NO
proof of prog.inttrs
# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty


Termination of the given IRSwT could be disproven:

(0) IRSwT
(1) IRSFormatTransformerProof [EQUIVALENT, 0 ms]
(2) IRSwT
(3) IRSwTTerminationDigraphProof [EQUIVALENT, 12.7 s]
(4) AND
    (5) IRSwT
        (6) IntTRSCompressionProof [EQUIVALENT, 0 ms]
        (7) IRSwT
        (8) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms]
        (9) IRSwT
        (10) FilterProof [EQUIVALENT, 0 ms]
        (11) IntTRS
        (12) IntTRSCompressionProof [EQUIVALENT, 0 ms]
        (13) IntTRS
        (14) IntTRSPeriodicNontermProof [COMPLETE, 0 ms]
        (15) NO
    (16) IRSwT
        (17) IntTRSCompressionProof [EQUIVALENT, 0 ms]
        (18) IRSwT
        (19) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 2 ms]
        (20) IRSwT
        (21) FilterProof [EQUIVALENT, 0 ms]
        (22) IntTRS
        (23) IntTRSCompressionProof [EQUIVALENT, 0 ms]
        (24) IntTRS
        (25) IntTRSPeriodicNontermProof [COMPLETE, 0 ms]
        (26) NO
    (27) IRSwT
        (28) IntTRSCompressionProof [EQUIVALENT, 0 ms]
        (29) IRSwT
        (30) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms]
        (31) IRSwT
        (32) FilterProof [EQUIVALENT, 0 ms]
        (33) IntTRS
        (34) IntTRSCompressionProof [EQUIVALENT, 0 ms]
        (35) IntTRS
        (36) IntTRSPeriodicNontermProof [COMPLETE, 0 ms]
        (37) NO
    (38) IRSwT
        (39) IntTRSCompressionProof [EQUIVALENT, 0 ms]
        (40) IRSwT
        (41) FilterProof [EQUIVALENT, 0 ms]
        (42) IntTRS
        (43) IntTRSCompressionProof [EQUIVALENT, 0 ms]
        (44) IntTRS
        (45) IntTRSPeriodicNontermProof [COMPLETE, 0 ms]
        (46) NO
    (47) IRSwT
        (48) IntTRSCompressionProof [EQUIVALENT, 0 ms]
        (49) IRSwT
        (50) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms]
        (51) IRSwT
        (52) FilterProof [EQUIVALENT, 0 ms]
        (53) IntTRS
        (54) IntTRSCompressionProof [EQUIVALENT, 0 ms]
        (55) IntTRS
        (56) RankingReductionPairProof [EQUIVALENT, 0 ms]
        (57) YES


