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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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, 17.5 s]
(4) AND
    (5) IRSwT
        (6) IntTRSCompressionProof [EQUIVALENT, 0 ms]
        (7) IRSwT
        (8) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms]
        (9) IRSwT
        (10) TempFilterProof [SOUND, 36 ms]
        (11) IntTRS
        (12) PolynomialOrderProcessor [EQUIVALENT, 0 ms]
        (13) YES
    (14) IRSwT
        (15) IntTRSCompressionProof [EQUIVALENT, 60 ms]
        (16) IRSwT
        (17) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms]
        (18) IRSwT
        (19) TempFilterProof [SOUND, 126 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) FilterProof [EQUIVALENT, 0 ms]
        (29) IntTRS
        (30) IntTRSCompressionProof [EQUIVALENT, 0 ms]
        (31) IntTRS
        (32) RankingReductionPairProof [EQUIVALENT, 0 ms]
        (33) YES
    (34) IRSwT
        (35) IntTRSCompressionProof [EQUIVALENT, 0 ms]
        (36) IRSwT
        (37) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms]
        (38) IRSwT
        (39) FilterProof [EQUIVALENT, 0 ms]
        (40) IntTRS
        (41) IntTRSCompressionProof [EQUIVALENT, 0 ms]
        (42) IntTRS
        (43) PolynomialOrderProcessor [EQUIVALENT, 0 ms]
        (44) YES


