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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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, 6923 ms]
(4) AND
    (5) IRSwT
        (6) IntTRSCompressionProof [EQUIVALENT, 0 ms]
        (7) IRSwT
        (8) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms]
        (9) IRSwT
        (10) TempFilterProof [SOUND, 56 ms]
        (11) IntTRS
        (12) PolynomialOrderProcessor [EQUIVALENT, 0 ms]
        (13) IntTRS
        (14) RankingReductionPairProof [EQUIVALENT, 6 ms]
        (15) YES
    (16) IRSwT
        (17) IntTRSCompressionProof [EQUIVALENT, 33 ms]
        (18) IRSwT
        (19) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms]
        (20) IRSwT
        (21) FilterProof [EQUIVALENT, 0 ms]
        (22) IntTRS
        (23) IntTRSCompressionProof [EQUIVALENT, 0 ms]
        (24) IntTRS
        (25) RankingReductionPairProof [EQUIVALENT, 28 ms]
        (26) YES


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(0)
Obligation:
Rules:
f1_0_main_Load(arg1, arg2, arg3, arg4, arg5, arg6, arg7) -> f2800_0_random_ArrayAccess(arg1P, arg2P, arg3P, arg4P, arg5P, arg6P, arg7P) :|: -1 <= x6 - 1 && 0 <= arg2 - 1 && 0 <= arg1 - 1 && 3 <= arg1P - 1 && arg2 = arg2P
f1260_0_create_Return(x, x1, x2, x3, x4, x5, x7) -> f2800_0_random_ArrayAccess(x8, x9, x10, x11, x12, x13, x14) :|: x4 = x11 && x3 = x10 && x3 + 5 <= x1 && x4 + 5 <= x1 && 3 <= x8 - 1 && 3 <= x1 - 1 && 0 <= x - 1 && x8 <= x1
f1_0_main_Load(x15, x16, x17, x21, x22, x23, x24) -> f2894_0_extendMatchingSubstitution_InvokeMethod(x25, x27, x28, x29, x30, x31, x32) :|: -1 <= x33 - 1 && 0 <= x16 - 1 && 0 <= x35 - 1 && x35 <= x16 - 1 && -1 <= x37 - 1 && x25 <= x15 && 0 <= x15 - 1 && 0 <= x25 - 1
f1262_0_create_Return(x38, x39, x40, x41, x42, x43, x45) -> f2894_0_extendMatchingSubstitution_InvokeMethod(x46, x47, x48, x49, x51, x53, x55) :|: 0 <= x46 - 1 && 0 <= x38 - 1 && x46 <= x38
f2800_0_random_ArrayAccess(x56, x57, x58, x59, x60, x61, x62) -> f3568_0_extendMatchingSubstitution_CheckCast(x63, x64, x65, x66, x67, x68, x69) :|: x70 <= x57 - 1 && 0 <= x70 - 1 && 0 <= x57 - 1 && -1 <= x71 - 1 && 1 <= x66 - 1 && x63 <= x56 && x64 + 3 <= x56 && x65 + 3 <= x56 && 3 <= x56 - 1 && 3 <= x63 - 1 && 0 <= x64 - 1 && 0 <= x65 - 1 && x59 + 5 <= x56 && x58 + 5 <= x56
f2800_0_random_ArrayAccess(x72, x73, x74, x75, x76, x77, x78) -> f3568_0_extendMatchingSubstitution_CheckCast(x79, x80, x81, x82, x83, x84, x85) :|: x86 <= x73 - 1 && 0 <= x86 - 1 && 0 <= x73 - 1 && -1 <= x87 - 1 && 1 <= x82 - 1 && x79 <= x72 && 3 <= x72 - 1 && 3 <= x79 - 1 && 3 <= x80 - 1 && 3 <= x81 - 1 && x75 + 5 <= x72 && x74 + 5 <= x72
f1_0_main_Load(x88, x89, x90, x91, x92, x93, x94) -> f648_0_create_GT(x95, x96, x97, x98, x99, x100, x101) :|: 1 = x97 && x89 = x96 && 0 <= x88 - 1 && 0 <= x89 - 1 && -1 <= x95 - 1
f1_0_main_Load(x102, x103, x104, x105, x106, x107, x108) -> f648_0_create_GT(x109, x110, x111, x112, x113, x114, x115) :|: -1 <= x116 - 1 && 0 <= x103 - 1 && 0 <= x117 - 1 && x117 <= x103 - 1 && -1 <= x109 - 1 && 0 <= x102 - 1 && x103 = x110 && x117 + 1 = x111
f2800_0_random_ArrayAccess(x118, x119, x120, x121, x122, x123, x124) -> f648_0_create_GT(x125, x126, x127, x128, x129, x130, x131) :|: x132 <= x119 - 1 && 0 <= x132 - 1 && 0 <= x119 - 1 && -1 <= x125 - 1 && 3 <= x118 - 1 && x121 + 5 <= x118 && x120 + 5 <= x118 && x119 = x126 && x132 + 1 = x127
