YES
proof of prog.inttrs
# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty


Termination of the given IRSwT could be proven:

(0) IRSwT
(1) IRSFormatTransformerProof [EQUIVALENT, 0 ms]
(2) IRSwT
(3) IRSwTTerminationDigraphProof [EQUIVALENT, 39.5 s]
(4) AND
    (5) IRSwT
        (6) IntTRSCompressionProof [EQUIVALENT, 0 ms]
        (7) IRSwT
        (8) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms]
        (9) IRSwT
        (10) FilterProof [EQUIVALENT, 10 ms]
        (11) IntTRS
        (12) IntTRSCompressionProof [EQUIVALENT, 0 ms]
        (13) IntTRS
        (14) RankingReductionPairProof [EQUIVALENT, 0 ms]
        (15) YES
    (16) IRSwT
        (17) IntTRSCompressionProof [EQUIVALENT, 0 ms]
        (18) IRSwT
        (19) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms]
        (20) IRSwT
        (21) TempFilterProof [SOUND, 20 ms]
        (22) IntTRS
        (23) RankingReductionPairProof [EQUIVALENT, 0 ms]
        (24) YES
    (25) IRSwT
        (26) IntTRSCompressionProof [EQUIVALENT, 0 ms]
        (27) IRSwT
        (28) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms]
        (29) IRSwT
        (30) TempFilterProof [SOUND, 11 ms]
        (31) IntTRS
        (32) PolynomialOrderProcessor [EQUIVALENT, 0 ms]
        (33) YES


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

(0)
Obligation:
Rules:
f1_0_main_Load(arg1, arg2, arg3, arg4, arg5) -> f392_0_createList_GT(arg1P, arg2P, arg3P, arg4P, arg5P) :|: 0 = arg3P && 0 = arg2P && 0 = arg1P && 0 = arg2 && 0 <= arg1 - 1
f1_0_main_Load(x, x1, x2, x3, x4) -> f89_0_main_InvokeMethod(x5, x6, x7, x8, x9) :|: 0 = x6 && 0 <= x5 - 1 && 0 <= x - 1 && 0 <= x1 - 1 && x5 <= x
f1_0_main_Load(x10, x11, x12, x13, x14) -> f89_0_main_InvokeMethod(x15, x16, x17, x19, x20) :|: 0 <= x15 - 1 && 0 <= x10 - 1 && x15 <= x10 && 0 <= x11 - 1 && -1 <= x16 - 1
f89_0_main_InvokeMethod(x21, x22, x24, x25, x26) -> f392_0_createList_GT(x27, x28, x30, x31, x32) :|: 1 = x30 && x22 = x27 && 0 <= x28 - 1 && 0 <= x21 - 1
f1_0_main_Load(x33, x34, x36, x37, x38) -> f730_0_quicksort_NONNULL(x39, x41, x42, x43, x44) :|: 0 = x34 && -1 <= x39 - 1 && 0 <= x33 - 1 && x39 + 1 <= x33
f89_0_main_InvokeMethod(x45, x46, x47, x48, x49) -> f730_0_quicksort_NONNULL(x50, x51, x52, x53, x55) :|: x50 + 1 <= x45 && 0 <= x56 - 1 && 0 <= x45 - 1 && -1 <= x50 - 1 && 0 = x46
f1_0_main_Load(x57, x58, x59, x60, x61) -> f730_0_quicksort_NONNULL(x62, x63, x64, x65, x66) :|: 0 = x58 && 1 <= x62 - 1 && 0 <= x57 - 1 && x62 - 1 <= x57
f89_0_main_InvokeMethod(x67, x68, x69, x70, x71) -> f703_0_main_InvokeMethod(x72, x73, x74, x75, x76) :|: x72 <= x67 && 0 <= x77 - 1 && 0 <= x67 - 1 && 0 <= x72 - 1 && 2 <= x73 - 1 && 0 = x74
f89_0_main_InvokeMethod(x78, x79, x80, x81, x82) -> f703_0_main_InvokeMethod(x83, x84, x85, x86, x87) :|: x83 <= x78 && 0 <= x88 - 1 && 0 <= x78 - 1 && 0 <= x83 - 1 && 2 <= x84 - 1
f89_0_main_InvokeMethod(x89, x90, x91, x92, x93) -> f703_0_main_InvokeMethod(x94, x95, x96, x97, x98) :|: x94 <= x89 && 0 <= x99 - 1 && 0 <= x89 - 1 && 0 <= x94 - 1 && 1 <= x95 - 1
f89_0_main_InvokeMethod(x100, x101, x102, x103, x104) -> f703_0_main_InvokeMethod(x106, x107, x108, x109, x111) :|: x106 <= x100 && 0 <= x112 - 1 && x107 - 1 <= x100 && 0 <= x100 - 1 && 0 <= x106 - 1 && 1 <= x107 - 1 && 0 = x108
f703_0_main_InvokeMethod(x113, x114, x116, x117, x118) -> f730_0_quicksort_NONNULL(x119, x120, x121, x122, x123) :|: x119 <= x114 && 0 <= x124 - 1 && 0 <= x113 - 1 && 0 <= x114 - 1 && 0 <= x119 - 1 && x116 + 2 <= x114
f392_0_createList_GT(x125, x126, x127, x128, x129) -> f392_0_createList_GT(x130, x131, x132, x133, x134) :|: x127 = x132 && x126 = x131 && x125 - 1 = x130 && x126 <= x127 && x125 - 1 <= x125 - 1 && -1 <= x126 - 1 && 0 <= x125 - 1
f392_0_createList_GT(x135, x136, x137, x138, x139) -> f501_0_createList_InvokeMethod(x141, x142, x143, x144, x146) :|: x137 + 1 = x144 && x136 = x143 && x135 - 1 = x142 && x135 = x141 && x137 <= x136 - 1 && -1 <= x137 - 1 && -1 <= x136 - 1 && 0 <= x135 - 1
f392_0_createList_GT(x147, x148, x149, x150, x151) -> f501_0_createList_InvokeMethod(x152, x153, x154, x155, x156) :|: 0 <= x147 - 1 && -1 <= x148 - 1 && x149 <= x148 - 1 && -1 <= x157 - 1 && -1 <= x149 - 1 && x147 = x152 && x147 - 1 = x153 && x148 = x154 && x149 + 1 = x155
f501_0_createList_InvokeMethod(x158, x159, x160, x161, x162) -> f392_0_createList_GT(x163, x165, x166, x167, x168) :|: x161 = x166 && x160 = x165 && x159 = x163 && x159 <= x158 - 1 && x161 <= x160 && 0 <= x160 - 1 && 0 <= x161 - 1 && 0 <= x158 - 1
f730_0_quicksort_NONNULL(x169, x170, x171, x172, x173) -> f790_0_sortedLow_NONNULL(x174, x175, x176, x177, x178) :|: x174 + 2 <= x169 && -1 <= x175 - 1 && 0 <= x169 - 1 && x175 + 1 <= x169
f730_0_quicksort_NONNULL(x179, x180, x181, x182, x183) -> f1140_0_sortedHigh_NONNULL(x184, x185, x186, x187, x188) :|: x184 + 2 <= x179 && -1 <= x185 - 1 && 1 <= x179 - 1 && x185 + 2 <= x179
f730_0_quicksort_NONNULL(x189, x190, x191, x192, x193) -> f1000_0_quicksort_InvokeMethod(x194, x196, x197, x198, x199) :|: x199 + 4 <= x189 && x198 + 2 <= x189 && 1 <= x196 - 1 && 3 <= x194 - 1 && 3 <= x189 - 1 && x196 + 2 <= x189 && x194 <= x189
f730_0_quicksort_NONNULL(x200, x201, x202, x203, x204) -> f1000_0_quicksort_InvokeMethod(x205, x206, x207, x208, x209) :|: x209 + 4 <= x200 && x208 + 2 <= x200 && 2 <= x206 - 1 && 4 <= x205 - 1 && 4 <= x200 - 1 && x206 + 2 <= x200 && x205 <= x200
f1000_0_quicksort_InvokeMethod(x210, x211, x212, x213, x214) -> f1140_0_sortedHigh_NONNULL(x215, x216, x217, x218, x219) :|: x212 = x217 && x213 = x215 && x214 + 2 <= x211 && x213 + 2 <= x210 && x214 + 4 <= x210 && 0 <= x216 - 1 && 0 <= x211 - 1 && 2 <= x210 - 1 && x216 <= x211 && x216 + 2 <= x210
f1000_0_quicksort_InvokeMethod(x220, x221, x222, x223, x224) -> f1287_0_quicksort_InvokeMethod(x225, x226, x227, x228, x229) :|: x224 + 2 <= x221 && x223 + 2 <= x220 && x224 + 4 <= x220 && 4 <= x225 - 1 && 2 <= x221 - 1 && 4 <= x220 - 1 && x225 <= x220
f1000_0_quicksort_InvokeMethod(x230, x231, x232, x233, x234) -> f1287_0_quicksort_InvokeMethod(x235, x236, x237, x238, x239) :|: x234 + 2 <= x231 && x233 + 2 <= x230 && x234 + 4 <= x230 && 3 <= x235 - 1 && 1 <= x231 - 1 && 3 <= x230 - 1 && x235 <= x230
f790_0_sortedLow_NONNULL(x240, x241, x242, x243, x244) -> f790_0_sortedLow_NONNULL(x245, x246, x247, x248, x249) :|: x246 + 1 <= x241 && x240 <= x250 - 1 && 0 <= x241 - 1 && -1 <= x246 - 1 && x240 = x245 && x242 = x247
f790_0_sortedLow_NONNULL(x251, x252, x253, x254, x255) -> f790_0_sortedLow_NONNULL(x256, x257, x258, x259, x260) :|: x257 + 1 <= x252 && x261 <= x251 && 0 <= x252 - 1 && -1 <= x257 - 1 && x251 = x256 && x253 = x258
f790_0_sortedLow_NONNULL(x262, x263, x264, x265, x266) -> f730_0_quicksort_NONNULL(x267, x268, x269, x270, x271) :|: x267 <= x263 && x272 <= x262 && 1 <= x263 - 1 && 1 <= x267 - 1
f790_0_sortedLow_NONNULL(x273, x274, x275, x276, x277) -> f1022_0_sortedLow_InvokeMethod(x278, x279, x280, x281, x282) :|: x275 = x280 && x281 + 4 <= x274 && x282 + 2 <= x274 && 1 <= x279 - 1 && 3 <= x278 - 1 && 3 <= x274 - 1 && x279 <= x274 && x282 <= x273 && x278 <= x274
f790_0_sortedLow_NONNULL(x283, x284, x285, x286, x287) -> f1022_0_sortedLow_InvokeMethod(x288, x289, x290, x291, x292) :|: x285 = x290 && x291 + 4 <= x284 && x292 + 2 <= x284 && 1 <= x289 - 1 && 4 <= x288 - 1 && 4 <= x284 - 1 && x289 <= x284 && x292 <= x283 && x288 <= x284
f1022_0_sortedLow_InvokeMethod(x293, x294, x295, x296, x297) -> f730_0_quicksort_NONNULL(x298, x299, x300, x301, x302) :|: x297 + 2 <= x294 && x297 + 2 <= x293 && x296 + 4 <= x293 && 1 <= x298 - 1 && 1 <= x294 - 1 && 2 <= x293 - 1 && x298 <= x294 && x298 <= x293
f1140_0_sortedHigh_NONNULL(x303, x304, x305, x306, x307) -> f1140_0_sortedHigh_NONNULL(x308, x309, x310, x311, x312) :|: x309 + 1 <= x304 && x313 <= x303 && 0 <= x304 - 1 && -1 <= x309 - 1 && x303 = x308 && x305 = x310
f1140_0_sortedHigh_NONNULL(x314, x315, x316, x317, x318) -> f1140_0_sortedHigh_NONNULL(x319, x320, x321, x322, x323) :|: x320 + 1 <= x315 && x314 <= x324 - 1 && 0 <= x315 - 1 && -1 <= x320 - 1 && x314 = x319 && x316 = x321
f1140_0_sortedHigh_NONNULL(x325, x326, x327, x328, x329) -> f1232_0_sortedHigh_InvokeMethod(x330, x331, x332, x333, x334) :|: x327 = x332 && x333 + 4 <= x326 && x334 + 2 <= x326 && 1 <= x331 - 1 && 3 <= x330 - 1 && 3 <= x326 - 1 && x331 <= x326 && x325 <= x334 - 1 && x330 <= x326
f1140_0_sortedHigh_NONNULL(x335, x336, x337, x338, x339) -> f1232_0_sortedHigh_InvokeMethod(x340, x341, x342, x343, x344) :|: x337 = x342 && x343 + 4 <= x336 && x344 + 2 <= x336 && 1 <= x341 - 1 && 4 <= x340 - 1 && 4 <= x336 - 1 && x341 <= x336 && x335 <= x344 - 1 && x340 <= x336
f1140_0_sortedHigh_NONNULL(x345, x346, x347, x348, x349) -> f730_0_quicksort_NONNULL(x350, x351, x352, x353, x354) :|: x350 <= x346 && x345 <= x355 - 1 && 1 <= x346 - 1 && 1 <= x350 - 1
f1232_0_sortedHigh_InvokeMethod(x356, x357, x358, x359, x360) -> f730_0_quicksort_NONNULL(x361, x362, x363, x364, x365) :|: x360 + 2 <= x357 && x360 + 2 <= x356 && x359 + 4 <= x356 && 1 <= x361 - 1 && 1 <= x357 - 1 && 2 <= x356 - 1 && x361 <= x357 && x361 <= x356
f1140_0_sortedHigh_NONNULL(x366, x367, x368, x369, x370) -> f1309_0_sortedHigh_InvokeMethod(x371, x372, x373, x374, x375) :|: x368 = x373 && x374 + 4 <= x367 && x375 + 2 <= x367 && 1 <= x372 - 1 && 3 <= x371 - 1 && 3 <= x367 - 1 && x372 <= x367 && x366 <= x375 - 1 && x371 <= x367
f1140_0_sortedHigh_NONNULL(x376, x377, x378, x379, x380) -> f1309_0_sortedHigh_InvokeMethod(x381, x382, x383, x384, x385) :|: x378 = x383 && x384 + 4 <= x377 && x385 + 2 <= x377 && 1 <= x382 - 1 && 4 <= x381 - 1 && 4 <= x377 - 1 && x382 <= x377 && x376 <= x385 - 1 && x381 <= x377
f1309_0_sortedHigh_InvokeMethod(x386, x387, x388, x389, x390) -> f730_0_quicksort_NONNULL(x391, x392, x393, x394, x395) :|: x390 + 2 <= x387 && x390 + 2 <= x386 && x389 + 4 <= x386 && 1 <= x391 - 1 && 1 <= x387 - 1 && 2 <= x386 - 1 && x391 <= x387 && x391 <= x386
__init(x396, x397, x398, x399, x400) -> f1_0_main_Load(x401, x402, x403, x404, x405) :|: 0 <= 0
Start term: __init(arg1, arg2, arg3, arg4, arg5)