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

(0)
Obligation:
Rules:
f83_0_mk_Return(arg1, arg2, arg3, arg4) -> f140_0_main_InvokeMethod(arg1P, arg2P, arg3P, arg4P) :|: arg3 = arg4P && arg3 + 3 = arg3P && -1 <= arg2P - 1 && 0 <= arg1P - 1 && -1 <= arg2 - 1 && 0 <= arg1 - 1 && arg2P <= arg2 && arg1P - 1 <= arg2 && -1 <= arg3 - 1 && arg1P <= arg1
f1_0_main_Load(x, x1, x2, x3) -> f140_0_main_InvokeMethod(x4, x5, x6, x7) :|: x1 = x7 && x1 + 3 = x6 && -1 <= x5 - 1 && 0 <= x4 - 1 && 0 <= x - 1 && -1 <= x1 - 1 && x4 <= x
f140_0_main_InvokeMethod(x8, x9, x10, x11) -> f183_0_main_InvokeMethod(x12, x13, x14, x15) :|: -1 <= x14 - 1 && -1 <= x13 - 1 && -1 <= x12 - 1 && -1 <= x9 - 1 && 0 <= x8 - 1 && x14 <= x9 && x11 <= x10 - 1 && 1 <= x10 - 1 && -1 <= x11 - 1 && x11 <= x11 + 5 - 1
f232_0_length_Return(x16, x17, x18, x19) -> f268_0_main_LE(x20, x21, x22, x23) :|: x19 = x23 && -1 <= x22 - 1 && -1 <= x21 - 1 && -1 <= x20 - 1 && -1 <= x18 - 1 && -1 <= x17 - 1 && -1 <= x16 - 1 && x22 <= x18 && x21 <= x17 && x20 <= x16
f183_0_main_InvokeMethod(x24, x25, x26, x27) -> f268_0_main_LE(x28, x29, x30, x31) :|: -1 <= x30 - 1 && -1 <= x29 - 1 && -1 <= x28 - 1 && -1 <= x26 - 1 && -1 <= x25 - 1 && -1 <= x24 - 1 && x30 <= x25 && x29 <= x24 && x28 <= x26
f268_0_main_LE(x32, x33, x34, x35) -> f268_0_main_LE'(x36, x37, x38, x39) :|: 0 <= x35 - 1 && 0 <= x40 - 3 * x41 - 1 && x42 <= x33 && x43 <= x34 && x44 <= x32 && -1 <= x32 - 1 && -1 <= x33 - 1 && -1 <= x34 - 1 && -1 <= x42 - 1 && -1 <= x43 - 1 && -1 <= x44 - 1 && x32 = x36 && x33 = x37 && x34 = x38 && x35 = x39
f268_0_main_LE'(x45, x46, x47, x48) -> f336_0_main_NE(x49, x50, x51, x52) :|: 0 <= x53 - 3 * x54 - 1 && 0 <= x48 - 1 && x49 <= x46 && x50 <= x47 && x51 <= x45 && -1 <= x45 - 1 && -1 <= x46 - 1 && -1 <= x47 - 1 && -1 <= x49 - 1 && -1 <= x50 - 1 && -1 <= x51 - 1 && x53 - 3 * x54 <= 2 && x55 - 5 * x56 <= 4 && 0 <= x55 - 5 * x56 && x55 - 5 * x56 = x52
f336_0_main_NE(x57, x58, x59, x60) -> f378_0_main_InvokeMethod(x61, x62, x63, x64) :|: -1 <= x63 - 1 && -1 <= x62 - 1 && -1 <= x61 - 1 && -1 <= x59 - 1 && -1 <= x58 - 1 && -1 <= x57 - 1 && x63 <= x57 && x62 <= x59 && 0 <= x60 - 1 && x61 <= x58
f268_0_main_LE(x65, x66, x69, x70) -> f268_0_main_LE'(x71, x72, x73, x74) :|: 0 <= x70 - 1 && x79 - 3 * x80 = 0 && x81 <= x66 && x82 <= x69 && x83 <= x65 && 0 <= x65 - 1 && -1 <= x66 - 1 && -1 <= x69 - 1 && -1 <= x81 - 1 && -1 <= x82 - 1 && 0 <= x83 - 1 && x65 = x71 && x66 = x72 && x69 = x73 && x70 = x74
f268_0_main_LE'(x84, x87, x88, x89) -> f336_0_main_NE(x90, x91, x92, x93) :|: 0 <= x89 - 1 && x94 - 3 * x95 = 0 && x90 <= x87 && x91 <= x88 && x92 <= x84 && 0 <= x84 - 1 && -1 <= x87 - 1 && -1 <= x88 - 1 && -1 <= x90 - 1 && -1 <= x91 - 1 && 0 <= x92 - 1 && 0 <= x94 - 3 * x95 && x94 - 3 * x95 <= 2 && x96 - 5 * x97 <= 4 && 0 <= x96 - 5 * x97 && x96 - 5 * x97 = x93
f336_0_main_NE(x98, x99, x100, x101) -> f378_0_main_InvokeMethod(x102, x103, x104, x105) :|: 0 = x101 && -1 <= x104 - 1 && -1 <= x103 - 1 && -1 <= x102 - 1 && 0 <= x100 - 1 && -1 <= x99 - 1 && -1 <= x98 - 1 && x104 <= x98 && x103 + 1 <= x100 && x102 <= x99
f378_0_main_InvokeMethod(x106, x107, x108, x109) -> f519_0_main_InvokeMethod(x110, x111, x112, x113) :|: x110 + 1 <= x108 && x114 <= x115 - 1 && x111 <= x106 && x112 <= x107 && -1 <= x106 - 1 && -1 <= x107 - 1 && 0 <= x108 - 1 && -1 <= x110 - 1 && -1 <= x111 - 1 && -1 <= x112 - 1
f378_0_main_InvokeMethod(x116, x117, x118, x119) -> f519_0_main_InvokeMethod(x120, x121, x122, x123) :|: x124 <= x125 - 1 && x126 <= x127 && x120 <= x118 && x121 <= x116 && x122 + 1 <= x117 && -1 <= x116 - 1 && 0 <= x117 - 1 && -1 <= x118 - 1 && -1 <= x120 - 1 && -1 <= x121 - 1 && -1 <= x122 - 1
f378_0_main_InvokeMethod(x128, x129, x130, x131) -> f519_0_main_InvokeMethod(x132, x133, x134, x135) :|: x132 <= x130 && x136 <= x137 && x133 + 1 <= x128 && x134 <= x129 && 0 <= x128 - 1 && -1 <= x129 - 1 && -1 <= x130 - 1 && -1 <= x132 - 1 && -1 <= x133 - 1 && -1 <= x134 - 1
f519_0_main_InvokeMethod(x138, x139, x140, x141) -> f183_0_main_InvokeMethod(x142, x143, x144, x147) :|: -1 <= x144 - 1 && -1 <= x143 - 1 && -1 <= x142 - 1 && -1 <= x140 - 1 && -1 <= x139 - 1 && -1 <= x138 - 1 && x144 <= x138 && x143 <= x140 && x142 <= x139
f1_0_main_Load(x148, x149, x150, x151) -> f161_0_mk_LE(x154, x155, x156, x157) :|: x149 = x155 && x149 - 1 = x154 && -1 <= x149 - 1 && 0 <= x148 - 1
f140_0_main_InvokeMethod(x158, x159, x160, x161) -> f161_0_mk_LE(x162, x163, x164, x165) :|: x160 = x163 && x160 - 1 = x162 && -1 <= x159 - 1 && 0 <= x158 - 1 && 1 <= x160 - 1 && x161 <= x160 - 1
f140_0_main_InvokeMethod(x166, x167, x168, x169) -> f161_0_mk_LE(x170, x176, x177, x178) :|: x169 + 5 = x176 && x169 + 4 = x170 && -1 <= x167 - 1 && 0 <= x166 - 1 && x169 <= x168 - 1 && 1 <= x168 - 1 && -1 <= x169 - 1 && x169 <= x169 + 5 - 1
f161_0_mk_LE(x179, x180, x181, x182) -> f161_0_mk_LE(x187, x188, x189, x190) :|: x179 = x188 && x179 - 1 = x187 && 0 <= x180 - 1
f183_0_main_InvokeMethod(x196, x197, x198, x199) -> f283_0_length_NULL(x200, x201, x202, x207) :|: -1 <= x201 - 1 && -1 <= x200 - 1 && -1 <= x198 - 1 && -1 <= x197 - 1 && -1 <= x196 - 1 && x201 <= x198 && x200 <= x198
f268_0_main_LE(x208, x209, x210, x211) -> f283_0_length_NULL(x212, x213, x214, x215) :|: -1 <= x213 - 1 && -1 <= x212 - 1 && -1 <= x210 - 1 && -1 <= x209 - 1 && -1 <= x208 - 1 && x213 <= x210 && 0 <= x211 - 1 && x212 <= x210
f268_0_main_LE(x216, x217, x218, x219) -> f268_0_main_LE'(x220, x225, x226, x227) :|: 0 <= x219 - 1 && 0 <= x228 - 3 * x229 - 1 && x230 <= x216 && x233 <= x216 && -1 <= x216 - 1 && -1 <= x217 - 1 && -1 <= x218 - 1 && -1 <= x230 - 1 && -1 <= x233 - 1 && x216 = x220 && x217 = x225 && x218 = x226 && x219 = x227
f268_0_main_LE'(x234, x235, x236, x241) -> f283_0_length_NULL(x242, x243, x244, x245) :|: 0 <= x246 - 3 * x249 - 1 && 0 <= x241 - 1 && x242 <= x234 && x243 <= x234 && -1 <= x234 - 1 && -1 <= x235 - 1 && -1 <= x236 - 1 && -1 <= x242 - 1 && -1 <= x243 - 1 && x246 - 3 * x249 <= 2
f268_0_main_LE(x250, x251, x252, x253) -> f268_0_main_LE'(x254, x255, x256, x257) :|: 0 <= x253 - 1 && x258 - 3 * x259 = 0 && x260 <= x250 && x261 <= x250 && 0 <= x250 - 1 && -1 <= x251 - 1 && -1 <= x252 - 1 && 0 <= x260 - 1 && 0 <= x261 - 1 && x250 = x254 && x251 = x255 && x252 = x256 && x253 = x257
f268_0_main_LE'(x262, x263, x264, x265) -> f283_0_length_NULL(x266, x267, x268, x269) :|: 0 <= x265 - 1 && x270 - 3 * x271 = 0 && x266 <= x262 && x267 <= x262 && 0 <= x262 - 1 && -1 <= x263 - 1 && -1 <= x264 - 1 && 0 <= x266 - 1 && 0 <= x267 - 1 && x270 - 3 * x271 <= 2 && 0 <= x270 - 3 * x271
f378_0_main_InvokeMethod(x272, x273, x274, x275) -> f283_0_length_NULL(x276, x277, x278, x279) :|: -1 <= x277 - 1 && -1 <= x276 - 1 && -1 <= x274 - 1 && -1 <= x273 - 1 && -1 <= x272 - 1 && x277 <= x274 && x276 <= x274
f378_0_main_InvokeMethod(x280, x281, x282, x283) -> f283_0_length_NULL(x284, x285, x286, x287) :|: -1 <= x285 - 1 && -1 <= x284 - 1 && -1 <= x282 - 1 && -1 <= x281 - 1 && -1 <= x280 - 1 && x285 <= x280 && x284 <= x280
f378_0_main_InvokeMethod(x288, x289, x290, x291) -> f283_0_length_NULL(x292, x293, x294, x295) :|: x292 <= x290 && x296 <= x297 && x293 <= x290 && -1 <= x288 - 1 && -1 <= x289 - 1 && -1 <= x290 - 1 && -1 <= x292 - 1 && -1 <= x293 - 1
f378_0_main_InvokeMethod(x298, x299, x300, x301) -> f283_0_length_NULL(x302, x303, x304, x305) :|: x302 <= x298 && x306 <= x307 && x303 <= x298 && -1 <= x298 - 1 && -1 <= x299 - 1 && -1 <= x300 - 1 && -1 <= x302 - 1 && -1 <= x303 - 1
f283_0_length_NULL(x308, x309, x310, x311) -> f283_0_length_NULL(x312, x313, x314, x315) :|: -1 <= x313 - 1 && -1 <= x312 - 1 && 0 <= x309 - 1 && 0 <= x308 - 1 && x313 + 1 <= x309 && x313 + 1 <= x308 && x312 + 1 <= x309 && x312 + 1 <= x308
f519_0_main_InvokeMethod(x316, x317, x318, x319) -> f632_0_test_NULL(x320, x321, x322, x323) :|: -1 <= x321 - 1 && -1 <= x320 - 1 && -1 <= x318 - 1 && -1 <= x317 - 1 && -1 <= x316 - 1 && x321 <= x316 && x320 <= x316
f632_0_test_NULL(x324, x325, x326, x327) -> f632_0_test_NULL(x328, x329, x330, x331) :|: -1 <= x329 - 1 && -1 <= x328 - 1 && 0 <= x325 - 1 && 0 <= x324 - 1 && x329 + 1 <= x325 && x329 + 1 <= x324 && x328 + 1 <= x325 && x328 + 1 <= x324
