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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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, 22.4 s]
(4) AND
    (5) IRSwT
        (6) IntTRSCompressionProof [EQUIVALENT, 35 ms]
        (7) IRSwT
        (8) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms]
        (9) IRSwT
        (10) TempFilterProof [SOUND, 38 ms]
        (11) IntTRS
        (12) RankingReductionPairProof [EQUIVALENT, 13 ms]
        (13) YES
    (14) IRSwT
        (15) IntTRSCompressionProof [EQUIVALENT, 27 ms]
        (16) IRSwT
        (17) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms]
        (18) IRSwT
        (19) TempFilterProof [SOUND, 170 ms]
        (20) IntTRS
        (21) RankingReductionPairProof [EQUIVALENT, 35 ms]
        (22) YES


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

(0)
Obligation:
Rules:
f242_0_createArray_Return(arg1, arg2, arg3, arg4, arg5, arg6, arg7) -> f382_0_random_ArrayAccess(arg1P, arg2P, arg3P, arg4P, arg5P, arg6P, arg7P) :|: arg4 = arg3P && 0 <= arg1P - 1 && 0 <= arg2 - 1 && 0 <= arg1 - 1 && arg1P <= arg2 && arg1P <= arg1
f1_0_main_Load(x, x1, x2, x3, x4, x5, x6) -> f382_0_random_ArrayAccess(x7, x8, x9, x10, x11, x12, x13) :|: x1 = x8 && 0 <= x7 - 1 && 0 <= x - 1 && x7 <= x
f1_0_main_Load(x14, x15, x16, x17, x18, x19, x20) -> f464_0_createArray_GE(x21, x23, x24, x25, x26, x27, x29) :|: 1 = x25 && x15 = x24 && 0 = x23 && 0 <= x21 - 1 && 0 <= x14 - 1 && x21 <= x14 && 0 <= x15 - 1 && -1 <= x26 - 1
f464_0_createArray_GE(x30, x31, x32, x33, x34, x35, x36) -> f464_0_createArray_GE(x37, x38, x39, x40, x41, x42, x43) :|: x34 = x41 && x33 + 1 = x40 && x32 = x39 && x31 + 1 = x38 && 0 <= x37 - 1 && 0 <= x30 - 1 && x37 <= x30 && -1 <= x34 - 1 && x31 <= x34 - 1 && 0 <= x33 - 1 && x33 <= x32 - 1
f382_0_random_ArrayAccess(x44, x45, x46, x47, x48, x49, x50) -> f826_0_binarySearch_LE(x51, x52, x53, x54, x55, x56, x57) :|: x58 <= x45 - 1 && 0 <= x58 - 1 && -1 <= x53 - 1 && 0 <= x45 - 1 && -1 <= x46 - 1 && 1 <= x59 - 1 && x52 <= x44 && 0 <= x44 - 1 && 0 <= x51 - 1 && 0 <= x52 - 1 && 0 = x54 && x46 = x55 && x46 = x56
f826_0_binarySearch_LE(x60, x61, x62, x63, x64, x65, x66) -> f826_0_binarySearch_LE'(x67, x68, x69, x70, x71, x73, x74) :|: x75 <= x64 - x63 && -1 <= x63 - 1 && -1 <= x64 - 1 && x63 <= x64 && -1 <= x75 - 1 && x63 + x75 <= x65 - 1 && 1 <= x76 - 1 && 0 <= x63 + x75 && x63 + x75 - 1 <= x63 + x75 - 1 && x77 <= x62 - 1 && x78 <= x60 && x78 <= x61 && x79 <= x60 && x79 <= x61 && 0 <= x60 - 1 && 0 <= x61 - 1 && 0 <= x78 - 1 && 0 <= x79 - 1 && x60 = x67 && x61 = x68 && x62 = x69 && x63 = x70 && x64 = x71 && x65 = x73
f826_0_binarySearch_LE(x80, x81, x82, x84, x85, x86, x87) -> f826_0_binarySearch_LE'(x88, x89, x90, x91, x92, x93, x95) :|: x96 <= x85 - x84 && -1 <= x84 - 1 && -1 <= x85 - 1 && x84 <= x85 && -1 <= x96 - 1 && x84 + x96 <= x86 - 1 && 1 <= x97 - 1 && 0 <= x84 + x96 && x84 + x96 - 1 <= x84 + x96 - 1 && x82 <= x98 - 1 && x99 <= x80 && x99 <= x81 && x100 <= x80 && x100 <= x81 && 0 <= x80 - 1 && 0 <= x81 - 1 && 0 <= x99 - 1 && 0 <= x100 - 1 && x80 = x88 && x81 = x89 && x82 = x90 && x84 = x91 && x85 = x92 && x86 = x93
f826_0_binarySearch_LE'(x101, x102, x103, x104, x106, x107, x108) -> f826_0_binarySearch_LE(x109, x110, x111, x112, x113, x114, x115) :|: x116 <= x106 - x104 && -1 <= x104 - 1 && -1 <= x106 - 1 && x104 <= x106 && -1 <= x116 - 1 && x104 + x116 <= x107 - 1 && 1 <= x117 - 1 && 0 <= x104 + x116 && x104 + x116 - 1 <= x104 + x116 - 1 && x118 <= x103 - 1 && x109 <= x101 && x109 <= x102 && x110 <= x101 && x110 <= x102 && 0 <= x101 - 1 && 0 <= x102 - 1 && 0 <= x109 - 1 && 0 <= x110 - 1 && x106 - x104 - 2 * x116 <= 1 && 0 <= x106 - x104 - 2 * x116 && x103 = x111 && x104 = x112 && x104 + x116 - 1 = x113 && x107 = x114
f826_0_binarySearch_LE'(x119, x120, x121, x122, x124, x125, x126) -> f826_0_binarySearch_LE(x127, x128, x129, x130, x131, x132, x133) :|: x134 <= x124 - x122 && -1 <= x122 - 1 && -1 <= x124 - 1 && x122 <= x124 && -1 <= x134 - 1 && x122 + x134 <= x125 - 1 && 1 <= x136 - 1 && 0 <= x122 + x134 && x122 + x134 - 1 <= x122 + x134 - 1 && x121 <= x137 - 1 && x127 <= x119 && x127 <= x120 && x128 <= x119 && x128 <= x120 && 0 <= x119 - 1 && 0 <= x120 - 1 && 0 <= x127 - 1 && 0 <= x128 - 1 && x124 - x122 - 2 * x134 <= 1 && 0 <= x124 - x122 - 2 * x134 && x121 = x129 && x122 = x130 && x122 + x134 - 1 = x131 && x125 = x132
f826_0_binarySearch_LE(x138, x139, x140, x141, x142, x143, x144) -> f826_0_binarySearch_LE'(x150, x151, x152, x153, x154, x155, x156) :|: x157 <= x142 - x141 && -1 <= x141 - 1 && -1 <= x142 - 1 && x141 <= x142 && -1 <= x157 - 1 && x141 + x157 <= x143 - 1 && 1 <= x161 - 1 && 0 <= x141 + x157 && x141 + x157 - 1 <= x141 + x157 - 1 && x162 <= x140 - 1 && x163 <= x138 && x163 <= x139 && 0 <= x138 - 1 && 0 <= x139 - 1 && 0 <= x163 - 1 && x138 = x150 && x139 = x151 && x140 = x152 && x141 = x153 && x142 = x154 && x143 = x155
f826_0_binarySearch_LE(x164, x165, x166, x167, x168, x172, x173) -> f826_0_binarySearch_LE'(x174, x175, x176, x177, x178, x179, x180) :|: x181 <= x168 - x167 && -1 <= x167 - 1 && -1 <= x168 - 1 && x167 <= x168 && -1 <= x181 - 1 && x167 + x181 <= x172 - 1 && 1 <= x182 - 1 && 0 <= x167 + x181 && x167 + x181 - 1 <= x167 + x181 - 1 && x166 <= x183 - 1 && x184 <= x164 && x184 <= x165 && 0 <= x164 - 1 && 0 <= x165 - 1 && 0 <= x184 - 1 && x164 = x174 && x165 = x175 && x166 = x176 && x167 = x177 && x168 = x178 && x172 = x179
f826_0_binarySearch_LE'(x185, x186, x187, x188, x189, x190, x191) -> f1076_0_binarySearch_EQ(x192, x193, x194, x195, x196, x197, x198) :|: x199 <= x189 - x188 && -1 <= x188 - 1 && -1 <= x189 - 1 && x188 <= x189 && -1 <= x199 - 1 && x188 + x199 <= x190 - 1 && 1 <= x200 - 1 && 0 <= x188 + x199 && x188 + x199 - 1 <= x188 + x199 - 1 && x201 <= x187 - 1 && x192 <= x185 && x192 <= x186 && 0 <= x185 - 1 && 0 <= x186 - 1 && 0 <= x192 - 1 && x189 - x188 - 2 * x199 <= 1 && 0 <= x189 - x188 - 2 * x199 && x187 = x193 && x189 = x194 && x188 + x199 = x195 && 0 = x196 && x190 = x198
f826_0_binarySearch_LE'(x202, x203, x204, x205, x206, x207, x208) -> f1076_0_binarySearch_EQ(x209, x210, x211, x212, x213, x214, x215) :|: x216 <= x206 - x205 && -1 <= x205 - 1 && -1 <= x206 - 1 && x205 <= x206 && -1 <= x216 - 1 && x205 + x216 <= x207 - 1 && 1 <= x217 - 1 && 0 <= x205 + x216 && x205 + x216 - 1 <= x205 + x216 - 1 && x204 <= x218 - 1 && x209 <= x202 && x209 <= x203 && 0 <= x202 - 1 && 0 <= x203 - 1 && 0 <= x209 - 1 && x206 - x205 - 2 * x216 <= 1 && 0 <= x206 - x205 - 2 * x216 && x204 = x210 && x206 = x211 && x205 + x216 = x212 && 0 = x213 && x207 = x215
f826_0_binarySearch_LE'(x219, x220, x221, x226, x227, x228, x229) -> f1078_0_binarySearch_EQ(x230, x231, x236, x237, x238, x239, x240) :|: x241 <= x227 - x226 && -1 <= x226 - 1 && -1 <= x227 - 1 && x226 <= x227 && -1 <= x241 - 1 && x226 + x241 <= x228 - 1 && 1 <= x242 - 1 && 0 <= x226 + x241 && x226 + x241 - 1 <= x226 + x241 - 1 && x244 <= x221 - 1 && x230 <= x219 && x230 <= x220 && 0 <= x219 - 1 && 0 <= x220 - 1 && 0 <= x230 - 1 && x227 - x226 - 2 * x241 <= 1 && 0 <= x227 - x226 - 2 * x241 && x221 = x231 && x227 = x236 && x226 + x241 = x237 && 0 = x238 && x228 = x240
f826_0_binarySearch_LE'(x247, x248, x249, x250, x251, x252, x253) -> f1078_0_binarySearch_EQ(x255, x258, x259, x260, x261, x262, x263) :|: x264 <= x251 - x250 && -1 <= x250 - 1 && -1 <= x251 - 1 && x250 <= x251 && -1 <= x264 - 1 && x250 + x264 <= x252 - 1 && 1 <= x265 - 1 && 0 <= x250 + x264 && x250 + x264 - 1 <= x250 + x264 - 1 && x249 <= x266 - 1 && x255 <= x247 && x255 <= x248 && 0 <= x247 - 1 && 0 <= x248 - 1 && 0 <= x255 - 1 && x251 - x250 - 2 * x264 <= 1 && 0 <= x251 - x250 - 2 * x264 && x249 = x258 && x251 = x259 && x250 + x264 = x260 && 0 = x261 && x252 = x263
f826_0_binarySearch_LE'(x267, x268, x269, x270, x271, x272, x273) -> f1076_0_binarySearch_EQ(x274, x275, x276, x277, x278, x279, x280) :|: x281 <= x271 - x270 && -1 <= x270 - 1 && -1 <= x271 - 1 && x270 <= x271 && -1 <= x281 - 1 && x270 + x281 <= x272 - 1 && 1 <= x282 - 1 && 0 <= x270 + x281 && x270 + x281 - 1 <= x270 + x281 - 1 && x283 <= x269 - 1 && x274 <= x267 && x274 <= x268 && 0 <= x267 - 1 && 0 <= x268 - 1 && 0 <= x274 - 1 && x271 - x270 - 2 * x281 <= 1 && 0 <= x271 - x270 - 2 * x281 && x269 = x275 && x271 = x276 && x270 + x281 = x277 && 1 = x278 && x272 = x280
f826_0_binarySearch_LE'(x284, x286, x289, x290, x291, x292, x293) -> f1076_0_binarySearch_EQ(x294, x295, x297, x300, x301, x302, x303) :|: x304 <= x291 - x290 && -1 <= x290 - 1 && -1 <= x291 - 1 && x290 <= x291 && -1 <= x304 - 1 && x290 + x304 <= x292 - 1 && 1 <= x305 - 1 && 0 <= x290 + x304 && x290 + x304 - 1 <= x290 + x304 - 1 && x289 <= x306 - 1 && x294 <= x284 && x294 <= x286 && 0 <= x284 - 1 && 0 <= x286 - 1 && 0 <= x294 - 1 && x291 - x290 - 2 * x304 <= 1 && 0 <= x291 - x290 - 2 * x304 && x289 = x295 && x291 = x297 && x290 + x304 = x300 && 1 = x301 && x292 = x303
f826_0_binarySearch_LE'(x307, x308, x309, x310, x311, x312, x313) -> f1078_0_binarySearch_EQ(x314, x315, x316, x317, x318, x319, x320) :|: x321 <= x311 - x310 && -1 <= x310 - 1 && -1 <= x311 - 1 && x310 <= x311 && -1 <= x321 - 1 && x310 + x321 <= x312 - 1 && 1 <= x322 - 1 && 0 <= x310 + x321 && x310 + x321 - 1 <= x310 + x321 - 1 && x323 <= x309 - 1 && x314 <= x307 && x314 <= x308 && 0 <= x307 - 1 && 0 <= x308 - 1 && 0 <= x314 - 1 && x311 - x310 - 2 * x321 <= 1 && 0 <= x311 - x310 - 2 * x321 && x309 = x315 && x311 = x316 && x310 + x321 = x317 && 1 = x318 && x312 = x320
f826_0_binarySearch_LE'(x324, x325, x326, x328, x331, x332, x333) -> f1078_0_binarySearch_EQ(x334, x335, x336, x337, x339, x342, x343) :|: x344 <= x331 - x328 && -1 <= x328 - 1 && -1 <= x331 - 1 && x328 <= x331 && -1 <= x344 - 1 && x328 + x344 <= x332 - 1 && 1 <= x345 - 1 && 0 <= x328 + x344 && x328 + x344 - 1 <= x328 + x344 - 1 && x326 <= x346 - 1 && x334 <= x324 && x334 <= x325 && 0 <= x324 - 1 && 0 <= x325 - 1 && 0 <= x334 - 1 && x331 - x328 - 2 * x344 <= 1 && 0 <= x331 - x328 - 2 * x344 && x326 = x335 && x331 = x336 && x328 + x344 = x337 && 1 = x339 && x332 = x343
f1078_0_binarySearch_EQ(x347, x348, x349, x350, x351, x352, x353) -> f826_0_binarySearch_LE(x354, x355, x356, x357, x358, x359, x360) :|: 1 <= x361 - 1 && -1 <= x350 - 1 && x354 <= x347 && x355 <= x347 && 0 <= x347 - 1 && 0 <= x354 - 1 && 0 <= x355 - 1 && 0 = x351 && x348 = x356 && x350 + 1 = x357 && x349 = x358 && x353 = x359
f1076_0_binarySearch_EQ(x362, x363, x364, x365, x366, x367, x368) -> f826_0_binarySearch_LE(x370, x373, x374, x375, x376, x377, x378) :|: 1 <= x379 - 1 && -1 <= x365 - 1 && x370 <= x362 && x373 <= x362 && 0 <= x362 - 1 && 0 <= x370 - 1 && 0 <= x373 - 1 && 0 = x366 && x363 = x374 && x365 + 1 = x375 && x364 = x376 && x368 = x377
f826_0_binarySearch_LE'(x381, x384, x385, x386, x387, x388, x389) -> f1076_0_binarySearch_EQ(x390, x391, x392, x394, x395, x396, x397) :|: x398 <= x387 - x386 && -1 <= x386 - 1 && -1 <= x387 - 1 && x386 <= x387 && -1 <= x398 - 1 && x386 + x398 <= x388 - 1 && 1 <= x399 - 1 && 0 <= x386 + x398 && x386 + x398 - 1 <= x386 + x398 - 1 && x400 <= x385 - 1 && x390 <= x381 && x390 <= x384 && 0 <= x381 - 1 && 0 <= x384 - 1 && 0 <= x390 - 1 && x387 - x386 - 2 * x398 <= 1 && 0 <= x387 - x386 - 2 * x398 && x385 = x391 && x387 = x392 && x386 + x398 = x394 && x388 = x397
f826_0_binarySearch_LE'(x401, x402, x403, x404, x405, x406, x407) -> f1076_0_binarySearch_EQ(x408, x409, x410, x411, x412, x413, x414) :|: x415 <= x405 - x404 && -1 <= x404 - 1 && -1 <= x405 - 1 && x404 <= x405 && -1 <= x415 - 1 && x404 + x415 <= x406 - 1 && 1 <= x416 - 1 && 0 <= x404 + x415 && x404 + x415 - 1 <= x404 + x415 - 1 && x403 <= x417 - 1 && x408 <= x401 && x408 <= x402 && 0 <= x401 - 1 && 0 <= x402 - 1 && 0 <= x408 - 1 && x405 - x404 - 2 * x415 <= 1 && 0 <= x405 - x404 - 2 * x415 && x403 = x409 && x405 = x410 && x404 + x415 = x411 && x406 = x414
f826_0_binarySearch_LE'(x418, x419, x420, x422, x423, x426, x427) -> f1078_0_binarySearch_EQ(x428, x429, x430, x431, x432, x434, x435) :|: x438 <= x423 - x422 && -1 <= x422 - 1 && -1 <= x423 - 1 && x422 <= x423 && -1 <= x438 - 1 && x422 + x438 <= x426 - 1 && 1 <= x439 - 1 && 0 <= x422 + x438 && x422 + x438 - 1 <= x422 + x438 - 1 && x440 <= x420 - 1 && x428 <= x418 && x428 <= x419 && 0 <= x418 - 1 && 0 <= x419 - 1 && 0 <= x428 - 1 && x423 - x422 - 2 * x438 <= 1 && 0 <= x423 - x422 - 2 * x438 && x420 = x429 && x423 = x430 && x422 + x438 = x431 && x426 = x435
f826_0_binarySearch_LE'(x441, x442, x443, x444, x445, x446, x447) -> f1078_0_binarySearch_EQ(x448, x449, x450, x451, x452, x453, x454) :|: x455 <= x445 - x444 && -1 <= x444 - 1 && -1 <= x445 - 1 && x444 <= x445 && -1 <= x455 - 1 && x444 + x455 <= x446 - 1 && 1 <= x456 - 1 && 0 <= x444 + x455 && x444 + x455 - 1 <= x444 + x455 - 1 && x443 <= x457 - 1 && x448 <= x441 && x448 <= x442 && 0 <= x441 - 1 && 0 <= x442 - 1 && 0 <= x448 - 1 && x445 - x444 - 2 * x455 <= 1 && 0 <= x445 - x444 - 2 * x455 && x443 = x449 && x445 = x450 && x444 + x455 = x451 && x446 = x454
__init(x458, x459, x460, x461, x462, x463, x464) -> f1_0_main_Load(x466, x467, x470, x471, x472, x473, x474) :|: 0 <= 0
Start term: __init(arg1, arg2, arg3, arg4, arg5, arg6, arg7)