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

(1) IRSFormatTransformerProof (EQUIVALENT)
Reformatted IRS to match normalized format (transformed away non-linear left-hand sides, !=, / and %).
----------------------------------------

(2)
Obligation:
Rules:
f1_0_main_Load(arg1, arg2, arg3, arg4, arg5) -> f392_0_createList_GT(arg1P, arg2P, arg3P, arg4P, arg5P) :|: 0 = arg3P && 0 = arg2P && 0 = arg1P && 0 = arg2 && 0 <= arg1 - 1
f1_0_main_Load(x, x1, x2, x3, x4) -> f89_0_main_InvokeMethod(x5, x6, x7, x8, x9) :|: 0 = x6 && 0 <= x5 - 1 && 0 <= x - 1 && 0 <= x1 - 1 && x5 <= x
f1_0_main_Load(x10, x11, x12, x13, x14) -> f89_0_main_InvokeMethod(x15, x16, x17, x19, x20) :|: 0 <= x15 - 1 && 0 <= x10 - 1 && x15 <= x10 && 0 <= x11 - 1 && -1 <= x16 - 1
f89_0_main_InvokeMethod(x21, x22, x24, x25, x26) -> f392_0_createList_GT(x27, x28, x30, x31, x32) :|: 1 = x30 && x22 = x27 && 0 <= x28 - 1 && 0 <= x21 - 1
f1_0_main_Load(x33, x34, x36, x37, x38) -> f730_0_quicksort_NONNULL(x39, x41, x42, x43, x44) :|: 0 = x34 && -1 <= x39 - 1 && 0 <= x33 - 1 && x39 + 1 <= x33
f89_0_main_InvokeMethod(x45, x46, x47, x48, x49) -> f730_0_quicksort_NONNULL(x50, x51, x52, x53, x55) :|: x50 + 1 <= x45 && 0 <= x56 - 1 && 0 <= x45 - 1 && -1 <= x50 - 1 && 0 = x46
f1_0_main_Load(x57, x58, x59, x60, x61) -> f730_0_quicksort_NONNULL(x62, x63, x64, x65, x66) :|: 0 = x58 && 1 <= x62 - 1 && 0 <= x57 - 1 && x62 - 1 <= x57
f89_0_main_InvokeMethod(x67, x68, x69, x70, x71) -> f703_0_main_InvokeMethod(x72, x73, x74, x75, x76) :|: x72 <= x67 && 0 <= x77 - 1 && 0 <= x67 - 1 && 0 <= x72 - 1 && 2 <= x73 - 1 && 0 = x74
f89_0_main_InvokeMethod(x78, x79, x80, x81, x82) -> f703_0_main_InvokeMethod(x83, x84, x85, x86, x87) :|: x83 <= x78 && 0 <= x88 - 1 && 0 <= x78 - 1 && 0 <= x83 - 1 && 2 <= x84 - 1
f89_0_main_InvokeMethod(x89, x90, x91, x92, x93) -> f703_0_main_InvokeMethod(x94, x95, x96, x97, x98) :|: x94 <= x89 && 0 <= x99 - 1 && 0 <= x89 - 1 && 0 <= x94 - 1 && 1 <= x95 - 1
f89_0_main_InvokeMethod(x100, x101, x102, x103, x104) -> f703_0_main_InvokeMethod(x106, x107, x108, x109, x111) :|: x106 <= x100 && 0 <= x112 - 1 && x107 - 1 <= x100 && 0 <= x100 - 1 && 0 <= x106 - 1 && 1 <= x107 - 1 && 0 = x108
f703_0_main_InvokeMethod(x113, x114, x116, x117, x118) -> f730_0_quicksort_NONNULL(x119, x120, x121, x122, x123) :|: x119 <= x114 && 0 <= x124 - 1 && 0 <= x113 - 1 && 0 <= x114 - 1 && 0 <= x119 - 1 && x116 + 2 <= x114
f392_0_createList_GT(x125, x126, x127, x128, x129) -> f392_0_createList_GT(x130, x131, x132, x133, x134) :|: x127 = x132 && x126 = x131 && x125 - 1 = x130 && x126 <= x127 && x125 - 1 <= x125 - 1 && -1 <= x126 - 1 && 0 <= x125 - 1
f392_0_createList_GT(x135, x136, x137, x138, x139) -> f501_0_createList_InvokeMethod(x141, x142, x143, x144, x146) :|: x137 + 1 = x144 && x136 = x143 && x135 - 1 = x142 && x135 = x141 && x137 <= x136 - 1 && -1 <= x137 - 1 && -1 <= x136 - 1 && 0 <= x135 - 1
f392_0_createList_GT(x147, x148, x149, x150, x151) -> f501_0_createList_InvokeMethod(x152, x153, x154, x155, x156) :|: 0 <= x147 - 1 && -1 <= x148 - 1 && x149 <= x148 - 1 && -1 <= x157 - 1 && -1 <= x149 - 1 && x147 = x152 && x147 - 1 = x153 && x148 = x154 && x149 + 1 = x155
f501_0_createList_InvokeMethod(x158, x159, x160, x161, x162) -> f392_0_createList_GT(x163, x165, x166, x167, x168) :|: x161 = x166 && x160 = x165 && x159 = x163 && x159 <= x158 - 1 && x161 <= x160 && 0 <= x160 - 1 && 0 <= x161 - 1 && 0 <= x158 - 1
f730_0_quicksort_NONNULL(x169, x170, x171, x172, x173) -> f790_0_sortedLow_NONNULL(x174, x175, x176, x177, x178) :|: x174 + 2 <= x169 && -1 <= x175 - 1 && 0 <= x169 - 1 && x175 + 1 <= x169
f730_0_quicksort_NONNULL(x179, x180, x181, x182, x183) -> f1140_0_sortedHigh_NONNULL(x184, x185, x186, x187, x188) :|: x184 + 2 <= x179 && -1 <= x185 - 1 && 1 <= x179 - 1 && x185 + 2 <= x179
f730_0_quicksort_NONNULL(x189, x190, x191, x192, x193) -> f1000_0_quicksort_InvokeMethod(x194, x196, x197, x198, x199) :|: x199 + 4 <= x189 && x198 + 2 <= x189 && 1 <= x196 - 1 && 3 <= x194 - 1 && 3 <= x189 - 1 && x196 + 2 <= x189 && x194 <= x189
f730_0_quicksort_NONNULL(x200, x201, x202, x203, x204) -> f1000_0_quicksort_InvokeMethod(x205, x206, x207, x208, x209) :|: x209 + 4 <= x200 && x208 + 2 <= x200 && 2 <= x206 - 1 && 4 <= x205 - 1 && 4 <= x200 - 1 && x206 + 2 <= x200 && x205 <= x200
f1000_0_quicksort_InvokeMethod(x210, x211, x212, x213, x214) -> f1140_0_sortedHigh_NONNULL(x215, x216, x217, x218, x219) :|: x212 = x217 && x213 = x215 && x214 + 2 <= x211 && x213 + 2 <= x210 && x214 + 4 <= x210 && 0 <= x216 - 1 && 0 <= x211 - 1 && 2 <= x210 - 1 && x216 <= x211 && x216 + 2 <= x210
f1000_0_quicksort_InvokeMethod(x220, x221, x222, x223, x224) -> f1287_0_quicksort_InvokeMethod(x225, x226, x227, x228, x229) :|: x224 + 2 <= x221 && x223 + 2 <= x220 && x224 + 4 <= x220 && 4 <= x225 - 1 && 2 <= x221 - 1 && 4 <= x220 - 1 && x225 <= x220
f1000_0_quicksort_InvokeMethod(x230, x231, x232, x233, x234) -> f1287_0_quicksort_InvokeMethod(x235, x236, x237, x238, x239) :|: x234 + 2 <= x231 && x233 + 2 <= x230 && x234 + 4 <= x230 && 3 <= x235 - 1 && 1 <= x231 - 1 && 3 <= x230 - 1 && x235 <= x230
f790_0_sortedLow_NONNULL(x240, x241, x242, x243, x244) -> f790_0_sortedLow_NONNULL(x245, x246, x247, x248, x249) :|: x246 + 1 <= x241 && x240 <= x250 - 1 && 0 <= x241 - 1 && -1 <= x246 - 1 && x240 = x245 && x242 = x247
f790_0_sortedLow_NONNULL(x251, x252, x253, x254, x255) -> f790_0_sortedLow_NONNULL(x256, x257, x258, x259, x260) :|: x257 + 1 <= x252 && x261 <= x251 && 0 <= x252 - 1 && -1 <= x257 - 1 && x251 = x256 && x253 = x258
f790_0_sortedLow_NONNULL(x262, x263, x264, x265, x266) -> f730_0_quicksort_NONNULL(x267, x268, x269, x270, x271) :|: x267 <= x263 && x272 <= x262 && 1 <= x263 - 1 && 1 <= x267 - 1
f790_0_sortedLow_NONNULL(x273, x274, x275, x276, x277) -> f1022_0_sortedLow_InvokeMethod(x278, x279, x280, x281, x282) :|: x275 = x280 && x281 + 4 <= x274 && x282 + 2 <= x274 && 1 <= x279 - 1 && 3 <= x278 - 1 && 3 <= x274 - 1 && x279 <= x274 && x282 <= x273 && x278 <= x274
f790_0_sortedLow_NONNULL(x283, x284, x285, x286, x287) -> f1022_0_sortedLow_InvokeMethod(x288, x289, x290, x291, x292) :|: x285 = x290 && x291 + 4 <= x284 && x292 + 2 <= x284 && 1 <= x289 - 1 && 4 <= x288 - 1 && 4 <= x284 - 1 && x289 <= x284 && x292 <= x283 && x288 <= x284
f1022_0_sortedLow_InvokeMethod(x293, x294, x295, x296, x297) -> f730_0_quicksort_NONNULL(x298, x299, x300, x301, x302) :|: x297 + 2 <= x294 && x297 + 2 <= x293 && x296 + 4 <= x293 && 1 <= x298 - 1 && 1 <= x294 - 1 && 2 <= x293 - 1 && x298 <= x294 && x298 <= x293
f1140_0_sortedHigh_NONNULL(x303, x304, x305, x306, x307) -> f1140_0_sortedHigh_NONNULL(x308, x309, x310, x311, x312) :|: x309 + 1 <= x304 && x313 <= x303 && 0 <= x304 - 1 && -1 <= x309 - 1 && x303 = x308 && x305 = x310
f1140_0_sortedHigh_NONNULL(x314, x315, x316, x317, x318) -> f1140_0_sortedHigh_NONNULL(x319, x320, x321, x322, x323) :|: x320 + 1 <= x315 && x314 <= x324 - 1 && 0 <= x315 - 1 && -1 <= x320 - 1 && x314 = x319 && x316 = x321
f1140_0_sortedHigh_NONNULL(x325, x326, x327, x328, x329) -> f1232_0_sortedHigh_InvokeMethod(x330, x331, x332, x333, x334) :|: x327 = x332 && x333 + 4 <= x326 && x334 + 2 <= x326 && 1 <= x331 - 1 && 3 <= x330 - 1 && 3 <= x326 - 1 && x331 <= x326 && x325 <= x334 - 1 && x330 <= x326
f1140_0_sortedHigh_NONNULL(x335, x336, x337, x338, x339) -> f1232_0_sortedHigh_InvokeMethod(x340, x341, x342, x343, x344) :|: x337 = x342 && x343 + 4 <= x336 && x344 + 2 <= x336 && 1 <= x341 - 1 && 4 <= x340 - 1 && 4 <= x336 - 1 && x341 <= x336 && x335 <= x344 - 1 && x340 <= x336
f1140_0_sortedHigh_NONNULL(x345, x346, x347, x348, x349) -> f730_0_quicksort_NONNULL(x350, x351, x352, x353, x354) :|: x350 <= x346 && x345 <= x355 - 1 && 1 <= x346 - 1 && 1 <= x350 - 1
f1232_0_sortedHigh_InvokeMethod(x356, x357, x358, x359, x360) -> f730_0_quicksort_NONNULL(x361, x362, x363, x364, x365) :|: x360 + 2 <= x357 && x360 + 2 <= x356 && x359 + 4 <= x356 && 1 <= x361 - 1 && 1 <= x357 - 1 && 2 <= x356 - 1 && x361 <= x357 && x361 <= x356
f1140_0_sortedHigh_NONNULL(x366, x367, x368, x369, x370) -> f1309_0_sortedHigh_InvokeMethod(x371, x372, x373, x374, x375) :|: x368 = x373 && x374 + 4 <= x367 && x375 + 2 <= x367 && 1 <= x372 - 1 && 3 <= x371 - 1 && 3 <= x367 - 1 && x372 <= x367 && x366 <= x375 - 1 && x371 <= x367
f1140_0_sortedHigh_NONNULL(x376, x377, x378, x379, x380) -> f1309_0_sortedHigh_InvokeMethod(x381, x382, x383, x384, x385) :|: x378 = x383 && x384 + 4 <= x377 && x385 + 2 <= x377 && 1 <= x382 - 1 && 4 <= x381 - 1 && 4 <= x377 - 1 && x382 <= x377 && x376 <= x385 - 1 && x381 <= x377
f1309_0_sortedHigh_InvokeMethod(x386, x387, x388, x389, x390) -> f730_0_quicksort_NONNULL(x391, x392, x393, x394, x395) :|: x390 + 2 <= x387 && x390 + 2 <= x386 && x389 + 4 <= x386 && 1 <= x391 - 1 && 1 <= x387 - 1 && 2 <= x386 - 1 && x391 <= x387 && x391 <= x386
__init(x396, x397, x398, x399, x400) -> f1_0_main_Load(x401, x402, x403, x404, x405) :|: 0 <= 0
Start term: __init(arg1, arg2, arg3, arg4, arg5)

