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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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, 2549 ms]
(4) AND
    (5) IRSwT
        (6) IntTRSCompressionProof [EQUIVALENT, 13 ms]
        (7) IRSwT
        (8) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms]
        (9) IRSwT
        (10) TempFilterProof [SOUND, 99 ms]
        (11) IntTRS
        (12) PolynomialOrderProcessor [EQUIVALENT, 0 ms]
        (13) YES
    (14) IRSwT
        (15) IntTRSCompressionProof [EQUIVALENT, 11 ms]
        (16) IRSwT
        (17) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms]
        (18) IRSwT
        (19) TempFilterProof [SOUND, 51 ms]
        (20) IntTRS
        (21) RankingReductionPairProof [EQUIVALENT, 0 ms]
        (22) YES


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

(0)
Obligation:
Rules:
f1_0_main_Load(arg1, arg2, arg3, arg4, arg5) -> f1938_0_main_InvokeMethod(arg1P, arg2P, arg3P, arg4P, arg5P) :|: 2 <= arg2P - 1 && 0 <= arg1P - 1 && 0 <= arg1 - 1 && arg1P <= arg1
f456_0_createTree_Return(x, x1, x2, x3, x4) -> f1938_0_main_InvokeMethod(x5, x6, x7, x8, x9) :|: x3 = x8 && x2 = x7 && x3 + 2 <= x1 && 2 <= x6 - 1 && 0 <= x5 - 1 && 2 <= x1 - 1 && 0 <= x - 1 && x6 <= x1 && x5 + 2 <= x1 && x5 <= x
f1_0_main_Load(x10, x11, x12, x13, x14) -> f1893_0_createTree_LE(x15, x16, x17, x18, x19) :|: 1 = x18 && 2 <= x16 - 1 && 2 <= x15 - 1 && 0 <= x10 - 1 && x16 - 2 <= x10 && x15 - 2 <= x10 && -1 <= x11 - 1 && 0 <= x17 - 1
f1893_0_createTree_LE(x20, x21, x22, x23, x24) -> f1893_0_createTree_LE(x25, x26, x27, x28, x29) :|: x23 + 1 = x28 && x22 - 1 = x27 && 0 <= x26 - 1 && 2 <= x25 - 1 && 2 <= x21 - 1 && 2 <= x20 - 1 && x26 + 2 <= x21 && x25 <= x20 && 0 <= x22 - 1 && -1 <= x23 - 1
f1893_0_createTree_LE(x31, x32, x33, x34, x35) -> f1893_0_createTree_LE(x36, x38, x39, x40, x41) :|: 0 <= x33 - 1 && 0 <= x42 - 1 && -1 <= x34 - 1 && x36 <= x31 && x38 + 2 <= x32 && 2 <= x31 - 1 && 2 <= x32 - 1 && 2 <= x36 - 1 && 0 <= x38 - 1 && x33 - 1 = x39 && x34 + 1 = x40
f1893_0_createTree_LE(x43, x44, x45, x46, x47) -> f1893_0_createTree_LE(x48, x49, x50, x51, x52) :|: 0 <= x45 - 1 && 0 <= x53 - 1 && -1 <= x46 - 1 && 2 <= x43 - 1 && 1 <= x44 - 1 && 2 <= x48 - 1 && 2 <= x49 - 1 && x45 - 1 = x50 && x46 + 1 = x51
f1893_0_createTree_LE(x54, x55, x57, x58, x59) -> f1893_0_createTree_LE(x60, x61, x62, x63, x64) :|: x58 + 1 = x63 && x57 - 1 = x62 && 2 <= x61 - 1 && 2 <= x60 - 1 && 1 <= x55 - 1 && 2 <= x54 - 1 && 0 <= x57 - 1 && -1 <= x58 - 1
f1893_0_createTree_LE(x65, x66, x67, x68, x69) -> f1893_0_createTree_LE(x70, x71, x72, x73, x74) :|: x68 + 1 = x73 && x67 - 1 = x72 && 4 <= x71 - 1 && 4 <= x70 - 1 && 2 <= x66 - 1 && 2 <= x65 - 1 && x71 - 2 <= x66 && x71 - 2 <= x65 && x70 - 2 <= x66 && x70 - 2 <= x65 && 0 <= x67 - 1 && -1 <= x68 - 1
