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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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, 35.0 s]
(4) AND
    (5) IRSwT
        (6) IntTRSCompressionProof [EQUIVALENT, 10 ms]
        (7) IRSwT
        (8) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms]
        (9) IRSwT
        (10) TempFilterProof [SOUND, 127 ms]
        (11) IntTRS
        (12) RankingReductionPairProof [EQUIVALENT, 0 ms]
        (13) IntTRS
        (14) RankingReductionPairProof [EQUIVALENT, 0 ms]
        (15) IntTRS
        (16) PolynomialOrderProcessor [EQUIVALENT, 0 ms]
        (17) YES
    (18) IRSwT
        (19) IntTRSCompressionProof [EQUIVALENT, 5 ms]
        (20) IRSwT
        (21) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms]
        (22) IRSwT
        (23) TempFilterProof [SOUND, 26 ms]
        (24) IntTRS
        (25) RankingReductionPairProof [EQUIVALENT, 0 ms]
        (26) YES
    (27) IRSwT
        (28) IntTRSCompressionProof [EQUIVALENT, 4 ms]
        (29) IRSwT
        (30) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms]
        (31) IRSwT
        (32) TempFilterProof [SOUND, 41 ms]
        (33) IntTRS
        (34) PolynomialOrderProcessor [EQUIVALENT, 0 ms]
        (35) YES
    (36) IRSwT
        (37) IntTRSCompressionProof [EQUIVALENT, 22 ms]
        (38) IRSwT
        (39) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms]
        (40) IRSwT
        (41) TempFilterProof [SOUND, 13 ms]
        (42) IntTRS
        (43) RankingReductionPairProof [EQUIVALENT, 0 ms]
        (44) YES
    (45) IRSwT
        (46) IntTRSCompressionProof [EQUIVALENT, 6 ms]
        (47) IRSwT
        (48) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms]
        (49) IRSwT
        (50) TempFilterProof [SOUND, 4 ms]
        (51) IntTRS
        (52) RankingReductionPairProof [EQUIVALENT, 0 ms]
        (53) YES
    (54) IRSwT
        (55) IntTRSCompressionProof [EQUIVALENT, 1 ms]
        (56) IRSwT
        (57) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms]
        (58) IRSwT
        (59) TempFilterProof [SOUND, 7 ms]
        (60) IntTRS
        (61) RankingReductionPairProof [EQUIVALENT, 0 ms]
        (62) YES


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

(0)
Obligation:
Rules:
f1_0_main_ConstantStackPush(arg1, arg2, arg3, arg4) -> f452_0_main_GE(arg1P, arg2P, arg3P, arg4P) :|: arg2 = arg3P && 0 = arg2P && 0 <= arg1P - 1 && 0 <= arg1 - 1 && -1 <= arg2 - 1 && arg1P <= arg1
f452_0_main_GE(x, x1, x2, x3) -> f452_0_main_GE'(x4, x5, x6, x7) :|: x1 <= x2 - 1 && 0 <= x2 - 1 && x1 - 2 * x8 = 0 && 0 <= x - 1 && x = x4 && x1 = x5 && x2 = x6
f452_0_main_GE'(x9, x10, x11, x12) -> f276_0_sin_GT(x13, x14, x15, x16) :|: x10 <= x11 - 1 && 0 <= x11 - 1 && x10 - 2 * x17 = 0 && 0 <= x9 - 1 && x10 - 2 * x17 <= 1 && 0 <= x10 - 2 * x17 && x11 = x13 && x10 = x14
f452_0_main_GE(x18, x19, x20, x21) -> f452_0_main_GE'(x22, x23, x24, x25) :|: x19 <= x20 - 1 && 0 <= x20 - 1 && x19 - 2 * x26 = 1 && x19 - 3 * x27 = 0 && 0 <= x18 - 1 && x18 = x22 && x19 = x23 && x20 = x24
f452_0_main_GE'(x28, x29, x30, x31) -> f307_0_cos_GT(x32, x33, x34, x35) :|: x29 <= x30 - 1 && 0 <= x30 - 1 && x29 - 2 * x36 = 1 && x29 - 3 * x37 = 0 && 0 <= x28 - 1 && 0 <= x29 - 2 * x36 && x29 - 2 * x36 <= 1 && x29 - 3 * x37 <= 2 && 0 <= x29 - 3 * x37 && x30 = x32 && x29 = x33
f452_0_main_GE(x38, x39, x40, x41) -> f452_0_main_GE'(x42, x43, x44, x45) :|: x39 <= x40 - 1 && 0 <= x40 - 1 && x39 - 2 * x46 = 1 && 0 <= x39 - 3 * x47 - 1 && x39 - 5 * x48 = 0 && 0 <= x38 - 1 && x38 = x42 && x39 = x43 && x40 = x44
f452_0_main_GE'(x49, x50, x51, x52) -> f342_0_exp_GT(x53, x54, x55, x56) :|: 0 <= x50 - 3 * x57 - 1 && x50 <= x51 - 1 && 0 <= x51 - 1 && x50 - 2 * x58 = 1 && x50 - 5 * x59 = 0 && 0 <= x49 - 1 && 0 <= x50 - 2 * x58 && x50 - 2 * x58 <= 1 && x50 - 3 * x57 <= 2 && x50 - 5 * x59 <= 4 && 0 <= x50 - 5 * x59 && x51 = x53 && x50 = x54
f452_0_main_GE(x60, x61, x62, x63) -> f452_0_main_GE'(x64, x65, x66, x67) :|: x61 - 2 * x68 = 1 && x61 <= x62 - 1 && 0 <= x61 - 5 * x69 - 1 && 0 <= x61 - 3 * x70 - 1 && x71 <= x60 && 0 <= x60 - 1 && 0 <= x71 - 1 && x60 = x64 && x61 = x65 && x62 = x66
f452_0_main_GE'(x72, x73, x74, x75) -> f697_0_main_GE(x76, x77, x78, x79) :|: 0 <= x73 - 5 * x80 - 1 && 0 <= x73 - 3 * x81 - 1 && x73 - 2 * x82 = 1 && x73 <= x74 - 1 && x76 <= x72 && 0 <= x72 - 1 && 0 <= x76 - 1 && 0 <= x73 - 2 * x82 && x73 - 2 * x82 <= 1 && x73 - 3 * x81 <= 2 && x73 - 5 * x80 <= 4 && x73 = x77 && 0 = x78 && x74 = x79
f697_0_main_GE(x83, x84, x85, x86) -> f697_0_main_GE(x87, x88, x89, x90) :|: x86 = x90 && x85 + 1 = x89 && x84 = x88 && 0 <= x87 - 1 && 0 <= x83 - 1 && x85 <= 99 && x87 <= x83
f452_0_main_GE(x92, x93, x94, x96) -> f452_0_main_GE(x97, x98, x101, x102) :|: x94 = x101 && 1 = x98 && 0 = x93 && 0 <= x97 - 1 && 0 <= x92 - 1 && 0 <= x94 - 1 && x97 <= x92
f697_0_main_GE(x103, x106, x107, x108) -> f452_0_main_GE(x112, x113, x114, x118) :|: x108 = x114 && x106 + 1 = x113 && 0 <= x112 - 1 && 0 <= x103 - 1 && x112 <= x103 && 99 <= x107 - 1 && -1 <= x108 - 1
f452_0_main_GE(x119, x120, x125, x126) -> f452_0_main_GE'(x127, x128, x132, x133) :|: x120 <= x125 - 1 && 0 <= x125 - 1 && x120 - 2 * x134 = 1 && 0 <= x120 - 3 * x139 - 1 && x120 - 5 * x140 = 0 && x141 <= x119 && 0 <= x119 - 1 && 0 <= x141 - 1 && x119 = x127 && x120 = x128 && x125 = x132
f452_0_main_GE'(x142, x146, x147, x148) -> f452_0_main_GE(x152, x153, x154, x155) :|: 0 <= x146 - 3 * x158 - 1 && x146 <= x147 - 1 && 0 <= x147 - 1 && x146 - 2 * x159 = 1 && x146 - 5 * x160 = 0 && x152 <= x142 && 0 <= x142 - 1 && 0 <= x152 - 1 && 0 <= x146 - 2 * x159 && x146 - 2 * x159 <= 1 && x146 - 3 * x158 <= 2 && x146 - 5 * x160 <= 4 && 0 <= x146 - 5 * x160 && x146 + 1 = x153 && x147 = x154
f452_0_main_GE(x163, x164, x165, x166) -> f452_0_main_GE'(x168, x169, x170, x174) :|: x164 <= x165 - 1 && 0 <= x165 - 1 && x164 - 2 * x175 = 1 && x164 - 3 * x176 = 0 && x180 <= x163 && 0 <= x163 - 1 && 0 <= x180 - 1 && x163 = x168 && x164 = x169 && x165 = x170
f452_0_main_GE'(x181, x185, x186, x190) -> f452_0_main_GE(x191, x192, x193, x194) :|: x185 <= x186 - 1 && 0 <= x186 - 1 && x185 - 2 * x195 = 1 && x185 - 3 * x196 = 0 && x191 <= x181 && 0 <= x181 - 1 && 0 <= x191 - 1 && 0 <= x185 - 2 * x195 && x185 - 2 * x195 <= 1 && x185 - 3 * x196 <= 2 && 0 <= x185 - 3 * x196 && x185 + 1 = x192 && x186 = x193
f452_0_main_GE(x197, x198, x199, x200) -> f452_0_main_GE'(x201, x202, x203, x204) :|: x198 <= x199 - 1 && 0 <= x199 - 1 && x198 - 2 * x205 = 0 && x206 <= x197 && 0 <= x197 - 1 && 0 <= x206 - 1 && x197 = x201 && x198 = x202 && x199 = x203
f452_0_main_GE'(x207, x208, x209, x210) -> f452_0_main_GE(x211, x212, x213, x214) :|: x208 <= x209 - 1 && 0 <= x209 - 1 && x208 - 2 * x215 = 0 && x211 <= x207 && 0 <= x207 - 1 && 0 <= x211 - 1 && x208 - 2 * x215 <= 1 && 0 <= x208 - 2 * x215 && x208 + 1 = x212 && x209 = x213
f276_0_sin_GT(x216, x217, x218, x219) -> f345_0_power_GT(x220, x221, x222, x223) :|: x217 = x220 && 0 <= x216 - 1 && 0 <= x217 - 1
f276_0_sin_GT(x224, x225, x226, x227) -> f566_0_sin_InvokeMethod(x228, x229, x230, x231) :|: 2 * x225 + 1 = x230 && x224 = x229 && x225 = x228 && 0 <= x225 - 1 && 0 <= 2 * x225 - 1 && 0 <= x224 - 1
f566_0_sin_InvokeMethod(x232, x233, x234, x235) -> f345_0_power_GT(x236, x237, x238, x239) :|: x234 = x236 && 0 <= x232 - 1 && 1 <= x234 - 1 && 0 <= x233 - 1
f566_0_sin_InvokeMethod(x240, x241, x242, x243) -> f453_0_fact_GT(x244, x245, x246, x247) :|: 2 * x240 + 1 = x244 && 1 <= x242 - 1 && 0 <= 2 * x240 - 1 && 0 <= x240 - 1 && 0 <= x241 - 1
f566_0_sin_InvokeMethod(x248, x249, x250, x251) -> f566_0_sin_InvokeMethod'(x252, x253, x254, x255) :|: x250 = x254 && x249 = x253 && x248 = x252 && 0 <= 2 * x248 - 1 && x248 - 1 <= x248 - 1 && 1 <= x250 - 1 && 0 <= x248 - 1 && 0 <= x249 - 1
f566_0_sin_InvokeMethod'(x256, x257, x258, x259) -> f276_0_sin_GT(x260, x261, x262, x263) :|: 0 <= x257 - 1 && 0 <= x256 - 1 && 1 <= x258 - 1 && 0 <= 2 * x256 - 1 && x256 - 1 <= x256 - 1 && x264 - x265 * x266 <= x265 - 1 && 0 <= x264 - x265 * x266 && x257 = x260 && x256 - 1 = x261
f307_0_cos_GT(x267, x268, x269, x270) -> f345_0_power_GT(x271, x272, x273, x274) :|: x268 = x271 && 0 <= x267 - 1 && 0 <= x268 - 1
f307_0_cos_GT(x275, x276, x277, x278) -> f552_0_cos_InvokeMethod(x279, x280, x281, x282) :|: 2 * x276 = x281 && x275 = x280 && x276 = x279 && 0 <= x275 - 1 && 0 <= x276 - 1
f552_0_cos_InvokeMethod(x283, x284, x285, x286) -> f345_0_power_GT(x287, x288, x289, x290) :|: x285 = x287 && 0 <= x283 - 1 && 0 <= x284 - 1 && 1 <= x285 - 1
f552_0_cos_InvokeMethod(x291, x292, x293, x294) -> f453_0_fact_GT(x295, x296, x297, x298) :|: 2 * x291 = x295 && 1 <= x293 - 1 && 1 <= 2 * x291 - 1 && 0 <= x291 - 1 && 0 <= x292 - 1
f552_0_cos_InvokeMethod(x299, x300, x301, x302) -> f552_0_cos_InvokeMethod'(x303, x304, x305, x306) :|: x301 = x305 && x300 = x304 && x299 = x303 && 1 <= 2 * x299 - 1 && x299 - 1 <= x299 - 1 && 1 <= x301 - 1 && 0 <= x299 - 1 && 0 <= x300 - 1
f552_0_cos_InvokeMethod'(x307, x308, x309, x310) -> f307_0_cos_GT(x311, x312, x313, x314) :|: 0 <= x308 - 1 && 0 <= x307 - 1 && 1 <= x309 - 1 && 1 <= 2 * x307 - 1 && x307 - 1 <= x307 - 1 && x315 - x316 * x317 <= x316 - 1 && 0 <= x315 - x316 * x317 && x308 = x311 && x307 - 1 = x312
f342_0_exp_GT(x318, x319, x320, x321) -> f345_0_power_GT(x322, x323, x324, x325) :|: x319 = x322 && 0 <= x318 - 1 && 0 <= x319 - 1
f638_0_exp_InvokeMethod(x326, x327, x328, x329) -> f342_0_exp_GT(x330, x331, x332, x333) :|: x328 = x331 && x327 = x330 && 0 <= x326 - 1 && 0 <= x327 - 1 && x328 <= x326 - 1
f345_0_power_GT(x334, x335, x336, x337) -> f345_0_power_GT(x338, x339, x340, x341) :|: x334 - 1 = x338 && 0 <= x334 - 1
f453_0_fact_GT(x342, x343, x344, x345) -> f453_0_fact_GT(x346, x347, x348, x349) :|: x342 - 1 = x346 && x342 - 1 <= x342 - 1 && 0 <= x342 - 1
f342_0_exp_GT(x350, x351, x352, x353) -> f453_0_fact_GT(x354, x355, x356, x357) :|: x351 = x354 && 0 <= x350 - 1 && 0 <= x351 - 1
f342_0_exp_GT(x358, x359, x360, x361) -> f342_0_exp_GT'(x362, x363, x364, x365) :|: x359 = x363 && x358 = x362 && 0 <= x358 - 1 && 0 <= x359 - 1
f342_0_exp_GT'(x366, x367, x368, x369) -> f638_0_exp_InvokeMethod(x370, x371, x372, x373) :|: 0 <= x366 - 1 && 0 <= x367 - 1 && x374 - x375 * x376 <= x375 - 1 && 0 <= x374 - x375 * x376 && x367 = x370 && x366 = x371 && x367 - 1 = x372
f342_0_exp_GT(x377, x378, x379, x380) -> f342_0_exp_GT'(x381, x382, x383, x384) :|: x378 = x382 && x377 = x381 && 0 <= x378 - 1 && 0 <= x377 - 1
f342_0_exp_GT'(x385, x386, x387, x388) -> f638_0_exp_InvokeMethod(x389, x390, x391, x392) :|: 0 <= x386 - 1 && 0 <= x385 - 1 && x393 - x394 * x395 <= x394 - 1 && 0 <= x393 - x394 * x395 && x386 = x389 && x385 = x390 && x386 - 1 = x391
__init(x396, x397, x398, x399) -> f1_0_main_ConstantStackPush(x400, x401, x402, x403) :|: 0 <= 0
Start term: __init(arg1, arg2, arg3, arg4)