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

(2)
Obligation:
Rules:
f242_0_createArray_Return(arg1, arg2, arg3, arg4, arg5, arg6, arg7) -> f382_0_random_ArrayAccess(arg1P, arg2P, arg3P, arg4P, arg5P, arg6P, arg7P) :|: arg4 = arg3P && 0 <= arg1P - 1 && 0 <= arg2 - 1 && 0 <= arg1 - 1 && arg1P <= arg2 && arg1P <= arg1
f1_0_main_Load(x, x1, x2, x3, x4, x5, x6) -> f382_0_random_ArrayAccess(x7, x8, x9, x10, x11, x12, x13) :|: x1 = x8 && 0 <= x7 - 1 && 0 <= x - 1 && x7 <= x
f1_0_main_Load(x14, x15, x16, x17, x18, x19, x20) -> f464_0_createArray_GE(x21, x23, x24, x25, x26, x27, x29) :|: 1 = x25 && x15 = x24 && 0 = x23 && 0 <= x21 - 1 && 0 <= x14 - 1 && x21 <= x14 && 0 <= x15 - 1 && -1 <= x26 - 1
f464_0_createArray_GE(x30, x31, x32, x33, x34, x35, x36) -> f464_0_createArray_GE(x37, x38, x39, x40, x41, x42, x43) :|: x34 = x41 && x33 + 1 = x40 && x32 = x39 && x31 + 1 = x38 && 0 <= x37 - 1 && 0 <= x30 - 1 && x37 <= x30 && -1 <= x34 - 1 && x31 <= x34 - 1 && 0 <= x33 - 1 && x33 <= x32 - 1
f382_0_random_ArrayAccess(x44, x45, x46, x47, x48, x49, x50) -> f826_0_binarySearch_LE(x51, x52, x53, x54, x55, x56, x57) :|: x58 <= x45 - 1 && 0 <= x58 - 1 && -1 <= x53 - 1 && 0 <= x45 - 1 && -1 <= x46 - 1 && 1 <= x59 - 1 && x52 <= x44 && 0 <= x44 - 1 && 0 <= x51 - 1 && 0 <= x52 - 1 && 0 = x54 && x46 = x55 && x46 = x56
f826_0_binarySearch_LE(x60, x61, x62, x63, x64, x65, x66) -> f826_0_binarySearch_LE'(x67, x68, x69, x70, x71, x73, x74) :|: x75 <= x64 - x63 && -1 <= x63 - 1 && -1 <= x64 - 1 && x63 <= x64 && -1 <= x75 - 1 && x63 + x75 <= x65 - 1 && 1 <= x76 - 1 && 0 <= x63 + x75 && x63 + x75 - 1 <= x63 + x75 - 1 && x77 <= x62 - 1 && x78 <= x60 && x78 <= x61 && x79 <= x60 && x79 <= x61 && 0 <= x60 - 1 && 0 <= x61 - 1 && 0 <= x78 - 1 && 0 <= x79 - 1 && x60 = x67 && x61 = x68 && x62 = x69 && x63 = x70 && x64 = x71 && x65 = x73
f826_0_binarySearch_LE(x80, x81, x82, x84, x85, x86, x87) -> f826_0_binarySearch_LE'(x88, x89, x90, x91, x92, x93, x95) :|: x96 <= x85 - x84 && -1 <= x84 - 1 && -1 <= x85 - 1 && x84 <= x85 && -1 <= x96 - 1 && x84 + x96 <= x86 - 1 && 1 <= x97 - 1 && 0 <= x84 + x96 && x84 + x96 - 1 <= x84 + x96 - 1 && x82 <= x98 - 1 && x99 <= x80 && x99 <= x81 && x100 <= x80 && x100 <= x81 && 0 <= x80 - 1 && 0 <= x81 - 1 && 0 <= x99 - 1 && 0 <= x100 - 1 && x80 = x88 && x81 = x89 && x82 = x90 && x84 = x91 && x85 = x92 && x86 = x93
f826_0_binarySearch_LE'(x101, x102, x103, x104, x106, x107, x108) -> f826_0_binarySearch_LE(x109, x110, x111, x112, x113, x114, x115) :|: x116 <= x106 - x104 && -1 <= x104 - 1 && -1 <= x106 - 1 && x104 <= x106 && -1 <= x116 - 1 && x104 + x116 <= x107 - 1 && 1 <= x117 - 1 && 0 <= x104 + x116 && x104 + x116 - 1 <= x104 + x116 - 1 && x118 <= x103 - 1 && x109 <= x101 && x109 <= x102 && x110 <= x101 && x110 <= x102 && 0 <= x101 - 1 && 0 <= x102 - 1 && 0 <= x109 - 1 && 0 <= x110 - 1 && x106 - x104 - 2 * x116 <= 1 && 0 <= x106 - x104 - 2 * x116 && x103 = x111 && x104 = x112 && x104 + x116 - 1 = x113 && x107 = x114
f826_0_binarySearch_LE'(x119, x120, x121, x122, x124, x125, x126) -> f826_0_binarySearch_LE(x127, x128, x129, x130, x131, x132, x133) :|: x134 <= x124 - x122 && -1 <= x122 - 1 && -1 <= x124 - 1 && x122 <= x124 && -1 <= x134 - 1 && x122 + x134 <= x125 - 1 && 1 <= x136 - 1 && 0 <= x122 + x134 && x122 + x134 - 1 <= x122 + x134 - 1 && x121 <= x137 - 1 && x127 <= x119 && x127 <= x120 && x128 <= x119 && x128 <= x120 && 0 <= x119 - 1 && 0 <= x120 - 1 && 0 <= x127 - 1 && 0 <= x128 - 1 && x124 - x122 - 2 * x134 <= 1 && 0 <= x124 - x122 - 2 * x134 && x121 = x129 && x122 = x130 && x122 + x134 - 1 = x131 && x125 = x132
f826_0_binarySearch_LE(x138, x139, x140, x141, x142, x143, x144) -> f826_0_binarySearch_LE'(x150, x151, x152, x153, x154, x155, x156) :|: x157 <= x142 - x141 && -1 <= x141 - 1 && -1 <= x142 - 1 && x141 <= x142 && -1 <= x157 - 1 && x141 + x157 <= x143 - 1 && 1 <= x161 - 1 && 0 <= x141 + x157 && x141 + x157 - 1 <= x141 + x157 - 1 && x162 <= x140 - 1 && x163 <= x138 && x163 <= x139 && 0 <= x138 - 1 && 0 <= x139 - 1 && 0 <= x163 - 1 && x138 = x150 && x139 = x151 && x140 = x152 && x141 = x153 && x142 = x154 && x143 = x155
f826_0_binarySearch_LE(x164, x165, x166, x167, x168, x172, x173) -> f826_0_binarySearch_LE'(x174, x175, x176, x177, x178, x179, x180) :|: x181 <= x168 - x167 && -1 <= x167 - 1 && -1 <= x168 - 1 && x167 <= x168 && -1 <= x181 - 1 && x167 + x181 <= x172 - 1 && 1 <= x182 - 1 && 0 <= x167 + x181 && x167 + x181 - 1 <= x167 + x181 - 1 && x166 <= x183 - 1 && x184 <= x164 && x184 <= x165 && 0 <= x164 - 1 && 0 <= x165 - 1 && 0 <= x184 - 1 && x164 = x174 && x165 = x175 && x166 = x176 && x167 = x177 && x168 = x178 && x172 = x179
f826_0_binarySearch_LE'(x185, x186, x187, x188, x189, x190, x191) -> f1076_0_binarySearch_EQ(x192, x193, x194, x195, x196, x197, x198) :|: x199 <= x189 - x188 && -1 <= x188 - 1 && -1 <= x189 - 1 && x188 <= x189 && -1 <= x199 - 1 && x188 + x199 <= x190 - 1 && 1 <= x200 - 1 && 0 <= x188 + x199 && x188 + x199 - 1 <= x188 + x199 - 1 && x201 <= x187 - 1 && x192 <= x185 && x192 <= x186 && 0 <= x185 - 1 && 0 <= x186 - 1 && 0 <= x192 - 1 && x189 - x188 - 2 * x199 <= 1 && 0 <= x189 - x188 - 2 * x199 && x187 = x193 && x189 = x194 && x188 + x199 = x195 && 0 = x196 && x190 = x198
f826_0_binarySearch_LE'(x202, x203, x204, x205, x206, x207, x208) -> f1076_0_binarySearch_EQ(x209, x210, x211, x212, x213, x214, x215) :|: x216 <= x206 - x205 && -1 <= x205 - 1 && -1 <= x206 - 1 && x205 <= x206 && -1 <= x216 - 1 && x205 + x216 <= x207 - 1 && 1 <= x217 - 1 && 0 <= x205 + x216 && x205 + x216 - 1 <= x205 + x216 - 1 && x204 <= x218 - 1 && x209 <= x202 && x209 <= x203 && 0 <= x202 - 1 && 0 <= x203 - 1 && 0 <= x209 - 1 && x206 - x205 - 2 * x216 <= 1 && 0 <= x206 - x205 - 2 * x216 && x204 = x210 && x206 = x211 && x205 + x216 = x212 && 0 = x213 && x207 = x215
f826_0_binarySearch_LE'(x219, x220, x221, x226, x227, x228, x229) -> f1078_0_binarySearch_EQ(x230, x231, x236, x237, x238, x239, x240) :|: x241 <= x227 - x226 && -1 <= x226 - 1 && -1 <= x227 - 1 && x226 <= x227 && -1 <= x241 - 1 && x226 + x241 <= x228 - 1 && 1 <= x242 - 1 && 0 <= x226 + x241 && x226 + x241 - 1 <= x226 + x241 - 1 && x244 <= x221 - 1 && x230 <= x219 && x230 <= x220 && 0 <= x219 - 1 && 0 <= x220 - 1 && 0 <= x230 - 1 && x227 - x226 - 2 * x241 <= 1 && 0 <= x227 - x226 - 2 * x241 && x221 = x231 && x227 = x236 && x226 + x241 = x237 && 0 = x238 && x228 = x240
f826_0_binarySearch_LE'(x247, x248, x249, x250, x251, x252, x253) -> f1078_0_binarySearch_EQ(x255, x258, x259, x260, x261, x262, x263) :|: x264 <= x251 - x250 && -1 <= x250 - 1 && -1 <= x251 - 1 && x250 <= x251 && -1 <= x264 - 1 && x250 + x264 <= x252 - 1 && 1 <= x265 - 1 && 0 <= x250 + x264 && x250 + x264 - 1 <= x250 + x264 - 1 && x249 <= x266 - 1 && x255 <= x247 && x255 <= x248 && 0 <= x247 - 1 && 0 <= x248 - 1 && 0 <= x255 - 1 && x251 - x250 - 2 * x264 <= 1 && 0 <= x251 - x250 - 2 * x264 && x249 = x258 && x251 = x259 && x250 + x264 = x260 && 0 = x261 && x252 = x263
f826_0_binarySearch_LE'(x267, x268, x269, x270, x271, x272, x273) -> f1076_0_binarySearch_EQ(x274, x275, x276, x277, x278, x279, x280) :|: x281 <= x271 - x270 && -1 <= x270 - 1 && -1 <= x271 - 1 && x270 <= x271 && -1 <= x281 - 1 && x270 + x281 <= x272 - 1 && 1 <= x282 - 1 && 0 <= x270 + x281 && x270 + x281 - 1 <= x270 + x281 - 1 && x283 <= x269 - 1 && x274 <= x267 && x274 <= x268 && 0 <= x267 - 1 && 0 <= x268 - 1 && 0 <= x274 - 1 && x271 - x270 - 2 * x281 <= 1 && 0 <= x271 - x270 - 2 * x281 && x269 = x275 && x271 = x276 && x270 + x281 = x277 && 1 = x278 && x272 = x280
f826_0_binarySearch_LE'(x284, x286, x289, x290, x291, x292, x293) -> f1076_0_binarySearch_EQ(x294, x295, x297, x300, x301, x302, x303) :|: x304 <= x291 - x290 && -1 <= x290 - 1 && -1 <= x291 - 1 && x290 <= x291 && -1 <= x304 - 1 && x290 + x304 <= x292 - 1 && 1 <= x305 - 1 && 0 <= x290 + x304 && x290 + x304 - 1 <= x290 + x304 - 1 && x289 <= x306 - 1 && x294 <= x284 && x294 <= x286 && 0 <= x284 - 1 && 0 <= x286 - 1 && 0 <= x294 - 1 && x291 - x290 - 2 * x304 <= 1 && 0 <= x291 - x290 - 2 * x304 && x289 = x295 && x291 = x297 && x290 + x304 = x300 && 1 = x301 && x292 = x303
f826_0_binarySearch_LE'(x307, x308, x309, x310, x311, x312, x313) -> f1078_0_binarySearch_EQ(x314, x315, x316, x317, x318, x319, x320) :|: x321 <= x311 - x310 && -1 <= x310 - 1 && -1 <= x311 - 1 && x310 <= x311 && -1 <= x321 - 1 && x310 + x321 <= x312 - 1 && 1 <= x322 - 1 && 0 <= x310 + x321 && x310 + x321 - 1 <= x310 + x321 - 1 && x323 <= x309 - 1 && x314 <= x307 && x314 <= x308 && 0 <= x307 - 1 && 0 <= x308 - 1 && 0 <= x314 - 1 && x311 - x310 - 2 * x321 <= 1 && 0 <= x311 - x310 - 2 * x321 && x309 = x315 && x311 = x316 && x310 + x321 = x317 && 1 = x318 && x312 = x320
f826_0_binarySearch_LE'(x324, x325, x326, x328, x331, x332, x333) -> f1078_0_binarySearch_EQ(x334, x335, x336, x337, x339, x342, x343) :|: x344 <= x331 - x328 && -1 <= x328 - 1 && -1 <= x331 - 1 && x328 <= x331 && -1 <= x344 - 1 && x328 + x344 <= x332 - 1 && 1 <= x345 - 1 && 0 <= x328 + x344 && x328 + x344 - 1 <= x328 + x344 - 1 && x326 <= x346 - 1 && x334 <= x324 && x334 <= x325 && 0 <= x324 - 1 && 0 <= x325 - 1 && 0 <= x334 - 1 && x331 - x328 - 2 * x344 <= 1 && 0 <= x331 - x328 - 2 * x344 && x326 = x335 && x331 = x336 && x328 + x344 = x337 && 1 = x339 && x332 = x343
f1078_0_binarySearch_EQ(x347, x348, x349, x350, x351, x352, x353) -> f826_0_binarySearch_LE(x354, x355, x356, x357, x358, x359, x360) :|: 1 <= x361 - 1 && -1 <= x350 - 1 && x354 <= x347 && x355 <= x347 && 0 <= x347 - 1 && 0 <= x354 - 1 && 0 <= x355 - 1 && 0 = x351 && x348 = x356 && x350 + 1 = x357 && x349 = x358 && x353 = x359
f1076_0_binarySearch_EQ(x362, x363, x364, x365, x366, x367, x368) -> f826_0_binarySearch_LE(x370, x373, x374, x375, x376, x377, x378) :|: 1 <= x379 - 1 && -1 <= x365 - 1 && x370 <= x362 && x373 <= x362 && 0 <= x362 - 1 && 0 <= x370 - 1 && 0 <= x373 - 1 && 0 = x366 && x363 = x374 && x365 + 1 = x375 && x364 = x376 && x368 = x377
f826_0_binarySearch_LE'(x381, x384, x385, x386, x387, x388, x389) -> f1076_0_binarySearch_EQ(x390, x391, x392, x394, x395, x396, x397) :|: x398 <= x387 - x386 && -1 <= x386 - 1 && -1 <= x387 - 1 && x386 <= x387 && -1 <= x398 - 1 && x386 + x398 <= x388 - 1 && 1 <= x399 - 1 && 0 <= x386 + x398 && x386 + x398 - 1 <= x386 + x398 - 1 && x400 <= x385 - 1 && x390 <= x381 && x390 <= x384 && 0 <= x381 - 1 && 0 <= x384 - 1 && 0 <= x390 - 1 && x387 - x386 - 2 * x398 <= 1 && 0 <= x387 - x386 - 2 * x398 && x385 = x391 && x387 = x392 && x386 + x398 = x394 && x388 = x397
f826_0_binarySearch_LE'(x401, x402, x403, x404, x405, x406, x407) -> f1076_0_binarySearch_EQ(x408, x409, x410, x411, x412, x413, x414) :|: x415 <= x405 - x404 && -1 <= x404 - 1 && -1 <= x405 - 1 && x404 <= x405 && -1 <= x415 - 1 && x404 + x415 <= x406 - 1 && 1 <= x416 - 1 && 0 <= x404 + x415 && x404 + x415 - 1 <= x404 + x415 - 1 && x403 <= x417 - 1 && x408 <= x401 && x408 <= x402 && 0 <= x401 - 1 && 0 <= x402 - 1 && 0 <= x408 - 1 && x405 - x404 - 2 * x415 <= 1 && 0 <= x405 - x404 - 2 * x415 && x403 = x409 && x405 = x410 && x404 + x415 = x411 && x406 = x414
f826_0_binarySearch_LE'(x418, x419, x420, x422, x423, x426, x427) -> f1078_0_binarySearch_EQ(x428, x429, x430, x431, x432, x434, x435) :|: x438 <= x423 - x422 && -1 <= x422 - 1 && -1 <= x423 - 1 && x422 <= x423 && -1 <= x438 - 1 && x422 + x438 <= x426 - 1 && 1 <= x439 - 1 && 0 <= x422 + x438 && x422 + x438 - 1 <= x422 + x438 - 1 && x440 <= x420 - 1 && x428 <= x418 && x428 <= x419 && 0 <= x418 - 1 && 0 <= x419 - 1 && 0 <= x428 - 1 && x423 - x422 - 2 * x438 <= 1 && 0 <= x423 - x422 - 2 * x438 && x420 = x429 && x423 = x430 && x422 + x438 = x431 && x426 = x435
f826_0_binarySearch_LE'(x441, x442, x443, x444, x445, x446, x447) -> f1078_0_binarySearch_EQ(x448, x449, x450, x451, x452, x453, x454) :|: x455 <= x445 - x444 && -1 <= x444 - 1 && -1 <= x445 - 1 && x444 <= x445 && -1 <= x455 - 1 && x444 + x455 <= x446 - 1 && 1 <= x456 - 1 && 0 <= x444 + x455 && x444 + x455 - 1 <= x444 + x455 - 1 && x443 <= x457 - 1 && x448 <= x441 && x448 <= x442 && 0 <= x441 - 1 && 0 <= x442 - 1 && 0 <= x448 - 1 && x445 - x444 - 2 * x455 <= 1 && 0 <= x445 - x444 - 2 * x455 && x443 = x449 && x445 = x450 && x444 + x455 = x451 && x446 = x454
__init(x458, x459, x460, x461, x462, x463, x464) -> f1_0_main_Load(x466, x467, x470, x471, x472, x473, x474) :|: 0 <= 0
Start term: __init(arg1, arg2, arg3, arg4, arg5, arg6, arg7)

