COND_MERGE_YS_ZS_2(False, Cons(S(S(z0)), x1), Cons(S(0), x3), S(S(z0)), x1, S(0), x3), LEQ#2(S(S(z0)), S(0)))
   MERGE#2(Cons(S(S(z0)), x1), Cons(S(S(z1)), x3)) -> c6(COND_MERGE_YS_ZS_2(leq#2(z0, z1), Cons(S(S(z0)), x1), Cons(S(S(z1)), x3), S(S(z0)), x1, S(S(z1)), x3), LEQ#2(S(S(z0)), S(S(z1))))
   MERGE#2(Cons(S(x0), x1), Cons(S(x2), x3)) -> c6(LEQ#2(S(x0), S(x2)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Cons(x2, Cons(z0, z1))))) -> c9(CONST_F#2(Cons(x0, Cons(x1, Cons(x2, Cons(z0, z1)))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Cons(x2, Cons(z0, z1)))), S(halve#1(S(S(length#1(z1)))))))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Cons(x2, Cons(z0, z1)))), S(halve#1(length#1(Cons(x2, Cons(z0, z1))))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Cons(z0, z1)))), S(halve#1(length#1(Cons(x2, Cons(z0, z1)))))), HALVE#1(length#1(Cons(x2, Cons(z0, z1)))), LENGTH#1(Cons(x2, Cons(z0, z1))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Cons(x2, x3)))) -> c9(MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Cons(x2, x3))), S(halve#1(length#1(Cons(x2, x3)))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, x3))), S(halve#1(length#1(Cons(x2, x3))))), HALVE#1(length#1(Cons(x2, x3))), LENGTH#1(Cons(x2, x3)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Nil))) -> c9(CONST_F#2(Cons(x0, Cons(x1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(0)), Cons(x0, Cons(x1, Nil))), Cons(drop#2(S(halve#1(0)), Cons(x0, Cons(x1, Nil))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Nil)), S(halve#1(length#1(Nil)))), HALVE#1(length#1(Nil)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Nil))) -> c9(CONST_F#2(Cons(x0, Cons(x1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Nil)), S(0)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Nil)), S(halve#1(length#1(Nil)))), HALVE#1(length#1(Nil)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> c9(CONST_F#2(Cons(z0, Cons(z1, z2)), Cons(dc#1(map, divisible, mergesort_zs_3, divide, const_f, take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2)))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(drop#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Nil))), DIVIDE_YS#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2)))), HALVE#1(length#1(z2)), LENGTH#1(z2))
   DIVIDE_YS#1(Cons(x0, Cons(x1, x2)), S(y11)) -> c(TAKE#2(S(y11), Cons(x0, Cons(x1, x2))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, x3))), S(y11)) -> c(TAKE#2(S(y11), Cons(x0, Cons(x1, Cons(x2, x3)))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Nil)), S(y10)) -> c(TAKE#2(S(y10), Cons(x0, Cons(x1, Nil))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Nil))), S(y7)) -> c(TAKE#2(S(y7), Cons(x0, Cons(x1, Cons(x2, Nil)))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4)))), S(y8)) -> c(TAKE#2(S(y8), Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4))))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, x2)), S(y11)) -> c1(DROP#2(S(y11), Cons(x0, Cons(x1, x2))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, x3))), S(y11)) -> c1(DROP#2(S(y11), Cons(x0, Cons(x1, Cons(x2, x3)))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Nil)), S(y10)) -> c1(DROP#2(S(y10), Cons(x0, Cons(x1, Nil))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Nil))), S(y7)) -> c1(DROP#2(S(y7), Cons(x0, Cons(x1, Cons(x2, Nil)))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4)))), S(y8)) -> c1(DROP#2(S(y8), Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4))))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> c9(CONST_F#2(Cons(z0, Cons(z1, z2)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(halve#1(length#1(z2)), Cons(z1, z2)), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Nil))), DIVIDE_YS#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2)))), HALVE#1(length#1(z2)), LENGTH#1(z2))
   COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(z2, z3), z4, Cons(0, y0), z6, z7) -> c2(MERGE#2(Cons(0, y0), Cons(z2, z3)))
   COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(0, z3), z4, Cons(S(y0), y1), z6, z7) -> c2(MERGE#2(Cons(S(y0), y1), Cons(0, z3)))
   COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(S(y1), z3), z4, Cons(S(0), y0), z6, z7) -> c2(MERGE#2(Cons(S(0), y0), Cons(S(y1), z3)))
   COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(S(0), z3), z4, Cons(S(S(y0)), y1), z6, z7) -> c2(MERGE#2(Cons(S(S(y0)), y1), Cons(S(0), z3)))
   COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(S(S(y2)), z3), z4, Cons(S(S(y0)), y1), z6, z7) -> c2(MERGE#2(Cons(S(S(y0)), y1), Cons(S(S(y2)), z3)))
   COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(S(y2), z3), z4, Cons(S(y0), y1), z6, z7) -> c2(MERGE#2(Cons(S(y0), y1), Cons(S(y2), z3)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, z3)))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Cons(z2, z3))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(Cons(z2, z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Cons(drop#2(S(halve#1(S(length#1(z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3)))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3))))), HALVE#1(S(length#1(z3))), LENGTH#1(Cons(z2, z3)))
   COND_MERGE_YS_ZS_2(False, Cons(S(x0), x1), Cons(0, x2), S(x0), x1, 0, x2) -> c3(MERGE#2(Cons(S(x0), x1), x2))
   COND_MERGE_YS_ZS_2(False, Cons(S(S(x0)), x1), Cons(S(0), x2), S(S(x0)), x1, S(0), x2) -> c3(MERGE#2(Cons(S(S(x0)), x1), x2))
   COND_MERGE_YS_ZS_2(False, Cons(S(S(x0)), x1), Cons(S(S(x2)), x3), S(S(x0)), x1, S(S(x2)), x3) -> c3(MERGE#2(Cons(S(S(x0)), x1), x3))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> c9(CONST_F#2(Cons(z0, Cons(z1, z2)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(Cons(z0, take#2(halve#1(length#1(z2)), Cons(z1, z2))), Cons(drop#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Nil))), DIVIDE_YS#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2)))), HALVE#1(length#1(z2)), LENGTH#1(z2))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, z3)))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Cons(z2, z3))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(S(length#1(z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Cons(drop#2(S(halve#1(length#1(Cons(z2, z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3)))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3))))), HALVE#1(S(length#1(z3))), LENGTH#1(Cons(z2, z3)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> c9(MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Nil))), DIVIDE_YS#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2)))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Nil))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(Nil))), Cons(z0, Cons(z1, Nil))), Cons(drop#2(S(halve#1(0)), Cons(z0, Cons(z1, Nil))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil)))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Nil))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(0)), Cons(z0, Cons(z1, Nil))), Cons(drop#2(S(halve#1(length#1(Nil))), Cons(z0, Cons(z1, Nil))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil)))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, z3)))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Cons(z2, z3))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(S(length#1(z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Cons(drop#2(S(halve#1(S(length#1(z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3)))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3))))), HALVE#1(S(length#1(z3))), LENGTH#1(Cons(z2, z3)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, Nil)))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Cons(z2, Nil))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, Nil))), S(halve#1(S(0)))))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, Nil))), S(halve#1(length#1(Cons(z2, Nil)))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, Nil))), S(halve#1(length#1(Cons(z2, Nil))))), HALVE#1(S(length#1(Nil))), LENGTH#1(Cons(z2, Nil)))
S tuples:
   DROP#2(S(z0), Cons(z1, z2)) -> c12(DROP#2(z0, z2))
   TAKE#2(S(z0), Cons(z1, z2)) -> c15(TAKE#2(z0, z2))
   HALVE#1(S(S(z0))) -> c18(HALVE#1(z0))
   CONST_F#2(z0, Cons(z1, Cons(z2, z3))) -> c19(MERGE#2(z1, z2))
   LEQ#2(S(z0), S(z1)) -> c22(LEQ#2(z0, z1))
   LENGTH#1(Cons(z0, z1)) -> c24(LENGTH#1(z1))
   MAP#2(dc(z0, z1, z2, z3, z4), Cons(z5, z6)) -> c26(DC#1(z0, z1, z2, z3, z4, z5))
   MAP#2(dc(z0, z1, z2, z3, z4), Cons(z5, z6)) -> c27(MAP#2(dc(z0, z1, z2, z3, z4), z6))
   MERGE#2(Cons(0, x1), Cons(z0, x3)) -> c6(COND_MERGE_YS_ZS_2(True, Cons(0, x1), Cons(z0, x3), 0, x1, z0, x3))
   MERGE#2(Cons(S(z0), x1), Cons(0, x3)) -> c6(COND_MERGE_YS_ZS_2(False, Cons(S(z0), x1), Cons(0, x3), S(z0), x1, 0, x3))
   MERGE#2(Cons(S(0), x1), Cons(S(z0), x3)) -> c6(COND_MERGE_YS_ZS_2(True, Cons(S(0), x1), Cons(S(z0), x3), S(0), x1, S(z0), x3), LEQ#2(S(0), S(z0)))
   MERGE#2(Cons(S(S(z0)), x1), Cons(S(0), x3)) -> c6(COND_MERGE_YS_ZS_2(False, Cons(S(S(z0)), x1), Cons(S(0), x3), S(S(z0)), x1, S(0), x3), LEQ#2(S(S(z0)), S(0)))
   MERGE#2(Cons(S(S(z0)), x1), Cons(S(S(z1)), x3)) -> c6(COND_MERGE_YS_ZS_2(leq#2(z0, z1), Cons(S(S(z0)), x1), Cons(S(S(z1)), x3), S(S(z0)), x1, S(S(z1)), x3), LEQ#2(S(S(z0)), S(S(z1))))
   MERGE#2(Cons(S(x0), x1), Cons(S(x2), x3)) -> c6(LEQ#2(S(x0), S(x2)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Cons(x2, Cons(z0, z1))))) -> c9(CONST_F#2(Cons(x0, Cons(x1, Cons(x2, Cons(z0, z1)))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Cons(x2, Cons(z0, z1)))), S(halve#1(S(S(length#1(z1)))))))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Cons(x2, Cons(z0, z1)))), S(halve#1(length#1(Cons(x2, Cons(z0, z1))))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Cons(z0, z1)))), S(halve#1(length#1(Cons(x2, Cons(z0, z1)))))), HALVE#1(length#1(Cons(x2, Cons(z0, z1)))), LENGTH#1(Cons(x2, Cons(z0, z1))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Cons(x2, x3)))) -> c9(MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Cons(x2, x3))), S(halve#1(length#1(Cons(x2, x3)))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, x3))), S(halve#1(length#1(Cons(x2, x3))))), HALVE#1(length#1(Cons(x2, x3))), LENGTH#1(Cons(x2, x3)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Nil))) -> c9(CONST_F#2(Cons(x0, Cons(x1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(0)), Cons(x0, Cons(x1, Nil))), Cons(drop#2(S(halve#1(0)), Cons(x0, Cons(x1, Nil))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Nil)), S(halve#1(length#1(Nil)))), HALVE#1(length#1(Nil)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Nil))) -> c9(CONST_F#2(Cons(x0, Cons(x1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Nil)), S(0)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Nil)), S(halve#1(length#1(Nil)))), HALVE#1(length#1(Nil)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> c9(CONST_F#2(Cons(z0, Cons(z1, z2)), Cons(dc#1(map, divisible, mergesort_zs_3, divide, const_f, take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2)))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(drop#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Nil))), DIVIDE_YS#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2)))), HALVE#1(length#1(z2)), LENGTH#1(z2))
   DIVIDE_YS#1(Cons(x0, Cons(x1, x2)), S(y11)) -> c(TAKE#2(S(y11), Cons(x0, Cons(x1, x2))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, x3))), S(y11)) -> c(TAKE#2(S(y11), Cons(x0, Cons(x1, Cons(x2, x3)))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Nil)), S(y10)) -> c(TAKE#2(S(y10), Cons(x0, Cons(x1, Nil))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Nil))), S(y7)) -> c(TAKE#2(S(y7), Cons(x0, Cons(x1, Cons(x2, Nil)))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4)))), S(y8)) -> c(TAKE#2(S(y8), Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4))))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, x2)), S(y11)) -> c1(DROP#2(S(y11), Cons(x0, Cons(x1, x2))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, x3))), S(y11)) -> c1(DROP#2(S(y11), Cons(x0, Cons(x1, Cons(x2, x3)))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Nil)), S(y10)) -> c1(DROP#2(S(y10), Cons(x0, Cons(x1, Nil))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Nil))), S(y7)) -> c1(DROP#2(S(y7), Cons(x0, Cons(x1, Cons(x2, Nil)))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4)))), S(y8)) -> c1(DROP#2(S(y8), Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4))))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> c9(CONST_F#2(Cons(z0, Cons(z1, z2)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(halve#1(length#1(z2)), Cons(z1, z2)), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Nil))), DIVIDE_YS#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2)))), HALVE#1(length#1(z2)), LENGTH#1(z2))
   COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(z2, z3), z4, Cons(0, y0), z6, z7) -> c2(MERGE#2(Cons(0, y0), Cons(z2, z3)))
   COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(0, z3), z4, Cons(S(y0), y1), z6, z7) -> c2(MERGE#2(Cons(S(y0), y1), Cons(0, z3)))
   COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(S(y1), z3), z4, Cons(S(0), y0), z6, z7) -> c2(MERGE#2(Cons(S(0), y0), Cons(S(y1), z3)))
   COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(S(0), z3), z4, Cons(S(S(y0)), y1), z6, z7) -> c2(MERGE#2(Cons(S(S(y0)), y1), Cons(S(0), z3)))
   COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(S(S(y2)), z3), z4, Cons(S(S(y0)), y1), z6, z7) -> c2(MERGE#2(Cons(S(S(y0)), y1), Cons(S(S(y2)), z3)))
   COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(S(y2), z3), z4, Cons(S(y0), y1), z6, z7) -> c2(MERGE#2(Cons(S(y0), y1), Cons(S(y2), z3)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, z3)))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Cons(z2, z3))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(Cons(z2, z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Cons(drop#2(S(halve#1(S(length#1(z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3)))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3))))), HALVE#1(S(length#1(z3))), LENGTH#1(Cons(z2, z3)))
   COND_MERGE_YS_ZS_2(False, Cons(S(x0), x1), Cons(0, x2), S(x0), x1, 0, x2) -> c3(MERGE#2(Cons(S(x0), x1), x2))
   COND_MERGE_YS_ZS_2(False, Cons(S(S(x0)), x1), Cons(S(0), x2), S(S(x0)), x1, S(0), x2) -> c3(MERGE#2(Cons(S(S(x0)), x1), x2))
   COND_MERGE_YS_ZS_2(False, Cons(S(S(x0)), x1), Cons(S(S(x2)), x3), S(S(x0)), x1, S(S(x2)), x3) -> c3(MERGE#2(Cons(S(S(x0)), x1), x3))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> c9(CONST_F#2(Cons(z0, Cons(z1, z2)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(Cons(z0, take#2(halve#1(length#1(z2)), Cons(z1, z2))), Cons(drop#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Nil))), DIVIDE_YS#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2)))), HALVE#1(length#1(z2)), LENGTH#1(z2))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, z3)))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Cons(z2, z3))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(S(length#1(z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Cons(drop#2(S(halve#1(length#1(Cons(z2, z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3)))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3))))), HALVE#1(S(length#1(z3))), LENGTH#1(Cons(z2, z3)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> c9(MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Nil))), DIVIDE_YS#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2)))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Nil))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(Nil))), Cons(z0, Cons(z1, Nil))), Cons(drop#2(S(halve#1(0)), Cons(z0, Cons(z1, Nil))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil)))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Nil))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(0)), Cons(z0, Cons(z1, Nil))), Cons(drop#2(S(halve#1(length#1(Nil))), Cons(z0, Cons(z1, Nil))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil)))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, z3)))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Cons(z2, z3))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(S(length#1(z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Cons(drop#2(S(halve#1(S(length#1(z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3)))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3))))), HALVE#1(S(length#1(z3))), LENGTH#1(Cons(z2, z3)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, Nil)))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Cons(z2, Nil))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, Nil))), S(halve#1(S(0)))))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, Nil))), S(halve#1(length#1(Cons(z2, Nil)))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, Nil))), S(halve#1(length#1(Cons(z2, Nil))))), HALVE#1(S(length#1(Nil))), LENGTH#1(Cons(z2, Nil)))
K tuples:none
Defined Rule Symbols:   leq#2_2, map#2_2, divide_ys#1_2, halve#1_1, length#1_1, take#2_2, drop#2_2, dc#1_6, const_f#2_2, merge#2_2, cond_merge_ys_zs_2_7

Defined Pair Symbols:   DROP#2_2, TAKE#2_2, HALVE#1_1, CONST_F#2_2, LEQ#2_2, LENGTH#1_1, MAP#2_2, MERGE#2_2, DC#1_6, DIVIDE_YS#1_2, COND_MERGE_YS_ZS_2_7

Compound Symbols:   c12_1, c15_1, c18_1, c19_1, c22_1, c24_1, c26_1, c27_1, c6_1, c6_2, c9_5, c9_4, c_1, c1_1, c2_1, c3_1, c9_2, c9_3


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

(133) CdtRewritingProof (BOTH BOUNDS(ID, ID))
Used rewriting to replace DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Cons(x2, Cons(z0, z1))))) -> c9(CONST_F#2(Cons(x0, Cons(x1, Cons(x2, Cons(z0, z1)))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Cons(x2, Cons(z0, z1)))), S(halve#1(S(S(length#1(z1)))))))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Cons(x2, Cons(z0, z1)))), S(halve#1(length#1(Cons(x2, Cons(z0, z1))))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Cons(z0, z1)))), S(halve#1(length#1(Cons(x2, Cons(z0, z1)))))), HALVE#1(length#1(Cons(x2, Cons(z0, z1)))), LENGTH#1(Cons(x2, Cons(z0, z1)))) by DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, Cons(z3, z4))))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Cons(z2, Cons(z3, z4)))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, Cons(z3, z4)))), S(halve#1(S(S(length#1(z4)))))))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, Cons(z3, z4)))), S(halve#1(length#1(Cons(z2, Cons(z3, z4))))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, Cons(z3, z4)))), S(halve#1(length#1(Cons(z2, Cons(z3, z4)))))), HALVE#1(S(length#1(Cons(z3, z4)))), LENGTH#1(Cons(z2, Cons(z3, z4))))
----------------------------------------

(134)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   leq#2(0, z0) -> True
   leq#2(S(z0), 0) -> False
   leq#2(S(z0), S(z1)) -> leq#2(z0, z1)
   map#2(dc(z0, z1, z2, z3, z4), Nil) -> Nil
   map#2(dc(z0, z1, z2, z3, z4), Cons(z5, z6)) -> Cons(dc#1(z0, z1, z2, z3, z4, z5), map#2(dc(z0, z1, z2, z3, z4), z6))
   divide_ys#1(z0, z1) -> Cons(take#2(z1, z0), Cons(drop#2(z1, z0), Nil))
   halve#1(0) -> 0
   halve#1(S(0)) -> S(0)
   halve#1(S(S(z0))) -> S(halve#1(z0))
   length#1(Nil) -> 0
   length#1(Cons(z0, z1)) -> S(length#1(z1))
   take#2(0, z0) -> Nil
   take#2(S(0), Nil) -> Cons(bot[0], Nil)
   take#2(S(z0), Cons(z1, z2)) -> Cons(z1, take#2(z0, z2))
   drop#2(0, z0) -> z0
   drop#2(S(0), Nil) -> bot[1]
   drop#2(S(z0), Cons(z1, z2)) -> drop#2(z0, z2)
   dc#1(map, divisible, mergesort_zs_3, divide, const_f, Nil) -> Nil
   dc#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Nil)) -> Cons(z0, Nil)
   dc#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> const_f#2(Cons(z0, Cons(z1, z2)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2))))))
   const_f#2(z0, Cons(z1, Cons(z2, z3))) -> merge#2(z1, z2)
   merge#2(Nil, z0) -> z0
   merge#2(Cons(z0, z1), Nil) -> Cons(z0, z1)
   merge#2(Cons(z0, z1), Cons(z2, z3)) -> cond_merge_ys_zs_2(leq#2(z0, z2), Cons(z0, z1), Cons(z2, z3), z0, z1, z2, z3)
   cond_merge_ys_zs_2(True, Cons(z0, z1), Cons(z2, z3), z4, z5, z6, z7) -> Cons(z4, merge#2(z5, Cons(z2, z3)))
   cond_merge_ys_zs_2(False, Cons(z0, z1), Cons(z2, z3), z4, z5, z6, z7) -> Cons(z6, merge#2(Cons(z0, z1), z7))
Tuples:
   DROP#2(S(z0), Cons(z1, z2)) -> c12(DROP#2(z0, z2))
   TAKE#2(S(z0), Cons(z1, z2)) -> c15(TAKE#2(z0, z2))
   HALVE#1(S(S(z0))) -> c18(HALVE#1(z0))
   CONST_F#2(z0, Cons(z1, Cons(z2, z3))) -> c19(MERGE#2(z1, z2))
   LEQ#2(S(z0), S(z1)) -> c22(LEQ#2(z0, z1))
   LENGTH#1(Cons(z0, z1)) -> c24(LENGTH#1(z1))
   MAP#2(dc(z0, z1, z2, z3, z4), Cons(z5, z6)) -> c26(DC#1(z0, z1, z2, z3, z4, z5))
   MAP#2(dc(z0, z1, z2, z3, z4), Cons(z5, z6)) -> c27(MAP#2(dc(z0, z1, z2, z3, z4), z6))
   MERGE#2(Cons(0, x1), Cons(z0, x3)) -> c6(COND_MERGE_YS_ZS_2(True, Cons(0, x1), Cons(z0, x3), 0, x1, z0, x3))
   MERGE#2(Cons(S(z0), x1), Cons(0, x3)) -> c6(COND_MERGE_YS_ZS_2(False, Cons(S(z0), x1), Cons(0, x3), S(z0), x1, 0, x3))
   MERGE#2(Cons(S(0), x1), Cons(S(z0), x3)) -> c6(COND_MERGE_YS_ZS_2(True, Cons(S(0), x1), Cons(S(z0), x3), S(0), x1, S(z0), x3), LEQ#2(S(0), S(z0)))
   MERGE#2(Cons(S(S(z0)), x1), Cons(S(0), x3)) -> c6(COND_MERGE_YS_ZS_2(False, Cons(S(S(z0)), x1), Cons(S(0), x3), S(S(z0)), x1, S(0), x3), LEQ#2(S(S(z0)), S(0)))
   MERGE#2(Cons(S(S(z0)), x1), Cons(S(S(z1)), x3)) -> c6(COND_MERGE_YS_ZS_2(leq#2(z0, z1), Cons(S(S(z0)), x1), Cons(S(S(z1)), x3), S(S(z0)), x1, S(S(z1)), x3), LEQ#2(S(S(z0)), S(S(z1))))
   MERGE#2(Cons(S(x0), x1), Cons(S(x2), x3)) -> c6(LEQ#2(S(x0), S(x2)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Cons(x2, x3)))) -> c9(MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Cons(x2, x3))), S(halve#1(length#1(Cons(x2, x3)))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, x3))), S(halve#1(length#1(Cons(x2, x3))))), HALVE#1(length#1(Cons(x2, x3))), LENGTH#1(Cons(x2, x3)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Nil))) -> c9(CONST_F#2(Cons(x0, Cons(x1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(0)), Cons(x0, Cons(x1, Nil))), Cons(drop#2(S(halve#1(0)), Cons(x0, Cons(x1, Nil))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Nil)), S(halve#1(length#1(Nil)))), HALVE#1(length#1(Nil)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Nil))) -> c9(CONST_F#2(Cons(x0, Cons(x1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Nil)), S(0)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Nil)), S(halve#1(length#1(Nil)))), HALVE#1(length#1(Nil)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> c9(CONST_F#2(Cons(z0, Cons(z1, z2)), Cons(dc#1(map, divisible, mergesort_zs_3, divide, const_f, take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2)))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(drop#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Nil))), DIVIDE_YS#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2)))), HALVE#1(length#1(z2)), LENGTH#1(z2))
   DIVIDE_YS#1(Cons(x0, Cons(x1, x2)), S(y11)) -> c(TAKE#2(S(y11), Cons(x0, Cons(x1, x2))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, x3))), S(y11)) -> c(TAKE#2(S(y11), Cons(x0, Cons(x1, Cons(x2, x3)))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Nil)), S(y10)) -> c(TAKE#2(S(y10), Cons(x0, Cons(x1, Nil))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Nil))), S(y7)) -> c(TAKE#2(S(y7), Cons(x0, Cons(x1, Cons(x2, Nil)))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4)))), S(y8)) -> c(TAKE#2(S(y8), Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4))))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, x2)), S(y11)) -> c1(DROP#2(S(y11), Cons(x0, Cons(x1, x2))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, x3))), S(y11)) -> c1(DROP#2(S(y11), Cons(x0, Cons(x1, Cons(x2, x3)))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Nil)), S(y10)) -> c1(DROP#2(S(y10), Cons(x0, Cons(x1, Nil))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Nil))), S(y7)) -> c1(DROP#2(S(y7), Cons(x0, Cons(x1, Cons(x2, Nil)))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4)))), S(y8)) -> c1(DROP#2(S(y8), Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4))))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> c9(CONST_F#2(Cons(z0, Cons(z1, z2)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(halve#1(length#1(z2)), Cons(z1, z2)), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Nil))), DIVIDE_YS#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2)))), HALVE#1(length#1(z2)), LENGTH#1(z2))
   COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(z2, z3), z4, Cons(0, y0), z6, z7) -> c2(MERGE#2(Cons(0, y0), Cons(z2, z3)))
   COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(0, z3), z4, Cons(S(y0), y1), z6, z7) -> c2(MERGE#2(Cons(S(y0), y1), Cons(0, z3)))
   COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(S(y1), z3), z4, Cons(S(0), y0), z6, z7) -> c2(MERGE#2(Cons(S(0), y0), Cons(S(y1), z3)))
   COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(S(0), z3), z4, Cons(S(S(y0)), y1), z6, z7) -> c2(MERGE#2(Cons(S(S(y0)), y1), Cons(S(0), z3)))
   COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(S(S(y2)), z3), z4, Cons(S(S(y0)), y1), z6, z7) -> c2(MERGE#2(Cons(S(S(y0)), y1), Cons(S(S(y2)), z3)))
   COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(S(y2), z3), z4, Cons(S(y0), y1), z6, z7) -> c2(MERGE#2(Cons(S(y0), y1), Cons(S(y2), z3)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, z3)))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Cons(z2, z3))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(Cons(z2, z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Cons(drop#2(S(halve#1(S(length#1(z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3)))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3))))), HALVE#1(S(length#1(z3))), LENGTH#1(Cons(z2, z3)))
   COND_MERGE_YS_ZS_2(False, Cons(S(x0), x1), Cons(0, x2), S(x0), x1, 0, x2) -> c3(MERGE#2(Cons(S(x0), x1), x2))
   COND_MERGE_YS_ZS_2(False, Cons(S(S(x0)), x1), Cons(S(0), x2), S(S(x0)), x1, S(0), x2) -> c3(MERGE#2(Cons(S(S(x0)), x1), x2))
   COND_MERGE_YS_ZS_2(False, Cons(S(S(x0)), x1), Cons(S(S(x2)), x3), S(S(x0)), x1, S(S(x2)), x3) -> c3(MERGE#2(Cons(S(S(x0)), x1), x3))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> c9(CONST_F#2(Cons(z0, Cons(z1, z2)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(Cons(z0, take#2(halve#1(length#1(z2)), Cons(z1, z2))), Cons(drop#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Nil))), DIVIDE_YS#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2)))), HALVE#1(length#1(z2)), LENGTH#1(z2))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, z3)))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Cons(z2, z3))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(S(length#1(z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Cons(drop#2(S(halve#1(length#1(Cons(z2, z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3)))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3))))), HALVE#1(S(length#1(z3))), LENGTH#1(Cons(z2, z3)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> c9(MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Nil))), DIVIDE_YS#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2)))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Nil))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(Nil))), Cons(z0, Cons(z1, Nil))), Cons(drop#2(S(halve#1(0)), Cons(z0, Cons(z1, Nil))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil)))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Nil))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(0)), Cons(z0, Cons(z1, Nil))), Cons(drop#2(S(halve#1(length#1(Nil))), Cons(z0, Cons(z1, Nil))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil)))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, z3)))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Cons(z2, z3))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(S(length#1(z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Cons(drop#2(S(halve#1(S(length#1(z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3)))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3))))), HALVE#1(S(length#1(z3))), LENGTH#1(Cons(z2, z3)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, Nil)))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Cons(z2, Nil))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, Nil))), S(halve#1(S(0)))))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, Nil))), S(halve#1(length#1(Cons(z2, Nil)))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, Nil))), S(halve#1(length#1(Cons(z2, Nil))))), HALVE#1(S(length#1(Nil))), LENGTH#1(Cons(z2, Nil)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, Cons(z3, z4))))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Cons(z2, Cons(z3, z4)))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, Cons(z3, z4)))), S(halve#1(S(S(length#1(z4)))))))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, Cons(z3, z4)))), S(halve#1(length#1(Cons(z2, Cons(z3, z4))))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, Cons(z3, z4)))), S(halve#1(length#1(Cons(z2, Cons(z3, z4)))))), HALVE#1(S(length#1(Cons(z3, z4)))), LENGTH#1(Cons(z2, Cons(z3, z4))))
S tuples:
   DROP#2(S(z0), Cons(z1, z2)) -> c12(DROP#2(z0, z2))
   TAKE#2(S(z0), Cons(z1, z2)) -> c15(TAKE#2(z0, z2))
   HALVE#1(S(S(z0))) -> c18(HALVE#1(z0))
   CONST_F#2(z0, Cons(z1, Cons(z2, z3))) -> c19(MERGE#2(z1, z2))
   LEQ#2(S(z0), S(z1)) -> c22(LEQ#2(z0, z1))
   LENGTH#1(Cons(z0, z1)) -> c24(LENGTH#1(z1))
   MAP#2(dc(z0, z1, z2, z3, z4), Cons(z5, z6)) -> c26(DC#1(z0, z1, z2, z3, z4, z5))
   MAP#2(dc(z0, z1, z2, z3, z4), Cons(z5, z6)) -> c27(MAP#2(dc(z0, z1, z2, z3, z4), z6))
   MERGE#2(Cons(0, x1), Cons(z0, x3)) -> c6(COND_MERGE_YS_ZS_2(True, Cons(0, x1), Cons(z0, x3), 0, x1, z0, x3))
   MERGE#2(Cons(S(z0), x1), Cons(0, x3)) -> c6(COND_MERGE_YS_ZS_2(False, Cons(S(z0), x1), Cons(0, x3), S(z0), x1, 0, x3))
   MERGE#2(Cons(S(0), x1), Cons(S(z0), x3)) -> c6(COND_MERGE_YS_ZS_2(True, Cons(S(0), x1), Cons(S(z0), x3), S(0), x1, S(z0), x3), LEQ#2(S(0), S(z0)))
   MERGE#2(Cons(S(S(z0)), x1), Cons(S(0), x3)) -> c6(COND_MERGE_YS_ZS_2(False, Cons(S(S(z0)), x1), Cons(S(0), x3), S(S(z0)), x1, S(0), x3), LEQ#2(S(S(z0)), S(0)))
   MERGE#2(Cons(S(S(z0)), x1), Cons(S(S(z1)), x3)) -> c6(COND_MERGE_YS_ZS_2(leq#2(z0, z1), Cons(S(S(z0)), x1), Cons(S(S(z1)), x3), S(S(z0)), x1, S(S(z1)), x3), LEQ#2(S(S(z0)), S(S(z1))))
   MERGE#2(Cons(S(x0), x1), Cons(S(x2), x3)) -> c6(LEQ#2(S(x0), S(x2)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Cons(x2, x3)))) -> c9(MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Cons(x2, x3))), S(halve#1(length#1(Cons(x2, x3)))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, x3))), S(halve#1(length#1(Cons(x2, x3))))), HALVE#1(length#1(Cons(x2, x3))), LENGTH#1(Cons(x2, x3)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Nil))) -> c9(CONST_F#2(Cons(x0, Cons(x1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(0)), Cons(x0, Cons(x1, Nil))), Cons(drop#2(S(halve#1(0)), Cons(x0, Cons(x1, Nil))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Nil)), S(halve#1(length#1(Nil)))), HALVE#1(length#1(Nil)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Nil))) -> c9(CONST_F#2(Cons(x0, Cons(x1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Nil)), S(0)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Nil)), S(halve#1(length#1(Nil)))), HALVE#1(length#1(Nil)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> c9(CONST_F#2(Cons(z0, Cons(z1, z2)), Cons(dc#1(map, divisible, mergesort_zs_3, divide, const_f, take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2)))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(drop#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Nil))), DIVIDE_YS#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2)))), HALVE#1(length#1(z2)), LENGTH#1(z2))
   DIVIDE_YS#1(Cons(x0, Cons(x1, x2)), S(y11)) -> c(TAKE#2(S(y11), Cons(x0, Cons(x1, x2))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, x3))), S(y11)) -> c(TAKE#2(S(y11), Cons(x0, Cons(x1, Cons(x2, x3)))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Nil)), S(y10)) -> c(TAKE#2(S(y10), Cons(x0, Cons(x1, Nil))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Nil))), S(y7)) -> c(TAKE#2(S(y7), Cons(x0, Cons(x1, Cons(x2, Nil)))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4)))), S(y8)) -> c(TAKE#2(S(y8), Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4))))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, x2)), S(y11)) -> c1(DROP#2(S(y11), Cons(x0, Cons(x1, x2))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, x3))), S(y11)) -> c1(DROP#2(S(y11), Cons(x0, Cons(x1, Cons(x2, x3)))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Nil)), S(y10)) -> c1(DROP#2(S(y10), Cons(x0, Cons(x1, Nil))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Nil))), S(y7)) -> c1(DROP#2(S(y7), Cons(x0, Cons(x1, Cons(x2, Nil)))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4)))), S(y8)) -> c1(DROP#2(S(y8), Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4))))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> c9(CONST_F#2(Cons(z0, Cons(z1, z2)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(halve#1(length#1(z2)), Cons(z1, z2)), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Nil))), DIVIDE_YS#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2)))), HALVE#1(length#1(z2)), LENGTH#1(z2))
   COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(z2, z3), z4, Cons(0, y0), z6, z7) -> c2(MERGE#2(Cons(0, y0), Cons(z2, z3)))
   COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(0, z3), z4, Cons(S(y0), y1), z6, z7) -> c2(MERGE#2(Cons(S(y0), y1), Cons(0, z3)))
   COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(S(y1), z3), z4, Cons(S(0), y0), z6, z7) -> c2(MERGE#2(Cons(S(0), y0), Cons(S(y1), z3)))
   COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(S(0), z3), z4, Cons(S(S(y0)), y1), z6, z7) -> c2(MERGE#2(Cons(S(S(y0)), y1), Cons(S(0), z3)))
   COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(S(S(y2)), z3), z4, Cons(S(S(y0)), y1), z6, z7) -> c2(MERGE#2(Cons(S(S(y0)), y1), Cons(S(S(y2)), z3)))
   COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(S(y2), z3), z4, Cons(S(y0), y1), z6, z7) -> c2(MERGE#2(Cons(S(y0), y1), Cons(S(y2), z3)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, z3)))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Cons(z2, z3))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(Cons(z2, z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Cons(drop#2(S(halve#1(S(length#1(z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3)))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3))))), HALVE#1(S(length#1(z3))), LENGTH#1(Cons(z2, z3)))
   COND_MERGE_YS_ZS_2(False, Cons(S(x0), x1), Cons(0, x2), S(x0), x1, 0, x2) -> c3(MERGE#2(Cons(S(x0), x1), x2))
   COND_MERGE_YS_ZS_2(False, Cons(S(S(x0)), x1), Cons(S(0), x2), S(S(x0)), x1, S(0), x2) -> c3(MERGE#2(Cons(S(S(x0)), x1), x2))
   COND_MERGE_YS_ZS_2(False, Cons(S(S(x0)), x1), Cons(S(S(x2)), x3), S(S(x0)), x1, S(S(x2)), x3) -> c3(MERGE#2(Cons(S(S(x0)), x1), x3))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> c9(CONST_F#2(Cons(z0, Cons(z1, z2)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(Cons(z0, take#2(halve#1(length#1(z2)), Cons(z1, z2))), Cons(drop#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Nil))), DIVIDE_YS#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2)))), HALVE#1(length#1(z2)), LENGTH#1(z2))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, z3)))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Cons(z2, z3))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(S(length#1(z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Cons(drop#2(S(halve#1(length#1(Cons(z2, z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3)))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3))))), HALVE#1(S(length#1(z3))), LENGTH#1(Cons(z2, z3)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> c9(MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Nil))), DIVIDE_YS#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2)))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Nil))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(Nil))), Cons(z0, Cons(z1, Nil))), Cons(drop#2(S(halve#1(0)), Cons(z0, Cons(z1, Nil))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil)))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Nil))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(0)), Cons(z0, Cons(z1, Nil))), Cons(drop#2(S(halve#1(length#1(Nil))), Cons(z0, Cons(z1, Nil))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil)))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, z3)))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Cons(z2, z3))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(S(length#1(z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Cons(drop#2(S(halve#1(S(length#1(z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3)))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3))))), HALVE#1(S(length#1(z3))), LENGTH#1(Cons(z2, z3)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, Nil)))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Cons(z2, Nil))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, Nil))), S(halve#1(S(0)))))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, Nil))), S(halve#1(length#1(Cons(z2, Nil)))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, Nil))), S(halve#1(length#1(Cons(z2, Nil))))), HALVE#1(S(length#1(Nil))), LENGTH#1(Cons(z2, Nil)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, Cons(z3, z4))))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Cons(z2, Cons(z3, z4)))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, Cons(z3, z4)))), S(halve#1(S(S(length#1(z4)))))))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, Cons(z3, z4)))), S(halve#1(length#1(Cons(z2, Cons(z3, z4))))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, Cons(z3, z4)))), S(halve#1(length#1(Cons(z2, Cons(z3, z4)))))), HALVE#1(S(length#1(Cons(z3, z4)))), LENGTH#1(Cons(z2, Cons(z3, z4))))
K tuples:none
Defined Rule Symbols:   leq#2_2, map#2_2, divide_ys#1_2, halve#1_1, length#1_1, take#2_2, drop#2_2, dc#1_6, const_f#2_2, merge#2_2, cond_merge_ys_zs_2_7

Defined Pair Symbols:   DROP#2_2, TAKE#2_2, HALVE#1_1, CONST_F#2_2, LEQ#2_2, LENGTH#1_1, MAP#2_2, MERGE#2_2, DC#1_6, DIVIDE_YS#1_2, COND_MERGE_YS_ZS_2_7

Compound Symbols:   c12_1, c15_1, c18_1, c19_1, c22_1, c24_1, c26_1, c27_1, c6_1, c6_2, c9_4, c9_5, c_1, c1_1, c2_1, c3_1, c9_2, c9_3


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

(135) CdtRewritingProof (BOTH BOUNDS(ID, ID))
Used rewriting to replace DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Cons(x2, x3)))) -> c9(MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Cons(x2, x3))), S(halve#1(length#1(Cons(x2, x3)))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, x3))), S(halve#1(length#1(Cons(x2, x3))))), HALVE#1(length#1(Cons(x2, x3))), LENGTH#1(Cons(x2, x3))) by DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, z3)))) -> c9(MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3)))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3))))), HALVE#1(S(length#1(z3))), LENGTH#1(Cons(z2, z3)))
----------------------------------------

(136)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   leq#2(0, z0) -> True
   leq#2(S(z0), 0) -> False
   leq#2(S(z0), S(z1)) -> leq#2(z0, z1)
   map#2(dc(z0, z1, z2, z3, z4), Nil) -> Nil
   map#2(dc(z0, z1, z2, z3, z4), Cons(z5, z6)) -> Cons(dc#1(z0, z1, z2, z3, z4, z5), map#2(dc(z0, z1, z2, z3, z4), z6))
   divide_ys#1(z0, z1) -> Cons(take#2(z1, z0), Cons(drop#2(z1, z0), Nil))
   halve#1(0) -> 0
   halve#1(S(0)) -> S(0)
   halve#1(S(S(z0))) -> S(halve#1(z0))
   length#1(Nil) -> 0
   length#1(Cons(z0, z1)) -> S(length#1(z1))
   take#2(0, z0) -> Nil
   take#2(S(0), Nil) -> Cons(bot[0], Nil)
   take#2(S(z0), Cons(z1, z2)) -> Cons(z1, take#2(z0, z2))
   drop#2(0, z0) -> z0
   drop#2(S(0), Nil) -> bot[1]
   drop#2(S(z0), Cons(z1, z2)) -> drop#2(z0, z2)
   dc#1(map, divisible, mergesort_zs_3, divide, const_f, Nil) -> Nil
   dc#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Nil)) -> Cons(z0, Nil)
   dc#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> const_f#2(Cons(z0, Cons(z1, z2)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2))))))
   const_f#2(z0, Cons(z1, Cons(z2, z3))) -> merge#2(z1, z2)
   merge#2(Nil, z0) -> z0
   merge#2(Cons(z0, z1), Nil) -> Cons(z0, z1)
   merge#2(Cons(z0, z1), Cons(z2, z3)) -> cond_merge_ys_zs_2(leq#2(z0, z2), Cons(z0, z1), Cons(z2, z3), z0, z1, z2, z3)
   cond_merge_ys_zs_2(True, Cons(z0, z1), Cons(z2, z3), z4, z5, z6, z7) -> Cons(z4, merge#2(z5, Cons(z2, z3)))
   cond_merge_ys_zs_2(False, Cons(z0, z1), Cons(z2, z3), z4, z5, z6, z7) -> Cons(z6, merge#2(Cons(z0, z1), z7))
Tuples:
   DROP#2(S(z0), Cons(z1, z2)) -> c12(DROP#2(z0, z2))
   TAKE#2(S(z0), Cons(z1, z2)) -> c15(TAKE#2(z0, z2))
   HALVE#1(S(S(z0))) -> c18(HALVE#1(z0))
   CONST_F#2(z0, Cons(z1, Cons(z2, z3))) -> c19(MERGE#2(z1, z2))
   LEQ#2(S(z0), S(z1)) -> c22(LEQ#2(z0, z1))
   LENGTH#1(Cons(z0, z1)) -> c24(LENGTH#1(z1))
   MAP#2(dc(z0, z1, z2, z3, z4), Cons(z5, z6)) -> c26(DC#1(z0, z1, z2, z3, z4, z5))
   MAP#2(dc(z0, z1, z2, z3, z4), Cons(z5, z6)) -> c27(MAP#2(dc(z0, z1, z2, z3, z4), z6))
   MERGE#2(Cons(0, x1), Cons(z0, x3)) -> c6(COND_MERGE_YS_ZS_2(True, Cons(0, x1), Cons(z0, x3), 0, x1, z0, x3))
   MERGE#2(Cons(S(z0), x1), Cons(0, x3)) -> c6(COND_MERGE_YS_ZS_2(False, Cons(S(z0), x1), Cons(0, x3), S(z0), x1, 0, x3))
   MERGE#2(Cons(S(0), x1), Cons(S(z0), x3)) -> c6(COND_MERGE_YS_ZS_2(True, Cons(S(0), x1), Cons(S(z0), x3), S(0), x1, S(z0), x3), LEQ#2(S(0), S(z0)))
   MERGE#2(Cons(S(S(z0)), x1), Cons(S(0), x3)) -> c6(COND_MERGE_YS_ZS_2(False, Cons(S(S(z0)), x1), Cons(S(0), x3), S(S(z0)), x1, S(0), x3), LEQ#2(S(S(z0)), S(0)))
   MERGE#2(Cons(S(S(z0)), x1), Cons(S(S(z1)), x3)) -> c6(COND_MERGE_YS_ZS_2(leq#2(z0, z1), Cons(S(S(z0)), x1), Cons(S(S(z1)), x3), S(S(z0)), x1, S(S(z1)), x3), LEQ#2(S(S(z0)), S(S(z1))))
   MERGE#2(Cons(S(x0), x1), Cons(S(x2), x3)) -> c6(LEQ#2(S(x0), S(x2)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Nil))) -> c9(CONST_F#2(Cons(x0, Cons(x1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(0)), Cons(x0, Cons(x1, Nil))), Cons(drop#2(S(halve#1(0)), Cons(x0, Cons(x1, Nil))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Nil)), S(halve#1(length#1(Nil)))), HALVE#1(length#1(Nil)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Nil))) -> c9(CONST_F#2(Cons(x0, Cons(x1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Nil)), S(0)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Nil)), S(halve#1(length#1(Nil)))), HALVE#1(length#1(Nil)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> c9(CONST_F#2(Cons(z0, Cons(z1, z2)), Cons(dc#1(map, divisible, mergesort_zs_3, divide, const_f, take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2)))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(drop#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Nil))), DIVIDE_YS#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2)))), HALVE#1(length#1(z2)), LENGTH#1(z2))
   DIVIDE_YS#1(Cons(x0, Cons(x1, x2)), S(y11)) -> c(TAKE#2(S(y11), Cons(x0, Cons(x1, x2))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, x3))), S(y11)) -> c(TAKE#2(S(y11), Cons(x0, Cons(x1, Cons(x2, x3)))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Nil)), S(y10)) -> c(TAKE#2(S(y10), Cons(x0, Cons(x1, Nil))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Nil))), S(y7)) -> c(TAKE#2(S(y7), Cons(x0, Cons(x1, Cons(x2, Nil)))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4)))), S(y8)) -> c(TAKE#2(S(y8), Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4))))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, x2)), S(y11)) -> c1(DROP#2(S(y11), Cons(x0, Cons(x1, x2))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, x3))), S(y11)) -> c1(DROP#2(S(y11), Cons(x0, Cons(x1, Cons(x2, x3)))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Nil)), S(y10)) -> c1(DROP#2(S(y10), Cons(x0, Cons(x1, Nil))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Nil))), S(y7)) -> c1(DROP#2(S(y7), Cons(x0, Cons(x1, Cons(x2, Nil)))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4)))), S(y8)) -> c1(DROP#2(S(y8), Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4))))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> c9(CONST_F#2(Cons(z0, Cons(z1, z2)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(halve#1(length#1(z2)), Cons(z1, z2)), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Nil))), DIVIDE_YS#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2)))), HALVE#1(length#1(z2)), LENGTH#1(z2))
   COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(z2, z3), z4, Cons(0, y0), z6, z7) -> c2(MERGE#2(Cons(0, y0), Cons(z2, z3)))
   COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(0, z3), z4, Cons(S(y0), y1), z6, z7) -> c2(MERGE#2(Cons(S(y0), y1), Cons(0, z3)))
   COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(S(y1), z3), z4, Cons(S(0), y0), z6, z7) -> c2(MERGE#2(Cons(S(0), y0), Cons(S(y1), z3)))
   COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(S(0), z3), z4, Cons(S(S(y0)), y1), z6, z7) -> c2(MERGE#2(Cons(S(S(y0)), y1), Cons(S(0), z3)))
   COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(S(S(y2)), z3), z4, Cons(S(S(y0)), y1), z6, z7) -> c2(MERGE#2(Cons(S(S(y0)), y1), Cons(S(S(y2)), z3)))
   COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(S(y2), z3), z4, Cons(S(y0), y1), z6, z7) -> c2(MERGE#2(Cons(S(y0), y1), Cons(S(y2), z3)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, z3)))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Cons(z2, z3))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(Cons(z2, z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Cons(drop#2(S(halve#1(S(length#1(z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3)))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3))))), HALVE#1(S(length#1(z3))), LENGTH#1(Cons(z2, z3)))
   COND_MERGE_YS_ZS_2(False, Cons(S(x0), x1), Cons(0, x2), S(x0), x1, 0, x2) -> c3(MERGE#2(Cons(S(x0), x1), x2))
   COND_MERGE_YS_ZS_2(False, Cons(S(S(x0)), x1), Cons(S(0), x2), S(S(x0)), x1, S(0), x2) -> c3(MERGE#2(Cons(S(S(x0)), x1), x2))
   COND_MERGE_YS_ZS_2(False, Cons(S(S(x0)), x1), Cons(S(S(x2)), x3), S(S(x0)), x1, S(S(x2)), x3) -> c3(MERGE#2(Cons(S(S(x0)), x1), x3))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> c9(CONST_F#2(Cons(z0, Cons(z1, z2)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(Cons(z0, take#2(halve#1(length#1(z2)), Cons(z1, z2))), Cons(drop#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Nil))), DIVIDE_YS#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2)))), HALVE#1(length#1(z2)), LENGTH#1(z2))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, z3)))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Cons(z2, z3))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(S(length#1(z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Cons(drop#2(S(halve#1(length#1(Cons(z2, z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3)))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3))))), HALVE#1(S(length#1(z3))), LENGTH#1(Cons(z2, z3)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> c9(MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Nil))), DIVIDE_YS#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2)))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Nil))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(Nil))), Cons(z0, Cons(z1, Nil))), Cons(drop#2(S(halve#1(0)), Cons(z0, Cons(z1, Nil))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil)))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Nil))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(0)), Cons(z0, Cons(z1, Nil))), Cons(drop#2(S(halve#1(length#1(Nil))), Cons(z0, Cons(z1, Nil))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil)))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, z3)))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Cons(z2, z3))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(S(length#1(z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Cons(drop#2(S(halve#1(S(length#1(z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3)))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3))))), HALVE#1(S(length#1(z3))), LENGTH#1(Cons(z2, z3)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, Nil)))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Cons(z2, Nil))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, Nil))), S(halve#1(S(0)))))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, Nil))), S(halve#1(length#1(Cons(z2, Nil)))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, Nil))), S(halve#1(length#1(Cons(z2, Nil))))), HALVE#1(S(length#1(Nil))), LENGTH#1(Cons(z2, Nil)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, Cons(z3, z4))))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Cons(z2, Cons(z3, z4)))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, Cons(z3, z4)))), S(halve#1(S(S(length#1(z4)))))))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, Cons(z3, z4)))), S(halve#1(length#1(Cons(z2, Cons(z3, z4))))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, Cons(z3, z4)))), S(halve#1(length#1(Cons(z2, Cons(z3, z4)))))), HALVE#1(S(length#1(Cons(z3, z4)))), LENGTH#1(Cons(z2, Cons(z3, z4))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, z3)))) -> c9(MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3)))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3))))), HALVE#1(S(length#1(z3))), LENGTH#1(Cons(z2, z3)))
S tuples:
   DROP#2(S(z0), Cons(z1, z2)) -> c12(DROP#2(z0, z2))
   TAKE#2(S(z0), Cons(z1, z2)) -> c15(TAKE#2(z0, z2))
   HALVE#1(S(S(z0))) -> c18(HALVE#1(z0))
   CONST_F#2(z0, Cons(z1, Cons(z2, z3))) -> c19(MERGE#2(z1, z2))
   LEQ#2(S(z0), S(z1)) -> c22(LEQ#2(z0, z1))
   LENGTH#1(Cons(z0, z1)) -> c24(LENGTH#1(z1))
   MAP#2(dc(z0, z1, z2, z3, z4), Cons(z5, z6)) -> c26(DC#1(z0, z1, z2, z3, z4, z5))
   MAP#2(dc(z0, z1, z2, z3, z4), Cons(z5, z6)) -> c27(MAP#2(dc(z0, z1, z2, z3, z4), z6))
   MERGE#2(Cons(0, x1), Cons(z0, x3)) -> c6(COND_MERGE_YS_ZS_2(True, Cons(0, x1), Cons(z0, x3), 0, x1, z0, x3))
   MERGE#2(Cons(S(z0), x1), Cons(0, x3)) -> c6(COND_MERGE_YS_ZS_2(False, Cons(S(z0), x1), Cons(0, x3), S(z0), x1, 0, x3))
   MERGE#2(Cons(S(0), x1), Cons(S(z0), x3)) -> c6(COND_MERGE_YS_ZS_2(True, Cons(S(0), x1), Cons(S(z0), x3), S(0), x1, S(z0), x3), LEQ#2(S(0), S(z0)))
   MERGE#2(Cons(S(S(z0)), x1), Cons(S(0), x3)) -> c6(COND_MERGE_YS_ZS_2(False, Cons(S(S(z0)), x1), Cons(S(0), x3), S(S(z0)), x1, S(0), x3), LEQ#2(S(S(z0)), S(0)))
   MERGE#2(Cons(S(S(z0)), x1), Cons(S(S(z1)), x3)) -> c6(COND_MERGE_YS_ZS_2(leq#2(z0, z1), Cons(S(S(z0)), x1), Cons(S(S(z1)), x3), S(S(z0)), x1, S(S(z1)), x3), LEQ#2(S(S(z0)), S(S(z1))))
   MERGE#2(Cons(S(x0), x1), Cons(S(x2), x3)) -> c6(LEQ#2(S(x0), S(x2)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Nil))) -> c9(CONST_F#2(Cons(x0, Cons(x1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(0)), Cons(x0, Cons(x1, Nil))), Cons(drop#2(S(halve#1(0)), Cons(x0, Cons(x1, Nil))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Nil)), S(halve#1(length#1(Nil)))), HALVE#1(length#1(Nil)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Nil))) -> c9(CONST_F#2(Cons(x0, Cons(x1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Nil)), S(0)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Nil)), S(halve#1(length#1(Nil)))), HALVE#1(length#1(Nil)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> c9(CONST_F#2(Cons(z0, Cons(z1, z2)), Cons(dc#1(map, divisible, mergesort_zs_3, divide, const_f, take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2)))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(drop#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Nil))), DIVIDE_YS#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2)))), HALVE#1(length#1(z2)), LENGTH#1(z2))
   DIVIDE_YS#1(Cons(x0, Cons(x1, x2)), S(y11)) -> c(TAKE#2(S(y11), Cons(x0, Cons(x1, x2))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, x3))), S(y11)) -> c(TAKE#2(S(y11), Cons(x0, Cons(x1, Cons(x2, x3)))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Nil)), S(y10)) -> c(TAKE#2(S(y10), Cons(x0, Cons(x1, Nil))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Nil))), S(y7)) -> c(TAKE#2(S(y7), Cons(x0, Cons(x1, Cons(x2, Nil)))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4)))), S(y8)) -> c(TAKE#2(S(y8), Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4))))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, x2)), S(y11)) -> c1(DROP#2(S(y11), Cons(x0, Cons(x1, x2))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, x3))), S(y11)) -> c1(DROP#2(S(y11), Cons(x0, Cons(x1, Cons(x2, x3)))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Nil)), S(y10)) -> c1(DROP#2(S(y10), Cons(x0, Cons(x1, Nil))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Nil))), S(y7)) -> c1(DROP#2(S(y7), Cons(x0, Cons(x1, Cons(x2, Nil)))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4)))), S(y8)) -> c1(DROP#2(S(y8), Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4))))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> c9(CONST_F#2(Cons(z0, Cons(z1, z2)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(halve#1(length#1(z2)), Cons(z1, z2)), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Nil))), DIVIDE_YS#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2)))), HALVE#1(length#1(z2)), LENGTH#1(z2))
   COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(z2, z3), z4, Cons(0, y0), z6, z7) -> c2(MERGE#2(Cons(0, y0), Cons(z2, z3)))
   COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(0, z3), z4, Cons(S(y0), y1), z6, z7) -> c2(MERGE#2(Cons(S(y0), y1), Cons(0, z3)))
   COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(S(y1), z3), z4, Cons(S(0), y0), z6, z7) -> c2(MERGE#2(Cons(S(0), y0), Cons(S(y1), z3)))
   COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(S(0), z3), z4, Cons(S(S(y0)), y1), z6, z7) -> c2(MERGE#2(Cons(S(S(y0)), y1), Cons(S(0), z3)))
   COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(S(S(y2)), z3), z4, Cons(S(S(y0)), y1), z6, z7) -> c2(MERGE#2(Cons(S(S(y0)), y1), Cons(S(S(y2)), z3)))
   COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(S(y2), z3), z4, Cons(S(y0), y1), z6, z7) -> c2(MERGE#2(Cons(S(y0), y1), Cons(S(y2), z3)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, z3)))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Cons(z2, z3))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(Cons(z2, z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Cons(drop#2(S(halve#1(S(length#1(z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3)))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3))))), HALVE#1(S(length#1(z3))), LENGTH#1(Cons(z2, z3)))
   COND_MERGE_YS_ZS_2(False, Cons(S(x0), x1), Cons(0, x2), S(x0), x1, 0, x2) -> c3(MERGE#2(Cons(S(x0), x1), x2))
   COND_MERGE_YS_ZS_2(False, Cons(S(S(x0)), x1), Cons(S(0), x2), S(S(x0)), x1, S(0), x2) -> c3(MERGE#2(Cons(S(S(x0)), x1), x2))
   COND_MERGE_YS_ZS_2(False, Cons(S(S(x0)), x1), Cons(S(S(x2)), x3), S(S(x0)), x1, S(S(x2)), x3) -> c3(MERGE#2(Cons(S(S(x0)), x1), x3))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> c9(CONST_F#2(Cons(z0, Cons(z1, z2)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(Cons(z0, take#2(halve#1(length#1(z2)), Cons(z1, z2))), Cons(drop#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Nil))), DIVIDE_YS#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2)))), HALVE#1(length#1(z2)), LENGTH#1(z2))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, z3)))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Cons(z2, z3))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(S(length#1(z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Cons(drop#2(S(halve#1(length#1(Cons(z2, z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3)))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3))))), HALVE#1(S(length#1(z3))), LENGTH#1(Cons(z2, z3)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> c9(MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Nil))), DIVIDE_YS#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2)))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Nil))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(Nil))), Cons(z0, Cons(z1, Nil))), Cons(drop#2(S(halve#1(0)), Cons(z0, Cons(z1, Nil))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil)))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Nil))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(0)), Cons(z0, Cons(z1, Nil))), Cons(drop#2(S(halve#1(length#1(Nil))), Cons(z0, Cons(z1, Nil))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil)))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, z3)))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Cons(z2, z3))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(S(length#1(z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Cons(drop#2(S(halve#1(S(length#1(z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3)))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3))))), HALVE#1(S(length#1(z3))), LENGTH#1(Cons(z2, z3)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, Nil)))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Cons(z2, Nil))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, Nil))), S(halve#1(S(0)))))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, Nil))), S(halve#1(length#1(Cons(z2, Nil)))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, Nil))), S(halve#1(length#1(Cons(z2, Nil))))), HALVE#1(S(length#1(Nil))), LENGTH#1(Cons(z2, Nil)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, Cons(z3, z4))))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Cons(z2, Cons(z3, z4)))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, Cons(z3, z4)))), S(halve#1(S(S(length#1(z4)))))))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, Cons(z3, z4)))), S(halve#1(length#1(Cons(z2, Cons(z3, z4))))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, Cons(z3, z4)))), S(halve#1(length#1(Cons(z2, Cons(z3, z4)))))), HALVE#1(S(length#1(Cons(z3, z4)))), LENGTH#1(Cons(z2, Cons(z3, z4))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, z3)))) -> c9(MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3)))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3))))), HALVE#1(S(length#1(z3))), LENGTH#1(Cons(z2, z3)))
K tuples:none
Defined Rule Symbols:   leq#2_2, map#2_2, divide_ys#1_2, halve#1_1, length#1_1, take#2_2, drop#2_2, dc#1_6, const_f#2_2, merge#2_2, cond_merge_ys_zs_2_7

Defined Pair Symbols:   DROP#2_2, TAKE#2_2, HALVE#1_1, CONST_F#2_2, LEQ#2_2, LENGTH#1_1, MAP#2_2, MERGE#2_2, DC#1_6, DIVIDE_YS#1_2, COND_MERGE_YS_ZS_2_7

Compound Symbols:   c12_1, c15_1, c18_1, c19_1, c22_1, c24_1, c26_1, c27_1, c6_1, c6_2, c9_4, c9_5, c_1, c1_1, c2_1, c3_1, c9_2, c9_3


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

(137) CdtRewritingProof (BOTH BOUNDS(ID, ID))
Used rewriting to replace DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Nil))) -> c9(CONST_F#2(Cons(x0, Cons(x1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(0)), Cons(x0, Cons(x1, Nil))), Cons(drop#2(S(halve#1(0)), Cons(x0, Cons(x1, Nil))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Nil)), S(halve#1(length#1(Nil)))), HALVE#1(length#1(Nil))) by DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Nil))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(0)), Cons(z0, Cons(z1, Nil))), Cons(drop#2(S(halve#1(0)), Cons(z0, Cons(z1, Nil))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil)))), HALVE#1(0))
----------------------------------------

(138)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   leq#2(0, z0) -> True
   leq#2(S(z0), 0) -> False
   leq#2(S(z0), S(z1)) -> leq#2(z0, z1)
   map#2(dc(z0, z1, z2, z3, z4), Nil) -> Nil
   map#2(dc(z0, z1, z2, z3, z4), Cons(z5, z6)) -> Cons(dc#1(z0, z1, z2, z3, z4, z5), map#2(dc(z0, z1, z2, z3, z4), z6))
   divide_ys#1(z0, z1) -> Cons(take#2(z1, z0), Cons(drop#2(z1, z0), Nil))
   halve#1(0) -> 0
   halve#1(S(0)) -> S(0)
   halve#1(S(S(z0))) -> S(halve#1(z0))
   length#1(Nil) -> 0
   length#1(Cons(z0, z1)) -> S(length#1(z1))
   take#2(0, z0) -> Nil
   take#2(S(0), Nil) -> Cons(bot[0], Nil)
   take#2(S(z0), Cons(z1, z2)) -> Cons(z1, take#2(z0, z2))
   drop#2(0, z0) -> z0
   drop#2(S(0), Nil) -> bot[1]
   drop#2(S(z0), Cons(z1, z2)) -> drop#2(z0, z2)
   dc#1(map, divisible, mergesort_zs_3, divide, const_f, Nil) -> Nil
   dc#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Nil)) -> Cons(z0, Nil)
   dc#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> const_f#2(Cons(z0, Cons(z1, z2)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2))))))
   const_f#2(z0, Cons(z1, Cons(z2, z3))) -> merge#2(z1, z2)
   merge#2(Nil, z0) -> z0
   merge#2(Cons(z0, z1), Nil) -> Cons(z0, z1)
   merge#2(Cons(z0, z1), Cons(z2, z3)) -> cond_merge_ys_zs_2(leq#2(z0, z2), Cons(z0, z1), Cons(z2, z3), z0, z1, z2, z3)
   cond_merge_ys_zs_2(True, Cons(z0, z1), Cons(z2, z3), z4, z5, z6, z7) -> Cons(z4, merge#2(z5, Cons(z2, z3)))
   cond_merge_ys_zs_2(False, Cons(z0, z1), Cons(z2, z3), z4, z5, z6, z7) -> Cons(z6, merge#2(Cons(z0, z1), z7))
Tuples:
   DROP#2(S(z0), Cons(z1, z2)) -> c12(DROP#2(z0, z2))
   TAKE#2(S(z0), Cons(z1, z2)) -> c15(TAKE#2(z0, z2))
   HALVE#1(S(S(z0))) -> c18(HALVE#1(z0))
   CONST_F#2(z0, Cons(z1, Cons(z2, z3))) -> c19(MERGE#2(z1, z2))
   LEQ#2(S(z0), S(z1)) -> c22(LEQ#2(z0, z1))
   LENGTH#1(Cons(z0, z1)) -> c24(LENGTH#1(z1))
   MAP#2(dc(z0, z1, z2, z3, z4), Cons(z5, z6)) -> c26(DC#1(z0, z1, z2, z3, z4, z5))
   MAP#2(dc(z0, z1, z2, z3, z4), Cons(z5, z6)) -> c27(MAP#2(dc(z0, z1, z2, z3, z4), z6))
   MERGE#2(Cons(0, x1), Cons(z0, x3)) -> c6(COND_MERGE_YS_ZS_2(True, Cons(0, x1), Cons(z0, x3), 0, x1, z0, x3))
   MERGE#2(Cons(S(z0), x1), Cons(0, x3)) -> c6(COND_MERGE_YS_ZS_2(False, Cons(S(z0), x1), Cons(0, x3), S(z0), x1, 0, x3))
   MERGE#2(Cons(S(0), x1), Cons(S(z0), x3)) -> c6(COND_MERGE_YS_ZS_2(True, Cons(S(0), x1), Cons(S(z0), x3), S(0), x1, S(z0), x3), LEQ#2(S(0), S(z0)))
   MERGE#2(Cons(S(S(z0)), x1), Cons(S(0), x3)) -> c6(COND_MERGE_YS_ZS_2(False, Cons(S(S(z0)), x1), Cons(S(0), x3), S(S(z0)), x1, S(0), x3), LEQ#2(S(S(z0)), S(0)))
   MERGE#2(Cons(S(S(z0)), x1), Cons(S(S(z1)), x3)) -> c6(COND_MERGE_YS_ZS_2(leq#2(z0, z1), Cons(S(S(z0)), x1), Cons(S(S(z1)), x3), S(S(z0)), x1, S(S(z1)), x3), LEQ#2(S(S(z0)), S(S(z1))))
   MERGE#2(Cons(S(x0), x1), Cons(S(x2), x3)) -> c6(LEQ#2(S(x0), S(x2)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Nil))) -> c9(CONST_F#2(Cons(x0, Cons(x1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Nil)), S(0)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Nil)), S(halve#1(length#1(Nil)))), HALVE#1(length#1(Nil)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> c9(CONST_F#2(Cons(z0, Cons(z1, z2)), Cons(dc#1(map, divisible, mergesort_zs_3, divide, const_f, take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2)))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(drop#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Nil))), DIVIDE_YS#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2)))), HALVE#1(length#1(z2)), LENGTH#1(z2))
   DIVIDE_YS#1(Cons(x0, Cons(x1, x2)), S(y11)) -> c(TAKE#2(S(y11), Cons(x0, Cons(x1, x2))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, x3))), S(y11)) -> c(TAKE#2(S(y11), Cons(x0, Cons(x1, Cons(x2, x3)))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Nil)), S(y10)) -> c(TAKE#2(S(y10), Cons(x0, Cons(x1, Nil))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Nil))), S(y7)) -> c(TAKE#2(S(y7), Cons(x0, Cons(x1, Cons(x2, Nil)))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4)))), S(y8)) -> c(TAKE#2(S(y8), Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4))))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, x2)), S(y11)) -> c1(DROP#2(S(y11), Cons(x0, Cons(x1, x2))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, x3))), S(y11)) -> c1(DROP#2(S(y11), Cons(x0, Cons(x1, Cons(x2, x3)))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Nil)), S(y10)) -> c1(DROP#2(S(y10), Cons(x0, Cons(x1, Nil))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Nil))), S(y7)) -> c1(DROP#2(S(y7), Cons(x0, Cons(x1, Cons(x2, Nil)))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4)))), S(y8)) -> c1(DROP#2(S(y8), Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4))))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> c9(CONST_F#2(Cons(z0, Cons(z1, z2)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(halve#1(length#1(z2)), Cons(z1, z2)), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Nil))), DIVIDE_YS#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2)))), HALVE#1(length#1(z2)), LENGTH#1(z2))
   COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(z2, z3), z4, Cons(0, y0), z6, z7) -> c2(MERGE#2(Cons(0, y0), Cons(z2, z3)))
   COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(0, z3), z4, Cons(S(y0), y1), z6, z7) -> c2(MERGE#2(Cons(S(y0), y1), Cons(0, z3)))
   COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(S(y1), z3), z4, Cons(S(0), y0), z6, z7) -> c2(MERGE#2(Cons(S(0), y0), Cons(S(y1), z3)))
   COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(S(0), z3), z4, Cons(S(S(y0)), y1), z6, z7) -> c2(MERGE#2(Cons(S(S(y0)), y1), Cons(S(0), z3)))
   COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(S(S(y2)), z3), z4, Cons(S(S(y0)), y1), z6, z7) -> c2(MERGE#2(Cons(S(S(y0)), y1), Cons(S(S(y2)), z3)))
   COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(S(y2), z3), z4, Cons(S(y0), y1), z6, z7) -> c2(MERGE#2(Cons(S(y0), y1), Cons(S(y2), z3)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, z3)))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Cons(z2, z3))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(Cons(z2, z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Cons(drop#2(S(halve#1(S(length#1(z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3)))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3))))), HALVE#1(S(length#1(z3))), LENGTH#1(Cons(z2, z3)))
   COND_MERGE_YS_ZS_2(False, Cons(S(x0), x1), Cons(0, x2), S(x0), x1, 0, x2) -> c3(MERGE#2(Cons(S(x0), x1), x2))
   COND_MERGE_YS_ZS_2(False, Cons(S(S(x0)), x1), Cons(S(0), x2), S(S(x0)), x1, S(0), x2) -> c3(MERGE#2(Cons(S(S(x0)), x1), x2))
   COND_MERGE_YS_ZS_2(False, Cons(S(S(x0)), x1), Cons(S(S(x2)), x3), S(S(x0)), x1, S(S(x2)), x3) -> c3(MERGE#2(Cons(S(S(x0)), x1), x3))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> c9(CONST_F#2(Cons(z0, Cons(z1, z2)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(Cons(z0, take#2(halve#1(length#1(z2)), Cons(z1, z2))), Cons(drop#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Nil))), DIVIDE_YS#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2)))), HALVE#1(length#1(z2)), LENGTH#1(z2))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, z3)))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Cons(z2, z3))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(S(length#1(z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Cons(drop#2(S(halve#1(length#1(Cons(z2, z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3)))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3))))), HALVE#1(S(length#1(z3))), LENGTH#1(Cons(z2, z3)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> c9(MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Nil))), DIVIDE_YS#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2)))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Nil))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(Nil))), Cons(z0, Cons(z1, Nil))), Cons(drop#2(S(halve#1(0)), Cons(z0, Cons(z1, Nil))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil)))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Nil))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(0)), Cons(z0, Cons(z1, Nil))), Cons(drop#2(S(halve#1(length#1(Nil))), Cons(z0, Cons(z1, Nil))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil)))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, z3)))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Cons(z2, z3))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(S(length#1(z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Cons(drop#2(S(halve#1(S(length#1(z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3)))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3))))), HALVE#1(S(length#1(z3))), LENGTH#1(Cons(z2, z3)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, Nil)))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Cons(z2, Nil))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, Nil))), S(halve#1(S(0)))))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, Nil))), S(halve#1(length#1(Cons(z2, Nil)))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, Nil))), S(halve#1(length#1(Cons(z2, Nil))))), HALVE#1(S(length#1(Nil))), LENGTH#1(Cons(z2, Nil)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, Cons(z3, z4))))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Cons(z2, Cons(z3, z4)))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, Cons(z3, z4)))), S(halve#1(S(S(length#1(z4)))))))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, Cons(z3, z4)))), S(halve#1(length#1(Cons(z2, Cons(z3, z4))))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, Cons(z3, z4)))), S(halve#1(length#1(Cons(z2, Cons(z3, z4)))))), HALVE#1(S(length#1(Cons(z3, z4)))), LENGTH#1(Cons(z2, Cons(z3, z4))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, z3)))) -> c9(MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3)))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3))))), HALVE#1(S(length#1(z3))), LENGTH#1(Cons(z2, z3)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Nil))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(0)), Cons(z0, Cons(z1, Nil))), Cons(drop#2(S(halve#1(0)), Cons(z0, Cons(z1, Nil))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil)))), HALVE#1(0))
S tuples:
   DROP#2(S(z0), Cons(z1, z2)) -> c12(DROP#2(z0, z2))
   TAKE#2(S(z0), Cons(z1, z2)) -> c15(TAKE#2(z0, z2))
   HALVE#1(S(S(z0))) -> c18(HALVE#1(z0))
   CONST_F#2(z0, Cons(z1, Cons(z2, z3))) -> c19(MERGE#2(z1, z2))
   LEQ#2(S(z0), S(z1)) -> c22(LEQ#2(z0, z1))
   LENGTH#1(Cons(z0, z1)) -> c24(LENGTH#1(z1))
   MAP#2(dc(z0, z1, z2, z3, z4), Cons(z5, z6)) -> c26(DC#1(z0, z1, z2, z3, z4, z5))
   MAP#2(dc(z0, z1, z2, z3, z4), Cons(z5, z6)) -> c27(MAP#2(dc(z0, z1, z2, z3, z4), z6))
   MERGE#2(Cons(0, x1), Cons(z0, x3)) -> c6(COND_MERGE_YS_ZS_2(True, Cons(0, x1), Cons(z0, x3), 0, x1, z0, x3))
   MERGE#2(Cons(S(z0), x1), Cons(0, x3)) -> c6(COND_MERGE_YS_ZS_2(False, Cons(S(z0), x1), Cons(0, x3), S(z0), x1, 0, x3))
   MERGE#2(Cons(S(0), x1), Cons(S(z0), x3)) -> c6(COND_MERGE_YS_ZS_2(True, Cons(S(0), x1), Cons(S(z0), x3), S(0), x1, S(z0), x3), LEQ#2(S(0), S(z0)))
   MERGE#2(Cons(S(S(z0)), x1), Cons(S(0), x3)) -> c6(COND_MERGE_YS_ZS_2(False, Cons(S(S(z0)), x1), Cons(S(0), x3), S(S(z0)), x1, S(0), x3), LEQ#2(S(S(z0)), S(0)))
   MERGE#2(Cons(S(S(z0)), x1), Cons(S(S(z1)), x3)) -> c6(COND_MERGE_YS_ZS_2(leq#2(z0, z1), Cons(S(S(z0)), x1), Cons(S(S(z1)), x3), S(S(z0)), x1, S(S(z1)), x3), LEQ#2(S(S(z0)), S(S(z1))))
   MERGE#2(Cons(S(x0), x1), Cons(S(x2), x3)) -> c6(LEQ#2(S(x0), S(x2)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Nil))) -> c9(CONST_F#2(Cons(x0, Cons(x1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Nil)), S(0)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Nil)), S(halve#1(length#1(Nil)))), HALVE#1(length#1(Nil)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> c9(CONST_F#2(Cons(z0, Cons(z1, z2)), Cons(dc#1(map, divisible, mergesort_zs_3, divide, const_f, take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2)))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(drop#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Nil))), DIVIDE_YS#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2)))), HALVE#1(length#1(z2)), LENGTH#1(z2))
   DIVIDE_YS#1(Cons(x0, Cons(x1, x2)), S(y11)) -> c(TAKE#2(S(y11), Cons(x0, Cons(x1, x2))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, x3))), S(y11)) -> c(TAKE#2(S(y11), Cons(x0, Cons(x1, Cons(x2, x3)))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Nil)), S(y10)) -> c(TAKE#2(S(y10), Cons(x0, Cons(x1, Nil))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Nil))), S(y7)) -> c(TAKE#2(S(y7), Cons(x0, Cons(x1, Cons(x2, Nil)))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4)))), S(y8)) -> c(TAKE#2(S(y8), Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4))))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, x2)), S(y11)) -> c1(DROP#2(S(y11), Cons(x0, Cons(x1, x2))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, x3))), S(y11)) -> c1(DROP#2(S(y11), Cons(x0, Cons(x1, Cons(x2, x3)))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Nil)), S(y10)) -> c1(DROP#2(S(y10), Cons(x0, Cons(x1, Nil))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Nil))), S(y7)) -> c1(DROP#2(S(y7), Cons(x0, Cons(x1, Cons(x2, Nil)))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4)))), S(y8)) -> c1(DROP#2(S(y8), Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4))))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> c9(CONST_F#2(Cons(z0, Cons(z1, z2)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(halve#1(length#1(z2)), Cons(z1, z2)), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Nil))), DIVIDE_YS#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2)))), HALVE#1(length#1(z2)), LENGTH#1(z2))
   COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(z2, z3), z4, Cons(0, y0), z6, z7) -> c2(MERGE#2(Cons(0, y0), Cons(z2, z3)))
   COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(0, z3), z4, Cons(S(y0), y1), z6, z7) -> c2(MERGE#2(Cons(S(y0), y1), Cons(0, z3)))
   COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(S(y1), z3), z4, Cons(S(0), y0), z6, z7) -> c2(MERGE#2(Cons(S(0), y0), Cons(S(y1), z3)))
   COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(S(0), z3), z4, Cons(S(S(y0)), y1), z6, z7) -> c2(MERGE#2(Cons(S(S(y0)), y1), Cons(S(0), z3)))
   COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(S(S(y2)), z3), z4, Cons(S(S(y0)), y1), z6, z7) -> c2(MERGE#2(Cons(S(S(y0)), y1), Cons(S(S(y2)), z3)))
   COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(S(y2), z3), z4, Cons(S(y0), y1), z6, z7) -> c2(MERGE#2(Cons(S(y0), y1), Cons(S(y2), z3)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, z3)))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Cons(z2, z3))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(Cons(z2, z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Cons(drop#2(S(halve#1(S(length#1(z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3)))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3))))), HALVE#1(S(length#1(z3))), LENGTH#1(Cons(z2, z3)))
   COND_MERGE_YS_ZS_2(False, Cons(S(x0), x1), Cons(0, x2), S(x0), x1, 0, x2) -> c3(MERGE#2(Cons(S(x0), x1), x2))
   COND_MERGE_YS_ZS_2(False, Cons(S(S(x0)), x1), Cons(S(0), x2), S(S(x0)), x1, S(0), x2) -> c3(MERGE#2(Cons(S(S(x0)), x1), x2))
   COND_MERGE_YS_ZS_2(False, Cons(S(S(x0)), x1), Cons(S(S(x2)), x3), S(S(x0)), x1, S(S(x2)), x3) -> c3(MERGE#2(Cons(S(S(x0)), x1), x3))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> c9(CONST_F#2(Cons(z0, Cons(z1, z2)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(Cons(z0, take#2(halve#1(length#1(z2)), Cons(z1, z2))), Cons(drop#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Nil))), DIVIDE_YS#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2)))), HALVE#1(length#1(z2)), LENGTH#1(z2))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, z3)))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Cons(z2, z3))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(S(length#1(z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Cons(drop#2(S(halve#1(length#1(Cons(z2, z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3)))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3))))), HALVE#1(S(length#1(z3))), LENGTH#1(Cons(z2, z3)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> c9(MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Nil))), DIVIDE_YS#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2)))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Nil))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(Nil))), Cons(z0, Cons(z1, Nil))), Cons(drop#2(S(halve#1(0)), Cons(z0, Cons(z1, Nil))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil)))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Nil))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(0)), Cons(z0, Cons(z1, Nil))), Cons(drop#2(S(halve#1(length#1(Nil))), Cons(z0, Cons(z1, Nil))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil)))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, z3)))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Cons(z2, z3))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(S(length#1(z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Cons(drop#2(S(halve#1(S(length#1(z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3)))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3))))), HALVE#1(S(length#1(z3))), LENGTH#1(Cons(z2, z3)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, Nil)))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Cons(z2, Nil))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, Nil))), S(halve#1(S(0)))))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, Nil))), S(halve#1(length#1(Cons(z2, Nil)))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, Nil))), S(halve#1(length#1(Cons(z2, Nil))))), HALVE#1(S(length#1(Nil))), LENGTH#1(Cons(z2, Nil)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, Cons(z3, z4))))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Cons(z2, Cons(z3, z4)))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, Cons(z3, z4)))), S(halve#1(S(S(length#1(z4)))))))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, Cons(z3, z4)))), S(halve#1(length#1(Cons(z2, Cons(z3, z4))))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, Cons(z3, z4)))), S(halve#1(length#1(Cons(z2, Cons(z3, z4)))))), HALVE#1(S(length#1(Cons(z3, z4)))), LENGTH#1(Cons(z2, Cons(z3, z4))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, z3)))) -> c9(MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3)))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3))))), HALVE#1(S(length#1(z3))), LENGTH#1(Cons(z2, z3)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Nil))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(0)), Cons(z0, Cons(z1, Nil))), Cons(drop#2(S(halve#1(0)), Cons(z0, Cons(z1, Nil))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil)))), HALVE#1(0))
K tuples:none
Defined Rule Symbols:   leq#2_2, map#2_2, divide_ys#1_2, halve#1_1, length#1_1, take#2_2, drop#2_2, dc#1_6, const_f#2_2, merge#2_2, cond_merge_ys_zs_2_7

Defined Pair Symbols:   DROP#2_2, TAKE#2_2, HALVE#1_1, CONST_F#2_2, LEQ#2_2, LENGTH#1_1, MAP#2_2, MERGE#2_2, DC#1_6, DIVIDE_YS#1_2, COND_MERGE_YS_ZS_2_7

Compound Symbols:   c12_1, c15_1, c18_1, c19_1, c22_1, c24_1, c26_1, c27_1, c6_1, c6_2, c9_4, c9_5, c_1, c1_1, c2_1, c3_1, c9_2, c9_3


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

(140)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   leq#2(0, z0) -> True
   leq#2(S(z0), 0) -> False
   leq#2(S(z0), S(z1)) -> leq#2(z0, z1)
   map#2(dc(z0, z1, z2, z3, z4), Nil) -> Nil
   map#2(dc(z0, z1, z2, z3, z4), Cons(z5, z6)) -> Cons(dc#1(z0, z1, z2, z3, z4, z5), map#2(dc(z0, z1, z2, z3, z4), z6))
   divide_ys#1(z0, z1) -> Cons(take#2(z1, z0), Cons(drop#2(z1, z0), Nil))
   halve#1(0) -> 0
   halve#1(S(0)) -> S(0)
   halve#1(S(S(z0))) -> S(halve#1(z0))
   length#1(Nil) -> 0
   length#1(Cons(z0, z1)) -> S(length#1(z1))
   take#2(0, z0) -> Nil
   take#2(S(0), Nil) -> Cons(bot[0], Nil)
   take#2(S(z0), Cons(z1, z2)) -> Cons(z1, take#2(z0, z2))
   drop#2(0, z0) -> z0
   drop#2(S(0), Nil) -> bot[1]
   drop#2(S(z0), Cons(z1, z2)) -> drop#2(z0, z2)
   dc#1(map, divisible, mergesort_zs_3, divide, const_f, Nil) -> Nil
   dc#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Nil)) -> Cons(z0, Nil)
   dc#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> const_f#2(Cons(z0, Cons(z1, z2)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2))))))
   const_f#2(z0, Cons(z1, Cons(z2, z3))) -> merge#2(z1, z2)
   merge#2(Nil, z0) -> z0
   merge#2(Cons(z0, z1), Nil) -> Cons(z0, z1)
   merge#2(Cons(z0, z1), Cons(z2, z3)) -> cond_merge_ys_zs_2(leq#2(z0, z2), Cons(z0, z1), Cons(z2, z3), z0, z1, z2, z3)
   cond_merge_ys_zs_2(True, Cons(z0, z1), Cons(z2, z3), z4, z5, z6, z7) -> Cons(z4, merge#2(z5, Cons(z2, z3)))
   cond_merge_ys_zs_2(False, Cons(z0, z1), Cons(z2, z3), z4, z5, z6, z7) -> Cons(z6, merge#2(Cons(z0, z1), z7))
Tuples:
   DROP#2(S(z0), Cons(z1, z2)) -> c12(DROP#2(z0, z2))
   TAKE#2(S(z0), Cons(z1, z2)) -> c15(TAKE#2(z0, z2))
   HALVE#1(S(S(z0))) -> c18(HALVE#1(z0))
   CONST_F#2(z0, Cons(z1, Cons(z2, z3))) -> c19(MERGE#2(z1, z2))
   LEQ#2(S(z0), S(z1)) -> c22(LEQ#2(z0, z1))
   LENGTH#1(Cons(z0, z1)) -> c24(LENGTH#1(z1))
   MAP#2(dc(z0, z1, z2, z3, z4), Cons(z5, z6)) -> c26(DC#1(z0, z1, z2, z3, z4, z5))
   MAP#2(dc(z0, z1, z2, z3, z4), Cons(z5, z6)) -> c27(MAP#2(dc(z0, z1, z2, z3, z4), z6))
   MERGE#2(Cons(0, x1), Cons(z0, x3)) -> c6(COND_MERGE_YS_ZS_2(True, Cons(0, x1), Cons(z0, x3), 0, x1, z0, x3))
   MERGE#2(Cons(S(z0), x1), Cons(0, x3)) -> c6(COND_MERGE_YS_ZS_2(False, Cons(S(z0), x1), Cons(0, x3), S(z0), x1, 0, x3))
   MERGE#2(Cons(S(0), x1), Cons(S(z0), x3)) -> c6(COND_MERGE_YS_ZS_2(True, Cons(S(0), x1), Cons(S(z0), x3), S(0), x1, S(z0), x3), LEQ#2(S(0), S(z0)))
   MERGE#2(Cons(S(S(z0)), x1), Cons(S(0), x3)) -> c6(COND_MERGE_YS_ZS_2(False, Cons(S(S(z0)), x1), Cons(S(0), x3), S(S(z0)), x1, S(0), x3), LEQ#2(S(S(z0)), S(0)))
   MERGE#2(Cons(S(S(z0)), x1), Cons(S(S(z1)), x3)) -> c6(COND_MERGE_YS_ZS_2(leq#2(z0, z1), Cons(S(S(z0)), x1), Cons(S(S(z1)), x3), S(S(z0)), x1, S(S(z1)), x3), LEQ#2(S(S(z0)), S(S(z1))))
   MERGE#2(Cons(S(x0), x1), Cons(S(x2), x3)) -> c6(LEQ#2(S(x0), S(x2)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Nil))) -> c9(CONST_F#2(Cons(x0, Cons(x1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Nil)), S(0)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Nil)), S(halve#1(length#1(Nil)))), HALVE#1(length#1(Nil)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> c9(CONST_F#2(Cons(z0, Cons(z1, z2)), Cons(dc#1(map, divisible, mergesort_zs_3, divide, const_f, take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2)))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(drop#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Nil))), DIVIDE_YS#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2)))), HALVE#1(length#1(z2)), LENGTH#1(z2))
   DIVIDE_YS#1(Cons(x0, Cons(x1, x2)), S(y11)) -> c(TAKE#2(S(y11), Cons(x0, Cons(x1, x2))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, x3))), S(y11)) -> c(TAKE#2(S(y11), Cons(x0, Cons(x1, Cons(x2, x3)))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Nil)), S(y10)) -> c(TAKE#2(S(y10), Cons(x0, Cons(x1, Nil))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Nil))), S(y7)) -> c(TAKE#2(S(y7), Cons(x0, Cons(x1, Cons(x2, Nil)))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4)))), S(y8)) -> c(TAKE#2(S(y8), Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4))))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, x2)), S(y11)) -> c1(DROP#2(S(y11), Cons(x0, Cons(x1, x2))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, x3))), S(y11)) -> c1(DROP#2(S(y11), Cons(x0, Cons(x1, Cons(x2, x3)))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Nil)), S(y10)) -> c1(DROP#2(S(y10), Cons(x0, Cons(x1, Nil))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Nil))), S(y7)) -> c1(DROP#2(S(y7), Cons(x0, Cons(x1, Cons(x2, Nil)))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4)))), S(y8)) -> c1(DROP#2(S(y8), Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4))))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> c9(CONST_F#2(Cons(z0, Cons(z1, z2)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(halve#1(length#1(z2)), Cons(z1, z2)), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Nil))), DIVIDE_YS#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2)))), HALVE#1(length#1(z2)), LENGTH#1(z2))
   COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(z2, z3), z4, Cons(0, y0), z6, z7) -> c2(MERGE#2(Cons(0, y0), Cons(z2, z3)))
   COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(0, z3), z4, Cons(S(y0), y1), z6, z7) -> c2(MERGE#2(Cons(S(y0), y1), Cons(0, z3)))
   COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(S(y1), z3), z4, Cons(S(0), y0), z6, z7) -> c2(MERGE#2(Cons(S(0), y0), Cons(S(y1), z3)))
   COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(S(0), z3), z4, Cons(S(S(y0)), y1), z6, z7) -> c2(MERGE#2(Cons(S(S(y0)), y1), Cons(S(0), z3)))
   COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(S(S(y2)), z3), z4, Cons(S(S(y0)), y1), z6, z7) -> c2(MERGE#2(Cons(S(S(y0)), y1), Cons(S(S(y2)), z3)))
   COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(S(y2), z3), z4, Cons(S(y0), y1), z6, z7) -> c2(MERGE#2(Cons(S(y0), y1), Cons(S(y2), z3)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, z3)))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Cons(z2, z3))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(Cons(z2, z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Cons(drop#2(S(halve#1(S(length#1(z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3)))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3))))), HALVE#1(S(length#1(z3))), LENGTH#1(Cons(z2, z3)))
   COND_MERGE_YS_ZS_2(False, Cons(S(x0), x1), Cons(0, x2), S(x0), x1, 0, x2) -> c3(MERGE#2(Cons(S(x0), x1), x2))
   COND_MERGE_YS_ZS_2(False, Cons(S(S(x0)), x1), Cons(S(0), x2), S(S(x0)), x1, S(0), x2) -> c3(MERGE#2(Cons(S(S(x0)), x1), x2))
   COND_MERGE_YS_ZS_2(False, Cons(S(S(x0)), x1), Cons(S(S(x2)), x3), S(S(x0)), x1, S(S(x2)), x3) -> c3(MERGE#2(Cons(S(S(x0)), x1), x3))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> c9(CONST_F#2(Cons(z0, Cons(z1, z2)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(Cons(z0, take#2(halve#1(length#1(z2)), Cons(z1, z2))), Cons(drop#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Nil))), DIVIDE_YS#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2)))), HALVE#1(length#1(z2)), LENGTH#1(z2))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, z3)))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Cons(z2, z3))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(S(length#1(z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Cons(drop#2(S(halve#1(length#1(Cons(z2, z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3)))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3))))), HALVE#1(S(length#1(z3))), LENGTH#1(Cons(z2, z3)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> c9(MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Nil))), DIVIDE_YS#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2)))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Nil))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(Nil))), Cons(z0, Cons(z1, Nil))), Cons(drop#2(S(halve#1(0)), Cons(z0, Cons(z1, Nil))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil)))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Nil))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(0)), Cons(z0, Cons(z1, Nil))), Cons(drop#2(S(halve#1(length#1(Nil))), Cons(z0, Cons(z1, Nil))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil)))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, z3)))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Cons(z2, z3))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(S(length#1(z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Cons(drop#2(S(halve#1(S(length#1(z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3)))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3))))), HALVE#1(S(length#1(z3))), LENGTH#1(Cons(z2, z3)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, Nil)))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Cons(z2, Nil))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, Nil))), S(halve#1(S(0)))))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, Nil))), S(halve#1(length#1(Cons(z2, Nil)))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, Nil))), S(halve#1(length#1(Cons(z2, Nil))))), HALVE#1(S(length#1(Nil))), LENGTH#1(Cons(z2, Nil)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, Cons(z3, z4))))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Cons(z2, Cons(z3, z4)))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, Cons(z3, z4)))), S(halve#1(S(S(length#1(z4)))))))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, Cons(z3, z4)))), S(halve#1(length#1(Cons(z2, Cons(z3, z4))))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, Cons(z3, z4)))), S(halve#1(length#1(Cons(z2, Cons(z3, z4)))))), HALVE#1(S(length#1(Cons(z3, z4)))), LENGTH#1(Cons(z2, Cons(z3, z4))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, z3)))) -> c9(MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3)))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3))))), HALVE#1(S(length#1(z3))), LENGTH#1(Cons(z2, z3)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Nil))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(0)), Cons(z0, Cons(z1, Nil))), Cons(drop#2(S(halve#1(0)), Cons(z0, Cons(z1, Nil))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil)))))
S tuples:
   DROP#2(S(z0), Cons(z1, z2)) -> c12(DROP#2(z0, z2))
   TAKE#2(S(z0), Cons(z1, z2)) -> c15(TAKE#2(z0, z2))
   HALVE#1(S(S(z0))) -> c18(HALVE#1(z0))
   CONST_F#2(z0, Cons(z1, Cons(z2, z3))) -> c19(MERGE#2(z1, z2))
   LEQ#2(S(z0), S(z1)) -> c22(LEQ#2(z0, z1))
   LENGTH#1(Cons(z0, z1)) -> c24(LENGTH#1(z1))
   MAP#2(dc(z0, z1, z2, z3, z4), Cons(z5, z6)) -> c26(DC#1(z0, z1, z2, z3, z4, z5))
   MAP#2(dc(z0, z1, z2, z3, z4), Cons(z5, z6)) -> c27(MAP#2(dc(z0, z1, z2, z3, z4), z6))
   MERGE#2(Cons(0, x1), Cons(z0, x3)) -> c6(COND_MERGE_YS_ZS_2(True, Cons(0, x1), Cons(z0, x3), 0, x1, z0, x3))
   MERGE#2(Cons(S(z0), x1), Cons(0, x3)) -> c6(COND_MERGE_YS_ZS_2(False, Cons(S(z0), x1), Cons(0, x3), S(z0), x1, 0, x3))
   MERGE#2(Cons(S(0), x1), Cons(S(z0), x3)) -> c6(COND_MERGE_YS_ZS_2(True, Cons(S(0), x1), Cons(S(z0), x3), S(0), x1, S(z0), x3), LEQ#2(S(0), S(z0)))
   MERGE#2(Cons(S(S(z0)), x1), Cons(S(0), x3)) -> c6(COND_MERGE_YS_ZS_2(False, Cons(S(S(z0)), x1), Cons(S(0), x3), S(S(z0)), x1, S(0), x3), LEQ#2(S(S(z0)), S(0)))
   MERGE#2(Cons(S(S(z0)), x1), Cons(S(S(z1)), x3)) -> c6(COND_MERGE_YS_ZS_2(leq#2(z0, z1), Cons(S(S(z0)), x1), Cons(S(S(z1)), x3), S(S(z0)), x1, S(S(z1)), x3), LEQ#2(S(S(z0)), S(S(z1))))
   MERGE#2(Cons(S(x0), x1), Cons(S(x2), x3)) -> c6(LEQ#2(S(x0), S(x2)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Nil))) -> c9(CONST_F#2(Cons(x0, Cons(x1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Nil)), S(0)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Nil)), S(halve#1(length#1(Nil)))), HALVE#1(length#1(Nil)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> c9(CONST_F#2(Cons(z0, Cons(z1, z2)), Cons(dc#1(map, divisible, mergesort_zs_3, divide, const_f, take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2)))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(drop#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Nil))), DIVIDE_YS#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2)))), HALVE#1(length#1(z2)), LENGTH#1(z2))
   DIVIDE_YS#1(Cons(x0, Cons(x1, x2)), S(y11)) -> c(TAKE#2(S(y11), Cons(x0, Cons(x1, x2))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, x3))), S(y11)) -> c(TAKE#2(S(y11), Cons(x0, Cons(x1, Cons(x2, x3)))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Nil)), S(y10)) -> c(TAKE#2(S(y10), Cons(x0, Cons(x1, Nil))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Nil))), S(y7)) -> c(TAKE#2(S(y7), Cons(x0, Cons(x1, Cons(x2, Nil)))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4)))), S(y8)) -> c(TAKE#2(S(y8), Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4))))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, x2)), S(y11)) -> c1(DROP#2(S(y11), Cons(x0, Cons(x1, x2))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, x3))), S(y11)) -> c1(DROP#2(S(y11), Cons(x0, Cons(x1, Cons(x2, x3)))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Nil)), S(y10)) -> c1(DROP#2(S(y10), Cons(x0, Cons(x1, Nil))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Nil))), S(y7)) -> c1(DROP#2(S(y7), Cons(x0, Cons(x1, Cons(x2, Nil)))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4)))), S(y8)) -> c1(DROP#2(S(y8), Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4))))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> c9(CONST_F#2(Cons(z0, Cons(z1, z2)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(halve#1(length#1(z2)), Cons(z1, z2)), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Nil))), DIVIDE_YS#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2)))), HALVE#1(length#1(z2)), LENGTH#1(z2))
   COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(z2, z3), z4, Cons(0, y0), z6, z7) -> c2(MERGE#2(Cons(0, y0), Cons(z2, z3)))
   COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(0, z3), z4, Cons(S(y0), y1), z6, z7) -> c2(MERGE#2(Cons(S(y0), y1), Cons(0, z3)))
   COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(S(y1), z3), z4, Cons(S(0), y0), z6, z7) -> c2(MERGE#2(Cons(S(0), y0), Cons(S(y1), z3)))
   COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(S(0), z3), z4, Cons(S(S(y0)), y1), z6, z7) -> c2(MERGE#2(Cons(S(S(y0)), y1), Cons(S(0), z3)))
   COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(S(S(y2)), z3), z4, Cons(S(S(y0)), y1), z6, z7) -> c2(MERGE#2(Cons(S(S(y0)), y1), Cons(S(S(y2)), z3)))
   COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(S(y2), z3), z4, Cons(S(y0), y1), z6, z7) -> c2(MERGE#2(Cons(S(y0), y1), Cons(S(y2), z3)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, z3)))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Cons(z2, z3))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(Cons(z2, z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Cons(drop#2(S(halve#1(S(length#1(z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3)))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3))))), HALVE#1(S(length#1(z3))), LENGTH#1(Cons(z2, z3)))
   COND_MERGE_YS_ZS_2(False, Cons(S(x0), x1), Cons(0, x2), S(x0), x1, 0, x2) -> c3(MERGE#2(Cons(S(x0), x1), x2))
   COND_MERGE_YS_ZS_2(False, Cons(S(S(x0)), x1), Cons(S(0), x2), S(S(x0)), x1, S(0), x2) -> c3(MERGE#2(Cons(S(S(x0)), x1), x2))
   COND_MERGE_YS_ZS_2(False, Cons(S(S(x0)), x1), Cons(S(S(x2)), x3), S(S(x0)), x1, S(S(x2)), x3) -> c3(MERGE#2(Cons(S(S(x0)), x1), x3))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> c9(CONST_F#2(Cons(z0, Cons(z1, z2)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(Cons(z0, take#2(halve#1(length#1(z2)), Cons(z1, z2))), Cons(drop#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Nil))), DIVIDE_YS#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2)))), HALVE#1(length#1(z2)), LENGTH#1(z2))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, z3)))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Cons(z2, z3))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(S(length#1(z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Cons(drop#2(S(halve#1(length#1(Cons(z2, z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3)))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3))))), HALVE#1(S(length#1(z3))), LENGTH#1(Cons(z2, z3)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> c9(MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Nil))), DIVIDE_YS#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2)))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Nil))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(Nil))), Cons(z0, Cons(z1, Nil))), Cons(drop#2(S(halve#1(0)), Cons(z0, Cons(z1, Nil))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil)))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Nil))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(0)), Cons(z0, Cons(z1, Nil))), Cons(drop#2(S(halve#1(length#1(Nil))), Cons(z0, Cons(z1, Nil))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil)))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, z3)))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Cons(z2, z3))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(S(length#1(z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Cons(drop#2(S(halve#1(S(length#1(z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3)))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3))))), HALVE#1(S(length#1(z3))), LENGTH#1(Cons(z2, z3)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, Nil)))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Cons(z2, Nil))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, Nil))), S(halve#1(S(0)))))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, Nil))), S(halve#1(length#1(Cons(z2, Nil)))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, Nil))), S(halve#1(length#1(Cons(z2, Nil))))), HALVE#1(S(length#1(Nil))), LENGTH#1(Cons(z2, Nil)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, Cons(z3, z4))))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Cons(z2, Cons(z3, z4)))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, Cons(z3, z4)))), S(halve#1(S(S(length#1(z4)))))))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, Cons(z3, z4)))), S(halve#1(length#1(Cons(z2, Cons(z3, z4))))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, Cons(z3, z4)))), S(halve#1(length#1(Cons(z2, Cons(z3, z4)))))), HALVE#1(S(length#1(Cons(z3, z4)))), LENGTH#1(Cons(z2, Cons(z3, z4))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, z3)))) -> c9(MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3)))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3))))), HALVE#1(S(length#1(z3))), LENGTH#1(Cons(z2, z3)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Nil))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(0)), Cons(z0, Cons(z1, Nil))), Cons(drop#2(S(halve#1(0)), Cons(z0, Cons(z1, Nil))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil)))))
K tuples:none
Defined Rule Symbols:   leq#2_2, map#2_2, divide_ys#1_2, halve#1_1, length#1_1, take#2_2, drop#2_2, dc#1_6, const_f#2_2, merge#2_2, cond_merge_ys_zs_2_7