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

(3) IRSwTTerminationDigraphProof (EQUIVALENT)
Constructed termination digraph!
Nodes:
(1) f1_0_main_Load(arg1, arg2, arg3, arg4, arg5) -> f392_0_createList_GT(arg1P, arg2P, arg3P, arg4P, arg5P) :|: 0 = arg3P && 0 = arg2P && 0 = arg1P && 0 = arg2 && 0 <= arg1 - 1
(2) f1_0_main_Load(x, x1, x2, x3, x4) -> f89_0_main_InvokeMethod(x5, x6, x7, x8, x9) :|: 0 = x6 && 0 <= x5 - 1 && 0 <= x - 1 && 0 <= x1 - 1 && x5 <= x
(3) f1_0_main_Load(x10, x11, x12, x13, x14) -> f89_0_main_InvokeMethod(x15, x16, x17, x19, x20) :|: 0 <= x15 - 1 && 0 <= x10 - 1 && x15 <= x10 && 0 <= x11 - 1 && -1 <= x16 - 1
(4) f89_0_main_InvokeMethod(x21, x22, x24, x25, x26) -> f392_0_createList_GT(x27, x28, x30, x31, x32) :|: 1 = x30 && x22 = x27 && 0 <= x28 - 1 && 0 <= x21 - 1
(5) f1_0_main_Load(x33, x34, x36, x37, x38) -> f730_0_quicksort_NONNULL(x39, x41, x42, x43, x44) :|: 0 = x34 && -1 <= x39 - 1 && 0 <= x33 - 1 && x39 + 1 <= x33
(6) f89_0_main_InvokeMethod(x45, x46, x47, x48, x49) -> f730_0_quicksort_NONNULL(x50, x51, x52, x53, x55) :|: x50 + 1 <= x45 && 0 <= x56 - 1 && 0 <= x45 - 1 && -1 <= x50 - 1 && 0 = x46
(7) f1_0_main_Load(x57, x58, x59, x60, x61) -> f730_0_quicksort_NONNULL(x62, x63, x64, x65, x66) :|: 0 = x58 && 1 <= x62 - 1 && 0 <= x57 - 1 && x62 - 1 <= x57
(8) f89_0_main_InvokeMethod(x67, x68, x69, x70, x71) -> f703_0_main_InvokeMethod(x72, x73, x74, x75, x76) :|: x72 <= x67 && 0 <= x77 - 1 && 0 <= x67 - 1 && 0 <= x72 - 1 && 2 <= x73 - 1 && 0 = x74
(9) f89_0_main_InvokeMethod(x78, x79, x80, x81, x82) -> f703_0_main_InvokeMethod(x83, x84, x85, x86, x87) :|: x83 <= x78 && 0 <= x88 - 1 && 0 <= x78 - 1 && 0 <= x83 - 1 && 2 <= x84 - 1
(10) f89_0_main_InvokeMethod(x89, x90, x91, x92, x93) -> f703_0_main_InvokeMethod(x94, x95, x96, x97, x98) :|: x94 <= x89 && 0 <= x99 - 1 && 0 <= x89 - 1 && 0 <= x94 - 1 && 1 <= x95 - 1
(11) f89_0_main_InvokeMethod(x100, x101, x102, x103, x104) -> f703_0_main_InvokeMethod(x106, x107, x108, x109, x111) :|: x106 <= x100 && 0 <= x112 - 1 && x107 - 1 <= x100 && 0 <= x100 - 1 && 0 <= x106 - 1 && 1 <= x107 - 1 && 0 = x108
(12) f703_0_main_InvokeMethod(x113, x114, x116, x117, x118) -> f730_0_quicksort_NONNULL(x119, x120, x121, x122, x123) :|: x119 <= x114 && 0 <= x124 - 1 && 0 <= x113 - 1 && 0 <= x114 - 1 && 0 <= x119 - 1 && x116 + 2 <= x114
(13) f392_0_createList_GT(x125, x126, x127, x128, x129) -> f392_0_createList_GT(x130, x131, x132, x133, x134) :|: x127 = x132 && x126 = x131 && x125 - 1 = x130 && x126 <= x127 && x125 - 1 <= x125 - 1 && -1 <= x126 - 1 && 0 <= x125 - 1
(14) f392_0_createList_GT(x135, x136, x137, x138, x139) -> f501_0_createList_InvokeMethod(x141, x142, x143, x144, x146) :|: x137 + 1 = x144 && x136 = x143 && x135 - 1 = x142 && x135 = x141 && x137 <= x136 - 1 && -1 <= x137 - 1 && -1 <= x136 - 1 && 0 <= x135 - 1
(15) f392_0_createList_GT(x147, x148, x149, x150, x151) -> f501_0_createList_InvokeMethod(x152, x153, x154, x155, x156) :|: 0 <= x147 - 1 && -1 <= x148 - 1 && x149 <= x148 - 1 && -1 <= x157 - 1 && -1 <= x149 - 1 && x147 = x152 && x147 - 1 = x153 && x148 = x154 && x149 + 1 = x155
(16) f501_0_createList_InvokeMethod(x158, x159, x160, x161, x162) -> f392_0_createList_GT(x163, x165, x166, x167, x168) :|: x161 = x166 && x160 = x165 && x159 = x163 && x159 <= x158 - 1 && x161 <= x160 && 0 <= x160 - 1 && 0 <= x161 - 1 && 0 <= x158 - 1
(17) f730_0_quicksort_NONNULL(x169, x170, x171, x172, x173) -> f790_0_sortedLow_NONNULL(x174, x175, x176, x177, x178) :|: x174 + 2 <= x169 && -1 <= x175 - 1 && 0 <= x169 - 1 && x175 + 1 <= x169
(18) f730_0_quicksort_NONNULL(x179, x180, x181, x182, x183) -> f1140_0_sortedHigh_NONNULL(x184, x185, x186, x187, x188) :|: x184 + 2 <= x179 && -1 <= x185 - 1 && 1 <= x179 - 1 && x185 + 2 <= x179
(19) f730_0_quicksort_NONNULL(x189, x190, x191, x192, x193) -> f1000_0_quicksort_InvokeMethod(x194, x196, x197, x198, x199) :|: x199 + 4 <= x189 && x198 + 2 <= x189 && 1 <= x196 - 1 && 3 <= x194 - 1 && 3 <= x189 - 1 && x196 + 2 <= x189 && x194 <= x189
(20) f730_0_quicksort_NONNULL(x200, x201, x202, x203, x204) -> f1000_0_quicksort_InvokeMethod(x205, x206, x207, x208, x209) :|: x209 + 4 <= x200 && x208 + 2 <= x200 && 2 <= x206 - 1 && 4 <= x205 - 1 && 4 <= x200 - 1 && x206 + 2 <= x200 && x205 <= x200
(21) f1000_0_quicksort_InvokeMethod(x210, x211, x212, x213, x214) -> f1140_0_sortedHigh_NONNULL(x215, x216, x217, x218, x219) :|: x212 = x217 && x213 = x215 && x214 + 2 <= x211 && x213 + 2 <= x210 && x214 + 4 <= x210 && 0 <= x216 - 1 && 0 <= x211 - 1 && 2 <= x210 - 1 && x216 <= x211 && x216 + 2 <= x210
(22) f1000_0_quicksort_InvokeMethod(x220, x221, x222, x223, x224) -> f1287_0_quicksort_InvokeMethod(x225, x226, x227, x228, x229) :|: x224 + 2 <= x221 && x223 + 2 <= x220 && x224 + 4 <= x220 && 4 <= x225 - 1 && 2 <= x221 - 1 && 4 <= x220 - 1 && x225 <= x220
(23) f1000_0_quicksort_InvokeMethod(x230, x231, x232, x233, x234) -> f1287_0_quicksort_InvokeMethod(x235, x236, x237, x238, x239) :|: x234 + 2 <= x231 && x233 + 2 <= x230 && x234 + 4 <= x230 && 3 <= x235 - 1 && 1 <= x231 - 1 && 3 <= x230 - 1 && x235 <= x230
(24) f790_0_sortedLow_NONNULL(x240, x241, x242, x243, x244) -> f790_0_sortedLow_NONNULL(x245, x246, x247, x248, x249) :|: x246 + 1 <= x241 && x240 <= x250 - 1 && 0 <= x241 - 1 && -1 <= x246 - 1 && x240 = x245 && x242 = x247
(25) f790_0_sortedLow_NONNULL(x251, x252, x253, x254, x255) -> f790_0_sortedLow_NONNULL(x256, x257, x258, x259, x260) :|: x257 + 1 <= x252 && x261 <= x251 && 0 <= x252 - 1 && -1 <= x257 - 1 && x251 = x256 && x253 = x258
(26) f790_0_sortedLow_NONNULL(x262, x263, x264, x265, x266) -> f730_0_quicksort_NONNULL(x267, x268, x269, x270, x271) :|: x267 <= x263 && x272 <= x262 && 1 <= x263 - 1 && 1 <= x267 - 1
(27) f790_0_sortedLow_NONNULL(x273, x274, x275, x276, x277) -> f1022_0_sortedLow_InvokeMethod(x278, x279, x280, x281, x282) :|: x275 = x280 && x281 + 4 <= x274 && x282 + 2 <= x274 && 1 <= x279 - 1 && 3 <= x278 - 1 && 3 <= x274 - 1 && x279 <= x274 && x282 <= x273 && x278 <= x274
(28) f790_0_sortedLow_NONNULL(x283, x284, x285, x286, x287) -> f1022_0_sortedLow_InvokeMethod(x288, x289, x290, x291, x292) :|: x285 = x290 && x291 + 4 <= x284 && x292 + 2 <= x284 && 1 <= x289 - 1 && 4 <= x288 - 1 && 4 <= x284 - 1 && x289 <= x284 && x292 <= x283 && x288 <= x284
(29) f1022_0_sortedLow_InvokeMethod(x293, x294, x295, x296, x297) -> f730_0_quicksort_NONNULL(x298, x299, x300, x301, x302) :|: x297 + 2 <= x294 && x297 + 2 <= x293 && x296 + 4 <= x293 && 1 <= x298 - 1 && 1 <= x294 - 1 && 2 <= x293 - 1 && x298 <= x294 && x298 <= x293
(30) f1140_0_sortedHigh_NONNULL(x303, x304, x305, x306, x307) -> f1140_0_sortedHigh_NONNULL(x308, x309, x310, x311, x312) :|: x309 + 1 <= x304 && x313 <= x303 && 0 <= x304 - 1 && -1 <= x309 - 1 && x303 = x308 && x305 = x310
(31) f1140_0_sortedHigh_NONNULL(x314, x315, x316, x317, x318) -> f1140_0_sortedHigh_NONNULL(x319, x320, x321, x322, x323) :|: x320 + 1 <= x315 && x314 <= x324 - 1 && 0 <= x315 - 1 && -1 <= x320 - 1 && x314 = x319 && x316 = x321
(32) f1140_0_sortedHigh_NONNULL(x325, x326, x327, x328, x329) -> f1232_0_sortedHigh_InvokeMethod(x330, x331, x332, x333, x334) :|: x327 = x332 && x333 + 4 <= x326 && x334 + 2 <= x326 && 1 <= x331 - 1 && 3 <= x330 - 1 && 3 <= x326 - 1 && x331 <= x326 && x325 <= x334 - 1 && x330 <= x326
(33) f1140_0_sortedHigh_NONNULL(x335, x336, x337, x338, x339) -> f1232_0_sortedHigh_InvokeMethod(x340, x341, x342, x343, x344) :|: x337 = x342 && x343 + 4 <= x336 && x344 + 2 <= x336 && 1 <= x341 - 1 && 4 <= x340 - 1 && 4 <= x336 - 1 && x341 <= x336 && x335 <= x344 - 1 && x340 <= x336
(34) f1140_0_sortedHigh_NONNULL(x345, x346, x347, x348, x349) -> f730_0_quicksort_NONNULL(x350, x351, x352, x353, x354) :|: x350 <= x346 && x345 <= x355 - 1 && 1 <= x346 - 1 && 1 <= x350 - 1
(35) f1232_0_sortedHigh_InvokeMethod(x356, x357, x358, x359, x360) -> f730_0_quicksort_NONNULL(x361, x362, x363, x364, x365) :|: x360 + 2 <= x357 && x360 + 2 <= x356 && x359 + 4 <= x356 && 1 <= x361 - 1 && 1 <= x357 - 1 && 2 <= x356 - 1 && x361 <= x357 && x361 <= x356
(36) f1140_0_sortedHigh_NONNULL(x366, x367, x368, x369, x370) -> f1309_0_sortedHigh_InvokeMethod(x371, x372, x373, x374, x375) :|: x368 = x373 && x374 + 4 <= x367 && x375 + 2 <= x367 && 1 <= x372 - 1 && 3 <= x371 - 1 && 3 <= x367 - 1 && x372 <= x367 && x366 <= x375 - 1 && x371 <= x367
(37) f1140_0_sortedHigh_NONNULL(x376, x377, x378, x379, x380) -> f1309_0_sortedHigh_InvokeMethod(x381, x382, x383, x384, x385) :|: x378 = x383 && x384 + 4 <= x377 && x385 + 2 <= x377 && 1 <= x382 - 1 && 4 <= x381 - 1 && 4 <= x377 - 1 && x382 <= x377 && x376 <= x385 - 1 && x381 <= x377
(38) f1309_0_sortedHigh_InvokeMethod(x386, x387, x388, x389, x390) -> f730_0_quicksort_NONNULL(x391, x392, x393, x394, x395) :|: x390 + 2 <= x387 && x390 + 2 <= x386 && x389 + 4 <= x386 && 1 <= x391 - 1 && 1 <= x387 - 1 && 2 <= x386 - 1 && x391 <= x387 && x391 <= x386
(39) __init(x396, x397, x398, x399, x400) -> f1_0_main_Load(x401, x402, x403, x404, x405) :|: 0 <= 0

