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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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, 26.2 s]
(4) AND
    (5) IRSwT
        (6) IntTRSCompressionProof [EQUIVALENT, 51 ms]
        (7) IRSwT
        (8) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms]
        (9) IRSwT
        (10) TempFilterProof [SOUND, 47 ms]
        (11) IntTRS
        (12) RankingReductionPairProof [EQUIVALENT, 0 ms]
        (13) IntTRS
        (14) RankingReductionPairProof [EQUIVALENT, 0 ms]
        (15) YES
    (16) IRSwT
        (17) IntTRSCompressionProof [EQUIVALENT, 22 ms]
        (18) IRSwT
        (19) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms]
        (20) IRSwT
        (21) TempFilterProof [SOUND, 69 ms]
        (22) IntTRS
        (23) RankingReductionPairProof [EQUIVALENT, 0 ms]
        (24) IntTRS
        (25) RankingReductionPairProof [EQUIVALENT, 0 ms]
        (26) IntTRS
        (27) RankingReductionPairProof [EQUIVALENT, 0 ms]
        (28) IntTRS
        (29) RankingReductionPairProof [EQUIVALENT, 0 ms]
        (30) YES


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

(0)
Obligation:
Rules:
l0(nDimHAT0, niHAT0, njHAT0, nkHAT0, tmpHAT0, tmp___0HAT0, tmp___1HAT0) -> l1(nDimHATpost, niHATpost, njHATpost, nkHATpost, tmpHATpost, tmp___0HATpost, tmp___1HATpost) :|: tmp___1HAT0 = tmp___1HATpost && tmp___0HAT0 = tmp___0HATpost && tmpHAT0 = tmpHATpost && nkHAT0 = nkHATpost && njHAT0 = njHATpost && niHAT0 = niHATpost && nDimHAT0 = nDimHATpost
l2(x, x1, x2, x3, x4, x5, x6) -> l3(x7, x8, x9, x10, x11, x12, x13) :|: x6 = x13 && x5 = x12 && x4 = x11 && x3 = x10 && x2 = x9 && x1 = x8 && x = x7
l4(x14, x15, x16, x17, x18, x19, x20) -> l5(x21, x22, x23, x24, x25, x26, x27) :|: x19 = x26 && x18 = x25 && x17 = x24 && x16 = x23 && x15 = x22 && x14 = x21 && x27 = 1
l6(x28, x29, x30, x31, x32, x33, x34) -> l5(x35, x36, x37, x38, x39, x40, x41) :|: x33 = x40 && x32 = x39 && x31 = x38 && x30 = x37 && x29 = x36 && x28 = x35 && x41 = 1
l7(x42, x43, x44, x45, x46, x47, x48) -> l5(x49, x50, x51, x52, x53, x54, x55) :|: x47 = x54 && x46 = x53 && x45 = x52 && x44 = x51 && x43 = x50 && x42 = x49 && x55 = 1
l8(x56, x57, x58, x59, x60, x61, x62) -> l5(x63, x64, x65, x66, x67, x68, x69) :|: x61 = x68 && x60 = x67 && x59 = x66 && x58 = x65 && x57 = x64 && x56 = x63 && x69 = 1
l5(x70, x71, x72, x73, x74, x75, x76) -> l9(x77, x78, x79, x80, x81, x82, x83) :|: x76 = x83 && x75 = x82 && x74 = x81 && x73 = x80 && x72 = x79 && x71 = x78 && x70 = x77
l10(x84, x85, x86, x87, x88, x89, x90) -> l8(x91, x92, x93, x94, x95, x96, x97) :|: x90 = x97 && x89 = x96 && x88 = x95 && x87 = x94 && x86 = x93 && x85 = x92 && x84 = x91
l10(x98, x99, x100, x101, x102, x103, x104) -> l5(x105, x106, x107, x108, x109, x110, x111) :|: x103 = x110 && x102 = x109 && x101 = x108 && x100 = x107 && x99 = x106 && x98 = x105 && x111 = 0
l11(x112, x113, x114, x115, x116, x117, x118) -> l7(x119, x120, x121, x122, x123, x124, x125) :|: x118 = x125 && x117 = x124 && x116 = x123 && x115 = x122 && x114 = x121 && x113 = x120 && x112 = x119
l11(x126, x127, x128, x129, x130, x131, x132) -> l10(x133, x134, x135, x136, x137, x138, x139) :|: x132 = x139 && x131 = x138 && x130 = x137 && x129 = x136 && x128 = x135 && x127 = x134 && x126 = x133
l12(x140, x141, x142, x143, x144, x145, x146) -> l6(x147, x148, x149, x150, x151, x152, x153) :|: x146 = x153 && x145 = x152 && x144 = x151 && x143 = x150 && x142 = x149 && x141 = x148 && x140 = x147
l12(x154, x155, x156, x157, x158, x159, x160) -> l11(x161, x162, x163, x164, x165, x166, x167) :|: x160 = x167 && x159 = x166 && x158 = x165 && x157 = x164 && x156 = x163 && x155 = x162 && x154 = x161