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

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

(2)
Obligation:
Rules:
f1_0_main_ConstantStackPush(arg1, arg2, arg3, arg4) -> f452_0_main_GE(arg1P, arg2P, arg3P, arg4P) :|: arg2 = arg3P && 0 = arg2P && 0 <= arg1P - 1 && 0 <= arg1 - 1 && -1 <= arg2 - 1 && arg1P <= arg1
f452_0_main_GE(x, x1, x2, x3) -> f452_0_main_GE'(x4, x5, x6, x7) :|: x1 <= x2 - 1 && 0 <= x2 - 1 && x1 - 2 * x8 = 0 && 0 <= x - 1 && x = x4 && x1 = x5 && x2 = x6
f452_0_main_GE'(x9, x10, x11, x12) -> f276_0_sin_GT(x13, x14, x15, x16) :|: x10 <= x11 - 1 && 0 <= x11 - 1 && x10 - 2 * x17 = 0 && 0 <= x9 - 1 && x10 - 2 * x17 <= 1 && 0 <= x10 - 2 * x17 && x11 = x13 && x10 = x14
f452_0_main_GE(x18, x19, x20, x21) -> f452_0_main_GE'(x22, x23, x24, x25) :|: x19 <= x20 - 1 && 0 <= x20 - 1 && x19 - 2 * x26 = 1 && x19 - 3 * x27 = 0 && 0 <= x18 - 1 && x18 = x22 && x19 = x23 && x20 = x24
f452_0_main_GE'(x28, x29, x30, x31) -> f307_0_cos_GT(x32, x33, x34, x35) :|: x29 <= x30 - 1 && 0 <= x30 - 1 && x29 - 2 * x36 = 1 && x29 - 3 * x37 = 0 && 0 <= x28 - 1 && 0 <= x29 - 2 * x36 && x29 - 2 * x36 <= 1 && x29 - 3 * x37 <= 2 && 0 <= x29 - 3 * x37 && x30 = x32 && x29 = x33
f452_0_main_GE(x38, x39, x40, x41) -> f452_0_main_GE'(x42, x43, x44, x45) :|: x39 <= x40 - 1 && 0 <= x40 - 1 && x39 - 2 * x46 = 1 && 0 <= x39 - 3 * x47 - 1 && x39 - 5 * x48 = 0 && 0 <= x38 - 1 && x38 = x42 && x39 = x43 && x40 = x44
f452_0_main_GE'(x49, x50, x51, x52) -> f342_0_exp_GT(x53, x54, x55, x56) :|: 0 <= x50 - 3 * x57 - 1 && x50 <= x51 - 1 && 0 <= x51 - 1 && x50 - 2 * x58 = 1 && x50 - 5 * x59 = 0 && 0 <= x49 - 1 && 0 <= x50 - 2 * x58 && x50 - 2 * x58 <= 1 && x50 - 3 * x57 <= 2 && x50 - 5 * x59 <= 4 && 0 <= x50 - 5 * x59 && x51 = x53 && x50 = x54
f452_0_main_GE(x60, x61, x62, x63) -> f452_0_main_GE'(x64, x65, x66, x67) :|: x61 - 2 * x68 = 1 && x61 <= x62 - 1 && 0 <= x61 - 5 * x69 - 1 && 0 <= x61 - 3 * x70 - 1 && x71 <= x60 && 0 <= x60 - 1 && 0 <= x71 - 1 && x60 = x64 && x61 = x65 && x62 = x66
f452_0_main_GE'(x72, x73, x74, x75) -> f697_0_main_GE(x76, x77, x78, x79) :|: 0 <= x73 - 5 * x80 - 1 && 0 <= x73 - 3 * x81 - 1 && x73 - 2 * x82 = 1 && x73 <= x74 - 1 && x76 <= x72 && 0 <= x72 - 1 && 0 <= x76 - 1 && 0 <= x73 - 2 * x82 && x73 - 2 * x82 <= 1 && x73 - 3 * x81 <= 2 && x73 - 5 * x80 <= 4 && x73 = x77 && 0 = x78 && x74 = x79
f697_0_main_GE(x83, x84, x85, x86) -> f697_0_main_GE(x87, x88, x89, x90) :|: x86 = x90 && x85 + 1 = x89 && x84 = x88 && 0 <= x87 - 1 && 0 <= x83 - 1 && x85 <= 99 && x87 <= x83
f452_0_main_GE(x92, x93, x94, x96) -> f452_0_main_GE(x97, x98, x101, x102) :|: x94 = x101 && 1 = x98 && 0 = x93 && 0 <= x97 - 1 && 0 <= x92 - 1 && 0 <= x94 - 1 && x97 <= x92
f697_0_main_GE(x103, x106, x107, x108) -> f452_0_main_GE(x112, x113, x114, x118) :|: x108 = x114 && x106 + 1 = x113 && 0 <= x112 - 1 && 0 <= x103 - 1 && x112 <= x103 && 99 <= x107 - 1 && -1 <= x108 - 1
f452_0_main_GE(x119, x120, x125, x126) -> f452_0_main_GE'(x127, x128, x132, x133) :|: x120 <= x125 - 1 && 0 <= x125 - 1 && x120 - 2 * x134 = 1 && 0 <= x120 - 3 * x139 - 1 && x120 - 5 * x140 = 0 && x141 <= x119 && 0 <= x119 - 1 && 0 <= x141 - 1 && x119 = x127 && x120 = x128 && x125 = x132
f452_0_main_GE'(x142, x146, x147, x148) -> f452_0_main_GE(x152, x153, x154, x155) :|: 0 <= x146 - 3 * x158 - 1 && x146 <= x147 - 1 && 0 <= x147 - 1 && x146 - 2 * x159 = 1 && x146 - 5 * x160 = 0 && x152 <= x142 && 0 <= x142 - 1 && 0 <= x152 - 1 && 0 <= x146 - 2 * x159 && x146 - 2 * x159 <= 1 && x146 - 3 * x158 <= 2 && x146 - 5 * x160 <= 4 && 0 <= x146 - 5 * x160 && x146 + 1 = x153 && x147 = x154
f452_0_main_GE(x163, x164, x165, x166) -> f452_0_main_GE'(x168, x169, x170, x174) :|: x164 <= x165 - 1 && 0 <= x165 - 1 && x164 - 2 * x175 = 1 && x164 - 3 * x176 = 0 && x180 <= x163 && 0 <= x163 - 1 && 0 <= x180 - 1 && x163 = x168 && x164 = x169 && x165 = x170
f452_0_main_GE'(x181, x185, x186, x190) -> f452_0_main_GE(x191, x192, x193, x194) :|: x185 <= x186 - 1 && 0 <= x186 - 1 && x185 - 2 * x195 = 1 && x185 - 3 * x196 = 0 && x191 <= x181 && 0 <= x181 - 1 && 0 <= x191 - 1 && 0 <= x185 - 2 * x195 && x185 - 2 * x195 <= 1 && x185 - 3 * x196 <= 2 && 0 <= x185 - 3 * x196 && x185 + 1 = x192 && x186 = x193
f452_0_main_GE(x197, x198, x199, x200) -> f452_0_main_GE'(x201, x202, x203, x204) :|: x198 <= x199 - 1 && 0 <= x199 - 1 && x198 - 2 * x205 = 0 && x206 <= x197 && 0 <= x197 - 1 && 0 <= x206 - 1 && x197 = x201 && x198 = x202 && x199 = x203
f452_0_main_GE'(x207, x208, x209, x210) -> f452_0_main_GE(x211, x212, x213, x214) :|: x208 <= x209 - 1 && 0 <= x209 - 1 && x208 - 2 * x215 = 0 && x211 <= x207 && 0 <= x207 - 1 && 0 <= x211 - 1 && x208 - 2 * x215 <= 1 && 0 <= x208 - 2 * x215 && x208 + 1 = x212 && x209 = x213
f276_0_sin_GT(x216, x217, x218, x219) -> f345_0_power_GT(x220, x221, x222, x223) :|: x217 = x220 && 0 <= x216 - 1 && 0 <= x217 - 1
f276_0_sin_GT(x224, x225, x226, x227) -> f566_0_sin_InvokeMethod(x228, x229, x230, x231) :|: 2 * x225 + 1 = x230 && x224 = x229 && x225 = x228 && 0 <= x225 - 1 && 0 <= 2 * x225 - 1 && 0 <= x224 - 1
f566_0_sin_InvokeMethod(x232, x233, x234, x235) -> f345_0_power_GT(x236, x237, x238, x239) :|: x234 = x236 && 0 <= x232 - 1 && 1 <= x234 - 1 && 0 <= x233 - 1
f566_0_sin_InvokeMethod(x240, x241, x242, x243) -> f453_0_fact_GT(x244, x245, x246, x247) :|: 2 * x240 + 1 = x244 && 1 <= x242 - 1 && 0 <= 2 * x240 - 1 && 0 <= x240 - 1 && 0 <= x241 - 1
f566_0_sin_InvokeMethod(x248, x249, x250, x251) -> f566_0_sin_InvokeMethod'(x252, x253, x254, x255) :|: x250 = x254 && x249 = x253 && x248 = x252 && 0 <= 2 * x248 - 1 && x248 - 1 <= x248 - 1 && 1 <= x250 - 1 && 0 <= x248 - 1 && 0 <= x249 - 1
f566_0_sin_InvokeMethod'(x256, x257, x258, x259) -> f276_0_sin_GT(x260, x261, x262, x263) :|: 0 <= x257 - 1 && 0 <= x256 - 1 && 1 <= x258 - 1 && 0 <= 2 * x256 - 1 && x256 - 1 <= x256 - 1 && x264 - x265 * x266 <= x265 - 1 && 0 <= x264 - x265 * x266 && x257 = x260 && x256 - 1 = x261
f307_0_cos_GT(x267, x268, x269, x270) -> f345_0_power_GT(x271, x272, x273, x274) :|: x268 = x271 && 0 <= x267 - 1 && 0 <= x268 - 1
f307_0_cos_GT(x275, x276, x277, x278) -> f552_0_cos_InvokeMethod(x279, x280, x281, x282) :|: 2 * x276 = x281 && x275 = x280 && x276 = x279 && 0 <= x275 - 1 && 0 <= x276 - 1
f552_0_cos_InvokeMethod(x283, x284, x285, x286) -> f345_0_power_GT(x287, x288, x289, x290) :|: x285 = x287 && 0 <= x283 - 1 && 0 <= x284 - 1 && 1 <= x285 - 1
f552_0_cos_InvokeMethod(x291, x292, x293, x294) -> f453_0_fact_GT(x295, x296, x297, x298) :|: 2 * x291 = x295 && 1 <= x293 - 1 && 1 <= 2 * x291 - 1 && 0 <= x291 - 1 && 0 <= x292 - 1
f552_0_cos_InvokeMethod(x299, x300, x301, x302) -> f552_0_cos_InvokeMethod'(x303, x304, x305, x306) :|: x301 = x305 && x300 = x304 && x299 = x303 && 1 <= 2 * x299 - 1 && x299 - 1 <= x299 - 1 && 1 <= x301 - 1 && 0 <= x299 - 1 && 0 <= x300 - 1
f552_0_cos_InvokeMethod'(x307, x308, x309, x310) -> f307_0_cos_GT(x311, x312, x313, x314) :|: 0 <= x308 - 1 && 0 <= x307 - 1 && 1 <= x309 - 1 && 1 <= 2 * x307 - 1 && x307 - 1 <= x307 - 1 && x315 - x316 * x317 <= x316 - 1 && 0 <= x315 - x316 * x317 && x308 = x311 && x307 - 1 = x312
f342_0_exp_GT(x318, x319, x320, x321) -> f345_0_power_GT(x322, x323, x324, x325) :|: x319 = x322 && 0 <= x318 - 1 && 0 <= x319 - 1
f638_0_exp_InvokeMethod(x326, x327, x328, x329) -> f342_0_exp_GT(x330, x331, x332, x333) :|: x328 = x331 && x327 = x330 && 0 <= x326 - 1 && 0 <= x327 - 1 && x328 <= x326 - 1
f345_0_power_GT(x334, x335, x336, x337) -> f345_0_power_GT(x338, x339, x340, x341) :|: x334 - 1 = x338 && 0 <= x334 - 1
f453_0_fact_GT(x342, x343, x344, x345) -> f453_0_fact_GT(x346, x347, x348, x349) :|: x342 - 1 = x346 && x342 - 1 <= x342 - 1 && 0 <= x342 - 1
f342_0_exp_GT(x350, x351, x352, x353) -> f453_0_fact_GT(x354, x355, x356, x357) :|: x351 = x354 && 0 <= x350 - 1 && 0 <= x351 - 1
f342_0_exp_GT(x358, x359, x360, x361) -> f342_0_exp_GT'(x362, x363, x364, x365) :|: x359 = x363 && x358 = x362 && 0 <= x358 - 1 && 0 <= x359 - 1
f342_0_exp_GT'(x366, x367, x368, x369) -> f638_0_exp_InvokeMethod(x370, x371, x372, x373) :|: 0 <= x366 - 1 && 0 <= x367 - 1 && x374 - x375 * x376 <= x375 - 1 && 0 <= x374 - x375 * x376 && x367 = x370 && x366 = x371 && x367 - 1 = x372
f342_0_exp_GT(x377, x378, x379, x380) -> f342_0_exp_GT'(x381, x382, x383, x384) :|: x378 = x382 && x377 = x381 && 0 <= x378 - 1 && 0 <= x377 - 1
f342_0_exp_GT'(x385, x386, x387, x388) -> f638_0_exp_InvokeMethod(x389, x390, x391, x392) :|: 0 <= x386 - 1 && 0 <= x385 - 1 && x393 - x394 * x395 <= x394 - 1 && 0 <= x393 - x394 * x395 && x386 = x389 && x385 = x390 && x386 - 1 = x391
__init(x396, x397, x398, x399) -> f1_0_main_ConstantStackPush(x400, x401, x402, x403) :|: 0 <= 0
Start term: __init(arg1, arg2, arg3, arg4)