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

(3) IRSwTTerminationDigraphProof (EQUIVALENT)
Constructed termination digraph!
Nodes:
(1) f242_0_createArray_Return(arg1, arg2, arg3, arg4, arg5, arg6, arg7) -> f382_0_random_ArrayAccess(arg1P, arg2P, arg3P, arg4P, arg5P, arg6P, arg7P) :|: arg4 = arg3P && 0 <= arg1P - 1 && 0 <= arg2 - 1 && 0 <= arg1 - 1 && arg1P <= arg2 && arg1P <= arg1
(2) f1_0_main_Load(x, x1, x2, x3, x4, x5, x6) -> f382_0_random_ArrayAccess(x7, x8, x9, x10, x11, x12, x13) :|: x1 = x8 && 0 <= x7 - 1 && 0 <= x - 1 && x7 <= x
(3) f1_0_main_Load(x14, x15, x16, x17, x18, x19, x20) -> f464_0_createArray_GE(x21, x23, x24, x25, x26, x27, x29) :|: 1 = x25 && x15 = x24 && 0 = x23 && 0 <= x21 - 1 && 0 <= x14 - 1 && x21 <= x14 && 0 <= x15 - 1 && -1 <= x26 - 1
(4) f464_0_createArray_GE(x30, x31, x32, x33, x34, x35, x36) -> f464_0_createArray_GE(x37, x38, x39, x40, x41, x42, x43) :|: x34 = x41 && x33 + 1 = x40 && x32 = x39 && x31 + 1 = x38 && 0 <= x37 - 1 && 0 <= x30 - 1 && x37 <= x30 && -1 <= x34 - 1 && x31 <= x34 - 1 && 0 <= x33 - 1 && x33 <= x32 - 1
(5) f382_0_random_ArrayAccess(x44, x45, x46, x47, x48, x49, x50) -> f826_0_binarySearch_LE(x51, x52, x53, x54, x55, x56, x57) :|: x58 <= x45 - 1 && 0 <= x58 - 1 && -1 <= x53 - 1 && 0 <= x45 - 1 && -1 <= x46 - 1 && 1 <= x59 - 1 && x52 <= x44 && 0 <= x44 - 1 && 0 <= x51 - 1 && 0 <= x52 - 1 && 0 = x54 && x46 = x55 && x46 = x56
(6) f826_0_binarySearch_LE(x60, x61, x62, x63, x64, x65, x66) -> f826_0_binarySearch_LE'(x67, x68, x69, x70, x71, x73, x74) :|: x75 <= x64 - x63 && -1 <= x63 - 1 && -1 <= x64 - 1 && x63 <= x64 && -1 <= x75 - 1 && x63 + x75 <= x65 - 1 && 1 <= x76 - 1 && 0 <= x63 + x75 && x63 + x75 - 1 <= x63 + x75 - 1 && x77 <= x62 - 1 && x78 <= x60 && x78 <= x61 && x79 <= x60 && x79 <= x61 && 0 <= x60 - 1 && 0 <= x61 - 1 && 0 <= x78 - 1 && 0 <= x79 - 1 && x60 = x67 && x61 = x68 && x62 = x69 && x63 = x70 && x64 = x71 && x65 = x73
(7) f826_0_binarySearch_LE(x80, x81, x82, x84, x85, x86, x87) -> f826_0_binarySearch_LE'(x88, x89, x90, x91, x92, x93, x95) :|: x96 <= x85 - x84 && -1 <= x84 - 1 && -1 <= x85 - 1 && x84 <= x85 && -1 <= x96 - 1 && x84 + x96 <= x86 - 1 && 1 <= x97 - 1 && 0 <= x84 + x96 && x84 + x96 - 1 <= x84 + x96 - 1 && x82 <= x98 - 1 && x99 <= x80 && x99 <= x81 && x100 <= x80 && x100 <= x81 && 0 <= x80 - 1 && 0 <= x81 - 1 && 0 <= x99 - 1 && 0 <= x100 - 1 && x80 = x88 && x81 = x89 && x82 = x90 && x84 = x91 && x85 = x92 && x86 = x93
(8) f826_0_binarySearch_LE'(x101, x102, x103, x104, x106, x107, x108) -> f826_0_binarySearch_LE(x109, x110, x111, x112, x113, x114, x115) :|: x116 <= x106 - x104 && -1 <= x104 - 1 && -1 <= x106 - 1 && x104 <= x106 && -1 <= x116 - 1 && x104 + x116 <= x107 - 1 && 1 <= x117 - 1 && 0 <= x104 + x116 && x104 + x116 - 1 <= x104 + x116 - 1 && x118 <= x103 - 1 && x109 <= x101 && x109 <= x102 && x110 <= x101 && x110 <= x102 && 0 <= x101 - 1 && 0 <= x102 - 1 && 0 <= x109 - 1 && 0 <= x110 - 1 && x106 - x104 - 2 * x116 <= 1 && 0 <= x106 - x104 - 2 * x116 && x103 = x111 && x104 = x112 && x104 + x116 - 1 = x113 && x107 = x114
(9) f826_0_binarySearch_LE'(x119, x120, x121, x122, x124, x125, x126) -> f826_0_binarySearch_LE(x127, x128, x129, x130, x131, x132, x133) :|: x134 <= x124 - x122 && -1 <= x122 - 1 && -1 <= x124 - 1 && x122 <= x124 && -1 <= x134 - 1 && x122 + x134 <= x125 - 1 && 1 <= x136 - 1 && 0 <= x122 + x134 && x122 + x134 - 1 <= x122 + x134 - 1 && x121 <= x137 - 1 && x127 <= x119 && x127 <= x120 && x128 <= x119 && x128 <= x120 && 0 <= x119 - 1 && 0 <= x120 - 1 && 0 <= x127 - 1 && 0 <= x128 - 1 && x124 - x122 - 2 * x134 <= 1 && 0 <= x124 - x122 - 2 * x134 && x121 = x129 && x122 = x130 && x122 + x134 - 1 = x131 && x125 = x132
(10) f826_0_binarySearch_LE(x138, x139, x140, x141, x142, x143, x144) -> f826_0_binarySearch_LE'(x150, x151, x152, x153, x154, x155, x156) :|: x157 <= x142 - x141 && -1 <= x141 - 1 && -1 <= x142 - 1 && x141 <= x142 && -1 <= x157 - 1 && x141 + x157 <= x143 - 1 && 1 <= x161 - 1 && 0 <= x141 + x157 && x141 + x157 - 1 <= x141 + x157 - 1 && x162 <= x140 - 1 && x163 <= x138 && x163 <= x139 && 0 <= x138 - 1 && 0 <= x139 - 1 && 0 <= x163 - 1 && x138 = x150 && x139 = x151 && x140 = x152 && x141 = x153 && x142 = x154 && x143 = x155
(11) f826_0_binarySearch_LE(x164, x165, x166, x167, x168, x172, x173) -> f826_0_binarySearch_LE'(x174, x175, x176, x177, x178, x179, x180) :|: x181 <= x168 - x167 && -1 <= x167 - 1 && -1 <= x168 - 1 && x167 <= x168 && -1 <= x181 - 1 && x167 + x181 <= x172 - 1 && 1 <= x182 - 1 && 0 <= x167 + x181 && x167 + x181 - 1 <= x167 + x181 - 1 && x166 <= x183 - 1 && x184 <= x164 && x184 <= x165 && 0 <= x164 - 1 && 0 <= x165 - 1 && 0 <= x184 - 1 && x164 = x174 && x165 = x175 && x166 = x176 && x167 = x177 && x168 = x178 && x172 = x179
(12) f826_0_binarySearch_LE'(x185, x186, x187, x188, x189, x190, x191) -> f1076_0_binarySearch_EQ(x192, x193, x194, x195, x196, x197, x198) :|: x199 <= x189 - x188 && -1 <= x188 - 1 && -1 <= x189 - 1 && x188 <= x189 && -1 <= x199 - 1 && x188 + x199 <= x190 - 1 && 1 <= x200 - 1 && 0 <= x188 + x199 && x188 + x199 - 1 <= x188 + x199 - 1 && x201 <= x187 - 1 && x192 <= x185 && x192 <= x186 && 0 <= x185 - 1 && 0 <= x186 - 1 && 0 <= x192 - 1 && x189 - x188 - 2 * x199 <= 1 && 0 <= x189 - x188 - 2 * x199 && x187 = x193 && x189 = x194 && x188 + x199 = x195 && 0 = x196 && x190 = x198
(13) f826_0_binarySearch_LE'(x202, x203, x204, x205, x206, x207, x208) -> f1076_0_binarySearch_EQ(x209, x210, x211, x212, x213, x214, x215) :|: x216 <= x206 - x205 && -1 <= x205 - 1 && -1 <= x206 - 1 && x205 <= x206 && -1 <= x216 - 1 && x205 + x216 <= x207 - 1 && 1 <= x217 - 1 && 0 <= x205 + x216 && x205 + x216 - 1 <= x205 + x216 - 1 && x204 <= x218 - 1 && x209 <= x202 && x209 <= x203 && 0 <= x202 - 1 && 0 <= x203 - 1 && 0 <= x209 - 1 && x206 - x205 - 2 * x216 <= 1 && 0 <= x206 - x205 - 2 * x216 && x204 = x210 && x206 = x211 && x205 + x216 = x212 && 0 = x213 && x207 = x215
(14) f826_0_binarySearch_LE'(x219, x220, x221, x226, x227, x228, x229) -> f1078_0_binarySearch_EQ(x230, x231, x236, x237, x238, x239, x240) :|: x241 <= x227 - x226 && -1 <= x226 - 1 && -1 <= x227 - 1 && x226 <= x227 && -1 <= x241 - 1 && x226 + x241 <= x228 - 1 && 1 <= x242 - 1 && 0 <= x226 + x241 && x226 + x241 - 1 <= x226 + x241 - 1 && x244 <= x221 - 1 && x230 <= x219 && x230 <= x220 && 0 <= x219 - 1 && 0 <= x220 - 1 && 0 <= x230 - 1 && x227 - x226 - 2 * x241 <= 1 && 0 <= x227 - x226 - 2 * x241 && x221 = x231 && x227 = x236 && x226 + x241 = x237 && 0 = x238 && x228 = x240
(15) f826_0_binarySearch_LE'(x247, x248, x249, x250, x251, x252, x253) -> f1078_0_binarySearch_EQ(x255, x258, x259, x260, x261, x262, x263) :|: x264 <= x251 - x250 && -1 <= x250 - 1 && -1 <= x251 - 1 && x250 <= x251 && -1 <= x264 - 1 && x250 + x264 <= x252 - 1 && 1 <= x265 - 1 && 0 <= x250 + x264 && x250 + x264 - 1 <= x250 + x264 - 1 && x249 <= x266 - 1 && x255 <= x247 && x255 <= x248 && 0 <= x247 - 1 && 0 <= x248 - 1 && 0 <= x255 - 1 && x251 - x250 - 2 * x264 <= 1 && 0 <= x251 - x250 - 2 * x264 && x249 = x258 && x251 = x259 && x250 + x264 = x260 && 0 = x261 && x252 = x263