l13(x168, x169, x170, x171, x172, x173, x174) -> l14(x175, x176, x177, x178, x179, x180, x181) :|: x174 = x181 && x173 = x180 && x172 = x179 && x171 = x178 && x170 = x177 && x169 = x176 && x168 = x175
l15(x182, x183, x184, x185, x186, x187, x188) -> l4(x189, x190, x191, x192, x193, x194, x195) :|: x188 = x195 && x187 = x194 && x186 = x193 && x185 = x192 && x184 = x191 && x183 = x190 && x182 = x189
l15(x196, x197, x198, x199, x200, x201, x202) -> l12(x203, x204, x205, x206, x207, x208, x209) :|: x202 = x209 && x201 = x208 && x200 = x207 && x199 = x206 && x198 = x205 && x197 = x204 && x196 = x203
l16(x210, x211, x212, x213, x214, x215, x216) -> l17(x217, x218, x219, x220, x221, x222, x223) :|: x216 = x223 && x215 = x222 && x214 = x221 && x213 = x220 && x211 = x218 && x210 = x217 && x219 = 1 + x212 && x210 <= x213
l16(x224, x225, x226, x227, x228, x229, x230) -> l18(x231, x232, x233, x234, x235, x236, x237) :|: x230 = x237 && x229 = x236 && x228 = x235 && x226 = x233 && x225 = x232 && x224 = x231 && x234 = 1 + x227 && 1 + x227 <= x224
l17(x238, x239, x240, x241, x242, x243, x244) -> l19(x245, x246, x247, x248, x249, x250, x251) :|: x244 = x251 && x243 = x250 && x242 = x249 && x241 = x248 && x240 = x247 && x239 = x246 && x238 = x245
l19(x252, x253, x254, x255, x256, x257, x258) -> l13(x259, x260, x261, x262, x263, x264, x265) :|: x258 = x265 && x257 = x264 && x256 = x263 && x255 = x262 && x254 = x261 && x252 = x259 && x260 = 1 + x253 && x252 <= x254
l19(x266, x267, x268, x269, x270, x271, x272) -> l18(x273, x274, x275, x276, x277, x278, x279) :|: x272 = x279 && x271 = x278 && x270 = x277 && x268 = x275 && x267 = x274 && x266 = x273 && x276 = 0 && 1 + x268 <= x266
l14(x280, x281, x282, x283, x284, x285, x286) -> l15(x287, x288, x289, x290, x291, x292, x293) :|: x286 = x293 && x285 = x292 && x284 = x291 && x283 = x290 && x282 = x289 && x281 = x288 && x280 = x287 && x280 <= x281
l14(x294, x295, x296, x297, x298, x299, x300) -> l17(x301, x302, x303, x304, x305, x306, x307) :|: x300 = x307 && x299 = x306 && x298 = x305 && x297 = x304 && x295 = x302 && x294 = x301 && x303 = 0 && 1 + x295 <= x294
l18(x308, x309, x310, x311, x312, x313, x314) -> l16(x315, x316, x317, x318, x319, x320, x321) :|: x314 = x321 && x313 = x320 && x312 = x319 && x311 = x318 && x310 = x317 && x309 = x316 && x308 = x315
l3(x322, x323, x324, x325, x326, x327, x328) -> l0(x329, x330, x331, x332, x333, x334, x335) :|: x328 = x335 && x327 = x334 && x326 = x333 && x325 = x332 && x324 = x331 && x322 = x329 && x330 = 1 + x323 && x322 <= x324
l3(x336, x337, x338, x339, x340, x341, x342) -> l2(x343, x344, x345, x346, x347, x348, x349) :|: x342 = x349 && x341 = x348 && x340 = x347 && x339 = x346 && x337 = x344 && x336 = x343 && x345 = 1 + x338 && 1 + x338 <= x336
l1(x350, x351, x352, x353, x354, x355, x356) -> l13(x357, x358, x359, x360, x361, x362, x363) :|: x356 = x363 && x355 = x362 && x354 = x361 && x353 = x360 && x352 = x359 && x350 = x357 && x358 = 0 && x350 <= x351
l1(x364, x365, x366, x367, x368, x369, x370) -> l2(x371, x372, x373, x374, x375, x376, x377) :|: x370 = x377 && x369 = x376 && x368 = x375 && x367 = x374 && x365 = x372 && x364 = x371 && x373 = 0 && 1 + x365 <= x364
l20(x378, x379, x380, x381, x382, x383, x384) -> l0(x385, x386, x387, x388, x389, x390, x391) :|: x384 = x391 && x381 = x388 && x380 = x387 && x386 = 0 && x390 = x390 && x389 = x389 && x385 = 2
l21(x392, x393, x394, x395, x396, x397, x398) -> l20(x399, x400, x401, x402, x403, x404, x405) :|: x398 = x405 && x397 = x404 && x396 = x403 && x395 = x402 && x394 = x401 && x393 = x400 && x392 = x399
Start term: l21(nDimHAT0, niHAT0, njHAT0, nkHAT0, tmpHAT0, tmp___0HAT0, tmp___1HAT0)