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

(0)
Obligation:
Rules:
f1_0_main_New(arg1, arg2, arg3, arg4, arg5) -> f217_0_merge_NONNULL(arg1P, arg2P, arg3P, arg4P, arg5P) :|: 9 <= arg1P - 1 && 6 <= arg2P - 1
f1_0_main_New(x, x1, x2, x3, x4) -> f561_0_main_FieldAccess(x5, x6, x7, x8, x9) :|: 1 = x8 && 3 = x7 && 4 <= x5 - 1 && 6 <= x6 - 1
f1_0_main_New(x10, x11, x12, x13, x14) -> f580_0_main_InvokeMethod(x15, x16, x17, x18, x19) :|: 5 = x19 && 6 <= x15 - 1 && 6 <= x16 - 1
f418_0_merge_Return(x20, x21, x22, x23, x24) -> f580_0_main_InvokeMethod(x25, x26, x27, x28, x29) :|: 5 = x29 && 5 = x22 && x21 + 2 <= x20 && 6 <= x26 - 1 && 6 <= x25 - 1 && 6 <= x20 - 1
f580_0_main_InvokeMethod(x30, x31, x32, x33, x34) -> f1500_0_main_InvokeMethod(x35, x36, x37, x38, x39) :|: 5 = x37 && 5 = x34 && x33 + 2 <= x31 && x32 + 2 <= x30 && 6 <= x35 - 1 && 6 <= x31 - 1 && 6 <= x30 - 1
f561_0_main_FieldAccess(x40, x41, x42, x43, x44) -> f1500_0_main_InvokeMethod(x45, x46, x47, x48, x49) :|: 5 = x47 && 6 = x46 && x42 + 4 <= x41 && x43 + 2 <= x41 && x42 + 2 <= x40 && 9 <= x45 - 1 && 2 <= x41 - 1 && 0 <= x40 - 1
f561_0_main_FieldAccess(x50, x51, x52, x55, x56) -> f1500_0_main_InvokeMethod(x57, x58, x61, x62, x63) :|: 5 = x61 && 6 = x58 && x52 + 4 <= x51 && x55 + 2 <= x51 && x52 + 2 <= x50 && 9 <= x57 - 1 && 2 <= x51 - 1 && 0 <= x50 - 1 && x57 - 7 <= x51 && x57 - 9 <= x50
f747_0_append_Return(x64, x65, x66, x67, x68) -> f1500_0_main_InvokeMethod(x69, x70, x71, x72, x73) :|: 5 = x71 && x66 = x70 && 5 = x67 && x66 + 4 <= x64 && x65 + 4 <= x64 && 6 <= x69 - 1 && 6 <= x64 - 1 && x69 <= x64
f749_0_append_Return(x74, x75, x76, x77, x78) -> f1500_0_main_InvokeMethod(x79, x80, x81, x82, x83) :|: 5 = x81 && 6 = x80 && 5 = x77 && 6 = x76 && x75 + 4 <= x74 && 9 <= x79 - 1 && 9 <= x74 - 1 && x79 <= x74
f1500_0_main_InvokeMethod(x84, x85, x86, x87, x88) -> f1650_0_main_InvokeMethod(x89, x90, x91, x92, x93) :|: 5 = x91 && x85 = x90 && 5 = x86 && x85 + 4 <= x84 && 6 <= x89 - 1 && 6 <= x84 - 1 && x89 <= x84
f217_0_merge_NONNULL(x94, x95, x96, x97, x98) -> f217_0_merge_NONNULL(x99, x100, x101, x102, x103) :|: x99 <= x94 && x104 <= x105 - 1 && x100 + 1 <= x95 && 0 <= x94 - 1 && 0 <= x95 - 1 && 0 <= x99 - 1 && -1 <= x100 - 1
f217_0_merge_NONNULL(x106, x107, x108, x109, x110) -> f217_0_merge_NONNULL(x111, x112, x113, x114, x115) :|: x111 + 2 <= x106 && x116 <= x117 && x112 <= x107 && 2 <= x106 - 1 && 0 <= x107 - 1 && 0 <= x111 - 1 && 0 <= x112 - 1
f580_0_main_InvokeMethod(x118, x119, x120, x121, x122) -> f1341_0_append_NONNULL(x123, x124, x125, x126, x127) :|: 1 = x127 && 5 = x126 && 5 = x122 && x121 + 2 <= x119 && x120 + 2 <= x118 && -1 <= x125 - 1 && 6 <= x124 - 1 && 6 <= x123 - 1 && 6 <= x119 - 1 && 6 <= x118 - 1 && x124 <= x119 && x124 <= x118
f561_0_main_FieldAccess(x128, x129, x130, x131, x132) -> f1341_0_append_NONNULL(x133, x134, x135, x136, x137) :|: x131 = x137 && 5 = x136 && x130 + 4 <= x129 && x131 + 2 <= x129 && x130 + 2 <= x128 && -1 <= x135 - 1 && 4 <= x134 - 1 && 9 <= x133 - 1 && 2 <= x129 - 1 && 0 <= x128 - 1 && x134 - 2 <= x129
f1341_0_append_NONNULL(x138, x139, x140, x141, x142) -> f1341_0_append_NONNULL(x143, x144, x145, x146, x147) :|: x142 = x147 && x142 + 2 <= x139 && x141 + 2 <= x138 && -1 <= x145 - 1 && 0 <= x144 - 1 && 0 <= x143 - 1 && 0 <= x140 - 1 && 0 <= x139 - 1 && 2 <= x138 - 1 && x144 <= x139
f580_0_main_InvokeMethod(x148, x149, x150, x151, x152) -> f1472_0_iter_NULL(x153, x154, x155, x156, x157) :|: 5 = x155 && 5 = x152 && x151 + 2 <= x149 && x150 + 2 <= x148 && -1 <= x154 - 1 && 6 <= x153 - 1 && 6 <= x149 - 1 && 6 <= x148 - 1 && x153 <= x149 && x153 <= x148
f1500_0_main_InvokeMethod(x158, x159, x160, x161, x162) -> f1472_0_iter_NULL(x163, x164, x165, x166, x167) :|: 5 = x165 && 5 = x160 && x159 + 4 <= x158 && -1 <= x164 - 1 && 6 <= x163 - 1 && 6 <= x158 - 1 && x163 <= x158
f1472_0_iter_NULL(x168, x169, x170, x171, x172) -> f1472_0_iter_NULL(x173, x174, x175, x176, x177) :|: x170 + 2 <= x168 && -1 <= x174 - 1 && 0 <= x173 - 1 && 0 <= x169 - 1 && 2 <= x168 - 1
f580_0_main_InvokeMethod(x178, x179, x180, x181, x182) -> f1570_0_reverseAcc_NONNULL(x183, x184, x185, x186, x187) :|: 5 = x185 && 5 = x182 && x181 + 2 <= x179 && x180 + 2 <= x178 && -1 <= x184 - 1 && 6 <= x183 - 1 && 6 <= x179 - 1 && 6 <= x178 - 1 && x183 <= x179 && x183 <= x178
f1500_0_main_InvokeMethod(x188, x189, x190, x191, x192) -> f1570_0_reverseAcc_NONNULL(x193, x194, x195, x196, x197) :|: 5 = x195 && 5 = x190 && x189 + 4 <= x188 && -1 <= x194 - 1 && 6 <= x193 - 1 && 6 <= x188 - 1 && x193 <= x188
f1570_0_reverseAcc_NONNULL(x198, x199, x200, x201, x202) -> f1570_0_reverseAcc_NONNULL(x203, x204, x205, x206, x207) :|: x200 + 2 <= x198 && -1 <= x204 - 1 && 0 <= x203 - 1 && 0 <= x199 - 1 && 2 <= x198 - 1
f580_0_main_InvokeMethod(x208, x209, x210, x211, x212) -> f1682_0_reverse_NONNULL(x213, x214, x215, x216, x217) :|: 5 = x215 && 5 = x212 && x211 + 2 <= x209 && x210 + 2 <= x208 && -1 <= x214 - 1 && 6 <= x213 - 1 && 6 <= x209 - 1 && 6 <= x208 - 1 && x213 <= x209 && x213 <= x208
f1650_0_main_InvokeMethod(x218, x219, x220, x221, x222) -> f1682_0_reverse_NONNULL(x223, x224, x225, x226, x227) :|: 5 = x225 && 5 = x220 && x219 + 4 <= x218 && -1 <= x224 - 1 && 6 <= x223 - 1 && 6 <= x218 - 1 && x223 <= x218
f1682_0_reverse_NONNULL(x228, x229, x230, x231, x232) -> f1682_0_reverse_NONNULL(x233, x234, x235, x236, x237) :|: x230 + 2 <= x228 && -1 <= x234 - 1 && 0 <= x233 - 1 && 0 <= x229 - 1 && 2 <= x228 - 1
f1682_0_reverse_NONNULL(x238, x239, x240, x241, x242) -> f1341_0_append_NONNULL(x243, x244, x245, x246, x247) :|: x240 = x247 && x240 + 2 <= x238 && -1 <= x245 - 1 && 1 <= x244 - 1 && 1 <= x243 - 1 && 0 <= x239 - 1 && 2 <= x238 - 1 && x244 <= x238
f1682_0_reverse_NONNULL(x248, x249, x250, x251, x252) -> f1748_0_reverse_InvokeMethod(x253, x254, x255, x256, x257) :|: x250 = x257 && x250 + 2 <= x248 && 1 <= x254 - 1 && 2 <= x253 - 1 && 0 <= x249 - 1 && 2 <= x248 - 1 && x254 <= x248
f1682_0_reverse_NONNULL(x258, x259, x260, x261, x262) -> f1748_0_reverse_InvokeMethod(x263, x264, x265, x266, x267) :|: x260 = x267 && x260 + 2 <= x258 && 1 <= x264 - 1 && 4 <= x263 - 1 && 0 <= x259 - 1 && 2 <= x258 - 1 && x264 <= x258
f1748_0_reverse_InvokeMethod(x268, x269, x270, x271, x272) -> f1341_0_append_NONNULL(x273, x274, x275, x276, x277) :|: x272 = x277 && x271 = x276 && x272 + 2 <= x269 && x271 + 2 <= x268 && x270 + 4 <= x268 && -1 <= x275 - 1 && 1 <= x274 - 1 && 2 <= x273 - 1 && 1 <= x269 - 1 && 2 <= x268 - 1 && x274 <= x269 && x273 <= x268
__init(x278, x279, x280, x281, x282) -> f1_0_main_New(x283, x284, x285, x286, x287) :|: 0 <= 0
Start term: __init(arg1, arg2, arg3, arg4, arg5)