Defined Pair Symbols:   DROP#2_2, TAKE#2_2, HALVE#1_1, CONST_F#2_2, LEQ#2_2, LENGTH#1_1, MAP#2_2, MERGE#2_2, DC#1_6, DIVIDE_YS#1_2, COND_MERGE_YS_ZS_2_7

Compound Symbols:   c12_1, c15_1, c18_1, c19_1, c22_1, c24_1, c26_1, c27_1, c6_1, c6_2, c9_4, c9_5, c_1, c1_1, c2_1, c3_1, c9_2, c9_3


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(141) CdtRewritingProof (BOTH BOUNDS(ID, ID))
Used rewriting to replace DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(x0, Cons(x1, Nil))) -> c9(CONST_F#2(Cons(x0, Cons(x1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Nil)), S(0)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(x0, Cons(x1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(x0, Cons(x1, Nil)), S(halve#1(length#1(Nil)))), HALVE#1(length#1(Nil))) by DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Nil))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Nil)), S(0)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil)))), HALVE#1(0))
----------------------------------------

(142)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   leq#2(0, z0) -> True
   leq#2(S(z0), 0) -> False
   leq#2(S(z0), S(z1)) -> leq#2(z0, z1)
   map#2(dc(z0, z1, z2, z3, z4), Nil) -> Nil
   map#2(dc(z0, z1, z2, z3, z4), Cons(z5, z6)) -> Cons(dc#1(z0, z1, z2, z3, z4, z5), map#2(dc(z0, z1, z2, z3, z4), z6))
   divide_ys#1(z0, z1) -> Cons(take#2(z1, z0), Cons(drop#2(z1, z0), Nil))
   halve#1(0) -> 0
   halve#1(S(0)) -> S(0)
   halve#1(S(S(z0))) -> S(halve#1(z0))
   length#1(Nil) -> 0
   length#1(Cons(z0, z1)) -> S(length#1(z1))
   take#2(0, z0) -> Nil
   take#2(S(0), Nil) -> Cons(bot[0], Nil)
   take#2(S(z0), Cons(z1, z2)) -> Cons(z1, take#2(z0, z2))
   drop#2(0, z0) -> z0
   drop#2(S(0), Nil) -> bot[1]
   drop#2(S(z0), Cons(z1, z2)) -> drop#2(z0, z2)
   dc#1(map, divisible, mergesort_zs_3, divide, const_f, Nil) -> Nil
   dc#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Nil)) -> Cons(z0, Nil)
   dc#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> const_f#2(Cons(z0, Cons(z1, z2)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2))))))
   const_f#2(z0, Cons(z1, Cons(z2, z3))) -> merge#2(z1, z2)
   merge#2(Nil, z0) -> z0
   merge#2(Cons(z0, z1), Nil) -> Cons(z0, z1)
   merge#2(Cons(z0, z1), Cons(z2, z3)) -> cond_merge_ys_zs_2(leq#2(z0, z2), Cons(z0, z1), Cons(z2, z3), z0, z1, z2, z3)
   cond_merge_ys_zs_2(True, Cons(z0, z1), Cons(z2, z3), z4, z5, z6, z7) -> Cons(z4, merge#2(z5, Cons(z2, z3)))
   cond_merge_ys_zs_2(False, Cons(z0, z1), Cons(z2, z3), z4, z5, z6, z7) -> Cons(z6, merge#2(Cons(z0, z1), z7))
Tuples:
   DROP#2(S(z0), Cons(z1, z2)) -> c12(DROP#2(z0, z2))
   TAKE#2(S(z0), Cons(z1, z2)) -> c15(TAKE#2(z0, z2))
   HALVE#1(S(S(z0))) -> c18(HALVE#1(z0))
   CONST_F#2(z0, Cons(z1, Cons(z2, z3))) -> c19(MERGE#2(z1, z2))
   LEQ#2(S(z0), S(z1)) -> c22(LEQ#2(z0, z1))
   LENGTH#1(Cons(z0, z1)) -> c24(LENGTH#1(z1))
   MAP#2(dc(z0, z1, z2, z3, z4), Cons(z5, z6)) -> c26(DC#1(z0, z1, z2, z3, z4, z5))
   MAP#2(dc(z0, z1, z2, z3, z4), Cons(z5, z6)) -> c27(MAP#2(dc(z0, z1, z2, z3, z4), z6))
   MERGE#2(Cons(0, x1), Cons(z0, x3)) -> c6(COND_MERGE_YS_ZS_2(True, Cons(0, x1), Cons(z0, x3), 0, x1, z0, x3))
   MERGE#2(Cons(S(z0), x1), Cons(0, x3)) -> c6(COND_MERGE_YS_ZS_2(False, Cons(S(z0), x1), Cons(0, x3), S(z0), x1, 0, x3))
   MERGE#2(Cons(S(0), x1), Cons(S(z0), x3)) -> c6(COND_MERGE_YS_ZS_2(True, Cons(S(0), x1), Cons(S(z0), x3), S(0), x1, S(z0), x3), LEQ#2(S(0), S(z0)))
   MERGE#2(Cons(S(S(z0)), x1), Cons(S(0), x3)) -> c6(COND_MERGE_YS_ZS_2(False, Cons(S(S(z0)), x1), Cons(S(0), x3), S(S(z0)), x1, S(0), x3), LEQ#2(S(S(z0)), S(0)))
   MERGE#2(Cons(S(S(z0)), x1), Cons(S(S(z1)), x3)) -> c6(COND_MERGE_YS_ZS_2(leq#2(z0, z1), Cons(S(S(z0)), x1), Cons(S(S(z1)), x3), S(S(z0)), x1, S(S(z1)), x3), LEQ#2(S(S(z0)), S(S(z1))))
   MERGE#2(Cons(S(x0), x1), Cons(S(x2), x3)) -> c6(LEQ#2(S(x0), S(x2)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> c9(CONST_F#2(Cons(z0, Cons(z1, z2)), Cons(dc#1(map, divisible, mergesort_zs_3, divide, const_f, take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2)))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(drop#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Nil))), DIVIDE_YS#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2)))), HALVE#1(length#1(z2)), LENGTH#1(z2))
   DIVIDE_YS#1(Cons(x0, Cons(x1, x2)), S(y11)) -> c(TAKE#2(S(y11), Cons(x0, Cons(x1, x2))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, x3))), S(y11)) -> c(TAKE#2(S(y11), Cons(x0, Cons(x1, Cons(x2, x3)))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Nil)), S(y10)) -> c(TAKE#2(S(y10), Cons(x0, Cons(x1, Nil))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Nil))), S(y7)) -> c(TAKE#2(S(y7), Cons(x0, Cons(x1, Cons(x2, Nil)))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4)))), S(y8)) -> c(TAKE#2(S(y8), Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4))))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, x2)), S(y11)) -> c1(DROP#2(S(y11), Cons(x0, Cons(x1, x2))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, x3))), S(y11)) -> c1(DROP#2(S(y11), Cons(x0, Cons(x1, Cons(x2, x3)))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Nil)), S(y10)) -> c1(DROP#2(S(y10), Cons(x0, Cons(x1, Nil))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Nil))), S(y7)) -> c1(DROP#2(S(y7), Cons(x0, Cons(x1, Cons(x2, Nil)))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4)))), S(y8)) -> c1(DROP#2(S(y8), Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4))))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> c9(CONST_F#2(Cons(z0, Cons(z1, z2)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(halve#1(length#1(z2)), Cons(z1, z2)), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Nil))), DIVIDE_YS#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2)))), HALVE#1(length#1(z2)), LENGTH#1(z2))
   COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(z2, z3), z4, Cons(0, y0), z6, z7) -> c2(MERGE#2(Cons(0, y0), Cons(z2, z3)))
   COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(0, z3), z4, Cons(S(y0), y1), z6, z7) -> c2(MERGE#2(Cons(S(y0), y1), Cons(0, z3)))
   COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(S(y1), z3), z4, Cons(S(0), y0), z6, z7) -> c2(MERGE#2(Cons(S(0), y0), Cons(S(y1), z3)))
   COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(S(0), z3), z4, Cons(S(S(y0)), y1), z6, z7) -> c2(MERGE#2(Cons(S(S(y0)), y1), Cons(S(0), z3)))
   COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(S(S(y2)), z3), z4, Cons(S(S(y0)), y1), z6, z7) -> c2(MERGE#2(Cons(S(S(y0)), y1), Cons(S(S(y2)), z3)))
   COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(S(y2), z3), z4, Cons(S(y0), y1), z6, z7) -> c2(MERGE#2(Cons(S(y0), y1), Cons(S(y2), z3)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, z3)))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Cons(z2, z3))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(Cons(z2, z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Cons(drop#2(S(halve#1(S(length#1(z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3)))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3))))), HALVE#1(S(length#1(z3))), LENGTH#1(Cons(z2, z3)))
   COND_MERGE_YS_ZS_2(False, Cons(S(x0), x1), Cons(0, x2), S(x0), x1, 0, x2) -> c3(MERGE#2(Cons(S(x0), x1), x2))
   COND_MERGE_YS_ZS_2(False, Cons(S(S(x0)), x1), Cons(S(0), x2), S(S(x0)), x1, S(0), x2) -> c3(MERGE#2(Cons(S(S(x0)), x1), x2))
   COND_MERGE_YS_ZS_2(False, Cons(S(S(x0)), x1), Cons(S(S(x2)), x3), S(S(x0)), x1, S(S(x2)), x3) -> c3(MERGE#2(Cons(S(S(x0)), x1), x3))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> c9(CONST_F#2(Cons(z0, Cons(z1, z2)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(Cons(z0, take#2(halve#1(length#1(z2)), Cons(z1, z2))), Cons(drop#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Nil))), DIVIDE_YS#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2)))), HALVE#1(length#1(z2)), LENGTH#1(z2))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, z3)))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Cons(z2, z3))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(S(length#1(z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Cons(drop#2(S(halve#1(length#1(Cons(z2, z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3)))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3))))), HALVE#1(S(length#1(z3))), LENGTH#1(Cons(z2, z3)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> c9(MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Nil))), DIVIDE_YS#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2)))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Nil))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(Nil))), Cons(z0, Cons(z1, Nil))), Cons(drop#2(S(halve#1(0)), Cons(z0, Cons(z1, Nil))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil)))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Nil))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(0)), Cons(z0, Cons(z1, Nil))), Cons(drop#2(S(halve#1(length#1(Nil))), Cons(z0, Cons(z1, Nil))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil)))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, z3)))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Cons(z2, z3))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(S(length#1(z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Cons(drop#2(S(halve#1(S(length#1(z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3)))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3))))), HALVE#1(S(length#1(z3))), LENGTH#1(Cons(z2, z3)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, Nil)))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Cons(z2, Nil))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, Nil))), S(halve#1(S(0)))))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, Nil))), S(halve#1(length#1(Cons(z2, Nil)))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, Nil))), S(halve#1(length#1(Cons(z2, Nil))))), HALVE#1(S(length#1(Nil))), LENGTH#1(Cons(z2, Nil)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, Cons(z3, z4))))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Cons(z2, Cons(z3, z4)))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, Cons(z3, z4)))), S(halve#1(S(S(length#1(z4)))))))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, Cons(z3, z4)))), S(halve#1(length#1(Cons(z2, Cons(z3, z4))))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, Cons(z3, z4)))), S(halve#1(length#1(Cons(z2, Cons(z3, z4)))))), HALVE#1(S(length#1(Cons(z3, z4)))), LENGTH#1(Cons(z2, Cons(z3, z4))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, z3)))) -> c9(MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3)))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3))))), HALVE#1(S(length#1(z3))), LENGTH#1(Cons(z2, z3)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Nil))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(0)), Cons(z0, Cons(z1, Nil))), Cons(drop#2(S(halve#1(0)), Cons(z0, Cons(z1, Nil))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil)))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Nil))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Nil)), S(0)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil)))), HALVE#1(0))
S tuples:
   DROP#2(S(z0), Cons(z1, z2)) -> c12(DROP#2(z0, z2))
   TAKE#2(S(z0), Cons(z1, z2)) -> c15(TAKE#2(z0, z2))
   HALVE#1(S(S(z0))) -> c18(HALVE#1(z0))
   CONST_F#2(z0, Cons(z1, Cons(z2, z3))) -> c19(MERGE#2(z1, z2))
   LEQ#2(S(z0), S(z1)) -> c22(LEQ#2(z0, z1))
   LENGTH#1(Cons(z0, z1)) -> c24(LENGTH#1(z1))
   MAP#2(dc(z0, z1, z2, z3, z4), Cons(z5, z6)) -> c26(DC#1(z0, z1, z2, z3, z4, z5))
   MAP#2(dc(z0, z1, z2, z3, z4), Cons(z5, z6)) -> c27(MAP#2(dc(z0, z1, z2, z3, z4), z6))
   MERGE#2(Cons(0, x1), Cons(z0, x3)) -> c6(COND_MERGE_YS_ZS_2(True, Cons(0, x1), Cons(z0, x3), 0, x1, z0, x3))
   MERGE#2(Cons(S(z0), x1), Cons(0, x3)) -> c6(COND_MERGE_YS_ZS_2(False, Cons(S(z0), x1), Cons(0, x3), S(z0), x1, 0, x3))
   MERGE#2(Cons(S(0), x1), Cons(S(z0), x3)) -> c6(COND_MERGE_YS_ZS_2(True, Cons(S(0), x1), Cons(S(z0), x3), S(0), x1, S(z0), x3), LEQ#2(S(0), S(z0)))
   MERGE#2(Cons(S(S(z0)), x1), Cons(S(0), x3)) -> c6(COND_MERGE_YS_ZS_2(False, Cons(S(S(z0)), x1), Cons(S(0), x3), S(S(z0)), x1, S(0), x3), LEQ#2(S(S(z0)), S(0)))
   MERGE#2(Cons(S(S(z0)), x1), Cons(S(S(z1)), x3)) -> c6(COND_MERGE_YS_ZS_2(leq#2(z0, z1), Cons(S(S(z0)), x1), Cons(S(S(z1)), x3), S(S(z0)), x1, S(S(z1)), x3), LEQ#2(S(S(z0)), S(S(z1))))
   MERGE#2(Cons(S(x0), x1), Cons(S(x2), x3)) -> c6(LEQ#2(S(x0), S(x2)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> c9(CONST_F#2(Cons(z0, Cons(z1, z2)), Cons(dc#1(map, divisible, mergesort_zs_3, divide, const_f, take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2)))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(drop#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Nil))), DIVIDE_YS#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2)))), HALVE#1(length#1(z2)), LENGTH#1(z2))
   DIVIDE_YS#1(Cons(x0, Cons(x1, x2)), S(y11)) -> c(TAKE#2(S(y11), Cons(x0, Cons(x1, x2))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, x3))), S(y11)) -> c(TAKE#2(S(y11), Cons(x0, Cons(x1, Cons(x2, x3)))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Nil)), S(y10)) -> c(TAKE#2(S(y10), Cons(x0, Cons(x1, Nil))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Nil))), S(y7)) -> c(TAKE#2(S(y7), Cons(x0, Cons(x1, Cons(x2, Nil)))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4)))), S(y8)) -> c(TAKE#2(S(y8), Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4))))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, x2)), S(y11)) -> c1(DROP#2(S(y11), Cons(x0, Cons(x1, x2))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, x3))), S(y11)) -> c1(DROP#2(S(y11), Cons(x0, Cons(x1, Cons(x2, x3)))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Nil)), S(y10)) -> c1(DROP#2(S(y10), Cons(x0, Cons(x1, Nil))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Nil))), S(y7)) -> c1(DROP#2(S(y7), Cons(x0, Cons(x1, Cons(x2, Nil)))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4)))), S(y8)) -> c1(DROP#2(S(y8), Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4))))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> c9(CONST_F#2(Cons(z0, Cons(z1, z2)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(halve#1(length#1(z2)), Cons(z1, z2)), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Nil))), DIVIDE_YS#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2)))), HALVE#1(length#1(z2)), LENGTH#1(z2))
   COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(z2, z3), z4, Cons(0, y0), z6, z7) -> c2(MERGE#2(Cons(0, y0), Cons(z2, z3)))
   COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(0, z3), z4, Cons(S(y0), y1), z6, z7) -> c2(MERGE#2(Cons(S(y0), y1), Cons(0, z3)))
   COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(S(y1), z3), z4, Cons(S(0), y0), z6, z7) -> c2(MERGE#2(Cons(S(0), y0), Cons(S(y1), z3)))
   COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(S(0), z3), z4, Cons(S(S(y0)), y1), z6, z7) -> c2(MERGE#2(Cons(S(S(y0)), y1), Cons(S(0), z3)))
   COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(S(S(y2)), z3), z4, Cons(S(S(y0)), y1), z6, z7) -> c2(MERGE#2(Cons(S(S(y0)), y1), Cons(S(S(y2)), z3)))
   COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(S(y2), z3), z4, Cons(S(y0), y1), z6, z7) -> c2(MERGE#2(Cons(S(y0), y1), Cons(S(y2), z3)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, z3)))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Cons(z2, z3))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(Cons(z2, z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Cons(drop#2(S(halve#1(S(length#1(z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3)))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3))))), HALVE#1(S(length#1(z3))), LENGTH#1(Cons(z2, z3)))
   COND_MERGE_YS_ZS_2(False, Cons(S(x0), x1), Cons(0, x2), S(x0), x1, 0, x2) -> c3(MERGE#2(Cons(S(x0), x1), x2))
   COND_MERGE_YS_ZS_2(False, Cons(S(S(x0)), x1), Cons(S(0), x2), S(S(x0)), x1, S(0), x2) -> c3(MERGE#2(Cons(S(S(x0)), x1), x2))
   COND_MERGE_YS_ZS_2(False, Cons(S(S(x0)), x1), Cons(S(S(x2)), x3), S(S(x0)), x1, S(S(x2)), x3) -> c3(MERGE#2(Cons(S(S(x0)), x1), x3))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> c9(CONST_F#2(Cons(z0, Cons(z1, z2)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(Cons(z0, take#2(halve#1(length#1(z2)), Cons(z1, z2))), Cons(drop#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Nil))), DIVIDE_YS#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2)))), HALVE#1(length#1(z2)), LENGTH#1(z2))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, z3)))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Cons(z2, z3))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(S(length#1(z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Cons(drop#2(S(halve#1(length#1(Cons(z2, z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3)))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3))))), HALVE#1(S(length#1(z3))), LENGTH#1(Cons(z2, z3)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> c9(MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Nil))), DIVIDE_YS#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2)))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Nil))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(Nil))), Cons(z0, Cons(z1, Nil))), Cons(drop#2(S(halve#1(0)), Cons(z0, Cons(z1, Nil))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil)))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Nil))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(0)), Cons(z0, Cons(z1, Nil))), Cons(drop#2(S(halve#1(length#1(Nil))), Cons(z0, Cons(z1, Nil))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil)))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, z3)))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Cons(z2, z3))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(S(length#1(z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Cons(drop#2(S(halve#1(S(length#1(z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3)))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3))))), HALVE#1(S(length#1(z3))), LENGTH#1(Cons(z2, z3)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, Nil)))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Cons(z2, Nil))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, Nil))), S(halve#1(S(0)))))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, Nil))), S(halve#1(length#1(Cons(z2, Nil)))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, Nil))), S(halve#1(length#1(Cons(z2, Nil))))), HALVE#1(S(length#1(Nil))), LENGTH#1(Cons(z2, Nil)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, Cons(z3, z4))))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Cons(z2, Cons(z3, z4)))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, Cons(z3, z4)))), S(halve#1(S(S(length#1(z4)))))))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, Cons(z3, z4)))), S(halve#1(length#1(Cons(z2, Cons(z3, z4))))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, Cons(z3, z4)))), S(halve#1(length#1(Cons(z2, Cons(z3, z4)))))), HALVE#1(S(length#1(Cons(z3, z4)))), LENGTH#1(Cons(z2, Cons(z3, z4))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, z3)))) -> c9(MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3)))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3))))), HALVE#1(S(length#1(z3))), LENGTH#1(Cons(z2, z3)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Nil))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(0)), Cons(z0, Cons(z1, Nil))), Cons(drop#2(S(halve#1(0)), Cons(z0, Cons(z1, Nil))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil)))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Nil))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Nil)), S(0)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil)))), HALVE#1(0))
K tuples:none
Defined Rule Symbols:   leq#2_2, map#2_2, divide_ys#1_2, halve#1_1, length#1_1, take#2_2, drop#2_2, dc#1_6, const_f#2_2, merge#2_2, cond_merge_ys_zs_2_7

Defined Pair Symbols:   DROP#2_2, TAKE#2_2, HALVE#1_1, CONST_F#2_2, LEQ#2_2, LENGTH#1_1, MAP#2_2, MERGE#2_2, DC#1_6, DIVIDE_YS#1_2, COND_MERGE_YS_ZS_2_7

Compound Symbols:   c12_1, c15_1, c18_1, c19_1, c22_1, c24_1, c26_1, c27_1, c6_1, c6_2, c9_5, c_1, c1_1, c2_1, c3_1, c9_2, c9_3, c9_4


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

(144)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   leq#2(0, z0) -> True
   leq#2(S(z0), 0) -> False
   leq#2(S(z0), S(z1)) -> leq#2(z0, z1)
   map#2(dc(z0, z1, z2, z3, z4), Nil) -> Nil
   map#2(dc(z0, z1, z2, z3, z4), Cons(z5, z6)) -> Cons(dc#1(z0, z1, z2, z3, z4, z5), map#2(dc(z0, z1, z2, z3, z4), z6))
   divide_ys#1(z0, z1) -> Cons(take#2(z1, z0), Cons(drop#2(z1, z0), Nil))
   halve#1(0) -> 0
   halve#1(S(0)) -> S(0)
   halve#1(S(S(z0))) -> S(halve#1(z0))
   length#1(Nil) -> 0
   length#1(Cons(z0, z1)) -> S(length#1(z1))
   take#2(0, z0) -> Nil
   take#2(S(0), Nil) -> Cons(bot[0], Nil)
   take#2(S(z0), Cons(z1, z2)) -> Cons(z1, take#2(z0, z2))
   drop#2(0, z0) -> z0
   drop#2(S(0), Nil) -> bot[1]
   drop#2(S(z0), Cons(z1, z2)) -> drop#2(z0, z2)
   dc#1(map, divisible, mergesort_zs_3, divide, const_f, Nil) -> Nil
   dc#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Nil)) -> Cons(z0, Nil)
   dc#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> const_f#2(Cons(z0, Cons(z1, z2)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2))))))
   const_f#2(z0, Cons(z1, Cons(z2, z3))) -> merge#2(z1, z2)
   merge#2(Nil, z0) -> z0
   merge#2(Cons(z0, z1), Nil) -> Cons(z0, z1)
   merge#2(Cons(z0, z1), Cons(z2, z3)) -> cond_merge_ys_zs_2(leq#2(z0, z2), Cons(z0, z1), Cons(z2, z3), z0, z1, z2, z3)
   cond_merge_ys_zs_2(True, Cons(z0, z1), Cons(z2, z3), z4, z5, z6, z7) -> Cons(z4, merge#2(z5, Cons(z2, z3)))
   cond_merge_ys_zs_2(False, Cons(z0, z1), Cons(z2, z3), z4, z5, z6, z7) -> Cons(z6, merge#2(Cons(z0, z1), z7))
Tuples:
   DROP#2(S(z0), Cons(z1, z2)) -> c12(DROP#2(z0, z2))
   TAKE#2(S(z0), Cons(z1, z2)) -> c15(TAKE#2(z0, z2))
   HALVE#1(S(S(z0))) -> c18(HALVE#1(z0))
   CONST_F#2(z0, Cons(z1, Cons(z2, z3))) -> c19(MERGE#2(z1, z2))
   LEQ#2(S(z0), S(z1)) -> c22(LEQ#2(z0, z1))
   LENGTH#1(Cons(z0, z1)) -> c24(LENGTH#1(z1))
   MAP#2(dc(z0, z1, z2, z3, z4), Cons(z5, z6)) -> c26(DC#1(z0, z1, z2, z3, z4, z5))
   MAP#2(dc(z0, z1, z2, z3, z4), Cons(z5, z6)) -> c27(MAP#2(dc(z0, z1, z2, z3, z4), z6))
   MERGE#2(Cons(0, x1), Cons(z0, x3)) -> c6(COND_MERGE_YS_ZS_2(True, Cons(0, x1), Cons(z0, x3), 0, x1, z0, x3))
   MERGE#2(Cons(S(z0), x1), Cons(0, x3)) -> c6(COND_MERGE_YS_ZS_2(False, Cons(S(z0), x1), Cons(0, x3), S(z0), x1, 0, x3))
   MERGE#2(Cons(S(0), x1), Cons(S(z0), x3)) -> c6(COND_MERGE_YS_ZS_2(True, Cons(S(0), x1), Cons(S(z0), x3), S(0), x1, S(z0), x3), LEQ#2(S(0), S(z0)))
   MERGE#2(Cons(S(S(z0)), x1), Cons(S(0), x3)) -> c6(COND_MERGE_YS_ZS_2(False, Cons(S(S(z0)), x1), Cons(S(0), x3), S(S(z0)), x1, S(0), x3), LEQ#2(S(S(z0)), S(0)))
   MERGE#2(Cons(S(S(z0)), x1), Cons(S(S(z1)), x3)) -> c6(COND_MERGE_YS_ZS_2(leq#2(z0, z1), Cons(S(S(z0)), x1), Cons(S(S(z1)), x3), S(S(z0)), x1, S(S(z1)), x3), LEQ#2(S(S(z0)), S(S(z1))))
   MERGE#2(Cons(S(x0), x1), Cons(S(x2), x3)) -> c6(LEQ#2(S(x0), S(x2)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> c9(CONST_F#2(Cons(z0, Cons(z1, z2)), Cons(dc#1(map, divisible, mergesort_zs_3, divide, const_f, take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2)))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(drop#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Nil))), DIVIDE_YS#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2)))), HALVE#1(length#1(z2)), LENGTH#1(z2))
   DIVIDE_YS#1(Cons(x0, Cons(x1, x2)), S(y11)) -> c(TAKE#2(S(y11), Cons(x0, Cons(x1, x2))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, x3))), S(y11)) -> c(TAKE#2(S(y11), Cons(x0, Cons(x1, Cons(x2, x3)))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Nil)), S(y10)) -> c(TAKE#2(S(y10), Cons(x0, Cons(x1, Nil))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Nil))), S(y7)) -> c(TAKE#2(S(y7), Cons(x0, Cons(x1, Cons(x2, Nil)))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4)))), S(y8)) -> c(TAKE#2(S(y8), Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4))))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, x2)), S(y11)) -> c1(DROP#2(S(y11), Cons(x0, Cons(x1, x2))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, x3))), S(y11)) -> c1(DROP#2(S(y11), Cons(x0, Cons(x1, Cons(x2, x3)))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Nil)), S(y10)) -> c1(DROP#2(S(y10), Cons(x0, Cons(x1, Nil))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Nil))), S(y7)) -> c1(DROP#2(S(y7), Cons(x0, Cons(x1, Cons(x2, Nil)))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4)))), S(y8)) -> c1(DROP#2(S(y8), Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4))))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> c9(CONST_F#2(Cons(z0, Cons(z1, z2)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(halve#1(length#1(z2)), Cons(z1, z2)), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Nil))), DIVIDE_YS#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2)))), HALVE#1(length#1(z2)), LENGTH#1(z2))
   COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(z2, z3), z4, Cons(0, y0), z6, z7) -> c2(MERGE#2(Cons(0, y0), Cons(z2, z3)))
   COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(0, z3), z4, Cons(S(y0), y1), z6, z7) -> c2(MERGE#2(Cons(S(y0), y1), Cons(0, z3)))
   COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(S(y1), z3), z4, Cons(S(0), y0), z6, z7) -> c2(MERGE#2(Cons(S(0), y0), Cons(S(y1), z3)))
   COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(S(0), z3), z4, Cons(S(S(y0)), y1), z6, z7) -> c2(MERGE#2(Cons(S(S(y0)), y1), Cons(S(0), z3)))
   COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(S(S(y2)), z3), z4, Cons(S(S(y0)), y1), z6, z7) -> c2(MERGE#2(Cons(S(S(y0)), y1), Cons(S(S(y2)), z3)))
   COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(S(y2), z3), z4, Cons(S(y0), y1), z6, z7) -> c2(MERGE#2(Cons(S(y0), y1), Cons(S(y2), z3)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, z3)))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Cons(z2, z3))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(Cons(z2, z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Cons(drop#2(S(halve#1(S(length#1(z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3)))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3))))), HALVE#1(S(length#1(z3))), LENGTH#1(Cons(z2, z3)))
   COND_MERGE_YS_ZS_2(False, Cons(S(x0), x1), Cons(0, x2), S(x0), x1, 0, x2) -> c3(MERGE#2(Cons(S(x0), x1), x2))
   COND_MERGE_YS_ZS_2(False, Cons(S(S(x0)), x1), Cons(S(0), x2), S(S(x0)), x1, S(0), x2) -> c3(MERGE#2(Cons(S(S(x0)), x1), x2))
   COND_MERGE_YS_ZS_2(False, Cons(S(S(x0)), x1), Cons(S(S(x2)), x3), S(S(x0)), x1, S(S(x2)), x3) -> c3(MERGE#2(Cons(S(S(x0)), x1), x3))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> c9(CONST_F#2(Cons(z0, Cons(z1, z2)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(Cons(z0, take#2(halve#1(length#1(z2)), Cons(z1, z2))), Cons(drop#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Nil))), DIVIDE_YS#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2)))), HALVE#1(length#1(z2)), LENGTH#1(z2))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, z3)))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Cons(z2, z3))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(S(length#1(z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Cons(drop#2(S(halve#1(length#1(Cons(z2, z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3)))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3))))), HALVE#1(S(length#1(z3))), LENGTH#1(Cons(z2, z3)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> c9(MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Nil))), DIVIDE_YS#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2)))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Nil))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(Nil))), Cons(z0, Cons(z1, Nil))), Cons(drop#2(S(halve#1(0)), Cons(z0, Cons(z1, Nil))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil)))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Nil))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(0)), Cons(z0, Cons(z1, Nil))), Cons(drop#2(S(halve#1(length#1(Nil))), Cons(z0, Cons(z1, Nil))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil)))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, z3)))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Cons(z2, z3))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(S(length#1(z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Cons(drop#2(S(halve#1(S(length#1(z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3)))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3))))), HALVE#1(S(length#1(z3))), LENGTH#1(Cons(z2, z3)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, Nil)))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Cons(z2, Nil))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, Nil))), S(halve#1(S(0)))))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, Nil))), S(halve#1(length#1(Cons(z2, Nil)))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, Nil))), S(halve#1(length#1(Cons(z2, Nil))))), HALVE#1(S(length#1(Nil))), LENGTH#1(Cons(z2, Nil)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, Cons(z3, z4))))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Cons(z2, Cons(z3, z4)))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, Cons(z3, z4)))), S(halve#1(S(S(length#1(z4)))))))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, Cons(z3, z4)))), S(halve#1(length#1(Cons(z2, Cons(z3, z4))))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, Cons(z3, z4)))), S(halve#1(length#1(Cons(z2, Cons(z3, z4)))))), HALVE#1(S(length#1(Cons(z3, z4)))), LENGTH#1(Cons(z2, Cons(z3, z4))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, z3)))) -> c9(MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3)))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3))))), HALVE#1(S(length#1(z3))), LENGTH#1(Cons(z2, z3)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Nil))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(0)), Cons(z0, Cons(z1, Nil))), Cons(drop#2(S(halve#1(0)), Cons(z0, Cons(z1, Nil))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil)))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Nil))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Nil)), S(0)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil)))))
S tuples:
   DROP#2(S(z0), Cons(z1, z2)) -> c12(DROP#2(z0, z2))
   TAKE#2(S(z0), Cons(z1, z2)) -> c15(TAKE#2(z0, z2))
   HALVE#1(S(S(z0))) -> c18(HALVE#1(z0))
   CONST_F#2(z0, Cons(z1, Cons(z2, z3))) -> c19(MERGE#2(z1, z2))
   LEQ#2(S(z0), S(z1)) -> c22(LEQ#2(z0, z1))
   LENGTH#1(Cons(z0, z1)) -> c24(LENGTH#1(z1))
   MAP#2(dc(z0, z1, z2, z3, z4), Cons(z5, z6)) -> c26(DC#1(z0, z1, z2, z3, z4, z5))
   MAP#2(dc(z0, z1, z2, z3, z4), Cons(z5, z6)) -> c27(MAP#2(dc(z0, z1, z2, z3, z4), z6))
   MERGE#2(Cons(0, x1), Cons(z0, x3)) -> c6(COND_MERGE_YS_ZS_2(True, Cons(0, x1), Cons(z0, x3), 0, x1, z0, x3))
   MERGE#2(Cons(S(z0), x1), Cons(0, x3)) -> c6(COND_MERGE_YS_ZS_2(False, Cons(S(z0), x1), Cons(0, x3), S(z0), x1, 0, x3))
   MERGE#2(Cons(S(0), x1), Cons(S(z0), x3)) -> c6(COND_MERGE_YS_ZS_2(True, Cons(S(0), x1), Cons(S(z0), x3), S(0), x1, S(z0), x3), LEQ#2(S(0), S(z0)))
   MERGE#2(Cons(S(S(z0)), x1), Cons(S(0), x3)) -> c6(COND_MERGE_YS_ZS_2(False, Cons(S(S(z0)), x1), Cons(S(0), x3), S(S(z0)), x1, S(0), x3), LEQ#2(S(S(z0)), S(0)))
   MERGE#2(Cons(S(S(z0)), x1), Cons(S(S(z1)), x3)) -> c6(COND_MERGE_YS_ZS_2(leq#2(z0, z1), Cons(S(S(z0)), x1), Cons(S(S(z1)), x3), S(S(z0)), x1, S(S(z1)), x3), LEQ#2(S(S(z0)), S(S(z1))))
   MERGE#2(Cons(S(x0), x1), Cons(S(x2), x3)) -> c6(LEQ#2(S(x0), S(x2)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> c9(CONST_F#2(Cons(z0, Cons(z1, z2)), Cons(dc#1(map, divisible, mergesort_zs_3, divide, const_f, take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2)))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(drop#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Nil))), DIVIDE_YS#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2)))), HALVE#1(length#1(z2)), LENGTH#1(z2))
   DIVIDE_YS#1(Cons(x0, Cons(x1, x2)), S(y11)) -> c(TAKE#2(S(y11), Cons(x0, Cons(x1, x2))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, x3))), S(y11)) -> c(TAKE#2(S(y11), Cons(x0, Cons(x1, Cons(x2, x3)))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Nil)), S(y10)) -> c(TAKE#2(S(y10), Cons(x0, Cons(x1, Nil))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Nil))), S(y7)) -> c(TAKE#2(S(y7), Cons(x0, Cons(x1, Cons(x2, Nil)))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4)))), S(y8)) -> c(TAKE#2(S(y8), Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4))))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, x2)), S(y11)) -> c1(DROP#2(S(y11), Cons(x0, Cons(x1, x2))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, x3))), S(y11)) -> c1(DROP#2(S(y11), Cons(x0, Cons(x1, Cons(x2, x3)))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Nil)), S(y10)) -> c1(DROP#2(S(y10), Cons(x0, Cons(x1, Nil))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Nil))), S(y7)) -> c1(DROP#2(S(y7), Cons(x0, Cons(x1, Cons(x2, Nil)))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4)))), S(y8)) -> c1(DROP#2(S(y8), Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4))))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> c9(CONST_F#2(Cons(z0, Cons(z1, z2)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(halve#1(length#1(z2)), Cons(z1, z2)), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Nil))), DIVIDE_YS#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2)))), HALVE#1(length#1(z2)), LENGTH#1(z2))
   COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(z2, z3), z4, Cons(0, y0), z6, z7) -> c2(MERGE#2(Cons(0, y0), Cons(z2, z3)))
   COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(0, z3), z4, Cons(S(y0), y1), z6, z7) -> c2(MERGE#2(Cons(S(y0), y1), Cons(0, z3)))
   COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(S(y1), z3), z4, Cons(S(0), y0), z6, z7) -> c2(MERGE#2(Cons(S(0), y0), Cons(S(y1), z3)))
   COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(S(0), z3), z4, Cons(S(S(y0)), y1), z6, z7) -> c2(MERGE#2(Cons(S(S(y0)), y1), Cons(S(0), z3)))
   COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(S(S(y2)), z3), z4, Cons(S(S(y0)), y1), z6, z7) -> c2(MERGE#2(Cons(S(S(y0)), y1), Cons(S(S(y2)), z3)))
   COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(S(y2), z3), z4, Cons(S(y0), y1), z6, z7) -> c2(MERGE#2(Cons(S(y0), y1), Cons(S(y2), z3)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, z3)))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Cons(z2, z3))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(Cons(z2, z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Cons(drop#2(S(halve#1(S(length#1(z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3)))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3))))), HALVE#1(S(length#1(z3))), LENGTH#1(Cons(z2, z3)))
   COND_MERGE_YS_ZS_2(False, Cons(S(x0), x1), Cons(0, x2), S(x0), x1, 0, x2) -> c3(MERGE#2(Cons(S(x0), x1), x2))
   COND_MERGE_YS_ZS_2(False, Cons(S(S(x0)), x1), Cons(S(0), x2), S(S(x0)), x1, S(0), x2) -> c3(MERGE#2(Cons(S(S(x0)), x1), x2))
   COND_MERGE_YS_ZS_2(False, Cons(S(S(x0)), x1), Cons(S(S(x2)), x3), S(S(x0)), x1, S(S(x2)), x3) -> c3(MERGE#2(Cons(S(S(x0)), x1), x3))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> c9(CONST_F#2(Cons(z0, Cons(z1, z2)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(Cons(z0, take#2(halve#1(length#1(z2)), Cons(z1, z2))), Cons(drop#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Nil))), DIVIDE_YS#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2)))), HALVE#1(length#1(z2)), LENGTH#1(z2))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, z3)))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Cons(z2, z3))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(S(length#1(z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Cons(drop#2(S(halve#1(length#1(Cons(z2, z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3)))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3))))), HALVE#1(S(length#1(z3))), LENGTH#1(Cons(z2, z3)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> c9(MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Nil))), DIVIDE_YS#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2)))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Nil))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(Nil))), Cons(z0, Cons(z1, Nil))), Cons(drop#2(S(halve#1(0)), Cons(z0, Cons(z1, Nil))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil)))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Nil))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(0)), Cons(z0, Cons(z1, Nil))), Cons(drop#2(S(halve#1(length#1(Nil))), Cons(z0, Cons(z1, Nil))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil)))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, z3)))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Cons(z2, z3))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(S(length#1(z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Cons(drop#2(S(halve#1(S(length#1(z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3)))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3))))), HALVE#1(S(length#1(z3))), LENGTH#1(Cons(z2, z3)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, Nil)))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Cons(z2, Nil))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, Nil))), S(halve#1(S(0)))))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, Nil))), S(halve#1(length#1(Cons(z2, Nil)))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, Nil))), S(halve#1(length#1(Cons(z2, Nil))))), HALVE#1(S(length#1(Nil))), LENGTH#1(Cons(z2, Nil)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, Cons(z3, z4))))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Cons(z2, Cons(z3, z4)))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, Cons(z3, z4)))), S(halve#1(S(S(length#1(z4)))))))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, Cons(z3, z4)))), S(halve#1(length#1(Cons(z2, Cons(z3, z4))))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, Cons(z3, z4)))), S(halve#1(length#1(Cons(z2, Cons(z3, z4)))))), HALVE#1(S(length#1(Cons(z3, z4)))), LENGTH#1(Cons(z2, Cons(z3, z4))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, z3)))) -> c9(MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3)))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3))))), HALVE#1(S(length#1(z3))), LENGTH#1(Cons(z2, z3)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Nil))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(0)), Cons(z0, Cons(z1, Nil))), Cons(drop#2(S(halve#1(0)), Cons(z0, Cons(z1, Nil))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil)))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Nil))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Nil)), S(0)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil)))))
K tuples:none
Defined Rule Symbols:   leq#2_2, map#2_2, divide_ys#1_2, halve#1_1, length#1_1, take#2_2, drop#2_2, dc#1_6, const_f#2_2, merge#2_2, cond_merge_ys_zs_2_7

Defined Pair Symbols:   DROP#2_2, TAKE#2_2, HALVE#1_1, CONST_F#2_2, LEQ#2_2, LENGTH#1_1, MAP#2_2, MERGE#2_2, DC#1_6, DIVIDE_YS#1_2, COND_MERGE_YS_ZS_2_7

Compound Symbols:   c12_1, c15_1, c18_1, c19_1, c22_1, c24_1, c26_1, c27_1, c6_1, c6_2, c9_5, c_1, c1_1, c2_1, c3_1, c9_2, c9_3, c9_4


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

(145) CdtRewritingProof (BOTH BOUNDS(ID, ID))
Used rewriting to replace DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> c9(CONST_F#2(Cons(z0, Cons(z1, z2)), Cons(dc#1(map, divisible, mergesort_zs_3, divide, const_f, take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2)))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(drop#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Nil))), DIVIDE_YS#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2)))), HALVE#1(length#1(z2)), LENGTH#1(z2)) by DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> c9(CONST_F#2(Cons(z0, Cons(z1, z2)), Cons(dc#1(map, divisible, mergesort_zs_3, divide, const_f, take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2)))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(drop#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(halve#1(length#1(z2)), Cons(z1, z2)), Nil))), DIVIDE_YS#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2)))), HALVE#1(length#1(z2)), LENGTH#1(z2))
----------------------------------------

(146)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   leq#2(0, z0) -> True
   leq#2(S(z0), 0) -> False
   leq#2(S(z0), S(z1)) -> leq#2(z0, z1)
   map#2(dc(z0, z1, z2, z3, z4), Nil) -> Nil
   map#2(dc(z0, z1, z2, z3, z4), Cons(z5, z6)) -> Cons(dc#1(z0, z1, z2, z3, z4, z5), map#2(dc(z0, z1, z2, z3, z4), z6))
   divide_ys#1(z0, z1) -> Cons(take#2(z1, z0), Cons(drop#2(z1, z0), Nil))
   halve#1(0) -> 0
   halve#1(S(0)) -> S(0)
   halve#1(S(S(z0))) -> S(halve#1(z0))
   length#1(Nil) -> 0
   length#1(Cons(z0, z1)) -> S(length#1(z1))
   take#2(0, z0) -> Nil
   take#2(S(0), Nil) -> Cons(bot[0], Nil)
   take#2(S(z0), Cons(z1, z2)) -> Cons(z1, take#2(z0, z2))
   drop#2(0, z0) -> z0
   drop#2(S(0), Nil) -> bot[1]
   drop#2(S(z0), Cons(z1, z2)) -> drop#2(z0, z2)
   dc#1(map, divisible, mergesort_zs_3, divide, const_f, Nil) -> Nil
   dc#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Nil)) -> Cons(z0, Nil)
   dc#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> const_f#2(Cons(z0, Cons(z1, z2)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2))))))
   const_f#2(z0, Cons(z1, Cons(z2, z3))) -> merge#2(z1, z2)
   merge#2(Nil, z0) -> z0
   merge#2(Cons(z0, z1), Nil) -> Cons(z0, z1)
   merge#2(Cons(z0, z1), Cons(z2, z3)) -> cond_merge_ys_zs_2(leq#2(z0, z2), Cons(z0, z1), Cons(z2, z3), z0, z1, z2, z3)
   cond_merge_ys_zs_2(True, Cons(z0, z1), Cons(z2, z3), z4, z5, z6, z7) -> Cons(z4, merge#2(z5, Cons(z2, z3)))
   cond_merge_ys_zs_2(False, Cons(z0, z1), Cons(z2, z3), z4, z5, z6, z7) -> Cons(z6, merge#2(Cons(z0, z1), z7))
Tuples:
   DROP#2(S(z0), Cons(z1, z2)) -> c12(DROP#2(z0, z2))
   TAKE#2(S(z0), Cons(z1, z2)) -> c15(TAKE#2(z0, z2))
   HALVE#1(S(S(z0))) -> c18(HALVE#1(z0))
   CONST_F#2(z0, Cons(z1, Cons(z2, z3))) -> c19(MERGE#2(z1, z2))
   LEQ#2(S(z0), S(z1)) -> c22(LEQ#2(z0, z1))
   LENGTH#1(Cons(z0, z1)) -> c24(LENGTH#1(z1))
   MAP#2(dc(z0, z1, z2, z3, z4), Cons(z5, z6)) -> c26(DC#1(z0, z1, z2, z3, z4, z5))
   MAP#2(dc(z0, z1, z2, z3, z4), Cons(z5, z6)) -> c27(MAP#2(dc(z0, z1, z2, z3, z4), z6))
   MERGE#2(Cons(0, x1), Cons(z0, x3)) -> c6(COND_MERGE_YS_ZS_2(True, Cons(0, x1), Cons(z0, x3), 0, x1, z0, x3))
   MERGE#2(Cons(S(z0), x1), Cons(0, x3)) -> c6(COND_MERGE_YS_ZS_2(False, Cons(S(z0), x1), Cons(0, x3), S(z0), x1, 0, x3))
   MERGE#2(Cons(S(0), x1), Cons(S(z0), x3)) -> c6(COND_MERGE_YS_ZS_2(True, Cons(S(0), x1), Cons(S(z0), x3), S(0), x1, S(z0), x3), LEQ#2(S(0), S(z0)))
   MERGE#2(Cons(S(S(z0)), x1), Cons(S(0), x3)) -> c6(COND_MERGE_YS_ZS_2(False, Cons(S(S(z0)), x1), Cons(S(0), x3), S(S(z0)), x1, S(0), x3), LEQ#2(S(S(z0)), S(0)))
   MERGE#2(Cons(S(S(z0)), x1), Cons(S(S(z1)), x3)) -> c6(COND_MERGE_YS_ZS_2(leq#2(z0, z1), Cons(S(S(z0)), x1), Cons(S(S(z1)), x3), S(S(z0)), x1, S(S(z1)), x3), LEQ#2(S(S(z0)), S(S(z1))))
   MERGE#2(Cons(S(x0), x1), Cons(S(x2), x3)) -> c6(LEQ#2(S(x0), S(x2)))
   DIVIDE_YS#1(Cons(x0, Cons(x1, x2)), S(y11)) -> c(TAKE#2(S(y11), Cons(x0, Cons(x1, x2))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, x3))), S(y11)) -> c(TAKE#2(S(y11), Cons(x0, Cons(x1, Cons(x2, x3)))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Nil)), S(y10)) -> c(TAKE#2(S(y10), Cons(x0, Cons(x1, Nil))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Nil))), S(y7)) -> c(TAKE#2(S(y7), Cons(x0, Cons(x1, Cons(x2, Nil)))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4)))), S(y8)) -> c(TAKE#2(S(y8), Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4))))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, x2)), S(y11)) -> c1(DROP#2(S(y11), Cons(x0, Cons(x1, x2))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, x3))), S(y11)) -> c1(DROP#2(S(y11), Cons(x0, Cons(x1, Cons(x2, x3)))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Nil)), S(y10)) -> c1(DROP#2(S(y10), Cons(x0, Cons(x1, Nil))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Nil))), S(y7)) -> c1(DROP#2(S(y7), Cons(x0, Cons(x1, Cons(x2, Nil)))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4)))), S(y8)) -> c1(DROP#2(S(y8), Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4))))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> c9(CONST_F#2(Cons(z0, Cons(z1, z2)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(halve#1(length#1(z2)), Cons(z1, z2)), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Nil))), DIVIDE_YS#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2)))), HALVE#1(length#1(z2)), LENGTH#1(z2))
   COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(z2, z3), z4, Cons(0, y0), z6, z7) -> c2(MERGE#2(Cons(0, y0), Cons(z2, z3)))
   COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(0, z3), z4, Cons(S(y0), y1), z6, z7) -> c2(MERGE#2(Cons(S(y0), y1), Cons(0, z3)))
   COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(S(y1), z3), z4, Cons(S(0), y0), z6, z7) -> c2(MERGE#2(Cons(S(0), y0), Cons(S(y1), z3)))
   COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(S(0), z3), z4, Cons(S(S(y0)), y1), z6, z7) -> c2(MERGE#2(Cons(S(S(y0)), y1), Cons(S(0), z3)))
   COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(S(S(y2)), z3), z4, Cons(S(S(y0)), y1), z6, z7) -> c2(MERGE#2(Cons(S(S(y0)), y1), Cons(S(S(y2)), z3)))
   COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(S(y2), z3), z4, Cons(S(y0), y1), z6, z7) -> c2(MERGE#2(Cons(S(y0), y1), Cons(S(y2), z3)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, z3)))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Cons(z2, z3))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(Cons(z2, z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Cons(drop#2(S(halve#1(S(length#1(z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3)))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3))))), HALVE#1(S(length#1(z3))), LENGTH#1(Cons(z2, z3)))
   COND_MERGE_YS_ZS_2(False, Cons(S(x0), x1), Cons(0, x2), S(x0), x1, 0, x2) -> c3(MERGE#2(Cons(S(x0), x1), x2))
   COND_MERGE_YS_ZS_2(False, Cons(S(S(x0)), x1), Cons(S(0), x2), S(S(x0)), x1, S(0), x2) -> c3(MERGE#2(Cons(S(S(x0)), x1), x2))
   COND_MERGE_YS_ZS_2(False, Cons(S(S(x0)), x1), Cons(S(S(x2)), x3), S(S(x0)), x1, S(S(x2)), x3) -> c3(MERGE#2(Cons(S(S(x0)), x1), x3))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> c9(CONST_F#2(Cons(z0, Cons(z1, z2)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(Cons(z0, take#2(halve#1(length#1(z2)), Cons(z1, z2))), Cons(drop#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Nil))), DIVIDE_YS#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2)))), HALVE#1(length#1(z2)), LENGTH#1(z2))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, z3)))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Cons(z2, z3))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(S(length#1(z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Cons(drop#2(S(halve#1(length#1(Cons(z2, z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3)))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3))))), HALVE#1(S(length#1(z3))), LENGTH#1(Cons(z2, z3)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> c9(MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Nil))), DIVIDE_YS#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2)))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Nil))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(Nil))), Cons(z0, Cons(z1, Nil))), Cons(drop#2(S(halve#1(0)), Cons(z0, Cons(z1, Nil))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil)))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Nil))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(0)), Cons(z0, Cons(z1, Nil))), Cons(drop#2(S(halve#1(length#1(Nil))), Cons(z0, Cons(z1, Nil))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil)))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, z3)))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Cons(z2, z3))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(S(length#1(z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Cons(drop#2(S(halve#1(S(length#1(z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3)))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3))))), HALVE#1(S(length#1(z3))), LENGTH#1(Cons(z2, z3)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, Nil)))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Cons(z2, Nil))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, Nil))), S(halve#1(S(0)))))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, Nil))), S(halve#1(length#1(Cons(z2, Nil)))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, Nil))), S(halve#1(length#1(Cons(z2, Nil))))), HALVE#1(S(length#1(Nil))), LENGTH#1(Cons(z2, Nil)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, Cons(z3, z4))))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Cons(z2, Cons(z3, z4)))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, Cons(z3, z4)))), S(halve#1(S(S(length#1(z4)))))))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, Cons(z3, z4)))), S(halve#1(length#1(Cons(z2, Cons(z3, z4))))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, Cons(z3, z4)))), S(halve#1(length#1(Cons(z2, Cons(z3, z4)))))), HALVE#1(S(length#1(Cons(z3, z4)))), LENGTH#1(Cons(z2, Cons(z3, z4))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, z3)))) -> c9(MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3)))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3))))), HALVE#1(S(length#1(z3))), LENGTH#1(Cons(z2, z3)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Nil))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(0)), Cons(z0, Cons(z1, Nil))), Cons(drop#2(S(halve#1(0)), Cons(z0, Cons(z1, Nil))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil)))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Nil))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Nil)), S(0)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil)))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> c9(CONST_F#2(Cons(z0, Cons(z1, z2)), Cons(dc#1(map, divisible, mergesort_zs_3, divide, const_f, take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2)))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(drop#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(halve#1(length#1(z2)), Cons(z1, z2)), Nil))), DIVIDE_YS#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2)))), HALVE#1(length#1(z2)), LENGTH#1(z2))
S tuples:
   DROP#2(S(z0), Cons(z1, z2)) -> c12(DROP#2(z0, z2))
   TAKE#2(S(z0), Cons(z1, z2)) -> c15(TAKE#2(z0, z2))
   HALVE#1(S(S(z0))) -> c18(HALVE#1(z0))
   CONST_F#2(z0, Cons(z1, Cons(z2, z3))) -> c19(MERGE#2(z1, z2))
   LEQ#2(S(z0), S(z1)) -> c22(LEQ#2(z0, z1))
   LENGTH#1(Cons(z0, z1)) -> c24(LENGTH#1(z1))
   MAP#2(dc(z0, z1, z2, z3, z4), Cons(z5, z6)) -> c26(DC#1(z0, z1, z2, z3, z4, z5))
   MAP#2(dc(z0, z1, z2, z3, z4), Cons(z5, z6)) -> c27(MAP#2(dc(z0, z1, z2, z3, z4), z6))
   MERGE#2(Cons(0, x1), Cons(z0, x3)) -> c6(COND_MERGE_YS_ZS_2(True, Cons(0, x1), Cons(z0, x3), 0, x1, z0, x3))
   MERGE#2(Cons(S(z0), x1), Cons(0, x3)) -> c6(COND_MERGE_YS_ZS_2(False, Cons(S(z0), x1), Cons(0, x3), S(z0), x1, 0, x3))
   MERGE#2(Cons(S(0), x1), Cons(S(z0), x3)) -> c6(COND_MERGE_YS_ZS_2(True, Cons(S(0), x1), Cons(S(z0), x3), S(0), x1, S(z0), x3), LEQ#2(S(0), S(z0)))
   MERGE#2(Cons(S(S(z0)), x1), Cons(S(0), x3)) -> c6(COND_MERGE_YS_ZS_2(False, Cons(S(S(z0)), x1), Cons(S(0), x3), S(S(z0)), x1, S(0), x3), LEQ#2(S(S(z0)), S(0)))
   MERGE#2(Cons(S(S(z0)), x1), Cons(S(S(z1)), x3)) -> c6(COND_MERGE_YS_ZS_2(leq#2(z0, z1), Cons(S(S(z0)), x1), Cons(S(S(z1)), x3), S(S(z0)), x1, S(S(z1)), x3), LEQ#2(S(S(z0)), S(S(z1))))
   MERGE#2(Cons(S(x0), x1), Cons(S(x2), x3)) -> c6(LEQ#2(S(x0), S(x2)))
   DIVIDE_YS#1(Cons(x0, Cons(x1, x2)), S(y11)) -> c(TAKE#2(S(y11), Cons(x0, Cons(x1, x2))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, x3))), S(y11)) -> c(TAKE#2(S(y11), Cons(x0, Cons(x1, Cons(x2, x3)))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Nil)), S(y10)) -> c(TAKE#2(S(y10), Cons(x0, Cons(x1, Nil))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Nil))), S(y7)) -> c(TAKE#2(S(y7), Cons(x0, Cons(x1, Cons(x2, Nil)))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4)))), S(y8)) -> c(TAKE#2(S(y8), Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4))))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, x2)), S(y11)) -> c1(DROP#2(S(y11), Cons(x0, Cons(x1, x2))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, x3))), S(y11)) -> c1(DROP#2(S(y11), Cons(x0, Cons(x1, Cons(x2, x3)))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Nil)), S(y10)) -> c1(DROP#2(S(y10), Cons(x0, Cons(x1, Nil))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Nil))), S(y7)) -> c1(DROP#2(S(y7), Cons(x0, Cons(x1, Cons(x2, Nil)))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4)))), S(y8)) -> c1(DROP#2(S(y8), Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4))))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> c9(CONST_F#2(Cons(z0, Cons(z1, z2)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(halve#1(length#1(z2)), Cons(z1, z2)), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Nil))), DIVIDE_YS#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2)))), HALVE#1(length#1(z2)), LENGTH#1(z2))
   COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(z2, z3), z4, Cons(0, y0), z6, z7) -> c2(MERGE#2(Cons(0, y0), Cons(z2, z3)))
   COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(0, z3), z4, Cons(S(y0), y1), z6, z7) -> c2(MERGE#2(Cons(S(y0), y1), Cons(0, z3)))
   COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(S(y1), z3), z4, Cons(S(0), y0), z6, z7) -> c2(MERGE#2(Cons(S(0), y0), Cons(S(y1), z3)))
   COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(S(0), z3), z4, Cons(S(S(y0)), y1), z6, z7) -> c2(MERGE#2(Cons(S(S(y0)), y1), Cons(S(0), z3)))
   COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(S(S(y2)), z3), z4, Cons(S(S(y0)), y1), z6, z7) -> c2(MERGE#2(Cons(S(S(y0)), y1), Cons(S(S(y2)), z3)))
   COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(S(y2), z3), z4, Cons(S(y0), y1), z6, z7) -> c2(MERGE#2(Cons(S(y0), y1), Cons(S(y2), z3)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, z3)))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Cons(z2, z3))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(Cons(z2, z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Cons(drop#2(S(halve#1(S(length#1(z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3)))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3))))), HALVE#1(S(length#1(z3))), LENGTH#1(Cons(z2, z3)))
   COND_MERGE_YS_ZS_2(False, Cons(S(x0), x1), Cons(0, x2), S(x0), x1, 0, x2) -> c3(MERGE#2(Cons(S(x0), x1), x2))
   COND_MERGE_YS_ZS_2(False, Cons(S(S(x0)), x1), Cons(S(0), x2), S(S(x0)), x1, S(0), x2) -> c3(MERGE#2(Cons(S(S(x0)), x1), x2))
   COND_MERGE_YS_ZS_2(False, Cons(S(S(x0)), x1), Cons(S(S(x2)), x3), S(S(x0)), x1, S(S(x2)), x3) -> c3(MERGE#2(Cons(S(S(x0)), x1), x3))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> c9(CONST_F#2(Cons(z0, Cons(z1, z2)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(Cons(z0, take#2(halve#1(length#1(z2)), Cons(z1, z2))), Cons(drop#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Nil))), DIVIDE_YS#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2)))), HALVE#1(length#1(z2)), LENGTH#1(z2))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, z3)))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Cons(z2, z3))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(S(length#1(z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Cons(drop#2(S(halve#1(length#1(Cons(z2, z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3)))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3))))), HALVE#1(S(length#1(z3))), LENGTH#1(Cons(z2, z3)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> c9(MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Nil))), DIVIDE_YS#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2)))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Nil))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(Nil))), Cons(z0, Cons(z1, Nil))), Cons(drop#2(S(halve#1(0)), Cons(z0, Cons(z1, Nil))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil)))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Nil))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(0)), Cons(z0, Cons(z1, Nil))), Cons(drop#2(S(halve#1(length#1(Nil))), Cons(z0, Cons(z1, Nil))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil)))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, z3)))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Cons(z2, z3))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(S(length#1(z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Cons(drop#2(S(halve#1(S(length#1(z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3)))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3))))), HALVE#1(S(length#1(z3))), LENGTH#1(Cons(z2, z3)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, Nil)))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Cons(z2, Nil))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, Nil))), S(halve#1(S(0)))))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, Nil))), S(halve#1(length#1(Cons(z2, Nil)))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, Nil))), S(halve#1(length#1(Cons(z2, Nil))))), HALVE#1(S(length#1(Nil))), LENGTH#1(Cons(z2, Nil)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, Cons(z3, z4))))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Cons(z2, Cons(z3, z4)))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, Cons(z3, z4)))), S(halve#1(S(S(length#1(z4)))))))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, Cons(z3, z4)))), S(halve#1(length#1(Cons(z2, Cons(z3, z4))))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, Cons(z3, z4)))), S(halve#1(length#1(Cons(z2, Cons(z3, z4)))))), HALVE#1(S(length#1(Cons(z3, z4)))), LENGTH#1(Cons(z2, Cons(z3, z4))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, z3)))) -> c9(MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3)))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3))))), HALVE#1(S(length#1(z3))), LENGTH#1(Cons(z2, z3)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Nil))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(0)), Cons(z0, Cons(z1, Nil))), Cons(drop#2(S(halve#1(0)), Cons(z0, Cons(z1, Nil))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil)))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Nil))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Nil)), S(0)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil)))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> c9(CONST_F#2(Cons(z0, Cons(z1, z2)), Cons(dc#1(map, divisible, mergesort_zs_3, divide, const_f, take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2)))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(drop#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(halve#1(length#1(z2)), Cons(z1, z2)), Nil))), DIVIDE_YS#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2)))), HALVE#1(length#1(z2)), LENGTH#1(z2))
K tuples:none
Defined Rule Symbols:   leq#2_2, map#2_2, divide_ys#1_2, halve#1_1, length#1_1, take#2_2, drop#2_2, dc#1_6, const_f#2_2, merge#2_2, cond_merge_ys_zs_2_7

Defined Pair Symbols:   DROP#2_2, TAKE#2_2, HALVE#1_1, CONST_F#2_2, LEQ#2_2, LENGTH#1_1, MAP#2_2, MERGE#2_2, DIVIDE_YS#1_2, DC#1_6, COND_MERGE_YS_ZS_2_7

Compound Symbols:   c12_1, c15_1, c18_1, c19_1, c22_1, c24_1, c26_1, c27_1, c6_1, c6_2, c_1, c1_1, c9_5, c2_1, c3_1, c9_2, c9_3, c9_4


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

(147) CdtInstantiationProof (BOTH BOUNDS(ID, ID))
Use instantiation to replace CONST_F#2(z0, Cons(z1, Cons(z2, z3))) -> c19(MERGE#2(z1, z2)) by 
   CONST_F#2(Cons(x0, Cons(x1, x2)), Cons(z1, Cons(z2, z3))) -> c19(MERGE#2(z1, z2))
   CONST_F#2(Cons(x0, Cons(x1, Cons(x2, x3))), Cons(z1, Cons(z2, z3))) -> c19(MERGE#2(z1, z2))
   CONST_F#2(Cons(x0, Cons(x1, Nil)), Cons(z1, Cons(z2, z3))) -> c19(MERGE#2(z1, z2))
   CONST_F#2(Cons(x0, Cons(x1, Cons(x2, Nil))), Cons(z1, Cons(z2, z3))) -> c19(MERGE#2(z1, z2))
   CONST_F#2(Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4)))), Cons(z1, Cons(z2, z3))) -> c19(MERGE#2(z1, z2))

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

(148)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   leq#2(0, z0) -> True
   leq#2(S(z0), 0) -> False
   leq#2(S(z0), S(z1)) -> leq#2(z0, z1)
   map#2(dc(z0, z1, z2, z3, z4), Nil) -> Nil
   map#2(dc(z0, z1, z2, z3, z4), Cons(z5, z6)) -> Cons(dc#1(z0, z1, z2, z3, z4, z5), map#2(dc(z0, z1, z2, z3, z4), z6))
   divide_ys#1(z0, z1) -> Cons(take#2(z1, z0), Cons(drop#2(z1, z0), Nil))
   halve#1(0) -> 0
   halve#1(S(0)) -> S(0)
   halve#1(S(S(z0))) -> S(halve#1(z0))
   length#1(Nil) -> 0
   length#1(Cons(z0, z1)) -> S(length#1(z1))
   take#2(0, z0) -> Nil
   take#2(S(0), Nil) -> Cons(bot[0], Nil)
   take#2(S(z0), Cons(z1, z2)) -> Cons(z1, take#2(z0, z2))
   drop#2(0, z0) -> z0
   drop#2(S(0), Nil) -> bot[1]
   drop#2(S(z0), Cons(z1, z2)) -> drop#2(z0, z2)
   dc#1(map, divisible, mergesort_zs_3, divide, const_f, Nil) -> Nil
   dc#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Nil)) -> Cons(z0, Nil)
   dc#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> const_f#2(Cons(z0, Cons(z1, z2)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2))))))
   const_f#2(z0, Cons(z1, Cons(z2, z3))) -> merge#2(z1, z2)
   merge#2(Nil, z0) -> z0
   merge#2(Cons(z0, z1), Nil) -> Cons(z0, z1)
   merge#2(Cons(z0, z1), Cons(z2, z3)) -> cond_merge_ys_zs_2(leq#2(z0, z2), Cons(z0, z1), Cons(z2, z3), z0, z1, z2, z3)
   cond_merge_ys_zs_2(True, Cons(z0, z1), Cons(z2, z3), z4, z5, z6, z7) -> Cons(z4, merge#2(z5, Cons(z2, z3)))
   cond_merge_ys_zs_2(False, Cons(z0, z1), Cons(z2, z3), z4, z5, z6, z7) -> Cons(z6, merge#2(Cons(z0, z1), z7))
Tuples:
   DROP#2(S(z0), Cons(z1, z2)) -> c12(DROP#2(z0, z2))
   TAKE#2(S(z0), Cons(z1, z2)) -> c15(TAKE#2(z0, z2))
   HALVE#1(S(S(z0))) -> c18(HALVE#1(z0))
   LEQ#2(S(z0), S(z1)) -> c22(LEQ#2(z0, z1))
   LENGTH#1(Cons(z0, z1)) -> c24(LENGTH#1(z1))
   MAP#2(dc(z0, z1, z2, z3, z4), Cons(z5, z6)) -> c26(DC#1(z0, z1, z2, z3, z4, z5))
   MAP#2(dc(z0, z1, z2, z3, z4), Cons(z5, z6)) -> c27(MAP#2(dc(z0, z1, z2, z3, z4), z6))
   MERGE#2(Cons(0, x1), Cons(z0, x3)) -> c6(COND_MERGE_YS_ZS_2(True, Cons(0, x1), Cons(z0, x3), 0, x1, z0, x3))
   MERGE#2(Cons(S(z0), x1), Cons(0, x3)) -> c6(COND_MERGE_YS_ZS_2(False, Cons(S(z0), x1), Cons(0, x3), S(z0), x1, 0, x3))
   MERGE#2(Cons(S(0), x1), Cons(S(z0), x3)) -> c6(COND_MERGE_YS_ZS_2(True, Cons(S(0), x1), Cons(S(z0), x3), S(0), x1, S(z0), x3), LEQ#2(S(0), S(z0)))
   MERGE#2(Cons(S(S(z0)), x1), Cons(S(0), x3)) -> c6(COND_MERGE_YS_ZS_2(False, Cons(S(S(z0)), x1), Cons(S(0), x3), S(S(z0)), x1, S(0), x3), LEQ#2(S(S(z0)), S(0)))
   MERGE#2(Cons(S(S(z0)), x1), Cons(S(S(z1)), x3)) -> c6(COND_MERGE_YS_ZS_2(leq#2(z0, z1), Cons(S(S(z0)), x1), Cons(S(S(z1)), x3), S(S(z0)), x1, S(S(z1)), x3), LEQ#2(S(S(z0)), S(S(z1))))
   MERGE#2(Cons(S(x0), x1), Cons(S(x2), x3)) -> c6(LEQ#2(S(x0), S(x2)))
   DIVIDE_YS#1(Cons(x0, Cons(x1, x2)), S(y11)) -> c(TAKE#2(S(y11), Cons(x0, Cons(x1, x2))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, x3))), S(y11)) -> c(TAKE#2(S(y11), Cons(x0, Cons(x1, Cons(x2, x3)))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Nil)), S(y10)) -> c(TAKE#2(S(y10), Cons(x0, Cons(x1, Nil))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Nil))), S(y7)) -> c(TAKE#2(S(y7), Cons(x0, Cons(x1, Cons(x2, Nil)))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4)))), S(y8)) -> c(TAKE#2(S(y8), Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4))))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, x2)), S(y11)) -> c1(DROP#2(S(y11), Cons(x0, Cons(x1, x2))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, x3))), S(y11)) -> c1(DROP#2(S(y11), Cons(x0, Cons(x1, Cons(x2, x3)))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Nil)), S(y10)) -> c1(DROP#2(S(y10), Cons(x0, Cons(x1, Nil))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Nil))), S(y7)) -> c1(DROP#2(S(y7), Cons(x0, Cons(x1, Cons(x2, Nil)))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4)))), S(y8)) -> c1(DROP#2(S(y8), Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4))))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> c9(CONST_F#2(Cons(z0, Cons(z1, z2)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(halve#1(length#1(z2)), Cons(z1, z2)), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Nil))), DIVIDE_YS#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2)))), HALVE#1(length#1(z2)), LENGTH#1(z2))
   COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(z2, z3), z4, Cons(0, y0), z6, z7) -> c2(MERGE#2(Cons(0, y0), Cons(z2, z3)))
   COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(0, z3), z4, Cons(S(y0), y1), z6, z7) -> c2(MERGE#2(Cons(S(y0), y1), Cons(0, z3)))
   COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(S(y1), z3), z4, Cons(S(0), y0), z6, z7) -> c2(MERGE#2(Cons(S(0), y0), Cons(S(y1), z3)))
   COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(S(0), z3), z4, Cons(S(S(y0)), y1), z6, z7) -> c2(MERGE#2(Cons(S(S(y0)), y1), Cons(S(0), z3)))
   COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(S(S(y2)), z3), z4, Cons(S(S(y0)), y1), z6, z7) -> c2(MERGE#2(Cons(S(S(y0)), y1), Cons(S(S(y2)), z3)))
   COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(S(y2), z3), z4, Cons(S(y0), y1), z6, z7) -> c2(MERGE#2(Cons(S(y0), y1), Cons(S(y2), z3)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, z3)))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Cons(z2, z3))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(Cons(z2, z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Cons(drop#2(S(halve#1(S(length#1(z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3)))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3))))), HALVE#1(S(length#1(z3))), LENGTH#1(Cons(z2, z3)))
   COND_MERGE_YS_ZS_2(False, Cons(S(x0), x1), Cons(0, x2), S(x0), x1, 0, x2) -> c3(MERGE#2(Cons(S(x0), x1), x2))
   COND_MERGE_YS_ZS_2(False, Cons(S(S(x0)), x1), Cons(S(0), x2), S(S(x0)), x1, S(0), x2) -> c3(MERGE#2(Cons(S(S(x0)), x1), x2))
   COND_MERGE_YS_ZS_2(False, Cons(S(S(x0)), x1), Cons(S(S(x2)), x3), S(S(x0)), x1, S(S(x2)), x3) -> c3(MERGE#2(Cons(S(S(x0)), x1), x3))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> c9(CONST_F#2(Cons(z0, Cons(z1, z2)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(Cons(z0, take#2(halve#1(length#1(z2)), Cons(z1, z2))), Cons(drop#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Nil))), DIVIDE_YS#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2)))), HALVE#1(length#1(z2)), LENGTH#1(z2))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, z3)))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Cons(z2, z3))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(S(length#1(z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Cons(drop#2(S(halve#1(length#1(Cons(z2, z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3)))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3))))), HALVE#1(S(length#1(z3))), LENGTH#1(Cons(z2, z3)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> c9(MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Nil))), DIVIDE_YS#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2)))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Nil))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(Nil))), Cons(z0, Cons(z1, Nil))), Cons(drop#2(S(halve#1(0)), Cons(z0, Cons(z1, Nil))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil)))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Nil))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(0)), Cons(z0, Cons(z1, Nil))), Cons(drop#2(S(halve#1(length#1(Nil))), Cons(z0, Cons(z1, Nil))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil)))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, z3)))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Cons(z2, z3))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(S(length#1(z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Cons(drop#2(S(halve#1(S(length#1(z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3)))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3))))), HALVE#1(S(length#1(z3))), LENGTH#1(Cons(z2, z3)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, Nil)))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Cons(z2, Nil))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, Nil))), S(halve#1(S(0)))))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, Nil))), S(halve#1(length#1(Cons(z2, Nil)))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, Nil))), S(halve#1(length#1(Cons(z2, Nil))))), HALVE#1(S(length#1(Nil))), LENGTH#1(Cons(z2, Nil)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, Cons(z3, z4))))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Cons(z2, Cons(z3, z4)))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, Cons(z3, z4)))), S(halve#1(S(S(length#1(z4)))))))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, Cons(z3, z4)))), S(halve#1(length#1(Cons(z2, Cons(z3, z4))))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, Cons(z3, z4)))), S(halve#1(length#1(Cons(z2, Cons(z3, z4)))))), HALVE#1(S(length#1(Cons(z3, z4)))), LENGTH#1(Cons(z2, Cons(z3, z4))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, z3)))) -> c9(MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3)))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3))))), HALVE#1(S(length#1(z3))), LENGTH#1(Cons(z2, z3)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Nil))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(0)), Cons(z0, Cons(z1, Nil))), Cons(drop#2(S(halve#1(0)), Cons(z0, Cons(z1, Nil))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil)))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Nil))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Nil)), S(0)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil)))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> c9(CONST_F#2(Cons(z0, Cons(z1, z2)), Cons(dc#1(map, divisible, mergesort_zs_3, divide, const_f, take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2)))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(drop#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(halve#1(length#1(z2)), Cons(z1, z2)), Nil))), DIVIDE_YS#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2)))), HALVE#1(length#1(z2)), LENGTH#1(z2))
   CONST_F#2(Cons(x0, Cons(x1, x2)), Cons(z1, Cons(z2, z3))) -> c19(MERGE#2(z1, z2))
   CONST_F#2(Cons(x0, Cons(x1, Cons(x2, x3))), Cons(z1, Cons(z2, z3))) -> c19(MERGE#2(z1, z2))
   CONST_F#2(Cons(x0, Cons(x1, Nil)), Cons(z1, Cons(z2, z3))) -> c19(MERGE#2(z1, z2))
   CONST_F#2(Cons(x0, Cons(x1, Cons(x2, Nil))), Cons(z1, Cons(z2, z3))) -> c19(MERGE#2(z1, z2))
   CONST_F#2(Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4)))), Cons(z1, Cons(z2, z3))) -> c19(MERGE#2(z1, z2))
S tuples:
   DROP#2(S(z0), Cons(z1, z2)) -> c12(DROP#2(z0, z2))
   TAKE#2(S(z0), Cons(z1, z2)) -> c15(TAKE#2(z0, z2))
   HALVE#1(S(S(z0))) -> c18(HALVE#1(z0))
   LEQ#2(S(z0), S(z1)) -> c22(LEQ#2(z0, z1))
   LENGTH#1(Cons(z0, z1)) -> c24(LENGTH#1(z1))
   MAP#2(dc(z0, z1, z2, z3, z4), Cons(z5, z6)) -> c26(DC#1(z0, z1, z2, z3, z4, z5))
   MAP#2(dc(z0, z1, z2, z3, z4), Cons(z5, z6)) -> c27(MAP#2(dc(z0, z1, z2, z3, z4), z6))
   MERGE#2(Cons(0, x1), Cons(z0, x3)) -> c6(COND_MERGE_YS_ZS_2(True, Cons(0, x1), Cons(z0, x3), 0, x1, z0, x3))
   MERGE#2(Cons(S(z0), x1), Cons(0, x3)) -> c6(COND_MERGE_YS_ZS_2(False, Cons(S(z0), x1), Cons(0, x3), S(z0), x1, 0, x3))
   MERGE#2(Cons(S(0), x1), Cons(S(z0), x3)) -> c6(COND_MERGE_YS_ZS_2(True, Cons(S(0), x1), Cons(S(z0), x3), S(0), x1, S(z0), x3), LEQ#2(S(0), S(z0)))
   MERGE#2(Cons(S(S(z0)), x1), Cons(S(0), x3)) -> c6(COND_MERGE_YS_ZS_2(False, Cons(S(S(z0)), x1), Cons(S(0), x3), S(S(z0)), x1, S(0), x3), LEQ#2(S(S(z0)), S(0)))
   MERGE#2(Cons(S(S(z0)), x1), Cons(S(S(z1)), x3)) -> c6(COND_MERGE_YS_ZS_2(leq#2(z0, z1), Cons(S(S(z0)), x1), Cons(S(S(z1)), x3), S(S(z0)), x1, S(S(z1)), x3), LEQ#2(S(S(z0)), S(S(z1))))
   MERGE#2(Cons(S(x0), x1), Cons(S(x2), x3)) -> c6(LEQ#2(S(x0), S(x2)))
   DIVIDE_YS#1(Cons(x0, Cons(x1, x2)), S(y11)) -> c(TAKE#2(S(y11), Cons(x0, Cons(x1, x2))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, x3))), S(y11)) -> c(TAKE#2(S(y11), Cons(x0, Cons(x1, Cons(x2, x3)))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Nil)), S(y10)) -> c(TAKE#2(S(y10), Cons(x0, Cons(x1, Nil))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Nil))), S(y7)) -> c(TAKE#2(S(y7), Cons(x0, Cons(x1, Cons(x2, Nil)))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4)))), S(y8)) -> c(TAKE#2(S(y8), Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4))))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, x2)), S(y11)) -> c1(DROP#2(S(y11), Cons(x0, Cons(x1, x2))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, x3))), S(y11)) -> c1(DROP#2(S(y11), Cons(x0, Cons(x1, Cons(x2, x3)))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Nil)), S(y10)) -> c1(DROP#2(S(y10), Cons(x0, Cons(x1, Nil))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Nil))), S(y7)) -> c1(DROP#2(S(y7), Cons(x0, Cons(x1, Cons(x2, Nil)))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4)))), S(y8)) -> c1(DROP#2(S(y8), Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4))))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> c9(CONST_F#2(Cons(z0, Cons(z1, z2)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(halve#1(length#1(z2)), Cons(z1, z2)), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Nil))), DIVIDE_YS#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2)))), HALVE#1(length#1(z2)), LENGTH#1(z2))
   COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(z2, z3), z4, Cons(0, y0), z6, z7) -> c2(MERGE#2(Cons(0, y0), Cons(z2, z3)))
   COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(0, z3), z4, Cons(S(y0), y1), z6, z7) -> c2(MERGE#2(Cons(S(y0), y1), Cons(0, z3)))
   COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(S(y1), z3), z4, Cons(S(0), y0), z6, z7) -> c2(MERGE#2(Cons(S(0), y0), Cons(S(y1), z3)))
   COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(S(0), z3), z4, Cons(S(S(y0)), y1), z6, z7) -> c2(MERGE#2(Cons(S(S(y0)), y1), Cons(S(0), z3)))
   COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(S(S(y2)), z3), z4, Cons(S(S(y0)), y1), z6, z7) -> c2(MERGE#2(Cons(S(S(y0)), y1), Cons(S(S(y2)), z3)))
   COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(S(y2), z3), z4, Cons(S(y0), y1), z6, z7) -> c2(MERGE#2(Cons(S(y0), y1), Cons(S(y2), z3)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, z3)))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Cons(z2, z3))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(Cons(z2, z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Cons(drop#2(S(halve#1(S(length#1(z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3)))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3))))), HALVE#1(S(length#1(z3))), LENGTH#1(Cons(z2, z3)))
   COND_MERGE_YS_ZS_2(False, Cons(S(x0), x1), Cons(0, x2), S(x0), x1, 0, x2) -> c3(MERGE#2(Cons(S(x0), x1), x2))
   COND_MERGE_YS_ZS_2(False, Cons(S(S(x0)), x1), Cons(S(0), x2), S(S(x0)), x1, S(0), x2) -> c3(MERGE#2(Cons(S(S(x0)), x1), x2))
   COND_MERGE_YS_ZS_2(False, Cons(S(S(x0)), x1), Cons(S(S(x2)), x3), S(S(x0)), x1, S(S(x2)), x3) -> c3(MERGE#2(Cons(S(S(x0)), x1), x3))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> c9(CONST_F#2(Cons(z0, Cons(z1, z2)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(Cons(z0, take#2(halve#1(length#1(z2)), Cons(z1, z2))), Cons(drop#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Nil))), DIVIDE_YS#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2)))), HALVE#1(length#1(z2)), LENGTH#1(z2))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, z3)))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Cons(z2, z3))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(S(length#1(z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Cons(drop#2(S(halve#1(length#1(Cons(z2, z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3)))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3))))), HALVE#1(S(length#1(z3))), LENGTH#1(Cons(z2, z3)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> c9(MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Nil))), DIVIDE_YS#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2)))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Nil))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(Nil))), Cons(z0, Cons(z1, Nil))), Cons(drop#2(S(halve#1(0)), Cons(z0, Cons(z1, Nil))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil)))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Nil))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(0)), Cons(z0, Cons(z1, Nil))), Cons(drop#2(S(halve#1(length#1(Nil))), Cons(z0, Cons(z1, Nil))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil)))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, z3)))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Cons(z2, z3))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(S(length#1(z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Cons(drop#2(S(halve#1(S(length#1(z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3)))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3))))), HALVE#1(S(length#1(z3))), LENGTH#1(Cons(z2, z3)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, Nil)))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Cons(z2, Nil))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, Nil))), S(halve#1(S(0)))))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, Nil))), S(halve#1(length#1(Cons(z2, Nil)))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, Nil))), S(halve#1(length#1(Cons(z2, Nil))))), HALVE#1(S(length#1(Nil))), LENGTH#1(Cons(z2, Nil)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, Cons(z3, z4))))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Cons(z2, Cons(z3, z4)))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, Cons(z3, z4)))), S(halve#1(S(S(length#1(z4)))))))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, Cons(z3, z4)))), S(halve#1(length#1(Cons(z2, Cons(z3, z4))))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, Cons(z3, z4)))), S(halve#1(length#1(Cons(z2, Cons(z3, z4)))))), HALVE#1(S(length#1(Cons(z3, z4)))), LENGTH#1(Cons(z2, Cons(z3, z4))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, z3)))) -> c9(MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3)))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3))))), HALVE#1(S(length#1(z3))), LENGTH#1(Cons(z2, z3)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Nil))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(0)), Cons(z0, Cons(z1, Nil))), Cons(drop#2(S(halve#1(0)), Cons(z0, Cons(z1, Nil))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil)))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Nil))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Nil)), S(0)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil)))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> c9(CONST_F#2(Cons(z0, Cons(z1, z2)), Cons(dc#1(map, divisible, mergesort_zs_3, divide, const_f, take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2)))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(drop#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(halve#1(length#1(z2)), Cons(z1, z2)), Nil))), DIVIDE_YS#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2)))), HALVE#1(length#1(z2)), LENGTH#1(z2))
   CONST_F#2(Cons(x0, Cons(x1, x2)), Cons(z1, Cons(z2, z3))) -> c19(MERGE#2(z1, z2))
   CONST_F#2(Cons(x0, Cons(x1, Cons(x2, x3))), Cons(z1, Cons(z2, z3))) -> c19(MERGE#2(z1, z2))
   CONST_F#2(Cons(x0, Cons(x1, Nil)), Cons(z1, Cons(z2, z3))) -> c19(MERGE#2(z1, z2))
   CONST_F#2(Cons(x0, Cons(x1, Cons(x2, Nil))), Cons(z1, Cons(z2, z3))) -> c19(MERGE#2(z1, z2))
   CONST_F#2(Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4)))), Cons(z1, Cons(z2, z3))) -> c19(MERGE#2(z1, z2))
K tuples:none
Defined Rule Symbols:   leq#2_2, map#2_2, divide_ys#1_2, halve#1_1, length#1_1, take#2_2, drop#2_2, dc#1_6, const_f#2_2, merge#2_2, cond_merge_ys_zs_2_7

Defined Pair Symbols:   DROP#2_2, TAKE#2_2, HALVE#1_1, LEQ#2_2, LENGTH#1_1, MAP#2_2, MERGE#2_2, DIVIDE_YS#1_2, DC#1_6, COND_MERGE_YS_ZS_2_7, CONST_F#2_2

Compound Symbols:   c12_1, c15_1, c18_1, c22_1, c24_1, c26_1, c27_1, c6_1, c6_2, c_1, c1_1, c9_5, c2_1, c3_1, c9_2, c9_3, c9_4, c19_1


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(149) CdtRewritingProof (BOTH BOUNDS(ID, ID))
Used rewriting to replace DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> c9(CONST_F#2(Cons(z0, Cons(z1, z2)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(halve#1(length#1(z2)), Cons(z1, z2)), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Nil))), DIVIDE_YS#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2)))), HALVE#1(length#1(z2)), LENGTH#1(z2)) by DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> c9(CONST_F#2(Cons(z0, Cons(z1, z2)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(halve#1(length#1(z2)), Cons(z1, z2)), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(halve#1(length#1(z2)), Cons(z1, z2)), Nil))), DIVIDE_YS#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2)))), HALVE#1(length#1(z2)), LENGTH#1(z2))
----------------------------------------