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

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

(2)
Obligation:
Rules:
l0(nDimHAT0, niHAT0, njHAT0, nkHAT0, tmpHAT0, tmp___0HAT0, tmp___1HAT0) -> l1(nDimHATpost, niHATpost, njHATpost, nkHATpost, tmpHATpost, tmp___0HATpost, tmp___1HATpost) :|: tmp___1HAT0 = tmp___1HATpost && tmp___0HAT0 = tmp___0HATpost && tmpHAT0 = tmpHATpost && nkHAT0 = nkHATpost && njHAT0 = njHATpost && niHAT0 = niHATpost && nDimHAT0 = nDimHATpost
l2(x, x1, x2, x3, x4, x5, x6) -> l3(x7, x8, x9, x10, x11, x12, x13) :|: x6 = x13 && x5 = x12 && x4 = x11 && x3 = x10 && x2 = x9 && x1 = x8 && x = x7
l4(x14, x15, x16, x17, x18, x19, x20) -> l5(x21, x22, x23, x24, x25, x26, x27) :|: x19 = x26 && x18 = x25 && x17 = x24 && x16 = x23 && x15 = x22 && x14 = x21 && x27 = 1
l6(x28, x29, x30, x31, x32, x33, x34) -> l5(x35, x36, x37, x38, x39, x40, x41) :|: x33 = x40 && x32 = x39 && x31 = x38 && x30 = x37 && x29 = x36 && x28 = x35 && x41 = 1
l7(x42, x43, x44, x45, x46, x47, x48) -> l5(x49, x50, x51, x52, x53, x54, x55) :|: x47 = x54 && x46 = x53 && x45 = x52 && x44 = x51 && x43 = x50 && x42 = x49 && x55 = 1
l8(x56, x57, x58, x59, x60, x61, x62) -> l5(x63, x64, x65, x66, x67, x68, x69) :|: x61 = x68 && x60 = x67 && x59 = x66 && x58 = x65 && x57 = x64 && x56 = x63 && x69 = 1
l5(x70, x71, x72, x73, x74, x75, x76) -> l9(x77, x78, x79, x80, x81, x82, x83) :|: x76 = x83 && x75 = x82 && x74 = x81 && x73 = x80 && x72 = x79 && x71 = x78 && x70 = x77
l10(x84, x85, x86, x87, x88, x89, x90) -> l8(x91, x92, x93, x94, x95, x96, x97) :|: x90 = x97 && x89 = x96 && x88 = x95 && x87 = x94 && x86 = x93 && x85 = x92 && x84 = x91
l10(x98, x99, x100, x101, x102, x103, x104) -> l5(x105, x106, x107, x108, x109, x110, x111) :|: x103 = x110 && x102 = x109 && x101 = x108 && x100 = x107 && x99 = x106 && x98 = x105 && x111 = 0
l11(x112, x113, x114, x115, x116, x117, x118) -> l7(x119, x120, x121, x122, x123, x124, x125) :|: x118 = x125 && x117 = x124 && x116 = x123 && x115 = x122 && x114 = x121 && x113 = x120 && x112 = x119
l11(x126, x127, x128, x129, x130, x131, x132) -> l10(x133, x134, x135, x136, x137, x138, x139) :|: x132 = x139 && x131 = x138 && x130 = x137 && x129 = x136 && x128 = x135 && x127 = x134 && x126 = x133
l12(x140, x141, x142, x143, x144, x145, x146) -> l6(x147, x148, x149, x150, x151, x152, x153) :|: x146 = x153 && x145 = x152 && x144 = x151 && x143 = x150 && x142 = x149 && x141 = x148 && x140 = x147
l12(x154, x155, x156, x157, x158, x159, x160) -> l11(x161, x162, x163, x164, x165, x166, x167) :|: x160 = x167 && x159 = x166 && x158 = x165 && x157 = x164 && x156 = x163 && x155 = x162 && x154 = x161
l13(x168, x169, x170, x171, x172, x173, x174) -> l14(x175, x176, x177, x178, x179, x180, x181) :|: x174 = x181 && x173 = x180 && x172 = x179 && x171 = x178 && x170 = x177 && x169 = x176 && x168 = x175
l15(x182, x183, x184, x185, x186, x187, x188) -> l4(x189, x190, x191, x192, x193, x194, x195) :|: x188 = x195 && x187 = x194 && x186 = x193 && x185 = x192 && x184 = x191 && x183 = x190 && x182 = x189
l15(x196, x197, x198, x199, x200, x201, x202) -> l12(x203, x204, x205, x206, x207, x208, x209) :|: x202 = x209 && x201 = x208 && x200 = x207 && x199 = x206 && x198 = x205 && x197 = x204 && x196 = x203
l16(x210, x211, x212, x213, x214, x215, x216) -> l17(x217, x218, x219, x220, x221, x222, x223) :|: x216 = x223 && x215 = x222 && x214 = x221 && x213 = x220 && x211 = x218 && x210 = x217 && x219 = 1 + x212 && x210 <= x213
l16(x224, x225, x226, x227, x228, x229, x230) -> l18(x231, x232, x233, x234, x235, x236, x237) :|: x230 = x237 && x229 = x236 && x228 = x235 && x226 = x233 && x225 = x232 && x224 = x231 && x234 = 1 + x227 && 1 + x227 <= x224
l17(x238, x239, x240, x241, x242, x243, x244) -> l19(x245, x246, x247, x248, x249, x250, x251) :|: x244 = x251 && x243 = x250 && x242 = x249 && x241 = x248 && x240 = x247 && x239 = x246 && x238 = x245
l19(x252, x253, x254, x255, x256, x257, x258) -> l13(x259, x260, x261, x262, x263, x264, x265) :|: x258 = x265 && x257 = x264 && x256 = x263 && x255 = x262 && x254 = x261 && x252 = x259 && x260 = 1 + x253 && x252 <= x254
l19(x266, x267, x268, x269, x270, x271, x272) -> l18(x273, x274, x275, x276, x277, x278, x279) :|: x272 = x279 && x271 = x278 && x270 = x277 && x268 = x275 && x267 = x274 && x266 = x273 && x276 = 0 && 1 + x268 <= x266
l14(x280, x281, x282, x283, x284, x285, x286) -> l15(x287, x288, x289, x290, x291, x292, x293) :|: x286 = x293 && x285 = x292 && x284 = x291 && x283 = x290 && x282 = x289 && x281 = x288 && x280 = x287 && x280 <= x281
l14(x294, x295, x296, x297, x298, x299, x300) -> l17(x301, x302, x303, x304, x305, x306, x307) :|: x300 = x307 && x299 = x306 && x298 = x305 && x297 = x304 && x295 = x302 && x294 = x301 && x303 = 0 && 1 + x295 <= x294
l18(x308, x309, x310, x311, x312, x313, x314) -> l16(x315, x316, x317, x318, x319, x320, x321) :|: x314 = x321 && x313 = x320 && x312 = x319 && x311 = x318 && x310 = x317 && x309 = x316 && x308 = x315
l3(x322, x323, x324, x325, x326, x327, x328) -> l0(x329, x330, x331, x332, x333, x334, x335) :|: x328 = x335 && x327 = x334 && x326 = x333 && x325 = x332 && x324 = x331 && x322 = x329 && x330 = 1 + x323 && x322 <= x324
l3(x336, x337, x338, x339, x340, x341, x342) -> l2(x343, x344, x345, x346, x347, x348, x349) :|: x342 = x349 && x341 = x348 && x340 = x347 && x339 = x346 && x337 = x344 && x336 = x343 && x345 = 1 + x338 && 1 + x338 <= x336
l1(x350, x351, x352, x353, x354, x355, x356) -> l13(x357, x358, x359, x360, x361, x362, x363) :|: x356 = x363 && x355 = x362 && x354 = x361 && x353 = x360 && x352 = x359 && x350 = x357 && x358 = 0 && x350 <= x351
l1(x364, x365, x366, x367, x368, x369, x370) -> l2(x371, x372, x373, x374, x375, x376, x377) :|: x370 = x377 && x369 = x376 && x368 = x375 && x367 = x374 && x365 = x372 && x364 = x371 && x373 = 0 && 1 + x365 <= x364
l20(x378, x379, x380, x381, x382, x383, x384) -> l0(x385, x386, x387, x388, x389, x390, x391) :|: x384 = x391 && x381 = x388 && x380 = x387 && x386 = 0 && x390 = x390 && x389 = x389 && x385 = 2
l21(x392, x393, x394, x395, x396, x397, x398) -> l20(x399, x400, x401, x402, x403, x404, x405) :|: x398 = x405 && x397 = x404 && x396 = x403 && x395 = x402 && x394 = x401 && x393 = x400 && x392 = x399
Start term: l21(nDimHAT0, niHAT0, njHAT0, nkHAT0, tmpHAT0, tmp___0HAT0, tmp___1HAT0)