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

(3) IRSwTTerminationDigraphProof (EQUIVALENT)
Constructed termination digraph!
Nodes:
(1) f1_0_main_ConstantStackPush(arg1, arg2, arg3, arg4) -> f452_0_main_GE(arg1P, arg2P, arg3P, arg4P) :|: arg2 = arg3P && 0 = arg2P && 0 <= arg1P - 1 && 0 <= arg1 - 1 && -1 <= arg2 - 1 && arg1P <= arg1
(2) f452_0_main_GE(x, x1, x2, x3) -> f452_0_main_GE'(x4, x5, x6, x7) :|: x1 <= x2 - 1 && 0 <= x2 - 1 && x1 - 2 * x8 = 0 && 0 <= x - 1 && x = x4 && x1 = x5 && x2 = x6
(3) f452_0_main_GE'(x9, x10, x11, x12) -> f276_0_sin_GT(x13, x14, x15, x16) :|: x10 <= x11 - 1 && 0 <= x11 - 1 && x10 - 2 * x17 = 0 && 0 <= x9 - 1 && x10 - 2 * x17 <= 1 && 0 <= x10 - 2 * x17 && x11 = x13 && x10 = x14
(4) f452_0_main_GE(x18, x19, x20, x21) -> f452_0_main_GE'(x22, x23, x24, x25) :|: x19 <= x20 - 1 && 0 <= x20 - 1 && x19 - 2 * x26 = 1 && x19 - 3 * x27 = 0 && 0 <= x18 - 1 && x18 = x22 && x19 = x23 && x20 = x24
(5) f452_0_main_GE'(x28, x29, x30, x31) -> f307_0_cos_GT(x32, x33, x34, x35) :|: x29 <= x30 - 1 && 0 <= x30 - 1 && x29 - 2 * x36 = 1 && x29 - 3 * x37 = 0 && 0 <= x28 - 1 && 0 <= x29 - 2 * x36 && x29 - 2 * x36 <= 1 && x29 - 3 * x37 <= 2 && 0 <= x29 - 3 * x37 && x30 = x32 && x29 = x33
(6) f452_0_main_GE(x38, x39, x40, x41) -> f452_0_main_GE'(x42, x43, x44, x45) :|: x39 <= x40 - 1 && 0 <= x40 - 1 && x39 - 2 * x46 = 1 && 0 <= x39 - 3 * x47 - 1 && x39 - 5 * x48 = 0 && 0 <= x38 - 1 && x38 = x42 && x39 = x43 && x40 = x44
(7) f452_0_main_GE'(x49, x50, x51, x52) -> f342_0_exp_GT(x53, x54, x55, x56) :|: 0 <= x50 - 3 * x57 - 1 && x50 <= x51 - 1 && 0 <= x51 - 1 && x50 - 2 * x58 = 1 && x50 - 5 * x59 = 0 && 0 <= x49 - 1 && 0 <= x50 - 2 * x58 && x50 - 2 * x58 <= 1 && x50 - 3 * x57 <= 2 && x50 - 5 * x59 <= 4 && 0 <= x50 - 5 * x59 && x51 = x53 && x50 = x54
(8) f452_0_main_GE(x60, x61, x62, x63) -> f452_0_main_GE'(x64, x65, x66, x67) :|: x61 - 2 * x68 = 1 && x61 <= x62 - 1 && 0 <= x61 - 5 * x69 - 1 && 0 <= x61 - 3 * x70 - 1 && x71 <= x60 && 0 <= x60 - 1 && 0 <= x71 - 1 && x60 = x64 && x61 = x65 && x62 = x66
(9) f452_0_main_GE'(x72, x73, x74, x75) -> f697_0_main_GE(x76, x77, x78, x79) :|: 0 <= x73 - 5 * x80 - 1 && 0 <= x73 - 3 * x81 - 1 && x73 - 2 * x82 = 1 && x73 <= x74 - 1 && x76 <= x72 && 0 <= x72 - 1 && 0 <= x76 - 1 && 0 <= x73 - 2 * x82 && x73 - 2 * x82 <= 1 && x73 - 3 * x81 <= 2 && x73 - 5 * x80 <= 4 && x73 = x77 && 0 = x78 && x74 = x79
(10) f697_0_main_GE(x83, x84, x85, x86) -> f697_0_main_GE(x87, x88, x89, x90) :|: x86 = x90 && x85 + 1 = x89 && x84 = x88 && 0 <= x87 - 1 && 0 <= x83 - 1 && x85 <= 99 && x87 <= x83
(11) f452_0_main_GE(x92, x93, x94, x96) -> f452_0_main_GE(x97, x98, x101, x102) :|: x94 = x101 && 1 = x98 && 0 = x93 && 0 <= x97 - 1 && 0 <= x92 - 1 && 0 <= x94 - 1 && x97 <= x92
(12) f697_0_main_GE(x103, x106, x107, x108) -> f452_0_main_GE(x112, x113, x114, x118) :|: x108 = x114 && x106 + 1 = x113 && 0 <= x112 - 1 && 0 <= x103 - 1 && x112 <= x103 && 99 <= x107 - 1 && -1 <= x108 - 1
(13) f452_0_main_GE(x119, x120, x125, x126) -> f452_0_main_GE'(x127, x128, x132, x133) :|: x120 <= x125 - 1 && 0 <= x125 - 1 && x120 - 2 * x134 = 1 && 0 <= x120 - 3 * x139 - 1 && x120 - 5 * x140 = 0 && x141 <= x119 && 0 <= x119 - 1 && 0 <= x141 - 1 && x119 = x127 && x120 = x128 && x125 = x132
(14) f452_0_main_GE'(x142, x146, x147, x148) -> f452_0_main_GE(x152, x153, x154, x155) :|: 0 <= x146 - 3 * x158 - 1 && x146 <= x147 - 1 && 0 <= x147 - 1 && x146 - 2 * x159 = 1 && x146 - 5 * x160 = 0 && x152 <= x142 && 0 <= x142 - 1 && 0 <= x152 - 1 && 0 <= x146 - 2 * x159 && x146 - 2 * x159 <= 1 && x146 - 3 * x158 <= 2 && x146 - 5 * x160 <= 4 && 0 <= x146 - 5 * x160 && x146 + 1 = x153 && x147 = x154
(15) f452_0_main_GE(x163, x164, x165, x166) -> f452_0_main_GE'(x168, x169, x170, x174) :|: x164 <= x165 - 1 && 0 <= x165 - 1 && x164 - 2 * x175 = 1 && x164 - 3 * x176 = 0 && x180 <= x163 && 0 <= x163 - 1 && 0 <= x180 - 1 && x163 = x168 && x164 = x169 && x165 = x170
(16) f452_0_main_GE'(x181, x185, x186, x190) -> f452_0_main_GE(x191, x192, x193, x194) :|: x185 <= x186 - 1 && 0 <= x186 - 1 && x185 - 2 * x195 = 1 && x185 - 3 * x196 = 0 && x191 <= x181 && 0 <= x181 - 1 && 0 <= x191 - 1 && 0 <= x185 - 2 * x195 && x185 - 2 * x195 <= 1 && x185 - 3 * x196 <= 2 && 0 <= x185 - 3 * x196 && x185 + 1 = x192 && x186 = x193
(17) f452_0_main_GE(x197, x198, x199, x200) -> f452_0_main_GE'(x201, x202, x203, x204) :|: x198 <= x199 - 1 && 0 <= x199 - 1 && x198 - 2 * x205 = 0 && x206 <= x197 && 0 <= x197 - 1 && 0 <= x206 - 1 && x197 = x201 && x198 = x202 && x199 = x203
(18) f452_0_main_GE'(x207, x208, x209, x210) -> f452_0_main_GE(x211, x212, x213, x214) :|: x208 <= x209 - 1 && 0 <= x209 - 1 && x208 - 2 * x215 = 0 && x211 <= x207 && 0 <= x207 - 1 && 0 <= x211 - 1 && x208 - 2 * x215 <= 1 && 0 <= x208 - 2 * x215 && x208 + 1 = x212 && x209 = x213
(19) f276_0_sin_GT(x216, x217, x218, x219) -> f345_0_power_GT(x220, x221, x222, x223) :|: x217 = x220 && 0 <= x216 - 1 && 0 <= x217 - 1
(20) f276_0_sin_GT(x224, x225, x226, x227) -> f566_0_sin_InvokeMethod(x228, x229, x230, x231) :|: 2 * x225 + 1 = x230 && x224 = x229 && x225 = x228 && 0 <= x225 - 1 && 0 <= 2 * x225 - 1 && 0 <= x224 - 1
(21) f566_0_sin_InvokeMethod(x232, x233, x234, x235) -> f345_0_power_GT(x236, x237, x238, x239) :|: x234 = x236 && 0 <= x232 - 1 && 1 <= x234 - 1 && 0 <= x233 - 1
(22) f566_0_sin_InvokeMethod(x240, x241, x242, x243) -> f453_0_fact_GT(x244, x245, x246, x247) :|: 2 * x240 + 1 = x244 && 1 <= x242 - 1 && 0 <= 2 * x240 - 1 && 0 <= x240 - 1 && 0 <= x241 - 1
(23) f566_0_sin_InvokeMethod(x248, x249, x250, x251) -> f566_0_sin_InvokeMethod'(x252, x253, x254, x255) :|: x250 = x254 && x249 = x253 && x248 = x252 && 0 <= 2 * x248 - 1 && x248 - 1 <= x248 - 1 && 1 <= x250 - 1 && 0 <= x248 - 1 && 0 <= x249 - 1
(24) f566_0_sin_InvokeMethod'(x256, x257, x258, x259) -> f276_0_sin_GT(x260, x261, x262, x263) :|: 0 <= x257 - 1 && 0 <= x256 - 1 && 1 <= x258 - 1 && 0 <= 2 * x256 - 1 && x256 - 1 <= x256 - 1 && x264 - x265 * x266 <= x265 - 1 && 0 <= x264 - x265 * x266 && x257 = x260 && x256 - 1 = x261
(25) f307_0_cos_GT(x267, x268, x269, x270) -> f345_0_power_GT(x271, x272, x273, x274) :|: x268 = x271 && 0 <= x267 - 1 && 0 <= x268 - 1
(26) f307_0_cos_GT(x275, x276, x277, x278) -> f552_0_cos_InvokeMethod(x279, x280, x281, x282) :|: 2 * x276 = x281 && x275 = x280 && x276 = x279 && 0 <= x275 - 1 && 0 <= x276 - 1
(27) f552_0_cos_InvokeMethod(x283, x284, x285, x286) -> f345_0_power_GT(x287, x288, x289, x290) :|: x285 = x287 && 0 <= x283 - 1 && 0 <= x284 - 1 && 1 <= x285 - 1
(28) f552_0_cos_InvokeMethod(x291, x292, x293, x294) -> f453_0_fact_GT(x295, x296, x297, x298) :|: 2 * x291 = x295 && 1 <= x293 - 1 && 1 <= 2 * x291 - 1 && 0 <= x291 - 1 && 0 <= x292 - 1
(29) f552_0_cos_InvokeMethod(x299, x300, x301, x302) -> f552_0_cos_InvokeMethod'(x303, x304, x305, x306) :|: x301 = x305 && x300 = x304 && x299 = x303 && 1 <= 2 * x299 - 1 && x299 - 1 <= x299 - 1 && 1 <= x301 - 1 && 0 <= x299 - 1 && 0 <= x300 - 1
(30) f552_0_cos_InvokeMethod'(x307, x308, x309, x310) -> f307_0_cos_GT(x311, x312, x313, x314) :|: 0 <= x308 - 1 && 0 <= x307 - 1 && 1 <= x309 - 1 && 1 <= 2 * x307 - 1 && x307 - 1 <= x307 - 1 && x315 - x316 * x317 <= x316 - 1 && 0 <= x315 - x316 * x317 && x308 = x311 && x307 - 1 = x312
(31) f342_0_exp_GT(x318, x319, x320, x321) -> f345_0_power_GT(x322, x323, x324, x325) :|: x319 = x322 && 0 <= x318 - 1 && 0 <= x319 - 1
(32) f638_0_exp_InvokeMethod(x326, x327, x328, x329) -> f342_0_exp_GT(x330, x331, x332, x333) :|: x328 = x331 && x327 = x330 && 0 <= x326 - 1 && 0 <= x327 - 1 && x328 <= x326 - 1
(33) f345_0_power_GT(x334, x335, x336, x337) -> f345_0_power_GT(x338, x339, x340, x341) :|: x334 - 1 = x338 && 0 <= x334 - 1
(34) f453_0_fact_GT(x342, x343, x344, x345) -> f453_0_fact_GT(x346, x347, x348, x349) :|: x342 - 1 = x346 && x342 - 1 <= x342 - 1 && 0 <= x342 - 1
(35) f342_0_exp_GT(x350, x351, x352, x353) -> f453_0_fact_GT(x354, x355, x356, x357) :|: x351 = x354 && 0 <= x350 - 1 && 0 <= x351 - 1
(36) f342_0_exp_GT(x358, x359, x360, x361) -> f342_0_exp_GT'(x362, x363, x364, x365) :|: x359 = x363 && x358 = x362 && 0 <= x358 - 1 && 0 <= x359 - 1
(37) f342_0_exp_GT'(x366, x367, x368, x369) -> f638_0_exp_InvokeMethod(x370, x371, x372, x373) :|: 0 <= x366 - 1 && 0 <= x367 - 1 && x374 - x375 * x376 <= x375 - 1 && 0 <= x374 - x375 * x376 && x367 = x370 && x366 = x371 && x367 - 1 = x372
(38) f342_0_exp_GT(x377, x378, x379, x380) -> f342_0_exp_GT'(x381, x382, x383, x384) :|: x378 = x382 && x377 = x381 && 0 <= x378 - 1 && 0 <= x377 - 1
(39) f342_0_exp_GT'(x385, x386, x387, x388) -> f638_0_exp_InvokeMethod(x389, x390, x391, x392) :|: 0 <= x386 - 1 && 0 <= x385 - 1 && x393 - x394 * x395 <= x394 - 1 && 0 <= x393 - x394 * x395 && x386 = x389 && x385 = x390 && x386 - 1 = x391
(40) __init(x396, x397, x398, x399) -> f1_0_main_ConstantStackPush(x400, x401, x402, x403) :|: 0 <= 0

