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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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, 23.5 s]
(4) AND
    (5) IRSwT
        (6) IntTRSCompressionProof [EQUIVALENT, 0 ms]
        (7) IRSwT
        (8) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms]
        (9) IRSwT
        (10) TempFilterProof [SOUND, 32 ms]
        (11) IntTRS
        (12) RankingReductionPairProof [EQUIVALENT, 13 ms]
        (13) YES
    (14) IRSwT
        (15) IntTRSCompressionProof [EQUIVALENT, 0 ms]
        (16) IRSwT
        (17) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms]
        (18) IRSwT
        (19) TempFilterProof [SOUND, 3 ms]
        (20) IntTRS
        (21) RankingReductionPairProof [EQUIVALENT, 0 ms]
        (22) YES
    (23) IRSwT
        (24) IntTRSCompressionProof [EQUIVALENT, 0 ms]
        (25) IRSwT
        (26) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms]
        (27) IRSwT
        (28) TempFilterProof [SOUND, 2 ms]
        (29) IntTRS
        (30) PolynomialOrderProcessor [EQUIVALENT, 0 ms]
        (31) YES
    (32) IRSwT
        (33) IntTRSCompressionProof [EQUIVALENT, 0 ms]
        (34) IRSwT
        (35) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms]
        (36) IRSwT
        (37) TempFilterProof [SOUND, 8 ms]
        (38) IntTRS
        (39) RankingReductionPairProof [EQUIVALENT, 0 ms]
        (40) YES
    (41) IRSwT
        (42) IntTRSCompressionProof [EQUIVALENT, 0 ms]
        (43) IRSwT
        (44) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms]
        (45) IRSwT
        (46) TempFilterProof [SOUND, 5 ms]
        (47) IntTRS
        (48) RankingReductionPairProof [EQUIVALENT, 3 ms]
        (49) YES
    (50) IRSwT
        (51) IntTRSCompressionProof [EQUIVALENT, 0 ms]
        (52) IRSwT
        (53) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms]
        (54) IRSwT
        (55) TempFilterProof [SOUND, 5 ms]
        (56) IntTRS
        (57) RankingReductionPairProof [EQUIVALENT, 0 ms]
        (58) YES
    (59) IRSwT
        (60) IntTRSCompressionProof [EQUIVALENT, 0 ms]
        (61) IRSwT
        (62) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms]
        (63) IRSwT
        (64) TempFilterProof [SOUND, 13 ms]
        (65) IntTRS
        (66) PolynomialOrderProcessor [EQUIVALENT, 0 ms]
        (67) YES
    (68) IRSwT
        (69) IntTRSCompressionProof [EQUIVALENT, 0 ms]
        (70) IRSwT
        (71) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms]
        (72) IRSwT
        (73) TempFilterProof [SOUND, 12 ms]
        (74) IntTRS
        (75) RankingReductionPairProof [EQUIVALENT, 0 ms]
        (76) YES


