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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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, 16.2 s]
(4) AND
    (5) IRSwT
        (6) IntTRSCompressionProof [EQUIVALENT, 61 ms]
        (7) IRSwT
        (8) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms]
        (9) IRSwT
        (10) TempFilterProof [SOUND, 24 ms]
        (11) IntTRS
        (12) RankingReductionPairProof [EQUIVALENT, 0 ms]
        (13) IntTRS
        (14) PolynomialOrderProcessor [EQUIVALENT, 0 ms]
        (15) YES
    (16) IRSwT
        (17) IntTRSCompressionProof [EQUIVALENT, 29 ms]
        (18) IRSwT
        (19) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms]
        (20) IRSwT
        (21) TempFilterProof [SOUND, 42 ms]
        (22) IntTRS
        (23) PolynomialOrderProcessor [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, ret_RandomInteger15HAT0) -> l1(Inner10HATpost, InnerIndex7HATpost, Ncnt14HATpost, NegcntHATpost, NegtotalHATpost, Ntotal12HATpost, Outer9HATpost, OuterIndex6HATpost, Pcnt13HATpost, PoscntHATpost, PostotalHATpost, Ptotal11HATpost, SeedHATpost, StartTime2HATpost, StopTime3HATpost, TotalTime4HATpost, ret_RandomInteger15HATpost) :|: ret_RandomInteger15HAT0 = ret_RandomInteger15HATpost && 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) -> l3(x17, x18, x19, x20, x21, x22, x23, x24, x25, x26, x27, x28, x29, x30, x31, x32, x33) :|: x16 = x33 && x15 = x32 && x14 = x31 && x13 = x30 && x12 = x29 && x11 = x28 && x10 = x27 && x9 = x26 && x8 = x25 && x7 = x24 && x6 = x23 && x5 = x22 && x4 = x21 && x3 = x20 && x2 = x19 && x1 = x18 && x17 = 1 + x
l4(x34, x35, x36, x37, x38, x39, x40, x41, x42, x43, x44, x45, x46, x47, x48, x49, x50) -> l5(x51, x52, x53, x54, x55, x56, x57, x58, x59, x60, x61, x62, x63, x64, x65, x66, x67) :|: x50 = x67 && x49 = x66 && x48 = x65 && x47 = x64 && x46 = x63 && x45 = x62 && x44 = x61 && x43 = x60 && x42 = x59 && x41 = x58 && x40 = x57 && x39 = x56 && x38 = x55 && x37 = x54 && x36 = x53 && x35 = x52 && x34 = x51
l6(x68, x69, x70, x71, x72, x73, x74, x75, x76, x77, x78, x79, x80, x81, x82, x83, x84) -> l2(x85, x86, x87, x88, x89, x90, x91, x92, x93, x94, x95, x96, x97, x98, x99, x100, x101) :|: x84 = x101 && x83 = x100 && x82 = x99 && x81 = x98 && x80 = x97 && x78 = x95 && x77 = x94 && x75 = x92 && x74 = x91 && x73 = x90 && x72 = x89 && x71 = x88 && x70 = x87 && x69 = x86 && x68 = x85 && x93 = 1 + x76 && x96 = x96
l6(x102, x103, x104, x105, x106, x107, x108, x109, x110, x111, x112, x113, x114, x115, x116, x117, x118) -> l2(x119, x120, x121, x122, x123, x124, x125, x126, x127, x128, x129, x130, x131, x132, x133, x134, x135) :|: x118 = x135 && x117 = x134 && x116 = x133 && x115 = x132 && x114 = x131 && x113 = x130 && x112 = x129 && x111 = x128 && x110 = x127 && x109 = x126 && x108 = x125 && x106 = x123 && x105 = x122 && x103 = x120 && x102 = x119 && x121 = 1 + x104 && x124 = x124
l7(x136, x137, x138, x139, x140, x141, x142, x143, x144, x145, x146, x147, x148, x149, x150, x151, x152) -> l8(x153, x154, x155, x156, x157, x158, x159, x160, x161, x162, x163, x164, x165, x166, x167, x168, x169) :|: x152 = x169 && x151 = x168 && x150 = x167 && x149 = x166 && x148 = x165 && x147 = x164 && x146 = x163 && x145 = x162 && x144 = x161 && x143 = x160 && x141 = x158 && x140 = x157 && x139 = x156 && x138 = x155 && x137 = x154 && x136 = x153 && x159 = 1 + x142 && 10 <= x136
l7(x170, x171, x172, x173, x174, x175, x176, x177, x178, x179, x180, x181, x182, x183, x184, x185, x186) -> l6(x187, x188, x189, x190, x191, x192, x193, x194, x195, x196, x197, x198, x199, x200, x201, x202, x203) :|: x186 = x203 && x185 = x202 && x184 = x201 && x183 = x200 && x182 = x199 && x181 = x198 && x180 = x197 && x179 = x196 && x178 = x195 && x177 = x194 && x176 = x193 && x175 = x192 && x174 = x191 && x173 = x190 && x172 = x189 && x171 = x188 && x170 = x187 && 1 + x170 <= 10
l9(x204, x205, x206, x207, x208, x209, x210, x211, x212, x213, x214, x215, x216, x217, x218, x219, x220) -> l10(x221, x222, x223, x224, x225, x226, x227, x228, x229, x230, x231, x232, x233, x234, x235, x236, x237) :|: x220 = x237 && x217 = x234 && x216 = x233 && x215 = x232 && x212 = x229 && x211 = x228 && x210 = x227 && x209 = x226 && x206 = x223 && x205 = x222 && x204 = x221 && x236 = x236 && x235 = 1500 && x224 = x206 && x225 = x209 && x230 = x212 && x231 = x215 && 10 <= x210
l9(x238, x239, x240, x241, x242, x243, x244, x245, x246, x247, x248, x249, x250, x251, x252, x253, x254) -> l3(x255, x256, x257, x258, x259, x260, x261, x262, x263, x264, x265, x266, x267, x268, x269, x270, x271) :|: x254 = x271 && x253 = x270 && x252 = x269 && x251 = x268 && x250 = x267 && x249 = x266 && x248 = x265 && x247 = x264 && x246 = x263 && x245 = x262 && x244 = x261 && x243 = x260 && x242 = x259 && x241 = x258 && x240 = x257 && x239 = x256 && x255 = 0 && 1 + x244 <= 10