Arcs:
(1) -> (2), (11), (17)
(2) -> (3), (18)
(3) -> (19), (20)
(4) -> (5), (16)
(5) -> (25), (26)
(6) -> (5), (7), (14), (16)
(7) -> (31), (35), (36), (38)
(8) -> (5), (7), (9), (14), (16)
(9) -> (10)
(10) -> (10), (12)
(11) -> (8)
(12) -> (2), (4), (6), (8), (11), (13), (15), (17)
(13) -> (5), (7), (14), (16)
(14) -> (2), (17)
(15) -> (5), (16)
(16) -> (2), (17)
(17) -> (3), (18)
(18) -> (4), (6), (8), (13), (15)
(19) -> (33)
(20) -> (21), (22), (23)
(21) -> (33)
(22) -> (34)
(23) -> (24)
(24) -> (19), (20)
(25) -> (33)
(26) -> (27), (28), (29)
(27) -> (33)
(28) -> (34)
(29) -> (30)
(30) -> (25), (26)
(31) -> (33)
(32) -> (31), (35), (36), (38)
(33) -> (33)
(34) -> (34)
(35) -> (34)
(36) -> (37), (39)
(37) -> (32)
(38) -> (37), (39)
(39) -> (32)
(40) -> (1)

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

(4)
Complex Obligation (AND)

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

(5)
Obligation:

Termination digraph:
Nodes:
(1) f452_0_main_GE(x, x1, x2, x3) -> f452_0_main_GE'(x4, x5, x6, x7) :|: x1 <= x2 - 1 && 0 <= x2 - 1 && x1 - 2 * x8 = 0 && 0 <= x - 1 && x = x4 && x1 = x5 && x2 = x6
(2) f697_0_main_GE(x103, x106, x107, x108) -> f452_0_main_GE(x112, x113, x114, x118) :|: x108 = x114 && x106 + 1 = x113 && 0 <= x112 - 1 && 0 <= x103 - 1 && x112 <= x103 && 99 <= x107 - 1 && -1 <= x108 - 1
(3) f697_0_main_GE(x83, x84, x85, x86) -> f697_0_main_GE(x87, x88, x89, x90) :|: x86 = x90 && x85 + 1 = x89 && x84 = x88 && 0 <= x87 - 1 && 0 <= x83 - 1 && x85 <= 99 && x87 <= x83
(4) f452_0_main_GE'(x72, x73, x74, x75) -> f697_0_main_GE(x76, x77, x78, x79) :|: 0 <= x73 - 5 * x80 - 1 && 0 <= x73 - 3 * x81 - 1 && x73 - 2 * x82 = 1 && x73 <= x74 - 1 && x76 <= x72 && 0 <= x72 - 1 && 0 <= x76 - 1 && 0 <= x73 - 2 * x82 && x73 - 2 * x82 <= 1 && x73 - 3 * x81 <= 2 && x73 - 5 * x80 <= 4 && x73 = x77 && 0 = x78 && x74 = x79
(5) f452_0_main_GE(x60, x61, x62, x63) -> f452_0_main_GE'(x64, x65, x66, x67) :|: x61 - 2 * x68 = 1 && x61 <= x62 - 1 && 0 <= x61 - 5 * x69 - 1 && 0 <= x61 - 3 * x70 - 1 && x71 <= x60 && 0 <= x60 - 1 && 0 <= x71 - 1 && x60 = x64 && x61 = x65 && x62 = x66
(6) f452_0_main_GE'(x207, x208, x209, x210) -> f452_0_main_GE(x211, x212, x213, x214) :|: x208 <= x209 - 1 && 0 <= x209 - 1 && x208 - 2 * x215 = 0 && x211 <= x207 && 0 <= x207 - 1 && 0 <= x211 - 1 && x208 - 2 * x215 <= 1 && 0 <= x208 - 2 * x215 && x208 + 1 = x212 && x209 = x213
(7) f452_0_main_GE(x197, x198, x199, x200) -> f452_0_main_GE'(x201, x202, x203, x204) :|: x198 <= x199 - 1 && 0 <= x199 - 1 && x198 - 2 * x205 = 0 && x206 <= x197 && 0 <= x197 - 1 && 0 <= x206 - 1 && x197 = x201 && x198 = x202 && x199 = x203
(8) f452_0_main_GE'(x181, x185, x186, x190) -> f452_0_main_GE(x191, x192, x193, x194) :|: x185 <= x186 - 1 && 0 <= x186 - 1 && x185 - 2 * x195 = 1 && x185 - 3 * x196 = 0 && x191 <= x181 && 0 <= x181 - 1 && 0 <= x191 - 1 && 0 <= x185 - 2 * x195 && x185 - 2 * x195 <= 1 && x185 - 3 * x196 <= 2 && 0 <= x185 - 3 * x196 && x185 + 1 = x192 && x186 = x193
(9) f452_0_main_GE(x163, x164, x165, x166) -> f452_0_main_GE'(x168, x169, x170, x174) :|: x164 <= x165 - 1 && 0 <= x165 - 1 && x164 - 2 * x175 = 1 && x164 - 3 * x176 = 0 && x180 <= x163 && 0 <= x163 - 1 && 0 <= x180 - 1 && x163 = x168 && x164 = x169 && x165 = x170
(10) f452_0_main_GE(x18, x19, x20, x21) -> f452_0_main_GE'(x22, x23, x24, x25) :|: x19 <= x20 - 1 && 0 <= x20 - 1 && x19 - 2 * x26 = 1 && x19 - 3 * x27 = 0 && 0 <= x18 - 1 && x18 = x22 && x19 = x23 && x20 = x24
(11) f452_0_main_GE'(x142, x146, x147, x148) -> f452_0_main_GE(x152, x153, x154, x155) :|: 0 <= x146 - 3 * x158 - 1 && x146 <= x147 - 1 && 0 <= x147 - 1 && x146 - 2 * x159 = 1 && x146 - 5 * x160 = 0 && x152 <= x142 && 0 <= x142 - 1 && 0 <= x152 - 1 && 0 <= x146 - 2 * x159 && x146 - 2 * x159 <= 1 && x146 - 3 * x158 <= 2 && x146 - 5 * x160 <= 4 && 0 <= x146 - 5 * x160 && x146 + 1 = x153 && x147 = x154
(12) f452_0_main_GE(x119, x120, x125, x126) -> f452_0_main_GE'(x127, x128, x132, x133) :|: x120 <= x125 - 1 && 0 <= x125 - 1 && x120 - 2 * x134 = 1 && 0 <= x120 - 3 * x139 - 1 && x120 - 5 * x140 = 0 && x141 <= x119 && 0 <= x119 - 1 && 0 <= x141 - 1 && x119 = x127 && x120 = x128 && x125 = x132
(13) f452_0_main_GE(x38, x39, x40, x41) -> f452_0_main_GE'(x42, x43, x44, x45) :|: x39 <= x40 - 1 && 0 <= x40 - 1 && x39 - 2 * x46 = 1 && 0 <= x39 - 3 * x47 - 1 && x39 - 5 * x48 = 0 && 0 <= x38 - 1 && x38 = x42 && x39 = x43 && x40 = x44
(14) f452_0_main_GE(x92, x93, x94, x96) -> f452_0_main_GE(x97, x98, x101, x102) :|: x94 = x101 && 1 = x98 && 0 = x93 && 0 <= x97 - 1 && 0 <= x92 - 1 && 0 <= x94 - 1 && x97 <= x92

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

This digraph is fully evaluated!