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

(0)
Obligation:
Rules:
l0(i11HAT0, i13HAT0, i15HAT0, i17HAT0, i7HAT0, i9HAT0, iHAT0, tmpHAT0, tmp___0HAT0) -> l1(i11HATpost, i13HATpost, i15HATpost, i17HATpost, i7HATpost, i9HATpost, iHATpost, tmpHATpost, tmp___0HATpost) :|: tmp___0HAT0 = tmp___0HATpost && tmpHAT0 = tmpHATpost && i9HAT0 = i9HATpost && i7HAT0 = i7HATpost && i17HAT0 = i17HATpost && i15HAT0 = i15HATpost && i13HAT0 = i13HATpost && i11HAT0 = i11HATpost && iHAT0 = iHATpost
l2(x, x1, x2, x3, x4, x5, x6, x7, x8) -> l3(x9, x10, x11, x12, x13, x14, x15, x16, x17) :|: x8 = x17 && x7 = x16 && x5 = x14 && x4 = x13 && x3 = x12 && x2 = x11 && x1 = x10 && x = x9 && x6 = x15 && 50 <= x6
l2(x18, x19, x20, x21, x22, x23, x24, x25, x26) -> l4(x27, x28, x29, x30, x31, x32, x33, x34, x35) :|: x26 = x35 && x25 = x34 && x23 = x32 && x22 = x31 && x21 = x30 && x20 = x29 && x19 = x28 && x18 = x27 && x33 = 1 + x24 && 1 + x24 <= 50
l5(x36, x37, x38, x39, x40, x41, x42, x43, x44) -> l6(x45, x46, x47, x48, x49, x50, x51, x52, x53) :|: x44 = x53 && x43 = x52 && x41 = x50 && x40 = x49 && x39 = x48 && x38 = x47 && x37 = x46 && x36 = x45 && x42 = x51
l7(x54, x55, x56, x57, x58, x59, x60, x61, x62) -> l4(x63, x64, x65, x66, x67, x68, x69, x70, x71) :|: x62 = x71 && x61 = x70 && x59 = x68 && x58 = x67 && x57 = x66 && x56 = x65 && x55 = x64 && x54 = x63 && x69 = 0 && 50 <= x57
l7(x72, x73, x74, x75, x76, x77, x78, x79, x80) -> l8(x81, x82, x83, x84, x85, x86, x87, x88, x89) :|: x80 = x89 && x79 = x88 && x77 = x86 && x76 = x85 && x74 = x83 && x73 = x82 && x72 = x81 && x78 = x87 && x84 = 1 + x75 && 1 + x75 <= 50
l9(x90, x91, x92, x93, x94, x95, x96, x97, x98) -> l10(x99, x100, x101, x102, x103, x104, x105, x106, x107) :|: x98 = x107 && x97 = x106 && x95 = x104 && x94 = x103 && x93 = x102 && x92 = x101 && x91 = x100 && x90 = x99 && x96 = x105
l11(x108, x109, x110, x111, x112, x113, x114, x115, x116) -> l8(x117, x118, x119, x120, x121, x122, x123, x124, x125) :|: 50 <= x110 && x126 = 0 && x120 = 0 && x114 = x123 && x108 = x117 && x109 = x118 && x110 = x119 && x112 = x121 && x113 = x122 && x115 = x124 && x116 = x125
l11(x127, x128, x129, x130, x131, x132, x133, x134, x135) -> l12(x136, x137, x138, x139, x140, x141, x142, x143, x144) :|: x135 = x144 && x134 = x143 && x132 = x141 && x131 = x140 && x130 = x139 && x128 = x137 && x127 = x136 && x133 = x142 && x138 = 1 + x129 && 1 + x129 <= 50
l13(x145, x146, x147, x148, x149, x150, x151, x152, x153) -> l14(x154, x155, x156, x157, x158, x159, x160, x161, x162) :|: x153 = x162 && x152 = x161 && x150 = x159 && x149 = x158 && x148 = x157 && x147 = x156 && x146 = x155 && x145 = x154 && x151 = x160
l15(x163, x164, x165, x166, x167, x168, x169, x170, x171) -> l12(x172, x173, x174, x175, x176, x177, x178, x179, x180) :|: 50 <= x164 && x181 = 0 && x174 = 0 && x169 = x178 && x163 = x172 && x164 = x173 && x166 = x175 && x167 = x176 && x168 = x177 && x170 = x179 && x171 = x180
l15(x182, x183, x184, x185, x186, x187, x188, x189, x190) -> l16(x191, x192, x193, x194, x195, x196, x197, x198, x199) :|: x190 = x199 && x189 = x198 && x187 = x196 && x186 = x195 && x185 = x194 && x184 = x193 && x182 = x191 && x188 = x197 && x192 = 1 + x183 && 1 + x183 <= 50
l16(x200, x201, x202, x203, x204, x205, x206, x207, x208) -> l15(x209, x210, x211, x212, x213, x214, x215, x216, x217) :|: x208 = x217 && x207 = x216 && x205 = x214 && x204 = x213 && x203 = x212 && x202 = x211 && x201 = x210 && x200 = x209 && x206 = x215
l14(x218, x219, x220, x221, x222, x223, x224, x225, x226) -> l16(x227, x228, x229, x230, x231, x232, x233, x234, x235) :|: 50 <= x224 && x236 = 0 && x228 = 0 && x224 = x233 && x218 = x227 && x220 = x229 && x221 = x230 && x222 = x231 && x223 = x232 && x225 = x234 && x226 = x235
l14(x237, x238, x239, x240, x241, x242, x243, x244, x245) -> l13(x246, x247, x248, x249, x250, x251, x252, x253, x254) :|: x245 = x254 && x244 = x253 && x242 = x251 && x241 = x250 && x240 = x249 && x239 = x248 && x238 = x247 && x237 = x246 && x252 = 1 + x243 && 1 + x243 <= 50
l12(x255, x256, x257, x258, x259, x260, x261, x262, x263) -> l11(x264, x265, x266, x267, x268, x269, x270, x271, x272) :|: x263 = x272 && x262 = x271 && x260 = x269 && x259 = x268 && x258 = x267 && x257 = x266 && x256 = x265 && x255 = x264 && x261 = x270
l10(x273, x274, x275, x276, x277, x278, x279, x280, x281) -> l13(x282, x283, x284, x285, x286, x287, x288, x289, x290) :|: x281 = x290 && x280 = x289 && x278 = x287 && x277 = x286 && x276 = x285 && x275 = x284 && x274 = x283 && x273 = x282 && x288 = 0 && 50 <= x273
l10(x291, x292, x293, x294, x295, x296, x297, x298, x299) -> l9(x300, x301, x302, x303, x304, x305, x306, x307, x308) :|: x299 = x308 && x298 = x307 && x296 = x305 && x295 = x304 && x294 = x303 && x293 = x302 && x292 = x301 && x297 = x306 && x300 = 1 + x291 && 1 + x291 <= 50
l8(x309, x310, x311, x312, x313, x314, x315, x316, x317) -> l7(x318, x319, x320, x321, x322, x323, x324, x325, x326) :|: x317 = x326 && x316 = x325 && x314 = x323 && x313 = x322 && x312 = x321 && x311 = x320 && x310 = x319 && x309 = x318 && x315 = x324
l6(x327, x328, x329, x330, x331, x332, x333, x334, x335) -> l9(x336, x337, x338, x339, x340, x341, x342, x343, x344) :|: 50 <= x332 && x345 = 0 && x336 = 0 && x333 = x342 && x328 = x337 && x329 = x338 && x330 = x339 && x331 = x340 && x332 = x341 && x334 = x343 && x335 = x344
l6(x346, x347, x348, x349, x350, x351, x352, x353, x354) -> l5(x355, x356, x357, x358, x359, x360, x361, x362, x363) :|: x354 = x363 && x353 = x362 && x350 = x359 && x349 = x358 && x348 = x357 && x347 = x356 && x346 = x355 && x352 = x361 && x360 = 1 + x351 && 1 + x351 <= 50
l4(x364, x365, x366, x367, x368, x369, x370, x371, x372) -> l2(x373, x374, x375, x376, x377, x378, x379, x380, x381) :|: x372 = x381 && x371 = x380 && x369 = x378 && x368 = x377 && x367 = x376 && x366 = x375 && x365 = x374 && x364 = x373 && x370 = x379
l1(x382, x383, x384, x385, x386, x387, x388, x389, x390) -> l5(x391, x392, x393, x394, x395, x396, x397, x398, x399) :|: 50 <= x386 && x400 = 0 && x396 = 0 && x388 = x397 && x382 = x391 && x383 = x392 && x384 = x393 && x385 = x394 && x386 = x395 && x389 = x398 && x390 = x399
l1(x401, x402, x403, x404, x405, x406, x407, x408, x409) -> l0(x410, x411, x412, x413, x414, x415, x416, x417, x418) :|: x409 = x418 && x408 = x417 && x406 = x415 && x404 = x413 && x403 = x412 && x402 = x411 && x401 = x410 && x407 = x416 && x414 = 1 + x405 && 1 + x405 <= 50
l17(x419, x420, x421, x422, x423, x424, x425, x426, x427) -> l0(x428, x429, x430, x431, x432, x433, x434, x435, x436) :|: x434 = 0 && x435 = x435 && x436 = x436 && x437 = 0 && x432 = 0 && x419 = x428 && x420 = x429 && x421 = x430 && x422 = x431 && x424 = x433
l18(x438, x439, x440, x441, x442, x443, x444, x445, x446) -> l17(x447, x448, x449, x450, x451, x452, x453, x454, x455) :|: x446 = x455 && x445 = x454 && x443 = x452 && x442 = x451 && x441 = x450 && x440 = x449 && x439 = x448 && x438 = x447 && x444 = x453
Start term: l18(i11HAT0, i13HAT0, i15HAT0, i17HAT0, i7HAT0, i9HAT0, iHAT0, tmpHAT0, tmp___0HAT0)