l8(x272, x273, x274, x275, x276, x277, x278, x279, x280, x281, x282, x283, x284, x285, x286, x287, x288) -> l9(x289, x290, x291, x292, x293, x294, x295, x296, x297, x298, x299, x300, x301, x302, x303, x304, x305) :|: x288 = x305 && x287 = x304 && x286 = x303 && x285 = x302 && x284 = x301 && x283 = x300 && x282 = x299 && x281 = x298 && x280 = x297 && x279 = x296 && x278 = x295 && x277 = x294 && x276 = x293 && x275 = x292 && x274 = x291 && x273 = x290 && x272 = x289
l3(x306, x307, x308, x309, x310, x311, x312, x313, x314, x315, x316, x317, x318, x319, x320, x321, x322) -> l7(x323, x324, x325, x326, x327, x328, x329, x330, x331, x332, x333, x334, x335, x336, x337, x338, x339) :|: x322 = x339 && x321 = x338 && x320 = x337 && x319 = x336 && x318 = x335 && x317 = x334 && x316 = x333 && x315 = x332 && x314 = x331 && x313 = x330 && x312 = x329 && x311 = x328 && x310 = x327 && x309 = x326 && x308 = x325 && x307 = x324 && x306 = x323
l5(x340, x341, x342, x343, x344, x345, x346, x347, x348, x349, x350, x351, x352, x353, x354, x355, x356) -> l0(x357, x358, x359, x360, x361, x362, x363, x364, x365, x366, x367, x368, x369, x370, x371, x372, x373) :|: x356 = x373 && x355 = x372 && x354 = x371 && x353 = x370 && x352 = x369 && x351 = x368 && x350 = x367 && x349 = x366 && x348 = x365 && x346 = x363 && x345 = x362 && x344 = x361 && x343 = x360 && x342 = x359 && x341 = x358 && x340 = x357 && x364 = 1 + x347 && 10 <= x341
l5(x374, x375, x376, x377, x378, x379, x380, x381, x382, x383, x384, x385, x386, x387, x388, x389, x390) -> l4(x391, x392, x393, x394, x395, x396, x397, x398, x399, x400, x401, x402, x403, x404, x405, x406, x407) :|: x389 = x406 && x388 = x405 && x387 = x404 && x385 = x402 && x384 = x401 && x383 = x400 && x382 = x399 && x381 = x398 && x380 = x397 && x379 = x396 && x378 = x395 && x377 = x394 && x376 = x393 && x374 = x391 && x392 = 1 + x375 && x407 = x403 && x403 = x403 && 1 + x375 <= 10
l1(x408, x409, x410, x411, x412, x413, x414, x415, x416, x417, x418, x419, x420, x421, x422, x423, x424) -> l8(x425, x426, x427, x428, x429, x430, x431, x432, x433, x434, x435, x436, x437, x438, x439, x440, x441) :|: x424 = x441 && x423 = x440 && x422 = x439 && x420 = x437 && x418 = x435 && x417 = x434 && x415 = x432 && x412 = x429 && x411 = x428 && x409 = x426 && x408 = x425 && x431 = 0 && x427 = 0 && x433 = 0 && x430 = 0 && x436 = 0 && x438 = 1000 && 10 <= x415
l1(x442, x443, x444, x445, x446, x447, x448, x449, x450, x451, x452, x453, x454, x455, x456, x457, x458) -> l4(x459, x460, x461, x462, x463, x464, x465, x466, x467, x468, x469, x470, x471, x472, x473, x474, x475) :|: x458 = x475 && x457 = x474 && x456 = x473 && x455 = x472 && x454 = x471 && x453 = x470 && x452 = x469 && x451 = x468 && x450 = x467 && x449 = x466 && x448 = x465 && x447 = x464 && x446 = x463 && x445 = x462 && x444 = x461 && x442 = x459 && x460 = 0 && 1 + x449 <= 10
l11(x476, x477, x478, x479, x480, x481, x482, x483, x484, x485, x486, x487, x488, x489, x490, x491, x492) -> l0(x493, x494, x495, x496, x497, x498, x499, x500, x501, x502, x503, x504, x505, x506, x507, x508, x509) :|: x492 = x509 && x491 = x508 && x490 = x507 && x489 = x506 && x487 = x504 && x486 = x503 && x485 = x502 && x484 = x501 && x482 = x499 && x481 = x498 && x480 = x497 && x479 = x496 && x478 = x495 && x477 = x494 && x476 = x493 && x500 = 0 && x505 = 0
l12(x510, x511, x512, x513, x514, x515, x516, x517, x518, x519, x520, x521, x522, x523, x524, x525, x526) -> l11(x527, x528, x529, x530, x531, x532, x533, x534, x535, x536, x537, x538, x539, x540, x541, x542, x543) :|: x526 = x543 && x525 = x542 && x524 = x541 && x523 = x540 && x522 = x539 && x521 = x538 && x520 = x537 && x519 = x536 && x518 = x535 && x517 = x534 && x516 = x533 && x515 = x532 && x514 = x531 && x513 = x530 && x512 = x529 && x511 = x528 && x510 = x527
Start term: l12(Inner10HAT0, InnerIndex7HAT0, Ncnt14HAT0, NegcntHAT0, NegtotalHAT0, Ntotal12HAT0, Outer9HAT0, OuterIndex6HAT0, Pcnt13HAT0, PoscntHAT0, PostotalHAT0, Ptotal11HAT0, SeedHAT0, StartTime2HAT0, StopTime3HAT0, TotalTime4HAT0, 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, ret_RandomInteger15HAT0) -> l1(Inner10HATpost, InnerIndex7HATpost, Ncnt14HATpost, NegcntHATpost, NegtotalHATpost, Ntotal12HATpost, Outer9HATpost, OuterIndex6HATpost, Pcnt13HATpost, PoscntHATpost, PostotalHATpost, Ptotal11HATpost, SeedHATpost, StartTime2HATpost, StopTime3HATpost, TotalTime4HATpost, ret_RandomInteger15HATpost) :|: ret_RandomInteger15HAT0 = ret_RandomInteger15HATpost && 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) -> l3(x17, x18, x19, x20, x21, x22, x23, x24, x25, x26, x27, x28, x29, x30, x31, x32, x33) :|: x16 = x33 && x15 = x32 && x14 = x31 && x13 = x30 && x12 = x29 && x11 = x28 && x10 = x27 && x9 = x26 && x8 = x25 && x7 = x24 && x6 = x23 && x5 = x22 && x4 = x21 && x3 = x20 && x2 = x19 && x1 = x18 && x17 = 1 + x
l4(x34, x35, x36, x37, x38, x39, x40, x41, x42, x43, x44, x45, x46, x47, x48, x49, x50) -> l5(x51, x52, x53, x54, x55, x56, x57, x58, x59, x60, x61, x62, x63, x64, x65, x66, x67) :|: x50 = x67 && x49 = x66 && x48 = x65 && x47 = x64 && x46 = x63 && x45 = x62 && x44 = x61 && x43 = x60 && x42 = x59 && x41 = x58 && x40 = x57 && x39 = x56 && x38 = x55 && x37 = x54 && x36 = x53 && x35 = x52 && x34 = x51