(150)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   leq#2(0, z0) -> True
   leq#2(S(z0), 0) -> False
   leq#2(S(z0), S(z1)) -> leq#2(z0, z1)
   map#2(dc(z0, z1, z2, z3, z4), Nil) -> Nil
   map#2(dc(z0, z1, z2, z3, z4), Cons(z5, z6)) -> Cons(dc#1(z0, z1, z2, z3, z4, z5), map#2(dc(z0, z1, z2, z3, z4), z6))
   divide_ys#1(z0, z1) -> Cons(take#2(z1, z0), Cons(drop#2(z1, z0), Nil))
   halve#1(0) -> 0
   halve#1(S(0)) -> S(0)
   halve#1(S(S(z0))) -> S(halve#1(z0))
   length#1(Nil) -> 0
   length#1(Cons(z0, z1)) -> S(length#1(z1))
   take#2(0, z0) -> Nil
   take#2(S(0), Nil) -> Cons(bot[0], Nil)
   take#2(S(z0), Cons(z1, z2)) -> Cons(z1, take#2(z0, z2))
   drop#2(0, z0) -> z0
   drop#2(S(0), Nil) -> bot[1]
   drop#2(S(z0), Cons(z1, z2)) -> drop#2(z0, z2)
   dc#1(map, divisible, mergesort_zs_3, divide, const_f, Nil) -> Nil
   dc#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Nil)) -> Cons(z0, Nil)
   dc#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> const_f#2(Cons(z0, Cons(z1, z2)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2))))))
   const_f#2(z0, Cons(z1, Cons(z2, z3))) -> merge#2(z1, z2)
   merge#2(Nil, z0) -> z0
   merge#2(Cons(z0, z1), Nil) -> Cons(z0, z1)
   merge#2(Cons(z0, z1), Cons(z2, z3)) -> cond_merge_ys_zs_2(leq#2(z0, z2), Cons(z0, z1), Cons(z2, z3), z0, z1, z2, z3)
   cond_merge_ys_zs_2(True, Cons(z0, z1), Cons(z2, z3), z4, z5, z6, z7) -> Cons(z4, merge#2(z5, Cons(z2, z3)))
   cond_merge_ys_zs_2(False, Cons(z0, z1), Cons(z2, z3), z4, z5, z6, z7) -> Cons(z6, merge#2(Cons(z0, z1), z7))
Tuples:
   DROP#2(S(z0), Cons(z1, z2)) -> c12(DROP#2(z0, z2))
   TAKE#2(S(z0), Cons(z1, z2)) -> c15(TAKE#2(z0, z2))
   HALVE#1(S(S(z0))) -> c18(HALVE#1(z0))
   LEQ#2(S(z0), S(z1)) -> c22(LEQ#2(z0, z1))
   LENGTH#1(Cons(z0, z1)) -> c24(LENGTH#1(z1))
   MAP#2(dc(z0, z1, z2, z3, z4), Cons(z5, z6)) -> c26(DC#1(z0, z1, z2, z3, z4, z5))
   MAP#2(dc(z0, z1, z2, z3, z4), Cons(z5, z6)) -> c27(MAP#2(dc(z0, z1, z2, z3, z4), z6))
   MERGE#2(Cons(0, x1), Cons(z0, x3)) -> c6(COND_MERGE_YS_ZS_2(True, Cons(0, x1), Cons(z0, x3), 0, x1, z0, x3))
   MERGE#2(Cons(S(z0), x1), Cons(0, x3)) -> c6(COND_MERGE_YS_ZS_2(False, Cons(S(z0), x1), Cons(0, x3), S(z0), x1, 0, x3))
   MERGE#2(Cons(S(0), x1), Cons(S(z0), x3)) -> c6(COND_MERGE_YS_ZS_2(True, Cons(S(0), x1), Cons(S(z0), x3), S(0), x1, S(z0), x3), LEQ#2(S(0), S(z0)))
   MERGE#2(Cons(S(S(z0)), x1), Cons(S(0), x3)) -> c6(COND_MERGE_YS_ZS_2(False, Cons(S(S(z0)), x1), Cons(S(0), x3), S(S(z0)), x1, S(0), x3), LEQ#2(S(S(z0)), S(0)))
   MERGE#2(Cons(S(S(z0)), x1), Cons(S(S(z1)), x3)) -> c6(COND_MERGE_YS_ZS_2(leq#2(z0, z1), Cons(S(S(z0)), x1), Cons(S(S(z1)), x3), S(S(z0)), x1, S(S(z1)), x3), LEQ#2(S(S(z0)), S(S(z1))))
   MERGE#2(Cons(S(x0), x1), Cons(S(x2), x3)) -> c6(LEQ#2(S(x0), S(x2)))
   DIVIDE_YS#1(Cons(x0, Cons(x1, x2)), S(y11)) -> c(TAKE#2(S(y11), Cons(x0, Cons(x1, x2))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, x3))), S(y11)) -> c(TAKE#2(S(y11), Cons(x0, Cons(x1, Cons(x2, x3)))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Nil)), S(y10)) -> c(TAKE#2(S(y10), Cons(x0, Cons(x1, Nil))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Nil))), S(y7)) -> c(TAKE#2(S(y7), Cons(x0, Cons(x1, Cons(x2, Nil)))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4)))), S(y8)) -> c(TAKE#2(S(y8), Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4))))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, x2)), S(y11)) -> c1(DROP#2(S(y11), Cons(x0, Cons(x1, x2))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, x3))), S(y11)) -> c1(DROP#2(S(y11), Cons(x0, Cons(x1, Cons(x2, x3)))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Nil)), S(y10)) -> c1(DROP#2(S(y10), Cons(x0, Cons(x1, Nil))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Nil))), S(y7)) -> c1(DROP#2(S(y7), Cons(x0, Cons(x1, Cons(x2, Nil)))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4)))), S(y8)) -> c1(DROP#2(S(y8), Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4))))))
   COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(z2, z3), z4, Cons(0, y0), z6, z7) -> c2(MERGE#2(Cons(0, y0), Cons(z2, z3)))
   COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(0, z3), z4, Cons(S(y0), y1), z6, z7) -> c2(MERGE#2(Cons(S(y0), y1), Cons(0, z3)))
   COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(S(y1), z3), z4, Cons(S(0), y0), z6, z7) -> c2(MERGE#2(Cons(S(0), y0), Cons(S(y1), z3)))
   COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(S(0), z3), z4, Cons(S(S(y0)), y1), z6, z7) -> c2(MERGE#2(Cons(S(S(y0)), y1), Cons(S(0), z3)))
   COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(S(S(y2)), z3), z4, Cons(S(S(y0)), y1), z6, z7) -> c2(MERGE#2(Cons(S(S(y0)), y1), Cons(S(S(y2)), z3)))
   COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(S(y2), z3), z4, Cons(S(y0), y1), z6, z7) -> c2(MERGE#2(Cons(S(y0), y1), Cons(S(y2), z3)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, z3)))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Cons(z2, z3))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(Cons(z2, z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Cons(drop#2(S(halve#1(S(length#1(z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3)))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3))))), HALVE#1(S(length#1(z3))), LENGTH#1(Cons(z2, z3)))
   COND_MERGE_YS_ZS_2(False, Cons(S(x0), x1), Cons(0, x2), S(x0), x1, 0, x2) -> c3(MERGE#2(Cons(S(x0), x1), x2))
   COND_MERGE_YS_ZS_2(False, Cons(S(S(x0)), x1), Cons(S(0), x2), S(S(x0)), x1, S(0), x2) -> c3(MERGE#2(Cons(S(S(x0)), x1), x2))
   COND_MERGE_YS_ZS_2(False, Cons(S(S(x0)), x1), Cons(S(S(x2)), x3), S(S(x0)), x1, S(S(x2)), x3) -> c3(MERGE#2(Cons(S(S(x0)), x1), x3))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> c9(CONST_F#2(Cons(z0, Cons(z1, z2)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(Cons(z0, take#2(halve#1(length#1(z2)), Cons(z1, z2))), Cons(drop#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Nil))), DIVIDE_YS#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2)))), HALVE#1(length#1(z2)), LENGTH#1(z2))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, z3)))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Cons(z2, z3))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(S(length#1(z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Cons(drop#2(S(halve#1(length#1(Cons(z2, z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3)))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3))))), HALVE#1(S(length#1(z3))), LENGTH#1(Cons(z2, z3)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> c9(MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Nil))), DIVIDE_YS#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2)))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Nil))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(Nil))), Cons(z0, Cons(z1, Nil))), Cons(drop#2(S(halve#1(0)), Cons(z0, Cons(z1, Nil))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil)))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Nil))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(0)), Cons(z0, Cons(z1, Nil))), Cons(drop#2(S(halve#1(length#1(Nil))), Cons(z0, Cons(z1, Nil))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil)))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, z3)))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Cons(z2, z3))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(S(length#1(z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Cons(drop#2(S(halve#1(S(length#1(z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3)))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3))))), HALVE#1(S(length#1(z3))), LENGTH#1(Cons(z2, z3)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, Nil)))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Cons(z2, Nil))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, Nil))), S(halve#1(S(0)))))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, Nil))), S(halve#1(length#1(Cons(z2, Nil)))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, Nil))), S(halve#1(length#1(Cons(z2, Nil))))), HALVE#1(S(length#1(Nil))), LENGTH#1(Cons(z2, Nil)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, Cons(z3, z4))))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Cons(z2, Cons(z3, z4)))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, Cons(z3, z4)))), S(halve#1(S(S(length#1(z4)))))))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, Cons(z3, z4)))), S(halve#1(length#1(Cons(z2, Cons(z3, z4))))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, Cons(z3, z4)))), S(halve#1(length#1(Cons(z2, Cons(z3, z4)))))), HALVE#1(S(length#1(Cons(z3, z4)))), LENGTH#1(Cons(z2, Cons(z3, z4))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, z3)))) -> c9(MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3)))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3))))), HALVE#1(S(length#1(z3))), LENGTH#1(Cons(z2, z3)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Nil))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(0)), Cons(z0, Cons(z1, Nil))), Cons(drop#2(S(halve#1(0)), Cons(z0, Cons(z1, Nil))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil)))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Nil))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Nil)), S(0)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil)))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> c9(CONST_F#2(Cons(z0, Cons(z1, z2)), Cons(dc#1(map, divisible, mergesort_zs_3, divide, const_f, take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2)))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(drop#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(halve#1(length#1(z2)), Cons(z1, z2)), Nil))), DIVIDE_YS#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2)))), HALVE#1(length#1(z2)), LENGTH#1(z2))
   CONST_F#2(Cons(x0, Cons(x1, x2)), Cons(z1, Cons(z2, z3))) -> c19(MERGE#2(z1, z2))
   CONST_F#2(Cons(x0, Cons(x1, Cons(x2, x3))), Cons(z1, Cons(z2, z3))) -> c19(MERGE#2(z1, z2))
   CONST_F#2(Cons(x0, Cons(x1, Nil)), Cons(z1, Cons(z2, z3))) -> c19(MERGE#2(z1, z2))
   CONST_F#2(Cons(x0, Cons(x1, Cons(x2, Nil))), Cons(z1, Cons(z2, z3))) -> c19(MERGE#2(z1, z2))
   CONST_F#2(Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4)))), Cons(z1, Cons(z2, z3))) -> c19(MERGE#2(z1, z2))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> c9(CONST_F#2(Cons(z0, Cons(z1, z2)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(halve#1(length#1(z2)), Cons(z1, z2)), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(halve#1(length#1(z2)), Cons(z1, z2)), Nil))), DIVIDE_YS#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2)))), HALVE#1(length#1(z2)), LENGTH#1(z2))
S tuples:
   DROP#2(S(z0), Cons(z1, z2)) -> c12(DROP#2(z0, z2))
   TAKE#2(S(z0), Cons(z1, z2)) -> c15(TAKE#2(z0, z2))
   HALVE#1(S(S(z0))) -> c18(HALVE#1(z0))
   LEQ#2(S(z0), S(z1)) -> c22(LEQ#2(z0, z1))
   LENGTH#1(Cons(z0, z1)) -> c24(LENGTH#1(z1))
   MAP#2(dc(z0, z1, z2, z3, z4), Cons(z5, z6)) -> c26(DC#1(z0, z1, z2, z3, z4, z5))
   MAP#2(dc(z0, z1, z2, z3, z4), Cons(z5, z6)) -> c27(MAP#2(dc(z0, z1, z2, z3, z4), z6))
   MERGE#2(Cons(0, x1), Cons(z0, x3)) -> c6(COND_MERGE_YS_ZS_2(True, Cons(0, x1), Cons(z0, x3), 0, x1, z0, x3))
   MERGE#2(Cons(S(z0), x1), Cons(0, x3)) -> c6(COND_MERGE_YS_ZS_2(False, Cons(S(z0), x1), Cons(0, x3), S(z0), x1, 0, x3))
   MERGE#2(Cons(S(0), x1), Cons(S(z0), x3)) -> c6(COND_MERGE_YS_ZS_2(True, Cons(S(0), x1), Cons(S(z0), x3), S(0), x1, S(z0), x3), LEQ#2(S(0), S(z0)))
   MERGE#2(Cons(S(S(z0)), x1), Cons(S(0), x3)) -> c6(COND_MERGE_YS_ZS_2(False, Cons(S(S(z0)), x1), Cons(S(0), x3), S(S(z0)), x1, S(0), x3), LEQ#2(S(S(z0)), S(0)))
   MERGE#2(Cons(S(S(z0)), x1), Cons(S(S(z1)), x3)) -> c6(COND_MERGE_YS_ZS_2(leq#2(z0, z1), Cons(S(S(z0)), x1), Cons(S(S(z1)), x3), S(S(z0)), x1, S(S(z1)), x3), LEQ#2(S(S(z0)), S(S(z1))))
   MERGE#2(Cons(S(x0), x1), Cons(S(x2), x3)) -> c6(LEQ#2(S(x0), S(x2)))
   DIVIDE_YS#1(Cons(x0, Cons(x1, x2)), S(y11)) -> c(TAKE#2(S(y11), Cons(x0, Cons(x1, x2))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, x3))), S(y11)) -> c(TAKE#2(S(y11), Cons(x0, Cons(x1, Cons(x2, x3)))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Nil)), S(y10)) -> c(TAKE#2(S(y10), Cons(x0, Cons(x1, Nil))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Nil))), S(y7)) -> c(TAKE#2(S(y7), Cons(x0, Cons(x1, Cons(x2, Nil)))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4)))), S(y8)) -> c(TAKE#2(S(y8), Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4))))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, x2)), S(y11)) -> c1(DROP#2(S(y11), Cons(x0, Cons(x1, x2))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, x3))), S(y11)) -> c1(DROP#2(S(y11), Cons(x0, Cons(x1, Cons(x2, x3)))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Nil)), S(y10)) -> c1(DROP#2(S(y10), Cons(x0, Cons(x1, Nil))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Nil))), S(y7)) -> c1(DROP#2(S(y7), Cons(x0, Cons(x1, Cons(x2, Nil)))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4)))), S(y8)) -> c1(DROP#2(S(y8), Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4))))))
   COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(z2, z3), z4, Cons(0, y0), z6, z7) -> c2(MERGE#2(Cons(0, y0), Cons(z2, z3)))
   COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(0, z3), z4, Cons(S(y0), y1), z6, z7) -> c2(MERGE#2(Cons(S(y0), y1), Cons(0, z3)))
   COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(S(y1), z3), z4, Cons(S(0), y0), z6, z7) -> c2(MERGE#2(Cons(S(0), y0), Cons(S(y1), z3)))
   COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(S(0), z3), z4, Cons(S(S(y0)), y1), z6, z7) -> c2(MERGE#2(Cons(S(S(y0)), y1), Cons(S(0), z3)))
   COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(S(S(y2)), z3), z4, Cons(S(S(y0)), y1), z6, z7) -> c2(MERGE#2(Cons(S(S(y0)), y1), Cons(S(S(y2)), z3)))
   COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(S(y2), z3), z4, Cons(S(y0), y1), z6, z7) -> c2(MERGE#2(Cons(S(y0), y1), Cons(S(y2), z3)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, z3)))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Cons(z2, z3))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(Cons(z2, z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Cons(drop#2(S(halve#1(S(length#1(z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3)))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3))))), HALVE#1(S(length#1(z3))), LENGTH#1(Cons(z2, z3)))
   COND_MERGE_YS_ZS_2(False, Cons(S(x0), x1), Cons(0, x2), S(x0), x1, 0, x2) -> c3(MERGE#2(Cons(S(x0), x1), x2))
   COND_MERGE_YS_ZS_2(False, Cons(S(S(x0)), x1), Cons(S(0), x2), S(S(x0)), x1, S(0), x2) -> c3(MERGE#2(Cons(S(S(x0)), x1), x2))
   COND_MERGE_YS_ZS_2(False, Cons(S(S(x0)), x1), Cons(S(S(x2)), x3), S(S(x0)), x1, S(S(x2)), x3) -> c3(MERGE#2(Cons(S(S(x0)), x1), x3))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> c9(CONST_F#2(Cons(z0, Cons(z1, z2)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(Cons(z0, take#2(halve#1(length#1(z2)), Cons(z1, z2))), Cons(drop#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Nil))), DIVIDE_YS#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2)))), HALVE#1(length#1(z2)), LENGTH#1(z2))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, z3)))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Cons(z2, z3))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(S(length#1(z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Cons(drop#2(S(halve#1(length#1(Cons(z2, z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3)))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3))))), HALVE#1(S(length#1(z3))), LENGTH#1(Cons(z2, z3)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> c9(MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Nil))), DIVIDE_YS#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2)))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Nil))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(Nil))), Cons(z0, Cons(z1, Nil))), Cons(drop#2(S(halve#1(0)), Cons(z0, Cons(z1, Nil))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil)))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Nil))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(0)), Cons(z0, Cons(z1, Nil))), Cons(drop#2(S(halve#1(length#1(Nil))), Cons(z0, Cons(z1, Nil))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil)))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, z3)))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Cons(z2, z3))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(S(length#1(z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Cons(drop#2(S(halve#1(S(length#1(z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3)))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3))))), HALVE#1(S(length#1(z3))), LENGTH#1(Cons(z2, z3)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, Nil)))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Cons(z2, Nil))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, Nil))), S(halve#1(S(0)))))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, Nil))), S(halve#1(length#1(Cons(z2, Nil)))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, Nil))), S(halve#1(length#1(Cons(z2, Nil))))), HALVE#1(S(length#1(Nil))), LENGTH#1(Cons(z2, Nil)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, Cons(z3, z4))))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Cons(z2, Cons(z3, z4)))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, Cons(z3, z4)))), S(halve#1(S(S(length#1(z4)))))))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, Cons(z3, z4)))), S(halve#1(length#1(Cons(z2, Cons(z3, z4))))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, Cons(z3, z4)))), S(halve#1(length#1(Cons(z2, Cons(z3, z4)))))), HALVE#1(S(length#1(Cons(z3, z4)))), LENGTH#1(Cons(z2, Cons(z3, z4))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, z3)))) -> c9(MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3)))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3))))), HALVE#1(S(length#1(z3))), LENGTH#1(Cons(z2, z3)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Nil))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(0)), Cons(z0, Cons(z1, Nil))), Cons(drop#2(S(halve#1(0)), Cons(z0, Cons(z1, Nil))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil)))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Nil))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Nil)), S(0)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil)))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> c9(CONST_F#2(Cons(z0, Cons(z1, z2)), Cons(dc#1(map, divisible, mergesort_zs_3, divide, const_f, take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2)))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(drop#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(halve#1(length#1(z2)), Cons(z1, z2)), Nil))), DIVIDE_YS#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2)))), HALVE#1(length#1(z2)), LENGTH#1(z2))
   CONST_F#2(Cons(x0, Cons(x1, x2)), Cons(z1, Cons(z2, z3))) -> c19(MERGE#2(z1, z2))
   CONST_F#2(Cons(x0, Cons(x1, Cons(x2, x3))), Cons(z1, Cons(z2, z3))) -> c19(MERGE#2(z1, z2))
   CONST_F#2(Cons(x0, Cons(x1, Nil)), Cons(z1, Cons(z2, z3))) -> c19(MERGE#2(z1, z2))
   CONST_F#2(Cons(x0, Cons(x1, Cons(x2, Nil))), Cons(z1, Cons(z2, z3))) -> c19(MERGE#2(z1, z2))
   CONST_F#2(Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4)))), Cons(z1, Cons(z2, z3))) -> c19(MERGE#2(z1, z2))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> c9(CONST_F#2(Cons(z0, Cons(z1, z2)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(halve#1(length#1(z2)), Cons(z1, z2)), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(halve#1(length#1(z2)), Cons(z1, z2)), Nil))), DIVIDE_YS#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2)))), HALVE#1(length#1(z2)), LENGTH#1(z2))
K tuples:none
Defined Rule Symbols:   leq#2_2, map#2_2, divide_ys#1_2, halve#1_1, length#1_1, take#2_2, drop#2_2, dc#1_6, const_f#2_2, merge#2_2, cond_merge_ys_zs_2_7

Defined Pair Symbols:   DROP#2_2, TAKE#2_2, HALVE#1_1, LEQ#2_2, LENGTH#1_1, MAP#2_2, MERGE#2_2, DIVIDE_YS#1_2, COND_MERGE_YS_ZS_2_7, DC#1_6, CONST_F#2_2

Compound Symbols:   c12_1, c15_1, c18_1, c22_1, c24_1, c26_1, c27_1, c6_1, c6_2, c_1, c1_1, c2_1, c9_5, c3_1, c9_2, c9_3, c9_4, c19_1


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

(151) CdtInstantiationProof (BOTH BOUNDS(ID, ID))
Use instantiation to replace COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(z2, z3), z4, Cons(0, y0), z6, z7) -> c2(MERGE#2(Cons(0, y0), Cons(z2, z3))) by 
   COND_MERGE_YS_ZS_2(True, Cons(0, Cons(0, z5)), Cons(x1, x2), 0, Cons(0, z5), x1, x2) -> c2(MERGE#2(Cons(0, z5), Cons(x1, x2)))
   COND_MERGE_YS_ZS_2(True, Cons(S(0), Cons(0, z5)), Cons(S(x1), x2), S(0), Cons(0, z5), S(x1), x2) -> c2(MERGE#2(Cons(0, z5), Cons(S(x1), x2)))
   COND_MERGE_YS_ZS_2(True, Cons(S(S(x0)), Cons(0, z5)), Cons(S(S(x2)), x3), S(S(x0)), Cons(0, z5), S(S(x2)), x3) -> c2(MERGE#2(Cons(0, z5), Cons(S(S(x2)), x3)))

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

(152)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   leq#2(0, z0) -> True
   leq#2(S(z0), 0) -> False
   leq#2(S(z0), S(z1)) -> leq#2(z0, z1)
   map#2(dc(z0, z1, z2, z3, z4), Nil) -> Nil
   map#2(dc(z0, z1, z2, z3, z4), Cons(z5, z6)) -> Cons(dc#1(z0, z1, z2, z3, z4, z5), map#2(dc(z0, z1, z2, z3, z4), z6))
   divide_ys#1(z0, z1) -> Cons(take#2(z1, z0), Cons(drop#2(z1, z0), Nil))
   halve#1(0) -> 0
   halve#1(S(0)) -> S(0)
   halve#1(S(S(z0))) -> S(halve#1(z0))
   length#1(Nil) -> 0
   length#1(Cons(z0, z1)) -> S(length#1(z1))
   take#2(0, z0) -> Nil
   take#2(S(0), Nil) -> Cons(bot[0], Nil)
   take#2(S(z0), Cons(z1, z2)) -> Cons(z1, take#2(z0, z2))
   drop#2(0, z0) -> z0
   drop#2(S(0), Nil) -> bot[1]
   drop#2(S(z0), Cons(z1, z2)) -> drop#2(z0, z2)
   dc#1(map, divisible, mergesort_zs_3, divide, const_f, Nil) -> Nil
   dc#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Nil)) -> Cons(z0, Nil)
   dc#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> const_f#2(Cons(z0, Cons(z1, z2)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2))))))
   const_f#2(z0, Cons(z1, Cons(z2, z3))) -> merge#2(z1, z2)
   merge#2(Nil, z0) -> z0
   merge#2(Cons(z0, z1), Nil) -> Cons(z0, z1)
   merge#2(Cons(z0, z1), Cons(z2, z3)) -> cond_merge_ys_zs_2(leq#2(z0, z2), Cons(z0, z1), Cons(z2, z3), z0, z1, z2, z3)
   cond_merge_ys_zs_2(True, Cons(z0, z1), Cons(z2, z3), z4, z5, z6, z7) -> Cons(z4, merge#2(z5, Cons(z2, z3)))
   cond_merge_ys_zs_2(False, Cons(z0, z1), Cons(z2, z3), z4, z5, z6, z7) -> Cons(z6, merge#2(Cons(z0, z1), z7))
Tuples:
   DROP#2(S(z0), Cons(z1, z2)) -> c12(DROP#2(z0, z2))
   TAKE#2(S(z0), Cons(z1, z2)) -> c15(TAKE#2(z0, z2))
   HALVE#1(S(S(z0))) -> c18(HALVE#1(z0))
   LEQ#2(S(z0), S(z1)) -> c22(LEQ#2(z0, z1))
   LENGTH#1(Cons(z0, z1)) -> c24(LENGTH#1(z1))
   MAP#2(dc(z0, z1, z2, z3, z4), Cons(z5, z6)) -> c26(DC#1(z0, z1, z2, z3, z4, z5))
   MAP#2(dc(z0, z1, z2, z3, z4), Cons(z5, z6)) -> c27(MAP#2(dc(z0, z1, z2, z3, z4), z6))
   MERGE#2(Cons(0, x1), Cons(z0, x3)) -> c6(COND_MERGE_YS_ZS_2(True, Cons(0, x1), Cons(z0, x3), 0, x1, z0, x3))
   MERGE#2(Cons(S(z0), x1), Cons(0, x3)) -> c6(COND_MERGE_YS_ZS_2(False, Cons(S(z0), x1), Cons(0, x3), S(z0), x1, 0, x3))
   MERGE#2(Cons(S(0), x1), Cons(S(z0), x3)) -> c6(COND_MERGE_YS_ZS_2(True, Cons(S(0), x1), Cons(S(z0), x3), S(0), x1, S(z0), x3), LEQ#2(S(0), S(z0)))
   MERGE#2(Cons(S(S(z0)), x1), Cons(S(0), x3)) -> c6(COND_MERGE_YS_ZS_2(False, Cons(S(S(z0)), x1), Cons(S(0), x3), S(S(z0)), x1, S(0), x3), LEQ#2(S(S(z0)), S(0)))
   MERGE#2(Cons(S(S(z0)), x1), Cons(S(S(z1)), x3)) -> c6(COND_MERGE_YS_ZS_2(leq#2(z0, z1), Cons(S(S(z0)), x1), Cons(S(S(z1)), x3), S(S(z0)), x1, S(S(z1)), x3), LEQ#2(S(S(z0)), S(S(z1))))
   MERGE#2(Cons(S(x0), x1), Cons(S(x2), x3)) -> c6(LEQ#2(S(x0), S(x2)))
   DIVIDE_YS#1(Cons(x0, Cons(x1, x2)), S(y11)) -> c(TAKE#2(S(y11), Cons(x0, Cons(x1, x2))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, x3))), S(y11)) -> c(TAKE#2(S(y11), Cons(x0, Cons(x1, Cons(x2, x3)))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Nil)), S(y10)) -> c(TAKE#2(S(y10), Cons(x0, Cons(x1, Nil))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Nil))), S(y7)) -> c(TAKE#2(S(y7), Cons(x0, Cons(x1, Cons(x2, Nil)))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4)))), S(y8)) -> c(TAKE#2(S(y8), Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4))))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, x2)), S(y11)) -> c1(DROP#2(S(y11), Cons(x0, Cons(x1, x2))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, x3))), S(y11)) -> c1(DROP#2(S(y11), Cons(x0, Cons(x1, Cons(x2, x3)))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Nil)), S(y10)) -> c1(DROP#2(S(y10), Cons(x0, Cons(x1, Nil))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Nil))), S(y7)) -> c1(DROP#2(S(y7), Cons(x0, Cons(x1, Cons(x2, Nil)))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4)))), S(y8)) -> c1(DROP#2(S(y8), Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4))))))
   COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(0, z3), z4, Cons(S(y0), y1), z6, z7) -> c2(MERGE#2(Cons(S(y0), y1), Cons(0, z3)))
   COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(S(y1), z3), z4, Cons(S(0), y0), z6, z7) -> c2(MERGE#2(Cons(S(0), y0), Cons(S(y1), z3)))
   COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(S(0), z3), z4, Cons(S(S(y0)), y1), z6, z7) -> c2(MERGE#2(Cons(S(S(y0)), y1), Cons(S(0), z3)))
   COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(S(S(y2)), z3), z4, Cons(S(S(y0)), y1), z6, z7) -> c2(MERGE#2(Cons(S(S(y0)), y1), Cons(S(S(y2)), z3)))
   COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(S(y2), z3), z4, Cons(S(y0), y1), z6, z7) -> c2(MERGE#2(Cons(S(y0), y1), Cons(S(y2), z3)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, z3)))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Cons(z2, z3))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(Cons(z2, z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Cons(drop#2(S(halve#1(S(length#1(z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3)))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3))))), HALVE#1(S(length#1(z3))), LENGTH#1(Cons(z2, z3)))
   COND_MERGE_YS_ZS_2(False, Cons(S(x0), x1), Cons(0, x2), S(x0), x1, 0, x2) -> c3(MERGE#2(Cons(S(x0), x1), x2))
   COND_MERGE_YS_ZS_2(False, Cons(S(S(x0)), x1), Cons(S(0), x2), S(S(x0)), x1, S(0), x2) -> c3(MERGE#2(Cons(S(S(x0)), x1), x2))
   COND_MERGE_YS_ZS_2(False, Cons(S(S(x0)), x1), Cons(S(S(x2)), x3), S(S(x0)), x1, S(S(x2)), x3) -> c3(MERGE#2(Cons(S(S(x0)), x1), x3))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> c9(CONST_F#2(Cons(z0, Cons(z1, z2)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(Cons(z0, take#2(halve#1(length#1(z2)), Cons(z1, z2))), Cons(drop#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Nil))), DIVIDE_YS#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2)))), HALVE#1(length#1(z2)), LENGTH#1(z2))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, z3)))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Cons(z2, z3))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(S(length#1(z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Cons(drop#2(S(halve#1(length#1(Cons(z2, z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3)))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3))))), HALVE#1(S(length#1(z3))), LENGTH#1(Cons(z2, z3)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> c9(MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Nil))), DIVIDE_YS#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2)))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Nil))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(Nil))), Cons(z0, Cons(z1, Nil))), Cons(drop#2(S(halve#1(0)), Cons(z0, Cons(z1, Nil))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil)))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Nil))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(0)), Cons(z0, Cons(z1, Nil))), Cons(drop#2(S(halve#1(length#1(Nil))), Cons(z0, Cons(z1, Nil))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil)))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, z3)))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Cons(z2, z3))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(S(length#1(z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Cons(drop#2(S(halve#1(S(length#1(z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3)))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3))))), HALVE#1(S(length#1(z3))), LENGTH#1(Cons(z2, z3)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, Nil)))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Cons(z2, Nil))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, Nil))), S(halve#1(S(0)))))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, Nil))), S(halve#1(length#1(Cons(z2, Nil)))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, Nil))), S(halve#1(length#1(Cons(z2, Nil))))), HALVE#1(S(length#1(Nil))), LENGTH#1(Cons(z2, Nil)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, Cons(z3, z4))))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Cons(z2, Cons(z3, z4)))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, Cons(z3, z4)))), S(halve#1(S(S(length#1(z4)))))))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, Cons(z3, z4)))), S(halve#1(length#1(Cons(z2, Cons(z3, z4))))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, Cons(z3, z4)))), S(halve#1(length#1(Cons(z2, Cons(z3, z4)))))), HALVE#1(S(length#1(Cons(z3, z4)))), LENGTH#1(Cons(z2, Cons(z3, z4))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, z3)))) -> c9(MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3)))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3))))), HALVE#1(S(length#1(z3))), LENGTH#1(Cons(z2, z3)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Nil))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(0)), Cons(z0, Cons(z1, Nil))), Cons(drop#2(S(halve#1(0)), Cons(z0, Cons(z1, Nil))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil)))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Nil))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Nil)), S(0)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil)))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> c9(CONST_F#2(Cons(z0, Cons(z1, z2)), Cons(dc#1(map, divisible, mergesort_zs_3, divide, const_f, take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2)))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(drop#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(halve#1(length#1(z2)), Cons(z1, z2)), Nil))), DIVIDE_YS#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2)))), HALVE#1(length#1(z2)), LENGTH#1(z2))
   CONST_F#2(Cons(x0, Cons(x1, x2)), Cons(z1, Cons(z2, z3))) -> c19(MERGE#2(z1, z2))
   CONST_F#2(Cons(x0, Cons(x1, Cons(x2, x3))), Cons(z1, Cons(z2, z3))) -> c19(MERGE#2(z1, z2))
   CONST_F#2(Cons(x0, Cons(x1, Nil)), Cons(z1, Cons(z2, z3))) -> c19(MERGE#2(z1, z2))
   CONST_F#2(Cons(x0, Cons(x1, Cons(x2, Nil))), Cons(z1, Cons(z2, z3))) -> c19(MERGE#2(z1, z2))
   CONST_F#2(Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4)))), Cons(z1, Cons(z2, z3))) -> c19(MERGE#2(z1, z2))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> c9(CONST_F#2(Cons(z0, Cons(z1, z2)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(halve#1(length#1(z2)), Cons(z1, z2)), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(halve#1(length#1(z2)), Cons(z1, z2)), Nil))), DIVIDE_YS#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2)))), HALVE#1(length#1(z2)), LENGTH#1(z2))
   COND_MERGE_YS_ZS_2(True, Cons(0, Cons(0, z5)), Cons(x1, x2), 0, Cons(0, z5), x1, x2) -> c2(MERGE#2(Cons(0, z5), Cons(x1, x2)))
   COND_MERGE_YS_ZS_2(True, Cons(S(0), Cons(0, z5)), Cons(S(x1), x2), S(0), Cons(0, z5), S(x1), x2) -> c2(MERGE#2(Cons(0, z5), Cons(S(x1), x2)))
   COND_MERGE_YS_ZS_2(True, Cons(S(S(x0)), Cons(0, z5)), Cons(S(S(x2)), x3), S(S(x0)), Cons(0, z5), S(S(x2)), x3) -> c2(MERGE#2(Cons(0, z5), Cons(S(S(x2)), x3)))
S tuples:
   DROP#2(S(z0), Cons(z1, z2)) -> c12(DROP#2(z0, z2))
   TAKE#2(S(z0), Cons(z1, z2)) -> c15(TAKE#2(z0, z2))
   HALVE#1(S(S(z0))) -> c18(HALVE#1(z0))
   LEQ#2(S(z0), S(z1)) -> c22(LEQ#2(z0, z1))
   LENGTH#1(Cons(z0, z1)) -> c24(LENGTH#1(z1))
   MAP#2(dc(z0, z1, z2, z3, z4), Cons(z5, z6)) -> c26(DC#1(z0, z1, z2, z3, z4, z5))
   MAP#2(dc(z0, z1, z2, z3, z4), Cons(z5, z6)) -> c27(MAP#2(dc(z0, z1, z2, z3, z4), z6))
   MERGE#2(Cons(0, x1), Cons(z0, x3)) -> c6(COND_MERGE_YS_ZS_2(True, Cons(0, x1), Cons(z0, x3), 0, x1, z0, x3))
   MERGE#2(Cons(S(z0), x1), Cons(0, x3)) -> c6(COND_MERGE_YS_ZS_2(False, Cons(S(z0), x1), Cons(0, x3), S(z0), x1, 0, x3))
   MERGE#2(Cons(S(0), x1), Cons(S(z0), x3)) -> c6(COND_MERGE_YS_ZS_2(True, Cons(S(0), x1), Cons(S(z0), x3), S(0), x1, S(z0), x3), LEQ#2(S(0), S(z0)))
   MERGE#2(Cons(S(S(z0)), x1), Cons(S(0), x3)) -> c6(COND_MERGE_YS_ZS_2(False, Cons(S(S(z0)), x1), Cons(S(0), x3), S(S(z0)), x1, S(0), x3), LEQ#2(S(S(z0)), S(0)))
   MERGE#2(Cons(S(S(z0)), x1), Cons(S(S(z1)), x3)) -> c6(COND_MERGE_YS_ZS_2(leq#2(z0, z1), Cons(S(S(z0)), x1), Cons(S(S(z1)), x3), S(S(z0)), x1, S(S(z1)), x3), LEQ#2(S(S(z0)), S(S(z1))))
   MERGE#2(Cons(S(x0), x1), Cons(S(x2), x3)) -> c6(LEQ#2(S(x0), S(x2)))
   DIVIDE_YS#1(Cons(x0, Cons(x1, x2)), S(y11)) -> c(TAKE#2(S(y11), Cons(x0, Cons(x1, x2))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, x3))), S(y11)) -> c(TAKE#2(S(y11), Cons(x0, Cons(x1, Cons(x2, x3)))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Nil)), S(y10)) -> c(TAKE#2(S(y10), Cons(x0, Cons(x1, Nil))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Nil))), S(y7)) -> c(TAKE#2(S(y7), Cons(x0, Cons(x1, Cons(x2, Nil)))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4)))), S(y8)) -> c(TAKE#2(S(y8), Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4))))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, x2)), S(y11)) -> c1(DROP#2(S(y11), Cons(x0, Cons(x1, x2))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, x3))), S(y11)) -> c1(DROP#2(S(y11), Cons(x0, Cons(x1, Cons(x2, x3)))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Nil)), S(y10)) -> c1(DROP#2(S(y10), Cons(x0, Cons(x1, Nil))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Nil))), S(y7)) -> c1(DROP#2(S(y7), Cons(x0, Cons(x1, Cons(x2, Nil)))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4)))), S(y8)) -> c1(DROP#2(S(y8), Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4))))))
   COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(0, z3), z4, Cons(S(y0), y1), z6, z7) -> c2(MERGE#2(Cons(S(y0), y1), Cons(0, z3)))
   COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(S(y1), z3), z4, Cons(S(0), y0), z6, z7) -> c2(MERGE#2(Cons(S(0), y0), Cons(S(y1), z3)))
   COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(S(0), z3), z4, Cons(S(S(y0)), y1), z6, z7) -> c2(MERGE#2(Cons(S(S(y0)), y1), Cons(S(0), z3)))
   COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(S(S(y2)), z3), z4, Cons(S(S(y0)), y1), z6, z7) -> c2(MERGE#2(Cons(S(S(y0)), y1), Cons(S(S(y2)), z3)))
   COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(S(y2), z3), z4, Cons(S(y0), y1), z6, z7) -> c2(MERGE#2(Cons(S(y0), y1), Cons(S(y2), z3)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, z3)))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Cons(z2, z3))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(Cons(z2, z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Cons(drop#2(S(halve#1(S(length#1(z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3)))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3))))), HALVE#1(S(length#1(z3))), LENGTH#1(Cons(z2, z3)))
   COND_MERGE_YS_ZS_2(False, Cons(S(x0), x1), Cons(0, x2), S(x0), x1, 0, x2) -> c3(MERGE#2(Cons(S(x0), x1), x2))
   COND_MERGE_YS_ZS_2(False, Cons(S(S(x0)), x1), Cons(S(0), x2), S(S(x0)), x1, S(0), x2) -> c3(MERGE#2(Cons(S(S(x0)), x1), x2))
   COND_MERGE_YS_ZS_2(False, Cons(S(S(x0)), x1), Cons(S(S(x2)), x3), S(S(x0)), x1, S(S(x2)), x3) -> c3(MERGE#2(Cons(S(S(x0)), x1), x3))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> c9(CONST_F#2(Cons(z0, Cons(z1, z2)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(Cons(z0, take#2(halve#1(length#1(z2)), Cons(z1, z2))), Cons(drop#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Nil))), DIVIDE_YS#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2)))), HALVE#1(length#1(z2)), LENGTH#1(z2))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, z3)))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Cons(z2, z3))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(S(length#1(z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Cons(drop#2(S(halve#1(length#1(Cons(z2, z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3)))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3))))), HALVE#1(S(length#1(z3))), LENGTH#1(Cons(z2, z3)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> c9(MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Nil))), DIVIDE_YS#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2)))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Nil))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(Nil))), Cons(z0, Cons(z1, Nil))), Cons(drop#2(S(halve#1(0)), Cons(z0, Cons(z1, Nil))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil)))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Nil))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(0)), Cons(z0, Cons(z1, Nil))), Cons(drop#2(S(halve#1(length#1(Nil))), Cons(z0, Cons(z1, Nil))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil)))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, z3)))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Cons(z2, z3))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(S(length#1(z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Cons(drop#2(S(halve#1(S(length#1(z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3)))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3))))), HALVE#1(S(length#1(z3))), LENGTH#1(Cons(z2, z3)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, Nil)))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Cons(z2, Nil))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, Nil))), S(halve#1(S(0)))))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, Nil))), S(halve#1(length#1(Cons(z2, Nil)))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, Nil))), S(halve#1(length#1(Cons(z2, Nil))))), HALVE#1(S(length#1(Nil))), LENGTH#1(Cons(z2, Nil)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, Cons(z3, z4))))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Cons(z2, Cons(z3, z4)))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, Cons(z3, z4)))), S(halve#1(S(S(length#1(z4)))))))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, Cons(z3, z4)))), S(halve#1(length#1(Cons(z2, Cons(z3, z4))))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, Cons(z3, z4)))), S(halve#1(length#1(Cons(z2, Cons(z3, z4)))))), HALVE#1(S(length#1(Cons(z3, z4)))), LENGTH#1(Cons(z2, Cons(z3, z4))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, z3)))) -> c9(MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3)))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3))))), HALVE#1(S(length#1(z3))), LENGTH#1(Cons(z2, z3)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Nil))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(0)), Cons(z0, Cons(z1, Nil))), Cons(drop#2(S(halve#1(0)), Cons(z0, Cons(z1, Nil))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil)))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Nil))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Nil)), S(0)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil)))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> c9(CONST_F#2(Cons(z0, Cons(z1, z2)), Cons(dc#1(map, divisible, mergesort_zs_3, divide, const_f, take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2)))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(drop#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(halve#1(length#1(z2)), Cons(z1, z2)), Nil))), DIVIDE_YS#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2)))), HALVE#1(length#1(z2)), LENGTH#1(z2))
   CONST_F#2(Cons(x0, Cons(x1, x2)), Cons(z1, Cons(z2, z3))) -> c19(MERGE#2(z1, z2))
   CONST_F#2(Cons(x0, Cons(x1, Cons(x2, x3))), Cons(z1, Cons(z2, z3))) -> c19(MERGE#2(z1, z2))
   CONST_F#2(Cons(x0, Cons(x1, Nil)), Cons(z1, Cons(z2, z3))) -> c19(MERGE#2(z1, z2))
   CONST_F#2(Cons(x0, Cons(x1, Cons(x2, Nil))), Cons(z1, Cons(z2, z3))) -> c19(MERGE#2(z1, z2))
   CONST_F#2(Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4)))), Cons(z1, Cons(z2, z3))) -> c19(MERGE#2(z1, z2))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> c9(CONST_F#2(Cons(z0, Cons(z1, z2)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(halve#1(length#1(z2)), Cons(z1, z2)), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(halve#1(length#1(z2)), Cons(z1, z2)), Nil))), DIVIDE_YS#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2)))), HALVE#1(length#1(z2)), LENGTH#1(z2))
   COND_MERGE_YS_ZS_2(True, Cons(0, Cons(0, z5)), Cons(x1, x2), 0, Cons(0, z5), x1, x2) -> c2(MERGE#2(Cons(0, z5), Cons(x1, x2)))
   COND_MERGE_YS_ZS_2(True, Cons(S(0), Cons(0, z5)), Cons(S(x1), x2), S(0), Cons(0, z5), S(x1), x2) -> c2(MERGE#2(Cons(0, z5), Cons(S(x1), x2)))
   COND_MERGE_YS_ZS_2(True, Cons(S(S(x0)), Cons(0, z5)), Cons(S(S(x2)), x3), S(S(x0)), Cons(0, z5), S(S(x2)), x3) -> c2(MERGE#2(Cons(0, z5), Cons(S(S(x2)), x3)))
K tuples:none
Defined Rule Symbols:   leq#2_2, map#2_2, divide_ys#1_2, halve#1_1, length#1_1, take#2_2, drop#2_2, dc#1_6, const_f#2_2, merge#2_2, cond_merge_ys_zs_2_7

Defined Pair Symbols:   DROP#2_2, TAKE#2_2, HALVE#1_1, LEQ#2_2, LENGTH#1_1, MAP#2_2, MERGE#2_2, DIVIDE_YS#1_2, COND_MERGE_YS_ZS_2_7, DC#1_6, CONST_F#2_2

Compound Symbols:   c12_1, c15_1, c18_1, c22_1, c24_1, c26_1, c27_1, c6_1, c6_2, c_1, c1_1, c2_1, c9_5, c3_1, c9_2, c9_3, c9_4, c19_1


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

(153) CdtRewritingProof (BOTH BOUNDS(ID, ID))
Used rewriting to replace DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, z3)))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Cons(z2, z3))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(Cons(z2, z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Cons(drop#2(S(halve#1(S(length#1(z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3)))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3))))), HALVE#1(S(length#1(z3))), LENGTH#1(Cons(z2, z3))) by DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, z3)))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Cons(z2, z3))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(Cons(z2, z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Cons(drop#2(S(halve#1(S(length#1(z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3)))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(S(length#1(z3))))), HALVE#1(S(length#1(z3))), LENGTH#1(Cons(z2, z3)))
----------------------------------------

(154)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   leq#2(0, z0) -> True
   leq#2(S(z0), 0) -> False
   leq#2(S(z0), S(z1)) -> leq#2(z0, z1)
   map#2(dc(z0, z1, z2, z3, z4), Nil) -> Nil
   map#2(dc(z0, z1, z2, z3, z4), Cons(z5, z6)) -> Cons(dc#1(z0, z1, z2, z3, z4, z5), map#2(dc(z0, z1, z2, z3, z4), z6))
   divide_ys#1(z0, z1) -> Cons(take#2(z1, z0), Cons(drop#2(z1, z0), Nil))
   halve#1(0) -> 0
   halve#1(S(0)) -> S(0)
   halve#1(S(S(z0))) -> S(halve#1(z0))
   length#1(Nil) -> 0
   length#1(Cons(z0, z1)) -> S(length#1(z1))
   take#2(0, z0) -> Nil
   take#2(S(0), Nil) -> Cons(bot[0], Nil)
   take#2(S(z0), Cons(z1, z2)) -> Cons(z1, take#2(z0, z2))
   drop#2(0, z0) -> z0
   drop#2(S(0), Nil) -> bot[1]
   drop#2(S(z0), Cons(z1, z2)) -> drop#2(z0, z2)
   dc#1(map, divisible, mergesort_zs_3, divide, const_f, Nil) -> Nil
   dc#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Nil)) -> Cons(z0, Nil)
   dc#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> const_f#2(Cons(z0, Cons(z1, z2)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2))))))
   const_f#2(z0, Cons(z1, Cons(z2, z3))) -> merge#2(z1, z2)
   merge#2(Nil, z0) -> z0
   merge#2(Cons(z0, z1), Nil) -> Cons(z0, z1)
   merge#2(Cons(z0, z1), Cons(z2, z3)) -> cond_merge_ys_zs_2(leq#2(z0, z2), Cons(z0, z1), Cons(z2, z3), z0, z1, z2, z3)
   cond_merge_ys_zs_2(True, Cons(z0, z1), Cons(z2, z3), z4, z5, z6, z7) -> Cons(z4, merge#2(z5, Cons(z2, z3)))
   cond_merge_ys_zs_2(False, Cons(z0, z1), Cons(z2, z3), z4, z5, z6, z7) -> Cons(z6, merge#2(Cons(z0, z1), z7))
Tuples:
   DROP#2(S(z0), Cons(z1, z2)) -> c12(DROP#2(z0, z2))
   TAKE#2(S(z0), Cons(z1, z2)) -> c15(TAKE#2(z0, z2))
   HALVE#1(S(S(z0))) -> c18(HALVE#1(z0))
   LEQ#2(S(z0), S(z1)) -> c22(LEQ#2(z0, z1))
   LENGTH#1(Cons(z0, z1)) -> c24(LENGTH#1(z1))
   MAP#2(dc(z0, z1, z2, z3, z4), Cons(z5, z6)) -> c26(DC#1(z0, z1, z2, z3, z4, z5))
   MAP#2(dc(z0, z1, z2, z3, z4), Cons(z5, z6)) -> c27(MAP#2(dc(z0, z1, z2, z3, z4), z6))
   MERGE#2(Cons(0, x1), Cons(z0, x3)) -> c6(COND_MERGE_YS_ZS_2(True, Cons(0, x1), Cons(z0, x3), 0, x1, z0, x3))
   MERGE#2(Cons(S(z0), x1), Cons(0, x3)) -> c6(COND_MERGE_YS_ZS_2(False, Cons(S(z0), x1), Cons(0, x3), S(z0), x1, 0, x3))
   MERGE#2(Cons(S(0), x1), Cons(S(z0), x3)) -> c6(COND_MERGE_YS_ZS_2(True, Cons(S(0), x1), Cons(S(z0), x3), S(0), x1, S(z0), x3), LEQ#2(S(0), S(z0)))
   MERGE#2(Cons(S(S(z0)), x1), Cons(S(0), x3)) -> c6(COND_MERGE_YS_ZS_2(False, Cons(S(S(z0)), x1), Cons(S(0), x3), S(S(z0)), x1, S(0), x3), LEQ#2(S(S(z0)), S(0)))
   MERGE#2(Cons(S(S(z0)), x1), Cons(S(S(z1)), x3)) -> c6(COND_MERGE_YS_ZS_2(leq#2(z0, z1), Cons(S(S(z0)), x1), Cons(S(S(z1)), x3), S(S(z0)), x1, S(S(z1)), x3), LEQ#2(S(S(z0)), S(S(z1))))
   MERGE#2(Cons(S(x0), x1), Cons(S(x2), x3)) -> c6(LEQ#2(S(x0), S(x2)))
   DIVIDE_YS#1(Cons(x0, Cons(x1, x2)), S(y11)) -> c(TAKE#2(S(y11), Cons(x0, Cons(x1, x2))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, x3))), S(y11)) -> c(TAKE#2(S(y11), Cons(x0, Cons(x1, Cons(x2, x3)))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Nil)), S(y10)) -> c(TAKE#2(S(y10), Cons(x0, Cons(x1, Nil))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Nil))), S(y7)) -> c(TAKE#2(S(y7), Cons(x0, Cons(x1, Cons(x2, Nil)))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4)))), S(y8)) -> c(TAKE#2(S(y8), Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4))))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, x2)), S(y11)) -> c1(DROP#2(S(y11), Cons(x0, Cons(x1, x2))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, x3))), S(y11)) -> c1(DROP#2(S(y11), Cons(x0, Cons(x1, Cons(x2, x3)))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Nil)), S(y10)) -> c1(DROP#2(S(y10), Cons(x0, Cons(x1, Nil))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Nil))), S(y7)) -> c1(DROP#2(S(y7), Cons(x0, Cons(x1, Cons(x2, Nil)))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4)))), S(y8)) -> c1(DROP#2(S(y8), Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4))))))
   COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(0, z3), z4, Cons(S(y0), y1), z6, z7) -> c2(MERGE#2(Cons(S(y0), y1), Cons(0, z3)))
   COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(S(y1), z3), z4, Cons(S(0), y0), z6, z7) -> c2(MERGE#2(Cons(S(0), y0), Cons(S(y1), z3)))
   COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(S(0), z3), z4, Cons(S(S(y0)), y1), z6, z7) -> c2(MERGE#2(Cons(S(S(y0)), y1), Cons(S(0), z3)))
   COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(S(S(y2)), z3), z4, Cons(S(S(y0)), y1), z6, z7) -> c2(MERGE#2(Cons(S(S(y0)), y1), Cons(S(S(y2)), z3)))
   COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(S(y2), z3), z4, Cons(S(y0), y1), z6, z7) -> c2(MERGE#2(Cons(S(y0), y1), Cons(S(y2), z3)))
   COND_MERGE_YS_ZS_2(False, Cons(S(x0), x1), Cons(0, x2), S(x0), x1, 0, x2) -> c3(MERGE#2(Cons(S(x0), x1), x2))
   COND_MERGE_YS_ZS_2(False, Cons(S(S(x0)), x1), Cons(S(0), x2), S(S(x0)), x1, S(0), x2) -> c3(MERGE#2(Cons(S(S(x0)), x1), x2))
   COND_MERGE_YS_ZS_2(False, Cons(S(S(x0)), x1), Cons(S(S(x2)), x3), S(S(x0)), x1, S(S(x2)), x3) -> c3(MERGE#2(Cons(S(S(x0)), x1), x3))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> c9(CONST_F#2(Cons(z0, Cons(z1, z2)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(Cons(z0, take#2(halve#1(length#1(z2)), Cons(z1, z2))), Cons(drop#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Nil))), DIVIDE_YS#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2)))), HALVE#1(length#1(z2)), LENGTH#1(z2))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, z3)))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Cons(z2, z3))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(S(length#1(z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Cons(drop#2(S(halve#1(length#1(Cons(z2, z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3)))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3))))), HALVE#1(S(length#1(z3))), LENGTH#1(Cons(z2, z3)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> c9(MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Nil))), DIVIDE_YS#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2)))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Nil))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(Nil))), Cons(z0, Cons(z1, Nil))), Cons(drop#2(S(halve#1(0)), Cons(z0, Cons(z1, Nil))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil)))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Nil))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(0)), Cons(z0, Cons(z1, Nil))), Cons(drop#2(S(halve#1(length#1(Nil))), Cons(z0, Cons(z1, Nil))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil)))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, z3)))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Cons(z2, z3))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(S(length#1(z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Cons(drop#2(S(halve#1(S(length#1(z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3)))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3))))), HALVE#1(S(length#1(z3))), LENGTH#1(Cons(z2, z3)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, Nil)))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Cons(z2, Nil))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, Nil))), S(halve#1(S(0)))))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, Nil))), S(halve#1(length#1(Cons(z2, Nil)))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, Nil))), S(halve#1(length#1(Cons(z2, Nil))))), HALVE#1(S(length#1(Nil))), LENGTH#1(Cons(z2, Nil)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, Cons(z3, z4))))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Cons(z2, Cons(z3, z4)))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, Cons(z3, z4)))), S(halve#1(S(S(length#1(z4)))))))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, Cons(z3, z4)))), S(halve#1(length#1(Cons(z2, Cons(z3, z4))))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, Cons(z3, z4)))), S(halve#1(length#1(Cons(z2, Cons(z3, z4)))))), HALVE#1(S(length#1(Cons(z3, z4)))), LENGTH#1(Cons(z2, Cons(z3, z4))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, z3)))) -> c9(MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3)))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3))))), HALVE#1(S(length#1(z3))), LENGTH#1(Cons(z2, z3)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Nil))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(0)), Cons(z0, Cons(z1, Nil))), Cons(drop#2(S(halve#1(0)), Cons(z0, Cons(z1, Nil))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil)))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Nil))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Nil)), S(0)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil)))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> c9(CONST_F#2(Cons(z0, Cons(z1, z2)), Cons(dc#1(map, divisible, mergesort_zs_3, divide, const_f, take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2)))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(drop#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(halve#1(length#1(z2)), Cons(z1, z2)), Nil))), DIVIDE_YS#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2)))), HALVE#1(length#1(z2)), LENGTH#1(z2))
   CONST_F#2(Cons(x0, Cons(x1, x2)), Cons(z1, Cons(z2, z3))) -> c19(MERGE#2(z1, z2))
   CONST_F#2(Cons(x0, Cons(x1, Cons(x2, x3))), Cons(z1, Cons(z2, z3))) -> c19(MERGE#2(z1, z2))
   CONST_F#2(Cons(x0, Cons(x1, Nil)), Cons(z1, Cons(z2, z3))) -> c19(MERGE#2(z1, z2))
   CONST_F#2(Cons(x0, Cons(x1, Cons(x2, Nil))), Cons(z1, Cons(z2, z3))) -> c19(MERGE#2(z1, z2))
   CONST_F#2(Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4)))), Cons(z1, Cons(z2, z3))) -> c19(MERGE#2(z1, z2))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> c9(CONST_F#2(Cons(z0, Cons(z1, z2)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(halve#1(length#1(z2)), Cons(z1, z2)), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(halve#1(length#1(z2)), Cons(z1, z2)), Nil))), DIVIDE_YS#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2)))), HALVE#1(length#1(z2)), LENGTH#1(z2))
   COND_MERGE_YS_ZS_2(True, Cons(0, Cons(0, z5)), Cons(x1, x2), 0, Cons(0, z5), x1, x2) -> c2(MERGE#2(Cons(0, z5), Cons(x1, x2)))
   COND_MERGE_YS_ZS_2(True, Cons(S(0), Cons(0, z5)), Cons(S(x1), x2), S(0), Cons(0, z5), S(x1), x2) -> c2(MERGE#2(Cons(0, z5), Cons(S(x1), x2)))
   COND_MERGE_YS_ZS_2(True, Cons(S(S(x0)), Cons(0, z5)), Cons(S(S(x2)), x3), S(S(x0)), Cons(0, z5), S(S(x2)), x3) -> c2(MERGE#2(Cons(0, z5), Cons(S(S(x2)), x3)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, z3)))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Cons(z2, z3))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(Cons(z2, z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Cons(drop#2(S(halve#1(S(length#1(z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3)))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(S(length#1(z3))))), HALVE#1(S(length#1(z3))), LENGTH#1(Cons(z2, z3)))
S tuples:
   DROP#2(S(z0), Cons(z1, z2)) -> c12(DROP#2(z0, z2))
   TAKE#2(S(z0), Cons(z1, z2)) -> c15(TAKE#2(z0, z2))
   HALVE#1(S(S(z0))) -> c18(HALVE#1(z0))
   LEQ#2(S(z0), S(z1)) -> c22(LEQ#2(z0, z1))
   LENGTH#1(Cons(z0, z1)) -> c24(LENGTH#1(z1))
   MAP#2(dc(z0, z1, z2, z3, z4), Cons(z5, z6)) -> c26(DC#1(z0, z1, z2, z3, z4, z5))
   MAP#2(dc(z0, z1, z2, z3, z4), Cons(z5, z6)) -> c27(MAP#2(dc(z0, z1, z2, z3, z4), z6))
   MERGE#2(Cons(0, x1), Cons(z0, x3)) -> c6(COND_MERGE_YS_ZS_2(True, Cons(0, x1), Cons(z0, x3), 0, x1, z0, x3))
   MERGE#2(Cons(S(z0), x1), Cons(0, x3)) -> c6(COND_MERGE_YS_ZS_2(False, Cons(S(z0), x1), Cons(0, x3), S(z0), x1, 0, x3))
   MERGE#2(Cons(S(0), x1), Cons(S(z0), x3)) -> c6(COND_MERGE_YS_ZS_2(True, Cons(S(0), x1), Cons(S(z0), x3), S(0), x1, S(z0), x3), LEQ#2(S(0), S(z0)))
   MERGE#2(Cons(S(S(z0)), x1), Cons(S(0), x3)) -> c6(COND_MERGE_YS_ZS_2(False, Cons(S(S(z0)), x1), Cons(S(0), x3), S(S(z0)), x1, S(0), x3), LEQ#2(S(S(z0)), S(0)))
   MERGE#2(Cons(S(S(z0)), x1), Cons(S(S(z1)), x3)) -> c6(COND_MERGE_YS_ZS_2(leq#2(z0, z1), Cons(S(S(z0)), x1), Cons(S(S(z1)), x3), S(S(z0)), x1, S(S(z1)), x3), LEQ#2(S(S(z0)), S(S(z1))))
   MERGE#2(Cons(S(x0), x1), Cons(S(x2), x3)) -> c6(LEQ#2(S(x0), S(x2)))
   DIVIDE_YS#1(Cons(x0, Cons(x1, x2)), S(y11)) -> c(TAKE#2(S(y11), Cons(x0, Cons(x1, x2))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, x3))), S(y11)) -> c(TAKE#2(S(y11), Cons(x0, Cons(x1, Cons(x2, x3)))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Nil)), S(y10)) -> c(TAKE#2(S(y10), Cons(x0, Cons(x1, Nil))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Nil))), S(y7)) -> c(TAKE#2(S(y7), Cons(x0, Cons(x1, Cons(x2, Nil)))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4)))), S(y8)) -> c(TAKE#2(S(y8), Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4))))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, x2)), S(y11)) -> c1(DROP#2(S(y11), Cons(x0, Cons(x1, x2))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, x3))), S(y11)) -> c1(DROP#2(S(y11), Cons(x0, Cons(x1, Cons(x2, x3)))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Nil)), S(y10)) -> c1(DROP#2(S(y10), Cons(x0, Cons(x1, Nil))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Nil))), S(y7)) -> c1(DROP#2(S(y7), Cons(x0, Cons(x1, Cons(x2, Nil)))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4)))), S(y8)) -> c1(DROP#2(S(y8), Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4))))))
   COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(0, z3), z4, Cons(S(y0), y1), z6, z7) -> c2(MERGE#2(Cons(S(y0), y1), Cons(0, z3)))
   COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(S(y1), z3), z4, Cons(S(0), y0), z6, z7) -> c2(MERGE#2(Cons(S(0), y0), Cons(S(y1), z3)))
   COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(S(0), z3), z4, Cons(S(S(y0)), y1), z6, z7) -> c2(MERGE#2(Cons(S(S(y0)), y1), Cons(S(0), z3)))
   COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(S(S(y2)), z3), z4, Cons(S(S(y0)), y1), z6, z7) -> c2(MERGE#2(Cons(S(S(y0)), y1), Cons(S(S(y2)), z3)))
   COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(S(y2), z3), z4, Cons(S(y0), y1), z6, z7) -> c2(MERGE#2(Cons(S(y0), y1), Cons(S(y2), z3)))
   COND_MERGE_YS_ZS_2(False, Cons(S(x0), x1), Cons(0, x2), S(x0), x1, 0, x2) -> c3(MERGE#2(Cons(S(x0), x1), x2))
   COND_MERGE_YS_ZS_2(False, Cons(S(S(x0)), x1), Cons(S(0), x2), S(S(x0)), x1, S(0), x2) -> c3(MERGE#2(Cons(S(S(x0)), x1), x2))
   COND_MERGE_YS_ZS_2(False, Cons(S(S(x0)), x1), Cons(S(S(x2)), x3), S(S(x0)), x1, S(S(x2)), x3) -> c3(MERGE#2(Cons(S(S(x0)), x1), x3))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> c9(CONST_F#2(Cons(z0, Cons(z1, z2)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(Cons(z0, take#2(halve#1(length#1(z2)), Cons(z1, z2))), Cons(drop#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Nil))), DIVIDE_YS#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2)))), HALVE#1(length#1(z2)), LENGTH#1(z2))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, z3)))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Cons(z2, z3))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(S(length#1(z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Cons(drop#2(S(halve#1(length#1(Cons(z2, z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3)))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3))))), HALVE#1(S(length#1(z3))), LENGTH#1(Cons(z2, z3)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> c9(MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Nil))), DIVIDE_YS#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2)))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Nil))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(Nil))), Cons(z0, Cons(z1, Nil))), Cons(drop#2(S(halve#1(0)), Cons(z0, Cons(z1, Nil))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil)))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Nil))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(0)), Cons(z0, Cons(z1, Nil))), Cons(drop#2(S(halve#1(length#1(Nil))), Cons(z0, Cons(z1, Nil))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil)))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, z3)))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Cons(z2, z3))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(S(length#1(z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Cons(drop#2(S(halve#1(S(length#1(z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3)))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3))))), HALVE#1(S(length#1(z3))), LENGTH#1(Cons(z2, z3)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, Nil)))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Cons(z2, Nil))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, Nil))), S(halve#1(S(0)))))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, Nil))), S(halve#1(length#1(Cons(z2, Nil)))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, Nil))), S(halve#1(length#1(Cons(z2, Nil))))), HALVE#1(S(length#1(Nil))), LENGTH#1(Cons(z2, Nil)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, Cons(z3, z4))))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Cons(z2, Cons(z3, z4)))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, Cons(z3, z4)))), S(halve#1(S(S(length#1(z4)))))))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, Cons(z3, z4)))), S(halve#1(length#1(Cons(z2, Cons(z3, z4))))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, Cons(z3, z4)))), S(halve#1(length#1(Cons(z2, Cons(z3, z4)))))), HALVE#1(S(length#1(Cons(z3, z4)))), LENGTH#1(Cons(z2, Cons(z3, z4))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, z3)))) -> c9(MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3)))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3))))), HALVE#1(S(length#1(z3))), LENGTH#1(Cons(z2, z3)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Nil))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(0)), Cons(z0, Cons(z1, Nil))), Cons(drop#2(S(halve#1(0)), Cons(z0, Cons(z1, Nil))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil)))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Nil))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Nil)), S(0)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil)))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> c9(CONST_F#2(Cons(z0, Cons(z1, z2)), Cons(dc#1(map, divisible, mergesort_zs_3, divide, const_f, take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2)))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(drop#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(halve#1(length#1(z2)), Cons(z1, z2)), Nil))), DIVIDE_YS#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2)))), HALVE#1(length#1(z2)), LENGTH#1(z2))
   CONST_F#2(Cons(x0, Cons(x1, x2)), Cons(z1, Cons(z2, z3))) -> c19(MERGE#2(z1, z2))
   CONST_F#2(Cons(x0, Cons(x1, Cons(x2, x3))), Cons(z1, Cons(z2, z3))) -> c19(MERGE#2(z1, z2))
   CONST_F#2(Cons(x0, Cons(x1, Nil)), Cons(z1, Cons(z2, z3))) -> c19(MERGE#2(z1, z2))
   CONST_F#2(Cons(x0, Cons(x1, Cons(x2, Nil))), Cons(z1, Cons(z2, z3))) -> c19(MERGE#2(z1, z2))
   CONST_F#2(Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4)))), Cons(z1, Cons(z2, z3))) -> c19(MERGE#2(z1, z2))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> c9(CONST_F#2(Cons(z0, Cons(z1, z2)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(halve#1(length#1(z2)), Cons(z1, z2)), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(halve#1(length#1(z2)), Cons(z1, z2)), Nil))), DIVIDE_YS#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2)))), HALVE#1(length#1(z2)), LENGTH#1(z2))
   COND_MERGE_YS_ZS_2(True, Cons(0, Cons(0, z5)), Cons(x1, x2), 0, Cons(0, z5), x1, x2) -> c2(MERGE#2(Cons(0, z5), Cons(x1, x2)))
   COND_MERGE_YS_ZS_2(True, Cons(S(0), Cons(0, z5)), Cons(S(x1), x2), S(0), Cons(0, z5), S(x1), x2) -> c2(MERGE#2(Cons(0, z5), Cons(S(x1), x2)))
   COND_MERGE_YS_ZS_2(True, Cons(S(S(x0)), Cons(0, z5)), Cons(S(S(x2)), x3), S(S(x0)), Cons(0, z5), S(S(x2)), x3) -> c2(MERGE#2(Cons(0, z5), Cons(S(S(x2)), x3)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, z3)))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Cons(z2, z3))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(Cons(z2, z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Cons(drop#2(S(halve#1(S(length#1(z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3)))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(S(length#1(z3))))), HALVE#1(S(length#1(z3))), LENGTH#1(Cons(z2, z3)))
K tuples:none
Defined Rule Symbols:   leq#2_2, map#2_2, divide_ys#1_2, halve#1_1, length#1_1, take#2_2, drop#2_2, dc#1_6, const_f#2_2, merge#2_2, cond_merge_ys_zs_2_7

Defined Pair Symbols:   DROP#2_2, TAKE#2_2, HALVE#1_1, LEQ#2_2, LENGTH#1_1, MAP#2_2, MERGE#2_2, DIVIDE_YS#1_2, COND_MERGE_YS_ZS_2_7, DC#1_6, CONST_F#2_2

Compound Symbols:   c12_1, c15_1, c18_1, c22_1, c24_1, c26_1, c27_1, c6_1, c6_2, c_1, c1_1, c2_1, c3_1, c9_5, c9_2, c9_3, c9_4, c19_1


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(155) CdtInstantiationProof (BOTH BOUNDS(ID, ID))
Use instantiation to replace COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(0, z3), z4, Cons(S(y0), y1), z6, z7) -> c2(MERGE#2(Cons(S(y0), y1), Cons(0, z3))) by 
   COND_MERGE_YS_ZS_2(True, Cons(0, Cons(S(z4), z5)), Cons(0, x2), 0, Cons(S(z4), z5), 0, x2) -> c2(MERGE#2(Cons(S(z4), z5), Cons(0, x2)))

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

(156)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   leq#2(0, z0) -> True
   leq#2(S(z0), 0) -> False
   leq#2(S(z0), S(z1)) -> leq#2(z0, z1)
   map#2(dc(z0, z1, z2, z3, z4), Nil) -> Nil
   map#2(dc(z0, z1, z2, z3, z4), Cons(z5, z6)) -> Cons(dc#1(z0, z1, z2, z3, z4, z5), map#2(dc(z0, z1, z2, z3, z4), z6))
   divide_ys#1(z0, z1) -> Cons(take#2(z1, z0), Cons(drop#2(z1, z0), Nil))
   halve#1(0) -> 0
   halve#1(S(0)) -> S(0)
   halve#1(S(S(z0))) -> S(halve#1(z0))
   length#1(Nil) -> 0
   length#1(Cons(z0, z1)) -> S(length#1(z1))
   take#2(0, z0) -> Nil
   take#2(S(0), Nil) -> Cons(bot[0], Nil)
   take#2(S(z0), Cons(z1, z2)) -> Cons(z1, take#2(z0, z2))
   drop#2(0, z0) -> z0
   drop#2(S(0), Nil) -> bot[1]
   drop#2(S(z0), Cons(z1, z2)) -> drop#2(z0, z2)
   dc#1(map, divisible, mergesort_zs_3, divide, const_f, Nil) -> Nil
   dc#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Nil)) -> Cons(z0, Nil)
   dc#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> const_f#2(Cons(z0, Cons(z1, z2)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2))))))
   const_f#2(z0, Cons(z1, Cons(z2, z3))) -> merge#2(z1, z2)
   merge#2(Nil, z0) -> z0
   merge#2(Cons(z0, z1), Nil) -> Cons(z0, z1)
   merge#2(Cons(z0, z1), Cons(z2, z3)) -> cond_merge_ys_zs_2(leq#2(z0, z2), Cons(z0, z1), Cons(z2, z3), z0, z1, z2, z3)
   cond_merge_ys_zs_2(True, Cons(z0, z1), Cons(z2, z3), z4, z5, z6, z7) -> Cons(z4, merge#2(z5, Cons(z2, z3)))
   cond_merge_ys_zs_2(False, Cons(z0, z1), Cons(z2, z3), z4, z5, z6, z7) -> Cons(z6, merge#2(Cons(z0, z1), z7))
Tuples:
   DROP#2(S(z0), Cons(z1, z2)) -> c12(DROP#2(z0, z2))
   TAKE#2(S(z0), Cons(z1, z2)) -> c15(TAKE#2(z0, z2))
   HALVE#1(S(S(z0))) -> c18(HALVE#1(z0))
   LEQ#2(S(z0), S(z1)) -> c22(LEQ#2(z0, z1))
   LENGTH#1(Cons(z0, z1)) -> c24(LENGTH#1(z1))
   MAP#2(dc(z0, z1, z2, z3, z4), Cons(z5, z6)) -> c26(DC#1(z0, z1, z2, z3, z4, z5))
   MAP#2(dc(z0, z1, z2, z3, z4), Cons(z5, z6)) -> c27(MAP#2(dc(z0, z1, z2, z3, z4), z6))
   MERGE#2(Cons(0, x1), Cons(z0, x3)) -> c6(COND_MERGE_YS_ZS_2(True, Cons(0, x1), Cons(z0, x3), 0, x1, z0, x3))
   MERGE#2(Cons(S(z0), x1), Cons(0, x3)) -> c6(COND_MERGE_YS_ZS_2(False, Cons(S(z0), x1), Cons(0, x3), S(z0), x1, 0, x3))
   MERGE#2(Cons(S(0), x1), Cons(S(z0), x3)) -> c6(COND_MERGE_YS_ZS_2(True, Cons(S(0), x1), Cons(S(z0), x3), S(0), x1, S(z0), x3), LEQ#2(S(0), S(z0)))
   MERGE#2(Cons(S(S(z0)), x1), Cons(S(0), x3)) -> c6(COND_MERGE_YS_ZS_2(False, Cons(S(S(z0)), x1), Cons(S(0), x3), S(S(z0)), x1, S(0), x3), LEQ#2(S(S(z0)), S(0)))
   MERGE#2(Cons(S(S(z0)), x1), Cons(S(S(z1)), x3)) -> c6(COND_MERGE_YS_ZS_2(leq#2(z0, z1), Cons(S(S(z0)), x1), Cons(S(S(z1)), x3), S(S(z0)), x1, S(S(z1)), x3), LEQ#2(S(S(z0)), S(S(z1))))
   MERGE#2(Cons(S(x0), x1), Cons(S(x2), x3)) -> c6(LEQ#2(S(x0), S(x2)))
   DIVIDE_YS#1(Cons(x0, Cons(x1, x2)), S(y11)) -> c(TAKE#2(S(y11), Cons(x0, Cons(x1, x2))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, x3))), S(y11)) -> c(TAKE#2(S(y11), Cons(x0, Cons(x1, Cons(x2, x3)))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Nil)), S(y10)) -> c(TAKE#2(S(y10), Cons(x0, Cons(x1, Nil))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Nil))), S(y7)) -> c(TAKE#2(S(y7), Cons(x0, Cons(x1, Cons(x2, Nil)))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4)))), S(y8)) -> c(TAKE#2(S(y8), Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4))))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, x2)), S(y11)) -> c1(DROP#2(S(y11), Cons(x0, Cons(x1, x2))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, x3))), S(y11)) -> c1(DROP#2(S(y11), Cons(x0, Cons(x1, Cons(x2, x3)))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Nil)), S(y10)) -> c1(DROP#2(S(y10), Cons(x0, Cons(x1, Nil))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Nil))), S(y7)) -> c1(DROP#2(S(y7), Cons(x0, Cons(x1, Cons(x2, Nil)))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4)))), S(y8)) -> c1(DROP#2(S(y8), Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4))))))
   COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(S(y1), z3), z4, Cons(S(0), y0), z6, z7) -> c2(MERGE#2(Cons(S(0), y0), Cons(S(y1), z3)))
   COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(S(0), z3), z4, Cons(S(S(y0)), y1), z6, z7) -> c2(MERGE#2(Cons(S(S(y0)), y1), Cons(S(0), z3)))
   COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(S(S(y2)), z3), z4, Cons(S(S(y0)), y1), z6, z7) -> c2(MERGE#2(Cons(S(S(y0)), y1), Cons(S(S(y2)), z3)))
   COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(S(y2), z3), z4, Cons(S(y0), y1), z6, z7) -> c2(MERGE#2(Cons(S(y0), y1), Cons(S(y2), z3)))
   COND_MERGE_YS_ZS_2(False, Cons(S(x0), x1), Cons(0, x2), S(x0), x1, 0, x2) -> c3(MERGE#2(Cons(S(x0), x1), x2))
   COND_MERGE_YS_ZS_2(False, Cons(S(S(x0)), x1), Cons(S(0), x2), S(S(x0)), x1, S(0), x2) -> c3(MERGE#2(Cons(S(S(x0)), x1), x2))
   COND_MERGE_YS_ZS_2(False, Cons(S(S(x0)), x1), Cons(S(S(x2)), x3), S(S(x0)), x1, S(S(x2)), x3) -> c3(MERGE#2(Cons(S(S(x0)), x1), x3))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> c9(CONST_F#2(Cons(z0, Cons(z1, z2)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(Cons(z0, take#2(halve#1(length#1(z2)), Cons(z1, z2))), Cons(drop#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Nil))), DIVIDE_YS#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2)))), HALVE#1(length#1(z2)), LENGTH#1(z2))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, z3)))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Cons(z2, z3))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(S(length#1(z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Cons(drop#2(S(halve#1(length#1(Cons(z2, z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3)))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3))))), HALVE#1(S(length#1(z3))), LENGTH#1(Cons(z2, z3)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> c9(MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Nil))), DIVIDE_YS#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2)))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Nil))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(Nil))), Cons(z0, Cons(z1, Nil))), Cons(drop#2(S(halve#1(0)), Cons(z0, Cons(z1, Nil))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil)))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Nil))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(0)), Cons(z0, Cons(z1, Nil))), Cons(drop#2(S(halve#1(length#1(Nil))), Cons(z0, Cons(z1, Nil))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil)))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, z3)))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Cons(z2, z3))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(S(length#1(z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Cons(drop#2(S(halve#1(S(length#1(z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3)))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3))))), HALVE#1(S(length#1(z3))), LENGTH#1(Cons(z2, z3)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, Nil)))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Cons(z2, Nil))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, Nil))), S(halve#1(S(0)))))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, Nil))), S(halve#1(length#1(Cons(z2, Nil)))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, Nil))), S(halve#1(length#1(Cons(z2, Nil))))), HALVE#1(S(length#1(Nil))), LENGTH#1(Cons(z2, Nil)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, Cons(z3, z4))))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Cons(z2, Cons(z3, z4)))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, Cons(z3, z4)))), S(halve#1(S(S(length#1(z4)))))))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, Cons(z3, z4)))), S(halve#1(length#1(Cons(z2, Cons(z3, z4))))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, Cons(z3, z4)))), S(halve#1(length#1(Cons(z2, Cons(z3, z4)))))), HALVE#1(S(length#1(Cons(z3, z4)))), LENGTH#1(Cons(z2, Cons(z3, z4))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, z3)))) -> c9(MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3)))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3))))), HALVE#1(S(length#1(z3))), LENGTH#1(Cons(z2, z3)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Nil))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(0)), Cons(z0, Cons(z1, Nil))), Cons(drop#2(S(halve#1(0)), Cons(z0, Cons(z1, Nil))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil)))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Nil))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Nil)), S(0)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil)))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> c9(CONST_F#2(Cons(z0, Cons(z1, z2)), Cons(dc#1(map, divisible, mergesort_zs_3, divide, const_f, take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2)))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(drop#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(halve#1(length#1(z2)), Cons(z1, z2)), Nil))), DIVIDE_YS#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2)))), HALVE#1(length#1(z2)), LENGTH#1(z2))
   CONST_F#2(Cons(x0, Cons(x1, x2)), Cons(z1, Cons(z2, z3))) -> c19(MERGE#2(z1, z2))
   CONST_F#2(Cons(x0, Cons(x1, Cons(x2, x3))), Cons(z1, Cons(z2, z3))) -> c19(MERGE#2(z1, z2))
   CONST_F#2(Cons(x0, Cons(x1, Nil)), Cons(z1, Cons(z2, z3))) -> c19(MERGE#2(z1, z2))
   CONST_F#2(Cons(x0, Cons(x1, Cons(x2, Nil))), Cons(z1, Cons(z2, z3))) -> c19(MERGE#2(z1, z2))
   CONST_F#2(Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4)))), Cons(z1, Cons(z2, z3))) -> c19(MERGE#2(z1, z2))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> c9(CONST_F#2(Cons(z0, Cons(z1, z2)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(halve#1(length#1(z2)), Cons(z1, z2)), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(halve#1(length#1(z2)), Cons(z1, z2)), Nil))), DIVIDE_YS#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2)))), HALVE#1(length#1(z2)), LENGTH#1(z2))
   COND_MERGE_YS_ZS_2(True, Cons(0, Cons(0, z5)), Cons(x1, x2), 0, Cons(0, z5), x1, x2) -> c2(MERGE#2(Cons(0, z5), Cons(x1, x2)))
   COND_MERGE_YS_ZS_2(True, Cons(S(0), Cons(0, z5)), Cons(S(x1), x2), S(0), Cons(0, z5), S(x1), x2) -> c2(MERGE#2(Cons(0, z5), Cons(S(x1), x2)))
   COND_MERGE_YS_ZS_2(True, Cons(S(S(x0)), Cons(0, z5)), Cons(S(S(x2)), x3), S(S(x0)), Cons(0, z5), S(S(x2)), x3) -> c2(MERGE#2(Cons(0, z5), Cons(S(S(x2)), x3)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, z3)))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Cons(z2, z3))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(Cons(z2, z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Cons(drop#2(S(halve#1(S(length#1(z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3)))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(S(length#1(z3))))), HALVE#1(S(length#1(z3))), LENGTH#1(Cons(z2, z3)))
   COND_MERGE_YS_ZS_2(True, Cons(0, Cons(S(z4), z5)), Cons(0, x2), 0, Cons(S(z4), z5), 0, x2) -> c2(MERGE#2(Cons(S(z4), z5), Cons(0, x2)))
S tuples:
   DROP#2(S(z0), Cons(z1, z2)) -> c12(DROP#2(z0, z2))
   TAKE#2(S(z0), Cons(z1, z2)) -> c15(TAKE#2(z0, z2))
   HALVE#1(S(S(z0))) -> c18(HALVE#1(z0))
   LEQ#2(S(z0), S(z1)) -> c22(LEQ#2(z0, z1))
   LENGTH#1(Cons(z0, z1)) -> c24(LENGTH#1(z1))
   MAP#2(dc(z0, z1, z2, z3, z4), Cons(z5, z6)) -> c26(DC#1(z0, z1, z2, z3, z4, z5))
   MAP#2(dc(z0, z1, z2, z3, z4), Cons(z5, z6)) -> c27(MAP#2(dc(z0, z1, z2, z3, z4), z6))
   MERGE#2(Cons(0, x1), Cons(z0, x3)) -> c6(COND_MERGE_YS_ZS_2(True, Cons(0, x1), Cons(z0, x3), 0, x1, z0, x3))
   MERGE#2(Cons(S(z0), x1), Cons(0, x3)) -> c6(COND_MERGE_YS_ZS_2(False, Cons(S(z0), x1), Cons(0, x3), S(z0), x1, 0, x3))
   MERGE#2(Cons(S(0), x1), Cons(S(z0), x3)) -> c6(COND_MERGE_YS_ZS_2(True, Cons(S(0), x1), Cons(S(z0), x3), S(0), x1, S(z0), x3), LEQ#2(S(0), S(z0)))
   MERGE#2(Cons(S(S(z0)), x1), Cons(S(0), x3)) -> c6(COND_MERGE_YS_ZS_2(False, Cons(S(S(z0)), x1), Cons(S(0), x3), S(S(z0)), x1, S(0), x3), LEQ#2(S(S(z0)), S(0)))
   MERGE#2(Cons(S(S(z0)), x1), Cons(S(S(z1)), x3)) -> c6(COND_MERGE_YS_ZS_2(leq#2(z0, z1), Cons(S(S(z0)), x1), Cons(S(S(z1)), x3), S(S(z0)), x1, S(S(z1)), x3), LEQ#2(S(S(z0)), S(S(z1))))
   MERGE#2(Cons(S(x0), x1), Cons(S(x2), x3)) -> c6(LEQ#2(S(x0), S(x2)))
   DIVIDE_YS#1(Cons(x0, Cons(x1, x2)), S(y11)) -> c(TAKE#2(S(y11), Cons(x0, Cons(x1, x2))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, x3))), S(y11)) -> c(TAKE#2(S(y11), Cons(x0, Cons(x1, Cons(x2, x3)))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Nil)), S(y10)) -> c(TAKE#2(S(y10), Cons(x0, Cons(x1, Nil))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Nil))), S(y7)) -> c(TAKE#2(S(y7), Cons(x0, Cons(x1, Cons(x2, Nil)))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4)))), S(y8)) -> c(TAKE#2(S(y8), Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4))))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, x2)), S(y11)) -> c1(DROP#2(S(y11), Cons(x0, Cons(x1, x2))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, x3))), S(y11)) -> c1(DROP#2(S(y11), Cons(x0, Cons(x1, Cons(x2, x3)))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Nil)), S(y10)) -> c1(DROP#2(S(y10), Cons(x0, Cons(x1, Nil))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Nil))), S(y7)) -> c1(DROP#2(S(y7), Cons(x0, Cons(x1, Cons(x2, Nil)))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4)))), S(y8)) -> c1(DROP#2(S(y8), Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4))))))
   COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(S(y1), z3), z4, Cons(S(0), y0), z6, z7) -> c2(MERGE#2(Cons(S(0), y0), Cons(S(y1), z3)))
   COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(S(0), z3), z4, Cons(S(S(y0)), y1), z6, z7) -> c2(MERGE#2(Cons(S(S(y0)), y1), Cons(S(0), z3)))
   COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(S(S(y2)), z3), z4, Cons(S(S(y0)), y1), z6, z7) -> c2(MERGE#2(Cons(S(S(y0)), y1), Cons(S(S(y2)), z3)))
   COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(S(y2), z3), z4, Cons(S(y0), y1), z6, z7) -> c2(MERGE#2(Cons(S(y0), y1), Cons(S(y2), z3)))
   COND_MERGE_YS_ZS_2(False, Cons(S(x0), x1), Cons(0, x2), S(x0), x1, 0, x2) -> c3(MERGE#2(Cons(S(x0), x1), x2))
   COND_MERGE_YS_ZS_2(False, Cons(S(S(x0)), x1), Cons(S(0), x2), S(S(x0)), x1, S(0), x2) -> c3(MERGE#2(Cons(S(S(x0)), x1), x2))
   COND_MERGE_YS_ZS_2(False, Cons(S(S(x0)), x1), Cons(S(S(x2)), x3), S(S(x0)), x1, S(S(x2)), x3) -> c3(MERGE#2(Cons(S(S(x0)), x1), x3))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> c9(CONST_F#2(Cons(z0, Cons(z1, z2)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(Cons(z0, take#2(halve#1(length#1(z2)), Cons(z1, z2))), Cons(drop#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Nil))), DIVIDE_YS#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2)))), HALVE#1(length#1(z2)), LENGTH#1(z2))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, z3)))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Cons(z2, z3))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(S(length#1(z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Cons(drop#2(S(halve#1(length#1(Cons(z2, z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3)))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3))))), HALVE#1(S(length#1(z3))), LENGTH#1(Cons(z2, z3)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> c9(MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Nil))), DIVIDE_YS#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2)))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Nil))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(Nil))), Cons(z0, Cons(z1, Nil))), Cons(drop#2(S(halve#1(0)), Cons(z0, Cons(z1, Nil))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil)))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Nil))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(0)), Cons(z0, Cons(z1, Nil))), Cons(drop#2(S(halve#1(length#1(Nil))), Cons(z0, Cons(z1, Nil))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil)))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, z3)))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Cons(z2, z3))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(S(length#1(z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Cons(drop#2(S(halve#1(S(length#1(z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3)))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3))))), HALVE#1(S(length#1(z3))), LENGTH#1(Cons(z2, z3)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, Nil)))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Cons(z2, Nil))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, Nil))), S(halve#1(S(0)))))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, Nil))), S(halve#1(length#1(Cons(z2, Nil)))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, Nil))), S(halve#1(length#1(Cons(z2, Nil))))), HALVE#1(S(length#1(Nil))), LENGTH#1(Cons(z2, Nil)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, Cons(z3, z4))))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Cons(z2, Cons(z3, z4)))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, Cons(z3, z4)))), S(halve#1(S(S(length#1(z4)))))))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, Cons(z3, z4)))), S(halve#1(length#1(Cons(z2, Cons(z3, z4))))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, Cons(z3, z4)))), S(halve#1(length#1(Cons(z2, Cons(z3, z4)))))), HALVE#1(S(length#1(Cons(z3, z4)))), LENGTH#1(Cons(z2, Cons(z3, z4))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, z3)))) -> c9(MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3)))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3))))), HALVE#1(S(length#1(z3))), LENGTH#1(Cons(z2, z3)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Nil))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(0)), Cons(z0, Cons(z1, Nil))), Cons(drop#2(S(halve#1(0)), Cons(z0, Cons(z1, Nil))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil)))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Nil))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Nil)), S(0)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil)))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> c9(CONST_F#2(Cons(z0, Cons(z1, z2)), Cons(dc#1(map, divisible, mergesort_zs_3, divide, const_f, take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2)))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(drop#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(halve#1(length#1(z2)), Cons(z1, z2)), Nil))), DIVIDE_YS#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2)))), HALVE#1(length#1(z2)), LENGTH#1(z2))
   CONST_F#2(Cons(x0, Cons(x1, x2)), Cons(z1, Cons(z2, z3))) -> c19(MERGE#2(z1, z2))
   CONST_F#2(Cons(x0, Cons(x1, Cons(x2, x3))), Cons(z1, Cons(z2, z3))) -> c19(MERGE#2(z1, z2))
   CONST_F#2(Cons(x0, Cons(x1, Nil)), Cons(z1, Cons(z2, z3))) -> c19(MERGE#2(z1, z2))
   CONST_F#2(Cons(x0, Cons(x1, Cons(x2, Nil))), Cons(z1, Cons(z2, z3))) -> c19(MERGE#2(z1, z2))
   CONST_F#2(Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4)))), Cons(z1, Cons(z2, z3))) -> c19(MERGE#2(z1, z2))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> c9(CONST_F#2(Cons(z0, Cons(z1, z2)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(halve#1(length#1(z2)), Cons(z1, z2)), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(halve#1(length#1(z2)), Cons(z1, z2)), Nil))), DIVIDE_YS#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2)))), HALVE#1(length#1(z2)), LENGTH#1(z2))
   COND_MERGE_YS_ZS_2(True, Cons(0, Cons(0, z5)), Cons(x1, x2), 0, Cons(0, z5), x1, x2) -> c2(MERGE#2(Cons(0, z5), Cons(x1, x2)))
   COND_MERGE_YS_ZS_2(True, Cons(S(0), Cons(0, z5)), Cons(S(x1), x2), S(0), Cons(0, z5), S(x1), x2) -> c2(MERGE#2(Cons(0, z5), Cons(S(x1), x2)))
   COND_MERGE_YS_ZS_2(True, Cons(S(S(x0)), Cons(0, z5)), Cons(S(S(x2)), x3), S(S(x0)), Cons(0, z5), S(S(x2)), x3) -> c2(MERGE#2(Cons(0, z5), Cons(S(S(x2)), x3)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, z3)))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Cons(z2, z3))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(Cons(z2, z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Cons(drop#2(S(halve#1(S(length#1(z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3)))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(S(length#1(z3))))), HALVE#1(S(length#1(z3))), LENGTH#1(Cons(z2, z3)))
   COND_MERGE_YS_ZS_2(True, Cons(0, Cons(S(z4), z5)), Cons(0, x2), 0, Cons(S(z4), z5), 0, x2) -> c2(MERGE#2(Cons(S(z4), z5), Cons(0, x2)))
K tuples:none
Defined Rule Symbols:   leq#2_2, map#2_2, divide_ys#1_2, halve#1_1, length#1_1, take#2_2, drop#2_2, dc#1_6, const_f#2_2, merge#2_2, cond_merge_ys_zs_2_7

Defined Pair Symbols:   DROP#2_2, TAKE#2_2, HALVE#1_1, LEQ#2_2, LENGTH#1_1, MAP#2_2, MERGE#2_2, DIVIDE_YS#1_2, COND_MERGE_YS_ZS_2_7, DC#1_6, CONST_F#2_2

Compound Symbols:   c12_1, c15_1, c18_1, c22_1, c24_1, c26_1, c27_1, c6_1, c6_2, c_1, c1_1, c2_1, c3_1, c9_5, c9_2, c9_3, c9_4, c19_1


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(157) CdtRewritingProof (BOTH BOUNDS(ID, ID))
Used rewriting to replace DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> c9(CONST_F#2(Cons(z0, Cons(z1, z2)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(Cons(z0, take#2(halve#1(length#1(z2)), Cons(z1, z2))), Cons(drop#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Nil))), DIVIDE_YS#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2)))), HALVE#1(length#1(z2)), LENGTH#1(z2)) by DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> c9(CONST_F#2(Cons(z0, Cons(z1, z2)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(Cons(z0, take#2(halve#1(length#1(z2)), Cons(z1, z2))), Cons(drop#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(halve#1(length#1(z2)), Cons(z1, z2)), Nil))), DIVIDE_YS#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2)))), HALVE#1(length#1(z2)), LENGTH#1(z2))
----------------------------------------