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

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

(2)
Obligation:
Rules:
l0(i11HAT0, i13HAT0, i15HAT0, i17HAT0, i7HAT0, i9HAT0, iHAT0, tmpHAT0, tmp___0HAT0) -> l1(i11HATpost, i13HATpost, i15HATpost, i17HATpost, i7HATpost, i9HATpost, iHATpost, tmpHATpost, tmp___0HATpost) :|: tmp___0HAT0 = tmp___0HATpost && tmpHAT0 = tmpHATpost && i9HAT0 = i9HATpost && i7HAT0 = i7HATpost && i17HAT0 = i17HATpost && i15HAT0 = i15HATpost && i13HAT0 = i13HATpost && i11HAT0 = i11HATpost && iHAT0 = iHATpost
l2(x, x1, x2, x3, x4, x5, x6, x7, x8) -> l3(x9, x10, x11, x12, x13, x14, x15, x16, x17) :|: x8 = x17 && x7 = x16 && x5 = x14 && x4 = x13 && x3 = x12 && x2 = x11 && x1 = x10 && x = x9 && x6 = x15 && 50 <= x6
l2(x18, x19, x20, x21, x22, x23, x24, x25, x26) -> l4(x27, x28, x29, x30, x31, x32, x33, x34, x35) :|: x26 = x35 && x25 = x34 && x23 = x32 && x22 = x31 && x21 = x30 && x20 = x29 && x19 = x28 && x18 = x27 && x33 = 1 + x24 && 1 + x24 <= 50
l5(x36, x37, x38, x39, x40, x41, x42, x43, x44) -> l6(x45, x46, x47, x48, x49, x50, x51, x52, x53) :|: x44 = x53 && x43 = x52 && x41 = x50 && x40 = x49 && x39 = x48 && x38 = x47 && x37 = x46 && x36 = x45 && x42 = x51
l7(x54, x55, x56, x57, x58, x59, x60, x61, x62) -> l4(x63, x64, x65, x66, x67, x68, x69, x70, x71) :|: x62 = x71 && x61 = x70 && x59 = x68 && x58 = x67 && x57 = x66 && x56 = x65 && x55 = x64 && x54 = x63 && x69 = 0 && 50 <= x57
l7(x72, x73, x74, x75, x76, x77, x78, x79, x80) -> l8(x81, x82, x83, x84, x85, x86, x87, x88, x89) :|: x80 = x89 && x79 = x88 && x77 = x86 && x76 = x85 && x74 = x83 && x73 = x82 && x72 = x81 && x78 = x87 && x84 = 1 + x75 && 1 + x75 <= 50
l9(x90, x91, x92, x93, x94, x95, x96, x97, x98) -> l10(x99, x100, x101, x102, x103, x104, x105, x106, x107) :|: x98 = x107 && x97 = x106 && x95 = x104 && x94 = x103 && x93 = x102 && x92 = x101 && x91 = x100 && x90 = x99 && x96 = x105
l11(x108, x109, x110, x111, x112, x113, x114, x115, x116) -> l8(x117, x118, x119, x120, x121, x122, x123, x124, x125) :|: 50 <= x110 && x126 = 0 && x120 = 0 && x114 = x123 && x108 = x117 && x109 = x118 && x110 = x119 && x112 = x121 && x113 = x122 && x115 = x124 && x116 = x125
l11(x127, x128, x129, x130, x131, x132, x133, x134, x135) -> l12(x136, x137, x138, x139, x140, x141, x142, x143, x144) :|: x135 = x144 && x134 = x143 && x132 = x141 && x131 = x140 && x130 = x139 && x128 = x137 && x127 = x136 && x133 = x142 && x138 = 1 + x129 && 1 + x129 <= 50
l13(x145, x146, x147, x148, x149, x150, x151, x152, x153) -> l14(x154, x155, x156, x157, x158, x159, x160, x161, x162) :|: x153 = x162 && x152 = x161 && x150 = x159 && x149 = x158 && x148 = x157 && x147 = x156 && x146 = x155 && x145 = x154 && x151 = x160
l15(x163, x164, x165, x166, x167, x168, x169, x170, x171) -> l12(x172, x173, x174, x175, x176, x177, x178, x179, x180) :|: 50 <= x164 && x181 = 0 && x174 = 0 && x169 = x178 && x163 = x172 && x164 = x173 && x166 = x175 && x167 = x176 && x168 = x177 && x170 = x179 && x171 = x180
l15(x182, x183, x184, x185, x186, x187, x188, x189, x190) -> l16(x191, x192, x193, x194, x195, x196, x197, x198, x199) :|: x190 = x199 && x189 = x198 && x187 = x196 && x186 = x195 && x185 = x194 && x184 = x193 && x182 = x191 && x188 = x197 && x192 = 1 + x183 && 1 + x183 <= 50
l16(x200, x201, x202, x203, x204, x205, x206, x207, x208) -> l15(x209, x210, x211, x212, x213, x214, x215, x216, x217) :|: x208 = x217 && x207 = x216 && x205 = x214 && x204 = x213 && x203 = x212 && x202 = x211 && x201 = x210 && x200 = x209 && x206 = x215
l14(x218, x219, x220, x221, x222, x223, x224, x225, x226) -> l16(x227, x228, x229, x230, x231, x232, x233, x234, x235) :|: 50 <= x224 && x236 = 0 && x228 = 0 && x224 = x233 && x218 = x227 && x220 = x229 && x221 = x230 && x222 = x231 && x223 = x232 && x225 = x234 && x226 = x235
l14(x237, x238, x239, x240, x241, x242, x243, x244, x245) -> l13(x246, x247, x248, x249, x250, x251, x252, x253, x254) :|: x245 = x254 && x244 = x253 && x242 = x251 && x241 = x250 && x240 = x249 && x239 = x248 && x238 = x247 && x237 = x246 && x252 = 1 + x243 && 1 + x243 <= 50
l12(x255, x256, x257, x258, x259, x260, x261, x262, x263) -> l11(x264, x265, x266, x267, x268, x269, x270, x271, x272) :|: x263 = x272 && x262 = x271 && x260 = x269 && x259 = x268 && x258 = x267 && x257 = x266 && x256 = x265 && x255 = x264 && x261 = x270
l10(x273, x274, x275, x276, x277, x278, x279, x280, x281) -> l13(x282, x283, x284, x285, x286, x287, x288, x289, x290) :|: x281 = x290 && x280 = x289 && x278 = x287 && x277 = x286 && x276 = x285 && x275 = x284 && x274 = x283 && x273 = x282 && x288 = 0 && 50 <= x273
l10(x291, x292, x293, x294, x295, x296, x297, x298, x299) -> l9(x300, x301, x302, x303, x304, x305, x306, x307, x308) :|: x299 = x308 && x298 = x307 && x296 = x305 && x295 = x304 && x294 = x303 && x293 = x302 && x292 = x301 && x297 = x306 && x300 = 1 + x291 && 1 + x291 <= 50
l8(x309, x310, x311, x312, x313, x314, x315, x316, x317) -> l7(x318, x319, x320, x321, x322, x323, x324, x325, x326) :|: x317 = x326 && x316 = x325 && x314 = x323 && x313 = x322 && x312 = x321 && x311 = x320 && x310 = x319 && x309 = x318 && x315 = x324
l6(x327, x328, x329, x330, x331, x332, x333, x334, x335) -> l9(x336, x337, x338, x339, x340, x341, x342, x343, x344) :|: 50 <= x332 && x345 = 0 && x336 = 0 && x333 = x342 && x328 = x337 && x329 = x338 && x330 = x339 && x331 = x340 && x332 = x341 && x334 = x343 && x335 = x344
l6(x346, x347, x348, x349, x350, x351, x352, x353, x354) -> l5(x355, x356, x357, x358, x359, x360, x361, x362, x363) :|: x354 = x363 && x353 = x362 && x350 = x359 && x349 = x358 && x348 = x357 && x347 = x356 && x346 = x355 && x352 = x361 && x360 = 1 + x351 && 1 + x351 <= 50
l4(x364, x365, x366, x367, x368, x369, x370, x371, x372) -> l2(x373, x374, x375, x376, x377, x378, x379, x380, x381) :|: x372 = x381 && x371 = x380 && x369 = x378 && x368 = x377 && x367 = x376 && x366 = x375 && x365 = x374 && x364 = x373 && x370 = x379
l1(x382, x383, x384, x385, x386, x387, x388, x389, x390) -> l5(x391, x392, x393, x394, x395, x396, x397, x398, x399) :|: 50 <= x386 && x400 = 0 && x396 = 0 && x388 = x397 && x382 = x391 && x383 = x392 && x384 = x393 && x385 = x394 && x386 = x395 && x389 = x398 && x390 = x399
l1(x401, x402, x403, x404, x405, x406, x407, x408, x409) -> l0(x410, x411, x412, x413, x414, x415, x416, x417, x418) :|: x409 = x418 && x408 = x417 && x406 = x415 && x404 = x413 && x403 = x412 && x402 = x411 && x401 = x410 && x407 = x416 && x414 = 1 + x405 && 1 + x405 <= 50
l17(x419, x420, x421, x422, x423, x424, x425, x426, x427) -> l0(x428, x429, x430, x431, x432, x433, x434, x435, x436) :|: x434 = 0 && x435 = x435 && x436 = x436 && x437 = 0 && x432 = 0 && x419 = x428 && x420 = x429 && x421 = x430 && x422 = x431 && x424 = x433
l18(x438, x439, x440, x441, x442, x443, x444, x445, x446) -> l17(x447, x448, x449, x450, x451, x452, x453, x454, x455) :|: x446 = x455 && x445 = x454 && x443 = x452 && x442 = x451 && x441 = x450 && x440 = x449 && x439 = x448 && x438 = x447 && x444 = x453
Start term: l18(i11HAT0, i13HAT0, i15HAT0, i17HAT0, i7HAT0, i9HAT0, iHAT0, tmpHAT0, tmp___0HAT0)