f648_0_create_GT(x133, x134, x135, x136, x137, x138, x139) -> f2576_0_create_GE(x140, x141, x142, x143, x144, x145, x146) :|: x135 + 1 = x144 && x134 = x143 && 0 = x141 && x133 = x140 && -1 <= x142 - 1 && x135 <= x134 - 1 && 0 <= x135 - 1 && 1 <= x133 - 1 && -1 <= x134 - 1
f2576_0_create_GE(x147, x148, x149, x150, x151, x152, x153) -> f648_0_create_GT(x154, x155, x156, x157, x158, x159, x160) :|: x151 = x156 && x150 = x155 && x147 - 1 = x154 && x147 - 1 <= x147 - 1 && 1 <= x151 - 1 && 0 <= x149 - 1 && 1 <= x147 - 1 && x148 <= x149 - 1
f2576_0_create_GE(x161, x162, x163, x164, x165, x166, x167) -> f2576_0_create_GE(x168, x169, x170, x171, x172, x173, x174) :|: x164 = x171 && x163 = x170 && x162 + 1 = x169 && x161 = x168 && x161 - 1 <= x161 - 1 && 1 <= x165 - 1 && 0 <= x163 - 1 && 1 <= x161 - 1 && x162 <= x163 - 1
f3568_0_extendMatchingSubstitution_CheckCast(x175, x176, x177, x178, x179, x180, x181) -> f3684_0_extendMatchingSubstitution_EQ(x182, x183, x184, x185, x186, x187, x188) :|: x178 = x186 && 0 = x184 && -1 <= x188 - 1 && -1 <= x187 - 1 && 0 <= x183 - 1 && 0 <= x182 - 1 && 0 <= x177 - 1 && 0 <= x176 - 1 && 0 <= x175 - 1 && x188 + 1 <= x177 && x188 + 1 <= x176 && x187 + 1 <= x175 && x183 <= x177 && x183 <= x176 && 1 <= x178 - 1 && x182 <= x175
f3568_0_extendMatchingSubstitution_CheckCast(x189, x190, x191, x192, x193, x194, x195) -> f3684_0_extendMatchingSubstitution_EQ(x196, x197, x198, x199, x200, x201, x202) :|: x192 = x200 && 1 = x198 && -1 <= x202 - 1 && -1 <= x201 - 1 && 0 <= x197 - 1 && 0 <= x196 - 1 && 0 <= x191 - 1 && 0 <= x190 - 1 && 0 <= x189 - 1 && x202 + 1 <= x191 && x202 + 1 <= x190 && x201 + 1 <= x189 && x197 <= x191 && x197 <= x190 && 1 <= x192 - 1 && x196 <= x189
f3684_0_extendMatchingSubstitution_EQ(x203, x204, x205, x206, x207, x208, x209) -> f3952_0_extendMatchingSubstitution_NULL(x210, x211, x212, x213, x214, x215, x216) :|: x207 = x213 && x206 = x212 && 1 = x205 && -1 <= x211 - 1 && -1 <= x210 - 1 && -1 <= x209 - 1 && -1 <= x208 - 1 && 0 <= x204 - 1 && 0 <= x203 - 1 && x211 <= x208 && x211 + 1 <= x203 && x210 <= x209 && x210 + 1 <= x204
f3952_0_extendMatchingSubstitution_NULL(x217, x218, x219, x220, x221, x222, x223) -> f3568_0_extendMatchingSubstitution_CheckCast(x224, x225, x226, x227, x228, x229, x230) :|: x220 = x227 && -1 <= x226 - 1 && -1 <= x225 - 1 && 0 <= x224 - 1 && 2 <= x218 - 1 && 1 <= x217 - 1 && x226 + 3 <= x218 && x226 + 2 <= x217 && x225 + 3 <= x218 && x225 + 2 <= x217 && 1 <= x220 - 1 && x224 + 2 <= x218
f3952_0_extendMatchingSubstitution_NULL(x231, x232, x233, x234, x235, x236, x237) -> f3568_0_extendMatchingSubstitution_CheckCast(x238, x239, x240, x241, x242, x243, x244) :|: x234 = x241 && 0 <= x240 - 1 && 0 <= x239 - 1 && 0 <= x238 - 1 && 2 <= x232 - 1 && 2 <= x231 - 1 && x240 + 2 <= x231 && x239 + 2 <= x231 && 1 <= x234 - 1 && x238 + 2 <= x232
f3952_0_extendMatchingSubstitution_NULL(x245, x246, x247, x248, x249, x250, x251) -> f3952_0_extendMatchingSubstitution_NULL(x252, x253, x254, x255, x256, x257, x258) :|: x248 = x255 && x247 = x254 && -1 <= x253 - 1 && -1 <= x252 - 1 && 2 <= x246 - 1 && 2 <= x245 - 1 && x253 + 2 <= x246 && 1 <= x248 - 1 && x252 + 2 <= x245
f3952_0_extendMatchingSubstitution_NULL(x259, x260, x261, x262, x263, x264, x265) -> f3952_0_extendMatchingSubstitution_NULL(x266, x267, x268, x269, x270, x271, x272) :|: x262 = x269 && x261 = x268 && -1 <= x267 - 1 && -1 <= x266 - 1 && 2 <= x260 - 1 && 1 <= x259 - 1 && x267 + 2 <= x260 && 1 <= x262 - 1 && x266 + 2 <= x259
__init(x273, x274, x275, x276, x277, x278, x279) -> f1_0_main_Load(x280, x281, x282, x283, x284, x285, x286) :|: 0 <= 0
Start term: __init(arg1, arg2, arg3, arg4, arg5, arg6, arg7)