(16) f826_0_binarySearch_LE'(x267, x268, x269, x270, x271, x272, x273) -> f1076_0_binarySearch_EQ(x274, x275, x276, x277, x278, x279, x280) :|: x281 <= x271 - x270 && -1 <= x270 - 1 && -1 <= x271 - 1 && x270 <= x271 && -1 <= x281 - 1 && x270 + x281 <= x272 - 1 && 1 <= x282 - 1 && 0 <= x270 + x281 && x270 + x281 - 1 <= x270 + x281 - 1 && x283 <= x269 - 1 && x274 <= x267 && x274 <= x268 && 0 <= x267 - 1 && 0 <= x268 - 1 && 0 <= x274 - 1 && x271 - x270 - 2 * x281 <= 1 && 0 <= x271 - x270 - 2 * x281 && x269 = x275 && x271 = x276 && x270 + x281 = x277 && 1 = x278 && x272 = x280
(17) f826_0_binarySearch_LE'(x284, x286, x289, x290, x291, x292, x293) -> f1076_0_binarySearch_EQ(x294, x295, x297, x300, x301, x302, x303) :|: x304 <= x291 - x290 && -1 <= x290 - 1 && -1 <= x291 - 1 && x290 <= x291 && -1 <= x304 - 1 && x290 + x304 <= x292 - 1 && 1 <= x305 - 1 && 0 <= x290 + x304 && x290 + x304 - 1 <= x290 + x304 - 1 && x289 <= x306 - 1 && x294 <= x284 && x294 <= x286 && 0 <= x284 - 1 && 0 <= x286 - 1 && 0 <= x294 - 1 && x291 - x290 - 2 * x304 <= 1 && 0 <= x291 - x290 - 2 * x304 && x289 = x295 && x291 = x297 && x290 + x304 = x300 && 1 = x301 && x292 = x303
(18) f826_0_binarySearch_LE'(x307, x308, x309, x310, x311, x312, x313) -> f1078_0_binarySearch_EQ(x314, x315, x316, x317, x318, x319, x320) :|: x321 <= x311 - x310 && -1 <= x310 - 1 && -1 <= x311 - 1 && x310 <= x311 && -1 <= x321 - 1 && x310 + x321 <= x312 - 1 && 1 <= x322 - 1 && 0 <= x310 + x321 && x310 + x321 - 1 <= x310 + x321 - 1 && x323 <= x309 - 1 && x314 <= x307 && x314 <= x308 && 0 <= x307 - 1 && 0 <= x308 - 1 && 0 <= x314 - 1 && x311 - x310 - 2 * x321 <= 1 && 0 <= x311 - x310 - 2 * x321 && x309 = x315 && x311 = x316 && x310 + x321 = x317 && 1 = x318 && x312 = x320
(19) f826_0_binarySearch_LE'(x324, x325, x326, x328, x331, x332, x333) -> f1078_0_binarySearch_EQ(x334, x335, x336, x337, x339, x342, x343) :|: x344 <= x331 - x328 && -1 <= x328 - 1 && -1 <= x331 - 1 && x328 <= x331 && -1 <= x344 - 1 && x328 + x344 <= x332 - 1 && 1 <= x345 - 1 && 0 <= x328 + x344 && x328 + x344 - 1 <= x328 + x344 - 1 && x326 <= x346 - 1 && x334 <= x324 && x334 <= x325 && 0 <= x324 - 1 && 0 <= x325 - 1 && 0 <= x334 - 1 && x331 - x328 - 2 * x344 <= 1 && 0 <= x331 - x328 - 2 * x344 && x326 = x335 && x331 = x336 && x328 + x344 = x337 && 1 = x339 && x332 = x343
(20) f1078_0_binarySearch_EQ(x347, x348, x349, x350, x351, x352, x353) -> f826_0_binarySearch_LE(x354, x355, x356, x357, x358, x359, x360) :|: 1 <= x361 - 1 && -1 <= x350 - 1 && x354 <= x347 && x355 <= x347 && 0 <= x347 - 1 && 0 <= x354 - 1 && 0 <= x355 - 1 && 0 = x351 && x348 = x356 && x350 + 1 = x357 && x349 = x358 && x353 = x359
(21) f1076_0_binarySearch_EQ(x362, x363, x364, x365, x366, x367, x368) -> f826_0_binarySearch_LE(x370, x373, x374, x375, x376, x377, x378) :|: 1 <= x379 - 1 && -1 <= x365 - 1 && x370 <= x362 && x373 <= x362 && 0 <= x362 - 1 && 0 <= x370 - 1 && 0 <= x373 - 1 && 0 = x366 && x363 = x374 && x365 + 1 = x375 && x364 = x376 && x368 = x377
(22) f826_0_binarySearch_LE'(x381, x384, x385, x386, x387, x388, x389) -> f1076_0_binarySearch_EQ(x390, x391, x392, x394, x395, x396, x397) :|: x398 <= x387 - x386 && -1 <= x386 - 1 && -1 <= x387 - 1 && x386 <= x387 && -1 <= x398 - 1 && x386 + x398 <= x388 - 1 && 1 <= x399 - 1 && 0 <= x386 + x398 && x386 + x398 - 1 <= x386 + x398 - 1 && x400 <= x385 - 1 && x390 <= x381 && x390 <= x384 && 0 <= x381 - 1 && 0 <= x384 - 1 && 0 <= x390 - 1 && x387 - x386 - 2 * x398 <= 1 && 0 <= x387 - x386 - 2 * x398 && x385 = x391 && x387 = x392 && x386 + x398 = x394 && x388 = x397
(23) f826_0_binarySearch_LE'(x401, x402, x403, x404, x405, x406, x407) -> f1076_0_binarySearch_EQ(x408, x409, x410, x411, x412, x413, x414) :|: x415 <= x405 - x404 && -1 <= x404 - 1 && -1 <= x405 - 1 && x404 <= x405 && -1 <= x415 - 1 && x404 + x415 <= x406 - 1 && 1 <= x416 - 1 && 0 <= x404 + x415 && x404 + x415 - 1 <= x404 + x415 - 1 && x403 <= x417 - 1 && x408 <= x401 && x408 <= x402 && 0 <= x401 - 1 && 0 <= x402 - 1 && 0 <= x408 - 1 && x405 - x404 - 2 * x415 <= 1 && 0 <= x405 - x404 - 2 * x415 && x403 = x409 && x405 = x410 && x404 + x415 = x411 && x406 = x414
(24) f826_0_binarySearch_LE'(x418, x419, x420, x422, x423, x426, x427) -> f1078_0_binarySearch_EQ(x428, x429, x430, x431, x432, x434, x435) :|: x438 <= x423 - x422 && -1 <= x422 - 1 && -1 <= x423 - 1 && x422 <= x423 && -1 <= x438 - 1 && x422 + x438 <= x426 - 1 && 1 <= x439 - 1 && 0 <= x422 + x438 && x422 + x438 - 1 <= x422 + x438 - 1 && x440 <= x420 - 1 && x428 <= x418 && x428 <= x419 && 0 <= x418 - 1 && 0 <= x419 - 1 && 0 <= x428 - 1 && x423 - x422 - 2 * x438 <= 1 && 0 <= x423 - x422 - 2 * x438 && x420 = x429 && x423 = x430 && x422 + x438 = x431 && x426 = x435
(25) f826_0_binarySearch_LE'(x441, x442, x443, x444, x445, x446, x447) -> f1078_0_binarySearch_EQ(x448, x449, x450, x451, x452, x453, x454) :|: x455 <= x445 - x444 && -1 <= x444 - 1 && -1 <= x445 - 1 && x444 <= x445 && -1 <= x455 - 1 && x444 + x455 <= x446 - 1 && 1 <= x456 - 1 && 0 <= x444 + x455 && x444 + x455 - 1 <= x444 + x455 - 1 && x443 <= x457 - 1 && x448 <= x441 && x448 <= x442 && 0 <= x441 - 1 && 0 <= x442 - 1 && 0 <= x448 - 1 && x445 - x444 - 2 * x455 <= 1 && 0 <= x445 - x444 - 2 * x455 && x443 = x449 && x445 = x450 && x444 + x455 = x451 && x446 = x454
(26) __init(x458, x459, x460, x461, x462, x463, x464) -> f1_0_main_Load(x466, x467, x470, x471, x472, x473, x474) :|: 0 <= 0

Arcs:
(1) -> (5)
(2) -> (5)
(3) -> (4)
(4) -> (4)
(5) -> (6), (7), (10), (11)
(6) -> (8), (9), (12), (13), (14), (15), (16), (17), (18), (19), (22), (23), (24), (25)
(7) -> (8), (9), (12), (13), (14), (15), (16), (17), (18), (19), (22), (23), (24), (25)
(8) -> (6), (7), (10), (11)
(9) -> (6), (7), (10), (11)
(10) -> (8), (9), (12), (13), (14), (15), (16), (17), (18), (19), (22), (23), (24), (25)
(11) -> (8), (9), (12), (13), (14), (15), (16), (17), (18), (19), (22), (23), (24), (25)
(12) -> (21)
(13) -> (21)
(14) -> (20)
(15) -> (20)
(20) -> (6), (7), (10), (11)
(21) -> (6), (7), (10), (11)
(22) -> (21)
(23) -> (21)
(24) -> (20)
(25) -> (20)
(26) -> (2), (3)

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

(4)
Complex Obligation (AND)

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

(5)
Obligation:

Termination digraph:
Nodes:
(1) f464_0_createArray_GE(x30, x31, x32, x33, x34, x35, x36) -> f464_0_createArray_GE(x37, x38, x39, x40, x41, x42, x43) :|: x34 = x41 && x33 + 1 = x40 && x32 = x39 && x31 + 1 = x38 && 0 <= x37 - 1 && 0 <= x30 - 1 && x37 <= x30 && -1 <= x34 - 1 && x31 <= x34 - 1 && 0 <= x33 - 1 && x33 <= x32 - 1

Arcs:
(1) -> (1)

This digraph is fully evaluated!