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

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

(7)
Obligation:
Rules:
f452_0_main_GE(x18:0, x19:0, x20:0, x21:0) -> f452_0_main_GE'(x18:0, x19:0, x20:0, x25:0) :|: x19:0 - 3 * x27:0 = 0 && x18:0 > 0 && x19:0 - 2 * x26:0 = 1 && x20:0 > 0 && x20:0 - 1 >= x19:0
f452_0_main_GE(x197:0, x198:0, x199:0, x200:0) -> f452_0_main_GE'(x197:0, x198:0, x199:0, x204:0) :|: x197:0 > 0 && x206:0 > 0 && x206:0 <= x197:0 && x198:0 - 2 * x205:0 = 0 && x199:0 > 0 && x199:0 - 1 >= x198:0
f452_0_main_GE(x38:0, x39:0, x40:0, x41:0) -> f452_0_main_GE'(x38:0, x39:0, x40:0, x45:0) :|: x39:0 - 5 * x48:0 = 0 && x38:0 > 0 && x39:0 - 3 * x47:0 >= 1 && x39:0 - 2 * x46:0 = 1 && x40:0 > 0 && x40:0 - 1 >= x39:0
f452_0_main_GE'(x142:0, x146:0, x147:0, x148:0) -> f452_0_main_GE(x152:0, x146:0 + 1, x147:0, x155:0) :|: x146:0 - 5 * x160:0 <= 4 && x146:0 - 5 * x160:0 >= 0 && x146:0 - 3 * x158:0 <= 2 && x146:0 - 2 * x159:0 <= 1 && x146:0 - 2 * x159:0 >= 0 && x152:0 > 0 && x142:0 > 0 && x152:0 <= x142:0 && x146:0 - 5 * x160:0 = 0 && x146:0 - 2 * x159:0 = 1 && x147:0 > 0 && x147:0 - 1 >= x146:0 && x146:0 - 3 * x158:0 >= 1
f452_0_main_GE(x4:0, x1:0, x2:0, x3:0) -> f452_0_main_GE'(x4:0, x1:0, x2:0, x7:0) :|: x1:0 - 2 * x8:0 = 0 && x4:0 > 0 && x2:0 > 0 && x2:0 - 1 >= x1:0
f452_0_main_GE(x119:0, x120:0, x125:0, x126:0) -> f452_0_main_GE'(x119:0, x120:0, x125:0, x133:0) :|: x119:0 > 0 && x141:0 > 0 && x141:0 <= x119:0 && x120:0 - 5 * x140:0 = 0 && x120:0 - 3 * x139:0 >= 1 && x120:0 - 2 * x134:0 = 1 && x125:0 > 0 && x125:0 - 1 >= x120:0
f452_0_main_GE'(x72:0, x73:0, x74:0, x75:0) -> f697_0_main_GE(x76:0, x73:0, 0, x74:0) :|: x73:0 - 3 * x81:0 <= 2 && x73:0 - 5 * x80:0 <= 4 && x73:0 - 2 * x82:0 <= 1 && x73:0 - 2 * x82:0 >= 0 && x76:0 > 0 && x72:0 > 0 && x76:0 <= x72:0 && x74:0 - 1 >= x73:0 && x73:0 - 2 * x82:0 = 1 && x73:0 - 3 * x81:0 >= 1 && x73:0 - 5 * x80:0 >= 1
f452_0_main_GE(x92:0, cons_0, x101:0, x96:0) -> f452_0_main_GE(x97:0, 1, x101:0, x102:0) :|: x101:0 > 0 && x97:0 <= x92:0 && x97:0 > 0 && x92:0 > 0 && cons_0 = 0
f697_0_main_GE(x103:0, x106:0, x107:0, x108:0) -> f452_0_main_GE(x112:0, x106:0 + 1, x108:0, x118:0) :|: x107:0 > 99 && x108:0 > -1 && x112:0 <= x103:0 && x112:0 > 0 && x103:0 > 0
f452_0_main_GE(x163:0, x164:0, x165:0, x166:0) -> f452_0_main_GE'(x163:0, x164:0, x165:0, x174:0) :|: x163:0 > 0 && x180:0 > 0 && x180:0 <= x163:0 && x164:0 - 3 * x176:0 = 0 && x164:0 - 2 * x175:0 = 1 && x165:0 > 0 && x165:0 - 1 >= x164:0
f452_0_main_GE(x60:0, x61:0, x62:0, x63:0) -> f452_0_main_GE'(x60:0, x61:0, x62:0, x67:0) :|: x60:0 > 0 && x71:0 > 0 && x71:0 <= x60:0 && x61:0 - 3 * x70:0 >= 1 && x61:0 - 5 * x69:0 >= 1 && x62:0 - 1 >= x61:0 && x61:0 - 2 * x68:0 = 1
f452_0_main_GE'(x207:0, x208:0, x209:0, x210:0) -> f452_0_main_GE(x211:0, x208:0 + 1, x209:0, x214:0) :|: x208:0 - 2 * x215:0 <= 1 && x208:0 - 2 * x215:0 >= 0 && x211:0 > 0 && x207:0 > 0 && x211:0 <= x207:0 && x208:0 - 2 * x215:0 = 0 && x209:0 > 0 && x209:0 - 1 >= x208:0
f697_0_main_GE(x83:0, x84:0, x85:0, x86:0) -> f697_0_main_GE(x87:0, x84:0, x85:0 + 1, x86:0) :|: x85:0 < 100 && x87:0 <= x83:0 && x87:0 > 0 && x83:0 > 0
f452_0_main_GE'(x181:0, x185:0, x186:0, x190:0) -> f452_0_main_GE(x191:0, x185:0 + 1, x186:0, x194:0) :|: x185:0 - 3 * x196:0 <= 2 && x185:0 - 3 * x196:0 >= 0 && x185:0 - 2 * x195:0 <= 1 && x185:0 - 2 * x195:0 >= 0 && x191:0 > 0 && x181:0 > 0 && x191:0 <= x181:0 && x185:0 - 3 * x196:0 = 0 && x185:0 - 2 * x195:0 = 1 && x186:0 > 0 && x186:0 - 1 >= x185:0

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

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

   f452_0_main_GE(x1, x2, x3, x4) -> f452_0_main_GE(x1, x2, x3)
   f452_0_main_GE'(x1, x2, x3, x4) -> f452_0_main_GE'(x1, x2, x3)

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

(9)
Obligation:
Rules:
f452_0_main_GE(x18:0, x19:0, x20:0) -> f452_0_main_GE'(x18:0, x19:0, x20:0) :|: x19:0 - 3 * x27:0 = 0 && x18:0 > 0 && x19:0 - 2 * x26:0 = 1 && x20:0 > 0 && x20:0 - 1 >= x19:0
f452_0_main_GE(x197:0, x198:0, x199:0) -> f452_0_main_GE'(x197:0, x198:0, x199:0) :|: x197:0 > 0 && x206:0 > 0 && x206:0 <= x197:0 && x198:0 - 2 * x205:0 = 0 && x199:0 > 0 && x199:0 - 1 >= x198:0
f452_0_main_GE(x38:0, x39:0, x40:0) -> f452_0_main_GE'(x38:0, x39:0, x40:0) :|: x39:0 - 5 * x48:0 = 0 && x38:0 > 0 && x39:0 - 3 * x47:0 >= 1 && x39:0 - 2 * x46:0 = 1 && x40:0 > 0 && x40:0 - 1 >= x39:0
f452_0_main_GE'(x142:0, x146:0, x147:0) -> f452_0_main_GE(x152:0, x146:0 + 1, x147:0) :|: x146:0 - 5 * x160:0 <= 4 && x146:0 - 5 * x160:0 >= 0 && x146:0 - 3 * x158:0 <= 2 && x146:0 - 2 * x159:0 <= 1 && x146:0 - 2 * x159:0 >= 0 && x152:0 > 0 && x142:0 > 0 && x152:0 <= x142:0 && x146:0 - 5 * x160:0 = 0 && x146:0 - 2 * x159:0 = 1 && x147:0 > 0 && x147:0 - 1 >= x146:0 && x146:0 - 3 * x158:0 >= 1
f452_0_main_GE(x4:0, x1:0, x2:0) -> f452_0_main_GE'(x4:0, x1:0, x2:0) :|: x1:0 - 2 * x8:0 = 0 && x4:0 > 0 && x2:0 > 0 && x2:0 - 1 >= x1:0
f452_0_main_GE(x119:0, x120:0, x125:0) -> f452_0_main_GE'(x119:0, x120:0, x125:0) :|: x119:0 > 0 && x141:0 > 0 && x141:0 <= x119:0 && x120:0 - 5 * x140:0 = 0 && x120:0 - 3 * x139:0 >= 1 && x120:0 - 2 * x134:0 = 1 && x125:0 > 0 && x125:0 - 1 >= x120:0
f452_0_main_GE'(x72:0, x73:0, x74:0) -> f697_0_main_GE(x76:0, x73:0, 0, x74:0) :|: x73:0 - 3 * x81:0 <= 2 && x73:0 - 5 * x80:0 <= 4 && x73:0 - 2 * x82:0 <= 1 && x73:0 - 2 * x82:0 >= 0 && x76:0 > 0 && x72:0 > 0 && x76:0 <= x72:0 && x74:0 - 1 >= x73:0 && x73:0 - 2 * x82:0 = 1 && x73:0 - 3 * x81:0 >= 1 && x73:0 - 5 * x80:0 >= 1
f452_0_main_GE(x92:0, cons_0, x101:0) -> f452_0_main_GE(x97:0, 1, x101:0) :|: x101:0 > 0 && x97:0 <= x92:0 && x97:0 > 0 && x92:0 > 0 && cons_0 = 0
f697_0_main_GE(x103:0, x106:0, x107:0, x108:0) -> f452_0_main_GE(x112:0, x106:0 + 1, x108:0) :|: x107:0 > 99 && x108:0 > -1 && x112:0 <= x103:0 && x112:0 > 0 && x103:0 > 0
f452_0_main_GE(x163:0, x164:0, x165:0) -> f452_0_main_GE'(x163:0, x164:0, x165:0) :|: x163:0 > 0 && x180:0 > 0 && x180:0 <= x163:0 && x164:0 - 3 * x176:0 = 0 && x164:0 - 2 * x175:0 = 1 && x165:0 > 0 && x165:0 - 1 >= x164:0
f452_0_main_GE(x60:0, x61:0, x62:0) -> f452_0_main_GE'(x60:0, x61:0, x62:0) :|: x60:0 > 0 && x71:0 > 0 && x71:0 <= x60:0 && x61:0 - 3 * x70:0 >= 1 && x61:0 - 5 * x69:0 >= 1 && x62:0 - 1 >= x61:0 && x61:0 - 2 * x68:0 = 1
f452_0_main_GE'(x207:0, x208:0, x209:0) -> f452_0_main_GE(x211:0, x208:0 + 1, x209:0) :|: x208:0 - 2 * x215:0 <= 1 && x208:0 - 2 * x215:0 >= 0 && x211:0 > 0 && x207:0 > 0 && x211:0 <= x207:0 && x208:0 - 2 * x215:0 = 0 && x209:0 > 0 && x209:0 - 1 >= x208:0
f697_0_main_GE(x83:0, x84:0, x85:0, x86:0) -> f697_0_main_GE(x87:0, x84:0, x85:0 + 1, x86:0) :|: x85:0 < 100 && x87:0 <= x83:0 && x87:0 > 0 && x83:0 > 0
f452_0_main_GE'(x181:0, x185:0, x186:0) -> f452_0_main_GE(x191:0, x185:0 + 1, x186:0) :|: x185:0 - 3 * x196:0 <= 2 && x185:0 - 3 * x196:0 >= 0 && x185:0 - 2 * x195:0 <= 1 && x185:0 - 2 * x195:0 >= 0 && x191:0 > 0 && x181:0 > 0 && x191:0 <= x181:0 && x185:0 - 3 * x196:0 = 0 && x185:0 - 2 * x195:0 = 1 && x186:0 > 0 && x186:0 - 1 >= x185:0

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

(10) TempFilterProof (SOUND)
Used the following sort dictionary for filtering: 
f452_0_main_GE(INTEGER, VARIABLE, INTEGER)
f452_0_main_GE'(INTEGER, INTEGER, INTEGER)
f697_0_main_GE(INTEGER, VARIABLE, VARIABLE, VARIABLE)
Replaced non-predefined constructor symbols by 0.
----------------------------------------