l6(x68, x69, x70, x71, x72, x73, x74, x75, x76, x77, x78, x79, x80, x81, x82, x83, x84) -> l2(x85, x86, x87, x88, x89, x90, x91, x92, x93, x94, x95, x96, x97, x98, x99, x100, x101) :|: x84 = x101 && x83 = x100 && x82 = x99 && x81 = x98 && x80 = x97 && x78 = x95 && x77 = x94 && x75 = x92 && x74 = x91 && x73 = x90 && x72 = x89 && x71 = x88 && x70 = x87 && x69 = x86 && x68 = x85 && x93 = 1 + x76 && x96 = x96
l6(x102, x103, x104, x105, x106, x107, x108, x109, x110, x111, x112, x113, x114, x115, x116, x117, x118) -> l2(x119, x120, x121, x122, x123, x124, x125, x126, x127, x128, x129, x130, x131, x132, x133, x134, x135) :|: x118 = x135 && x117 = x134 && x116 = x133 && x115 = x132 && x114 = x131 && x113 = x130 && x112 = x129 && x111 = x128 && x110 = x127 && x109 = x126 && x108 = x125 && x106 = x123 && x105 = x122 && x103 = x120 && x102 = x119 && x121 = 1 + x104 && x124 = x124
l7(x136, x137, x138, x139, x140, x141, x142, x143, x144, x145, x146, x147, x148, x149, x150, x151, x152) -> l8(x153, x154, x155, x156, x157, x158, x159, x160, x161, x162, x163, x164, x165, x166, x167, x168, x169) :|: x152 = x169 && x151 = x168 && x150 = x167 && x149 = x166 && x148 = x165 && x147 = x164 && x146 = x163 && x145 = x162 && x144 = x161 && x143 = x160 && x141 = x158 && x140 = x157 && x139 = x156 && x138 = x155 && x137 = x154 && x136 = x153 && x159 = 1 + x142 && 10 <= x136
l7(x170, x171, x172, x173, x174, x175, x176, x177, x178, x179, x180, x181, x182, x183, x184, x185, x186) -> l6(x187, x188, x189, x190, x191, x192, x193, x194, x195, x196, x197, x198, x199, x200, x201, x202, x203) :|: x186 = x203 && x185 = x202 && x184 = x201 && x183 = x200 && x182 = x199 && x181 = x198 && x180 = x197 && x179 = x196 && x178 = x195 && x177 = x194 && x176 = x193 && x175 = x192 && x174 = x191 && x173 = x190 && x172 = x189 && x171 = x188 && x170 = x187 && 1 + x170 <= 10
l9(x204, x205, x206, x207, x208, x209, x210, x211, x212, x213, x214, x215, x216, x217, x218, x219, x220) -> l10(x221, x222, x223, x224, x225, x226, x227, x228, x229, x230, x231, x232, x233, x234, x235, x236, x237) :|: x220 = x237 && x217 = x234 && x216 = x233 && x215 = x232 && x212 = x229 && x211 = x228 && x210 = x227 && x209 = x226 && x206 = x223 && x205 = x222 && x204 = x221 && x236 = x236 && x235 = 1500 && x224 = x206 && x225 = x209 && x230 = x212 && x231 = x215 && 10 <= x210
l9(x238, x239, x240, x241, x242, x243, x244, x245, x246, x247, x248, x249, x250, x251, x252, x253, x254) -> l3(x255, x256, x257, x258, x259, x260, x261, x262, x263, x264, x265, x266, x267, x268, x269, x270, x271) :|: x254 = x271 && x253 = x270 && x252 = x269 && x251 = x268 && x250 = x267 && x249 = x266 && x248 = x265 && x247 = x264 && x246 = x263 && x245 = x262 && x244 = x261 && x243 = x260 && x242 = x259 && x241 = x258 && x240 = x257 && x239 = x256 && x255 = 0 && 1 + x244 <= 10
l8(x272, x273, x274, x275, x276, x277, x278, x279, x280, x281, x282, x283, x284, x285, x286, x287, x288) -> l9(x289, x290, x291, x292, x293, x294, x295, x296, x297, x298, x299, x300, x301, x302, x303, x304, x305) :|: x288 = x305 && x287 = x304 && x286 = x303 && x285 = x302 && x284 = x301 && x283 = x300 && x282 = x299 && x281 = x298 && x280 = x297 && x279 = x296 && x278 = x295 && x277 = x294 && x276 = x293 && x275 = x292 && x274 = x291 && x273 = x290 && x272 = x289
l3(x306, x307, x308, x309, x310, x311, x312, x313, x314, x315, x316, x317, x318, x319, x320, x321, x322) -> l7(x323, x324, x325, x326, x327, x328, x329, x330, x331, x332, x333, x334, x335, x336, x337, x338, x339) :|: x322 = x339 && x321 = x338 && x320 = x337 && x319 = x336 && x318 = x335 && x317 = x334 && x316 = x333 && x315 = x332 && x314 = x331 && x313 = x330 && x312 = x329 && x311 = x328 && x310 = x327 && x309 = x326 && x308 = x325 && x307 = x324 && x306 = x323
l5(x340, x341, x342, x343, x344, x345, x346, x347, x348, x349, x350, x351, x352, x353, x354, x355, x356) -> l0(x357, x358, x359, x360, x361, x362, x363, x364, x365, x366, x367, x368, x369, x370, x371, x372, x373) :|: x356 = x373 && x355 = x372 && x354 = x371 && x353 = x370 && x352 = x369 && x351 = x368 && x350 = x367 && x349 = x366 && x348 = x365 && x346 = x363 && x345 = x362 && x344 = x361 && x343 = x360 && x342 = x359 && x341 = x358 && x340 = x357 && x364 = 1 + x347 && 10 <= x341
l5(x374, x375, x376, x377, x378, x379, x380, x381, x382, x383, x384, x385, x386, x387, x388, x389, x390) -> l4(x391, x392, x393, x394, x395, x396, x397, x398, x399, x400, x401, x402, x403, x404, x405, x406, x407) :|: x389 = x406 && x388 = x405 && x387 = x404 && x385 = x402 && x384 = x401 && x383 = x400 && x382 = x399 && x381 = x398 && x380 = x397 && x379 = x396 && x378 = x395 && x377 = x394 && x376 = x393 && x374 = x391 && x392 = 1 + x375 && x407 = x403 && x403 = x403 && 1 + x375 <= 10