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

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

(7)
Obligation:
Rules:
f464_0_createArray_GE(x30:0, x31:0, x32:0, x33:0, x34:0, x35:0, x36:0) -> f464_0_createArray_GE(x37:0, x31:0 + 1, x32:0, x33:0 + 1, x34:0, x42:0, x43:0) :|: x33:0 > 0 && x33:0 <= x32:0 - 1 && x34:0 - 1 >= x31:0 && x34:0 > -1 && x37:0 <= x30:0 && x37:0 > 0 && x30:0 > 0

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

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

   f464_0_createArray_GE(x1, x2, x3, x4, x5, x6, x7) -> f464_0_createArray_GE(x1, x2, x3, x4, x5)

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

(9)
Obligation:
Rules:
f464_0_createArray_GE(x30:0, x31:0, x32:0, x33:0, x34:0) -> f464_0_createArray_GE(x37:0, x31:0 + 1, x32:0, x33:0 + 1, x34:0) :|: x33:0 > 0 && x33:0 <= x32:0 - 1 && x34:0 - 1 >= x31:0 && x34:0 > -1 && x37:0 <= x30:0 && x37:0 > 0 && x30:0 > 0

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

(10) TempFilterProof (SOUND)
Used the following sort dictionary for filtering: 
f464_0_createArray_GE(INTEGER, INTEGER, INTEGER, INTEGER, INTEGER)
Replaced non-predefined constructor symbols by 0.
----------------------------------------

(11)
Obligation:
Rules:
f464_0_createArray_GE(x30:0, x31:0, x32:0, x33:0, x34:0) -> f464_0_createArray_GE(x37:0, c, x32:0, c1, x34:0) :|: c1 = x33:0 + 1 && c = x31:0 + 1 && (x33:0 > 0 && x33:0 <= x32:0 - 1 && x34:0 - 1 >= x31:0 && x34:0 > -1 && x37:0 <= x30:0 && x37:0 > 0 && x30:0 > 0)

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

(12) RankingReductionPairProof (EQUIVALENT)
Interpretation:
[ f464_0_createArray_GE ] = -1*f464_0_createArray_GE_4 + f464_0_createArray_GE_3

The following rules are decreasing:
f464_0_createArray_GE(x30:0, x31:0, x32:0, x33:0, x34:0) -> f464_0_createArray_GE(x37:0, c, x32:0, c1, x34:0) :|: c1 = x33:0 + 1 && c = x31:0 + 1 && (x33:0 > 0 && x33:0 <= x32:0 - 1 && x34:0 - 1 >= x31:0 && x34:0 > -1 && x37:0 <= x30:0 && x37:0 > 0 && x30:0 > 0)

The following rules are bounded:
f464_0_createArray_GE(x30:0, x31:0, x32:0, x33:0, x34:0) -> f464_0_createArray_GE(x37:0, c, x32:0, c1, x34:0) :|: c1 = x33:0 + 1 && c = x31:0 + 1 && (x33:0 > 0 && x33:0 <= x32:0 - 1 && x34:0 - 1 >= x31:0 && x34:0 > -1 && x37:0 <= x30:0 && x37:0 > 0 && x30:0 > 0)


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

(13)
YES

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

(14)
Obligation:

Termination digraph:
Nodes:
(1) f826_0_binarySearch_LE(x60, x61, x62, x63, x64, x65, x66) -> f826_0_binarySearch_LE'(x67, x68, x69, x70, x71, x73, x74) :|: x75 <= x64 - x63 && -1 <= x63 - 1 && -1 <= x64 - 1 && x63 <= x64 && -1 <= x75 - 1 && x63 + x75 <= x65 - 1 && 1 <= x76 - 1 && 0 <= x63 + x75 && x63 + x75 - 1 <= x63 + x75 - 1 && x77 <= x62 - 1 && x78 <= x60 && x78 <= x61 && x79 <= x60 && x79 <= x61 && 0 <= x60 - 1 && 0 <= x61 - 1 && 0 <= x78 - 1 && 0 <= x79 - 1 && x60 = x67 && x61 = x68 && x62 = x69 && x63 = x70 && x64 = x71 && x65 = x73
(2) f826_0_binarySearch_LE'(x101, x102, x103, x104, x106, x107, x108) -> f826_0_binarySearch_LE(x109, x110, x111, x112, x113, x114, x115) :|: x116 <= x106 - x104 && -1 <= x104 - 1 && -1 <= x106 - 1 && x104 <= x106 && -1 <= x116 - 1 && x104 + x116 <= x107 - 1 && 1 <= x117 - 1 && 0 <= x104 + x116 && x104 + x116 - 1 <= x104 + x116 - 1 && x118 <= x103 - 1 && x109 <= x101 && x109 <= x102 && x110 <= x101 && x110 <= x102 && 0 <= x101 - 1 && 0 <= x102 - 1 && 0 <= x109 - 1 && 0 <= x110 - 1 && x106 - x104 - 2 * x116 <= 1 && 0 <= x106 - x104 - 2 * x116 && x103 = x111 && x104 = x112 && x104 + x116 - 1 = x113 && x107 = x114
(3) f826_0_binarySearch_LE(x80, x81, x82, x84, x85, x86, x87) -> f826_0_binarySearch_LE'(x88, x89, x90, x91, x92, x93, x95) :|: x96 <= x85 - x84 && -1 <= x84 - 1 && -1 <= x85 - 1 && x84 <= x85 && -1 <= x96 - 1 && x84 + x96 <= x86 - 1 && 1 <= x97 - 1 && 0 <= x84 + x96 && x84 + x96 - 1 <= x84 + x96 - 1 && x82 <= x98 - 1 && x99 <= x80 && x99 <= x81 && x100 <= x80 && x100 <= x81 && 0 <= x80 - 1 && 0 <= x81 - 1 && 0 <= x99 - 1 && 0 <= x100 - 1 && x80 = x88 && x81 = x89 && x82 = x90 && x84 = x91 && x85 = x92 && x86 = x93
(4) f826_0_binarySearch_LE'(x119, x120, x121, x122, x124, x125, x126) -> f826_0_binarySearch_LE(x127, x128, x129, x130, x131, x132, x133) :|: x134 <= x124 - x122 && -1 <= x122 - 1 && -1 <= x124 - 1 && x122 <= x124 && -1 <= x134 - 1 && x122 + x134 <= x125 - 1 && 1 <= x136 - 1 && 0 <= x122 + x134 && x122 + x134 - 1 <= x122 + x134 - 1 && x121 <= x137 - 1 && x127 <= x119 && x127 <= x120 && x128 <= x119 && x128 <= x120 && 0 <= x119 - 1 && 0 <= x120 - 1 && 0 <= x127 - 1 && 0 <= x128 - 1 && x124 - x122 - 2 * x134 <= 1 && 0 <= x124 - x122 - 2 * x134 && x121 = x129 && x122 = x130 && x122 + x134 - 1 = x131 && x125 = x132
(5) f826_0_binarySearch_LE(x138, x139, x140, x141, x142, x143, x144) -> f826_0_binarySearch_LE'(x150, x151, x152, x153, x154, x155, x156) :|: x157 <= x142 - x141 && -1 <= x141 - 1 && -1 <= x142 - 1 && x141 <= x142 && -1 <= x157 - 1 && x141 + x157 <= x143 - 1 && 1 <= x161 - 1 && 0 <= x141 + x157 && x141 + x157 - 1 <= x141 + x157 - 1 && x162 <= x140 - 1 && x163 <= x138 && x163 <= x139 && 0 <= x138 - 1 && 0 <= x139 - 1 && 0 <= x163 - 1 && x138 = x150 && x139 = x151 && x140 = x152 && x141 = x153 && x142 = x154 && x143 = x155
(6) f1078_0_binarySearch_EQ(x347, x348, x349, x350, x351, x352, x353) -> f826_0_binarySearch_LE(x354, x355, x356, x357, x358, x359, x360) :|: 1 <= x361 - 1 && -1 <= x350 - 1 && x354 <= x347 && x355 <= x347 && 0 <= x347 - 1 && 0 <= x354 - 1 && 0 <= x355 - 1 && 0 = x351 && x348 = x356 && x350 + 1 = x357 && x349 = x358 && x353 = x359
(7) f826_0_binarySearch_LE'(x441, x442, x443, x444, x445, x446, x447) -> f1078_0_binarySearch_EQ(x448, x449, x450, x451, x452, x453, x454) :|: x455 <= x445 - x444 && -1 <= x444 - 1 && -1 <= x445 - 1 && x444 <= x445 && -1 <= x455 - 1 && x444 + x455 <= x446 - 1 && 1 <= x456 - 1 && 0 <= x444 + x455 && x444 + x455 - 1 <= x444 + x455 - 1 && x443 <= x457 - 1 && x448 <= x441 && x448 <= x442 && 0 <= x441 - 1 && 0 <= x442 - 1 && 0 <= x448 - 1 && x445 - x444 - 2 * x455 <= 1 && 0 <= x445 - x444 - 2 * x455 && x443 = x449 && x445 = x450 && x444 + x455 = x451 && x446 = x454
(8) f826_0_binarySearch_LE'(x418, x419, x420, x422, x423, x426, x427) -> f1078_0_binarySearch_EQ(x428, x429, x430, x431, x432, x434, x435) :|: x438 <= x423 - x422 && -1 <= x422 - 1 && -1 <= x423 - 1 && x422 <= x423 && -1 <= x438 - 1 && x422 + x438 <= x426 - 1 && 1 <= x439 - 1 && 0 <= x422 + x438 && x422 + x438 - 1 <= x422 + x438 - 1 && x440 <= x420 - 1 && x428 <= x418 && x428 <= x419 && 0 <= x418 - 1 && 0 <= x419 - 1 && 0 <= x428 - 1 && x423 - x422 - 2 * x438 <= 1 && 0 <= x423 - x422 - 2 * x438 && x420 = x429 && x423 = x430 && x422 + x438 = x431 && x426 = x435
(9) f826_0_binarySearch_LE'(x247, x248, x249, x250, x251, x252, x253) -> f1078_0_binarySearch_EQ(x255, x258, x259, x260, x261, x262, x263) :|: x264 <= x251 - x250 && -1 <= x250 - 1 && -1 <= x251 - 1 && x250 <= x251 && -1 <= x264 - 1 && x250 + x264 <= x252 - 1 && 1 <= x265 - 1 && 0 <= x250 + x264 && x250 + x264 - 1 <= x250 + x264 - 1 && x249 <= x266 - 1 && x255 <= x247 && x255 <= x248 && 0 <= x247 - 1 && 0 <= x248 - 1 && 0 <= x255 - 1 && x251 - x250 - 2 * x264 <= 1 && 0 <= x251 - x250 - 2 * x264 && x249 = x258 && x251 = x259 && x250 + x264 = x260 && 0 = x261 && x252 = x263
(10) f826_0_binarySearch_LE'(x219, x220, x221, x226, x227, x228, x229) -> f1078_0_binarySearch_EQ(x230, x231, x236, x237, x238, x239, x240) :|: x241 <= x227 - x226 && -1 <= x226 - 1 && -1 <= x227 - 1 && x226 <= x227 && -1 <= x241 - 1 && x226 + x241 <= x228 - 1 && 1 <= x242 - 1 && 0 <= x226 + x241 && x226 + x241 - 1 <= x226 + x241 - 1 && x244 <= x221 - 1 && x230 <= x219 && x230 <= x220 && 0 <= x219 - 1 && 0 <= x220 - 1 && 0 <= x230 - 1 && x227 - x226 - 2 * x241 <= 1 && 0 <= x227 - x226 - 2 * x241 && x221 = x231 && x227 = x236 && x226 + x241 = x237 && 0 = x238 && x228 = x240
(11) f826_0_binarySearch_LE(x164, x165, x166, x167, x168, x172, x173) -> f826_0_binarySearch_LE'(x174, x175, x176, x177, x178, x179, x180) :|: x181 <= x168 - x167 && -1 <= x167 - 1 && -1 <= x168 - 1 && x167 <= x168 && -1 <= x181 - 1 && x167 + x181 <= x172 - 1 && 1 <= x182 - 1 && 0 <= x167 + x181 && x167 + x181 - 1 <= x167 + x181 - 1 && x166 <= x183 - 1 && x184 <= x164 && x184 <= x165 && 0 <= x164 - 1 && 0 <= x165 - 1 && 0 <= x184 - 1 && x164 = x174 && x165 = x175 && x166 = x176 && x167 = x177 && x168 = x178 && x172 = x179
(12) f1076_0_binarySearch_EQ(x362, x363, x364, x365, x366, x367, x368) -> f826_0_binarySearch_LE(x370, x373, x374, x375, x376, x377, x378) :|: 1 <= x379 - 1 && -1 <= x365 - 1 && x370 <= x362 && x373 <= x362 && 0 <= x362 - 1 && 0 <= x370 - 1 && 0 <= x373 - 1 && 0 = x366 && x363 = x374 && x365 + 1 = x375 && x364 = x376 && x368 = x377
(13) f826_0_binarySearch_LE'(x401, x402, x403, x404, x405, x406, x407) -> f1076_0_binarySearch_EQ(x408, x409, x410, x411, x412, x413, x414) :|: x415 <= x405 - x404 && -1 <= x404 - 1 && -1 <= x405 - 1 && x404 <= x405 && -1 <= x415 - 1 && x404 + x415 <= x406 - 1 && 1 <= x416 - 1 && 0 <= x404 + x415 && x404 + x415 - 1 <= x404 + x415 - 1 && x403 <= x417 - 1 && x408 <= x401 && x408 <= x402 && 0 <= x401 - 1 && 0 <= x402 - 1 && 0 <= x408 - 1 && x405 - x404 - 2 * x415 <= 1 && 0 <= x405 - x404 - 2 * x415 && x403 = x409 && x405 = x410 && x404 + x415 = x411 && x406 = x414
(14) f826_0_binarySearch_LE'(x381, x384, x385, x386, x387, x388, x389) -> f1076_0_binarySearch_EQ(x390, x391, x392, x394, x395, x396, x397) :|: x398 <= x387 - x386 && -1 <= x386 - 1 && -1 <= x387 - 1 && x386 <= x387 && -1 <= x398 - 1 && x386 + x398 <= x388 - 1 && 1 <= x399 - 1 && 0 <= x386 + x398 && x386 + x398 - 1 <= x386 + x398 - 1 && x400 <= x385 - 1 && x390 <= x381 && x390 <= x384 && 0 <= x381 - 1 && 0 <= x384 - 1 && 0 <= x390 - 1 && x387 - x386 - 2 * x398 <= 1 && 0 <= x387 - x386 - 2 * x398 && x385 = x391 && x387 = x392 && x386 + x398 = x394 && x388 = x397
(15) f826_0_binarySearch_LE'(x202, x203, x204, x205, x206, x207, x208) -> f1076_0_binarySearch_EQ(x209, x210, x211, x212, x213, x214, x215) :|: x216 <= x206 - x205 && -1 <= x205 - 1 && -1 <= x206 - 1 && x205 <= x206 && -1 <= x216 - 1 && x205 + x216 <= x207 - 1 && 1 <= x217 - 1 && 0 <= x205 + x216 && x205 + x216 - 1 <= x205 + x216 - 1 && x204 <= x218 - 1 && x209 <= x202 && x209 <= x203 && 0 <= x202 - 1 && 0 <= x203 - 1 && 0 <= x209 - 1 && x206 - x205 - 2 * x216 <= 1 && 0 <= x206 - x205 - 2 * x216 && x204 = x210 && x206 = x211 && x205 + x216 = x212 && 0 = x213 && x207 = x215
(16) f826_0_binarySearch_LE'(x185, x186, x187, x188, x189, x190, x191) -> f1076_0_binarySearch_EQ(x192, x193, x194, x195, x196, x197, x198) :|: x199 <= x189 - x188 && -1 <= x188 - 1 && -1 <= x189 - 1 && x188 <= x189 && -1 <= x199 - 1 && x188 + x199 <= x190 - 1 && 1 <= x200 - 1 && 0 <= x188 + x199 && x188 + x199 - 1 <= x188 + x199 - 1 && x201 <= x187 - 1 && x192 <= x185 && x192 <= x186 && 0 <= x185 - 1 && 0 <= x186 - 1 && 0 <= x192 - 1 && x189 - x188 - 2 * x199 <= 1 && 0 <= x189 - x188 - 2 * x199 && x187 = x193 && x189 = x194 && x188 + x199 = x195 && 0 = x196 && x190 = x198

