YES proof of prog.inttrs # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty Termination of the given IRSwT could be proven: (0) IRSwT (1) IRSFormatTransformerProof [EQUIVALENT, 0 ms] (2) IRSwT (3) IRSwTTerminationDigraphProof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, 22.8 s] (4) AND (5) IRSwT (6) IntTRSCompressionProof [EQUIVALENT, 67 ms] (7) IRSwT (8) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms] (9) IRSwT (10) TempFilterProof [SOUND, 43 ms] (11) IntTRS (12) PolynomialOrderProcessor [EQUIVALENT, 16 ms] (13) IntTRS (14) RankingReductionPairProof [EQUIVALENT, 0 ms] (15) YES (16) IRSwT (17) IntTRSCompressionProof [EQUIVALENT, 27 ms] (18) IRSwT (19) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms] (20) IRSwT (21) TempFilterProof [SOUND, 24 ms] (22) IntTRS (23) PolynomialOrderProcessor [EQUIVALENT, 0 ms] (24) IntTRS (25) RankingReductionPairProof [EQUIVALENT, 0 ms] (26) YES (27) IRSwT (28) IntTRSCompressionProof [EQUIVALENT, 23 ms] (29) IRSwT (30) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms] (31) IRSwT (32) TempFilterProof [SOUND, 58 ms] (33) IntTRS (34) RankingReductionPairProof [EQUIVALENT, 18 ms] (35) IntTRS (36) RankingReductionPairProof [EQUIVALENT, 0 ms] (37) IntTRS (38) RankingReductionPairProof [EQUIVALENT, 0 ms] (39) IntTRS (40) PolynomialOrderProcessor [EQUIVALENT, 0 ms] (41) YES ---------------------------------------- (0) Obligation: Rules: l0(Index15HAT0, Inner14HAT0, InnerIndex6HAT0, InnerIndex9HAT0, Outer13HAT0, OuterIndex5HAT0, OuterIndex8HAT0, SeedHAT0, __const_20HAT0, ret_RandomInteger16HAT0, ret_RandomInteger17HAT0) -> l1(Index15HATpost, Inner14HATpost, InnerIndex6HATpost, InnerIndex9HATpost, Outer13HATpost, OuterIndex5HATpost, OuterIndex8HATpost, SeedHATpost, __const_20HATpost, ret_RandomInteger16HATpost, ret_RandomInteger17HATpost) :|: ret_RandomInteger17HAT0 = ret_RandomInteger17HATpost && ret_RandomInteger16HAT0 = ret_RandomInteger16HATpost && __const_20HAT0 = __const_20HATpost && SeedHAT0 = SeedHATpost && OuterIndex8HAT0 = OuterIndex8HATpost && OuterIndex5HAT0 = OuterIndex5HATpost && Outer13HAT0 = Outer13HATpost && InnerIndex9HAT0 = InnerIndex9HATpost && InnerIndex6HAT0 = InnerIndex6HATpost && Inner14HAT0 = Inner14HATpost && Index15HAT0 = Index15HATpost l2(x, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10) -> l3(x11, x12, x13, x14, x15, x16, x17, x18, x19, x20, x21) :|: x10 = x21 && x9 = x20 && x8 = x19 && x7 = x18 && x6 = x17 && x5 = x16 && x4 = x15 && x3 = x14 && x2 = x13 && x1 = x12 && x = x11 l4(x22, x23, x24, x25, x26, x27, x28, x29, x30, x31, x32) -> l5(x33, x34, x35, x36, x37, x38, x39, x40, x41, x42, x43) :|: x32 = x43 && x31 = x42 && x30 = x41 && x29 = x40 && x28 = x39 && x27 = x38 && x26 = x37 && x25 = x36 && x24 = x35 && x23 = x34 && x22 = x33 l6(x44, x45, x46, x47, x48, x49, x50, x51, x52, x53, x54) -> l7(x55, x56, x57, x58, x59, x60, x61, x62, x63, x64, x65) :|: x54 = x65 && x53 = x64 && x52 = x63 && x51 = x62 && x50 = x61 && x49 = x60 && x48 = x59 && x47 = x58 && x46 = x57 && x44 = x55 && x56 = 1 + x45 && x52 <= x44 l6(x66, x67, x68, x69, x70, x71, x72, x73, x74, x75, x76) -> l8(x77, x78, x79, x80, x81, x82, x83, x84, x85, x86, x87) :|: x76 = x87 && x75 = x86 && x74 = x85 && x73 = x84 && x72 = x83 && x71 = x82 && x70 = x81 && x69 = x80 && x68 = x79 && x67 = x78 && x77 = 1 + x66 && 1 + x66 <= x74 l9(x88, x89, x90, x91, x92, x93, x94, x95, x96, x97, x98) -> l10(x99, x100, x101, x102, x103, x104, x105, x106, x107, x108, x109) :|: x98 = x109 && x97 = x108 && x96 = x107 && x95 = x106 && x94 = x105 && x93 = x104 && x91 = x102 && x90 = x101 && x89 = x100 && x88 = x99 && x103 = 1 + x92 && x96 <= x89 l9(x110, x111, x112, x113, x114, x115, x116, x117, x118, x119, x120) -> l8(x121, x122, x123, x124, x125, x126, x127, x128, x129, x130, x131) :|: x120 = x131 && x119 = x130 && x118 = x129 && x117 = x128 && x116 = x127 && x115 = x126 && x114 = x125 && x113 = x124 && x112 = x123 && x111 = x122 && x121 = 0 && 1 + x111 <= x118 l11(x132, x133, x134, x135, x136, x137, x138, x139, x140, x141, x142) -> l12(x143, x144, x145, x146, x147, x148, x149, x150, x151, x152, x153) :|: x142 = x153 && x141 = x152 && x140 = x151 && x139 = x150 && x138 = x149 && x137 = x148 && x136 = x147 && x135 = x146 && x134 = x145 && x133 = x144 && x132 = x143 && x140 <= x136 l11(x154, x155, x156, x157, x158, x159, x160, x161, x162, x163, x164) -> l7(x165, x166, x167, x168, x169, x170, x171, x172, x173, x174, x175) :|: x164 = x175 && x163 = x174 && x162 = x173 && x161 = x172 && x160 = x171 && x159 = x170 && x158 = x169 && x157 = x168 && x156 = x167 && x154 = x165 && x166 = 0 && 1 + x158 <= x162 l13(x176, x177, x178, x179, x180, x181, x182, x183, x184, x185, x186) -> l14(x187, x188, x189, x190, x191, x192, x193, x194, x195, x196, x197) :|: x186 = x197 && x185 = x196 && x184 = x195 && x183 = x194 && x182 = x193 && x181 = x192 && x180 = x191 && x179 = x190 && x178 = x189 && x177 = x188 && x176 = x187 l10(x198, x199, x200, x201, x202, x203, x204, x205, x206, x207, x208) -> l11(x209, x210, x211, x212, x213, x214, x215, x216, x217, x218, x219) :|: x208 = x219 && x207 = x218 && x206 = x217 && x205 = x216 && x204 = x215 && x203 = x214 && x202 = x213 && x201 = x212 && x200 = x211 && x199 = x210 && x198 = x209 l14(x220, x221, x222, x223, x224, x225, x226, x227, x228, x229, x230) -> l4(x231, x232, x233, x234, x235, x236, x237, x238, x239, x240, x241) :|: x230 = x241 && x229 = x240 && x228 = x239 && x227 = x238 && x225 = x236 && x224 = x235 && x223 = x234 && x222 = x233 && x221 = x232 && x220 = x231 && x237 = 1 + x226 && x228 <= x223 l14(x242, x243, x244, x245, x246, x247, x248, x249, x250, x251, x252) -> l13(x253, x254, x255, x256, x257, x258, x259, x260, x261, x262, x263) :|: x251 = x262 && x250 = x261 && x248 = x259 && x247 = x258 && x246 = x257 && x244 = x255 && x243 = x254 && x242 = x253 && x256 = 1 + x245 && x263 = x260 && x260 = x260 && 1 + x245 <= x250 l5(x264, x265, x266, x267, x268, x269, x270, x271, x272, x273, x274) -> l10(x275, x276, x277, x278, x279, x280, x281, x282, x283, x284, x285) :|: x274 = x285 && x273 = x284 && x272 = x283 && x271 = x282 && x270 = x281 && x269 = x280 && x267 = x278 && x266 = x277 && x265 = x276 && x264 = x275 && x279 = 0 && x272 <= x270 l5(x286, x287, x288, x289, x290, x291, x292, x293, x294, x295, x296) -> l13(x297, x298, x299, x300, x301, x302, x303, x304, x305, x306, x307) :|: x296 = x307 && x295 = x306 && x294 = x305 && x293 = x304 && x292 = x303 && x291 = x302 && x290 = x301 && x288 = x299 && x287 = x298 && x286 = x297 && x300 = 0 && 1 + x292 <= x294 l7(x308, x309, x310, x311, x312, x313, x314, x315, x316, x317, x318) -> l9(x319, x320, x321, x322, x323, x324, x325, x326, x327, x328, x329) :|: x318 = x329 && x317 = x328 && x316 = x327 && x315 = x326 && x314 = x325 && x313 = x324 && x312 = x323 && x311 = x322 && x310 = x321 && x309 = x320 && x308 = x319 l8(x330, x331, x332, x333, x334, x335, x336, x337, x338, x339, x340) -> l6(x341, x342, x343, x344, x345, x346, x347, x348, x349, x350, x351) :|: x340 = x351 && x339 = x350 && x338 = x349 && x337 = x348 && x336 = x347 && x335 = x346 && x334 = x345 && x333 = x344 && x332 = x343 && x331 = x342 && x330 = x341 l3(x352, x353, x354, x355, x356, x357, x358, x359, x360, x361, x362) -> l0(x363, x364, x365, x366, x367, x368, x369, x370, x371, x372, x373) :|: x362 = x373 && x361 = x372 && x360 = x371 && x359 = x370 && x358 = x369 && x356 = x367 && x355 = x366 && x354 = x365 && x353 = x364 && x352 = x363 && x368 = 1 + x357 && x360 <= x354 l3(x374, x375, x376, x377, x378, x379, x380, x381, x382, x383, x384) -> l2(x385, x386, x387, x388, x389, x390, x391, x392, x393, x394, x395) :|: x384 = x395 && x382 = x393 && x380 = x391 && x379 = x390 && x378 = x389 && x377 = x388 && x375 = x386 && x374 = x385 && x387 = 1 + x376 && x394 = x392 && x392 = x392 && 1 + x376 <= x382 l1(x396, x397, x398, x399, x400, x401, x402, x403, x404, x405, x406) -> l4(x407, x408, x409, x410, x411, x412, x413, x414, x415, x416, x417) :|: x406 = x417 && x405 = x416 && x404 = x415 && x403 = x414 && x401 = x412 && x400 = x411 && x399 = x410 && x398 = x409 && x397 = x408 && x396 = x407 && x413 = 0 && x404 <= x401 l1(x418, x419, x420, x421, x422, x423, x424, x425, x426, x427, x428) -> l2(x429, x430, x431, x432, x433, x434, x435, x436, x437, x438, x439) :|: x428 = x439 && x427 = x438 && x426 = x437 && x425 = x436 && x424 = x435 && x423 = x434 && x422 = x433 && x421 = x432 && x419 = x430 && x418 = x429 && x431 = 0 && 1 + x423 <= x426 l15(x440, x441, x442, x443, x444, x445, x446, x447, x448, x449, x450) -> l0(x451, x452, x453, x454, x455, x456, x457, x458, x459, x460, x461) :|: x450 = x461 && x449 = x460 && x448 = x459 && x446 = x457 && x444 = x455 && x443 = x454 && x442 = x453 && x441 = x452 && x440 = x451 && x456 = 0 && x458 = 0 l16(x462, x463, x464, x465, x466, x467, x468, x469, x470, x471, x472) -> l15(x473, x474, x475, x476, x477, x478, x479, x480, x481, x482, x483) :|: x472 = x483 && x471 = x482 && x470 = x481 && x469 = x480 && x468 = x479 && x467 = x478 && x466 = x477 && x465 = x476 && x464 = x475 && x463 = x474 && x462 = x473 Start term: l16(Index15HAT0, Inner14HAT0, InnerIndex6HAT0, InnerIndex9HAT0, Outer13HAT0, OuterIndex5HAT0, OuterIndex8HAT0, SeedHAT0, __const_20HAT0, ret_RandomInteger16HAT0, ret_RandomInteger17HAT0) ---------------------------------------- (1) IRSFormatTransformerProof (EQUIVALENT) Reformatted IRS to match normalized format (transformed away non-linear left-hand sides, !=, / and %). ---------------------------------------- (2) Obligation: Rules: l0(Index15HAT0, Inner14HAT0, InnerIndex6HAT0, InnerIndex9HAT0, Outer13HAT0, OuterIndex5HAT0, OuterIndex8HAT0, SeedHAT0, __const_20HAT0, ret_RandomInteger16HAT0, ret_RandomInteger17HAT0) -> l1(Index15HATpost, Inner14HATpost, InnerIndex6HATpost, InnerIndex9HATpost, Outer13HATpost, OuterIndex5HATpost, OuterIndex8HATpost, SeedHATpost, __const_20HATpost, ret_RandomInteger16HATpost, ret_RandomInteger17HATpost) :|: ret_RandomInteger17HAT0 = ret_RandomInteger17HATpost && ret_RandomInteger16HAT0 = ret_RandomInteger16HATpost && __const_20HAT0 = __const_20HATpost && SeedHAT0 = SeedHATpost && OuterIndex8HAT0 = OuterIndex8HATpost && OuterIndex5HAT0 = OuterIndex5HATpost && Outer13HAT0 = Outer13HATpost && InnerIndex9HAT0 = InnerIndex9HATpost && InnerIndex6HAT0 = InnerIndex6HATpost && Inner14HAT0 = Inner14HATpost && Index15HAT0 = Index15HATpost l2(x, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10) -> l3(x11, x12, x13, x14, x15, x16, x17, x18, x19, x20, x21) :|: x10 = x21 && x9 = x20 && x8 = x19 && x7 = x18 && x6 = x17 && x5 = x16 && x4 = x15 && x3 = x14 && x2 = x13 && x1 = x12 && x = x11 l4(x22, x23, x24, x25, x26, x27, x28, x29, x30, x31, x32) -> l5(x33, x34, x35, x36, x37, x38, x39, x40, x41, x42, x43) :|: x32 = x43 && x31 = x42 && x30 = x41 && x29 = x40 && x28 = x39 && x27 = x38 && x26 = x37 && x25 = x36 && x24 = x35 && x23 = x34 && x22 = x33 l6(x44, x45, x46, x47, x48, x49, x50, x51, x52, x53, x54) -> l7(x55, x56, x57, x58, x59, x60, x61, x62, x63, x64, x65) :|: x54 = x65 && x53 = x64 && x52 = x63 && x51 = x62 && x50 = x61 && x49 = x60 && x48 = x59 && x47 = x58 && x46 = x57 && x44 = x55 && x56 = 1 + x45 && x52 <= x44 l6(x66, x67, x68, x69, x70, x71, x72, x73, x74, x75, x76) -> l8(x77, x78, x79, x80, x81, x82, x83, x84, x85, x86, x87) :|: x76 = x87 && x75 = x86 && x74 = x85 && x73 = x84 && x72 = x83 && x71 = x82 && x70 = x81 && x69 = x80 && x68 = x79 && x67 = x78 && x77 = 1 + x66 && 1 + x66 <= x74 l9(x88, x89, x90, x91, x92, x93, x94, x95, x96, x97, x98) -> l10(x99, x100, x101, x102, x103, x104, x105, x106, x107, x108, x109) :|: x98 = x109 && x97 = x108 && x96 = x107 && x95 = x106 && x94 = x105 && x93 = x104 && x91 = x102 && x90 = x101 && x89 = x100 && x88 = x99 && x103 = 1 + x92 && x96 <= x89 l9(x110, x111, x112, x113, x114, x115, x116, x117, x118, x119, x120) -> l8(x121, x122, x123, x124, x125, x126, x127, x128, x129, x130, x131) :|: x120 = x131 && x119 = x130 && x118 = x129 && x117 = x128 && x116 = x127 && x115 = x126 && x114 = x125 && x113 = x124 && x112 = x123 && x111 = x122 && x121 = 0 && 1 + x111 <= x118 l11(x132, x133, x134, x135, x136, x137, x138, x139, x140, x141, x142) -> l12(x143, x144, x145, x146, x147, x148, x149, x150, x151, x152, x153) :|: x142 = x153 && x141 = x152 && x140 = x151 && x139 = x150 && x138 = x149 && x137 = x148 && x136 = x147 && x135 = x146 && x134 = x145 && x133 = x144 && x132 = x143 && x140 <= x136 l11(x154, x155, x156, x157, x158, x159, x160, x161, x162, x163, x164) -> l7(x165, x166, x167, x168, x169, x170, x171, x172, x173, x174, x175) :|: x164 = x175 && x163 = x174 && x162 = x173 && x161 = x172 && x160 = x171 && x159 = x170 && x158 = x169 && x157 = x168 && x156 = x167 && x154 = x165 && x166 = 0 && 1 + x158 <= x162 l13(x176, x177, x178, x179, x180, x181, x182, x183, x184, x185, x186) -> l14(x187, x188, x189, x190, x191, x192, x193, x194, x195, x196, x197) :|: x186 = x197 && x185 = x196 && x184 = x195 && x183 = x194 && x182 = x193 && x181 = x192 && x180 = x191 && x179 = x190 && x178 = x189 && x177 = x188 && x176 = x187 l10(x198, x199, x200, x201, x202, x203, x204, x205, x206, x207, x208) -> l11(x209, x210, x211, x212, x213, x214, x215, x216, x217, x218, x219) :|: x208 = x219 && x207 = x218 && x206 = x217 && x205 = x216 && x204 = x215 && x203 = x214 && x202 = x213 && x201 = x212 && x200 = x211 && x199 = x210 && x198 = x209 l14(x220, x221, x222, x223, x224, x225, x226, x227, x228, x229, x230) -> l4(x231, x232, x233, x234, x235, x236, x237, x238, x239, x240, x241) :|: x230 = x241 && x229 = x240 && x228 = x239 && x227 = x238 && x225 = x236 && x224 = x235 && x223 = x234 && x222 = x233 && x221 = x232 && x220 = x231 && x237 = 1 + x226 && x228 <= x223 l14(x242, x243, x244, x245, x246, x247, x248, x249, x250, x251, x252) -> l13(x253, x254, x255, x256, x257, x258, x259, x260, x261, x262, x263) :|: x251 = x262 && x250 = x261 && x248 = x259 && x247 = x258 && x246 = x257 && x244 = x255 && x243 = x254 && x242 = x253 && x256 = 1 + x245 && x263 = x260 && x260 = x260 && 1 + x245 <= x250 l5(x264, x265, x266, x267, x268, x269, x270, x271, x272, x273, x274) -> l10(x275, x276, x277, x278, x279, x280, x281, x282, x283, x284, x285) :|: x274 = x285 && x273 = x284 && x272 = x283 && x271 = x282 && x270 = x281 && x269 = x280 && x267 = x278 && x266 = x277 && x265 = x276 && x264 = x275 && x279 = 0 && x272 <= x270 l5(x286, x287, x288, x289, x290, x291, x292, x293, x294, x295, x296) -> l13(x297, x298, x299, x300, x301, x302, x303, x304, x305, x306, x307) :|: x296 = x307 && x295 = x306 && x294 = x305 && x293 = x304 && x292 = x303 && x291 = x302 && x290 = x301 && x288 = x299 && x287 = x298 && x286 = x297 && x300 = 0 && 1 + x292 <= x294 l7(x308, x309, x310, x311, x312, x313, x314, x315, x316, x317, x318) -> l9(x319, x320, x321, x322, x323, x324, x325, x326, x327, x328, x329) :|: x318 = x329 && x317 = x328 && x316 = x327 && x315 = x326 && x314 = x325 && x313 = x324 && x312 = x323 && x311 = x322 && x310 = x321 && x309 = x320 && x308 = x319 l8(x330, x331, x332, x333, x334, x335, x336, x337, x338, x339, x340) -> l6(x341, x342, x343, x344, x345, x346, x347, x348, x349, x350, x351) :|: x340 = x351 && x339 = x350 && x338 = x349 && x337 = x348 && x336 = x347 && x335 = x346 && x334 = x345 && x333 = x344 && x332 = x343 && x331 = x342 && x330 = x341 l3(x352, x353, x354, x355, x356, x357, x358, x359, x360, x361, x362) -> l0(x363, x364, x365, x366, x367, x368, x369, x370, x371, x372, x373) :|: x362 = x373 && x361 = x372 && x360 = x371 && x359 = x370 && x358 = x369 && x356 = x367 && x355 = x366 && x354 = x365 && x353 = x364 && x352 = x363 && x368 = 1 + x357 && x360 <= x354 l3(x374, x375, x376, x377, x378, x379, x380, x381, x382, x383, x384) -> l2(x385, x386, x387, x388, x389, x390, x391, x392, x393, x394, x395) :|: x384 = x395 && x382 = x393 && x380 = x391 && x379 = x390 && x378 = x389 && x377 = x388 && x375 = x386 && x374 = x385 && x387 = 1 + x376 && x394 = x392 && x392 = x392 && 1 + x376 <= x382 l1(x396, x397, x398, x399, x400, x401, x402, x403, x404, x405, x406) -> l4(x407, x408, x409, x410, x411, x412, x413, x414, x415, x416, x417) :|: x406 = x417 && x405 = x416 && x404 = x415 && x403 = x414 && x401 = x412 && x400 = x411 && x399 = x410 && x398 = x409 && x397 = x408 && x396 = x407 && x413 = 0 && x404 <= x401 l1(x418, x419, x420, x421, x422, x423, x424, x425, x426, x427, x428) -> l2(x429, x430, x431, x432, x433, x434, x435, x436, x437, x438, x439) :|: x428 = x439 && x427 = x438 && x426 = x437 && x425 = x436 && x424 = x435 && x423 = x434 && x422 = x433 && x421 = x432 && x419 = x430 && x418 = x429 && x431 = 0 && 1 + x423 <= x426 l15(x440, x441, x442, x443, x444, x445, x446, x447, x448, x449, x450) -> l0(x451, x452, x453, x454, x455, x456, x457, x458, x459, x460, x461) :|: x450 = x461 && x449 = x460 && x448 = x459 && x446 = x457 && x444 = x455 && x443 = x454 && x442 = x453 && x441 = x452 && x440 = x451 && x456 = 0 && x458 = 0 l16(x462, x463, x464, x465, x466, x467, x468, x469, x470, x471, x472) -> l15(x473, x474, x475, x476, x477, x478, x479, x480, x481, x482, x483) :|: x472 = x483 && x471 = x482 && x470 = x481 && x469 = x480 && x468 = x479 && x467 = x478 && x466 = x477 && x465 = x476 && x464 = x475 && x463 = x474 && x462 = x473 Start term: l16(Index15HAT0, Inner14HAT0, InnerIndex6HAT0, InnerIndex9HAT0, Outer13HAT0, OuterIndex5HAT0, OuterIndex8HAT0, SeedHAT0, __const_20HAT0, ret_RandomInteger16HAT0, ret_RandomInteger17HAT0) ---------------------------------------- (3) IRSwTTerminationDigraphProof (EQUIVALENT) Constructed termination digraph! Nodes: (1) l0(Index15HAT0, Inner14HAT0, InnerIndex6HAT0, InnerIndex9HAT0, Outer13HAT0, OuterIndex5HAT0, OuterIndex8HAT0, SeedHAT0, __const_20HAT0, ret_RandomInteger16HAT0, ret_RandomInteger17HAT0) -> l1(Index15HATpost, Inner14HATpost, InnerIndex6HATpost, InnerIndex9HATpost, Outer13HATpost, OuterIndex5HATpost, OuterIndex8HATpost, SeedHATpost, __const_20HATpost, ret_RandomInteger16HATpost, ret_RandomInteger17HATpost) :|: ret_RandomInteger17HAT0 = ret_RandomInteger17HATpost && ret_RandomInteger16HAT0 = ret_RandomInteger16HATpost && __const_20HAT0 = __const_20HATpost && SeedHAT0 = SeedHATpost && OuterIndex8HAT0 = OuterIndex8HATpost && OuterIndex5HAT0 = OuterIndex5HATpost && Outer13HAT0 = Outer13HATpost && InnerIndex9HAT0 = InnerIndex9HATpost && InnerIndex6HAT0 = InnerIndex6HATpost && Inner14HAT0 = Inner14HATpost && Index15HAT0 = Index15HATpost (2) l2(x, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10) -> l3(x11, x12, x13, x14, x15, x16, x17, x18, x19, x20, x21) :|: x10 = x21 && x9 = x20 && x8 = x19 && x7 = x18 && x6 = x17 && x5 = x16 && x4 = x15 && x3 = x14 && x2 = x13 && x1 = x12 && x = x11 (3) l4(x22, x23, x24, x25, x26, x27, x28, x29, x30, x31, x32) -> l5(x33, x34, x35, x36, x37, x38, x39, x40, x41, x42, x43) :|: x32 = x43 && x31 = x42 && x30 = x41 && x29 = x40 && x28 = x39 && x27 = x38 && x26 = x37 && x25 = x36 && x24 = x35 && x23 = x34 && x22 = x33 (4) l6(x44, x45, x46, x47, x48, x49, x50, x51, x52, x53, x54) -> l7(x55, x56, x57, x58, x59, x60, x61, x62, x63, x64, x65) :|: x54 = x65 && x53 = x64 && x52 = x63 && x51 = x62 && x50 = x61 && x49 = x60 && x48 = x59 && x47 = x58 && x46 = x57 && x44 = x55 && x56 = 1 + x45 && x52 <= x44 (5) l6(x66, x67, x68, x69, x70, x71, x72, x73, x74, x75, x76) -> l8(x77, x78, x79, x80, x81, x82, x83, x84, x85, x86, x87) :|: x76 = x87 && x75 = x86 && x74 = x85 && x73 = x84 && x72 = x83 && x71 = x82 && x70 = x81 && x69 = x80 && x68 = x79 && x67 = x78 && x77 = 1 + x66 && 1 + x66 <= x74 (6) l9(x88, x89, x90, x91, x92, x93, x94, x95, x96, x97, x98) -> l10(x99, x100, x101, x102, x103, x104, x105, x106, x107, x108, x109) :|: x98 = x109 && x97 = x108 && x96 = x107 && x95 = x106 && x94 = x105 && x93 = x104 && x91 = x102 && x90 = x101 && x89 = x100 && x88 = x99 && x103 = 1 + x92 && x96 <= x89 (7) l9(x110, x111, x112, x113, x114, x115, x116, x117, x118, x119, x120) -> l8(x121, x122, x123, x124, x125, x126, x127, x128, x129, x130, x131) :|: x120 = x131 && x119 = x130 && x118 = x129 && x117 = x128 && x116 = x127 && x115 = x126 && x114 = x125 && x113 = x124 && x112 = x123 && x111 = x122 && x121 = 0 && 1 + x111 <= x118 (8) l11(x132, x133, x134, x135, x136, x137, x138, x139, x140, x141, x142) -> l12(x143, x144, x145, x146, x147, x148, x149, x150, x151, x152, x153) :|: x142 = x153 && x141 = x152 && x140 = x151 && x139 = x150 && x138 = x149 && x137 = x148 && x136 = x147 && x135 = x146 && x134 = x145 && x133 = x144 && x132 = x143 && x140 <= x136 (9) l11(x154, x155, x156, x157, x158, x159, x160, x161, x162, x163, x164) -> l7(x165, x166, x167, x168, x169, x170, x171, x172, x173, x174, x175) :|: x164 = x175 && x163 = x174 && x162 = x173 && x161 = x172 && x160 = x171 && x159 = x170 && x158 = x169 && x157 = x168 && x156 = x167 && x154 = x165 && x166 = 0 && 1 + x158 <= x162 (10) l13(x176, x177, x178, x179, x180, x181, x182, x183, x184, x185, x186) -> l14(x187, x188, x189, x190, x191, x192, x193, x194, x195, x196, x197) :|: x186 = x197 && x185 = x196 && x184 = x195 && x183 = x194 && x182 = x193 && x181 = x192 && x180 = x191 && x179 = x190 && x178 = x189 && x177 = x188 && x176 = x187 (11) l10(x198, x199, x200, x201, x202, x203, x204, x205, x206, x207, x208) -> l11(x209, x210, x211, x212, x213, x214, x215, x216, x217, x218, x219) :|: x208 = x219 && x207 = x218 && x206 = x217 && x205 = x216 && x204 = x215 && x203 = x214 && x202 = x213 && x201 = x212 && x200 = x211 && x199 = x210 && x198 = x209 (12) l14(x220, x221, x222, x223, x224, x225, x226, x227, x228, x229, x230) -> l4(x231, x232, x233, x234, x235, x236, x237, x238, x239, x240, x241) :|: x230 = x241 && x229 = x240 && x228 = x239 && x227 = x238 && x225 = x236 && x224 = x235 && x223 = x234 && x222 = x233 && x221 = x232 && x220 = x231 && x237 = 1 + x226 && x228 <= x223 (13) l14(x242, x243, x244, x245, x246, x247, x248, x249, x250, x251, x252) -> l13(x253, x254, x255, x256, x257, x258, x259, x260, x261, x262, x263) :|: x251 = x262 && x250 = x261 && x248 = x259 && x247 = x258 && x246 = x257 && x244 = x255 && x243 = x254 && x242 = x253 && x256 = 1 + x245 && x263 = x260 && x260 = x260 && 1 + x245 <= x250 (14) l5(x264, x265, x266, x267, x268, x269, x270, x271, x272, x273, x274) -> l10(x275, x276, x277, x278, x279, x280, x281, x282, x283, x284, x285) :|: x274 = x285 && x273 = x284 && x272 = x283 && x271 = x282 && x270 = x281 && x269 = x280 && x267 = x278 && x266 = x277 && x265 = x276 && x264 = x275 && x279 = 0 && x272 <= x270 (15) l5(x286, x287, x288, x289, x290, x291, x292, x293, x294, x295, x296) -> l13(x297, x298, x299, x300, x301, x302, x303, x304, x305, x306, x307) :|: x296 = x307 && x295 = x306 && x294 = x305 && x293 = x304 && x292 = x303 && x291 = x302 && x290 = x301 && x288 = x299 && x287 = x298 && x286 = x297 && x300 = 0 && 1 + x292 <= x294 (16) l7(x308, x309, x310, x311, x312, x313, x314, x315, x316, x317, x318) -> l9(x319, x320, x321, x322, x323, x324, x325, x326, x327, x328, x329) :|: x318 = x329 && x317 = x328 && x316 = x327 && x315 = x326 && x314 = x325 && x313 = x324 && x312 = x323 && x311 = x322 && x310 = x321 && x309 = x320 && x308 = x319 (17) l8(x330, x331, x332, x333, x334, x335, x336, x337, x338, x339, x340) -> l6(x341, x342, x343, x344, x345, x346, x347, x348, x349, x350, x351) :|: x340 = x351 && x339 = x350 && x338 = x349 && x337 = x348 && x336 = x347 && x335 = x346 && x334 = x345 && x333 = x344 && x332 = x343 && x331 = x342 && x330 = x341 (18) l3(x352, x353, x354, x355, x356, x357, x358, x359, x360, x361, x362) -> l0(x363, x364, x365, x366, x367, x368, x369, x370, x371, x372, x373) :|: x362 = x373 && x361 = x372 && x360 = x371 && x359 = x370 && x358 = x369 && x356 = x367 && x355 = x366 && x354 = x365 && x353 = x364 && x352 = x363 && x368 = 1 + x357 && x360 <= x354 (19) l3(x374, x375, x376, x377, x378, x379, x380, x381, x382, x383, x384) -> l2(x385, x386, x387, x388, x389, x390, x391, x392, x393, x394, x395) :|: x384 = x395 && x382 = x393 && x380 = x391 && x379 = x390 && x378 = x389 && x377 = x388 && x375 = x386 && x374 = x385 && x387 = 1 + x376 && x394 = x392 && x392 = x392 && 1 + x376 <= x382 (20) l1(x396, x397, x398, x399, x400, x401, x402, x403, x404, x405, x406) -> l4(x407, x408, x409, x410, x411, x412, x413, x414, x415, x416, x417) :|: x406 = x417 && x405 = x416 && x404 = x415 && x403 = x414 && x401 = x412 && x400 = x411 && x399 = x410 && x398 = x409 && x397 = x408 && x396 = x407 && x413 = 0 && x404 <= x401 (21) l1(x418, x419, x420, x421, x422, x423, x424, x425, x426, x427, x428) -> l2(x429, x430, x431, x432, x433, x434, x435, x436, x437, x438, x439) :|: x428 = x439 && x427 = x438 && x426 = x437 && x425 = x436 && x424 = x435 && x423 = x434 && x422 = x433 && x421 = x432 && x419 = x430 && x418 = x429 && x431 = 0 && 1 + x423 <= x426 (22) l15(x440, x441, x442, x443, x444, x445, x446, x447, x448, x449, x450) -> l0(x451, x452, x453, x454, x455, x456, x457, x458, x459, x460, x461) :|: x450 = x461 && x449 = x460 && x448 = x459 && x446 = x457 && x444 = x455 && x443 = x454 && x442 = x453 && x441 = x452 && x440 = x451 && x456 = 0 && x458 = 0 (23) l16(x462, x463, x464, x465, x466, x467, x468, x469, x470, x471, x472) -> l15(x473, x474, x475, x476, x477, x478, x479, x480, x481, x482, x483) :|: x472 = x483 && x471 = x482 && x470 = x481 && x469 = x480 && x468 = x479 && x467 = x478 && x466 = x477 && x465 = x476 && x464 = x475 && x463 = x474 && x462 = x473 Arcs: (1) -> (20), (21) (2) -> (18), (19) (3) -> (14), (15) (4) -> (16) (5) -> (17) (6) -> (11) (7) -> (17) (9) -> (16) (10) -> (12), (13) (11) -> (8), (9) (12) -> (3) (13) -> (10) (14) -> (11) (15) -> (10) (16) -> (6), (7) (17) -> (4), (5) (18) -> (1) (19) -> (2) (20) -> (3) (21) -> (2) (22) -> (1) (23) -> (22) This digraph is fully evaluated! ---------------------------------------- (4) Complex Obligation (AND) ---------------------------------------- (5) Obligation: Termination digraph: Nodes: (1) l0(Index15HAT0, Inner14HAT0, InnerIndex6HAT0, InnerIndex9HAT0, Outer13HAT0, OuterIndex5HAT0, OuterIndex8HAT0, SeedHAT0, __const_20HAT0, ret_RandomInteger16HAT0, ret_RandomInteger17HAT0) -> l1(Index15HATpost, Inner14HATpost, InnerIndex6HATpost, InnerIndex9HATpost, Outer13HATpost, OuterIndex5HATpost, OuterIndex8HATpost, SeedHATpost, __const_20HATpost, ret_RandomInteger16HATpost, ret_RandomInteger17HATpost) :|: ret_RandomInteger17HAT0 = ret_RandomInteger17HATpost && ret_RandomInteger16HAT0 = ret_RandomInteger16HATpost && __const_20HAT0 = __const_20HATpost && SeedHAT0 = SeedHATpost && OuterIndex8HAT0 = OuterIndex8HATpost && OuterIndex5HAT0 = OuterIndex5HATpost && Outer13HAT0 = Outer13HATpost && InnerIndex9HAT0 = InnerIndex9HATpost && InnerIndex6HAT0 = InnerIndex6HATpost && Inner14HAT0 = Inner14HATpost && Index15HAT0 = Index15HATpost (2) l3(x352, x353, x354, x355, x356, x357, x358, x359, x360, x361, x362) -> l0(x363, x364, x365, x366, x367, x368, x369, x370, x371, x372, x373) :|: x362 = x373 && x361 = x372 && x360 = x371 && x359 = x370 && x358 = x369 && x356 = x367 && x355 = x366 && x354 = x365 && x353 = x364 && x352 = x363 && x368 = 1 + x357 && x360 <= x354 (3) l2(x, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10) -> l3(x11, x12, x13, x14, x15, x16, x17, x18, x19, x20, x21) :|: x10 = x21 && x9 = x20 && x8 = x19 && x7 = x18 && x6 = x17 && x5 = x16 && x4 = x15 && x3 = x14 && x2 = x13 && x1 = x12 && x = x11 (4) l1(x418, x419, x420, x421, x422, x423, x424, x425, x426, x427, x428) -> l2(x429, x430, x431, x432, x433, x434, x435, x436, x437, x438, x439) :|: x428 = x439 && x427 = x438 && x426 = x437 && x425 = x436 && x424 = x435 && x423 = x434 && x422 = x433 && x421 = x432 && x419 = x430 && x418 = x429 && x431 = 0 && 1 + x423 <= x426 (5) l3(x374, x375, x376, x377, x378, x379, x380, x381, x382, x383, x384) -> l2(x385, x386, x387, x388, x389, x390, x391, x392, x393, x394, x395) :|: x384 = x395 && x382 = x393 && x380 = x391 && x379 = x390 && x378 = x389 && x377 = x388 && x375 = x386 && x374 = x385 && x387 = 1 + x376 && x394 = x392 && x392 = x392 && 1 + x376 <= x382 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: l2(Index15HATpost:0, Inner14HATpost:0, InnerIndex6HATpost:0, InnerIndex9HATpost:0, Outer13HATpost:0, x16:0, OuterIndex8HATpost:0, SeedHATpost:0, __const_20HATpost:0, ret_RandomInteger16HATpost:0, ret_RandomInteger17HATpost:0) -> l2(Index15HATpost:0, Inner14HATpost:0, 0, InnerIndex9HATpost:0, Outer13HATpost:0, 1 + x16:0, OuterIndex8HATpost:0, SeedHATpost:0, __const_20HATpost:0, ret_RandomInteger16HATpost:0, ret_RandomInteger17HATpost:0) :|: __const_20HATpost:0 <= InnerIndex6HATpost:0 && __const_20HATpost:0 >= 1 + (1 + x16:0) l2(x, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10) -> l2(x, x1, 1 + x2, x3, x4, x5, x6, x11, x8, x11, x10) :|: x8 >= 1 + x2 ---------------------------------------- (8) IntTRSUnneededArgumentFilterProof (EQUIVALENT) Some arguments are removed because they cannot influence termination. We removed arguments according to the following replacements: l2(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11) -> l2(x3, x6, x9) ---------------------------------------- (9) Obligation: Rules: l2(InnerIndex6HATpost:0, x16:0, __const_20HATpost:0) -> l2(0, 1 + x16:0, __const_20HATpost:0) :|: __const_20HATpost:0 <= InnerIndex6HATpost:0 && __const_20HATpost:0 >= 1 + (1 + x16:0) l2(x2, x5, x8) -> l2(1 + x2, x5, x8) :|: x8 >= 1 + x2 ---------------------------------------- (10) TempFilterProof (SOUND) Used the following sort dictionary for filtering: l2(VARIABLE, VARIABLE, INTEGER) Replaced non-predefined constructor symbols by 0. ---------------------------------------- (11) Obligation: Rules: l2(InnerIndex6HATpost:0, x16:0, __const_20HATpost:0) -> l2(c, c1, __const_20HATpost:0) :|: c1 = 1 + x16:0 && c = 0 && (__const_20HATpost:0 <= InnerIndex6HATpost:0 && __const_20HATpost:0 >= 1 + (1 + x16:0)) l2(x2, x5, x8) -> l2(c2, x5, x8) :|: c2 = 1 + x2 && x8 >= 1 + x2 ---------------------------------------- (12) PolynomialOrderProcessor (EQUIVALENT) Found the following polynomial interpretation: [l2(x, x1, x2)] = -2 - x1 + x2 The following rules are decreasing: l2(InnerIndex6HATpost:0, x16:0, __const_20HATpost:0) -> l2(c, c1, __const_20HATpost:0) :|: c1 = 1 + x16:0 && c = 0 && (__const_20HATpost:0 <= InnerIndex6HATpost:0 && __const_20HATpost:0 >= 1 + (1 + x16:0)) The following rules are bounded: l2(InnerIndex6HATpost:0, x16:0, __const_20HATpost:0) -> l2(c, c1, __const_20HATpost:0) :|: c1 = 1 + x16:0 && c = 0 && (__const_20HATpost:0 <= InnerIndex6HATpost:0 && __const_20HATpost:0 >= 1 + (1 + x16:0)) ---------------------------------------- (13) Obligation: Rules: l2(x2, x5, x8) -> l2(c2, x5, x8) :|: c2 = 1 + x2 && x8 >= 1 + x2 ---------------------------------------- (14) RankingReductionPairProof (EQUIVALENT) Interpretation: [ l2 ] = l2_3 + -1*l2_1 The following rules are decreasing: l2(x2, x5, x8) -> l2(c2, x5, x8) :|: c2 = 1 + x2 && x8 >= 1 + x2 The following rules are bounded: l2(x2, x5, x8) -> l2(c2, x5, x8) :|: c2 = 1 + x2 && x8 >= 1 + x2 ---------------------------------------- (15) YES ---------------------------------------- (16) Obligation: Termination digraph: Nodes: (1) l4(x22, x23, x24, x25, x26, x27, x28, x29, x30, x31, x32) -> l5(x33, x34, x35, x36, x37, x38, x39, x40, x41, x42, x43) :|: x32 = x43 && x31 = x42 && x30 = x41 && x29 = x40 && x28 = x39 && x27 = x38 && x26 = x37 && x25 = x36 && x24 = x35 && x23 = x34 && x22 = x33 (2) l14(x220, x221, x222, x223, x224, x225, x226, x227, x228, x229, x230) -> l4(x231, x232, x233, x234, x235, x236, x237, x238, x239, x240, x241) :|: x230 = x241 && x229 = x240 && x228 = x239 && x227 = x238 && x225 = x236 && x224 = x235 && x223 = x234 && x222 = x233 && x221 = x232 && x220 = x231 && x237 = 1 + x226 && x228 <= x223 (3) l13(x176, x177, x178, x179, x180, x181, x182, x183, x184, x185, x186) -> l14(x187, x188, x189, x190, x191, x192, x193, x194, x195, x196, x197) :|: x186 = x197 && x185 = x196 && x184 = x195 && x183 = x194 && x182 = x193 && x181 = x192 && x180 = x191 && x179 = x190 && x178 = x189 && x177 = x188 && x176 = x187 (4) l5(x286, x287, x288, x289, x290, x291, x292, x293, x294, x295, x296) -> l13(x297, x298, x299, x300, x301, x302, x303, x304, x305, x306, x307) :|: x296 = x307 && x295 = x306 && x294 = x305 && x293 = x304 && x292 = x303 && x291 = x302 && x290 = x301 && x288 = x299 && x287 = x298 && x286 = x297 && x300 = 0 && 1 + x292 <= x294 (5) l14(x242, x243, x244, x245, x246, x247, x248, x249, x250, x251, x252) -> l13(x253, x254, x255, x256, x257, x258, x259, x260, x261, x262, x263) :|: x251 = x262 && x250 = x261 && x248 = x259 && x247 = x258 && x246 = x257 && x244 = x255 && x243 = x254 && x242 = x253 && x256 = 1 + x245 && x263 = x260 && x260 = x260 && 1 + x245 <= x250 Arcs: (1) -> (4) (2) -> (1) (3) -> (2), (5) (4) -> (3) (5) -> (3) This digraph is fully evaluated! ---------------------------------------- (17) IntTRSCompressionProof (EQUIVALENT) Compressed rules. ---------------------------------------- (18) Obligation: Rules: l13(x176:0, x177:0, x178:0, x179:0, x180:0, x181:0, x182:0, x183:0, x184:0, x185:0, x186:0) -> l13(x176:0, x177:0, x178:0, 0, x180:0, x181:0, 1 + x182:0, x183:0, x184:0, x185:0, x186:0) :|: x184:0 <= x179:0 && x184:0 >= 1 + (1 + x182:0) l13(x, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10) -> l13(x, x1, x2, 1 + x3, x4, x5, x6, x11, x8, x9, x11) :|: x8 >= 1 + x3 ---------------------------------------- (19) IntTRSUnneededArgumentFilterProof (EQUIVALENT) Some arguments are removed because they cannot influence termination. We removed arguments according to the following replacements: l13(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11) -> l13(x4, x7, x9) ---------------------------------------- (20) Obligation: Rules: l13(x179:0, x182:0, x184:0) -> l13(0, 1 + x182:0, x184:0) :|: x184:0 <= x179:0 && x184:0 >= 1 + (1 + x182:0) l13(x3, x6, x8) -> l13(1 + x3, x6, x8) :|: x8 >= 1 + x3 ---------------------------------------- (21) TempFilterProof (SOUND) Used the following sort dictionary for filtering: l13(VARIABLE, VARIABLE, INTEGER) Replaced non-predefined constructor symbols by 0. ---------------------------------------- (22) Obligation: Rules: l13(x179:0, x182:0, x184:0) -> l13(c, c1, x184:0) :|: c1 = 1 + x182:0 && c = 0 && (x184:0 <= x179:0 && x184:0 >= 1 + (1 + x182:0)) l13(x3, x6, x8) -> l13(c2, x6, x8) :|: c2 = 1 + x3 && x8 >= 1 + x3 ---------------------------------------- (23) PolynomialOrderProcessor (EQUIVALENT) Found the following polynomial interpretation: [l13(x, x1, x2)] = -2 - x1 + x2 The following rules are decreasing: l13(x179:0, x182:0, x184:0) -> l13(c, c1, x184:0) :|: c1 = 1 + x182:0 && c = 0 && (x184:0 <= x179:0 && x184:0 >= 1 + (1 + x182:0)) The following rules are bounded: l13(x179:0, x182:0, x184:0) -> l13(c, c1, x184:0) :|: c1 = 1 + x182:0 && c = 0 && (x184:0 <= x179:0 && x184:0 >= 1 + (1 + x182:0)) ---------------------------------------- (24) Obligation: Rules: l13(x3, x6, x8) -> l13(c2, x6, x8) :|: c2 = 1 + x3 && x8 >= 1 + x3 ---------------------------------------- (25) RankingReductionPairProof (EQUIVALENT) Interpretation: [ l13 ] = l13_3 + -1*l13_1 The following rules are decreasing: l13(x3, x6, x8) -> l13(c2, x6, x8) :|: c2 = 1 + x3 && x8 >= 1 + x3 The following rules are bounded: l13(x3, x6, x8) -> l13(c2, x6, x8) :|: c2 = 1 + x3 && x8 >= 1 + x3 ---------------------------------------- (26) YES ---------------------------------------- (27) Obligation: Termination digraph: Nodes: (1) l10(x198, x199, x200, x201, x202, x203, x204, x205, x206, x207, x208) -> l11(x209, x210, x211, x212, x213, x214, x215, x216, x217, x218, x219) :|: x208 = x219 && x207 = x218 && x206 = x217 && x205 = x216 && x204 = x215 && x203 = x214 && x202 = x213 && x201 = x212 && x200 = x211 && x199 = x210 && x198 = x209 (2) l9(x88, x89, x90, x91, x92, x93, x94, x95, x96, x97, x98) -> l10(x99, x100, x101, x102, x103, x104, x105, x106, x107, x108, x109) :|: x98 = x109 && x97 = x108 && x96 = x107 && x95 = x106 && x94 = x105 && x93 = x104 && x91 = x102 && x90 = x101 && x89 = x100 && x88 = x99 && x103 = 1 + x92 && x96 <= x89 (3) l7(x308, x309, x310, x311, x312, x313, x314, x315, x316, x317, x318) -> l9(x319, x320, x321, x322, x323, x324, x325, x326, x327, x328, x329) :|: x318 = x329 && x317 = x328 && x316 = x327 && x315 = x326 && x314 = x325 && x313 = x324 && x312 = x323 && x311 = x322 && x310 = x321 && x309 = x320 && x308 = x319 (4) l11(x154, x155, x156, x157, x158, x159, x160, x161, x162, x163, x164) -> l7(x165, x166, x167, x168, x169, x170, x171, x172, x173, x174, x175) :|: x164 = x175 && x163 = x174 && x162 = x173 && x161 = x172 && x160 = x171 && x159 = x170 && x158 = x169 && x157 = x168 && x156 = x167 && x154 = x165 && x166 = 0 && 1 + x158 <= x162 (5) l6(x44, x45, x46, x47, x48, x49, x50, x51, x52, x53, x54) -> l7(x55, x56, x57, x58, x59, x60, x61, x62, x63, x64, x65) :|: x54 = x65 && x53 = x64 && x52 = x63 && x51 = x62 && x50 = x61 && x49 = x60 && x48 = x59 && x47 = x58 && x46 = x57 && x44 = x55 && x56 = 1 + x45 && x52 <= x44 (6) l8(x330, x331, x332, x333, x334, x335, x336, x337, x338, x339, x340) -> l6(x341, x342, x343, x344, x345, x346, x347, x348, x349, x350, x351) :|: x340 = x351 && x339 = x350 && x338 = x349 && x337 = x348 && x336 = x347 && x335 = x346 && x334 = x345 && x333 = x344 && x332 = x343 && x331 = x342 && x330 = x341 (7) l9(x110, x111, x112, x113, x114, x115, x116, x117, x118, x119, x120) -> l8(x121, x122, x123, x124, x125, x126, x127, x128, x129, x130, x131) :|: x120 = x131 && x119 = x130 && x118 = x129 && x117 = x128 && x116 = x127 && x115 = x126 && x114 = x125 && x113 = x124 && x112 = x123 && x111 = x122 && x121 = 0 && 1 + x111 <= x118 (8) l6(x66, x67, x68, x69, x70, x71, x72, x73, x74, x75, x76) -> l8(x77, x78, x79, x80, x81, x82, x83, x84, x85, x86, x87) :|: x76 = x87 && x75 = x86 && x74 = x85 && x73 = x84 && x72 = x83 && x71 = x82 && x70 = x81 && x69 = x80 && x68 = x79 && x67 = x78 && x77 = 1 + x66 && 1 + x66 <= x74 Arcs: (1) -> (4) (2) -> (1) (3) -> (2), (7) (4) -> (3) (5) -> (3) (6) -> (5), (8) (7) -> (6) (8) -> (6) This digraph is fully evaluated! ---------------------------------------- (28) IntTRSCompressionProof (EQUIVALENT) Compressed rules. ---------------------------------------- (29) Obligation: Rules: l7(x308:0, x122:0, x123:0, x124:0, x125:0, x126:0, x127:0, x128:0, x129:0, x130:0, x131:0) -> l8(0, x122:0, x123:0, x124:0, x125:0, x126:0, x127:0, x128:0, x129:0, x130:0, x131:0) :|: x129:0 >= 1 + x122:0 l8(x330:0, x331:0, x332:0, x333:0, x334:0, x335:0, x336:0, x337:0, x338:0, x339:0, x340:0) -> l8(1 + x330:0, x331:0, x332:0, x333:0, x334:0, x335:0, x336:0, x337:0, x338:0, x339:0, x340:0) :|: x338:0 >= 1 + x330:0 l8(x, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10) -> l7(x, 1 + x1, x2, x3, x4, x5, x6, x7, x8, x9, x10) :|: x8 <= x l7(x165:0, x100:0, x101:0, x102:0, x312:0, x104:0, x105:0, x106:0, x107:0, x108:0, x109:0) -> l7(x165:0, 0, x101:0, x102:0, 1 + x312:0, x104:0, x105:0, x106:0, x107:0, x108:0, x109:0) :|: x107:0 <= x100:0 && x107:0 >= 1 + (1 + x312:0) ---------------------------------------- (30) IntTRSUnneededArgumentFilterProof (EQUIVALENT) Some arguments are removed because they cannot influence termination. We removed arguments according to the following replacements: l7(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11) -> l7(x2, x5, x9) l8(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11) -> l8(x1, x2, x5, x9) ---------------------------------------- (31) Obligation: Rules: l7(x122:0, x125:0, x129:0) -> l8(0, x122:0, x125:0, x129:0) :|: x129:0 >= 1 + x122:0 l8(x330:0, x331:0, x334:0, x338:0) -> l8(1 + x330:0, x331:0, x334:0, x338:0) :|: x338:0 >= 1 + x330:0 l8(x, x1, x4, x8) -> l7(1 + x1, x4, x8) :|: x8 <= x l7(x100:0, x312:0, x107:0) -> l7(0, 1 + x312:0, x107:0) :|: x107:0 <= x100:0 && x107:0 >= 1 + (1 + x312:0) ---------------------------------------- (32) TempFilterProof (SOUND) Used the following sort dictionary for filtering: l7(VARIABLE, VARIABLE, INTEGER) l8(VARIABLE, VARIABLE, VARIABLE, INTEGER) Replaced non-predefined constructor symbols by 0. ---------------------------------------- (33) Obligation: Rules: l7(x122:0, x125:0, x129:0) -> l8(c, x122:0, x125:0, x129:0) :|: c = 0 && x129:0 >= 1 + x122:0 l8(x330:0, x331:0, x334:0, x338:0) -> l8(c1, x331:0, x334:0, x338:0) :|: c1 = 1 + x330:0 && x338:0 >= 1 + x330:0 l8(x, x1, x4, x8) -> l7(c2, x4, x8) :|: c2 = 1 + x1 && x8 <= x l7(x100:0, x312:0, x107:0) -> l7(c3, c4, x107:0) :|: c4 = 1 + x312:0 && c3 = 0 && (x107:0 <= x100:0 && x107:0 >= 1 + (1 + x312:0)) ---------------------------------------- (34) RankingReductionPairProof (EQUIVALENT) Interpretation: [ l7 ] = 3*l7_3 + -3*l7_2 + 1 [ l8 ] = -3*l8_3 + 3*l8_4 + 1 The following rules are decreasing: l7(x100:0, x312:0, x107:0) -> l7(c3, c4, x107:0) :|: c4 = 1 + x312:0 && c3 = 0 && (x107:0 <= x100:0 && x107:0 >= 1 + (1 + x312:0)) The following rules are bounded: l7(x100:0, x312:0, x107:0) -> l7(c3, c4, x107:0) :|: c4 = 1 + x312:0 && c3 = 0 && (x107:0 <= x100:0 && x107:0 >= 1 + (1 + x312:0)) ---------------------------------------- (35) Obligation: Rules: l7(x122:0, x125:0, x129:0) -> l8(c, x122:0, x125:0, x129:0) :|: c = 0 && x129:0 >= 1 + x122:0 l8(x330:0, x331:0, x334:0, x338:0) -> l8(c1, x331:0, x334:0, x338:0) :|: c1 = 1 + x330:0 && x338:0 >= 1 + x330:0 l8(x, x1, x4, x8) -> l7(c2, x4, x8) :|: c2 = 1 + x1 && x8 <= x ---------------------------------------- (36) RankingReductionPairProof (EQUIVALENT) Interpretation: [ l7 ] = 3*l7_3 + -3*l7_1 [ l8 ] = -3*l8_2 + 3*l8_4 + -1 The following rules are decreasing: l7(x122:0, x125:0, x129:0) -> l8(c, x122:0, x125:0, x129:0) :|: c = 0 && x129:0 >= 1 + x122:0 l8(x, x1, x4, x8) -> l7(c2, x4, x8) :|: c2 = 1 + x1 && x8 <= x The following rules are bounded: l7(x122:0, x125:0, x129:0) -> l8(c, x122:0, x125:0, x129:0) :|: c = 0 && x129:0 >= 1 + x122:0 ---------------------------------------- (37) Obligation: Rules: l8(x330:0, x331:0, x334:0, x338:0) -> l8(c1, x331:0, x334:0, x338:0) :|: c1 = 1 + x330:0 && x338:0 >= 1 + x330:0 l8(x, x1, x4, x8) -> l7(c2, x4, x8) :|: c2 = 1 + x1 && x8 <= x ---------------------------------------- (38) RankingReductionPairProof (EQUIVALENT) Interpretation: [ l8 ] = 0 [ l7 ] = -1 The following rules are decreasing: l8(x, x1, x4, x8) -> l7(c2, x4, x8) :|: c2 = 1 + x1 && x8 <= x The following rules are bounded: l8(x330:0, x331:0, x334:0, x338:0) -> l8(c1, x331:0, x334:0, x338:0) :|: c1 = 1 + x330:0 && x338:0 >= 1 + x330:0 l8(x, x1, x4, x8) -> l7(c2, x4, x8) :|: c2 = 1 + x1 && x8 <= x ---------------------------------------- (39) Obligation: Rules: l8(x330:0, x331:0, x334:0, x338:0) -> l8(c1, x331:0, x334:0, x338:0) :|: c1 = 1 + x330:0 && x338:0 >= 1 + x330:0 ---------------------------------------- (40) PolynomialOrderProcessor (EQUIVALENT) Found the following polynomial interpretation: [l8(x, x1, x2, x3)] = -x + x3 The following rules are decreasing: l8(x330:0, x331:0, x334:0, x338:0) -> l8(c1, x331:0, x334:0, x338:0) :|: c1 = 1 + x330:0 && x338:0 >= 1 + x330:0 The following rules are bounded: l8(x330:0, x331:0, x334:0, x338:0) -> l8(c1, x331:0, x334:0, x338:0) :|: c1 = 1 + x330:0 && x338:0 >= 1 + x330:0 ---------------------------------------- (41) YES