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

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

(2)
Obligation:
Rules:
f1_0_main_New(arg1, arg2, arg3, arg4, arg5) -> f217_0_merge_NONNULL(arg1P, arg2P, arg3P, arg4P, arg5P) :|: 9 <= arg1P - 1 && 6 <= arg2P - 1
f1_0_main_New(x, x1, x2, x3, x4) -> f561_0_main_FieldAccess(x5, x6, x7, x8, x9) :|: 1 = x8 && 3 = x7 && 4 <= x5 - 1 && 6 <= x6 - 1
f1_0_main_New(x10, x11, x12, x13, x14) -> f580_0_main_InvokeMethod(x15, x16, x17, x18, x19) :|: 5 = x19 && 6 <= x15 - 1 && 6 <= x16 - 1
f418_0_merge_Return(x20, x21, x22, x23, x24) -> f580_0_main_InvokeMethod(x25, x26, x27, x28, x29) :|: 5 = x29 && 5 = x22 && x21 + 2 <= x20 && 6 <= x26 - 1 && 6 <= x25 - 1 && 6 <= x20 - 1
f580_0_main_InvokeMethod(x30, x31, x32, x33, x34) -> f1500_0_main_InvokeMethod(x35, x36, x37, x38, x39) :|: 5 = x37 && 5 = x34 && x33 + 2 <= x31 && x32 + 2 <= x30 && 6 <= x35 - 1 && 6 <= x31 - 1 && 6 <= x30 - 1
f561_0_main_FieldAccess(x40, x41, x42, x43, x44) -> f1500_0_main_InvokeMethod(x45, x46, x47, x48, x49) :|: 5 = x47 && 6 = x46 && x42 + 4 <= x41 && x43 + 2 <= x41 && x42 + 2 <= x40 && 9 <= x45 - 1 && 2 <= x41 - 1 && 0 <= x40 - 1
f561_0_main_FieldAccess(x50, x51, x52, x55, x56) -> f1500_0_main_InvokeMethod(x57, x58, x61, x62, x63) :|: 5 = x61 && 6 = x58 && x52 + 4 <= x51 && x55 + 2 <= x51 && x52 + 2 <= x50 && 9 <= x57 - 1 && 2 <= x51 - 1 && 0 <= x50 - 1 && x57 - 7 <= x51 && x57 - 9 <= x50
f747_0_append_Return(x64, x65, x66, x67, x68) -> f1500_0_main_InvokeMethod(x69, x70, x71, x72, x73) :|: 5 = x71 && x66 = x70 && 5 = x67 && x66 + 4 <= x64 && x65 + 4 <= x64 && 6 <= x69 - 1 && 6 <= x64 - 1 && x69 <= x64
f749_0_append_Return(x74, x75, x76, x77, x78) -> f1500_0_main_InvokeMethod(x79, x80, x81, x82, x83) :|: 5 = x81 && 6 = x80 && 5 = x77 && 6 = x76 && x75 + 4 <= x74 && 9 <= x79 - 1 && 9 <= x74 - 1 && x79 <= x74
f1500_0_main_InvokeMethod(x84, x85, x86, x87, x88) -> f1650_0_main_InvokeMethod(x89, x90, x91, x92, x93) :|: 5 = x91 && x85 = x90 && 5 = x86 && x85 + 4 <= x84 && 6 <= x89 - 1 && 6 <= x84 - 1 && x89 <= x84
f217_0_merge_NONNULL(x94, x95, x96, x97, x98) -> f217_0_merge_NONNULL(x99, x100, x101, x102, x103) :|: x99 <= x94 && x104 <= x105 - 1 && x100 + 1 <= x95 && 0 <= x94 - 1 && 0 <= x95 - 1 && 0 <= x99 - 1 && -1 <= x100 - 1
f217_0_merge_NONNULL(x106, x107, x108, x109, x110) -> f217_0_merge_NONNULL(x111, x112, x113, x114, x115) :|: x111 + 2 <= x106 && x116 <= x117 && x112 <= x107 && 2 <= x106 - 1 && 0 <= x107 - 1 && 0 <= x111 - 1 && 0 <= x112 - 1
f580_0_main_InvokeMethod(x118, x119, x120, x121, x122) -> f1341_0_append_NONNULL(x123, x124, x125, x126, x127) :|: 1 = x127 && 5 = x126 && 5 = x122 && x121 + 2 <= x119 && x120 + 2 <= x118 && -1 <= x125 - 1 && 6 <= x124 - 1 && 6 <= x123 - 1 && 6 <= x119 - 1 && 6 <= x118 - 1 && x124 <= x119 && x124 <= x118
f561_0_main_FieldAccess(x128, x129, x130, x131, x132) -> f1341_0_append_NONNULL(x133, x134, x135, x136, x137) :|: x131 = x137 && 5 = x136 && x130 + 4 <= x129 && x131 + 2 <= x129 && x130 + 2 <= x128 && -1 <= x135 - 1 && 4 <= x134 - 1 && 9 <= x133 - 1 && 2 <= x129 - 1 && 0 <= x128 - 1 && x134 - 2 <= x129
f1341_0_append_NONNULL(x138, x139, x140, x141, x142) -> f1341_0_append_NONNULL(x143, x144, x145, x146, x147) :|: x142 = x147 && x142 + 2 <= x139 && x141 + 2 <= x138 && -1 <= x145 - 1 && 0 <= x144 - 1 && 0 <= x143 - 1 && 0 <= x140 - 1 && 0 <= x139 - 1 && 2 <= x138 - 1 && x144 <= x139
f580_0_main_InvokeMethod(x148, x149, x150, x151, x152) -> f1472_0_iter_NULL(x153, x154, x155, x156, x157) :|: 5 = x155 && 5 = x152 && x151 + 2 <= x149 && x150 + 2 <= x148 && -1 <= x154 - 1 && 6 <= x153 - 1 && 6 <= x149 - 1 && 6 <= x148 - 1 && x153 <= x149 && x153 <= x148
f1500_0_main_InvokeMethod(x158, x159, x160, x161, x162) -> f1472_0_iter_NULL(x163, x164, x165, x166, x167) :|: 5 = x165 && 5 = x160 && x159 + 4 <= x158 && -1 <= x164 - 1 && 6 <= x163 - 1 && 6 <= x158 - 1 && x163 <= x158
f1472_0_iter_NULL(x168, x169, x170, x171, x172) -> f1472_0_iter_NULL(x173, x174, x175, x176, x177) :|: x170 + 2 <= x168 && -1 <= x174 - 1 && 0 <= x173 - 1 && 0 <= x169 - 1 && 2 <= x168 - 1
f580_0_main_InvokeMethod(x178, x179, x180, x181, x182) -> f1570_0_reverseAcc_NONNULL(x183, x184, x185, x186, x187) :|: 5 = x185 && 5 = x182 && x181 + 2 <= x179 && x180 + 2 <= x178 && -1 <= x184 - 1 && 6 <= x183 - 1 && 6 <= x179 - 1 && 6 <= x178 - 1 && x183 <= x179 && x183 <= x178
f1500_0_main_InvokeMethod(x188, x189, x190, x191, x192) -> f1570_0_reverseAcc_NONNULL(x193, x194, x195, x196, x197) :|: 5 = x195 && 5 = x190 && x189 + 4 <= x188 && -1 <= x194 - 1 && 6 <= x193 - 1 && 6 <= x188 - 1 && x193 <= x188
f1570_0_reverseAcc_NONNULL(x198, x199, x200, x201, x202) -> f1570_0_reverseAcc_NONNULL(x203, x204, x205, x206, x207) :|: x200 + 2 <= x198 && -1 <= x204 - 1 && 0 <= x203 - 1 && 0 <= x199 - 1 && 2 <= x198 - 1
f580_0_main_InvokeMethod(x208, x209, x210, x211, x212) -> f1682_0_reverse_NONNULL(x213, x214, x215, x216, x217) :|: 5 = x215 && 5 = x212 && x211 + 2 <= x209 && x210 + 2 <= x208 && -1 <= x214 - 1 && 6 <= x213 - 1 && 6 <= x209 - 1 && 6 <= x208 - 1 && x213 <= x209 && x213 <= x208
f1650_0_main_InvokeMethod(x218, x219, x220, x221, x222) -> f1682_0_reverse_NONNULL(x223, x224, x225, x226, x227) :|: 5 = x225 && 5 = x220 && x219 + 4 <= x218 && -1 <= x224 - 1 && 6 <= x223 - 1 && 6 <= x218 - 1 && x223 <= x218
f1682_0_reverse_NONNULL(x228, x229, x230, x231, x232) -> f1682_0_reverse_NONNULL(x233, x234, x235, x236, x237) :|: x230 + 2 <= x228 && -1 <= x234 - 1 && 0 <= x233 - 1 && 0 <= x229 - 1 && 2 <= x228 - 1
f1682_0_reverse_NONNULL(x238, x239, x240, x241, x242) -> f1341_0_append_NONNULL(x243, x244, x245, x246, x247) :|: x240 = x247 && x240 + 2 <= x238 && -1 <= x245 - 1 && 1 <= x244 - 1 && 1 <= x243 - 1 && 0 <= x239 - 1 && 2 <= x238 - 1 && x244 <= x238
f1682_0_reverse_NONNULL(x248, x249, x250, x251, x252) -> f1748_0_reverse_InvokeMethod(x253, x254, x255, x256, x257) :|: x250 = x257 && x250 + 2 <= x248 && 1 <= x254 - 1 && 2 <= x253 - 1 && 0 <= x249 - 1 && 2 <= x248 - 1 && x254 <= x248
f1682_0_reverse_NONNULL(x258, x259, x260, x261, x262) -> f1748_0_reverse_InvokeMethod(x263, x264, x265, x266, x267) :|: x260 = x267 && x260 + 2 <= x258 && 1 <= x264 - 1 && 4 <= x263 - 1 && 0 <= x259 - 1 && 2 <= x258 - 1 && x264 <= x258
f1748_0_reverse_InvokeMethod(x268, x269, x270, x271, x272) -> f1341_0_append_NONNULL(x273, x274, x275, x276, x277) :|: x272 = x277 && x271 = x276 && x272 + 2 <= x269 && x271 + 2 <= x268 && x270 + 4 <= x268 && -1 <= x275 - 1 && 1 <= x274 - 1 && 2 <= x273 - 1 && 1 <= x269 - 1 && 2 <= x268 - 1 && x274 <= x269 && x273 <= x268
__init(x278, x279, x280, x281, x282) -> f1_0_main_New(x283, x284, x285, x286, x287) :|: 0 <= 0
Start term: __init(arg1, arg2, arg3, arg4, arg5)