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

(3) IRSwTTerminationDigraphProof (EQUIVALENT)
Constructed termination digraph!
Nodes:
(1) l0(nDimHAT0, niHAT0, njHAT0, nkHAT0, tmpHAT0, tmp___0HAT0, tmp___1HAT0) -> l1(nDimHATpost, niHATpost, njHATpost, nkHATpost, tmpHATpost, tmp___0HATpost, tmp___1HATpost) :|: tmp___1HAT0 = tmp___1HATpost && tmp___0HAT0 = tmp___0HATpost && tmpHAT0 = tmpHATpost && nkHAT0 = nkHATpost && njHAT0 = njHATpost && niHAT0 = niHATpost && nDimHAT0 = nDimHATpost
(2) l2(x, x1, x2, x3, x4, x5, x6) -> l3(x7, x8, x9, x10, x11, x12, x13) :|: x6 = x13 && x5 = x12 && x4 = x11 && x3 = x10 && x2 = x9 && x1 = x8 && x = x7
(3) l4(x14, x15, x16, x17, x18, x19, x20) -> l5(x21, x22, x23, x24, x25, x26, x27) :|: x19 = x26 && x18 = x25 && x17 = x24 && x16 = x23 && x15 = x22 && x14 = x21 && x27 = 1
(4) l6(x28, x29, x30, x31, x32, x33, x34) -> l5(x35, x36, x37, x38, x39, x40, x41) :|: x33 = x40 && x32 = x39 && x31 = x38 && x30 = x37 && x29 = x36 && x28 = x35 && x41 = 1
(5) l7(x42, x43, x44, x45, x46, x47, x48) -> l5(x49, x50, x51, x52, x53, x54, x55) :|: x47 = x54 && x46 = x53 && x45 = x52 && x44 = x51 && x43 = x50 && x42 = x49 && x55 = 1
(6) l8(x56, x57, x58, x59, x60, x61, x62) -> l5(x63, x64, x65, x66, x67, x68, x69) :|: x61 = x68 && x60 = x67 && x59 = x66 && x58 = x65 && x57 = x64 && x56 = x63 && x69 = 1
(7) l5(x70, x71, x72, x73, x74, x75, x76) -> l9(x77, x78, x79, x80, x81, x82, x83) :|: x76 = x83 && x75 = x82 && x74 = x81 && x73 = x80 && x72 = x79 && x71 = x78 && x70 = x77
(8) l10(x84, x85, x86, x87, x88, x89, x90) -> l8(x91, x92, x93, x94, x95, x96, x97) :|: x90 = x97 && x89 = x96 && x88 = x95 && x87 = x94 && x86 = x93 && x85 = x92 && x84 = x91
(9) l10(x98, x99, x100, x101, x102, x103, x104) -> l5(x105, x106, x107, x108, x109, x110, x111) :|: x103 = x110 && x102 = x109 && x101 = x108 && x100 = x107 && x99 = x106 && x98 = x105 && x111 = 0
(10) l11(x112, x113, x114, x115, x116, x117, x118) -> l7(x119, x120, x121, x122, x123, x124, x125) :|: x118 = x125 && x117 = x124 && x116 = x123 && x115 = x122 && x114 = x121 && x113 = x120 && x112 = x119
(11) l11(x126, x127, x128, x129, x130, x131, x132) -> l10(x133, x134, x135, x136, x137, x138, x139) :|: x132 = x139 && x131 = x138 && x130 = x137 && x129 = x136 && x128 = x135 && x127 = x134 && x126 = x133
(12) l12(x140, x141, x142, x143, x144, x145, x146) -> l6(x147, x148, x149, x150, x151, x152, x153) :|: x146 = x153 && x145 = x152 && x144 = x151 && x143 = x150 && x142 = x149 && x141 = x148 && x140 = x147
(13) l12(x154, x155, x156, x157, x158, x159, x160) -> l11(x161, x162, x163, x164, x165, x166, x167) :|: x160 = x167 && x159 = x166 && x158 = x165 && x157 = x164 && x156 = x163 && x155 = x162 && x154 = x161
(14) l13(x168, x169, x170, x171, x172, x173, x174) -> l14(x175, x176, x177, x178, x179, x180, x181) :|: x174 = x181 && x173 = x180 && x172 = x179 && x171 = x178 && x170 = x177 && x169 = x176 && x168 = x175
(15) l15(x182, x183, x184, x185, x186, x187, x188) -> l4(x189, x190, x191, x192, x193, x194, x195) :|: x188 = x195 && x187 = x194 && x186 = x193 && x185 = x192 && x184 = x191 && x183 = x190 && x182 = x189