(158)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   leq#2(0, z0) -> True
   leq#2(S(z0), 0) -> False
   leq#2(S(z0), S(z1)) -> leq#2(z0, z1)
   map#2(dc(z0, z1, z2, z3, z4), Nil) -> Nil
   map#2(dc(z0, z1, z2, z3, z4), Cons(z5, z6)) -> Cons(dc#1(z0, z1, z2, z3, z4, z5), map#2(dc(z0, z1, z2, z3, z4), z6))
   divide_ys#1(z0, z1) -> Cons(take#2(z1, z0), Cons(drop#2(z1, z0), Nil))
   halve#1(0) -> 0
   halve#1(S(0)) -> S(0)
   halve#1(S(S(z0))) -> S(halve#1(z0))
   length#1(Nil) -> 0
   length#1(Cons(z0, z1)) -> S(length#1(z1))
   take#2(0, z0) -> Nil
   take#2(S(0), Nil) -> Cons(bot[0], Nil)
   take#2(S(z0), Cons(z1, z2)) -> Cons(z1, take#2(z0, z2))
   drop#2(0, z0) -> z0
   drop#2(S(0), Nil) -> bot[1]
   drop#2(S(z0), Cons(z1, z2)) -> drop#2(z0, z2)
   dc#1(map, divisible, mergesort_zs_3, divide, const_f, Nil) -> Nil
   dc#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Nil)) -> Cons(z0, Nil)
   dc#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> const_f#2(Cons(z0, Cons(z1, z2)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2))))))
   const_f#2(z0, Cons(z1, Cons(z2, z3))) -> merge#2(z1, z2)
   merge#2(Nil, z0) -> z0
   merge#2(Cons(z0, z1), Nil) -> Cons(z0, z1)
   merge#2(Cons(z0, z1), Cons(z2, z3)) -> cond_merge_ys_zs_2(leq#2(z0, z2), Cons(z0, z1), Cons(z2, z3), z0, z1, z2, z3)
   cond_merge_ys_zs_2(True, Cons(z0, z1), Cons(z2, z3), z4, z5, z6, z7) -> Cons(z4, merge#2(z5, Cons(z2, z3)))
   cond_merge_ys_zs_2(False, Cons(z0, z1), Cons(z2, z3), z4, z5, z6, z7) -> Cons(z6, merge#2(Cons(z0, z1), z7))
Tuples:
   DROP#2(S(z0), Cons(z1, z2)) -> c12(DROP#2(z0, z2))
   TAKE#2(S(z0), Cons(z1, z2)) -> c15(TAKE#2(z0, z2))
   HALVE#1(S(S(z0))) -> c18(HALVE#1(z0))
   LEQ#2(S(z0), S(z1)) -> c22(LEQ#2(z0, z1))
   LENGTH#1(Cons(z0, z1)) -> c24(LENGTH#1(z1))
   MAP#2(dc(z0, z1, z2, z3, z4), Cons(z5, z6)) -> c26(DC#1(z0, z1, z2, z3, z4, z5))
   MAP#2(dc(z0, z1, z2, z3, z4), Cons(z5, z6)) -> c27(MAP#2(dc(z0, z1, z2, z3, z4), z6))
   MERGE#2(Cons(0, x1), Cons(z0, x3)) -> c6(COND_MERGE_YS_ZS_2(True, Cons(0, x1), Cons(z0, x3), 0, x1, z0, x3))
   MERGE#2(Cons(S(z0), x1), Cons(0, x3)) -> c6(COND_MERGE_YS_ZS_2(False, Cons(S(z0), x1), Cons(0, x3), S(z0), x1, 0, x3))
   MERGE#2(Cons(S(0), x1), Cons(S(z0), x3)) -> c6(COND_MERGE_YS_ZS_2(True, Cons(S(0), x1), Cons(S(z0), x3), S(0), x1, S(z0), x3), LEQ#2(S(0), S(z0)))
   MERGE#2(Cons(S(S(z0)), x1), Cons(S(0), x3)) -> c6(COND_MERGE_YS_ZS_2(False, Cons(S(S(z0)), x1), Cons(S(0), x3), S(S(z0)), x1, S(0), x3), LEQ#2(S(S(z0)), S(0)))
   MERGE#2(Cons(S(S(z0)), x1), Cons(S(S(z1)), x3)) -> c6(COND_MERGE_YS_ZS_2(leq#2(z0, z1), Cons(S(S(z0)), x1), Cons(S(S(z1)), x3), S(S(z0)), x1, S(S(z1)), x3), LEQ#2(S(S(z0)), S(S(z1))))
   MERGE#2(Cons(S(x0), x1), Cons(S(x2), x3)) -> c6(LEQ#2(S(x0), S(x2)))
   DIVIDE_YS#1(Cons(x0, Cons(x1, x2)), S(y11)) -> c(TAKE#2(S(y11), Cons(x0, Cons(x1, x2))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, x3))), S(y11)) -> c(TAKE#2(S(y11), Cons(x0, Cons(x1, Cons(x2, x3)))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Nil)), S(y10)) -> c(TAKE#2(S(y10), Cons(x0, Cons(x1, Nil))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Nil))), S(y7)) -> c(TAKE#2(S(y7), Cons(x0, Cons(x1, Cons(x2, Nil)))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4)))), S(y8)) -> c(TAKE#2(S(y8), Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4))))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, x2)), S(y11)) -> c1(DROP#2(S(y11), Cons(x0, Cons(x1, x2))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, x3))), S(y11)) -> c1(DROP#2(S(y11), Cons(x0, Cons(x1, Cons(x2, x3)))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Nil)), S(y10)) -> c1(DROP#2(S(y10), Cons(x0, Cons(x1, Nil))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Nil))), S(y7)) -> c1(DROP#2(S(y7), Cons(x0, Cons(x1, Cons(x2, Nil)))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4)))), S(y8)) -> c1(DROP#2(S(y8), Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4))))))
   COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(S(y1), z3), z4, Cons(S(0), y0), z6, z7) -> c2(MERGE#2(Cons(S(0), y0), Cons(S(y1), z3)))
   COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(S(0), z3), z4, Cons(S(S(y0)), y1), z6, z7) -> c2(MERGE#2(Cons(S(S(y0)), y1), Cons(S(0), z3)))
   COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(S(S(y2)), z3), z4, Cons(S(S(y0)), y1), z6, z7) -> c2(MERGE#2(Cons(S(S(y0)), y1), Cons(S(S(y2)), z3)))
   COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(S(y2), z3), z4, Cons(S(y0), y1), z6, z7) -> c2(MERGE#2(Cons(S(y0), y1), Cons(S(y2), z3)))
   COND_MERGE_YS_ZS_2(False, Cons(S(x0), x1), Cons(0, x2), S(x0), x1, 0, x2) -> c3(MERGE#2(Cons(S(x0), x1), x2))
   COND_MERGE_YS_ZS_2(False, Cons(S(S(x0)), x1), Cons(S(0), x2), S(S(x0)), x1, S(0), x2) -> c3(MERGE#2(Cons(S(S(x0)), x1), x2))
   COND_MERGE_YS_ZS_2(False, Cons(S(S(x0)), x1), Cons(S(S(x2)), x3), S(S(x0)), x1, S(S(x2)), x3) -> c3(MERGE#2(Cons(S(S(x0)), x1), x3))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, z3)))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Cons(z2, z3))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(S(length#1(z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Cons(drop#2(S(halve#1(length#1(Cons(z2, z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3)))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3))))), HALVE#1(S(length#1(z3))), LENGTH#1(Cons(z2, z3)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> c9(MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Nil))), DIVIDE_YS#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2)))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Nil))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(Nil))), Cons(z0, Cons(z1, Nil))), Cons(drop#2(S(halve#1(0)), Cons(z0, Cons(z1, Nil))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil)))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Nil))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(0)), Cons(z0, Cons(z1, Nil))), Cons(drop#2(S(halve#1(length#1(Nil))), Cons(z0, Cons(z1, Nil))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil)))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, z3)))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Cons(z2, z3))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(S(length#1(z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Cons(drop#2(S(halve#1(S(length#1(z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3)))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3))))), HALVE#1(S(length#1(z3))), LENGTH#1(Cons(z2, z3)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, Nil)))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Cons(z2, Nil))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, Nil))), S(halve#1(S(0)))))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, Nil))), S(halve#1(length#1(Cons(z2, Nil)))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, Nil))), S(halve#1(length#1(Cons(z2, Nil))))), HALVE#1(S(length#1(Nil))), LENGTH#1(Cons(z2, Nil)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, Cons(z3, z4))))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Cons(z2, Cons(z3, z4)))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, Cons(z3, z4)))), S(halve#1(S(S(length#1(z4)))))))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, Cons(z3, z4)))), S(halve#1(length#1(Cons(z2, Cons(z3, z4))))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, Cons(z3, z4)))), S(halve#1(length#1(Cons(z2, Cons(z3, z4)))))), HALVE#1(S(length#1(Cons(z3, z4)))), LENGTH#1(Cons(z2, Cons(z3, z4))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, z3)))) -> c9(MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3)))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3))))), HALVE#1(S(length#1(z3))), LENGTH#1(Cons(z2, z3)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Nil))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(0)), Cons(z0, Cons(z1, Nil))), Cons(drop#2(S(halve#1(0)), Cons(z0, Cons(z1, Nil))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil)))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Nil))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Nil)), S(0)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil)))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> c9(CONST_F#2(Cons(z0, Cons(z1, z2)), Cons(dc#1(map, divisible, mergesort_zs_3, divide, const_f, take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2)))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(drop#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(halve#1(length#1(z2)), Cons(z1, z2)), Nil))), DIVIDE_YS#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2)))), HALVE#1(length#1(z2)), LENGTH#1(z2))
   CONST_F#2(Cons(x0, Cons(x1, x2)), Cons(z1, Cons(z2, z3))) -> c19(MERGE#2(z1, z2))
   CONST_F#2(Cons(x0, Cons(x1, Cons(x2, x3))), Cons(z1, Cons(z2, z3))) -> c19(MERGE#2(z1, z2))
   CONST_F#2(Cons(x0, Cons(x1, Nil)), Cons(z1, Cons(z2, z3))) -> c19(MERGE#2(z1, z2))
   CONST_F#2(Cons(x0, Cons(x1, Cons(x2, Nil))), Cons(z1, Cons(z2, z3))) -> c19(MERGE#2(z1, z2))
   CONST_F#2(Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4)))), Cons(z1, Cons(z2, z3))) -> c19(MERGE#2(z1, z2))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> c9(CONST_F#2(Cons(z0, Cons(z1, z2)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(halve#1(length#1(z2)), Cons(z1, z2)), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(halve#1(length#1(z2)), Cons(z1, z2)), Nil))), DIVIDE_YS#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2)))), HALVE#1(length#1(z2)), LENGTH#1(z2))
   COND_MERGE_YS_ZS_2(True, Cons(0, Cons(0, z5)), Cons(x1, x2), 0, Cons(0, z5), x1, x2) -> c2(MERGE#2(Cons(0, z5), Cons(x1, x2)))
   COND_MERGE_YS_ZS_2(True, Cons(S(0), Cons(0, z5)), Cons(S(x1), x2), S(0), Cons(0, z5), S(x1), x2) -> c2(MERGE#2(Cons(0, z5), Cons(S(x1), x2)))
   COND_MERGE_YS_ZS_2(True, Cons(S(S(x0)), Cons(0, z5)), Cons(S(S(x2)), x3), S(S(x0)), Cons(0, z5), S(S(x2)), x3) -> c2(MERGE#2(Cons(0, z5), Cons(S(S(x2)), x3)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, z3)))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Cons(z2, z3))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(Cons(z2, z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Cons(drop#2(S(halve#1(S(length#1(z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3)))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(S(length#1(z3))))), HALVE#1(S(length#1(z3))), LENGTH#1(Cons(z2, z3)))
   COND_MERGE_YS_ZS_2(True, Cons(0, Cons(S(z4), z5)), Cons(0, x2), 0, Cons(S(z4), z5), 0, x2) -> c2(MERGE#2(Cons(S(z4), z5), Cons(0, x2)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> c9(CONST_F#2(Cons(z0, Cons(z1, z2)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(Cons(z0, take#2(halve#1(length#1(z2)), Cons(z1, z2))), Cons(drop#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(halve#1(length#1(z2)), Cons(z1, z2)), Nil))), DIVIDE_YS#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2)))), HALVE#1(length#1(z2)), LENGTH#1(z2))
S tuples:
   DROP#2(S(z0), Cons(z1, z2)) -> c12(DROP#2(z0, z2))
   TAKE#2(S(z0), Cons(z1, z2)) -> c15(TAKE#2(z0, z2))
   HALVE#1(S(S(z0))) -> c18(HALVE#1(z0))
   LEQ#2(S(z0), S(z1)) -> c22(LEQ#2(z0, z1))
   LENGTH#1(Cons(z0, z1)) -> c24(LENGTH#1(z1))
   MAP#2(dc(z0, z1, z2, z3, z4), Cons(z5, z6)) -> c26(DC#1(z0, z1, z2, z3, z4, z5))
   MAP#2(dc(z0, z1, z2, z3, z4), Cons(z5, z6)) -> c27(MAP#2(dc(z0, z1, z2, z3, z4), z6))
   MERGE#2(Cons(0, x1), Cons(z0, x3)) -> c6(COND_MERGE_YS_ZS_2(True, Cons(0, x1), Cons(z0, x3), 0, x1, z0, x3))
   MERGE#2(Cons(S(z0), x1), Cons(0, x3)) -> c6(COND_MERGE_YS_ZS_2(False, Cons(S(z0), x1), Cons(0, x3), S(z0), x1, 0, x3))
   MERGE#2(Cons(S(0), x1), Cons(S(z0), x3)) -> c6(COND_MERGE_YS_ZS_2(True, Cons(S(0), x1), Cons(S(z0), x3), S(0), x1, S(z0), x3), LEQ#2(S(0), S(z0)))
   MERGE#2(Cons(S(S(z0)), x1), Cons(S(0), x3)) -> c6(COND_MERGE_YS_ZS_2(False, Cons(S(S(z0)), x1), Cons(S(0), x3), S(S(z0)), x1, S(0), x3), LEQ#2(S(S(z0)), S(0)))
   MERGE#2(Cons(S(S(z0)), x1), Cons(S(S(z1)), x3)) -> c6(COND_MERGE_YS_ZS_2(leq#2(z0, z1), Cons(S(S(z0)), x1), Cons(S(S(z1)), x3), S(S(z0)), x1, S(S(z1)), x3), LEQ#2(S(S(z0)), S(S(z1))))
   MERGE#2(Cons(S(x0), x1), Cons(S(x2), x3)) -> c6(LEQ#2(S(x0), S(x2)))
   DIVIDE_YS#1(Cons(x0, Cons(x1, x2)), S(y11)) -> c(TAKE#2(S(y11), Cons(x0, Cons(x1, x2))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, x3))), S(y11)) -> c(TAKE#2(S(y11), Cons(x0, Cons(x1, Cons(x2, x3)))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Nil)), S(y10)) -> c(TAKE#2(S(y10), Cons(x0, Cons(x1, Nil))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Nil))), S(y7)) -> c(TAKE#2(S(y7), Cons(x0, Cons(x1, Cons(x2, Nil)))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4)))), S(y8)) -> c(TAKE#2(S(y8), Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4))))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, x2)), S(y11)) -> c1(DROP#2(S(y11), Cons(x0, Cons(x1, x2))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, x3))), S(y11)) -> c1(DROP#2(S(y11), Cons(x0, Cons(x1, Cons(x2, x3)))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Nil)), S(y10)) -> c1(DROP#2(S(y10), Cons(x0, Cons(x1, Nil))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Nil))), S(y7)) -> c1(DROP#2(S(y7), Cons(x0, Cons(x1, Cons(x2, Nil)))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4)))), S(y8)) -> c1(DROP#2(S(y8), Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4))))))
   COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(S(y1), z3), z4, Cons(S(0), y0), z6, z7) -> c2(MERGE#2(Cons(S(0), y0), Cons(S(y1), z3)))
   COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(S(0), z3), z4, Cons(S(S(y0)), y1), z6, z7) -> c2(MERGE#2(Cons(S(S(y0)), y1), Cons(S(0), z3)))
   COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(S(S(y2)), z3), z4, Cons(S(S(y0)), y1), z6, z7) -> c2(MERGE#2(Cons(S(S(y0)), y1), Cons(S(S(y2)), z3)))
   COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(S(y2), z3), z4, Cons(S(y0), y1), z6, z7) -> c2(MERGE#2(Cons(S(y0), y1), Cons(S(y2), z3)))
   COND_MERGE_YS_ZS_2(False, Cons(S(x0), x1), Cons(0, x2), S(x0), x1, 0, x2) -> c3(MERGE#2(Cons(S(x0), x1), x2))
   COND_MERGE_YS_ZS_2(False, Cons(S(S(x0)), x1), Cons(S(0), x2), S(S(x0)), x1, S(0), x2) -> c3(MERGE#2(Cons(S(S(x0)), x1), x2))
   COND_MERGE_YS_ZS_2(False, Cons(S(S(x0)), x1), Cons(S(S(x2)), x3), S(S(x0)), x1, S(S(x2)), x3) -> c3(MERGE#2(Cons(S(S(x0)), x1), x3))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, z3)))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Cons(z2, z3))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(S(length#1(z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Cons(drop#2(S(halve#1(length#1(Cons(z2, z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3)))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3))))), HALVE#1(S(length#1(z3))), LENGTH#1(Cons(z2, z3)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> c9(MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Nil))), DIVIDE_YS#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2)))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Nil))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(Nil))), Cons(z0, Cons(z1, Nil))), Cons(drop#2(S(halve#1(0)), Cons(z0, Cons(z1, Nil))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil)))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Nil))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(0)), Cons(z0, Cons(z1, Nil))), Cons(drop#2(S(halve#1(length#1(Nil))), Cons(z0, Cons(z1, Nil))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil)))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, z3)))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Cons(z2, z3))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(S(length#1(z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Cons(drop#2(S(halve#1(S(length#1(z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3)))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3))))), HALVE#1(S(length#1(z3))), LENGTH#1(Cons(z2, z3)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, Nil)))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Cons(z2, Nil))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, Nil))), S(halve#1(S(0)))))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, Nil))), S(halve#1(length#1(Cons(z2, Nil)))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, Nil))), S(halve#1(length#1(Cons(z2, Nil))))), HALVE#1(S(length#1(Nil))), LENGTH#1(Cons(z2, Nil)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, Cons(z3, z4))))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Cons(z2, Cons(z3, z4)))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, Cons(z3, z4)))), S(halve#1(S(S(length#1(z4)))))))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, Cons(z3, z4)))), S(halve#1(length#1(Cons(z2, Cons(z3, z4))))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, Cons(z3, z4)))), S(halve#1(length#1(Cons(z2, Cons(z3, z4)))))), HALVE#1(S(length#1(Cons(z3, z4)))), LENGTH#1(Cons(z2, Cons(z3, z4))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, z3)))) -> c9(MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3)))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3))))), HALVE#1(S(length#1(z3))), LENGTH#1(Cons(z2, z3)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Nil))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(0)), Cons(z0, Cons(z1, Nil))), Cons(drop#2(S(halve#1(0)), Cons(z0, Cons(z1, Nil))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil)))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Nil))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Nil)), S(0)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil)))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> c9(CONST_F#2(Cons(z0, Cons(z1, z2)), Cons(dc#1(map, divisible, mergesort_zs_3, divide, const_f, take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2)))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(drop#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(halve#1(length#1(z2)), Cons(z1, z2)), Nil))), DIVIDE_YS#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2)))), HALVE#1(length#1(z2)), LENGTH#1(z2))
   CONST_F#2(Cons(x0, Cons(x1, x2)), Cons(z1, Cons(z2, z3))) -> c19(MERGE#2(z1, z2))
   CONST_F#2(Cons(x0, Cons(x1, Cons(x2, x3))), Cons(z1, Cons(z2, z3))) -> c19(MERGE#2(z1, z2))
   CONST_F#2(Cons(x0, Cons(x1, Nil)), Cons(z1, Cons(z2, z3))) -> c19(MERGE#2(z1, z2))
   CONST_F#2(Cons(x0, Cons(x1, Cons(x2, Nil))), Cons(z1, Cons(z2, z3))) -> c19(MERGE#2(z1, z2))
   CONST_F#2(Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4)))), Cons(z1, Cons(z2, z3))) -> c19(MERGE#2(z1, z2))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> c9(CONST_F#2(Cons(z0, Cons(z1, z2)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(halve#1(length#1(z2)), Cons(z1, z2)), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(halve#1(length#1(z2)), Cons(z1, z2)), Nil))), DIVIDE_YS#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2)))), HALVE#1(length#1(z2)), LENGTH#1(z2))
   COND_MERGE_YS_ZS_2(True, Cons(0, Cons(0, z5)), Cons(x1, x2), 0, Cons(0, z5), x1, x2) -> c2(MERGE#2(Cons(0, z5), Cons(x1, x2)))
   COND_MERGE_YS_ZS_2(True, Cons(S(0), Cons(0, z5)), Cons(S(x1), x2), S(0), Cons(0, z5), S(x1), x2) -> c2(MERGE#2(Cons(0, z5), Cons(S(x1), x2)))
   COND_MERGE_YS_ZS_2(True, Cons(S(S(x0)), Cons(0, z5)), Cons(S(S(x2)), x3), S(S(x0)), Cons(0, z5), S(S(x2)), x3) -> c2(MERGE#2(Cons(0, z5), Cons(S(S(x2)), x3)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, z3)))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Cons(z2, z3))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(Cons(z2, z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Cons(drop#2(S(halve#1(S(length#1(z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3)))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(S(length#1(z3))))), HALVE#1(S(length#1(z3))), LENGTH#1(Cons(z2, z3)))
   COND_MERGE_YS_ZS_2(True, Cons(0, Cons(S(z4), z5)), Cons(0, x2), 0, Cons(S(z4), z5), 0, x2) -> c2(MERGE#2(Cons(S(z4), z5), Cons(0, x2)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> c9(CONST_F#2(Cons(z0, Cons(z1, z2)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(Cons(z0, take#2(halve#1(length#1(z2)), Cons(z1, z2))), Cons(drop#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(halve#1(length#1(z2)), Cons(z1, z2)), Nil))), DIVIDE_YS#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2)))), HALVE#1(length#1(z2)), LENGTH#1(z2))
K tuples:none
Defined Rule Symbols:   leq#2_2, map#2_2, divide_ys#1_2, halve#1_1, length#1_1, take#2_2, drop#2_2, dc#1_6, const_f#2_2, merge#2_2, cond_merge_ys_zs_2_7

Defined Pair Symbols:   DROP#2_2, TAKE#2_2, HALVE#1_1, LEQ#2_2, LENGTH#1_1, MAP#2_2, MERGE#2_2, DIVIDE_YS#1_2, COND_MERGE_YS_ZS_2_7, DC#1_6, CONST_F#2_2

Compound Symbols:   c12_1, c15_1, c18_1, c22_1, c24_1, c26_1, c27_1, c6_1, c6_2, c_1, c1_1, c2_1, c3_1, c9_5, c9_2, c9_3, c9_4, c19_1


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(159) CdtInstantiationProof (BOTH BOUNDS(ID, ID))
Use instantiation to replace COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(S(y1), z3), z4, Cons(S(0), y0), z6, z7) -> c2(MERGE#2(Cons(S(0), y0), Cons(S(y1), z3))) by 
   COND_MERGE_YS_ZS_2(True, Cons(0, Cons(S(0), z5)), Cons(S(z2), x2), 0, Cons(S(0), z5), S(z2), x2) -> c2(MERGE#2(Cons(S(0), z5), Cons(S(z2), x2)))
   COND_MERGE_YS_ZS_2(True, Cons(S(0), Cons(S(0), z5)), Cons(S(x1), x2), S(0), Cons(S(0), z5), S(x1), x2) -> c2(MERGE#2(Cons(S(0), z5), Cons(S(x1), x2)))
   COND_MERGE_YS_ZS_2(True, Cons(S(S(x0)), Cons(S(0), z5)), Cons(S(S(x2)), x3), S(S(x0)), Cons(S(0), z5), S(S(x2)), x3) -> c2(MERGE#2(Cons(S(0), z5), Cons(S(S(x2)), x3)))

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(160)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   leq#2(0, z0) -> True
   leq#2(S(z0), 0) -> False
   leq#2(S(z0), S(z1)) -> leq#2(z0, z1)
   map#2(dc(z0, z1, z2, z3, z4), Nil) -> Nil
   map#2(dc(z0, z1, z2, z3, z4), Cons(z5, z6)) -> Cons(dc#1(z0, z1, z2, z3, z4, z5), map#2(dc(z0, z1, z2, z3, z4), z6))
   divide_ys#1(z0, z1) -> Cons(take#2(z1, z0), Cons(drop#2(z1, z0), Nil))
   halve#1(0) -> 0
   halve#1(S(0)) -> S(0)
   halve#1(S(S(z0))) -> S(halve#1(z0))
   length#1(Nil) -> 0
   length#1(Cons(z0, z1)) -> S(length#1(z1))
   take#2(0, z0) -> Nil
   take#2(S(0), Nil) -> Cons(bot[0], Nil)
   take#2(S(z0), Cons(z1, z2)) -> Cons(z1, take#2(z0, z2))
   drop#2(0, z0) -> z0
   drop#2(S(0), Nil) -> bot[1]
   drop#2(S(z0), Cons(z1, z2)) -> drop#2(z0, z2)
   dc#1(map, divisible, mergesort_zs_3, divide, const_f, Nil) -> Nil
   dc#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Nil)) -> Cons(z0, Nil)
   dc#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> const_f#2(Cons(z0, Cons(z1, z2)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2))))))
   const_f#2(z0, Cons(z1, Cons(z2, z3))) -> merge#2(z1, z2)
   merge#2(Nil, z0) -> z0
   merge#2(Cons(z0, z1), Nil) -> Cons(z0, z1)
   merge#2(Cons(z0, z1), Cons(z2, z3)) -> cond_merge_ys_zs_2(leq#2(z0, z2), Cons(z0, z1), Cons(z2, z3), z0, z1, z2, z3)
   cond_merge_ys_zs_2(True, Cons(z0, z1), Cons(z2, z3), z4, z5, z6, z7) -> Cons(z4, merge#2(z5, Cons(z2, z3)))
   cond_merge_ys_zs_2(False, Cons(z0, z1), Cons(z2, z3), z4, z5, z6, z7) -> Cons(z6, merge#2(Cons(z0, z1), z7))
Tuples:
   DROP#2(S(z0), Cons(z1, z2)) -> c12(DROP#2(z0, z2))
   TAKE#2(S(z0), Cons(z1, z2)) -> c15(TAKE#2(z0, z2))
   HALVE#1(S(S(z0))) -> c18(HALVE#1(z0))
   LEQ#2(S(z0), S(z1)) -> c22(LEQ#2(z0, z1))
   LENGTH#1(Cons(z0, z1)) -> c24(LENGTH#1(z1))
   MAP#2(dc(z0, z1, z2, z3, z4), Cons(z5, z6)) -> c26(DC#1(z0, z1, z2, z3, z4, z5))
   MAP#2(dc(z0, z1, z2, z3, z4), Cons(z5, z6)) -> c27(MAP#2(dc(z0, z1, z2, z3, z4), z6))
   MERGE#2(Cons(0, x1), Cons(z0, x3)) -> c6(COND_MERGE_YS_ZS_2(True, Cons(0, x1), Cons(z0, x3), 0, x1, z0, x3))
   MERGE#2(Cons(S(z0), x1), Cons(0, x3)) -> c6(COND_MERGE_YS_ZS_2(False, Cons(S(z0), x1), Cons(0, x3), S(z0), x1, 0, x3))
   MERGE#2(Cons(S(0), x1), Cons(S(z0), x3)) -> c6(COND_MERGE_YS_ZS_2(True, Cons(S(0), x1), Cons(S(z0), x3), S(0), x1, S(z0), x3), LEQ#2(S(0), S(z0)))
   MERGE#2(Cons(S(S(z0)), x1), Cons(S(0), x3)) -> c6(COND_MERGE_YS_ZS_2(False, Cons(S(S(z0)), x1), Cons(S(0), x3), S(S(z0)), x1, S(0), x3), LEQ#2(S(S(z0)), S(0)))
   MERGE#2(Cons(S(S(z0)), x1), Cons(S(S(z1)), x3)) -> c6(COND_MERGE_YS_ZS_2(leq#2(z0, z1), Cons(S(S(z0)), x1), Cons(S(S(z1)), x3), S(S(z0)), x1, S(S(z1)), x3), LEQ#2(S(S(z0)), S(S(z1))))
   MERGE#2(Cons(S(x0), x1), Cons(S(x2), x3)) -> c6(LEQ#2(S(x0), S(x2)))
   DIVIDE_YS#1(Cons(x0, Cons(x1, x2)), S(y11)) -> c(TAKE#2(S(y11), Cons(x0, Cons(x1, x2))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, x3))), S(y11)) -> c(TAKE#2(S(y11), Cons(x0, Cons(x1, Cons(x2, x3)))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Nil)), S(y10)) -> c(TAKE#2(S(y10), Cons(x0, Cons(x1, Nil))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Nil))), S(y7)) -> c(TAKE#2(S(y7), Cons(x0, Cons(x1, Cons(x2, Nil)))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4)))), S(y8)) -> c(TAKE#2(S(y8), Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4))))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, x2)), S(y11)) -> c1(DROP#2(S(y11), Cons(x0, Cons(x1, x2))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, x3))), S(y11)) -> c1(DROP#2(S(y11), Cons(x0, Cons(x1, Cons(x2, x3)))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Nil)), S(y10)) -> c1(DROP#2(S(y10), Cons(x0, Cons(x1, Nil))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Nil))), S(y7)) -> c1(DROP#2(S(y7), Cons(x0, Cons(x1, Cons(x2, Nil)))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4)))), S(y8)) -> c1(DROP#2(S(y8), Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4))))))
   COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(S(0), z3), z4, Cons(S(S(y0)), y1), z6, z7) -> c2(MERGE#2(Cons(S(S(y0)), y1), Cons(S(0), z3)))
   COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(S(S(y2)), z3), z4, Cons(S(S(y0)), y1), z6, z7) -> c2(MERGE#2(Cons(S(S(y0)), y1), Cons(S(S(y2)), z3)))
   COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(S(y2), z3), z4, Cons(S(y0), y1), z6, z7) -> c2(MERGE#2(Cons(S(y0), y1), Cons(S(y2), z3)))
   COND_MERGE_YS_ZS_2(False, Cons(S(x0), x1), Cons(0, x2), S(x0), x1, 0, x2) -> c3(MERGE#2(Cons(S(x0), x1), x2))
   COND_MERGE_YS_ZS_2(False, Cons(S(S(x0)), x1), Cons(S(0), x2), S(S(x0)), x1, S(0), x2) -> c3(MERGE#2(Cons(S(S(x0)), x1), x2))
   COND_MERGE_YS_ZS_2(False, Cons(S(S(x0)), x1), Cons(S(S(x2)), x3), S(S(x0)), x1, S(S(x2)), x3) -> c3(MERGE#2(Cons(S(S(x0)), x1), x3))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, z3)))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Cons(z2, z3))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(S(length#1(z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Cons(drop#2(S(halve#1(length#1(Cons(z2, z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3)))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3))))), HALVE#1(S(length#1(z3))), LENGTH#1(Cons(z2, z3)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> c9(MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Nil))), DIVIDE_YS#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2)))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Nil))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(Nil))), Cons(z0, Cons(z1, Nil))), Cons(drop#2(S(halve#1(0)), Cons(z0, Cons(z1, Nil))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil)))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Nil))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(0)), Cons(z0, Cons(z1, Nil))), Cons(drop#2(S(halve#1(length#1(Nil))), Cons(z0, Cons(z1, Nil))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil)))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, z3)))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Cons(z2, z3))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(S(length#1(z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Cons(drop#2(S(halve#1(S(length#1(z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3)))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3))))), HALVE#1(S(length#1(z3))), LENGTH#1(Cons(z2, z3)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, Nil)))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Cons(z2, Nil))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, Nil))), S(halve#1(S(0)))))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, Nil))), S(halve#1(length#1(Cons(z2, Nil)))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, Nil))), S(halve#1(length#1(Cons(z2, Nil))))), HALVE#1(S(length#1(Nil))), LENGTH#1(Cons(z2, Nil)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, Cons(z3, z4))))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Cons(z2, Cons(z3, z4)))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, Cons(z3, z4)))), S(halve#1(S(S(length#1(z4)))))))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, Cons(z3, z4)))), S(halve#1(length#1(Cons(z2, Cons(z3, z4))))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, Cons(z3, z4)))), S(halve#1(length#1(Cons(z2, Cons(z3, z4)))))), HALVE#1(S(length#1(Cons(z3, z4)))), LENGTH#1(Cons(z2, Cons(z3, z4))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, z3)))) -> c9(MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3)))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3))))), HALVE#1(S(length#1(z3))), LENGTH#1(Cons(z2, z3)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Nil))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(0)), Cons(z0, Cons(z1, Nil))), Cons(drop#2(S(halve#1(0)), Cons(z0, Cons(z1, Nil))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil)))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Nil))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Nil)), S(0)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil)))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> c9(CONST_F#2(Cons(z0, Cons(z1, z2)), Cons(dc#1(map, divisible, mergesort_zs_3, divide, const_f, take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2)))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(drop#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(halve#1(length#1(z2)), Cons(z1, z2)), Nil))), DIVIDE_YS#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2)))), HALVE#1(length#1(z2)), LENGTH#1(z2))
   CONST_F#2(Cons(x0, Cons(x1, x2)), Cons(z1, Cons(z2, z3))) -> c19(MERGE#2(z1, z2))
   CONST_F#2(Cons(x0, Cons(x1, Cons(x2, x3))), Cons(z1, Cons(z2, z3))) -> c19(MERGE#2(z1, z2))
   CONST_F#2(Cons(x0, Cons(x1, Nil)), Cons(z1, Cons(z2, z3))) -> c19(MERGE#2(z1, z2))
   CONST_F#2(Cons(x0, Cons(x1, Cons(x2, Nil))), Cons(z1, Cons(z2, z3))) -> c19(MERGE#2(z1, z2))
   CONST_F#2(Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4)))), Cons(z1, Cons(z2, z3))) -> c19(MERGE#2(z1, z2))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> c9(CONST_F#2(Cons(z0, Cons(z1, z2)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(halve#1(length#1(z2)), Cons(z1, z2)), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(halve#1(length#1(z2)), Cons(z1, z2)), Nil))), DIVIDE_YS#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2)))), HALVE#1(length#1(z2)), LENGTH#1(z2))
   COND_MERGE_YS_ZS_2(True, Cons(0, Cons(0, z5)), Cons(x1, x2), 0, Cons(0, z5), x1, x2) -> c2(MERGE#2(Cons(0, z5), Cons(x1, x2)))
   COND_MERGE_YS_ZS_2(True, Cons(S(0), Cons(0, z5)), Cons(S(x1), x2), S(0), Cons(0, z5), S(x1), x2) -> c2(MERGE#2(Cons(0, z5), Cons(S(x1), x2)))
   COND_MERGE_YS_ZS_2(True, Cons(S(S(x0)), Cons(0, z5)), Cons(S(S(x2)), x3), S(S(x0)), Cons(0, z5), S(S(x2)), x3) -> c2(MERGE#2(Cons(0, z5), Cons(S(S(x2)), x3)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, z3)))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Cons(z2, z3))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(Cons(z2, z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Cons(drop#2(S(halve#1(S(length#1(z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3)))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(S(length#1(z3))))), HALVE#1(S(length#1(z3))), LENGTH#1(Cons(z2, z3)))
   COND_MERGE_YS_ZS_2(True, Cons(0, Cons(S(z4), z5)), Cons(0, x2), 0, Cons(S(z4), z5), 0, x2) -> c2(MERGE#2(Cons(S(z4), z5), Cons(0, x2)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> c9(CONST_F#2(Cons(z0, Cons(z1, z2)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(Cons(z0, take#2(halve#1(length#1(z2)), Cons(z1, z2))), Cons(drop#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(halve#1(length#1(z2)), Cons(z1, z2)), Nil))), DIVIDE_YS#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2)))), HALVE#1(length#1(z2)), LENGTH#1(z2))
   COND_MERGE_YS_ZS_2(True, Cons(0, Cons(S(0), z5)), Cons(S(z2), x2), 0, Cons(S(0), z5), S(z2), x2) -> c2(MERGE#2(Cons(S(0), z5), Cons(S(z2), x2)))
   COND_MERGE_YS_ZS_2(True, Cons(S(0), Cons(S(0), z5)), Cons(S(x1), x2), S(0), Cons(S(0), z5), S(x1), x2) -> c2(MERGE#2(Cons(S(0), z5), Cons(S(x1), x2)))
   COND_MERGE_YS_ZS_2(True, Cons(S(S(x0)), Cons(S(0), z5)), Cons(S(S(x2)), x3), S(S(x0)), Cons(S(0), z5), S(S(x2)), x3) -> c2(MERGE#2(Cons(S(0), z5), Cons(S(S(x2)), x3)))
S tuples:
   DROP#2(S(z0), Cons(z1, z2)) -> c12(DROP#2(z0, z2))
   TAKE#2(S(z0), Cons(z1, z2)) -> c15(TAKE#2(z0, z2))
   HALVE#1(S(S(z0))) -> c18(HALVE#1(z0))
   LEQ#2(S(z0), S(z1)) -> c22(LEQ#2(z0, z1))
   LENGTH#1(Cons(z0, z1)) -> c24(LENGTH#1(z1))
   MAP#2(dc(z0, z1, z2, z3, z4), Cons(z5, z6)) -> c26(DC#1(z0, z1, z2, z3, z4, z5))
   MAP#2(dc(z0, z1, z2, z3, z4), Cons(z5, z6)) -> c27(MAP#2(dc(z0, z1, z2, z3, z4), z6))
   MERGE#2(Cons(0, x1), Cons(z0, x3)) -> c6(COND_MERGE_YS_ZS_2(True, Cons(0, x1), Cons(z0, x3), 0, x1, z0, x3))
   MERGE#2(Cons(S(z0), x1), Cons(0, x3)) -> c6(COND_MERGE_YS_ZS_2(False, Cons(S(z0), x1), Cons(0, x3), S(z0), x1, 0, x3))
   MERGE#2(Cons(S(0), x1), Cons(S(z0), x3)) -> c6(COND_MERGE_YS_ZS_2(True, Cons(S(0), x1), Cons(S(z0), x3), S(0), x1, S(z0), x3), LEQ#2(S(0), S(z0)))
   MERGE#2(Cons(S(S(z0)), x1), Cons(S(0), x3)) -> c6(COND_MERGE_YS_ZS_2(False, Cons(S(S(z0)), x1), Cons(S(0), x3), S(S(z0)), x1, S(0), x3), LEQ#2(S(S(z0)), S(0)))
   MERGE#2(Cons(S(S(z0)), x1), Cons(S(S(z1)), x3)) -> c6(COND_MERGE_YS_ZS_2(leq#2(z0, z1), Cons(S(S(z0)), x1), Cons(S(S(z1)), x3), S(S(z0)), x1, S(S(z1)), x3), LEQ#2(S(S(z0)), S(S(z1))))
   MERGE#2(Cons(S(x0), x1), Cons(S(x2), x3)) -> c6(LEQ#2(S(x0), S(x2)))
   DIVIDE_YS#1(Cons(x0, Cons(x1, x2)), S(y11)) -> c(TAKE#2(S(y11), Cons(x0, Cons(x1, x2))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, x3))), S(y11)) -> c(TAKE#2(S(y11), Cons(x0, Cons(x1, Cons(x2, x3)))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Nil)), S(y10)) -> c(TAKE#2(S(y10), Cons(x0, Cons(x1, Nil))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Nil))), S(y7)) -> c(TAKE#2(S(y7), Cons(x0, Cons(x1, Cons(x2, Nil)))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4)))), S(y8)) -> c(TAKE#2(S(y8), Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4))))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, x2)), S(y11)) -> c1(DROP#2(S(y11), Cons(x0, Cons(x1, x2))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, x3))), S(y11)) -> c1(DROP#2(S(y11), Cons(x0, Cons(x1, Cons(x2, x3)))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Nil)), S(y10)) -> c1(DROP#2(S(y10), Cons(x0, Cons(x1, Nil))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Nil))), S(y7)) -> c1(DROP#2(S(y7), Cons(x0, Cons(x1, Cons(x2, Nil)))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4)))), S(y8)) -> c1(DROP#2(S(y8), Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4))))))
   COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(S(0), z3), z4, Cons(S(S(y0)), y1), z6, z7) -> c2(MERGE#2(Cons(S(S(y0)), y1), Cons(S(0), z3)))
   COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(S(S(y2)), z3), z4, Cons(S(S(y0)), y1), z6, z7) -> c2(MERGE#2(Cons(S(S(y0)), y1), Cons(S(S(y2)), z3)))
   COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(S(y2), z3), z4, Cons(S(y0), y1), z6, z7) -> c2(MERGE#2(Cons(S(y0), y1), Cons(S(y2), z3)))
   COND_MERGE_YS_ZS_2(False, Cons(S(x0), x1), Cons(0, x2), S(x0), x1, 0, x2) -> c3(MERGE#2(Cons(S(x0), x1), x2))
   COND_MERGE_YS_ZS_2(False, Cons(S(S(x0)), x1), Cons(S(0), x2), S(S(x0)), x1, S(0), x2) -> c3(MERGE#2(Cons(S(S(x0)), x1), x2))
   COND_MERGE_YS_ZS_2(False, Cons(S(S(x0)), x1), Cons(S(S(x2)), x3), S(S(x0)), x1, S(S(x2)), x3) -> c3(MERGE#2(Cons(S(S(x0)), x1), x3))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, z3)))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Cons(z2, z3))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(S(length#1(z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Cons(drop#2(S(halve#1(length#1(Cons(z2, z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3)))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3))))), HALVE#1(S(length#1(z3))), LENGTH#1(Cons(z2, z3)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> c9(MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Nil))), DIVIDE_YS#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2)))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Nil))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(Nil))), Cons(z0, Cons(z1, Nil))), Cons(drop#2(S(halve#1(0)), Cons(z0, Cons(z1, Nil))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil)))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Nil))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(0)), Cons(z0, Cons(z1, Nil))), Cons(drop#2(S(halve#1(length#1(Nil))), Cons(z0, Cons(z1, Nil))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil)))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, z3)))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Cons(z2, z3))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(S(length#1(z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Cons(drop#2(S(halve#1(S(length#1(z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3)))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3))))), HALVE#1(S(length#1(z3))), LENGTH#1(Cons(z2, z3)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, Nil)))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Cons(z2, Nil))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, Nil))), S(halve#1(S(0)))))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, Nil))), S(halve#1(length#1(Cons(z2, Nil)))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, Nil))), S(halve#1(length#1(Cons(z2, Nil))))), HALVE#1(S(length#1(Nil))), LENGTH#1(Cons(z2, Nil)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, Cons(z3, z4))))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Cons(z2, Cons(z3, z4)))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, Cons(z3, z4)))), S(halve#1(S(S(length#1(z4)))))))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, Cons(z3, z4)))), S(halve#1(length#1(Cons(z2, Cons(z3, z4))))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, Cons(z3, z4)))), S(halve#1(length#1(Cons(z2, Cons(z3, z4)))))), HALVE#1(S(length#1(Cons(z3, z4)))), LENGTH#1(Cons(z2, Cons(z3, z4))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, z3)))) -> c9(MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3)))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3))))), HALVE#1(S(length#1(z3))), LENGTH#1(Cons(z2, z3)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Nil))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(0)), Cons(z0, Cons(z1, Nil))), Cons(drop#2(S(halve#1(0)), Cons(z0, Cons(z1, Nil))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil)))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Nil))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Nil)), S(0)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil)))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> c9(CONST_F#2(Cons(z0, Cons(z1, z2)), Cons(dc#1(map, divisible, mergesort_zs_3, divide, const_f, take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2)))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(drop#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(halve#1(length#1(z2)), Cons(z1, z2)), Nil))), DIVIDE_YS#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2)))), HALVE#1(length#1(z2)), LENGTH#1(z2))
   CONST_F#2(Cons(x0, Cons(x1, x2)), Cons(z1, Cons(z2, z3))) -> c19(MERGE#2(z1, z2))
   CONST_F#2(Cons(x0, Cons(x1, Cons(x2, x3))), Cons(z1, Cons(z2, z3))) -> c19(MERGE#2(z1, z2))
   CONST_F#2(Cons(x0, Cons(x1, Nil)), Cons(z1, Cons(z2, z3))) -> c19(MERGE#2(z1, z2))
   CONST_F#2(Cons(x0, Cons(x1, Cons(x2, Nil))), Cons(z1, Cons(z2, z3))) -> c19(MERGE#2(z1, z2))
   CONST_F#2(Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4)))), Cons(z1, Cons(z2, z3))) -> c19(MERGE#2(z1, z2))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> c9(CONST_F#2(Cons(z0, Cons(z1, z2)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(halve#1(length#1(z2)), Cons(z1, z2)), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(halve#1(length#1(z2)), Cons(z1, z2)), Nil))), DIVIDE_YS#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2)))), HALVE#1(length#1(z2)), LENGTH#1(z2))
   COND_MERGE_YS_ZS_2(True, Cons(0, Cons(0, z5)), Cons(x1, x2), 0, Cons(0, z5), x1, x2) -> c2(MERGE#2(Cons(0, z5), Cons(x1, x2)))
   COND_MERGE_YS_ZS_2(True, Cons(S(0), Cons(0, z5)), Cons(S(x1), x2), S(0), Cons(0, z5), S(x1), x2) -> c2(MERGE#2(Cons(0, z5), Cons(S(x1), x2)))
   COND_MERGE_YS_ZS_2(True, Cons(S(S(x0)), Cons(0, z5)), Cons(S(S(x2)), x3), S(S(x0)), Cons(0, z5), S(S(x2)), x3) -> c2(MERGE#2(Cons(0, z5), Cons(S(S(x2)), x3)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, z3)))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Cons(z2, z3))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(Cons(z2, z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Cons(drop#2(S(halve#1(S(length#1(z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3)))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(S(length#1(z3))))), HALVE#1(S(length#1(z3))), LENGTH#1(Cons(z2, z3)))
   COND_MERGE_YS_ZS_2(True, Cons(0, Cons(S(z4), z5)), Cons(0, x2), 0, Cons(S(z4), z5), 0, x2) -> c2(MERGE#2(Cons(S(z4), z5), Cons(0, x2)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> c9(CONST_F#2(Cons(z0, Cons(z1, z2)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(Cons(z0, take#2(halve#1(length#1(z2)), Cons(z1, z2))), Cons(drop#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(halve#1(length#1(z2)), Cons(z1, z2)), Nil))), DIVIDE_YS#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2)))), HALVE#1(length#1(z2)), LENGTH#1(z2))
   COND_MERGE_YS_ZS_2(True, Cons(0, Cons(S(0), z5)), Cons(S(z2), x2), 0, Cons(S(0), z5), S(z2), x2) -> c2(MERGE#2(Cons(S(0), z5), Cons(S(z2), x2)))
   COND_MERGE_YS_ZS_2(True, Cons(S(0), Cons(S(0), z5)), Cons(S(x1), x2), S(0), Cons(S(0), z5), S(x1), x2) -> c2(MERGE#2(Cons(S(0), z5), Cons(S(x1), x2)))
   COND_MERGE_YS_ZS_2(True, Cons(S(S(x0)), Cons(S(0), z5)), Cons(S(S(x2)), x3), S(S(x0)), Cons(S(0), z5), S(S(x2)), x3) -> c2(MERGE#2(Cons(S(0), z5), Cons(S(S(x2)), x3)))
K tuples:none
Defined Rule Symbols:   leq#2_2, map#2_2, divide_ys#1_2, halve#1_1, length#1_1, take#2_2, drop#2_2, dc#1_6, const_f#2_2, merge#2_2, cond_merge_ys_zs_2_7

Defined Pair Symbols:   DROP#2_2, TAKE#2_2, HALVE#1_1, LEQ#2_2, LENGTH#1_1, MAP#2_2, MERGE#2_2, DIVIDE_YS#1_2, COND_MERGE_YS_ZS_2_7, DC#1_6, CONST_F#2_2

Compound Symbols:   c12_1, c15_1, c18_1, c22_1, c24_1, c26_1, c27_1, c6_1, c6_2, c_1, c1_1, c2_1, c3_1, c9_5, c9_2, c9_3, c9_4, c19_1


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

(161) CdtRewritingProof (BOTH BOUNDS(ID, ID))
Used rewriting to replace DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, z3)))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Cons(z2, z3))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(S(length#1(z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Cons(drop#2(S(halve#1(length#1(Cons(z2, z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3)))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3))))), HALVE#1(S(length#1(z3))), LENGTH#1(Cons(z2, z3))) by DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, z3)))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Cons(z2, z3))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(S(length#1(z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Cons(drop#2(S(halve#1(length#1(Cons(z2, z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3)))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(S(length#1(z3))))), HALVE#1(S(length#1(z3))), LENGTH#1(Cons(z2, z3)))
----------------------------------------

(162)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   leq#2(0, z0) -> True
   leq#2(S(z0), 0) -> False
   leq#2(S(z0), S(z1)) -> leq#2(z0, z1)
   map#2(dc(z0, z1, z2, z3, z4), Nil) -> Nil
   map#2(dc(z0, z1, z2, z3, z4), Cons(z5, z6)) -> Cons(dc#1(z0, z1, z2, z3, z4, z5), map#2(dc(z0, z1, z2, z3, z4), z6))
   divide_ys#1(z0, z1) -> Cons(take#2(z1, z0), Cons(drop#2(z1, z0), Nil))
   halve#1(0) -> 0
   halve#1(S(0)) -> S(0)
   halve#1(S(S(z0))) -> S(halve#1(z0))
   length#1(Nil) -> 0
   length#1(Cons(z0, z1)) -> S(length#1(z1))
   take#2(0, z0) -> Nil
   take#2(S(0), Nil) -> Cons(bot[0], Nil)
   take#2(S(z0), Cons(z1, z2)) -> Cons(z1, take#2(z0, z2))
   drop#2(0, z0) -> z0
   drop#2(S(0), Nil) -> bot[1]
   drop#2(S(z0), Cons(z1, z2)) -> drop#2(z0, z2)
   dc#1(map, divisible, mergesort_zs_3, divide, const_f, Nil) -> Nil
   dc#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Nil)) -> Cons(z0, Nil)
   dc#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> const_f#2(Cons(z0, Cons(z1, z2)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2))))))
   const_f#2(z0, Cons(z1, Cons(z2, z3))) -> merge#2(z1, z2)
   merge#2(Nil, z0) -> z0
   merge#2(Cons(z0, z1), Nil) -> Cons(z0, z1)
   merge#2(Cons(z0, z1), Cons(z2, z3)) -> cond_merge_ys_zs_2(leq#2(z0, z2), Cons(z0, z1), Cons(z2, z3), z0, z1, z2, z3)
   cond_merge_ys_zs_2(True, Cons(z0, z1), Cons(z2, z3), z4, z5, z6, z7) -> Cons(z4, merge#2(z5, Cons(z2, z3)))
   cond_merge_ys_zs_2(False, Cons(z0, z1), Cons(z2, z3), z4, z5, z6, z7) -> Cons(z6, merge#2(Cons(z0, z1), z7))
Tuples:
   DROP#2(S(z0), Cons(z1, z2)) -> c12(DROP#2(z0, z2))
   TAKE#2(S(z0), Cons(z1, z2)) -> c15(TAKE#2(z0, z2))
   HALVE#1(S(S(z0))) -> c18(HALVE#1(z0))
   LEQ#2(S(z0), S(z1)) -> c22(LEQ#2(z0, z1))
   LENGTH#1(Cons(z0, z1)) -> c24(LENGTH#1(z1))
   MAP#2(dc(z0, z1, z2, z3, z4), Cons(z5, z6)) -> c26(DC#1(z0, z1, z2, z3, z4, z5))
   MAP#2(dc(z0, z1, z2, z3, z4), Cons(z5, z6)) -> c27(MAP#2(dc(z0, z1, z2, z3, z4), z6))
   MERGE#2(Cons(0, x1), Cons(z0, x3)) -> c6(COND_MERGE_YS_ZS_2(True, Cons(0, x1), Cons(z0, x3), 0, x1, z0, x3))
   MERGE#2(Cons(S(z0), x1), Cons(0, x3)) -> c6(COND_MERGE_YS_ZS_2(False, Cons(S(z0), x1), Cons(0, x3), S(z0), x1, 0, x3))
   MERGE#2(Cons(S(0), x1), Cons(S(z0), x3)) -> c6(COND_MERGE_YS_ZS_2(True, Cons(S(0), x1), Cons(S(z0), x3), S(0), x1, S(z0), x3), LEQ#2(S(0), S(z0)))
   MERGE#2(Cons(S(S(z0)), x1), Cons(S(0), x3)) -> c6(COND_MERGE_YS_ZS_2(False, Cons(S(S(z0)), x1), Cons(S(0), x3), S(S(z0)), x1, S(0), x3), LEQ#2(S(S(z0)), S(0)))
   MERGE#2(Cons(S(S(z0)), x1), Cons(S(S(z1)), x3)) -> c6(COND_MERGE_YS_ZS_2(leq#2(z0, z1), Cons(S(S(z0)), x1), Cons(S(S(z1)), x3), S(S(z0)), x1, S(S(z1)), x3), LEQ#2(S(S(z0)), S(S(z1))))
   MERGE#2(Cons(S(x0), x1), Cons(S(x2), x3)) -> c6(LEQ#2(S(x0), S(x2)))
   DIVIDE_YS#1(Cons(x0, Cons(x1, x2)), S(y11)) -> c(TAKE#2(S(y11), Cons(x0, Cons(x1, x2))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, x3))), S(y11)) -> c(TAKE#2(S(y11), Cons(x0, Cons(x1, Cons(x2, x3)))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Nil)), S(y10)) -> c(TAKE#2(S(y10), Cons(x0, Cons(x1, Nil))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Nil))), S(y7)) -> c(TAKE#2(S(y7), Cons(x0, Cons(x1, Cons(x2, Nil)))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4)))), S(y8)) -> c(TAKE#2(S(y8), Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4))))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, x2)), S(y11)) -> c1(DROP#2(S(y11), Cons(x0, Cons(x1, x2))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, x3))), S(y11)) -> c1(DROP#2(S(y11), Cons(x0, Cons(x1, Cons(x2, x3)))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Nil)), S(y10)) -> c1(DROP#2(S(y10), Cons(x0, Cons(x1, Nil))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Nil))), S(y7)) -> c1(DROP#2(S(y7), Cons(x0, Cons(x1, Cons(x2, Nil)))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4)))), S(y8)) -> c1(DROP#2(S(y8), Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4))))))
   COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(S(0), z3), z4, Cons(S(S(y0)), y1), z6, z7) -> c2(MERGE#2(Cons(S(S(y0)), y1), Cons(S(0), z3)))
   COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(S(S(y2)), z3), z4, Cons(S(S(y0)), y1), z6, z7) -> c2(MERGE#2(Cons(S(S(y0)), y1), Cons(S(S(y2)), z3)))
   COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(S(y2), z3), z4, Cons(S(y0), y1), z6, z7) -> c2(MERGE#2(Cons(S(y0), y1), Cons(S(y2), z3)))
   COND_MERGE_YS_ZS_2(False, Cons(S(x0), x1), Cons(0, x2), S(x0), x1, 0, x2) -> c3(MERGE#2(Cons(S(x0), x1), x2))
   COND_MERGE_YS_ZS_2(False, Cons(S(S(x0)), x1), Cons(S(0), x2), S(S(x0)), x1, S(0), x2) -> c3(MERGE#2(Cons(S(S(x0)), x1), x2))
   COND_MERGE_YS_ZS_2(False, Cons(S(S(x0)), x1), Cons(S(S(x2)), x3), S(S(x0)), x1, S(S(x2)), x3) -> c3(MERGE#2(Cons(S(S(x0)), x1), x3))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> c9(MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Nil))), DIVIDE_YS#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2)))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Nil))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(Nil))), Cons(z0, Cons(z1, Nil))), Cons(drop#2(S(halve#1(0)), Cons(z0, Cons(z1, Nil))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil)))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Nil))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(0)), Cons(z0, Cons(z1, Nil))), Cons(drop#2(S(halve#1(length#1(Nil))), Cons(z0, Cons(z1, Nil))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil)))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, z3)))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Cons(z2, z3))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(S(length#1(z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Cons(drop#2(S(halve#1(S(length#1(z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3)))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3))))), HALVE#1(S(length#1(z3))), LENGTH#1(Cons(z2, z3)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, Nil)))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Cons(z2, Nil))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, Nil))), S(halve#1(S(0)))))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, Nil))), S(halve#1(length#1(Cons(z2, Nil)))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, Nil))), S(halve#1(length#1(Cons(z2, Nil))))), HALVE#1(S(length#1(Nil))), LENGTH#1(Cons(z2, Nil)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, Cons(z3, z4))))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Cons(z2, Cons(z3, z4)))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, Cons(z3, z4)))), S(halve#1(S(S(length#1(z4)))))))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, Cons(z3, z4)))), S(halve#1(length#1(Cons(z2, Cons(z3, z4))))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, Cons(z3, z4)))), S(halve#1(length#1(Cons(z2, Cons(z3, z4)))))), HALVE#1(S(length#1(Cons(z3, z4)))), LENGTH#1(Cons(z2, Cons(z3, z4))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, z3)))) -> c9(MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3)))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3))))), HALVE#1(S(length#1(z3))), LENGTH#1(Cons(z2, z3)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Nil))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(0)), Cons(z0, Cons(z1, Nil))), Cons(drop#2(S(halve#1(0)), Cons(z0, Cons(z1, Nil))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil)))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Nil))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Nil)), S(0)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil)))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> c9(CONST_F#2(Cons(z0, Cons(z1, z2)), Cons(dc#1(map, divisible, mergesort_zs_3, divide, const_f, take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2)))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(drop#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(halve#1(length#1(z2)), Cons(z1, z2)), Nil))), DIVIDE_YS#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2)))), HALVE#1(length#1(z2)), LENGTH#1(z2))
   CONST_F#2(Cons(x0, Cons(x1, x2)), Cons(z1, Cons(z2, z3))) -> c19(MERGE#2(z1, z2))
   CONST_F#2(Cons(x0, Cons(x1, Cons(x2, x3))), Cons(z1, Cons(z2, z3))) -> c19(MERGE#2(z1, z2))
   CONST_F#2(Cons(x0, Cons(x1, Nil)), Cons(z1, Cons(z2, z3))) -> c19(MERGE#2(z1, z2))
   CONST_F#2(Cons(x0, Cons(x1, Cons(x2, Nil))), Cons(z1, Cons(z2, z3))) -> c19(MERGE#2(z1, z2))
   CONST_F#2(Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4)))), Cons(z1, Cons(z2, z3))) -> c19(MERGE#2(z1, z2))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> c9(CONST_F#2(Cons(z0, Cons(z1, z2)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(halve#1(length#1(z2)), Cons(z1, z2)), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(halve#1(length#1(z2)), Cons(z1, z2)), Nil))), DIVIDE_YS#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2)))), HALVE#1(length#1(z2)), LENGTH#1(z2))
   COND_MERGE_YS_ZS_2(True, Cons(0, Cons(0, z5)), Cons(x1, x2), 0, Cons(0, z5), x1, x2) -> c2(MERGE#2(Cons(0, z5), Cons(x1, x2)))
   COND_MERGE_YS_ZS_2(True, Cons(S(0), Cons(0, z5)), Cons(S(x1), x2), S(0), Cons(0, z5), S(x1), x2) -> c2(MERGE#2(Cons(0, z5), Cons(S(x1), x2)))
   COND_MERGE_YS_ZS_2(True, Cons(S(S(x0)), Cons(0, z5)), Cons(S(S(x2)), x3), S(S(x0)), Cons(0, z5), S(S(x2)), x3) -> c2(MERGE#2(Cons(0, z5), Cons(S(S(x2)), x3)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, z3)))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Cons(z2, z3))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(Cons(z2, z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Cons(drop#2(S(halve#1(S(length#1(z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3)))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(S(length#1(z3))))), HALVE#1(S(length#1(z3))), LENGTH#1(Cons(z2, z3)))
   COND_MERGE_YS_ZS_2(True, Cons(0, Cons(S(z4), z5)), Cons(0, x2), 0, Cons(S(z4), z5), 0, x2) -> c2(MERGE#2(Cons(S(z4), z5), Cons(0, x2)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> c9(CONST_F#2(Cons(z0, Cons(z1, z2)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(Cons(z0, take#2(halve#1(length#1(z2)), Cons(z1, z2))), Cons(drop#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(halve#1(length#1(z2)), Cons(z1, z2)), Nil))), DIVIDE_YS#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2)))), HALVE#1(length#1(z2)), LENGTH#1(z2))
   COND_MERGE_YS_ZS_2(True, Cons(0, Cons(S(0), z5)), Cons(S(z2), x2), 0, Cons(S(0), z5), S(z2), x2) -> c2(MERGE#2(Cons(S(0), z5), Cons(S(z2), x2)))
   COND_MERGE_YS_ZS_2(True, Cons(S(0), Cons(S(0), z5)), Cons(S(x1), x2), S(0), Cons(S(0), z5), S(x1), x2) -> c2(MERGE#2(Cons(S(0), z5), Cons(S(x1), x2)))
   COND_MERGE_YS_ZS_2(True, Cons(S(S(x0)), Cons(S(0), z5)), Cons(S(S(x2)), x3), S(S(x0)), Cons(S(0), z5), S(S(x2)), x3) -> c2(MERGE#2(Cons(S(0), z5), Cons(S(S(x2)), x3)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, z3)))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Cons(z2, z3))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(S(length#1(z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Cons(drop#2(S(halve#1(length#1(Cons(z2, z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3)))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(S(length#1(z3))))), HALVE#1(S(length#1(z3))), LENGTH#1(Cons(z2, z3)))
S tuples:
   DROP#2(S(z0), Cons(z1, z2)) -> c12(DROP#2(z0, z2))
   TAKE#2(S(z0), Cons(z1, z2)) -> c15(TAKE#2(z0, z2))
   HALVE#1(S(S(z0))) -> c18(HALVE#1(z0))
   LEQ#2(S(z0), S(z1)) -> c22(LEQ#2(z0, z1))
   LENGTH#1(Cons(z0, z1)) -> c24(LENGTH#1(z1))
   MAP#2(dc(z0, z1, z2, z3, z4), Cons(z5, z6)) -> c26(DC#1(z0, z1, z2, z3, z4, z5))
   MAP#2(dc(z0, z1, z2, z3, z4), Cons(z5, z6)) -> c27(MAP#2(dc(z0, z1, z2, z3, z4), z6))
   MERGE#2(Cons(0, x1), Cons(z0, x3)) -> c6(COND_MERGE_YS_ZS_2(True, Cons(0, x1), Cons(z0, x3), 0, x1, z0, x3))
   MERGE#2(Cons(S(z0), x1), Cons(0, x3)) -> c6(COND_MERGE_YS_ZS_2(False, Cons(S(z0), x1), Cons(0, x3), S(z0), x1, 0, x3))
   MERGE#2(Cons(S(0), x1), Cons(S(z0), x3)) -> c6(COND_MERGE_YS_ZS_2(True, Cons(S(0), x1), Cons(S(z0), x3), S(0), x1, S(z0), x3), LEQ#2(S(0), S(z0)))
   MERGE#2(Cons(S(S(z0)), x1), Cons(S(0), x3)) -> c6(COND_MERGE_YS_ZS_2(False, Cons(S(S(z0)), x1), Cons(S(0), x3), S(S(z0)), x1, S(0), x3), LEQ#2(S(S(z0)), S(0)))
   MERGE#2(Cons(S(S(z0)), x1), Cons(S(S(z1)), x3)) -> c6(COND_MERGE_YS_ZS_2(leq#2(z0, z1), Cons(S(S(z0)), x1), Cons(S(S(z1)), x3), S(S(z0)), x1, S(S(z1)), x3), LEQ#2(S(S(z0)), S(S(z1))))
   MERGE#2(Cons(S(x0), x1), Cons(S(x2), x3)) -> c6(LEQ#2(S(x0), S(x2)))
   DIVIDE_YS#1(Cons(x0, Cons(x1, x2)), S(y11)) -> c(TAKE#2(S(y11), Cons(x0, Cons(x1, x2))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, x3))), S(y11)) -> c(TAKE#2(S(y11), Cons(x0, Cons(x1, Cons(x2, x3)))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Nil)), S(y10)) -> c(TAKE#2(S(y10), Cons(x0, Cons(x1, Nil))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Nil))), S(y7)) -> c(TAKE#2(S(y7), Cons(x0, Cons(x1, Cons(x2, Nil)))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4)))), S(y8)) -> c(TAKE#2(S(y8), Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4))))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, x2)), S(y11)) -> c1(DROP#2(S(y11), Cons(x0, Cons(x1, x2))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, x3))), S(y11)) -> c1(DROP#2(S(y11), Cons(x0, Cons(x1, Cons(x2, x3)))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Nil)), S(y10)) -> c1(DROP#2(S(y10), Cons(x0, Cons(x1, Nil))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Nil))), S(y7)) -> c1(DROP#2(S(y7), Cons(x0, Cons(x1, Cons(x2, Nil)))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4)))), S(y8)) -> c1(DROP#2(S(y8), Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4))))))
   COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(S(0), z3), z4, Cons(S(S(y0)), y1), z6, z7) -> c2(MERGE#2(Cons(S(S(y0)), y1), Cons(S(0), z3)))
   COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(S(S(y2)), z3), z4, Cons(S(S(y0)), y1), z6, z7) -> c2(MERGE#2(Cons(S(S(y0)), y1), Cons(S(S(y2)), z3)))
   COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(S(y2), z3), z4, Cons(S(y0), y1), z6, z7) -> c2(MERGE#2(Cons(S(y0), y1), Cons(S(y2), z3)))
   COND_MERGE_YS_ZS_2(False, Cons(S(x0), x1), Cons(0, x2), S(x0), x1, 0, x2) -> c3(MERGE#2(Cons(S(x0), x1), x2))
   COND_MERGE_YS_ZS_2(False, Cons(S(S(x0)), x1), Cons(S(0), x2), S(S(x0)), x1, S(0), x2) -> c3(MERGE#2(Cons(S(S(x0)), x1), x2))
   COND_MERGE_YS_ZS_2(False, Cons(S(S(x0)), x1), Cons(S(S(x2)), x3), S(S(x0)), x1, S(S(x2)), x3) -> c3(MERGE#2(Cons(S(S(x0)), x1), x3))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> c9(MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Nil))), DIVIDE_YS#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2)))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Nil))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(Nil))), Cons(z0, Cons(z1, Nil))), Cons(drop#2(S(halve#1(0)), Cons(z0, Cons(z1, Nil))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil)))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Nil))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(0)), Cons(z0, Cons(z1, Nil))), Cons(drop#2(S(halve#1(length#1(Nil))), Cons(z0, Cons(z1, Nil))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil)))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, z3)))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Cons(z2, z3))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(S(length#1(z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Cons(drop#2(S(halve#1(S(length#1(z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3)))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3))))), HALVE#1(S(length#1(z3))), LENGTH#1(Cons(z2, z3)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, Nil)))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Cons(z2, Nil))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, Nil))), S(halve#1(S(0)))))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, Nil))), S(halve#1(length#1(Cons(z2, Nil)))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, Nil))), S(halve#1(length#1(Cons(z2, Nil))))), HALVE#1(S(length#1(Nil))), LENGTH#1(Cons(z2, Nil)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, Cons(z3, z4))))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Cons(z2, Cons(z3, z4)))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, Cons(z3, z4)))), S(halve#1(S(S(length#1(z4)))))))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, Cons(z3, z4)))), S(halve#1(length#1(Cons(z2, Cons(z3, z4))))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, Cons(z3, z4)))), S(halve#1(length#1(Cons(z2, Cons(z3, z4)))))), HALVE#1(S(length#1(Cons(z3, z4)))), LENGTH#1(Cons(z2, Cons(z3, z4))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, z3)))) -> c9(MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3)))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3))))), HALVE#1(S(length#1(z3))), LENGTH#1(Cons(z2, z3)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Nil))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(0)), Cons(z0, Cons(z1, Nil))), Cons(drop#2(S(halve#1(0)), Cons(z0, Cons(z1, Nil))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil)))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Nil))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Nil)), S(0)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil)))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> c9(CONST_F#2(Cons(z0, Cons(z1, z2)), Cons(dc#1(map, divisible, mergesort_zs_3, divide, const_f, take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2)))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(drop#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(halve#1(length#1(z2)), Cons(z1, z2)), Nil))), DIVIDE_YS#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2)))), HALVE#1(length#1(z2)), LENGTH#1(z2))
   CONST_F#2(Cons(x0, Cons(x1, x2)), Cons(z1, Cons(z2, z3))) -> c19(MERGE#2(z1, z2))
   CONST_F#2(Cons(x0, Cons(x1, Cons(x2, x3))), Cons(z1, Cons(z2, z3))) -> c19(MERGE#2(z1, z2))
   CONST_F#2(Cons(x0, Cons(x1, Nil)), Cons(z1, Cons(z2, z3))) -> c19(MERGE#2(z1, z2))
   CONST_F#2(Cons(x0, Cons(x1, Cons(x2, Nil))), Cons(z1, Cons(z2, z3))) -> c19(MERGE#2(z1, z2))
   CONST_F#2(Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4)))), Cons(z1, Cons(z2, z3))) -> c19(MERGE#2(z1, z2))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> c9(CONST_F#2(Cons(z0, Cons(z1, z2)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(halve#1(length#1(z2)), Cons(z1, z2)), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(halve#1(length#1(z2)), Cons(z1, z2)), Nil))), DIVIDE_YS#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2)))), HALVE#1(length#1(z2)), LENGTH#1(z2))
   COND_MERGE_YS_ZS_2(True, Cons(0, Cons(0, z5)), Cons(x1, x2), 0, Cons(0, z5), x1, x2) -> c2(MERGE#2(Cons(0, z5), Cons(x1, x2)))
   COND_MERGE_YS_ZS_2(True, Cons(S(0), Cons(0, z5)), Cons(S(x1), x2), S(0), Cons(0, z5), S(x1), x2) -> c2(MERGE#2(Cons(0, z5), Cons(S(x1), x2)))
   COND_MERGE_YS_ZS_2(True, Cons(S(S(x0)), Cons(0, z5)), Cons(S(S(x2)), x3), S(S(x0)), Cons(0, z5), S(S(x2)), x3) -> c2(MERGE#2(Cons(0, z5), Cons(S(S(x2)), x3)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, z3)))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Cons(z2, z3))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(Cons(z2, z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Cons(drop#2(S(halve#1(S(length#1(z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3)))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(S(length#1(z3))))), HALVE#1(S(length#1(z3))), LENGTH#1(Cons(z2, z3)))
   COND_MERGE_YS_ZS_2(True, Cons(0, Cons(S(z4), z5)), Cons(0, x2), 0, Cons(S(z4), z5), 0, x2) -> c2(MERGE#2(Cons(S(z4), z5), Cons(0, x2)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> c9(CONST_F#2(Cons(z0, Cons(z1, z2)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(Cons(z0, take#2(halve#1(length#1(z2)), Cons(z1, z2))), Cons(drop#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(halve#1(length#1(z2)), Cons(z1, z2)), Nil))), DIVIDE_YS#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2)))), HALVE#1(length#1(z2)), LENGTH#1(z2))
   COND_MERGE_YS_ZS_2(True, Cons(0, Cons(S(0), z5)), Cons(S(z2), x2), 0, Cons(S(0), z5), S(z2), x2) -> c2(MERGE#2(Cons(S(0), z5), Cons(S(z2), x2)))
   COND_MERGE_YS_ZS_2(True, Cons(S(0), Cons(S(0), z5)), Cons(S(x1), x2), S(0), Cons(S(0), z5), S(x1), x2) -> c2(MERGE#2(Cons(S(0), z5), Cons(S(x1), x2)))
   COND_MERGE_YS_ZS_2(True, Cons(S(S(x0)), Cons(S(0), z5)), Cons(S(S(x2)), x3), S(S(x0)), Cons(S(0), z5), S(S(x2)), x3) -> c2(MERGE#2(Cons(S(0), z5), Cons(S(S(x2)), x3)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, z3)))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Cons(z2, z3))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(S(length#1(z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Cons(drop#2(S(halve#1(length#1(Cons(z2, z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3)))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(S(length#1(z3))))), HALVE#1(S(length#1(z3))), LENGTH#1(Cons(z2, z3)))
K tuples:none
Defined Rule Symbols:   leq#2_2, map#2_2, divide_ys#1_2, halve#1_1, length#1_1, take#2_2, drop#2_2, dc#1_6, const_f#2_2, merge#2_2, cond_merge_ys_zs_2_7

Defined Pair Symbols:   DROP#2_2, TAKE#2_2, HALVE#1_1, LEQ#2_2, LENGTH#1_1, MAP#2_2, MERGE#2_2, DIVIDE_YS#1_2, COND_MERGE_YS_ZS_2_7, DC#1_6, CONST_F#2_2

Compound Symbols:   c12_1, c15_1, c18_1, c22_1, c24_1, c26_1, c27_1, c6_1, c6_2, c_1, c1_1, c2_1, c3_1, c9_2, c9_3, c9_5, c9_4, c19_1


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(163) CdtInstantiationProof (BOTH BOUNDS(ID, ID))
Use instantiation to replace COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(S(0), z3), z4, Cons(S(S(y0)), y1), z6, z7) -> c2(MERGE#2(Cons(S(S(y0)), y1), Cons(S(0), z3))) by 
   COND_MERGE_YS_ZS_2(True, Cons(0, Cons(S(S(z4)), z5)), Cons(S(0), x2), 0, Cons(S(S(z4)), z5), S(0), x2) -> c2(MERGE#2(Cons(S(S(z4)), z5), Cons(S(0), x2)))
   COND_MERGE_YS_ZS_2(True, Cons(S(0), Cons(S(S(z4)), z5)), Cons(S(0), x2), S(0), Cons(S(S(z4)), z5), S(0), x2) -> c2(MERGE#2(Cons(S(S(z4)), z5), Cons(S(0), x2)))

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

(164)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   leq#2(0, z0) -> True
   leq#2(S(z0), 0) -> False
   leq#2(S(z0), S(z1)) -> leq#2(z0, z1)
   map#2(dc(z0, z1, z2, z3, z4), Nil) -> Nil
   map#2(dc(z0, z1, z2, z3, z4), Cons(z5, z6)) -> Cons(dc#1(z0, z1, z2, z3, z4, z5), map#2(dc(z0, z1, z2, z3, z4), z6))
   divide_ys#1(z0, z1) -> Cons(take#2(z1, z0), Cons(drop#2(z1, z0), Nil))
   halve#1(0) -> 0
   halve#1(S(0)) -> S(0)
   halve#1(S(S(z0))) -> S(halve#1(z0))
   length#1(Nil) -> 0
   length#1(Cons(z0, z1)) -> S(length#1(z1))
   take#2(0, z0) -> Nil
   take#2(S(0), Nil) -> Cons(bot[0], Nil)
   take#2(S(z0), Cons(z1, z2)) -> Cons(z1, take#2(z0, z2))
   drop#2(0, z0) -> z0
   drop#2(S(0), Nil) -> bot[1]
   drop#2(S(z0), Cons(z1, z2)) -> drop#2(z0, z2)
   dc#1(map, divisible, mergesort_zs_3, divide, const_f, Nil) -> Nil
   dc#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Nil)) -> Cons(z0, Nil)
   dc#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> const_f#2(Cons(z0, Cons(z1, z2)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2))))))
   const_f#2(z0, Cons(z1, Cons(z2, z3))) -> merge#2(z1, z2)
   merge#2(Nil, z0) -> z0
   merge#2(Cons(z0, z1), Nil) -> Cons(z0, z1)
   merge#2(Cons(z0, z1), Cons(z2, z3)) -> cond_merge_ys_zs_2(leq#2(z0, z2), Cons(z0, z1), Cons(z2, z3), z0, z1, z2, z3)
   cond_merge_ys_zs_2(True, Cons(z0, z1), Cons(z2, z3), z4, z5, z6, z7) -> Cons(z4, merge#2(z5, Cons(z2, z3)))
   cond_merge_ys_zs_2(False, Cons(z0, z1), Cons(z2, z3), z4, z5, z6, z7) -> Cons(z6, merge#2(Cons(z0, z1), z7))
Tuples:
   DROP#2(S(z0), Cons(z1, z2)) -> c12(DROP#2(z0, z2))
   TAKE#2(S(z0), Cons(z1, z2)) -> c15(TAKE#2(z0, z2))
   HALVE#1(S(S(z0))) -> c18(HALVE#1(z0))
   LEQ#2(S(z0), S(z1)) -> c22(LEQ#2(z0, z1))
   LENGTH#1(Cons(z0, z1)) -> c24(LENGTH#1(z1))
   MAP#2(dc(z0, z1, z2, z3, z4), Cons(z5, z6)) -> c26(DC#1(z0, z1, z2, z3, z4, z5))
   MAP#2(dc(z0, z1, z2, z3, z4), Cons(z5, z6)) -> c27(MAP#2(dc(z0, z1, z2, z3, z4), z6))
   MERGE#2(Cons(0, x1), Cons(z0, x3)) -> c6(COND_MERGE_YS_ZS_2(True, Cons(0, x1), Cons(z0, x3), 0, x1, z0, x3))
   MERGE#2(Cons(S(z0), x1), Cons(0, x3)) -> c6(COND_MERGE_YS_ZS_2(False, Cons(S(z0), x1), Cons(0, x3), S(z0), x1, 0, x3))
   MERGE#2(Cons(S(0), x1), Cons(S(z0), x3)) -> c6(COND_MERGE_YS_ZS_2(True, Cons(S(0), x1), Cons(S(z0), x3), S(0), x1, S(z0), x3), LEQ#2(S(0), S(z0)))
   MERGE#2(Cons(S(S(z0)), x1), Cons(S(0), x3)) -> c6(COND_MERGE_YS_ZS_2(False, Cons(S(S(z0)), x1), Cons(S(0), x3), S(S(z0)), x1, S(0), x3), LEQ#2(S(S(z0)), S(0)))
   MERGE#2(Cons(S(S(z0)), x1), Cons(S(S(z1)), x3)) -> c6(COND_MERGE_YS_ZS_2(leq#2(z0, z1), Cons(S(S(z0)), x1), Cons(S(S(z1)), x3), S(S(z0)), x1, S(S(z1)), x3), LEQ#2(S(S(z0)), S(S(z1))))
   MERGE#2(Cons(S(x0), x1), Cons(S(x2), x3)) -> c6(LEQ#2(S(x0), S(x2)))
   DIVIDE_YS#1(Cons(x0, Cons(x1, x2)), S(y11)) -> c(TAKE#2(S(y11), Cons(x0, Cons(x1, x2))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, x3))), S(y11)) -> c(TAKE#2(S(y11), Cons(x0, Cons(x1, Cons(x2, x3)))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Nil)), S(y10)) -> c(TAKE#2(S(y10), Cons(x0, Cons(x1, Nil))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Nil))), S(y7)) -> c(TAKE#2(S(y7), Cons(x0, Cons(x1, Cons(x2, Nil)))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4)))), S(y8)) -> c(TAKE#2(S(y8), Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4))))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, x2)), S(y11)) -> c1(DROP#2(S(y11), Cons(x0, Cons(x1, x2))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, x3))), S(y11)) -> c1(DROP#2(S(y11), Cons(x0, Cons(x1, Cons(x2, x3)))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Nil)), S(y10)) -> c1(DROP#2(S(y10), Cons(x0, Cons(x1, Nil))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Nil))), S(y7)) -> c1(DROP#2(S(y7), Cons(x0, Cons(x1, Cons(x2, Nil)))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4)))), S(y8)) -> c1(DROP#2(S(y8), Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4))))))
   COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(S(S(y2)), z3), z4, Cons(S(S(y0)), y1), z6, z7) -> c2(MERGE#2(Cons(S(S(y0)), y1), Cons(S(S(y2)), z3)))
   COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(S(y2), z3), z4, Cons(S(y0), y1), z6, z7) -> c2(MERGE#2(Cons(S(y0), y1), Cons(S(y2), z3)))
   COND_MERGE_YS_ZS_2(False, Cons(S(x0), x1), Cons(0, x2), S(x0), x1, 0, x2) -> c3(MERGE#2(Cons(S(x0), x1), x2))
   COND_MERGE_YS_ZS_2(False, Cons(S(S(x0)), x1), Cons(S(0), x2), S(S(x0)), x1, S(0), x2) -> c3(MERGE#2(Cons(S(S(x0)), x1), x2))
   COND_MERGE_YS_ZS_2(False, Cons(S(S(x0)), x1), Cons(S(S(x2)), x3), S(S(x0)), x1, S(S(x2)), x3) -> c3(MERGE#2(Cons(S(S(x0)), x1), x3))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> c9(MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Nil))), DIVIDE_YS#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2)))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Nil))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(Nil))), Cons(z0, Cons(z1, Nil))), Cons(drop#2(S(halve#1(0)), Cons(z0, Cons(z1, Nil))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil)))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Nil))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(0)), Cons(z0, Cons(z1, Nil))), Cons(drop#2(S(halve#1(length#1(Nil))), Cons(z0, Cons(z1, Nil))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil)))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, z3)))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Cons(z2, z3))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(S(length#1(z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Cons(drop#2(S(halve#1(S(length#1(z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3)))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3))))), HALVE#1(S(length#1(z3))), LENGTH#1(Cons(z2, z3)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, Nil)))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Cons(z2, Nil))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, Nil))), S(halve#1(S(0)))))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, Nil))), S(halve#1(length#1(Cons(z2, Nil)))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, Nil))), S(halve#1(length#1(Cons(z2, Nil))))), HALVE#1(S(length#1(Nil))), LENGTH#1(Cons(z2, Nil)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, Cons(z3, z4))))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Cons(z2, Cons(z3, z4)))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, Cons(z3, z4)))), S(halve#1(S(S(length#1(z4)))))))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, Cons(z3, z4)))), S(halve#1(length#1(Cons(z2, Cons(z3, z4))))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, Cons(z3, z4)))), S(halve#1(length#1(Cons(z2, Cons(z3, z4)))))), HALVE#1(S(length#1(Cons(z3, z4)))), LENGTH#1(Cons(z2, Cons(z3, z4))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, z3)))) -> c9(MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3)))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3))))), HALVE#1(S(length#1(z3))), LENGTH#1(Cons(z2, z3)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Nil))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(0)), Cons(z0, Cons(z1, Nil))), Cons(drop#2(S(halve#1(0)), Cons(z0, Cons(z1, Nil))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil)))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Nil))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Nil)), S(0)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil)))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> c9(CONST_F#2(Cons(z0, Cons(z1, z2)), Cons(dc#1(map, divisible, mergesort_zs_3, divide, const_f, take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2)))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(drop#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(halve#1(length#1(z2)), Cons(z1, z2)), Nil))), DIVIDE_YS#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2)))), HALVE#1(length#1(z2)), LENGTH#1(z2))
   CONST_F#2(Cons(x0, Cons(x1, x2)), Cons(z1, Cons(z2, z3))) -> c19(MERGE#2(z1, z2))
   CONST_F#2(Cons(x0, Cons(x1, Cons(x2, x3))), Cons(z1, Cons(z2, z3))) -> c19(MERGE#2(z1, z2))
   CONST_F#2(Cons(x0, Cons(x1, Nil)), Cons(z1, Cons(z2, z3))) -> c19(MERGE#2(z1, z2))
   CONST_F#2(Cons(x0, Cons(x1, Cons(x2, Nil))), Cons(z1, Cons(z2, z3))) -> c19(MERGE#2(z1, z2))
   CONST_F#2(Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4)))), Cons(z1, Cons(z2, z3))) -> c19(MERGE#2(z1, z2))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> c9(CONST_F#2(Cons(z0, Cons(z1, z2)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(halve#1(length#1(z2)), Cons(z1, z2)), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(halve#1(length#1(z2)), Cons(z1, z2)), Nil))), DIVIDE_YS#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2)))), HALVE#1(length#1(z2)), LENGTH#1(z2))
   COND_MERGE_YS_ZS_2(True, Cons(0, Cons(0, z5)), Cons(x1, x2), 0, Cons(0, z5), x1, x2) -> c2(MERGE#2(Cons(0, z5), Cons(x1, x2)))
   COND_MERGE_YS_ZS_2(True, Cons(S(0), Cons(0, z5)), Cons(S(x1), x2), S(0), Cons(0, z5), S(x1), x2) -> c2(MERGE#2(Cons(0, z5), Cons(S(x1), x2)))
   COND_MERGE_YS_ZS_2(True, Cons(S(S(x0)), Cons(0, z5)), Cons(S(S(x2)), x3), S(S(x0)), Cons(0, z5), S(S(x2)), x3) -> c2(MERGE#2(Cons(0, z5), Cons(S(S(x2)), x3)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, z3)))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Cons(z2, z3))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(Cons(z2, z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Cons(drop#2(S(halve#1(S(length#1(z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3)))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(S(length#1(z3))))), HALVE#1(S(length#1(z3))), LENGTH#1(Cons(z2, z3)))
   COND_MERGE_YS_ZS_2(True, Cons(0, Cons(S(z4), z5)), Cons(0, x2), 0, Cons(S(z4), z5), 0, x2) -> c2(MERGE#2(Cons(S(z4), z5), Cons(0, x2)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> c9(CONST_F#2(Cons(z0, Cons(z1, z2)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(Cons(z0, take#2(halve#1(length#1(z2)), Cons(z1, z2))), Cons(drop#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(halve#1(length#1(z2)), Cons(z1, z2)), Nil))), DIVIDE_YS#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2)))), HALVE#1(length#1(z2)), LENGTH#1(z2))
   COND_MERGE_YS_ZS_2(True, Cons(0, Cons(S(0), z5)), Cons(S(z2), x2), 0, Cons(S(0), z5), S(z2), x2) -> c2(MERGE#2(Cons(S(0), z5), Cons(S(z2), x2)))
   COND_MERGE_YS_ZS_2(True, Cons(S(0), Cons(S(0), z5)), Cons(S(x1), x2), S(0), Cons(S(0), z5), S(x1), x2) -> c2(MERGE#2(Cons(S(0), z5), Cons(S(x1), x2)))
   COND_MERGE_YS_ZS_2(True, Cons(S(S(x0)), Cons(S(0), z5)), Cons(S(S(x2)), x3), S(S(x0)), Cons(S(0), z5), S(S(x2)), x3) -> c2(MERGE#2(Cons(S(0), z5), Cons(S(S(x2)), x3)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, z3)))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Cons(z2, z3))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(S(length#1(z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Cons(drop#2(S(halve#1(length#1(Cons(z2, z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3)))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(S(length#1(z3))))), HALVE#1(S(length#1(z3))), LENGTH#1(Cons(z2, z3)))
   COND_MERGE_YS_ZS_2(True, Cons(0, Cons(S(S(z4)), z5)), Cons(S(0), x2), 0, Cons(S(S(z4)), z5), S(0), x2) -> c2(MERGE#2(Cons(S(S(z4)), z5), Cons(S(0), x2)))
   COND_MERGE_YS_ZS_2(True, Cons(S(0), Cons(S(S(z4)), z5)), Cons(S(0), x2), S(0), Cons(S(S(z4)), z5), S(0), x2) -> c2(MERGE#2(Cons(S(S(z4)), z5), Cons(S(0), x2)))
S tuples:
   DROP#2(S(z0), Cons(z1, z2)) -> c12(DROP#2(z0, z2))
   TAKE#2(S(z0), Cons(z1, z2)) -> c15(TAKE#2(z0, z2))
   HALVE#1(S(S(z0))) -> c18(HALVE#1(z0))
   LEQ#2(S(z0), S(z1)) -> c22(LEQ#2(z0, z1))
   LENGTH#1(Cons(z0, z1)) -> c24(LENGTH#1(z1))
   MAP#2(dc(z0, z1, z2, z3, z4), Cons(z5, z6)) -> c26(DC#1(z0, z1, z2, z3, z4, z5))
   MAP#2(dc(z0, z1, z2, z3, z4), Cons(z5, z6)) -> c27(MAP#2(dc(z0, z1, z2, z3, z4), z6))
   MERGE#2(Cons(0, x1), Cons(z0, x3)) -> c6(COND_MERGE_YS_ZS_2(True, Cons(0, x1), Cons(z0, x3), 0, x1, z0, x3))
   MERGE#2(Cons(S(z0), x1), Cons(0, x3)) -> c6(COND_MERGE_YS_ZS_2(False, Cons(S(z0), x1), Cons(0, x3), S(z0), x1, 0, x3))
   MERGE#2(Cons(S(0), x1), Cons(S(z0), x3)) -> c6(COND_MERGE_YS_ZS_2(True, Cons(S(0), x1), Cons(S(z0), x3), S(0), x1, S(z0), x3), LEQ#2(S(0), S(z0)))
   MERGE#2(Cons(S(S(z0)), x1), Cons(S(0), x3)) -> c6(COND_MERGE_YS_ZS_2(False, Cons(S(S(z0)), x1), Cons(S(0), x3), S(S(z0)), x1, S(0), x3), LEQ#2(S(S(z0)), S(0)))
   MERGE#2(Cons(S(S(z0)), x1), Cons(S(S(z1)), x3)) -> c6(COND_MERGE_YS_ZS_2(leq#2(z0, z1), Cons(S(S(z0)), x1), Cons(S(S(z1)), x3), S(S(z0)), x1, S(S(z1)), x3), LEQ#2(S(S(z0)), S(S(z1))))
   MERGE#2(Cons(S(x0), x1), Cons(S(x2), x3)) -> c6(LEQ#2(S(x0), S(x2)))
   DIVIDE_YS#1(Cons(x0, Cons(x1, x2)), S(y11)) -> c(TAKE#2(S(y11), Cons(x0, Cons(x1, x2))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, x3))), S(y11)) -> c(TAKE#2(S(y11), Cons(x0, Cons(x1, Cons(x2, x3)))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Nil)), S(y10)) -> c(TAKE#2(S(y10), Cons(x0, Cons(x1, Nil))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Nil))), S(y7)) -> c(TAKE#2(S(y7), Cons(x0, Cons(x1, Cons(x2, Nil)))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4)))), S(y8)) -> c(TAKE#2(S(y8), Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4))))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, x2)), S(y11)) -> c1(DROP#2(S(y11), Cons(x0, Cons(x1, x2))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, x3))), S(y11)) -> c1(DROP#2(S(y11), Cons(x0, Cons(x1, Cons(x2, x3)))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Nil)), S(y10)) -> c1(DROP#2(S(y10), Cons(x0, Cons(x1, Nil))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Nil))), S(y7)) -> c1(DROP#2(S(y7), Cons(x0, Cons(x1, Cons(x2, Nil)))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4)))), S(y8)) -> c1(DROP#2(S(y8), Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4))))))
   COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(S(S(y2)), z3), z4, Cons(S(S(y0)), y1), z6, z7) -> c2(MERGE#2(Cons(S(S(y0)), y1), Cons(S(S(y2)), z3)))
   COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(S(y2), z3), z4, Cons(S(y0), y1), z6, z7) -> c2(MERGE#2(Cons(S(y0), y1), Cons(S(y2), z3)))
   COND_MERGE_YS_ZS_2(False, Cons(S(x0), x1), Cons(0, x2), S(x0), x1, 0, x2) -> c3(MERGE#2(Cons(S(x0), x1), x2))
   COND_MERGE_YS_ZS_2(False, Cons(S(S(x0)), x1), Cons(S(0), x2), S(S(x0)), x1, S(0), x2) -> c3(MERGE#2(Cons(S(S(x0)), x1), x2))
   COND_MERGE_YS_ZS_2(False, Cons(S(S(x0)), x1), Cons(S(S(x2)), x3), S(S(x0)), x1, S(S(x2)), x3) -> c3(MERGE#2(Cons(S(S(x0)), x1), x3))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> c9(MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Nil))), DIVIDE_YS#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2)))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Nil))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(Nil))), Cons(z0, Cons(z1, Nil))), Cons(drop#2(S(halve#1(0)), Cons(z0, Cons(z1, Nil))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil)))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Nil))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(0)), Cons(z0, Cons(z1, Nil))), Cons(drop#2(S(halve#1(length#1(Nil))), Cons(z0, Cons(z1, Nil))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil)))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, z3)))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Cons(z2, z3))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(S(length#1(z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Cons(drop#2(S(halve#1(S(length#1(z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3)))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3))))), HALVE#1(S(length#1(z3))), LENGTH#1(Cons(z2, z3)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, Nil)))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Cons(z2, Nil))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, Nil))), S(halve#1(S(0)))))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, Nil))), S(halve#1(length#1(Cons(z2, Nil)))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, Nil))), S(halve#1(length#1(Cons(z2, Nil))))), HALVE#1(S(length#1(Nil))), LENGTH#1(Cons(z2, Nil)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, Cons(z3, z4))))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Cons(z2, Cons(z3, z4)))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, Cons(z3, z4)))), S(halve#1(S(S(length#1(z4)))))))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, Cons(z3, z4)))), S(halve#1(length#1(Cons(z2, Cons(z3, z4))))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, Cons(z3, z4)))), S(halve#1(length#1(Cons(z2, Cons(z3, z4)))))), HALVE#1(S(length#1(Cons(z3, z4)))), LENGTH#1(Cons(z2, Cons(z3, z4))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, z3)))) -> c9(MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3)))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3))))), HALVE#1(S(length#1(z3))), LENGTH#1(Cons(z2, z3)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Nil))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(0)), Cons(z0, Cons(z1, Nil))), Cons(drop#2(S(halve#1(0)), Cons(z0, Cons(z1, Nil))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil)))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Nil))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Nil)), S(0)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil)))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> c9(CONST_F#2(Cons(z0, Cons(z1, z2)), Cons(dc#1(map, divisible, mergesort_zs_3, divide, const_f, take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2)))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(drop#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(halve#1(length#1(z2)), Cons(z1, z2)), Nil))), DIVIDE_YS#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2)))), HALVE#1(length#1(z2)), LENGTH#1(z2))
   CONST_F#2(Cons(x0, Cons(x1, x2)), Cons(z1, Cons(z2, z3))) -> c19(MERGE#2(z1, z2))
   CONST_F#2(Cons(x0, Cons(x1, Cons(x2, x3))), Cons(z1, Cons(z2, z3))) -> c19(MERGE#2(z1, z2))
   CONST_F#2(Cons(x0, Cons(x1, Nil)), Cons(z1, Cons(z2, z3))) -> c19(MERGE#2(z1, z2))
   CONST_F#2(Cons(x0, Cons(x1, Cons(x2, Nil))), Cons(z1, Cons(z2, z3))) -> c19(MERGE#2(z1, z2))
   CONST_F#2(Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4)))), Cons(z1, Cons(z2, z3))) -> c19(MERGE#2(z1, z2))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> c9(CONST_F#2(Cons(z0, Cons(z1, z2)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(halve#1(length#1(z2)), Cons(z1, z2)), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(halve#1(length#1(z2)), Cons(z1, z2)), Nil))), DIVIDE_YS#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2)))), HALVE#1(length#1(z2)), LENGTH#1(z2))
   COND_MERGE_YS_ZS_2(True, Cons(0, Cons(0, z5)), Cons(x1, x2), 0, Cons(0, z5), x1, x2) -> c2(MERGE#2(Cons(0, z5), Cons(x1, x2)))
   COND_MERGE_YS_ZS_2(True, Cons(S(0), Cons(0, z5)), Cons(S(x1), x2), S(0), Cons(0, z5), S(x1), x2) -> c2(MERGE#2(Cons(0, z5), Cons(S(x1), x2)))
   COND_MERGE_YS_ZS_2(True, Cons(S(S(x0)), Cons(0, z5)), Cons(S(S(x2)), x3), S(S(x0)), Cons(0, z5), S(S(x2)), x3) -> c2(MERGE#2(Cons(0, z5), Cons(S(S(x2)), x3)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, z3)))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Cons(z2, z3))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(Cons(z2, z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Cons(drop#2(S(halve#1(S(length#1(z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3)))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(S(length#1(z3))))), HALVE#1(S(length#1(z3))), LENGTH#1(Cons(z2, z3)))
   COND_MERGE_YS_ZS_2(True, Cons(0, Cons(S(z4), z5)), Cons(0, x2), 0, Cons(S(z4), z5), 0, x2) -> c2(MERGE#2(Cons(S(z4), z5), Cons(0, x2)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> c9(CONST_F#2(Cons(z0, Cons(z1, z2)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(Cons(z0, take#2(halve#1(length#1(z2)), Cons(z1, z2))), Cons(drop#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(halve#1(length#1(z2)), Cons(z1, z2)), Nil))), DIVIDE_YS#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2)))), HALVE#1(length#1(z2)), LENGTH#1(z2))
   COND_MERGE_YS_ZS_2(True, Cons(0, Cons(S(0), z5)), Cons(S(z2), x2), 0, Cons(S(0), z5), S(z2), x2) -> c2(MERGE#2(Cons(S(0), z5), Cons(S(z2), x2)))
   COND_MERGE_YS_ZS_2(True, Cons(S(0), Cons(S(0), z5)), Cons(S(x1), x2), S(0), Cons(S(0), z5), S(x1), x2) -> c2(MERGE#2(Cons(S(0), z5), Cons(S(x1), x2)))
   COND_MERGE_YS_ZS_2(True, Cons(S(S(x0)), Cons(S(0), z5)), Cons(S(S(x2)), x3), S(S(x0)), Cons(S(0), z5), S(S(x2)), x3) -> c2(MERGE#2(Cons(S(0), z5), Cons(S(S(x2)), x3)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, z3)))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Cons(z2, z3))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(S(length#1(z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Cons(drop#2(S(halve#1(length#1(Cons(z2, z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3)))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(S(length#1(z3))))), HALVE#1(S(length#1(z3))), LENGTH#1(Cons(z2, z3)))
   COND_MERGE_YS_ZS_2(True, Cons(0, Cons(S(S(z4)), z5)), Cons(S(0), x2), 0, Cons(S(S(z4)), z5), S(0), x2) -> c2(MERGE#2(Cons(S(S(z4)), z5), Cons(S(0), x2)))
   COND_MERGE_YS_ZS_2(True, Cons(S(0), Cons(S(S(z4)), z5)), Cons(S(0), x2), S(0), Cons(S(S(z4)), z5), S(0), x2) -> c2(MERGE#2(Cons(S(S(z4)), z5), Cons(S(0), x2)))
K tuples:none
Defined Rule Symbols:   leq#2_2, map#2_2, divide_ys#1_2, halve#1_1, length#1_1, take#2_2, drop#2_2, dc#1_6, const_f#2_2, merge#2_2, cond_merge_ys_zs_2_7