f1893_0_createTree_LE(x76, x77, x78, x79, x80) -> f1893_0_createTree_LE(x81, x82, x84, x85, x86) :|: 0 <= x78 - 1 && 0 <= x87 - 1 && -1 <= x79 - 1 && x81 - 2 <= x76 && x81 - 2 <= x77 && x82 - 2 <= x76 && x82 - 2 <= x77 && 2 <= x76 - 1 && 2 <= x77 - 1 && 4 <= x81 - 1 && 4 <= x82 - 1 && x78 - 1 = x84 && x79 + 1 = x85
f1_0_main_Load(x88, x89, x91, x92, x93) -> f1821_0_duplicateRandomPath_NULL(x94, x95, x96, x97, x98) :|: 1 = x97 && x89 = x96 && -1 <= x95 - 1 && -1 <= x94 - 1 && 0 <= x88 - 1 && x95 + 1 <= x88 && 0 <= x89 - 1 && x94 + 1 <= x88
f1938_0_main_InvokeMethod(x99, x100, x101, x102, x103) -> f1821_0_duplicateRandomPath_NULL(x104, x105, x106, x107, x108) :|: x101 = x107 && x102 + 2 <= x100 && 2 <= x105 - 1 && 2 <= x104 - 1 && 2 <= x100 - 1 && 0 <= x99 - 1 && x105 <= x100 && 0 <= x106 - 1 && x104 <= x100
f1821_0_duplicateRandomPath_NULL(x109, x110, x111, x112, x113) -> f1989_0_duplicateRandomPath_NULL(x114, x115, x116, x117, x118) :|: -1 <= x111 - 1 && 41 <= x119 - 1 && -1 <= x112 - 1 && x114 <= x109 && x114 <= x110 && x115 + 1 <= x109 && x115 + 1 <= x110 && 0 <= x109 - 1 && 0 <= x110 - 1 && 0 <= x114 - 1 && -1 <= x115 - 1 && x118 + 2 <= x109 && x118 + 2 <= x110 && x111 = x116 && x112 + 1 = x117
f1821_0_duplicateRandomPath_NULL(x120, x121, x122, x123, x124) -> f1989_0_duplicateRandomPath_NULL(x125, x126, x127, x128, x129) :|: -1 <= x122 - 1 && -1 <= x123 - 1 && x130 <= 41 && -1 <= x130 - 1 && x125 <= x120 && x125 <= x121 && x126 + 2 <= x120 && x126 + 2 <= x121 && 1 <= x120 - 1 && 1 <= x121 - 1 && 1 <= x125 - 1 && -1 <= x126 - 1 && x129 + 2 <= x120 && x129 + 2 <= x121 && x122 = x127 && x123 + 1 = x128
f1821_0_duplicateRandomPath_NULL(x131, x132, x133, x134, x135) -> f1821_0_duplicateRandomPath_NULL(x136, x137, x138, x139, x140) :|: -1 <= x133 - 1 && -1 <= x134 - 1 && x141 <= 41 && -1 <= x141 - 1 && x136 + 2 <= x131 && x136 + 2 <= x132 && x137 + 2 <= x131 && x137 + 2 <= x132 && 2 <= x131 - 1 && 2 <= x132 - 1 && 0 <= x136 - 1 && 0 <= x137 - 1 && x133 = x138 && x134 + 1 = x139
f1989_0_duplicateRandomPath_NULL(x142, x143, x144, x145, x146) -> f1821_0_duplicateRandomPath_NULL(x147, x148, x149, x150, x151) :|: x145 = x150 && x144 = x149 && x146 + 2 <= x142 && 0 <= x148 - 1 && 0 <= x147 - 1 && 0 <= x143 - 1 && 2 <= x142 - 1 && x148 <= x143 && x148 + 2 <= x142 && x147 <= x143 && x147 + 2 <= x142
__init(x152, x153, x154, x155, x156) -> f1_0_main_Load(x157, x158, x159, x160, x161) :|: 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_Load(arg1, arg2, arg3, arg4, arg5) -> f1938_0_main_InvokeMethod(arg1P, arg2P, arg3P, arg4P, arg5P) :|: 2 <= arg2P - 1 && 0 <= arg1P - 1 && 0 <= arg1 - 1 && arg1P <= arg1
f456_0_createTree_Return(x, x1, x2, x3, x4) -> f1938_0_main_InvokeMethod(x5, x6, x7, x8, x9) :|: x3 = x8 && x2 = x7 && x3 + 2 <= x1 && 2 <= x6 - 1 && 0 <= x5 - 1 && 2 <= x1 - 1 && 0 <= x - 1 && x6 <= x1 && x5 + 2 <= x1 && x5 <= x
