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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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, 22.0 s]
(4) AND
    (5) IRSwT
        (6) IntTRSCompressionProof [EQUIVALENT, 115 ms]
        (7) IRSwT
        (8) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms]
        (9) IRSwT
        (10) TempFilterProof [SOUND, 48 ms]
        (11) IntTRS
        (12) PolynomialOrderProcessor [EQUIVALENT, 0 ms]
        (13) IntTRS
        (14) RankingReductionPairProof [EQUIVALENT, 0 ms]
        (15) YES
    (16) IRSwT
        (17) IntTRSCompressionProof [EQUIVALENT, 74 ms]
        (18) IRSwT
        (19) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms]
        (20) IRSwT
        (21) TempFilterProof [SOUND, 23 ms]
        (22) IntTRS
        (23) RankingReductionPairProof [EQUIVALENT, 0 ms]
        (24) IntTRS
        (25) RankingReductionPairProof [EQUIVALENT, 0 ms]
        (26) YES


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

(0)
Obligation:
Rules:
l0(Inner10HAT0, InnerIndex7HAT0, Ncnt14HAT0, NegcntHAT0, NegtotalHAT0, Ntotal12HAT0, Outer9HAT0, OuterIndex6HAT0, Pcnt13HAT0, PoscntHAT0, PostotalHAT0, Ptotal11HAT0, SeedHAT0, StartTime2HAT0, StopTime3HAT0, TotalTime4HAT0, __const_1000HAT0, __const_10HAT0, __const_1500HAT0, ret_RandomInteger15HAT0) -> l1(Inner10HATpost, InnerIndex7HATpost, Ncnt14HATpost, NegcntHATpost, NegtotalHATpost, Ntotal12HATpost, Outer9HATpost, OuterIndex6HATpost, Pcnt13HATpost, PoscntHATpost, PostotalHATpost, Ptotal11HATpost, SeedHATpost, StartTime2HATpost, StopTime3HATpost, TotalTime4HATpost, __const_1000HATpost, __const_10HATpost, __const_1500HATpost, ret_RandomInteger15HATpost) :|: ret_RandomInteger15HAT0 = ret_RandomInteger15HATpost && __const_1500HAT0 = __const_1500HATpost && __const_1000HAT0 = __const_1000HATpost && __const_10HAT0 = __const_10HATpost && TotalTime4HAT0 = TotalTime4HATpost && StopTime3HAT0 = StopTime3HATpost && StartTime2HAT0 = StartTime2HATpost && SeedHAT0 = SeedHATpost && Ptotal11HAT0 = Ptotal11HATpost && PostotalHAT0 = PostotalHATpost && PoscntHAT0 = PoscntHATpost && Pcnt13HAT0 = Pcnt13HATpost && OuterIndex6HAT0 = OuterIndex6HATpost && Outer9HAT0 = Outer9HATpost && Ntotal12HAT0 = Ntotal12HATpost && NegtotalHAT0 = NegtotalHATpost && NegcntHAT0 = NegcntHATpost && Ncnt14HAT0 = Ncnt14HATpost && InnerIndex7HAT0 = InnerIndex7HATpost && Inner10HAT0 = Inner10HATpost
l2(x, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15, x16, x17, x18, x19) -> l3(x20, x21, x22, x23, x24, x25, x26, x27, x28, x29, x30, x31, x32, x33, x34, x35, x36, x37, x38, x39) :|: x19 = x39 && x18 = x38 && x16 = x36 && x17 = x37 && x15 = x35 && x14 = x34 && x13 = x33 && x12 = x32 && x11 = x31 && x10 = x30 && x9 = x29 && x8 = x28 && x7 = x27 && x6 = x26 && x5 = x25 && x4 = x24 && x3 = x23 && x2 = x22 && x1 = x21 && x20 = 1 + x
l4(x40, x41, x42, x43, x44, x45, x46, x47, x48, x49, x50, x51, x52, x53, x54, x55, x56, x57, x58, x59) -> l5(x60, x61, x62, x63, x64, x65, x66, x67, x68, x69, x70, x71, x72, x73, x74, x75, x76, x77, x78, x79) :|: x59 = x79 && x58 = x78 && x56 = x76 && x57 = x77 && x55 = x75 && x54 = x74 && x53 = x73 && x52 = x72 && x51 = x71 && x50 = x70 && x49 = x69 && x48 = x68 && x47 = x67 && x46 = x66 && x45 = x65 && x44 = x64 && x43 = x63 && x42 = x62 && x41 = x61 && x40 = x60
l6(x80, x81, x82, x83, x84, x85, x86, x87, x88, x89, x90, x91, x92, x93, x94, x95, x96, x97, x98, x99) -> l2(x100, x101, x102, x103, x104, x105, x106, x107, x108, x109, x110, x111, x112, x113, x114, x115, x116, x117, x118, x119) :|: x99 = x119 && x98 = x118 && x96 = x116 && x97 = x117 && x95 = x115 && x94 = x114 && x93 = x113 && x92 = x112 && x90 = x110 && x89 = x109 && x87 = x107 && x86 = x106 && x85 = x105 && x84 = x104 && x83 = x103 && x82 = x102 && x81 = x101 && x80 = x100 && x108 = 1 + x88 && x111 = x111
l6(x120, x121, x122, x123, x124, x125, x126, x127, x128, x129, x130, x131, x132, x133, x134, x135, x136, x137, x138, x139) -> l2(x140, x141, x142, x143, x144, x145, x146, x147, x148, x149, x150, x151, x152, x153, x154, x155, x156, x157, x158, x159) :|: x139 = x159 && x138 = x158 && x136 = x156 && x137 = x157 && x135 = x155 && x134 = x154 && x133 = x153 && x132 = x152 && x131 = x151 && x130 = x150 && x129 = x149 && x128 = x148 && x127 = x147 && x126 = x146 && x124 = x144 && x123 = x143 && x121 = x141 && x120 = x140 && x142 = 1 + x122 && x145 = x145
l7(x160, x161, x162, x163, x164, x165, x166, x167, x168, x169, x170, x171, x172, x173, x174, x175, x176, x177, x178, x179) -> l8(x180, x181, x182, x183, x184, x185, x186, x187, x188, x189, x190, x191, x192, x193, x194, x195, x196, x197, x198, x199) :|: x179 = x199 && x178 = x198 && x176 = x196 && x177 = x197 && x175 = x195 && x174 = x194 && x173 = x193 && x172 = x192 && x171 = x191 && x170 = x190 && x169 = x189 && x168 = x188 && x167 = x187 && x165 = x185 && x164 = x184 && x163 = x183 && x162 = x182 && x161 = x181 && x160 = x180 && x186 = 1 + x166 && x177 <= x160
l7(x200, x201, x202, x203, x204, x205, x206, x207, x208, x209, x210, x211, x212, x213, x214, x215, x216, x217, x218, x219) -> l6(x220, x221, x222, x223, x224, x225, x226, x227, x228, x229, x230, x231, x232, x233, x234, x235, x236, x237, x238, x239) :|: x219 = x239 && x218 = x238 && x216 = x236 && x217 = x237 && x215 = x235 && x214 = x234 && x213 = x233 && x212 = x232 && x211 = x231 && x210 = x230 && x209 = x229 && x208 = x228 && x207 = x227 && x206 = x226 && x205 = x225 && x204 = x224 && x203 = x223 && x202 = x222 && x201 = x221 && x200 = x220 && 1 + x200 <= x217