Defined Pair Symbols:   DROP#2_2, TAKE#2_2, HALVE#1_1, LEQ#2_2, LENGTH#1_1, MAP#2_2, MERGE#2_2, DIVIDE_YS#1_2, COND_MERGE_YS_ZS_2_7, DC#1_6, CONST_F#2_2

Compound Symbols:   c12_1, c15_1, c18_1, c22_1, c24_1, c26_1, c27_1, c6_1, c6_2, c_1, c1_1, c2_1, c3_1, c9_2, c9_3, c9_5, c9_4, c19_1


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

(165) CdtRewritingProof (BOTH BOUNDS(ID, ID))
Used rewriting to replace DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> c9(MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Nil))), DIVIDE_YS#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2))))) by DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> c9(MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(halve#1(length#1(z2)), Cons(z1, z2)), Nil))), DIVIDE_YS#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2)))))
----------------------------------------

(166)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   leq#2(0, z0) -> True
   leq#2(S(z0), 0) -> False
   leq#2(S(z0), S(z1)) -> leq#2(z0, z1)
   map#2(dc(z0, z1, z2, z3, z4), Nil) -> Nil
   map#2(dc(z0, z1, z2, z3, z4), Cons(z5, z6)) -> Cons(dc#1(z0, z1, z2, z3, z4, z5), map#2(dc(z0, z1, z2, z3, z4), z6))
   divide_ys#1(z0, z1) -> Cons(take#2(z1, z0), Cons(drop#2(z1, z0), Nil))
   halve#1(0) -> 0
   halve#1(S(0)) -> S(0)
   halve#1(S(S(z0))) -> S(halve#1(z0))
   length#1(Nil) -> 0
   length#1(Cons(z0, z1)) -> S(length#1(z1))
   take#2(0, z0) -> Nil
   take#2(S(0), Nil) -> Cons(bot[0], Nil)
   take#2(S(z0), Cons(z1, z2)) -> Cons(z1, take#2(z0, z2))
   drop#2(0, z0) -> z0
   drop#2(S(0), Nil) -> bot[1]
   drop#2(S(z0), Cons(z1, z2)) -> drop#2(z0, z2)
   dc#1(map, divisible, mergesort_zs_3, divide, const_f, Nil) -> Nil
   dc#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Nil)) -> Cons(z0, Nil)
   dc#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> const_f#2(Cons(z0, Cons(z1, z2)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2))))))
   const_f#2(z0, Cons(z1, Cons(z2, z3))) -> merge#2(z1, z2)
   merge#2(Nil, z0) -> z0
   merge#2(Cons(z0, z1), Nil) -> Cons(z0, z1)
   merge#2(Cons(z0, z1), Cons(z2, z3)) -> cond_merge_ys_zs_2(leq#2(z0, z2), Cons(z0, z1), Cons(z2, z3), z0, z1, z2, z3)
   cond_merge_ys_zs_2(True, Cons(z0, z1), Cons(z2, z3), z4, z5, z6, z7) -> Cons(z4, merge#2(z5, Cons(z2, z3)))
   cond_merge_ys_zs_2(False, Cons(z0, z1), Cons(z2, z3), z4, z5, z6, z7) -> Cons(z6, merge#2(Cons(z0, z1), z7))
Tuples:
   DROP#2(S(z0), Cons(z1, z2)) -> c12(DROP#2(z0, z2))
   TAKE#2(S(z0), Cons(z1, z2)) -> c15(TAKE#2(z0, z2))
   HALVE#1(S(S(z0))) -> c18(HALVE#1(z0))
   LEQ#2(S(z0), S(z1)) -> c22(LEQ#2(z0, z1))
   LENGTH#1(Cons(z0, z1)) -> c24(LENGTH#1(z1))
   MAP#2(dc(z0, z1, z2, z3, z4), Cons(z5, z6)) -> c26(DC#1(z0, z1, z2, z3, z4, z5))
   MAP#2(dc(z0, z1, z2, z3, z4), Cons(z5, z6)) -> c27(MAP#2(dc(z0, z1, z2, z3, z4), z6))
   MERGE#2(Cons(0, x1), Cons(z0, x3)) -> c6(COND_MERGE_YS_ZS_2(True, Cons(0, x1), Cons(z0, x3), 0, x1, z0, x3))
   MERGE#2(Cons(S(z0), x1), Cons(0, x3)) -> c6(COND_MERGE_YS_ZS_2(False, Cons(S(z0), x1), Cons(0, x3), S(z0), x1, 0, x3))
   MERGE#2(Cons(S(0), x1), Cons(S(z0), x3)) -> c6(COND_MERGE_YS_ZS_2(True, Cons(S(0), x1), Cons(S(z0), x3), S(0), x1, S(z0), x3), LEQ#2(S(0), S(z0)))
   MERGE#2(Cons(S(S(z0)), x1), Cons(S(0), x3)) -> c6(COND_MERGE_YS_ZS_2(False, Cons(S(S(z0)), x1), Cons(S(0), x3), S(S(z0)), x1, S(0), x3), LEQ#2(S(S(z0)), S(0)))
   MERGE#2(Cons(S(S(z0)), x1), Cons(S(S(z1)), x3)) -> c6(COND_MERGE_YS_ZS_2(leq#2(z0, z1), Cons(S(S(z0)), x1), Cons(S(S(z1)), x3), S(S(z0)), x1, S(S(z1)), x3), LEQ#2(S(S(z0)), S(S(z1))))
   MERGE#2(Cons(S(x0), x1), Cons(S(x2), x3)) -> c6(LEQ#2(S(x0), S(x2)))
   DIVIDE_YS#1(Cons(x0, Cons(x1, x2)), S(y11)) -> c(TAKE#2(S(y11), Cons(x0, Cons(x1, x2))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, x3))), S(y11)) -> c(TAKE#2(S(y11), Cons(x0, Cons(x1, Cons(x2, x3)))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Nil)), S(y10)) -> c(TAKE#2(S(y10), Cons(x0, Cons(x1, Nil))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Nil))), S(y7)) -> c(TAKE#2(S(y7), Cons(x0, Cons(x1, Cons(x2, Nil)))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4)))), S(y8)) -> c(TAKE#2(S(y8), Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4))))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, x2)), S(y11)) -> c1(DROP#2(S(y11), Cons(x0, Cons(x1, x2))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, x3))), S(y11)) -> c1(DROP#2(S(y11), Cons(x0, Cons(x1, Cons(x2, x3)))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Nil)), S(y10)) -> c1(DROP#2(S(y10), Cons(x0, Cons(x1, Nil))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Nil))), S(y7)) -> c1(DROP#2(S(y7), Cons(x0, Cons(x1, Cons(x2, Nil)))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4)))), S(y8)) -> c1(DROP#2(S(y8), Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4))))))
   COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(S(S(y2)), z3), z4, Cons(S(S(y0)), y1), z6, z7) -> c2(MERGE#2(Cons(S(S(y0)), y1), Cons(S(S(y2)), z3)))
   COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(S(y2), z3), z4, Cons(S(y0), y1), z6, z7) -> c2(MERGE#2(Cons(S(y0), y1), Cons(S(y2), z3)))
   COND_MERGE_YS_ZS_2(False, Cons(S(x0), x1), Cons(0, x2), S(x0), x1, 0, x2) -> c3(MERGE#2(Cons(S(x0), x1), x2))
   COND_MERGE_YS_ZS_2(False, Cons(S(S(x0)), x1), Cons(S(0), x2), S(S(x0)), x1, S(0), x2) -> c3(MERGE#2(Cons(S(S(x0)), x1), x2))
   COND_MERGE_YS_ZS_2(False, Cons(S(S(x0)), x1), Cons(S(S(x2)), x3), S(S(x0)), x1, S(S(x2)), x3) -> c3(MERGE#2(Cons(S(S(x0)), x1), x3))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Nil))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(Nil))), Cons(z0, Cons(z1, Nil))), Cons(drop#2(S(halve#1(0)), Cons(z0, Cons(z1, Nil))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil)))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Nil))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(0)), Cons(z0, Cons(z1, Nil))), Cons(drop#2(S(halve#1(length#1(Nil))), Cons(z0, Cons(z1, Nil))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil)))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, z3)))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Cons(z2, z3))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(S(length#1(z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Cons(drop#2(S(halve#1(S(length#1(z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3)))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3))))), HALVE#1(S(length#1(z3))), LENGTH#1(Cons(z2, z3)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, Nil)))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Cons(z2, Nil))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, Nil))), S(halve#1(S(0)))))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, Nil))), S(halve#1(length#1(Cons(z2, Nil)))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, Nil))), S(halve#1(length#1(Cons(z2, Nil))))), HALVE#1(S(length#1(Nil))), LENGTH#1(Cons(z2, Nil)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, Cons(z3, z4))))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Cons(z2, Cons(z3, z4)))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, Cons(z3, z4)))), S(halve#1(S(S(length#1(z4)))))))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, Cons(z3, z4)))), S(halve#1(length#1(Cons(z2, Cons(z3, z4))))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, Cons(z3, z4)))), S(halve#1(length#1(Cons(z2, Cons(z3, z4)))))), HALVE#1(S(length#1(Cons(z3, z4)))), LENGTH#1(Cons(z2, Cons(z3, z4))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, z3)))) -> c9(MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3)))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3))))), HALVE#1(S(length#1(z3))), LENGTH#1(Cons(z2, z3)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Nil))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(0)), Cons(z0, Cons(z1, Nil))), Cons(drop#2(S(halve#1(0)), Cons(z0, Cons(z1, Nil))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil)))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Nil))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Nil)), S(0)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil)))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> c9(CONST_F#2(Cons(z0, Cons(z1, z2)), Cons(dc#1(map, divisible, mergesort_zs_3, divide, const_f, take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2)))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(drop#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(halve#1(length#1(z2)), Cons(z1, z2)), Nil))), DIVIDE_YS#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2)))), HALVE#1(length#1(z2)), LENGTH#1(z2))
   CONST_F#2(Cons(x0, Cons(x1, x2)), Cons(z1, Cons(z2, z3))) -> c19(MERGE#2(z1, z2))
   CONST_F#2(Cons(x0, Cons(x1, Cons(x2, x3))), Cons(z1, Cons(z2, z3))) -> c19(MERGE#2(z1, z2))
   CONST_F#2(Cons(x0, Cons(x1, Nil)), Cons(z1, Cons(z2, z3))) -> c19(MERGE#2(z1, z2))
   CONST_F#2(Cons(x0, Cons(x1, Cons(x2, Nil))), Cons(z1, Cons(z2, z3))) -> c19(MERGE#2(z1, z2))
   CONST_F#2(Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4)))), Cons(z1, Cons(z2, z3))) -> c19(MERGE#2(z1, z2))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> c9(CONST_F#2(Cons(z0, Cons(z1, z2)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(halve#1(length#1(z2)), Cons(z1, z2)), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(halve#1(length#1(z2)), Cons(z1, z2)), Nil))), DIVIDE_YS#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2)))), HALVE#1(length#1(z2)), LENGTH#1(z2))
   COND_MERGE_YS_ZS_2(True, Cons(0, Cons(0, z5)), Cons(x1, x2), 0, Cons(0, z5), x1, x2) -> c2(MERGE#2(Cons(0, z5), Cons(x1, x2)))
   COND_MERGE_YS_ZS_2(True, Cons(S(0), Cons(0, z5)), Cons(S(x1), x2), S(0), Cons(0, z5), S(x1), x2) -> c2(MERGE#2(Cons(0, z5), Cons(S(x1), x2)))
   COND_MERGE_YS_ZS_2(True, Cons(S(S(x0)), Cons(0, z5)), Cons(S(S(x2)), x3), S(S(x0)), Cons(0, z5), S(S(x2)), x3) -> c2(MERGE#2(Cons(0, z5), Cons(S(S(x2)), x3)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, z3)))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Cons(z2, z3))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(Cons(z2, z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Cons(drop#2(S(halve#1(S(length#1(z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3)))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(S(length#1(z3))))), HALVE#1(S(length#1(z3))), LENGTH#1(Cons(z2, z3)))
   COND_MERGE_YS_ZS_2(True, Cons(0, Cons(S(z4), z5)), Cons(0, x2), 0, Cons(S(z4), z5), 0, x2) -> c2(MERGE#2(Cons(S(z4), z5), Cons(0, x2)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> c9(CONST_F#2(Cons(z0, Cons(z1, z2)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(Cons(z0, take#2(halve#1(length#1(z2)), Cons(z1, z2))), Cons(drop#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(halve#1(length#1(z2)), Cons(z1, z2)), Nil))), DIVIDE_YS#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2)))), HALVE#1(length#1(z2)), LENGTH#1(z2))
   COND_MERGE_YS_ZS_2(True, Cons(0, Cons(S(0), z5)), Cons(S(z2), x2), 0, Cons(S(0), z5), S(z2), x2) -> c2(MERGE#2(Cons(S(0), z5), Cons(S(z2), x2)))
   COND_MERGE_YS_ZS_2(True, Cons(S(0), Cons(S(0), z5)), Cons(S(x1), x2), S(0), Cons(S(0), z5), S(x1), x2) -> c2(MERGE#2(Cons(S(0), z5), Cons(S(x1), x2)))
   COND_MERGE_YS_ZS_2(True, Cons(S(S(x0)), Cons(S(0), z5)), Cons(S(S(x2)), x3), S(S(x0)), Cons(S(0), z5), S(S(x2)), x3) -> c2(MERGE#2(Cons(S(0), z5), Cons(S(S(x2)), x3)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, z3)))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Cons(z2, z3))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(S(length#1(z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Cons(drop#2(S(halve#1(length#1(Cons(z2, z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3)))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(S(length#1(z3))))), HALVE#1(S(length#1(z3))), LENGTH#1(Cons(z2, z3)))
   COND_MERGE_YS_ZS_2(True, Cons(0, Cons(S(S(z4)), z5)), Cons(S(0), x2), 0, Cons(S(S(z4)), z5), S(0), x2) -> c2(MERGE#2(Cons(S(S(z4)), z5), Cons(S(0), x2)))
   COND_MERGE_YS_ZS_2(True, Cons(S(0), Cons(S(S(z4)), z5)), Cons(S(0), x2), S(0), Cons(S(S(z4)), z5), S(0), x2) -> c2(MERGE#2(Cons(S(S(z4)), z5), Cons(S(0), x2)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> c9(MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(halve#1(length#1(z2)), Cons(z1, z2)), Nil))), DIVIDE_YS#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2)))))
S tuples:
   DROP#2(S(z0), Cons(z1, z2)) -> c12(DROP#2(z0, z2))
   TAKE#2(S(z0), Cons(z1, z2)) -> c15(TAKE#2(z0, z2))
   HALVE#1(S(S(z0))) -> c18(HALVE#1(z0))
   LEQ#2(S(z0), S(z1)) -> c22(LEQ#2(z0, z1))
   LENGTH#1(Cons(z0, z1)) -> c24(LENGTH#1(z1))
   MAP#2(dc(z0, z1, z2, z3, z4), Cons(z5, z6)) -> c26(DC#1(z0, z1, z2, z3, z4, z5))
   MAP#2(dc(z0, z1, z2, z3, z4), Cons(z5, z6)) -> c27(MAP#2(dc(z0, z1, z2, z3, z4), z6))
   MERGE#2(Cons(0, x1), Cons(z0, x3)) -> c6(COND_MERGE_YS_ZS_2(True, Cons(0, x1), Cons(z0, x3), 0, x1, z0, x3))
   MERGE#2(Cons(S(z0), x1), Cons(0, x3)) -> c6(COND_MERGE_YS_ZS_2(False, Cons(S(z0), x1), Cons(0, x3), S(z0), x1, 0, x3))
   MERGE#2(Cons(S(0), x1), Cons(S(z0), x3)) -> c6(COND_MERGE_YS_ZS_2(True, Cons(S(0), x1), Cons(S(z0), x3), S(0), x1, S(z0), x3), LEQ#2(S(0), S(z0)))
   MERGE#2(Cons(S(S(z0)), x1), Cons(S(0), x3)) -> c6(COND_MERGE_YS_ZS_2(False, Cons(S(S(z0)), x1), Cons(S(0), x3), S(S(z0)), x1, S(0), x3), LEQ#2(S(S(z0)), S(0)))
   MERGE#2(Cons(S(S(z0)), x1), Cons(S(S(z1)), x3)) -> c6(COND_MERGE_YS_ZS_2(leq#2(z0, z1), Cons(S(S(z0)), x1), Cons(S(S(z1)), x3), S(S(z0)), x1, S(S(z1)), x3), LEQ#2(S(S(z0)), S(S(z1))))
   MERGE#2(Cons(S(x0), x1), Cons(S(x2), x3)) -> c6(LEQ#2(S(x0), S(x2)))
   DIVIDE_YS#1(Cons(x0, Cons(x1, x2)), S(y11)) -> c(TAKE#2(S(y11), Cons(x0, Cons(x1, x2))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, x3))), S(y11)) -> c(TAKE#2(S(y11), Cons(x0, Cons(x1, Cons(x2, x3)))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Nil)), S(y10)) -> c(TAKE#2(S(y10), Cons(x0, Cons(x1, Nil))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Nil))), S(y7)) -> c(TAKE#2(S(y7), Cons(x0, Cons(x1, Cons(x2, Nil)))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4)))), S(y8)) -> c(TAKE#2(S(y8), Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4))))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, x2)), S(y11)) -> c1(DROP#2(S(y11), Cons(x0, Cons(x1, x2))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, x3))), S(y11)) -> c1(DROP#2(S(y11), Cons(x0, Cons(x1, Cons(x2, x3)))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Nil)), S(y10)) -> c1(DROP#2(S(y10), Cons(x0, Cons(x1, Nil))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Nil))), S(y7)) -> c1(DROP#2(S(y7), Cons(x0, Cons(x1, Cons(x2, Nil)))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4)))), S(y8)) -> c1(DROP#2(S(y8), Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4))))))
   COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(S(S(y2)), z3), z4, Cons(S(S(y0)), y1), z6, z7) -> c2(MERGE#2(Cons(S(S(y0)), y1), Cons(S(S(y2)), z3)))
   COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(S(y2), z3), z4, Cons(S(y0), y1), z6, z7) -> c2(MERGE#2(Cons(S(y0), y1), Cons(S(y2), z3)))
   COND_MERGE_YS_ZS_2(False, Cons(S(x0), x1), Cons(0, x2), S(x0), x1, 0, x2) -> c3(MERGE#2(Cons(S(x0), x1), x2))
   COND_MERGE_YS_ZS_2(False, Cons(S(S(x0)), x1), Cons(S(0), x2), S(S(x0)), x1, S(0), x2) -> c3(MERGE#2(Cons(S(S(x0)), x1), x2))
   COND_MERGE_YS_ZS_2(False, Cons(S(S(x0)), x1), Cons(S(S(x2)), x3), S(S(x0)), x1, S(S(x2)), x3) -> c3(MERGE#2(Cons(S(S(x0)), x1), x3))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Nil))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(Nil))), Cons(z0, Cons(z1, Nil))), Cons(drop#2(S(halve#1(0)), Cons(z0, Cons(z1, Nil))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil)))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Nil))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(0)), Cons(z0, Cons(z1, Nil))), Cons(drop#2(S(halve#1(length#1(Nil))), Cons(z0, Cons(z1, Nil))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil)))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, z3)))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Cons(z2, z3))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(S(length#1(z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Cons(drop#2(S(halve#1(S(length#1(z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3)))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3))))), HALVE#1(S(length#1(z3))), LENGTH#1(Cons(z2, z3)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, Nil)))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Cons(z2, Nil))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, Nil))), S(halve#1(S(0)))))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, Nil))), S(halve#1(length#1(Cons(z2, Nil)))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, Nil))), S(halve#1(length#1(Cons(z2, Nil))))), HALVE#1(S(length#1(Nil))), LENGTH#1(Cons(z2, Nil)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, Cons(z3, z4))))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Cons(z2, Cons(z3, z4)))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, Cons(z3, z4)))), S(halve#1(S(S(length#1(z4)))))))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, Cons(z3, z4)))), S(halve#1(length#1(Cons(z2, Cons(z3, z4))))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, Cons(z3, z4)))), S(halve#1(length#1(Cons(z2, Cons(z3, z4)))))), HALVE#1(S(length#1(Cons(z3, z4)))), LENGTH#1(Cons(z2, Cons(z3, z4))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, z3)))) -> c9(MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3)))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3))))), HALVE#1(S(length#1(z3))), LENGTH#1(Cons(z2, z3)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Nil))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(0)), Cons(z0, Cons(z1, Nil))), Cons(drop#2(S(halve#1(0)), Cons(z0, Cons(z1, Nil))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil)))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Nil))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Nil)), S(0)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil)))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> c9(CONST_F#2(Cons(z0, Cons(z1, z2)), Cons(dc#1(map, divisible, mergesort_zs_3, divide, const_f, take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2)))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(drop#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(halve#1(length#1(z2)), Cons(z1, z2)), Nil))), DIVIDE_YS#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2)))), HALVE#1(length#1(z2)), LENGTH#1(z2))
   CONST_F#2(Cons(x0, Cons(x1, x2)), Cons(z1, Cons(z2, z3))) -> c19(MERGE#2(z1, z2))
   CONST_F#2(Cons(x0, Cons(x1, Cons(x2, x3))), Cons(z1, Cons(z2, z3))) -> c19(MERGE#2(z1, z2))
   CONST_F#2(Cons(x0, Cons(x1, Nil)), Cons(z1, Cons(z2, z3))) -> c19(MERGE#2(z1, z2))
   CONST_F#2(Cons(x0, Cons(x1, Cons(x2, Nil))), Cons(z1, Cons(z2, z3))) -> c19(MERGE#2(z1, z2))
   CONST_F#2(Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4)))), Cons(z1, Cons(z2, z3))) -> c19(MERGE#2(z1, z2))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> c9(CONST_F#2(Cons(z0, Cons(z1, z2)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(halve#1(length#1(z2)), Cons(z1, z2)), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(halve#1(length#1(z2)), Cons(z1, z2)), Nil))), DIVIDE_YS#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2)))), HALVE#1(length#1(z2)), LENGTH#1(z2))
   COND_MERGE_YS_ZS_2(True, Cons(0, Cons(0, z5)), Cons(x1, x2), 0, Cons(0, z5), x1, x2) -> c2(MERGE#2(Cons(0, z5), Cons(x1, x2)))
   COND_MERGE_YS_ZS_2(True, Cons(S(0), Cons(0, z5)), Cons(S(x1), x2), S(0), Cons(0, z5), S(x1), x2) -> c2(MERGE#2(Cons(0, z5), Cons(S(x1), x2)))
   COND_MERGE_YS_ZS_2(True, Cons(S(S(x0)), Cons(0, z5)), Cons(S(S(x2)), x3), S(S(x0)), Cons(0, z5), S(S(x2)), x3) -> c2(MERGE#2(Cons(0, z5), Cons(S(S(x2)), x3)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, z3)))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Cons(z2, z3))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(Cons(z2, z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Cons(drop#2(S(halve#1(S(length#1(z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3)))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(S(length#1(z3))))), HALVE#1(S(length#1(z3))), LENGTH#1(Cons(z2, z3)))
   COND_MERGE_YS_ZS_2(True, Cons(0, Cons(S(z4), z5)), Cons(0, x2), 0, Cons(S(z4), z5), 0, x2) -> c2(MERGE#2(Cons(S(z4), z5), Cons(0, x2)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> c9(CONST_F#2(Cons(z0, Cons(z1, z2)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(Cons(z0, take#2(halve#1(length#1(z2)), Cons(z1, z2))), Cons(drop#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(halve#1(length#1(z2)), Cons(z1, z2)), Nil))), DIVIDE_YS#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2)))), HALVE#1(length#1(z2)), LENGTH#1(z2))
   COND_MERGE_YS_ZS_2(True, Cons(0, Cons(S(0), z5)), Cons(S(z2), x2), 0, Cons(S(0), z5), S(z2), x2) -> c2(MERGE#2(Cons(S(0), z5), Cons(S(z2), x2)))
   COND_MERGE_YS_ZS_2(True, Cons(S(0), Cons(S(0), z5)), Cons(S(x1), x2), S(0), Cons(S(0), z5), S(x1), x2) -> c2(MERGE#2(Cons(S(0), z5), Cons(S(x1), x2)))
   COND_MERGE_YS_ZS_2(True, Cons(S(S(x0)), Cons(S(0), z5)), Cons(S(S(x2)), x3), S(S(x0)), Cons(S(0), z5), S(S(x2)), x3) -> c2(MERGE#2(Cons(S(0), z5), Cons(S(S(x2)), x3)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, z3)))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Cons(z2, z3))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(S(length#1(z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Cons(drop#2(S(halve#1(length#1(Cons(z2, z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3)))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(S(length#1(z3))))), HALVE#1(S(length#1(z3))), LENGTH#1(Cons(z2, z3)))
   COND_MERGE_YS_ZS_2(True, Cons(0, Cons(S(S(z4)), z5)), Cons(S(0), x2), 0, Cons(S(S(z4)), z5), S(0), x2) -> c2(MERGE#2(Cons(S(S(z4)), z5), Cons(S(0), x2)))
   COND_MERGE_YS_ZS_2(True, Cons(S(0), Cons(S(S(z4)), z5)), Cons(S(0), x2), S(0), Cons(S(S(z4)), z5), S(0), x2) -> c2(MERGE#2(Cons(S(S(z4)), z5), Cons(S(0), x2)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> c9(MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(halve#1(length#1(z2)), Cons(z1, z2)), Nil))), DIVIDE_YS#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2)))))
K tuples:none
Defined Rule Symbols:   leq#2_2, map#2_2, divide_ys#1_2, halve#1_1, length#1_1, take#2_2, drop#2_2, dc#1_6, const_f#2_2, merge#2_2, cond_merge_ys_zs_2_7

Defined Pair Symbols:   DROP#2_2, TAKE#2_2, HALVE#1_1, LEQ#2_2, LENGTH#1_1, MAP#2_2, MERGE#2_2, DIVIDE_YS#1_2, COND_MERGE_YS_ZS_2_7, DC#1_6, CONST_F#2_2

Compound Symbols:   c12_1, c15_1, c18_1, c22_1, c24_1, c26_1, c27_1, c6_1, c6_2, c_1, c1_1, c2_1, c3_1, c9_3, c9_5, c9_4, c19_1, c9_2


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

(167) CdtRewritingProof (BOTH BOUNDS(ID, ID))
Used rewriting to replace DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Nil))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(Nil))), Cons(z0, Cons(z1, Nil))), Cons(drop#2(S(halve#1(0)), Cons(z0, Cons(z1, Nil))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil))))) by DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Nil))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(Nil))), Cons(z0, Cons(z1, Nil))), Cons(drop#2(S(halve#1(0)), Cons(z0, Cons(z1, Nil))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Nil)), S(halve#1(0))))
----------------------------------------

(168)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   leq#2(0, z0) -> True
   leq#2(S(z0), 0) -> False
   leq#2(S(z0), S(z1)) -> leq#2(z0, z1)
   map#2(dc(z0, z1, z2, z3, z4), Nil) -> Nil
   map#2(dc(z0, z1, z2, z3, z4), Cons(z5, z6)) -> Cons(dc#1(z0, z1, z2, z3, z4, z5), map#2(dc(z0, z1, z2, z3, z4), z6))
   divide_ys#1(z0, z1) -> Cons(take#2(z1, z0), Cons(drop#2(z1, z0), Nil))
   halve#1(0) -> 0
   halve#1(S(0)) -> S(0)
   halve#1(S(S(z0))) -> S(halve#1(z0))
   length#1(Nil) -> 0
   length#1(Cons(z0, z1)) -> S(length#1(z1))
   take#2(0, z0) -> Nil
   take#2(S(0), Nil) -> Cons(bot[0], Nil)
   take#2(S(z0), Cons(z1, z2)) -> Cons(z1, take#2(z0, z2))
   drop#2(0, z0) -> z0
   drop#2(S(0), Nil) -> bot[1]
   drop#2(S(z0), Cons(z1, z2)) -> drop#2(z0, z2)
   dc#1(map, divisible, mergesort_zs_3, divide, const_f, Nil) -> Nil
   dc#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Nil)) -> Cons(z0, Nil)
   dc#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> const_f#2(Cons(z0, Cons(z1, z2)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2))))))
   const_f#2(z0, Cons(z1, Cons(z2, z3))) -> merge#2(z1, z2)
   merge#2(Nil, z0) -> z0
   merge#2(Cons(z0, z1), Nil) -> Cons(z0, z1)
   merge#2(Cons(z0, z1), Cons(z2, z3)) -> cond_merge_ys_zs_2(leq#2(z0, z2), Cons(z0, z1), Cons(z2, z3), z0, z1, z2, z3)
   cond_merge_ys_zs_2(True, Cons(z0, z1), Cons(z2, z3), z4, z5, z6, z7) -> Cons(z4, merge#2(z5, Cons(z2, z3)))
   cond_merge_ys_zs_2(False, Cons(z0, z1), Cons(z2, z3), z4, z5, z6, z7) -> Cons(z6, merge#2(Cons(z0, z1), z7))
Tuples:
   DROP#2(S(z0), Cons(z1, z2)) -> c12(DROP#2(z0, z2))
   TAKE#2(S(z0), Cons(z1, z2)) -> c15(TAKE#2(z0, z2))
   HALVE#1(S(S(z0))) -> c18(HALVE#1(z0))
   LEQ#2(S(z0), S(z1)) -> c22(LEQ#2(z0, z1))
   LENGTH#1(Cons(z0, z1)) -> c24(LENGTH#1(z1))
   MAP#2(dc(z0, z1, z2, z3, z4), Cons(z5, z6)) -> c26(DC#1(z0, z1, z2, z3, z4, z5))
   MAP#2(dc(z0, z1, z2, z3, z4), Cons(z5, z6)) -> c27(MAP#2(dc(z0, z1, z2, z3, z4), z6))
   MERGE#2(Cons(0, x1), Cons(z0, x3)) -> c6(COND_MERGE_YS_ZS_2(True, Cons(0, x1), Cons(z0, x3), 0, x1, z0, x3))
   MERGE#2(Cons(S(z0), x1), Cons(0, x3)) -> c6(COND_MERGE_YS_ZS_2(False, Cons(S(z0), x1), Cons(0, x3), S(z0), x1, 0, x3))
   MERGE#2(Cons(S(0), x1), Cons(S(z0), x3)) -> c6(COND_MERGE_YS_ZS_2(True, Cons(S(0), x1), Cons(S(z0), x3), S(0), x1, S(z0), x3), LEQ#2(S(0), S(z0)))
   MERGE#2(Cons(S(S(z0)), x1), Cons(S(0), x3)) -> c6(COND_MERGE_YS_ZS_2(False, Cons(S(S(z0)), x1), Cons(S(0), x3), S(S(z0)), x1, S(0), x3), LEQ#2(S(S(z0)), S(0)))
   MERGE#2(Cons(S(S(z0)), x1), Cons(S(S(z1)), x3)) -> c6(COND_MERGE_YS_ZS_2(leq#2(z0, z1), Cons(S(S(z0)), x1), Cons(S(S(z1)), x3), S(S(z0)), x1, S(S(z1)), x3), LEQ#2(S(S(z0)), S(S(z1))))
   MERGE#2(Cons(S(x0), x1), Cons(S(x2), x3)) -> c6(LEQ#2(S(x0), S(x2)))
   DIVIDE_YS#1(Cons(x0, Cons(x1, x2)), S(y11)) -> c(TAKE#2(S(y11), Cons(x0, Cons(x1, x2))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, x3))), S(y11)) -> c(TAKE#2(S(y11), Cons(x0, Cons(x1, Cons(x2, x3)))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Nil)), S(y10)) -> c(TAKE#2(S(y10), Cons(x0, Cons(x1, Nil))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Nil))), S(y7)) -> c(TAKE#2(S(y7), Cons(x0, Cons(x1, Cons(x2, Nil)))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4)))), S(y8)) -> c(TAKE#2(S(y8), Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4))))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, x2)), S(y11)) -> c1(DROP#2(S(y11), Cons(x0, Cons(x1, x2))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, x3))), S(y11)) -> c1(DROP#2(S(y11), Cons(x0, Cons(x1, Cons(x2, x3)))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Nil)), S(y10)) -> c1(DROP#2(S(y10), Cons(x0, Cons(x1, Nil))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Nil))), S(y7)) -> c1(DROP#2(S(y7), Cons(x0, Cons(x1, Cons(x2, Nil)))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4)))), S(y8)) -> c1(DROP#2(S(y8), Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4))))))
   COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(S(S(y2)), z3), z4, Cons(S(S(y0)), y1), z6, z7) -> c2(MERGE#2(Cons(S(S(y0)), y1), Cons(S(S(y2)), z3)))
   COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(S(y2), z3), z4, Cons(S(y0), y1), z6, z7) -> c2(MERGE#2(Cons(S(y0), y1), Cons(S(y2), z3)))
   COND_MERGE_YS_ZS_2(False, Cons(S(x0), x1), Cons(0, x2), S(x0), x1, 0, x2) -> c3(MERGE#2(Cons(S(x0), x1), x2))
   COND_MERGE_YS_ZS_2(False, Cons(S(S(x0)), x1), Cons(S(0), x2), S(S(x0)), x1, S(0), x2) -> c3(MERGE#2(Cons(S(S(x0)), x1), x2))
   COND_MERGE_YS_ZS_2(False, Cons(S(S(x0)), x1), Cons(S(S(x2)), x3), S(S(x0)), x1, S(S(x2)), x3) -> c3(MERGE#2(Cons(S(S(x0)), x1), x3))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Nil))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(0)), Cons(z0, Cons(z1, Nil))), Cons(drop#2(S(halve#1(length#1(Nil))), Cons(z0, Cons(z1, Nil))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil)))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, z3)))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Cons(z2, z3))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(S(length#1(z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Cons(drop#2(S(halve#1(S(length#1(z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3)))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3))))), HALVE#1(S(length#1(z3))), LENGTH#1(Cons(z2, z3)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, Nil)))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Cons(z2, Nil))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, Nil))), S(halve#1(S(0)))))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, Nil))), S(halve#1(length#1(Cons(z2, Nil)))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, Nil))), S(halve#1(length#1(Cons(z2, Nil))))), HALVE#1(S(length#1(Nil))), LENGTH#1(Cons(z2, Nil)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, Cons(z3, z4))))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Cons(z2, Cons(z3, z4)))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, Cons(z3, z4)))), S(halve#1(S(S(length#1(z4)))))))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, Cons(z3, z4)))), S(halve#1(length#1(Cons(z2, Cons(z3, z4))))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, Cons(z3, z4)))), S(halve#1(length#1(Cons(z2, Cons(z3, z4)))))), HALVE#1(S(length#1(Cons(z3, z4)))), LENGTH#1(Cons(z2, Cons(z3, z4))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, z3)))) -> c9(MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3)))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3))))), HALVE#1(S(length#1(z3))), LENGTH#1(Cons(z2, z3)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Nil))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(0)), Cons(z0, Cons(z1, Nil))), Cons(drop#2(S(halve#1(0)), Cons(z0, Cons(z1, Nil))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil)))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Nil))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Nil)), S(0)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil)))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> c9(CONST_F#2(Cons(z0, Cons(z1, z2)), Cons(dc#1(map, divisible, mergesort_zs_3, divide, const_f, take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2)))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(drop#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(halve#1(length#1(z2)), Cons(z1, z2)), Nil))), DIVIDE_YS#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2)))), HALVE#1(length#1(z2)), LENGTH#1(z2))
   CONST_F#2(Cons(x0, Cons(x1, x2)), Cons(z1, Cons(z2, z3))) -> c19(MERGE#2(z1, z2))
   CONST_F#2(Cons(x0, Cons(x1, Cons(x2, x3))), Cons(z1, Cons(z2, z3))) -> c19(MERGE#2(z1, z2))
   CONST_F#2(Cons(x0, Cons(x1, Nil)), Cons(z1, Cons(z2, z3))) -> c19(MERGE#2(z1, z2))
   CONST_F#2(Cons(x0, Cons(x1, Cons(x2, Nil))), Cons(z1, Cons(z2, z3))) -> c19(MERGE#2(z1, z2))
   CONST_F#2(Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4)))), Cons(z1, Cons(z2, z3))) -> c19(MERGE#2(z1, z2))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> c9(CONST_F#2(Cons(z0, Cons(z1, z2)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(halve#1(length#1(z2)), Cons(z1, z2)), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(halve#1(length#1(z2)), Cons(z1, z2)), Nil))), DIVIDE_YS#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2)))), HALVE#1(length#1(z2)), LENGTH#1(z2))
   COND_MERGE_YS_ZS_2(True, Cons(0, Cons(0, z5)), Cons(x1, x2), 0, Cons(0, z5), x1, x2) -> c2(MERGE#2(Cons(0, z5), Cons(x1, x2)))
   COND_MERGE_YS_ZS_2(True, Cons(S(0), Cons(0, z5)), Cons(S(x1), x2), S(0), Cons(0, z5), S(x1), x2) -> c2(MERGE#2(Cons(0, z5), Cons(S(x1), x2)))
   COND_MERGE_YS_ZS_2(True, Cons(S(S(x0)), Cons(0, z5)), Cons(S(S(x2)), x3), S(S(x0)), Cons(0, z5), S(S(x2)), x3) -> c2(MERGE#2(Cons(0, z5), Cons(S(S(x2)), x3)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, z3)))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Cons(z2, z3))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(Cons(z2, z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Cons(drop#2(S(halve#1(S(length#1(z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3)))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(S(length#1(z3))))), HALVE#1(S(length#1(z3))), LENGTH#1(Cons(z2, z3)))
   COND_MERGE_YS_ZS_2(True, Cons(0, Cons(S(z4), z5)), Cons(0, x2), 0, Cons(S(z4), z5), 0, x2) -> c2(MERGE#2(Cons(S(z4), z5), Cons(0, x2)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> c9(CONST_F#2(Cons(z0, Cons(z1, z2)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(Cons(z0, take#2(halve#1(length#1(z2)), Cons(z1, z2))), Cons(drop#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(halve#1(length#1(z2)), Cons(z1, z2)), Nil))), DIVIDE_YS#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2)))), HALVE#1(length#1(z2)), LENGTH#1(z2))
   COND_MERGE_YS_ZS_2(True, Cons(0, Cons(S(0), z5)), Cons(S(z2), x2), 0, Cons(S(0), z5), S(z2), x2) -> c2(MERGE#2(Cons(S(0), z5), Cons(S(z2), x2)))
   COND_MERGE_YS_ZS_2(True, Cons(S(0), Cons(S(0), z5)), Cons(S(x1), x2), S(0), Cons(S(0), z5), S(x1), x2) -> c2(MERGE#2(Cons(S(0), z5), Cons(S(x1), x2)))
   COND_MERGE_YS_ZS_2(True, Cons(S(S(x0)), Cons(S(0), z5)), Cons(S(S(x2)), x3), S(S(x0)), Cons(S(0), z5), S(S(x2)), x3) -> c2(MERGE#2(Cons(S(0), z5), Cons(S(S(x2)), x3)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, z3)))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Cons(z2, z3))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(S(length#1(z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Cons(drop#2(S(halve#1(length#1(Cons(z2, z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3)))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(S(length#1(z3))))), HALVE#1(S(length#1(z3))), LENGTH#1(Cons(z2, z3)))
   COND_MERGE_YS_ZS_2(True, Cons(0, Cons(S(S(z4)), z5)), Cons(S(0), x2), 0, Cons(S(S(z4)), z5), S(0), x2) -> c2(MERGE#2(Cons(S(S(z4)), z5), Cons(S(0), x2)))
   COND_MERGE_YS_ZS_2(True, Cons(S(0), Cons(S(S(z4)), z5)), Cons(S(0), x2), S(0), Cons(S(S(z4)), z5), S(0), x2) -> c2(MERGE#2(Cons(S(S(z4)), z5), Cons(S(0), x2)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> c9(MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(halve#1(length#1(z2)), Cons(z1, z2)), Nil))), DIVIDE_YS#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2)))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Nil))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(Nil))), Cons(z0, Cons(z1, Nil))), Cons(drop#2(S(halve#1(0)), Cons(z0, Cons(z1, Nil))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Nil)), S(halve#1(0))))
S tuples:
   DROP#2(S(z0), Cons(z1, z2)) -> c12(DROP#2(z0, z2))
   TAKE#2(S(z0), Cons(z1, z2)) -> c15(TAKE#2(z0, z2))
   HALVE#1(S(S(z0))) -> c18(HALVE#1(z0))
   LEQ#2(S(z0), S(z1)) -> c22(LEQ#2(z0, z1))
   LENGTH#1(Cons(z0, z1)) -> c24(LENGTH#1(z1))
   MAP#2(dc(z0, z1, z2, z3, z4), Cons(z5, z6)) -> c26(DC#1(z0, z1, z2, z3, z4, z5))
   MAP#2(dc(z0, z1, z2, z3, z4), Cons(z5, z6)) -> c27(MAP#2(dc(z0, z1, z2, z3, z4), z6))
   MERGE#2(Cons(0, x1), Cons(z0, x3)) -> c6(COND_MERGE_YS_ZS_2(True, Cons(0, x1), Cons(z0, x3), 0, x1, z0, x3))
   MERGE#2(Cons(S(z0), x1), Cons(0, x3)) -> c6(COND_MERGE_YS_ZS_2(False, Cons(S(z0), x1), Cons(0, x3), S(z0), x1, 0, x3))
   MERGE#2(Cons(S(0), x1), Cons(S(z0), x3)) -> c6(COND_MERGE_YS_ZS_2(True, Cons(S(0), x1), Cons(S(z0), x3), S(0), x1, S(z0), x3), LEQ#2(S(0), S(z0)))
   MERGE#2(Cons(S(S(z0)), x1), Cons(S(0), x3)) -> c6(COND_MERGE_YS_ZS_2(False, Cons(S(S(z0)), x1), Cons(S(0), x3), S(S(z0)), x1, S(0), x3), LEQ#2(S(S(z0)), S(0)))
   MERGE#2(Cons(S(S(z0)), x1), Cons(S(S(z1)), x3)) -> c6(COND_MERGE_YS_ZS_2(leq#2(z0, z1), Cons(S(S(z0)), x1), Cons(S(S(z1)), x3), S(S(z0)), x1, S(S(z1)), x3), LEQ#2(S(S(z0)), S(S(z1))))
   MERGE#2(Cons(S(x0), x1), Cons(S(x2), x3)) -> c6(LEQ#2(S(x0), S(x2)))
   DIVIDE_YS#1(Cons(x0, Cons(x1, x2)), S(y11)) -> c(TAKE#2(S(y11), Cons(x0, Cons(x1, x2))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, x3))), S(y11)) -> c(TAKE#2(S(y11), Cons(x0, Cons(x1, Cons(x2, x3)))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Nil)), S(y10)) -> c(TAKE#2(S(y10), Cons(x0, Cons(x1, Nil))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Nil))), S(y7)) -> c(TAKE#2(S(y7), Cons(x0, Cons(x1, Cons(x2, Nil)))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4)))), S(y8)) -> c(TAKE#2(S(y8), Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4))))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, x2)), S(y11)) -> c1(DROP#2(S(y11), Cons(x0, Cons(x1, x2))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, x3))), S(y11)) -> c1(DROP#2(S(y11), Cons(x0, Cons(x1, Cons(x2, x3)))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Nil)), S(y10)) -> c1(DROP#2(S(y10), Cons(x0, Cons(x1, Nil))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Nil))), S(y7)) -> c1(DROP#2(S(y7), Cons(x0, Cons(x1, Cons(x2, Nil)))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4)))), S(y8)) -> c1(DROP#2(S(y8), Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4))))))
   COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(S(S(y2)), z3), z4, Cons(S(S(y0)), y1), z6, z7) -> c2(MERGE#2(Cons(S(S(y0)), y1), Cons(S(S(y2)), z3)))
   COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(S(y2), z3), z4, Cons(S(y0), y1), z6, z7) -> c2(MERGE#2(Cons(S(y0), y1), Cons(S(y2), z3)))
   COND_MERGE_YS_ZS_2(False, Cons(S(x0), x1), Cons(0, x2), S(x0), x1, 0, x2) -> c3(MERGE#2(Cons(S(x0), x1), x2))
   COND_MERGE_YS_ZS_2(False, Cons(S(S(x0)), x1), Cons(S(0), x2), S(S(x0)), x1, S(0), x2) -> c3(MERGE#2(Cons(S(S(x0)), x1), x2))
   COND_MERGE_YS_ZS_2(False, Cons(S(S(x0)), x1), Cons(S(S(x2)), x3), S(S(x0)), x1, S(S(x2)), x3) -> c3(MERGE#2(Cons(S(S(x0)), x1), x3))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Nil))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(0)), Cons(z0, Cons(z1, Nil))), Cons(drop#2(S(halve#1(length#1(Nil))), Cons(z0, Cons(z1, Nil))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil)))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, z3)))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Cons(z2, z3))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(S(length#1(z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Cons(drop#2(S(halve#1(S(length#1(z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3)))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3))))), HALVE#1(S(length#1(z3))), LENGTH#1(Cons(z2, z3)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, Nil)))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Cons(z2, Nil))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, Nil))), S(halve#1(S(0)))))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, Nil))), S(halve#1(length#1(Cons(z2, Nil)))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, Nil))), S(halve#1(length#1(Cons(z2, Nil))))), HALVE#1(S(length#1(Nil))), LENGTH#1(Cons(z2, Nil)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, Cons(z3, z4))))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Cons(z2, Cons(z3, z4)))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, Cons(z3, z4)))), S(halve#1(S(S(length#1(z4)))))))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, Cons(z3, z4)))), S(halve#1(length#1(Cons(z2, Cons(z3, z4))))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, Cons(z3, z4)))), S(halve#1(length#1(Cons(z2, Cons(z3, z4)))))), HALVE#1(S(length#1(Cons(z3, z4)))), LENGTH#1(Cons(z2, Cons(z3, z4))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, z3)))) -> c9(MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3)))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3))))), HALVE#1(S(length#1(z3))), LENGTH#1(Cons(z2, z3)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Nil))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(0)), Cons(z0, Cons(z1, Nil))), Cons(drop#2(S(halve#1(0)), Cons(z0, Cons(z1, Nil))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil)))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Nil))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Nil)), S(0)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil)))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> c9(CONST_F#2(Cons(z0, Cons(z1, z2)), Cons(dc#1(map, divisible, mergesort_zs_3, divide, const_f, take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2)))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(drop#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(halve#1(length#1(z2)), Cons(z1, z2)), Nil))), DIVIDE_YS#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2)))), HALVE#1(length#1(z2)), LENGTH#1(z2))
   CONST_F#2(Cons(x0, Cons(x1, x2)), Cons(z1, Cons(z2, z3))) -> c19(MERGE#2(z1, z2))
   CONST_F#2(Cons(x0, Cons(x1, Cons(x2, x3))), Cons(z1, Cons(z2, z3))) -> c19(MERGE#2(z1, z2))
   CONST_F#2(Cons(x0, Cons(x1, Nil)), Cons(z1, Cons(z2, z3))) -> c19(MERGE#2(z1, z2))
   CONST_F#2(Cons(x0, Cons(x1, Cons(x2, Nil))), Cons(z1, Cons(z2, z3))) -> c19(MERGE#2(z1, z2))
   CONST_F#2(Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4)))), Cons(z1, Cons(z2, z3))) -> c19(MERGE#2(z1, z2))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> c9(CONST_F#2(Cons(z0, Cons(z1, z2)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(halve#1(length#1(z2)), Cons(z1, z2)), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(halve#1(length#1(z2)), Cons(z1, z2)), Nil))), DIVIDE_YS#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2)))), HALVE#1(length#1(z2)), LENGTH#1(z2))
   COND_MERGE_YS_ZS_2(True, Cons(0, Cons(0, z5)), Cons(x1, x2), 0, Cons(0, z5), x1, x2) -> c2(MERGE#2(Cons(0, z5), Cons(x1, x2)))
   COND_MERGE_YS_ZS_2(True, Cons(S(0), Cons(0, z5)), Cons(S(x1), x2), S(0), Cons(0, z5), S(x1), x2) -> c2(MERGE#2(Cons(0, z5), Cons(S(x1), x2)))
   COND_MERGE_YS_ZS_2(True, Cons(S(S(x0)), Cons(0, z5)), Cons(S(S(x2)), x3), S(S(x0)), Cons(0, z5), S(S(x2)), x3) -> c2(MERGE#2(Cons(0, z5), Cons(S(S(x2)), x3)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, z3)))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Cons(z2, z3))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(Cons(z2, z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Cons(drop#2(S(halve#1(S(length#1(z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3)))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(S(length#1(z3))))), HALVE#1(S(length#1(z3))), LENGTH#1(Cons(z2, z3)))
   COND_MERGE_YS_ZS_2(True, Cons(0, Cons(S(z4), z5)), Cons(0, x2), 0, Cons(S(z4), z5), 0, x2) -> c2(MERGE#2(Cons(S(z4), z5), Cons(0, x2)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> c9(CONST_F#2(Cons(z0, Cons(z1, z2)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(Cons(z0, take#2(halve#1(length#1(z2)), Cons(z1, z2))), Cons(drop#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(halve#1(length#1(z2)), Cons(z1, z2)), Nil))), DIVIDE_YS#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2)))), HALVE#1(length#1(z2)), LENGTH#1(z2))
   COND_MERGE_YS_ZS_2(True, Cons(0, Cons(S(0), z5)), Cons(S(z2), x2), 0, Cons(S(0), z5), S(z2), x2) -> c2(MERGE#2(Cons(S(0), z5), Cons(S(z2), x2)))
   COND_MERGE_YS_ZS_2(True, Cons(S(0), Cons(S(0), z5)), Cons(S(x1), x2), S(0), Cons(S(0), z5), S(x1), x2) -> c2(MERGE#2(Cons(S(0), z5), Cons(S(x1), x2)))
   COND_MERGE_YS_ZS_2(True, Cons(S(S(x0)), Cons(S(0), z5)), Cons(S(S(x2)), x3), S(S(x0)), Cons(S(0), z5), S(S(x2)), x3) -> c2(MERGE#2(Cons(S(0), z5), Cons(S(S(x2)), x3)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, z3)))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Cons(z2, z3))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(S(length#1(z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Cons(drop#2(S(halve#1(length#1(Cons(z2, z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3)))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(S(length#1(z3))))), HALVE#1(S(length#1(z3))), LENGTH#1(Cons(z2, z3)))
   COND_MERGE_YS_ZS_2(True, Cons(0, Cons(S(S(z4)), z5)), Cons(S(0), x2), 0, Cons(S(S(z4)), z5), S(0), x2) -> c2(MERGE#2(Cons(S(S(z4)), z5), Cons(S(0), x2)))
   COND_MERGE_YS_ZS_2(True, Cons(S(0), Cons(S(S(z4)), z5)), Cons(S(0), x2), S(0), Cons(S(S(z4)), z5), S(0), x2) -> c2(MERGE#2(Cons(S(S(z4)), z5), Cons(S(0), x2)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> c9(MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(halve#1(length#1(z2)), Cons(z1, z2)), Nil))), DIVIDE_YS#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2)))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Nil))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(Nil))), Cons(z0, Cons(z1, Nil))), Cons(drop#2(S(halve#1(0)), Cons(z0, Cons(z1, Nil))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Nil)), S(halve#1(0))))
K tuples:none
Defined Rule Symbols:   leq#2_2, map#2_2, divide_ys#1_2, halve#1_1, length#1_1, take#2_2, drop#2_2, dc#1_6, const_f#2_2, merge#2_2, cond_merge_ys_zs_2_7

Defined Pair Symbols:   DROP#2_2, TAKE#2_2, HALVE#1_1, LEQ#2_2, LENGTH#1_1, MAP#2_2, MERGE#2_2, DIVIDE_YS#1_2, COND_MERGE_YS_ZS_2_7, DC#1_6, CONST_F#2_2

Compound Symbols:   c12_1, c15_1, c18_1, c22_1, c24_1, c26_1, c27_1, c6_1, c6_2, c_1, c1_1, c2_1, c3_1, c9_3, c9_5, c9_4, c19_1, c9_2


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

(169) CdtRewritingProof (BOTH BOUNDS(ID, ID))
Used rewriting to replace DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Nil))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(0)), Cons(z0, Cons(z1, Nil))), Cons(drop#2(S(halve#1(length#1(Nil))), Cons(z0, Cons(z1, Nil))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil))))) by DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Nil))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(0)), Cons(z0, Cons(z1, Nil))), Cons(drop#2(S(halve#1(length#1(Nil))), Cons(z0, Cons(z1, Nil))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Nil)), S(halve#1(0))))
----------------------------------------

(170)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   leq#2(0, z0) -> True
   leq#2(S(z0), 0) -> False
   leq#2(S(z0), S(z1)) -> leq#2(z0, z1)
   map#2(dc(z0, z1, z2, z3, z4), Nil) -> Nil
   map#2(dc(z0, z1, z2, z3, z4), Cons(z5, z6)) -> Cons(dc#1(z0, z1, z2, z3, z4, z5), map#2(dc(z0, z1, z2, z3, z4), z6))
   divide_ys#1(z0, z1) -> Cons(take#2(z1, z0), Cons(drop#2(z1, z0), Nil))
   halve#1(0) -> 0
   halve#1(S(0)) -> S(0)
   halve#1(S(S(z0))) -> S(halve#1(z0))
   length#1(Nil) -> 0
   length#1(Cons(z0, z1)) -> S(length#1(z1))
   take#2(0, z0) -> Nil
   take#2(S(0), Nil) -> Cons(bot[0], Nil)
   take#2(S(z0), Cons(z1, z2)) -> Cons(z1, take#2(z0, z2))
   drop#2(0, z0) -> z0
   drop#2(S(0), Nil) -> bot[1]
   drop#2(S(z0), Cons(z1, z2)) -> drop#2(z0, z2)
   dc#1(map, divisible, mergesort_zs_3, divide, const_f, Nil) -> Nil
   dc#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Nil)) -> Cons(z0, Nil)
   dc#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> const_f#2(Cons(z0, Cons(z1, z2)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2))))))
   const_f#2(z0, Cons(z1, Cons(z2, z3))) -> merge#2(z1, z2)
   merge#2(Nil, z0) -> z0
   merge#2(Cons(z0, z1), Nil) -> Cons(z0, z1)
   merge#2(Cons(z0, z1), Cons(z2, z3)) -> cond_merge_ys_zs_2(leq#2(z0, z2), Cons(z0, z1), Cons(z2, z3), z0, z1, z2, z3)
   cond_merge_ys_zs_2(True, Cons(z0, z1), Cons(z2, z3), z4, z5, z6, z7) -> Cons(z4, merge#2(z5, Cons(z2, z3)))
   cond_merge_ys_zs_2(False, Cons(z0, z1), Cons(z2, z3), z4, z5, z6, z7) -> Cons(z6, merge#2(Cons(z0, z1), z7))
Tuples:
   DROP#2(S(z0), Cons(z1, z2)) -> c12(DROP#2(z0, z2))
   TAKE#2(S(z0), Cons(z1, z2)) -> c15(TAKE#2(z0, z2))
   HALVE#1(S(S(z0))) -> c18(HALVE#1(z0))
   LEQ#2(S(z0), S(z1)) -> c22(LEQ#2(z0, z1))
   LENGTH#1(Cons(z0, z1)) -> c24(LENGTH#1(z1))
   MAP#2(dc(z0, z1, z2, z3, z4), Cons(z5, z6)) -> c26(DC#1(z0, z1, z2, z3, z4, z5))
   MAP#2(dc(z0, z1, z2, z3, z4), Cons(z5, z6)) -> c27(MAP#2(dc(z0, z1, z2, z3, z4), z6))
   MERGE#2(Cons(0, x1), Cons(z0, x3)) -> c6(COND_MERGE_YS_ZS_2(True, Cons(0, x1), Cons(z0, x3), 0, x1, z0, x3))
   MERGE#2(Cons(S(z0), x1), Cons(0, x3)) -> c6(COND_MERGE_YS_ZS_2(False, Cons(S(z0), x1), Cons(0, x3), S(z0), x1, 0, x3))
   MERGE#2(Cons(S(0), x1), Cons(S(z0), x3)) -> c6(COND_MERGE_YS_ZS_2(True, Cons(S(0), x1), Cons(S(z0), x3), S(0), x1, S(z0), x3), LEQ#2(S(0), S(z0)))
   MERGE#2(Cons(S(S(z0)), x1), Cons(S(0), x3)) -> c6(COND_MERGE_YS_ZS_2(False, Cons(S(S(z0)), x1), Cons(S(0), x3), S(S(z0)), x1, S(0), x3), LEQ#2(S(S(z0)), S(0)))
   MERGE#2(Cons(S(S(z0)), x1), Cons(S(S(z1)), x3)) -> c6(COND_MERGE_YS_ZS_2(leq#2(z0, z1), Cons(S(S(z0)), x1), Cons(S(S(z1)), x3), S(S(z0)), x1, S(S(z1)), x3), LEQ#2(S(S(z0)), S(S(z1))))
   MERGE#2(Cons(S(x0), x1), Cons(S(x2), x3)) -> c6(LEQ#2(S(x0), S(x2)))
   DIVIDE_YS#1(Cons(x0, Cons(x1, x2)), S(y11)) -> c(TAKE#2(S(y11), Cons(x0, Cons(x1, x2))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, x3))), S(y11)) -> c(TAKE#2(S(y11), Cons(x0, Cons(x1, Cons(x2, x3)))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Nil)), S(y10)) -> c(TAKE#2(S(y10), Cons(x0, Cons(x1, Nil))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Nil))), S(y7)) -> c(TAKE#2(S(y7), Cons(x0, Cons(x1, Cons(x2, Nil)))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4)))), S(y8)) -> c(TAKE#2(S(y8), Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4))))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, x2)), S(y11)) -> c1(DROP#2(S(y11), Cons(x0, Cons(x1, x2))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, x3))), S(y11)) -> c1(DROP#2(S(y11), Cons(x0, Cons(x1, Cons(x2, x3)))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Nil)), S(y10)) -> c1(DROP#2(S(y10), Cons(x0, Cons(x1, Nil))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Nil))), S(y7)) -> c1(DROP#2(S(y7), Cons(x0, Cons(x1, Cons(x2, Nil)))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4)))), S(y8)) -> c1(DROP#2(S(y8), Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4))))))
   COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(S(S(y2)), z3), z4, Cons(S(S(y0)), y1), z6, z7) -> c2(MERGE#2(Cons(S(S(y0)), y1), Cons(S(S(y2)), z3)))
   COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(S(y2), z3), z4, Cons(S(y0), y1), z6, z7) -> c2(MERGE#2(Cons(S(y0), y1), Cons(S(y2), z3)))
   COND_MERGE_YS_ZS_2(False, Cons(S(x0), x1), Cons(0, x2), S(x0), x1, 0, x2) -> c3(MERGE#2(Cons(S(x0), x1), x2))
   COND_MERGE_YS_ZS_2(False, Cons(S(S(x0)), x1), Cons(S(0), x2), S(S(x0)), x1, S(0), x2) -> c3(MERGE#2(Cons(S(S(x0)), x1), x2))
   COND_MERGE_YS_ZS_2(False, Cons(S(S(x0)), x1), Cons(S(S(x2)), x3), S(S(x0)), x1, S(S(x2)), x3) -> c3(MERGE#2(Cons(S(S(x0)), x1), x3))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, z3)))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Cons(z2, z3))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(S(length#1(z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Cons(drop#2(S(halve#1(S(length#1(z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3)))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3))))), HALVE#1(S(length#1(z3))), LENGTH#1(Cons(z2, z3)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, Nil)))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Cons(z2, Nil))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, Nil))), S(halve#1(S(0)))))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, Nil))), S(halve#1(length#1(Cons(z2, Nil)))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, Nil))), S(halve#1(length#1(Cons(z2, Nil))))), HALVE#1(S(length#1(Nil))), LENGTH#1(Cons(z2, Nil)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, Cons(z3, z4))))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Cons(z2, Cons(z3, z4)))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, Cons(z3, z4)))), S(halve#1(S(S(length#1(z4)))))))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, Cons(z3, z4)))), S(halve#1(length#1(Cons(z2, Cons(z3, z4))))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, Cons(z3, z4)))), S(halve#1(length#1(Cons(z2, Cons(z3, z4)))))), HALVE#1(S(length#1(Cons(z3, z4)))), LENGTH#1(Cons(z2, Cons(z3, z4))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, z3)))) -> c9(MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3)))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3))))), HALVE#1(S(length#1(z3))), LENGTH#1(Cons(z2, z3)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Nil))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(0)), Cons(z0, Cons(z1, Nil))), Cons(drop#2(S(halve#1(0)), Cons(z0, Cons(z1, Nil))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil)))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Nil))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Nil)), S(0)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil)))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> c9(CONST_F#2(Cons(z0, Cons(z1, z2)), Cons(dc#1(map, divisible, mergesort_zs_3, divide, const_f, take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2)))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(drop#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(halve#1(length#1(z2)), Cons(z1, z2)), Nil))), DIVIDE_YS#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2)))), HALVE#1(length#1(z2)), LENGTH#1(z2))
   CONST_F#2(Cons(x0, Cons(x1, x2)), Cons(z1, Cons(z2, z3))) -> c19(MERGE#2(z1, z2))
   CONST_F#2(Cons(x0, Cons(x1, Cons(x2, x3))), Cons(z1, Cons(z2, z3))) -> c19(MERGE#2(z1, z2))
   CONST_F#2(Cons(x0, Cons(x1, Nil)), Cons(z1, Cons(z2, z3))) -> c19(MERGE#2(z1, z2))
   CONST_F#2(Cons(x0, Cons(x1, Cons(x2, Nil))), Cons(z1, Cons(z2, z3))) -> c19(MERGE#2(z1, z2))
   CONST_F#2(Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4)))), Cons(z1, Cons(z2, z3))) -> c19(MERGE#2(z1, z2))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> c9(CONST_F#2(Cons(z0, Cons(z1, z2)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(halve#1(length#1(z2)), Cons(z1, z2)), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(halve#1(length#1(z2)), Cons(z1, z2)), Nil))), DIVIDE_YS#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2)))), HALVE#1(length#1(z2)), LENGTH#1(z2))
   COND_MERGE_YS_ZS_2(True, Cons(0, Cons(0, z5)), Cons(x1, x2), 0, Cons(0, z5), x1, x2) -> c2(MERGE#2(Cons(0, z5), Cons(x1, x2)))
   COND_MERGE_YS_ZS_2(True, Cons(S(0), Cons(0, z5)), Cons(S(x1), x2), S(0), Cons(0, z5), S(x1), x2) -> c2(MERGE#2(Cons(0, z5), Cons(S(x1), x2)))
   COND_MERGE_YS_ZS_2(True, Cons(S(S(x0)), Cons(0, z5)), Cons(S(S(x2)), x3), S(S(x0)), Cons(0, z5), S(S(x2)), x3) -> c2(MERGE#2(Cons(0, z5), Cons(S(S(x2)), x3)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, z3)))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Cons(z2, z3))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(Cons(z2, z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Cons(drop#2(S(halve#1(S(length#1(z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3)))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(S(length#1(z3))))), HALVE#1(S(length#1(z3))), LENGTH#1(Cons(z2, z3)))
   COND_MERGE_YS_ZS_2(True, Cons(0, Cons(S(z4), z5)), Cons(0, x2), 0, Cons(S(z4), z5), 0, x2) -> c2(MERGE#2(Cons(S(z4), z5), Cons(0, x2)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> c9(CONST_F#2(Cons(z0, Cons(z1, z2)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(Cons(z0, take#2(halve#1(length#1(z2)), Cons(z1, z2))), Cons(drop#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(halve#1(length#1(z2)), Cons(z1, z2)), Nil))), DIVIDE_YS#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2)))), HALVE#1(length#1(z2)), LENGTH#1(z2))
   COND_MERGE_YS_ZS_2(True, Cons(0, Cons(S(0), z5)), Cons(S(z2), x2), 0, Cons(S(0), z5), S(z2), x2) -> c2(MERGE#2(Cons(S(0), z5), Cons(S(z2), x2)))
   COND_MERGE_YS_ZS_2(True, Cons(S(0), Cons(S(0), z5)), Cons(S(x1), x2), S(0), Cons(S(0), z5), S(x1), x2) -> c2(MERGE#2(Cons(S(0), z5), Cons(S(x1), x2)))
   COND_MERGE_YS_ZS_2(True, Cons(S(S(x0)), Cons(S(0), z5)), Cons(S(S(x2)), x3), S(S(x0)), Cons(S(0), z5), S(S(x2)), x3) -> c2(MERGE#2(Cons(S(0), z5), Cons(S(S(x2)), x3)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, z3)))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Cons(z2, z3))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(S(length#1(z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Cons(drop#2(S(halve#1(length#1(Cons(z2, z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3)))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(S(length#1(z3))))), HALVE#1(S(length#1(z3))), LENGTH#1(Cons(z2, z3)))
   COND_MERGE_YS_ZS_2(True, Cons(0, Cons(S(S(z4)), z5)), Cons(S(0), x2), 0, Cons(S(S(z4)), z5), S(0), x2) -> c2(MERGE#2(Cons(S(S(z4)), z5), Cons(S(0), x2)))
   COND_MERGE_YS_ZS_2(True, Cons(S(0), Cons(S(S(z4)), z5)), Cons(S(0), x2), S(0), Cons(S(S(z4)), z5), S(0), x2) -> c2(MERGE#2(Cons(S(S(z4)), z5), Cons(S(0), x2)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> c9(MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(halve#1(length#1(z2)), Cons(z1, z2)), Nil))), DIVIDE_YS#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2)))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Nil))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(Nil))), Cons(z0, Cons(z1, Nil))), Cons(drop#2(S(halve#1(0)), Cons(z0, Cons(z1, Nil))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Nil)), S(halve#1(0))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Nil))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(0)), Cons(z0, Cons(z1, Nil))), Cons(drop#2(S(halve#1(length#1(Nil))), Cons(z0, Cons(z1, Nil))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Nil)), S(halve#1(0))))
S tuples:
   DROP#2(S(z0), Cons(z1, z2)) -> c12(DROP#2(z0, z2))
   TAKE#2(S(z0), Cons(z1, z2)) -> c15(TAKE#2(z0, z2))
   HALVE#1(S(S(z0))) -> c18(HALVE#1(z0))
   LEQ#2(S(z0), S(z1)) -> c22(LEQ#2(z0, z1))
   LENGTH#1(Cons(z0, z1)) -> c24(LENGTH#1(z1))
   MAP#2(dc(z0, z1, z2, z3, z4), Cons(z5, z6)) -> c26(DC#1(z0, z1, z2, z3, z4, z5))
   MAP#2(dc(z0, z1, z2, z3, z4), Cons(z5, z6)) -> c27(MAP#2(dc(z0, z1, z2, z3, z4), z6))
   MERGE#2(Cons(0, x1), Cons(z0, x3)) -> c6(COND_MERGE_YS_ZS_2(True, Cons(0, x1), Cons(z0, x3), 0, x1, z0, x3))
   MERGE#2(Cons(S(z0), x1), Cons(0, x3)) -> c6(COND_MERGE_YS_ZS_2(False, Cons(S(z0), x1), Cons(0, x3), S(z0), x1, 0, x3))
   MERGE#2(Cons(S(0), x1), Cons(S(z0), x3)) -> c6(COND_MERGE_YS_ZS_2(True, Cons(S(0), x1), Cons(S(z0), x3), S(0), x1, S(z0), x3), LEQ#2(S(0), S(z0)))
   MERGE#2(Cons(S(S(z0)), x1), Cons(S(0), x3)) -> c6(COND_MERGE_YS_ZS_2(False, Cons(S(S(z0)), x1), Cons(S(0), x3), S(S(z0)), x1, S(0), x3), LEQ#2(S(S(z0)), S(0)))
   MERGE#2(Cons(S(S(z0)), x1), Cons(S(S(z1)), x3)) -> c6(COND_MERGE_YS_ZS_2(leq#2(z0, z1), Cons(S(S(z0)), x1), Cons(S(S(z1)), x3), S(S(z0)), x1, S(S(z1)), x3), LEQ#2(S(S(z0)), S(S(z1))))
   MERGE#2(Cons(S(x0), x1), Cons(S(x2), x3)) -> c6(LEQ#2(S(x0), S(x2)))
   DIVIDE_YS#1(Cons(x0, Cons(x1, x2)), S(y11)) -> c(TAKE#2(S(y11), Cons(x0, Cons(x1, x2))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, x3))), S(y11)) -> c(TAKE#2(S(y11), Cons(x0, Cons(x1, Cons(x2, x3)))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Nil)), S(y10)) -> c(TAKE#2(S(y10), Cons(x0, Cons(x1, Nil))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Nil))), S(y7)) -> c(TAKE#2(S(y7), Cons(x0, Cons(x1, Cons(x2, Nil)))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4)))), S(y8)) -> c(TAKE#2(S(y8), Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4))))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, x2)), S(y11)) -> c1(DROP#2(S(y11), Cons(x0, Cons(x1, x2))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, x3))), S(y11)) -> c1(DROP#2(S(y11), Cons(x0, Cons(x1, Cons(x2, x3)))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Nil)), S(y10)) -> c1(DROP#2(S(y10), Cons(x0, Cons(x1, Nil))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Nil))), S(y7)) -> c1(DROP#2(S(y7), Cons(x0, Cons(x1, Cons(x2, Nil)))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4)))), S(y8)) -> c1(DROP#2(S(y8), Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4))))))
   COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(S(S(y2)), z3), z4, Cons(S(S(y0)), y1), z6, z7) -> c2(MERGE#2(Cons(S(S(y0)), y1), Cons(S(S(y2)), z3)))
   COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(S(y2), z3), z4, Cons(S(y0), y1), z6, z7) -> c2(MERGE#2(Cons(S(y0), y1), Cons(S(y2), z3)))
   COND_MERGE_YS_ZS_2(False, Cons(S(x0), x1), Cons(0, x2), S(x0), x1, 0, x2) -> c3(MERGE#2(Cons(S(x0), x1), x2))
   COND_MERGE_YS_ZS_2(False, Cons(S(S(x0)), x1), Cons(S(0), x2), S(S(x0)), x1, S(0), x2) -> c3(MERGE#2(Cons(S(S(x0)), x1), x2))
   COND_MERGE_YS_ZS_2(False, Cons(S(S(x0)), x1), Cons(S(S(x2)), x3), S(S(x0)), x1, S(S(x2)), x3) -> c3(MERGE#2(Cons(S(S(x0)), x1), x3))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, z3)))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Cons(z2, z3))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(S(length#1(z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Cons(drop#2(S(halve#1(S(length#1(z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3)))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3))))), HALVE#1(S(length#1(z3))), LENGTH#1(Cons(z2, z3)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, Nil)))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Cons(z2, Nil))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, Nil))), S(halve#1(S(0)))))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, Nil))), S(halve#1(length#1(Cons(z2, Nil)))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, Nil))), S(halve#1(length#1(Cons(z2, Nil))))), HALVE#1(S(length#1(Nil))), LENGTH#1(Cons(z2, Nil)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, Cons(z3, z4))))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Cons(z2, Cons(z3, z4)))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, Cons(z3, z4)))), S(halve#1(S(S(length#1(z4)))))))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, Cons(z3, z4)))), S(halve#1(length#1(Cons(z2, Cons(z3, z4))))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, Cons(z3, z4)))), S(halve#1(length#1(Cons(z2, Cons(z3, z4)))))), HALVE#1(S(length#1(Cons(z3, z4)))), LENGTH#1(Cons(z2, Cons(z3, z4))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, z3)))) -> c9(MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3)))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3))))), HALVE#1(S(length#1(z3))), LENGTH#1(Cons(z2, z3)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Nil))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(0)), Cons(z0, Cons(z1, Nil))), Cons(drop#2(S(halve#1(0)), Cons(z0, Cons(z1, Nil))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil)))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Nil))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Nil)), S(0)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil)))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> c9(CONST_F#2(Cons(z0, Cons(z1, z2)), Cons(dc#1(map, divisible, mergesort_zs_3, divide, const_f, take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2)))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(drop#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(halve#1(length#1(z2)), Cons(z1, z2)), Nil))), DIVIDE_YS#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2)))), HALVE#1(length#1(z2)), LENGTH#1(z2))
   CONST_F#2(Cons(x0, Cons(x1, x2)), Cons(z1, Cons(z2, z3))) -> c19(MERGE#2(z1, z2))
   CONST_F#2(Cons(x0, Cons(x1, Cons(x2, x3))), Cons(z1, Cons(z2, z3))) -> c19(MERGE#2(z1, z2))
   CONST_F#2(Cons(x0, Cons(x1, Nil)), Cons(z1, Cons(z2, z3))) -> c19(MERGE#2(z1, z2))
   CONST_F#2(Cons(x0, Cons(x1, Cons(x2, Nil))), Cons(z1, Cons(z2, z3))) -> c19(MERGE#2(z1, z2))
   CONST_F#2(Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4)))), Cons(z1, Cons(z2, z3))) -> c19(MERGE#2(z1, z2))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> c9(CONST_F#2(Cons(z0, Cons(z1, z2)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(halve#1(length#1(z2)), Cons(z1, z2)), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(halve#1(length#1(z2)), Cons(z1, z2)), Nil))), DIVIDE_YS#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2)))), HALVE#1(length#1(z2)), LENGTH#1(z2))
   COND_MERGE_YS_ZS_2(True, Cons(0, Cons(0, z5)), Cons(x1, x2), 0, Cons(0, z5), x1, x2) -> c2(MERGE#2(Cons(0, z5), Cons(x1, x2)))
   COND_MERGE_YS_ZS_2(True, Cons(S(0), Cons(0, z5)), Cons(S(x1), x2), S(0), Cons(0, z5), S(x1), x2) -> c2(MERGE#2(Cons(0, z5), Cons(S(x1), x2)))
   COND_MERGE_YS_ZS_2(True, Cons(S(S(x0)), Cons(0, z5)), Cons(S(S(x2)), x3), S(S(x0)), Cons(0, z5), S(S(x2)), x3) -> c2(MERGE#2(Cons(0, z5), Cons(S(S(x2)), x3)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, z3)))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Cons(z2, z3))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(Cons(z2, z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Cons(drop#2(S(halve#1(S(length#1(z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3)))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(S(length#1(z3))))), HALVE#1(S(length#1(z3))), LENGTH#1(Cons(z2, z3)))
   COND_MERGE_YS_ZS_2(True, Cons(0, Cons(S(z4), z5)), Cons(0, x2), 0, Cons(S(z4), z5), 0, x2) -> c2(MERGE#2(Cons(S(z4), z5), Cons(0, x2)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> c9(CONST_F#2(Cons(z0, Cons(z1, z2)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(Cons(z0, take#2(halve#1(length#1(z2)), Cons(z1, z2))), Cons(drop#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(halve#1(length#1(z2)), Cons(z1, z2)), Nil))), DIVIDE_YS#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2)))), HALVE#1(length#1(z2)), LENGTH#1(z2))
   COND_MERGE_YS_ZS_2(True, Cons(0, Cons(S(0), z5)), Cons(S(z2), x2), 0, Cons(S(0), z5), S(z2), x2) -> c2(MERGE#2(Cons(S(0), z5), Cons(S(z2), x2)))
   COND_MERGE_YS_ZS_2(True, Cons(S(0), Cons(S(0), z5)), Cons(S(x1), x2), S(0), Cons(S(0), z5), S(x1), x2) -> c2(MERGE#2(Cons(S(0), z5), Cons(S(x1), x2)))
   COND_MERGE_YS_ZS_2(True, Cons(S(S(x0)), Cons(S(0), z5)), Cons(S(S(x2)), x3), S(S(x0)), Cons(S(0), z5), S(S(x2)), x3) -> c2(MERGE#2(Cons(S(0), z5), Cons(S(S(x2)), x3)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, z3)))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Cons(z2, z3))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(S(length#1(z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Cons(drop#2(S(halve#1(length#1(Cons(z2, z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3)))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(S(length#1(z3))))), HALVE#1(S(length#1(z3))), LENGTH#1(Cons(z2, z3)))
   COND_MERGE_YS_ZS_2(True, Cons(0, Cons(S(S(z4)), z5)), Cons(S(0), x2), 0, Cons(S(S(z4)), z5), S(0), x2) -> c2(MERGE#2(Cons(S(S(z4)), z5), Cons(S(0), x2)))
   COND_MERGE_YS_ZS_2(True, Cons(S(0), Cons(S(S(z4)), z5)), Cons(S(0), x2), S(0), Cons(S(S(z4)), z5), S(0), x2) -> c2(MERGE#2(Cons(S(S(z4)), z5), Cons(S(0), x2)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> c9(MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(halve#1(length#1(z2)), Cons(z1, z2)), Nil))), DIVIDE_YS#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2)))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Nil))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(Nil))), Cons(z0, Cons(z1, Nil))), Cons(drop#2(S(halve#1(0)), Cons(z0, Cons(z1, Nil))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Nil)), S(halve#1(0))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Nil))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(0)), Cons(z0, Cons(z1, Nil))), Cons(drop#2(S(halve#1(length#1(Nil))), Cons(z0, Cons(z1, Nil))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Nil)), S(halve#1(0))))
K tuples:none
Defined Rule Symbols:   leq#2_2, map#2_2, divide_ys#1_2, halve#1_1, length#1_1, take#2_2, drop#2_2, dc#1_6, const_f#2_2, merge#2_2, cond_merge_ys_zs_2_7

Defined Pair Symbols:   DROP#2_2, TAKE#2_2, HALVE#1_1, LEQ#2_2, LENGTH#1_1, MAP#2_2, MERGE#2_2, DIVIDE_YS#1_2, COND_MERGE_YS_ZS_2_7, DC#1_6, CONST_F#2_2

Compound Symbols:   c12_1, c15_1, c18_1, c22_1, c24_1, c26_1, c27_1, c6_1, c6_2, c_1, c1_1, c2_1, c3_1, c9_5, c9_4, c9_3, c19_1, c9_2


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

(171) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID))
Use forward instantiation to replace DROP#2(S(z0), Cons(z1, z2)) -> c12(DROP#2(z0, z2)) by 
   DROP#2(S(S(y0)), Cons(z1, Cons(y1, y2))) -> c12(DROP#2(S(y0), Cons(y1, y2)))