(11)
Obligation:
Rules:
f452_0_main_GE(x18:0, x19:0, x20:0) -> f452_0_main_GE'(x18:0, x19:0, x20:0) :|: x19:0 - 3 * x27:0 = 0 && x18:0 > 0 && x19:0 - 2 * x26:0 = 1 && x20:0 > 0 && x20:0 - 1 >= x19:0
f452_0_main_GE(x197:0, x198:0, x199:0) -> f452_0_main_GE'(x197:0, x198:0, x199:0) :|: x197:0 > 0 && x206:0 > 0 && x206:0 <= x197:0 && x198:0 - 2 * x205:0 = 0 && x199:0 > 0 && x199:0 - 1 >= x198:0
f452_0_main_GE(x38:0, x39:0, x40:0) -> f452_0_main_GE'(x38:0, x39:0, x40:0) :|: x39:0 - 5 * x48:0 = 0 && x38:0 > 0 && x39:0 - 3 * x47:0 >= 1 && x39:0 - 2 * x46:0 = 1 && x40:0 > 0 && x40:0 - 1 >= x39:0
f452_0_main_GE'(x142:0, x146:0, x147:0) -> f452_0_main_GE(x152:0, c, x147:0) :|: c = x146:0 + 1 && (x146:0 - 5 * x160:0 <= 4 && x146:0 - 5 * x160:0 >= 0 && x146:0 - 3 * x158:0 <= 2 && x146:0 - 2 * x159:0 <= 1 && x146:0 - 2 * x159:0 >= 0 && x152:0 > 0 && x142:0 > 0 && x152:0 <= x142:0 && x146:0 - 5 * x160:0 = 0 && x146:0 - 2 * x159:0 = 1 && x147:0 > 0 && x147:0 - 1 >= x146:0 && x146:0 - 3 * x158:0 >= 1)
f452_0_main_GE(x4:0, x1:0, x2:0) -> f452_0_main_GE'(x4:0, x1:0, x2:0) :|: x1:0 - 2 * x8:0 = 0 && x4:0 > 0 && x2:0 > 0 && x2:0 - 1 >= x1:0
f452_0_main_GE(x119:0, x120:0, x125:0) -> f452_0_main_GE'(x119:0, x120:0, x125:0) :|: x119:0 > 0 && x141:0 > 0 && x141:0 <= x119:0 && x120:0 - 5 * x140:0 = 0 && x120:0 - 3 * x139:0 >= 1 && x120:0 - 2 * x134:0 = 1 && x125:0 > 0 && x125:0 - 1 >= x120:0
f452_0_main_GE'(x72:0, x73:0, x74:0) -> f697_0_main_GE(x76:0, x73:0, c1, x74:0) :|: c1 = 0 && (x73:0 - 3 * x81:0 <= 2 && x73:0 - 5 * x80:0 <= 4 && x73:0 - 2 * x82:0 <= 1 && x73:0 - 2 * x82:0 >= 0 && x76:0 > 0 && x72:0 > 0 && x76:0 <= x72:0 && x74:0 - 1 >= x73:0 && x73:0 - 2 * x82:0 = 1 && x73:0 - 3 * x81:0 >= 1 && x73:0 - 5 * x80:0 >= 1)
f452_0_main_GE(x92:0, c2, x101:0) -> f452_0_main_GE(x97:0, c3, x101:0) :|: c3 = 1 && c2 = 0 && (x101:0 > 0 && x97:0 <= x92:0 && x97:0 > 0 && x92:0 > 0 && cons_0 = 0)
f697_0_main_GE(x103:0, x106:0, x107:0, x108:0) -> f452_0_main_GE(x112:0, c4, x108:0) :|: c4 = x106:0 + 1 && (x107:0 > 99 && x108:0 > -1 && x112:0 <= x103:0 && x112:0 > 0 && x103:0 > 0)
f452_0_main_GE(x163:0, x164:0, x165:0) -> f452_0_main_GE'(x163:0, x164:0, x165:0) :|: x163:0 > 0 && x180:0 > 0 && x180:0 <= x163:0 && x164:0 - 3 * x176:0 = 0 && x164:0 - 2 * x175:0 = 1 && x165:0 > 0 && x165:0 - 1 >= x164:0
f452_0_main_GE(x60:0, x61:0, x62:0) -> f452_0_main_GE'(x60:0, x61:0, x62:0) :|: x60:0 > 0 && x71:0 > 0 && x71:0 <= x60:0 && x61:0 - 3 * x70:0 >= 1 && x61:0 - 5 * x69:0 >= 1 && x62:0 - 1 >= x61:0 && x61:0 - 2 * x68:0 = 1
f452_0_main_GE'(x207:0, x208:0, x209:0) -> f452_0_main_GE(x211:0, c5, x209:0) :|: c5 = x208:0 + 1 && (x208:0 - 2 * x215:0 <= 1 && x208:0 - 2 * x215:0 >= 0 && x211:0 > 0 && x207:0 > 0 && x211:0 <= x207:0 && x208:0 - 2 * x215:0 = 0 && x209:0 > 0 && x209:0 - 1 >= x208:0)
f697_0_main_GE(x83:0, x84:0, x85:0, x86:0) -> f697_0_main_GE(x87:0, x84:0, c6, x86:0) :|: c6 = x85:0 + 1 && (x85:0 < 100 && x87:0 <= x83:0 && x87:0 > 0 && x83:0 > 0)
f452_0_main_GE'(x181:0, x185:0, x186:0) -> f452_0_main_GE(x191:0, c7, x186:0) :|: c7 = x185:0 + 1 && (x185:0 - 3 * x196:0 <= 2 && x185:0 - 3 * x196:0 >= 0 && x185:0 - 2 * x195:0 <= 1 && x185:0 - 2 * x195:0 >= 0 && x191:0 > 0 && x181:0 > 0 && x191:0 <= x181:0 && x185:0 - 3 * x196:0 = 0 && x185:0 - 2 * x195:0 = 1 && x186:0 > 0 && x186:0 - 1 >= x185:0)

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

(12) RankingReductionPairProof (EQUIVALENT)
Interpretation:
[ f452_0_main_GE ] = 3*f452_0_main_GE_3 + -3*f452_0_main_GE_2 + 1
[ f452_0_main_GE' ] = -3*f452_0_main_GE'_2 + 3*f452_0_main_GE'_3
[ f697_0_main_GE ] = -3*f697_0_main_GE_2 + 3*f697_0_main_GE_4 + -1

The following rules are decreasing:
f452_0_main_GE(x18:0, x19:0, x20:0) -> f452_0_main_GE'(x18:0, x19:0, x20:0) :|: x19:0 - 3 * x27:0 = 0 && x18:0 > 0 && x19:0 - 2 * x26:0 = 1 && x20:0 > 0 && x20:0 - 1 >= x19:0
f452_0_main_GE(x197:0, x198:0, x199:0) -> f452_0_main_GE'(x197:0, x198:0, x199:0) :|: x197:0 > 0 && x206:0 > 0 && x206:0 <= x197:0 && x198:0 - 2 * x205:0 = 0 && x199:0 > 0 && x199:0 - 1 >= x198:0
f452_0_main_GE(x38:0, x39:0, x40:0) -> f452_0_main_GE'(x38:0, x39:0, x40:0) :|: x39:0 - 5 * x48:0 = 0 && x38:0 > 0 && x39:0 - 3 * x47:0 >= 1 && x39:0 - 2 * x46:0 = 1 && x40:0 > 0 && x40:0 - 1 >= x39:0
f452_0_main_GE'(x142:0, x146:0, x147:0) -> f452_0_main_GE(x152:0, c, x147:0) :|: c = x146:0 + 1 && (x146:0 - 5 * x160:0 <= 4 && x146:0 - 5 * x160:0 >= 0 && x146:0 - 3 * x158:0 <= 2 && x146:0 - 2 * x159:0 <= 1 && x146:0 - 2 * x159:0 >= 0 && x152:0 > 0 && x142:0 > 0 && x152:0 <= x142:0 && x146:0 - 5 * x160:0 = 0 && x146:0 - 2 * x159:0 = 1 && x147:0 > 0 && x147:0 - 1 >= x146:0 && x146:0 - 3 * x158:0 >= 1)
f452_0_main_GE(x4:0, x1:0, x2:0) -> f452_0_main_GE'(x4:0, x1:0, x2:0) :|: x1:0 - 2 * x8:0 = 0 && x4:0 > 0 && x2:0 > 0 && x2:0 - 1 >= x1:0
f452_0_main_GE(x119:0, x120:0, x125:0) -> f452_0_main_GE'(x119:0, x120:0, x125:0) :|: x119:0 > 0 && x141:0 > 0 && x141:0 <= x119:0 && x120:0 - 5 * x140:0 = 0 && x120:0 - 3 * x139:0 >= 1 && x120:0 - 2 * x134:0 = 1 && x125:0 > 0 && x125:0 - 1 >= x120:0
f452_0_main_GE'(x72:0, x73:0, x74:0) -> f697_0_main_GE(x76:0, x73:0, c1, x74:0) :|: c1 = 0 && (x73:0 - 3 * x81:0 <= 2 && x73:0 - 5 * x80:0 <= 4 && x73:0 - 2 * x82:0 <= 1 && x73:0 - 2 * x82:0 >= 0 && x76:0 > 0 && x72:0 > 0 && x76:0 <= x72:0 && x74:0 - 1 >= x73:0 && x73:0 - 2 * x82:0 = 1 && x73:0 - 3 * x81:0 >= 1 && x73:0 - 5 * x80:0 >= 1)
f452_0_main_GE(x92:0, c2, x101:0) -> f452_0_main_GE(x97:0, c3, x101:0) :|: c3 = 1 && c2 = 0 && (x101:0 > 0 && x97:0 <= x92:0 && x97:0 > 0 && x92:0 > 0 && cons_0 = 0)
f697_0_main_GE(x103:0, x106:0, x107:0, x108:0) -> f452_0_main_GE(x112:0, c4, x108:0) :|: c4 = x106:0 + 1 && (x107:0 > 99 && x108:0 > -1 && x112:0 <= x103:0 && x112:0 > 0 && x103:0 > 0)
f452_0_main_GE(x163:0, x164:0, x165:0) -> f452_0_main_GE'(x163:0, x164:0, x165:0) :|: x163:0 > 0 && x180:0 > 0 && x180:0 <= x163:0 && x164:0 - 3 * x176:0 = 0 && x164:0 - 2 * x175:0 = 1 && x165:0 > 0 && x165:0 - 1 >= x164:0
f452_0_main_GE(x60:0, x61:0, x62:0) -> f452_0_main_GE'(x60:0, x61:0, x62:0) :|: x60:0 > 0 && x71:0 > 0 && x71:0 <= x60:0 && x61:0 - 3 * x70:0 >= 1 && x61:0 - 5 * x69:0 >= 1 && x62:0 - 1 >= x61:0 && x61:0 - 2 * x68:0 = 1
f452_0_main_GE'(x207:0, x208:0, x209:0) -> f452_0_main_GE(x211:0, c5, x209:0) :|: c5 = x208:0 + 1 && (x208:0 - 2 * x215:0 <= 1 && x208:0 - 2 * x215:0 >= 0 && x211:0 > 0 && x207:0 > 0 && x211:0 <= x207:0 && x208:0 - 2 * x215:0 = 0 && x209:0 > 0 && x209:0 - 1 >= x208:0)
f452_0_main_GE'(x181:0, x185:0, x186:0) -> f452_0_main_GE(x191:0, c7, x186:0) :|: c7 = x185:0 + 1 && (x185:0 - 3 * x196:0 <= 2 && x185:0 - 3 * x196:0 >= 0 && x185:0 - 2 * x195:0 <= 1 && x185:0 - 2 * x195:0 >= 0 && x191:0 > 0 && x181:0 > 0 && x191:0 <= x181:0 && x185:0 - 3 * x196:0 = 0 && x185:0 - 2 * x195:0 = 1 && x186:0 > 0 && x186:0 - 1 >= x185:0)

The following rules are bounded:
f452_0_main_GE(x18:0, x19:0, x20:0) -> f452_0_main_GE'(x18:0, x19:0, x20:0) :|: x19:0 - 3 * x27:0 = 0 && x18:0 > 0 && x19:0 - 2 * x26:0 = 1 && x20:0 > 0 && x20:0 - 1 >= x19:0
f452_0_main_GE(x197:0, x198:0, x199:0) -> f452_0_main_GE'(x197:0, x198:0, x199:0) :|: x197:0 > 0 && x206:0 > 0 && x206:0 <= x197:0 && x198:0 - 2 * x205:0 = 0 && x199:0 > 0 && x199:0 - 1 >= x198:0
f452_0_main_GE(x38:0, x39:0, x40:0) -> f452_0_main_GE'(x38:0, x39:0, x40:0) :|: x39:0 - 5 * x48:0 = 0 && x38:0 > 0 && x39:0 - 3 * x47:0 >= 1 && x39:0 - 2 * x46:0 = 1 && x40:0 > 0 && x40:0 - 1 >= x39:0
f452_0_main_GE'(x142:0, x146:0, x147:0) -> f452_0_main_GE(x152:0, c, x147:0) :|: c = x146:0 + 1 && (x146:0 - 5 * x160:0 <= 4 && x146:0 - 5 * x160:0 >= 0 && x146:0 - 3 * x158:0 <= 2 && x146:0 - 2 * x159:0 <= 1 && x146:0 - 2 * x159:0 >= 0 && x152:0 > 0 && x142:0 > 0 && x152:0 <= x142:0 && x146:0 - 5 * x160:0 = 0 && x146:0 - 2 * x159:0 = 1 && x147:0 > 0 && x147:0 - 1 >= x146:0 && x146:0 - 3 * x158:0 >= 1)
f452_0_main_GE(x4:0, x1:0, x2:0) -> f452_0_main_GE'(x4:0, x1:0, x2:0) :|: x1:0 - 2 * x8:0 = 0 && x4:0 > 0 && x2:0 > 0 && x2:0 - 1 >= x1:0
f452_0_main_GE(x119:0, x120:0, x125:0) -> f452_0_main_GE'(x119:0, x120:0, x125:0) :|: x119:0 > 0 && x141:0 > 0 && x141:0 <= x119:0 && x120:0 - 5 * x140:0 = 0 && x120:0 - 3 * x139:0 >= 1 && x120:0 - 2 * x134:0 = 1 && x125:0 > 0 && x125:0 - 1 >= x120:0
f452_0_main_GE'(x72:0, x73:0, x74:0) -> f697_0_main_GE(x76:0, x73:0, c1, x74:0) :|: c1 = 0 && (x73:0 - 3 * x81:0 <= 2 && x73:0 - 5 * x80:0 <= 4 && x73:0 - 2 * x82:0 <= 1 && x73:0 - 2 * x82:0 >= 0 && x76:0 > 0 && x72:0 > 0 && x76:0 <= x72:0 && x74:0 - 1 >= x73:0 && x73:0 - 2 * x82:0 = 1 && x73:0 - 3 * x81:0 >= 1 && x73:0 - 5 * x80:0 >= 1)
f452_0_main_GE(x92:0, c2, x101:0) -> f452_0_main_GE(x97:0, c3, x101:0) :|: c3 = 1 && c2 = 0 && (x101:0 > 0 && x97:0 <= x92:0 && x97:0 > 0 && x92:0 > 0 && cons_0 = 0)
f452_0_main_GE(x163:0, x164:0, x165:0) -> f452_0_main_GE'(x163:0, x164:0, x165:0) :|: x163:0 > 0 && x180:0 > 0 && x180:0 <= x163:0 && x164:0 - 3 * x176:0 = 0 && x164:0 - 2 * x175:0 = 1 && x165:0 > 0 && x165:0 - 1 >= x164:0
f452_0_main_GE(x60:0, x61:0, x62:0) -> f452_0_main_GE'(x60:0, x61:0, x62:0) :|: x60:0 > 0 && x71:0 > 0 && x71:0 <= x60:0 && x61:0 - 3 * x70:0 >= 1 && x61:0 - 5 * x69:0 >= 1 && x62:0 - 1 >= x61:0 && x61:0 - 2 * x68:0 = 1
f452_0_main_GE'(x207:0, x208:0, x209:0) -> f452_0_main_GE(x211:0, c5, x209:0) :|: c5 = x208:0 + 1 && (x208:0 - 2 * x215:0 <= 1 && x208:0 - 2 * x215:0 >= 0 && x211:0 > 0 && x207:0 > 0 && x211:0 <= x207:0 && x208:0 - 2 * x215:0 = 0 && x209:0 > 0 && x209:0 - 1 >= x208:0)
f452_0_main_GE'(x181:0, x185:0, x186:0) -> f452_0_main_GE(x191:0, c7, x186:0) :|: c7 = x185:0 + 1 && (x185:0 - 3 * x196:0 <= 2 && x185:0 - 3 * x196:0 >= 0 && x185:0 - 2 * x195:0 <= 1 && x185:0 - 2 * x195:0 >= 0 && x191:0 > 0 && x181:0 > 0 && x191:0 <= x181:0 && x185:0 - 3 * x196:0 = 0 && x185:0 - 2 * x195:0 = 1 && x186:0 > 0 && x186:0 - 1 >= x185:0)