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

This digraph is fully evaluated!

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

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

(16)
Obligation:
Rules:
f826_0_binarySearch_LE'(x119:0, x120:0, x121:0, x122:0, x124:0, x125:0, x126:0) -> f826_0_binarySearch_LE(x127:0, x128:0, x121:0, x122:0, x122:0 + x134:0 - 1, x125:0, x133:0) :|: x124:0 - x122:0 - 2 * x134:0 <= 1 && x124:0 - x122:0 - 2 * x134:0 >= 0 && x128:0 > 0 && x127:0 > 0 && x120:0 > 0 && x119:0 > 0 && x128:0 <= x120:0 && x128:0 <= x119:0 && x127:0 <= x120:0 && x127:0 <= x119:0 && x137:0 - 1 >= x121:0 && x122:0 + x134:0 >= 0 && x136:0 > 1 && x125:0 - 1 >= x122:0 + x134:0 && x134:0 > -1 && x124:0 >= x122:0 && x124:0 > -1 && x122:0 > -1 && x134:0 <= x124:0 - x122:0
f826_0_binarySearch_LE'(x418:0, x419:0, x356:0, x422:0, x358:0, x359:0, x427:0) -> f826_0_binarySearch_LE(x354:0, x355:0, x356:0, x422:0 + x438:0 + 1, x358:0, x359:0, x360:0) :|: x358:0 - x422:0 - 2 * x438:0 <= 1 && x358:0 - x422:0 - 2 * x438:0 >= 0 && x355:0 > 0 && x354:0 > 0 && x419:0 > 0 && x428:0 > 0 && x418:0 > 0 && x428:0 >= x355:0 && x428:0 <= x419:0 && x428:0 >= x354:0 && x428:0 <= x418:0 && x361:0 > 1 && x440:0 <= x356:0 - 1 && x439:0 > 1 && x422:0 + x438:0 <= x359:0 - 1 && x438:0 > -1 && x422:0 <= x358:0 && x358:0 > -1 && x438:0 <= x358:0 - x422:0 && x422:0 + x438:0 >= 0 && x422:0 > -1
f826_0_binarySearch_LE(x80:0, x81:0, x82:0, x84:0, x85:0, x86:0, x87:0) -> f826_0_binarySearch_LE'(x80:0, x81:0, x82:0, x84:0, x85:0, x86:0, x95:0) :|: x99:0 > 0 && x100:0 > 0 && x81:0 > 0 && x80:0 > 0 && x81:0 >= x100:0 && x80:0 >= x100:0 && x99:0 <= x81:0 && x99:0 <= x80:0 && x98:0 - 1 >= x82:0 && x84:0 + x96:0 >= 0 && x97:0 > 1 && x86:0 - 1 >= x84:0 + x96:0 && x96:0 > -1 && x85:0 >= x84:0 && x85:0 > -1 && x84:0 > -1 && x96:0 <= x85:0 - x84:0
f826_0_binarySearch_LE'(x, x1, x2, x3, x4, x5, x6) -> f826_0_binarySearch_LE(x7, x8, x2, x3 + x9 + 1, x4, x5, x10) :|: x8 > 0 && x4 - x3 - 2 * x9 >= 0 && x4 - x3 - 2 * x9 <= 1 && x7 > 0 && x11 > 0 && x1 > 0 && x8 <= x11 && x > 0 && x7 <= x11 && x11 <= x1 && x12 > 1 && x11 <= x && x13 - 1 >= x2 && x14 > 1 && x5 - 1 >= x3 + x9 && x9 > -1 && x4 >= x3 && x4 > -1 && x9 <= x4 - x3 && x3 + x9 >= 0 && x3 > -1
f826_0_binarySearch_LE'(x15, x16, x17, x18, x19, x20, x21) -> f826_0_binarySearch_LE(x22, x23, x17, x18 + x24 + 1, x19, x20, x25) :|: x23 > 0 && x19 - x18 - 2 * x24 >= 0 && x19 - x18 - 2 * x24 <= 1 && x22 > 0 && x26 > 0 && x16 > 0 && x23 <= x26 && x15 > 0 && x22 <= x26 && x26 <= x16 && x27 > 1 && x26 <= x15 && x28 <= x17 - 1 && x29 > 1 && x20 - 1 >= x18 + x24 && x24 > -1 && x19 >= x18 && x19 > -1 && x24 <= x19 - x18 && x18 + x24 >= 0 && x18 > -1
f826_0_binarySearch_LE'(x101:0, x102:0, x103:0, x104:0, x106:0, x107:0, x108:0) -> f826_0_binarySearch_LE(x109:0, x110:0, x103:0, x104:0, x104:0 + x116:0 - 1, x107:0, x115:0) :|: x106:0 - x104:0 - 2 * x116:0 <= 1 && x106:0 - x104:0 - 2 * x116:0 >= 0 && x110:0 > 0 && x109:0 > 0 && x102:0 > 0 && x101:0 > 0 && x110:0 <= x102:0 && x110:0 <= x101:0 && x109:0 <= x102:0 && x109:0 <= x101:0 && x118:0 <= x103:0 - 1 && x104:0 + x116:0 >= 0 && x117:0 > 1 && x107:0 - 1 >= x104:0 + x116:0 && x116:0 > -1 && x106:0 >= x104:0 && x106:0 > -1 && x104:0 > -1 && x116:0 <= x106:0 - x104:0
f826_0_binarySearch_LE(x164:0, x165:0, x166:0, x167:0, x168:0, x172:0, x173:0) -> f826_0_binarySearch_LE'(x164:0, x165:0, x166:0, x167:0, x168:0, x172:0, x180:0) :|: x165:0 > 0 && x184:0 > 0 && x164:0 > 0 && x184:0 <= x165:0 && x184:0 <= x164:0 && x183:0 - 1 >= x166:0 && x167:0 + x181:0 >= 0 && x182:0 > 1 && x172:0 - 1 >= x167:0 + x181:0 && x181:0 > -1 && x168:0 >= x167:0 && x168:0 > -1 && x167:0 > -1 && x181:0 <= x168:0 - x167:0
f826_0_binarySearch_LE(x60:0, x61:0, x62:0, x63:0, x64:0, x65:0, x66:0) -> f826_0_binarySearch_LE'(x60:0, x61:0, x62:0, x63:0, x64:0, x65:0, x74:0) :|: x78:0 > 0 && x79:0 > 0 && x61:0 > 0 && x60:0 > 0 && x79:0 <= x61:0 && x79:0 <= x60:0 && x78:0 <= x61:0 && x78:0 <= x60:0 && x77:0 <= x62:0 - 1 && x63:0 + x75:0 >= 0 && x76:0 > 1 && x65:0 - 1 >= x63:0 + x75:0 && x75:0 > -1 && x64:0 >= x63:0 && x64:0 > -1 && x63:0 > -1 && x75:0 <= x64:0 - x63:0
f826_0_binarySearch_LE'(x30, x31, x32, x33, x34, x35, x36) -> f826_0_binarySearch_LE(x37, x38, x32, x33 + x39 + 1, x34, x35, x40) :|: x34 - x33 - 2 * x39 <= 1 && x34 - x33 - 2 * x39 >= 0 && x38 > 0 && x37 > 0 && x31 > 0 && x41 > 0 && x30 > 0 && x41 >= x38 && x41 <= x31 && x41 >= x37 && x41 <= x30 && x42 > 1 && x43 - 1 >= x32 && x44 > 1 && x33 + x39 <= x35 - 1 && x39 > -1 && x33 <= x34 && x34 > -1 && x39 <= x34 - x33 && x33 + x39 >= 0 && x33 > -1
f826_0_binarySearch_LE(x138:0, x139:0, x140:0, x141:0, x142:0, x143:0, x144:0) -> f826_0_binarySearch_LE'(x138:0, x139:0, x140:0, x141:0, x142:0, x143:0, x156:0) :|: x139:0 > 0 && x163:0 > 0 && x138:0 > 0 && x163:0 <= x139:0 && x163:0 <= x138:0 && x162:0 <= x140:0 - 1 && x141:0 + x157:0 >= 0 && x161:0 > 1 && x143:0 - 1 >= x141:0 + x157:0 && x157:0 > -1 && x142:0 >= x141:0 && x142:0 > -1 && x141:0 > -1 && x157:0 <= x142:0 - x141:0

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

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

   f826_0_binarySearch_LE'(x1, x2, x3, x4, x5, x6, x7) -> f826_0_binarySearch_LE'(x1, x2, x3, x4, x5, x6)
   f826_0_binarySearch_LE(x1, x2, x3, x4, x5, x6, x7) -> f826_0_binarySearch_LE(x1, x2, x3, x4, x5, x6)