l9(x240, x241, x242, x243, x244, x245, x246, x247, x248, x249, x250, x251, x252, x253, x254, x255, x256, x257, x258, x259) -> l10(x260, x261, x262, x263, x264, x265, x266, x267, x268, x269, x270, x271, x272, x273, x274, x275, x276, x277, x278, x279) :|: x259 = x279 && x258 = x278 && x256 = x276 && x257 = x277 && x253 = x273 && x252 = x272 && x251 = x271 && x248 = x268 && x247 = x267 && x246 = x266 && x245 = x265 && x242 = x262 && x241 = x261 && x240 = x260 && x275 = x275 && x274 = x258 && x263 = x242 && x264 = x245 && x269 = x248 && x270 = x251 && x257 <= x246
l9(x280, x281, x282, x283, x284, x285, x286, x287, x288, x289, x290, x291, x292, x293, x294, x295, x296, x297, x298, x299) -> l3(x300, x301, x302, x303, x304, x305, x306, x307, x308, x309, x310, x311, x312, x313, x314, x315, x316, x317, x318, x319) :|: x299 = x319 && x298 = x318 && x296 = x316 && x297 = x317 && x295 = x315 && x294 = x314 && x293 = x313 && x292 = x312 && x291 = x311 && x290 = x310 && x289 = x309 && x288 = x308 && x287 = x307 && x286 = x306 && x285 = x305 && x284 = x304 && x283 = x303 && x282 = x302 && x281 = x301 && x300 = 0 && 1 + x286 <= x297
l8(x320, x321, x322, x323, x324, x325, x326, x327, x328, x329, x330, x331, x332, x333, x334, x335, x336, x337, x338, x339) -> l9(x340, x341, x342, x343, x344, x345, x346, x347, x348, x349, x350, x351, x352, x353, x354, x355, x356, x357, x358, x359) :|: x339 = x359 && x338 = x358 && x336 = x356 && x337 = x357 && x335 = x355 && x334 = x354 && x333 = x353 && x332 = x352 && x331 = x351 && x330 = x350 && x329 = x349 && x328 = x348 && x327 = x347 && x326 = x346 && x325 = x345 && x324 = x344 && x323 = x343 && x322 = x342 && x321 = x341 && x320 = x340
l3(x360, x361, x362, x363, x364, x365, x366, x367, x368, x369, x370, x371, x372, x373, x374, x375, x376, x377, x378, x379) -> l7(x380, x381, x382, x383, x384, x385, x386, x387, x388, x389, x390, x391, x392, x393, x394, x395, x396, x397, x398, x399) :|: x379 = x399 && x378 = x398 && x376 = x396 && x377 = x397 && x375 = x395 && x374 = x394 && x373 = x393 && x372 = x392 && x371 = x391 && x370 = x390 && x369 = x389 && x368 = x388 && x367 = x387 && x366 = x386 && x365 = x385 && x364 = x384 && x363 = x383 && x362 = x382 && x361 = x381 && x360 = x380
l5(x400, x401, x402, x403, x404, x405, x406, x407, x408, x409, x410, x411, x412, x413, x414, x415, x416, x417, x418, x419) -> l0(x420, x421, x422, x423, x424, x425, x426, x427, x428, x429, x430, x431, x432, x433, x434, x435, x436, x437, x438, x439) :|: x419 = x439 && x418 = x438 && x416 = x436 && x417 = x437 && x415 = x435 && x414 = x434 && x413 = x433 && x412 = x432 && x411 = x431 && x410 = x430 && x409 = x429 && x408 = x428 && x406 = x426 && x405 = x425 && x404 = x424 && x403 = x423 && x402 = x422 && x401 = x421 && x400 = x420 && x427 = 1 + x407 && x417 <= x401
l5(x440, x441, x442, x443, x444, x445, x446, x447, x448, x449, x450, x451, x452, x453, x454, x455, x456, x457, x458, x459) -> l4(x460, x461, x462, x463, x464, x465, x466, x467, x468, x469, x470, x471, x472, x473, x474, x475, x476, x477, x478, x479) :|: x458 = x478 && x456 = x476 && x457 = x477 && x455 = x475 && x454 = x474 && x453 = x473 && x451 = x471 && x450 = x470 && x449 = x469 && x448 = x468 && x447 = x467 && x446 = x466 && x445 = x465 && x444 = x464 && x443 = x463 && x442 = x462 && x440 = x460 && x461 = 1 + x441 && x479 = x472 && x472 = x472 && 1 + x441 <= x457
l1(x480, x481, x482, x483, x484, x485, x486, x487, x488, x489, x490, x491, x492, x493, x494, x495, x496, x497, x498, x499) -> l8(x500, x501, x502, x503, x504, x505, x506, x507, x508, x509, x510, x511, x512, x513, x514, x515, x516, x517, x518, x519) :|: x499 = x519 && x498 = x518 && x496 = x516 && x497 = x517 && x495 = x515 && x494 = x514 && x492 = x512 && x490 = x510 && x489 = x509 && x487 = x507 && x484 = x504 && x483 = x503 && x481 = x501 && x480 = x500 && x506 = 0 && x502 = 0 && x508 = 0 && x505 = 0 && x511 = 0 && x513 = x496 && x497 <= x487
l1(x520, x521, x522, x523, x524, x525, x526, x527, x528, x529, x530, x531, x532, x533, x534, x535, x536, x537, x538, x539) -> l4(x540, x541, x542, x543, x544, x545, x546, x547, x548, x549, x550, x551, x552, x553, x554, x555, x556, x557, x558, x559) :|: x539 = x559 && x538 = x558 && x536 = x556 && x537 = x557 && x535 = x555 && x534 = x554 && x533 = x553 && x532 = x552 && x531 = x551 && x530 = x550 && x529 = x549 && x528 = x548 && x527 = x547 && x526 = x546 && x525 = x545 && x524 = x544 && x523 = x543 && x522 = x542 && x520 = x540 && x541 = 0 && 1 + x527 <= x537
l11(x560, x561, x562, x563, x564, x565, x566, x567, x568, x569, x570, x571, x572, x573, x574, x575, x576, x577, x578, x579) -> l0(x580, x581, x582, x583, x584, x585, x586, x587, x588, x589, x590, x591, x592, x593, x594, x595, x596, x597, x598, x599) :|: x579 = x599 && x578 = x598 && x576 = x596 && x577 = x597 && x575 = x595 && x574 = x594 && x573 = x593 && x571 = x591 && x570 = x590 && x569 = x589 && x568 = x588 && x566 = x586 && x565 = x585 && x564 = x584 && x563 = x583 && x562 = x582 && x561 = x581 && x560 = x580 && x587 = 0 && x592 = 0
l12(x600, x601, x602, x603, x604, x605, x606, x607, x608, x609, x610, x611, x612, x613, x614, x615, x616, x617, x618, x619) -> l11(x620, x621, x622, x623, x624, x625, x626, x627, x628, x629, x630, x631, x632, x633, x634, x635, x636, x637, x638, x639) :|: x619 = x639 && x618 = x638 && x616 = x636 && x617 = x637 && x615 = x635 && x614 = x634 && x613 = x633 && x612 = x632 && x611 = x631 && x610 = x630 && x609 = x629 && x608 = x628 && x607 = x627 && x606 = x626 && x605 = x625 && x604 = x624 && x603 = x623 && x602 = x622 && x601 = x621 && x600 = x620
Start term: l12(Inner10HAT0, InnerIndex7HAT0, Ncnt14HAT0, NegcntHAT0, NegtotalHAT0, Ntotal12HAT0, Outer9HAT0, OuterIndex6HAT0, Pcnt13HAT0, PoscntHAT0, PostotalHAT0, Ptotal11HAT0, SeedHAT0, StartTime2HAT0, StopTime3HAT0, TotalTime4HAT0, __const_1000HAT0, __const_10HAT0, __const_1500HAT0, ret_RandomInteger15HAT0)