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

(2)
Obligation:
Rules:
f1_0_main_Load(arg1, arg2, arg3, arg4, arg5, arg6, arg7) -> f2800_0_random_ArrayAccess(arg1P, arg2P, arg3P, arg4P, arg5P, arg6P, arg7P) :|: -1 <= x6 - 1 && 0 <= arg2 - 1 && 0 <= arg1 - 1 && 3 <= arg1P - 1 && arg2 = arg2P
f1260_0_create_Return(x, x1, x2, x3, x4, x5, x7) -> f2800_0_random_ArrayAccess(x8, x9, x10, x11, x12, x13, x14) :|: x4 = x11 && x3 = x10 && x3 + 5 <= x1 && x4 + 5 <= x1 && 3 <= x8 - 1 && 3 <= x1 - 1 && 0 <= x - 1 && x8 <= x1
f1_0_main_Load(x15, x16, x17, x21, x22, x23, x24) -> f2894_0_extendMatchingSubstitution_InvokeMethod(x25, x27, x28, x29, x30, x31, x32) :|: -1 <= x33 - 1 && 0 <= x16 - 1 && 0 <= x35 - 1 && x35 <= x16 - 1 && -1 <= x37 - 1 && x25 <= x15 && 0 <= x15 - 1 && 0 <= x25 - 1
f1262_0_create_Return(x38, x39, x40, x41, x42, x43, x45) -> f2894_0_extendMatchingSubstitution_InvokeMethod(x46, x47, x48, x49, x51, x53, x55) :|: 0 <= x46 - 1 && 0 <= x38 - 1 && x46 <= x38
f2800_0_random_ArrayAccess(x56, x57, x58, x59, x60, x61, x62) -> f3568_0_extendMatchingSubstitution_CheckCast(x63, x64, x65, x66, x67, x68, x69) :|: x70 <= x57 - 1 && 0 <= x70 - 1 && 0 <= x57 - 1 && -1 <= x71 - 1 && 1 <= x66 - 1 && x63 <= x56 && x64 + 3 <= x56 && x65 + 3 <= x56 && 3 <= x56 - 1 && 3 <= x63 - 1 && 0 <= x64 - 1 && 0 <= x65 - 1 && x59 + 5 <= x56 && x58 + 5 <= x56
f2800_0_random_ArrayAccess(x72, x73, x74, x75, x76, x77, x78) -> f3568_0_extendMatchingSubstitution_CheckCast(x79, x80, x81, x82, x83, x84, x85) :|: x86 <= x73 - 1 && 0 <= x86 - 1 && 0 <= x73 - 1 && -1 <= x87 - 1 && 1 <= x82 - 1 && x79 <= x72 && 3 <= x72 - 1 && 3 <= x79 - 1 && 3 <= x80 - 1 && 3 <= x81 - 1 && x75 + 5 <= x72 && x74 + 5 <= x72
f1_0_main_Load(x88, x89, x90, x91, x92, x93, x94) -> f648_0_create_GT(x95, x96, x97, x98, x99, x100, x101) :|: 1 = x97 && x89 = x96 && 0 <= x88 - 1 && 0 <= x89 - 1 && -1 <= x95 - 1
f1_0_main_Load(x102, x103, x104, x105, x106, x107, x108) -> f648_0_create_GT(x109, x110, x111, x112, x113, x114, x115) :|: -1 <= x116 - 1 && 0 <= x103 - 1 && 0 <= x117 - 1 && x117 <= x103 - 1 && -1 <= x109 - 1 && 0 <= x102 - 1 && x103 = x110 && x117 + 1 = x111
f2800_0_random_ArrayAccess(x118, x119, x120, x121, x122, x123, x124) -> f648_0_create_GT(x125, x126, x127, x128, x129, x130, x131) :|: x132 <= x119 - 1 && 0 <= x132 - 1 && 0 <= x119 - 1 && -1 <= x125 - 1 && 3 <= x118 - 1 && x121 + 5 <= x118 && x120 + 5 <= x118 && x119 = x126 && x132 + 1 = x127
f648_0_create_GT(x133, x134, x135, x136, x137, x138, x139) -> f2576_0_create_GE(x140, x141, x142, x143, x144, x145, x146) :|: x135 + 1 = x144 && x134 = x143 && 0 = x141 && x133 = x140 && -1 <= x142 - 1 && x135 <= x134 - 1 && 0 <= x135 - 1 && 1 <= x133 - 1 && -1 <= x134 - 1
f2576_0_create_GE(x147, x148, x149, x150, x151, x152, x153) -> f648_0_create_GT(x154, x155, x156, x157, x158, x159, x160) :|: x151 = x156 && x150 = x155 && x147 - 1 = x154 && x147 - 1 <= x147 - 1 && 1 <= x151 - 1 && 0 <= x149 - 1 && 1 <= x147 - 1 && x148 <= x149 - 1
f2576_0_create_GE(x161, x162, x163, x164, x165, x166, x167) -> f2576_0_create_GE(x168, x169, x170, x171, x172, x173, x174) :|: x164 = x171 && x163 = x170 && x162 + 1 = x169 && x161 = x168 && x161 - 1 <= x161 - 1 && 1 <= x165 - 1 && 0 <= x163 - 1 && 1 <= x161 - 1 && x162 <= x163 - 1
f3568_0_extendMatchingSubstitution_CheckCast(x175, x176, x177, x178, x179, x180, x181) -> f3684_0_extendMatchingSubstitution_EQ(x182, x183, x184, x185, x186, x187, x188) :|: x178 = x186 && 0 = x184 && -1 <= x188 - 1 && -1 <= x187 - 1 && 0 <= x183 - 1 && 0 <= x182 - 1 && 0 <= x177 - 1 && 0 <= x176 - 1 && 0 <= x175 - 1 && x188 + 1 <= x177 && x188 + 1 <= x176 && x187 + 1 <= x175 && x183 <= x177 && x183 <= x176 && 1 <= x178 - 1 && x182 <= x175
f3568_0_extendMatchingSubstitution_CheckCast(x189, x190, x191, x192, x193, x194, x195) -> f3684_0_extendMatchingSubstitution_EQ(x196, x197, x198, x199, x200, x201, x202) :|: x192 = x200 && 1 = x198 && -1 <= x202 - 1 && -1 <= x201 - 1 && 0 <= x197 - 1 && 0 <= x196 - 1 && 0 <= x191 - 1 && 0 <= x190 - 1 && 0 <= x189 - 1 && x202 + 1 <= x191 && x202 + 1 <= x190 && x201 + 1 <= x189 && x197 <= x191 && x197 <= x190 && 1 <= x192 - 1 && x196 <= x189
f3684_0_extendMatchingSubstitution_EQ(x203, x204, x205, x206, x207, x208, x209) -> f3952_0_extendMatchingSubstitution_NULL(x210, x211, x212, x213, x214, x215, x216) :|: x207 = x213 && x206 = x212 && 1 = x205 && -1 <= x211 - 1 && -1 <= x210 - 1 && -1 <= x209 - 1 && -1 <= x208 - 1 && 0 <= x204 - 1 && 0 <= x203 - 1 && x211 <= x208 && x211 + 1 <= x203 && x210 <= x209 && x210 + 1 <= x204
f3952_0_extendMatchingSubstitution_NULL(x217, x218, x219, x220, x221, x222, x223) -> f3568_0_extendMatchingSubstitution_CheckCast(x224, x225, x226, x227, x228, x229, x230) :|: x220 = x227 && -1 <= x226 - 1 && -1 <= x225 - 1 && 0 <= x224 - 1 && 2 <= x218 - 1 && 1 <= x217 - 1 && x226 + 3 <= x218 && x226 + 2 <= x217 && x225 + 3 <= x218 && x225 + 2 <= x217 && 1 <= x220 - 1 && x224 + 2 <= x218
f3952_0_extendMatchingSubstitution_NULL(x231, x232, x233, x234, x235, x236, x237) -> f3568_0_extendMatchingSubstitution_CheckCast(x238, x239, x240, x241, x242, x243, x244) :|: x234 = x241 && 0 <= x240 - 1 && 0 <= x239 - 1 && 0 <= x238 - 1 && 2 <= x232 - 1 && 2 <= x231 - 1 && x240 + 2 <= x231 && x239 + 2 <= x231 && 1 <= x234 - 1 && x238 + 2 <= x232
f3952_0_extendMatchingSubstitution_NULL(x245, x246, x247, x248, x249, x250, x251) -> f3952_0_extendMatchingSubstitution_NULL(x252, x253, x254, x255, x256, x257, x258) :|: x248 = x255 && x247 = x254 && -1 <= x253 - 1 && -1 <= x252 - 1 && 2 <= x246 - 1 && 2 <= x245 - 1 && x253 + 2 <= x246 && 1 <= x248 - 1 && x252 + 2 <= x245
f3952_0_extendMatchingSubstitution_NULL(x259, x260, x261, x262, x263, x264, x265) -> f3952_0_extendMatchingSubstitution_NULL(x266, x267, x268, x269, x270, x271, x272) :|: x262 = x269 && x261 = x268 && -1 <= x267 - 1 && -1 <= x266 - 1 && 2 <= x260 - 1 && 1 <= x259 - 1 && x267 + 2 <= x260 && 1 <= x262 - 1 && x266 + 2 <= x259
__init(x273, x274, x275, x276, x277, x278, x279) -> f1_0_main_Load(x280, x281, x282, x283, x284, x285, x286) :|: 0 <= 0
Start term: __init(arg1, arg2, arg3, arg4, arg5, arg6, arg7)