Arcs:
(2) -> (4), (6), (8), (9), (10), (11)
(3) -> (4), (6), (8), (9), (10), (11)
(4) -> (13), (14), (15)
(5) -> (17), (18), (19), (20)
(6) -> (17), (18), (19), (20)
(7) -> (17), (18), (19), (20)
(8) -> (12)
(9) -> (12)
(10) -> (12)
(11) -> (12)
(12) -> (17), (18), (19), (20)
(13) -> (13)
(14) -> (16)
(15) -> (16)
(16) -> (13), (14), (15)
(17) -> (24), (25), (26), (27), (28)
(18) -> (30), (31), (32), (33), (34), (36), (37)
(19) -> (21), (22), (23)
(20) -> (21), (22), (23)
(21) -> (30), (31), (32), (33), (34), (36), (37)
(24) -> (24), (25), (26), (27), (28)
(25) -> (24), (25), (26), (27), (28)
(26) -> (17), (18), (19), (20)
(27) -> (29)
(28) -> (29)
(29) -> (17), (18), (19), (20)
(30) -> (30), (31), (32), (33), (34), (36), (37)
(31) -> (30), (31), (32), (33), (34), (36), (37)
(32) -> (35)
(33) -> (35)
(34) -> (17), (18), (19), (20)
(35) -> (17), (18), (19), (20)
(36) -> (38)
(37) -> (38)
(38) -> (17), (18), (19), (20)
(39) -> (1), (2), (3), (5), (7)

This digraph is fully evaluated!
----------------------------------------

(4)
Complex Obligation (AND)

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

(5)
Obligation:

Termination digraph:
Nodes:
(1) f730_0_quicksort_NONNULL(x169, x170, x171, x172, x173) -> f790_0_sortedLow_NONNULL(x174, x175, x176, x177, x178) :|: x174 + 2 <= x169 && -1 <= x175 - 1 && 0 <= x169 - 1 && x175 + 1 <= x169
(2) f1140_0_sortedHigh_NONNULL(x345, x346, x347, x348, x349) -> f730_0_quicksort_NONNULL(x350, x351, x352, x353, x354) :|: x350 <= x346 && x345 <= x355 - 1 && 1 <= x346 - 1 && 1 <= x350 - 1
(3) f730_0_quicksort_NONNULL(x179, x180, x181, x182, x183) -> f1140_0_sortedHigh_NONNULL(x184, x185, x186, x187, x188) :|: x184 + 2 <= x179 && -1 <= x185 - 1 && 1 <= x179 - 1 && x185 + 2 <= x179
(4) f1232_0_sortedHigh_InvokeMethod(x356, x357, x358, x359, x360) -> f730_0_quicksort_NONNULL(x361, x362, x363, x364, x365) :|: x360 + 2 <= x357 && x360 + 2 <= x356 && x359 + 4 <= x356 && 1 <= x361 - 1 && 1 <= x357 - 1 && 2 <= x356 - 1 && x361 <= x357 && x361 <= x356
(5) f1140_0_sortedHigh_NONNULL(x335, x336, x337, x338, x339) -> f1232_0_sortedHigh_InvokeMethod(x340, x341, x342, x343, x344) :|: x337 = x342 && x343 + 4 <= x336 && x344 + 2 <= x336 && 1 <= x341 - 1 && 4 <= x340 - 1 && 4 <= x336 - 1 && x341 <= x336 && x335 <= x344 - 1 && x340 <= x336
(6) f1140_0_sortedHigh_NONNULL(x325, x326, x327, x328, x329) -> f1232_0_sortedHigh_InvokeMethod(x330, x331, x332, x333, x334) :|: x327 = x332 && x333 + 4 <= x326 && x334 + 2 <= x326 && 1 <= x331 - 1 && 3 <= x330 - 1 && 3 <= x326 - 1 && x331 <= x326 && x325 <= x334 - 1 && x330 <= x326
(7) f1000_0_quicksort_InvokeMethod(x210, x211, x212, x213, x214) -> f1140_0_sortedHigh_NONNULL(x215, x216, x217, x218, x219) :|: x212 = x217 && x213 = x215 && x214 + 2 <= x211 && x213 + 2 <= x210 && x214 + 4 <= x210 && 0 <= x216 - 1 && 0 <= x211 - 1 && 2 <= x210 - 1 && x216 <= x211 && x216 + 2 <= x210
(8) f730_0_quicksort_NONNULL(x200, x201, x202, x203, x204) -> f1000_0_quicksort_InvokeMethod(x205, x206, x207, x208, x209) :|: x209 + 4 <= x200 && x208 + 2 <= x200 && 2 <= x206 - 1 && 4 <= x205 - 1 && 4 <= x200 - 1 && x206 + 2 <= x200 && x205 <= x200
(9) f730_0_quicksort_NONNULL(x189, x190, x191, x192, x193) -> f1000_0_quicksort_InvokeMethod(x194, x196, x197, x198, x199) :|: x199 + 4 <= x189 && x198 + 2 <= x189 && 1 <= x196 - 1 && 3 <= x194 - 1 && 3 <= x189 - 1 && x196 + 2 <= x189 && x194 <= x189
(10) f1309_0_sortedHigh_InvokeMethod(x386, x387, x388, x389, x390) -> f730_0_quicksort_NONNULL(x391, x392, x393, x394, x395) :|: x390 + 2 <= x387 && x390 + 2 <= x386 && x389 + 4 <= x386 && 1 <= x391 - 1 && 1 <= x387 - 1 && 2 <= x386 - 1 && x391 <= x387 && x391 <= x386
(11) f1140_0_sortedHigh_NONNULL(x376, x377, x378, x379, x380) -> f1309_0_sortedHigh_InvokeMethod(x381, x382, x383, x384, x385) :|: x378 = x383 && x384 + 4 <= x377 && x385 + 2 <= x377 && 1 <= x382 - 1 && 4 <= x381 - 1 && 4 <= x377 - 1 && x382 <= x377 && x376 <= x385 - 1 && x381 <= x377
(12) f1140_0_sortedHigh_NONNULL(x366, x367, x368, x369, x370) -> f1309_0_sortedHigh_InvokeMethod(x371, x372, x373, x374, x375) :|: x368 = x373 && x374 + 4 <= x367 && x375 + 2 <= x367 && 1 <= x372 - 1 && 3 <= x371 - 1 && 3 <= x367 - 1 && x372 <= x367 && x366 <= x375 - 1 && x371 <= x367
(13) f1140_0_sortedHigh_NONNULL(x303, x304, x305, x306, x307) -> f1140_0_sortedHigh_NONNULL(x308, x309, x310, x311, x312) :|: x309 + 1 <= x304 && x313 <= x303 && 0 <= x304 - 1 && -1 <= x309 - 1 && x303 = x308 && x305 = x310
(14) f1140_0_sortedHigh_NONNULL(x314, x315, x316, x317, x318) -> f1140_0_sortedHigh_NONNULL(x319, x320, x321, x322, x323) :|: x320 + 1 <= x315 && x314 <= x324 - 1 && 0 <= x315 - 1 && -1 <= x320 - 1 && x314 = x319 && x316 = x321
(15) f1022_0_sortedLow_InvokeMethod(x293, x294, x295, x296, x297) -> f730_0_quicksort_NONNULL(x298, x299, x300, x301, x302) :|: x297 + 2 <= x294 && x297 + 2 <= x293 && x296 + 4 <= x293 && 1 <= x298 - 1 && 1 <= x294 - 1 && 2 <= x293 - 1 && x298 <= x294 && x298 <= x293
(16) f790_0_sortedLow_NONNULL(x283, x284, x285, x286, x287) -> f1022_0_sortedLow_InvokeMethod(x288, x289, x290, x291, x292) :|: x285 = x290 && x291 + 4 <= x284 && x292 + 2 <= x284 && 1 <= x289 - 1 && 4 <= x288 - 1 && 4 <= x284 - 1 && x289 <= x284 && x292 <= x283 && x288 <= x284
(17) f790_0_sortedLow_NONNULL(x273, x274, x275, x276, x277) -> f1022_0_sortedLow_InvokeMethod(x278, x279, x280, x281, x282) :|: x275 = x280 && x281 + 4 <= x274 && x282 + 2 <= x274 && 1 <= x279 - 1 && 3 <= x278 - 1 && 3 <= x274 - 1 && x279 <= x274 && x282 <= x273 && x278 <= x274
(18) f790_0_sortedLow_NONNULL(x262, x263, x264, x265, x266) -> f730_0_quicksort_NONNULL(x267, x268, x269, x270, x271) :|: x267 <= x263 && x272 <= x262 && 1 <= x263 - 1 && 1 <= x267 - 1
(19) f790_0_sortedLow_NONNULL(x240, x241, x242, x243, x244) -> f790_0_sortedLow_NONNULL(x245, x246, x247, x248, x249) :|: x246 + 1 <= x241 && x240 <= x250 - 1 && 0 <= x241 - 1 && -1 <= x246 - 1 && x240 = x245 && x242 = x247
(20) f790_0_sortedLow_NONNULL(x251, x252, x253, x254, x255) -> f790_0_sortedLow_NONNULL(x256, x257, x258, x259, x260) :|: x257 + 1 <= x252 && x261 <= x251 && 0 <= x252 - 1 && -1 <= x257 - 1 && x251 = x256 && x253 = x258