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

(172)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   leq#2(0, z0) -> True
   leq#2(S(z0), 0) -> False
   leq#2(S(z0), S(z1)) -> leq#2(z0, z1)
   map#2(dc(z0, z1, z2, z3, z4), Nil) -> Nil
   map#2(dc(z0, z1, z2, z3, z4), Cons(z5, z6)) -> Cons(dc#1(z0, z1, z2, z3, z4, z5), map#2(dc(z0, z1, z2, z3, z4), z6))
   divide_ys#1(z0, z1) -> Cons(take#2(z1, z0), Cons(drop#2(z1, z0), Nil))
   halve#1(0) -> 0
   halve#1(S(0)) -> S(0)
   halve#1(S(S(z0))) -> S(halve#1(z0))
   length#1(Nil) -> 0
   length#1(Cons(z0, z1)) -> S(length#1(z1))
   take#2(0, z0) -> Nil
   take#2(S(0), Nil) -> Cons(bot[0], Nil)
   take#2(S(z0), Cons(z1, z2)) -> Cons(z1, take#2(z0, z2))
   drop#2(0, z0) -> z0
   drop#2(S(0), Nil) -> bot[1]
   drop#2(S(z0), Cons(z1, z2)) -> drop#2(z0, z2)
   dc#1(map, divisible, mergesort_zs_3, divide, const_f, Nil) -> Nil
   dc#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Nil)) -> Cons(z0, Nil)
   dc#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> const_f#2(Cons(z0, Cons(z1, z2)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2))))))
   const_f#2(z0, Cons(z1, Cons(z2, z3))) -> merge#2(z1, z2)
   merge#2(Nil, z0) -> z0
   merge#2(Cons(z0, z1), Nil) -> Cons(z0, z1)
   merge#2(Cons(z0, z1), Cons(z2, z3)) -> cond_merge_ys_zs_2(leq#2(z0, z2), Cons(z0, z1), Cons(z2, z3), z0, z1, z2, z3)
   cond_merge_ys_zs_2(True, Cons(z0, z1), Cons(z2, z3), z4, z5, z6, z7) -> Cons(z4, merge#2(z5, Cons(z2, z3)))
   cond_merge_ys_zs_2(False, Cons(z0, z1), Cons(z2, z3), z4, z5, z6, z7) -> Cons(z6, merge#2(Cons(z0, z1), z7))
Tuples:
   TAKE#2(S(z0), Cons(z1, z2)) -> c15(TAKE#2(z0, z2))
   HALVE#1(S(S(z0))) -> c18(HALVE#1(z0))
   LEQ#2(S(z0), S(z1)) -> c22(LEQ#2(z0, z1))
   LENGTH#1(Cons(z0, z1)) -> c24(LENGTH#1(z1))
   MAP#2(dc(z0, z1, z2, z3, z4), Cons(z5, z6)) -> c26(DC#1(z0, z1, z2, z3, z4, z5))
   MAP#2(dc(z0, z1, z2, z3, z4), Cons(z5, z6)) -> c27(MAP#2(dc(z0, z1, z2, z3, z4), z6))
   MERGE#2(Cons(0, x1), Cons(z0, x3)) -> c6(COND_MERGE_YS_ZS_2(True, Cons(0, x1), Cons(z0, x3), 0, x1, z0, x3))
   MERGE#2(Cons(S(z0), x1), Cons(0, x3)) -> c6(COND_MERGE_YS_ZS_2(False, Cons(S(z0), x1), Cons(0, x3), S(z0), x1, 0, x3))
   MERGE#2(Cons(S(0), x1), Cons(S(z0), x3)) -> c6(COND_MERGE_YS_ZS_2(True, Cons(S(0), x1), Cons(S(z0), x3), S(0), x1, S(z0), x3), LEQ#2(S(0), S(z0)))
   MERGE#2(Cons(S(S(z0)), x1), Cons(S(0), x3)) -> c6(COND_MERGE_YS_ZS_2(False, Cons(S(S(z0)), x1), Cons(S(0), x3), S(S(z0)), x1, S(0), x3), LEQ#2(S(S(z0)), S(0)))
   MERGE#2(Cons(S(S(z0)), x1), Cons(S(S(z1)), x3)) -> c6(COND_MERGE_YS_ZS_2(leq#2(z0, z1), Cons(S(S(z0)), x1), Cons(S(S(z1)), x3), S(S(z0)), x1, S(S(z1)), x3), LEQ#2(S(S(z0)), S(S(z1))))
   MERGE#2(Cons(S(x0), x1), Cons(S(x2), x3)) -> c6(LEQ#2(S(x0), S(x2)))
   DIVIDE_YS#1(Cons(x0, Cons(x1, x2)), S(y11)) -> c(TAKE#2(S(y11), Cons(x0, Cons(x1, x2))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, x3))), S(y11)) -> c(TAKE#2(S(y11), Cons(x0, Cons(x1, Cons(x2, x3)))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Nil)), S(y10)) -> c(TAKE#2(S(y10), Cons(x0, Cons(x1, Nil))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Nil))), S(y7)) -> c(TAKE#2(S(y7), Cons(x0, Cons(x1, Cons(x2, Nil)))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4)))), S(y8)) -> c(TAKE#2(S(y8), Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4))))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, x2)), S(y11)) -> c1(DROP#2(S(y11), Cons(x0, Cons(x1, x2))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, x3))), S(y11)) -> c1(DROP#2(S(y11), Cons(x0, Cons(x1, Cons(x2, x3)))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Nil)), S(y10)) -> c1(DROP#2(S(y10), Cons(x0, Cons(x1, Nil))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Nil))), S(y7)) -> c1(DROP#2(S(y7), Cons(x0, Cons(x1, Cons(x2, Nil)))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4)))), S(y8)) -> c1(DROP#2(S(y8), Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4))))))
   COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(S(S(y2)), z3), z4, Cons(S(S(y0)), y1), z6, z7) -> c2(MERGE#2(Cons(S(S(y0)), y1), Cons(S(S(y2)), z3)))
   COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(S(y2), z3), z4, Cons(S(y0), y1), z6, z7) -> c2(MERGE#2(Cons(S(y0), y1), Cons(S(y2), z3)))
   COND_MERGE_YS_ZS_2(False, Cons(S(x0), x1), Cons(0, x2), S(x0), x1, 0, x2) -> c3(MERGE#2(Cons(S(x0), x1), x2))
   COND_MERGE_YS_ZS_2(False, Cons(S(S(x0)), x1), Cons(S(0), x2), S(S(x0)), x1, S(0), x2) -> c3(MERGE#2(Cons(S(S(x0)), x1), x2))
   COND_MERGE_YS_ZS_2(False, Cons(S(S(x0)), x1), Cons(S(S(x2)), x3), S(S(x0)), x1, S(S(x2)), x3) -> c3(MERGE#2(Cons(S(S(x0)), x1), x3))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, z3)))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Cons(z2, z3))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(S(length#1(z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Cons(drop#2(S(halve#1(S(length#1(z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3)))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3))))), HALVE#1(S(length#1(z3))), LENGTH#1(Cons(z2, z3)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, Nil)))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Cons(z2, Nil))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, Nil))), S(halve#1(S(0)))))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, Nil))), S(halve#1(length#1(Cons(z2, Nil)))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, Nil))), S(halve#1(length#1(Cons(z2, Nil))))), HALVE#1(S(length#1(Nil))), LENGTH#1(Cons(z2, Nil)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, Cons(z3, z4))))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Cons(z2, Cons(z3, z4)))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, Cons(z3, z4)))), S(halve#1(S(S(length#1(z4)))))))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, Cons(z3, z4)))), S(halve#1(length#1(Cons(z2, Cons(z3, z4))))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, Cons(z3, z4)))), S(halve#1(length#1(Cons(z2, Cons(z3, z4)))))), HALVE#1(S(length#1(Cons(z3, z4)))), LENGTH#1(Cons(z2, Cons(z3, z4))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, z3)))) -> c9(MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3)))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3))))), HALVE#1(S(length#1(z3))), LENGTH#1(Cons(z2, z3)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Nil))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(0)), Cons(z0, Cons(z1, Nil))), Cons(drop#2(S(halve#1(0)), Cons(z0, Cons(z1, Nil))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil)))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Nil))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Nil)), S(0)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil)))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> c9(CONST_F#2(Cons(z0, Cons(z1, z2)), Cons(dc#1(map, divisible, mergesort_zs_3, divide, const_f, take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2)))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(drop#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(halve#1(length#1(z2)), Cons(z1, z2)), Nil))), DIVIDE_YS#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2)))), HALVE#1(length#1(z2)), LENGTH#1(z2))
   CONST_F#2(Cons(x0, Cons(x1, x2)), Cons(z1, Cons(z2, z3))) -> c19(MERGE#2(z1, z2))
   CONST_F#2(Cons(x0, Cons(x1, Cons(x2, x3))), Cons(z1, Cons(z2, z3))) -> c19(MERGE#2(z1, z2))
   CONST_F#2(Cons(x0, Cons(x1, Nil)), Cons(z1, Cons(z2, z3))) -> c19(MERGE#2(z1, z2))
   CONST_F#2(Cons(x0, Cons(x1, Cons(x2, Nil))), Cons(z1, Cons(z2, z3))) -> c19(MERGE#2(z1, z2))
   CONST_F#2(Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4)))), Cons(z1, Cons(z2, z3))) -> c19(MERGE#2(z1, z2))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> c9(CONST_F#2(Cons(z0, Cons(z1, z2)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(halve#1(length#1(z2)), Cons(z1, z2)), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(halve#1(length#1(z2)), Cons(z1, z2)), Nil))), DIVIDE_YS#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2)))), HALVE#1(length#1(z2)), LENGTH#1(z2))
   COND_MERGE_YS_ZS_2(True, Cons(0, Cons(0, z5)), Cons(x1, x2), 0, Cons(0, z5), x1, x2) -> c2(MERGE#2(Cons(0, z5), Cons(x1, x2)))
   COND_MERGE_YS_ZS_2(True, Cons(S(0), Cons(0, z5)), Cons(S(x1), x2), S(0), Cons(0, z5), S(x1), x2) -> c2(MERGE#2(Cons(0, z5), Cons(S(x1), x2)))
   COND_MERGE_YS_ZS_2(True, Cons(S(S(x0)), Cons(0, z5)), Cons(S(S(x2)), x3), S(S(x0)), Cons(0, z5), S(S(x2)), x3) -> c2(MERGE#2(Cons(0, z5), Cons(S(S(x2)), x3)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, z3)))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Cons(z2, z3))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(Cons(z2, z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Cons(drop#2(S(halve#1(S(length#1(z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3)))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(S(length#1(z3))))), HALVE#1(S(length#1(z3))), LENGTH#1(Cons(z2, z3)))
   COND_MERGE_YS_ZS_2(True, Cons(0, Cons(S(z4), z5)), Cons(0, x2), 0, Cons(S(z4), z5), 0, x2) -> c2(MERGE#2(Cons(S(z4), z5), Cons(0, x2)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> c9(CONST_F#2(Cons(z0, Cons(z1, z2)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(Cons(z0, take#2(halve#1(length#1(z2)), Cons(z1, z2))), Cons(drop#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(halve#1(length#1(z2)), Cons(z1, z2)), Nil))), DIVIDE_YS#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2)))), HALVE#1(length#1(z2)), LENGTH#1(z2))
   COND_MERGE_YS_ZS_2(True, Cons(0, Cons(S(0), z5)), Cons(S(z2), x2), 0, Cons(S(0), z5), S(z2), x2) -> c2(MERGE#2(Cons(S(0), z5), Cons(S(z2), x2)))
   COND_MERGE_YS_ZS_2(True, Cons(S(0), Cons(S(0), z5)), Cons(S(x1), x2), S(0), Cons(S(0), z5), S(x1), x2) -> c2(MERGE#2(Cons(S(0), z5), Cons(S(x1), x2)))
   COND_MERGE_YS_ZS_2(True, Cons(S(S(x0)), Cons(S(0), z5)), Cons(S(S(x2)), x3), S(S(x0)), Cons(S(0), z5), S(S(x2)), x3) -> c2(MERGE#2(Cons(S(0), z5), Cons(S(S(x2)), x3)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, z3)))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Cons(z2, z3))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(S(length#1(z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Cons(drop#2(S(halve#1(length#1(Cons(z2, z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3)))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(S(length#1(z3))))), HALVE#1(S(length#1(z3))), LENGTH#1(Cons(z2, z3)))
   COND_MERGE_YS_ZS_2(True, Cons(0, Cons(S(S(z4)), z5)), Cons(S(0), x2), 0, Cons(S(S(z4)), z5), S(0), x2) -> c2(MERGE#2(Cons(S(S(z4)), z5), Cons(S(0), x2)))
   COND_MERGE_YS_ZS_2(True, Cons(S(0), Cons(S(S(z4)), z5)), Cons(S(0), x2), S(0), Cons(S(S(z4)), z5), S(0), x2) -> c2(MERGE#2(Cons(S(S(z4)), z5), Cons(S(0), x2)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> c9(MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(halve#1(length#1(z2)), Cons(z1, z2)), Nil))), DIVIDE_YS#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2)))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Nil))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(Nil))), Cons(z0, Cons(z1, Nil))), Cons(drop#2(S(halve#1(0)), Cons(z0, Cons(z1, Nil))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Nil)), S(halve#1(0))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Nil))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(0)), Cons(z0, Cons(z1, Nil))), Cons(drop#2(S(halve#1(length#1(Nil))), Cons(z0, Cons(z1, Nil))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Nil)), S(halve#1(0))))
   DROP#2(S(S(y0)), Cons(z1, Cons(y1, y2))) -> c12(DROP#2(S(y0), Cons(y1, y2)))
S tuples:
   TAKE#2(S(z0), Cons(z1, z2)) -> c15(TAKE#2(z0, z2))
   HALVE#1(S(S(z0))) -> c18(HALVE#1(z0))
   LEQ#2(S(z0), S(z1)) -> c22(LEQ#2(z0, z1))
   LENGTH#1(Cons(z0, z1)) -> c24(LENGTH#1(z1))
   MAP#2(dc(z0, z1, z2, z3, z4), Cons(z5, z6)) -> c26(DC#1(z0, z1, z2, z3, z4, z5))
   MAP#2(dc(z0, z1, z2, z3, z4), Cons(z5, z6)) -> c27(MAP#2(dc(z0, z1, z2, z3, z4), z6))
   MERGE#2(Cons(0, x1), Cons(z0, x3)) -> c6(COND_MERGE_YS_ZS_2(True, Cons(0, x1), Cons(z0, x3), 0, x1, z0, x3))
   MERGE#2(Cons(S(z0), x1), Cons(0, x3)) -> c6(COND_MERGE_YS_ZS_2(False, Cons(S(z0), x1), Cons(0, x3), S(z0), x1, 0, x3))
   MERGE#2(Cons(S(0), x1), Cons(S(z0), x3)) -> c6(COND_MERGE_YS_ZS_2(True, Cons(S(0), x1), Cons(S(z0), x3), S(0), x1, S(z0), x3), LEQ#2(S(0), S(z0)))
   MERGE#2(Cons(S(S(z0)), x1), Cons(S(0), x3)) -> c6(COND_MERGE_YS_ZS_2(False, Cons(S(S(z0)), x1), Cons(S(0), x3), S(S(z0)), x1, S(0), x3), LEQ#2(S(S(z0)), S(0)))
   MERGE#2(Cons(S(S(z0)), x1), Cons(S(S(z1)), x3)) -> c6(COND_MERGE_YS_ZS_2(leq#2(z0, z1), Cons(S(S(z0)), x1), Cons(S(S(z1)), x3), S(S(z0)), x1, S(S(z1)), x3), LEQ#2(S(S(z0)), S(S(z1))))
   MERGE#2(Cons(S(x0), x1), Cons(S(x2), x3)) -> c6(LEQ#2(S(x0), S(x2)))
   DIVIDE_YS#1(Cons(x0, Cons(x1, x2)), S(y11)) -> c(TAKE#2(S(y11), Cons(x0, Cons(x1, x2))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, x3))), S(y11)) -> c(TAKE#2(S(y11), Cons(x0, Cons(x1, Cons(x2, x3)))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Nil)), S(y10)) -> c(TAKE#2(S(y10), Cons(x0, Cons(x1, Nil))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Nil))), S(y7)) -> c(TAKE#2(S(y7), Cons(x0, Cons(x1, Cons(x2, Nil)))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4)))), S(y8)) -> c(TAKE#2(S(y8), Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4))))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, x2)), S(y11)) -> c1(DROP#2(S(y11), Cons(x0, Cons(x1, x2))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, x3))), S(y11)) -> c1(DROP#2(S(y11), Cons(x0, Cons(x1, Cons(x2, x3)))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Nil)), S(y10)) -> c1(DROP#2(S(y10), Cons(x0, Cons(x1, Nil))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Nil))), S(y7)) -> c1(DROP#2(S(y7), Cons(x0, Cons(x1, Cons(x2, Nil)))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4)))), S(y8)) -> c1(DROP#2(S(y8), Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4))))))
   COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(S(S(y2)), z3), z4, Cons(S(S(y0)), y1), z6, z7) -> c2(MERGE#2(Cons(S(S(y0)), y1), Cons(S(S(y2)), z3)))
   COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(S(y2), z3), z4, Cons(S(y0), y1), z6, z7) -> c2(MERGE#2(Cons(S(y0), y1), Cons(S(y2), z3)))
   COND_MERGE_YS_ZS_2(False, Cons(S(x0), x1), Cons(0, x2), S(x0), x1, 0, x2) -> c3(MERGE#2(Cons(S(x0), x1), x2))
   COND_MERGE_YS_ZS_2(False, Cons(S(S(x0)), x1), Cons(S(0), x2), S(S(x0)), x1, S(0), x2) -> c3(MERGE#2(Cons(S(S(x0)), x1), x2))
   COND_MERGE_YS_ZS_2(False, Cons(S(S(x0)), x1), Cons(S(S(x2)), x3), S(S(x0)), x1, S(S(x2)), x3) -> c3(MERGE#2(Cons(S(S(x0)), x1), x3))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, z3)))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Cons(z2, z3))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(S(length#1(z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Cons(drop#2(S(halve#1(S(length#1(z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3)))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3))))), HALVE#1(S(length#1(z3))), LENGTH#1(Cons(z2, z3)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, Nil)))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Cons(z2, Nil))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, Nil))), S(halve#1(S(0)))))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, Nil))), S(halve#1(length#1(Cons(z2, Nil)))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, Nil))), S(halve#1(length#1(Cons(z2, Nil))))), HALVE#1(S(length#1(Nil))), LENGTH#1(Cons(z2, Nil)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, Cons(z3, z4))))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Cons(z2, Cons(z3, z4)))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, Cons(z3, z4)))), S(halve#1(S(S(length#1(z4)))))))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, Cons(z3, z4)))), S(halve#1(length#1(Cons(z2, Cons(z3, z4))))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, Cons(z3, z4)))), S(halve#1(length#1(Cons(z2, Cons(z3, z4)))))), HALVE#1(S(length#1(Cons(z3, z4)))), LENGTH#1(Cons(z2, Cons(z3, z4))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, z3)))) -> c9(MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3)))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3))))), HALVE#1(S(length#1(z3))), LENGTH#1(Cons(z2, z3)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Nil))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(0)), Cons(z0, Cons(z1, Nil))), Cons(drop#2(S(halve#1(0)), Cons(z0, Cons(z1, Nil))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil)))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Nil))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Nil)), S(0)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil)))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> c9(CONST_F#2(Cons(z0, Cons(z1, z2)), Cons(dc#1(map, divisible, mergesort_zs_3, divide, const_f, take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2)))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(drop#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(halve#1(length#1(z2)), Cons(z1, z2)), Nil))), DIVIDE_YS#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2)))), HALVE#1(length#1(z2)), LENGTH#1(z2))
   CONST_F#2(Cons(x0, Cons(x1, x2)), Cons(z1, Cons(z2, z3))) -> c19(MERGE#2(z1, z2))
   CONST_F#2(Cons(x0, Cons(x1, Cons(x2, x3))), Cons(z1, Cons(z2, z3))) -> c19(MERGE#2(z1, z2))
   CONST_F#2(Cons(x0, Cons(x1, Nil)), Cons(z1, Cons(z2, z3))) -> c19(MERGE#2(z1, z2))
   CONST_F#2(Cons(x0, Cons(x1, Cons(x2, Nil))), Cons(z1, Cons(z2, z3))) -> c19(MERGE#2(z1, z2))
   CONST_F#2(Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4)))), Cons(z1, Cons(z2, z3))) -> c19(MERGE#2(z1, z2))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> c9(CONST_F#2(Cons(z0, Cons(z1, z2)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(halve#1(length#1(z2)), Cons(z1, z2)), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(halve#1(length#1(z2)), Cons(z1, z2)), Nil))), DIVIDE_YS#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2)))), HALVE#1(length#1(z2)), LENGTH#1(z2))
   COND_MERGE_YS_ZS_2(True, Cons(0, Cons(0, z5)), Cons(x1, x2), 0, Cons(0, z5), x1, x2) -> c2(MERGE#2(Cons(0, z5), Cons(x1, x2)))
   COND_MERGE_YS_ZS_2(True, Cons(S(0), Cons(0, z5)), Cons(S(x1), x2), S(0), Cons(0, z5), S(x1), x2) -> c2(MERGE#2(Cons(0, z5), Cons(S(x1), x2)))
   COND_MERGE_YS_ZS_2(True, Cons(S(S(x0)), Cons(0, z5)), Cons(S(S(x2)), x3), S(S(x0)), Cons(0, z5), S(S(x2)), x3) -> c2(MERGE#2(Cons(0, z5), Cons(S(S(x2)), x3)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, z3)))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Cons(z2, z3))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(Cons(z2, z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Cons(drop#2(S(halve#1(S(length#1(z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3)))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(S(length#1(z3))))), HALVE#1(S(length#1(z3))), LENGTH#1(Cons(z2, z3)))
   COND_MERGE_YS_ZS_2(True, Cons(0, Cons(S(z4), z5)), Cons(0, x2), 0, Cons(S(z4), z5), 0, x2) -> c2(MERGE#2(Cons(S(z4), z5), Cons(0, x2)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> c9(CONST_F#2(Cons(z0, Cons(z1, z2)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(Cons(z0, take#2(halve#1(length#1(z2)), Cons(z1, z2))), Cons(drop#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(halve#1(length#1(z2)), Cons(z1, z2)), Nil))), DIVIDE_YS#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2)))), HALVE#1(length#1(z2)), LENGTH#1(z2))
   COND_MERGE_YS_ZS_2(True, Cons(0, Cons(S(0), z5)), Cons(S(z2), x2), 0, Cons(S(0), z5), S(z2), x2) -> c2(MERGE#2(Cons(S(0), z5), Cons(S(z2), x2)))
   COND_MERGE_YS_ZS_2(True, Cons(S(0), Cons(S(0), z5)), Cons(S(x1), x2), S(0), Cons(S(0), z5), S(x1), x2) -> c2(MERGE#2(Cons(S(0), z5), Cons(S(x1), x2)))
   COND_MERGE_YS_ZS_2(True, Cons(S(S(x0)), Cons(S(0), z5)), Cons(S(S(x2)), x3), S(S(x0)), Cons(S(0), z5), S(S(x2)), x3) -> c2(MERGE#2(Cons(S(0), z5), Cons(S(S(x2)), x3)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, z3)))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Cons(z2, z3))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(S(length#1(z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Cons(drop#2(S(halve#1(length#1(Cons(z2, z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3)))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(S(length#1(z3))))), HALVE#1(S(length#1(z3))), LENGTH#1(Cons(z2, z3)))
   COND_MERGE_YS_ZS_2(True, Cons(0, Cons(S(S(z4)), z5)), Cons(S(0), x2), 0, Cons(S(S(z4)), z5), S(0), x2) -> c2(MERGE#2(Cons(S(S(z4)), z5), Cons(S(0), x2)))
   COND_MERGE_YS_ZS_2(True, Cons(S(0), Cons(S(S(z4)), z5)), Cons(S(0), x2), S(0), Cons(S(S(z4)), z5), S(0), x2) -> c2(MERGE#2(Cons(S(S(z4)), z5), Cons(S(0), x2)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> c9(MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(halve#1(length#1(z2)), Cons(z1, z2)), Nil))), DIVIDE_YS#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2)))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Nil))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(Nil))), Cons(z0, Cons(z1, Nil))), Cons(drop#2(S(halve#1(0)), Cons(z0, Cons(z1, Nil))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Nil)), S(halve#1(0))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Nil))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(0)), Cons(z0, Cons(z1, Nil))), Cons(drop#2(S(halve#1(length#1(Nil))), Cons(z0, Cons(z1, Nil))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Nil)), S(halve#1(0))))
   DROP#2(S(S(y0)), Cons(z1, Cons(y1, y2))) -> c12(DROP#2(S(y0), Cons(y1, y2)))
K tuples:none
Defined Rule Symbols:   leq#2_2, map#2_2, divide_ys#1_2, halve#1_1, length#1_1, take#2_2, drop#2_2, dc#1_6, const_f#2_2, merge#2_2, cond_merge_ys_zs_2_7

Defined Pair Symbols:   TAKE#2_2, HALVE#1_1, LEQ#2_2, LENGTH#1_1, MAP#2_2, MERGE#2_2, DIVIDE_YS#1_2, COND_MERGE_YS_ZS_2_7, DC#1_6, CONST_F#2_2, DROP#2_2

Compound Symbols:   c15_1, c18_1, c22_1, c24_1, c26_1, c27_1, c6_1, c6_2, c_1, c1_1, c2_1, c3_1, c9_5, c9_4, c9_3, c19_1, c9_2, c12_1


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(173) CdtInstantiationProof (BOTH BOUNDS(ID, ID))
Use instantiation to replace COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(S(S(y2)), z3), z4, Cons(S(S(y0)), y1), z6, z7) -> c2(MERGE#2(Cons(S(S(y0)), y1), Cons(S(S(y2)), z3))) by 
   COND_MERGE_YS_ZS_2(True, Cons(0, Cons(S(S(z5)), z6)), Cons(S(S(z2)), x2), 0, Cons(S(S(z5)), z6), S(S(z2)), x2) -> c2(MERGE#2(Cons(S(S(z5)), z6), Cons(S(S(z2)), x2)))
   COND_MERGE_YS_ZS_2(True, Cons(S(0), Cons(S(S(z5)), z6)), Cons(S(S(z2)), x2), S(0), Cons(S(S(z5)), z6), S(S(z2)), x2) -> c2(MERGE#2(Cons(S(S(z5)), z6), Cons(S(S(z2)), x2)))
   COND_MERGE_YS_ZS_2(True, Cons(S(S(x0)), Cons(S(S(z5)), z6)), Cons(S(S(x2)), x3), S(S(x0)), Cons(S(S(z5)), z6), S(S(x2)), x3) -> c2(MERGE#2(Cons(S(S(z5)), z6), Cons(S(S(x2)), x3)))

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

(174)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   leq#2(0, z0) -> True
   leq#2(S(z0), 0) -> False
   leq#2(S(z0), S(z1)) -> leq#2(z0, z1)
   map#2(dc(z0, z1, z2, z3, z4), Nil) -> Nil
   map#2(dc(z0, z1, z2, z3, z4), Cons(z5, z6)) -> Cons(dc#1(z0, z1, z2, z3, z4, z5), map#2(dc(z0, z1, z2, z3, z4), z6))
   divide_ys#1(z0, z1) -> Cons(take#2(z1, z0), Cons(drop#2(z1, z0), Nil))
   halve#1(0) -> 0
   halve#1(S(0)) -> S(0)
   halve#1(S(S(z0))) -> S(halve#1(z0))
   length#1(Nil) -> 0
   length#1(Cons(z0, z1)) -> S(length#1(z1))
   take#2(0, z0) -> Nil
   take#2(S(0), Nil) -> Cons(bot[0], Nil)
   take#2(S(z0), Cons(z1, z2)) -> Cons(z1, take#2(z0, z2))
   drop#2(0, z0) -> z0
   drop#2(S(0), Nil) -> bot[1]
   drop#2(S(z0), Cons(z1, z2)) -> drop#2(z0, z2)
   dc#1(map, divisible, mergesort_zs_3, divide, const_f, Nil) -> Nil
   dc#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Nil)) -> Cons(z0, Nil)
   dc#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> const_f#2(Cons(z0, Cons(z1, z2)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2))))))
   const_f#2(z0, Cons(z1, Cons(z2, z3))) -> merge#2(z1, z2)
   merge#2(Nil, z0) -> z0
   merge#2(Cons(z0, z1), Nil) -> Cons(z0, z1)
   merge#2(Cons(z0, z1), Cons(z2, z3)) -> cond_merge_ys_zs_2(leq#2(z0, z2), Cons(z0, z1), Cons(z2, z3), z0, z1, z2, z3)
   cond_merge_ys_zs_2(True, Cons(z0, z1), Cons(z2, z3), z4, z5, z6, z7) -> Cons(z4, merge#2(z5, Cons(z2, z3)))
   cond_merge_ys_zs_2(False, Cons(z0, z1), Cons(z2, z3), z4, z5, z6, z7) -> Cons(z6, merge#2(Cons(z0, z1), z7))
Tuples:
   TAKE#2(S(z0), Cons(z1, z2)) -> c15(TAKE#2(z0, z2))
   HALVE#1(S(S(z0))) -> c18(HALVE#1(z0))
   LEQ#2(S(z0), S(z1)) -> c22(LEQ#2(z0, z1))
   LENGTH#1(Cons(z0, z1)) -> c24(LENGTH#1(z1))
   MAP#2(dc(z0, z1, z2, z3, z4), Cons(z5, z6)) -> c26(DC#1(z0, z1, z2, z3, z4, z5))
   MAP#2(dc(z0, z1, z2, z3, z4), Cons(z5, z6)) -> c27(MAP#2(dc(z0, z1, z2, z3, z4), z6))
   MERGE#2(Cons(0, x1), Cons(z0, x3)) -> c6(COND_MERGE_YS_ZS_2(True, Cons(0, x1), Cons(z0, x3), 0, x1, z0, x3))
   MERGE#2(Cons(S(z0), x1), Cons(0, x3)) -> c6(COND_MERGE_YS_ZS_2(False, Cons(S(z0), x1), Cons(0, x3), S(z0), x1, 0, x3))
   MERGE#2(Cons(S(0), x1), Cons(S(z0), x3)) -> c6(COND_MERGE_YS_ZS_2(True, Cons(S(0), x1), Cons(S(z0), x3), S(0), x1, S(z0), x3), LEQ#2(S(0), S(z0)))
   MERGE#2(Cons(S(S(z0)), x1), Cons(S(0), x3)) -> c6(COND_MERGE_YS_ZS_2(False, Cons(S(S(z0)), x1), Cons(S(0), x3), S(S(z0)), x1, S(0), x3), LEQ#2(S(S(z0)), S(0)))
   MERGE#2(Cons(S(S(z0)), x1), Cons(S(S(z1)), x3)) -> c6(COND_MERGE_YS_ZS_2(leq#2(z0, z1), Cons(S(S(z0)), x1), Cons(S(S(z1)), x3), S(S(z0)), x1, S(S(z1)), x3), LEQ#2(S(S(z0)), S(S(z1))))
   MERGE#2(Cons(S(x0), x1), Cons(S(x2), x3)) -> c6(LEQ#2(S(x0), S(x2)))
   DIVIDE_YS#1(Cons(x0, Cons(x1, x2)), S(y11)) -> c(TAKE#2(S(y11), Cons(x0, Cons(x1, x2))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, x3))), S(y11)) -> c(TAKE#2(S(y11), Cons(x0, Cons(x1, Cons(x2, x3)))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Nil)), S(y10)) -> c(TAKE#2(S(y10), Cons(x0, Cons(x1, Nil))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Nil))), S(y7)) -> c(TAKE#2(S(y7), Cons(x0, Cons(x1, Cons(x2, Nil)))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4)))), S(y8)) -> c(TAKE#2(S(y8), Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4))))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, x2)), S(y11)) -> c1(DROP#2(S(y11), Cons(x0, Cons(x1, x2))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, x3))), S(y11)) -> c1(DROP#2(S(y11), Cons(x0, Cons(x1, Cons(x2, x3)))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Nil)), S(y10)) -> c1(DROP#2(S(y10), Cons(x0, Cons(x1, Nil))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Nil))), S(y7)) -> c1(DROP#2(S(y7), Cons(x0, Cons(x1, Cons(x2, Nil)))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4)))), S(y8)) -> c1(DROP#2(S(y8), Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4))))))
   COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(S(y2), z3), z4, Cons(S(y0), y1), z6, z7) -> c2(MERGE#2(Cons(S(y0), y1), Cons(S(y2), z3)))
   COND_MERGE_YS_ZS_2(False, Cons(S(x0), x1), Cons(0, x2), S(x0), x1, 0, x2) -> c3(MERGE#2(Cons(S(x0), x1), x2))
   COND_MERGE_YS_ZS_2(False, Cons(S(S(x0)), x1), Cons(S(0), x2), S(S(x0)), x1, S(0), x2) -> c3(MERGE#2(Cons(S(S(x0)), x1), x2))
   COND_MERGE_YS_ZS_2(False, Cons(S(S(x0)), x1), Cons(S(S(x2)), x3), S(S(x0)), x1, S(S(x2)), x3) -> c3(MERGE#2(Cons(S(S(x0)), x1), x3))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, z3)))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Cons(z2, z3))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(S(length#1(z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Cons(drop#2(S(halve#1(S(length#1(z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3)))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3))))), HALVE#1(S(length#1(z3))), LENGTH#1(Cons(z2, z3)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, Nil)))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Cons(z2, Nil))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, Nil))), S(halve#1(S(0)))))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, Nil))), S(halve#1(length#1(Cons(z2, Nil)))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, Nil))), S(halve#1(length#1(Cons(z2, Nil))))), HALVE#1(S(length#1(Nil))), LENGTH#1(Cons(z2, Nil)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, Cons(z3, z4))))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Cons(z2, Cons(z3, z4)))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, Cons(z3, z4)))), S(halve#1(S(S(length#1(z4)))))))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, Cons(z3, z4)))), S(halve#1(length#1(Cons(z2, Cons(z3, z4))))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, Cons(z3, z4)))), S(halve#1(length#1(Cons(z2, Cons(z3, z4)))))), HALVE#1(S(length#1(Cons(z3, z4)))), LENGTH#1(Cons(z2, Cons(z3, z4))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, z3)))) -> c9(MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3)))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3))))), HALVE#1(S(length#1(z3))), LENGTH#1(Cons(z2, z3)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Nil))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(0)), Cons(z0, Cons(z1, Nil))), Cons(drop#2(S(halve#1(0)), Cons(z0, Cons(z1, Nil))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil)))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Nil))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Nil)), S(0)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil)))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> c9(CONST_F#2(Cons(z0, Cons(z1, z2)), Cons(dc#1(map, divisible, mergesort_zs_3, divide, const_f, take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2)))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(drop#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(halve#1(length#1(z2)), Cons(z1, z2)), Nil))), DIVIDE_YS#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2)))), HALVE#1(length#1(z2)), LENGTH#1(z2))
   CONST_F#2(Cons(x0, Cons(x1, x2)), Cons(z1, Cons(z2, z3))) -> c19(MERGE#2(z1, z2))
   CONST_F#2(Cons(x0, Cons(x1, Cons(x2, x3))), Cons(z1, Cons(z2, z3))) -> c19(MERGE#2(z1, z2))
   CONST_F#2(Cons(x0, Cons(x1, Nil)), Cons(z1, Cons(z2, z3))) -> c19(MERGE#2(z1, z2))
   CONST_F#2(Cons(x0, Cons(x1, Cons(x2, Nil))), Cons(z1, Cons(z2, z3))) -> c19(MERGE#2(z1, z2))
   CONST_F#2(Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4)))), Cons(z1, Cons(z2, z3))) -> c19(MERGE#2(z1, z2))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> c9(CONST_F#2(Cons(z0, Cons(z1, z2)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(halve#1(length#1(z2)), Cons(z1, z2)), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(halve#1(length#1(z2)), Cons(z1, z2)), Nil))), DIVIDE_YS#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2)))), HALVE#1(length#1(z2)), LENGTH#1(z2))
   COND_MERGE_YS_ZS_2(True, Cons(0, Cons(0, z5)), Cons(x1, x2), 0, Cons(0, z5), x1, x2) -> c2(MERGE#2(Cons(0, z5), Cons(x1, x2)))
   COND_MERGE_YS_ZS_2(True, Cons(S(0), Cons(0, z5)), Cons(S(x1), x2), S(0), Cons(0, z5), S(x1), x2) -> c2(MERGE#2(Cons(0, z5), Cons(S(x1), x2)))
   COND_MERGE_YS_ZS_2(True, Cons(S(S(x0)), Cons(0, z5)), Cons(S(S(x2)), x3), S(S(x0)), Cons(0, z5), S(S(x2)), x3) -> c2(MERGE#2(Cons(0, z5), Cons(S(S(x2)), x3)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, z3)))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Cons(z2, z3))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(Cons(z2, z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Cons(drop#2(S(halve#1(S(length#1(z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3)))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(S(length#1(z3))))), HALVE#1(S(length#1(z3))), LENGTH#1(Cons(z2, z3)))
   COND_MERGE_YS_ZS_2(True, Cons(0, Cons(S(z4), z5)), Cons(0, x2), 0, Cons(S(z4), z5), 0, x2) -> c2(MERGE#2(Cons(S(z4), z5), Cons(0, x2)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> c9(CONST_F#2(Cons(z0, Cons(z1, z2)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(Cons(z0, take#2(halve#1(length#1(z2)), Cons(z1, z2))), Cons(drop#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(halve#1(length#1(z2)), Cons(z1, z2)), Nil))), DIVIDE_YS#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2)))), HALVE#1(length#1(z2)), LENGTH#1(z2))
   COND_MERGE_YS_ZS_2(True, Cons(0, Cons(S(0), z5)), Cons(S(z2), x2), 0, Cons(S(0), z5), S(z2), x2) -> c2(MERGE#2(Cons(S(0), z5), Cons(S(z2), x2)))
   COND_MERGE_YS_ZS_2(True, Cons(S(0), Cons(S(0), z5)), Cons(S(x1), x2), S(0), Cons(S(0), z5), S(x1), x2) -> c2(MERGE#2(Cons(S(0), z5), Cons(S(x1), x2)))
   COND_MERGE_YS_ZS_2(True, Cons(S(S(x0)), Cons(S(0), z5)), Cons(S(S(x2)), x3), S(S(x0)), Cons(S(0), z5), S(S(x2)), x3) -> c2(MERGE#2(Cons(S(0), z5), Cons(S(S(x2)), x3)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, z3)))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Cons(z2, z3))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(S(length#1(z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Cons(drop#2(S(halve#1(length#1(Cons(z2, z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3)))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(S(length#1(z3))))), HALVE#1(S(length#1(z3))), LENGTH#1(Cons(z2, z3)))
   COND_MERGE_YS_ZS_2(True, Cons(0, Cons(S(S(z4)), z5)), Cons(S(0), x2), 0, Cons(S(S(z4)), z5), S(0), x2) -> c2(MERGE#2(Cons(S(S(z4)), z5), Cons(S(0), x2)))
   COND_MERGE_YS_ZS_2(True, Cons(S(0), Cons(S(S(z4)), z5)), Cons(S(0), x2), S(0), Cons(S(S(z4)), z5), S(0), x2) -> c2(MERGE#2(Cons(S(S(z4)), z5), Cons(S(0), x2)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> c9(MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(halve#1(length#1(z2)), Cons(z1, z2)), Nil))), DIVIDE_YS#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2)))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Nil))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(Nil))), Cons(z0, Cons(z1, Nil))), Cons(drop#2(S(halve#1(0)), Cons(z0, Cons(z1, Nil))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Nil)), S(halve#1(0))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Nil))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(0)), Cons(z0, Cons(z1, Nil))), Cons(drop#2(S(halve#1(length#1(Nil))), Cons(z0, Cons(z1, Nil))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Nil)), S(halve#1(0))))
   DROP#2(S(S(y0)), Cons(z1, Cons(y1, y2))) -> c12(DROP#2(S(y0), Cons(y1, y2)))
   COND_MERGE_YS_ZS_2(True, Cons(0, Cons(S(S(z5)), z6)), Cons(S(S(z2)), x2), 0, Cons(S(S(z5)), z6), S(S(z2)), x2) -> c2(MERGE#2(Cons(S(S(z5)), z6), Cons(S(S(z2)), x2)))
   COND_MERGE_YS_ZS_2(True, Cons(S(0), Cons(S(S(z5)), z6)), Cons(S(S(z2)), x2), S(0), Cons(S(S(z5)), z6), S(S(z2)), x2) -> c2(MERGE#2(Cons(S(S(z5)), z6), Cons(S(S(z2)), x2)))
   COND_MERGE_YS_ZS_2(True, Cons(S(S(x0)), Cons(S(S(z5)), z6)), Cons(S(S(x2)), x3), S(S(x0)), Cons(S(S(z5)), z6), S(S(x2)), x3) -> c2(MERGE#2(Cons(S(S(z5)), z6), Cons(S(S(x2)), x3)))
S tuples:
   TAKE#2(S(z0), Cons(z1, z2)) -> c15(TAKE#2(z0, z2))
   HALVE#1(S(S(z0))) -> c18(HALVE#1(z0))
   LEQ#2(S(z0), S(z1)) -> c22(LEQ#2(z0, z1))
   LENGTH#1(Cons(z0, z1)) -> c24(LENGTH#1(z1))
   MAP#2(dc(z0, z1, z2, z3, z4), Cons(z5, z6)) -> c26(DC#1(z0, z1, z2, z3, z4, z5))
   MAP#2(dc(z0, z1, z2, z3, z4), Cons(z5, z6)) -> c27(MAP#2(dc(z0, z1, z2, z3, z4), z6))
   MERGE#2(Cons(0, x1), Cons(z0, x3)) -> c6(COND_MERGE_YS_ZS_2(True, Cons(0, x1), Cons(z0, x3), 0, x1, z0, x3))
   MERGE#2(Cons(S(z0), x1), Cons(0, x3)) -> c6(COND_MERGE_YS_ZS_2(False, Cons(S(z0), x1), Cons(0, x3), S(z0), x1, 0, x3))
   MERGE#2(Cons(S(0), x1), Cons(S(z0), x3)) -> c6(COND_MERGE_YS_ZS_2(True, Cons(S(0), x1), Cons(S(z0), x3), S(0), x1, S(z0), x3), LEQ#2(S(0), S(z0)))
   MERGE#2(Cons(S(S(z0)), x1), Cons(S(0), x3)) -> c6(COND_MERGE_YS_ZS_2(False, Cons(S(S(z0)), x1), Cons(S(0), x3), S(S(z0)), x1, S(0), x3), LEQ#2(S(S(z0)), S(0)))
   MERGE#2(Cons(S(S(z0)), x1), Cons(S(S(z1)), x3)) -> c6(COND_MERGE_YS_ZS_2(leq#2(z0, z1), Cons(S(S(z0)), x1), Cons(S(S(z1)), x3), S(S(z0)), x1, S(S(z1)), x3), LEQ#2(S(S(z0)), S(S(z1))))
   MERGE#2(Cons(S(x0), x1), Cons(S(x2), x3)) -> c6(LEQ#2(S(x0), S(x2)))
   DIVIDE_YS#1(Cons(x0, Cons(x1, x2)), S(y11)) -> c(TAKE#2(S(y11), Cons(x0, Cons(x1, x2))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, x3))), S(y11)) -> c(TAKE#2(S(y11), Cons(x0, Cons(x1, Cons(x2, x3)))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Nil)), S(y10)) -> c(TAKE#2(S(y10), Cons(x0, Cons(x1, Nil))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Nil))), S(y7)) -> c(TAKE#2(S(y7), Cons(x0, Cons(x1, Cons(x2, Nil)))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4)))), S(y8)) -> c(TAKE#2(S(y8), Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4))))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, x2)), S(y11)) -> c1(DROP#2(S(y11), Cons(x0, Cons(x1, x2))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, x3))), S(y11)) -> c1(DROP#2(S(y11), Cons(x0, Cons(x1, Cons(x2, x3)))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Nil)), S(y10)) -> c1(DROP#2(S(y10), Cons(x0, Cons(x1, Nil))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Nil))), S(y7)) -> c1(DROP#2(S(y7), Cons(x0, Cons(x1, Cons(x2, Nil)))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4)))), S(y8)) -> c1(DROP#2(S(y8), Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4))))))
   COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(S(y2), z3), z4, Cons(S(y0), y1), z6, z7) -> c2(MERGE#2(Cons(S(y0), y1), Cons(S(y2), z3)))
   COND_MERGE_YS_ZS_2(False, Cons(S(x0), x1), Cons(0, x2), S(x0), x1, 0, x2) -> c3(MERGE#2(Cons(S(x0), x1), x2))
   COND_MERGE_YS_ZS_2(False, Cons(S(S(x0)), x1), Cons(S(0), x2), S(S(x0)), x1, S(0), x2) -> c3(MERGE#2(Cons(S(S(x0)), x1), x2))
   COND_MERGE_YS_ZS_2(False, Cons(S(S(x0)), x1), Cons(S(S(x2)), x3), S(S(x0)), x1, S(S(x2)), x3) -> c3(MERGE#2(Cons(S(S(x0)), x1), x3))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, z3)))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Cons(z2, z3))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(S(length#1(z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Cons(drop#2(S(halve#1(S(length#1(z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3)))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3))))), HALVE#1(S(length#1(z3))), LENGTH#1(Cons(z2, z3)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, Nil)))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Cons(z2, Nil))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, Nil))), S(halve#1(S(0)))))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, Nil))), S(halve#1(length#1(Cons(z2, Nil)))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, Nil))), S(halve#1(length#1(Cons(z2, Nil))))), HALVE#1(S(length#1(Nil))), LENGTH#1(Cons(z2, Nil)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, Cons(z3, z4))))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Cons(z2, Cons(z3, z4)))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, Cons(z3, z4)))), S(halve#1(S(S(length#1(z4)))))))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, Cons(z3, z4)))), S(halve#1(length#1(Cons(z2, Cons(z3, z4))))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, Cons(z3, z4)))), S(halve#1(length#1(Cons(z2, Cons(z3, z4)))))), HALVE#1(S(length#1(Cons(z3, z4)))), LENGTH#1(Cons(z2, Cons(z3, z4))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, z3)))) -> c9(MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3)))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3))))), HALVE#1(S(length#1(z3))), LENGTH#1(Cons(z2, z3)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Nil))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(0)), Cons(z0, Cons(z1, Nil))), Cons(drop#2(S(halve#1(0)), Cons(z0, Cons(z1, Nil))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil)))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Nil))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Nil)), S(0)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil)))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> c9(CONST_F#2(Cons(z0, Cons(z1, z2)), Cons(dc#1(map, divisible, mergesort_zs_3, divide, const_f, take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2)))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(drop#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(halve#1(length#1(z2)), Cons(z1, z2)), Nil))), DIVIDE_YS#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2)))), HALVE#1(length#1(z2)), LENGTH#1(z2))
   CONST_F#2(Cons(x0, Cons(x1, x2)), Cons(z1, Cons(z2, z3))) -> c19(MERGE#2(z1, z2))
   CONST_F#2(Cons(x0, Cons(x1, Cons(x2, x3))), Cons(z1, Cons(z2, z3))) -> c19(MERGE#2(z1, z2))
   CONST_F#2(Cons(x0, Cons(x1, Nil)), Cons(z1, Cons(z2, z3))) -> c19(MERGE#2(z1, z2))
   CONST_F#2(Cons(x0, Cons(x1, Cons(x2, Nil))), Cons(z1, Cons(z2, z3))) -> c19(MERGE#2(z1, z2))
   CONST_F#2(Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4)))), Cons(z1, Cons(z2, z3))) -> c19(MERGE#2(z1, z2))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> c9(CONST_F#2(Cons(z0, Cons(z1, z2)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(halve#1(length#1(z2)), Cons(z1, z2)), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(halve#1(length#1(z2)), Cons(z1, z2)), Nil))), DIVIDE_YS#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2)))), HALVE#1(length#1(z2)), LENGTH#1(z2))
   COND_MERGE_YS_ZS_2(True, Cons(0, Cons(0, z5)), Cons(x1, x2), 0, Cons(0, z5), x1, x2) -> c2(MERGE#2(Cons(0, z5), Cons(x1, x2)))
   COND_MERGE_YS_ZS_2(True, Cons(S(0), Cons(0, z5)), Cons(S(x1), x2), S(0), Cons(0, z5), S(x1), x2) -> c2(MERGE#2(Cons(0, z5), Cons(S(x1), x2)))
   COND_MERGE_YS_ZS_2(True, Cons(S(S(x0)), Cons(0, z5)), Cons(S(S(x2)), x3), S(S(x0)), Cons(0, z5), S(S(x2)), x3) -> c2(MERGE#2(Cons(0, z5), Cons(S(S(x2)), x3)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, z3)))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Cons(z2, z3))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(Cons(z2, z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Cons(drop#2(S(halve#1(S(length#1(z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3)))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(S(length#1(z3))))), HALVE#1(S(length#1(z3))), LENGTH#1(Cons(z2, z3)))
   COND_MERGE_YS_ZS_2(True, Cons(0, Cons(S(z4), z5)), Cons(0, x2), 0, Cons(S(z4), z5), 0, x2) -> c2(MERGE#2(Cons(S(z4), z5), Cons(0, x2)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> c9(CONST_F#2(Cons(z0, Cons(z1, z2)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(Cons(z0, take#2(halve#1(length#1(z2)), Cons(z1, z2))), Cons(drop#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(halve#1(length#1(z2)), Cons(z1, z2)), Nil))), DIVIDE_YS#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2)))), HALVE#1(length#1(z2)), LENGTH#1(z2))
   COND_MERGE_YS_ZS_2(True, Cons(0, Cons(S(0), z5)), Cons(S(z2), x2), 0, Cons(S(0), z5), S(z2), x2) -> c2(MERGE#2(Cons(S(0), z5), Cons(S(z2), x2)))
   COND_MERGE_YS_ZS_2(True, Cons(S(0), Cons(S(0), z5)), Cons(S(x1), x2), S(0), Cons(S(0), z5), S(x1), x2) -> c2(MERGE#2(Cons(S(0), z5), Cons(S(x1), x2)))
   COND_MERGE_YS_ZS_2(True, Cons(S(S(x0)), Cons(S(0), z5)), Cons(S(S(x2)), x3), S(S(x0)), Cons(S(0), z5), S(S(x2)), x3) -> c2(MERGE#2(Cons(S(0), z5), Cons(S(S(x2)), x3)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, z3)))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Cons(z2, z3))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(S(length#1(z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Cons(drop#2(S(halve#1(length#1(Cons(z2, z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3)))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(S(length#1(z3))))), HALVE#1(S(length#1(z3))), LENGTH#1(Cons(z2, z3)))
   COND_MERGE_YS_ZS_2(True, Cons(0, Cons(S(S(z4)), z5)), Cons(S(0), x2), 0, Cons(S(S(z4)), z5), S(0), x2) -> c2(MERGE#2(Cons(S(S(z4)), z5), Cons(S(0), x2)))
   COND_MERGE_YS_ZS_2(True, Cons(S(0), Cons(S(S(z4)), z5)), Cons(S(0), x2), S(0), Cons(S(S(z4)), z5), S(0), x2) -> c2(MERGE#2(Cons(S(S(z4)), z5), Cons(S(0), x2)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> c9(MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(halve#1(length#1(z2)), Cons(z1, z2)), Nil))), DIVIDE_YS#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2)))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Nil))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(Nil))), Cons(z0, Cons(z1, Nil))), Cons(drop#2(S(halve#1(0)), Cons(z0, Cons(z1, Nil))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Nil)), S(halve#1(0))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Nil))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(0)), Cons(z0, Cons(z1, Nil))), Cons(drop#2(S(halve#1(length#1(Nil))), Cons(z0, Cons(z1, Nil))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Nil)), S(halve#1(0))))
   DROP#2(S(S(y0)), Cons(z1, Cons(y1, y2))) -> c12(DROP#2(S(y0), Cons(y1, y2)))
   COND_MERGE_YS_ZS_2(True, Cons(0, Cons(S(S(z5)), z6)), Cons(S(S(z2)), x2), 0, Cons(S(S(z5)), z6), S(S(z2)), x2) -> c2(MERGE#2(Cons(S(S(z5)), z6), Cons(S(S(z2)), x2)))
   COND_MERGE_YS_ZS_2(True, Cons(S(0), Cons(S(S(z5)), z6)), Cons(S(S(z2)), x2), S(0), Cons(S(S(z5)), z6), S(S(z2)), x2) -> c2(MERGE#2(Cons(S(S(z5)), z6), Cons(S(S(z2)), x2)))
   COND_MERGE_YS_ZS_2(True, Cons(S(S(x0)), Cons(S(S(z5)), z6)), Cons(S(S(x2)), x3), S(S(x0)), Cons(S(S(z5)), z6), S(S(x2)), x3) -> c2(MERGE#2(Cons(S(S(z5)), z6), Cons(S(S(x2)), x3)))
K tuples:none
Defined Rule Symbols:   leq#2_2, map#2_2, divide_ys#1_2, halve#1_1, length#1_1, take#2_2, drop#2_2, dc#1_6, const_f#2_2, merge#2_2, cond_merge_ys_zs_2_7

Defined Pair Symbols:   TAKE#2_2, HALVE#1_1, LEQ#2_2, LENGTH#1_1, MAP#2_2, MERGE#2_2, DIVIDE_YS#1_2, COND_MERGE_YS_ZS_2_7, DC#1_6, CONST_F#2_2, DROP#2_2

Compound Symbols:   c15_1, c18_1, c22_1, c24_1, c26_1, c27_1, c6_1, c6_2, c_1, c1_1, c2_1, c3_1, c9_5, c9_4, c9_3, c19_1, c9_2, c12_1


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(175) CdtInstantiationProof (BOTH BOUNDS(ID, ID))
Use instantiation to replace COND_MERGE_YS_ZS_2(True, Cons(z0, z1), Cons(S(y2), z3), z4, Cons(S(y0), y1), z6, z7) -> c2(MERGE#2(Cons(S(y0), y1), Cons(S(y2), z3))) by 
   COND_MERGE_YS_ZS_2(True, Cons(0, Cons(S(z5), z6)), Cons(S(z2), x2), 0, Cons(S(z5), z6), S(z2), x2) -> c2(MERGE#2(Cons(S(z5), z6), Cons(S(z2), x2)))
   COND_MERGE_YS_ZS_2(True, Cons(S(0), Cons(S(z5), z6)), Cons(S(x1), x2), S(0), Cons(S(z5), z6), S(x1), x2) -> c2(MERGE#2(Cons(S(z5), z6), Cons(S(x1), x2)))
   COND_MERGE_YS_ZS_2(True, Cons(S(S(x0)), Cons(S(z5), z6)), Cons(S(S(x2)), x3), S(S(x0)), Cons(S(z5), z6), S(S(x2)), x3) -> c2(MERGE#2(Cons(S(z5), z6), Cons(S(S(x2)), x3)))

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

(176)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   leq#2(0, z0) -> True
   leq#2(S(z0), 0) -> False
   leq#2(S(z0), S(z1)) -> leq#2(z0, z1)
   map#2(dc(z0, z1, z2, z3, z4), Nil) -> Nil
   map#2(dc(z0, z1, z2, z3, z4), Cons(z5, z6)) -> Cons(dc#1(z0, z1, z2, z3, z4, z5), map#2(dc(z0, z1, z2, z3, z4), z6))
   divide_ys#1(z0, z1) -> Cons(take#2(z1, z0), Cons(drop#2(z1, z0), Nil))
   halve#1(0) -> 0
   halve#1(S(0)) -> S(0)
   halve#1(S(S(z0))) -> S(halve#1(z0))
   length#1(Nil) -> 0
   length#1(Cons(z0, z1)) -> S(length#1(z1))
   take#2(0, z0) -> Nil
   take#2(S(0), Nil) -> Cons(bot[0], Nil)
   take#2(S(z0), Cons(z1, z2)) -> Cons(z1, take#2(z0, z2))
   drop#2(0, z0) -> z0
   drop#2(S(0), Nil) -> bot[1]
   drop#2(S(z0), Cons(z1, z2)) -> drop#2(z0, z2)
   dc#1(map, divisible, mergesort_zs_3, divide, const_f, Nil) -> Nil
   dc#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Nil)) -> Cons(z0, Nil)
   dc#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> const_f#2(Cons(z0, Cons(z1, z2)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2))))))
   const_f#2(z0, Cons(z1, Cons(z2, z3))) -> merge#2(z1, z2)
   merge#2(Nil, z0) -> z0
   merge#2(Cons(z0, z1), Nil) -> Cons(z0, z1)
   merge#2(Cons(z0, z1), Cons(z2, z3)) -> cond_merge_ys_zs_2(leq#2(z0, z2), Cons(z0, z1), Cons(z2, z3), z0, z1, z2, z3)
   cond_merge_ys_zs_2(True, Cons(z0, z1), Cons(z2, z3), z4, z5, z6, z7) -> Cons(z4, merge#2(z5, Cons(z2, z3)))
   cond_merge_ys_zs_2(False, Cons(z0, z1), Cons(z2, z3), z4, z5, z6, z7) -> Cons(z6, merge#2(Cons(z0, z1), z7))
Tuples:
   TAKE#2(S(z0), Cons(z1, z2)) -> c15(TAKE#2(z0, z2))
   HALVE#1(S(S(z0))) -> c18(HALVE#1(z0))
   LEQ#2(S(z0), S(z1)) -> c22(LEQ#2(z0, z1))
   LENGTH#1(Cons(z0, z1)) -> c24(LENGTH#1(z1))
   MAP#2(dc(z0, z1, z2, z3, z4), Cons(z5, z6)) -> c26(DC#1(z0, z1, z2, z3, z4, z5))
   MAP#2(dc(z0, z1, z2, z3, z4), Cons(z5, z6)) -> c27(MAP#2(dc(z0, z1, z2, z3, z4), z6))
   MERGE#2(Cons(0, x1), Cons(z0, x3)) -> c6(COND_MERGE_YS_ZS_2(True, Cons(0, x1), Cons(z0, x3), 0, x1, z0, x3))
   MERGE#2(Cons(S(z0), x1), Cons(0, x3)) -> c6(COND_MERGE_YS_ZS_2(False, Cons(S(z0), x1), Cons(0, x3), S(z0), x1, 0, x3))
   MERGE#2(Cons(S(0), x1), Cons(S(z0), x3)) -> c6(COND_MERGE_YS_ZS_2(True, Cons(S(0), x1), Cons(S(z0), x3), S(0), x1, S(z0), x3), LEQ#2(S(0), S(z0)))
   MERGE#2(Cons(S(S(z0)), x1), Cons(S(0), x3)) -> c6(COND_MERGE_YS_ZS_2(False, Cons(S(S(z0)), x1), Cons(S(0), x3), S(S(z0)), x1, S(0), x3), LEQ#2(S(S(z0)), S(0)))
   MERGE#2(Cons(S(S(z0)), x1), Cons(S(S(z1)), x3)) -> c6(COND_MERGE_YS_ZS_2(leq#2(z0, z1), Cons(S(S(z0)), x1), Cons(S(S(z1)), x3), S(S(z0)), x1, S(S(z1)), x3), LEQ#2(S(S(z0)), S(S(z1))))
   MERGE#2(Cons(S(x0), x1), Cons(S(x2), x3)) -> c6(LEQ#2(S(x0), S(x2)))
   DIVIDE_YS#1(Cons(x0, Cons(x1, x2)), S(y11)) -> c(TAKE#2(S(y11), Cons(x0, Cons(x1, x2))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, x3))), S(y11)) -> c(TAKE#2(S(y11), Cons(x0, Cons(x1, Cons(x2, x3)))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Nil)), S(y10)) -> c(TAKE#2(S(y10), Cons(x0, Cons(x1, Nil))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Nil))), S(y7)) -> c(TAKE#2(S(y7), Cons(x0, Cons(x1, Cons(x2, Nil)))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4)))), S(y8)) -> c(TAKE#2(S(y8), Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4))))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, x2)), S(y11)) -> c1(DROP#2(S(y11), Cons(x0, Cons(x1, x2))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, x3))), S(y11)) -> c1(DROP#2(S(y11), Cons(x0, Cons(x1, Cons(x2, x3)))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Nil)), S(y10)) -> c1(DROP#2(S(y10), Cons(x0, Cons(x1, Nil))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Nil))), S(y7)) -> c1(DROP#2(S(y7), Cons(x0, Cons(x1, Cons(x2, Nil)))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4)))), S(y8)) -> c1(DROP#2(S(y8), Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4))))))
   COND_MERGE_YS_ZS_2(False, Cons(S(x0), x1), Cons(0, x2), S(x0), x1, 0, x2) -> c3(MERGE#2(Cons(S(x0), x1), x2))
   COND_MERGE_YS_ZS_2(False, Cons(S(S(x0)), x1), Cons(S(0), x2), S(S(x0)), x1, S(0), x2) -> c3(MERGE#2(Cons(S(S(x0)), x1), x2))
   COND_MERGE_YS_ZS_2(False, Cons(S(S(x0)), x1), Cons(S(S(x2)), x3), S(S(x0)), x1, S(S(x2)), x3) -> c3(MERGE#2(Cons(S(S(x0)), x1), x3))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, z3)))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Cons(z2, z3))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(S(length#1(z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Cons(drop#2(S(halve#1(S(length#1(z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3)))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3))))), HALVE#1(S(length#1(z3))), LENGTH#1(Cons(z2, z3)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, Nil)))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Cons(z2, Nil))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, Nil))), S(halve#1(S(0)))))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, Nil))), S(halve#1(length#1(Cons(z2, Nil)))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, Nil))), S(halve#1(length#1(Cons(z2, Nil))))), HALVE#1(S(length#1(Nil))), LENGTH#1(Cons(z2, Nil)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, Cons(z3, z4))))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Cons(z2, Cons(z3, z4)))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, Cons(z3, z4)))), S(halve#1(S(S(length#1(z4)))))))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, Cons(z3, z4)))), S(halve#1(length#1(Cons(z2, Cons(z3, z4))))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, Cons(z3, z4)))), S(halve#1(length#1(Cons(z2, Cons(z3, z4)))))), HALVE#1(S(length#1(Cons(z3, z4)))), LENGTH#1(Cons(z2, Cons(z3, z4))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, z3)))) -> c9(MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3)))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3))))), HALVE#1(S(length#1(z3))), LENGTH#1(Cons(z2, z3)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Nil))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(0)), Cons(z0, Cons(z1, Nil))), Cons(drop#2(S(halve#1(0)), Cons(z0, Cons(z1, Nil))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil)))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Nil))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Nil)), S(0)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil)))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> c9(CONST_F#2(Cons(z0, Cons(z1, z2)), Cons(dc#1(map, divisible, mergesort_zs_3, divide, const_f, take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2)))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(drop#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(halve#1(length#1(z2)), Cons(z1, z2)), Nil))), DIVIDE_YS#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2)))), HALVE#1(length#1(z2)), LENGTH#1(z2))
   CONST_F#2(Cons(x0, Cons(x1, x2)), Cons(z1, Cons(z2, z3))) -> c19(MERGE#2(z1, z2))
   CONST_F#2(Cons(x0, Cons(x1, Cons(x2, x3))), Cons(z1, Cons(z2, z3))) -> c19(MERGE#2(z1, z2))
   CONST_F#2(Cons(x0, Cons(x1, Nil)), Cons(z1, Cons(z2, z3))) -> c19(MERGE#2(z1, z2))
   CONST_F#2(Cons(x0, Cons(x1, Cons(x2, Nil))), Cons(z1, Cons(z2, z3))) -> c19(MERGE#2(z1, z2))
   CONST_F#2(Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4)))), Cons(z1, Cons(z2, z3))) -> c19(MERGE#2(z1, z2))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> c9(CONST_F#2(Cons(z0, Cons(z1, z2)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(halve#1(length#1(z2)), Cons(z1, z2)), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(halve#1(length#1(z2)), Cons(z1, z2)), Nil))), DIVIDE_YS#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2)))), HALVE#1(length#1(z2)), LENGTH#1(z2))
   COND_MERGE_YS_ZS_2(True, Cons(0, Cons(0, z5)), Cons(x1, x2), 0, Cons(0, z5), x1, x2) -> c2(MERGE#2(Cons(0, z5), Cons(x1, x2)))
   COND_MERGE_YS_ZS_2(True, Cons(S(0), Cons(0, z5)), Cons(S(x1), x2), S(0), Cons(0, z5), S(x1), x2) -> c2(MERGE#2(Cons(0, z5), Cons(S(x1), x2)))
   COND_MERGE_YS_ZS_2(True, Cons(S(S(x0)), Cons(0, z5)), Cons(S(S(x2)), x3), S(S(x0)), Cons(0, z5), S(S(x2)), x3) -> c2(MERGE#2(Cons(0, z5), Cons(S(S(x2)), x3)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, z3)))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Cons(z2, z3))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(Cons(z2, z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Cons(drop#2(S(halve#1(S(length#1(z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3)))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(S(length#1(z3))))), HALVE#1(S(length#1(z3))), LENGTH#1(Cons(z2, z3)))
   COND_MERGE_YS_ZS_2(True, Cons(0, Cons(S(z4), z5)), Cons(0, x2), 0, Cons(S(z4), z5), 0, x2) -> c2(MERGE#2(Cons(S(z4), z5), Cons(0, x2)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> c9(CONST_F#2(Cons(z0, Cons(z1, z2)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(Cons(z0, take#2(halve#1(length#1(z2)), Cons(z1, z2))), Cons(drop#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(halve#1(length#1(z2)), Cons(z1, z2)), Nil))), DIVIDE_YS#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2)))), HALVE#1(length#1(z2)), LENGTH#1(z2))
   COND_MERGE_YS_ZS_2(True, Cons(0, Cons(S(0), z5)), Cons(S(z2), x2), 0, Cons(S(0), z5), S(z2), x2) -> c2(MERGE#2(Cons(S(0), z5), Cons(S(z2), x2)))
   COND_MERGE_YS_ZS_2(True, Cons(S(0), Cons(S(0), z5)), Cons(S(x1), x2), S(0), Cons(S(0), z5), S(x1), x2) -> c2(MERGE#2(Cons(S(0), z5), Cons(S(x1), x2)))
   COND_MERGE_YS_ZS_2(True, Cons(S(S(x0)), Cons(S(0), z5)), Cons(S(S(x2)), x3), S(S(x0)), Cons(S(0), z5), S(S(x2)), x3) -> c2(MERGE#2(Cons(S(0), z5), Cons(S(S(x2)), x3)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, z3)))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Cons(z2, z3))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(S(length#1(z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Cons(drop#2(S(halve#1(length#1(Cons(z2, z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3)))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(S(length#1(z3))))), HALVE#1(S(length#1(z3))), LENGTH#1(Cons(z2, z3)))
   COND_MERGE_YS_ZS_2(True, Cons(0, Cons(S(S(z4)), z5)), Cons(S(0), x2), 0, Cons(S(S(z4)), z5), S(0), x2) -> c2(MERGE#2(Cons(S(S(z4)), z5), Cons(S(0), x2)))
   COND_MERGE_YS_ZS_2(True, Cons(S(0), Cons(S(S(z4)), z5)), Cons(S(0), x2), S(0), Cons(S(S(z4)), z5), S(0), x2) -> c2(MERGE#2(Cons(S(S(z4)), z5), Cons(S(0), x2)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> c9(MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(halve#1(length#1(z2)), Cons(z1, z2)), Nil))), DIVIDE_YS#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2)))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Nil))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(Nil))), Cons(z0, Cons(z1, Nil))), Cons(drop#2(S(halve#1(0)), Cons(z0, Cons(z1, Nil))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Nil)), S(halve#1(0))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Nil))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(0)), Cons(z0, Cons(z1, Nil))), Cons(drop#2(S(halve#1(length#1(Nil))), Cons(z0, Cons(z1, Nil))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Nil)), S(halve#1(0))))
   DROP#2(S(S(y0)), Cons(z1, Cons(y1, y2))) -> c12(DROP#2(S(y0), Cons(y1, y2)))
   COND_MERGE_YS_ZS_2(True, Cons(0, Cons(S(S(z5)), z6)), Cons(S(S(z2)), x2), 0, Cons(S(S(z5)), z6), S(S(z2)), x2) -> c2(MERGE#2(Cons(S(S(z5)), z6), Cons(S(S(z2)), x2)))
   COND_MERGE_YS_ZS_2(True, Cons(S(0), Cons(S(S(z5)), z6)), Cons(S(S(z2)), x2), S(0), Cons(S(S(z5)), z6), S(S(z2)), x2) -> c2(MERGE#2(Cons(S(S(z5)), z6), Cons(S(S(z2)), x2)))
   COND_MERGE_YS_ZS_2(True, Cons(S(S(x0)), Cons(S(S(z5)), z6)), Cons(S(S(x2)), x3), S(S(x0)), Cons(S(S(z5)), z6), S(S(x2)), x3) -> c2(MERGE#2(Cons(S(S(z5)), z6), Cons(S(S(x2)), x3)))
   COND_MERGE_YS_ZS_2(True, Cons(0, Cons(S(z5), z6)), Cons(S(z2), x2), 0, Cons(S(z5), z6), S(z2), x2) -> c2(MERGE#2(Cons(S(z5), z6), Cons(S(z2), x2)))
   COND_MERGE_YS_ZS_2(True, Cons(S(0), Cons(S(z5), z6)), Cons(S(x1), x2), S(0), Cons(S(z5), z6), S(x1), x2) -> c2(MERGE#2(Cons(S(z5), z6), Cons(S(x1), x2)))
   COND_MERGE_YS_ZS_2(True, Cons(S(S(x0)), Cons(S(z5), z6)), Cons(S(S(x2)), x3), S(S(x0)), Cons(S(z5), z6), S(S(x2)), x3) -> c2(MERGE#2(Cons(S(z5), z6), Cons(S(S(x2)), x3)))
S tuples:
   TAKE#2(S(z0), Cons(z1, z2)) -> c15(TAKE#2(z0, z2))
   HALVE#1(S(S(z0))) -> c18(HALVE#1(z0))
   LEQ#2(S(z0), S(z1)) -> c22(LEQ#2(z0, z1))
   LENGTH#1(Cons(z0, z1)) -> c24(LENGTH#1(z1))
   MAP#2(dc(z0, z1, z2, z3, z4), Cons(z5, z6)) -> c26(DC#1(z0, z1, z2, z3, z4, z5))
   MAP#2(dc(z0, z1, z2, z3, z4), Cons(z5, z6)) -> c27(MAP#2(dc(z0, z1, z2, z3, z4), z6))
   MERGE#2(Cons(0, x1), Cons(z0, x3)) -> c6(COND_MERGE_YS_ZS_2(True, Cons(0, x1), Cons(z0, x3), 0, x1, z0, x3))
   MERGE#2(Cons(S(z0), x1), Cons(0, x3)) -> c6(COND_MERGE_YS_ZS_2(False, Cons(S(z0), x1), Cons(0, x3), S(z0), x1, 0, x3))
   MERGE#2(Cons(S(0), x1), Cons(S(z0), x3)) -> c6(COND_MERGE_YS_ZS_2(True, Cons(S(0), x1), Cons(S(z0), x3), S(0), x1, S(z0), x3), LEQ#2(S(0), S(z0)))
   MERGE#2(Cons(S(S(z0)), x1), Cons(S(0), x3)) -> c6(COND_MERGE_YS_ZS_2(False, Cons(S(S(z0)), x1), Cons(S(0), x3), S(S(z0)), x1, S(0), x3), LEQ#2(S(S(z0)), S(0)))
   MERGE#2(Cons(S(S(z0)), x1), Cons(S(S(z1)), x3)) -> c6(COND_MERGE_YS_ZS_2(leq#2(z0, z1), Cons(S(S(z0)), x1), Cons(S(S(z1)), x3), S(S(z0)), x1, S(S(z1)), x3), LEQ#2(S(S(z0)), S(S(z1))))
   MERGE#2(Cons(S(x0), x1), Cons(S(x2), x3)) -> c6(LEQ#2(S(x0), S(x2)))
   DIVIDE_YS#1(Cons(x0, Cons(x1, x2)), S(y11)) -> c(TAKE#2(S(y11), Cons(x0, Cons(x1, x2))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, x3))), S(y11)) -> c(TAKE#2(S(y11), Cons(x0, Cons(x1, Cons(x2, x3)))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Nil)), S(y10)) -> c(TAKE#2(S(y10), Cons(x0, Cons(x1, Nil))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Nil))), S(y7)) -> c(TAKE#2(S(y7), Cons(x0, Cons(x1, Cons(x2, Nil)))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4)))), S(y8)) -> c(TAKE#2(S(y8), Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4))))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, x2)), S(y11)) -> c1(DROP#2(S(y11), Cons(x0, Cons(x1, x2))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, x3))), S(y11)) -> c1(DROP#2(S(y11), Cons(x0, Cons(x1, Cons(x2, x3)))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Nil)), S(y10)) -> c1(DROP#2(S(y10), Cons(x0, Cons(x1, Nil))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Nil))), S(y7)) -> c1(DROP#2(S(y7), Cons(x0, Cons(x1, Cons(x2, Nil)))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4)))), S(y8)) -> c1(DROP#2(S(y8), Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4))))))
   COND_MERGE_YS_ZS_2(False, Cons(S(x0), x1), Cons(0, x2), S(x0), x1, 0, x2) -> c3(MERGE#2(Cons(S(x0), x1), x2))
   COND_MERGE_YS_ZS_2(False, Cons(S(S(x0)), x1), Cons(S(0), x2), S(S(x0)), x1, S(0), x2) -> c3(MERGE#2(Cons(S(S(x0)), x1), x2))
   COND_MERGE_YS_ZS_2(False, Cons(S(S(x0)), x1), Cons(S(S(x2)), x3), S(S(x0)), x1, S(S(x2)), x3) -> c3(MERGE#2(Cons(S(S(x0)), x1), x3))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, z3)))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Cons(z2, z3))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(S(length#1(z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Cons(drop#2(S(halve#1(S(length#1(z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3)))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3))))), HALVE#1(S(length#1(z3))), LENGTH#1(Cons(z2, z3)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, Nil)))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Cons(z2, Nil))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, Nil))), S(halve#1(S(0)))))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, Nil))), S(halve#1(length#1(Cons(z2, Nil)))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, Nil))), S(halve#1(length#1(Cons(z2, Nil))))), HALVE#1(S(length#1(Nil))), LENGTH#1(Cons(z2, Nil)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, Cons(z3, z4))))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Cons(z2, Cons(z3, z4)))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, Cons(z3, z4)))), S(halve#1(S(S(length#1(z4)))))))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, Cons(z3, z4)))), S(halve#1(length#1(Cons(z2, Cons(z3, z4))))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, Cons(z3, z4)))), S(halve#1(length#1(Cons(z2, Cons(z3, z4)))))), HALVE#1(S(length#1(Cons(z3, z4)))), LENGTH#1(Cons(z2, Cons(z3, z4))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, z3)))) -> c9(MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3)))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3))))), HALVE#1(S(length#1(z3))), LENGTH#1(Cons(z2, z3)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Nil))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(0)), Cons(z0, Cons(z1, Nil))), Cons(drop#2(S(halve#1(0)), Cons(z0, Cons(z1, Nil))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil)))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Nil))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Nil)), S(0)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil)))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> c9(CONST_F#2(Cons(z0, Cons(z1, z2)), Cons(dc#1(map, divisible, mergesort_zs_3, divide, const_f, take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2)))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(drop#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(halve#1(length#1(z2)), Cons(z1, z2)), Nil))), DIVIDE_YS#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2)))), HALVE#1(length#1(z2)), LENGTH#1(z2))
   CONST_F#2(Cons(x0, Cons(x1, x2)), Cons(z1, Cons(z2, z3))) -> c19(MERGE#2(z1, z2))
   CONST_F#2(Cons(x0, Cons(x1, Cons(x2, x3))), Cons(z1, Cons(z2, z3))) -> c19(MERGE#2(z1, z2))
   CONST_F#2(Cons(x0, Cons(x1, Nil)), Cons(z1, Cons(z2, z3))) -> c19(MERGE#2(z1, z2))
   CONST_F#2(Cons(x0, Cons(x1, Cons(x2, Nil))), Cons(z1, Cons(z2, z3))) -> c19(MERGE#2(z1, z2))
   CONST_F#2(Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4)))), Cons(z1, Cons(z2, z3))) -> c19(MERGE#2(z1, z2))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> c9(CONST_F#2(Cons(z0, Cons(z1, z2)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(halve#1(length#1(z2)), Cons(z1, z2)), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(halve#1(length#1(z2)), Cons(z1, z2)), Nil))), DIVIDE_YS#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2)))), HALVE#1(length#1(z2)), LENGTH#1(z2))
   COND_MERGE_YS_ZS_2(True, Cons(0, Cons(0, z5)), Cons(x1, x2), 0, Cons(0, z5), x1, x2) -> c2(MERGE#2(Cons(0, z5), Cons(x1, x2)))
   COND_MERGE_YS_ZS_2(True, Cons(S(0), Cons(0, z5)), Cons(S(x1), x2), S(0), Cons(0, z5), S(x1), x2) -> c2(MERGE#2(Cons(0, z5), Cons(S(x1), x2)))
   COND_MERGE_YS_ZS_2(True, Cons(S(S(x0)), Cons(0, z5)), Cons(S(S(x2)), x3), S(S(x0)), Cons(0, z5), S(S(x2)), x3) -> c2(MERGE#2(Cons(0, z5), Cons(S(S(x2)), x3)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, z3)))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Cons(z2, z3))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(Cons(z2, z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Cons(drop#2(S(halve#1(S(length#1(z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3)))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(S(length#1(z3))))), HALVE#1(S(length#1(z3))), LENGTH#1(Cons(z2, z3)))
   COND_MERGE_YS_ZS_2(True, Cons(0, Cons(S(z4), z5)), Cons(0, x2), 0, Cons(S(z4), z5), 0, x2) -> c2(MERGE#2(Cons(S(z4), z5), Cons(0, x2)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> c9(CONST_F#2(Cons(z0, Cons(z1, z2)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(Cons(z0, take#2(halve#1(length#1(z2)), Cons(z1, z2))), Cons(drop#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(halve#1(length#1(z2)), Cons(z1, z2)), Nil))), DIVIDE_YS#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2)))), HALVE#1(length#1(z2)), LENGTH#1(z2))
   COND_MERGE_YS_ZS_2(True, Cons(0, Cons(S(0), z5)), Cons(S(z2), x2), 0, Cons(S(0), z5), S(z2), x2) -> c2(MERGE#2(Cons(S(0), z5), Cons(S(z2), x2)))
   COND_MERGE_YS_ZS_2(True, Cons(S(0), Cons(S(0), z5)), Cons(S(x1), x2), S(0), Cons(S(0), z5), S(x1), x2) -> c2(MERGE#2(Cons(S(0), z5), Cons(S(x1), x2)))
   COND_MERGE_YS_ZS_2(True, Cons(S(S(x0)), Cons(S(0), z5)), Cons(S(S(x2)), x3), S(S(x0)), Cons(S(0), z5), S(S(x2)), x3) -> c2(MERGE#2(Cons(S(0), z5), Cons(S(S(x2)), x3)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, z3)))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Cons(z2, z3))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(S(length#1(z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Cons(drop#2(S(halve#1(length#1(Cons(z2, z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3)))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(S(length#1(z3))))), HALVE#1(S(length#1(z3))), LENGTH#1(Cons(z2, z3)))
   COND_MERGE_YS_ZS_2(True, Cons(0, Cons(S(S(z4)), z5)), Cons(S(0), x2), 0, Cons(S(S(z4)), z5), S(0), x2) -> c2(MERGE#2(Cons(S(S(z4)), z5), Cons(S(0), x2)))
   COND_MERGE_YS_ZS_2(True, Cons(S(0), Cons(S(S(z4)), z5)), Cons(S(0), x2), S(0), Cons(S(S(z4)), z5), S(0), x2) -> c2(MERGE#2(Cons(S(S(z4)), z5), Cons(S(0), x2)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> c9(MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(halve#1(length#1(z2)), Cons(z1, z2)), Nil))), DIVIDE_YS#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2)))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Nil))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(Nil))), Cons(z0, Cons(z1, Nil))), Cons(drop#2(S(halve#1(0)), Cons(z0, Cons(z1, Nil))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Nil)), S(halve#1(0))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Nil))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(0)), Cons(z0, Cons(z1, Nil))), Cons(drop#2(S(halve#1(length#1(Nil))), Cons(z0, Cons(z1, Nil))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Nil)), S(halve#1(0))))
   DROP#2(S(S(y0)), Cons(z1, Cons(y1, y2))) -> c12(DROP#2(S(y0), Cons(y1, y2)))
   COND_MERGE_YS_ZS_2(True, Cons(0, Cons(S(S(z5)), z6)), Cons(S(S(z2)), x2), 0, Cons(S(S(z5)), z6), S(S(z2)), x2) -> c2(MERGE#2(Cons(S(S(z5)), z6), Cons(S(S(z2)), x2)))
   COND_MERGE_YS_ZS_2(True, Cons(S(0), Cons(S(S(z5)), z6)), Cons(S(S(z2)), x2), S(0), Cons(S(S(z5)), z6), S(S(z2)), x2) -> c2(MERGE#2(Cons(S(S(z5)), z6), Cons(S(S(z2)), x2)))
   COND_MERGE_YS_ZS_2(True, Cons(S(S(x0)), Cons(S(S(z5)), z6)), Cons(S(S(x2)), x3), S(S(x0)), Cons(S(S(z5)), z6), S(S(x2)), x3) -> c2(MERGE#2(Cons(S(S(z5)), z6), Cons(S(S(x2)), x3)))
   COND_MERGE_YS_ZS_2(True, Cons(0, Cons(S(z5), z6)), Cons(S(z2), x2), 0, Cons(S(z5), z6), S(z2), x2) -> c2(MERGE#2(Cons(S(z5), z6), Cons(S(z2), x2)))
   COND_MERGE_YS_ZS_2(True, Cons(S(0), Cons(S(z5), z6)), Cons(S(x1), x2), S(0), Cons(S(z5), z6), S(x1), x2) -> c2(MERGE#2(Cons(S(z5), z6), Cons(S(x1), x2)))
   COND_MERGE_YS_ZS_2(True, Cons(S(S(x0)), Cons(S(z5), z6)), Cons(S(S(x2)), x3), S(S(x0)), Cons(S(z5), z6), S(S(x2)), x3) -> c2(MERGE#2(Cons(S(z5), z6), Cons(S(S(x2)), x3)))
K tuples:none
Defined Rule Symbols:   leq#2_2, map#2_2, divide_ys#1_2, halve#1_1, length#1_1, take#2_2, drop#2_2, dc#1_6, const_f#2_2, merge#2_2, cond_merge_ys_zs_2_7

Defined Pair Symbols:   TAKE#2_2, HALVE#1_1, LEQ#2_2, LENGTH#1_1, MAP#2_2, MERGE#2_2, DIVIDE_YS#1_2, COND_MERGE_YS_ZS_2_7, DC#1_6, CONST_F#2_2, DROP#2_2

Compound Symbols:   c15_1, c18_1, c22_1, c24_1, c26_1, c27_1, c6_1, c6_2, c_1, c1_1, c3_1, c9_5, c9_4, c9_3, c19_1, c2_1, c9_2, c12_1


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

(177) CdtRewritingProof (BOTH BOUNDS(ID, ID))
Used rewriting to replace DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, z3)))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Cons(z2, z3))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(S(length#1(z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Cons(drop#2(S(halve#1(S(length#1(z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3)))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3))))), HALVE#1(S(length#1(z3))), LENGTH#1(Cons(z2, z3))) by DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, z3)))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Cons(z2, z3))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(S(length#1(z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Cons(drop#2(S(halve#1(S(length#1(z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3)))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(S(length#1(z3))))), HALVE#1(S(length#1(z3))), LENGTH#1(Cons(z2, z3)))
----------------------------------------

(178)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   leq#2(0, z0) -> True
   leq#2(S(z0), 0) -> False
   leq#2(S(z0), S(z1)) -> leq#2(z0, z1)
   map#2(dc(z0, z1, z2, z3, z4), Nil) -> Nil
   map#2(dc(z0, z1, z2, z3, z4), Cons(z5, z6)) -> Cons(dc#1(z0, z1, z2, z3, z4, z5), map#2(dc(z0, z1, z2, z3, z4), z6))
   divide_ys#1(z0, z1) -> Cons(take#2(z1, z0), Cons(drop#2(z1, z0), Nil))
   halve#1(0) -> 0
   halve#1(S(0)) -> S(0)
   halve#1(S(S(z0))) -> S(halve#1(z0))
   length#1(Nil) -> 0
   length#1(Cons(z0, z1)) -> S(length#1(z1))
   take#2(0, z0) -> Nil
   take#2(S(0), Nil) -> Cons(bot[0], Nil)
   take#2(S(z0), Cons(z1, z2)) -> Cons(z1, take#2(z0, z2))
   drop#2(0, z0) -> z0
   drop#2(S(0), Nil) -> bot[1]
   drop#2(S(z0), Cons(z1, z2)) -> drop#2(z0, z2)
   dc#1(map, divisible, mergesort_zs_3, divide, const_f, Nil) -> Nil
   dc#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Nil)) -> Cons(z0, Nil)
   dc#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> const_f#2(Cons(z0, Cons(z1, z2)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2))))))
   const_f#2(z0, Cons(z1, Cons(z2, z3))) -> merge#2(z1, z2)
   merge#2(Nil, z0) -> z0
   merge#2(Cons(z0, z1), Nil) -> Cons(z0, z1)
   merge#2(Cons(z0, z1), Cons(z2, z3)) -> cond_merge_ys_zs_2(leq#2(z0, z2), Cons(z0, z1), Cons(z2, z3), z0, z1, z2, z3)
   cond_merge_ys_zs_2(True, Cons(z0, z1), Cons(z2, z3), z4, z5, z6, z7) -> Cons(z4, merge#2(z5, Cons(z2, z3)))
   cond_merge_ys_zs_2(False, Cons(z0, z1), Cons(z2, z3), z4, z5, z6, z7) -> Cons(z6, merge#2(Cons(z0, z1), z7))
Tuples:
   TAKE#2(S(z0), Cons(z1, z2)) -> c15(TAKE#2(z0, z2))
   HALVE#1(S(S(z0))) -> c18(HALVE#1(z0))
   LEQ#2(S(z0), S(z1)) -> c22(LEQ#2(z0, z1))
   LENGTH#1(Cons(z0, z1)) -> c24(LENGTH#1(z1))
   MAP#2(dc(z0, z1, z2, z3, z4), Cons(z5, z6)) -> c26(DC#1(z0, z1, z2, z3, z4, z5))
   MAP#2(dc(z0, z1, z2, z3, z4), Cons(z5, z6)) -> c27(MAP#2(dc(z0, z1, z2, z3, z4), z6))
   MERGE#2(Cons(0, x1), Cons(z0, x3)) -> c6(COND_MERGE_YS_ZS_2(True, Cons(0, x1), Cons(z0, x3), 0, x1, z0, x3))
   MERGE#2(Cons(S(z0), x1), Cons(0, x3)) -> c6(COND_MERGE_YS_ZS_2(False, Cons(S(z0), x1), Cons(0, x3), S(z0), x1, 0, x3))
   MERGE#2(Cons(S(0), x1), Cons(S(z0), x3)) -> c6(COND_MERGE_YS_ZS_2(True, Cons(S(0), x1), Cons(S(z0), x3), S(0), x1, S(z0), x3), LEQ#2(S(0), S(z0)))
   MERGE#2(Cons(S(S(z0)), x1), Cons(S(0), x3)) -> c6(COND_MERGE_YS_ZS_2(False, Cons(S(S(z0)), x1), Cons(S(0), x3), S(S(z0)), x1, S(0), x3), LEQ#2(S(S(z0)), S(0)))
   MERGE#2(Cons(S(S(z0)), x1), Cons(S(S(z1)), x3)) -> c6(COND_MERGE_YS_ZS_2(leq#2(z0, z1), Cons(S(S(z0)), x1), Cons(S(S(z1)), x3), S(S(z0)), x1, S(S(z1)), x3), LEQ#2(S(S(z0)), S(S(z1))))
   MERGE#2(Cons(S(x0), x1), Cons(S(x2), x3)) -> c6(LEQ#2(S(x0), S(x2)))
   DIVIDE_YS#1(Cons(x0, Cons(x1, x2)), S(y11)) -> c(TAKE#2(S(y11), Cons(x0, Cons(x1, x2))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, x3))), S(y11)) -> c(TAKE#2(S(y11), Cons(x0, Cons(x1, Cons(x2, x3)))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Nil)), S(y10)) -> c(TAKE#2(S(y10), Cons(x0, Cons(x1, Nil))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Nil))), S(y7)) -> c(TAKE#2(S(y7), Cons(x0, Cons(x1, Cons(x2, Nil)))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4)))), S(y8)) -> c(TAKE#2(S(y8), Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4))))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, x2)), S(y11)) -> c1(DROP#2(S(y11), Cons(x0, Cons(x1, x2))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, x3))), S(y11)) -> c1(DROP#2(S(y11), Cons(x0, Cons(x1, Cons(x2, x3)))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Nil)), S(y10)) -> c1(DROP#2(S(y10), Cons(x0, Cons(x1, Nil))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Nil))), S(y7)) -> c1(DROP#2(S(y7), Cons(x0, Cons(x1, Cons(x2, Nil)))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4)))), S(y8)) -> c1(DROP#2(S(y8), Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4))))))
   COND_MERGE_YS_ZS_2(False, Cons(S(x0), x1), Cons(0, x2), S(x0), x1, 0, x2) -> c3(MERGE#2(Cons(S(x0), x1), x2))
   COND_MERGE_YS_ZS_2(False, Cons(S(S(x0)), x1), Cons(S(0), x2), S(S(x0)), x1, S(0), x2) -> c3(MERGE#2(Cons(S(S(x0)), x1), x2))
   COND_MERGE_YS_ZS_2(False, Cons(S(S(x0)), x1), Cons(S(S(x2)), x3), S(S(x0)), x1, S(S(x2)), x3) -> c3(MERGE#2(Cons(S(S(x0)), x1), x3))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, Nil)))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Cons(z2, Nil))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, Nil))), S(halve#1(S(0)))))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, Nil))), S(halve#1(length#1(Cons(z2, Nil)))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, Nil))), S(halve#1(length#1(Cons(z2, Nil))))), HALVE#1(S(length#1(Nil))), LENGTH#1(Cons(z2, Nil)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, Cons(z3, z4))))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Cons(z2, Cons(z3, z4)))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, Cons(z3, z4)))), S(halve#1(S(S(length#1(z4)))))))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, Cons(z3, z4)))), S(halve#1(length#1(Cons(z2, Cons(z3, z4))))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, Cons(z3, z4)))), S(halve#1(length#1(Cons(z2, Cons(z3, z4)))))), HALVE#1(S(length#1(Cons(z3, z4)))), LENGTH#1(Cons(z2, Cons(z3, z4))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, z3)))) -> c9(MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3)))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3))))), HALVE#1(S(length#1(z3))), LENGTH#1(Cons(z2, z3)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Nil))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(0)), Cons(z0, Cons(z1, Nil))), Cons(drop#2(S(halve#1(0)), Cons(z0, Cons(z1, Nil))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil)))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Nil))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Nil)), S(0)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil)))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> c9(CONST_F#2(Cons(z0, Cons(z1, z2)), Cons(dc#1(map, divisible, mergesort_zs_3, divide, const_f, take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2)))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(drop#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(halve#1(length#1(z2)), Cons(z1, z2)), Nil))), DIVIDE_YS#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2)))), HALVE#1(length#1(z2)), LENGTH#1(z2))
   CONST_F#2(Cons(x0, Cons(x1, x2)), Cons(z1, Cons(z2, z3))) -> c19(MERGE#2(z1, z2))
   CONST_F#2(Cons(x0, Cons(x1, Cons(x2, x3))), Cons(z1, Cons(z2, z3))) -> c19(MERGE#2(z1, z2))
   CONST_F#2(Cons(x0, Cons(x1, Nil)), Cons(z1, Cons(z2, z3))) -> c19(MERGE#2(z1, z2))
   CONST_F#2(Cons(x0, Cons(x1, Cons(x2, Nil))), Cons(z1, Cons(z2, z3))) -> c19(MERGE#2(z1, z2))
   CONST_F#2(Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4)))), Cons(z1, Cons(z2, z3))) -> c19(MERGE#2(z1, z2))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> c9(CONST_F#2(Cons(z0, Cons(z1, z2)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(halve#1(length#1(z2)), Cons(z1, z2)), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(halve#1(length#1(z2)), Cons(z1, z2)), Nil))), DIVIDE_YS#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2)))), HALVE#1(length#1(z2)), LENGTH#1(z2))
   COND_MERGE_YS_ZS_2(True, Cons(0, Cons(0, z5)), Cons(x1, x2), 0, Cons(0, z5), x1, x2) -> c2(MERGE#2(Cons(0, z5), Cons(x1, x2)))
   COND_MERGE_YS_ZS_2(True, Cons(S(0), Cons(0, z5)), Cons(S(x1), x2), S(0), Cons(0, z5), S(x1), x2) -> c2(MERGE#2(Cons(0, z5), Cons(S(x1), x2)))
   COND_MERGE_YS_ZS_2(True, Cons(S(S(x0)), Cons(0, z5)), Cons(S(S(x2)), x3), S(S(x0)), Cons(0, z5), S(S(x2)), x3) -> c2(MERGE#2(Cons(0, z5), Cons(S(S(x2)), x3)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, z3)))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Cons(z2, z3))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(Cons(z2, z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Cons(drop#2(S(halve#1(S(length#1(z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3)))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(S(length#1(z3))))), HALVE#1(S(length#1(z3))), LENGTH#1(Cons(z2, z3)))
   COND_MERGE_YS_ZS_2(True, Cons(0, Cons(S(z4), z5)), Cons(0, x2), 0, Cons(S(z4), z5), 0, x2) -> c2(MERGE#2(Cons(S(z4), z5), Cons(0, x2)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> c9(CONST_F#2(Cons(z0, Cons(z1, z2)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(Cons(z0, take#2(halve#1(length#1(z2)), Cons(z1, z2))), Cons(drop#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(halve#1(length#1(z2)), Cons(z1, z2)), Nil))), DIVIDE_YS#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2)))), HALVE#1(length#1(z2)), LENGTH#1(z2))
   COND_MERGE_YS_ZS_2(True, Cons(0, Cons(S(0), z5)), Cons(S(z2), x2), 0, Cons(S(0), z5), S(z2), x2) -> c2(MERGE#2(Cons(S(0), z5), Cons(S(z2), x2)))
   COND_MERGE_YS_ZS_2(True, Cons(S(0), Cons(S(0), z5)), Cons(S(x1), x2), S(0), Cons(S(0), z5), S(x1), x2) -> c2(MERGE#2(Cons(S(0), z5), Cons(S(x1), x2)))
   COND_MERGE_YS_ZS_2(True, Cons(S(S(x0)), Cons(S(0), z5)), Cons(S(S(x2)), x3), S(S(x0)), Cons(S(0), z5), S(S(x2)), x3) -> c2(MERGE#2(Cons(S(0), z5), Cons(S(S(x2)), x3)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, z3)))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Cons(z2, z3))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(S(length#1(z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Cons(drop#2(S(halve#1(length#1(Cons(z2, z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3)))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(S(length#1(z3))))), HALVE#1(S(length#1(z3))), LENGTH#1(Cons(z2, z3)))
   COND_MERGE_YS_ZS_2(True, Cons(0, Cons(S(S(z4)), z5)), Cons(S(0), x2), 0, Cons(S(S(z4)), z5), S(0), x2) -> c2(MERGE#2(Cons(S(S(z4)), z5), Cons(S(0), x2)))
   COND_MERGE_YS_ZS_2(True, Cons(S(0), Cons(S(S(z4)), z5)), Cons(S(0), x2), S(0), Cons(S(S(z4)), z5), S(0), x2) -> c2(MERGE#2(Cons(S(S(z4)), z5), Cons(S(0), x2)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> c9(MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(halve#1(length#1(z2)), Cons(z1, z2)), Nil))), DIVIDE_YS#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2)))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Nil))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(Nil))), Cons(z0, Cons(z1, Nil))), Cons(drop#2(S(halve#1(0)), Cons(z0, Cons(z1, Nil))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Nil)), S(halve#1(0))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Nil))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(0)), Cons(z0, Cons(z1, Nil))), Cons(drop#2(S(halve#1(length#1(Nil))), Cons(z0, Cons(z1, Nil))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Nil)), S(halve#1(0))))
   DROP#2(S(S(y0)), Cons(z1, Cons(y1, y2))) -> c12(DROP#2(S(y0), Cons(y1, y2)))
   COND_MERGE_YS_ZS_2(True, Cons(0, Cons(S(S(z5)), z6)), Cons(S(S(z2)), x2), 0, Cons(S(S(z5)), z6), S(S(z2)), x2) -> c2(MERGE#2(Cons(S(S(z5)), z6), Cons(S(S(z2)), x2)))
   COND_MERGE_YS_ZS_2(True, Cons(S(0), Cons(S(S(z5)), z6)), Cons(S(S(z2)), x2), S(0), Cons(S(S(z5)), z6), S(S(z2)), x2) -> c2(MERGE#2(Cons(S(S(z5)), z6), Cons(S(S(z2)), x2)))
   COND_MERGE_YS_ZS_2(True, Cons(S(S(x0)), Cons(S(S(z5)), z6)), Cons(S(S(x2)), x3), S(S(x0)), Cons(S(S(z5)), z6), S(S(x2)), x3) -> c2(MERGE#2(Cons(S(S(z5)), z6), Cons(S(S(x2)), x3)))
   COND_MERGE_YS_ZS_2(True, Cons(0, Cons(S(z5), z6)), Cons(S(z2), x2), 0, Cons(S(z5), z6), S(z2), x2) -> c2(MERGE#2(Cons(S(z5), z6), Cons(S(z2), x2)))
   COND_MERGE_YS_ZS_2(True, Cons(S(0), Cons(S(z5), z6)), Cons(S(x1), x2), S(0), Cons(S(z5), z6), S(x1), x2) -> c2(MERGE#2(Cons(S(z5), z6), Cons(S(x1), x2)))
   COND_MERGE_YS_ZS_2(True, Cons(S(S(x0)), Cons(S(z5), z6)), Cons(S(S(x2)), x3), S(S(x0)), Cons(S(z5), z6), S(S(x2)), x3) -> c2(MERGE#2(Cons(S(z5), z6), Cons(S(S(x2)), x3)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, z3)))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Cons(z2, z3))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(S(length#1(z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Cons(drop#2(S(halve#1(S(length#1(z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3)))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(S(length#1(z3))))), HALVE#1(S(length#1(z3))), LENGTH#1(Cons(z2, z3)))
S tuples:
   TAKE#2(S(z0), Cons(z1, z2)) -> c15(TAKE#2(z0, z2))
   HALVE#1(S(S(z0))) -> c18(HALVE#1(z0))
   LEQ#2(S(z0), S(z1)) -> c22(LEQ#2(z0, z1))
   LENGTH#1(Cons(z0, z1)) -> c24(LENGTH#1(z1))
   MAP#2(dc(z0, z1, z2, z3, z4), Cons(z5, z6)) -> c26(DC#1(z0, z1, z2, z3, z4, z5))
   MAP#2(dc(z0, z1, z2, z3, z4), Cons(z5, z6)) -> c27(MAP#2(dc(z0, z1, z2, z3, z4), z6))
   MERGE#2(Cons(0, x1), Cons(z0, x3)) -> c6(COND_MERGE_YS_ZS_2(True, Cons(0, x1), Cons(z0, x3), 0, x1, z0, x3))
   MERGE#2(Cons(S(z0), x1), Cons(0, x3)) -> c6(COND_MERGE_YS_ZS_2(False, Cons(S(z0), x1), Cons(0, x3), S(z0), x1, 0, x3))
   MERGE#2(Cons(S(0), x1), Cons(S(z0), x3)) -> c6(COND_MERGE_YS_ZS_2(True, Cons(S(0), x1), Cons(S(z0), x3), S(0), x1, S(z0), x3), LEQ#2(S(0), S(z0)))
   MERGE#2(Cons(S(S(z0)), x1), Cons(S(0), x3)) -> c6(COND_MERGE_YS_ZS_2(False, Cons(S(S(z0)), x1), Cons(S(0), x3), S(S(z0)), x1, S(0), x3), LEQ#2(S(S(z0)), S(0)))
   MERGE#2(Cons(S(S(z0)), x1), Cons(S(S(z1)), x3)) -> c6(COND_MERGE_YS_ZS_2(leq#2(z0, z1), Cons(S(S(z0)), x1), Cons(S(S(z1)), x3), S(S(z0)), x1, S(S(z1)), x3), LEQ#2(S(S(z0)), S(S(z1))))
   MERGE#2(Cons(S(x0), x1), Cons(S(x2), x3)) -> c6(LEQ#2(S(x0), S(x2)))
   DIVIDE_YS#1(Cons(x0, Cons(x1, x2)), S(y11)) -> c(TAKE#2(S(y11), Cons(x0, Cons(x1, x2))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, x3))), S(y11)) -> c(TAKE#2(S(y11), Cons(x0, Cons(x1, Cons(x2, x3)))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Nil)), S(y10)) -> c(TAKE#2(S(y10), Cons(x0, Cons(x1, Nil))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Nil))), S(y7)) -> c(TAKE#2(S(y7), Cons(x0, Cons(x1, Cons(x2, Nil)))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4)))), S(y8)) -> c(TAKE#2(S(y8), Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4))))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, x2)), S(y11)) -> c1(DROP#2(S(y11), Cons(x0, Cons(x1, x2))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, x3))), S(y11)) -> c1(DROP#2(S(y11), Cons(x0, Cons(x1, Cons(x2, x3)))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Nil)), S(y10)) -> c1(DROP#2(S(y10), Cons(x0, Cons(x1, Nil))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Nil))), S(y7)) -> c1(DROP#2(S(y7), Cons(x0, Cons(x1, Cons(x2, Nil)))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4)))), S(y8)) -> c1(DROP#2(S(y8), Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4))))))
   COND_MERGE_YS_ZS_2(False, Cons(S(x0), x1), Cons(0, x2), S(x0), x1, 0, x2) -> c3(MERGE#2(Cons(S(x0), x1), x2))
   COND_MERGE_YS_ZS_2(False, Cons(S(S(x0)), x1), Cons(S(0), x2), S(S(x0)), x1, S(0), x2) -> c3(MERGE#2(Cons(S(S(x0)), x1), x2))
   COND_MERGE_YS_ZS_2(False, Cons(S(S(x0)), x1), Cons(S(S(x2)), x3), S(S(x0)), x1, S(S(x2)), x3) -> c3(MERGE#2(Cons(S(S(x0)), x1), x3))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, Nil)))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Cons(z2, Nil))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, Nil))), S(halve#1(S(0)))))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, Nil))), S(halve#1(length#1(Cons(z2, Nil)))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, Nil))), S(halve#1(length#1(Cons(z2, Nil))))), HALVE#1(S(length#1(Nil))), LENGTH#1(Cons(z2, Nil)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, Cons(z3, z4))))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Cons(z2, Cons(z3, z4)))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, Cons(z3, z4)))), S(halve#1(S(S(length#1(z4)))))))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, Cons(z3, z4)))), S(halve#1(length#1(Cons(z2, Cons(z3, z4))))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, Cons(z3, z4)))), S(halve#1(length#1(Cons(z2, Cons(z3, z4)))))), HALVE#1(S(length#1(Cons(z3, z4)))), LENGTH#1(Cons(z2, Cons(z3, z4))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, z3)))) -> c9(MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3)))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3))))), HALVE#1(S(length#1(z3))), LENGTH#1(Cons(z2, z3)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Nil))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(0)), Cons(z0, Cons(z1, Nil))), Cons(drop#2(S(halve#1(0)), Cons(z0, Cons(z1, Nil))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil)))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Nil))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Nil)), S(0)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil)))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> c9(CONST_F#2(Cons(z0, Cons(z1, z2)), Cons(dc#1(map, divisible, mergesort_zs_3, divide, const_f, take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2)))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(drop#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(halve#1(length#1(z2)), Cons(z1, z2)), Nil))), DIVIDE_YS#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2)))), HALVE#1(length#1(z2)), LENGTH#1(z2))
   CONST_F#2(Cons(x0, Cons(x1, x2)), Cons(z1, Cons(z2, z3))) -> c19(MERGE#2(z1, z2))
   CONST_F#2(Cons(x0, Cons(x1, Cons(x2, x3))), Cons(z1, Cons(z2, z3))) -> c19(MERGE#2(z1, z2))
   CONST_F#2(Cons(x0, Cons(x1, Nil)), Cons(z1, Cons(z2, z3))) -> c19(MERGE#2(z1, z2))
   CONST_F#2(Cons(x0, Cons(x1, Cons(x2, Nil))), Cons(z1, Cons(z2, z3))) -> c19(MERGE#2(z1, z2))
   CONST_F#2(Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4)))), Cons(z1, Cons(z2, z3))) -> c19(MERGE#2(z1, z2))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> c9(CONST_F#2(Cons(z0, Cons(z1, z2)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(halve#1(length#1(z2)), Cons(z1, z2)), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(halve#1(length#1(z2)), Cons(z1, z2)), Nil))), DIVIDE_YS#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2)))), HALVE#1(length#1(z2)), LENGTH#1(z2))
   COND_MERGE_YS_ZS_2(True, Cons(0, Cons(0, z5)), Cons(x1, x2), 0, Cons(0, z5), x1, x2) -> c2(MERGE#2(Cons(0, z5), Cons(x1, x2)))
   COND_MERGE_YS_ZS_2(True, Cons(S(0), Cons(0, z5)), Cons(S(x1), x2), S(0), Cons(0, z5), S(x1), x2) -> c2(MERGE#2(Cons(0, z5), Cons(S(x1), x2)))
   COND_MERGE_YS_ZS_2(True, Cons(S(S(x0)), Cons(0, z5)), Cons(S(S(x2)), x3), S(S(x0)), Cons(0, z5), S(S(x2)), x3) -> c2(MERGE#2(Cons(0, z5), Cons(S(S(x2)), x3)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, z3)))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Cons(z2, z3))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(Cons(z2, z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Cons(drop#2(S(halve#1(S(length#1(z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3)))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(S(length#1(z3))))), HALVE#1(S(length#1(z3))), LENGTH#1(Cons(z2, z3)))
   COND_MERGE_YS_ZS_2(True, Cons(0, Cons(S(z4), z5)), Cons(0, x2), 0, Cons(S(z4), z5), 0, x2) -> c2(MERGE#2(Cons(S(z4), z5), Cons(0, x2)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> c9(CONST_F#2(Cons(z0, Cons(z1, z2)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(Cons(z0, take#2(halve#1(length#1(z2)), Cons(z1, z2))), Cons(drop#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(halve#1(length#1(z2)), Cons(z1, z2)), Nil))), DIVIDE_YS#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2)))), HALVE#1(length#1(z2)), LENGTH#1(z2))
   COND_MERGE_YS_ZS_2(True, Cons(0, Cons(S(0), z5)), Cons(S(z2), x2), 0, Cons(S(0), z5), S(z2), x2) -> c2(MERGE#2(Cons(S(0), z5), Cons(S(z2), x2)))
   COND_MERGE_YS_ZS_2(True, Cons(S(0), Cons(S(0), z5)), Cons(S(x1), x2), S(0), Cons(S(0), z5), S(x1), x2) -> c2(MERGE#2(Cons(S(0), z5), Cons(S(x1), x2)))
   COND_MERGE_YS_ZS_2(True, Cons(S(S(x0)), Cons(S(0), z5)), Cons(S(S(x2)), x3), S(S(x0)), Cons(S(0), z5), S(S(x2)), x3) -> c2(MERGE#2(Cons(S(0), z5), Cons(S(S(x2)), x3)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, z3)))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Cons(z2, z3))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(S(length#1(z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Cons(drop#2(S(halve#1(length#1(Cons(z2, z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3)))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(S(length#1(z3))))), HALVE#1(S(length#1(z3))), LENGTH#1(Cons(z2, z3)))
   COND_MERGE_YS_ZS_2(True, Cons(0, Cons(S(S(z4)), z5)), Cons(S(0), x2), 0, Cons(S(S(z4)), z5), S(0), x2) -> c2(MERGE#2(Cons(S(S(z4)), z5), Cons(S(0), x2)))
   COND_MERGE_YS_ZS_2(True, Cons(S(0), Cons(S(S(z4)), z5)), Cons(S(0), x2), S(0), Cons(S(S(z4)), z5), S(0), x2) -> c2(MERGE#2(Cons(S(S(z4)), z5), Cons(S(0), x2)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> c9(MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(halve#1(length#1(z2)), Cons(z1, z2)), Nil))), DIVIDE_YS#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2)))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Nil))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(Nil))), Cons(z0, Cons(z1, Nil))), Cons(drop#2(S(halve#1(0)), Cons(z0, Cons(z1, Nil))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Nil)), S(halve#1(0))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Nil))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(0)), Cons(z0, Cons(z1, Nil))), Cons(drop#2(S(halve#1(length#1(Nil))), Cons(z0, Cons(z1, Nil))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Nil)), S(halve#1(0))))
   DROP#2(S(S(y0)), Cons(z1, Cons(y1, y2))) -> c12(DROP#2(S(y0), Cons(y1, y2)))
   COND_MERGE_YS_ZS_2(True, Cons(0, Cons(S(S(z5)), z6)), Cons(S(S(z2)), x2), 0, Cons(S(S(z5)), z6), S(S(z2)), x2) -> c2(MERGE#2(Cons(S(S(z5)), z6), Cons(S(S(z2)), x2)))
   COND_MERGE_YS_ZS_2(True, Cons(S(0), Cons(S(S(z5)), z6)), Cons(S(S(z2)), x2), S(0), Cons(S(S(z5)), z6), S(S(z2)), x2) -> c2(MERGE#2(Cons(S(S(z5)), z6), Cons(S(S(z2)), x2)))
   COND_MERGE_YS_ZS_2(True, Cons(S(S(x0)), Cons(S(S(z5)), z6)), Cons(S(S(x2)), x3), S(S(x0)), Cons(S(S(z5)), z6), S(S(x2)), x3) -> c2(MERGE#2(Cons(S(S(z5)), z6), Cons(S(S(x2)), x3)))
   COND_MERGE_YS_ZS_2(True, Cons(0, Cons(S(z5), z6)), Cons(S(z2), x2), 0, Cons(S(z5), z6), S(z2), x2) -> c2(MERGE#2(Cons(S(z5), z6), Cons(S(z2), x2)))
   COND_MERGE_YS_ZS_2(True, Cons(S(0), Cons(S(z5), z6)), Cons(S(x1), x2), S(0), Cons(S(z5), z6), S(x1), x2) -> c2(MERGE#2(Cons(S(z5), z6), Cons(S(x1), x2)))
   COND_MERGE_YS_ZS_2(True, Cons(S(S(x0)), Cons(S(z5), z6)), Cons(S(S(x2)), x3), S(S(x0)), Cons(S(z5), z6), S(S(x2)), x3) -> c2(MERGE#2(Cons(S(z5), z6), Cons(S(S(x2)), x3)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, z3)))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Cons(z2, z3))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(S(length#1(z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Cons(drop#2(S(halve#1(S(length#1(z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3)))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(S(length#1(z3))))), HALVE#1(S(length#1(z3))), LENGTH#1(Cons(z2, z3)))
K tuples:none
Defined Rule Symbols:   leq#2_2, map#2_2, divide_ys#1_2, halve#1_1, length#1_1, take#2_2, drop#2_2, dc#1_6, const_f#2_2, merge#2_2, cond_merge_ys_zs_2_7