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

(3) IRSwTTerminationDigraphProof (EQUIVALENT)
Constructed termination digraph!
Nodes:
(1) f1_0_main_Load(arg1, arg2, arg3, arg4, arg5, arg6, arg7) -> f2800_0_random_ArrayAccess(arg1P, arg2P, arg3P, arg4P, arg5P, arg6P, arg7P) :|: -1 <= x6 - 1 && 0 <= arg2 - 1 && 0 <= arg1 - 1 && 3 <= arg1P - 1 && arg2 = arg2P
(2) f1260_0_create_Return(x, x1, x2, x3, x4, x5, x7) -> f2800_0_random_ArrayAccess(x8, x9, x10, x11, x12, x13, x14) :|: x4 = x11 && x3 = x10 && x3 + 5 <= x1 && x4 + 5 <= x1 && 3 <= x8 - 1 && 3 <= x1 - 1 && 0 <= x - 1 && x8 <= x1
(3) f1_0_main_Load(x15, x16, x17, x21, x22, x23, x24) -> f2894_0_extendMatchingSubstitution_InvokeMethod(x25, x27, x28, x29, x30, x31, x32) :|: -1 <= x33 - 1 && 0 <= x16 - 1 && 0 <= x35 - 1 && x35 <= x16 - 1 && -1 <= x37 - 1 && x25 <= x15 && 0 <= x15 - 1 && 0 <= x25 - 1
(4) f1262_0_create_Return(x38, x39, x40, x41, x42, x43, x45) -> f2894_0_extendMatchingSubstitution_InvokeMethod(x46, x47, x48, x49, x51, x53, x55) :|: 0 <= x46 - 1 && 0 <= x38 - 1 && x46 <= x38
(5) f2800_0_random_ArrayAccess(x56, x57, x58, x59, x60, x61, x62) -> f3568_0_extendMatchingSubstitution_CheckCast(x63, x64, x65, x66, x67, x68, x69) :|: x70 <= x57 - 1 && 0 <= x70 - 1 && 0 <= x57 - 1 && -1 <= x71 - 1 && 1 <= x66 - 1 && x63 <= x56 && x64 + 3 <= x56 && x65 + 3 <= x56 && 3 <= x56 - 1 && 3 <= x63 - 1 && 0 <= x64 - 1 && 0 <= x65 - 1 && x59 + 5 <= x56 && x58 + 5 <= x56
(6) f2800_0_random_ArrayAccess(x72, x73, x74, x75, x76, x77, x78) -> f3568_0_extendMatchingSubstitution_CheckCast(x79, x80, x81, x82, x83, x84, x85) :|: x86 <= x73 - 1 && 0 <= x86 - 1 && 0 <= x73 - 1 && -1 <= x87 - 1 && 1 <= x82 - 1 && x79 <= x72 && 3 <= x72 - 1 && 3 <= x79 - 1 && 3 <= x80 - 1 && 3 <= x81 - 1 && x75 + 5 <= x72 && x74 + 5 <= x72
(7) f1_0_main_Load(x88, x89, x90, x91, x92, x93, x94) -> f648_0_create_GT(x95, x96, x97, x98, x99, x100, x101) :|: 1 = x97 && x89 = x96 && 0 <= x88 - 1 && 0 <= x89 - 1 && -1 <= x95 - 1
(8) f1_0_main_Load(x102, x103, x104, x105, x106, x107, x108) -> f648_0_create_GT(x109, x110, x111, x112, x113, x114, x115) :|: -1 <= x116 - 1 && 0 <= x103 - 1 && 0 <= x117 - 1 && x117 <= x103 - 1 && -1 <= x109 - 1 && 0 <= x102 - 1 && x103 = x110 && x117 + 1 = x111
(9) f2800_0_random_ArrayAccess(x118, x119, x120, x121, x122, x123, x124) -> f648_0_create_GT(x125, x126, x127, x128, x129, x130, x131) :|: x132 <= x119 - 1 && 0 <= x132 - 1 && 0 <= x119 - 1 && -1 <= x125 - 1 && 3 <= x118 - 1 && x121 + 5 <= x118 && x120 + 5 <= x118 && x119 = x126 && x132 + 1 = x127
(10) f648_0_create_GT(x133, x134, x135, x136, x137, x138, x139) -> f2576_0_create_GE(x140, x141, x142, x143, x144, x145, x146) :|: x135 + 1 = x144 && x134 = x143 && 0 = x141 && x133 = x140 && -1 <= x142 - 1 && x135 <= x134 - 1 && 0 <= x135 - 1 && 1 <= x133 - 1 && -1 <= x134 - 1
(11) f2576_0_create_GE(x147, x148, x149, x150, x151, x152, x153) -> f648_0_create_GT(x154, x155, x156, x157, x158, x159, x160) :|: x151 = x156 && x150 = x155 && x147 - 1 = x154 && x147 - 1 <= x147 - 1 && 1 <= x151 - 1 && 0 <= x149 - 1 && 1 <= x147 - 1 && x148 <= x149 - 1
(12) f2576_0_create_GE(x161, x162, x163, x164, x165, x166, x167) -> f2576_0_create_GE(x168, x169, x170, x171, x172, x173, x174) :|: x164 = x171 && x163 = x170 && x162 + 1 = x169 && x161 = x168 && x161 - 1 <= x161 - 1 && 1 <= x165 - 1 && 0 <= x163 - 1 && 1 <= x161 - 1 && x162 <= x163 - 1
(13) f3568_0_extendMatchingSubstitution_CheckCast(x175, x176, x177, x178, x179, x180, x181) -> f3684_0_extendMatchingSubstitution_EQ(x182, x183, x184, x185, x186, x187, x188) :|: x178 = x186 && 0 = x184 && -1 <= x188 - 1 && -1 <= x187 - 1 && 0 <= x183 - 1 && 0 <= x182 - 1 && 0 <= x177 - 1 && 0 <= x176 - 1 && 0 <= x175 - 1 && x188 + 1 <= x177 && x188 + 1 <= x176 && x187 + 1 <= x175 && x183 <= x177 && x183 <= x176 && 1 <= x178 - 1 && x182 <= x175
(14) f3568_0_extendMatchingSubstitution_CheckCast(x189, x190, x191, x192, x193, x194, x195) -> f3684_0_extendMatchingSubstitution_EQ(x196, x197, x198, x199, x200, x201, x202) :|: x192 = x200 && 1 = x198 && -1 <= x202 - 1 && -1 <= x201 - 1 && 0 <= x197 - 1 && 0 <= x196 - 1 && 0 <= x191 - 1 && 0 <= x190 - 1 && 0 <= x189 - 1 && x202 + 1 <= x191 && x202 + 1 <= x190 && x201 + 1 <= x189 && x197 <= x191 && x197 <= x190 && 1 <= x192 - 1 && x196 <= x189
(15) f3684_0_extendMatchingSubstitution_EQ(x203, x204, x205, x206, x207, x208, x209) -> f3952_0_extendMatchingSubstitution_NULL(x210, x211, x212, x213, x214, x215, x216) :|: x207 = x213 && x206 = x212 && 1 = x205 && -1 <= x211 - 1 && -1 <= x210 - 1 && -1 <= x209 - 1 && -1 <= x208 - 1 && 0 <= x204 - 1 && 0 <= x203 - 1 && x211 <= x208 && x211 + 1 <= x203 && x210 <= x209 && x210 + 1 <= x204
(16) f3952_0_extendMatchingSubstitution_NULL(x217, x218, x219, x220, x221, x222, x223) -> f3568_0_extendMatchingSubstitution_CheckCast(x224, x225, x226, x227, x228, x229, x230) :|: x220 = x227 && -1 <= x226 - 1 && -1 <= x225 - 1 && 0 <= x224 - 1 && 2 <= x218 - 1 && 1 <= x217 - 1 && x226 + 3 <= x218 && x226 + 2 <= x217 && x225 + 3 <= x218 && x225 + 2 <= x217 && 1 <= x220 - 1 && x224 + 2 <= x218
(17) f3952_0_extendMatchingSubstitution_NULL(x231, x232, x233, x234, x235, x236, x237) -> f3568_0_extendMatchingSubstitution_CheckCast(x238, x239, x240, x241, x242, x243, x244) :|: x234 = x241 && 0 <= x240 - 1 && 0 <= x239 - 1 && 0 <= x238 - 1 && 2 <= x232 - 1 && 2 <= x231 - 1 && x240 + 2 <= x231 && x239 + 2 <= x231 && 1 <= x234 - 1 && x238 + 2 <= x232
(18) f3952_0_extendMatchingSubstitution_NULL(x245, x246, x247, x248, x249, x250, x251) -> f3952_0_extendMatchingSubstitution_NULL(x252, x253, x254, x255, x256, x257, x258) :|: x248 = x255 && x247 = x254 && -1 <= x253 - 1 && -1 <= x252 - 1 && 2 <= x246 - 1 && 2 <= x245 - 1 && x253 + 2 <= x246 && 1 <= x248 - 1 && x252 + 2 <= x245
(19) f3952_0_extendMatchingSubstitution_NULL(x259, x260, x261, x262, x263, x264, x265) -> f3952_0_extendMatchingSubstitution_NULL(x266, x267, x268, x269, x270, x271, x272) :|: x262 = x269 && x261 = x268 && -1 <= x267 - 1 && -1 <= x266 - 1 && 2 <= x260 - 1 && 1 <= x259 - 1 && x267 + 2 <= x260 && 1 <= x262 - 1 && x266 + 2 <= x259
(20) __init(x273, x274, x275, x276, x277, x278, x279) -> f1_0_main_Load(x280, x281, x282, x283, x284, x285, x286) :|: 0 <= 0