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

(13)
Obligation:
Rules:
f697_0_main_GE(x103:0, x106:0, x107:0, x108:0) -> f452_0_main_GE(x112:0, c4, x108:0) :|: c4 = x106:0 + 1 && (x107:0 > 99 && x108:0 > -1 && x112:0 <= x103:0 && x112:0 > 0 && x103:0 > 0)
f697_0_main_GE(x83:0, x84:0, x85:0, x86:0) -> f697_0_main_GE(x87:0, x84:0, c6, x86:0) :|: c6 = x85:0 + 1 && (x85:0 < 100 && x87:0 <= x83:0 && x87:0 > 0 && x83:0 > 0)

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

(14) RankingReductionPairProof (EQUIVALENT)
Interpretation:
[ f697_0_main_GE ] = 0
[ f452_0_main_GE ] = -1*f452_0_main_GE_1

The following rules are decreasing:
f697_0_main_GE(x103:0, x106:0, x107:0, x108:0) -> f452_0_main_GE(x112:0, c4, x108:0) :|: c4 = x106:0 + 1 && (x107:0 > 99 && x108:0 > -1 && x112:0 <= x103:0 && x112:0 > 0 && x103:0 > 0)

The following rules are bounded:
f697_0_main_GE(x103:0, x106:0, x107:0, x108:0) -> f452_0_main_GE(x112:0, c4, x108:0) :|: c4 = x106:0 + 1 && (x107:0 > 99 && x108:0 > -1 && x112:0 <= x103:0 && x112:0 > 0 && x103:0 > 0)
f697_0_main_GE(x83:0, x84:0, x85:0, x86:0) -> f697_0_main_GE(x87:0, x84:0, c6, x86:0) :|: c6 = x85:0 + 1 && (x85:0 < 100 && x87:0 <= x83:0 && x87:0 > 0 && x83:0 > 0)


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

(15)
Obligation:
Rules:
f697_0_main_GE(x83:0, x84:0, x85:0, x86:0) -> f697_0_main_GE(x87:0, x84:0, c6, x86:0) :|: c6 = x85:0 + 1 && (x85:0 < 100 && x87:0 <= x83:0 && x87:0 > 0 && x83:0 > 0)

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

(16) PolynomialOrderProcessor (EQUIVALENT)
Found the following polynomial interpretation:
[f697_0_main_GE(x, x1, x2, x3)] = 99 - x2

The following rules are decreasing:
f697_0_main_GE(x83:0, x84:0, x85:0, x86:0) -> f697_0_main_GE(x87:0, x84:0, c6, x86:0) :|: c6 = x85:0 + 1 && (x85:0 < 100 && x87:0 <= x83:0 && x87:0 > 0 && x83:0 > 0)
The following rules are bounded:
f697_0_main_GE(x83:0, x84:0, x85:0, x86:0) -> f697_0_main_GE(x87:0, x84:0, c6, x86:0) :|: c6 = x85:0 + 1 && (x85:0 < 100 && x87:0 <= x83:0 && x87:0 > 0 && x83:0 > 0)

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

(17)
YES

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

(18)
Obligation:

Termination digraph:
Nodes:
(1) f342_0_exp_GT(x358, x359, x360, x361) -> f342_0_exp_GT'(x362, x363, x364, x365) :|: x359 = x363 && x358 = x362 && 0 <= x358 - 1 && 0 <= x359 - 1
(2) f638_0_exp_InvokeMethod(x326, x327, x328, x329) -> f342_0_exp_GT(x330, x331, x332, x333) :|: x328 = x331 && x327 = x330 && 0 <= x326 - 1 && 0 <= x327 - 1 && x328 <= x326 - 1
(3) f342_0_exp_GT'(x385, x386, x387, x388) -> f638_0_exp_InvokeMethod(x389, x390, x391, x392) :|: 0 <= x386 - 1 && 0 <= x385 - 1 && x393 - x394 * x395 <= x394 - 1 && 0 <= x393 - x394 * x395 && x386 = x389 && x385 = x390 && x386 - 1 = x391
(4) f342_0_exp_GT'(x366, x367, x368, x369) -> f638_0_exp_InvokeMethod(x370, x371, x372, x373) :|: 0 <= x366 - 1 && 0 <= x367 - 1 && x374 - x375 * x376 <= x375 - 1 && 0 <= x374 - x375 * x376 && x367 = x370 && x366 = x371 && x367 - 1 = x372
(5) f342_0_exp_GT(x377, x378, x379, x380) -> f342_0_exp_GT'(x381, x382, x383, x384) :|: x378 = x382 && x377 = x381 && 0 <= x378 - 1 && 0 <= x377 - 1

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

This digraph is fully evaluated!

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

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

(20)
Obligation:
Rules:
f638_0_exp_InvokeMethod(x326:0, x327:0, x328:0, x329:0) -> f342_0_exp_GT'(x327:0, x328:0, x383:0, x384:0) :|: x328:0 <= x326:0 - 1 && x327:0 > 0 && x326:0 > 0 && x328:0 > 0
f638_0_exp_InvokeMethod(x, x1, x2, x3) -> f342_0_exp_GT'(x1, x2, x4, x5) :|: x2 > 0 && x2 <= x - 1 && x > 0 && x1 > 0
f342_0_exp_GT'(x385:0, x386:0, x387:0, x388:0) -> f638_0_exp_InvokeMethod(x386:0, x385:0, x386:0 - 1, x392:0) :|: x394:0 - 1 >= x393:0 - x394:0 * x395:0 && x393:0 - x394:0 * x395:0 >= 0 && x385:0 > 0 && x386:0 > 0
f342_0_exp_GT'(x366:0, x367:0, x368:0, x369:0) -> f638_0_exp_InvokeMethod(x367:0, x366:0, x367:0 - 1, x373:0) :|: x375:0 - 1 >= x374:0 - x375:0 * x376:0 && x374:0 - x375:0 * x376:0 >= 0 && x367:0 > 0 && x366:0 > 0

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

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

   f638_0_exp_InvokeMethod(x1, x2, x3, x4) -> f638_0_exp_InvokeMethod(x1, x2, x3)
   f342_0_exp_GT'(x1, x2, x3, x4) -> f342_0_exp_GT'(x1, x2)

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

(22)
Obligation:
Rules:
f638_0_exp_InvokeMethod(x326:0, x327:0, x328:0) -> f342_0_exp_GT'(x327:0, x328:0) :|: x328:0 <= x326:0 - 1 && x327:0 > 0 && x326:0 > 0 && x328:0 > 0
f638_0_exp_InvokeMethod(x, x1, x2) -> f342_0_exp_GT'(x1, x2) :|: x2 > 0 && x2 <= x - 1 && x > 0 && x1 > 0
f342_0_exp_GT'(x385:0, x386:0) -> f638_0_exp_InvokeMethod(x386:0, x385:0, x386:0 - 1) :|: x394:0 - 1 >= x393:0 - x394:0 * x395:0 && x393:0 - x394:0 * x395:0 >= 0 && x385:0 > 0 && x386:0 > 0
f342_0_exp_GT'(x366:0, x367:0) -> f638_0_exp_InvokeMethod(x367:0, x366:0, x367:0 - 1) :|: x375:0 - 1 >= x374:0 - x375:0 * x376:0 && x374:0 - x375:0 * x376:0 >= 0 && x367:0 > 0 && x366:0 > 0

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

(23) TempFilterProof (SOUND)
Used the following sort dictionary for filtering: 
f638_0_exp_InvokeMethod(INTEGER, INTEGER, INTEGER)
f342_0_exp_GT'(INTEGER, INTEGER)
Replaced non-predefined constructor symbols by 0.
----------------------------------------

(24)
Obligation:
Rules:
f638_0_exp_InvokeMethod(x326:0, x327:0, x328:0) -> f342_0_exp_GT'(x327:0, x328:0) :|: x328:0 <= x326:0 - 1 && x327:0 > 0 && x326:0 > 0 && x328:0 > 0
f638_0_exp_InvokeMethod(x, x1, x2) -> f342_0_exp_GT'(x1, x2) :|: x2 > 0 && x2 <= x - 1 && x > 0 && x1 > 0
f342_0_exp_GT'(x385:0, x386:0) -> f638_0_exp_InvokeMethod(x386:0, x385:0, c) :|: c = x386:0 - 1 && (x394:0 - 1 >= x393:0 - x394:0 * x395:0 && x393:0 - x394:0 * x395:0 >= 0 && x385:0 > 0 && x386:0 > 0)
f342_0_exp_GT'(x366:0, x367:0) -> f638_0_exp_InvokeMethod(x367:0, x366:0, c1) :|: c1 = x367:0 - 1 && (x375:0 - 1 >= x374:0 - x375:0 * x376:0 && x374:0 - x375:0 * x376:0 >= 0 && x367:0 > 0 && x366:0 > 0)

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

(25) RankingReductionPairProof (EQUIVALENT)
Interpretation:
[ f638_0_exp_InvokeMethod ] = 2*f638_0_exp_InvokeMethod_1 + -1
[ f342_0_exp_GT' ] = 2*f342_0_exp_GT'_2

The following rules are decreasing:
f638_0_exp_InvokeMethod(x326:0, x327:0, x328:0) -> f342_0_exp_GT'(x327:0, x328:0) :|: x328:0 <= x326:0 - 1 && x327:0 > 0 && x326:0 > 0 && x328:0 > 0
f638_0_exp_InvokeMethod(x, x1, x2) -> f342_0_exp_GT'(x1, x2) :|: x2 > 0 && x2 <= x - 1 && x > 0 && x1 > 0
f342_0_exp_GT'(x385:0, x386:0) -> f638_0_exp_InvokeMethod(x386:0, x385:0, c) :|: c = x386:0 - 1 && (x394:0 - 1 >= x393:0 - x394:0 * x395:0 && x393:0 - x394:0 * x395:0 >= 0 && x385:0 > 0 && x386:0 > 0)
f342_0_exp_GT'(x366:0, x367:0) -> f638_0_exp_InvokeMethod(x367:0, x366:0, c1) :|: c1 = x367:0 - 1 && (x375:0 - 1 >= x374:0 - x375:0 * x376:0 && x374:0 - x375:0 * x376:0 >= 0 && x367:0 > 0 && x366:0 > 0)

The following rules are bounded:
f638_0_exp_InvokeMethod(x326:0, x327:0, x328:0) -> f342_0_exp_GT'(x327:0, x328:0) :|: x328:0 <= x326:0 - 1 && x327:0 > 0 && x326:0 > 0 && x328:0 > 0
f638_0_exp_InvokeMethod(x, x1, x2) -> f342_0_exp_GT'(x1, x2) :|: x2 > 0 && x2 <= x - 1 && x > 0 && x1 > 0
f342_0_exp_GT'(x385:0, x386:0) -> f638_0_exp_InvokeMethod(x386:0, x385:0, c) :|: c = x386:0 - 1 && (x394:0 - 1 >= x393:0 - x394:0 * x395:0 && x393:0 - x394:0 * x395:0 >= 0 && x385:0 > 0 && x386:0 > 0)
f342_0_exp_GT'(x366:0, x367:0) -> f638_0_exp_InvokeMethod(x367:0, x366:0, c1) :|: c1 = x367:0 - 1 && (x375:0 - 1 >= x374:0 - x375:0 * x376:0 && x374:0 - x375:0 * x376:0 >= 0 && x367:0 > 0 && x366:0 > 0)


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

(26)
YES

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

(27)
Obligation:

Termination digraph:
Nodes:
(1) f307_0_cos_GT(x275, x276, x277, x278) -> f552_0_cos_InvokeMethod(x279, x280, x281, x282) :|: 2 * x276 = x281 && x275 = x280 && x276 = x279 && 0 <= x275 - 1 && 0 <= x276 - 1
(2) f552_0_cos_InvokeMethod'(x307, x308, x309, x310) -> f307_0_cos_GT(x311, x312, x313, x314) :|: 0 <= x308 - 1 && 0 <= x307 - 1 && 1 <= x309 - 1 && 1 <= 2 * x307 - 1 && x307 - 1 <= x307 - 1 && x315 - x316 * x317 <= x316 - 1 && 0 <= x315 - x316 * x317 && x308 = x311 && x307 - 1 = x312
(3) f552_0_cos_InvokeMethod(x299, x300, x301, x302) -> f552_0_cos_InvokeMethod'(x303, x304, x305, x306) :|: x301 = x305 && x300 = x304 && x299 = x303 && 1 <= 2 * x299 - 1 && x299 - 1 <= x299 - 1 && 1 <= x301 - 1 && 0 <= x299 - 1 && 0 <= x300 - 1

Arcs:
(1) -> (3)
(2) -> (1)
(3) -> (2)

This digraph is fully evaluated!