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

(18)
Obligation:
Rules:
f826_0_binarySearch_LE'(x119:0, x120:0, x121:0, x122:0, x124:0, x125:0) -> f826_0_binarySearch_LE(x127:0, x128:0, x121:0, x122:0, x122:0 + x134:0 - 1, x125:0) :|: x124:0 - x122:0 - 2 * x134:0 <= 1 && x124:0 - x122:0 - 2 * x134:0 >= 0 && x128:0 > 0 && x127:0 > 0 && x120:0 > 0 && x119:0 > 0 && x128:0 <= x120:0 && x128:0 <= x119:0 && x127:0 <= x120:0 && x127:0 <= x119:0 && x137:0 - 1 >= x121:0 && x122:0 + x134:0 >= 0 && x136:0 > 1 && x125:0 - 1 >= x122:0 + x134:0 && x134:0 > -1 && x124:0 >= x122:0 && x124:0 > -1 && x122:0 > -1 && x134:0 <= x124:0 - x122:0
f826_0_binarySearch_LE'(x418:0, x419:0, x356:0, x422:0, x358:0, x359:0) -> f826_0_binarySearch_LE(x354:0, x355:0, x356:0, x422:0 + x438:0 + 1, x358:0, x359:0) :|: x358:0 - x422:0 - 2 * x438:0 <= 1 && x358:0 - x422:0 - 2 * x438:0 >= 0 && x355:0 > 0 && x354:0 > 0 && x419:0 > 0 && x428:0 > 0 && x418:0 > 0 && x428:0 >= x355:0 && x428:0 <= x419:0 && x428:0 >= x354:0 && x428:0 <= x418:0 && x361:0 > 1 && x440:0 <= x356:0 - 1 && x439:0 > 1 && x422:0 + x438:0 <= x359:0 - 1 && x438:0 > -1 && x422:0 <= x358:0 && x358:0 > -1 && x438:0 <= x358:0 - x422:0 && x422:0 + x438:0 >= 0 && x422:0 > -1
f826_0_binarySearch_LE(x80:0, x81:0, x82:0, x84:0, x85:0, x86:0) -> f826_0_binarySearch_LE'(x80:0, x81:0, x82:0, x84:0, x85:0, x86:0) :|: x99:0 > 0 && x100:0 > 0 && x81:0 > 0 && x80:0 > 0 && x81:0 >= x100:0 && x80:0 >= x100:0 && x99:0 <= x81:0 && x99:0 <= x80:0 && x98:0 - 1 >= x82:0 && x84:0 + x96:0 >= 0 && x97:0 > 1 && x86:0 - 1 >= x84:0 + x96:0 && x96:0 > -1 && x85:0 >= x84:0 && x85:0 > -1 && x84:0 > -1 && x96:0 <= x85:0 - x84:0
f826_0_binarySearch_LE'(x, x1, x2, x3, x4, x5) -> f826_0_binarySearch_LE(x7, x8, x2, x3 + x9 + 1, x4, x5) :|: x8 > 0 && x4 - x3 - 2 * x9 >= 0 && x4 - x3 - 2 * x9 <= 1 && x7 > 0 && x11 > 0 && x1 > 0 && x8 <= x11 && x > 0 && x7 <= x11 && x11 <= x1 && x12 > 1 && x11 <= x && x13 - 1 >= x2 && x14 > 1 && x5 - 1 >= x3 + x9 && x9 > -1 && x4 >= x3 && x4 > -1 && x9 <= x4 - x3 && x3 + x9 >= 0 && x3 > -1
f826_0_binarySearch_LE'(x15, x16, x17, x18, x19, x20) -> f826_0_binarySearch_LE(x22, x23, x17, x18 + x24 + 1, x19, x20) :|: x23 > 0 && x19 - x18 - 2 * x24 >= 0 && x19 - x18 - 2 * x24 <= 1 && x22 > 0 && x26 > 0 && x16 > 0 && x23 <= x26 && x15 > 0 && x22 <= x26 && x26 <= x16 && x27 > 1 && x26 <= x15 && x28 <= x17 - 1 && x29 > 1 && x20 - 1 >= x18 + x24 && x24 > -1 && x19 >= x18 && x19 > -1 && x24 <= x19 - x18 && x18 + x24 >= 0 && x18 > -1
f826_0_binarySearch_LE'(x101:0, x102:0, x103:0, x104:0, x106:0, x107:0) -> f826_0_binarySearch_LE(x109:0, x110:0, x103:0, x104:0, x104:0 + x116:0 - 1, x107:0) :|: x106:0 - x104:0 - 2 * x116:0 <= 1 && x106:0 - x104:0 - 2 * x116:0 >= 0 && x110:0 > 0 && x109:0 > 0 && x102:0 > 0 && x101:0 > 0 && x110:0 <= x102:0 && x110:0 <= x101:0 && x109:0 <= x102:0 && x109:0 <= x101:0 && x118:0 <= x103:0 - 1 && x104:0 + x116:0 >= 0 && x117:0 > 1 && x107:0 - 1 >= x104:0 + x116:0 && x116:0 > -1 && x106:0 >= x104:0 && x106:0 > -1 && x104:0 > -1 && x116:0 <= x106:0 - x104:0
f826_0_binarySearch_LE(x164:0, x165:0, x166:0, x167:0, x168:0, x172:0) -> f826_0_binarySearch_LE'(x164:0, x165:0, x166:0, x167:0, x168:0, x172:0) :|: x165:0 > 0 && x184:0 > 0 && x164:0 > 0 && x184:0 <= x165:0 && x184:0 <= x164:0 && x183:0 - 1 >= x166:0 && x167:0 + x181:0 >= 0 && x182:0 > 1 && x172:0 - 1 >= x167:0 + x181:0 && x181:0 > -1 && x168:0 >= x167:0 && x168:0 > -1 && x167:0 > -1 && x181:0 <= x168:0 - x167:0
f826_0_binarySearch_LE(x60:0, x61:0, x62:0, x63:0, x64:0, x65:0) -> f826_0_binarySearch_LE'(x60:0, x61:0, x62:0, x63:0, x64:0, x65:0) :|: x78:0 > 0 && x79:0 > 0 && x61:0 > 0 && x60:0 > 0 && x79:0 <= x61:0 && x79:0 <= x60:0 && x78:0 <= x61:0 && x78:0 <= x60:0 && x77:0 <= x62:0 - 1 && x63:0 + x75:0 >= 0 && x76:0 > 1 && x65:0 - 1 >= x63:0 + x75:0 && x75:0 > -1 && x64:0 >= x63:0 && x64:0 > -1 && x63:0 > -1 && x75:0 <= x64:0 - x63:0
f826_0_binarySearch_LE'(x30, x31, x32, x33, x34, x35) -> f826_0_binarySearch_LE(x37, x38, x32, x33 + x39 + 1, x34, x35) :|: x34 - x33 - 2 * x39 <= 1 && x34 - x33 - 2 * x39 >= 0 && x38 > 0 && x37 > 0 && x31 > 0 && x41 > 0 && x30 > 0 && x41 >= x38 && x41 <= x31 && x41 >= x37 && x41 <= x30 && x42 > 1 && x43 - 1 >= x32 && x44 > 1 && x33 + x39 <= x35 - 1 && x39 > -1 && x33 <= x34 && x34 > -1 && x39 <= x34 - x33 && x33 + x39 >= 0 && x33 > -1
f826_0_binarySearch_LE(x138:0, x139:0, x140:0, x141:0, x142:0, x143:0) -> f826_0_binarySearch_LE'(x138:0, x139:0, x140:0, x141:0, x142:0, x143:0) :|: x139:0 > 0 && x163:0 > 0 && x138:0 > 0 && x163:0 <= x139:0 && x163:0 <= x138:0 && x162:0 <= x140:0 - 1 && x141:0 + x157:0 >= 0 && x161:0 > 1 && x143:0 - 1 >= x141:0 + x157:0 && x157:0 > -1 && x142:0 >= x141:0 && x142:0 > -1 && x141:0 > -1 && x157:0 <= x142:0 - x141:0

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

(19) TempFilterProof (SOUND)
Used the following sort dictionary for filtering: 
f826_0_binarySearch_LE'(INTEGER, INTEGER, INTEGER, INTEGER, INTEGER, INTEGER)
f826_0_binarySearch_LE(INTEGER, INTEGER, INTEGER, INTEGER, INTEGER, INTEGER)
Replaced non-predefined constructor symbols by 0.
----------------------------------------

(20)
Obligation:
Rules:
f826_0_binarySearch_LE'(x119:0, x120:0, x121:0, x122:0, x124:0, x125:0) -> f826_0_binarySearch_LE(x127:0, x128:0, x121:0, x122:0, c, x125:0) :|: c = x122:0 + x134:0 - 1 && (x124:0 - x122:0 - 2 * x134:0 <= 1 && x124:0 - x122:0 - 2 * x134:0 >= 0 && x128:0 > 0 && x127:0 > 0 && x120:0 > 0 && x119:0 > 0 && x128:0 <= x120:0 && x128:0 <= x119:0 && x127:0 <= x120:0 && x127:0 <= x119:0 && x137:0 - 1 >= x121:0 && x122:0 + x134:0 >= 0 && x136:0 > 1 && x125:0 - 1 >= x122:0 + x134:0 && x134:0 > -1 && x124:0 >= x122:0 && x124:0 > -1 && x122:0 > -1 && x134:0 <= x124:0 - x122:0)
f826_0_binarySearch_LE'(x418:0, x419:0, x356:0, x422:0, x358:0, x359:0) -> f826_0_binarySearch_LE(x354:0, x355:0, x356:0, c1, x358:0, x359:0) :|: c1 = x422:0 + x438:0 + 1 && (x358:0 - x422:0 - 2 * x438:0 <= 1 && x358:0 - x422:0 - 2 * x438:0 >= 0 && x355:0 > 0 && x354:0 > 0 && x419:0 > 0 && x428:0 > 0 && x418:0 > 0 && x428:0 >= x355:0 && x428:0 <= x419:0 && x428:0 >= x354:0 && x428:0 <= x418:0 && x361:0 > 1 && x440:0 <= x356:0 - 1 && x439:0 > 1 && x422:0 + x438:0 <= x359:0 - 1 && x438:0 > -1 && x422:0 <= x358:0 && x358:0 > -1 && x438:0 <= x358:0 - x422:0 && x422:0 + x438:0 >= 0 && x422:0 > -1)
f826_0_binarySearch_LE(x80:0, x81:0, x82:0, x84:0, x85:0, x86:0) -> f826_0_binarySearch_LE'(x80:0, x81:0, x82:0, x84:0, x85:0, x86:0) :|: x99:0 > 0 && x100:0 > 0 && x81:0 > 0 && x80:0 > 0 && x81:0 >= x100:0 && x80:0 >= x100:0 && x99:0 <= x81:0 && x99:0 <= x80:0 && x98:0 - 1 >= x82:0 && x84:0 + x96:0 >= 0 && x97:0 > 1 && x86:0 - 1 >= x84:0 + x96:0 && x96:0 > -1 && x85:0 >= x84:0 && x85:0 > -1 && x84:0 > -1 && x96:0 <= x85:0 - x84:0
f826_0_binarySearch_LE'(x, x1, x2, x3, x4, x5) -> f826_0_binarySearch_LE(x7, x8, x2, c2, x4, x5) :|: c2 = x3 + x9 + 1 && (x8 > 0 && x4 - x3 - 2 * x9 >= 0 && x4 - x3 - 2 * x9 <= 1 && x7 > 0 && x11 > 0 && x1 > 0 && x8 <= x11 && x > 0 && x7 <= x11 && x11 <= x1 && x12 > 1 && x11 <= x && x13 - 1 >= x2 && x14 > 1 && x5 - 1 >= x3 + x9 && x9 > -1 && x4 >= x3 && x4 > -1 && x9 <= x4 - x3 && x3 + x9 >= 0 && x3 > -1)
f826_0_binarySearch_LE'(x15, x16, x17, x18, x19, x20) -> f826_0_binarySearch_LE(x22, x23, x17, c3, x19, x20) :|: c3 = x18 + x24 + 1 && (x23 > 0 && x19 - x18 - 2 * x24 >= 0 && x19 - x18 - 2 * x24 <= 1 && x22 > 0 && x26 > 0 && x16 > 0 && x23 <= x26 && x15 > 0 && x22 <= x26 && x26 <= x16 && x27 > 1 && x26 <= x15 && x28 <= x17 - 1 && x29 > 1 && x20 - 1 >= x18 + x24 && x24 > -1 && x19 >= x18 && x19 > -1 && x24 <= x19 - x18 && x18 + x24 >= 0 && x18 > -1)
f826_0_binarySearch_LE'(x101:0, x102:0, x103:0, x104:0, x106:0, x107:0) -> f826_0_binarySearch_LE(x109:0, x110:0, x103:0, x104:0, c4, x107:0) :|: c4 = x104:0 + x116:0 - 1 && (x106:0 - x104:0 - 2 * x116:0 <= 1 && x106:0 - x104:0 - 2 * x116:0 >= 0 && x110:0 > 0 && x109:0 > 0 && x102:0 > 0 && x101:0 > 0 && x110:0 <= x102:0 && x110:0 <= x101:0 && x109:0 <= x102:0 && x109:0 <= x101:0 && x118:0 <= x103:0 - 1 && x104:0 + x116:0 >= 0 && x117:0 > 1 && x107:0 - 1 >= x104:0 + x116:0 && x116:0 > -1 && x106:0 >= x104:0 && x106:0 > -1 && x104:0 > -1 && x116:0 <= x106:0 - x104:0)
f826_0_binarySearch_LE(x164:0, x165:0, x166:0, x167:0, x168:0, x172:0) -> f826_0_binarySearch_LE'(x164:0, x165:0, x166:0, x167:0, x168:0, x172:0) :|: x165:0 > 0 && x184:0 > 0 && x164:0 > 0 && x184:0 <= x165:0 && x184:0 <= x164:0 && x183:0 - 1 >= x166:0 && x167:0 + x181:0 >= 0 && x182:0 > 1 && x172:0 - 1 >= x167:0 + x181:0 && x181:0 > -1 && x168:0 >= x167:0 && x168:0 > -1 && x167:0 > -1 && x181:0 <= x168:0 - x167:0
f826_0_binarySearch_LE(x60:0, x61:0, x62:0, x63:0, x64:0, x65:0) -> f826_0_binarySearch_LE'(x60:0, x61:0, x62:0, x63:0, x64:0, x65:0) :|: x78:0 > 0 && x79:0 > 0 && x61:0 > 0 && x60:0 > 0 && x79:0 <= x61:0 && x79:0 <= x60:0 && x78:0 <= x61:0 && x78:0 <= x60:0 && x77:0 <= x62:0 - 1 && x63:0 + x75:0 >= 0 && x76:0 > 1 && x65:0 - 1 >= x63:0 + x75:0 && x75:0 > -1 && x64:0 >= x63:0 && x64:0 > -1 && x63:0 > -1 && x75:0 <= x64:0 - x63:0
f826_0_binarySearch_LE'(x30, x31, x32, x33, x34, x35) -> f826_0_binarySearch_LE(x37, x38, x32, c5, x34, x35) :|: c5 = x33 + x39 + 1 && (x34 - x33 - 2 * x39 <= 1 && x34 - x33 - 2 * x39 >= 0 && x38 > 0 && x37 > 0 && x31 > 0 && x41 > 0 && x30 > 0 && x41 >= x38 && x41 <= x31 && x41 >= x37 && x41 <= x30 && x42 > 1 && x43 - 1 >= x32 && x44 > 1 && x33 + x39 <= x35 - 1 && x39 > -1 && x33 <= x34 && x34 > -1 && x39 <= x34 - x33 && x33 + x39 >= 0 && x33 > -1)
f826_0_binarySearch_LE(x138:0, x139:0, x140:0, x141:0, x142:0, x143:0) -> f826_0_binarySearch_LE'(x138:0, x139:0, x140:0, x141:0, x142:0, x143:0) :|: x139:0 > 0 && x163:0 > 0 && x138:0 > 0 && x163:0 <= x139:0 && x163:0 <= x138:0 && x162:0 <= x140:0 - 1 && x141:0 + x157:0 >= 0 && x161:0 > 1 && x143:0 - 1 >= x141:0 + x157:0 && x157:0 > -1 && x142:0 >= x141:0 && x142:0 > -1 && x141:0 > -1 && x157:0 <= x142:0 - x141:0

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

(21) RankingReductionPairProof (EQUIVALENT)
Interpretation:
[ f826_0_binarySearch_LE' ] = 2*f826_0_binarySearch_LE'_5 + -2*f826_0_binarySearch_LE'_4 + -1
[ f826_0_binarySearch_LE ] = -2*f826_0_binarySearch_LE_4 + 2*f826_0_binarySearch_LE_5