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

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

(2)
Obligation:
Rules:
l0(Inner10HAT0, InnerIndex7HAT0, Ncnt14HAT0, NegcntHAT0, NegtotalHAT0, Ntotal12HAT0, Outer9HAT0, OuterIndex6HAT0, Pcnt13HAT0, PoscntHAT0, PostotalHAT0, Ptotal11HAT0, SeedHAT0, StartTime2HAT0, StopTime3HAT0, TotalTime4HAT0, __const_1000HAT0, __const_10HAT0, __const_1500HAT0, ret_RandomInteger15HAT0) -> l1(Inner10HATpost, InnerIndex7HATpost, Ncnt14HATpost, NegcntHATpost, NegtotalHATpost, Ntotal12HATpost, Outer9HATpost, OuterIndex6HATpost, Pcnt13HATpost, PoscntHATpost, PostotalHATpost, Ptotal11HATpost, SeedHATpost, StartTime2HATpost, StopTime3HATpost, TotalTime4HATpost, __const_1000HATpost, __const_10HATpost, __const_1500HATpost, ret_RandomInteger15HATpost) :|: ret_RandomInteger15HAT0 = ret_RandomInteger15HATpost && __const_1500HAT0 = __const_1500HATpost && __const_1000HAT0 = __const_1000HATpost && __const_10HAT0 = __const_10HATpost && TotalTime4HAT0 = TotalTime4HATpost && StopTime3HAT0 = StopTime3HATpost && StartTime2HAT0 = StartTime2HATpost && SeedHAT0 = SeedHATpost && Ptotal11HAT0 = Ptotal11HATpost && PostotalHAT0 = PostotalHATpost && PoscntHAT0 = PoscntHATpost && Pcnt13HAT0 = Pcnt13HATpost && OuterIndex6HAT0 = OuterIndex6HATpost && Outer9HAT0 = Outer9HATpost && Ntotal12HAT0 = Ntotal12HATpost && NegtotalHAT0 = NegtotalHATpost && NegcntHAT0 = NegcntHATpost && Ncnt14HAT0 = Ncnt14HATpost && InnerIndex7HAT0 = InnerIndex7HATpost && Inner10HAT0 = Inner10HATpost
l2(x, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15, x16, x17, x18, x19) -> l3(x20, x21, x22, x23, x24, x25, x26, x27, x28, x29, x30, x31, x32, x33, x34, x35, x36, x37, x38, x39) :|: x19 = x39 && x18 = x38 && x16 = x36 && x17 = x37 && x15 = x35 && x14 = x34 && x13 = x33 && x12 = x32 && x11 = x31 && x10 = x30 && x9 = x29 && x8 = x28 && x7 = x27 && x6 = x26 && x5 = x25 && x4 = x24 && x3 = x23 && x2 = x22 && x1 = x21 && x20 = 1 + x
l4(x40, x41, x42, x43, x44, x45, x46, x47, x48, x49, x50, x51, x52, x53, x54, x55, x56, x57, x58, x59) -> l5(x60, x61, x62, x63, x64, x65, x66, x67, x68, x69, x70, x71, x72, x73, x74, x75, x76, x77, x78, x79) :|: x59 = x79 && x58 = x78 && x56 = x76 && x57 = x77 && x55 = x75 && x54 = x74 && x53 = x73 && x52 = x72 && x51 = x71 && x50 = x70 && x49 = x69 && x48 = x68 && x47 = x67 && x46 = x66 && x45 = x65 && x44 = x64 && x43 = x63 && x42 = x62 && x41 = x61 && x40 = x60
l6(x80, x81, x82, x83, x84, x85, x86, x87, x88, x89, x90, x91, x92, x93, x94, x95, x96, x97, x98, x99) -> l2(x100, x101, x102, x103, x104, x105, x106, x107, x108, x109, x110, x111, x112, x113, x114, x115, x116, x117, x118, x119) :|: x99 = x119 && x98 = x118 && x96 = x116 && x97 = x117 && x95 = x115 && x94 = x114 && x93 = x113 && x92 = x112 && x90 = x110 && x89 = x109 && x87 = x107 && x86 = x106 && x85 = x105 && x84 = x104 && x83 = x103 && x82 = x102 && x81 = x101 && x80 = x100 && x108 = 1 + x88 && x111 = x111
l6(x120, x121, x122, x123, x124, x125, x126, x127, x128, x129, x130, x131, x132, x133, x134, x135, x136, x137, x138, x139) -> l2(x140, x141, x142, x143, x144, x145, x146, x147, x148, x149, x150, x151, x152, x153, x154, x155, x156, x157, x158, x159) :|: x139 = x159 && x138 = x158 && x136 = x156 && x137 = x157 && x135 = x155 && x134 = x154 && x133 = x153 && x132 = x152 && x131 = x151 && x130 = x150 && x129 = x149 && x128 = x148 && x127 = x147 && x126 = x146 && x124 = x144 && x123 = x143 && x121 = x141 && x120 = x140 && x142 = 1 + x122 && x145 = x145
l7(x160, x161, x162, x163, x164, x165, x166, x167, x168, x169, x170, x171, x172, x173, x174, x175, x176, x177, x178, x179) -> l8(x180, x181, x182, x183, x184, x185, x186, x187, x188, x189, x190, x191, x192, x193, x194, x195, x196, x197, x198, x199) :|: x179 = x199 && x178 = x198 && x176 = x196 && x177 = x197 && x175 = x195 && x174 = x194 && x173 = x193 && x172 = x192 && x171 = x191 && x170 = x190 && x169 = x189 && x168 = x188 && x167 = x187 && x165 = x185 && x164 = x184 && x163 = x183 && x162 = x182 && x161 = x181 && x160 = x180 && x186 = 1 + x166 && x177 <= x160
l7(x200, x201, x202, x203, x204, x205, x206, x207, x208, x209, x210, x211, x212, x213, x214, x215, x216, x217, x218, x219) -> l6(x220, x221, x222, x223, x224, x225, x226, x227, x228, x229, x230, x231, x232, x233, x234, x235, x236, x237, x238, x239) :|: x219 = x239 && x218 = x238 && x216 = x236 && x217 = x237 && x215 = x235 && x214 = x234 && x213 = x233 && x212 = x232 && x211 = x231 && x210 = x230 && x209 = x229 && x208 = x228 && x207 = x227 && x206 = x226 && x205 = x225 && x204 = x224 && x203 = x223 && x202 = x222 && x201 = x221 && x200 = x220 && 1 + x200 <= x217
l9(x240, x241, x242, x243, x244, x245, x246, x247, x248, x249, x250, x251, x252, x253, x254, x255, x256, x257, x258, x259) -> l10(x260, x261, x262, x263, x264, x265, x266, x267, x268, x269, x270, x271, x272, x273, x274, x275, x276, x277, x278, x279) :|: x259 = x279 && x258 = x278 && x256 = x276 && x257 = x277 && x253 = x273 && x252 = x272 && x251 = x271 && x248 = x268 && x247 = x267 && x246 = x266 && x245 = x265 && x242 = x262 && x241 = x261 && x240 = x260 && x275 = x275 && x274 = x258 && x263 = x242 && x264 = x245 && x269 = x248 && x270 = x251 && x257 <= x246