Arcs:
(1) -> (16), (17), (18), (19), (20)
(2) -> (1), (3), (8), (9)
(3) -> (2), (5), (6), (11), (12), (13), (14)
(4) -> (1), (3), (8), (9)
(5) -> (4)
(6) -> (4)
(7) -> (2), (5), (6), (11), (12), (13), (14)
(8) -> (7)
(9) -> (7)
(10) -> (1), (3), (8), (9)
(11) -> (10)
(12) -> (10)
(13) -> (2), (5), (6), (11), (12), (13), (14)
(14) -> (2), (5), (6), (11), (12), (13), (14)
(15) -> (1), (3), (8), (9)
(16) -> (15)
(17) -> (15)
(18) -> (1), (3), (8), (9)
(19) -> (16), (17), (18), (19), (20)
(20) -> (16), (17), (18), (19), (20)

This digraph is fully evaluated!

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

(6) IntTRSCompressionProof (EQUIVALENT)
Compressed rules.
----------------------------------------

(7)
Obligation:
Rules:
f730_0_quicksort_NONNULL(x200:0, x201:0, x202:0, x203:0, x204:0) -> f1140_0_sortedHigh_NONNULL(x208:0, x216:0, x207:0, x218:0, x219:0) :|: x216:0 + 2 <= x205:0 && x205:0 <= x200:0 && x206:0 + 2 <= x200:0 && x216:0 <= x206:0 && x200:0 > 4 && x216:0 > 0 && x209:0 + 4 <= x200:0 && x208:0 + 2 <= x200:0 && x209:0 + 4 <= x205:0 && x208:0 + 2 <= x205:0 && x209:0 + 2 <= x206:0 && x206:0 > 2 && x205:0 > 4
f790_0_sortedLow_NONNULL(x262:0, x263:0, x264:0, x265:0, x266:0) -> f730_0_quicksort_NONNULL(x267:0, x268:0, x269:0, x270:0, x271:0) :|: x263:0 > 1 && x267:0 > 1 && x272:0 <= x262:0 && x267:0 <= x263:0
f1140_0_sortedHigh_NONNULL(x325:0, x326:0, x327:0, x328:0, x329:0) -> f730_0_quicksort_NONNULL(x361:0, x362:0, x363:0, x364:0, x365:0) :|: x361:0 <= x330:0 && x330:0 <= x326:0 && x334:0 - 1 >= x325:0 && x361:0 <= x331:0 && x331:0 <= x326:0 && x326:0 > 3 && x361:0 > 1 && x331:0 > 1 && x333:0 + 4 <= x330:0 && x334:0 + 2 <= x326:0 && x334:0 + 2 <= x331:0 && x334:0 + 2 <= x330:0 && x330:0 > 3 && x333:0 + 4 <= x326:0
f730_0_quicksort_NONNULL(x169:0, x170:0, x171:0, x172:0, x173:0) -> f790_0_sortedLow_NONNULL(x174:0, x175:0, x176:0, x177:0, x178:0) :|: x169:0 > 0 && x175:0 + 1 <= x169:0 && x175:0 > -1 && x174:0 + 2 <= x169:0
f730_0_quicksort_NONNULL(x179:0, x180:0, x181:0, x182:0, x183:0) -> f1140_0_sortedHigh_NONNULL(x184:0, x185:0, x186:0, x187:0, x188:0) :|: x179:0 > 1 && x185:0 + 2 <= x179:0 && x185:0 > -1 && x184:0 + 2 <= x179:0
f730_0_quicksort_NONNULL(x, x1, x2, x3, x4) -> f1140_0_sortedHigh_NONNULL(x5, x6, x7, x8, x9) :|: x6 + 2 <= x10 && x10 <= x && x11 + 2 <= x && x6 <= x11 && x > 3 && x6 > 0 && x12 + 4 <= x && x5 + 2 <= x && x12 + 4 <= x10 && x5 + 2 <= x10 && x12 + 2 <= x11 && x11 > 1 && x10 > 3
f790_0_sortedLow_NONNULL(x273:0, x274:0, x275:0, x276:0, x277:0) -> f730_0_quicksort_NONNULL(x298:0, x299:0, x300:0, x301:0, x302:0) :|: x298:0 <= x278:0 && x278:0 <= x274:0 && x282:0 <= x273:0 && x298:0 <= x279:0 && x279:0 <= x274:0 && x274:0 > 3 && x298:0 > 1 && x279:0 > 1 && x281:0 + 4 <= x278:0 && x282:0 + 2 <= x274:0 && x282:0 + 2 <= x279:0 && x282:0 + 2 <= x278:0 && x278:0 > 3 && x281:0 + 4 <= x274:0
f1140_0_sortedHigh_NONNULL(x345:0, x346:0, x347:0, x348:0, x349:0) -> f730_0_quicksort_NONNULL(x350:0, x351:0, x352:0, x353:0, x354:0) :|: x346:0 > 1 && x350:0 > 1 && x355:0 - 1 >= x345:0 && x350:0 <= x346:0
f1140_0_sortedHigh_NONNULL(x303:0, x304:0, x305:0, x306:0, x307:0) -> f1140_0_sortedHigh_NONNULL(x303:0, x309:0, x305:0, x311:0, x312:0) :|: x304:0 > 0 && x309:0 > -1 && x313:0 <= x303:0 && x309:0 + 1 <= x304:0
f1140_0_sortedHigh_NONNULL(x13, x14, x15, x16, x17) -> f730_0_quicksort_NONNULL(x18, x19, x20, x21, x22) :|: x18 <= x23 && x23 <= x14 && x24 - 1 >= x13 && x18 <= x25 && x25 <= x14 && x14 > 4 && x18 > 1 && x25 > 1 && x26 + 4 <= x23 && x24 + 2 <= x14 && x24 + 2 <= x25 && x24 + 2 <= x23 && x23 > 4 && x26 + 4 <= x14
f1140_0_sortedHigh_NONNULL(x314:0, x315:0, x316:0, x317:0, x318:0) -> f1140_0_sortedHigh_NONNULL(x314:0, x320:0, x316:0, x322:0, x323:0) :|: x315:0 > 0 && x320:0 > -1 && x324:0 - 1 >= x314:0 && x320:0 + 1 <= x315:0
f790_0_sortedLow_NONNULL(x27, x28, x29, x30, x31) -> f730_0_quicksort_NONNULL(x32, x33, x34, x35, x36) :|: x32 <= x37 && x37 <= x28 && x38 <= x27 && x32 <= x39 && x39 <= x28 && x28 > 4 && x32 > 1 && x39 > 1 && x40 + 4 <= x37 && x38 + 2 <= x28 && x38 + 2 <= x39 && x38 + 2 <= x37 && x37 > 4 && x40 + 4 <= x28
f790_0_sortedLow_NONNULL(x251:0, x252:0, x253:0, x254:0, x255:0) -> f790_0_sortedLow_NONNULL(x251:0, x257:0, x253:0, x259:0, x260:0) :|: x252:0 > 0 && x257:0 > -1 && x261:0 <= x251:0 && x257:0 + 1 <= x252:0
f790_0_sortedLow_NONNULL(x240:0, x241:0, x242:0, x243:0, x244:0) -> f790_0_sortedLow_NONNULL(x240:0, x246:0, x242:0, x248:0, x249:0) :|: x241:0 > 0 && x246:0 > -1 && x250:0 - 1 >= x240:0 && x246:0 + 1 <= x241:0

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

(8) IntTRSUnneededArgumentFilterProof (EQUIVALENT)
Some arguments are removed because they cannot influence termination. We removed arguments according to the following replacements:

   f730_0_quicksort_NONNULL(x1, x2, x3, x4, x5) -> f730_0_quicksort_NONNULL(x1)
   f790_0_sortedLow_NONNULL(x1, x2, x3, x4, x5) -> f790_0_sortedLow_NONNULL(x1, x2)
   f1140_0_sortedHigh_NONNULL(x1, x2, x3, x4, x5) -> f1140_0_sortedHigh_NONNULL(x1, x2)