(16) l15(x196, x197, x198, x199, x200, x201, x202) -> l12(x203, x204, x205, x206, x207, x208, x209) :|: x202 = x209 && x201 = x208 && x200 = x207 && x199 = x206 && x198 = x205 && x197 = x204 && x196 = x203
(17) l16(x210, x211, x212, x213, x214, x215, x216) -> l17(x217, x218, x219, x220, x221, x222, x223) :|: x216 = x223 && x215 = x222 && x214 = x221 && x213 = x220 && x211 = x218 && x210 = x217 && x219 = 1 + x212 && x210 <= x213
(18) l16(x224, x225, x226, x227, x228, x229, x230) -> l18(x231, x232, x233, x234, x235, x236, x237) :|: x230 = x237 && x229 = x236 && x228 = x235 && x226 = x233 && x225 = x232 && x224 = x231 && x234 = 1 + x227 && 1 + x227 <= x224
(19) l17(x238, x239, x240, x241, x242, x243, x244) -> l19(x245, x246, x247, x248, x249, x250, x251) :|: x244 = x251 && x243 = x250 && x242 = x249 && x241 = x248 && x240 = x247 && x239 = x246 && x238 = x245
(20) l19(x252, x253, x254, x255, x256, x257, x258) -> l13(x259, x260, x261, x262, x263, x264, x265) :|: x258 = x265 && x257 = x264 && x256 = x263 && x255 = x262 && x254 = x261 && x252 = x259 && x260 = 1 + x253 && x252 <= x254
(21) l19(x266, x267, x268, x269, x270, x271, x272) -> l18(x273, x274, x275, x276, x277, x278, x279) :|: x272 = x279 && x271 = x278 && x270 = x277 && x268 = x275 && x267 = x274 && x266 = x273 && x276 = 0 && 1 + x268 <= x266
(22) l14(x280, x281, x282, x283, x284, x285, x286) -> l15(x287, x288, x289, x290, x291, x292, x293) :|: x286 = x293 && x285 = x292 && x284 = x291 && x283 = x290 && x282 = x289 && x281 = x288 && x280 = x287 && x280 <= x281
(23) l14(x294, x295, x296, x297, x298, x299, x300) -> l17(x301, x302, x303, x304, x305, x306, x307) :|: x300 = x307 && x299 = x306 && x298 = x305 && x297 = x304 && x295 = x302 && x294 = x301 && x303 = 0 && 1 + x295 <= x294
(24) l18(x308, x309, x310, x311, x312, x313, x314) -> l16(x315, x316, x317, x318, x319, x320, x321) :|: x314 = x321 && x313 = x320 && x312 = x319 && x311 = x318 && x310 = x317 && x309 = x316 && x308 = x315
(25) l3(x322, x323, x324, x325, x326, x327, x328) -> l0(x329, x330, x331, x332, x333, x334, x335) :|: x328 = x335 && x327 = x334 && x326 = x333 && x325 = x332 && x324 = x331 && x322 = x329 && x330 = 1 + x323 && x322 <= x324
(26) l3(x336, x337, x338, x339, x340, x341, x342) -> l2(x343, x344, x345, x346, x347, x348, x349) :|: x342 = x349 && x341 = x348 && x340 = x347 && x339 = x346 && x337 = x344 && x336 = x343 && x345 = 1 + x338 && 1 + x338 <= x336
(27) l1(x350, x351, x352, x353, x354, x355, x356) -> l13(x357, x358, x359, x360, x361, x362, x363) :|: x356 = x363 && x355 = x362 && x354 = x361 && x353 = x360 && x352 = x359 && x350 = x357 && x358 = 0 && x350 <= x351
(28) l1(x364, x365, x366, x367, x368, x369, x370) -> l2(x371, x372, x373, x374, x375, x376, x377) :|: x370 = x377 && x369 = x376 && x368 = x375 && x367 = x374 && x365 = x372 && x364 = x371 && x373 = 0 && 1 + x365 <= x364
(29) l20(x378, x379, x380, x381, x382, x383, x384) -> l0(x385, x386, x387, x388, x389, x390, x391) :|: x384 = x391 && x381 = x388 && x380 = x387 && x386 = 0 && x390 = x390 && x389 = x389 && x385 = 2
(30) l21(x392, x393, x394, x395, x396, x397, x398) -> l20(x399, x400, x401, x402, x403, x404, x405) :|: x398 = x405 && x397 = x404 && x396 = x403 && x395 = x402 && x394 = x401 && x393 = x400 && x392 = x399