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

(3) IRSwTTerminationDigraphProof (EQUIVALENT)
Constructed termination digraph!
Nodes:
(1) f1_0_main_New(arg1, arg2, arg3, arg4, arg5) -> f217_0_merge_NONNULL(arg1P, arg2P, arg3P, arg4P, arg5P) :|: 9 <= arg1P - 1 && 6 <= arg2P - 1
(2) f1_0_main_New(x, x1, x2, x3, x4) -> f561_0_main_FieldAccess(x5, x6, x7, x8, x9) :|: 1 = x8 && 3 = x7 && 4 <= x5 - 1 && 6 <= x6 - 1
(3) f1_0_main_New(x10, x11, x12, x13, x14) -> f580_0_main_InvokeMethod(x15, x16, x17, x18, x19) :|: 5 = x19 && 6 <= x15 - 1 && 6 <= x16 - 1
(4) f418_0_merge_Return(x20, x21, x22, x23, x24) -> f580_0_main_InvokeMethod(x25, x26, x27, x28, x29) :|: 5 = x29 && 5 = x22 && x21 + 2 <= x20 && 6 <= x26 - 1 && 6 <= x25 - 1 && 6 <= x20 - 1
(5) f580_0_main_InvokeMethod(x30, x31, x32, x33, x34) -> f1500_0_main_InvokeMethod(x35, x36, x37, x38, x39) :|: 5 = x37 && 5 = x34 && x33 + 2 <= x31 && x32 + 2 <= x30 && 6 <= x35 - 1 && 6 <= x31 - 1 && 6 <= x30 - 1
(6) f561_0_main_FieldAccess(x40, x41, x42, x43, x44) -> f1500_0_main_InvokeMethod(x45, x46, x47, x48, x49) :|: 5 = x47 && 6 = x46 && x42 + 4 <= x41 && x43 + 2 <= x41 && x42 + 2 <= x40 && 9 <= x45 - 1 && 2 <= x41 - 1 && 0 <= x40 - 1
(7) f561_0_main_FieldAccess(x50, x51, x52, x55, x56) -> f1500_0_main_InvokeMethod(x57, x58, x61, x62, x63) :|: 5 = x61 && 6 = x58 && x52 + 4 <= x51 && x55 + 2 <= x51 && x52 + 2 <= x50 && 9 <= x57 - 1 && 2 <= x51 - 1 && 0 <= x50 - 1 && x57 - 7 <= x51 && x57 - 9 <= x50
(8) f747_0_append_Return(x64, x65, x66, x67, x68) -> f1500_0_main_InvokeMethod(x69, x70, x71, x72, x73) :|: 5 = x71 && x66 = x70 && 5 = x67 && x66 + 4 <= x64 && x65 + 4 <= x64 && 6 <= x69 - 1 && 6 <= x64 - 1 && x69 <= x64
(9) f749_0_append_Return(x74, x75, x76, x77, x78) -> f1500_0_main_InvokeMethod(x79, x80, x81, x82, x83) :|: 5 = x81 && 6 = x80 && 5 = x77 && 6 = x76 && x75 + 4 <= x74 && 9 <= x79 - 1 && 9 <= x74 - 1 && x79 <= x74
(10) f1500_0_main_InvokeMethod(x84, x85, x86, x87, x88) -> f1650_0_main_InvokeMethod(x89, x90, x91, x92, x93) :|: 5 = x91 && x85 = x90 && 5 = x86 && x85 + 4 <= x84 && 6 <= x89 - 1 && 6 <= x84 - 1 && x89 <= x84
(11) f217_0_merge_NONNULL(x94, x95, x96, x97, x98) -> f217_0_merge_NONNULL(x99, x100, x101, x102, x103) :|: x99 <= x94 && x104 <= x105 - 1 && x100 + 1 <= x95 && 0 <= x94 - 1 && 0 <= x95 - 1 && 0 <= x99 - 1 && -1 <= x100 - 1
(12) f217_0_merge_NONNULL(x106, x107, x108, x109, x110) -> f217_0_merge_NONNULL(x111, x112, x113, x114, x115) :|: x111 + 2 <= x106 && x116 <= x117 && x112 <= x107 && 2 <= x106 - 1 && 0 <= x107 - 1 && 0 <= x111 - 1 && 0 <= x112 - 1
(13) f580_0_main_InvokeMethod(x118, x119, x120, x121, x122) -> f1341_0_append_NONNULL(x123, x124, x125, x126, x127) :|: 1 = x127 && 5 = x126 && 5 = x122 && x121 + 2 <= x119 && x120 + 2 <= x118 && -1 <= x125 - 1 && 6 <= x124 - 1 && 6 <= x123 - 1 && 6 <= x119 - 1 && 6 <= x118 - 1 && x124 <= x119 && x124 <= x118
(14) f561_0_main_FieldAccess(x128, x129, x130, x131, x132) -> f1341_0_append_NONNULL(x133, x134, x135, x136, x137) :|: x131 = x137 && 5 = x136 && x130 + 4 <= x129 && x131 + 2 <= x129 && x130 + 2 <= x128 && -1 <= x135 - 1 && 4 <= x134 - 1 && 9 <= x133 - 1 && 2 <= x129 - 1 && 0 <= x128 - 1 && x134 - 2 <= x129
(15) f1341_0_append_NONNULL(x138, x139, x140, x141, x142) -> f1341_0_append_NONNULL(x143, x144, x145, x146, x147) :|: x142 = x147 && x142 + 2 <= x139 && x141 + 2 <= x138 && -1 <= x145 - 1 && 0 <= x144 - 1 && 0 <= x143 - 1 && 0 <= x140 - 1 && 0 <= x139 - 1 && 2 <= x138 - 1 && x144 <= x139