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

(9)
Obligation:
Rules:
f730_0_quicksort_NONNULL(x200:0) -> f1140_0_sortedHigh_NONNULL(x208:0, x216:0) :|: x216:0 + 2 <= x205:0 && x205:0 <= x200:0 && x206:0 + 2 <= x200:0 && x216:0 <= x206:0 && x200:0 > 4 && x216:0 > 0 && x209:0 + 4 <= x200:0 && x208:0 + 2 <= x200:0 && x209:0 + 4 <= x205:0 && x208:0 + 2 <= x205:0 && x209:0 + 2 <= x206:0 && x206:0 > 2 && x205:0 > 4
f790_0_sortedLow_NONNULL(x262:0, x263:0) -> f730_0_quicksort_NONNULL(x267:0) :|: x263:0 > 1 && x267:0 > 1 && x272:0 <= x262:0 && x267:0 <= x263:0
f1140_0_sortedHigh_NONNULL(x325:0, x326:0) -> f730_0_quicksort_NONNULL(x361:0) :|: x361:0 <= x330:0 && x330:0 <= x326:0 && x334:0 - 1 >= x325:0 && x361:0 <= x331:0 && x331:0 <= x326:0 && x326:0 > 3 && x361:0 > 1 && x331:0 > 1 && x333:0 + 4 <= x330:0 && x334:0 + 2 <= x326:0 && x334:0 + 2 <= x331:0 && x334:0 + 2 <= x330:0 && x330:0 > 3 && x333:0 + 4 <= x326:0
f730_0_quicksort_NONNULL(x169:0) -> f790_0_sortedLow_NONNULL(x174:0, x175:0) :|: x169:0 > 0 && x175:0 + 1 <= x169:0 && x175:0 > -1 && x174:0 + 2 <= x169:0
f730_0_quicksort_NONNULL(x179:0) -> f1140_0_sortedHigh_NONNULL(x184:0, x185:0) :|: x179:0 > 1 && x185:0 + 2 <= x179:0 && x185:0 > -1 && x184:0 + 2 <= x179:0
f730_0_quicksort_NONNULL(x) -> f1140_0_sortedHigh_NONNULL(x5, x6) :|: x6 + 2 <= x10 && x10 <= x && x11 + 2 <= x && x6 <= x11 && x > 3 && x6 > 0 && x12 + 4 <= x && x5 + 2 <= x && x12 + 4 <= x10 && x5 + 2 <= x10 && x12 + 2 <= x11 && x11 > 1 && x10 > 3
f790_0_sortedLow_NONNULL(x273:0, x274:0) -> f730_0_quicksort_NONNULL(x298:0) :|: x298:0 <= x278:0 && x278:0 <= x274:0 && x282:0 <= x273:0 && x298:0 <= x279:0 && x279:0 <= x274:0 && x274:0 > 3 && x298:0 > 1 && x279:0 > 1 && x281:0 + 4 <= x278:0 && x282:0 + 2 <= x274:0 && x282:0 + 2 <= x279:0 && x282:0 + 2 <= x278:0 && x278:0 > 3 && x281:0 + 4 <= x274:0
f1140_0_sortedHigh_NONNULL(x345:0, x346:0) -> f730_0_quicksort_NONNULL(x350:0) :|: x346:0 > 1 && x350:0 > 1 && x355:0 - 1 >= x345:0 && x350:0 <= x346:0
f1140_0_sortedHigh_NONNULL(x303:0, x304:0) -> f1140_0_sortedHigh_NONNULL(x303:0, x309:0) :|: x304:0 > 0 && x309:0 > -1 && x313:0 <= x303:0 && x309:0 + 1 <= x304:0
f1140_0_sortedHigh_NONNULL(x13, x14) -> f730_0_quicksort_NONNULL(x18) :|: x18 <= x23 && x23 <= x14 && x24 - 1 >= x13 && x18 <= x25 && x25 <= x14 && x14 > 4 && x18 > 1 && x25 > 1 && x26 + 4 <= x23 && x24 + 2 <= x14 && x24 + 2 <= x25 && x24 + 2 <= x23 && x23 > 4 && x26 + 4 <= x14
f1140_0_sortedHigh_NONNULL(x314:0, x315:0) -> f1140_0_sortedHigh_NONNULL(x314:0, x320:0) :|: x315:0 > 0 && x320:0 > -1 && x324:0 - 1 >= x314:0 && x320:0 + 1 <= x315:0
f790_0_sortedLow_NONNULL(x27, x28) -> f730_0_quicksort_NONNULL(x32) :|: x32 <= x37 && x37 <= x28 && x38 <= x27 && x32 <= x39 && x39 <= x28 && x28 > 4 && x32 > 1 && x39 > 1 && x40 + 4 <= x37 && x38 + 2 <= x28 && x38 + 2 <= x39 && x38 + 2 <= x37 && x37 > 4 && x40 + 4 <= x28
f790_0_sortedLow_NONNULL(x251:0, x252:0) -> f790_0_sortedLow_NONNULL(x251:0, x257:0) :|: x252:0 > 0 && x257:0 > -1 && x261:0 <= x251:0 && x257:0 + 1 <= x252:0
f790_0_sortedLow_NONNULL(x240:0, x241:0) -> f790_0_sortedLow_NONNULL(x240:0, x246:0) :|: x241:0 > 0 && x246:0 > -1 && x250:0 - 1 >= x240:0 && x246:0 + 1 <= x241:0

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

(10) FilterProof (EQUIVALENT)
Used the following sort dictionary for filtering: 
f730_0_quicksort_NONNULL(INTEGER)
f1140_0_sortedHigh_NONNULL(INTEGER, INTEGER)
f790_0_sortedLow_NONNULL(INTEGER, INTEGER)
Replaced non-predefined constructor symbols by 0.
----------------------------------------

(11)
Obligation:
Rules:
f730_0_quicksort_NONNULL(x200:0) -> f1140_0_sortedHigh_NONNULL(x208:0, x216:0) :|: x216:0 + 2 <= x205:0 && x205:0 <= x200:0 && x206:0 + 2 <= x200:0 && x216:0 <= x206:0 && x200:0 > 4 && x216:0 > 0 && x209:0 + 4 <= x200:0 && x208:0 + 2 <= x200:0 && x209:0 + 4 <= x205:0 && x208:0 + 2 <= x205:0 && x209:0 + 2 <= x206:0 && x206:0 > 2 && x205:0 > 4
f790_0_sortedLow_NONNULL(x262:0, x263:0) -> f730_0_quicksort_NONNULL(x267:0) :|: x263:0 > 1 && x267:0 > 1 && x272:0 <= x262:0 && x267:0 <= x263:0
f1140_0_sortedHigh_NONNULL(x325:0, x326:0) -> f730_0_quicksort_NONNULL(x361:0) :|: x361:0 <= x330:0 && x330:0 <= x326:0 && x334:0 - 1 >= x325:0 && x361:0 <= x331:0 && x331:0 <= x326:0 && x326:0 > 3 && x361:0 > 1 && x331:0 > 1 && x333:0 + 4 <= x330:0 && x334:0 + 2 <= x326:0 && x334:0 + 2 <= x331:0 && x334:0 + 2 <= x330:0 && x330:0 > 3 && x333:0 + 4 <= x326:0
f730_0_quicksort_NONNULL(x169:0) -> f790_0_sortedLow_NONNULL(x174:0, x175:0) :|: x169:0 > 0 && x175:0 + 1 <= x169:0 && x175:0 > -1 && x174:0 + 2 <= x169:0
f730_0_quicksort_NONNULL(x179:0) -> f1140_0_sortedHigh_NONNULL(x184:0, x185:0) :|: x179:0 > 1 && x185:0 + 2 <= x179:0 && x185:0 > -1 && x184:0 + 2 <= x179:0
f730_0_quicksort_NONNULL(x) -> f1140_0_sortedHigh_NONNULL(x5, x6) :|: x6 + 2 <= x10 && x10 <= x && x11 + 2 <= x && x6 <= x11 && x > 3 && x6 > 0 && x12 + 4 <= x && x5 + 2 <= x && x12 + 4 <= x10 && x5 + 2 <= x10 && x12 + 2 <= x11 && x11 > 1 && x10 > 3
f790_0_sortedLow_NONNULL(x273:0, x274:0) -> f730_0_quicksort_NONNULL(x298:0) :|: x298:0 <= x278:0 && x278:0 <= x274:0 && x282:0 <= x273:0 && x298:0 <= x279:0 && x279:0 <= x274:0 && x274:0 > 3 && x298:0 > 1 && x279:0 > 1 && x281:0 + 4 <= x278:0 && x282:0 + 2 <= x274:0 && x282:0 + 2 <= x279:0 && x282:0 + 2 <= x278:0 && x278:0 > 3 && x281:0 + 4 <= x274:0
f1140_0_sortedHigh_NONNULL(x345:0, x346:0) -> f730_0_quicksort_NONNULL(x350:0) :|: x346:0 > 1 && x350:0 > 1 && x355:0 - 1 >= x345:0 && x350:0 <= x346:0
f1140_0_sortedHigh_NONNULL(x303:0, x304:0) -> f1140_0_sortedHigh_NONNULL(x303:0, x309:0) :|: x304:0 > 0 && x309:0 > -1 && x313:0 <= x303:0 && x309:0 + 1 <= x304:0
f1140_0_sortedHigh_NONNULL(x13, x14) -> f730_0_quicksort_NONNULL(x18) :|: x18 <= x23 && x23 <= x14 && x24 - 1 >= x13 && x18 <= x25 && x25 <= x14 && x14 > 4 && x18 > 1 && x25 > 1 && x26 + 4 <= x23 && x24 + 2 <= x14 && x24 + 2 <= x25 && x24 + 2 <= x23 && x23 > 4 && x26 + 4 <= x14
f1140_0_sortedHigh_NONNULL(x314:0, x315:0) -> f1140_0_sortedHigh_NONNULL(x314:0, x320:0) :|: x315:0 > 0 && x320:0 > -1 && x324:0 - 1 >= x314:0 && x320:0 + 1 <= x315:0
f790_0_sortedLow_NONNULL(x27, x28) -> f730_0_quicksort_NONNULL(x32) :|: x32 <= x37 && x37 <= x28 && x38 <= x27 && x32 <= x39 && x39 <= x28 && x28 > 4 && x32 > 1 && x39 > 1 && x40 + 4 <= x37 && x38 + 2 <= x28 && x38 + 2 <= x39 && x38 + 2 <= x37 && x37 > 4 && x40 + 4 <= x28
f790_0_sortedLow_NONNULL(x251:0, x252:0) -> f790_0_sortedLow_NONNULL(x251:0, x257:0) :|: x252:0 > 0 && x257:0 > -1 && x261:0 <= x251:0 && x257:0 + 1 <= x252:0
f790_0_sortedLow_NONNULL(x240:0, x241:0) -> f790_0_sortedLow_NONNULL(x240:0, x246:0) :|: x241:0 > 0 && x246:0 > -1 && x250:0 - 1 >= x240:0 && x246:0 + 1 <= x241:0

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

(12) IntTRSCompressionProof (EQUIVALENT)
Compressed rules.
----------------------------------------

(13)
Obligation:
Rules:
f790_0_sortedLow_NONNULL(x251:0:0, x252:0:0) -> f790_0_sortedLow_NONNULL(x251:0:0, x257:0:0) :|: x261:0:0 <= x251:0:0 && x257:0:0 + 1 <= x252:0:0 && x257:0:0 > -1 && x252:0:0 > 0
f790_0_sortedLow_NONNULL(x273:0:0, x274:0:0) -> f730_0_quicksort_NONNULL(x298:0:0) :|: x278:0:0 > 3 && x281:0:0 + 4 <= x274:0:0 && x282:0:0 + 2 <= x278:0:0 && x282:0:0 + 2 <= x279:0:0 && x282:0:0 + 2 <= x274:0:0 && x281:0:0 + 4 <= x278:0:0 && x279:0:0 > 1 && x298:0:0 > 1 && x274:0:0 > 3 && x279:0:0 <= x274:0:0 && x298:0:0 <= x279:0:0 && x282:0:0 <= x273:0:0 && x278:0:0 <= x274:0:0 && x298:0:0 <= x278:0:0
f1140_0_sortedHigh_NONNULL(x325:0:0, x326:0:0) -> f730_0_quicksort_NONNULL(x361:0:0) :|: x330:0:0 > 3 && x333:0:0 + 4 <= x326:0:0 && x334:0:0 + 2 <= x330:0:0 && x334:0:0 + 2 <= x331:0:0 && x334:0:0 + 2 <= x326:0:0 && x333:0:0 + 4 <= x330:0:0 && x331:0:0 > 1 && x361:0:0 > 1 && x326:0:0 > 3 && x331:0:0 <= x326:0:0 && x361:0:0 <= x331:0:0 && x334:0:0 - 1 >= x325:0:0 && x330:0:0 <= x326:0:0 && x361:0:0 <= x330:0:0
f1140_0_sortedHigh_NONNULL(x314:0:0, x315:0:0) -> f1140_0_sortedHigh_NONNULL(x314:0:0, x320:0:0) :|: x324:0:0 - 1 >= x314:0:0 && x320:0:0 + 1 <= x315:0:0 && x320:0:0 > -1 && x315:0:0 > 0
f1140_0_sortedHigh_NONNULL(x345:0:0, x346:0:0) -> f730_0_quicksort_NONNULL(x350:0:0) :|: x355:0:0 - 1 >= x345:0:0 && x350:0:0 <= x346:0:0 && x350:0:0 > 1 && x346:0:0 > 1
f1140_0_sortedHigh_NONNULL(x303:0:0, x304:0:0) -> f1140_0_sortedHigh_NONNULL(x303:0:0, x309:0:0) :|: x313:0:0 <= x303:0:0 && x309:0:0 + 1 <= x304:0:0 && x309:0:0 > -1 && x304:0:0 > 0
f730_0_quicksort_NONNULL(x:0) -> f1140_0_sortedHigh_NONNULL(x5:0, x6:0) :|: x11:0 > 1 && x10:0 > 3 && x12:0 + 2 <= x11:0 && x5:0 + 2 <= x10:0 && x12:0 + 4 <= x10:0 && x:0 >= x5:0 + 2 && x:0 >= x12:0 + 4 && x6:0 > 0 && x:0 > 3 && x6:0 <= x11:0 && x:0 >= x11:0 + 2 && x:0 >= x10:0 && x6:0 + 2 <= x10:0
f790_0_sortedLow_NONNULL(x240:0:0, x241:0:0) -> f790_0_sortedLow_NONNULL(x240:0:0, x246:0:0) :|: x250:0:0 - 1 >= x240:0:0 && x246:0:0 + 1 <= x241:0:0 && x246:0:0 > -1 && x241:0:0 > 0
f730_0_quicksort_NONNULL(x200:0:0) -> f1140_0_sortedHigh_NONNULL(x208:0:0, x216:0:0) :|: x206:0:0 > 2 && x205:0:0 > 4 && x209:0:0 + 2 <= x206:0:0 && x208:0:0 + 2 <= x205:0:0 && x209:0:0 + 4 <= x205:0:0 && x208:0:0 + 2 <= x200:0:0 && x209:0:0 + 4 <= x200:0:0 && x216:0:0 > 0 && x200:0:0 > 4 && x216:0:0 <= x206:0:0 && x206:0:0 + 2 <= x200:0:0 && x205:0:0 <= x200:0:0 && x216:0:0 + 2 <= x205:0:0
f730_0_quicksort_NONNULL(x169:0:0) -> f790_0_sortedLow_NONNULL(x174:0:0, x175:0:0) :|: x175:0:0 > -1 && x174:0:0 + 2 <= x169:0:0 && x175:0:0 + 1 <= x169:0:0 && x169:0:0 > 0
f790_0_sortedLow_NONNULL(x27:0, x28:0) -> f730_0_quicksort_NONNULL(x32:0) :|: x37:0 > 4 && x40:0 + 4 <= x28:0 && x38:0 + 2 <= x37:0 && x39:0 >= x38:0 + 2 && x38:0 + 2 <= x28:0 && x40:0 + 4 <= x37:0 && x39:0 > 1 && x32:0 > 1 && x28:0 > 4 && x39:0 <= x28:0 && x39:0 >= x32:0 && x38:0 <= x27:0 && x37:0 <= x28:0 && x37:0 >= x32:0
f1140_0_sortedHigh_NONNULL(x13:0, x14:0) -> f730_0_quicksort_NONNULL(x18:0) :|: x23:0 > 4 && x26:0 + 4 <= x14:0 && x24:0 + 2 <= x23:0 && x25:0 >= x24:0 + 2 && x24:0 + 2 <= x14:0 && x26:0 + 4 <= x23:0 && x25:0 > 1 && x18:0 > 1 && x14:0 > 4 && x25:0 <= x14:0 && x25:0 >= x18:0 && x24:0 - 1 >= x13:0 && x23:0 <= x14:0 && x23:0 >= x18:0
f730_0_quicksort_NONNULL(x179:0:0) -> f1140_0_sortedHigh_NONNULL(x184:0:0, x185:0:0) :|: x185:0:0 > -1 && x184:0:0 + 2 <= x179:0:0 && x185:0:0 + 2 <= x179:0:0 && x179:0:0 > 1
f790_0_sortedLow_NONNULL(x262:0:0, x263:0:0) -> f730_0_quicksort_NONNULL(x267:0:0) :|: x272:0:0 <= x262:0:0 && x267:0:0 <= x263:0:0 && x267:0:0 > 1 && x263:0:0 > 1