Defined Pair Symbols:   TAKE#2_2, HALVE#1_1, LEQ#2_2, LENGTH#1_1, MAP#2_2, MERGE#2_2, DIVIDE_YS#1_2, COND_MERGE_YS_ZS_2_7, DC#1_6, CONST_F#2_2, DROP#2_2

Compound Symbols:   c15_1, c18_1, c22_1, c24_1, c26_1, c27_1, c6_1, c6_2, c_1, c1_1, c3_1, c9_5, c9_4, c9_3, c19_1, c2_1, c9_2, c12_1


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

(179) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID))
Use forward instantiation to replace TAKE#2(S(z0), Cons(z1, z2)) -> c15(TAKE#2(z0, z2)) by 
   TAKE#2(S(S(y0)), Cons(z1, Cons(y1, y2))) -> c15(TAKE#2(S(y0), Cons(y1, y2)))

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

(180)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   leq#2(0, z0) -> True
   leq#2(S(z0), 0) -> False
   leq#2(S(z0), S(z1)) -> leq#2(z0, z1)
   map#2(dc(z0, z1, z2, z3, z4), Nil) -> Nil
   map#2(dc(z0, z1, z2, z3, z4), Cons(z5, z6)) -> Cons(dc#1(z0, z1, z2, z3, z4, z5), map#2(dc(z0, z1, z2, z3, z4), z6))
   divide_ys#1(z0, z1) -> Cons(take#2(z1, z0), Cons(drop#2(z1, z0), Nil))
   halve#1(0) -> 0
   halve#1(S(0)) -> S(0)
   halve#1(S(S(z0))) -> S(halve#1(z0))
   length#1(Nil) -> 0
   length#1(Cons(z0, z1)) -> S(length#1(z1))
   take#2(0, z0) -> Nil
   take#2(S(0), Nil) -> Cons(bot[0], Nil)
   take#2(S(z0), Cons(z1, z2)) -> Cons(z1, take#2(z0, z2))
   drop#2(0, z0) -> z0
   drop#2(S(0), Nil) -> bot[1]
   drop#2(S(z0), Cons(z1, z2)) -> drop#2(z0, z2)
   dc#1(map, divisible, mergesort_zs_3, divide, const_f, Nil) -> Nil
   dc#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Nil)) -> Cons(z0, Nil)
   dc#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> const_f#2(Cons(z0, Cons(z1, z2)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2))))))
   const_f#2(z0, Cons(z1, Cons(z2, z3))) -> merge#2(z1, z2)
   merge#2(Nil, z0) -> z0
   merge#2(Cons(z0, z1), Nil) -> Cons(z0, z1)
   merge#2(Cons(z0, z1), Cons(z2, z3)) -> cond_merge_ys_zs_2(leq#2(z0, z2), Cons(z0, z1), Cons(z2, z3), z0, z1, z2, z3)
   cond_merge_ys_zs_2(True, Cons(z0, z1), Cons(z2, z3), z4, z5, z6, z7) -> Cons(z4, merge#2(z5, Cons(z2, z3)))
   cond_merge_ys_zs_2(False, Cons(z0, z1), Cons(z2, z3), z4, z5, z6, z7) -> Cons(z6, merge#2(Cons(z0, z1), z7))
Tuples:
   HALVE#1(S(S(z0))) -> c18(HALVE#1(z0))
   LEQ#2(S(z0), S(z1)) -> c22(LEQ#2(z0, z1))
   LENGTH#1(Cons(z0, z1)) -> c24(LENGTH#1(z1))
   MAP#2(dc(z0, z1, z2, z3, z4), Cons(z5, z6)) -> c26(DC#1(z0, z1, z2, z3, z4, z5))
   MAP#2(dc(z0, z1, z2, z3, z4), Cons(z5, z6)) -> c27(MAP#2(dc(z0, z1, z2, z3, z4), z6))
   MERGE#2(Cons(0, x1), Cons(z0, x3)) -> c6(COND_MERGE_YS_ZS_2(True, Cons(0, x1), Cons(z0, x3), 0, x1, z0, x3))
   MERGE#2(Cons(S(z0), x1), Cons(0, x3)) -> c6(COND_MERGE_YS_ZS_2(False, Cons(S(z0), x1), Cons(0, x3), S(z0), x1, 0, x3))
   MERGE#2(Cons(S(0), x1), Cons(S(z0), x3)) -> c6(COND_MERGE_YS_ZS_2(True, Cons(S(0), x1), Cons(S(z0), x3), S(0), x1, S(z0), x3), LEQ#2(S(0), S(z0)))
   MERGE#2(Cons(S(S(z0)), x1), Cons(S(0), x3)) -> c6(COND_MERGE_YS_ZS_2(False, Cons(S(S(z0)), x1), Cons(S(0), x3), S(S(z0)), x1, S(0), x3), LEQ#2(S(S(z0)), S(0)))
   MERGE#2(Cons(S(S(z0)), x1), Cons(S(S(z1)), x3)) -> c6(COND_MERGE_YS_ZS_2(leq#2(z0, z1), Cons(S(S(z0)), x1), Cons(S(S(z1)), x3), S(S(z0)), x1, S(S(z1)), x3), LEQ#2(S(S(z0)), S(S(z1))))
   MERGE#2(Cons(S(x0), x1), Cons(S(x2), x3)) -> c6(LEQ#2(S(x0), S(x2)))
   DIVIDE_YS#1(Cons(x0, Cons(x1, x2)), S(y11)) -> c(TAKE#2(S(y11), Cons(x0, Cons(x1, x2))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, x3))), S(y11)) -> c(TAKE#2(S(y11), Cons(x0, Cons(x1, Cons(x2, x3)))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Nil)), S(y10)) -> c(TAKE#2(S(y10), Cons(x0, Cons(x1, Nil))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Nil))), S(y7)) -> c(TAKE#2(S(y7), Cons(x0, Cons(x1, Cons(x2, Nil)))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4)))), S(y8)) -> c(TAKE#2(S(y8), Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4))))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, x2)), S(y11)) -> c1(DROP#2(S(y11), Cons(x0, Cons(x1, x2))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, x3))), S(y11)) -> c1(DROP#2(S(y11), Cons(x0, Cons(x1, Cons(x2, x3)))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Nil)), S(y10)) -> c1(DROP#2(S(y10), Cons(x0, Cons(x1, Nil))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Nil))), S(y7)) -> c1(DROP#2(S(y7), Cons(x0, Cons(x1, Cons(x2, Nil)))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4)))), S(y8)) -> c1(DROP#2(S(y8), Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4))))))
   COND_MERGE_YS_ZS_2(False, Cons(S(x0), x1), Cons(0, x2), S(x0), x1, 0, x2) -> c3(MERGE#2(Cons(S(x0), x1), x2))
   COND_MERGE_YS_ZS_2(False, Cons(S(S(x0)), x1), Cons(S(0), x2), S(S(x0)), x1, S(0), x2) -> c3(MERGE#2(Cons(S(S(x0)), x1), x2))
   COND_MERGE_YS_ZS_2(False, Cons(S(S(x0)), x1), Cons(S(S(x2)), x3), S(S(x0)), x1, S(S(x2)), x3) -> c3(MERGE#2(Cons(S(S(x0)), x1), x3))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, Nil)))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Cons(z2, Nil))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, Nil))), S(halve#1(S(0)))))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, Nil))), S(halve#1(length#1(Cons(z2, Nil)))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, Nil))), S(halve#1(length#1(Cons(z2, Nil))))), HALVE#1(S(length#1(Nil))), LENGTH#1(Cons(z2, Nil)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, Cons(z3, z4))))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Cons(z2, Cons(z3, z4)))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, Cons(z3, z4)))), S(halve#1(S(S(length#1(z4)))))))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, Cons(z3, z4)))), S(halve#1(length#1(Cons(z2, Cons(z3, z4))))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, Cons(z3, z4)))), S(halve#1(length#1(Cons(z2, Cons(z3, z4)))))), HALVE#1(S(length#1(Cons(z3, z4)))), LENGTH#1(Cons(z2, Cons(z3, z4))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, z3)))) -> c9(MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3)))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3))))), HALVE#1(S(length#1(z3))), LENGTH#1(Cons(z2, z3)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Nil))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(0)), Cons(z0, Cons(z1, Nil))), Cons(drop#2(S(halve#1(0)), Cons(z0, Cons(z1, Nil))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil)))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Nil))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Nil)), S(0)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil)))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> c9(CONST_F#2(Cons(z0, Cons(z1, z2)), Cons(dc#1(map, divisible, mergesort_zs_3, divide, const_f, take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2)))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(drop#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(halve#1(length#1(z2)), Cons(z1, z2)), Nil))), DIVIDE_YS#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2)))), HALVE#1(length#1(z2)), LENGTH#1(z2))
   CONST_F#2(Cons(x0, Cons(x1, x2)), Cons(z1, Cons(z2, z3))) -> c19(MERGE#2(z1, z2))
   CONST_F#2(Cons(x0, Cons(x1, Cons(x2, x3))), Cons(z1, Cons(z2, z3))) -> c19(MERGE#2(z1, z2))
   CONST_F#2(Cons(x0, Cons(x1, Nil)), Cons(z1, Cons(z2, z3))) -> c19(MERGE#2(z1, z2))
   CONST_F#2(Cons(x0, Cons(x1, Cons(x2, Nil))), Cons(z1, Cons(z2, z3))) -> c19(MERGE#2(z1, z2))
   CONST_F#2(Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4)))), Cons(z1, Cons(z2, z3))) -> c19(MERGE#2(z1, z2))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> c9(CONST_F#2(Cons(z0, Cons(z1, z2)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(halve#1(length#1(z2)), Cons(z1, z2)), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(halve#1(length#1(z2)), Cons(z1, z2)), Nil))), DIVIDE_YS#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2)))), HALVE#1(length#1(z2)), LENGTH#1(z2))
   COND_MERGE_YS_ZS_2(True, Cons(0, Cons(0, z5)), Cons(x1, x2), 0, Cons(0, z5), x1, x2) -> c2(MERGE#2(Cons(0, z5), Cons(x1, x2)))
   COND_MERGE_YS_ZS_2(True, Cons(S(0), Cons(0, z5)), Cons(S(x1), x2), S(0), Cons(0, z5), S(x1), x2) -> c2(MERGE#2(Cons(0, z5), Cons(S(x1), x2)))
   COND_MERGE_YS_ZS_2(True, Cons(S(S(x0)), Cons(0, z5)), Cons(S(S(x2)), x3), S(S(x0)), Cons(0, z5), S(S(x2)), x3) -> c2(MERGE#2(Cons(0, z5), Cons(S(S(x2)), x3)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, z3)))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Cons(z2, z3))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(Cons(z2, z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Cons(drop#2(S(halve#1(S(length#1(z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3)))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(S(length#1(z3))))), HALVE#1(S(length#1(z3))), LENGTH#1(Cons(z2, z3)))
   COND_MERGE_YS_ZS_2(True, Cons(0, Cons(S(z4), z5)), Cons(0, x2), 0, Cons(S(z4), z5), 0, x2) -> c2(MERGE#2(Cons(S(z4), z5), Cons(0, x2)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> c9(CONST_F#2(Cons(z0, Cons(z1, z2)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(Cons(z0, take#2(halve#1(length#1(z2)), Cons(z1, z2))), Cons(drop#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(halve#1(length#1(z2)), Cons(z1, z2)), Nil))), DIVIDE_YS#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2)))), HALVE#1(length#1(z2)), LENGTH#1(z2))
   COND_MERGE_YS_ZS_2(True, Cons(0, Cons(S(0), z5)), Cons(S(z2), x2), 0, Cons(S(0), z5), S(z2), x2) -> c2(MERGE#2(Cons(S(0), z5), Cons(S(z2), x2)))
   COND_MERGE_YS_ZS_2(True, Cons(S(0), Cons(S(0), z5)), Cons(S(x1), x2), S(0), Cons(S(0), z5), S(x1), x2) -> c2(MERGE#2(Cons(S(0), z5), Cons(S(x1), x2)))
   COND_MERGE_YS_ZS_2(True, Cons(S(S(x0)), Cons(S(0), z5)), Cons(S(S(x2)), x3), S(S(x0)), Cons(S(0), z5), S(S(x2)), x3) -> c2(MERGE#2(Cons(S(0), z5), Cons(S(S(x2)), x3)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, z3)))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Cons(z2, z3))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(S(length#1(z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Cons(drop#2(S(halve#1(length#1(Cons(z2, z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3)))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(S(length#1(z3))))), HALVE#1(S(length#1(z3))), LENGTH#1(Cons(z2, z3)))
   COND_MERGE_YS_ZS_2(True, Cons(0, Cons(S(S(z4)), z5)), Cons(S(0), x2), 0, Cons(S(S(z4)), z5), S(0), x2) -> c2(MERGE#2(Cons(S(S(z4)), z5), Cons(S(0), x2)))
   COND_MERGE_YS_ZS_2(True, Cons(S(0), Cons(S(S(z4)), z5)), Cons(S(0), x2), S(0), Cons(S(S(z4)), z5), S(0), x2) -> c2(MERGE#2(Cons(S(S(z4)), z5), Cons(S(0), x2)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> c9(MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(halve#1(length#1(z2)), Cons(z1, z2)), Nil))), DIVIDE_YS#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2)))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Nil))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(Nil))), Cons(z0, Cons(z1, Nil))), Cons(drop#2(S(halve#1(0)), Cons(z0, Cons(z1, Nil))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Nil)), S(halve#1(0))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Nil))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(0)), Cons(z0, Cons(z1, Nil))), Cons(drop#2(S(halve#1(length#1(Nil))), Cons(z0, Cons(z1, Nil))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Nil)), S(halve#1(0))))
   DROP#2(S(S(y0)), Cons(z1, Cons(y1, y2))) -> c12(DROP#2(S(y0), Cons(y1, y2)))
   COND_MERGE_YS_ZS_2(True, Cons(0, Cons(S(S(z5)), z6)), Cons(S(S(z2)), x2), 0, Cons(S(S(z5)), z6), S(S(z2)), x2) -> c2(MERGE#2(Cons(S(S(z5)), z6), Cons(S(S(z2)), x2)))
   COND_MERGE_YS_ZS_2(True, Cons(S(0), Cons(S(S(z5)), z6)), Cons(S(S(z2)), x2), S(0), Cons(S(S(z5)), z6), S(S(z2)), x2) -> c2(MERGE#2(Cons(S(S(z5)), z6), Cons(S(S(z2)), x2)))
   COND_MERGE_YS_ZS_2(True, Cons(S(S(x0)), Cons(S(S(z5)), z6)), Cons(S(S(x2)), x3), S(S(x0)), Cons(S(S(z5)), z6), S(S(x2)), x3) -> c2(MERGE#2(Cons(S(S(z5)), z6), Cons(S(S(x2)), x3)))
   COND_MERGE_YS_ZS_2(True, Cons(0, Cons(S(z5), z6)), Cons(S(z2), x2), 0, Cons(S(z5), z6), S(z2), x2) -> c2(MERGE#2(Cons(S(z5), z6), Cons(S(z2), x2)))
   COND_MERGE_YS_ZS_2(True, Cons(S(0), Cons(S(z5), z6)), Cons(S(x1), x2), S(0), Cons(S(z5), z6), S(x1), x2) -> c2(MERGE#2(Cons(S(z5), z6), Cons(S(x1), x2)))
   COND_MERGE_YS_ZS_2(True, Cons(S(S(x0)), Cons(S(z5), z6)), Cons(S(S(x2)), x3), S(S(x0)), Cons(S(z5), z6), S(S(x2)), x3) -> c2(MERGE#2(Cons(S(z5), z6), Cons(S(S(x2)), x3)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, z3)))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Cons(z2, z3))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(S(length#1(z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Cons(drop#2(S(halve#1(S(length#1(z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3)))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(S(length#1(z3))))), HALVE#1(S(length#1(z3))), LENGTH#1(Cons(z2, z3)))
   TAKE#2(S(S(y0)), Cons(z1, Cons(y1, y2))) -> c15(TAKE#2(S(y0), Cons(y1, y2)))
S tuples:
   HALVE#1(S(S(z0))) -> c18(HALVE#1(z0))
   LEQ#2(S(z0), S(z1)) -> c22(LEQ#2(z0, z1))
   LENGTH#1(Cons(z0, z1)) -> c24(LENGTH#1(z1))
   MAP#2(dc(z0, z1, z2, z3, z4), Cons(z5, z6)) -> c26(DC#1(z0, z1, z2, z3, z4, z5))
   MAP#2(dc(z0, z1, z2, z3, z4), Cons(z5, z6)) -> c27(MAP#2(dc(z0, z1, z2, z3, z4), z6))
   MERGE#2(Cons(0, x1), Cons(z0, x3)) -> c6(COND_MERGE_YS_ZS_2(True, Cons(0, x1), Cons(z0, x3), 0, x1, z0, x3))
   MERGE#2(Cons(S(z0), x1), Cons(0, x3)) -> c6(COND_MERGE_YS_ZS_2(False, Cons(S(z0), x1), Cons(0, x3), S(z0), x1, 0, x3))
   MERGE#2(Cons(S(0), x1), Cons(S(z0), x3)) -> c6(COND_MERGE_YS_ZS_2(True, Cons(S(0), x1), Cons(S(z0), x3), S(0), x1, S(z0), x3), LEQ#2(S(0), S(z0)))
   MERGE#2(Cons(S(S(z0)), x1), Cons(S(0), x3)) -> c6(COND_MERGE_YS_ZS_2(False, Cons(S(S(z0)), x1), Cons(S(0), x3), S(S(z0)), x1, S(0), x3), LEQ#2(S(S(z0)), S(0)))
   MERGE#2(Cons(S(S(z0)), x1), Cons(S(S(z1)), x3)) -> c6(COND_MERGE_YS_ZS_2(leq#2(z0, z1), Cons(S(S(z0)), x1), Cons(S(S(z1)), x3), S(S(z0)), x1, S(S(z1)), x3), LEQ#2(S(S(z0)), S(S(z1))))
   MERGE#2(Cons(S(x0), x1), Cons(S(x2), x3)) -> c6(LEQ#2(S(x0), S(x2)))
   DIVIDE_YS#1(Cons(x0, Cons(x1, x2)), S(y11)) -> c(TAKE#2(S(y11), Cons(x0, Cons(x1, x2))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, x3))), S(y11)) -> c(TAKE#2(S(y11), Cons(x0, Cons(x1, Cons(x2, x3)))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Nil)), S(y10)) -> c(TAKE#2(S(y10), Cons(x0, Cons(x1, Nil))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Nil))), S(y7)) -> c(TAKE#2(S(y7), Cons(x0, Cons(x1, Cons(x2, Nil)))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4)))), S(y8)) -> c(TAKE#2(S(y8), Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4))))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, x2)), S(y11)) -> c1(DROP#2(S(y11), Cons(x0, Cons(x1, x2))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, x3))), S(y11)) -> c1(DROP#2(S(y11), Cons(x0, Cons(x1, Cons(x2, x3)))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Nil)), S(y10)) -> c1(DROP#2(S(y10), Cons(x0, Cons(x1, Nil))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Nil))), S(y7)) -> c1(DROP#2(S(y7), Cons(x0, Cons(x1, Cons(x2, Nil)))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4)))), S(y8)) -> c1(DROP#2(S(y8), Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4))))))
   COND_MERGE_YS_ZS_2(False, Cons(S(x0), x1), Cons(0, x2), S(x0), x1, 0, x2) -> c3(MERGE#2(Cons(S(x0), x1), x2))
   COND_MERGE_YS_ZS_2(False, Cons(S(S(x0)), x1), Cons(S(0), x2), S(S(x0)), x1, S(0), x2) -> c3(MERGE#2(Cons(S(S(x0)), x1), x2))
   COND_MERGE_YS_ZS_2(False, Cons(S(S(x0)), x1), Cons(S(S(x2)), x3), S(S(x0)), x1, S(S(x2)), x3) -> c3(MERGE#2(Cons(S(S(x0)), x1), x3))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, Nil)))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Cons(z2, Nil))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, Nil))), S(halve#1(S(0)))))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, Nil))), S(halve#1(length#1(Cons(z2, Nil)))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, Nil))), S(halve#1(length#1(Cons(z2, Nil))))), HALVE#1(S(length#1(Nil))), LENGTH#1(Cons(z2, Nil)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, Cons(z3, z4))))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Cons(z2, Cons(z3, z4)))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, Cons(z3, z4)))), S(halve#1(S(S(length#1(z4)))))))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, Cons(z3, z4)))), S(halve#1(length#1(Cons(z2, Cons(z3, z4))))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, Cons(z3, z4)))), S(halve#1(length#1(Cons(z2, Cons(z3, z4)))))), HALVE#1(S(length#1(Cons(z3, z4)))), LENGTH#1(Cons(z2, Cons(z3, z4))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, z3)))) -> c9(MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3)))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3))))), HALVE#1(S(length#1(z3))), LENGTH#1(Cons(z2, z3)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Nil))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(0)), Cons(z0, Cons(z1, Nil))), Cons(drop#2(S(halve#1(0)), Cons(z0, Cons(z1, Nil))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil)))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Nil))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Nil)), S(0)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil)))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> c9(CONST_F#2(Cons(z0, Cons(z1, z2)), Cons(dc#1(map, divisible, mergesort_zs_3, divide, const_f, take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2)))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(drop#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(halve#1(length#1(z2)), Cons(z1, z2)), Nil))), DIVIDE_YS#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2)))), HALVE#1(length#1(z2)), LENGTH#1(z2))
   CONST_F#2(Cons(x0, Cons(x1, x2)), Cons(z1, Cons(z2, z3))) -> c19(MERGE#2(z1, z2))
   CONST_F#2(Cons(x0, Cons(x1, Cons(x2, x3))), Cons(z1, Cons(z2, z3))) -> c19(MERGE#2(z1, z2))
   CONST_F#2(Cons(x0, Cons(x1, Nil)), Cons(z1, Cons(z2, z3))) -> c19(MERGE#2(z1, z2))
   CONST_F#2(Cons(x0, Cons(x1, Cons(x2, Nil))), Cons(z1, Cons(z2, z3))) -> c19(MERGE#2(z1, z2))
   CONST_F#2(Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4)))), Cons(z1, Cons(z2, z3))) -> c19(MERGE#2(z1, z2))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> c9(CONST_F#2(Cons(z0, Cons(z1, z2)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(halve#1(length#1(z2)), Cons(z1, z2)), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(halve#1(length#1(z2)), Cons(z1, z2)), Nil))), DIVIDE_YS#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2)))), HALVE#1(length#1(z2)), LENGTH#1(z2))
   COND_MERGE_YS_ZS_2(True, Cons(0, Cons(0, z5)), Cons(x1, x2), 0, Cons(0, z5), x1, x2) -> c2(MERGE#2(Cons(0, z5), Cons(x1, x2)))
   COND_MERGE_YS_ZS_2(True, Cons(S(0), Cons(0, z5)), Cons(S(x1), x2), S(0), Cons(0, z5), S(x1), x2) -> c2(MERGE#2(Cons(0, z5), Cons(S(x1), x2)))
   COND_MERGE_YS_ZS_2(True, Cons(S(S(x0)), Cons(0, z5)), Cons(S(S(x2)), x3), S(S(x0)), Cons(0, z5), S(S(x2)), x3) -> c2(MERGE#2(Cons(0, z5), Cons(S(S(x2)), x3)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, z3)))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Cons(z2, z3))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(Cons(z2, z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Cons(drop#2(S(halve#1(S(length#1(z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3)))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(S(length#1(z3))))), HALVE#1(S(length#1(z3))), LENGTH#1(Cons(z2, z3)))
   COND_MERGE_YS_ZS_2(True, Cons(0, Cons(S(z4), z5)), Cons(0, x2), 0, Cons(S(z4), z5), 0, x2) -> c2(MERGE#2(Cons(S(z4), z5), Cons(0, x2)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> c9(CONST_F#2(Cons(z0, Cons(z1, z2)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(Cons(z0, take#2(halve#1(length#1(z2)), Cons(z1, z2))), Cons(drop#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(halve#1(length#1(z2)), Cons(z1, z2)), Nil))), DIVIDE_YS#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2)))), HALVE#1(length#1(z2)), LENGTH#1(z2))
   COND_MERGE_YS_ZS_2(True, Cons(0, Cons(S(0), z5)), Cons(S(z2), x2), 0, Cons(S(0), z5), S(z2), x2) -> c2(MERGE#2(Cons(S(0), z5), Cons(S(z2), x2)))
   COND_MERGE_YS_ZS_2(True, Cons(S(0), Cons(S(0), z5)), Cons(S(x1), x2), S(0), Cons(S(0), z5), S(x1), x2) -> c2(MERGE#2(Cons(S(0), z5), Cons(S(x1), x2)))
   COND_MERGE_YS_ZS_2(True, Cons(S(S(x0)), Cons(S(0), z5)), Cons(S(S(x2)), x3), S(S(x0)), Cons(S(0), z5), S(S(x2)), x3) -> c2(MERGE#2(Cons(S(0), z5), Cons(S(S(x2)), x3)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, z3)))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Cons(z2, z3))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(S(length#1(z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Cons(drop#2(S(halve#1(length#1(Cons(z2, z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3)))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(S(length#1(z3))))), HALVE#1(S(length#1(z3))), LENGTH#1(Cons(z2, z3)))
   COND_MERGE_YS_ZS_2(True, Cons(0, Cons(S(S(z4)), z5)), Cons(S(0), x2), 0, Cons(S(S(z4)), z5), S(0), x2) -> c2(MERGE#2(Cons(S(S(z4)), z5), Cons(S(0), x2)))
   COND_MERGE_YS_ZS_2(True, Cons(S(0), Cons(S(S(z4)), z5)), Cons(S(0), x2), S(0), Cons(S(S(z4)), z5), S(0), x2) -> c2(MERGE#2(Cons(S(S(z4)), z5), Cons(S(0), x2)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> c9(MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(halve#1(length#1(z2)), Cons(z1, z2)), Nil))), DIVIDE_YS#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2)))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Nil))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(Nil))), Cons(z0, Cons(z1, Nil))), Cons(drop#2(S(halve#1(0)), Cons(z0, Cons(z1, Nil))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Nil)), S(halve#1(0))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Nil))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(0)), Cons(z0, Cons(z1, Nil))), Cons(drop#2(S(halve#1(length#1(Nil))), Cons(z0, Cons(z1, Nil))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Nil)), S(halve#1(0))))
   DROP#2(S(S(y0)), Cons(z1, Cons(y1, y2))) -> c12(DROP#2(S(y0), Cons(y1, y2)))
   COND_MERGE_YS_ZS_2(True, Cons(0, Cons(S(S(z5)), z6)), Cons(S(S(z2)), x2), 0, Cons(S(S(z5)), z6), S(S(z2)), x2) -> c2(MERGE#2(Cons(S(S(z5)), z6), Cons(S(S(z2)), x2)))
   COND_MERGE_YS_ZS_2(True, Cons(S(0), Cons(S(S(z5)), z6)), Cons(S(S(z2)), x2), S(0), Cons(S(S(z5)), z6), S(S(z2)), x2) -> c2(MERGE#2(Cons(S(S(z5)), z6), Cons(S(S(z2)), x2)))
   COND_MERGE_YS_ZS_2(True, Cons(S(S(x0)), Cons(S(S(z5)), z6)), Cons(S(S(x2)), x3), S(S(x0)), Cons(S(S(z5)), z6), S(S(x2)), x3) -> c2(MERGE#2(Cons(S(S(z5)), z6), Cons(S(S(x2)), x3)))
   COND_MERGE_YS_ZS_2(True, Cons(0, Cons(S(z5), z6)), Cons(S(z2), x2), 0, Cons(S(z5), z6), S(z2), x2) -> c2(MERGE#2(Cons(S(z5), z6), Cons(S(z2), x2)))
   COND_MERGE_YS_ZS_2(True, Cons(S(0), Cons(S(z5), z6)), Cons(S(x1), x2), S(0), Cons(S(z5), z6), S(x1), x2) -> c2(MERGE#2(Cons(S(z5), z6), Cons(S(x1), x2)))
   COND_MERGE_YS_ZS_2(True, Cons(S(S(x0)), Cons(S(z5), z6)), Cons(S(S(x2)), x3), S(S(x0)), Cons(S(z5), z6), S(S(x2)), x3) -> c2(MERGE#2(Cons(S(z5), z6), Cons(S(S(x2)), x3)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, z3)))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Cons(z2, z3))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(S(length#1(z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Cons(drop#2(S(halve#1(S(length#1(z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3)))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(S(length#1(z3))))), HALVE#1(S(length#1(z3))), LENGTH#1(Cons(z2, z3)))
   TAKE#2(S(S(y0)), Cons(z1, Cons(y1, y2))) -> c15(TAKE#2(S(y0), Cons(y1, y2)))
K tuples:none
Defined Rule Symbols:   leq#2_2, map#2_2, divide_ys#1_2, halve#1_1, length#1_1, take#2_2, drop#2_2, dc#1_6, const_f#2_2, merge#2_2, cond_merge_ys_zs_2_7

Defined Pair Symbols:   HALVE#1_1, LEQ#2_2, LENGTH#1_1, MAP#2_2, MERGE#2_2, DIVIDE_YS#1_2, COND_MERGE_YS_ZS_2_7, DC#1_6, CONST_F#2_2, DROP#2_2, TAKE#2_2

Compound Symbols:   c18_1, c22_1, c24_1, c26_1, c27_1, c6_1, c6_2, c_1, c1_1, c3_1, c9_5, c9_4, c9_3, c19_1, c2_1, c9_2, c12_1, c15_1


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

(181) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID))
Use forward instantiation to replace HALVE#1(S(S(z0))) -> c18(HALVE#1(z0)) by 
   HALVE#1(S(S(S(S(y0))))) -> c18(HALVE#1(S(S(y0))))

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

(182)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   leq#2(0, z0) -> True
   leq#2(S(z0), 0) -> False
   leq#2(S(z0), S(z1)) -> leq#2(z0, z1)
   map#2(dc(z0, z1, z2, z3, z4), Nil) -> Nil
   map#2(dc(z0, z1, z2, z3, z4), Cons(z5, z6)) -> Cons(dc#1(z0, z1, z2, z3, z4, z5), map#2(dc(z0, z1, z2, z3, z4), z6))
   divide_ys#1(z0, z1) -> Cons(take#2(z1, z0), Cons(drop#2(z1, z0), Nil))
   halve#1(0) -> 0
   halve#1(S(0)) -> S(0)
   halve#1(S(S(z0))) -> S(halve#1(z0))
   length#1(Nil) -> 0
   length#1(Cons(z0, z1)) -> S(length#1(z1))
   take#2(0, z0) -> Nil
   take#2(S(0), Nil) -> Cons(bot[0], Nil)
   take#2(S(z0), Cons(z1, z2)) -> Cons(z1, take#2(z0, z2))
   drop#2(0, z0) -> z0
   drop#2(S(0), Nil) -> bot[1]
   drop#2(S(z0), Cons(z1, z2)) -> drop#2(z0, z2)
   dc#1(map, divisible, mergesort_zs_3, divide, const_f, Nil) -> Nil
   dc#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Nil)) -> Cons(z0, Nil)
   dc#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> const_f#2(Cons(z0, Cons(z1, z2)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2))))))
   const_f#2(z0, Cons(z1, Cons(z2, z3))) -> merge#2(z1, z2)
   merge#2(Nil, z0) -> z0
   merge#2(Cons(z0, z1), Nil) -> Cons(z0, z1)
   merge#2(Cons(z0, z1), Cons(z2, z3)) -> cond_merge_ys_zs_2(leq#2(z0, z2), Cons(z0, z1), Cons(z2, z3), z0, z1, z2, z3)
   cond_merge_ys_zs_2(True, Cons(z0, z1), Cons(z2, z3), z4, z5, z6, z7) -> Cons(z4, merge#2(z5, Cons(z2, z3)))
   cond_merge_ys_zs_2(False, Cons(z0, z1), Cons(z2, z3), z4, z5, z6, z7) -> Cons(z6, merge#2(Cons(z0, z1), z7))
Tuples:
   LEQ#2(S(z0), S(z1)) -> c22(LEQ#2(z0, z1))
   LENGTH#1(Cons(z0, z1)) -> c24(LENGTH#1(z1))
   MAP#2(dc(z0, z1, z2, z3, z4), Cons(z5, z6)) -> c26(DC#1(z0, z1, z2, z3, z4, z5))
   MAP#2(dc(z0, z1, z2, z3, z4), Cons(z5, z6)) -> c27(MAP#2(dc(z0, z1, z2, z3, z4), z6))
   MERGE#2(Cons(0, x1), Cons(z0, x3)) -> c6(COND_MERGE_YS_ZS_2(True, Cons(0, x1), Cons(z0, x3), 0, x1, z0, x3))
   MERGE#2(Cons(S(z0), x1), Cons(0, x3)) -> c6(COND_MERGE_YS_ZS_2(False, Cons(S(z0), x1), Cons(0, x3), S(z0), x1, 0, x3))
   MERGE#2(Cons(S(0), x1), Cons(S(z0), x3)) -> c6(COND_MERGE_YS_ZS_2(True, Cons(S(0), x1), Cons(S(z0), x3), S(0), x1, S(z0), x3), LEQ#2(S(0), S(z0)))
   MERGE#2(Cons(S(S(z0)), x1), Cons(S(0), x3)) -> c6(COND_MERGE_YS_ZS_2(False, Cons(S(S(z0)), x1), Cons(S(0), x3), S(S(z0)), x1, S(0), x3), LEQ#2(S(S(z0)), S(0)))
   MERGE#2(Cons(S(S(z0)), x1), Cons(S(S(z1)), x3)) -> c6(COND_MERGE_YS_ZS_2(leq#2(z0, z1), Cons(S(S(z0)), x1), Cons(S(S(z1)), x3), S(S(z0)), x1, S(S(z1)), x3), LEQ#2(S(S(z0)), S(S(z1))))
   MERGE#2(Cons(S(x0), x1), Cons(S(x2), x3)) -> c6(LEQ#2(S(x0), S(x2)))
   DIVIDE_YS#1(Cons(x0, Cons(x1, x2)), S(y11)) -> c(TAKE#2(S(y11), Cons(x0, Cons(x1, x2))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, x3))), S(y11)) -> c(TAKE#2(S(y11), Cons(x0, Cons(x1, Cons(x2, x3)))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Nil)), S(y10)) -> c(TAKE#2(S(y10), Cons(x0, Cons(x1, Nil))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Nil))), S(y7)) -> c(TAKE#2(S(y7), Cons(x0, Cons(x1, Cons(x2, Nil)))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4)))), S(y8)) -> c(TAKE#2(S(y8), Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4))))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, x2)), S(y11)) -> c1(DROP#2(S(y11), Cons(x0, Cons(x1, x2))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, x3))), S(y11)) -> c1(DROP#2(S(y11), Cons(x0, Cons(x1, Cons(x2, x3)))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Nil)), S(y10)) -> c1(DROP#2(S(y10), Cons(x0, Cons(x1, Nil))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Nil))), S(y7)) -> c1(DROP#2(S(y7), Cons(x0, Cons(x1, Cons(x2, Nil)))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4)))), S(y8)) -> c1(DROP#2(S(y8), Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4))))))
   COND_MERGE_YS_ZS_2(False, Cons(S(x0), x1), Cons(0, x2), S(x0), x1, 0, x2) -> c3(MERGE#2(Cons(S(x0), x1), x2))
   COND_MERGE_YS_ZS_2(False, Cons(S(S(x0)), x1), Cons(S(0), x2), S(S(x0)), x1, S(0), x2) -> c3(MERGE#2(Cons(S(S(x0)), x1), x2))
   COND_MERGE_YS_ZS_2(False, Cons(S(S(x0)), x1), Cons(S(S(x2)), x3), S(S(x0)), x1, S(S(x2)), x3) -> c3(MERGE#2(Cons(S(S(x0)), x1), x3))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, Nil)))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Cons(z2, Nil))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, Nil))), S(halve#1(S(0)))))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, Nil))), S(halve#1(length#1(Cons(z2, Nil)))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, Nil))), S(halve#1(length#1(Cons(z2, Nil))))), HALVE#1(S(length#1(Nil))), LENGTH#1(Cons(z2, Nil)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, Cons(z3, z4))))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Cons(z2, Cons(z3, z4)))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, Cons(z3, z4)))), S(halve#1(S(S(length#1(z4)))))))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, Cons(z3, z4)))), S(halve#1(length#1(Cons(z2, Cons(z3, z4))))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, Cons(z3, z4)))), S(halve#1(length#1(Cons(z2, Cons(z3, z4)))))), HALVE#1(S(length#1(Cons(z3, z4)))), LENGTH#1(Cons(z2, Cons(z3, z4))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, z3)))) -> c9(MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3)))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3))))), HALVE#1(S(length#1(z3))), LENGTH#1(Cons(z2, z3)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Nil))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(0)), Cons(z0, Cons(z1, Nil))), Cons(drop#2(S(halve#1(0)), Cons(z0, Cons(z1, Nil))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil)))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Nil))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Nil)), S(0)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil)))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> c9(CONST_F#2(Cons(z0, Cons(z1, z2)), Cons(dc#1(map, divisible, mergesort_zs_3, divide, const_f, take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2)))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(drop#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(halve#1(length#1(z2)), Cons(z1, z2)), Nil))), DIVIDE_YS#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2)))), HALVE#1(length#1(z2)), LENGTH#1(z2))
   CONST_F#2(Cons(x0, Cons(x1, x2)), Cons(z1, Cons(z2, z3))) -> c19(MERGE#2(z1, z2))
   CONST_F#2(Cons(x0, Cons(x1, Cons(x2, x3))), Cons(z1, Cons(z2, z3))) -> c19(MERGE#2(z1, z2))
   CONST_F#2(Cons(x0, Cons(x1, Nil)), Cons(z1, Cons(z2, z3))) -> c19(MERGE#2(z1, z2))
   CONST_F#2(Cons(x0, Cons(x1, Cons(x2, Nil))), Cons(z1, Cons(z2, z3))) -> c19(MERGE#2(z1, z2))
   CONST_F#2(Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4)))), Cons(z1, Cons(z2, z3))) -> c19(MERGE#2(z1, z2))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> c9(CONST_F#2(Cons(z0, Cons(z1, z2)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(halve#1(length#1(z2)), Cons(z1, z2)), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(halve#1(length#1(z2)), Cons(z1, z2)), Nil))), DIVIDE_YS#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2)))), HALVE#1(length#1(z2)), LENGTH#1(z2))
   COND_MERGE_YS_ZS_2(True, Cons(0, Cons(0, z5)), Cons(x1, x2), 0, Cons(0, z5), x1, x2) -> c2(MERGE#2(Cons(0, z5), Cons(x1, x2)))
   COND_MERGE_YS_ZS_2(True, Cons(S(0), Cons(0, z5)), Cons(S(x1), x2), S(0), Cons(0, z5), S(x1), x2) -> c2(MERGE#2(Cons(0, z5), Cons(S(x1), x2)))
   COND_MERGE_YS_ZS_2(True, Cons(S(S(x0)), Cons(0, z5)), Cons(S(S(x2)), x3), S(S(x0)), Cons(0, z5), S(S(x2)), x3) -> c2(MERGE#2(Cons(0, z5), Cons(S(S(x2)), x3)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, z3)))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Cons(z2, z3))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(Cons(z2, z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Cons(drop#2(S(halve#1(S(length#1(z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3)))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(S(length#1(z3))))), HALVE#1(S(length#1(z3))), LENGTH#1(Cons(z2, z3)))
   COND_MERGE_YS_ZS_2(True, Cons(0, Cons(S(z4), z5)), Cons(0, x2), 0, Cons(S(z4), z5), 0, x2) -> c2(MERGE#2(Cons(S(z4), z5), Cons(0, x2)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> c9(CONST_F#2(Cons(z0, Cons(z1, z2)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(Cons(z0, take#2(halve#1(length#1(z2)), Cons(z1, z2))), Cons(drop#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(halve#1(length#1(z2)), Cons(z1, z2)), Nil))), DIVIDE_YS#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2)))), HALVE#1(length#1(z2)), LENGTH#1(z2))
   COND_MERGE_YS_ZS_2(True, Cons(0, Cons(S(0), z5)), Cons(S(z2), x2), 0, Cons(S(0), z5), S(z2), x2) -> c2(MERGE#2(Cons(S(0), z5), Cons(S(z2), x2)))
   COND_MERGE_YS_ZS_2(True, Cons(S(0), Cons(S(0), z5)), Cons(S(x1), x2), S(0), Cons(S(0), z5), S(x1), x2) -> c2(MERGE#2(Cons(S(0), z5), Cons(S(x1), x2)))
   COND_MERGE_YS_ZS_2(True, Cons(S(S(x0)), Cons(S(0), z5)), Cons(S(S(x2)), x3), S(S(x0)), Cons(S(0), z5), S(S(x2)), x3) -> c2(MERGE#2(Cons(S(0), z5), Cons(S(S(x2)), x3)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, z3)))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Cons(z2, z3))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(S(length#1(z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Cons(drop#2(S(halve#1(length#1(Cons(z2, z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3)))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(S(length#1(z3))))), HALVE#1(S(length#1(z3))), LENGTH#1(Cons(z2, z3)))
   COND_MERGE_YS_ZS_2(True, Cons(0, Cons(S(S(z4)), z5)), Cons(S(0), x2), 0, Cons(S(S(z4)), z5), S(0), x2) -> c2(MERGE#2(Cons(S(S(z4)), z5), Cons(S(0), x2)))
   COND_MERGE_YS_ZS_2(True, Cons(S(0), Cons(S(S(z4)), z5)), Cons(S(0), x2), S(0), Cons(S(S(z4)), z5), S(0), x2) -> c2(MERGE#2(Cons(S(S(z4)), z5), Cons(S(0), x2)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> c9(MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(halve#1(length#1(z2)), Cons(z1, z2)), Nil))), DIVIDE_YS#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2)))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Nil))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(Nil))), Cons(z0, Cons(z1, Nil))), Cons(drop#2(S(halve#1(0)), Cons(z0, Cons(z1, Nil))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Nil)), S(halve#1(0))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Nil))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(0)), Cons(z0, Cons(z1, Nil))), Cons(drop#2(S(halve#1(length#1(Nil))), Cons(z0, Cons(z1, Nil))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Nil)), S(halve#1(0))))
   DROP#2(S(S(y0)), Cons(z1, Cons(y1, y2))) -> c12(DROP#2(S(y0), Cons(y1, y2)))
   COND_MERGE_YS_ZS_2(True, Cons(0, Cons(S(S(z5)), z6)), Cons(S(S(z2)), x2), 0, Cons(S(S(z5)), z6), S(S(z2)), x2) -> c2(MERGE#2(Cons(S(S(z5)), z6), Cons(S(S(z2)), x2)))
   COND_MERGE_YS_ZS_2(True, Cons(S(0), Cons(S(S(z5)), z6)), Cons(S(S(z2)), x2), S(0), Cons(S(S(z5)), z6), S(S(z2)), x2) -> c2(MERGE#2(Cons(S(S(z5)), z6), Cons(S(S(z2)), x2)))
   COND_MERGE_YS_ZS_2(True, Cons(S(S(x0)), Cons(S(S(z5)), z6)), Cons(S(S(x2)), x3), S(S(x0)), Cons(S(S(z5)), z6), S(S(x2)), x3) -> c2(MERGE#2(Cons(S(S(z5)), z6), Cons(S(S(x2)), x3)))
   COND_MERGE_YS_ZS_2(True, Cons(0, Cons(S(z5), z6)), Cons(S(z2), x2), 0, Cons(S(z5), z6), S(z2), x2) -> c2(MERGE#2(Cons(S(z5), z6), Cons(S(z2), x2)))
   COND_MERGE_YS_ZS_2(True, Cons(S(0), Cons(S(z5), z6)), Cons(S(x1), x2), S(0), Cons(S(z5), z6), S(x1), x2) -> c2(MERGE#2(Cons(S(z5), z6), Cons(S(x1), x2)))
   COND_MERGE_YS_ZS_2(True, Cons(S(S(x0)), Cons(S(z5), z6)), Cons(S(S(x2)), x3), S(S(x0)), Cons(S(z5), z6), S(S(x2)), x3) -> c2(MERGE#2(Cons(S(z5), z6), Cons(S(S(x2)), x3)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, z3)))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Cons(z2, z3))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(S(length#1(z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Cons(drop#2(S(halve#1(S(length#1(z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3)))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(S(length#1(z3))))), HALVE#1(S(length#1(z3))), LENGTH#1(Cons(z2, z3)))
   TAKE#2(S(S(y0)), Cons(z1, Cons(y1, y2))) -> c15(TAKE#2(S(y0), Cons(y1, y2)))
   HALVE#1(S(S(S(S(y0))))) -> c18(HALVE#1(S(S(y0))))
S tuples:
   LEQ#2(S(z0), S(z1)) -> c22(LEQ#2(z0, z1))
   LENGTH#1(Cons(z0, z1)) -> c24(LENGTH#1(z1))
   MAP#2(dc(z0, z1, z2, z3, z4), Cons(z5, z6)) -> c26(DC#1(z0, z1, z2, z3, z4, z5))
   MAP#2(dc(z0, z1, z2, z3, z4), Cons(z5, z6)) -> c27(MAP#2(dc(z0, z1, z2, z3, z4), z6))
   MERGE#2(Cons(0, x1), Cons(z0, x3)) -> c6(COND_MERGE_YS_ZS_2(True, Cons(0, x1), Cons(z0, x3), 0, x1, z0, x3))
   MERGE#2(Cons(S(z0), x1), Cons(0, x3)) -> c6(COND_MERGE_YS_ZS_2(False, Cons(S(z0), x1), Cons(0, x3), S(z0), x1, 0, x3))
   MERGE#2(Cons(S(0), x1), Cons(S(z0), x3)) -> c6(COND_MERGE_YS_ZS_2(True, Cons(S(0), x1), Cons(S(z0), x3), S(0), x1, S(z0), x3), LEQ#2(S(0), S(z0)))
   MERGE#2(Cons(S(S(z0)), x1), Cons(S(0), x3)) -> c6(COND_MERGE_YS_ZS_2(False, Cons(S(S(z0)), x1), Cons(S(0), x3), S(S(z0)), x1, S(0), x3), LEQ#2(S(S(z0)), S(0)))
   MERGE#2(Cons(S(S(z0)), x1), Cons(S(S(z1)), x3)) -> c6(COND_MERGE_YS_ZS_2(leq#2(z0, z1), Cons(S(S(z0)), x1), Cons(S(S(z1)), x3), S(S(z0)), x1, S(S(z1)), x3), LEQ#2(S(S(z0)), S(S(z1))))
   MERGE#2(Cons(S(x0), x1), Cons(S(x2), x3)) -> c6(LEQ#2(S(x0), S(x2)))
   DIVIDE_YS#1(Cons(x0, Cons(x1, x2)), S(y11)) -> c(TAKE#2(S(y11), Cons(x0, Cons(x1, x2))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, x3))), S(y11)) -> c(TAKE#2(S(y11), Cons(x0, Cons(x1, Cons(x2, x3)))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Nil)), S(y10)) -> c(TAKE#2(S(y10), Cons(x0, Cons(x1, Nil))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Nil))), S(y7)) -> c(TAKE#2(S(y7), Cons(x0, Cons(x1, Cons(x2, Nil)))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4)))), S(y8)) -> c(TAKE#2(S(y8), Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4))))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, x2)), S(y11)) -> c1(DROP#2(S(y11), Cons(x0, Cons(x1, x2))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, x3))), S(y11)) -> c1(DROP#2(S(y11), Cons(x0, Cons(x1, Cons(x2, x3)))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Nil)), S(y10)) -> c1(DROP#2(S(y10), Cons(x0, Cons(x1, Nil))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Nil))), S(y7)) -> c1(DROP#2(S(y7), Cons(x0, Cons(x1, Cons(x2, Nil)))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4)))), S(y8)) -> c1(DROP#2(S(y8), Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4))))))
   COND_MERGE_YS_ZS_2(False, Cons(S(x0), x1), Cons(0, x2), S(x0), x1, 0, x2) -> c3(MERGE#2(Cons(S(x0), x1), x2))
   COND_MERGE_YS_ZS_2(False, Cons(S(S(x0)), x1), Cons(S(0), x2), S(S(x0)), x1, S(0), x2) -> c3(MERGE#2(Cons(S(S(x0)), x1), x2))
   COND_MERGE_YS_ZS_2(False, Cons(S(S(x0)), x1), Cons(S(S(x2)), x3), S(S(x0)), x1, S(S(x2)), x3) -> c3(MERGE#2(Cons(S(S(x0)), x1), x3))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, Nil)))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Cons(z2, Nil))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, Nil))), S(halve#1(S(0)))))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, Nil))), S(halve#1(length#1(Cons(z2, Nil)))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, Nil))), S(halve#1(length#1(Cons(z2, Nil))))), HALVE#1(S(length#1(Nil))), LENGTH#1(Cons(z2, Nil)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, Cons(z3, z4))))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Cons(z2, Cons(z3, z4)))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, Cons(z3, z4)))), S(halve#1(S(S(length#1(z4)))))))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, Cons(z3, z4)))), S(halve#1(length#1(Cons(z2, Cons(z3, z4))))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, Cons(z3, z4)))), S(halve#1(length#1(Cons(z2, Cons(z3, z4)))))), HALVE#1(S(length#1(Cons(z3, z4)))), LENGTH#1(Cons(z2, Cons(z3, z4))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, z3)))) -> c9(MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3)))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3))))), HALVE#1(S(length#1(z3))), LENGTH#1(Cons(z2, z3)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Nil))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(0)), Cons(z0, Cons(z1, Nil))), Cons(drop#2(S(halve#1(0)), Cons(z0, Cons(z1, Nil))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil)))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Nil))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Nil)), S(0)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil)))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> c9(CONST_F#2(Cons(z0, Cons(z1, z2)), Cons(dc#1(map, divisible, mergesort_zs_3, divide, const_f, take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2)))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(drop#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(halve#1(length#1(z2)), Cons(z1, z2)), Nil))), DIVIDE_YS#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2)))), HALVE#1(length#1(z2)), LENGTH#1(z2))
   CONST_F#2(Cons(x0, Cons(x1, x2)), Cons(z1, Cons(z2, z3))) -> c19(MERGE#2(z1, z2))
   CONST_F#2(Cons(x0, Cons(x1, Cons(x2, x3))), Cons(z1, Cons(z2, z3))) -> c19(MERGE#2(z1, z2))
   CONST_F#2(Cons(x0, Cons(x1, Nil)), Cons(z1, Cons(z2, z3))) -> c19(MERGE#2(z1, z2))
   CONST_F#2(Cons(x0, Cons(x1, Cons(x2, Nil))), Cons(z1, Cons(z2, z3))) -> c19(MERGE#2(z1, z2))
   CONST_F#2(Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4)))), Cons(z1, Cons(z2, z3))) -> c19(MERGE#2(z1, z2))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> c9(CONST_F#2(Cons(z0, Cons(z1, z2)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(halve#1(length#1(z2)), Cons(z1, z2)), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(halve#1(length#1(z2)), Cons(z1, z2)), Nil))), DIVIDE_YS#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2)))), HALVE#1(length#1(z2)), LENGTH#1(z2))
   COND_MERGE_YS_ZS_2(True, Cons(0, Cons(0, z5)), Cons(x1, x2), 0, Cons(0, z5), x1, x2) -> c2(MERGE#2(Cons(0, z5), Cons(x1, x2)))
   COND_MERGE_YS_ZS_2(True, Cons(S(0), Cons(0, z5)), Cons(S(x1), x2), S(0), Cons(0, z5), S(x1), x2) -> c2(MERGE#2(Cons(0, z5), Cons(S(x1), x2)))
   COND_MERGE_YS_ZS_2(True, Cons(S(S(x0)), Cons(0, z5)), Cons(S(S(x2)), x3), S(S(x0)), Cons(0, z5), S(S(x2)), x3) -> c2(MERGE#2(Cons(0, z5), Cons(S(S(x2)), x3)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, z3)))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Cons(z2, z3))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(Cons(z2, z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Cons(drop#2(S(halve#1(S(length#1(z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3)))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(S(length#1(z3))))), HALVE#1(S(length#1(z3))), LENGTH#1(Cons(z2, z3)))
   COND_MERGE_YS_ZS_2(True, Cons(0, Cons(S(z4), z5)), Cons(0, x2), 0, Cons(S(z4), z5), 0, x2) -> c2(MERGE#2(Cons(S(z4), z5), Cons(0, x2)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> c9(CONST_F#2(Cons(z0, Cons(z1, z2)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(Cons(z0, take#2(halve#1(length#1(z2)), Cons(z1, z2))), Cons(drop#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(halve#1(length#1(z2)), Cons(z1, z2)), Nil))), DIVIDE_YS#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2)))), HALVE#1(length#1(z2)), LENGTH#1(z2))
   COND_MERGE_YS_ZS_2(True, Cons(0, Cons(S(0), z5)), Cons(S(z2), x2), 0, Cons(S(0), z5), S(z2), x2) -> c2(MERGE#2(Cons(S(0), z5), Cons(S(z2), x2)))
   COND_MERGE_YS_ZS_2(True, Cons(S(0), Cons(S(0), z5)), Cons(S(x1), x2), S(0), Cons(S(0), z5), S(x1), x2) -> c2(MERGE#2(Cons(S(0), z5), Cons(S(x1), x2)))
   COND_MERGE_YS_ZS_2(True, Cons(S(S(x0)), Cons(S(0), z5)), Cons(S(S(x2)), x3), S(S(x0)), Cons(S(0), z5), S(S(x2)), x3) -> c2(MERGE#2(Cons(S(0), z5), Cons(S(S(x2)), x3)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, z3)))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Cons(z2, z3))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(S(length#1(z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Cons(drop#2(S(halve#1(length#1(Cons(z2, z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3)))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(S(length#1(z3))))), HALVE#1(S(length#1(z3))), LENGTH#1(Cons(z2, z3)))
   COND_MERGE_YS_ZS_2(True, Cons(0, Cons(S(S(z4)), z5)), Cons(S(0), x2), 0, Cons(S(S(z4)), z5), S(0), x2) -> c2(MERGE#2(Cons(S(S(z4)), z5), Cons(S(0), x2)))
   COND_MERGE_YS_ZS_2(True, Cons(S(0), Cons(S(S(z4)), z5)), Cons(S(0), x2), S(0), Cons(S(S(z4)), z5), S(0), x2) -> c2(MERGE#2(Cons(S(S(z4)), z5), Cons(S(0), x2)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> c9(MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(halve#1(length#1(z2)), Cons(z1, z2)), Nil))), DIVIDE_YS#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2)))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Nil))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(Nil))), Cons(z0, Cons(z1, Nil))), Cons(drop#2(S(halve#1(0)), Cons(z0, Cons(z1, Nil))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Nil)), S(halve#1(0))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Nil))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(0)), Cons(z0, Cons(z1, Nil))), Cons(drop#2(S(halve#1(length#1(Nil))), Cons(z0, Cons(z1, Nil))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Nil)), S(halve#1(0))))
   DROP#2(S(S(y0)), Cons(z1, Cons(y1, y2))) -> c12(DROP#2(S(y0), Cons(y1, y2)))
   COND_MERGE_YS_ZS_2(True, Cons(0, Cons(S(S(z5)), z6)), Cons(S(S(z2)), x2), 0, Cons(S(S(z5)), z6), S(S(z2)), x2) -> c2(MERGE#2(Cons(S(S(z5)), z6), Cons(S(S(z2)), x2)))
   COND_MERGE_YS_ZS_2(True, Cons(S(0), Cons(S(S(z5)), z6)), Cons(S(S(z2)), x2), S(0), Cons(S(S(z5)), z6), S(S(z2)), x2) -> c2(MERGE#2(Cons(S(S(z5)), z6), Cons(S(S(z2)), x2)))
   COND_MERGE_YS_ZS_2(True, Cons(S(S(x0)), Cons(S(S(z5)), z6)), Cons(S(S(x2)), x3), S(S(x0)), Cons(S(S(z5)), z6), S(S(x2)), x3) -> c2(MERGE#2(Cons(S(S(z5)), z6), Cons(S(S(x2)), x3)))
   COND_MERGE_YS_ZS_2(True, Cons(0, Cons(S(z5), z6)), Cons(S(z2), x2), 0, Cons(S(z5), z6), S(z2), x2) -> c2(MERGE#2(Cons(S(z5), z6), Cons(S(z2), x2)))
   COND_MERGE_YS_ZS_2(True, Cons(S(0), Cons(S(z5), z6)), Cons(S(x1), x2), S(0), Cons(S(z5), z6), S(x1), x2) -> c2(MERGE#2(Cons(S(z5), z6), Cons(S(x1), x2)))
   COND_MERGE_YS_ZS_2(True, Cons(S(S(x0)), Cons(S(z5), z6)), Cons(S(S(x2)), x3), S(S(x0)), Cons(S(z5), z6), S(S(x2)), x3) -> c2(MERGE#2(Cons(S(z5), z6), Cons(S(S(x2)), x3)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, z3)))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Cons(z2, z3))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(S(length#1(z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Cons(drop#2(S(halve#1(S(length#1(z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3)))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(S(length#1(z3))))), HALVE#1(S(length#1(z3))), LENGTH#1(Cons(z2, z3)))
   TAKE#2(S(S(y0)), Cons(z1, Cons(y1, y2))) -> c15(TAKE#2(S(y0), Cons(y1, y2)))
   HALVE#1(S(S(S(S(y0))))) -> c18(HALVE#1(S(S(y0))))
K tuples:none
Defined Rule Symbols:   leq#2_2, map#2_2, divide_ys#1_2, halve#1_1, length#1_1, take#2_2, drop#2_2, dc#1_6, const_f#2_2, merge#2_2, cond_merge_ys_zs_2_7

Defined Pair Symbols:   LEQ#2_2, LENGTH#1_1, MAP#2_2, MERGE#2_2, DIVIDE_YS#1_2, COND_MERGE_YS_ZS_2_7, DC#1_6, CONST_F#2_2, DROP#2_2, TAKE#2_2, HALVE#1_1

Compound Symbols:   c22_1, c24_1, c26_1, c27_1, c6_1, c6_2, c_1, c1_1, c3_1, c9_5, c9_4, c9_3, c19_1, c2_1, c9_2, c12_1, c15_1, c18_1


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

(183) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID))
Use forward instantiation to replace LEQ#2(S(z0), S(z1)) -> c22(LEQ#2(z0, z1)) by 
   LEQ#2(S(S(y0)), S(S(y1))) -> c22(LEQ#2(S(y0), S(y1)))

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

(184)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   leq#2(0, z0) -> True
   leq#2(S(z0), 0) -> False
   leq#2(S(z0), S(z1)) -> leq#2(z0, z1)
   map#2(dc(z0, z1, z2, z3, z4), Nil) -> Nil
   map#2(dc(z0, z1, z2, z3, z4), Cons(z5, z6)) -> Cons(dc#1(z0, z1, z2, z3, z4, z5), map#2(dc(z0, z1, z2, z3, z4), z6))
   divide_ys#1(z0, z1) -> Cons(take#2(z1, z0), Cons(drop#2(z1, z0), Nil))
   halve#1(0) -> 0
   halve#1(S(0)) -> S(0)
   halve#1(S(S(z0))) -> S(halve#1(z0))
   length#1(Nil) -> 0
   length#1(Cons(z0, z1)) -> S(length#1(z1))
   take#2(0, z0) -> Nil
   take#2(S(0), Nil) -> Cons(bot[0], Nil)
   take#2(S(z0), Cons(z1, z2)) -> Cons(z1, take#2(z0, z2))
   drop#2(0, z0) -> z0
   drop#2(S(0), Nil) -> bot[1]
   drop#2(S(z0), Cons(z1, z2)) -> drop#2(z0, z2)
   dc#1(map, divisible, mergesort_zs_3, divide, const_f, Nil) -> Nil
   dc#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Nil)) -> Cons(z0, Nil)
   dc#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> const_f#2(Cons(z0, Cons(z1, z2)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2))))))
   const_f#2(z0, Cons(z1, Cons(z2, z3))) -> merge#2(z1, z2)
   merge#2(Nil, z0) -> z0
   merge#2(Cons(z0, z1), Nil) -> Cons(z0, z1)
   merge#2(Cons(z0, z1), Cons(z2, z3)) -> cond_merge_ys_zs_2(leq#2(z0, z2), Cons(z0, z1), Cons(z2, z3), z0, z1, z2, z3)
   cond_merge_ys_zs_2(True, Cons(z0, z1), Cons(z2, z3), z4, z5, z6, z7) -> Cons(z4, merge#2(z5, Cons(z2, z3)))
   cond_merge_ys_zs_2(False, Cons(z0, z1), Cons(z2, z3), z4, z5, z6, z7) -> Cons(z6, merge#2(Cons(z0, z1), z7))
Tuples:
   LENGTH#1(Cons(z0, z1)) -> c24(LENGTH#1(z1))
   MAP#2(dc(z0, z1, z2, z3, z4), Cons(z5, z6)) -> c26(DC#1(z0, z1, z2, z3, z4, z5))
   MAP#2(dc(z0, z1, z2, z3, z4), Cons(z5, z6)) -> c27(MAP#2(dc(z0, z1, z2, z3, z4), z6))
   MERGE#2(Cons(0, x1), Cons(z0, x3)) -> c6(COND_MERGE_YS_ZS_2(True, Cons(0, x1), Cons(z0, x3), 0, x1, z0, x3))
   MERGE#2(Cons(S(z0), x1), Cons(0, x3)) -> c6(COND_MERGE_YS_ZS_2(False, Cons(S(z0), x1), Cons(0, x3), S(z0), x1, 0, x3))
   MERGE#2(Cons(S(0), x1), Cons(S(z0), x3)) -> c6(COND_MERGE_YS_ZS_2(True, Cons(S(0), x1), Cons(S(z0), x3), S(0), x1, S(z0), x3), LEQ#2(S(0), S(z0)))
   MERGE#2(Cons(S(S(z0)), x1), Cons(S(0), x3)) -> c6(COND_MERGE_YS_ZS_2(False, Cons(S(S(z0)), x1), Cons(S(0), x3), S(S(z0)), x1, S(0), x3), LEQ#2(S(S(z0)), S(0)))
   MERGE#2(Cons(S(S(z0)), x1), Cons(S(S(z1)), x3)) -> c6(COND_MERGE_YS_ZS_2(leq#2(z0, z1), Cons(S(S(z0)), x1), Cons(S(S(z1)), x3), S(S(z0)), x1, S(S(z1)), x3), LEQ#2(S(S(z0)), S(S(z1))))
   MERGE#2(Cons(S(x0), x1), Cons(S(x2), x3)) -> c6(LEQ#2(S(x0), S(x2)))
   DIVIDE_YS#1(Cons(x0, Cons(x1, x2)), S(y11)) -> c(TAKE#2(S(y11), Cons(x0, Cons(x1, x2))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, x3))), S(y11)) -> c(TAKE#2(S(y11), Cons(x0, Cons(x1, Cons(x2, x3)))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Nil)), S(y10)) -> c(TAKE#2(S(y10), Cons(x0, Cons(x1, Nil))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Nil))), S(y7)) -> c(TAKE#2(S(y7), Cons(x0, Cons(x1, Cons(x2, Nil)))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4)))), S(y8)) -> c(TAKE#2(S(y8), Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4))))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, x2)), S(y11)) -> c1(DROP#2(S(y11), Cons(x0, Cons(x1, x2))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, x3))), S(y11)) -> c1(DROP#2(S(y11), Cons(x0, Cons(x1, Cons(x2, x3)))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Nil)), S(y10)) -> c1(DROP#2(S(y10), Cons(x0, Cons(x1, Nil))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Nil))), S(y7)) -> c1(DROP#2(S(y7), Cons(x0, Cons(x1, Cons(x2, Nil)))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4)))), S(y8)) -> c1(DROP#2(S(y8), Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4))))))
   COND_MERGE_YS_ZS_2(False, Cons(S(x0), x1), Cons(0, x2), S(x0), x1, 0, x2) -> c3(MERGE#2(Cons(S(x0), x1), x2))
   COND_MERGE_YS_ZS_2(False, Cons(S(S(x0)), x1), Cons(S(0), x2), S(S(x0)), x1, S(0), x2) -> c3(MERGE#2(Cons(S(S(x0)), x1), x2))
   COND_MERGE_YS_ZS_2(False, Cons(S(S(x0)), x1), Cons(S(S(x2)), x3), S(S(x0)), x1, S(S(x2)), x3) -> c3(MERGE#2(Cons(S(S(x0)), x1), x3))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, Nil)))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Cons(z2, Nil))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, Nil))), S(halve#1(S(0)))))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, Nil))), S(halve#1(length#1(Cons(z2, Nil)))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, Nil))), S(halve#1(length#1(Cons(z2, Nil))))), HALVE#1(S(length#1(Nil))), LENGTH#1(Cons(z2, Nil)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, Cons(z3, z4))))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Cons(z2, Cons(z3, z4)))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, Cons(z3, z4)))), S(halve#1(S(S(length#1(z4)))))))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, Cons(z3, z4)))), S(halve#1(length#1(Cons(z2, Cons(z3, z4))))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, Cons(z3, z4)))), S(halve#1(length#1(Cons(z2, Cons(z3, z4)))))), HALVE#1(S(length#1(Cons(z3, z4)))), LENGTH#1(Cons(z2, Cons(z3, z4))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, z3)))) -> c9(MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3)))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3))))), HALVE#1(S(length#1(z3))), LENGTH#1(Cons(z2, z3)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Nil))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(0)), Cons(z0, Cons(z1, Nil))), Cons(drop#2(S(halve#1(0)), Cons(z0, Cons(z1, Nil))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil)))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Nil))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Nil)), S(0)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil)))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> c9(CONST_F#2(Cons(z0, Cons(z1, z2)), Cons(dc#1(map, divisible, mergesort_zs_3, divide, const_f, take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2)))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(drop#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(halve#1(length#1(z2)), Cons(z1, z2)), Nil))), DIVIDE_YS#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2)))), HALVE#1(length#1(z2)), LENGTH#1(z2))
   CONST_F#2(Cons(x0, Cons(x1, x2)), Cons(z1, Cons(z2, z3))) -> c19(MERGE#2(z1, z2))
   CONST_F#2(Cons(x0, Cons(x1, Cons(x2, x3))), Cons(z1, Cons(z2, z3))) -> c19(MERGE#2(z1, z2))
   CONST_F#2(Cons(x0, Cons(x1, Nil)), Cons(z1, Cons(z2, z3))) -> c19(MERGE#2(z1, z2))
   CONST_F#2(Cons(x0, Cons(x1, Cons(x2, Nil))), Cons(z1, Cons(z2, z3))) -> c19(MERGE#2(z1, z2))
   CONST_F#2(Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4)))), Cons(z1, Cons(z2, z3))) -> c19(MERGE#2(z1, z2))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> c9(CONST_F#2(Cons(z0, Cons(z1, z2)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(halve#1(length#1(z2)), Cons(z1, z2)), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(halve#1(length#1(z2)), Cons(z1, z2)), Nil))), DIVIDE_YS#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2)))), HALVE#1(length#1(z2)), LENGTH#1(z2))
   COND_MERGE_YS_ZS_2(True, Cons(0, Cons(0, z5)), Cons(x1, x2), 0, Cons(0, z5), x1, x2) -> c2(MERGE#2(Cons(0, z5), Cons(x1, x2)))
   COND_MERGE_YS_ZS_2(True, Cons(S(0), Cons(0, z5)), Cons(S(x1), x2), S(0), Cons(0, z5), S(x1), x2) -> c2(MERGE#2(Cons(0, z5), Cons(S(x1), x2)))
   COND_MERGE_YS_ZS_2(True, Cons(S(S(x0)), Cons(0, z5)), Cons(S(S(x2)), x3), S(S(x0)), Cons(0, z5), S(S(x2)), x3) -> c2(MERGE#2(Cons(0, z5), Cons(S(S(x2)), x3)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, z3)))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Cons(z2, z3))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(Cons(z2, z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Cons(drop#2(S(halve#1(S(length#1(z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3)))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(S(length#1(z3))))), HALVE#1(S(length#1(z3))), LENGTH#1(Cons(z2, z3)))
   COND_MERGE_YS_ZS_2(True, Cons(0, Cons(S(z4), z5)), Cons(0, x2), 0, Cons(S(z4), z5), 0, x2) -> c2(MERGE#2(Cons(S(z4), z5), Cons(0, x2)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> c9(CONST_F#2(Cons(z0, Cons(z1, z2)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(Cons(z0, take#2(halve#1(length#1(z2)), Cons(z1, z2))), Cons(drop#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(halve#1(length#1(z2)), Cons(z1, z2)), Nil))), DIVIDE_YS#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2)))), HALVE#1(length#1(z2)), LENGTH#1(z2))
   COND_MERGE_YS_ZS_2(True, Cons(0, Cons(S(0), z5)), Cons(S(z2), x2), 0, Cons(S(0), z5), S(z2), x2) -> c2(MERGE#2(Cons(S(0), z5), Cons(S(z2), x2)))
   COND_MERGE_YS_ZS_2(True, Cons(S(0), Cons(S(0), z5)), Cons(S(x1), x2), S(0), Cons(S(0), z5), S(x1), x2) -> c2(MERGE#2(Cons(S(0), z5), Cons(S(x1), x2)))
   COND_MERGE_YS_ZS_2(True, Cons(S(S(x0)), Cons(S(0), z5)), Cons(S(S(x2)), x3), S(S(x0)), Cons(S(0), z5), S(S(x2)), x3) -> c2(MERGE#2(Cons(S(0), z5), Cons(S(S(x2)), x3)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, z3)))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Cons(z2, z3))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(S(length#1(z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Cons(drop#2(S(halve#1(length#1(Cons(z2, z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3)))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(S(length#1(z3))))), HALVE#1(S(length#1(z3))), LENGTH#1(Cons(z2, z3)))
   COND_MERGE_YS_ZS_2(True, Cons(0, Cons(S(S(z4)), z5)), Cons(S(0), x2), 0, Cons(S(S(z4)), z5), S(0), x2) -> c2(MERGE#2(Cons(S(S(z4)), z5), Cons(S(0), x2)))
   COND_MERGE_YS_ZS_2(True, Cons(S(0), Cons(S(S(z4)), z5)), Cons(S(0), x2), S(0), Cons(S(S(z4)), z5), S(0), x2) -> c2(MERGE#2(Cons(S(S(z4)), z5), Cons(S(0), x2)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> c9(MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(halve#1(length#1(z2)), Cons(z1, z2)), Nil))), DIVIDE_YS#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2)))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Nil))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(Nil))), Cons(z0, Cons(z1, Nil))), Cons(drop#2(S(halve#1(0)), Cons(z0, Cons(z1, Nil))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Nil)), S(halve#1(0))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Nil))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(0)), Cons(z0, Cons(z1, Nil))), Cons(drop#2(S(halve#1(length#1(Nil))), Cons(z0, Cons(z1, Nil))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Nil)), S(halve#1(0))))
   DROP#2(S(S(y0)), Cons(z1, Cons(y1, y2))) -> c12(DROP#2(S(y0), Cons(y1, y2)))
   COND_MERGE_YS_ZS_2(True, Cons(0, Cons(S(S(z5)), z6)), Cons(S(S(z2)), x2), 0, Cons(S(S(z5)), z6), S(S(z2)), x2) -> c2(MERGE#2(Cons(S(S(z5)), z6), Cons(S(S(z2)), x2)))
   COND_MERGE_YS_ZS_2(True, Cons(S(0), Cons(S(S(z5)), z6)), Cons(S(S(z2)), x2), S(0), Cons(S(S(z5)), z6), S(S(z2)), x2) -> c2(MERGE#2(Cons(S(S(z5)), z6), Cons(S(S(z2)), x2)))
   COND_MERGE_YS_ZS_2(True, Cons(S(S(x0)), Cons(S(S(z5)), z6)), Cons(S(S(x2)), x3), S(S(x0)), Cons(S(S(z5)), z6), S(S(x2)), x3) -> c2(MERGE#2(Cons(S(S(z5)), z6), Cons(S(S(x2)), x3)))
   COND_MERGE_YS_ZS_2(True, Cons(0, Cons(S(z5), z6)), Cons(S(z2), x2), 0, Cons(S(z5), z6), S(z2), x2) -> c2(MERGE#2(Cons(S(z5), z6), Cons(S(z2), x2)))
   COND_MERGE_YS_ZS_2(True, Cons(S(0), Cons(S(z5), z6)), Cons(S(x1), x2), S(0), Cons(S(z5), z6), S(x1), x2) -> c2(MERGE#2(Cons(S(z5), z6), Cons(S(x1), x2)))
   COND_MERGE_YS_ZS_2(True, Cons(S(S(x0)), Cons(S(z5), z6)), Cons(S(S(x2)), x3), S(S(x0)), Cons(S(z5), z6), S(S(x2)), x3) -> c2(MERGE#2(Cons(S(z5), z6), Cons(S(S(x2)), x3)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, z3)))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Cons(z2, z3))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(S(length#1(z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Cons(drop#2(S(halve#1(S(length#1(z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3)))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(S(length#1(z3))))), HALVE#1(S(length#1(z3))), LENGTH#1(Cons(z2, z3)))
   TAKE#2(S(S(y0)), Cons(z1, Cons(y1, y2))) -> c15(TAKE#2(S(y0), Cons(y1, y2)))
   HALVE#1(S(S(S(S(y0))))) -> c18(HALVE#1(S(S(y0))))
   LEQ#2(S(S(y0)), S(S(y1))) -> c22(LEQ#2(S(y0), S(y1)))
S tuples:
   LENGTH#1(Cons(z0, z1)) -> c24(LENGTH#1(z1))
   MAP#2(dc(z0, z1, z2, z3, z4), Cons(z5, z6)) -> c26(DC#1(z0, z1, z2, z3, z4, z5))
   MAP#2(dc(z0, z1, z2, z3, z4), Cons(z5, z6)) -> c27(MAP#2(dc(z0, z1, z2, z3, z4), z6))
   MERGE#2(Cons(0, x1), Cons(z0, x3)) -> c6(COND_MERGE_YS_ZS_2(True, Cons(0, x1), Cons(z0, x3), 0, x1, z0, x3))
   MERGE#2(Cons(S(z0), x1), Cons(0, x3)) -> c6(COND_MERGE_YS_ZS_2(False, Cons(S(z0), x1), Cons(0, x3), S(z0), x1, 0, x3))
   MERGE#2(Cons(S(0), x1), Cons(S(z0), x3)) -> c6(COND_MERGE_YS_ZS_2(True, Cons(S(0), x1), Cons(S(z0), x3), S(0), x1, S(z0), x3), LEQ#2(S(0), S(z0)))
   MERGE#2(Cons(S(S(z0)), x1), Cons(S(0), x3)) -> c6(COND_MERGE_YS_ZS_2(False, Cons(S(S(z0)), x1), Cons(S(0), x3), S(S(z0)), x1, S(0), x3), LEQ#2(S(S(z0)), S(0)))
   MERGE#2(Cons(S(S(z0)), x1), Cons(S(S(z1)), x3)) -> c6(COND_MERGE_YS_ZS_2(leq#2(z0, z1), Cons(S(S(z0)), x1), Cons(S(S(z1)), x3), S(S(z0)), x1, S(S(z1)), x3), LEQ#2(S(S(z0)), S(S(z1))))
   MERGE#2(Cons(S(x0), x1), Cons(S(x2), x3)) -> c6(LEQ#2(S(x0), S(x2)))
   DIVIDE_YS#1(Cons(x0, Cons(x1, x2)), S(y11)) -> c(TAKE#2(S(y11), Cons(x0, Cons(x1, x2))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, x3))), S(y11)) -> c(TAKE#2(S(y11), Cons(x0, Cons(x1, Cons(x2, x3)))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Nil)), S(y10)) -> c(TAKE#2(S(y10), Cons(x0, Cons(x1, Nil))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Nil))), S(y7)) -> c(TAKE#2(S(y7), Cons(x0, Cons(x1, Cons(x2, Nil)))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4)))), S(y8)) -> c(TAKE#2(S(y8), Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4))))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, x2)), S(y11)) -> c1(DROP#2(S(y11), Cons(x0, Cons(x1, x2))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, x3))), S(y11)) -> c1(DROP#2(S(y11), Cons(x0, Cons(x1, Cons(x2, x3)))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Nil)), S(y10)) -> c1(DROP#2(S(y10), Cons(x0, Cons(x1, Nil))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Nil))), S(y7)) -> c1(DROP#2(S(y7), Cons(x0, Cons(x1, Cons(x2, Nil)))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4)))), S(y8)) -> c1(DROP#2(S(y8), Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4))))))
   COND_MERGE_YS_ZS_2(False, Cons(S(x0), x1), Cons(0, x2), S(x0), x1, 0, x2) -> c3(MERGE#2(Cons(S(x0), x1), x2))
   COND_MERGE_YS_ZS_2(False, Cons(S(S(x0)), x1), Cons(S(0), x2), S(S(x0)), x1, S(0), x2) -> c3(MERGE#2(Cons(S(S(x0)), x1), x2))
   COND_MERGE_YS_ZS_2(False, Cons(S(S(x0)), x1), Cons(S(S(x2)), x3), S(S(x0)), x1, S(S(x2)), x3) -> c3(MERGE#2(Cons(S(S(x0)), x1), x3))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, Nil)))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Cons(z2, Nil))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, Nil))), S(halve#1(S(0)))))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, Nil))), S(halve#1(length#1(Cons(z2, Nil)))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, Nil))), S(halve#1(length#1(Cons(z2, Nil))))), HALVE#1(S(length#1(Nil))), LENGTH#1(Cons(z2, Nil)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, Cons(z3, z4))))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Cons(z2, Cons(z3, z4)))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, Cons(z3, z4)))), S(halve#1(S(S(length#1(z4)))))))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, Cons(z3, z4)))), S(halve#1(length#1(Cons(z2, Cons(z3, z4))))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, Cons(z3, z4)))), S(halve#1(length#1(Cons(z2, Cons(z3, z4)))))), HALVE#1(S(length#1(Cons(z3, z4)))), LENGTH#1(Cons(z2, Cons(z3, z4))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, z3)))) -> c9(MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3)))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3))))), HALVE#1(S(length#1(z3))), LENGTH#1(Cons(z2, z3)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Nil))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(0)), Cons(z0, Cons(z1, Nil))), Cons(drop#2(S(halve#1(0)), Cons(z0, Cons(z1, Nil))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil)))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Nil))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Nil)), S(0)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil)))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> c9(CONST_F#2(Cons(z0, Cons(z1, z2)), Cons(dc#1(map, divisible, mergesort_zs_3, divide, const_f, take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2)))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(drop#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(halve#1(length#1(z2)), Cons(z1, z2)), Nil))), DIVIDE_YS#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2)))), HALVE#1(length#1(z2)), LENGTH#1(z2))
   CONST_F#2(Cons(x0, Cons(x1, x2)), Cons(z1, Cons(z2, z3))) -> c19(MERGE#2(z1, z2))
   CONST_F#2(Cons(x0, Cons(x1, Cons(x2, x3))), Cons(z1, Cons(z2, z3))) -> c19(MERGE#2(z1, z2))
   CONST_F#2(Cons(x0, Cons(x1, Nil)), Cons(z1, Cons(z2, z3))) -> c19(MERGE#2(z1, z2))
   CONST_F#2(Cons(x0, Cons(x1, Cons(x2, Nil))), Cons(z1, Cons(z2, z3))) -> c19(MERGE#2(z1, z2))
   CONST_F#2(Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4)))), Cons(z1, Cons(z2, z3))) -> c19(MERGE#2(z1, z2))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> c9(CONST_F#2(Cons(z0, Cons(z1, z2)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(halve#1(length#1(z2)), Cons(z1, z2)), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(halve#1(length#1(z2)), Cons(z1, z2)), Nil))), DIVIDE_YS#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2)))), HALVE#1(length#1(z2)), LENGTH#1(z2))
   COND_MERGE_YS_ZS_2(True, Cons(0, Cons(0, z5)), Cons(x1, x2), 0, Cons(0, z5), x1, x2) -> c2(MERGE#2(Cons(0, z5), Cons(x1, x2)))
   COND_MERGE_YS_ZS_2(True, Cons(S(0), Cons(0, z5)), Cons(S(x1), x2), S(0), Cons(0, z5), S(x1), x2) -> c2(MERGE#2(Cons(0, z5), Cons(S(x1), x2)))
   COND_MERGE_YS_ZS_2(True, Cons(S(S(x0)), Cons(0, z5)), Cons(S(S(x2)), x3), S(S(x0)), Cons(0, z5), S(S(x2)), x3) -> c2(MERGE#2(Cons(0, z5), Cons(S(S(x2)), x3)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, z3)))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Cons(z2, z3))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(Cons(z2, z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Cons(drop#2(S(halve#1(S(length#1(z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3)))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(S(length#1(z3))))), HALVE#1(S(length#1(z3))), LENGTH#1(Cons(z2, z3)))
   COND_MERGE_YS_ZS_2(True, Cons(0, Cons(S(z4), z5)), Cons(0, x2), 0, Cons(S(z4), z5), 0, x2) -> c2(MERGE#2(Cons(S(z4), z5), Cons(0, x2)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> c9(CONST_F#2(Cons(z0, Cons(z1, z2)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(Cons(z0, take#2(halve#1(length#1(z2)), Cons(z1, z2))), Cons(drop#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(halve#1(length#1(z2)), Cons(z1, z2)), Nil))), DIVIDE_YS#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2)))), HALVE#1(length#1(z2)), LENGTH#1(z2))
   COND_MERGE_YS_ZS_2(True, Cons(0, Cons(S(0), z5)), Cons(S(z2), x2), 0, Cons(S(0), z5), S(z2), x2) -> c2(MERGE#2(Cons(S(0), z5), Cons(S(z2), x2)))
   COND_MERGE_YS_ZS_2(True, Cons(S(0), Cons(S(0), z5)), Cons(S(x1), x2), S(0), Cons(S(0), z5), S(x1), x2) -> c2(MERGE#2(Cons(S(0), z5), Cons(S(x1), x2)))
   COND_MERGE_YS_ZS_2(True, Cons(S(S(x0)), Cons(S(0), z5)), Cons(S(S(x2)), x3), S(S(x0)), Cons(S(0), z5), S(S(x2)), x3) -> c2(MERGE#2(Cons(S(0), z5), Cons(S(S(x2)), x3)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, z3)))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Cons(z2, z3))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(S(length#1(z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Cons(drop#2(S(halve#1(length#1(Cons(z2, z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3)))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(S(length#1(z3))))), HALVE#1(S(length#1(z3))), LENGTH#1(Cons(z2, z3)))
   COND_MERGE_YS_ZS_2(True, Cons(0, Cons(S(S(z4)), z5)), Cons(S(0), x2), 0, Cons(S(S(z4)), z5), S(0), x2) -> c2(MERGE#2(Cons(S(S(z4)), z5), Cons(S(0), x2)))
   COND_MERGE_YS_ZS_2(True, Cons(S(0), Cons(S(S(z4)), z5)), Cons(S(0), x2), S(0), Cons(S(S(z4)), z5), S(0), x2) -> c2(MERGE#2(Cons(S(S(z4)), z5), Cons(S(0), x2)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> c9(MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(halve#1(length#1(z2)), Cons(z1, z2)), Nil))), DIVIDE_YS#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2)))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Nil))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(Nil))), Cons(z0, Cons(z1, Nil))), Cons(drop#2(S(halve#1(0)), Cons(z0, Cons(z1, Nil))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Nil)), S(halve#1(0))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Nil))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(0)), Cons(z0, Cons(z1, Nil))), Cons(drop#2(S(halve#1(length#1(Nil))), Cons(z0, Cons(z1, Nil))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Nil)), S(halve#1(0))))
   DROP#2(S(S(y0)), Cons(z1, Cons(y1, y2))) -> c12(DROP#2(S(y0), Cons(y1, y2)))
   COND_MERGE_YS_ZS_2(True, Cons(0, Cons(S(S(z5)), z6)), Cons(S(S(z2)), x2), 0, Cons(S(S(z5)), z6), S(S(z2)), x2) -> c2(MERGE#2(Cons(S(S(z5)), z6), Cons(S(S(z2)), x2)))
   COND_MERGE_YS_ZS_2(True, Cons(S(0), Cons(S(S(z5)), z6)), Cons(S(S(z2)), x2), S(0), Cons(S(S(z5)), z6), S(S(z2)), x2) -> c2(MERGE#2(Cons(S(S(z5)), z6), Cons(S(S(z2)), x2)))
   COND_MERGE_YS_ZS_2(True, Cons(S(S(x0)), Cons(S(S(z5)), z6)), Cons(S(S(x2)), x3), S(S(x0)), Cons(S(S(z5)), z6), S(S(x2)), x3) -> c2(MERGE#2(Cons(S(S(z5)), z6), Cons(S(S(x2)), x3)))
   COND_MERGE_YS_ZS_2(True, Cons(0, Cons(S(z5), z6)), Cons(S(z2), x2), 0, Cons(S(z5), z6), S(z2), x2) -> c2(MERGE#2(Cons(S(z5), z6), Cons(S(z2), x2)))
   COND_MERGE_YS_ZS_2(True, Cons(S(0), Cons(S(z5), z6)), Cons(S(x1), x2), S(0), Cons(S(z5), z6), S(x1), x2) -> c2(MERGE#2(Cons(S(z5), z6), Cons(S(x1), x2)))
   COND_MERGE_YS_ZS_2(True, Cons(S(S(x0)), Cons(S(z5), z6)), Cons(S(S(x2)), x3), S(S(x0)), Cons(S(z5), z6), S(S(x2)), x3) -> c2(MERGE#2(Cons(S(z5), z6), Cons(S(S(x2)), x3)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, z3)))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Cons(z2, z3))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(S(length#1(z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Cons(drop#2(S(halve#1(S(length#1(z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3)))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(S(length#1(z3))))), HALVE#1(S(length#1(z3))), LENGTH#1(Cons(z2, z3)))
   TAKE#2(S(S(y0)), Cons(z1, Cons(y1, y2))) -> c15(TAKE#2(S(y0), Cons(y1, y2)))
   HALVE#1(S(S(S(S(y0))))) -> c18(HALVE#1(S(S(y0))))
   LEQ#2(S(S(y0)), S(S(y1))) -> c22(LEQ#2(S(y0), S(y1)))
K tuples:none
Defined Rule Symbols:   leq#2_2, map#2_2, divide_ys#1_2, halve#1_1, length#1_1, take#2_2, drop#2_2, dc#1_6, const_f#2_2, merge#2_2, cond_merge_ys_zs_2_7