l1(x408, x409, x410, x411, x412, x413, x414, x415, x416, x417, x418, x419, x420, x421, x422, x423, x424) -> l8(x425, x426, x427, x428, x429, x430, x431, x432, x433, x434, x435, x436, x437, x438, x439, x440, x441) :|: x424 = x441 && x423 = x440 && x422 = x439 && x420 = x437 && x418 = x435 && x417 = x434 && x415 = x432 && x412 = x429 && x411 = x428 && x409 = x426 && x408 = x425 && x431 = 0 && x427 = 0 && x433 = 0 && x430 = 0 && x436 = 0 && x438 = 1000 && 10 <= x415
l1(x442, x443, x444, x445, x446, x447, x448, x449, x450, x451, x452, x453, x454, x455, x456, x457, x458) -> l4(x459, x460, x461, x462, x463, x464, x465, x466, x467, x468, x469, x470, x471, x472, x473, x474, x475) :|: x458 = x475 && x457 = x474 && x456 = x473 && x455 = x472 && x454 = x471 && x453 = x470 && x452 = x469 && x451 = x468 && x450 = x467 && x449 = x466 && x448 = x465 && x447 = x464 && x446 = x463 && x445 = x462 && x444 = x461 && x442 = x459 && x460 = 0 && 1 + x449 <= 10
l11(x476, x477, x478, x479, x480, x481, x482, x483, x484, x485, x486, x487, x488, x489, x490, x491, x492) -> l0(x493, x494, x495, x496, x497, x498, x499, x500, x501, x502, x503, x504, x505, x506, x507, x508, x509) :|: x492 = x509 && x491 = x508 && x490 = x507 && x489 = x506 && x487 = x504 && x486 = x503 && x485 = x502 && x484 = x501 && x482 = x499 && x481 = x498 && x480 = x497 && x479 = x496 && x478 = x495 && x477 = x494 && x476 = x493 && x500 = 0 && x505 = 0
l12(x510, x511, x512, x513, x514, x515, x516, x517, x518, x519, x520, x521, x522, x523, x524, x525, x526) -> l11(x527, x528, x529, x530, x531, x532, x533, x534, x535, x536, x537, x538, x539, x540, x541, x542, x543) :|: x526 = x543 && x525 = x542 && x524 = x541 && x523 = x540 && x522 = x539 && x521 = x538 && x520 = x537 && x519 = x536 && x518 = x535 && x517 = x534 && x516 = x533 && x515 = x532 && x514 = x531 && x513 = x530 && x512 = x529 && x511 = x528 && x510 = x527
Start term: l12(Inner10HAT0, InnerIndex7HAT0, Ncnt14HAT0, NegcntHAT0, NegtotalHAT0, Ntotal12HAT0, Outer9HAT0, OuterIndex6HAT0, Pcnt13HAT0, PoscntHAT0, PostotalHAT0, Ptotal11HAT0, SeedHAT0, StartTime2HAT0, StopTime3HAT0, TotalTime4HAT0, 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, ret_RandomInteger15HAT0) -> l1(Inner10HATpost, InnerIndex7HATpost, Ncnt14HATpost, NegcntHATpost, NegtotalHATpost, Ntotal12HATpost, Outer9HATpost, OuterIndex6HATpost, Pcnt13HATpost, PoscntHATpost, PostotalHATpost, Ptotal11HATpost, SeedHATpost, StartTime2HATpost, StopTime3HATpost, TotalTime4HATpost, ret_RandomInteger15HATpost) :|: ret_RandomInteger15HAT0 = ret_RandomInteger15HATpost && 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) -> l3(x17, x18, x19, x20, x21, x22, x23, x24, x25, x26, x27, x28, x29, x30, x31, x32, x33) :|: x16 = x33 && x15 = x32 && x14 = x31 && x13 = x30 && x12 = x29 && x11 = x28 && x10 = x27 && x9 = x26 && x8 = x25 && x7 = x24 && x6 = x23 && x5 = x22 && x4 = x21 && x3 = x20 && x2 = x19 && x1 = x18 && x17 = 1 + x
(3) l4(x34, x35, x36, x37, x38, x39, x40, x41, x42, x43, x44, x45, x46, x47, x48, x49, x50) -> l5(x51, x52, x53, x54, x55, x56, x57, x58, x59, x60, x61, x62, x63, x64, x65, x66, x67) :|: x50 = x67 && x49 = x66 && x48 = x65 && x47 = x64 && x46 = x63 && x45 = x62 && x44 = x61 && x43 = x60 && x42 = x59 && x41 = x58 && x40 = x57 && x39 = x56 && x38 = x55 && x37 = x54 && x36 = x53 && x35 = x52 && x34 = x51
(4) l6(x68, x69, x70, x71, x72, x73, x74, x75, x76, x77, x78, x79, x80, x81, x82, x83, x84) -> l2(x85, x86, x87, x88, x89, x90, x91, x92, x93, x94, x95, x96, x97, x98, x99, x100, x101) :|: x84 = x101 && x83 = x100 && x82 = x99 && x81 = x98 && x80 = x97 && x78 = x95 && x77 = x94 && x75 = x92 && x74 = x91 && x73 = x90 && x72 = x89 && x71 = x88 && x70 = x87 && x69 = x86 && x68 = x85 && x93 = 1 + x76 && x96 = x96
(5) l6(x102, x103, x104, x105, x106, x107, x108, x109, x110, x111, x112, x113, x114, x115, x116, x117, x118) -> l2(x119, x120, x121, x122, x123, x124, x125, x126, x127, x128, x129, x130, x131, x132, x133, x134, x135) :|: x118 = x135 && x117 = x134 && x116 = x133 && x115 = x132 && x114 = x131 && x113 = x130 && x112 = x129 && x111 = x128 && x110 = x127 && x109 = x126 && x108 = x125 && x106 = x123 && x105 = x122 && x103 = x120 && x102 = x119 && x121 = 1 + x104 && x124 = x124
(6) l7(x136, x137, x138, x139, x140, x141, x142, x143, x144, x145, x146, x147, x148, x149, x150, x151, x152) -> l8(x153, x154, x155, x156, x157, x158, x159, x160, x161, x162, x163, x164, x165, x166, x167, x168, x169) :|: x152 = x169 && x151 = x168 && x150 = x167 && x149 = x166 && x148 = x165 && x147 = x164 && x146 = x163 && x145 = x162 && x144 = x161 && x143 = x160 && x141 = x158 && x140 = x157 && x139 = x156 && x138 = x155 && x137 = x154 && x136 = x153 && x159 = 1 + x142 && 10 <= x136
(7) l7(x170, x171, x172, x173, x174, x175, x176, x177, x178, x179, x180, x181, x182, x183, x184, x185, x186) -> l6(x187, x188, x189, x190, x191, x192, x193, x194, x195, x196, x197, x198, x199, x200, x201, x202, x203) :|: x186 = x203 && x185 = x202 && x184 = x201 && x183 = x200 && x182 = x199 && x181 = x198 && x180 = x197 && x179 = x196 && x178 = x195 && x177 = x194 && x176 = x193 && x175 = x192 && x174 = x191 && x173 = x190 && x172 = x189 && x171 = x188 && x170 = x187 && 1 + x170 <= 10