(16) f580_0_main_InvokeMethod(x148, x149, x150, x151, x152) -> f1472_0_iter_NULL(x153, x154, x155, x156, x157) :|: 5 = x155 && 5 = x152 && x151 + 2 <= x149 && x150 + 2 <= x148 && -1 <= x154 - 1 && 6 <= x153 - 1 && 6 <= x149 - 1 && 6 <= x148 - 1 && x153 <= x149 && x153 <= x148
(17) f1500_0_main_InvokeMethod(x158, x159, x160, x161, x162) -> f1472_0_iter_NULL(x163, x164, x165, x166, x167) :|: 5 = x165 && 5 = x160 && x159 + 4 <= x158 && -1 <= x164 - 1 && 6 <= x163 - 1 && 6 <= x158 - 1 && x163 <= x158
(18) f1472_0_iter_NULL(x168, x169, x170, x171, x172) -> f1472_0_iter_NULL(x173, x174, x175, x176, x177) :|: x170 + 2 <= x168 && -1 <= x174 - 1 && 0 <= x173 - 1 && 0 <= x169 - 1 && 2 <= x168 - 1
(19) f580_0_main_InvokeMethod(x178, x179, x180, x181, x182) -> f1570_0_reverseAcc_NONNULL(x183, x184, x185, x186, x187) :|: 5 = x185 && 5 = x182 && x181 + 2 <= x179 && x180 + 2 <= x178 && -1 <= x184 - 1 && 6 <= x183 - 1 && 6 <= x179 - 1 && 6 <= x178 - 1 && x183 <= x179 && x183 <= x178
(20) f1500_0_main_InvokeMethod(x188, x189, x190, x191, x192) -> f1570_0_reverseAcc_NONNULL(x193, x194, x195, x196, x197) :|: 5 = x195 && 5 = x190 && x189 + 4 <= x188 && -1 <= x194 - 1 && 6 <= x193 - 1 && 6 <= x188 - 1 && x193 <= x188
(21) f1570_0_reverseAcc_NONNULL(x198, x199, x200, x201, x202) -> f1570_0_reverseAcc_NONNULL(x203, x204, x205, x206, x207) :|: x200 + 2 <= x198 && -1 <= x204 - 1 && 0 <= x203 - 1 && 0 <= x199 - 1 && 2 <= x198 - 1
(22) f580_0_main_InvokeMethod(x208, x209, x210, x211, x212) -> f1682_0_reverse_NONNULL(x213, x214, x215, x216, x217) :|: 5 = x215 && 5 = x212 && x211 + 2 <= x209 && x210 + 2 <= x208 && -1 <= x214 - 1 && 6 <= x213 - 1 && 6 <= x209 - 1 && 6 <= x208 - 1 && x213 <= x209 && x213 <= x208
(23) f1650_0_main_InvokeMethod(x218, x219, x220, x221, x222) -> f1682_0_reverse_NONNULL(x223, x224, x225, x226, x227) :|: 5 = x225 && 5 = x220 && x219 + 4 <= x218 && -1 <= x224 - 1 && 6 <= x223 - 1 && 6 <= x218 - 1 && x223 <= x218
(24) f1682_0_reverse_NONNULL(x228, x229, x230, x231, x232) -> f1682_0_reverse_NONNULL(x233, x234, x235, x236, x237) :|: x230 + 2 <= x228 && -1 <= x234 - 1 && 0 <= x233 - 1 && 0 <= x229 - 1 && 2 <= x228 - 1
(25) f1682_0_reverse_NONNULL(x238, x239, x240, x241, x242) -> f1341_0_append_NONNULL(x243, x244, x245, x246, x247) :|: x240 = x247 && x240 + 2 <= x238 && -1 <= x245 - 1 && 1 <= x244 - 1 && 1 <= x243 - 1 && 0 <= x239 - 1 && 2 <= x238 - 1 && x244 <= x238
(26) f1682_0_reverse_NONNULL(x248, x249, x250, x251, x252) -> f1748_0_reverse_InvokeMethod(x253, x254, x255, x256, x257) :|: x250 = x257 && x250 + 2 <= x248 && 1 <= x254 - 1 && 2 <= x253 - 1 && 0 <= x249 - 1 && 2 <= x248 - 1 && x254 <= x248
(27) f1682_0_reverse_NONNULL(x258, x259, x260, x261, x262) -> f1748_0_reverse_InvokeMethod(x263, x264, x265, x266, x267) :|: x260 = x267 && x260 + 2 <= x258 && 1 <= x264 - 1 && 4 <= x263 - 1 && 0 <= x259 - 1 && 2 <= x258 - 1 && x264 <= x258
(28) f1748_0_reverse_InvokeMethod(x268, x269, x270, x271, x272) -> f1341_0_append_NONNULL(x273, x274, x275, x276, x277) :|: x272 = x277 && x271 = x276 && x272 + 2 <= x269 && x271 + 2 <= x268 && x270 + 4 <= x268 && -1 <= x275 - 1 && 1 <= x274 - 1 && 2 <= x273 - 1 && 1 <= x269 - 1 && 2 <= x268 - 1 && x274 <= x269 && x273 <= x268
(29) __init(x278, x279, x280, x281, x282) -> f1_0_main_New(x283, x284, x285, x286, x287) :|: 0 <= 0