Defined Pair Symbols:   LENGTH#1_1, MAP#2_2, MERGE#2_2, DIVIDE_YS#1_2, COND_MERGE_YS_ZS_2_7, DC#1_6, CONST_F#2_2, DROP#2_2, TAKE#2_2, HALVE#1_1, LEQ#2_2

Compound Symbols:   c24_1, c26_1, c27_1, c6_1, c6_2, c_1, c1_1, c3_1, c9_5, c9_4, c9_3, c19_1, c2_1, c9_2, c12_1, c15_1, c18_1, c22_1


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(185) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID))
Removed 2 trailing tuple parts
----------------------------------------

(186)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   leq#2(0, z0) -> True
   leq#2(S(z0), 0) -> False
   leq#2(S(z0), S(z1)) -> leq#2(z0, z1)
   map#2(dc(z0, z1, z2, z3, z4), Nil) -> Nil
   map#2(dc(z0, z1, z2, z3, z4), Cons(z5, z6)) -> Cons(dc#1(z0, z1, z2, z3, z4, z5), map#2(dc(z0, z1, z2, z3, z4), z6))
   divide_ys#1(z0, z1) -> Cons(take#2(z1, z0), Cons(drop#2(z1, z0), Nil))
   halve#1(0) -> 0
   halve#1(S(0)) -> S(0)
   halve#1(S(S(z0))) -> S(halve#1(z0))
   length#1(Nil) -> 0
   length#1(Cons(z0, z1)) -> S(length#1(z1))
   take#2(0, z0) -> Nil
   take#2(S(0), Nil) -> Cons(bot[0], Nil)
   take#2(S(z0), Cons(z1, z2)) -> Cons(z1, take#2(z0, z2))
   drop#2(0, z0) -> z0
   drop#2(S(0), Nil) -> bot[1]
   drop#2(S(z0), Cons(z1, z2)) -> drop#2(z0, z2)
   dc#1(map, divisible, mergesort_zs_3, divide, const_f, Nil) -> Nil
   dc#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Nil)) -> Cons(z0, Nil)
   dc#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> const_f#2(Cons(z0, Cons(z1, z2)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2))))))
   const_f#2(z0, Cons(z1, Cons(z2, z3))) -> merge#2(z1, z2)
   merge#2(Nil, z0) -> z0
   merge#2(Cons(z0, z1), Nil) -> Cons(z0, z1)
   merge#2(Cons(z0, z1), Cons(z2, z3)) -> cond_merge_ys_zs_2(leq#2(z0, z2), Cons(z0, z1), Cons(z2, z3), z0, z1, z2, z3)
   cond_merge_ys_zs_2(True, Cons(z0, z1), Cons(z2, z3), z4, z5, z6, z7) -> Cons(z4, merge#2(z5, Cons(z2, z3)))
   cond_merge_ys_zs_2(False, Cons(z0, z1), Cons(z2, z3), z4, z5, z6, z7) -> Cons(z6, merge#2(Cons(z0, z1), z7))
Tuples:
   LENGTH#1(Cons(z0, z1)) -> c24(LENGTH#1(z1))
   MAP#2(dc(z0, z1, z2, z3, z4), Cons(z5, z6)) -> c26(DC#1(z0, z1, z2, z3, z4, z5))
   MAP#2(dc(z0, z1, z2, z3, z4), Cons(z5, z6)) -> c27(MAP#2(dc(z0, z1, z2, z3, z4), z6))
   MERGE#2(Cons(0, x1), Cons(z0, x3)) -> c6(COND_MERGE_YS_ZS_2(True, Cons(0, x1), Cons(z0, x3), 0, x1, z0, x3))
   MERGE#2(Cons(S(z0), x1), Cons(0, x3)) -> c6(COND_MERGE_YS_ZS_2(False, Cons(S(z0), x1), Cons(0, x3), S(z0), x1, 0, x3))
   MERGE#2(Cons(S(S(z0)), x1), Cons(S(S(z1)), x3)) -> c6(COND_MERGE_YS_ZS_2(leq#2(z0, z1), Cons(S(S(z0)), x1), Cons(S(S(z1)), x3), S(S(z0)), x1, S(S(z1)), x3), LEQ#2(S(S(z0)), S(S(z1))))
   MERGE#2(Cons(S(x0), x1), Cons(S(x2), x3)) -> c6(LEQ#2(S(x0), S(x2)))
   DIVIDE_YS#1(Cons(x0, Cons(x1, x2)), S(y11)) -> c(TAKE#2(S(y11), Cons(x0, Cons(x1, x2))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, x3))), S(y11)) -> c(TAKE#2(S(y11), Cons(x0, Cons(x1, Cons(x2, x3)))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Nil)), S(y10)) -> c(TAKE#2(S(y10), Cons(x0, Cons(x1, Nil))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Nil))), S(y7)) -> c(TAKE#2(S(y7), Cons(x0, Cons(x1, Cons(x2, Nil)))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4)))), S(y8)) -> c(TAKE#2(S(y8), Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4))))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, x2)), S(y11)) -> c1(DROP#2(S(y11), Cons(x0, Cons(x1, x2))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, x3))), S(y11)) -> c1(DROP#2(S(y11), Cons(x0, Cons(x1, Cons(x2, x3)))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Nil)), S(y10)) -> c1(DROP#2(S(y10), Cons(x0, Cons(x1, Nil))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Nil))), S(y7)) -> c1(DROP#2(S(y7), Cons(x0, Cons(x1, Cons(x2, Nil)))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4)))), S(y8)) -> c1(DROP#2(S(y8), Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4))))))
   COND_MERGE_YS_ZS_2(False, Cons(S(x0), x1), Cons(0, x2), S(x0), x1, 0, x2) -> c3(MERGE#2(Cons(S(x0), x1), x2))
   COND_MERGE_YS_ZS_2(False, Cons(S(S(x0)), x1), Cons(S(0), x2), S(S(x0)), x1, S(0), x2) -> c3(MERGE#2(Cons(S(S(x0)), x1), x2))
   COND_MERGE_YS_ZS_2(False, Cons(S(S(x0)), x1), Cons(S(S(x2)), x3), S(S(x0)), x1, S(S(x2)), x3) -> c3(MERGE#2(Cons(S(S(x0)), x1), x3))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, Nil)))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Cons(z2, Nil))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, Nil))), S(halve#1(S(0)))))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, Nil))), S(halve#1(length#1(Cons(z2, Nil)))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, Nil))), S(halve#1(length#1(Cons(z2, Nil))))), HALVE#1(S(length#1(Nil))), LENGTH#1(Cons(z2, Nil)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, Cons(z3, z4))))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Cons(z2, Cons(z3, z4)))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, Cons(z3, z4)))), S(halve#1(S(S(length#1(z4)))))))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, Cons(z3, z4)))), S(halve#1(length#1(Cons(z2, Cons(z3, z4))))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, Cons(z3, z4)))), S(halve#1(length#1(Cons(z2, Cons(z3, z4)))))), HALVE#1(S(length#1(Cons(z3, z4)))), LENGTH#1(Cons(z2, Cons(z3, z4))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, z3)))) -> c9(MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3)))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3))))), HALVE#1(S(length#1(z3))), LENGTH#1(Cons(z2, z3)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Nil))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(0)), Cons(z0, Cons(z1, Nil))), Cons(drop#2(S(halve#1(0)), Cons(z0, Cons(z1, Nil))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil)))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Nil))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Nil)), S(0)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil)))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> c9(CONST_F#2(Cons(z0, Cons(z1, z2)), Cons(dc#1(map, divisible, mergesort_zs_3, divide, const_f, take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2)))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(drop#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(halve#1(length#1(z2)), Cons(z1, z2)), Nil))), DIVIDE_YS#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2)))), HALVE#1(length#1(z2)), LENGTH#1(z2))
   CONST_F#2(Cons(x0, Cons(x1, x2)), Cons(z1, Cons(z2, z3))) -> c19(MERGE#2(z1, z2))
   CONST_F#2(Cons(x0, Cons(x1, Cons(x2, x3))), Cons(z1, Cons(z2, z3))) -> c19(MERGE#2(z1, z2))
   CONST_F#2(Cons(x0, Cons(x1, Nil)), Cons(z1, Cons(z2, z3))) -> c19(MERGE#2(z1, z2))
   CONST_F#2(Cons(x0, Cons(x1, Cons(x2, Nil))), Cons(z1, Cons(z2, z3))) -> c19(MERGE#2(z1, z2))
   CONST_F#2(Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4)))), Cons(z1, Cons(z2, z3))) -> c19(MERGE#2(z1, z2))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> c9(CONST_F#2(Cons(z0, Cons(z1, z2)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(halve#1(length#1(z2)), Cons(z1, z2)), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(halve#1(length#1(z2)), Cons(z1, z2)), Nil))), DIVIDE_YS#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2)))), HALVE#1(length#1(z2)), LENGTH#1(z2))
   COND_MERGE_YS_ZS_2(True, Cons(0, Cons(0, z5)), Cons(x1, x2), 0, Cons(0, z5), x1, x2) -> c2(MERGE#2(Cons(0, z5), Cons(x1, x2)))
   COND_MERGE_YS_ZS_2(True, Cons(S(0), Cons(0, z5)), Cons(S(x1), x2), S(0), Cons(0, z5), S(x1), x2) -> c2(MERGE#2(Cons(0, z5), Cons(S(x1), x2)))
   COND_MERGE_YS_ZS_2(True, Cons(S(S(x0)), Cons(0, z5)), Cons(S(S(x2)), x3), S(S(x0)), Cons(0, z5), S(S(x2)), x3) -> c2(MERGE#2(Cons(0, z5), Cons(S(S(x2)), x3)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, z3)))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Cons(z2, z3))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(Cons(z2, z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Cons(drop#2(S(halve#1(S(length#1(z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3)))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(S(length#1(z3))))), HALVE#1(S(length#1(z3))), LENGTH#1(Cons(z2, z3)))
   COND_MERGE_YS_ZS_2(True, Cons(0, Cons(S(z4), z5)), Cons(0, x2), 0, Cons(S(z4), z5), 0, x2) -> c2(MERGE#2(Cons(S(z4), z5), Cons(0, x2)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> c9(CONST_F#2(Cons(z0, Cons(z1, z2)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(Cons(z0, take#2(halve#1(length#1(z2)), Cons(z1, z2))), Cons(drop#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(halve#1(length#1(z2)), Cons(z1, z2)), Nil))), DIVIDE_YS#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2)))), HALVE#1(length#1(z2)), LENGTH#1(z2))
   COND_MERGE_YS_ZS_2(True, Cons(0, Cons(S(0), z5)), Cons(S(z2), x2), 0, Cons(S(0), z5), S(z2), x2) -> c2(MERGE#2(Cons(S(0), z5), Cons(S(z2), x2)))
   COND_MERGE_YS_ZS_2(True, Cons(S(0), Cons(S(0), z5)), Cons(S(x1), x2), S(0), Cons(S(0), z5), S(x1), x2) -> c2(MERGE#2(Cons(S(0), z5), Cons(S(x1), x2)))
   COND_MERGE_YS_ZS_2(True, Cons(S(S(x0)), Cons(S(0), z5)), Cons(S(S(x2)), x3), S(S(x0)), Cons(S(0), z5), S(S(x2)), x3) -> c2(MERGE#2(Cons(S(0), z5), Cons(S(S(x2)), x3)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, z3)))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Cons(z2, z3))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(S(length#1(z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Cons(drop#2(S(halve#1(length#1(Cons(z2, z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3)))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(S(length#1(z3))))), HALVE#1(S(length#1(z3))), LENGTH#1(Cons(z2, z3)))
   COND_MERGE_YS_ZS_2(True, Cons(0, Cons(S(S(z4)), z5)), Cons(S(0), x2), 0, Cons(S(S(z4)), z5), S(0), x2) -> c2(MERGE#2(Cons(S(S(z4)), z5), Cons(S(0), x2)))
   COND_MERGE_YS_ZS_2(True, Cons(S(0), Cons(S(S(z4)), z5)), Cons(S(0), x2), S(0), Cons(S(S(z4)), z5), S(0), x2) -> c2(MERGE#2(Cons(S(S(z4)), z5), Cons(S(0), x2)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> c9(MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(halve#1(length#1(z2)), Cons(z1, z2)), Nil))), DIVIDE_YS#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2)))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Nil))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(Nil))), Cons(z0, Cons(z1, Nil))), Cons(drop#2(S(halve#1(0)), Cons(z0, Cons(z1, Nil))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Nil)), S(halve#1(0))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Nil))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(0)), Cons(z0, Cons(z1, Nil))), Cons(drop#2(S(halve#1(length#1(Nil))), Cons(z0, Cons(z1, Nil))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Nil)), S(halve#1(0))))
   DROP#2(S(S(y0)), Cons(z1, Cons(y1, y2))) -> c12(DROP#2(S(y0), Cons(y1, y2)))
   COND_MERGE_YS_ZS_2(True, Cons(0, Cons(S(S(z5)), z6)), Cons(S(S(z2)), x2), 0, Cons(S(S(z5)), z6), S(S(z2)), x2) -> c2(MERGE#2(Cons(S(S(z5)), z6), Cons(S(S(z2)), x2)))
   COND_MERGE_YS_ZS_2(True, Cons(S(0), Cons(S(S(z5)), z6)), Cons(S(S(z2)), x2), S(0), Cons(S(S(z5)), z6), S(S(z2)), x2) -> c2(MERGE#2(Cons(S(S(z5)), z6), Cons(S(S(z2)), x2)))
   COND_MERGE_YS_ZS_2(True, Cons(S(S(x0)), Cons(S(S(z5)), z6)), Cons(S(S(x2)), x3), S(S(x0)), Cons(S(S(z5)), z6), S(S(x2)), x3) -> c2(MERGE#2(Cons(S(S(z5)), z6), Cons(S(S(x2)), x3)))
   COND_MERGE_YS_ZS_2(True, Cons(0, Cons(S(z5), z6)), Cons(S(z2), x2), 0, Cons(S(z5), z6), S(z2), x2) -> c2(MERGE#2(Cons(S(z5), z6), Cons(S(z2), x2)))
   COND_MERGE_YS_ZS_2(True, Cons(S(0), Cons(S(z5), z6)), Cons(S(x1), x2), S(0), Cons(S(z5), z6), S(x1), x2) -> c2(MERGE#2(Cons(S(z5), z6), Cons(S(x1), x2)))
   COND_MERGE_YS_ZS_2(True, Cons(S(S(x0)), Cons(S(z5), z6)), Cons(S(S(x2)), x3), S(S(x0)), Cons(S(z5), z6), S(S(x2)), x3) -> c2(MERGE#2(Cons(S(z5), z6), Cons(S(S(x2)), x3)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, z3)))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Cons(z2, z3))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(S(length#1(z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Cons(drop#2(S(halve#1(S(length#1(z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3)))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(S(length#1(z3))))), HALVE#1(S(length#1(z3))), LENGTH#1(Cons(z2, z3)))
   TAKE#2(S(S(y0)), Cons(z1, Cons(y1, y2))) -> c15(TAKE#2(S(y0), Cons(y1, y2)))
   HALVE#1(S(S(S(S(y0))))) -> c18(HALVE#1(S(S(y0))))
   LEQ#2(S(S(y0)), S(S(y1))) -> c22(LEQ#2(S(y0), S(y1)))
   MERGE#2(Cons(S(0), x1), Cons(S(z0), x3)) -> c6(COND_MERGE_YS_ZS_2(True, Cons(S(0), x1), Cons(S(z0), x3), S(0), x1, S(z0), x3))
   MERGE#2(Cons(S(S(z0)), x1), Cons(S(0), x3)) -> c6(COND_MERGE_YS_ZS_2(False, Cons(S(S(z0)), x1), Cons(S(0), x3), S(S(z0)), x1, S(0), x3))
S tuples:
   LENGTH#1(Cons(z0, z1)) -> c24(LENGTH#1(z1))
   MAP#2(dc(z0, z1, z2, z3, z4), Cons(z5, z6)) -> c26(DC#1(z0, z1, z2, z3, z4, z5))
   MAP#2(dc(z0, z1, z2, z3, z4), Cons(z5, z6)) -> c27(MAP#2(dc(z0, z1, z2, z3, z4), z6))
   MERGE#2(Cons(0, x1), Cons(z0, x3)) -> c6(COND_MERGE_YS_ZS_2(True, Cons(0, x1), Cons(z0, x3), 0, x1, z0, x3))
   MERGE#2(Cons(S(z0), x1), Cons(0, x3)) -> c6(COND_MERGE_YS_ZS_2(False, Cons(S(z0), x1), Cons(0, x3), S(z0), x1, 0, x3))
   MERGE#2(Cons(S(S(z0)), x1), Cons(S(S(z1)), x3)) -> c6(COND_MERGE_YS_ZS_2(leq#2(z0, z1), Cons(S(S(z0)), x1), Cons(S(S(z1)), x3), S(S(z0)), x1, S(S(z1)), x3), LEQ#2(S(S(z0)), S(S(z1))))
   MERGE#2(Cons(S(x0), x1), Cons(S(x2), x3)) -> c6(LEQ#2(S(x0), S(x2)))
   DIVIDE_YS#1(Cons(x0, Cons(x1, x2)), S(y11)) -> c(TAKE#2(S(y11), Cons(x0, Cons(x1, x2))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, x3))), S(y11)) -> c(TAKE#2(S(y11), Cons(x0, Cons(x1, Cons(x2, x3)))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Nil)), S(y10)) -> c(TAKE#2(S(y10), Cons(x0, Cons(x1, Nil))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Nil))), S(y7)) -> c(TAKE#2(S(y7), Cons(x0, Cons(x1, Cons(x2, Nil)))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4)))), S(y8)) -> c(TAKE#2(S(y8), Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4))))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, x2)), S(y11)) -> c1(DROP#2(S(y11), Cons(x0, Cons(x1, x2))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, x3))), S(y11)) -> c1(DROP#2(S(y11), Cons(x0, Cons(x1, Cons(x2, x3)))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Nil)), S(y10)) -> c1(DROP#2(S(y10), Cons(x0, Cons(x1, Nil))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Nil))), S(y7)) -> c1(DROP#2(S(y7), Cons(x0, Cons(x1, Cons(x2, Nil)))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4)))), S(y8)) -> c1(DROP#2(S(y8), Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4))))))
   COND_MERGE_YS_ZS_2(False, Cons(S(x0), x1), Cons(0, x2), S(x0), x1, 0, x2) -> c3(MERGE#2(Cons(S(x0), x1), x2))
   COND_MERGE_YS_ZS_2(False, Cons(S(S(x0)), x1), Cons(S(0), x2), S(S(x0)), x1, S(0), x2) -> c3(MERGE#2(Cons(S(S(x0)), x1), x2))
   COND_MERGE_YS_ZS_2(False, Cons(S(S(x0)), x1), Cons(S(S(x2)), x3), S(S(x0)), x1, S(S(x2)), x3) -> c3(MERGE#2(Cons(S(S(x0)), x1), x3))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, Nil)))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Cons(z2, Nil))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, Nil))), S(halve#1(S(0)))))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, Nil))), S(halve#1(length#1(Cons(z2, Nil)))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, Nil))), S(halve#1(length#1(Cons(z2, Nil))))), HALVE#1(S(length#1(Nil))), LENGTH#1(Cons(z2, Nil)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, Cons(z3, z4))))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Cons(z2, Cons(z3, z4)))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, Cons(z3, z4)))), S(halve#1(S(S(length#1(z4)))))))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, Cons(z3, z4)))), S(halve#1(length#1(Cons(z2, Cons(z3, z4))))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, Cons(z3, z4)))), S(halve#1(length#1(Cons(z2, Cons(z3, z4)))))), HALVE#1(S(length#1(Cons(z3, z4)))), LENGTH#1(Cons(z2, Cons(z3, z4))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, z3)))) -> c9(MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3)))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3))))), HALVE#1(S(length#1(z3))), LENGTH#1(Cons(z2, z3)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Nil))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(0)), Cons(z0, Cons(z1, Nil))), Cons(drop#2(S(halve#1(0)), Cons(z0, Cons(z1, Nil))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil)))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Nil))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Nil)), S(0)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil)))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> c9(CONST_F#2(Cons(z0, Cons(z1, z2)), Cons(dc#1(map, divisible, mergesort_zs_3, divide, const_f, take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2)))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(drop#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(halve#1(length#1(z2)), Cons(z1, z2)), Nil))), DIVIDE_YS#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2)))), HALVE#1(length#1(z2)), LENGTH#1(z2))
   CONST_F#2(Cons(x0, Cons(x1, x2)), Cons(z1, Cons(z2, z3))) -> c19(MERGE#2(z1, z2))
   CONST_F#2(Cons(x0, Cons(x1, Cons(x2, x3))), Cons(z1, Cons(z2, z3))) -> c19(MERGE#2(z1, z2))
   CONST_F#2(Cons(x0, Cons(x1, Nil)), Cons(z1, Cons(z2, z3))) -> c19(MERGE#2(z1, z2))
   CONST_F#2(Cons(x0, Cons(x1, Cons(x2, Nil))), Cons(z1, Cons(z2, z3))) -> c19(MERGE#2(z1, z2))
   CONST_F#2(Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4)))), Cons(z1, Cons(z2, z3))) -> c19(MERGE#2(z1, z2))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> c9(CONST_F#2(Cons(z0, Cons(z1, z2)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(halve#1(length#1(z2)), Cons(z1, z2)), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(halve#1(length#1(z2)), Cons(z1, z2)), Nil))), DIVIDE_YS#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2)))), HALVE#1(length#1(z2)), LENGTH#1(z2))
   COND_MERGE_YS_ZS_2(True, Cons(0, Cons(0, z5)), Cons(x1, x2), 0, Cons(0, z5), x1, x2) -> c2(MERGE#2(Cons(0, z5), Cons(x1, x2)))
   COND_MERGE_YS_ZS_2(True, Cons(S(0), Cons(0, z5)), Cons(S(x1), x2), S(0), Cons(0, z5), S(x1), x2) -> c2(MERGE#2(Cons(0, z5), Cons(S(x1), x2)))
   COND_MERGE_YS_ZS_2(True, Cons(S(S(x0)), Cons(0, z5)), Cons(S(S(x2)), x3), S(S(x0)), Cons(0, z5), S(S(x2)), x3) -> c2(MERGE#2(Cons(0, z5), Cons(S(S(x2)), x3)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, z3)))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Cons(z2, z3))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(Cons(z2, z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Cons(drop#2(S(halve#1(S(length#1(z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3)))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(S(length#1(z3))))), HALVE#1(S(length#1(z3))), LENGTH#1(Cons(z2, z3)))
   COND_MERGE_YS_ZS_2(True, Cons(0, Cons(S(z4), z5)), Cons(0, x2), 0, Cons(S(z4), z5), 0, x2) -> c2(MERGE#2(Cons(S(z4), z5), Cons(0, x2)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> c9(CONST_F#2(Cons(z0, Cons(z1, z2)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(Cons(z0, take#2(halve#1(length#1(z2)), Cons(z1, z2))), Cons(drop#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(halve#1(length#1(z2)), Cons(z1, z2)), Nil))), DIVIDE_YS#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2)))), HALVE#1(length#1(z2)), LENGTH#1(z2))
   COND_MERGE_YS_ZS_2(True, Cons(0, Cons(S(0), z5)), Cons(S(z2), x2), 0, Cons(S(0), z5), S(z2), x2) -> c2(MERGE#2(Cons(S(0), z5), Cons(S(z2), x2)))
   COND_MERGE_YS_ZS_2(True, Cons(S(0), Cons(S(0), z5)), Cons(S(x1), x2), S(0), Cons(S(0), z5), S(x1), x2) -> c2(MERGE#2(Cons(S(0), z5), Cons(S(x1), x2)))
   COND_MERGE_YS_ZS_2(True, Cons(S(S(x0)), Cons(S(0), z5)), Cons(S(S(x2)), x3), S(S(x0)), Cons(S(0), z5), S(S(x2)), x3) -> c2(MERGE#2(Cons(S(0), z5), Cons(S(S(x2)), x3)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, z3)))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Cons(z2, z3))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(S(length#1(z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Cons(drop#2(S(halve#1(length#1(Cons(z2, z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3)))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(S(length#1(z3))))), HALVE#1(S(length#1(z3))), LENGTH#1(Cons(z2, z3)))
   COND_MERGE_YS_ZS_2(True, Cons(0, Cons(S(S(z4)), z5)), Cons(S(0), x2), 0, Cons(S(S(z4)), z5), S(0), x2) -> c2(MERGE#2(Cons(S(S(z4)), z5), Cons(S(0), x2)))
   COND_MERGE_YS_ZS_2(True, Cons(S(0), Cons(S(S(z4)), z5)), Cons(S(0), x2), S(0), Cons(S(S(z4)), z5), S(0), x2) -> c2(MERGE#2(Cons(S(S(z4)), z5), Cons(S(0), x2)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> c9(MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(halve#1(length#1(z2)), Cons(z1, z2)), Nil))), DIVIDE_YS#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2)))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Nil))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(Nil))), Cons(z0, Cons(z1, Nil))), Cons(drop#2(S(halve#1(0)), Cons(z0, Cons(z1, Nil))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Nil)), S(halve#1(0))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Nil))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(0)), Cons(z0, Cons(z1, Nil))), Cons(drop#2(S(halve#1(length#1(Nil))), Cons(z0, Cons(z1, Nil))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Nil)), S(halve#1(0))))
   DROP#2(S(S(y0)), Cons(z1, Cons(y1, y2))) -> c12(DROP#2(S(y0), Cons(y1, y2)))
   COND_MERGE_YS_ZS_2(True, Cons(0, Cons(S(S(z5)), z6)), Cons(S(S(z2)), x2), 0, Cons(S(S(z5)), z6), S(S(z2)), x2) -> c2(MERGE#2(Cons(S(S(z5)), z6), Cons(S(S(z2)), x2)))
   COND_MERGE_YS_ZS_2(True, Cons(S(0), Cons(S(S(z5)), z6)), Cons(S(S(z2)), x2), S(0), Cons(S(S(z5)), z6), S(S(z2)), x2) -> c2(MERGE#2(Cons(S(S(z5)), z6), Cons(S(S(z2)), x2)))
   COND_MERGE_YS_ZS_2(True, Cons(S(S(x0)), Cons(S(S(z5)), z6)), Cons(S(S(x2)), x3), S(S(x0)), Cons(S(S(z5)), z6), S(S(x2)), x3) -> c2(MERGE#2(Cons(S(S(z5)), z6), Cons(S(S(x2)), x3)))
   COND_MERGE_YS_ZS_2(True, Cons(0, Cons(S(z5), z6)), Cons(S(z2), x2), 0, Cons(S(z5), z6), S(z2), x2) -> c2(MERGE#2(Cons(S(z5), z6), Cons(S(z2), x2)))
   COND_MERGE_YS_ZS_2(True, Cons(S(0), Cons(S(z5), z6)), Cons(S(x1), x2), S(0), Cons(S(z5), z6), S(x1), x2) -> c2(MERGE#2(Cons(S(z5), z6), Cons(S(x1), x2)))
   COND_MERGE_YS_ZS_2(True, Cons(S(S(x0)), Cons(S(z5), z6)), Cons(S(S(x2)), x3), S(S(x0)), Cons(S(z5), z6), S(S(x2)), x3) -> c2(MERGE#2(Cons(S(z5), z6), Cons(S(S(x2)), x3)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, z3)))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Cons(z2, z3))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(S(length#1(z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Cons(drop#2(S(halve#1(S(length#1(z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3)))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(S(length#1(z3))))), HALVE#1(S(length#1(z3))), LENGTH#1(Cons(z2, z3)))
   TAKE#2(S(S(y0)), Cons(z1, Cons(y1, y2))) -> c15(TAKE#2(S(y0), Cons(y1, y2)))
   HALVE#1(S(S(S(S(y0))))) -> c18(HALVE#1(S(S(y0))))
   LEQ#2(S(S(y0)), S(S(y1))) -> c22(LEQ#2(S(y0), S(y1)))
   MERGE#2(Cons(S(0), x1), Cons(S(z0), x3)) -> c6(COND_MERGE_YS_ZS_2(True, Cons(S(0), x1), Cons(S(z0), x3), S(0), x1, S(z0), x3))
   MERGE#2(Cons(S(S(z0)), x1), Cons(S(0), x3)) -> c6(COND_MERGE_YS_ZS_2(False, Cons(S(S(z0)), x1), Cons(S(0), x3), S(S(z0)), x1, S(0), x3))
K tuples:none
Defined Rule Symbols:   leq#2_2, map#2_2, divide_ys#1_2, halve#1_1, length#1_1, take#2_2, drop#2_2, dc#1_6, const_f#2_2, merge#2_2, cond_merge_ys_zs_2_7

Defined Pair Symbols:   LENGTH#1_1, MAP#2_2, MERGE#2_2, DIVIDE_YS#1_2, COND_MERGE_YS_ZS_2_7, DC#1_6, CONST_F#2_2, DROP#2_2, TAKE#2_2, HALVE#1_1, LEQ#2_2

Compound Symbols:   c24_1, c26_1, c27_1, c6_1, c6_2, c_1, c1_1, c3_1, c9_5, c9_4, c9_3, c19_1, c2_1, c9_2, c12_1, c15_1, c18_1, c22_1


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

(187) CdtRewritingProof (BOTH BOUNDS(ID, ID))
Used rewriting to replace DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, Nil)))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Cons(z2, Nil))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, Nil))), S(halve#1(S(0)))))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, Nil))), S(halve#1(length#1(Cons(z2, Nil)))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, Nil))), S(halve#1(length#1(Cons(z2, Nil))))), HALVE#1(S(length#1(Nil))), LENGTH#1(Cons(z2, Nil))) by DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, Nil)))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Cons(z2, Nil))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, Nil))), S(halve#1(S(0)))))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, Nil))), S(halve#1(length#1(Cons(z2, Nil)))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, Nil))), S(halve#1(length#1(Cons(z2, Nil))))), HALVE#1(S(0)), LENGTH#1(Cons(z2, Nil)))
----------------------------------------

(188)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   leq#2(0, z0) -> True
   leq#2(S(z0), 0) -> False
   leq#2(S(z0), S(z1)) -> leq#2(z0, z1)
   map#2(dc(z0, z1, z2, z3, z4), Nil) -> Nil
   map#2(dc(z0, z1, z2, z3, z4), Cons(z5, z6)) -> Cons(dc#1(z0, z1, z2, z3, z4, z5), map#2(dc(z0, z1, z2, z3, z4), z6))
   divide_ys#1(z0, z1) -> Cons(take#2(z1, z0), Cons(drop#2(z1, z0), Nil))
   halve#1(0) -> 0
   halve#1(S(0)) -> S(0)
   halve#1(S(S(z0))) -> S(halve#1(z0))
   length#1(Nil) -> 0
   length#1(Cons(z0, z1)) -> S(length#1(z1))
   take#2(0, z0) -> Nil
   take#2(S(0), Nil) -> Cons(bot[0], Nil)
   take#2(S(z0), Cons(z1, z2)) -> Cons(z1, take#2(z0, z2))
   drop#2(0, z0) -> z0
   drop#2(S(0), Nil) -> bot[1]
   drop#2(S(z0), Cons(z1, z2)) -> drop#2(z0, z2)
   dc#1(map, divisible, mergesort_zs_3, divide, const_f, Nil) -> Nil
   dc#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Nil)) -> Cons(z0, Nil)
   dc#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> const_f#2(Cons(z0, Cons(z1, z2)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2))))))
   const_f#2(z0, Cons(z1, Cons(z2, z3))) -> merge#2(z1, z2)
   merge#2(Nil, z0) -> z0
   merge#2(Cons(z0, z1), Nil) -> Cons(z0, z1)
   merge#2(Cons(z0, z1), Cons(z2, z3)) -> cond_merge_ys_zs_2(leq#2(z0, z2), Cons(z0, z1), Cons(z2, z3), z0, z1, z2, z3)
   cond_merge_ys_zs_2(True, Cons(z0, z1), Cons(z2, z3), z4, z5, z6, z7) -> Cons(z4, merge#2(z5, Cons(z2, z3)))
   cond_merge_ys_zs_2(False, Cons(z0, z1), Cons(z2, z3), z4, z5, z6, z7) -> Cons(z6, merge#2(Cons(z0, z1), z7))
Tuples:
   LENGTH#1(Cons(z0, z1)) -> c24(LENGTH#1(z1))
   MAP#2(dc(z0, z1, z2, z3, z4), Cons(z5, z6)) -> c26(DC#1(z0, z1, z2, z3, z4, z5))
   MAP#2(dc(z0, z1, z2, z3, z4), Cons(z5, z6)) -> c27(MAP#2(dc(z0, z1, z2, z3, z4), z6))
   MERGE#2(Cons(0, x1), Cons(z0, x3)) -> c6(COND_MERGE_YS_ZS_2(True, Cons(0, x1), Cons(z0, x3), 0, x1, z0, x3))
   MERGE#2(Cons(S(z0), x1), Cons(0, x3)) -> c6(COND_MERGE_YS_ZS_2(False, Cons(S(z0), x1), Cons(0, x3), S(z0), x1, 0, x3))
   MERGE#2(Cons(S(S(z0)), x1), Cons(S(S(z1)), x3)) -> c6(COND_MERGE_YS_ZS_2(leq#2(z0, z1), Cons(S(S(z0)), x1), Cons(S(S(z1)), x3), S(S(z0)), x1, S(S(z1)), x3), LEQ#2(S(S(z0)), S(S(z1))))
   MERGE#2(Cons(S(x0), x1), Cons(S(x2), x3)) -> c6(LEQ#2(S(x0), S(x2)))
   DIVIDE_YS#1(Cons(x0, Cons(x1, x2)), S(y11)) -> c(TAKE#2(S(y11), Cons(x0, Cons(x1, x2))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, x3))), S(y11)) -> c(TAKE#2(S(y11), Cons(x0, Cons(x1, Cons(x2, x3)))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Nil)), S(y10)) -> c(TAKE#2(S(y10), Cons(x0, Cons(x1, Nil))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Nil))), S(y7)) -> c(TAKE#2(S(y7), Cons(x0, Cons(x1, Cons(x2, Nil)))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4)))), S(y8)) -> c(TAKE#2(S(y8), Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4))))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, x2)), S(y11)) -> c1(DROP#2(S(y11), Cons(x0, Cons(x1, x2))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, x3))), S(y11)) -> c1(DROP#2(S(y11), Cons(x0, Cons(x1, Cons(x2, x3)))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Nil)), S(y10)) -> c1(DROP#2(S(y10), Cons(x0, Cons(x1, Nil))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Nil))), S(y7)) -> c1(DROP#2(S(y7), Cons(x0, Cons(x1, Cons(x2, Nil)))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4)))), S(y8)) -> c1(DROP#2(S(y8), Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4))))))
   COND_MERGE_YS_ZS_2(False, Cons(S(x0), x1), Cons(0, x2), S(x0), x1, 0, x2) -> c3(MERGE#2(Cons(S(x0), x1), x2))
   COND_MERGE_YS_ZS_2(False, Cons(S(S(x0)), x1), Cons(S(0), x2), S(S(x0)), x1, S(0), x2) -> c3(MERGE#2(Cons(S(S(x0)), x1), x2))
   COND_MERGE_YS_ZS_2(False, Cons(S(S(x0)), x1), Cons(S(S(x2)), x3), S(S(x0)), x1, S(S(x2)), x3) -> c3(MERGE#2(Cons(S(S(x0)), x1), x3))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, Cons(z3, z4))))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Cons(z2, Cons(z3, z4)))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, Cons(z3, z4)))), S(halve#1(S(S(length#1(z4)))))))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, Cons(z3, z4)))), S(halve#1(length#1(Cons(z2, Cons(z3, z4))))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, Cons(z3, z4)))), S(halve#1(length#1(Cons(z2, Cons(z3, z4)))))), HALVE#1(S(length#1(Cons(z3, z4)))), LENGTH#1(Cons(z2, Cons(z3, z4))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, z3)))) -> c9(MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3)))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3))))), HALVE#1(S(length#1(z3))), LENGTH#1(Cons(z2, z3)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Nil))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(0)), Cons(z0, Cons(z1, Nil))), Cons(drop#2(S(halve#1(0)), Cons(z0, Cons(z1, Nil))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil)))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Nil))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Nil)), S(0)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil)))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> c9(CONST_F#2(Cons(z0, Cons(z1, z2)), Cons(dc#1(map, divisible, mergesort_zs_3, divide, const_f, take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2)))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(drop#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(halve#1(length#1(z2)), Cons(z1, z2)), Nil))), DIVIDE_YS#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2)))), HALVE#1(length#1(z2)), LENGTH#1(z2))
   CONST_F#2(Cons(x0, Cons(x1, x2)), Cons(z1, Cons(z2, z3))) -> c19(MERGE#2(z1, z2))
   CONST_F#2(Cons(x0, Cons(x1, Cons(x2, x3))), Cons(z1, Cons(z2, z3))) -> c19(MERGE#2(z1, z2))
   CONST_F#2(Cons(x0, Cons(x1, Nil)), Cons(z1, Cons(z2, z3))) -> c19(MERGE#2(z1, z2))
   CONST_F#2(Cons(x0, Cons(x1, Cons(x2, Nil))), Cons(z1, Cons(z2, z3))) -> c19(MERGE#2(z1, z2))
   CONST_F#2(Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4)))), Cons(z1, Cons(z2, z3))) -> c19(MERGE#2(z1, z2))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> c9(CONST_F#2(Cons(z0, Cons(z1, z2)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(halve#1(length#1(z2)), Cons(z1, z2)), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(halve#1(length#1(z2)), Cons(z1, z2)), Nil))), DIVIDE_YS#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2)))), HALVE#1(length#1(z2)), LENGTH#1(z2))
   COND_MERGE_YS_ZS_2(True, Cons(0, Cons(0, z5)), Cons(x1, x2), 0, Cons(0, z5), x1, x2) -> c2(MERGE#2(Cons(0, z5), Cons(x1, x2)))
   COND_MERGE_YS_ZS_2(True, Cons(S(0), Cons(0, z5)), Cons(S(x1), x2), S(0), Cons(0, z5), S(x1), x2) -> c2(MERGE#2(Cons(0, z5), Cons(S(x1), x2)))
   COND_MERGE_YS_ZS_2(True, Cons(S(S(x0)), Cons(0, z5)), Cons(S(S(x2)), x3), S(S(x0)), Cons(0, z5), S(S(x2)), x3) -> c2(MERGE#2(Cons(0, z5), Cons(S(S(x2)), x3)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, z3)))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Cons(z2, z3))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(Cons(z2, z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Cons(drop#2(S(halve#1(S(length#1(z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3)))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(S(length#1(z3))))), HALVE#1(S(length#1(z3))), LENGTH#1(Cons(z2, z3)))
   COND_MERGE_YS_ZS_2(True, Cons(0, Cons(S(z4), z5)), Cons(0, x2), 0, Cons(S(z4), z5), 0, x2) -> c2(MERGE#2(Cons(S(z4), z5), Cons(0, x2)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> c9(CONST_F#2(Cons(z0, Cons(z1, z2)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(Cons(z0, take#2(halve#1(length#1(z2)), Cons(z1, z2))), Cons(drop#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(halve#1(length#1(z2)), Cons(z1, z2)), Nil))), DIVIDE_YS#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2)))), HALVE#1(length#1(z2)), LENGTH#1(z2))
   COND_MERGE_YS_ZS_2(True, Cons(0, Cons(S(0), z5)), Cons(S(z2), x2), 0, Cons(S(0), z5), S(z2), x2) -> c2(MERGE#2(Cons(S(0), z5), Cons(S(z2), x2)))
   COND_MERGE_YS_ZS_2(True, Cons(S(0), Cons(S(0), z5)), Cons(S(x1), x2), S(0), Cons(S(0), z5), S(x1), x2) -> c2(MERGE#2(Cons(S(0), z5), Cons(S(x1), x2)))
   COND_MERGE_YS_ZS_2(True, Cons(S(S(x0)), Cons(S(0), z5)), Cons(S(S(x2)), x3), S(S(x0)), Cons(S(0), z5), S(S(x2)), x3) -> c2(MERGE#2(Cons(S(0), z5), Cons(S(S(x2)), x3)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, z3)))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Cons(z2, z3))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(S(length#1(z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Cons(drop#2(S(halve#1(length#1(Cons(z2, z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3)))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(S(length#1(z3))))), HALVE#1(S(length#1(z3))), LENGTH#1(Cons(z2, z3)))
   COND_MERGE_YS_ZS_2(True, Cons(0, Cons(S(S(z4)), z5)), Cons(S(0), x2), 0, Cons(S(S(z4)), z5), S(0), x2) -> c2(MERGE#2(Cons(S(S(z4)), z5), Cons(S(0), x2)))
   COND_MERGE_YS_ZS_2(True, Cons(S(0), Cons(S(S(z4)), z5)), Cons(S(0), x2), S(0), Cons(S(S(z4)), z5), S(0), x2) -> c2(MERGE#2(Cons(S(S(z4)), z5), Cons(S(0), x2)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> c9(MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(halve#1(length#1(z2)), Cons(z1, z2)), Nil))), DIVIDE_YS#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2)))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Nil))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(Nil))), Cons(z0, Cons(z1, Nil))), Cons(drop#2(S(halve#1(0)), Cons(z0, Cons(z1, Nil))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Nil)), S(halve#1(0))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Nil))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(0)), Cons(z0, Cons(z1, Nil))), Cons(drop#2(S(halve#1(length#1(Nil))), Cons(z0, Cons(z1, Nil))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Nil)), S(halve#1(0))))
   DROP#2(S(S(y0)), Cons(z1, Cons(y1, y2))) -> c12(DROP#2(S(y0), Cons(y1, y2)))
   COND_MERGE_YS_ZS_2(True, Cons(0, Cons(S(S(z5)), z6)), Cons(S(S(z2)), x2), 0, Cons(S(S(z5)), z6), S(S(z2)), x2) -> c2(MERGE#2(Cons(S(S(z5)), z6), Cons(S(S(z2)), x2)))
   COND_MERGE_YS_ZS_2(True, Cons(S(0), Cons(S(S(z5)), z6)), Cons(S(S(z2)), x2), S(0), Cons(S(S(z5)), z6), S(S(z2)), x2) -> c2(MERGE#2(Cons(S(S(z5)), z6), Cons(S(S(z2)), x2)))
   COND_MERGE_YS_ZS_2(True, Cons(S(S(x0)), Cons(S(S(z5)), z6)), Cons(S(S(x2)), x3), S(S(x0)), Cons(S(S(z5)), z6), S(S(x2)), x3) -> c2(MERGE#2(Cons(S(S(z5)), z6), Cons(S(S(x2)), x3)))
   COND_MERGE_YS_ZS_2(True, Cons(0, Cons(S(z5), z6)), Cons(S(z2), x2), 0, Cons(S(z5), z6), S(z2), x2) -> c2(MERGE#2(Cons(S(z5), z6), Cons(S(z2), x2)))
   COND_MERGE_YS_ZS_2(True, Cons(S(0), Cons(S(z5), z6)), Cons(S(x1), x2), S(0), Cons(S(z5), z6), S(x1), x2) -> c2(MERGE#2(Cons(S(z5), z6), Cons(S(x1), x2)))
   COND_MERGE_YS_ZS_2(True, Cons(S(S(x0)), Cons(S(z5), z6)), Cons(S(S(x2)), x3), S(S(x0)), Cons(S(z5), z6), S(S(x2)), x3) -> c2(MERGE#2(Cons(S(z5), z6), Cons(S(S(x2)), x3)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, z3)))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Cons(z2, z3))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(S(length#1(z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Cons(drop#2(S(halve#1(S(length#1(z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3)))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(S(length#1(z3))))), HALVE#1(S(length#1(z3))), LENGTH#1(Cons(z2, z3)))
   TAKE#2(S(S(y0)), Cons(z1, Cons(y1, y2))) -> c15(TAKE#2(S(y0), Cons(y1, y2)))
   HALVE#1(S(S(S(S(y0))))) -> c18(HALVE#1(S(S(y0))))
   LEQ#2(S(S(y0)), S(S(y1))) -> c22(LEQ#2(S(y0), S(y1)))
   MERGE#2(Cons(S(0), x1), Cons(S(z0), x3)) -> c6(COND_MERGE_YS_ZS_2(True, Cons(S(0), x1), Cons(S(z0), x3), S(0), x1, S(z0), x3))
   MERGE#2(Cons(S(S(z0)), x1), Cons(S(0), x3)) -> c6(COND_MERGE_YS_ZS_2(False, Cons(S(S(z0)), x1), Cons(S(0), x3), S(S(z0)), x1, S(0), x3))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, Nil)))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Cons(z2, Nil))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, Nil))), S(halve#1(S(0)))))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, Nil))), S(halve#1(length#1(Cons(z2, Nil)))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, Nil))), S(halve#1(length#1(Cons(z2, Nil))))), HALVE#1(S(0)), LENGTH#1(Cons(z2, Nil)))
S tuples:
   LENGTH#1(Cons(z0, z1)) -> c24(LENGTH#1(z1))
   MAP#2(dc(z0, z1, z2, z3, z4), Cons(z5, z6)) -> c26(DC#1(z0, z1, z2, z3, z4, z5))
   MAP#2(dc(z0, z1, z2, z3, z4), Cons(z5, z6)) -> c27(MAP#2(dc(z0, z1, z2, z3, z4), z6))
   MERGE#2(Cons(0, x1), Cons(z0, x3)) -> c6(COND_MERGE_YS_ZS_2(True, Cons(0, x1), Cons(z0, x3), 0, x1, z0, x3))
   MERGE#2(Cons(S(z0), x1), Cons(0, x3)) -> c6(COND_MERGE_YS_ZS_2(False, Cons(S(z0), x1), Cons(0, x3), S(z0), x1, 0, x3))
   MERGE#2(Cons(S(S(z0)), x1), Cons(S(S(z1)), x3)) -> c6(COND_MERGE_YS_ZS_2(leq#2(z0, z1), Cons(S(S(z0)), x1), Cons(S(S(z1)), x3), S(S(z0)), x1, S(S(z1)), x3), LEQ#2(S(S(z0)), S(S(z1))))
   MERGE#2(Cons(S(x0), x1), Cons(S(x2), x3)) -> c6(LEQ#2(S(x0), S(x2)))
   DIVIDE_YS#1(Cons(x0, Cons(x1, x2)), S(y11)) -> c(TAKE#2(S(y11), Cons(x0, Cons(x1, x2))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, x3))), S(y11)) -> c(TAKE#2(S(y11), Cons(x0, Cons(x1, Cons(x2, x3)))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Nil)), S(y10)) -> c(TAKE#2(S(y10), Cons(x0, Cons(x1, Nil))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Nil))), S(y7)) -> c(TAKE#2(S(y7), Cons(x0, Cons(x1, Cons(x2, Nil)))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4)))), S(y8)) -> c(TAKE#2(S(y8), Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4))))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, x2)), S(y11)) -> c1(DROP#2(S(y11), Cons(x0, Cons(x1, x2))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, x3))), S(y11)) -> c1(DROP#2(S(y11), Cons(x0, Cons(x1, Cons(x2, x3)))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Nil)), S(y10)) -> c1(DROP#2(S(y10), Cons(x0, Cons(x1, Nil))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Nil))), S(y7)) -> c1(DROP#2(S(y7), Cons(x0, Cons(x1, Cons(x2, Nil)))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4)))), S(y8)) -> c1(DROP#2(S(y8), Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4))))))
   COND_MERGE_YS_ZS_2(False, Cons(S(x0), x1), Cons(0, x2), S(x0), x1, 0, x2) -> c3(MERGE#2(Cons(S(x0), x1), x2))
   COND_MERGE_YS_ZS_2(False, Cons(S(S(x0)), x1), Cons(S(0), x2), S(S(x0)), x1, S(0), x2) -> c3(MERGE#2(Cons(S(S(x0)), x1), x2))
   COND_MERGE_YS_ZS_2(False, Cons(S(S(x0)), x1), Cons(S(S(x2)), x3), S(S(x0)), x1, S(S(x2)), x3) -> c3(MERGE#2(Cons(S(S(x0)), x1), x3))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, Cons(z3, z4))))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Cons(z2, Cons(z3, z4)))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, Cons(z3, z4)))), S(halve#1(S(S(length#1(z4)))))))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, Cons(z3, z4)))), S(halve#1(length#1(Cons(z2, Cons(z3, z4))))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, Cons(z3, z4)))), S(halve#1(length#1(Cons(z2, Cons(z3, z4)))))), HALVE#1(S(length#1(Cons(z3, z4)))), LENGTH#1(Cons(z2, Cons(z3, z4))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, z3)))) -> c9(MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3)))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3))))), HALVE#1(S(length#1(z3))), LENGTH#1(Cons(z2, z3)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Nil))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(0)), Cons(z0, Cons(z1, Nil))), Cons(drop#2(S(halve#1(0)), Cons(z0, Cons(z1, Nil))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil)))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Nil))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Nil)), S(0)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil)))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> c9(CONST_F#2(Cons(z0, Cons(z1, z2)), Cons(dc#1(map, divisible, mergesort_zs_3, divide, const_f, take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2)))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(drop#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(halve#1(length#1(z2)), Cons(z1, z2)), Nil))), DIVIDE_YS#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2)))), HALVE#1(length#1(z2)), LENGTH#1(z2))
   CONST_F#2(Cons(x0, Cons(x1, x2)), Cons(z1, Cons(z2, z3))) -> c19(MERGE#2(z1, z2))
   CONST_F#2(Cons(x0, Cons(x1, Cons(x2, x3))), Cons(z1, Cons(z2, z3))) -> c19(MERGE#2(z1, z2))
   CONST_F#2(Cons(x0, Cons(x1, Nil)), Cons(z1, Cons(z2, z3))) -> c19(MERGE#2(z1, z2))
   CONST_F#2(Cons(x0, Cons(x1, Cons(x2, Nil))), Cons(z1, Cons(z2, z3))) -> c19(MERGE#2(z1, z2))
   CONST_F#2(Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4)))), Cons(z1, Cons(z2, z3))) -> c19(MERGE#2(z1, z2))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> c9(CONST_F#2(Cons(z0, Cons(z1, z2)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(halve#1(length#1(z2)), Cons(z1, z2)), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(halve#1(length#1(z2)), Cons(z1, z2)), Nil))), DIVIDE_YS#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2)))), HALVE#1(length#1(z2)), LENGTH#1(z2))
   COND_MERGE_YS_ZS_2(True, Cons(0, Cons(0, z5)), Cons(x1, x2), 0, Cons(0, z5), x1, x2) -> c2(MERGE#2(Cons(0, z5), Cons(x1, x2)))
   COND_MERGE_YS_ZS_2(True, Cons(S(0), Cons(0, z5)), Cons(S(x1), x2), S(0), Cons(0, z5), S(x1), x2) -> c2(MERGE#2(Cons(0, z5), Cons(S(x1), x2)))
   COND_MERGE_YS_ZS_2(True, Cons(S(S(x0)), Cons(0, z5)), Cons(S(S(x2)), x3), S(S(x0)), Cons(0, z5), S(S(x2)), x3) -> c2(MERGE#2(Cons(0, z5), Cons(S(S(x2)), x3)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, z3)))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Cons(z2, z3))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(Cons(z2, z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Cons(drop#2(S(halve#1(S(length#1(z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3)))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(S(length#1(z3))))), HALVE#1(S(length#1(z3))), LENGTH#1(Cons(z2, z3)))
   COND_MERGE_YS_ZS_2(True, Cons(0, Cons(S(z4), z5)), Cons(0, x2), 0, Cons(S(z4), z5), 0, x2) -> c2(MERGE#2(Cons(S(z4), z5), Cons(0, x2)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> c9(CONST_F#2(Cons(z0, Cons(z1, z2)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(Cons(z0, take#2(halve#1(length#1(z2)), Cons(z1, z2))), Cons(drop#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(halve#1(length#1(z2)), Cons(z1, z2)), Nil))), DIVIDE_YS#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2)))), HALVE#1(length#1(z2)), LENGTH#1(z2))
   COND_MERGE_YS_ZS_2(True, Cons(0, Cons(S(0), z5)), Cons(S(z2), x2), 0, Cons(S(0), z5), S(z2), x2) -> c2(MERGE#2(Cons(S(0), z5), Cons(S(z2), x2)))
   COND_MERGE_YS_ZS_2(True, Cons(S(0), Cons(S(0), z5)), Cons(S(x1), x2), S(0), Cons(S(0), z5), S(x1), x2) -> c2(MERGE#2(Cons(S(0), z5), Cons(S(x1), x2)))
   COND_MERGE_YS_ZS_2(True, Cons(S(S(x0)), Cons(S(0), z5)), Cons(S(S(x2)), x3), S(S(x0)), Cons(S(0), z5), S(S(x2)), x3) -> c2(MERGE#2(Cons(S(0), z5), Cons(S(S(x2)), x3)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, z3)))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Cons(z2, z3))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(S(length#1(z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Cons(drop#2(S(halve#1(length#1(Cons(z2, z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3)))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(S(length#1(z3))))), HALVE#1(S(length#1(z3))), LENGTH#1(Cons(z2, z3)))
   COND_MERGE_YS_ZS_2(True, Cons(0, Cons(S(S(z4)), z5)), Cons(S(0), x2), 0, Cons(S(S(z4)), z5), S(0), x2) -> c2(MERGE#2(Cons(S(S(z4)), z5), Cons(S(0), x2)))
   COND_MERGE_YS_ZS_2(True, Cons(S(0), Cons(S(S(z4)), z5)), Cons(S(0), x2), S(0), Cons(S(S(z4)), z5), S(0), x2) -> c2(MERGE#2(Cons(S(S(z4)), z5), Cons(S(0), x2)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> c9(MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(halve#1(length#1(z2)), Cons(z1, z2)), Nil))), DIVIDE_YS#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2)))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Nil))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(Nil))), Cons(z0, Cons(z1, Nil))), Cons(drop#2(S(halve#1(0)), Cons(z0, Cons(z1, Nil))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Nil)), S(halve#1(0))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Nil))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(0)), Cons(z0, Cons(z1, Nil))), Cons(drop#2(S(halve#1(length#1(Nil))), Cons(z0, Cons(z1, Nil))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Nil)), S(halve#1(0))))
   DROP#2(S(S(y0)), Cons(z1, Cons(y1, y2))) -> c12(DROP#2(S(y0), Cons(y1, y2)))
   COND_MERGE_YS_ZS_2(True, Cons(0, Cons(S(S(z5)), z6)), Cons(S(S(z2)), x2), 0, Cons(S(S(z5)), z6), S(S(z2)), x2) -> c2(MERGE#2(Cons(S(S(z5)), z6), Cons(S(S(z2)), x2)))
   COND_MERGE_YS_ZS_2(True, Cons(S(0), Cons(S(S(z5)), z6)), Cons(S(S(z2)), x2), S(0), Cons(S(S(z5)), z6), S(S(z2)), x2) -> c2(MERGE#2(Cons(S(S(z5)), z6), Cons(S(S(z2)), x2)))
   COND_MERGE_YS_ZS_2(True, Cons(S(S(x0)), Cons(S(S(z5)), z6)), Cons(S(S(x2)), x3), S(S(x0)), Cons(S(S(z5)), z6), S(S(x2)), x3) -> c2(MERGE#2(Cons(S(S(z5)), z6), Cons(S(S(x2)), x3)))
   COND_MERGE_YS_ZS_2(True, Cons(0, Cons(S(z5), z6)), Cons(S(z2), x2), 0, Cons(S(z5), z6), S(z2), x2) -> c2(MERGE#2(Cons(S(z5), z6), Cons(S(z2), x2)))
   COND_MERGE_YS_ZS_2(True, Cons(S(0), Cons(S(z5), z6)), Cons(S(x1), x2), S(0), Cons(S(z5), z6), S(x1), x2) -> c2(MERGE#2(Cons(S(z5), z6), Cons(S(x1), x2)))
   COND_MERGE_YS_ZS_2(True, Cons(S(S(x0)), Cons(S(z5), z6)), Cons(S(S(x2)), x3), S(S(x0)), Cons(S(z5), z6), S(S(x2)), x3) -> c2(MERGE#2(Cons(S(z5), z6), Cons(S(S(x2)), x3)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, z3)))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Cons(z2, z3))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(S(length#1(z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Cons(drop#2(S(halve#1(S(length#1(z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3)))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(S(length#1(z3))))), HALVE#1(S(length#1(z3))), LENGTH#1(Cons(z2, z3)))
   TAKE#2(S(S(y0)), Cons(z1, Cons(y1, y2))) -> c15(TAKE#2(S(y0), Cons(y1, y2)))
   HALVE#1(S(S(S(S(y0))))) -> c18(HALVE#1(S(S(y0))))
   LEQ#2(S(S(y0)), S(S(y1))) -> c22(LEQ#2(S(y0), S(y1)))
   MERGE#2(Cons(S(0), x1), Cons(S(z0), x3)) -> c6(COND_MERGE_YS_ZS_2(True, Cons(S(0), x1), Cons(S(z0), x3), S(0), x1, S(z0), x3))
   MERGE#2(Cons(S(S(z0)), x1), Cons(S(0), x3)) -> c6(COND_MERGE_YS_ZS_2(False, Cons(S(S(z0)), x1), Cons(S(0), x3), S(S(z0)), x1, S(0), x3))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, Nil)))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Cons(z2, Nil))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, Nil))), S(halve#1(S(0)))))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, Nil))), S(halve#1(length#1(Cons(z2, Nil)))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, Nil))), S(halve#1(length#1(Cons(z2, Nil))))), HALVE#1(S(0)), LENGTH#1(Cons(z2, Nil)))
K tuples:none
Defined Rule Symbols:   leq#2_2, map#2_2, divide_ys#1_2, halve#1_1, length#1_1, take#2_2, drop#2_2, dc#1_6, const_f#2_2, merge#2_2, cond_merge_ys_zs_2_7

Defined Pair Symbols:   LENGTH#1_1, MAP#2_2, MERGE#2_2, DIVIDE_YS#1_2, COND_MERGE_YS_ZS_2_7, DC#1_6, CONST_F#2_2, DROP#2_2, TAKE#2_2, HALVE#1_1, LEQ#2_2

Compound Symbols:   c24_1, c26_1, c27_1, c6_1, c6_2, c_1, c1_1, c3_1, c9_5, c9_4, c9_3, c19_1, c2_1, c9_2, c12_1, c15_1, c18_1, c22_1


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

(190)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   leq#2(0, z0) -> True
   leq#2(S(z0), 0) -> False
   leq#2(S(z0), S(z1)) -> leq#2(z0, z1)
   map#2(dc(z0, z1, z2, z3, z4), Nil) -> Nil
   map#2(dc(z0, z1, z2, z3, z4), Cons(z5, z6)) -> Cons(dc#1(z0, z1, z2, z3, z4, z5), map#2(dc(z0, z1, z2, z3, z4), z6))
   divide_ys#1(z0, z1) -> Cons(take#2(z1, z0), Cons(drop#2(z1, z0), Nil))
   halve#1(0) -> 0
   halve#1(S(0)) -> S(0)
   halve#1(S(S(z0))) -> S(halve#1(z0))
   length#1(Nil) -> 0
   length#1(Cons(z0, z1)) -> S(length#1(z1))
   take#2(0, z0) -> Nil
   take#2(S(0), Nil) -> Cons(bot[0], Nil)
   take#2(S(z0), Cons(z1, z2)) -> Cons(z1, take#2(z0, z2))
   drop#2(0, z0) -> z0
   drop#2(S(0), Nil) -> bot[1]
   drop#2(S(z0), Cons(z1, z2)) -> drop#2(z0, z2)
   dc#1(map, divisible, mergesort_zs_3, divide, const_f, Nil) -> Nil
   dc#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Nil)) -> Cons(z0, Nil)
   dc#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> const_f#2(Cons(z0, Cons(z1, z2)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2))))))
   const_f#2(z0, Cons(z1, Cons(z2, z3))) -> merge#2(z1, z2)
   merge#2(Nil, z0) -> z0
   merge#2(Cons(z0, z1), Nil) -> Cons(z0, z1)
   merge#2(Cons(z0, z1), Cons(z2, z3)) -> cond_merge_ys_zs_2(leq#2(z0, z2), Cons(z0, z1), Cons(z2, z3), z0, z1, z2, z3)
   cond_merge_ys_zs_2(True, Cons(z0, z1), Cons(z2, z3), z4, z5, z6, z7) -> Cons(z4, merge#2(z5, Cons(z2, z3)))
   cond_merge_ys_zs_2(False, Cons(z0, z1), Cons(z2, z3), z4, z5, z6, z7) -> Cons(z6, merge#2(Cons(z0, z1), z7))
Tuples:
   LENGTH#1(Cons(z0, z1)) -> c24(LENGTH#1(z1))
   MAP#2(dc(z0, z1, z2, z3, z4), Cons(z5, z6)) -> c26(DC#1(z0, z1, z2, z3, z4, z5))
   MAP#2(dc(z0, z1, z2, z3, z4), Cons(z5, z6)) -> c27(MAP#2(dc(z0, z1, z2, z3, z4), z6))
   MERGE#2(Cons(0, x1), Cons(z0, x3)) -> c6(COND_MERGE_YS_ZS_2(True, Cons(0, x1), Cons(z0, x3), 0, x1, z0, x3))
   MERGE#2(Cons(S(z0), x1), Cons(0, x3)) -> c6(COND_MERGE_YS_ZS_2(False, Cons(S(z0), x1), Cons(0, x3), S(z0), x1, 0, x3))
   MERGE#2(Cons(S(S(z0)), x1), Cons(S(S(z1)), x3)) -> c6(COND_MERGE_YS_ZS_2(leq#2(z0, z1), Cons(S(S(z0)), x1), Cons(S(S(z1)), x3), S(S(z0)), x1, S(S(z1)), x3), LEQ#2(S(S(z0)), S(S(z1))))
   MERGE#2(Cons(S(x0), x1), Cons(S(x2), x3)) -> c6(LEQ#2(S(x0), S(x2)))
   DIVIDE_YS#1(Cons(x0, Cons(x1, x2)), S(y11)) -> c(TAKE#2(S(y11), Cons(x0, Cons(x1, x2))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, x3))), S(y11)) -> c(TAKE#2(S(y11), Cons(x0, Cons(x1, Cons(x2, x3)))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Nil)), S(y10)) -> c(TAKE#2(S(y10), Cons(x0, Cons(x1, Nil))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Nil))), S(y7)) -> c(TAKE#2(S(y7), Cons(x0, Cons(x1, Cons(x2, Nil)))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4)))), S(y8)) -> c(TAKE#2(S(y8), Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4))))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, x2)), S(y11)) -> c1(DROP#2(S(y11), Cons(x0, Cons(x1, x2))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, x3))), S(y11)) -> c1(DROP#2(S(y11), Cons(x0, Cons(x1, Cons(x2, x3)))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Nil)), S(y10)) -> c1(DROP#2(S(y10), Cons(x0, Cons(x1, Nil))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Nil))), S(y7)) -> c1(DROP#2(S(y7), Cons(x0, Cons(x1, Cons(x2, Nil)))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4)))), S(y8)) -> c1(DROP#2(S(y8), Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4))))))
   COND_MERGE_YS_ZS_2(False, Cons(S(x0), x1), Cons(0, x2), S(x0), x1, 0, x2) -> c3(MERGE#2(Cons(S(x0), x1), x2))
   COND_MERGE_YS_ZS_2(False, Cons(S(S(x0)), x1), Cons(S(0), x2), S(S(x0)), x1, S(0), x2) -> c3(MERGE#2(Cons(S(S(x0)), x1), x2))
   COND_MERGE_YS_ZS_2(False, Cons(S(S(x0)), x1), Cons(S(S(x2)), x3), S(S(x0)), x1, S(S(x2)), x3) -> c3(MERGE#2(Cons(S(S(x0)), x1), x3))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, Cons(z3, z4))))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Cons(z2, Cons(z3, z4)))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, Cons(z3, z4)))), S(halve#1(S(S(length#1(z4)))))))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, Cons(z3, z4)))), S(halve#1(length#1(Cons(z2, Cons(z3, z4))))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, Cons(z3, z4)))), S(halve#1(length#1(Cons(z2, Cons(z3, z4)))))), HALVE#1(S(length#1(Cons(z3, z4)))), LENGTH#1(Cons(z2, Cons(z3, z4))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, z3)))) -> c9(MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3)))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3))))), HALVE#1(S(length#1(z3))), LENGTH#1(Cons(z2, z3)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Nil))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(0)), Cons(z0, Cons(z1, Nil))), Cons(drop#2(S(halve#1(0)), Cons(z0, Cons(z1, Nil))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil)))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Nil))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Nil)), S(0)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil)))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> c9(CONST_F#2(Cons(z0, Cons(z1, z2)), Cons(dc#1(map, divisible, mergesort_zs_3, divide, const_f, take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2)))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(drop#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(halve#1(length#1(z2)), Cons(z1, z2)), Nil))), DIVIDE_YS#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2)))), HALVE#1(length#1(z2)), LENGTH#1(z2))
   CONST_F#2(Cons(x0, Cons(x1, x2)), Cons(z1, Cons(z2, z3))) -> c19(MERGE#2(z1, z2))
   CONST_F#2(Cons(x0, Cons(x1, Cons(x2, x3))), Cons(z1, Cons(z2, z3))) -> c19(MERGE#2(z1, z2))
   CONST_F#2(Cons(x0, Cons(x1, Nil)), Cons(z1, Cons(z2, z3))) -> c19(MERGE#2(z1, z2))
   CONST_F#2(Cons(x0, Cons(x1, Cons(x2, Nil))), Cons(z1, Cons(z2, z3))) -> c19(MERGE#2(z1, z2))
   CONST_F#2(Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4)))), Cons(z1, Cons(z2, z3))) -> c19(MERGE#2(z1, z2))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> c9(CONST_F#2(Cons(z0, Cons(z1, z2)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(halve#1(length#1(z2)), Cons(z1, z2)), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(halve#1(length#1(z2)), Cons(z1, z2)), Nil))), DIVIDE_YS#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2)))), HALVE#1(length#1(z2)), LENGTH#1(z2))
   COND_MERGE_YS_ZS_2(True, Cons(0, Cons(0, z5)), Cons(x1, x2), 0, Cons(0, z5), x1, x2) -> c2(MERGE#2(Cons(0, z5), Cons(x1, x2)))
   COND_MERGE_YS_ZS_2(True, Cons(S(0), Cons(0, z5)), Cons(S(x1), x2), S(0), Cons(0, z5), S(x1), x2) -> c2(MERGE#2(Cons(0, z5), Cons(S(x1), x2)))
   COND_MERGE_YS_ZS_2(True, Cons(S(S(x0)), Cons(0, z5)), Cons(S(S(x2)), x3), S(S(x0)), Cons(0, z5), S(S(x2)), x3) -> c2(MERGE#2(Cons(0, z5), Cons(S(S(x2)), x3)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, z3)))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Cons(z2, z3))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(Cons(z2, z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Cons(drop#2(S(halve#1(S(length#1(z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3)))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(S(length#1(z3))))), HALVE#1(S(length#1(z3))), LENGTH#1(Cons(z2, z3)))
   COND_MERGE_YS_ZS_2(True, Cons(0, Cons(S(z4), z5)), Cons(0, x2), 0, Cons(S(z4), z5), 0, x2) -> c2(MERGE#2(Cons(S(z4), z5), Cons(0, x2)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> c9(CONST_F#2(Cons(z0, Cons(z1, z2)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(Cons(z0, take#2(halve#1(length#1(z2)), Cons(z1, z2))), Cons(drop#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(halve#1(length#1(z2)), Cons(z1, z2)), Nil))), DIVIDE_YS#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2)))), HALVE#1(length#1(z2)), LENGTH#1(z2))
   COND_MERGE_YS_ZS_2(True, Cons(0, Cons(S(0), z5)), Cons(S(z2), x2), 0, Cons(S(0), z5), S(z2), x2) -> c2(MERGE#2(Cons(S(0), z5), Cons(S(z2), x2)))
   COND_MERGE_YS_ZS_2(True, Cons(S(0), Cons(S(0), z5)), Cons(S(x1), x2), S(0), Cons(S(0), z5), S(x1), x2) -> c2(MERGE#2(Cons(S(0), z5), Cons(S(x1), x2)))
   COND_MERGE_YS_ZS_2(True, Cons(S(S(x0)), Cons(S(0), z5)), Cons(S(S(x2)), x3), S(S(x0)), Cons(S(0), z5), S(S(x2)), x3) -> c2(MERGE#2(Cons(S(0), z5), Cons(S(S(x2)), x3)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, z3)))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Cons(z2, z3))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(S(length#1(z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Cons(drop#2(S(halve#1(length#1(Cons(z2, z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3)))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(S(length#1(z3))))), HALVE#1(S(length#1(z3))), LENGTH#1(Cons(z2, z3)))
   COND_MERGE_YS_ZS_2(True, Cons(0, Cons(S(S(z4)), z5)), Cons(S(0), x2), 0, Cons(S(S(z4)), z5), S(0), x2) -> c2(MERGE#2(Cons(S(S(z4)), z5), Cons(S(0), x2)))
   COND_MERGE_YS_ZS_2(True, Cons(S(0), Cons(S(S(z4)), z5)), Cons(S(0), x2), S(0), Cons(S(S(z4)), z5), S(0), x2) -> c2(MERGE#2(Cons(S(S(z4)), z5), Cons(S(0), x2)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> c9(MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(halve#1(length#1(z2)), Cons(z1, z2)), Nil))), DIVIDE_YS#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2)))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Nil))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(Nil))), Cons(z0, Cons(z1, Nil))), Cons(drop#2(S(halve#1(0)), Cons(z0, Cons(z1, Nil))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Nil)), S(halve#1(0))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Nil))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(0)), Cons(z0, Cons(z1, Nil))), Cons(drop#2(S(halve#1(length#1(Nil))), Cons(z0, Cons(z1, Nil))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Nil)), S(halve#1(0))))
   DROP#2(S(S(y0)), Cons(z1, Cons(y1, y2))) -> c12(DROP#2(S(y0), Cons(y1, y2)))
   COND_MERGE_YS_ZS_2(True, Cons(0, Cons(S(S(z5)), z6)), Cons(S(S(z2)), x2), 0, Cons(S(S(z5)), z6), S(S(z2)), x2) -> c2(MERGE#2(Cons(S(S(z5)), z6), Cons(S(S(z2)), x2)))
   COND_MERGE_YS_ZS_2(True, Cons(S(0), Cons(S(S(z5)), z6)), Cons(S(S(z2)), x2), S(0), Cons(S(S(z5)), z6), S(S(z2)), x2) -> c2(MERGE#2(Cons(S(S(z5)), z6), Cons(S(S(z2)), x2)))
   COND_MERGE_YS_ZS_2(True, Cons(S(S(x0)), Cons(S(S(z5)), z6)), Cons(S(S(x2)), x3), S(S(x0)), Cons(S(S(z5)), z6), S(S(x2)), x3) -> c2(MERGE#2(Cons(S(S(z5)), z6), Cons(S(S(x2)), x3)))
   COND_MERGE_YS_ZS_2(True, Cons(0, Cons(S(z5), z6)), Cons(S(z2), x2), 0, Cons(S(z5), z6), S(z2), x2) -> c2(MERGE#2(Cons(S(z5), z6), Cons(S(z2), x2)))
   COND_MERGE_YS_ZS_2(True, Cons(S(0), Cons(S(z5), z6)), Cons(S(x1), x2), S(0), Cons(S(z5), z6), S(x1), x2) -> c2(MERGE#2(Cons(S(z5), z6), Cons(S(x1), x2)))
   COND_MERGE_YS_ZS_2(True, Cons(S(S(x0)), Cons(S(z5), z6)), Cons(S(S(x2)), x3), S(S(x0)), Cons(S(z5), z6), S(S(x2)), x3) -> c2(MERGE#2(Cons(S(z5), z6), Cons(S(S(x2)), x3)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, z3)))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Cons(z2, z3))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(S(length#1(z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Cons(drop#2(S(halve#1(S(length#1(z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3)))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(S(length#1(z3))))), HALVE#1(S(length#1(z3))), LENGTH#1(Cons(z2, z3)))
   TAKE#2(S(S(y0)), Cons(z1, Cons(y1, y2))) -> c15(TAKE#2(S(y0), Cons(y1, y2)))
   HALVE#1(S(S(S(S(y0))))) -> c18(HALVE#1(S(S(y0))))
   LEQ#2(S(S(y0)), S(S(y1))) -> c22(LEQ#2(S(y0), S(y1)))
   MERGE#2(Cons(S(0), x1), Cons(S(z0), x3)) -> c6(COND_MERGE_YS_ZS_2(True, Cons(S(0), x1), Cons(S(z0), x3), S(0), x1, S(z0), x3))
   MERGE#2(Cons(S(S(z0)), x1), Cons(S(0), x3)) -> c6(COND_MERGE_YS_ZS_2(False, Cons(S(S(z0)), x1), Cons(S(0), x3), S(S(z0)), x1, S(0), x3))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, Nil)))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Cons(z2, Nil))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, Nil))), S(halve#1(S(0)))))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, Nil))), S(halve#1(length#1(Cons(z2, Nil)))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, Nil))), S(halve#1(length#1(Cons(z2, Nil))))), LENGTH#1(Cons(z2, Nil)))
S tuples:
   LENGTH#1(Cons(z0, z1)) -> c24(LENGTH#1(z1))
   MAP#2(dc(z0, z1, z2, z3, z4), Cons(z5, z6)) -> c26(DC#1(z0, z1, z2, z3, z4, z5))
   MAP#2(dc(z0, z1, z2, z3, z4), Cons(z5, z6)) -> c27(MAP#2(dc(z0, z1, z2, z3, z4), z6))
   MERGE#2(Cons(0, x1), Cons(z0, x3)) -> c6(COND_MERGE_YS_ZS_2(True, Cons(0, x1), Cons(z0, x3), 0, x1, z0, x3))
   MERGE#2(Cons(S(z0), x1), Cons(0, x3)) -> c6(COND_MERGE_YS_ZS_2(False, Cons(S(z0), x1), Cons(0, x3), S(z0), x1, 0, x3))
   MERGE#2(Cons(S(S(z0)), x1), Cons(S(S(z1)), x3)) -> c6(COND_MERGE_YS_ZS_2(leq#2(z0, z1), Cons(S(S(z0)), x1), Cons(S(S(z1)), x3), S(S(z0)), x1, S(S(z1)), x3), LEQ#2(S(S(z0)), S(S(z1))))
   MERGE#2(Cons(S(x0), x1), Cons(S(x2), x3)) -> c6(LEQ#2(S(x0), S(x2)))
   DIVIDE_YS#1(Cons(x0, Cons(x1, x2)), S(y11)) -> c(TAKE#2(S(y11), Cons(x0, Cons(x1, x2))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, x3))), S(y11)) -> c(TAKE#2(S(y11), Cons(x0, Cons(x1, Cons(x2, x3)))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Nil)), S(y10)) -> c(TAKE#2(S(y10), Cons(x0, Cons(x1, Nil))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Nil))), S(y7)) -> c(TAKE#2(S(y7), Cons(x0, Cons(x1, Cons(x2, Nil)))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4)))), S(y8)) -> c(TAKE#2(S(y8), Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4))))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, x2)), S(y11)) -> c1(DROP#2(S(y11), Cons(x0, Cons(x1, x2))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, x3))), S(y11)) -> c1(DROP#2(S(y11), Cons(x0, Cons(x1, Cons(x2, x3)))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Nil)), S(y10)) -> c1(DROP#2(S(y10), Cons(x0, Cons(x1, Nil))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Nil))), S(y7)) -> c1(DROP#2(S(y7), Cons(x0, Cons(x1, Cons(x2, Nil)))))
   DIVIDE_YS#1(Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4)))), S(y8)) -> c1(DROP#2(S(y8), Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4))))))
   COND_MERGE_YS_ZS_2(False, Cons(S(x0), x1), Cons(0, x2), S(x0), x1, 0, x2) -> c3(MERGE#2(Cons(S(x0), x1), x2))
   COND_MERGE_YS_ZS_2(False, Cons(S(S(x0)), x1), Cons(S(0), x2), S(S(x0)), x1, S(0), x2) -> c3(MERGE#2(Cons(S(S(x0)), x1), x2))
   COND_MERGE_YS_ZS_2(False, Cons(S(S(x0)), x1), Cons(S(S(x2)), x3), S(S(x0)), x1, S(S(x2)), x3) -> c3(MERGE#2(Cons(S(S(x0)), x1), x3))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, Cons(z3, z4))))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Cons(z2, Cons(z3, z4)))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, Cons(z3, z4)))), S(halve#1(S(S(length#1(z4)))))))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, Cons(z3, z4)))), S(halve#1(length#1(Cons(z2, Cons(z3, z4))))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, Cons(z3, z4)))), S(halve#1(length#1(Cons(z2, Cons(z3, z4)))))), HALVE#1(S(length#1(Cons(z3, z4)))), LENGTH#1(Cons(z2, Cons(z3, z4))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, z3)))) -> c9(MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3)))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3))))), HALVE#1(S(length#1(z3))), LENGTH#1(Cons(z2, z3)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Nil))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(0)), Cons(z0, Cons(z1, Nil))), Cons(drop#2(S(halve#1(0)), Cons(z0, Cons(z1, Nil))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil)))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Nil))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Nil)), S(0)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil)))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> c9(CONST_F#2(Cons(z0, Cons(z1, z2)), Cons(dc#1(map, divisible, mergesort_zs_3, divide, const_f, take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2)))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(drop#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(halve#1(length#1(z2)), Cons(z1, z2)), Nil))), DIVIDE_YS#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2)))), HALVE#1(length#1(z2)), LENGTH#1(z2))
   CONST_F#2(Cons(x0, Cons(x1, x2)), Cons(z1, Cons(z2, z3))) -> c19(MERGE#2(z1, z2))
   CONST_F#2(Cons(x0, Cons(x1, Cons(x2, x3))), Cons(z1, Cons(z2, z3))) -> c19(MERGE#2(z1, z2))
   CONST_F#2(Cons(x0, Cons(x1, Nil)), Cons(z1, Cons(z2, z3))) -> c19(MERGE#2(z1, z2))
   CONST_F#2(Cons(x0, Cons(x1, Cons(x2, Nil))), Cons(z1, Cons(z2, z3))) -> c19(MERGE#2(z1, z2))
   CONST_F#2(Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4)))), Cons(z1, Cons(z2, z3))) -> c19(MERGE#2(z1, z2))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> c9(CONST_F#2(Cons(z0, Cons(z1, z2)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(halve#1(length#1(z2)), Cons(z1, z2)), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(halve#1(length#1(z2)), Cons(z1, z2)), Nil))), DIVIDE_YS#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2)))), HALVE#1(length#1(z2)), LENGTH#1(z2))
   COND_MERGE_YS_ZS_2(True, Cons(0, Cons(0, z5)), Cons(x1, x2), 0, Cons(0, z5), x1, x2) -> c2(MERGE#2(Cons(0, z5), Cons(x1, x2)))
   COND_MERGE_YS_ZS_2(True, Cons(S(0), Cons(0, z5)), Cons(S(x1), x2), S(0), Cons(0, z5), S(x1), x2) -> c2(MERGE#2(Cons(0, z5), Cons(S(x1), x2)))
   COND_MERGE_YS_ZS_2(True, Cons(S(S(x0)), Cons(0, z5)), Cons(S(S(x2)), x3), S(S(x0)), Cons(0, z5), S(S(x2)), x3) -> c2(MERGE#2(Cons(0, z5), Cons(S(S(x2)), x3)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, z3)))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Cons(z2, z3))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(Cons(z2, z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Cons(drop#2(S(halve#1(S(length#1(z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3)))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(S(length#1(z3))))), HALVE#1(S(length#1(z3))), LENGTH#1(Cons(z2, z3)))
   COND_MERGE_YS_ZS_2(True, Cons(0, Cons(S(z4), z5)), Cons(0, x2), 0, Cons(S(z4), z5), 0, x2) -> c2(MERGE#2(Cons(S(z4), z5), Cons(0, x2)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> c9(CONST_F#2(Cons(z0, Cons(z1, z2)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(Cons(z0, take#2(halve#1(length#1(z2)), Cons(z1, z2))), Cons(drop#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(halve#1(length#1(z2)), Cons(z1, z2)), Nil))), DIVIDE_YS#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2)))), HALVE#1(length#1(z2)), LENGTH#1(z2))
   COND_MERGE_YS_ZS_2(True, Cons(0, Cons(S(0), z5)), Cons(S(z2), x2), 0, Cons(S(0), z5), S(z2), x2) -> c2(MERGE#2(Cons(S(0), z5), Cons(S(z2), x2)))
   COND_MERGE_YS_ZS_2(True, Cons(S(0), Cons(S(0), z5)), Cons(S(x1), x2), S(0), Cons(S(0), z5), S(x1), x2) -> c2(MERGE#2(Cons(S(0), z5), Cons(S(x1), x2)))
   COND_MERGE_YS_ZS_2(True, Cons(S(S(x0)), Cons(S(0), z5)), Cons(S(S(x2)), x3), S(S(x0)), Cons(S(0), z5), S(S(x2)), x3) -> c2(MERGE#2(Cons(S(0), z5), Cons(S(S(x2)), x3)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, z3)))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Cons(z2, z3))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(S(length#1(z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Cons(drop#2(S(halve#1(length#1(Cons(z2, z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3)))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(S(length#1(z3))))), HALVE#1(S(length#1(z3))), LENGTH#1(Cons(z2, z3)))
   COND_MERGE_YS_ZS_2(True, Cons(0, Cons(S(S(z4)), z5)), Cons(S(0), x2), 0, Cons(S(S(z4)), z5), S(0), x2) -> c2(MERGE#2(Cons(S(S(z4)), z5), Cons(S(0), x2)))
   COND_MERGE_YS_ZS_2(True, Cons(S(0), Cons(S(S(z4)), z5)), Cons(S(0), x2), S(0), Cons(S(S(z4)), z5), S(0), x2) -> c2(MERGE#2(Cons(S(S(z4)), z5), Cons(S(0), x2)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, z2))) -> c9(MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(z2))), Cons(z0, Cons(z1, z2))), Cons(drop#2(halve#1(length#1(z2)), Cons(z1, z2)), Nil))), DIVIDE_YS#1(Cons(z0, Cons(z1, z2)), S(halve#1(length#1(z2)))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Nil))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(length#1(Nil))), Cons(z0, Cons(z1, Nil))), Cons(drop#2(S(halve#1(0)), Cons(z0, Cons(z1, Nil))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Nil)), S(halve#1(0))))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Nil))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Nil)), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(0)), Cons(z0, Cons(z1, Nil))), Cons(drop#2(S(halve#1(length#1(Nil))), Cons(z0, Cons(z1, Nil))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Nil)), S(halve#1(length#1(Nil))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Nil)), S(halve#1(0))))
   DROP#2(S(S(y0)), Cons(z1, Cons(y1, y2))) -> c12(DROP#2(S(y0), Cons(y1, y2)))
   COND_MERGE_YS_ZS_2(True, Cons(0, Cons(S(S(z5)), z6)), Cons(S(S(z2)), x2), 0, Cons(S(S(z5)), z6), S(S(z2)), x2) -> c2(MERGE#2(Cons(S(S(z5)), z6), Cons(S(S(z2)), x2)))
   COND_MERGE_YS_ZS_2(True, Cons(S(0), Cons(S(S(z5)), z6)), Cons(S(S(z2)), x2), S(0), Cons(S(S(z5)), z6), S(S(z2)), x2) -> c2(MERGE#2(Cons(S(S(z5)), z6), Cons(S(S(z2)), x2)))
   COND_MERGE_YS_ZS_2(True, Cons(S(S(x0)), Cons(S(S(z5)), z6)), Cons(S(S(x2)), x3), S(S(x0)), Cons(S(S(z5)), z6), S(S(x2)), x3) -> c2(MERGE#2(Cons(S(S(z5)), z6), Cons(S(S(x2)), x3)))
   COND_MERGE_YS_ZS_2(True, Cons(0, Cons(S(z5), z6)), Cons(S(z2), x2), 0, Cons(S(z5), z6), S(z2), x2) -> c2(MERGE#2(Cons(S(z5), z6), Cons(S(z2), x2)))
   COND_MERGE_YS_ZS_2(True, Cons(S(0), Cons(S(z5), z6)), Cons(S(x1), x2), S(0), Cons(S(z5), z6), S(x1), x2) -> c2(MERGE#2(Cons(S(z5), z6), Cons(S(x1), x2)))
   COND_MERGE_YS_ZS_2(True, Cons(S(S(x0)), Cons(S(z5), z6)), Cons(S(S(x2)), x3), S(S(x0)), Cons(S(z5), z6), S(S(x2)), x3) -> c2(MERGE#2(Cons(S(z5), z6), Cons(S(S(x2)), x3)))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, z3)))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Cons(z2, z3))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), Cons(take#2(S(halve#1(S(length#1(z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Cons(drop#2(S(halve#1(S(length#1(z3)))), Cons(z0, Cons(z1, Cons(z2, z3)))), Nil)))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(length#1(Cons(z2, z3)))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, z3))), S(halve#1(S(length#1(z3))))), HALVE#1(S(length#1(z3))), LENGTH#1(Cons(z2, z3)))
   TAKE#2(S(S(y0)), Cons(z1, Cons(y1, y2))) -> c15(TAKE#2(S(y0), Cons(y1, y2)))
   HALVE#1(S(S(S(S(y0))))) -> c18(HALVE#1(S(S(y0))))
   LEQ#2(S(S(y0)), S(S(y1))) -> c22(LEQ#2(S(y0), S(y1)))
   MERGE#2(Cons(S(0), x1), Cons(S(z0), x3)) -> c6(COND_MERGE_YS_ZS_2(True, Cons(S(0), x1), Cons(S(z0), x3), S(0), x1, S(z0), x3))
   MERGE#2(Cons(S(S(z0)), x1), Cons(S(0), x3)) -> c6(COND_MERGE_YS_ZS_2(False, Cons(S(S(z0)), x1), Cons(S(0), x3), S(S(z0)), x1, S(0), x3))
   DC#1(map, divisible, mergesort_zs_3, divide, const_f, Cons(z0, Cons(z1, Cons(z2, Nil)))) -> c9(CONST_F#2(Cons(z0, Cons(z1, Cons(z2, Nil))), map#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, Nil))), S(halve#1(S(0)))))), MAP#2(dc(map, divisible, mergesort_zs_3, divide, const_f), divide_ys#1(Cons(z0, Cons(z1, Cons(z2, Nil))), S(halve#1(length#1(Cons(z2, Nil)))))), DIVIDE_YS#1(Cons(z0, Cons(z1, Cons(z2, Nil))), S(halve#1(length#1(Cons(z2, Nil))))), LENGTH#1(Cons(z2, Nil)))
K tuples:none
Defined Rule Symbols:   leq#2_2, map#2_2, divide_ys#1_2, halve#1_1, length#1_1, take#2_2, drop#2_2, dc#1_6, const_f#2_2, merge#2_2, cond_merge_ys_zs_2_7

Defined Pair Symbols:   LENGTH#1_1, MAP#2_2, MERGE#2_2, DIVIDE_YS#1_2, COND_MERGE_YS_ZS_2_7, DC#1_6, CONST_F#2_2, DROP#2_2, TAKE#2_2, HALVE#1_1, LEQ#2_2

Compound Symbols:   c24_1, c26_1, c27_1, c6_1, c6_2, c_1, c1_1, c3_1, c9_5, c9_4, c9_3, c19_1, c2_1, c9_2, c12_1, c15_1, c18_1, c22_1