__init(x332, x333, x334, x335) -> f1_0_main_Load(x336, x337, x338, x339) :|: 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:
f83_0_mk_Return(arg1, arg2, arg3, arg4) -> f140_0_main_InvokeMethod(arg1P, arg2P, arg3P, arg4P) :|: arg3 = arg4P && arg3 + 3 = arg3P && -1 <= arg2P - 1 && 0 <= arg1P - 1 && -1 <= arg2 - 1 && 0 <= arg1 - 1 && arg2P <= arg2 && arg1P - 1 <= arg2 && -1 <= arg3 - 1 && arg1P <= arg1
f1_0_main_Load(x, x1, x2, x3) -> f140_0_main_InvokeMethod(x4, x5, x6, x7) :|: x1 = x7 && x1 + 3 = x6 && -1 <= x5 - 1 && 0 <= x4 - 1 && 0 <= x - 1 && -1 <= x1 - 1 && x4 <= x
f140_0_main_InvokeMethod(x8, x9, x10, x11) -> f183_0_main_InvokeMethod(x12, x13, x14, x15) :|: -1 <= x14 - 1 && -1 <= x13 - 1 && -1 <= x12 - 1 && -1 <= x9 - 1 && 0 <= x8 - 1 && x14 <= x9 && x11 <= x10 - 1 && 1 <= x10 - 1 && -1 <= x11 - 1 && x11 <= x11 + 5 - 1
f232_0_length_Return(x16, x17, x18, x19) -> f268_0_main_LE(x20, x21, x22, x23) :|: x19 = x23 && -1 <= x22 - 1 && -1 <= x21 - 1 && -1 <= x20 - 1 && -1 <= x18 - 1 && -1 <= x17 - 1 && -1 <= x16 - 1 && x22 <= x18 && x21 <= x17 && x20 <= x16
f183_0_main_InvokeMethod(x24, x25, x26, x27) -> f268_0_main_LE(x28, x29, x30, x31) :|: -1 <= x30 - 1 && -1 <= x29 - 1 && -1 <= x28 - 1 && -1 <= x26 - 1 && -1 <= x25 - 1 && -1 <= x24 - 1 && x30 <= x25 && x29 <= x24 && x28 <= x26
f268_0_main_LE(x32, x33, x34, x35) -> f268_0_main_LE'(x36, x37, x38, x39) :|: 0 <= x35 - 1 && 0 <= x40 - 3 * x41 - 1 && x42 <= x33 && x43 <= x34 && x44 <= x32 && -1 <= x32 - 1 && -1 <= x33 - 1 && -1 <= x34 - 1 && -1 <= x42 - 1 && -1 <= x43 - 1 && -1 <= x44 - 1 && x32 = x36 && x33 = x37 && x34 = x38 && x35 = x39
f268_0_main_LE'(x45, x46, x47, x48) -> f336_0_main_NE(x49, x50, x51, x52) :|: 0 <= x53 - 3 * x54 - 1 && 0 <= x48 - 1 && x49 <= x46 && x50 <= x47 && x51 <= x45 && -1 <= x45 - 1 && -1 <= x46 - 1 && -1 <= x47 - 1 && -1 <= x49 - 1 && -1 <= x50 - 1 && -1 <= x51 - 1 && x53 - 3 * x54 <= 2 && x55 - 5 * x56 <= 4 && 0 <= x55 - 5 * x56 && x55 - 5 * x56 = x52
f336_0_main_NE(x57, x58, x59, x60) -> f378_0_main_InvokeMethod(x61, x62, x63, x64) :|: -1 <= x63 - 1 && -1 <= x62 - 1 && -1 <= x61 - 1 && -1 <= x59 - 1 && -1 <= x58 - 1 && -1 <= x57 - 1 && x63 <= x57 && x62 <= x59 && 0 <= x60 - 1 && x61 <= x58
f268_0_main_LE(x65, x66, x69, x70) -> f268_0_main_LE'(x71, x72, x73, x74) :|: 0 <= x70 - 1 && x79 - 3 * x80 = 0 && x81 <= x66 && x82 <= x69 && x83 <= x65 && 0 <= x65 - 1 && -1 <= x66 - 1 && -1 <= x69 - 1 && -1 <= x81 - 1 && -1 <= x82 - 1 && 0 <= x83 - 1 && x65 = x71 && x66 = x72 && x69 = x73 && x70 = x74
f268_0_main_LE'(x84, x87, x88, x89) -> f336_0_main_NE(x90, x91, x92, x93) :|: 0 <= x89 - 1 && x94 - 3 * x95 = 0 && x90 <= x87 && x91 <= x88 && x92 <= x84 && 0 <= x84 - 1 && -1 <= x87 - 1 && -1 <= x88 - 1 && -1 <= x90 - 1 && -1 <= x91 - 1 && 0 <= x92 - 1 && 0 <= x94 - 3 * x95 && x94 - 3 * x95 <= 2 && x96 - 5 * x97 <= 4 && 0 <= x96 - 5 * x97 && x96 - 5 * x97 = x93
f336_0_main_NE(x98, x99, x100, x101) -> f378_0_main_InvokeMethod(x102, x103, x104, x105) :|: 0 = x101 && -1 <= x104 - 1 && -1 <= x103 - 1 && -1 <= x102 - 1 && 0 <= x100 - 1 && -1 <= x99 - 1 && -1 <= x98 - 1 && x104 <= x98 && x103 + 1 <= x100 && x102 <= x99
f378_0_main_InvokeMethod(x106, x107, x108, x109) -> f519_0_main_InvokeMethod(x110, x111, x112, x113) :|: x110 + 1 <= x108 && x114 <= x115 - 1 && x111 <= x106 && x112 <= x107 && -1 <= x106 - 1 && -1 <= x107 - 1 && 0 <= x108 - 1 && -1 <= x110 - 1 && -1 <= x111 - 1 && -1 <= x112 - 1
f378_0_main_InvokeMethod(x116, x117, x118, x119) -> f519_0_main_InvokeMethod(x120, x121, x122, x123) :|: x124 <= x125 - 1 && x126 <= x127 && x120 <= x118 && x121 <= x116 && x122 + 1 <= x117 && -1 <= x116 - 1 && 0 <= x117 - 1 && -1 <= x118 - 1 && -1 <= x120 - 1 && -1 <= x121 - 1 && -1 <= x122 - 1
f378_0_main_InvokeMethod(x128, x129, x130, x131) -> f519_0_main_InvokeMethod(x132, x133, x134, x135) :|: x132 <= x130 && x136 <= x137 && x133 + 1 <= x128 && x134 <= x129 && 0 <= x128 - 1 && -1 <= x129 - 1 && -1 <= x130 - 1 && -1 <= x132 - 1 && -1 <= x133 - 1 && -1 <= x134 - 1
f519_0_main_InvokeMethod(x138, x139, x140, x141) -> f183_0_main_InvokeMethod(x142, x143, x144, x147) :|: -1 <= x144 - 1 && -1 <= x143 - 1 && -1 <= x142 - 1 && -1 <= x140 - 1 && -1 <= x139 - 1 && -1 <= x138 - 1 && x144 <= x138 && x143 <= x140 && x142 <= x139
f1_0_main_Load(x148, x149, x150, x151) -> f161_0_mk_LE(x154, x155, x156, x157) :|: x149 = x155 && x149 - 1 = x154 && -1 <= x149 - 1 && 0 <= x148 - 1
f140_0_main_InvokeMethod(x158, x159, x160, x161) -> f161_0_mk_LE(x162, x163, x164, x165) :|: x160 = x163 && x160 - 1 = x162 && -1 <= x159 - 1 && 0 <= x158 - 1 && 1 <= x160 - 1 && x161 <= x160 - 1
f140_0_main_InvokeMethod(x166, x167, x168, x169) -> f161_0_mk_LE(x170, x176, x177, x178) :|: x169 + 5 = x176 && x169 + 4 = x170 && -1 <= x167 - 1 && 0 <= x166 - 1 && x169 <= x168 - 1 && 1 <= x168 - 1 && -1 <= x169 - 1 && x169 <= x169 + 5 - 1
f161_0_mk_LE(x179, x180, x181, x182) -> f161_0_mk_LE(x187, x188, x189, x190) :|: x179 = x188 && x179 - 1 = x187 && 0 <= x180 - 1
f183_0_main_InvokeMethod(x196, x197, x198, x199) -> f283_0_length_NULL(x200, x201, x202, x207) :|: -1 <= x201 - 1 && -1 <= x200 - 1 && -1 <= x198 - 1 && -1 <= x197 - 1 && -1 <= x196 - 1 && x201 <= x198 && x200 <= x198
f268_0_main_LE(x208, x209, x210, x211) -> f283_0_length_NULL(x212, x213, x214, x215) :|: -1 <= x213 - 1 && -1 <= x212 - 1 && -1 <= x210 - 1 && -1 <= x209 - 1 && -1 <= x208 - 1 && x213 <= x210 && 0 <= x211 - 1 && x212 <= x210
f268_0_main_LE(x216, x217, x218, x219) -> f268_0_main_LE'(x220, x225, x226, x227) :|: 0 <= x219 - 1 && 0 <= x228 - 3 * x229 - 1 && x230 <= x216 && x233 <= x216 && -1 <= x216 - 1 && -1 <= x217 - 1 && -1 <= x218 - 1 && -1 <= x230 - 1 && -1 <= x233 - 1 && x216 = x220 && x217 = x225 && x218 = x226 && x219 = x227
f268_0_main_LE'(x234, x235, x236, x241) -> f283_0_length_NULL(x242, x243, x244, x245) :|: 0 <= x246 - 3 * x249 - 1 && 0 <= x241 - 1 && x242 <= x234 && x243 <= x234 && -1 <= x234 - 1 && -1 <= x235 - 1 && -1 <= x236 - 1 && -1 <= x242 - 1 && -1 <= x243 - 1 && x246 - 3 * x249 <= 2
f268_0_main_LE(x250, x251, x252, x253) -> f268_0_main_LE'(x254, x255, x256, x257) :|: 0 <= x253 - 1 && x258 - 3 * x259 = 0 && x260 <= x250 && x261 <= x250 && 0 <= x250 - 1 && -1 <= x251 - 1 && -1 <= x252 - 1 && 0 <= x260 - 1 && 0 <= x261 - 1 && x250 = x254 && x251 = x255 && x252 = x256 && x253 = x257
f268_0_main_LE'(x262, x263, x264, x265) -> f283_0_length_NULL(x266, x267, x268, x269) :|: 0 <= x265 - 1 && x270 - 3 * x271 = 0 && x266 <= x262 && x267 <= x262 && 0 <= x262 - 1 && -1 <= x263 - 1 && -1 <= x264 - 1 && 0 <= x266 - 1 && 0 <= x267 - 1 && x270 - 3 * x271 <= 2 && 0 <= x270 - 3 * x271
f378_0_main_InvokeMethod(x272, x273, x274, x275) -> f283_0_length_NULL(x276, x277, x278, x279) :|: -1 <= x277 - 1 && -1 <= x276 - 1 && -1 <= x274 - 1 && -1 <= x273 - 1 && -1 <= x272 - 1 && x277 <= x274 && x276 <= x274
f378_0_main_InvokeMethod(x280, x281, x282, x283) -> f283_0_length_NULL(x284, x285, x286, x287) :|: -1 <= x285 - 1 && -1 <= x284 - 1 && -1 <= x282 - 1 && -1 <= x281 - 1 && -1 <= x280 - 1 && x285 <= x280 && x284 <= x280
f378_0_main_InvokeMethod(x288, x289, x290, x291) -> f283_0_length_NULL(x292, x293, x294, x295) :|: x292 <= x290 && x296 <= x297 && x293 <= x290 && -1 <= x288 - 1 && -1 <= x289 - 1 && -1 <= x290 - 1 && -1 <= x292 - 1 && -1 <= x293 - 1
f378_0_main_InvokeMethod(x298, x299, x300, x301) -> f283_0_length_NULL(x302, x303, x304, x305) :|: x302 <= x298 && x306 <= x307 && x303 <= x298 && -1 <= x298 - 1 && -1 <= x299 - 1 && -1 <= x300 - 1 && -1 <= x302 - 1 && -1 <= x303 - 1
f283_0_length_NULL(x308, x309, x310, x311) -> f283_0_length_NULL(x312, x313, x314, x315) :|: -1 <= x313 - 1 && -1 <= x312 - 1 && 0 <= x309 - 1 && 0 <= x308 - 1 && x313 + 1 <= x309 && x313 + 1 <= x308 && x312 + 1 <= x309 && x312 + 1 <= x308
f519_0_main_InvokeMethod(x316, x317, x318, x319) -> f632_0_test_NULL(x320, x321, x322, x323) :|: -1 <= x321 - 1 && -1 <= x320 - 1 && -1 <= x318 - 1 && -1 <= x317 - 1 && -1 <= x316 - 1 && x321 <= x316 && x320 <= x316
f632_0_test_NULL(x324, x325, x326, x327) -> f632_0_test_NULL(x328, x329, x330, x331) :|: -1 <= x329 - 1 && -1 <= x328 - 1 && 0 <= x325 - 1 && 0 <= x324 - 1 && x329 + 1 <= x325 && x329 + 1 <= x324 && x328 + 1 <= x325 && x328 + 1 <= x324
__init(x332, x333, x334, x335) -> f1_0_main_Load(x336, x337, x338, x339) :|: 0 <= 0
Start term: __init(arg1, arg2, arg3, arg4)