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

(3) IRSwTTerminationDigraphProof (EQUIVALENT)
Constructed termination digraph!
Nodes:
(1) l0(i11HAT0, i13HAT0, i15HAT0, i17HAT0, i7HAT0, i9HAT0, iHAT0, tmpHAT0, tmp___0HAT0) -> l1(i11HATpost, i13HATpost, i15HATpost, i17HATpost, i7HATpost, i9HATpost, iHATpost, tmpHATpost, tmp___0HATpost) :|: tmp___0HAT0 = tmp___0HATpost && tmpHAT0 = tmpHATpost && i9HAT0 = i9HATpost && i7HAT0 = i7HATpost && i17HAT0 = i17HATpost && i15HAT0 = i15HATpost && i13HAT0 = i13HATpost && i11HAT0 = i11HATpost && iHAT0 = iHATpost
(2) l2(x, x1, x2, x3, x4, x5, x6, x7, x8) -> l3(x9, x10, x11, x12, x13, x14, x15, x16, x17) :|: x8 = x17 && x7 = x16 && x5 = x14 && x4 = x13 && x3 = x12 && x2 = x11 && x1 = x10 && x = x9 && x6 = x15 && 50 <= x6
(3) l2(x18, x19, x20, x21, x22, x23, x24, x25, x26) -> l4(x27, x28, x29, x30, x31, x32, x33, x34, x35) :|: x26 = x35 && x25 = x34 && x23 = x32 && x22 = x31 && x21 = x30 && x20 = x29 && x19 = x28 && x18 = x27 && x33 = 1 + x24 && 1 + x24 <= 50
(4) l5(x36, x37, x38, x39, x40, x41, x42, x43, x44) -> l6(x45, x46, x47, x48, x49, x50, x51, x52, x53) :|: x44 = x53 && x43 = x52 && x41 = x50 && x40 = x49 && x39 = x48 && x38 = x47 && x37 = x46 && x36 = x45 && x42 = x51
(5) l7(x54, x55, x56, x57, x58, x59, x60, x61, x62) -> l4(x63, x64, x65, x66, x67, x68, x69, x70, x71) :|: x62 = x71 && x61 = x70 && x59 = x68 && x58 = x67 && x57 = x66 && x56 = x65 && x55 = x64 && x54 = x63 && x69 = 0 && 50 <= x57
(6) l7(x72, x73, x74, x75, x76, x77, x78, x79, x80) -> l8(x81, x82, x83, x84, x85, x86, x87, x88, x89) :|: x80 = x89 && x79 = x88 && x77 = x86 && x76 = x85 && x74 = x83 && x73 = x82 && x72 = x81 && x78 = x87 && x84 = 1 + x75 && 1 + x75 <= 50
(7) l9(x90, x91, x92, x93, x94, x95, x96, x97, x98) -> l10(x99, x100, x101, x102, x103, x104, x105, x106, x107) :|: x98 = x107 && x97 = x106 && x95 = x104 && x94 = x103 && x93 = x102 && x92 = x101 && x91 = x100 && x90 = x99 && x96 = x105
(8) l11(x108, x109, x110, x111, x112, x113, x114, x115, x116) -> l8(x117, x118, x119, x120, x121, x122, x123, x124, x125) :|: 50 <= x110 && x126 = 0 && x120 = 0 && x114 = x123 && x108 = x117 && x109 = x118 && x110 = x119 && x112 = x121 && x113 = x122 && x115 = x124 && x116 = x125
(9) l11(x127, x128, x129, x130, x131, x132, x133, x134, x135) -> l12(x136, x137, x138, x139, x140, x141, x142, x143, x144) :|: x135 = x144 && x134 = x143 && x132 = x141 && x131 = x140 && x130 = x139 && x128 = x137 && x127 = x136 && x133 = x142 && x138 = 1 + x129 && 1 + x129 <= 50
(10) l13(x145, x146, x147, x148, x149, x150, x151, x152, x153) -> l14(x154, x155, x156, x157, x158, x159, x160, x161, x162) :|: x153 = x162 && x152 = x161 && x150 = x159 && x149 = x158 && x148 = x157 && x147 = x156 && x146 = x155 && x145 = x154 && x151 = x160
(11) l15(x163, x164, x165, x166, x167, x168, x169, x170, x171) -> l12(x172, x173, x174, x175, x176, x177, x178, x179, x180) :|: 50 <= x164 && x181 = 0 && x174 = 0 && x169 = x178 && x163 = x172 && x164 = x173 && x166 = x175 && x167 = x176 && x168 = x177 && x170 = x179 && x171 = x180
(12) l15(x182, x183, x184, x185, x186, x187, x188, x189, x190) -> l16(x191, x192, x193, x194, x195, x196, x197, x198, x199) :|: x190 = x199 && x189 = x198 && x187 = x196 && x186 = x195 && x185 = x194 && x184 = x193 && x182 = x191 && x188 = x197 && x192 = 1 + x183 && 1 + x183 <= 50
(13) l16(x200, x201, x202, x203, x204, x205, x206, x207, x208) -> l15(x209, x210, x211, x212, x213, x214, x215, x216, x217) :|: x208 = x217 && x207 = x216 && x205 = x214 && x204 = x213 && x203 = x212 && x202 = x211 && x201 = x210 && x200 = x209 && x206 = x215