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

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

(4)
Complex Obligation (AND)

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

(5)
Obligation:

Termination digraph:
Nodes:
(1) l0(nDimHAT0, niHAT0, njHAT0, nkHAT0, tmpHAT0, tmp___0HAT0, tmp___1HAT0) -> l1(nDimHATpost, niHATpost, njHATpost, nkHATpost, tmpHATpost, tmp___0HATpost, tmp___1HATpost) :|: tmp___1HAT0 = tmp___1HATpost && tmp___0HAT0 = tmp___0HATpost && tmpHAT0 = tmpHATpost && nkHAT0 = nkHATpost && njHAT0 = njHATpost && niHAT0 = niHATpost && nDimHAT0 = nDimHATpost
(2) l3(x322, x323, x324, x325, x326, x327, x328) -> l0(x329, x330, x331, x332, x333, x334, x335) :|: x328 = x335 && x327 = x334 && x326 = x333 && x325 = x332 && x324 = x331 && x322 = x329 && x330 = 1 + x323 && x322 <= x324
(3) l2(x, x1, x2, x3, x4, x5, x6) -> l3(x7, x8, x9, x10, x11, x12, x13) :|: x6 = x13 && x5 = x12 && x4 = x11 && x3 = x10 && x2 = x9 && x1 = x8 && x = x7
(4) l1(x364, x365, x366, x367, x368, x369, x370) -> l2(x371, x372, x373, x374, x375, x376, x377) :|: x370 = x377 && x369 = x376 && x368 = x375 && x367 = x374 && x365 = x372 && x364 = x371 && x373 = 0 && 1 + x365 <= x364
(5) l3(x336, x337, x338, x339, x340, x341, x342) -> l2(x343, x344, x345, x346, x347, x348, x349) :|: x342 = x349 && x341 = x348 && x340 = x347 && x339 = x346 && x337 = x344 && x336 = x343 && x345 = 1 + x338 && 1 + x338 <= x336

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(x343:0, x1:0, x2:0, x10:0, x11:0, x12:0, x13:0) -> l2(x343:0, x1:0, 1 + x2:0, x10:0, x11:0, x12:0, x13:0) :|: x343:0 >= 1 + x2:0
l2(x, x1, x2, x3, x4, x5, x6) -> l2(x, 1 + x1, 0, x3, x4, x5, x6) :|: x2 >= x && x >= 1 + (1 + x1)

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

(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) -> l2(x1, x2, x3)

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

(9)
Obligation:
Rules:
l2(x343:0, x1:0, x2:0) -> l2(x343:0, x1:0, 1 + x2:0) :|: x343:0 >= 1 + x2:0
l2(x, x1, x2) -> l2(x, 1 + x1, 0) :|: x2 >= x && x >= 1 + (1 + x1)

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

(10) TempFilterProof (SOUND)
Used the following sort dictionary for filtering: 
l2(INTEGER, VARIABLE, VARIABLE)
Replaced non-predefined constructor symbols by 0.
----------------------------------------

(11)
Obligation:
Rules:
l2(x343:0, x1:0, x2:0) -> l2(x343:0, x1:0, c) :|: c = 1 + x2:0 && x343:0 >= 1 + x2:0
l2(x, x1, x2) -> l2(x, c1, c2) :|: c2 = 0 && c1 = 1 + x1 && (x2 >= x && x >= 1 + (1 + x1))

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

(12) RankingReductionPairProof (EQUIVALENT)
Interpretation:
[ l2 ] = l2_1 + -1*l2_2 + 1