f1_0_main_Load(x10, x11, x12, x13, x14) -> f1893_0_createTree_LE(x15, x16, x17, x18, x19) :|: 1 = x18 && 2 <= x16 - 1 && 2 <= x15 - 1 && 0 <= x10 - 1 && x16 - 2 <= x10 && x15 - 2 <= x10 && -1 <= x11 - 1 && 0 <= x17 - 1
f1893_0_createTree_LE(x20, x21, x22, x23, x24) -> f1893_0_createTree_LE(x25, x26, x27, x28, x29) :|: x23 + 1 = x28 && x22 - 1 = x27 && 0 <= x26 - 1 && 2 <= x25 - 1 && 2 <= x21 - 1 && 2 <= x20 - 1 && x26 + 2 <= x21 && x25 <= x20 && 0 <= x22 - 1 && -1 <= x23 - 1
f1893_0_createTree_LE(x31, x32, x33, x34, x35) -> f1893_0_createTree_LE(x36, x38, x39, x40, x41) :|: 0 <= x33 - 1 && 0 <= x42 - 1 && -1 <= x34 - 1 && x36 <= x31 && x38 + 2 <= x32 && 2 <= x31 - 1 && 2 <= x32 - 1 && 2 <= x36 - 1 && 0 <= x38 - 1 && x33 - 1 = x39 && x34 + 1 = x40
f1893_0_createTree_LE(x43, x44, x45, x46, x47) -> f1893_0_createTree_LE(x48, x49, x50, x51, x52) :|: 0 <= x45 - 1 && 0 <= x53 - 1 && -1 <= x46 - 1 && 2 <= x43 - 1 && 1 <= x44 - 1 && 2 <= x48 - 1 && 2 <= x49 - 1 && x45 - 1 = x50 && x46 + 1 = x51
f1893_0_createTree_LE(x54, x55, x57, x58, x59) -> f1893_0_createTree_LE(x60, x61, x62, x63, x64) :|: x58 + 1 = x63 && x57 - 1 = x62 && 2 <= x61 - 1 && 2 <= x60 - 1 && 1 <= x55 - 1 && 2 <= x54 - 1 && 0 <= x57 - 1 && -1 <= x58 - 1
f1893_0_createTree_LE(x65, x66, x67, x68, x69) -> f1893_0_createTree_LE(x70, x71, x72, x73, x74) :|: x68 + 1 = x73 && x67 - 1 = x72 && 4 <= x71 - 1 && 4 <= x70 - 1 && 2 <= x66 - 1 && 2 <= x65 - 1 && x71 - 2 <= x66 && x71 - 2 <= x65 && x70 - 2 <= x66 && x70 - 2 <= x65 && 0 <= x67 - 1 && -1 <= x68 - 1
f1893_0_createTree_LE(x76, x77, x78, x79, x80) -> f1893_0_createTree_LE(x81, x82, x84, x85, x86) :|: 0 <= x78 - 1 && 0 <= x87 - 1 && -1 <= x79 - 1 && x81 - 2 <= x76 && x81 - 2 <= x77 && x82 - 2 <= x76 && x82 - 2 <= x77 && 2 <= x76 - 1 && 2 <= x77 - 1 && 4 <= x81 - 1 && 4 <= x82 - 1 && x78 - 1 = x84 && x79 + 1 = x85
f1_0_main_Load(x88, x89, x91, x92, x93) -> f1821_0_duplicateRandomPath_NULL(x94, x95, x96, x97, x98) :|: 1 = x97 && x89 = x96 && -1 <= x95 - 1 && -1 <= x94 - 1 && 0 <= x88 - 1 && x95 + 1 <= x88 && 0 <= x89 - 1 && x94 + 1 <= x88
f1938_0_main_InvokeMethod(x99, x100, x101, x102, x103) -> f1821_0_duplicateRandomPath_NULL(x104, x105, x106, x107, x108) :|: x101 = x107 && x102 + 2 <= x100 && 2 <= x105 - 1 && 2 <= x104 - 1 && 2 <= x100 - 1 && 0 <= x99 - 1 && x105 <= x100 && 0 <= x106 - 1 && x104 <= x100
f1821_0_duplicateRandomPath_NULL(x109, x110, x111, x112, x113) -> f1989_0_duplicateRandomPath_NULL(x114, x115, x116, x117, x118) :|: -1 <= x111 - 1 && 41 <= x119 - 1 && -1 <= x112 - 1 && x114 <= x109 && x114 <= x110 && x115 + 1 <= x109 && x115 + 1 <= x110 && 0 <= x109 - 1 && 0 <= x110 - 1 && 0 <= x114 - 1 && -1 <= x115 - 1 && x118 + 2 <= x109 && x118 + 2 <= x110 && x111 = x116 && x112 + 1 = x117