Arcs:
(1) -> (5), (6), (9)
(2) -> (5), (6), (9)
(5) -> (13), (14)
(6) -> (13), (14)
(7) -> (10)
(8) -> (10)
(9) -> (10)
(10) -> (11), (12)
(11) -> (10)
(12) -> (11), (12)
(14) -> (15)
(15) -> (16), (17), (18), (19)
(16) -> (13), (14)
(17) -> (13), (14)
(18) -> (16), (17), (18), (19)
(19) -> (16), (17), (18), (19)
(20) -> (1), (3), (7), (8)

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

(4)
Complex Obligation (AND)

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

(5)
Obligation:

Termination digraph:
Nodes:
(1) f648_0_create_GT(x133, x134, x135, x136, x137, x138, x139) -> f2576_0_create_GE(x140, x141, x142, x143, x144, x145, x146) :|: x135 + 1 = x144 && x134 = x143 && 0 = x141 && x133 = x140 && -1 <= x142 - 1 && x135 <= x134 - 1 && 0 <= x135 - 1 && 1 <= x133 - 1 && -1 <= x134 - 1
(2) f2576_0_create_GE(x147, x148, x149, x150, x151, x152, x153) -> f648_0_create_GT(x154, x155, x156, x157, x158, x159, x160) :|: x151 = x156 && x150 = x155 && x147 - 1 = x154 && x147 - 1 <= x147 - 1 && 1 <= x151 - 1 && 0 <= x149 - 1 && 1 <= x147 - 1 && x148 <= x149 - 1
(3) f2576_0_create_GE(x161, x162, x163, x164, x165, x166, x167) -> f2576_0_create_GE(x168, x169, x170, x171, x172, x173, x174) :|: x164 = x171 && x163 = x170 && x162 + 1 = x169 && x161 = x168 && x161 - 1 <= x161 - 1 && 1 <= x165 - 1 && 0 <= x163 - 1 && 1 <= x161 - 1 && x162 <= x163 - 1

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

This digraph is fully evaluated!

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

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

(7)
Obligation:
Rules:
f2576_0_create_GE(x147:0, x148:0, x149:0, x143:0, x151:0, x152:0, x153:0) -> f2576_0_create_GE(x147:0 - 1, 0, x142:0, x143:0, x151:0 + 1, x145:0, x146:0) :|: x143:0 > -1 && x149:0 - 1 >= x148:0 && x149:0 > 0 && x151:0 <= x143:0 - 1 && x142:0 > -1 && x151:0 > 1 && x147:0 > 2
f2576_0_create_GE(x161:0, x162:0, x163:0, x164:0, x165:0, x166:0, x167:0) -> f2576_0_create_GE(x161:0, x162:0 + 1, x163:0, x164:0, x172:0, x173:0, x174:0) :|: x161:0 > 1 && x163:0 - 1 >= x162:0 && x165:0 > 1 && x163:0 > 0

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

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

   f2576_0_create_GE(x1, x2, x3, x4, x5, x6, x7) -> f2576_0_create_GE(x1, x2, x3, x4, x5)

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

(9)
Obligation:
Rules:
f2576_0_create_GE(x147:0, x148:0, x149:0, x143:0, x151:0) -> f2576_0_create_GE(x147:0 - 1, 0, x142:0, x143:0, x151:0 + 1) :|: x143:0 > -1 && x149:0 - 1 >= x148:0 && x149:0 > 0 && x151:0 <= x143:0 - 1 && x142:0 > -1 && x151:0 > 1 && x147:0 > 2
f2576_0_create_GE(x161:0, x162:0, x163:0, x164:0, x165:0) -> f2576_0_create_GE(x161:0, x162:0 + 1, x163:0, x164:0, x172:0) :|: x161:0 > 1 && x163:0 - 1 >= x162:0 && x165:0 > 1 && x163:0 > 0

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

(10) TempFilterProof (SOUND)
Used the following sort dictionary for filtering: 
f2576_0_create_GE(INTEGER, VARIABLE, INTEGER, VARIABLE, VARIABLE)
Replaced non-predefined constructor symbols by 0.
----------------------------------------

(11)
Obligation:
Rules:
f2576_0_create_GE(x147:0, x148:0, x149:0, x143:0, x151:0) -> f2576_0_create_GE(c, c1, x142:0, x143:0, c2) :|: c2 = x151:0 + 1 && (c1 = 0 && c = x147:0 - 1) && (x143:0 > -1 && x149:0 - 1 >= x148:0 && x149:0 > 0 && x151:0 <= x143:0 - 1 && x142:0 > -1 && x151:0 > 1 && x147:0 > 2)
f2576_0_create_GE(x161:0, x162:0, x163:0, x164:0, x165:0) -> f2576_0_create_GE(x161:0, c3, x163:0, x164:0, x172:0) :|: c3 = x162:0 + 1 && (x161:0 > 1 && x163:0 - 1 >= x162:0 && x165:0 > 1 && x163:0 > 0)

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

(12) PolynomialOrderProcessor (EQUIVALENT)
Found the following polynomial interpretation:
[f2576_0_create_GE(x, x1, x2, x3, x4)] = x

The following rules are decreasing:
f2576_0_create_GE(x147:0, x148:0, x149:0, x143:0, x151:0) -> f2576_0_create_GE(c, c1, x142:0, x143:0, c2) :|: c2 = x151:0 + 1 && (c1 = 0 && c = x147:0 - 1) && (x143:0 > -1 && x149:0 - 1 >= x148:0 && x149:0 > 0 && x151:0 <= x143:0 - 1 && x142:0 > -1 && x151:0 > 1 && x147:0 > 2)
The following rules are bounded:
f2576_0_create_GE(x147:0, x148:0, x149:0, x143:0, x151:0) -> f2576_0_create_GE(c, c1, x142:0, x143:0, c2) :|: c2 = x151:0 + 1 && (c1 = 0 && c = x147:0 - 1) && (x143:0 > -1 && x149:0 - 1 >= x148:0 && x149:0 > 0 && x151:0 <= x143:0 - 1 && x142:0 > -1 && x151:0 > 1 && x147:0 > 2)
f2576_0_create_GE(x161:0, x162:0, x163:0, x164:0, x165:0) -> f2576_0_create_GE(x161:0, c3, x163:0, x164:0, x172:0) :|: c3 = x162:0 + 1 && (x161:0 > 1 && x163:0 - 1 >= x162:0 && x165:0 > 1 && x163:0 > 0)

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

(13)
Obligation:
Rules:
f2576_0_create_GE(x161:0, x162:0, x163:0, x164:0, x165:0) -> f2576_0_create_GE(x161:0, c3, x163:0, x164:0, x172:0) :|: c3 = x162:0 + 1 && (x161:0 > 1 && x163:0 - 1 >= x162:0 && x165:0 > 1 && x163:0 > 0)

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

(14) RankingReductionPairProof (EQUIVALENT)
Interpretation:
[ f2576_0_create_GE ] = f2576_0_create_GE_3 + -1*f2576_0_create_GE_2

The following rules are decreasing:
f2576_0_create_GE(x161:0, x162:0, x163:0, x164:0, x165:0) -> f2576_0_create_GE(x161:0, c3, x163:0, x164:0, x172:0) :|: c3 = x162:0 + 1 && (x161:0 > 1 && x163:0 - 1 >= x162:0 && x165:0 > 1 && x163:0 > 0)

The following rules are bounded:
f2576_0_create_GE(x161:0, x162:0, x163:0, x164:0, x165:0) -> f2576_0_create_GE(x161:0, c3, x163:0, x164:0, x172:0) :|: c3 = x162:0 + 1 && (x161:0 > 1 && x163:0 - 1 >= x162:0 && x165:0 > 1 && x163:0 > 0)