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

(14) RankingReductionPairProof (EQUIVALENT)
Interpretation:
[ f790_0_sortedLow_NONNULL ] = 2*f790_0_sortedLow_NONNULL_2
[ f730_0_quicksort_NONNULL ] = 2*f730_0_quicksort_NONNULL_1 + -1
[ f1140_0_sortedHigh_NONNULL ] = 2*f1140_0_sortedHigh_NONNULL_2

The following rules are decreasing:
f790_0_sortedLow_NONNULL(x251:0:0, x252:0:0) -> f790_0_sortedLow_NONNULL(x251:0:0, x257:0:0) :|: x261:0:0 <= x251:0:0 && x257:0:0 + 1 <= x252:0:0 && x257:0:0 > -1 && x252:0:0 > 0
f790_0_sortedLow_NONNULL(x273:0:0, x274:0:0) -> f730_0_quicksort_NONNULL(x298:0:0) :|: x278:0:0 > 3 && x281:0:0 + 4 <= x274:0:0 && x282:0:0 + 2 <= x278:0:0 && x282:0:0 + 2 <= x279:0:0 && x282:0:0 + 2 <= x274:0:0 && x281:0:0 + 4 <= x278:0:0 && x279:0:0 > 1 && x298:0:0 > 1 && x274:0:0 > 3 && x279:0:0 <= x274:0:0 && x298:0:0 <= x279:0:0 && x282:0:0 <= x273:0:0 && x278:0:0 <= x274:0:0 && x298:0:0 <= x278:0:0
f1140_0_sortedHigh_NONNULL(x325:0:0, x326:0:0) -> f730_0_quicksort_NONNULL(x361:0:0) :|: x330:0:0 > 3 && x333:0:0 + 4 <= x326:0:0 && x334:0:0 + 2 <= x330:0:0 && x334:0:0 + 2 <= x331:0:0 && x334:0:0 + 2 <= x326:0:0 && x333:0:0 + 4 <= x330:0:0 && x331:0:0 > 1 && x361:0:0 > 1 && x326:0:0 > 3 && x331:0:0 <= x326:0:0 && x361:0:0 <= x331:0:0 && x334:0:0 - 1 >= x325:0:0 && x330:0:0 <= x326:0:0 && x361:0:0 <= x330:0:0
f1140_0_sortedHigh_NONNULL(x314:0:0, x315:0:0) -> f1140_0_sortedHigh_NONNULL(x314:0:0, x320:0:0) :|: x324:0:0 - 1 >= x314:0:0 && x320:0:0 + 1 <= x315:0:0 && x320:0:0 > -1 && x315:0:0 > 0
f1140_0_sortedHigh_NONNULL(x345:0:0, x346:0:0) -> f730_0_quicksort_NONNULL(x350:0:0) :|: x355:0:0 - 1 >= x345:0:0 && x350:0:0 <= x346:0:0 && x350:0:0 > 1 && x346:0:0 > 1
f1140_0_sortedHigh_NONNULL(x303:0:0, x304:0:0) -> f1140_0_sortedHigh_NONNULL(x303:0:0, x309:0:0) :|: x313:0:0 <= x303:0:0 && x309:0:0 + 1 <= x304:0:0 && x309:0:0 > -1 && x304:0:0 > 0
f730_0_quicksort_NONNULL(x:0) -> f1140_0_sortedHigh_NONNULL(x5:0, x6:0) :|: x11:0 > 1 && x10:0 > 3 && x12:0 + 2 <= x11:0 && x5:0 + 2 <= x10:0 && x12:0 + 4 <= x10:0 && x:0 >= x5:0 + 2 && x:0 >= x12:0 + 4 && x6:0 > 0 && x:0 > 3 && x6:0 <= x11:0 && x:0 >= x11:0 + 2 && x:0 >= x10:0 && x6:0 + 2 <= x10:0
f790_0_sortedLow_NONNULL(x240:0:0, x241:0:0) -> f790_0_sortedLow_NONNULL(x240:0:0, x246:0:0) :|: x250:0:0 - 1 >= x240:0:0 && x246:0:0 + 1 <= x241:0:0 && x246:0:0 > -1 && x241:0:0 > 0
f730_0_quicksort_NONNULL(x200:0:0) -> f1140_0_sortedHigh_NONNULL(x208:0:0, x216:0:0) :|: x206:0:0 > 2 && x205:0:0 > 4 && x209:0:0 + 2 <= x206:0:0 && x208:0:0 + 2 <= x205:0:0 && x209:0:0 + 4 <= x205:0:0 && x208:0:0 + 2 <= x200:0:0 && x209:0:0 + 4 <= x200:0:0 && x216:0:0 > 0 && x200:0:0 > 4 && x216:0:0 <= x206:0:0 && x206:0:0 + 2 <= x200:0:0 && x205:0:0 <= x200:0:0 && x216:0:0 + 2 <= x205:0:0
f730_0_quicksort_NONNULL(x169:0:0) -> f790_0_sortedLow_NONNULL(x174:0:0, x175:0:0) :|: x175:0:0 > -1 && x174:0:0 + 2 <= x169:0:0 && x175:0:0 + 1 <= x169:0:0 && x169:0:0 > 0
f790_0_sortedLow_NONNULL(x27:0, x28:0) -> f730_0_quicksort_NONNULL(x32:0) :|: x37:0 > 4 && x40:0 + 4 <= x28:0 && x38:0 + 2 <= x37:0 && x39:0 >= x38:0 + 2 && x38:0 + 2 <= x28:0 && x40:0 + 4 <= x37:0 && x39:0 > 1 && x32:0 > 1 && x28:0 > 4 && x39:0 <= x28:0 && x39:0 >= x32:0 && x38:0 <= x27:0 && x37:0 <= x28:0 && x37:0 >= x32:0
f1140_0_sortedHigh_NONNULL(x13:0, x14:0) -> f730_0_quicksort_NONNULL(x18:0) :|: x23:0 > 4 && x26:0 + 4 <= x14:0 && x24:0 + 2 <= x23:0 && x25:0 >= x24:0 + 2 && x24:0 + 2 <= x14:0 && x26:0 + 4 <= x23:0 && x25:0 > 1 && x18:0 > 1 && x14:0 > 4 && x25:0 <= x14:0 && x25:0 >= x18:0 && x24:0 - 1 >= x13:0 && x23:0 <= x14:0 && x23:0 >= x18:0
f730_0_quicksort_NONNULL(x179:0:0) -> f1140_0_sortedHigh_NONNULL(x184:0:0, x185:0:0) :|: x185:0:0 > -1 && x184:0:0 + 2 <= x179:0:0 && x185:0:0 + 2 <= x179:0:0 && x179:0:0 > 1
f790_0_sortedLow_NONNULL(x262:0:0, x263:0:0) -> f730_0_quicksort_NONNULL(x267:0:0) :|: x272:0:0 <= x262:0:0 && x267:0:0 <= x263:0:0 && x267:0:0 > 1 && x263:0:0 > 1