(8) l9(x204, x205, x206, x207, x208, x209, x210, x211, x212, x213, x214, x215, x216, x217, x218, x219, x220) -> l10(x221, x222, x223, x224, x225, x226, x227, x228, x229, x230, x231, x232, x233, x234, x235, x236, x237) :|: x220 = x237 && x217 = x234 && x216 = x233 && x215 = x232 && x212 = x229 && x211 = x228 && x210 = x227 && x209 = x226 && x206 = x223 && x205 = x222 && x204 = x221 && x236 = x236 && x235 = 1500 && x224 = x206 && x225 = x209 && x230 = x212 && x231 = x215 && 10 <= x210
(9) l9(x238, x239, x240, x241, x242, x243, x244, x245, x246, x247, x248, x249, x250, x251, x252, x253, x254) -> l3(x255, x256, x257, x258, x259, x260, x261, x262, x263, x264, x265, x266, x267, x268, x269, x270, x271) :|: x254 = x271 && x253 = x270 && x252 = x269 && x251 = x268 && x250 = x267 && x249 = x266 && x248 = x265 && x247 = x264 && x246 = x263 && x245 = x262 && x244 = x261 && x243 = x260 && x242 = x259 && x241 = x258 && x240 = x257 && x239 = x256 && x255 = 0 && 1 + x244 <= 10
(10) l8(x272, x273, x274, x275, x276, x277, x278, x279, x280, x281, x282, x283, x284, x285, x286, x287, x288) -> l9(x289, x290, x291, x292, x293, x294, x295, x296, x297, x298, x299, x300, x301, x302, x303, x304, x305) :|: x288 = x305 && x287 = x304 && x286 = x303 && x285 = x302 && x284 = x301 && x283 = x300 && x282 = x299 && x281 = x298 && x280 = x297 && x279 = x296 && x278 = x295 && x277 = x294 && x276 = x293 && x275 = x292 && x274 = x291 && x273 = x290 && x272 = x289
(11) l3(x306, x307, x308, x309, x310, x311, x312, x313, x314, x315, x316, x317, x318, x319, x320, x321, x322) -> l7(x323, x324, x325, x326, x327, x328, x329, x330, x331, x332, x333, x334, x335, x336, x337, x338, x339) :|: x322 = x339 && x321 = x338 && x320 = x337 && x319 = x336 && x318 = x335 && x317 = x334 && x316 = x333 && x315 = x332 && x314 = x331 && x313 = x330 && x312 = x329 && x311 = x328 && x310 = x327 && x309 = x326 && x308 = x325 && x307 = x324 && x306 = x323
(12) l5(x340, x341, x342, x343, x344, x345, x346, x347, x348, x349, x350, x351, x352, x353, x354, x355, x356) -> l0(x357, x358, x359, x360, x361, x362, x363, x364, x365, x366, x367, x368, x369, x370, x371, x372, x373) :|: x356 = x373 && x355 = x372 && x354 = x371 && x353 = x370 && x352 = x369 && x351 = x368 && x350 = x367 && x349 = x366 && x348 = x365 && x346 = x363 && x345 = x362 && x344 = x361 && x343 = x360 && x342 = x359 && x341 = x358 && x340 = x357 && x364 = 1 + x347 && 10 <= x341
(13) l5(x374, x375, x376, x377, x378, x379, x380, x381, x382, x383, x384, x385, x386, x387, x388, x389, x390) -> l4(x391, x392, x393, x394, x395, x396, x397, x398, x399, x400, x401, x402, x403, x404, x405, x406, x407) :|: x389 = x406 && x388 = x405 && x387 = x404 && x385 = x402 && x384 = x401 && x383 = x400 && x382 = x399 && x381 = x398 && x380 = x397 && x379 = x396 && x378 = x395 && x377 = x394 && x376 = x393 && x374 = x391 && x392 = 1 + x375 && x407 = x403 && x403 = x403 && 1 + x375 <= 10
(14) l1(x408, x409, x410, x411, x412, x413, x414, x415, x416, x417, x418, x419, x420, x421, x422, x423, x424) -> l8(x425, x426, x427, x428, x429, x430, x431, x432, x433, x434, x435, x436, x437, x438, x439, x440, x441) :|: x424 = x441 && x423 = x440 && x422 = x439 && x420 = x437 && x418 = x435 && x417 = x434 && x415 = x432 && x412 = x429 && x411 = x428 && x409 = x426 && x408 = x425 && x431 = 0 && x427 = 0 && x433 = 0 && x430 = 0 && x436 = 0 && x438 = 1000 && 10 <= x415
(15) l1(x442, x443, x444, x445, x446, x447, x448, x449, x450, x451, x452, x453, x454, x455, x456, x457, x458) -> l4(x459, x460, x461, x462, x463, x464, x465, x466, x467, x468, x469, x470, x471, x472, x473, x474, x475) :|: x458 = x475 && x457 = x474 && x456 = x473 && x455 = x472 && x454 = x471 && x453 = x470 && x452 = x469 && x451 = x468 && x450 = x467 && x449 = x466 && x448 = x465 && x447 = x464 && x446 = x463 && x445 = x462 && x444 = x461 && x442 = x459 && x460 = 0 && 1 + x449 <= 10
(16) l11(x476, x477, x478, x479, x480, x481, x482, x483, x484, x485, x486, x487, x488, x489, x490, x491, x492) -> l0(x493, x494, x495, x496, x497, x498, x499, x500, x501, x502, x503, x504, x505, x506, x507, x508, x509) :|: x492 = x509 && x491 = x508 && x490 = x507 && x489 = x506 && x487 = x504 && x486 = x503 && x485 = x502 && x484 = x501 && x482 = x499 && x481 = x498 && x480 = x497 && x479 = x496 && x478 = x495 && x477 = x494 && x476 = x493 && x500 = 0 && x505 = 0
(17) l12(x510, x511, x512, x513, x514, x515, x516, x517, x518, x519, x520, x521, x522, x523, x524, x525, x526) -> l11(x527, x528, x529, x530, x531, x532, x533, x534, x535, x536, x537, x538, x539, x540, x541, x542, x543) :|: x526 = x543 && x525 = x542 && x524 = x541 && x523 = x540 && x522 = x539 && x521 = x538 && x520 = x537 && x519 = x536 && x518 = x535 && x517 = x534 && x516 = x533 && x515 = x532 && x514 = x531 && x513 = x530 && x512 = x529 && x511 = x528 && x510 = x527