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

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

(29)
Obligation:
Rules:
f552_0_cos_InvokeMethod'(x307:0, x280:0, x309:0, x310:0) -> f552_0_cos_InvokeMethod'(x307:0 - 1, x280:0, 2 * (x307:0 - 1), x306:0) :|: x315:0 - x316:0 * x317:0 >= 0 && x316:0 - 1 >= x315:0 - x316:0 * x317:0 && 2 * x307:0 >= 2 && x309:0 > 1 && x280:0 > 0 && 2 * (x307:0 - 1) >= 2 && x307:0 > 1

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

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

   f552_0_cos_InvokeMethod'(x1, x2, x3, x4) -> f552_0_cos_InvokeMethod'(x1, x2, x3)

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

(31)
Obligation:
Rules:
f552_0_cos_InvokeMethod'(x307:0, x280:0, x309:0) -> f552_0_cos_InvokeMethod'(x307:0 - 1, x280:0, 2 * (x307:0 - 1)) :|: x315:0 - x316:0 * x317:0 >= 0 && x316:0 - 1 >= x315:0 - x316:0 * x317:0 && 2 * x307:0 >= 2 && x309:0 > 1 && x280:0 > 0 && 2 * (x307:0 - 1) >= 2 && x307:0 > 1

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

(32) TempFilterProof (SOUND)
Used the following sort dictionary for filtering: 
f552_0_cos_InvokeMethod'(INTEGER, INTEGER, INTEGER)
Replaced non-predefined constructor symbols by 0.
----------------------------------------

(33)
Obligation:
Rules:
f552_0_cos_InvokeMethod'(x307:0, x280:0, x309:0) -> f552_0_cos_InvokeMethod'(c, x280:0, c1) :|: c1 = 2 * (x307:0 - 1) && c = x307:0 - 1 && (x315:0 - x316:0 * x317:0 >= 0 && x316:0 - 1 >= x315:0 - x316:0 * x317:0 && 2 * x307:0 >= 2 && x309:0 > 1 && x280:0 > 0 && 2 * (x307:0 - 1) >= 2 && x307:0 > 1)

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

(34) PolynomialOrderProcessor (EQUIVALENT)
Found the following polynomial interpretation:
[f552_0_cos_InvokeMethod'(x, x1, x2)] = x

The following rules are decreasing:
f552_0_cos_InvokeMethod'(x307:0, x280:0, x309:0) -> f552_0_cos_InvokeMethod'(c, x280:0, c1) :|: c1 = 2 * (x307:0 - 1) && c = x307:0 - 1 && (x315:0 - x316:0 * x317:0 >= 0 && x316:0 - 1 >= x315:0 - x316:0 * x317:0 && 2 * x307:0 >= 2 && x309:0 > 1 && x280:0 > 0 && 2 * (x307:0 - 1) >= 2 && x307:0 > 1)
The following rules are bounded:
f552_0_cos_InvokeMethod'(x307:0, x280:0, x309:0) -> f552_0_cos_InvokeMethod'(c, x280:0, c1) :|: c1 = 2 * (x307:0 - 1) && c = x307:0 - 1 && (x315:0 - x316:0 * x317:0 >= 0 && x316:0 - 1 >= x315:0 - x316:0 * x317:0 && 2 * x307:0 >= 2 && x309:0 > 1 && x280:0 > 0 && 2 * (x307:0 - 1) >= 2 && x307:0 > 1)

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

(35)
YES

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

(36)
Obligation:

Termination digraph:
Nodes:
(1) f276_0_sin_GT(x224, x225, x226, x227) -> f566_0_sin_InvokeMethod(x228, x229, x230, x231) :|: 2 * x225 + 1 = x230 && x224 = x229 && x225 = x228 && 0 <= x225 - 1 && 0 <= 2 * x225 - 1 && 0 <= x224 - 1
(2) f566_0_sin_InvokeMethod'(x256, x257, x258, x259) -> f276_0_sin_GT(x260, x261, x262, x263) :|: 0 <= x257 - 1 && 0 <= x256 - 1 && 1 <= x258 - 1 && 0 <= 2 * x256 - 1 && x256 - 1 <= x256 - 1 && x264 - x265 * x266 <= x265 - 1 && 0 <= x264 - x265 * x266 && x257 = x260 && x256 - 1 = x261
(3) f566_0_sin_InvokeMethod(x248, x249, x250, x251) -> f566_0_sin_InvokeMethod'(x252, x253, x254, x255) :|: x250 = x254 && x249 = x253 && x248 = x252 && 0 <= 2 * x248 - 1 && x248 - 1 <= x248 - 1 && 1 <= x250 - 1 && 0 <= x248 - 1 && 0 <= x249 - 1

Arcs:
(1) -> (3)
(2) -> (1)
(3) -> (2)

This digraph is fully evaluated!

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

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

(38)
Obligation:
Rules:
f566_0_sin_InvokeMethod'(x256:0, x229:0, x258:0, x259:0) -> f566_0_sin_InvokeMethod'(x256:0 - 1, x229:0, 2 * (x256:0 - 1) + 1, x255:0) :|: x264:0 - x265:0 * x266:0 >= 0 && x265:0 - 1 >= x264:0 - x265:0 * x266:0 && 2 * x256:0 >= 1 && x258:0 > 1 && x229:0 > 0 && 2 * (x256:0 - 1) >= 1 && x256:0 > 1

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

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

   f566_0_sin_InvokeMethod'(x1, x2, x3, x4) -> f566_0_sin_InvokeMethod'(x1, x2, x3)

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

(40)
Obligation:
Rules:
f566_0_sin_InvokeMethod'(x256:0, x229:0, x258:0) -> f566_0_sin_InvokeMethod'(x256:0 - 1, x229:0, 2 * (x256:0 - 1) + 1) :|: x264:0 - x265:0 * x266:0 >= 0 && x265:0 - 1 >= x264:0 - x265:0 * x266:0 && 2 * x256:0 >= 1 && x258:0 > 1 && x229:0 > 0 && 2 * (x256:0 - 1) >= 1 && x256:0 > 1

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

(41) TempFilterProof (SOUND)
Used the following sort dictionary for filtering: 
f566_0_sin_InvokeMethod'(INTEGER, INTEGER, INTEGER)
Replaced non-predefined constructor symbols by 0.
----------------------------------------

(42)
Obligation:
Rules:
f566_0_sin_InvokeMethod'(x256:0, x229:0, x258:0) -> f566_0_sin_InvokeMethod'(c, x229:0, c1) :|: c1 = 2 * (x256:0 - 1) + 1 && c = x256:0 - 1 && (x264:0 - x265:0 * x266:0 >= 0 && x265:0 - 1 >= x264:0 - x265:0 * x266:0 && 2 * x256:0 >= 1 && x258:0 > 1 && x229:0 > 0 && 2 * (x256:0 - 1) >= 1 && x256:0 > 1)

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

(43) RankingReductionPairProof (EQUIVALENT)
Interpretation:
[ f566_0_sin_InvokeMethod' ] = f566_0_sin_InvokeMethod'_1

The following rules are decreasing:
f566_0_sin_InvokeMethod'(x256:0, x229:0, x258:0) -> f566_0_sin_InvokeMethod'(c, x229:0, c1) :|: c1 = 2 * (x256:0 - 1) + 1 && c = x256:0 - 1 && (x264:0 - x265:0 * x266:0 >= 0 && x265:0 - 1 >= x264:0 - x265:0 * x266:0 && 2 * x256:0 >= 1 && x258:0 > 1 && x229:0 > 0 && 2 * (x256:0 - 1) >= 1 && x256:0 > 1)

The following rules are bounded:
f566_0_sin_InvokeMethod'(x256:0, x229:0, x258:0) -> f566_0_sin_InvokeMethod'(c, x229:0, c1) :|: c1 = 2 * (x256:0 - 1) + 1 && c = x256:0 - 1 && (x264:0 - x265:0 * x266:0 >= 0 && x265:0 - 1 >= x264:0 - x265:0 * x266:0 && 2 * x256:0 >= 1 && x258:0 > 1 && x229:0 > 0 && 2 * (x256:0 - 1) >= 1 && x256:0 > 1)


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(44)
YES

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(45)
Obligation:

Termination digraph:
Nodes:
(1) f453_0_fact_GT(x342, x343, x344, x345) -> f453_0_fact_GT(x346, x347, x348, x349) :|: x342 - 1 = x346 && x342 - 1 <= x342 - 1 && 0 <= x342 - 1

Arcs:
(1) -> (1)

This digraph is fully evaluated!

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(46) IntTRSCompressionProof (EQUIVALENT)
Compressed rules.
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(47)
Obligation:
Rules:
f453_0_fact_GT(x342:0, x343:0, x344:0, x345:0) -> f453_0_fact_GT(x342:0 - 1, x347:0, x348:0, x349:0) :|: x342:0 > 0

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

   f453_0_fact_GT(x1, x2, x3, x4) -> f453_0_fact_GT(x1)

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(49)
Obligation:
Rules:
f453_0_fact_GT(x342:0) -> f453_0_fact_GT(x342:0 - 1) :|: x342:0 > 0

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(50) TempFilterProof (SOUND)
Used the following sort dictionary for filtering: 
f453_0_fact_GT(INTEGER)
Replaced non-predefined constructor symbols by 0.
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(51)
Obligation:
Rules:
f453_0_fact_GT(x342:0) -> f453_0_fact_GT(c) :|: c = x342:0 - 1 && x342:0 > 0

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(52) RankingReductionPairProof (EQUIVALENT)
Interpretation:
[ f453_0_fact_GT ] = f453_0_fact_GT_1

The following rules are decreasing:
f453_0_fact_GT(x342:0) -> f453_0_fact_GT(c) :|: c = x342:0 - 1 && x342:0 > 0

The following rules are bounded:
f453_0_fact_GT(x342:0) -> f453_0_fact_GT(c) :|: c = x342:0 - 1 && x342:0 > 0


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(53)
YES

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(54)
Obligation:

Termination digraph:
Nodes:
(1) f345_0_power_GT(x334, x335, x336, x337) -> f345_0_power_GT(x338, x339, x340, x341) :|: x334 - 1 = x338 && 0 <= x334 - 1

Arcs:
(1) -> (1)

This digraph is fully evaluated!

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

(56)
Obligation:
Rules:
f345_0_power_GT(x334:0, x335:0, x336:0, x337:0) -> f345_0_power_GT(x334:0 - 1, x339:0, x340:0, x341:0) :|: x334:0 > 0

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

   f345_0_power_GT(x1, x2, x3, x4) -> f345_0_power_GT(x1)

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(58)
Obligation:
Rules:
f345_0_power_GT(x334:0) -> f345_0_power_GT(x334:0 - 1) :|: x334:0 > 0

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(59) TempFilterProof (SOUND)
Used the following sort dictionary for filtering: 
f345_0_power_GT(INTEGER)
Replaced non-predefined constructor symbols by 0.
----------------------------------------

(60)
Obligation:
Rules:
f345_0_power_GT(x334:0) -> f345_0_power_GT(c) :|: c = x334:0 - 1 && x334:0 > 0

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(61) RankingReductionPairProof (EQUIVALENT)
Interpretation:
[ f345_0_power_GT ] = f345_0_power_GT_1

The following rules are decreasing:
f345_0_power_GT(x334:0) -> f345_0_power_GT(c) :|: c = x334:0 - 1 && x334:0 > 0

The following rules are bounded:
f345_0_power_GT(x334:0) -> f345_0_power_GT(c) :|: c = x334:0 - 1 && x334:0 > 0


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(62)
YES