l9(x280, x281, x282, x283, x284, x285, x286, x287, x288, x289, x290, x291, x292, x293, x294, x295, x296, x297, x298, x299) -> l3(x300, x301, x302, x303, x304, x305, x306, x307, x308, x309, x310, x311, x312, x313, x314, x315, x316, x317, x318, x319) :|: x299 = x319 && x298 = x318 && x296 = x316 && x297 = x317 && x295 = x315 && x294 = x314 && x293 = x313 && x292 = x312 && x291 = x311 && x290 = x310 && x289 = x309 && x288 = x308 && x287 = x307 && x286 = x306 && x285 = x305 && x284 = x304 && x283 = x303 && x282 = x302 && x281 = x301 && x300 = 0 && 1 + x286 <= x297
l8(x320, x321, x322, x323, x324, x325, x326, x327, x328, x329, x330, x331, x332, x333, x334, x335, x336, x337, x338, x339) -> l9(x340, x341, x342, x343, x344, x345, x346, x347, x348, x349, x350, x351, x352, x353, x354, x355, x356, x357, x358, x359) :|: x339 = x359 && x338 = x358 && x336 = x356 && x337 = x357 && x335 = x355 && x334 = x354 && x333 = x353 && x332 = x352 && x331 = x351 && x330 = x350 && x329 = x349 && x328 = x348 && x327 = x347 && x326 = x346 && x325 = x345 && x324 = x344 && x323 = x343 && x322 = x342 && x321 = x341 && x320 = x340
l3(x360, x361, x362, x363, x364, x365, x366, x367, x368, x369, x370, x371, x372, x373, x374, x375, x376, x377, x378, x379) -> l7(x380, x381, x382, x383, x384, x385, x386, x387, x388, x389, x390, x391, x392, x393, x394, x395, x396, x397, x398, x399) :|: x379 = x399 && x378 = x398 && x376 = x396 && x377 = x397 && x375 = x395 && x374 = x394 && x373 = x393 && x372 = x392 && x371 = x391 && x370 = x390 && x369 = x389 && x368 = x388 && x367 = x387 && x366 = x386 && x365 = x385 && x364 = x384 && x363 = x383 && x362 = x382 && x361 = x381 && x360 = x380
l5(x400, x401, x402, x403, x404, x405, x406, x407, x408, x409, x410, x411, x412, x413, x414, x415, x416, x417, x418, x419) -> l0(x420, x421, x422, x423, x424, x425, x426, x427, x428, x429, x430, x431, x432, x433, x434, x435, x436, x437, x438, x439) :|: x419 = x439 && x418 = x438 && x416 = x436 && x417 = x437 && x415 = x435 && x414 = x434 && x413 = x433 && x412 = x432 && x411 = x431 && x410 = x430 && x409 = x429 && x408 = x428 && x406 = x426 && x405 = x425 && x404 = x424 && x403 = x423 && x402 = x422 && x401 = x421 && x400 = x420 && x427 = 1 + x407 && x417 <= x401
l5(x440, x441, x442, x443, x444, x445, x446, x447, x448, x449, x450, x451, x452, x453, x454, x455, x456, x457, x458, x459) -> l4(x460, x461, x462, x463, x464, x465, x466, x467, x468, x469, x470, x471, x472, x473, x474, x475, x476, x477, x478, x479) :|: x458 = x478 && x456 = x476 && x457 = x477 && x455 = x475 && x454 = x474 && x453 = x473 && x451 = x471 && x450 = x470 && x449 = x469 && x448 = x468 && x447 = x467 && x446 = x466 && x445 = x465 && x444 = x464 && x443 = x463 && x442 = x462 && x440 = x460 && x461 = 1 + x441 && x479 = x472 && x472 = x472 && 1 + x441 <= x457
l1(x480, x481, x482, x483, x484, x485, x486, x487, x488, x489, x490, x491, x492, x493, x494, x495, x496, x497, x498, x499) -> l8(x500, x501, x502, x503, x504, x505, x506, x507, x508, x509, x510, x511, x512, x513, x514, x515, x516, x517, x518, x519) :|: x499 = x519 && x498 = x518 && x496 = x516 && x497 = x517 && x495 = x515 && x494 = x514 && x492 = x512 && x490 = x510 && x489 = x509 && x487 = x507 && x484 = x504 && x483 = x503 && x481 = x501 && x480 = x500 && x506 = 0 && x502 = 0 && x508 = 0 && x505 = 0 && x511 = 0 && x513 = x496 && x497 <= x487
l1(x520, x521, x522, x523, x524, x525, x526, x527, x528, x529, x530, x531, x532, x533, x534, x535, x536, x537, x538, x539) -> l4(x540, x541, x542, x543, x544, x545, x546, x547, x548, x549, x550, x551, x552, x553, x554, x555, x556, x557, x558, x559) :|: x539 = x559 && x538 = x558 && x536 = x556 && x537 = x557 && x535 = x555 && x534 = x554 && x533 = x553 && x532 = x552 && x531 = x551 && x530 = x550 && x529 = x549 && x528 = x548 && x527 = x547 && x526 = x546 && x525 = x545 && x524 = x544 && x523 = x543 && x522 = x542 && x520 = x540 && x541 = 0 && 1 + x527 <= x537
l11(x560, x561, x562, x563, x564, x565, x566, x567, x568, x569, x570, x571, x572, x573, x574, x575, x576, x577, x578, x579) -> l0(x580, x581, x582, x583, x584, x585, x586, x587, x588, x589, x590, x591, x592, x593, x594, x595, x596, x597, x598, x599) :|: x579 = x599 && x578 = x598 && x576 = x596 && x577 = x597 && x575 = x595 && x574 = x594 && x573 = x593 && x571 = x591 && x570 = x590 && x569 = x589 && x568 = x588 && x566 = x586 && x565 = x585 && x564 = x584 && x563 = x583 && x562 = x582 && x561 = x581 && x560 = x580 && x587 = 0 && x592 = 0
l12(x600, x601, x602, x603, x604, x605, x606, x607, x608, x609, x610, x611, x612, x613, x614, x615, x616, x617, x618, x619) -> l11(x620, x621, x622, x623, x624, x625, x626, x627, x628, x629, x630, x631, x632, x633, x634, x635, x636, x637, x638, x639) :|: x619 = x639 && x618 = x638 && x616 = x636 && x617 = x637 && x615 = x635 && x614 = x634 && x613 = x633 && x612 = x632 && x611 = x631 && x610 = x630 && x609 = x629 && x608 = x628 && x607 = x627 && x606 = x626 && x605 = x625 && x604 = x624 && x603 = x623 && x602 = x622 && x601 = x621 && x600 = x620
Start term: l12(Inner10HAT0, InnerIndex7HAT0, Ncnt14HAT0, NegcntHAT0, NegtotalHAT0, Ntotal12HAT0, Outer9HAT0, OuterIndex6HAT0, Pcnt13HAT0, PoscntHAT0, PostotalHAT0, Ptotal11HAT0, SeedHAT0, StartTime2HAT0, StopTime3HAT0, TotalTime4HAT0, __const_1000HAT0, __const_10HAT0, __const_1500HAT0, ret_RandomInteger15HAT0)