The following rules are decreasing:
l2(x, x1, x2) -> l2(x, c1, c2) :|: c2 = 0 && c1 = 1 + x1 && (x2 >= x && x >= 1 + (1 + x1))

The following rules are bounded:
l2(x, x1, x2) -> l2(x, c1, c2) :|: c2 = 0 && c1 = 1 + x1 && (x2 >= x && x >= 1 + (1 + x1))


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

(13)
Obligation:
Rules:
l2(x343:0, x1:0, x2:0) -> l2(x343:0, x1:0, c) :|: c = 1 + x2:0 && x343:0 >= 1 + x2:0

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

(14) RankingReductionPairProof (EQUIVALENT)
Interpretation:
[ l2 ] = l2_1 + -1*l2_3

The following rules are decreasing:
l2(x343:0, x1:0, x2:0) -> l2(x343:0, x1:0, c) :|: c = 1 + x2:0 && x343:0 >= 1 + x2:0

The following rules are bounded:
l2(x343:0, x1:0, x2:0) -> l2(x343:0, x1:0, c) :|: c = 1 + x2:0 && x343:0 >= 1 + x2:0


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

(15)
YES

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

(16)
Obligation:

Termination digraph:
Nodes:
(1) l13(x168, x169, x170, x171, x172, x173, x174) -> l14(x175, x176, x177, x178, x179, x180, x181) :|: x174 = x181 && x173 = x180 && x172 = x179 && x171 = x178 && x170 = x177 && x169 = x176 && x168 = x175
(2) l19(x252, x253, x254, x255, x256, x257, x258) -> l13(x259, x260, x261, x262, x263, x264, x265) :|: x258 = x265 && x257 = x264 && x256 = x263 && x255 = x262 && x254 = x261 && x252 = x259 && x260 = 1 + x253 && x252 <= x254
(3) l17(x238, x239, x240, x241, x242, x243, x244) -> l19(x245, x246, x247, x248, x249, x250, x251) :|: x244 = x251 && x243 = x250 && x242 = x249 && x241 = x248 && x240 = x247 && x239 = x246 && x238 = x245
(4) l14(x294, x295, x296, x297, x298, x299, x300) -> l17(x301, x302, x303, x304, x305, x306, x307) :|: x300 = x307 && x299 = x306 && x298 = x305 && x297 = x304 && x295 = x302 && x294 = x301 && x303 = 0 && 1 + x295 <= x294
(5) l16(x210, x211, x212, x213, x214, x215, x216) -> l17(x217, x218, x219, x220, x221, x222, x223) :|: x216 = x223 && x215 = x222 && x214 = x221 && x213 = x220 && x211 = x218 && x210 = x217 && x219 = 1 + x212 && x210 <= x213
(6) l18(x308, x309, x310, x311, x312, x313, x314) -> l16(x315, x316, x317, x318, x319, x320, x321) :|: x314 = x321 && x313 = x320 && x312 = x319 && x311 = x318 && x310 = x317 && x309 = x316 && x308 = x315
(7) l19(x266, x267, x268, x269, x270, x271, x272) -> l18(x273, x274, x275, x276, x277, x278, x279) :|: x272 = x279 && x271 = x278 && x270 = x277 && x268 = x275 && x267 = x274 && x266 = x273 && x276 = 0 && 1 + x268 <= x266
(8) l16(x224, x225, x226, x227, x228, x229, x230) -> l18(x231, x232, x233, x234, x235, x236, x237) :|: x230 = x237 && x229 = x236 && x228 = x235 && x226 = x233 && x225 = x232 && x224 = x231 && x234 = 1 + x227 && 1 + x227 <= x224

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

This digraph is fully evaluated!

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

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

(18)
Obligation:
Rules:
l18(x217:0, x218:0, x310:0, x220:0, x221:0, x222:0, x223:0) -> l17(x217:0, x218:0, 1 + x310:0, x220:0, x221:0, x222:0, x223:0) :|: x220:0 >= x217:0
l17(x238:0, x239:0, x240:0, x241:0, x242:0, x243:0, x244:0) -> l18(x238:0, x239:0, x240:0, 0, x242:0, x243:0, x244:0) :|: x238:0 >= 1 + x240:0
l18(x231:0, x232:0, x233:0, x311:0, x235:0, x236:0, x237:0) -> l18(x231:0, x232:0, x233:0, 1 + x311:0, x235:0, x236:0, x237:0) :|: x231:0 >= 1 + x311:0
l17(x, x1, x2, x3, x4, x5, x6) -> l17(x, 1 + x1, 0, x3, x4, x5, x6) :|: x2 >= x && x >= 1 + (1 + x1)

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

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

   l18(x1, x2, x3, x4, x5, x6, x7) -> l18(x1, x2, x3, x4)
   l17(x1, x2, x3, x4, x5, x6, x7) -> l17(x1, x2, x3)

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

(20)
Obligation:
Rules:
l18(x217:0, x218:0, x310:0, x220:0) -> l17(x217:0, x218:0, 1 + x310:0) :|: x220:0 >= x217:0
l17(x238:0, x239:0, x240:0) -> l18(x238:0, x239:0, x240:0, 0) :|: x238:0 >= 1 + x240:0
l18(x231:0, x232:0, x233:0, x311:0) -> l18(x231:0, x232:0, x233:0, 1 + x311:0) :|: x231:0 >= 1 + x311:0
l17(x, x1, x2) -> l17(x, 1 + x1, 0) :|: x2 >= x && x >= 1 + (1 + x1)