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

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

(4)
Complex Obligation (AND)

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

(5)
Obligation:

Termination digraph:
Nodes:
(1) f1570_0_reverseAcc_NONNULL(x198, x199, x200, x201, x202) -> f1570_0_reverseAcc_NONNULL(x203, x204, x205, x206, x207) :|: x200 + 2 <= x198 && -1 <= x204 - 1 && 0 <= x203 - 1 && 0 <= x199 - 1 && 2 <= x198 - 1

Arcs:
(1) -> (1)

This digraph is fully evaluated!

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

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

(7)
Obligation:
Rules:
f1570_0_reverseAcc_NONNULL(x198:0, x199:0, x200:0, x201:0, x202:0) -> f1570_0_reverseAcc_NONNULL(x203:0, x204:0, x205:0, x206:0, x207:0) :|: x199:0 > 0 && x198:0 > 2 && x203:0 > 0 && x204:0 > -1 && x200:0 + 2 <= x198:0

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

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

   f1570_0_reverseAcc_NONNULL(x1, x2, x3, x4, x5) -> f1570_0_reverseAcc_NONNULL(x1, x2, x3)

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

(9)
Obligation:
Rules:
f1570_0_reverseAcc_NONNULL(x198:0, x199:0, x200:0) -> f1570_0_reverseAcc_NONNULL(x203:0, x204:0, x205:0) :|: x199:0 > 0 && x198:0 > 2 && x203:0 > 0 && x204:0 > -1 && x200:0 + 2 <= x198:0

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

(10) FilterProof (EQUIVALENT)
Used the following sort dictionary for filtering: 
f1570_0_reverseAcc_NONNULL(INTEGER, INTEGER, VARIABLE)
Replaced non-predefined constructor symbols by 0.
----------------------------------------

(11)
Obligation:
Rules:
f1570_0_reverseAcc_NONNULL(x198:0, x199:0, x200:0) -> f1570_0_reverseAcc_NONNULL(x203:0, x204:0, x205:0) :|: x199:0 > 0 && x198:0 > 2 && x203:0 > 0 && x204:0 > -1 && x200:0 + 2 <= x198:0

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

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

(13)
Obligation:
Rules:
f1570_0_reverseAcc_NONNULL(x198:0:0, x199:0:0, x200:0:0) -> f1570_0_reverseAcc_NONNULL(x203:0:0, x204:0:0, x205:0:0) :|: x204:0:0 > -1 && x200:0:0 + 2 <= x198:0:0 && x203:0:0 > 0 && x198:0:0 > 2 && x199:0:0 > 0

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

(14) IntTRSPeriodicNontermProof (COMPLETE)
Normalized system to the following form:
f(pc, x198:0:0, x199:0:0, x200:0:0) -> f(1, x203:0:0, x204:0:0, x205:0:0) :|: pc = 1 && (x204:0:0 > -1 && x200:0:0 + 2 <= x198:0:0 && x203:0:0 > 0 && x198:0:0 > 2 && x199:0:0 > 0)
Witness term starting non-terminating reduction: f(1, 15, 15, -8)
----------------------------------------

(15)
NO

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

(16)
Obligation:

Termination digraph:
Nodes:
(1) f1472_0_iter_NULL(x168, x169, x170, x171, x172) -> f1472_0_iter_NULL(x173, x174, x175, x176, x177) :|: x170 + 2 <= x168 && -1 <= x174 - 1 && 0 <= x173 - 1 && 0 <= x169 - 1 && 2 <= x168 - 1

Arcs:
(1) -> (1)

This digraph is fully evaluated!

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

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

(18)
Obligation:
Rules:
f1472_0_iter_NULL(x168:0, x169:0, x170:0, x171:0, x172:0) -> f1472_0_iter_NULL(x173:0, x174:0, x175:0, x176:0, x177:0) :|: x169:0 > 0 && x168:0 > 2 && x173:0 > 0 && x174:0 > -1 && x170:0 + 2 <= x168:0

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

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

   f1472_0_iter_NULL(x1, x2, x3, x4, x5) -> f1472_0_iter_NULL(x1, x2, x3)

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

(20)
Obligation:
Rules:
f1472_0_iter_NULL(x168:0, x169:0, x170:0) -> f1472_0_iter_NULL(x173:0, x174:0, x175:0) :|: x169:0 > 0 && x168:0 > 2 && x173:0 > 0 && x174:0 > -1 && x170:0 + 2 <= x168:0

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

(21) FilterProof (EQUIVALENT)
Used the following sort dictionary for filtering: 
f1472_0_iter_NULL(INTEGER, INTEGER, VARIABLE)
Replaced non-predefined constructor symbols by 0.
----------------------------------------

(22)
Obligation:
Rules:
f1472_0_iter_NULL(x168:0, x169:0, x170:0) -> f1472_0_iter_NULL(x173:0, x174:0, x175:0) :|: x169:0 > 0 && x168:0 > 2 && x173:0 > 0 && x174:0 > -1 && x170:0 + 2 <= x168:0