(14) l14(x218, x219, x220, x221, x222, x223, x224, x225, x226) -> l16(x227, x228, x229, x230, x231, x232, x233, x234, x235) :|: 50 <= x224 && x236 = 0 && x228 = 0 && x224 = x233 && x218 = x227 && x220 = x229 && x221 = x230 && x222 = x231 && x223 = x232 && x225 = x234 && x226 = x235
(15) l14(x237, x238, x239, x240, x241, x242, x243, x244, x245) -> l13(x246, x247, x248, x249, x250, x251, x252, x253, x254) :|: x245 = x254 && x244 = x253 && x242 = x251 && x241 = x250 && x240 = x249 && x239 = x248 && x238 = x247 && x237 = x246 && x252 = 1 + x243 && 1 + x243 <= 50
(16) l12(x255, x256, x257, x258, x259, x260, x261, x262, x263) -> l11(x264, x265, x266, x267, x268, x269, x270, x271, x272) :|: x263 = x272 && x262 = x271 && x260 = x269 && x259 = x268 && x258 = x267 && x257 = x266 && x256 = x265 && x255 = x264 && x261 = x270
(17) l10(x273, x274, x275, x276, x277, x278, x279, x280, x281) -> l13(x282, x283, x284, x285, x286, x287, x288, x289, x290) :|: x281 = x290 && x280 = x289 && x278 = x287 && x277 = x286 && x276 = x285 && x275 = x284 && x274 = x283 && x273 = x282 && x288 = 0 && 50 <= x273
(18) l10(x291, x292, x293, x294, x295, x296, x297, x298, x299) -> l9(x300, x301, x302, x303, x304, x305, x306, x307, x308) :|: x299 = x308 && x298 = x307 && x296 = x305 && x295 = x304 && x294 = x303 && x293 = x302 && x292 = x301 && x297 = x306 && x300 = 1 + x291 && 1 + x291 <= 50
(19) l8(x309, x310, x311, x312, x313, x314, x315, x316, x317) -> l7(x318, x319, x320, x321, x322, x323, x324, x325, x326) :|: x317 = x326 && x316 = x325 && x314 = x323 && x313 = x322 && x312 = x321 && x311 = x320 && x310 = x319 && x309 = x318 && x315 = x324
(20) l6(x327, x328, x329, x330, x331, x332, x333, x334, x335) -> l9(x336, x337, x338, x339, x340, x341, x342, x343, x344) :|: 50 <= x332 && x345 = 0 && x336 = 0 && x333 = x342 && x328 = x337 && x329 = x338 && x330 = x339 && x331 = x340 && x332 = x341 && x334 = x343 && x335 = x344
(21) l6(x346, x347, x348, x349, x350, x351, x352, x353, x354) -> l5(x355, x356, x357, x358, x359, x360, x361, x362, x363) :|: x354 = x363 && x353 = x362 && x350 = x359 && x349 = x358 && x348 = x357 && x347 = x356 && x346 = x355 && x352 = x361 && x360 = 1 + x351 && 1 + x351 <= 50
(22) l4(x364, x365, x366, x367, x368, x369, x370, x371, x372) -> l2(x373, x374, x375, x376, x377, x378, x379, x380, x381) :|: x372 = x381 && x371 = x380 && x369 = x378 && x368 = x377 && x367 = x376 && x366 = x375 && x365 = x374 && x364 = x373 && x370 = x379
(23) l1(x382, x383, x384, x385, x386, x387, x388, x389, x390) -> l5(x391, x392, x393, x394, x395, x396, x397, x398, x399) :|: 50 <= x386 && x400 = 0 && x396 = 0 && x388 = x397 && x382 = x391 && x383 = x392 && x384 = x393 && x385 = x394 && x386 = x395 && x389 = x398 && x390 = x399
(24) l1(x401, x402, x403, x404, x405, x406, x407, x408, x409) -> l0(x410, x411, x412, x413, x414, x415, x416, x417, x418) :|: x409 = x418 && x408 = x417 && x406 = x415 && x404 = x413 && x403 = x412 && x402 = x411 && x401 = x410 && x407 = x416 && x414 = 1 + x405 && 1 + x405 <= 50
(25) l17(x419, x420, x421, x422, x423, x424, x425, x426, x427) -> l0(x428, x429, x430, x431, x432, x433, x434, x435, x436) :|: x434 = 0 && x435 = x435 && x436 = x436 && x437 = 0 && x432 = 0 && x419 = x428 && x420 = x429 && x421 = x430 && x422 = x431 && x424 = x433
(26) l18(x438, x439, x440, x441, x442, x443, x444, x445, x446) -> l17(x447, x448, x449, x450, x451, x452, x453, x454, x455) :|: x446 = x455 && x445 = x454 && x443 = x452 && x442 = x451 && x441 = x450 && x440 = x449 && x439 = x448 && x438 = x447 && x444 = x453