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

(21) TempFilterProof (SOUND)
Used the following sort dictionary for filtering: 
l18(INTEGER, VARIABLE, VARIABLE, VARIABLE)
l17(INTEGER, VARIABLE, VARIABLE)
Replaced non-predefined constructor symbols by 0.
----------------------------------------

(22)
Obligation:
Rules:
l18(x217:0, x218:0, x310:0, x220:0) -> l17(x217:0, x218:0, c) :|: c = 1 + x310:0 && x220:0 >= x217:0
l17(x238:0, x239:0, x240:0) -> l18(x238:0, x239:0, x240:0, c1) :|: c1 = 0 && x238:0 >= 1 + x240:0
l18(x231:0, x232:0, x233:0, x311:0) -> l18(x231:0, x232:0, x233:0, c2) :|: c2 = 1 + x311:0 && x231:0 >= 1 + x311:0
l17(x, x1, x2) -> l17(x, c3, c4) :|: c4 = 0 && c3 = 1 + x1 && (x2 >= x && x >= 1 + (1 + x1))

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

(23) RankingReductionPairProof (EQUIVALENT)
Interpretation:
[ l18 ] = 3*l18_1 + -3*l18_2 + 1
[ l17 ] = 3*l17_1 + -3*l17_2 + 1

The following rules are decreasing:
l17(x, x1, x2) -> l17(x, c3, c4) :|: c4 = 0 && c3 = 1 + x1 && (x2 >= x && x >= 1 + (1 + x1))

The following rules are bounded:
l17(x, x1, x2) -> l17(x, c3, c4) :|: c4 = 0 && c3 = 1 + x1 && (x2 >= x && x >= 1 + (1 + x1))


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

(24)
Obligation:
Rules:
l18(x217:0, x218:0, x310:0, x220:0) -> l17(x217:0, x218:0, c) :|: c = 1 + x310:0 && x220:0 >= x217:0
l17(x238:0, x239:0, x240:0) -> l18(x238:0, x239:0, x240:0, c1) :|: c1 = 0 && x238:0 >= 1 + x240:0
l18(x231:0, x232:0, x233:0, x311:0) -> l18(x231:0, x232:0, x233:0, c2) :|: c2 = 1 + x311:0 && x231:0 >= 1 + x311:0

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

(25) RankingReductionPairProof (EQUIVALENT)
Interpretation:
[ l18 ] = 3*l18_1 + -3*l18_3 + -1
[ l17 ] = 3*l17_1 + -3*l17_3

The following rules are decreasing:
l18(x217:0, x218:0, x310:0, x220:0) -> l17(x217:0, x218:0, c) :|: c = 1 + x310:0 && x220:0 >= x217:0
l17(x238:0, x239:0, x240:0) -> l18(x238:0, x239:0, x240:0, c1) :|: c1 = 0 && x238:0 >= 1 + x240:0

The following rules are bounded:
l17(x238:0, x239:0, x240:0) -> l18(x238:0, x239:0, x240:0, c1) :|: c1 = 0 && x238:0 >= 1 + x240:0


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

(26)
Obligation:
Rules:
l18(x217:0, x218:0, x310:0, x220:0) -> l17(x217:0, x218:0, c) :|: c = 1 + x310:0 && x220:0 >= x217:0
l18(x231:0, x232:0, x233:0, x311:0) -> l18(x231:0, x232:0, x233:0, c2) :|: c2 = 1 + x311:0 && x231:0 >= 1 + x311:0

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

(27) RankingReductionPairProof (EQUIVALENT)
Interpretation:
[ l18 ] = 0
[ l17 ] = -1

The following rules are decreasing:
l18(x217:0, x218:0, x310:0, x220:0) -> l17(x217:0, x218:0, c) :|: c = 1 + x310:0 && x220:0 >= x217:0

The following rules are bounded:
l18(x217:0, x218:0, x310:0, x220:0) -> l17(x217:0, x218:0, c) :|: c = 1 + x310:0 && x220:0 >= x217:0
l18(x231:0, x232:0, x233:0, x311:0) -> l18(x231:0, x232:0, x233:0, c2) :|: c2 = 1 + x311:0 && x231:0 >= 1 + x311:0


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

(28)
Obligation:
Rules:
l18(x231:0, x232:0, x233:0, x311:0) -> l18(x231:0, x232:0, x233:0, c2) :|: c2 = 1 + x311:0 && x231:0 >= 1 + x311:0

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

(29) RankingReductionPairProof (EQUIVALENT)
Interpretation:
[ l18 ] = l18_1 + -1*l18_4

The following rules are decreasing:
l18(x231:0, x232:0, x233:0, x311:0) -> l18(x231:0, x232:0, x233:0, c2) :|: c2 = 1 + x311:0 && x231:0 >= 1 + x311:0

The following rules are bounded:
l18(x231:0, x232:0, x233:0, x311:0) -> l18(x231:0, x232:0, x233:0, c2) :|: c2 = 1 + x311:0 && x231:0 >= 1 + x311:0


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

(30)
YES