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

(3) IRSwTTerminationDigraphProof (EQUIVALENT)
Constructed termination digraph!
Nodes:
(1) f83_0_mk_Return(arg1, arg2, arg3, arg4) -> f140_0_main_InvokeMethod(arg1P, arg2P, arg3P, arg4P) :|: arg3 = arg4P && arg3 + 3 = arg3P && -1 <= arg2P - 1 && 0 <= arg1P - 1 && -1 <= arg2 - 1 && 0 <= arg1 - 1 && arg2P <= arg2 && arg1P - 1 <= arg2 && -1 <= arg3 - 1 && arg1P <= arg1
(2) f1_0_main_Load(x, x1, x2, x3) -> f140_0_main_InvokeMethod(x4, x5, x6, x7) :|: x1 = x7 && x1 + 3 = x6 && -1 <= x5 - 1 && 0 <= x4 - 1 && 0 <= x - 1 && -1 <= x1 - 1 && x4 <= x
(3) f140_0_main_InvokeMethod(x8, x9, x10, x11) -> f183_0_main_InvokeMethod(x12, x13, x14, x15) :|: -1 <= x14 - 1 && -1 <= x13 - 1 && -1 <= x12 - 1 && -1 <= x9 - 1 && 0 <= x8 - 1 && x14 <= x9 && x11 <= x10 - 1 && 1 <= x10 - 1 && -1 <= x11 - 1 && x11 <= x11 + 5 - 1
(4) f232_0_length_Return(x16, x17, x18, x19) -> f268_0_main_LE(x20, x21, x22, x23) :|: x19 = x23 && -1 <= x22 - 1 && -1 <= x21 - 1 && -1 <= x20 - 1 && -1 <= x18 - 1 && -1 <= x17 - 1 && -1 <= x16 - 1 && x22 <= x18 && x21 <= x17 && x20 <= x16
(5) f183_0_main_InvokeMethod(x24, x25, x26, x27) -> f268_0_main_LE(x28, x29, x30, x31) :|: -1 <= x30 - 1 && -1 <= x29 - 1 && -1 <= x28 - 1 && -1 <= x26 - 1 && -1 <= x25 - 1 && -1 <= x24 - 1 && x30 <= x25 && x29 <= x24 && x28 <= x26
(6) f268_0_main_LE(x32, x33, x34, x35) -> f268_0_main_LE'(x36, x37, x38, x39) :|: 0 <= x35 - 1 && 0 <= x40 - 3 * x41 - 1 && x42 <= x33 && x43 <= x34 && x44 <= x32 && -1 <= x32 - 1 && -1 <= x33 - 1 && -1 <= x34 - 1 && -1 <= x42 - 1 && -1 <= x43 - 1 && -1 <= x44 - 1 && x32 = x36 && x33 = x37 && x34 = x38 && x35 = x39
(7) f268_0_main_LE'(x45, x46, x47, x48) -> f336_0_main_NE(x49, x50, x51, x52) :|: 0 <= x53 - 3 * x54 - 1 && 0 <= x48 - 1 && x49 <= x46 && x50 <= x47 && x51 <= x45 && -1 <= x45 - 1 && -1 <= x46 - 1 && -1 <= x47 - 1 && -1 <= x49 - 1 && -1 <= x50 - 1 && -1 <= x51 - 1 && x53 - 3 * x54 <= 2 && x55 - 5 * x56 <= 4 && 0 <= x55 - 5 * x56 && x55 - 5 * x56 = x52
(8) f336_0_main_NE(x57, x58, x59, x60) -> f378_0_main_InvokeMethod(x61, x62, x63, x64) :|: -1 <= x63 - 1 && -1 <= x62 - 1 && -1 <= x61 - 1 && -1 <= x59 - 1 && -1 <= x58 - 1 && -1 <= x57 - 1 && x63 <= x57 && x62 <= x59 && 0 <= x60 - 1 && x61 <= x58
(9) f268_0_main_LE(x65, x66, x69, x70) -> f268_0_main_LE'(x71, x72, x73, x74) :|: 0 <= x70 - 1 && x79 - 3 * x80 = 0 && x81 <= x66 && x82 <= x69 && x83 <= x65 && 0 <= x65 - 1 && -1 <= x66 - 1 && -1 <= x69 - 1 && -1 <= x81 - 1 && -1 <= x82 - 1 && 0 <= x83 - 1 && x65 = x71 && x66 = x72 && x69 = x73 && x70 = x74
(10) f268_0_main_LE'(x84, x87, x88, x89) -> f336_0_main_NE(x90, x91, x92, x93) :|: 0 <= x89 - 1 && x94 - 3 * x95 = 0 && x90 <= x87 && x91 <= x88 && x92 <= x84 && 0 <= x84 - 1 && -1 <= x87 - 1 && -1 <= x88 - 1 && -1 <= x90 - 1 && -1 <= x91 - 1 && 0 <= x92 - 1 && 0 <= x94 - 3 * x95 && x94 - 3 * x95 <= 2 && x96 - 5 * x97 <= 4 && 0 <= x96 - 5 * x97 && x96 - 5 * x97 = x93
(11) f336_0_main_NE(x98, x99, x100, x101) -> f378_0_main_InvokeMethod(x102, x103, x104, x105) :|: 0 = x101 && -1 <= x104 - 1 && -1 <= x103 - 1 && -1 <= x102 - 1 && 0 <= x100 - 1 && -1 <= x99 - 1 && -1 <= x98 - 1 && x104 <= x98 && x103 + 1 <= x100 && x102 <= x99
(12) f378_0_main_InvokeMethod(x106, x107, x108, x109) -> f519_0_main_InvokeMethod(x110, x111, x112, x113) :|: x110 + 1 <= x108 && x114 <= x115 - 1 && x111 <= x106 && x112 <= x107 && -1 <= x106 - 1 && -1 <= x107 - 1 && 0 <= x108 - 1 && -1 <= x110 - 1 && -1 <= x111 - 1 && -1 <= x112 - 1
(13) f378_0_main_InvokeMethod(x116, x117, x118, x119) -> f519_0_main_InvokeMethod(x120, x121, x122, x123) :|: x124 <= x125 - 1 && x126 <= x127 && x120 <= x118 && x121 <= x116 && x122 + 1 <= x117 && -1 <= x116 - 1 && 0 <= x117 - 1 && -1 <= x118 - 1 && -1 <= x120 - 1 && -1 <= x121 - 1 && -1 <= x122 - 1
(14) f378_0_main_InvokeMethod(x128, x129, x130, x131) -> f519_0_main_InvokeMethod(x132, x133, x134, x135) :|: x132 <= x130 && x136 <= x137 && x133 + 1 <= x128 && x134 <= x129 && 0 <= x128 - 1 && -1 <= x129 - 1 && -1 <= x130 - 1 && -1 <= x132 - 1 && -1 <= x133 - 1 && -1 <= x134 - 1
(15) f519_0_main_InvokeMethod(x138, x139, x140, x141) -> f183_0_main_InvokeMethod(x142, x143, x144, x147) :|: -1 <= x144 - 1 && -1 <= x143 - 1 && -1 <= x142 - 1 && -1 <= x140 - 1 && -1 <= x139 - 1 && -1 <= x138 - 1 && x144 <= x138 && x143 <= x140 && x142 <= x139
(16) f1_0_main_Load(x148, x149, x150, x151) -> f161_0_mk_LE(x154, x155, x156, x157) :|: x149 = x155 && x149 - 1 = x154 && -1 <= x149 - 1 && 0 <= x148 - 1
(17) f140_0_main_InvokeMethod(x158, x159, x160, x161) -> f161_0_mk_LE(x162, x163, x164, x165) :|: x160 = x163 && x160 - 1 = x162 && -1 <= x159 - 1 && 0 <= x158 - 1 && 1 <= x160 - 1 && x161 <= x160 - 1
(18) f140_0_main_InvokeMethod(x166, x167, x168, x169) -> f161_0_mk_LE(x170, x176, x177, x178) :|: x169 + 5 = x176 && x169 + 4 = x170 && -1 <= x167 - 1 && 0 <= x166 - 1 && x169 <= x168 - 1 && 1 <= x168 - 1 && -1 <= x169 - 1 && x169 <= x169 + 5 - 1
(19) f161_0_mk_LE(x179, x180, x181, x182) -> f161_0_mk_LE(x187, x188, x189, x190) :|: x179 = x188 && x179 - 1 = x187 && 0 <= x180 - 1
(20) f183_0_main_InvokeMethod(x196, x197, x198, x199) -> f283_0_length_NULL(x200, x201, x202, x207) :|: -1 <= x201 - 1 && -1 <= x200 - 1 && -1 <= x198 - 1 && -1 <= x197 - 1 && -1 <= x196 - 1 && x201 <= x198 && x200 <= x198
(21) f268_0_main_LE(x208, x209, x210, x211) -> f283_0_length_NULL(x212, x213, x214, x215) :|: -1 <= x213 - 1 && -1 <= x212 - 1 && -1 <= x210 - 1 && -1 <= x209 - 1 && -1 <= x208 - 1 && x213 <= x210 && 0 <= x211 - 1 && x212 <= x210
(22) f268_0_main_LE(x216, x217, x218, x219) -> f268_0_main_LE'(x220, x225, x226, x227) :|: 0 <= x219 - 1 && 0 <= x228 - 3 * x229 - 1 && x230 <= x216 && x233 <= x216 && -1 <= x216 - 1 && -1 <= x217 - 1 && -1 <= x218 - 1 && -1 <= x230 - 1 && -1 <= x233 - 1 && x216 = x220 && x217 = x225 && x218 = x226 && x219 = x227
(23) f268_0_main_LE'(x234, x235, x236, x241) -> f283_0_length_NULL(x242, x243, x244, x245) :|: 0 <= x246 - 3 * x249 - 1 && 0 <= x241 - 1 && x242 <= x234 && x243 <= x234 && -1 <= x234 - 1 && -1 <= x235 - 1 && -1 <= x236 - 1 && -1 <= x242 - 1 && -1 <= x243 - 1 && x246 - 3 * x249 <= 2
(24) f268_0_main_LE(x250, x251, x252, x253) -> f268_0_main_LE'(x254, x255, x256, x257) :|: 0 <= x253 - 1 && x258 - 3 * x259 = 0 && x260 <= x250 && x261 <= x250 && 0 <= x250 - 1 && -1 <= x251 - 1 && -1 <= x252 - 1 && 0 <= x260 - 1 && 0 <= x261 - 1 && x250 = x254 && x251 = x255 && x252 = x256 && x253 = x257
(25) f268_0_main_LE'(x262, x263, x264, x265) -> f283_0_length_NULL(x266, x267, x268, x269) :|: 0 <= x265 - 1 && x270 - 3 * x271 = 0 && x266 <= x262 && x267 <= x262 && 0 <= x262 - 1 && -1 <= x263 - 1 && -1 <= x264 - 1 && 0 <= x266 - 1 && 0 <= x267 - 1 && x270 - 3 * x271 <= 2 && 0 <= x270 - 3 * x271
(26) f378_0_main_InvokeMethod(x272, x273, x274, x275) -> f283_0_length_NULL(x276, x277, x278, x279) :|: -1 <= x277 - 1 && -1 <= x276 - 1 && -1 <= x274 - 1 && -1 <= x273 - 1 && -1 <= x272 - 1 && x277 <= x274 && x276 <= x274
(27) f378_0_main_InvokeMethod(x280, x281, x282, x283) -> f283_0_length_NULL(x284, x285, x286, x287) :|: -1 <= x285 - 1 && -1 <= x284 - 1 && -1 <= x282 - 1 && -1 <= x281 - 1 && -1 <= x280 - 1 && x285 <= x280 && x284 <= x280
(28) f378_0_main_InvokeMethod(x288, x289, x290, x291) -> f283_0_length_NULL(x292, x293, x294, x295) :|: x292 <= x290 && x296 <= x297 && x293 <= x290 && -1 <= x288 - 1 && -1 <= x289 - 1 && -1 <= x290 - 1 && -1 <= x292 - 1 && -1 <= x293 - 1
(29) f378_0_main_InvokeMethod(x298, x299, x300, x301) -> f283_0_length_NULL(x302, x303, x304, x305) :|: x302 <= x298 && x306 <= x307 && x303 <= x298 && -1 <= x298 - 1 && -1 <= x299 - 1 && -1 <= x300 - 1 && -1 <= x302 - 1 && -1 <= x303 - 1
(30) f283_0_length_NULL(x308, x309, x310, x311) -> f283_0_length_NULL(x312, x313, x314, x315) :|: -1 <= x313 - 1 && -1 <= x312 - 1 && 0 <= x309 - 1 && 0 <= x308 - 1 && x313 + 1 <= x309 && x313 + 1 <= x308 && x312 + 1 <= x309 && x312 + 1 <= x308
(31) f519_0_main_InvokeMethod(x316, x317, x318, x319) -> f632_0_test_NULL(x320, x321, x322, x323) :|: -1 <= x321 - 1 && -1 <= x320 - 1 && -1 <= x318 - 1 && -1 <= x317 - 1 && -1 <= x316 - 1 && x321 <= x316 && x320 <= x316
(32) f632_0_test_NULL(x324, x325, x326, x327) -> f632_0_test_NULL(x328, x329, x330, x331) :|: -1 <= x329 - 1 && -1 <= x328 - 1 && 0 <= x325 - 1 && 0 <= x324 - 1 && x329 + 1 <= x325 && x329 + 1 <= x324 && x328 + 1 <= x325 && x328 + 1 <= x324
(33) __init(x332, x333, x334, x335) -> f1_0_main_Load(x336, x337, x338, x339) :|: 0 <= 0

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

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

(4)
Complex Obligation (AND)

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

(5)
Obligation:

Termination digraph:
Nodes:
(1) f161_0_mk_LE(x179, x180, x181, x182) -> f161_0_mk_LE(x187, x188, x189, x190) :|: x179 = x188 && x179 - 1 = x187 && 0 <= x180 - 1

Arcs:
(1) -> (1)

This digraph is fully evaluated!

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

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

(7)
Obligation:
Rules:
f161_0_mk_LE(x179:0, x180:0, x181:0, x182:0) -> f161_0_mk_LE(x179:0 - 1, x179:0, x189:0, x190:0) :|: x180:0 > 0

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

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

   f161_0_mk_LE(x1, x2, x3, x4) -> f161_0_mk_LE(x1, x2)

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

(9)
Obligation:
Rules:
f161_0_mk_LE(x179:0, x180:0) -> f161_0_mk_LE(x179:0 - 1, x179:0) :|: x180:0 > 0

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

(10) TempFilterProof (SOUND)
Used the following sort dictionary for filtering: 
f161_0_mk_LE(VARIABLE, VARIABLE)
Replaced non-predefined constructor symbols by 0.
----------------------------------------

(11)
Obligation:
Rules:
f161_0_mk_LE(x179:0, x180:0) -> f161_0_mk_LE(c, x179:0) :|: c = x179:0 - 1 && x180:0 > 0

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

(12) PolynomialOrderProcessor (EQUIVALENT)
Found the following polynomial interpretation:
[f161_0_mk_LE(x, x1)] = x^2 + 2*x1

The following rules are decreasing:
f161_0_mk_LE(x179:0, x180:0) -> f161_0_mk_LE(c, x179:0) :|: c = x179:0 - 1 && x180:0 > 0
The following rules are bounded:
f161_0_mk_LE(x179:0, x180:0) -> f161_0_mk_LE(c, x179:0) :|: c = x179:0 - 1 && x180:0 > 0

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

(13)
YES

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

(14)
Obligation:

Termination digraph:
Nodes:
(1) f183_0_main_InvokeMethod(x24, x25, x26, x27) -> f268_0_main_LE(x28, x29, x30, x31) :|: -1 <= x30 - 1 && -1 <= x29 - 1 && -1 <= x28 - 1 && -1 <= x26 - 1 && -1 <= x25 - 1 && -1 <= x24 - 1 && x30 <= x25 && x29 <= x24 && x28 <= x26
(2) f519_0_main_InvokeMethod(x138, x139, x140, x141) -> f183_0_main_InvokeMethod(x142, x143, x144, x147) :|: -1 <= x144 - 1 && -1 <= x143 - 1 && -1 <= x142 - 1 && -1 <= x140 - 1 && -1 <= x139 - 1 && -1 <= x138 - 1 && x144 <= x138 && x143 <= x140 && x142 <= x139
(3) f378_0_main_InvokeMethod(x128, x129, x130, x131) -> f519_0_main_InvokeMethod(x132, x133, x134, x135) :|: x132 <= x130 && x136 <= x137 && x133 + 1 <= x128 && x134 <= x129 && 0 <= x128 - 1 && -1 <= x129 - 1 && -1 <= x130 - 1 && -1 <= x132 - 1 && -1 <= x133 - 1 && -1 <= x134 - 1
(4) f378_0_main_InvokeMethod(x116, x117, x118, x119) -> f519_0_main_InvokeMethod(x120, x121, x122, x123) :|: x124 <= x125 - 1 && x126 <= x127 && x120 <= x118 && x121 <= x116 && x122 + 1 <= x117 && -1 <= x116 - 1 && 0 <= x117 - 1 && -1 <= x118 - 1 && -1 <= x120 - 1 && -1 <= x121 - 1 && -1 <= x122 - 1
(5) f378_0_main_InvokeMethod(x106, x107, x108, x109) -> f519_0_main_InvokeMethod(x110, x111, x112, x113) :|: x110 + 1 <= x108 && x114 <= x115 - 1 && x111 <= x106 && x112 <= x107 && -1 <= x106 - 1 && -1 <= x107 - 1 && 0 <= x108 - 1 && -1 <= x110 - 1 && -1 <= x111 - 1 && -1 <= x112 - 1
(6) f336_0_main_NE(x98, x99, x100, x101) -> f378_0_main_InvokeMethod(x102, x103, x104, x105) :|: 0 = x101 && -1 <= x104 - 1 && -1 <= x103 - 1 && -1 <= x102 - 1 && 0 <= x100 - 1 && -1 <= x99 - 1 && -1 <= x98 - 1 && x104 <= x98 && x103 + 1 <= x100 && x102 <= x99
(7) f336_0_main_NE(x57, x58, x59, x60) -> f378_0_main_InvokeMethod(x61, x62, x63, x64) :|: -1 <= x63 - 1 && -1 <= x62 - 1 && -1 <= x61 - 1 && -1 <= x59 - 1 && -1 <= x58 - 1 && -1 <= x57 - 1 && x63 <= x57 && x62 <= x59 && 0 <= x60 - 1 && x61 <= x58
(8) f268_0_main_LE'(x84, x87, x88, x89) -> f336_0_main_NE(x90, x91, x92, x93) :|: 0 <= x89 - 1 && x94 - 3 * x95 = 0 && x90 <= x87 && x91 <= x88 && x92 <= x84 && 0 <= x84 - 1 && -1 <= x87 - 1 && -1 <= x88 - 1 && -1 <= x90 - 1 && -1 <= x91 - 1 && 0 <= x92 - 1 && 0 <= x94 - 3 * x95 && x94 - 3 * x95 <= 2 && x96 - 5 * x97 <= 4 && 0 <= x96 - 5 * x97 && x96 - 5 * x97 = x93
(9) f268_0_main_LE'(x45, x46, x47, x48) -> f336_0_main_NE(x49, x50, x51, x52) :|: 0 <= x53 - 3 * x54 - 1 && 0 <= x48 - 1 && x49 <= x46 && x50 <= x47 && x51 <= x45 && -1 <= x45 - 1 && -1 <= x46 - 1 && -1 <= x47 - 1 && -1 <= x49 - 1 && -1 <= x50 - 1 && -1 <= x51 - 1 && x53 - 3 * x54 <= 2 && x55 - 5 * x56 <= 4 && 0 <= x55 - 5 * x56 && x55 - 5 * x56 = x52
(10) f268_0_main_LE(x250, x251, x252, x253) -> f268_0_main_LE'(x254, x255, x256, x257) :|: 0 <= x253 - 1 && x258 - 3 * x259 = 0 && x260 <= x250 && x261 <= x250 && 0 <= x250 - 1 && -1 <= x251 - 1 && -1 <= x252 - 1 && 0 <= x260 - 1 && 0 <= x261 - 1 && x250 = x254 && x251 = x255 && x252 = x256 && x253 = x257
(11) f268_0_main_LE(x216, x217, x218, x219) -> f268_0_main_LE'(x220, x225, x226, x227) :|: 0 <= x219 - 1 && 0 <= x228 - 3 * x229 - 1 && x230 <= x216 && x233 <= x216 && -1 <= x216 - 1 && -1 <= x217 - 1 && -1 <= x218 - 1 && -1 <= x230 - 1 && -1 <= x233 - 1 && x216 = x220 && x217 = x225 && x218 = x226 && x219 = x227
(12) f268_0_main_LE(x65, x66, x69, x70) -> f268_0_main_LE'(x71, x72, x73, x74) :|: 0 <= x70 - 1 && x79 - 3 * x80 = 0 && x81 <= x66 && x82 <= x69 && x83 <= x65 && 0 <= x65 - 1 && -1 <= x66 - 1 && -1 <= x69 - 1 && -1 <= x81 - 1 && -1 <= x82 - 1 && 0 <= x83 - 1 && x65 = x71 && x66 = x72 && x69 = x73 && x70 = x74
(13) f268_0_main_LE(x32, x33, x34, x35) -> f268_0_main_LE'(x36, x37, x38, x39) :|: 0 <= x35 - 1 && 0 <= x40 - 3 * x41 - 1 && x42 <= x33 && x43 <= x34 && x44 <= x32 && -1 <= x32 - 1 && -1 <= x33 - 1 && -1 <= x34 - 1 && -1 <= x42 - 1 && -1 <= x43 - 1 && -1 <= x44 - 1 && x32 = x36 && x33 = x37 && x34 = x38 && x35 = x39

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

This digraph is fully evaluated!

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

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

(16)
Obligation:
Rules:
f378_0_main_InvokeMethod(x128:0, x129:0, x130:0, x131:0) -> f519_0_main_InvokeMethod(x132:0, x133:0, x134:0, x135:0) :|: x133:0 > -1 && x134:0 > -1 && x132:0 > -1 && x130:0 > -1 && x129:0 > -1 && x128:0 > 0 && x134:0 <= x129:0 && x133:0 + 1 <= x128:0 && x137:0 >= x136:0 && x132:0 <= x130:0
f336_0_main_NE(x98:0, x99:0, x100:0, cons_0) -> f378_0_main_InvokeMethod(x102:0, x103:0, x104:0, x105:0) :|: x103:0 + 1 <= x100:0 && x99:0 >= x102:0 && x98:0 >= x104:0 && x98:0 > -1 && x99:0 > -1 && x100:0 > 0 && x102:0 > -1 && x104:0 > -1 && x103:0 > -1 && cons_0 = 0
f519_0_main_InvokeMethod(x138:0, x139:0, x140:0, x141:0) -> f268_0_main_LE'(x220:0, x225:0, x226:0, x227:0) :|: x143:0 <= x140:0 && x142:0 <= x139:0 && x220:0 <= x144:0 && x144:0 <= x138:0 && x225:0 <= x142:0 && x138:0 > -1 && x226:0 <= x143:0 && x139:0 > -1 && x140:0 > -1 && x233:0 > -1 && x142:0 > -1 && x230:0 > -1 && x144:0 > -1 && x143:0 > -1 && x226:0 > -1 && x225:0 > -1 && x220:0 > -1 && x233:0 <= x220:0 && x230:0 <= x220:0 && x228:0 - 3 * x229:0 >= 1 && x227:0 > 0
f336_0_main_NE(x57:0, x58:0, x59:0, x60:0) -> f378_0_main_InvokeMethod(x61:0, x62:0, x63:0, x64:0) :|: x60:0 > 0 && x61:0 <= x58:0 && x62:0 <= x59:0 && x63:0 <= x57:0 && x57:0 > -1 && x58:0 > -1 && x59:0 > -1 && x61:0 > -1 && x62:0 > -1 && x63:0 > -1
f268_0_main_LE'(x45:0, x46:0, x47:0, x48:0) -> f336_0_main_NE(x49:0, x50:0, x51:0, x55:0 - 5 * x56:0) :|: x55:0 - 5 * x56:0 <= 4 && x55:0 - 5 * x56:0 >= 0 && x53:0 - 3 * x54:0 <= 2 && x51:0 > -1 && x50:0 > -1 && x49:0 > -1 && x47:0 > -1 && x46:0 > -1 && x45:0 > -1 && x51:0 <= x45:0 && x50:0 <= x47:0 && x49:0 <= x46:0 && x48:0 > 0 && x53:0 - 3 * x54:0 >= 1
f378_0_main_InvokeMethod(x106:0, x107:0, x108:0, x109:0) -> f519_0_main_InvokeMethod(x110:0, x111:0, x112:0, x113:0) :|: x111:0 > -1 && x112:0 > -1 && x110:0 > -1 && x108:0 > 0 && x107:0 > -1 && x106:0 > -1 && x112:0 <= x107:0 && x111:0 <= x106:0 && x115:0 - 1 >= x114:0 && x110:0 + 1 <= x108:0
f378_0_main_InvokeMethod(x116:0, x117:0, x118:0, x119:0) -> f519_0_main_InvokeMethod(x120:0, x121:0, x122:0, x123:0) :|: x121:0 > -1 && x122:0 > -1 && x120:0 > -1 && x118:0 > -1 && x117:0 > 0 && x116:0 > -1 && x122:0 + 1 <= x117:0 && x121:0 <= x116:0 && x120:0 <= x118:0 && x127:0 >= x126:0 && x125:0 - 1 >= x124:0
f519_0_main_InvokeMethod(x, x1, x2, x3) -> f268_0_main_LE'(x4, x5, x6, x7) :|: x8 <= x2 && x9 <= x1 && x4 <= x10 && x10 <= x && x5 <= x9 && x > -1 && x6 <= x8 && x1 > -1 && x2 > -1 && x11 > 0 && x9 > -1 && x12 > 0 && x10 > -1 && x8 > -1 && x6 > -1 && x5 > -1 && x11 <= x4 && x12 <= x4 && x7 > 0 && x4 > 0 && x13 - 3 * x14 = 0
f519_0_main_InvokeMethod(x15, x16, x17, x18) -> f268_0_main_LE'(x19, x20, x21, x22) :|: x23 <= x17 && x24 <= x16 && x19 <= x25 && x25 <= x15 && x20 <= x24 && x15 > -1 && x21 <= x23 && x16 > -1 && x17 > -1 && x26 > -1 && x24 > -1 && x27 > -1 && x25 > -1 && x23 > -1 && x28 > -1 && x21 > -1 && x20 > -1 && x19 > -1 && x26 <= x19 && x27 <= x21 && x28 <= x20 && x29 - 3 * x30 >= 1 && x22 > 0
f519_0_main_InvokeMethod(x31, x32, x33, x34) -> f268_0_main_LE'(x35, x36, x37, x38) :|: x39 <= x33 && x40 <= x32 && x35 <= x41 && x41 <= x31 && x36 <= x40 && x31 > -1 && x37 <= x39 && x32 > -1 && x33 > -1 && x42 > 0 && x40 > -1 && x43 > -1 && x41 > -1 && x39 > -1 && x44 > -1 && x37 > -1 && x36 > -1 && x42 <= x35 && x43 <= x37 && x44 <= x36 && x38 > 0 && x35 > 0 && x45 - 3 * x46 = 0
f268_0_main_LE'(x84:0, x87:0, x88:0, x89:0) -> f336_0_main_NE(x90:0, x91:0, x92:0, x96:0 - 5 * x97:0) :|: x96:0 - 5 * x97:0 <= 4 && x96:0 - 5 * x97:0 >= 0 && x94:0 - 3 * x95:0 <= 2 && x94:0 - 3 * x95:0 >= 0 && x92:0 > 0 && x91:0 > -1 && x90:0 > -1 && x88:0 > -1 && x87:0 > -1 && x84:0 > 0 && x92:0 <= x84:0 && x91:0 <= x88:0 && x90:0 <= x87:0 && x94:0 - 3 * x95:0 = 0 && x89:0 > 0

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

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

   f378_0_main_InvokeMethod(x1, x2, x3, x4) -> f378_0_main_InvokeMethod(x1, x2, x3)
   f519_0_main_InvokeMethod(x1, x2, x3, x4) -> f519_0_main_InvokeMethod(x1, x2, x3)