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

This digraph is fully evaluated!
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(4)
Complex Obligation (AND)

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(5)
Obligation:

Termination digraph:
Nodes:
(1) l0(i11HAT0, i13HAT0, i15HAT0, i17HAT0, i7HAT0, i9HAT0, iHAT0, tmpHAT0, tmp___0HAT0) -> l1(i11HATpost, i13HATpost, i15HATpost, i17HATpost, i7HATpost, i9HATpost, iHATpost, tmpHATpost, tmp___0HATpost) :|: tmp___0HAT0 = tmp___0HATpost && tmpHAT0 = tmpHATpost && i9HAT0 = i9HATpost && i7HAT0 = i7HATpost && i17HAT0 = i17HATpost && i15HAT0 = i15HATpost && i13HAT0 = i13HATpost && i11HAT0 = i11HATpost && iHAT0 = iHATpost
(2) l1(x401, x402, x403, x404, x405, x406, x407, x408, x409) -> l0(x410, x411, x412, x413, x414, x415, x416, x417, x418) :|: x409 = x418 && x408 = x417 && x406 = x415 && x404 = x413 && x403 = x412 && x402 = x411 && x401 = x410 && x407 = x416 && x414 = 1 + x405 && 1 + x405 <= 50

Arcs:
(1) -> (2)
(2) -> (1)

This digraph is fully evaluated!

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

(7)
Obligation:
Rules:
l0(i11HAT0:0, i13HAT0:0, i15HAT0:0, i17HAT0:0, i7HAT0:0, i9HAT0:0, iHAT0:0, tmpHAT0:0, tmp___0HAT0:0) -> l0(i11HAT0:0, i13HAT0:0, i15HAT0:0, i17HAT0:0, 1 + i7HAT0:0, i9HAT0:0, iHAT0:0, tmpHAT0:0, tmp___0HAT0:0) :|: i7HAT0:0 < 50

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

   l0(x1, x2, x3, x4, x5, x6, x7, x8, x9) -> l0(x5)

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(9)
Obligation:
Rules:
l0(i7HAT0:0) -> l0(1 + i7HAT0:0) :|: i7HAT0:0 < 50

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(10) TempFilterProof (SOUND)
Used the following sort dictionary for filtering: 
l0(INTEGER)
Replaced non-predefined constructor symbols by 0.
----------------------------------------

(11)
Obligation:
Rules:
l0(i7HAT0:0) -> l0(c) :|: c = 1 + i7HAT0:0 && i7HAT0:0 < 50

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(12) RankingReductionPairProof (EQUIVALENT)
Interpretation:
[ l0 ] = -1*l0_1

The following rules are decreasing:
l0(i7HAT0:0) -> l0(c) :|: c = 1 + i7HAT0:0 && i7HAT0:0 < 50

The following rules are bounded:
l0(i7HAT0:0) -> l0(c) :|: c = 1 + i7HAT0:0 && i7HAT0:0 < 50


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(13)
YES

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(14)
Obligation:

Termination digraph:
Nodes:
(1) l5(x36, x37, x38, x39, x40, x41, x42, x43, x44) -> l6(x45, x46, x47, x48, x49, x50, x51, x52, x53) :|: x44 = x53 && x43 = x52 && x41 = x50 && x40 = x49 && x39 = x48 && x38 = x47 && x37 = x46 && x36 = x45 && x42 = x51
(2) l6(x346, x347, x348, x349, x350, x351, x352, x353, x354) -> l5(x355, x356, x357, x358, x359, x360, x361, x362, x363) :|: x354 = x363 && x353 = x362 && x350 = x359 && x349 = x358 && x348 = x357 && x347 = x356 && x346 = x355 && x352 = x361 && x360 = 1 + x351 && 1 + x351 <= 50

Arcs:
(1) -> (2)
(2) -> (1)

This digraph is fully evaluated!

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

(16)
Obligation:
Rules:
l5(x355:0, x356:0, x357:0, x358:0, x359:0, x41:0, x361:0, x362:0, x363:0) -> l5(x355:0, x356:0, x357:0, x358:0, x359:0, 1 + x41:0, x361:0, x362:0, x363:0) :|: x41:0 < 50

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

   l5(x1, x2, x3, x4, x5, x6, x7, x8, x9) -> l5(x6)

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(18)
Obligation:
Rules:
l5(x41:0) -> l5(1 + x41:0) :|: x41:0 < 50

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(19) TempFilterProof (SOUND)
Used the following sort dictionary for filtering: 
l5(INTEGER)
Replaced non-predefined constructor symbols by 0.
----------------------------------------

(20)
Obligation:
Rules:
l5(x41:0) -> l5(c) :|: c = 1 + x41:0 && x41:0 < 50

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(21) RankingReductionPairProof (EQUIVALENT)
Interpretation:
[ l5 ] = -1*l5_1

The following rules are decreasing:
l5(x41:0) -> l5(c) :|: c = 1 + x41:0 && x41:0 < 50

The following rules are bounded:
l5(x41:0) -> l5(c) :|: c = 1 + x41:0 && x41:0 < 50


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(22)
YES

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

(23)
Obligation:

Termination digraph:
Nodes:
(1) l9(x90, x91, x92, x93, x94, x95, x96, x97, x98) -> l10(x99, x100, x101, x102, x103, x104, x105, x106, x107) :|: x98 = x107 && x97 = x106 && x95 = x104 && x94 = x103 && x93 = x102 && x92 = x101 && x91 = x100 && x90 = x99 && x96 = x105
(2) l10(x291, x292, x293, x294, x295, x296, x297, x298, x299) -> l9(x300, x301, x302, x303, x304, x305, x306, x307, x308) :|: x299 = x308 && x298 = x307 && x296 = x305 && x295 = x304 && x294 = x303 && x293 = x302 && x292 = x301 && x297 = x306 && x300 = 1 + x291 && 1 + x291 <= 50

Arcs:
(1) -> (2)
(2) -> (1)

This digraph is fully evaluated!