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

(3) IRSwTTerminationDigraphProof (EQUIVALENT)
Constructed termination digraph!
Nodes:
(1) l0(Inner10HAT0, InnerIndex7HAT0, Ncnt14HAT0, NegcntHAT0, NegtotalHAT0, Ntotal12HAT0, Outer9HAT0, OuterIndex6HAT0, Pcnt13HAT0, PoscntHAT0, PostotalHAT0, Ptotal11HAT0, SeedHAT0, StartTime2HAT0, StopTime3HAT0, TotalTime4HAT0, __const_1000HAT0, __const_10HAT0, __const_1500HAT0, ret_RandomInteger15HAT0) -> l1(Inner10HATpost, InnerIndex7HATpost, Ncnt14HATpost, NegcntHATpost, NegtotalHATpost, Ntotal12HATpost, Outer9HATpost, OuterIndex6HATpost, Pcnt13HATpost, PoscntHATpost, PostotalHATpost, Ptotal11HATpost, SeedHATpost, StartTime2HATpost, StopTime3HATpost, TotalTime4HATpost, __const_1000HATpost, __const_10HATpost, __const_1500HATpost, ret_RandomInteger15HATpost) :|: ret_RandomInteger15HAT0 = ret_RandomInteger15HATpost && __const_1500HAT0 = __const_1500HATpost && __const_1000HAT0 = __const_1000HATpost && __const_10HAT0 = __const_10HATpost && TotalTime4HAT0 = TotalTime4HATpost && StopTime3HAT0 = StopTime3HATpost && StartTime2HAT0 = StartTime2HATpost && SeedHAT0 = SeedHATpost && Ptotal11HAT0 = Ptotal11HATpost && PostotalHAT0 = PostotalHATpost && PoscntHAT0 = PoscntHATpost && Pcnt13HAT0 = Pcnt13HATpost && OuterIndex6HAT0 = OuterIndex6HATpost && Outer9HAT0 = Outer9HATpost && Ntotal12HAT0 = Ntotal12HATpost && NegtotalHAT0 = NegtotalHATpost && NegcntHAT0 = NegcntHATpost && Ncnt14HAT0 = Ncnt14HATpost && InnerIndex7HAT0 = InnerIndex7HATpost && Inner10HAT0 = Inner10HATpost
(2) l2(x, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15, x16, x17, x18, x19) -> l3(x20, x21, x22, x23, x24, x25, x26, x27, x28, x29, x30, x31, x32, x33, x34, x35, x36, x37, x38, x39) :|: x19 = x39 && x18 = x38 && x16 = x36 && x17 = x37 && x15 = x35 && x14 = x34 && x13 = x33 && x12 = x32 && x11 = x31 && x10 = x30 && x9 = x29 && x8 = x28 && x7 = x27 && x6 = x26 && x5 = x25 && x4 = x24 && x3 = x23 && x2 = x22 && x1 = x21 && x20 = 1 + x
(3) l4(x40, x41, x42, x43, x44, x45, x46, x47, x48, x49, x50, x51, x52, x53, x54, x55, x56, x57, x58, x59) -> l5(x60, x61, x62, x63, x64, x65, x66, x67, x68, x69, x70, x71, x72, x73, x74, x75, x76, x77, x78, x79) :|: x59 = x79 && x58 = x78 && x56 = x76 && x57 = x77 && x55 = x75 && x54 = x74 && x53 = x73 && x52 = x72 && x51 = x71 && x50 = x70 && x49 = x69 && x48 = x68 && x47 = x67 && x46 = x66 && x45 = x65 && x44 = x64 && x43 = x63 && x42 = x62 && x41 = x61 && x40 = x60
(4) l6(x80, x81, x82, x83, x84, x85, x86, x87, x88, x89, x90, x91, x92, x93, x94, x95, x96, x97, x98, x99) -> l2(x100, x101, x102, x103, x104, x105, x106, x107, x108, x109, x110, x111, x112, x113, x114, x115, x116, x117, x118, x119) :|: x99 = x119 && x98 = x118 && x96 = x116 && x97 = x117 && x95 = x115 && x94 = x114 && x93 = x113 && x92 = x112 && x90 = x110 && x89 = x109 && x87 = x107 && x86 = x106 && x85 = x105 && x84 = x104 && x83 = x103 && x82 = x102 && x81 = x101 && x80 = x100 && x108 = 1 + x88 && x111 = x111
(5) l6(x120, x121, x122, x123, x124, x125, x126, x127, x128, x129, x130, x131, x132, x133, x134, x135, x136, x137, x138, x139) -> l2(x140, x141, x142, x143, x144, x145, x146, x147, x148, x149, x150, x151, x152, x153, x154, x155, x156, x157, x158, x159) :|: x139 = x159 && x138 = x158 && x136 = x156 && x137 = x157 && x135 = x155 && x134 = x154 && x133 = x153 && x132 = x152 && x131 = x151 && x130 = x150 && x129 = x149 && x128 = x148 && x127 = x147 && x126 = x146 && x124 = x144 && x123 = x143 && x121 = x141 && x120 = x140 && x142 = 1 + x122 && x145 = x145
(6) l7(x160, x161, x162, x163, x164, x165, x166, x167, x168, x169, x170, x171, x172, x173, x174, x175, x176, x177, x178, x179) -> l8(x180, x181, x182, x183, x184, x185, x186, x187, x188, x189, x190, x191, x192, x193, x194, x195, x196, x197, x198, x199) :|: x179 = x199 && x178 = x198 && x176 = x196 && x177 = x197 && x175 = x195 && x174 = x194 && x173 = x193 && x172 = x192 && x171 = x191 && x170 = x190 && x169 = x189 && x168 = x188 && x167 = x187 && x165 = x185 && x164 = x184 && x163 = x183 && x162 = x182 && x161 = x181 && x160 = x180 && x186 = 1 + x166 && x177 <= x160
(7) l7(x200, x201, x202, x203, x204, x205, x206, x207, x208, x209, x210, x211, x212, x213, x214, x215, x216, x217, x218, x219) -> l6(x220, x221, x222, x223, x224, x225, x226, x227, x228, x229, x230, x231, x232, x233, x234, x235, x236, x237, x238, x239) :|: x219 = x239 && x218 = x238 && x216 = x236 && x217 = x237 && x215 = x235 && x214 = x234 && x213 = x233 && x212 = x232 && x211 = x231 && x210 = x230 && x209 = x229 && x208 = x228 && x207 = x227 && x206 = x226 && x205 = x225 && x204 = x224 && x203 = x223 && x202 = x222 && x201 = x221 && x200 = x220 && 1 + x200 <= x217
(8) l9(x240, x241, x242, x243, x244, x245, x246, x247, x248, x249, x250, x251, x252, x253, x254, x255, x256, x257, x258, x259) -> l10(x260, x261, x262, x263, x264, x265, x266, x267, x268, x269, x270, x271, x272, x273, x274, x275, x276, x277, x278, x279) :|: x259 = x279 && x258 = x278 && x256 = x276 && x257 = x277 && x253 = x273 && x252 = x272 && x251 = x271 && x248 = x268 && x247 = x267 && x246 = x266 && x245 = x265 && x242 = x262 && x241 = x261 && x240 = x260 && x275 = x275 && x274 = x258 && x263 = x242 && x264 = x245 && x269 = x248 && x270 = x251 && x257 <= x246
(9) l9(x280, x281, x282, x283, x284, x285, x286, x287, x288, x289, x290, x291, x292, x293, x294, x295, x296, x297, x298, x299) -> l3(x300, x301, x302, x303, x304, x305, x306, x307, x308, x309, x310, x311, x312, x313, x314, x315, x316, x317, x318, x319) :|: x299 = x319 && x298 = x318 && x296 = x316 && x297 = x317 && x295 = x315 && x294 = x314 && x293 = x313 && x292 = x312 && x291 = x311 && x290 = x310 && x289 = x309 && x288 = x308 && x287 = x307 && x286 = x306 && x285 = x305 && x284 = x304 && x283 = x303 && x282 = x302 && x281 = x301 && x300 = 0 && 1 + x286 <= x297
(10) l8(x320, x321, x322, x323, x324, x325, x326, x327, x328, x329, x330, x331, x332, x333, x334, x335, x336, x337, x338, x339) -> l9(x340, x341, x342, x343, x344, x345, x346, x347, x348, x349, x350, x351, x352, x353, x354, x355, x356, x357, x358, x359) :|: x339 = x359 && x338 = x358 && x336 = x356 && x337 = x357 && x335 = x355 && x334 = x354 && x333 = x353 && x332 = x352 && x331 = x351 && x330 = x350 && x329 = x349 && x328 = x348 && x327 = x347 && x326 = x346 && x325 = x345 && x324 = x344 && x323 = x343 && x322 = x342 && x321 = x341 && x320 = x340
(11) l3(x360, x361, x362, x363, x364, x365, x366, x367, x368, x369, x370, x371, x372, x373, x374, x375, x376, x377, x378, x379) -> l7(x380, x381, x382, x383, x384, x385, x386, x387, x388, x389, x390, x391, x392, x393, x394, x395, x396, x397, x398, x399) :|: x379 = x399 && x378 = x398 && x376 = x396 && x377 = x397 && x375 = x395 && x374 = x394 && x373 = x393 && x372 = x392 && x371 = x391 && x370 = x390 && x369 = x389 && x368 = x388 && x367 = x387 && x366 = x386 && x365 = x385 && x364 = x384 && x363 = x383 && x362 = x382 && x361 = x381 && x360 = x380
(12) l5(x400, x401, x402, x403, x404, x405, x406, x407, x408, x409, x410, x411, x412, x413, x414, x415, x416, x417, x418, x419) -> l0(x420, x421, x422, x423, x424, x425, x426, x427, x428, x429, x430, x431, x432, x433, x434, x435, x436, x437, x438, x439) :|: x419 = x439 && x418 = x438 && x416 = x436 && x417 = x437 && x415 = x435 && x414 = x434 && x413 = x433 && x412 = x432 && x411 = x431 && x410 = x430 && x409 = x429 && x408 = x428 && x406 = x426 && x405 = x425 && x404 = x424 && x403 = x423 && x402 = x422 && x401 = x421 && x400 = x420 && x427 = 1 + x407 && x417 <= x401
(13) l5(x440, x441, x442, x443, x444, x445, x446, x447, x448, x449, x450, x451, x452, x453, x454, x455, x456, x457, x458, x459) -> l4(x460, x461, x462, x463, x464, x465, x466, x467, x468, x469, x470, x471, x472, x473, x474, x475, x476, x477, x478, x479) :|: x458 = x478 && x456 = x476 && x457 = x477 && x455 = x475 && x454 = x474 && x453 = x473 && x451 = x471 && x450 = x470 && x449 = x469 && x448 = x468 && x447 = x467 && x446 = x466 && x445 = x465 && x444 = x464 && x443 = x463 && x442 = x462 && x440 = x460 && x461 = 1 + x441 && x479 = x472 && x472 = x472 && 1 + x441 <= x457
(14) l1(x480, x481, x482, x483, x484, x485, x486, x487, x488, x489, x490, x491, x492, x493, x494, x495, x496, x497, x498, x499) -> l8(x500, x501, x502, x503, x504, x505, x506, x507, x508, x509, x510, x511, x512, x513, x514, x515, x516, x517, x518, x519) :|: x499 = x519 && x498 = x518 && x496 = x516 && x497 = x517 && x495 = x515 && x494 = x514 && x492 = x512 && x490 = x510 && x489 = x509 && x487 = x507 && x484 = x504 && x483 = x503 && x481 = x501 && x480 = x500 && x506 = 0 && x502 = 0 && x508 = 0 && x505 = 0 && x511 = 0 && x513 = x496 && x497 <= x487
(15) l1(x520, x521, x522, x523, x524, x525, x526, x527, x528, x529, x530, x531, x532, x533, x534, x535, x536, x537, x538, x539) -> l4(x540, x541, x542, x543, x544, x545, x546, x547, x548, x549, x550, x551, x552, x553, x554, x555, x556, x557, x558, x559) :|: x539 = x559 && x538 = x558 && x536 = x556 && x537 = x557 && x535 = x555 && x534 = x554 && x533 = x553 && x532 = x552 && x531 = x551 && x530 = x550 && x529 = x549 && x528 = x548 && x527 = x547 && x526 = x546 && x525 = x545 && x524 = x544 && x523 = x543 && x522 = x542 && x520 = x540 && x541 = 0 && 1 + x527 <= x537
(16) l11(x560, x561, x562, x563, x564, x565, x566, x567, x568, x569, x570, x571, x572, x573, x574, x575, x576, x577, x578, x579) -> l0(x580, x581, x582, x583, x584, x585, x586, x587, x588, x589, x590, x591, x592, x593, x594, x595, x596, x597, x598, x599) :|: x579 = x599 && x578 = x598 && x576 = x596 && x577 = x597 && x575 = x595 && x574 = x594 && x573 = x593 && x571 = x591 && x570 = x590 && x569 = x589 && x568 = x588 && x566 = x586 && x565 = x585 && x564 = x584 && x563 = x583 && x562 = x582 && x561 = x581 && x560 = x580 && x587 = 0 && x592 = 0
(17) l12(x600, x601, x602, x603, x604, x605, x606, x607, x608, x609, x610, x611, x612, x613, x614, x615, x616, x617, x618, x619) -> l11(x620, x621, x622, x623, x624, x625, x626, x627, x628, x629, x630, x631, x632, x633, x634, x635, x636, x637, x638, x639) :|: x619 = x639 && x618 = x638 && x616 = x636 && x617 = x637 && x615 = x635 && x614 = x634 && x613 = x633 && x612 = x632 && x611 = x631 && x610 = x630 && x609 = x629 && x608 = x628 && x607 = x627 && x606 = x626 && x605 = x625 && x604 = x624 && x603 = x623 && x602 = x622 && x601 = x621 && x600 = x620