The following rules are decreasing:
f826_0_binarySearch_LE'(x119:0, x120:0, x121:0, x122:0, x124:0, x125:0) -> f826_0_binarySearch_LE(x127:0, x128:0, x121:0, x122:0, c, x125:0) :|: c = x122:0 + x134:0 - 1 && (x124:0 - x122:0 - 2 * x134:0 <= 1 && x124:0 - x122:0 - 2 * x134:0 >= 0 && x128:0 > 0 && x127:0 > 0 && x120:0 > 0 && x119:0 > 0 && x128:0 <= x120:0 && x128:0 <= x119:0 && x127:0 <= x120:0 && x127:0 <= x119:0 && x137:0 - 1 >= x121:0 && x122:0 + x134:0 >= 0 && x136:0 > 1 && x125:0 - 1 >= x122:0 + x134:0 && x134:0 > -1 && x124:0 >= x122:0 && x124:0 > -1 && x122:0 > -1 && x134:0 <= x124:0 - x122:0)
f826_0_binarySearch_LE'(x418:0, x419:0, x356:0, x422:0, x358:0, x359:0) -> f826_0_binarySearch_LE(x354:0, x355:0, x356:0, c1, x358:0, x359:0) :|: c1 = x422:0 + x438:0 + 1 && (x358:0 - x422:0 - 2 * x438:0 <= 1 && x358:0 - x422:0 - 2 * x438:0 >= 0 && x355:0 > 0 && x354:0 > 0 && x419:0 > 0 && x428:0 > 0 && x418:0 > 0 && x428:0 >= x355:0 && x428:0 <= x419:0 && x428:0 >= x354:0 && x428:0 <= x418:0 && x361:0 > 1 && x440:0 <= x356:0 - 1 && x439:0 > 1 && x422:0 + x438:0 <= x359:0 - 1 && x438:0 > -1 && x422:0 <= x358:0 && x358:0 > -1 && x438:0 <= x358:0 - x422:0 && x422:0 + x438:0 >= 0 && x422:0 > -1)
f826_0_binarySearch_LE(x80:0, x81:0, x82:0, x84:0, x85:0, x86:0) -> f826_0_binarySearch_LE'(x80:0, x81:0, x82:0, x84:0, x85:0, x86:0) :|: x99:0 > 0 && x100:0 > 0 && x81:0 > 0 && x80:0 > 0 && x81:0 >= x100:0 && x80:0 >= x100:0 && x99:0 <= x81:0 && x99:0 <= x80:0 && x98:0 - 1 >= x82:0 && x84:0 + x96:0 >= 0 && x97:0 > 1 && x86:0 - 1 >= x84:0 + x96:0 && x96:0 > -1 && x85:0 >= x84:0 && x85:0 > -1 && x84:0 > -1 && x96:0 <= x85:0 - x84:0
f826_0_binarySearch_LE'(x, x1, x2, x3, x4, x5) -> f826_0_binarySearch_LE(x7, x8, x2, c2, x4, x5) :|: c2 = x3 + x9 + 1 && (x8 > 0 && x4 - x3 - 2 * x9 >= 0 && x4 - x3 - 2 * x9 <= 1 && x7 > 0 && x11 > 0 && x1 > 0 && x8 <= x11 && x > 0 && x7 <= x11 && x11 <= x1 && x12 > 1 && x11 <= x && x13 - 1 >= x2 && x14 > 1 && x5 - 1 >= x3 + x9 && x9 > -1 && x4 >= x3 && x4 > -1 && x9 <= x4 - x3 && x3 + x9 >= 0 && x3 > -1)
f826_0_binarySearch_LE'(x15, x16, x17, x18, x19, x20) -> f826_0_binarySearch_LE(x22, x23, x17, c3, x19, x20) :|: c3 = x18 + x24 + 1 && (x23 > 0 && x19 - x18 - 2 * x24 >= 0 && x19 - x18 - 2 * x24 <= 1 && x22 > 0 && x26 > 0 && x16 > 0 && x23 <= x26 && x15 > 0 && x22 <= x26 && x26 <= x16 && x27 > 1 && x26 <= x15 && x28 <= x17 - 1 && x29 > 1 && x20 - 1 >= x18 + x24 && x24 > -1 && x19 >= x18 && x19 > -1 && x24 <= x19 - x18 && x18 + x24 >= 0 && x18 > -1)
f826_0_binarySearch_LE'(x101:0, x102:0, x103:0, x104:0, x106:0, x107:0) -> f826_0_binarySearch_LE(x109:0, x110:0, x103:0, x104:0, c4, x107:0) :|: c4 = x104:0 + x116:0 - 1 && (x106:0 - x104:0 - 2 * x116:0 <= 1 && x106:0 - x104:0 - 2 * x116:0 >= 0 && x110:0 > 0 && x109:0 > 0 && x102:0 > 0 && x101:0 > 0 && x110:0 <= x102:0 && x110:0 <= x101:0 && x109:0 <= x102:0 && x109:0 <= x101:0 && x118:0 <= x103:0 - 1 && x104:0 + x116:0 >= 0 && x117:0 > 1 && x107:0 - 1 >= x104:0 + x116:0 && x116:0 > -1 && x106:0 >= x104:0 && x106:0 > -1 && x104:0 > -1 && x116:0 <= x106:0 - x104:0)
f826_0_binarySearch_LE(x164:0, x165:0, x166:0, x167:0, x168:0, x172:0) -> f826_0_binarySearch_LE'(x164:0, x165:0, x166:0, x167:0, x168:0, x172:0) :|: x165:0 > 0 && x184:0 > 0 && x164:0 > 0 && x184:0 <= x165:0 && x184:0 <= x164:0 && x183:0 - 1 >= x166:0 && x167:0 + x181:0 >= 0 && x182:0 > 1 && x172:0 - 1 >= x167:0 + x181:0 && x181:0 > -1 && x168:0 >= x167:0 && x168:0 > -1 && x167:0 > -1 && x181:0 <= x168:0 - x167:0
f826_0_binarySearch_LE(x60:0, x61:0, x62:0, x63:0, x64:0, x65:0) -> f826_0_binarySearch_LE'(x60:0, x61:0, x62:0, x63:0, x64:0, x65:0) :|: x78:0 > 0 && x79:0 > 0 && x61:0 > 0 && x60:0 > 0 && x79:0 <= x61:0 && x79:0 <= x60:0 && x78:0 <= x61:0 && x78:0 <= x60:0 && x77:0 <= x62:0 - 1 && x63:0 + x75:0 >= 0 && x76:0 > 1 && x65:0 - 1 >= x63:0 + x75:0 && x75:0 > -1 && x64:0 >= x63:0 && x64:0 > -1 && x63:0 > -1 && x75:0 <= x64:0 - x63:0
f826_0_binarySearch_LE'(x30, x31, x32, x33, x34, x35) -> f826_0_binarySearch_LE(x37, x38, x32, c5, x34, x35) :|: c5 = x33 + x39 + 1 && (x34 - x33 - 2 * x39 <= 1 && x34 - x33 - 2 * x39 >= 0 && x38 > 0 && x37 > 0 && x31 > 0 && x41 > 0 && x30 > 0 && x41 >= x38 && x41 <= x31 && x41 >= x37 && x41 <= x30 && x42 > 1 && x43 - 1 >= x32 && x44 > 1 && x33 + x39 <= x35 - 1 && x39 > -1 && x33 <= x34 && x34 > -1 && x39 <= x34 - x33 && x33 + x39 >= 0 && x33 > -1)
f826_0_binarySearch_LE(x138:0, x139:0, x140:0, x141:0, x142:0, x143:0) -> f826_0_binarySearch_LE'(x138:0, x139:0, x140:0, x141:0, x142:0, x143:0) :|: x139:0 > 0 && x163:0 > 0 && x138:0 > 0 && x163:0 <= x139:0 && x163:0 <= x138:0 && x162:0 <= x140:0 - 1 && x141:0 + x157:0 >= 0 && x161:0 > 1 && x143:0 - 1 >= x141:0 + x157:0 && x157:0 > -1 && x142:0 >= x141:0 && x142:0 > -1 && x141:0 > -1 && x157:0 <= x142:0 - x141:0

The following rules are bounded:
f826_0_binarySearch_LE'(x119:0, x120:0, x121:0, x122:0, x124:0, x125:0) -> f826_0_binarySearch_LE(x127:0, x128:0, x121:0, x122:0, c, x125:0) :|: c = x122:0 + x134:0 - 1 && (x124:0 - x122:0 - 2 * x134:0 <= 1 && x124:0 - x122:0 - 2 * x134:0 >= 0 && x128:0 > 0 && x127:0 > 0 && x120:0 > 0 && x119:0 > 0 && x128:0 <= x120:0 && x128:0 <= x119:0 && x127:0 <= x120:0 && x127:0 <= x119:0 && x137:0 - 1 >= x121:0 && x122:0 + x134:0 >= 0 && x136:0 > 1 && x125:0 - 1 >= x122:0 + x134:0 && x134:0 > -1 && x124:0 >= x122:0 && x124:0 > -1 && x122:0 > -1 && x134:0 <= x124:0 - x122:0)
f826_0_binarySearch_LE'(x418:0, x419:0, x356:0, x422:0, x358:0, x359:0) -> f826_0_binarySearch_LE(x354:0, x355:0, x356:0, c1, x358:0, x359:0) :|: c1 = x422:0 + x438:0 + 1 && (x358:0 - x422:0 - 2 * x438:0 <= 1 && x358:0 - x422:0 - 2 * x438:0 >= 0 && x355:0 > 0 && x354:0 > 0 && x419:0 > 0 && x428:0 > 0 && x418:0 > 0 && x428:0 >= x355:0 && x428:0 <= x419:0 && x428:0 >= x354:0 && x428:0 <= x418:0 && x361:0 > 1 && x440:0 <= x356:0 - 1 && x439:0 > 1 && x422:0 + x438:0 <= x359:0 - 1 && x438:0 > -1 && x422:0 <= x358:0 && x358:0 > -1 && x438:0 <= x358:0 - x422:0 && x422:0 + x438:0 >= 0 && x422:0 > -1)
f826_0_binarySearch_LE(x80:0, x81:0, x82:0, x84:0, x85:0, x86:0) -> f826_0_binarySearch_LE'(x80:0, x81:0, x82:0, x84:0, x85:0, x86:0) :|: x99:0 > 0 && x100:0 > 0 && x81:0 > 0 && x80:0 > 0 && x81:0 >= x100:0 && x80:0 >= x100:0 && x99:0 <= x81:0 && x99:0 <= x80:0 && x98:0 - 1 >= x82:0 && x84:0 + x96:0 >= 0 && x97:0 > 1 && x86:0 - 1 >= x84:0 + x96:0 && x96:0 > -1 && x85:0 >= x84:0 && x85:0 > -1 && x84:0 > -1 && x96:0 <= x85:0 - x84:0
f826_0_binarySearch_LE'(x, x1, x2, x3, x4, x5) -> f826_0_binarySearch_LE(x7, x8, x2, c2, x4, x5) :|: c2 = x3 + x9 + 1 && (x8 > 0 && x4 - x3 - 2 * x9 >= 0 && x4 - x3 - 2 * x9 <= 1 && x7 > 0 && x11 > 0 && x1 > 0 && x8 <= x11 && x > 0 && x7 <= x11 && x11 <= x1 && x12 > 1 && x11 <= x && x13 - 1 >= x2 && x14 > 1 && x5 - 1 >= x3 + x9 && x9 > -1 && x4 >= x3 && x4 > -1 && x9 <= x4 - x3 && x3 + x9 >= 0 && x3 > -1)
f826_0_binarySearch_LE'(x15, x16, x17, x18, x19, x20) -> f826_0_binarySearch_LE(x22, x23, x17, c3, x19, x20) :|: c3 = x18 + x24 + 1 && (x23 > 0 && x19 - x18 - 2 * x24 >= 0 && x19 - x18 - 2 * x24 <= 1 && x22 > 0 && x26 > 0 && x16 > 0 && x23 <= x26 && x15 > 0 && x22 <= x26 && x26 <= x16 && x27 > 1 && x26 <= x15 && x28 <= x17 - 1 && x29 > 1 && x20 - 1 >= x18 + x24 && x24 > -1 && x19 >= x18 && x19 > -1 && x24 <= x19 - x18 && x18 + x24 >= 0 && x18 > -1)
f826_0_binarySearch_LE'(x101:0, x102:0, x103:0, x104:0, x106:0, x107:0) -> f826_0_binarySearch_LE(x109:0, x110:0, x103:0, x104:0, c4, x107:0) :|: c4 = x104:0 + x116:0 - 1 && (x106:0 - x104:0 - 2 * x116:0 <= 1 && x106:0 - x104:0 - 2 * x116:0 >= 0 && x110:0 > 0 && x109:0 > 0 && x102:0 > 0 && x101:0 > 0 && x110:0 <= x102:0 && x110:0 <= x101:0 && x109:0 <= x102:0 && x109:0 <= x101:0 && x118:0 <= x103:0 - 1 && x104:0 + x116:0 >= 0 && x117:0 > 1 && x107:0 - 1 >= x104:0 + x116:0 && x116:0 > -1 && x106:0 >= x104:0 && x106:0 > -1 && x104:0 > -1 && x116:0 <= x106:0 - x104:0)
f826_0_binarySearch_LE(x164:0, x165:0, x166:0, x167:0, x168:0, x172:0) -> f826_0_binarySearch_LE'(x164:0, x165:0, x166:0, x167:0, x168:0, x172:0) :|: x165:0 > 0 && x184:0 > 0 && x164:0 > 0 && x184:0 <= x165:0 && x184:0 <= x164:0 && x183:0 - 1 >= x166:0 && x167:0 + x181:0 >= 0 && x182:0 > 1 && x172:0 - 1 >= x167:0 + x181:0 && x181:0 > -1 && x168:0 >= x167:0 && x168:0 > -1 && x167:0 > -1 && x181:0 <= x168:0 - x167:0
f826_0_binarySearch_LE(x60:0, x61:0, x62:0, x63:0, x64:0, x65:0) -> f826_0_binarySearch_LE'(x60:0, x61:0, x62:0, x63:0, x64:0, x65:0) :|: x78:0 > 0 && x79:0 > 0 && x61:0 > 0 && x60:0 > 0 && x79:0 <= x61:0 && x79:0 <= x60:0 && x78:0 <= x61:0 && x78:0 <= x60:0 && x77:0 <= x62:0 - 1 && x63:0 + x75:0 >= 0 && x76:0 > 1 && x65:0 - 1 >= x63:0 + x75:0 && x75:0 > -1 && x64:0 >= x63:0 && x64:0 > -1 && x63:0 > -1 && x75:0 <= x64:0 - x63:0
f826_0_binarySearch_LE'(x30, x31, x32, x33, x34, x35) -> f826_0_binarySearch_LE(x37, x38, x32, c5, x34, x35) :|: c5 = x33 + x39 + 1 && (x34 - x33 - 2 * x39 <= 1 && x34 - x33 - 2 * x39 >= 0 && x38 > 0 && x37 > 0 && x31 > 0 && x41 > 0 && x30 > 0 && x41 >= x38 && x41 <= x31 && x41 >= x37 && x41 <= x30 && x42 > 1 && x43 - 1 >= x32 && x44 > 1 && x33 + x39 <= x35 - 1 && x39 > -1 && x33 <= x34 && x34 > -1 && x39 <= x34 - x33 && x33 + x39 >= 0 && x33 > -1)
f826_0_binarySearch_LE(x138:0, x139:0, x140:0, x141:0, x142:0, x143:0) -> f826_0_binarySearch_LE'(x138:0, x139:0, x140:0, x141:0, x142:0, x143:0) :|: x139:0 > 0 && x163:0 > 0 && x138:0 > 0 && x163:0 <= x139:0 && x163:0 <= x138:0 && x162:0 <= x140:0 - 1 && x141:0 + x157:0 >= 0 && x161:0 > 1 && x143:0 - 1 >= x141:0 + x157:0 && x157:0 > -1 && x142:0 >= x141:0 && x142:0 > -1 && x141:0 > -1 && x157:0 <= x142:0 - x141:0


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