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

(15)
YES

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

(16)
Obligation:

Termination digraph:
Nodes:
(1) f3568_0_extendMatchingSubstitution_CheckCast(x189, x190, x191, x192, x193, x194, x195) -> f3684_0_extendMatchingSubstitution_EQ(x196, x197, x198, x199, x200, x201, x202) :|: x192 = x200 && 1 = x198 && -1 <= x202 - 1 && -1 <= x201 - 1 && 0 <= x197 - 1 && 0 <= x196 - 1 && 0 <= x191 - 1 && 0 <= x190 - 1 && 0 <= x189 - 1 && x202 + 1 <= x191 && x202 + 1 <= x190 && x201 + 1 <= x189 && x197 <= x191 && x197 <= x190 && 1 <= x192 - 1 && x196 <= x189
(2) f3952_0_extendMatchingSubstitution_NULL(x231, x232, x233, x234, x235, x236, x237) -> f3568_0_extendMatchingSubstitution_CheckCast(x238, x239, x240, x241, x242, x243, x244) :|: x234 = x241 && 0 <= x240 - 1 && 0 <= x239 - 1 && 0 <= x238 - 1 && 2 <= x232 - 1 && 2 <= x231 - 1 && x240 + 2 <= x231 && x239 + 2 <= x231 && 1 <= x234 - 1 && x238 + 2 <= x232
(3) f3952_0_extendMatchingSubstitution_NULL(x217, x218, x219, x220, x221, x222, x223) -> f3568_0_extendMatchingSubstitution_CheckCast(x224, x225, x226, x227, x228, x229, x230) :|: x220 = x227 && -1 <= x226 - 1 && -1 <= x225 - 1 && 0 <= x224 - 1 && 2 <= x218 - 1 && 1 <= x217 - 1 && x226 + 3 <= x218 && x226 + 2 <= x217 && x225 + 3 <= x218 && x225 + 2 <= x217 && 1 <= x220 - 1 && x224 + 2 <= x218
(4) f3952_0_extendMatchingSubstitution_NULL(x245, x246, x247, x248, x249, x250, x251) -> f3952_0_extendMatchingSubstitution_NULL(x252, x253, x254, x255, x256, x257, x258) :|: x248 = x255 && x247 = x254 && -1 <= x253 - 1 && -1 <= x252 - 1 && 2 <= x246 - 1 && 2 <= x245 - 1 && x253 + 2 <= x246 && 1 <= x248 - 1 && x252 + 2 <= x245
(5) f3952_0_extendMatchingSubstitution_NULL(x259, x260, x261, x262, x263, x264, x265) -> f3952_0_extendMatchingSubstitution_NULL(x266, x267, x268, x269, x270, x271, x272) :|: x262 = x269 && x261 = x268 && -1 <= x267 - 1 && -1 <= x266 - 1 && 2 <= x260 - 1 && 1 <= x259 - 1 && x267 + 2 <= x260 && 1 <= x262 - 1 && x266 + 2 <= x259
(6) f3684_0_extendMatchingSubstitution_EQ(x203, x204, x205, x206, x207, x208, x209) -> f3952_0_extendMatchingSubstitution_NULL(x210, x211, x212, x213, x214, x215, x216) :|: x207 = x213 && x206 = x212 && 1 = x205 && -1 <= x211 - 1 && -1 <= x210 - 1 && -1 <= x209 - 1 && -1 <= x208 - 1 && 0 <= x204 - 1 && 0 <= x203 - 1 && x211 <= x208 && x211 + 1 <= x203 && x210 <= x209 && x210 + 1 <= x204

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

This digraph is fully evaluated!

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

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

(18)
Obligation:
Rules:
f3952_0_extendMatchingSubstitution_NULL(x259:0, x260:0, x261:0, x262:0, x263:0, x264:0, x265:0) -> f3952_0_extendMatchingSubstitution_NULL(x266:0, x267:0, x261:0, x262:0, x270:0, x271:0, x272:0) :|: x262:0 > 1 && x266:0 + 2 <= x259:0 && x267:0 + 2 <= x260:0 && x259:0 > 1 && x260:0 > 2 && x267:0 > -1 && x266:0 > -1
f3952_0_extendMatchingSubstitution_NULL(x245:0, x246:0, x247:0, x248:0, x249:0, x250:0, x251:0) -> f3952_0_extendMatchingSubstitution_NULL(x252:0, x253:0, x247:0, x248:0, x256:0, x257:0, x258:0) :|: x248:0 > 1 && x252:0 + 2 <= x245:0 && x253:0 + 2 <= x246:0 && x245:0 > 2 && x246:0 > 2 && x253:0 > -1 && x252:0 > -1
f3952_0_extendMatchingSubstitution_NULL(x217:0, x218:0, x219:0, x200:0, x221:0, x222:0, x223:0) -> f3952_0_extendMatchingSubstitution_NULL(x210:0, x211:0, x199:0, x200:0, x214:0, x215:0, x216:0) :|: x224:0 + 2 <= x218:0 && x224:0 >= x196:0 && x210:0 + 1 <= x197:0 && x225:0 + 2 <= x217:0 && x200:0 > 1 && x210:0 <= x202:0 && x225:0 + 3 <= x218:0 && x225:0 >= x197:0 && x211:0 + 1 <= x196:0 && x226:0 + 2 <= x217:0 && x226:0 >= x197:0 && x211:0 <= x201:0 && x226:0 + 3 <= x218:0 && x224:0 >= x201:0 + 1 && x217:0 > 1 && x225:0 >= x202:0 + 1 && x218:0 > 2 && x226:0 >= x202:0 + 1 && x224:0 > 0 && x210:0 > -1 && x211:0 > -1 && x196:0 > 0 && x197:0 > 0 && x201:0 > -1 && x202:0 > -1 && x226:0 > 0 && x225:0 > 0
f3952_0_extendMatchingSubstitution_NULL(x, x1, x2, x3, x4, x5, x6) -> f3952_0_extendMatchingSubstitution_NULL(x7, x8, x9, x3, x10, x11, x12) :|: x13 + 2 <= x1 && x13 >= x14 && x7 + 1 <= x15 && x16 + 2 <= x && x3 > 1 && x7 <= x17 && x18 + 2 <= x && x16 >= x15 && x8 + 1 <= x14 && x > 2 && x18 >= x15 && x8 <= x19 && x1 > 2 && x13 >= x19 + 1 && x16 >= x17 + 1 && x18 >= x17 + 1 && x13 > 0 && x16 > 0 && x7 > -1 && x18 > 0 && x8 > -1 && x14 > 0 && x15 > 0 && x17 > -1 && x19 > -1

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

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

   f3952_0_extendMatchingSubstitution_NULL(x1, x2, x3, x4, x5, x6, x7) -> f3952_0_extendMatchingSubstitution_NULL(x1, x2, x4)