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

(18)
Obligation:
Rules:
f378_0_main_InvokeMethod(x128:0, x129:0, x130:0) -> f519_0_main_InvokeMethod(x132:0, x133:0, x134:0) :|: x133:0 > -1 && x134:0 > -1 && x132:0 > -1 && x130:0 > -1 && x129:0 > -1 && x128:0 > 0 && x134:0 <= x129:0 && x133:0 + 1 <= x128:0 && x137:0 >= x136:0 && x132:0 <= x130:0
f336_0_main_NE(x98:0, x99:0, x100:0, cons_0) -> f378_0_main_InvokeMethod(x102:0, x103:0, x104:0) :|: x103:0 + 1 <= x100:0 && x99:0 >= x102:0 && x98:0 >= x104:0 && x98:0 > -1 && x99:0 > -1 && x100:0 > 0 && x102:0 > -1 && x104:0 > -1 && x103:0 > -1 && cons_0 = 0
f519_0_main_InvokeMethod(x138:0, x139:0, x140:0) -> f268_0_main_LE'(x220:0, x225:0, x226:0, x227:0) :|: x143:0 <= x140:0 && x142:0 <= x139:0 && x220:0 <= x144:0 && x144:0 <= x138:0 && x225:0 <= x142:0 && x138:0 > -1 && x226:0 <= x143:0 && x139:0 > -1 && x140:0 > -1 && x233:0 > -1 && x142:0 > -1 && x230:0 > -1 && x144:0 > -1 && x143:0 > -1 && x226:0 > -1 && x225:0 > -1 && x220:0 > -1 && x233:0 <= x220:0 && x230:0 <= x220:0 && x228:0 - 3 * x229:0 >= 1 && x227:0 > 0
f336_0_main_NE(x57:0, x58:0, x59:0, x60:0) -> f378_0_main_InvokeMethod(x61:0, x62:0, x63:0) :|: x60:0 > 0 && x61:0 <= x58:0 && x62:0 <= x59:0 && x63:0 <= x57:0 && x57:0 > -1 && x58:0 > -1 && x59:0 > -1 && x61:0 > -1 && x62:0 > -1 && x63:0 > -1
f268_0_main_LE'(x45:0, x46:0, x47:0, x48:0) -> f336_0_main_NE(x49:0, x50:0, x51:0, x55:0 - 5 * x56:0) :|: x55:0 - 5 * x56:0 <= 4 && x55:0 - 5 * x56:0 >= 0 && x53:0 - 3 * x54:0 <= 2 && x51:0 > -1 && x50:0 > -1 && x49:0 > -1 && x47:0 > -1 && x46:0 > -1 && x45:0 > -1 && x51:0 <= x45:0 && x50:0 <= x47:0 && x49:0 <= x46:0 && x48:0 > 0 && x53:0 - 3 * x54:0 >= 1
f378_0_main_InvokeMethod(x106:0, x107:0, x108:0) -> f519_0_main_InvokeMethod(x110:0, x111:0, x112:0) :|: x111:0 > -1 && x112:0 > -1 && x110:0 > -1 && x108:0 > 0 && x107:0 > -1 && x106:0 > -1 && x112:0 <= x107:0 && x111:0 <= x106:0 && x115:0 - 1 >= x114:0 && x110:0 + 1 <= x108:0
f378_0_main_InvokeMethod(x116:0, x117:0, x118:0) -> f519_0_main_InvokeMethod(x120:0, x121:0, x122:0) :|: x121:0 > -1 && x122:0 > -1 && x120:0 > -1 && x118:0 > -1 && x117:0 > 0 && x116:0 > -1 && x122:0 + 1 <= x117:0 && x121:0 <= x116:0 && x120:0 <= x118:0 && x127:0 >= x126:0 && x125:0 - 1 >= x124:0
f519_0_main_InvokeMethod(x, x1, x2) -> f268_0_main_LE'(x4, x5, x6, x7) :|: x8 <= x2 && x9 <= x1 && x4 <= x10 && x10 <= x && x5 <= x9 && x > -1 && x6 <= x8 && x1 > -1 && x2 > -1 && x11 > 0 && x9 > -1 && x12 > 0 && x10 > -1 && x8 > -1 && x6 > -1 && x5 > -1 && x11 <= x4 && x12 <= x4 && x7 > 0 && x4 > 0 && x13 - 3 * x14 = 0
f519_0_main_InvokeMethod(x15, x16, x17) -> f268_0_main_LE'(x19, x20, x21, x22) :|: x23 <= x17 && x24 <= x16 && x19 <= x25 && x25 <= x15 && x20 <= x24 && x15 > -1 && x21 <= x23 && x16 > -1 && x17 > -1 && x26 > -1 && x24 > -1 && x27 > -1 && x25 > -1 && x23 > -1 && x28 > -1 && x21 > -1 && x20 > -1 && x19 > -1 && x26 <= x19 && x27 <= x21 && x28 <= x20 && x29 - 3 * x30 >= 1 && x22 > 0
f519_0_main_InvokeMethod(x31, x32, x33) -> f268_0_main_LE'(x35, x36, x37, x38) :|: x39 <= x33 && x40 <= x32 && x35 <= x41 && x41 <= x31 && x36 <= x40 && x31 > -1 && x37 <= x39 && x32 > -1 && x33 > -1 && x42 > 0 && x40 > -1 && x43 > -1 && x41 > -1 && x39 > -1 && x44 > -1 && x37 > -1 && x36 > -1 && x42 <= x35 && x43 <= x37 && x44 <= x36 && x38 > 0 && x35 > 0 && x45 - 3 * x46 = 0
f268_0_main_LE'(x84:0, x87:0, x88:0, x89:0) -> f336_0_main_NE(x90:0, x91:0, x92:0, x96:0 - 5 * x97:0) :|: x96:0 - 5 * x97:0 <= 4 && x96:0 - 5 * x97:0 >= 0 && x94:0 - 3 * x95:0 <= 2 && x94:0 - 3 * x95:0 >= 0 && x92:0 > 0 && x91:0 > -1 && x90:0 > -1 && x88:0 > -1 && x87:0 > -1 && x84:0 > 0 && x92:0 <= x84:0 && x91:0 <= x88:0 && x90:0 <= x87:0 && x94:0 - 3 * x95:0 = 0 && x89:0 > 0

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

(19) TempFilterProof (SOUND)
Used the following sort dictionary for filtering: 
f378_0_main_InvokeMethod(INTEGER, INTEGER, INTEGER)
f519_0_main_InvokeMethod(INTEGER, INTEGER, INTEGER)
f336_0_main_NE(INTEGER, INTEGER, INTEGER, INTEGER)
f268_0_main_LE'(INTEGER, INTEGER, INTEGER, INTEGER)
Replaced non-predefined constructor symbols by 0.
----------------------------------------

(20)
Obligation:
Rules:
f378_0_main_InvokeMethod(x128:0, x129:0, x130:0) -> f519_0_main_InvokeMethod(x132:0, x133:0, x134:0) :|: x133:0 > -1 && x134:0 > -1 && x132:0 > -1 && x130:0 > -1 && x129:0 > -1 && x128:0 > 0 && x134:0 <= x129:0 && x133:0 + 1 <= x128:0 && x137:0 >= x136:0 && x132:0 <= x130:0
f336_0_main_NE(x98:0, x99:0, x100:0, c) -> f378_0_main_InvokeMethod(x102:0, x103:0, x104:0) :|: c = 0 && (x103:0 + 1 <= x100:0 && x99:0 >= x102:0 && x98:0 >= x104:0 && x98:0 > -1 && x99:0 > -1 && x100:0 > 0 && x102:0 > -1 && x104:0 > -1 && x103:0 > -1 && cons_0 = 0)
f519_0_main_InvokeMethod(x138:0, x139:0, x140:0) -> f268_0_main_LE'(x220:0, x225:0, x226:0, x227:0) :|: x143:0 <= x140:0 && x142:0 <= x139:0 && x220:0 <= x144:0 && x144:0 <= x138:0 && x225:0 <= x142:0 && x138:0 > -1 && x226:0 <= x143:0 && x139:0 > -1 && x140:0 > -1 && x233:0 > -1 && x142:0 > -1 && x230:0 > -1 && x144:0 > -1 && x143:0 > -1 && x226:0 > -1 && x225:0 > -1 && x220:0 > -1 && x233:0 <= x220:0 && x230:0 <= x220:0 && x228:0 - 3 * x229:0 >= 1 && x227:0 > 0
f336_0_main_NE(x57:0, x58:0, x59:0, x60:0) -> f378_0_main_InvokeMethod(x61:0, x62:0, x63:0) :|: x60:0 > 0 && x61:0 <= x58:0 && x62:0 <= x59:0 && x63:0 <= x57:0 && x57:0 > -1 && x58:0 > -1 && x59:0 > -1 && x61:0 > -1 && x62:0 > -1 && x63:0 > -1
f268_0_main_LE'(x45:0, x46:0, x47:0, x48:0) -> f336_0_main_NE(x49:0, x50:0, x51:0, c1) :|: c1 = x55:0 - 5 * x56:0 && (x55:0 - 5 * x56:0 <= 4 && x55:0 - 5 * x56:0 >= 0 && x53:0 - 3 * x54:0 <= 2 && x51:0 > -1 && x50:0 > -1 && x49:0 > -1 && x47:0 > -1 && x46:0 > -1 && x45:0 > -1 && x51:0 <= x45:0 && x50:0 <= x47:0 && x49:0 <= x46:0 && x48:0 > 0 && x53:0 - 3 * x54:0 >= 1)
f378_0_main_InvokeMethod(x106:0, x107:0, x108:0) -> f519_0_main_InvokeMethod(x110:0, x111:0, x112:0) :|: x111:0 > -1 && x112:0 > -1 && x110:0 > -1 && x108:0 > 0 && x107:0 > -1 && x106:0 > -1 && x112:0 <= x107:0 && x111:0 <= x106:0 && x115:0 - 1 >= x114:0 && x110:0 + 1 <= x108:0
f378_0_main_InvokeMethod(x116:0, x117:0, x118:0) -> f519_0_main_InvokeMethod(x120:0, x121:0, x122:0) :|: x121:0 > -1 && x122:0 > -1 && x120:0 > -1 && x118:0 > -1 && x117:0 > 0 && x116:0 > -1 && x122:0 + 1 <= x117:0 && x121:0 <= x116:0 && x120:0 <= x118:0 && x127:0 >= x126:0 && x125:0 - 1 >= x124:0
f519_0_main_InvokeMethod(x, x1, x2) -> f268_0_main_LE'(x4, x5, x6, x7) :|: x8 <= x2 && x9 <= x1 && x4 <= x10 && x10 <= x && x5 <= x9 && x > -1 && x6 <= x8 && x1 > -1 && x2 > -1 && x11 > 0 && x9 > -1 && x12 > 0 && x10 > -1 && x8 > -1 && x6 > -1 && x5 > -1 && x11 <= x4 && x12 <= x4 && x7 > 0 && x4 > 0 && x13 - 3 * x14 = 0
f519_0_main_InvokeMethod(x15, x16, x17) -> f268_0_main_LE'(x19, x20, x21, x22) :|: x23 <= x17 && x24 <= x16 && x19 <= x25 && x25 <= x15 && x20 <= x24 && x15 > -1 && x21 <= x23 && x16 > -1 && x17 > -1 && x26 > -1 && x24 > -1 && x27 > -1 && x25 > -1 && x23 > -1 && x28 > -1 && x21 > -1 && x20 > -1 && x19 > -1 && x26 <= x19 && x27 <= x21 && x28 <= x20 && x29 - 3 * x30 >= 1 && x22 > 0
f519_0_main_InvokeMethod(x31, x32, x33) -> f268_0_main_LE'(x35, x36, x37, x38) :|: x39 <= x33 && x40 <= x32 && x35 <= x41 && x41 <= x31 && x36 <= x40 && x31 > -1 && x37 <= x39 && x32 > -1 && x33 > -1 && x42 > 0 && x40 > -1 && x43 > -1 && x41 > -1 && x39 > -1 && x44 > -1 && x37 > -1 && x36 > -1 && x42 <= x35 && x43 <= x37 && x44 <= x36 && x38 > 0 && x35 > 0 && x45 - 3 * x46 = 0
f268_0_main_LE'(x84:0, x87:0, x88:0, x89:0) -> f336_0_main_NE(x90:0, x91:0, x92:0, c2) :|: c2 = x96:0 - 5 * x97:0 && (x96:0 - 5 * x97:0 <= 4 && x96:0 - 5 * x97:0 >= 0 && x94:0 - 3 * x95:0 <= 2 && x94:0 - 3 * x95:0 >= 0 && x92:0 > 0 && x91:0 > -1 && x90:0 > -1 && x88:0 > -1 && x87:0 > -1 && x84:0 > 0 && x92:0 <= x84:0 && x91:0 <= x88:0 && x90:0 <= x87:0 && x94:0 - 3 * x95:0 = 0 && x89:0 > 0)