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

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

(24)
Obligation:
Rules:
f1472_0_iter_NULL(x168:0:0, x169:0:0, x170:0:0) -> f1472_0_iter_NULL(x173:0:0, x174:0:0, x175:0:0) :|: x174:0:0 > -1 && x170:0:0 + 2 <= x168:0:0 && x173:0:0 > 0 && x168:0:0 > 2 && x169:0:0 > 0

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

(25) IntTRSPeriodicNontermProof (COMPLETE)
Normalized system to the following form:
f(pc, x168:0:0, x169:0:0, x170:0:0) -> f(1, x173:0:0, x174:0:0, x175:0:0) :|: pc = 1 && (x174:0:0 > -1 && x170:0:0 + 2 <= x168:0:0 && x173:0:0 > 0 && x168:0:0 > 2 && x169:0:0 > 0)
Witness term starting non-terminating reduction: f(1, 15, 15, -8)
----------------------------------------

(26)
NO

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

(27)
Obligation:

Termination digraph:
Nodes:
(1) f1682_0_reverse_NONNULL(x228, x229, x230, x231, x232) -> f1682_0_reverse_NONNULL(x233, x234, x235, x236, x237) :|: x230 + 2 <= x228 && -1 <= x234 - 1 && 0 <= x233 - 1 && 0 <= x229 - 1 && 2 <= x228 - 1

Arcs:
(1) -> (1)

This digraph is fully evaluated!

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

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

(29)
Obligation:
Rules:
f1682_0_reverse_NONNULL(x228:0, x229:0, x230:0, x231:0, x232:0) -> f1682_0_reverse_NONNULL(x233:0, x234:0, x235:0, x236:0, x237:0) :|: x229:0 > 0 && x228:0 > 2 && x233:0 > 0 && x234:0 > -1 && x230:0 + 2 <= x228:0

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

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

   f1682_0_reverse_NONNULL(x1, x2, x3, x4, x5) -> f1682_0_reverse_NONNULL(x1, x2, x3)

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

(31)
Obligation:
Rules:
f1682_0_reverse_NONNULL(x228:0, x229:0, x230:0) -> f1682_0_reverse_NONNULL(x233:0, x234:0, x235:0) :|: x229:0 > 0 && x228:0 > 2 && x233:0 > 0 && x234:0 > -1 && x230:0 + 2 <= x228:0

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

(32) FilterProof (EQUIVALENT)
Used the following sort dictionary for filtering: 
f1682_0_reverse_NONNULL(INTEGER, INTEGER, VARIABLE)
Replaced non-predefined constructor symbols by 0.
----------------------------------------

(33)
Obligation:
Rules:
f1682_0_reverse_NONNULL(x228:0, x229:0, x230:0) -> f1682_0_reverse_NONNULL(x233:0, x234:0, x235:0) :|: x229:0 > 0 && x228:0 > 2 && x233:0 > 0 && x234:0 > -1 && x230:0 + 2 <= x228:0

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

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

(35)
Obligation:
Rules:
f1682_0_reverse_NONNULL(x228:0:0, x229:0:0, x230:0:0) -> f1682_0_reverse_NONNULL(x233:0:0, x234:0:0, x235:0:0) :|: x234:0:0 > -1 && x230:0:0 + 2 <= x228:0:0 && x233:0:0 > 0 && x228:0:0 > 2 && x229:0:0 > 0

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

(36) IntTRSPeriodicNontermProof (COMPLETE)
Normalized system to the following form:
f(pc, x228:0:0, x229:0:0, x230:0:0) -> f(1, x233:0:0, x234:0:0, x235:0:0) :|: pc = 1 && (x234:0:0 > -1 && x230:0:0 + 2 <= x228:0:0 && x233:0:0 > 0 && x228:0:0 > 2 && x229:0:0 > 0)
Witness term starting non-terminating reduction: f(1, 15, 15, -8)
----------------------------------------

(37)
NO

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

(38)
Obligation:

Termination digraph:
Nodes:
(1) f1341_0_append_NONNULL(x138, x139, x140, x141, x142) -> f1341_0_append_NONNULL(x143, x144, x145, x146, x147) :|: x142 = x147 && x142 + 2 <= x139 && x141 + 2 <= x138 && -1 <= x145 - 1 && 0 <= x144 - 1 && 0 <= x143 - 1 && 0 <= x140 - 1 && 0 <= x139 - 1 && 2 <= x138 - 1 && x144 <= x139

Arcs:
(1) -> (1)

This digraph is fully evaluated!

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

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

(40)
Obligation:
Rules:
f1341_0_append_NONNULL(x138:0, x139:0, x140:0, x141:0, x142:0) -> f1341_0_append_NONNULL(x143:0, x144:0, x145:0, x146:0, x142:0) :|: x138:0 > 2 && x144:0 <= x139:0 && x139:0 > 0 && x140:0 > 0 && x143:0 > 0 && x144:0 > 0 && x145:0 > -1 && x142:0 + 2 <= x139:0 && x141:0 + 2 <= x138:0

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

(41) FilterProof (EQUIVALENT)
Used the following sort dictionary for filtering: 
f1341_0_append_NONNULL(INTEGER, INTEGER, INTEGER, VARIABLE, INTEGER)
Replaced non-predefined constructor symbols by 0.
----------------------------------------

(42)
Obligation:
Rules:
f1341_0_append_NONNULL(x138:0, x139:0, x140:0, x141:0, x142:0) -> f1341_0_append_NONNULL(x143:0, x144:0, x145:0, x146:0, x142:0) :|: x138:0 > 2 && x144:0 <= x139:0 && x139:0 > 0 && x140:0 > 0 && x143:0 > 0 && x144:0 > 0 && x145:0 > -1 && x142:0 + 2 <= x139:0 && x141:0 + 2 <= x138:0

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

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

(44)
Obligation:
Rules:
f1341_0_append_NONNULL(x138:0:0, x139:0:0, x140:0:0, x141:0:0, x142:0:0) -> f1341_0_append_NONNULL(x143:0:0, x144:0:0, x145:0:0, x146:0:0, x142:0:0) :|: x142:0:0 + 2 <= x139:0:0 && x141:0:0 + 2 <= x138:0:0 && x145:0:0 > -1 && x144:0:0 > 0 && x143:0:0 > 0 && x140:0:0 > 0 && x139:0:0 > 0 && x144:0:0 <= x139:0:0 && x138:0:0 > 2

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

(45) IntTRSPeriodicNontermProof (COMPLETE)
Normalized system to the following form:
f(pc, x138:0:0, x139:0:0, x140:0:0, x141:0:0, x142:0:0) -> f(1, x143:0:0, x144:0:0, x145:0:0, x146:0:0, x142:0:0) :|: pc = 1 && (x142:0:0 + 2 <= x139:0:0 && x141:0:0 + 2 <= x138:0:0 && x145:0:0 > -1 && x144:0:0 > 0 && x143:0:0 > 0 && x140:0:0 > 0 && x139:0:0 > 0 && x144:0:0 <= x139:0:0 && x138:0:0 > 2)
Witness term starting non-terminating reduction: f(1, 15, 16, 15, -6, -2)
----------------------------------------