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

(20)
Obligation:
Rules:
f3952_0_extendMatchingSubstitution_NULL(x259:0, x260:0, x262:0) -> f3952_0_extendMatchingSubstitution_NULL(x266:0, x267:0, x262:0) :|: x262:0 > 1 && x266:0 + 2 <= x259:0 && x267:0 + 2 <= x260:0 && x259:0 > 1 && x260:0 > 2 && x267:0 > -1 && x266:0 > -1
f3952_0_extendMatchingSubstitution_NULL(x245:0, x246:0, x248:0) -> f3952_0_extendMatchingSubstitution_NULL(x252:0, x253:0, x248:0) :|: x248:0 > 1 && x252:0 + 2 <= x245:0 && x253:0 + 2 <= x246:0 && x245:0 > 2 && x246:0 > 2 && x253:0 > -1 && x252:0 > -1
f3952_0_extendMatchingSubstitution_NULL(x217:0, x218:0, x200:0) -> f3952_0_extendMatchingSubstitution_NULL(x210:0, x211:0, x200:0) :|: x224:0 + 2 <= x218:0 && x224:0 >= x196:0 && x210:0 + 1 <= x197:0 && x225:0 + 2 <= x217:0 && x200:0 > 1 && x210:0 <= x202:0 && x225:0 + 3 <= x218:0 && x225:0 >= x197:0 && x211:0 + 1 <= x196:0 && x226:0 + 2 <= x217:0 && x226:0 >= x197:0 && x211:0 <= x201:0 && x226:0 + 3 <= x218:0 && x224:0 >= x201:0 + 1 && x217:0 > 1 && x225:0 >= x202:0 + 1 && x218:0 > 2 && x226:0 >= x202:0 + 1 && x224:0 > 0 && x210:0 > -1 && x211:0 > -1 && x196:0 > 0 && x197:0 > 0 && x201:0 > -1 && x202:0 > -1 && x226:0 > 0 && x225:0 > 0
f3952_0_extendMatchingSubstitution_NULL(x, x1, x3) -> f3952_0_extendMatchingSubstitution_NULL(x7, x8, x3) :|: x13 + 2 <= x1 && x13 >= x14 && x7 + 1 <= x15 && x16 + 2 <= x && x3 > 1 && x7 <= x17 && x18 + 2 <= x && x16 >= x15 && x8 + 1 <= x14 && x > 2 && x18 >= x15 && x8 <= x19 && x1 > 2 && x13 >= x19 + 1 && x16 >= x17 + 1 && x18 >= x17 + 1 && x13 > 0 && x16 > 0 && x7 > -1 && x18 > 0 && x8 > -1 && x14 > 0 && x15 > 0 && x17 > -1 && x19 > -1

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

(21) FilterProof (EQUIVALENT)
Used the following sort dictionary for filtering: 
f3952_0_extendMatchingSubstitution_NULL(INTEGER, INTEGER, INTEGER)
Replaced non-predefined constructor symbols by 0.
----------------------------------------

(22)
Obligation:
Rules:
f3952_0_extendMatchingSubstitution_NULL(x259:0, x260:0, x262:0) -> f3952_0_extendMatchingSubstitution_NULL(x266:0, x267:0, x262:0) :|: x262:0 > 1 && x266:0 + 2 <= x259:0 && x267:0 + 2 <= x260:0 && x259:0 > 1 && x260:0 > 2 && x267:0 > -1 && x266:0 > -1
f3952_0_extendMatchingSubstitution_NULL(x245:0, x246:0, x248:0) -> f3952_0_extendMatchingSubstitution_NULL(x252:0, x253:0, x248:0) :|: x248:0 > 1 && x252:0 + 2 <= x245:0 && x253:0 + 2 <= x246:0 && x245:0 > 2 && x246:0 > 2 && x253:0 > -1 && x252:0 > -1
f3952_0_extendMatchingSubstitution_NULL(x217:0, x218:0, x200:0) -> f3952_0_extendMatchingSubstitution_NULL(x210:0, x211:0, x200:0) :|: x224:0 + 2 <= x218:0 && x224:0 >= x196:0 && x210:0 + 1 <= x197:0 && x225:0 + 2 <= x217:0 && x200:0 > 1 && x210:0 <= x202:0 && x225:0 + 3 <= x218:0 && x225:0 >= x197:0 && x211:0 + 1 <= x196:0 && x226:0 + 2 <= x217:0 && x226:0 >= x197:0 && x211:0 <= x201:0 && x226:0 + 3 <= x218:0 && x224:0 >= x201:0 + 1 && x217:0 > 1 && x225:0 >= x202:0 + 1 && x218:0 > 2 && x226:0 >= x202:0 + 1 && x224:0 > 0 && x210:0 > -1 && x211:0 > -1 && x196:0 > 0 && x197:0 > 0 && x201:0 > -1 && x202:0 > -1 && x226:0 > 0 && x225:0 > 0
f3952_0_extendMatchingSubstitution_NULL(x, x1, x3) -> f3952_0_extendMatchingSubstitution_NULL(x7, x8, x3) :|: x13 + 2 <= x1 && x13 >= x14 && x7 + 1 <= x15 && x16 + 2 <= x && x3 > 1 && x7 <= x17 && x18 + 2 <= x && x16 >= x15 && x8 + 1 <= x14 && x > 2 && x18 >= x15 && x8 <= x19 && x1 > 2 && x13 >= x19 + 1 && x16 >= x17 + 1 && x18 >= x17 + 1 && x13 > 0 && x16 > 0 && x7 > -1 && x18 > 0 && x8 > -1 && x14 > 0 && x15 > 0 && x17 > -1 && x19 > -1

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

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

(24)
Obligation:
Rules:
f3952_0_extendMatchingSubstitution_NULL(x245:0:0, x246:0:0, x248:0:0) -> f3952_0_extendMatchingSubstitution_NULL(x252:0:0, x253:0:0, x248:0:0) :|: x253:0:0 > -1 && x252:0:0 > -1 && x246:0:0 > 2 && x245:0:0 > 2 && x253:0:0 + 2 <= x246:0:0 && x252:0:0 + 2 <= x245:0:0 && x248:0:0 > 1
f3952_0_extendMatchingSubstitution_NULL(x259:0:0, x260:0:0, x262:0:0) -> f3952_0_extendMatchingSubstitution_NULL(x266:0:0, x267:0:0, x262:0:0) :|: x267:0:0 > -1 && x266:0:0 > -1 && x260:0:0 > 2 && x259:0:0 > 1 && x267:0:0 + 2 <= x260:0:0 && x266:0:0 + 2 <= x259:0:0 && x262:0:0 > 1
f3952_0_extendMatchingSubstitution_NULL(x:0, x1:0, x3:0) -> f3952_0_extendMatchingSubstitution_NULL(x7:0, x8:0, x3:0) :|: x17:0 > -1 && x19:0 > -1 && x15:0 > 0 && x14:0 > 0 && x8:0 > -1 && x18:0 > 0 && x7:0 > -1 && x16:0 > 0 && x13:0 > 0 && x18:0 >= x17:0 + 1 && x17:0 + 1 <= x16:0 && x19:0 + 1 <= x13:0 && x1:0 > 2 && x8:0 <= x19:0 && x18:0 >= x15:0 && x:0 > 2 && x8:0 + 1 <= x14:0 && x16:0 >= x15:0 && x:0 >= x18:0 + 2 && x7:0 <= x17:0 && x3:0 > 1 && x:0 >= x16:0 + 2 && x7:0 + 1 <= x15:0 && x14:0 <= x13:0 && x1:0 >= x13:0 + 2
f3952_0_extendMatchingSubstitution_NULL(x217:0:0, x218:0:0, x200:0:0) -> f3952_0_extendMatchingSubstitution_NULL(x210:0:0, x211:0:0, x200:0:0) :|: x226:0:0 > 0 && x225:0:0 > 0 && x202:0:0 > -1 && x201:0:0 > -1 && x197:0:0 > 0 && x196:0:0 > 0 && x211:0:0 > -1 && x210:0:0 > -1 && x224:0:0 > 0 && x226:0:0 >= x202:0:0 + 1 && x218:0:0 > 2 && x225:0:0 >= x202:0:0 + 1 && x217:0:0 > 1 && x224:0:0 >= x201:0:0 + 1 && x226:0:0 + 3 <= x218:0:0 && x211:0:0 <= x201:0:0 && x226:0:0 >= x197:0:0 && x226:0:0 + 2 <= x217:0:0 && x211:0:0 + 1 <= x196:0:0 && x225:0:0 >= x197:0:0 && x225:0:0 + 3 <= x218:0:0 && x210:0:0 <= x202:0:0 && x200:0:0 > 1 && x225:0:0 + 2 <= x217:0:0 && x210:0:0 + 1 <= x197:0:0 && x224:0:0 >= x196:0:0 && x224:0:0 + 2 <= x218:0:0