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

(21) RankingReductionPairProof (EQUIVALENT)
Interpretation:
[ f378_0_main_InvokeMethod ] = 4*f378_0_main_InvokeMethod_3 + 4*f378_0_main_InvokeMethod_2 + 4*f378_0_main_InvokeMethod_1 + -2
[ f519_0_main_InvokeMethod ] = 4*f519_0_main_InvokeMethod_2 + 4*f519_0_main_InvokeMethod_3 + 4*f519_0_main_InvokeMethod_1 + 1
[ f336_0_main_NE ] = 4*f336_0_main_NE_1 + 4*f336_0_main_NE_2 + 4*f336_0_main_NE_3 + -1
[ f268_0_main_LE' ] = 4*f268_0_main_LE'_1 + 4*f268_0_main_LE'_2 + 4*f268_0_main_LE'_3

The following rules are decreasing:
f378_0_main_InvokeMethod(x128:0, x129:0, x130:0) -> f519_0_main_InvokeMethod(x132:0, x133:0, x134:0) :|: x133:0 > -1 && x134:0 > -1 && x132:0 > -1 && x130:0 > -1 && x129:0 > -1 && x128:0 > 0 && x134:0 <= x129:0 && x133:0 + 1 <= x128:0 && x137:0 >= x136:0 && x132:0 <= x130:0
f336_0_main_NE(x98:0, x99:0, x100:0, c) -> f378_0_main_InvokeMethod(x102:0, x103:0, x104:0) :|: c = 0 && (x103:0 + 1 <= x100:0 && x99:0 >= x102:0 && x98:0 >= x104:0 && x98:0 > -1 && x99:0 > -1 && x100:0 > 0 && x102:0 > -1 && x104:0 > -1 && x103:0 > -1 && cons_0 = 0)
f519_0_main_InvokeMethod(x138:0, x139:0, x140:0) -> f268_0_main_LE'(x220:0, x225:0, x226:0, x227:0) :|: x143:0 <= x140:0 && x142:0 <= x139:0 && x220:0 <= x144:0 && x144:0 <= x138:0 && x225:0 <= x142:0 && x138:0 > -1 && x226:0 <= x143:0 && x139:0 > -1 && x140:0 > -1 && x233:0 > -1 && x142:0 > -1 && x230:0 > -1 && x144:0 > -1 && x143:0 > -1 && x226:0 > -1 && x225:0 > -1 && x220:0 > -1 && x233:0 <= x220:0 && x230:0 <= x220:0 && x228:0 - 3 * x229:0 >= 1 && x227:0 > 0
f336_0_main_NE(x57:0, x58:0, x59:0, x60:0) -> f378_0_main_InvokeMethod(x61:0, x62:0, x63:0) :|: x60:0 > 0 && x61:0 <= x58:0 && x62:0 <= x59:0 && x63:0 <= x57:0 && x57:0 > -1 && x58:0 > -1 && x59:0 > -1 && x61:0 > -1 && x62:0 > -1 && x63:0 > -1
f268_0_main_LE'(x45:0, x46:0, x47:0, x48:0) -> f336_0_main_NE(x49:0, x50:0, x51:0, c1) :|: c1 = x55:0 - 5 * x56:0 && (x55:0 - 5 * x56:0 <= 4 && x55:0 - 5 * x56:0 >= 0 && x53:0 - 3 * x54:0 <= 2 && x51:0 > -1 && x50:0 > -1 && x49:0 > -1 && x47:0 > -1 && x46:0 > -1 && x45:0 > -1 && x51:0 <= x45:0 && x50:0 <= x47:0 && x49:0 <= x46:0 && x48:0 > 0 && x53:0 - 3 * x54:0 >= 1)
f378_0_main_InvokeMethod(x106:0, x107:0, x108:0) -> f519_0_main_InvokeMethod(x110:0, x111:0, x112:0) :|: x111:0 > -1 && x112:0 > -1 && x110:0 > -1 && x108:0 > 0 && x107:0 > -1 && x106:0 > -1 && x112:0 <= x107:0 && x111:0 <= x106:0 && x115:0 - 1 >= x114:0 && x110:0 + 1 <= x108:0
f378_0_main_InvokeMethod(x116:0, x117:0, x118:0) -> f519_0_main_InvokeMethod(x120:0, x121:0, x122:0) :|: x121:0 > -1 && x122:0 > -1 && x120:0 > -1 && x118:0 > -1 && x117:0 > 0 && x116:0 > -1 && x122:0 + 1 <= x117:0 && x121:0 <= x116:0 && x120:0 <= x118:0 && x127:0 >= x126:0 && x125:0 - 1 >= x124:0
f519_0_main_InvokeMethod(x, x1, x2) -> f268_0_main_LE'(x4, x5, x6, x7) :|: x8 <= x2 && x9 <= x1 && x4 <= x10 && x10 <= x && x5 <= x9 && x > -1 && x6 <= x8 && x1 > -1 && x2 > -1 && x11 > 0 && x9 > -1 && x12 > 0 && x10 > -1 && x8 > -1 && x6 > -1 && x5 > -1 && x11 <= x4 && x12 <= x4 && x7 > 0 && x4 > 0 && x13 - 3 * x14 = 0
f519_0_main_InvokeMethod(x15, x16, x17) -> f268_0_main_LE'(x19, x20, x21, x22) :|: x23 <= x17 && x24 <= x16 && x19 <= x25 && x25 <= x15 && x20 <= x24 && x15 > -1 && x21 <= x23 && x16 > -1 && x17 > -1 && x26 > -1 && x24 > -1 && x27 > -1 && x25 > -1 && x23 > -1 && x28 > -1 && x21 > -1 && x20 > -1 && x19 > -1 && x26 <= x19 && x27 <= x21 && x28 <= x20 && x29 - 3 * x30 >= 1 && x22 > 0
f519_0_main_InvokeMethod(x31, x32, x33) -> f268_0_main_LE'(x35, x36, x37, x38) :|: x39 <= x33 && x40 <= x32 && x35 <= x41 && x41 <= x31 && x36 <= x40 && x31 > -1 && x37 <= x39 && x32 > -1 && x33 > -1 && x42 > 0 && x40 > -1 && x43 > -1 && x41 > -1 && x39 > -1 && x44 > -1 && x37 > -1 && x36 > -1 && x42 <= x35 && x43 <= x37 && x44 <= x36 && x38 > 0 && x35 > 0 && x45 - 3 * x46 = 0
f268_0_main_LE'(x84:0, x87:0, x88:0, x89:0) -> f336_0_main_NE(x90:0, x91:0, x92:0, c2) :|: c2 = x96:0 - 5 * x97:0 && (x96:0 - 5 * x97:0 <= 4 && x96:0 - 5 * x97:0 >= 0 && x94:0 - 3 * x95:0 <= 2 && x94:0 - 3 * x95:0 >= 0 && x92:0 > 0 && x91:0 > -1 && x90:0 > -1 && x88:0 > -1 && x87:0 > -1 && x84:0 > 0 && x92:0 <= x84:0 && x91:0 <= x88:0 && x90:0 <= x87:0 && x94:0 - 3 * x95:0 = 0 && x89:0 > 0)