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

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

(4)
Complex Obligation (AND)

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

(5)
Obligation:

Termination digraph:
Nodes:
(1) l0(Inner10HAT0, InnerIndex7HAT0, Ncnt14HAT0, NegcntHAT0, NegtotalHAT0, Ntotal12HAT0, Outer9HAT0, OuterIndex6HAT0, Pcnt13HAT0, PoscntHAT0, PostotalHAT0, Ptotal11HAT0, SeedHAT0, StartTime2HAT0, StopTime3HAT0, TotalTime4HAT0, __const_1000HAT0, __const_10HAT0, __const_1500HAT0, ret_RandomInteger15HAT0) -> l1(Inner10HATpost, InnerIndex7HATpost, Ncnt14HATpost, NegcntHATpost, NegtotalHATpost, Ntotal12HATpost, Outer9HATpost, OuterIndex6HATpost, Pcnt13HATpost, PoscntHATpost, PostotalHATpost, Ptotal11HATpost, SeedHATpost, StartTime2HATpost, StopTime3HATpost, TotalTime4HATpost, __const_1000HATpost, __const_10HATpost, __const_1500HATpost, ret_RandomInteger15HATpost) :|: ret_RandomInteger15HAT0 = ret_RandomInteger15HATpost && __const_1500HAT0 = __const_1500HATpost && __const_1000HAT0 = __const_1000HATpost && __const_10HAT0 = __const_10HATpost && TotalTime4HAT0 = TotalTime4HATpost && StopTime3HAT0 = StopTime3HATpost && StartTime2HAT0 = StartTime2HATpost && SeedHAT0 = SeedHATpost && Ptotal11HAT0 = Ptotal11HATpost && PostotalHAT0 = PostotalHATpost && PoscntHAT0 = PoscntHATpost && Pcnt13HAT0 = Pcnt13HATpost && OuterIndex6HAT0 = OuterIndex6HATpost && Outer9HAT0 = Outer9HATpost && Ntotal12HAT0 = Ntotal12HATpost && NegtotalHAT0 = NegtotalHATpost && NegcntHAT0 = NegcntHATpost && Ncnt14HAT0 = Ncnt14HATpost && InnerIndex7HAT0 = InnerIndex7HATpost && Inner10HAT0 = Inner10HATpost
(2) l5(x400, x401, x402, x403, x404, x405, x406, x407, x408, x409, x410, x411, x412, x413, x414, x415, x416, x417, x418, x419) -> l0(x420, x421, x422, x423, x424, x425, x426, x427, x428, x429, x430, x431, x432, x433, x434, x435, x436, x437, x438, x439) :|: x419 = x439 && x418 = x438 && x416 = x436 && x417 = x437 && x415 = x435 && x414 = x434 && x413 = x433 && x412 = x432 && x411 = x431 && x410 = x430 && x409 = x429 && x408 = x428 && x406 = x426 && x405 = x425 && x404 = x424 && x403 = x423 && x402 = x422 && x401 = x421 && x400 = x420 && x427 = 1 + x407 && x417 <= x401
(3) l4(x40, x41, x42, x43, x44, x45, x46, x47, x48, x49, x50, x51, x52, x53, x54, x55, x56, x57, x58, x59) -> l5(x60, x61, x62, x63, x64, x65, x66, x67, x68, x69, x70, x71, x72, x73, x74, x75, x76, x77, x78, x79) :|: x59 = x79 && x58 = x78 && x56 = x76 && x57 = x77 && x55 = x75 && x54 = x74 && x53 = x73 && x52 = x72 && x51 = x71 && x50 = x70 && x49 = x69 && x48 = x68 && x47 = x67 && x46 = x66 && x45 = x65 && x44 = x64 && x43 = x63 && x42 = x62 && x41 = x61 && x40 = x60
(4) l1(x520, x521, x522, x523, x524, x525, x526, x527, x528, x529, x530, x531, x532, x533, x534, x535, x536, x537, x538, x539) -> l4(x540, x541, x542, x543, x544, x545, x546, x547, x548, x549, x550, x551, x552, x553, x554, x555, x556, x557, x558, x559) :|: x539 = x559 && x538 = x558 && x536 = x556 && x537 = x557 && x535 = x555 && x534 = x554 && x533 = x553 && x532 = x552 && x531 = x551 && x530 = x550 && x529 = x549 && x528 = x548 && x527 = x547 && x526 = x546 && x525 = x545 && x524 = x544 && x523 = x543 && x522 = x542 && x520 = x540 && x541 = 0 && 1 + x527 <= x537
(5) l5(x440, x441, x442, x443, x444, x445, x446, x447, x448, x449, x450, x451, x452, x453, x454, x455, x456, x457, x458, x459) -> l4(x460, x461, x462, x463, x464, x465, x466, x467, x468, x469, x470, x471, x472, x473, x474, x475, x476, x477, x478, x479) :|: x458 = x478 && x456 = x476 && x457 = x477 && x455 = x475 && x454 = x474 && x453 = x473 && x451 = x471 && x450 = x470 && x449 = x469 && x448 = x468 && x447 = x467 && x446 = x466 && x445 = x465 && x444 = x464 && x443 = x463 && x442 = x462 && x440 = x460 && x461 = 1 + x441 && x479 = x472 && x472 = x472 && 1 + x441 <= x457

Arcs:
(1) -> (4)
(2) -> (1)
(3) -> (2), (5)
(4) -> (3)
(5) -> (3)

This digraph is fully evaluated!