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(25) RankingReductionPairProof (EQUIVALENT)
Interpretation:
[ f3952_0_extendMatchingSubstitution_NULL ] = 1/2*f3952_0_extendMatchingSubstitution_NULL_2

The following rules are decreasing:
f3952_0_extendMatchingSubstitution_NULL(x245:0:0, x246:0:0, x248:0:0) -> f3952_0_extendMatchingSubstitution_NULL(x252:0:0, x253:0:0, x248:0:0) :|: x253:0:0 > -1 && x252:0:0 > -1 && x246:0:0 > 2 && x245:0:0 > 2 && x253:0:0 + 2 <= x246:0:0 && x252:0:0 + 2 <= x245:0:0 && x248:0:0 > 1
f3952_0_extendMatchingSubstitution_NULL(x259:0:0, x260:0:0, x262:0:0) -> f3952_0_extendMatchingSubstitution_NULL(x266:0:0, x267:0:0, x262:0:0) :|: x267:0:0 > -1 && x266:0:0 > -1 && x260:0:0 > 2 && x259:0:0 > 1 && x267:0:0 + 2 <= x260:0:0 && x266:0:0 + 2 <= x259:0:0 && x262:0:0 > 1
f3952_0_extendMatchingSubstitution_NULL(x:0, x1:0, x3:0) -> f3952_0_extendMatchingSubstitution_NULL(x7:0, x8:0, x3:0) :|: x17:0 > -1 && x19:0 > -1 && x15:0 > 0 && x14:0 > 0 && x8:0 > -1 && x18:0 > 0 && x7:0 > -1 && x16:0 > 0 && x13:0 > 0 && x18:0 >= x17:0 + 1 && x17:0 + 1 <= x16:0 && x19:0 + 1 <= x13:0 && x1:0 > 2 && x8:0 <= x19:0 && x18:0 >= x15:0 && x:0 > 2 && x8:0 + 1 <= x14:0 && x16:0 >= x15:0 && x:0 >= x18:0 + 2 && x7:0 <= x17:0 && x3:0 > 1 && x:0 >= x16:0 + 2 && x7:0 + 1 <= x15:0 && x14:0 <= x13:0 && x1:0 >= x13:0 + 2
f3952_0_extendMatchingSubstitution_NULL(x217:0:0, x218:0:0, x200:0:0) -> f3952_0_extendMatchingSubstitution_NULL(x210:0:0, x211:0:0, x200:0:0) :|: x226:0:0 > 0 && x225:0:0 > 0 && x202:0:0 > -1 && x201:0:0 > -1 && x197:0:0 > 0 && x196:0:0 > 0 && x211:0:0 > -1 && x210:0:0 > -1 && x224:0:0 > 0 && x226:0:0 >= x202:0:0 + 1 && x218:0:0 > 2 && x225:0:0 >= x202:0:0 + 1 && x217:0:0 > 1 && x224:0:0 >= x201:0:0 + 1 && x226:0:0 + 3 <= x218:0:0 && x211:0:0 <= x201:0:0 && x226:0:0 >= x197:0:0 && x226:0:0 + 2 <= x217:0:0 && x211:0:0 + 1 <= x196:0:0 && x225:0:0 >= x197:0:0 && x225:0:0 + 3 <= x218:0:0 && x210:0:0 <= x202:0:0 && x200:0:0 > 1 && x225:0:0 + 2 <= x217:0:0 && x210:0:0 + 1 <= x197:0:0 && x224:0:0 >= x196:0:0 && x224:0:0 + 2 <= x218:0:0

The following rules are bounded:
f3952_0_extendMatchingSubstitution_NULL(x245:0:0, x246:0:0, x248:0:0) -> f3952_0_extendMatchingSubstitution_NULL(x252:0:0, x253:0:0, x248:0:0) :|: x253:0:0 > -1 && x252:0:0 > -1 && x246:0:0 > 2 && x245:0:0 > 2 && x253:0:0 + 2 <= x246:0:0 && x252:0:0 + 2 <= x245:0:0 && x248:0:0 > 1
f3952_0_extendMatchingSubstitution_NULL(x259:0:0, x260:0:0, x262:0:0) -> f3952_0_extendMatchingSubstitution_NULL(x266:0:0, x267:0:0, x262:0:0) :|: x267:0:0 > -1 && x266:0:0 > -1 && x260:0:0 > 2 && x259:0:0 > 1 && x267:0:0 + 2 <= x260:0:0 && x266:0:0 + 2 <= x259:0:0 && x262:0:0 > 1
f3952_0_extendMatchingSubstitution_NULL(x:0, x1:0, x3:0) -> f3952_0_extendMatchingSubstitution_NULL(x7:0, x8:0, x3:0) :|: x17:0 > -1 && x19:0 > -1 && x15:0 > 0 && x14:0 > 0 && x8:0 > -1 && x18:0 > 0 && x7:0 > -1 && x16:0 > 0 && x13:0 > 0 && x18:0 >= x17:0 + 1 && x17:0 + 1 <= x16:0 && x19:0 + 1 <= x13:0 && x1:0 > 2 && x8:0 <= x19:0 && x18:0 >= x15:0 && x:0 > 2 && x8:0 + 1 <= x14:0 && x16:0 >= x15:0 && x:0 >= x18:0 + 2 && x7:0 <= x17:0 && x3:0 > 1 && x:0 >= x16:0 + 2 && x7:0 + 1 <= x15:0 && x14:0 <= x13:0 && x1:0 >= x13:0 + 2
f3952_0_extendMatchingSubstitution_NULL(x217:0:0, x218:0:0, x200:0:0) -> f3952_0_extendMatchingSubstitution_NULL(x210:0:0, x211:0:0, x200:0:0) :|: x226:0:0 > 0 && x225:0:0 > 0 && x202:0:0 > -1 && x201:0:0 > -1 && x197:0:0 > 0 && x196:0:0 > 0 && x211:0:0 > -1 && x210:0:0 > -1 && x224:0:0 > 0 && x226:0:0 >= x202:0:0 + 1 && x218:0:0 > 2 && x225:0:0 >= x202:0:0 + 1 && x217:0:0 > 1 && x224:0:0 >= x201:0:0 + 1 && x226:0:0 + 3 <= x218:0:0 && x211:0:0 <= x201:0:0 && x226:0:0 >= x197:0:0 && x226:0:0 + 2 <= x217:0:0 && x211:0:0 + 1 <= x196:0:0 && x225:0:0 >= x197:0:0 && x225:0:0 + 3 <= x218:0:0 && x210:0:0 <= x202:0:0 && x200:0:0 > 1 && x225:0:0 + 2 <= x217:0:0 && x210:0:0 + 1 <= x197:0:0 && x224:0:0 >= x196:0:0 && x224:0:0 + 2 <= x218:0:0


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(26)
YES