The following rules are bounded:
f378_0_main_InvokeMethod(x128:0, x129:0, x130:0) -> f519_0_main_InvokeMethod(x132:0, x133:0, x134:0) :|: x133:0 > -1 && x134:0 > -1 && x132:0 > -1 && x130:0 > -1 && x129:0 > -1 && x128:0 > 0 && x134:0 <= x129:0 && x133:0 + 1 <= x128:0 && x137:0 >= x136:0 && x132:0 <= x130:0
f336_0_main_NE(x98:0, x99:0, x100:0, c) -> f378_0_main_InvokeMethod(x102:0, x103:0, x104:0) :|: c = 0 && (x103:0 + 1 <= x100:0 && x99:0 >= x102:0 && x98:0 >= x104:0 && x98:0 > -1 && x99:0 > -1 && x100:0 > 0 && x102:0 > -1 && x104:0 > -1 && x103:0 > -1 && cons_0 = 0)
f519_0_main_InvokeMethod(x138:0, x139:0, x140:0) -> f268_0_main_LE'(x220:0, x225:0, x226:0, x227:0) :|: x143:0 <= x140:0 && x142:0 <= x139:0 && x220:0 <= x144:0 && x144:0 <= x138:0 && x225:0 <= x142:0 && x138:0 > -1 && x226:0 <= x143:0 && x139:0 > -1 && x140:0 > -1 && x233:0 > -1 && x142:0 > -1 && x230:0 > -1 && x144:0 > -1 && x143:0 > -1 && x226:0 > -1 && x225:0 > -1 && x220:0 > -1 && x233:0 <= x220:0 && x230:0 <= x220:0 && x228:0 - 3 * x229:0 >= 1 && x227:0 > 0
f336_0_main_NE(x57:0, x58:0, x59:0, x60:0) -> f378_0_main_InvokeMethod(x61:0, x62:0, x63:0) :|: x60:0 > 0 && x61:0 <= x58:0 && x62:0 <= x59:0 && x63:0 <= x57:0 && x57:0 > -1 && x58:0 > -1 && x59:0 > -1 && x61:0 > -1 && x62:0 > -1 && x63:0 > -1
f268_0_main_LE'(x45:0, x46:0, x47:0, x48:0) -> f336_0_main_NE(x49:0, x50:0, x51:0, c1) :|: c1 = x55:0 - 5 * x56:0 && (x55:0 - 5 * x56:0 <= 4 && x55:0 - 5 * x56:0 >= 0 && x53:0 - 3 * x54:0 <= 2 && x51:0 > -1 && x50:0 > -1 && x49:0 > -1 && x47:0 > -1 && x46:0 > -1 && x45:0 > -1 && x51:0 <= x45:0 && x50:0 <= x47:0 && x49:0 <= x46:0 && x48:0 > 0 && x53:0 - 3 * x54:0 >= 1)
f378_0_main_InvokeMethod(x106:0, x107:0, x108:0) -> f519_0_main_InvokeMethod(x110:0, x111:0, x112:0) :|: x111:0 > -1 && x112:0 > -1 && x110:0 > -1 && x108:0 > 0 && x107:0 > -1 && x106:0 > -1 && x112:0 <= x107:0 && x111:0 <= x106:0 && x115:0 - 1 >= x114:0 && x110:0 + 1 <= x108:0
f378_0_main_InvokeMethod(x116:0, x117:0, x118:0) -> f519_0_main_InvokeMethod(x120:0, x121:0, x122:0) :|: x121:0 > -1 && x122:0 > -1 && x120:0 > -1 && x118:0 > -1 && x117:0 > 0 && x116:0 > -1 && x122:0 + 1 <= x117:0 && x121:0 <= x116:0 && x120:0 <= x118:0 && x127:0 >= x126:0 && x125:0 - 1 >= x124:0
f519_0_main_InvokeMethod(x, x1, x2) -> f268_0_main_LE'(x4, x5, x6, x7) :|: x8 <= x2 && x9 <= x1 && x4 <= x10 && x10 <= x && x5 <= x9 && x > -1 && x6 <= x8 && x1 > -1 && x2 > -1 && x11 > 0 && x9 > -1 && x12 > 0 && x10 > -1 && x8 > -1 && x6 > -1 && x5 > -1 && x11 <= x4 && x12 <= x4 && x7 > 0 && x4 > 0 && x13 - 3 * x14 = 0
f519_0_main_InvokeMethod(x15, x16, x17) -> f268_0_main_LE'(x19, x20, x21, x22) :|: x23 <= x17 && x24 <= x16 && x19 <= x25 && x25 <= x15 && x20 <= x24 && x15 > -1 && x21 <= x23 && x16 > -1 && x17 > -1 && x26 > -1 && x24 > -1 && x27 > -1 && x25 > -1 && x23 > -1 && x28 > -1 && x21 > -1 && x20 > -1 && x19 > -1 && x26 <= x19 && x27 <= x21 && x28 <= x20 && x29 - 3 * x30 >= 1 && x22 > 0
f519_0_main_InvokeMethod(x31, x32, x33) -> f268_0_main_LE'(x35, x36, x37, x38) :|: x39 <= x33 && x40 <= x32 && x35 <= x41 && x41 <= x31 && x36 <= x40 && x31 > -1 && x37 <= x39 && x32 > -1 && x33 > -1 && x42 > 0 && x40 > -1 && x43 > -1 && x41 > -1 && x39 > -1 && x44 > -1 && x37 > -1 && x36 > -1 && x42 <= x35 && x43 <= x37 && x44 <= x36 && x38 > 0 && x35 > 0 && x45 - 3 * x46 = 0
f268_0_main_LE'(x84:0, x87:0, x88:0, x89:0) -> f336_0_main_NE(x90:0, x91:0, x92:0, c2) :|: c2 = x96:0 - 5 * x97:0 && (x96:0 - 5 * x97:0 <= 4 && x96:0 - 5 * x97:0 >= 0 && x94:0 - 3 * x95:0 <= 2 && x94:0 - 3 * x95:0 >= 0 && x92:0 > 0 && x91:0 > -1 && x90:0 > -1 && x88:0 > -1 && x87:0 > -1 && x84:0 > 0 && x92:0 <= x84:0 && x91:0 <= x88:0 && x90:0 <= x87:0 && x94:0 - 3 * x95:0 = 0 && x89:0 > 0)


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

(22)
YES

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

(23)
Obligation:

Termination digraph:
Nodes:
(1) f632_0_test_NULL(x324, x325, x326, x327) -> f632_0_test_NULL(x328, x329, x330, x331) :|: -1 <= x329 - 1 && -1 <= x328 - 1 && 0 <= x325 - 1 && 0 <= x324 - 1 && x329 + 1 <= x325 && x329 + 1 <= x324 && x328 + 1 <= x325 && x328 + 1 <= x324

Arcs:
(1) -> (1)

This digraph is fully evaluated!

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

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

(25)
Obligation:
Rules:
f632_0_test_NULL(x324:0, x325:0, x326:0, x327:0) -> f632_0_test_NULL(x328:0, x329:0, x330:0, x331:0) :|: x328:0 + 1 <= x325:0 && x328:0 + 1 <= x324:0 && x329:0 + 1 <= x324:0 && x329:0 + 1 <= x325:0 && x324:0 > 0 && x325:0 > 0 && x328:0 > -1 && x329:0 > -1

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

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

   f632_0_test_NULL(x1, x2, x3, x4) -> f632_0_test_NULL(x1, x2)

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

(27)
Obligation:
Rules:
f632_0_test_NULL(x324:0, x325:0) -> f632_0_test_NULL(x328:0, x329:0) :|: x328:0 + 1 <= x325:0 && x328:0 + 1 <= x324:0 && x329:0 + 1 <= x324:0 && x329:0 + 1 <= x325:0 && x324:0 > 0 && x325:0 > 0 && x328:0 > -1 && x329:0 > -1

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

(28) FilterProof (EQUIVALENT)
Used the following sort dictionary for filtering: 
f632_0_test_NULL(INTEGER, INTEGER)
Replaced non-predefined constructor symbols by 0.
----------------------------------------

(29)
Obligation:
Rules:
f632_0_test_NULL(x324:0, x325:0) -> f632_0_test_NULL(x328:0, x329:0) :|: x328:0 + 1 <= x325:0 && x328:0 + 1 <= x324:0 && x329:0 + 1 <= x324:0 && x329:0 + 1 <= x325:0 && x324:0 > 0 && x325:0 > 0 && x328:0 > -1 && x329:0 > -1

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

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

(31)
Obligation:
Rules:
f632_0_test_NULL(x324:0:0, x325:0:0) -> f632_0_test_NULL(x328:0:0, x329:0:0) :|: x328:0:0 > -1 && x329:0:0 > -1 && x325:0:0 > 0 && x324:0:0 > 0 && x329:0:0 + 1 <= x325:0:0 && x329:0:0 + 1 <= x324:0:0 && x328:0:0 + 1 <= x324:0:0 && x328:0:0 + 1 <= x325:0:0

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

(32) RankingReductionPairProof (EQUIVALENT)
Interpretation:
[ f632_0_test_NULL ] = f632_0_test_NULL_1

The following rules are decreasing:
f632_0_test_NULL(x324:0:0, x325:0:0) -> f632_0_test_NULL(x328:0:0, x329:0:0) :|: x328:0:0 > -1 && x329:0:0 > -1 && x325:0:0 > 0 && x324:0:0 > 0 && x329:0:0 + 1 <= x325:0:0 && x329:0:0 + 1 <= x324:0:0 && x328:0:0 + 1 <= x324:0:0 && x328:0:0 + 1 <= x325:0:0

The following rules are bounded:
f632_0_test_NULL(x324:0:0, x325:0:0) -> f632_0_test_NULL(x328:0:0, x329:0:0) :|: x328:0:0 > -1 && x329:0:0 > -1 && x325:0:0 > 0 && x324:0:0 > 0 && x329:0:0 + 1 <= x325:0:0 && x329:0:0 + 1 <= x324:0:0 && x328:0:0 + 1 <= x324:0:0 && x328:0:0 + 1 <= x325:0:0


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

(33)
YES

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

(34)
Obligation:

Termination digraph:
Nodes:
(1) f283_0_length_NULL(x308, x309, x310, x311) -> f283_0_length_NULL(x312, x313, x314, x315) :|: -1 <= x313 - 1 && -1 <= x312 - 1 && 0 <= x309 - 1 && 0 <= x308 - 1 && x313 + 1 <= x309 && x313 + 1 <= x308 && x312 + 1 <= x309 && x312 + 1 <= x308

Arcs:
(1) -> (1)

This digraph is fully evaluated!

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

(36)
Obligation:
Rules:
f283_0_length_NULL(x308:0, x309:0, x310:0, x311:0) -> f283_0_length_NULL(x312:0, x313:0, x314:0, x315:0) :|: x312:0 + 1 <= x309:0 && x312:0 + 1 <= x308:0 && x313:0 + 1 <= x308:0 && x313:0 + 1 <= x309:0 && x308:0 > 0 && x309:0 > 0 && x312:0 > -1 && x313:0 > -1

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

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

   f283_0_length_NULL(x1, x2, x3, x4) -> f283_0_length_NULL(x1, x2)

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

(38)
Obligation:
Rules:
f283_0_length_NULL(x308:0, x309:0) -> f283_0_length_NULL(x312:0, x313:0) :|: x312:0 + 1 <= x309:0 && x312:0 + 1 <= x308:0 && x313:0 + 1 <= x308:0 && x313:0 + 1 <= x309:0 && x308:0 > 0 && x309:0 > 0 && x312:0 > -1 && x313:0 > -1

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

(39) FilterProof (EQUIVALENT)
Used the following sort dictionary for filtering: 
f283_0_length_NULL(INTEGER, INTEGER)
Replaced non-predefined constructor symbols by 0.
----------------------------------------

(40)
Obligation:
Rules:
f283_0_length_NULL(x308:0, x309:0) -> f283_0_length_NULL(x312:0, x313:0) :|: x312:0 + 1 <= x309:0 && x312:0 + 1 <= x308:0 && x313:0 + 1 <= x308:0 && x313:0 + 1 <= x309:0 && x308:0 > 0 && x309:0 > 0 && x312:0 > -1 && x313:0 > -1

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

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

(42)
Obligation:
Rules:
f283_0_length_NULL(x308:0:0, x309:0:0) -> f283_0_length_NULL(x312:0:0, x313:0:0) :|: x312:0:0 > -1 && x313:0:0 > -1 && x309:0:0 > 0 && x308:0:0 > 0 && x313:0:0 + 1 <= x309:0:0 && x313:0:0 + 1 <= x308:0:0 && x312:0:0 + 1 <= x308:0:0 && x312:0:0 + 1 <= x309:0:0

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(43) PolynomialOrderProcessor (EQUIVALENT)
Found the following polynomial interpretation:
[f283_0_length_NULL(x, x1)] = -1 + x + x1

The following rules are decreasing:
f283_0_length_NULL(x308:0:0, x309:0:0) -> f283_0_length_NULL(x312:0:0, x313:0:0) :|: x312:0:0 > -1 && x313:0:0 > -1 && x309:0:0 > 0 && x308:0:0 > 0 && x313:0:0 + 1 <= x309:0:0 && x313:0:0 + 1 <= x308:0:0 && x312:0:0 + 1 <= x308:0:0 && x312:0:0 + 1 <= x309:0:0
The following rules are bounded:
f283_0_length_NULL(x308:0:0, x309:0:0) -> f283_0_length_NULL(x312:0:0, x313:0:0) :|: x312:0:0 > -1 && x313:0:0 > -1 && x309:0:0 > 0 && x308:0:0 > 0 && x313:0:0 + 1 <= x309:0:0 && x313:0:0 + 1 <= x308:0:0 && x312:0:0 + 1 <= x308:0:0 && x312:0:0 + 1 <= x309:0:0

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

(44)
YES