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

(25)
Obligation:
Rules:
l9(x90:0, x100:0, x101:0, x102:0, x103:0, x104:0, x105:0, x106:0, x107:0) -> l9(1 + x90:0, x100:0, x101:0, x102:0, x103:0, x104:0, x105:0, x106:0, x107:0) :|: x90:0 < 50

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

   l9(x1, x2, x3, x4, x5, x6, x7, x8, x9) -> l9(x1)

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(27)
Obligation:
Rules:
l9(x90:0) -> l9(1 + x90:0) :|: x90:0 < 50

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(28) TempFilterProof (SOUND)
Used the following sort dictionary for filtering: 
l9(INTEGER)
Replaced non-predefined constructor symbols by 0.
----------------------------------------

(29)
Obligation:
Rules:
l9(x90:0) -> l9(c) :|: c = 1 + x90:0 && x90:0 < 50

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(30) PolynomialOrderProcessor (EQUIVALENT)
Found the following polynomial interpretation:
[l9(x)] = 49 - x

The following rules are decreasing:
l9(x90:0) -> l9(c) :|: c = 1 + x90:0 && x90:0 < 50
The following rules are bounded:
l9(x90:0) -> l9(c) :|: c = 1 + x90:0 && x90:0 < 50

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(31)
YES

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(32)
Obligation:

Termination digraph:
Nodes:
(1) l13(x145, x146, x147, x148, x149, x150, x151, x152, x153) -> l14(x154, x155, x156, x157, x158, x159, x160, x161, x162) :|: x153 = x162 && x152 = x161 && x150 = x159 && x149 = x158 && x148 = x157 && x147 = x156 && x146 = x155 && x145 = x154 && x151 = x160
(2) l14(x237, x238, x239, x240, x241, x242, x243, x244, x245) -> l13(x246, x247, x248, x249, x250, x251, x252, x253, x254) :|: x245 = x254 && x244 = x253 && x242 = x251 && x241 = x250 && x240 = x249 && x239 = x248 && x238 = x247 && x237 = x246 && x252 = 1 + x243 && 1 + x243 <= 50

Arcs:
(1) -> (2)
(2) -> (1)

This digraph is fully evaluated!

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

(34)
Obligation:
Rules:
l13(x145:0, x146:0, x147:0, x148:0, x149:0, x150:0, x151:0, x152:0, x153:0) -> l13(x145:0, x146:0, x147:0, x148:0, x149:0, x150:0, 1 + x151:0, x152:0, x153:0) :|: x151:0 < 50

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(35) 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) -> l13(x7)

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(36)
Obligation:
Rules:
l13(x151:0) -> l13(1 + x151:0) :|: x151:0 < 50

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(37) TempFilterProof (SOUND)
Used the following sort dictionary for filtering: 
l13(INTEGER)
Replaced non-predefined constructor symbols by 0.
----------------------------------------

(38)
Obligation:
Rules:
l13(x151:0) -> l13(c) :|: c = 1 + x151:0 && x151:0 < 50

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(39) RankingReductionPairProof (EQUIVALENT)
Interpretation:
[ l13 ] = -1*l13_1

The following rules are decreasing:
l13(x151:0) -> l13(c) :|: c = 1 + x151:0 && x151:0 < 50

The following rules are bounded:
l13(x151:0) -> l13(c) :|: c = 1 + x151:0 && x151:0 < 50


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(40)
YES

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

(41)
Obligation:

Termination digraph:
Nodes:
(1) l16(x200, x201, x202, x203, x204, x205, x206, x207, x208) -> l15(x209, x210, x211, x212, x213, x214, x215, x216, x217) :|: x208 = x217 && x207 = x216 && x205 = x214 && x204 = x213 && x203 = x212 && x202 = x211 && x201 = x210 && x200 = x209 && x206 = x215
(2) l15(x182, x183, x184, x185, x186, x187, x188, x189, x190) -> l16(x191, x192, x193, x194, x195, x196, x197, x198, x199) :|: x190 = x199 && x189 = x198 && x187 = x196 && x186 = x195 && x185 = x194 && x184 = x193 && x182 = x191 && x188 = x197 && x192 = 1 + x183 && 1 + x183 <= 50

Arcs:
(1) -> (2)
(2) -> (1)

This digraph is fully evaluated!

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

(43)
Obligation:
Rules:
l16(x191:0, x201:0, x193:0, x194:0, x195:0, x196:0, x197:0, x198:0, x199:0) -> l16(x191:0, 1 + x201:0, x193:0, x194:0, x195:0, x196:0, x197:0, x198:0, x199:0) :|: x201:0 < 50

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

   l16(x1, x2, x3, x4, x5, x6, x7, x8, x9) -> l16(x2)

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(45)
Obligation:
Rules:
l16(x201:0) -> l16(1 + x201:0) :|: x201:0 < 50

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

(46) TempFilterProof (SOUND)
Used the following sort dictionary for filtering: 
l16(INTEGER)
Replaced non-predefined constructor symbols by 0.
----------------------------------------

(47)
Obligation:
Rules:
l16(x201:0) -> l16(c) :|: c = 1 + x201:0 && x201:0 < 50

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(48) RankingReductionPairProof (EQUIVALENT)
Interpretation:
[ l16 ] = -1*l16_1

The following rules are decreasing:
l16(x201:0) -> l16(c) :|: c = 1 + x201:0 && x201:0 < 50

The following rules are bounded:
l16(x201:0) -> l16(c) :|: c = 1 + x201:0 && x201:0 < 50