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, ret_RandomInteger15HAT0) -> l1(Inner10HATpost, InnerIndex7HATpost, Ncnt14HATpost, NegcntHATpost, NegtotalHATpost, Ntotal12HATpost, Outer9HATpost, OuterIndex6HATpost, Pcnt13HATpost, PoscntHATpost, PostotalHATpost, Ptotal11HATpost, SeedHATpost, StartTime2HATpost, StopTime3HATpost, TotalTime4HATpost, ret_RandomInteger15HATpost) :|: ret_RandomInteger15HAT0 = ret_RandomInteger15HATpost && 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(x340, x341, x342, x343, x344, x345, x346, x347, x348, x349, x350, x351, x352, x353, x354, x355, x356) -> l0(x357, x358, x359, x360, x361, x362, x363, x364, x365, x366, x367, x368, x369, x370, x371, x372, x373) :|: x356 = x373 && x355 = x372 && x354 = x371 && x353 = x370 && x352 = x369 && x351 = x368 && x350 = x367 && x349 = x366 && x348 = x365 && x346 = x363 && x345 = x362 && x344 = x361 && x343 = x360 && x342 = x359 && x341 = x358 && x340 = x357 && x364 = 1 + x347 && 10 <= x341
(3) l4(x34, x35, x36, x37, x38, x39, x40, x41, x42, x43, x44, x45, x46, x47, x48, x49, x50) -> l5(x51, x52, x53, x54, x55, x56, x57, x58, x59, x60, x61, x62, x63, x64, x65, x66, x67) :|: x50 = x67 && x49 = x66 && x48 = x65 && x47 = x64 && x46 = x63 && x45 = x62 && x44 = x61 && x43 = x60 && x42 = x59 && x41 = x58 && x40 = x57 && x39 = x56 && x38 = x55 && x37 = x54 && x36 = x53 && x35 = x52 && x34 = x51
(4) l1(x442, x443, x444, x445, x446, x447, x448, x449, x450, x451, x452, x453, x454, x455, x456, x457, x458) -> l4(x459, x460, x461, x462, x463, x464, x465, x466, x467, x468, x469, x470, x471, x472, x473, x474, x475) :|: x458 = x475 && x457 = x474 && x456 = x473 && x455 = x472 && x454 = x471 && x453 = x470 && x452 = x469 && x451 = x468 && x450 = x467 && x449 = x466 && x448 = x465 && x447 = x464 && x446 = x463 && x445 = x462 && x444 = x461 && x442 = x459 && x460 = 0 && 1 + x449 <= 10
(5) l5(x374, x375, x376, x377, x378, x379, x380, x381, x382, x383, x384, x385, x386, x387, x388, x389, x390) -> l4(x391, x392, x393, x394, x395, x396, x397, x398, x399, x400, x401, x402, x403, x404, x405, x406, x407) :|: x389 = x406 && x388 = x405 && x387 = x404 && x385 = x402 && x384 = x401 && x383 = x400 && x382 = x399 && x381 = x398 && x380 = x397 && x379 = x396 && x378 = x395 && x377 = x394 && x376 = x393 && x374 = x391 && x392 = 1 + x375 && x407 = x403 && x403 = x403 && 1 + x375 <= 10