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

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

(7)
Obligation:
Rules:
l4(Inner10HATpost:0, InnerIndex7HATpost:0, Ncnt14HATpost:0, NegcntHATpost:0, NegtotalHATpost:0, Ntotal12HATpost:0, Outer9HATpost:0, x47:0, Pcnt13HATpost:0, PoscntHATpost:0, PostotalHATpost:0, Ptotal11HATpost:0, SeedHATpost:0, StartTime2HATpost:0, StopTime3HATpost:0, TotalTime4HATpost:0, __const_1000HATpost:0, __const_10HATpost:0, __const_1500HATpost:0, ret_RandomInteger15HATpost:0) -> l4(Inner10HATpost:0, 0, Ncnt14HATpost:0, NegcntHATpost:0, NegtotalHATpost:0, Ntotal12HATpost:0, Outer9HATpost:0, 1 + x47:0, Pcnt13HATpost:0, PoscntHATpost:0, PostotalHATpost:0, Ptotal11HATpost:0, SeedHATpost:0, StartTime2HATpost:0, StopTime3HATpost:0, TotalTime4HATpost:0, __const_1000HATpost:0, __const_10HATpost:0, __const_1500HATpost:0, ret_RandomInteger15HATpost:0) :|: __const_10HATpost:0 <= InnerIndex7HATpost:0 && __const_10HATpost:0 >= 1 + (1 + x47:0)
l4(x40:0, x41:0, x42:0, x43:0, x44:0, x45:0, x466:0, x467:0, x468:0, x469:0, x470:0, x471:0, x52:0, x473:0, x474:0, x475:0, x476:0, x477:0, x478:0, x59:0) -> l4(x40:0, 1 + x41:0, x42:0, x43:0, x44:0, x45:0, x466:0, x467:0, x468:0, x469:0, x470:0, x471:0, x472:0, x473:0, x474:0, x475:0, x476:0, x477:0, x478:0, x472:0) :|: x477:0 >= 1 + x41:0

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

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

   l4(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15, x16, x17, x18, x19, x20) -> l4(x2, x8, x18)

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

(9)
Obligation:
Rules:
l4(InnerIndex7HATpost:0, x47:0, __const_10HATpost:0) -> l4(0, 1 + x47:0, __const_10HATpost:0) :|: __const_10HATpost:0 <= InnerIndex7HATpost:0 && __const_10HATpost:0 >= 1 + (1 + x47:0)
l4(x41:0, x467:0, x477:0) -> l4(1 + x41:0, x467:0, x477:0) :|: x477:0 >= 1 + x41:0

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

(10) TempFilterProof (SOUND)
Used the following sort dictionary for filtering: 
l4(VARIABLE, VARIABLE, INTEGER)
Replaced non-predefined constructor symbols by 0.
----------------------------------------

(11)
Obligation:
Rules:
l4(InnerIndex7HATpost:0, x47:0, __const_10HATpost:0) -> l4(c, c1, __const_10HATpost:0) :|: c1 = 1 + x47:0 && c = 0 && (__const_10HATpost:0 <= InnerIndex7HATpost:0 && __const_10HATpost:0 >= 1 + (1 + x47:0))
l4(x41:0, x467:0, x477:0) -> l4(c2, x467:0, x477:0) :|: c2 = 1 + x41:0 && x477:0 >= 1 + x41:0

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

(12) PolynomialOrderProcessor (EQUIVALENT)
Found the following polynomial interpretation:
[l4(x, x1, x2)] = -2 - x1 + x2

The following rules are decreasing:
l4(InnerIndex7HATpost:0, x47:0, __const_10HATpost:0) -> l4(c, c1, __const_10HATpost:0) :|: c1 = 1 + x47:0 && c = 0 && (__const_10HATpost:0 <= InnerIndex7HATpost:0 && __const_10HATpost:0 >= 1 + (1 + x47:0))
The following rules are bounded:
l4(InnerIndex7HATpost:0, x47:0, __const_10HATpost:0) -> l4(c, c1, __const_10HATpost:0) :|: c1 = 1 + x47:0 && c = 0 && (__const_10HATpost:0 <= InnerIndex7HATpost:0 && __const_10HATpost:0 >= 1 + (1 + x47:0))

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

(13)
Obligation:
Rules:
l4(x41:0, x467:0, x477:0) -> l4(c2, x467:0, x477:0) :|: c2 = 1 + x41:0 && x477:0 >= 1 + x41:0

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

(14) RankingReductionPairProof (EQUIVALENT)
Interpretation:
[ l4 ] = l4_3 + -1*l4_1

The following rules are decreasing:
l4(x41:0, x467:0, x477:0) -> l4(c2, x467:0, x477:0) :|: c2 = 1 + x41:0 && x477:0 >= 1 + x41:0

The following rules are bounded:
l4(x41:0, x467:0, x477:0) -> l4(c2, x467:0, x477:0) :|: c2 = 1 + x41:0 && x477:0 >= 1 + x41:0


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

(15)
YES

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

(16)
Obligation:

Termination digraph:
Nodes:
(1) l8(x320, x321, x322, x323, x324, x325, x326, x327, x328, x329, x330, x331, x332, x333, x334, x335, x336, x337, x338, x339) -> l9(x340, x341, x342, x343, x344, x345, x346, x347, x348, x349, x350, x351, x352, x353, x354, x355, x356, x357, x358, x359) :|: x339 = x359 && x338 = x358 && x336 = x356 && x337 = x357 && x335 = x355 && x334 = x354 && x333 = x353 && x332 = x352 && x331 = x351 && x330 = x350 && x329 = x349 && x328 = x348 && x327 = x347 && x326 = x346 && x325 = x345 && x324 = x344 && x323 = x343 && x322 = x342 && x321 = x341 && x320 = x340
(2) l7(x160, x161, x162, x163, x164, x165, x166, x167, x168, x169, x170, x171, x172, x173, x174, x175, x176, x177, x178, x179) -> l8(x180, x181, x182, x183, x184, x185, x186, x187, x188, x189, x190, x191, x192, x193, x194, x195, x196, x197, x198, x199) :|: x179 = x199 && x178 = x198 && x176 = x196 && x177 = x197 && x175 = x195 && x174 = x194 && x173 = x193 && x172 = x192 && x171 = x191 && x170 = x190 && x169 = x189 && x168 = x188 && x167 = x187 && x165 = x185 && x164 = x184 && x163 = x183 && x162 = x182 && x161 = x181 && x160 = x180 && x186 = 1 + x166 && x177 <= x160
(3) l3(x360, x361, x362, x363, x364, x365, x366, x367, x368, x369, x370, x371, x372, x373, x374, x375, x376, x377, x378, x379) -> l7(x380, x381, x382, x383, x384, x385, x386, x387, x388, x389, x390, x391, x392, x393, x394, x395, x396, x397, x398, x399) :|: x379 = x399 && x378 = x398 && x376 = x396 && x377 = x397 && x375 = x395 && x374 = x394 && x373 = x393 && x372 = x392 && x371 = x391 && x370 = x390 && x369 = x389 && x368 = x388 && x367 = x387 && x366 = x386 && x365 = x385 && x364 = x384 && x363 = x383 && x362 = x382 && x361 = x381 && x360 = x380
(4) l9(x280, x281, x282, x283, x284, x285, x286, x287, x288, x289, x290, x291, x292, x293, x294, x295, x296, x297, x298, x299) -> l3(x300, x301, x302, x303, x304, x305, x306, x307, x308, x309, x310, x311, x312, x313, x314, x315, x316, x317, x318, x319) :|: x299 = x319 && x298 = x318 && x296 = x316 && x297 = x317 && x295 = x315 && x294 = x314 && x293 = x313 && x292 = x312 && x291 = x311 && x290 = x310 && x289 = x309 && x288 = x308 && x287 = x307 && x286 = x306 && x285 = x305 && x284 = x304 && x283 = x303 && x282 = x302 && x281 = x301 && x300 = 0 && 1 + x286 <= x297
(5) l2(x, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15, x16, x17, x18, x19) -> l3(x20, x21, x22, x23, x24, x25, x26, x27, x28, x29, x30, x31, x32, x33, x34, x35, x36, x37, x38, x39) :|: x19 = x39 && x18 = x38 && x16 = x36 && x17 = x37 && x15 = x35 && x14 = x34 && x13 = x33 && x12 = x32 && x11 = x31 && x10 = x30 && x9 = x29 && x8 = x28 && x7 = x27 && x6 = x26 && x5 = x25 && x4 = x24 && x3 = x23 && x2 = x22 && x1 = x21 && x20 = 1 + x
(6) l6(x120, x121, x122, x123, x124, x125, x126, x127, x128, x129, x130, x131, x132, x133, x134, x135, x136, x137, x138, x139) -> l2(x140, x141, x142, x143, x144, x145, x146, x147, x148, x149, x150, x151, x152, x153, x154, x155, x156, x157, x158, x159) :|: x139 = x159 && x138 = x158 && x136 = x156 && x137 = x157 && x135 = x155 && x134 = x154 && x133 = x153 && x132 = x152 && x131 = x151 && x130 = x150 && x129 = x149 && x128 = x148 && x127 = x147 && x126 = x146 && x124 = x144 && x123 = x143 && x121 = x141 && x120 = x140 && x142 = 1 + x122 && x145 = x145
(7) l6(x80, x81, x82, x83, x84, x85, x86, x87, x88, x89, x90, x91, x92, x93, x94, x95, x96, x97, x98, x99) -> l2(x100, x101, x102, x103, x104, x105, x106, x107, x108, x109, x110, x111, x112, x113, x114, x115, x116, x117, x118, x119) :|: x99 = x119 && x98 = x118 && x96 = x116 && x97 = x117 && x95 = x115 && x94 = x114 && x93 = x113 && x92 = x112 && x90 = x110 && x89 = x109 && x87 = x107 && x86 = x106 && x85 = x105 && x84 = x104 && x83 = x103 && x82 = x102 && x81 = x101 && x80 = x100 && x108 = 1 + x88 && x111 = x111
(8) l7(x200, x201, x202, x203, x204, x205, x206, x207, x208, x209, x210, x211, x212, x213, x214, x215, x216, x217, x218, x219) -> l6(x220, x221, x222, x223, x224, x225, x226, x227, x228, x229, x230, x231, x232, x233, x234, x235, x236, x237, x238, x239) :|: x219 = x239 && x218 = x238 && x216 = x236 && x217 = x237 && x215 = x235 && x214 = x234 && x213 = x233 && x212 = x232 && x211 = x231 && x210 = x230 && x209 = x229 && x208 = x228 && x207 = x227 && x206 = x226 && x205 = x225 && x204 = x224 && x203 = x223 && x202 = x222 && x201 = x221 && x200 = x220 && 1 + x200 <= x217

Arcs:
(1) -> (4)
(2) -> (1)
(3) -> (2), (8)
(4) -> (3)
(5) -> (3)
(6) -> (5)
(7) -> (5)
(8) -> (6), (7)

This digraph is fully evaluated!

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

(18)
Obligation:
Rules:
l3(x100:0, x101:0, x102:0, x103:0, x104:0, x105:0, x106:0, x107:0, x228:0, x109:0, x110:0, x231:0, x112:0, x113:0, x114:0, x115:0, x116:0, x117:0, x118:0, x119:0) -> l3(1 + x100:0, x101:0, x102:0, x103:0, x104:0, x105:0, x106:0, x107:0, 1 + x228:0, x109:0, x110:0, x111:0, x112:0, x113:0, x114:0, x115:0, x116:0, x117:0, x118:0, x119:0) :|: x117:0 >= 1 + x100:0
l3(x180:0, x181:0, x182:0, x183:0, x184:0, x185:0, x366:0, x187:0, x188:0, x189:0, x190:0, x191:0, x192:0, x193:0, x194:0, x195:0, x196:0, x197:0, x198:0, x199:0) -> l3(0, x181:0, x182:0, x183:0, x184:0, x185:0, 1 + x366:0, x187:0, x188:0, x189:0, x190:0, x191:0, x192:0, x193:0, x194:0, x195:0, x196:0, x197:0, x198:0, x199:0) :|: x197:0 <= x180:0 && x197:0 >= 1 + (1 + x366:0)
l3(x140:0, x141:0, x222:0, x143:0, x144:0, x225:0, x146:0, x147:0, x148:0, x149:0, x150:0, x151:0, x152:0, x153:0, x154:0, x155:0, x156:0, x157:0, x158:0, x159:0) -> l3(1 + x140:0, x141:0, 1 + x222:0, x143:0, x144:0, x145:0, x146:0, x147:0, x148:0, x149:0, x150:0, x151:0, x152:0, x153:0, x154:0, x155:0, x156:0, x157:0, x158:0, x159:0) :|: x157:0 >= 1 + x140:0

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

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

   l3(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15, x16, x17, x18, x19, x20) -> l3(x1, x7, x18)

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

(20)
Obligation:
Rules:
l3(x100:0, x106:0, x117:0) -> l3(1 + x100:0, x106:0, x117:0) :|: x117:0 >= 1 + x100:0
l3(x180:0, x366:0, x197:0) -> l3(0, 1 + x366:0, x197:0) :|: x197:0 <= x180:0 && x197:0 >= 1 + (1 + x366:0)

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

(21) TempFilterProof (SOUND)
Used the following sort dictionary for filtering: 
l3(VARIABLE, VARIABLE, INTEGER)
Replaced non-predefined constructor symbols by 0.
----------------------------------------

(22)
Obligation:
Rules:
l3(x100:0, x106:0, x117:0) -> l3(c, x106:0, x117:0) :|: c = 1 + x100:0 && x117:0 >= 1 + x100:0
l3(x180:0, x366:0, x197:0) -> l3(c1, c2, x197:0) :|: c2 = 1 + x366:0 && c1 = 0 && (x197:0 <= x180:0 && x197:0 >= 1 + (1 + x366:0))

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

(23) RankingReductionPairProof (EQUIVALENT)
Interpretation:
[ l3 ] = l3_3 + -1*l3_2

The following rules are decreasing:
l3(x180:0, x366:0, x197:0) -> l3(c1, c2, x197:0) :|: c2 = 1 + x366:0 && c1 = 0 && (x197:0 <= x180:0 && x197:0 >= 1 + (1 + x366:0))

The following rules are bounded:
l3(x180:0, x366:0, x197:0) -> l3(c1, c2, x197:0) :|: c2 = 1 + x366:0 && c1 = 0 && (x197:0 <= x180:0 && x197:0 >= 1 + (1 + x366:0))


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

(24)
Obligation:
Rules:
l3(x100:0, x106:0, x117:0) -> l3(c, x106:0, x117:0) :|: c = 1 + x100:0 && x117:0 >= 1 + x100:0

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

(25) RankingReductionPairProof (EQUIVALENT)
Interpretation:
[ l3 ] = l3_3 + -1*l3_1

The following rules are decreasing:
l3(x100:0, x106:0, x117:0) -> l3(c, x106:0, x117:0) :|: c = 1 + x100:0 && x117:0 >= 1 + x100:0

The following rules are bounded:
l3(x100:0, x106:0, x117:0) -> l3(c, x106:0, x117:0) :|: c = 1 + x100:0 && x117:0 >= 1 + x100:0


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(26)
YES