(46)
NO

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

(47)
Obligation:

Termination digraph:
Nodes:
(1) f217_0_merge_NONNULL(x94, x95, x96, x97, x98) -> f217_0_merge_NONNULL(x99, x100, x101, x102, x103) :|: x99 <= x94 && x104 <= x105 - 1 && x100 + 1 <= x95 && 0 <= x94 - 1 && 0 <= x95 - 1 && 0 <= x99 - 1 && -1 <= x100 - 1
(2) f217_0_merge_NONNULL(x106, x107, x108, x109, x110) -> f217_0_merge_NONNULL(x111, x112, x113, x114, x115) :|: x111 + 2 <= x106 && x116 <= x117 && x112 <= x107 && 2 <= x106 - 1 && 0 <= x107 - 1 && 0 <= x111 - 1 && 0 <= x112 - 1

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

This digraph is fully evaluated!

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

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

(49)
Obligation:
Rules:
f217_0_merge_NONNULL(x106:0, x107:0, x108:0, x109:0, x110:0) -> f217_0_merge_NONNULL(x111:0, x112:0, x113:0, x114:0, x115:0) :|: x111:0 > 0 && x112:0 > 0 && x107:0 > 0 && x106:0 > 2 && x112:0 <= x107:0 && x117:0 >= x116:0 && x111:0 + 2 <= x106:0
f217_0_merge_NONNULL(x94:0, x95:0, x96:0, x97:0, x98:0) -> f217_0_merge_NONNULL(x99:0, x100:0, x101:0, x102:0, x103:0) :|: x99:0 > 0 && x100:0 > -1 && x95:0 > 0 && x94:0 > 0 && x95:0 >= x100:0 + 1 && x105:0 - 1 >= x104:0 && x99:0 <= x94:0

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

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

   f217_0_merge_NONNULL(x1, x2, x3, x4, x5) -> f217_0_merge_NONNULL(x1, x2)

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

(51)
Obligation:
Rules:
f217_0_merge_NONNULL(x106:0, x107:0) -> f217_0_merge_NONNULL(x111:0, x112:0) :|: x111:0 > 0 && x112:0 > 0 && x107:0 > 0 && x106:0 > 2 && x112:0 <= x107:0 && x117:0 >= x116:0 && x111:0 + 2 <= x106:0
f217_0_merge_NONNULL(x94:0, x95:0) -> f217_0_merge_NONNULL(x99:0, x100:0) :|: x99:0 > 0 && x100:0 > -1 && x95:0 > 0 && x94:0 > 0 && x95:0 >= x100:0 + 1 && x105:0 - 1 >= x104:0 && x99:0 <= x94:0

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

(52) FilterProof (EQUIVALENT)
Used the following sort dictionary for filtering: 
f217_0_merge_NONNULL(INTEGER, INTEGER)
Replaced non-predefined constructor symbols by 0.
----------------------------------------

(53)
Obligation:
Rules:
f217_0_merge_NONNULL(x106:0, x107:0) -> f217_0_merge_NONNULL(x111:0, x112:0) :|: x111:0 > 0 && x112:0 > 0 && x107:0 > 0 && x106:0 > 2 && x112:0 <= x107:0 && x117:0 >= x116:0 && x111:0 + 2 <= x106:0
f217_0_merge_NONNULL(x94:0, x95:0) -> f217_0_merge_NONNULL(x99:0, x100:0) :|: x99:0 > 0 && x100:0 > -1 && x95:0 > 0 && x94:0 > 0 && x95:0 >= x100:0 + 1 && x105:0 - 1 >= x104:0 && x99:0 <= x94:0

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(54) IntTRSCompressionProof (EQUIVALENT)
Compressed rules.
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(55)
Obligation:
Rules:
f217_0_merge_NONNULL(x94:0:0, x95:0:0) -> f217_0_merge_NONNULL(x99:0:0, x100:0:0) :|: x105:0:0 - 1 >= x104:0:0 && x99:0:0 <= x94:0:0 && x95:0:0 >= x100:0:0 + 1 && x94:0:0 > 0 && x95:0:0 > 0 && x100:0:0 > -1 && x99:0:0 > 0
f217_0_merge_NONNULL(x106:0:0, x107:0:0) -> f217_0_merge_NONNULL(x111:0:0, x112:0:0) :|: x117:0:0 >= x116:0:0 && x111:0:0 + 2 <= x106:0:0 && x112:0:0 <= x107:0:0 && x106:0:0 > 2 && x107:0:0 > 0 && x112:0:0 > 0 && x111:0:0 > 0

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(56) RankingReductionPairProof (EQUIVALENT)
Interpretation:
[ f217_0_merge_NONNULL ] = 1/2*f217_0_merge_NONNULL_1 + f217_0_merge_NONNULL_2

The following rules are decreasing:
f217_0_merge_NONNULL(x94:0:0, x95:0:0) -> f217_0_merge_NONNULL(x99:0:0, x100:0:0) :|: x105:0:0 - 1 >= x104:0:0 && x99:0:0 <= x94:0:0 && x95:0:0 >= x100:0:0 + 1 && x94:0:0 > 0 && x95:0:0 > 0 && x100:0:0 > -1 && x99:0:0 > 0
f217_0_merge_NONNULL(x106:0:0, x107:0:0) -> f217_0_merge_NONNULL(x111:0:0, x112:0:0) :|: x117:0:0 >= x116:0:0 && x111:0:0 + 2 <= x106:0:0 && x112:0:0 <= x107:0:0 && x106:0:0 > 2 && x107:0:0 > 0 && x112:0:0 > 0 && x111:0:0 > 0

The following rules are bounded:
f217_0_merge_NONNULL(x94:0:0, x95:0:0) -> f217_0_merge_NONNULL(x99:0:0, x100:0:0) :|: x105:0:0 - 1 >= x104:0:0 && x99:0:0 <= x94:0:0 && x95:0:0 >= x100:0:0 + 1 && x94:0:0 > 0 && x95:0:0 > 0 && x100:0:0 > -1 && x99:0:0 > 0
f217_0_merge_NONNULL(x106:0:0, x107:0:0) -> f217_0_merge_NONNULL(x111:0:0, x112:0:0) :|: x117:0:0 >= x116:0:0 && x111:0:0 + 2 <= x106:0:0 && x112:0:0 <= x107:0:0 && x106:0:0 > 2 && x107:0:0 > 0 && x112:0:0 > 0 && x111:0:0 > 0


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(57)
YES