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

This digraph is fully evaluated!

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

(7)
Obligation:
Rules:
l4(Inner10HATpost:0, InnerIndex7HATpost:0, Ncnt14HATpost:0, NegcntHATpost:0, NegtotalHATpost:0, Ntotal12HATpost:0, Outer9HATpost:0, x41:0, Pcnt13HATpost:0, PoscntHATpost:0, PostotalHATpost:0, Ptotal11HATpost:0, SeedHATpost:0, StartTime2HATpost:0, StopTime3HATpost:0, TotalTime4HATpost:0, ret_RandomInteger15HATpost:0) -> l4(Inner10HATpost:0, 0, Ncnt14HATpost:0, NegcntHATpost:0, NegtotalHATpost:0, Ntotal12HATpost:0, Outer9HATpost:0, 1 + x41:0, Pcnt13HATpost:0, PoscntHATpost:0, PostotalHATpost:0, Ptotal11HATpost:0, SeedHATpost:0, StartTime2HATpost:0, StopTime3HATpost:0, TotalTime4HATpost:0, ret_RandomInteger15HATpost:0) :|: InnerIndex7HATpost:0 > 9 && x41:0 < 9
l4(x34:0, x35:0, x36:0, x37:0, x38:0, x396:0, x397:0, x398:0, x399:0, x400:0, x401:0, x402:0, x46:0, x404:0, x405:0, x406:0, x50:0) -> l4(x34:0, 1 + x35:0, x36:0, x37:0, x38:0, x396:0, x397:0, x398:0, x399:0, x400:0, x401:0, x402:0, x403:0, x404:0, x405:0, x406:0, x403:0) :|: x35:0 < 10

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(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) -> l4(x2, x8)

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

(9)
Obligation:
Rules:
l4(InnerIndex7HATpost:0, x41:0) -> l4(0, 1 + x41:0) :|: InnerIndex7HATpost:0 > 9 && x41:0 < 9
l4(x35:0, x398:0) -> l4(1 + x35:0, x398:0) :|: x35:0 < 10

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

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

(11)
Obligation:
Rules:
l4(InnerIndex7HATpost:0, x41:0) -> l4(c, c1) :|: c1 = 1 + x41:0 && c = 0 && (InnerIndex7HATpost:0 > 9 && x41:0 < 9)
l4(x35:0, x398:0) -> l4(c2, x398:0) :|: c2 = 1 + x35:0 && x35:0 < 10

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

(12) RankingReductionPairProof (EQUIVALENT)
Interpretation:
[ l4 ] = -1*l4_2

The following rules are decreasing:
l4(InnerIndex7HATpost:0, x41:0) -> l4(c, c1) :|: c1 = 1 + x41:0 && c = 0 && (InnerIndex7HATpost:0 > 9 && x41:0 < 9)

The following rules are bounded:
l4(InnerIndex7HATpost:0, x41:0) -> l4(c, c1) :|: c1 = 1 + x41:0 && c = 0 && (InnerIndex7HATpost:0 > 9 && x41:0 < 9)


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

(13)
Obligation:
Rules:
l4(x35:0, x398:0) -> l4(c2, x398:0) :|: c2 = 1 + x35:0 && x35:0 < 10

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

(14) PolynomialOrderProcessor (EQUIVALENT)
Found the following polynomial interpretation:
[l4(x, x1)] = 9 - x

The following rules are decreasing:
l4(x35:0, x398:0) -> l4(c2, x398:0) :|: c2 = 1 + x35:0 && x35:0 < 10
The following rules are bounded:
l4(x35:0, x398:0) -> l4(c2, x398:0) :|: c2 = 1 + x35:0 && x35:0 < 10

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

(15)
YES

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

(16)
Obligation:

Termination digraph:
Nodes:
(1) l8(x272, x273, x274, x275, x276, x277, x278, x279, x280, x281, x282, x283, x284, x285, x286, x287, x288) -> l9(x289, x290, x291, x292, x293, x294, x295, x296, x297, x298, x299, x300, x301, x302, x303, x304, x305) :|: x288 = x305 && x287 = x304 && x286 = x303 && x285 = x302 && x284 = x301 && x283 = x300 && x282 = x299 && x281 = x298 && x280 = x297 && x279 = x296 && x278 = x295 && x277 = x294 && x276 = x293 && x275 = x292 && x274 = x291 && x273 = x290 && x272 = x289
(2) l7(x136, x137, x138, x139, x140, x141, x142, x143, x144, x145, x146, x147, x148, x149, x150, x151, x152) -> l8(x153, x154, x155, x156, x157, x158, x159, x160, x161, x162, x163, x164, x165, x166, x167, x168, x169) :|: x152 = x169 && x151 = x168 && x150 = x167 && x149 = x166 && x148 = x165 && x147 = x164 && x146 = x163 && x145 = x162 && x144 = x161 && x143 = x160 && x141 = x158 && x140 = x157 && x139 = x156 && x138 = x155 && x137 = x154 && x136 = x153 && x159 = 1 + x142 && 10 <= x136
(3) l3(x306, x307, x308, x309, x310, x311, x312, x313, x314, x315, x316, x317, x318, x319, x320, x321, x322) -> l7(x323, x324, x325, x326, x327, x328, x329, x330, x331, x332, x333, x334, x335, x336, x337, x338, x339) :|: x322 = x339 && x321 = x338 && x320 = x337 && x319 = x336 && x318 = x335 && x317 = x334 && x316 = x333 && x315 = x332 && x314 = x331 && x313 = x330 && x312 = x329 && x311 = x328 && x310 = x327 && x309 = x326 && x308 = x325 && x307 = x324 && x306 = x323
(4) l9(x238, x239, x240, x241, x242, x243, x244, x245, x246, x247, x248, x249, x250, x251, x252, x253, x254) -> l3(x255, x256, x257, x258, x259, x260, x261, x262, x263, x264, x265, x266, x267, x268, x269, x270, x271) :|: x254 = x271 && x253 = x270 && x252 = x269 && x251 = x268 && x250 = x267 && x249 = x266 && x248 = x265 && x247 = x264 && x246 = x263 && x245 = x262 && x244 = x261 && x243 = x260 && x242 = x259 && x241 = x258 && x240 = x257 && x239 = x256 && x255 = 0 && 1 + x244 <= 10
(5) l2(x, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15, x16) -> l3(x17, x18, x19, x20, x21, x22, x23, x24, x25, x26, x27, x28, x29, x30, x31, x32, x33) :|: x16 = x33 && x15 = x32 && x14 = x31 && x13 = x30 && x12 = x29 && x11 = x28 && x10 = x27 && x9 = x26 && x8 = x25 && x7 = x24 && x6 = x23 && x5 = x22 && x4 = x21 && x3 = x20 && x2 = x19 && x1 = x18 && x17 = 1 + x
(6) l6(x102, x103, x104, x105, x106, x107, x108, x109, x110, x111, x112, x113, x114, x115, x116, x117, x118) -> l2(x119, x120, x121, x122, x123, x124, x125, x126, x127, x128, x129, x130, x131, x132, x133, x134, x135) :|: x118 = x135 && x117 = x134 && x116 = x133 && x115 = x132 && x114 = x131 && x113 = x130 && x112 = x129 && x111 = x128 && x110 = x127 && x109 = x126 && x108 = x125 && x106 = x123 && x105 = x122 && x103 = x120 && x102 = x119 && x121 = 1 + x104 && x124 = x124
(7) l6(x68, x69, x70, x71, x72, x73, x74, x75, x76, x77, x78, x79, x80, x81, x82, x83, x84) -> l2(x85, x86, x87, x88, x89, x90, x91, x92, x93, x94, x95, x96, x97, x98, x99, x100, x101) :|: x84 = x101 && x83 = x100 && x82 = x99 && x81 = x98 && x80 = x97 && x78 = x95 && x77 = x94 && x75 = x92 && x74 = x91 && x73 = x90 && x72 = x89 && x71 = x88 && x70 = x87 && x69 = x86 && x68 = x85 && x93 = 1 + x76 && x96 = x96
(8) l7(x170, x171, x172, x173, x174, x175, x176, x177, x178, x179, x180, x181, x182, x183, x184, x185, x186) -> l6(x187, x188, x189, x190, x191, x192, x193, x194, x195, x196, x197, x198, x199, x200, x201, x202, x203) :|: x186 = x203 && x185 = x202 && x184 = x201 && x183 = x200 && x182 = x199 && x181 = x198 && x180 = x197 && x179 = x196 && x178 = x195 && x177 = x194 && x176 = x193 && x175 = x192 && x174 = x191 && x173 = x190 && x172 = x189 && x171 = x188 && x170 = x187 && 1 + x170 <= 10

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.
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(18)
Obligation:
Rules:
l3(x119:0, x120:0, x189:0, x122:0, x123:0, x192:0, x125:0, x126:0, x127:0, x128:0, x129:0, x130:0, x131:0, x132:0, x133:0, x134:0, x135:0) -> l3(1 + x119:0, x120:0, 1 + x189:0, x122:0, x123:0, x124:0, x125:0, x126:0, x127:0, x128:0, x129:0, x130:0, x131:0, x132:0, x133:0, x134:0, x135:0) :|: x119:0 < 10
l3(x153:0, x154:0, x155:0, x156:0, x157:0, x158:0, x312:0, x160:0, x161:0, x162:0, x163:0, x164:0, x165:0, x166:0, x167:0, x168:0, x169:0) -> l3(0, x154:0, x155:0, x156:0, x157:0, x158:0, 1 + x312:0, x160:0, x161:0, x162:0, x163:0, x164:0, x165:0, x166:0, x167:0, x168:0, x169:0) :|: x153:0 > 9 && x312:0 < 9
l3(x, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15, x16) -> l3(1 + x, x1, x2, x3, x4, x5, x6, x7, 1 + x8, x9, x10, x17, x12, x13, x14, x15, x16) :|: x < 10

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(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) -> l3(x1, x7)

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(20)
Obligation:
Rules:
l3(x119:0, x125:0) -> l3(1 + x119:0, x125:0) :|: x119:0 < 10
l3(x153:0, x312:0) -> l3(0, 1 + x312:0) :|: x153:0 > 9 && x312:0 < 9

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(21) TempFilterProof (SOUND)
Used the following sort dictionary for filtering: 
l3(VARIABLE, VARIABLE)
Replaced non-predefined constructor symbols by 0.
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(22)
Obligation:
Rules:
l3(x119:0, x125:0) -> l3(c, x125:0) :|: c = 1 + x119:0 && x119:0 < 10
l3(x153:0, x312:0) -> l3(c1, c2) :|: c2 = 1 + x312:0 && c1 = 0 && (x153:0 > 9 && x312:0 < 9)

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(23) PolynomialOrderProcessor (EQUIVALENT)
Found the following polynomial interpretation:
[l3(x, x1)] = 8 - x1

The following rules are decreasing:
l3(x153:0, x312:0) -> l3(c1, c2) :|: c2 = 1 + x312:0 && c1 = 0 && (x153:0 > 9 && x312:0 < 9)
The following rules are bounded:
l3(x153:0, x312:0) -> l3(c1, c2) :|: c2 = 1 + x312:0 && c1 = 0 && (x153:0 > 9 && x312:0 < 9)

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(24)
Obligation:
Rules:
l3(x119:0, x125:0) -> l3(c, x125:0) :|: c = 1 + x119:0 && x119:0 < 10

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

The following rules are decreasing:
l3(x119:0, x125:0) -> l3(c, x125:0) :|: c = 1 + x119:0 && x119:0 < 10

The following rules are bounded:
l3(x119:0, x125:0) -> l3(c, x125:0) :|: c = 1 + x119:0 && x119:0 < 10


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(26)
YES