The following rules are bounded:
f790_0_sortedLow_NONNULL(x251:0:0, x252:0:0) -> f790_0_sortedLow_NONNULL(x251:0:0, x257:0:0) :|: x261:0:0 <= x251:0:0 && x257:0:0 + 1 <= x252:0:0 && x257:0:0 > -1 && x252:0:0 > 0
f790_0_sortedLow_NONNULL(x273:0:0, x274:0:0) -> f730_0_quicksort_NONNULL(x298:0:0) :|: x278:0:0 > 3 && x281:0:0 + 4 <= x274:0:0 && x282:0:0 + 2 <= x278:0:0 && x282:0:0 + 2 <= x279:0:0 && x282:0:0 + 2 <= x274:0:0 && x281:0:0 + 4 <= x278:0:0 && x279:0:0 > 1 && x298:0:0 > 1 && x274:0:0 > 3 && x279:0:0 <= x274:0:0 && x298:0:0 <= x279:0:0 && x282:0:0 <= x273:0:0 && x278:0:0 <= x274:0:0 && x298:0:0 <= x278:0:0
f1140_0_sortedHigh_NONNULL(x325:0:0, x326:0:0) -> f730_0_quicksort_NONNULL(x361:0:0) :|: x330:0:0 > 3 && x333:0:0 + 4 <= x326:0:0 && x334:0:0 + 2 <= x330:0:0 && x334:0:0 + 2 <= x331:0:0 && x334:0:0 + 2 <= x326:0:0 && x333:0:0 + 4 <= x330:0:0 && x331:0:0 > 1 && x361:0:0 > 1 && x326:0:0 > 3 && x331:0:0 <= x326:0:0 && x361:0:0 <= x331:0:0 && x334:0:0 - 1 >= x325:0:0 && x330:0:0 <= x326:0:0 && x361:0:0 <= x330:0:0
f1140_0_sortedHigh_NONNULL(x314:0:0, x315:0:0) -> f1140_0_sortedHigh_NONNULL(x314:0:0, x320:0:0) :|: x324:0:0 - 1 >= x314:0:0 && x320:0:0 + 1 <= x315:0:0 && x320:0:0 > -1 && x315:0:0 > 0
f1140_0_sortedHigh_NONNULL(x345:0:0, x346:0:0) -> f730_0_quicksort_NONNULL(x350:0:0) :|: x355:0:0 - 1 >= x345:0:0 && x350:0:0 <= x346:0:0 && x350:0:0 > 1 && x346:0:0 > 1
f1140_0_sortedHigh_NONNULL(x303:0:0, x304:0:0) -> f1140_0_sortedHigh_NONNULL(x303:0:0, x309:0:0) :|: x313:0:0 <= x303:0:0 && x309:0:0 + 1 <= x304:0:0 && x309:0:0 > -1 && x304:0:0 > 0
f730_0_quicksort_NONNULL(x:0) -> f1140_0_sortedHigh_NONNULL(x5:0, x6:0) :|: x11:0 > 1 && x10:0 > 3 && x12:0 + 2 <= x11:0 && x5:0 + 2 <= x10:0 && x12:0 + 4 <= x10:0 && x:0 >= x5:0 + 2 && x:0 >= x12:0 + 4 && x6:0 > 0 && x:0 > 3 && x6:0 <= x11:0 && x:0 >= x11:0 + 2 && x:0 >= x10:0 && x6:0 + 2 <= x10:0
f790_0_sortedLow_NONNULL(x240:0:0, x241:0:0) -> f790_0_sortedLow_NONNULL(x240:0:0, x246:0:0) :|: x250:0:0 - 1 >= x240:0:0 && x246:0:0 + 1 <= x241:0:0 && x246:0:0 > -1 && x241:0:0 > 0
f730_0_quicksort_NONNULL(x200:0:0) -> f1140_0_sortedHigh_NONNULL(x208:0:0, x216:0:0) :|: x206:0:0 > 2 && x205:0:0 > 4 && x209:0:0 + 2 <= x206:0:0 && x208:0:0 + 2 <= x205:0:0 && x209:0:0 + 4 <= x205:0:0 && x208:0:0 + 2 <= x200:0:0 && x209:0:0 + 4 <= x200:0:0 && x216:0:0 > 0 && x200:0:0 > 4 && x216:0:0 <= x206:0:0 && x206:0:0 + 2 <= x200:0:0 && x205:0:0 <= x200:0:0 && x216:0:0 + 2 <= x205:0:0
f730_0_quicksort_NONNULL(x169:0:0) -> f790_0_sortedLow_NONNULL(x174:0:0, x175:0:0) :|: x175:0:0 > -1 && x174:0:0 + 2 <= x169:0:0 && x175:0:0 + 1 <= x169:0:0 && x169:0:0 > 0
f790_0_sortedLow_NONNULL(x27:0, x28:0) -> f730_0_quicksort_NONNULL(x32:0) :|: x37:0 > 4 && x40:0 + 4 <= x28:0 && x38:0 + 2 <= x37:0 && x39:0 >= x38:0 + 2 && x38:0 + 2 <= x28:0 && x40:0 + 4 <= x37:0 && x39:0 > 1 && x32:0 > 1 && x28:0 > 4 && x39:0 <= x28:0 && x39:0 >= x32:0 && x38:0 <= x27:0 && x37:0 <= x28:0 && x37:0 >= x32:0
f1140_0_sortedHigh_NONNULL(x13:0, x14:0) -> f730_0_quicksort_NONNULL(x18:0) :|: x23:0 > 4 && x26:0 + 4 <= x14:0 && x24:0 + 2 <= x23:0 && x25:0 >= x24:0 + 2 && x24:0 + 2 <= x14:0 && x26:0 + 4 <= x23:0 && x25:0 > 1 && x18:0 > 1 && x14:0 > 4 && x25:0 <= x14:0 && x25:0 >= x18:0 && x24:0 - 1 >= x13:0 && x23:0 <= x14:0 && x23:0 >= x18:0
f730_0_quicksort_NONNULL(x179:0:0) -> f1140_0_sortedHigh_NONNULL(x184:0:0, x185:0:0) :|: x185:0:0 > -1 && x184:0:0 + 2 <= x179:0:0 && x185:0:0 + 2 <= x179:0:0 && x179:0:0 > 1
f790_0_sortedLow_NONNULL(x262:0:0, x263:0:0) -> f730_0_quicksort_NONNULL(x267:0:0) :|: x272:0:0 <= x262:0:0 && x267:0:0 <= x263:0:0 && x267:0:0 > 1 && x263:0:0 > 1


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

(15)
YES

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

(16)
Obligation:

Termination digraph:
Nodes:
(1) f392_0_createList_GT(x135, x136, x137, x138, x139) -> f501_0_createList_InvokeMethod(x141, x142, x143, x144, x146) :|: x137 + 1 = x144 && x136 = x143 && x135 - 1 = x142 && x135 = x141 && x137 <= x136 - 1 && -1 <= x137 - 1 && -1 <= x136 - 1 && 0 <= x135 - 1
(2) f501_0_createList_InvokeMethod(x158, x159, x160, x161, x162) -> f392_0_createList_GT(x163, x165, x166, x167, x168) :|: x161 = x166 && x160 = x165 && x159 = x163 && x159 <= x158 - 1 && x161 <= x160 && 0 <= x160 - 1 && 0 <= x161 - 1 && 0 <= x158 - 1
(3) f392_0_createList_GT(x147, x148, x149, x150, x151) -> f501_0_createList_InvokeMethod(x152, x153, x154, x155, x156) :|: 0 <= x147 - 1 && -1 <= x148 - 1 && x149 <= x148 - 1 && -1 <= x157 - 1 && -1 <= x149 - 1 && x147 = x152 && x147 - 1 = x153 && x148 = x154 && x149 + 1 = x155

Arcs:
(1) -> (2)
(2) -> (1), (3)
(3) -> (2)

This digraph is fully evaluated!

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

(17) IntTRSCompressionProof (EQUIVALENT)
Compressed rules.
----------------------------------------

(18)
Obligation:
Rules:
f392_0_createList_GT(x135:0, x136:0, x137:0, x138:0, x139:0) -> f392_0_createList_GT(x135:0 - 1, x136:0, x137:0 + 1, x167:0, x168:0) :|: x135:0 > 0 && x137:0 > -1 && x137:0 <= x136:0 - 1 && x136:0 > 0 && x137:0 + 1 <= x136:0
f392_0_createList_GT(x, x1, x2, x3, x4) -> f392_0_createList_GT(x - 1, x1, x2 + 1, x5, x6) :|: x2 + 1 <= x1 && x2 > -1 && x7 > -1 && x2 <= x1 - 1 && x1 > 0 && x > 0

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

(19) IntTRSUnneededArgumentFilterProof (EQUIVALENT)
Some arguments are removed because they cannot influence termination. We removed arguments according to the following replacements:

   f392_0_createList_GT(x1, x2, x3, x4, x5) -> f392_0_createList_GT(x1, x2, x3)

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

(20)
Obligation:
Rules:
f392_0_createList_GT(x135:0, x136:0, x137:0) -> f392_0_createList_GT(x135:0 - 1, x136:0, x137:0 + 1) :|: x135:0 > 0 && x137:0 > -1 && x137:0 <= x136:0 - 1 && x136:0 > 0 && x137:0 + 1 <= x136:0
f392_0_createList_GT(x, x1, x2) -> f392_0_createList_GT(x - 1, x1, x2 + 1) :|: x2 + 1 <= x1 && x2 > -1 && x7 > -1 && x2 <= x1 - 1 && x1 > 0 && x > 0

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

(21) TempFilterProof (SOUND)
Used the following sort dictionary for filtering: 
f392_0_createList_GT(INTEGER, INTEGER, INTEGER)
Replaced non-predefined constructor symbols by 0.
----------------------------------------

(22)
Obligation:
Rules:
f392_0_createList_GT(x135:0, x136:0, x137:0) -> f392_0_createList_GT(c, x136:0, c1) :|: c1 = x137:0 + 1 && c = x135:0 - 1 && (x135:0 > 0 && x137:0 > -1 && x137:0 <= x136:0 - 1 && x136:0 > 0 && x137:0 + 1 <= x136:0)
f392_0_createList_GT(x, x1, x2) -> f392_0_createList_GT(c2, x1, c3) :|: c3 = x2 + 1 && c2 = x - 1 && (x2 + 1 <= x1 && x2 > -1 && x7 > -1 && x2 <= x1 - 1 && x1 > 0 && x > 0)

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

(23) RankingReductionPairProof (EQUIVALENT)
Interpretation:
[ f392_0_createList_GT ] = f392_0_createList_GT_1

The following rules are decreasing:
f392_0_createList_GT(x135:0, x136:0, x137:0) -> f392_0_createList_GT(c, x136:0, c1) :|: c1 = x137:0 + 1 && c = x135:0 - 1 && (x135:0 > 0 && x137:0 > -1 && x137:0 <= x136:0 - 1 && x136:0 > 0 && x137:0 + 1 <= x136:0)
f392_0_createList_GT(x, x1, x2) -> f392_0_createList_GT(c2, x1, c3) :|: c3 = x2 + 1 && c2 = x - 1 && (x2 + 1 <= x1 && x2 > -1 && x7 > -1 && x2 <= x1 - 1 && x1 > 0 && x > 0)

The following rules are bounded:
f392_0_createList_GT(x135:0, x136:0, x137:0) -> f392_0_createList_GT(c, x136:0, c1) :|: c1 = x137:0 + 1 && c = x135:0 - 1 && (x135:0 > 0 && x137:0 > -1 && x137:0 <= x136:0 - 1 && x136:0 > 0 && x137:0 + 1 <= x136:0)
f392_0_createList_GT(x, x1, x2) -> f392_0_createList_GT(c2, x1, c3) :|: c3 = x2 + 1 && c2 = x - 1 && (x2 + 1 <= x1 && x2 > -1 && x7 > -1 && x2 <= x1 - 1 && x1 > 0 && x > 0)


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

(24)
YES

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

(25)
Obligation:

Termination digraph:
Nodes:
(1) f392_0_createList_GT(x125, x126, x127, x128, x129) -> f392_0_createList_GT(x130, x131, x132, x133, x134) :|: x127 = x132 && x126 = x131 && x125 - 1 = x130 && x126 <= x127 && x125 - 1 <= x125 - 1 && -1 <= x126 - 1 && 0 <= x125 - 1

Arcs:
(1) -> (1)

This digraph is fully evaluated!

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

(26) IntTRSCompressionProof (EQUIVALENT)
Compressed rules.
----------------------------------------

(27)
Obligation:
Rules:
f392_0_createList_GT(x125:0, x126:0, x127:0, x128:0, x129:0) -> f392_0_createList_GT(x125:0 - 1, x126:0, x127:0, x133:0, x134:0) :|: x126:0 > -1 && x127:0 >= x126:0 && x125:0 > 0

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

(28) IntTRSUnneededArgumentFilterProof (EQUIVALENT)
Some arguments are removed because they cannot influence termination. We removed arguments according to the following replacements:

   f392_0_createList_GT(x1, x2, x3, x4, x5) -> f392_0_createList_GT(x1, x2, x3)

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

(29)
Obligation:
Rules:
f392_0_createList_GT(x125:0, x126:0, x127:0) -> f392_0_createList_GT(x125:0 - 1, x126:0, x127:0) :|: x126:0 > -1 && x127:0 >= x126:0 && x125:0 > 0

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

(30) TempFilterProof (SOUND)
Used the following sort dictionary for filtering: 
f392_0_createList_GT(INTEGER, INTEGER, INTEGER)
Replaced non-predefined constructor symbols by 0.
----------------------------------------

(31)
Obligation:
Rules:
f392_0_createList_GT(x125:0, x126:0, x127:0) -> f392_0_createList_GT(c, x126:0, x127:0) :|: c = x125:0 - 1 && (x126:0 > -1 && x127:0 >= x126:0 && x125:0 > 0)

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

(32) PolynomialOrderProcessor (EQUIVALENT)
Found the following polynomial interpretation:
[f392_0_createList_GT(x, x1, x2)] = x

The following rules are decreasing:
f392_0_createList_GT(x125:0, x126:0, x127:0) -> f392_0_createList_GT(c, x126:0, x127:0) :|: c = x125:0 - 1 && (x126:0 > -1 && x127:0 >= x126:0 && x125:0 > 0)
The following rules are bounded:
f392_0_createList_GT(x125:0, x126:0, x127:0) -> f392_0_createList_GT(c, x126:0, x127:0) :|: c = x125:0 - 1 && (x126:0 > -1 && x127:0 >= x126:0 && x125:0 > 0)

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

(33)
YES