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(49)
YES

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(50)
Obligation:

Termination digraph:
Nodes:
(1) l12(x255, x256, x257, x258, x259, x260, x261, x262, x263) -> l11(x264, x265, x266, x267, x268, x269, x270, x271, x272) :|: x263 = x272 && x262 = x271 && x260 = x269 && x259 = x268 && x258 = x267 && x257 = x266 && x256 = x265 && x255 = x264 && x261 = x270
(2) l11(x127, x128, x129, x130, x131, x132, x133, x134, x135) -> l12(x136, x137, x138, x139, x140, x141, x142, x143, x144) :|: x135 = x144 && x134 = x143 && x132 = x141 && x131 = x140 && x130 = x139 && x128 = x137 && x127 = x136 && x133 = x142 && x138 = 1 + x129 && 1 + x129 <= 50

Arcs:
(1) -> (2)
(2) -> (1)

This digraph is fully evaluated!

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(51) IntTRSCompressionProof (EQUIVALENT)
Compressed rules.
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(52)
Obligation:
Rules:
l12(x136:0, x137:0, x257:0, x139:0, x140:0, x141:0, x142:0, x143:0, x144:0) -> l12(x136:0, x137:0, 1 + x257:0, x139:0, x140:0, x141:0, x142:0, x143:0, x144:0) :|: x257:0 < 50

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

   l12(x1, x2, x3, x4, x5, x6, x7, x8, x9) -> l12(x3)

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(54)
Obligation:
Rules:
l12(x257:0) -> l12(1 + x257:0) :|: x257:0 < 50

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(55) TempFilterProof (SOUND)
Used the following sort dictionary for filtering: 
l12(INTEGER)
Replaced non-predefined constructor symbols by 0.
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(56)
Obligation:
Rules:
l12(x257:0) -> l12(c) :|: c = 1 + x257:0 && x257:0 < 50

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(57) RankingReductionPairProof (EQUIVALENT)
Interpretation:
[ l12 ] = -1*l12_1

The following rules are decreasing:
l12(x257:0) -> l12(c) :|: c = 1 + x257:0 && x257:0 < 50

The following rules are bounded:
l12(x257:0) -> l12(c) :|: c = 1 + x257:0 && x257:0 < 50


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(58)
YES

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(59)
Obligation:

Termination digraph:
Nodes:
(1) l8(x309, x310, x311, x312, x313, x314, x315, x316, x317) -> l7(x318, x319, x320, x321, x322, x323, x324, x325, x326) :|: x317 = x326 && x316 = x325 && x314 = x323 && x313 = x322 && x312 = x321 && x311 = x320 && x310 = x319 && x309 = x318 && x315 = x324
(2) l7(x72, x73, x74, x75, x76, x77, x78, x79, x80) -> l8(x81, x82, x83, x84, x85, x86, x87, x88, x89) :|: x80 = x89 && x79 = x88 && x77 = x86 && x76 = x85 && x74 = x83 && x73 = x82 && x72 = x81 && x78 = x87 && x84 = 1 + x75 && 1 + x75 <= 50

Arcs:
(1) -> (2)
(2) -> (1)

This digraph is fully evaluated!

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

(61)
Obligation:
Rules:
l8(x309:0, x310:0, x311:0, x312:0, x313:0, x314:0, x315:0, x316:0, x317:0) -> l8(x309:0, x310:0, x311:0, 1 + x312:0, x313:0, x314:0, x315:0, x316:0, x317:0) :|: x312:0 < 50

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

   l8(x1, x2, x3, x4, x5, x6, x7, x8, x9) -> l8(x4)

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(63)
Obligation:
Rules:
l8(x312:0) -> l8(1 + x312:0) :|: x312:0 < 50

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(64) TempFilterProof (SOUND)
Used the following sort dictionary for filtering: 
l8(INTEGER)
Replaced non-predefined constructor symbols by 0.
----------------------------------------

(65)
Obligation:
Rules:
l8(x312:0) -> l8(c) :|: c = 1 + x312:0 && x312:0 < 50

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(66) PolynomialOrderProcessor (EQUIVALENT)
Found the following polynomial interpretation:
[l8(x)] = 49 - x

The following rules are decreasing:
l8(x312:0) -> l8(c) :|: c = 1 + x312:0 && x312:0 < 50
The following rules are bounded:
l8(x312:0) -> l8(c) :|: c = 1 + x312:0 && x312:0 < 50

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(67)
YES

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(68)
Obligation:

Termination digraph:
Nodes:
(1) l4(x364, x365, x366, x367, x368, x369, x370, x371, x372) -> l2(x373, x374, x375, x376, x377, x378, x379, x380, x381) :|: x372 = x381 && x371 = x380 && x369 = x378 && x368 = x377 && x367 = x376 && x366 = x375 && x365 = x374 && x364 = x373 && x370 = x379
(2) l2(x18, x19, x20, x21, x22, x23, x24, x25, x26) -> l4(x27, x28, x29, x30, x31, x32, x33, x34, x35) :|: x26 = x35 && x25 = x34 && x23 = x32 && x22 = x31 && x21 = x30 && x20 = x29 && x19 = x28 && x18 = x27 && x33 = 1 + x24 && 1 + x24 <= 50

Arcs:
(1) -> (2)
(2) -> (1)

This digraph is fully evaluated!

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

(70)
Obligation:
Rules:
l4(x27:0, x28:0, x29:0, x30:0, x31:0, x32:0, x370:0, x34:0, x35:0) -> l4(x27:0, x28:0, x29:0, x30:0, x31:0, x32:0, 1 + x370:0, x34:0, x35:0) :|: x370:0 < 50

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(71) 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) -> l4(x7)

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(72)
Obligation:
Rules:
l4(x370:0) -> l4(1 + x370:0) :|: x370:0 < 50

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

(74)
Obligation:
Rules:
l4(x370:0) -> l4(c) :|: c = 1 + x370:0 && x370:0 < 50

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(75) RankingReductionPairProof (EQUIVALENT)
Interpretation:
[ l4 ] = -1*l4_1

The following rules are decreasing:
l4(x370:0) -> l4(c) :|: c = 1 + x370:0 && x370:0 < 50

The following rules are bounded:
l4(x370:0) -> l4(c) :|: c = 1 + x370:0 && x370:0 < 50


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(76)
YES