f1821_0_duplicateRandomPath_NULL(x120, x121, x122, x123, x124) -> f1989_0_duplicateRandomPath_NULL(x125, x126, x127, x128, x129) :|: -1 <= x122 - 1 && -1 <= x123 - 1 && x130 <= 41 && -1 <= x130 - 1 && x125 <= x120 && x125 <= x121 && x126 + 2 <= x120 && x126 + 2 <= x121 && 1 <= x120 - 1 && 1 <= x121 - 1 && 1 <= x125 - 1 && -1 <= x126 - 1 && x129 + 2 <= x120 && x129 + 2 <= x121 && x122 = x127 && x123 + 1 = x128
f1821_0_duplicateRandomPath_NULL(x131, x132, x133, x134, x135) -> f1821_0_duplicateRandomPath_NULL(x136, x137, x138, x139, x140) :|: -1 <= x133 - 1 && -1 <= x134 - 1 && x141 <= 41 && -1 <= x141 - 1 && x136 + 2 <= x131 && x136 + 2 <= x132 && x137 + 2 <= x131 && x137 + 2 <= x132 && 2 <= x131 - 1 && 2 <= x132 - 1 && 0 <= x136 - 1 && 0 <= x137 - 1 && x133 = x138 && x134 + 1 = x139
f1989_0_duplicateRandomPath_NULL(x142, x143, x144, x145, x146) -> f1821_0_duplicateRandomPath_NULL(x147, x148, x149, x150, x151) :|: x145 = x150 && x144 = x149 && x146 + 2 <= x142 && 0 <= x148 - 1 && 0 <= x147 - 1 && 0 <= x143 - 1 && 2 <= x142 - 1 && x148 <= x143 && x148 + 2 <= x142 && x147 <= x143 && x147 + 2 <= x142
__init(x152, x153, x154, x155, x156) -> f1_0_main_Load(x157, x158, x159, x160, x161) :|: 0 <= 0
Start term: __init(arg1, arg2, arg3, arg4, arg5)

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

(3) IRSwTTerminationDigraphProof (EQUIVALENT)
Constructed termination digraph!
Nodes:
(1) f1_0_main_Load(arg1, arg2, arg3, arg4, arg5) -> f1938_0_main_InvokeMethod(arg1P, arg2P, arg3P, arg4P, arg5P) :|: 2 <= arg2P - 1 && 0 <= arg1P - 1 && 0 <= arg1 - 1 && arg1P <= arg1
(2) f456_0_createTree_Return(x, x1, x2, x3, x4) -> f1938_0_main_InvokeMethod(x5, x6, x7, x8, x9) :|: x3 = x8 && x2 = x7 && x3 + 2 <= x1 && 2 <= x6 - 1 && 0 <= x5 - 1 && 2 <= x1 - 1 && 0 <= x - 1 && x6 <= x1 && x5 + 2 <= x1 && x5 <= x
(3) f1_0_main_Load(x10, x11, x12, x13, x14) -> f1893_0_createTree_LE(x15, x16, x17, x18, x19) :|: 1 = x18 && 2 <= x16 - 1 && 2 <= x15 - 1 && 0 <= x10 - 1 && x16 - 2 <= x10 && x15 - 2 <= x10 && -1 <= x11 - 1 && 0 <= x17 - 1
(4) f1893_0_createTree_LE(x20, x21, x22, x23, x24) -> f1893_0_createTree_LE(x25, x26, x27, x28, x29) :|: x23 + 1 = x28 && x22 - 1 = x27 && 0 <= x26 - 1 && 2 <= x25 - 1 && 2 <= x21 - 1 && 2 <= x20 - 1 && x26 + 2 <= x21 && x25 <= x20 && 0 <= x22 - 1 && -1 <= x23 - 1
(5) f1893_0_createTree_LE(x31, x32, x33, x34, x35) -> f1893_0_createTree_LE(x36, x38, x39, x40, x41) :|: 0 <= x33 - 1 && 0 <= x42 - 1 && -1 <= x34 - 1 && x36 <= x31 && x38 + 2 <= x32 && 2 <= x31 - 1 && 2 <= x32 - 1 && 2 <= x36 - 1 && 0 <= x38 - 1 && x33 - 1 = x39 && x34 + 1 = x40
(6) f1893_0_createTree_LE(x43, x44, x45, x46, x47) -> f1893_0_createTree_LE(x48, x49, x50, x51, x52) :|: 0 <= x45 - 1 && 0 <= x53 - 1 && -1 <= x46 - 1 && 2 <= x43 - 1 && 1 <= x44 - 1 && 2 <= x48 - 1 && 2 <= x49 - 1 && x45 - 1 = x50 && x46 + 1 = x51
(7) f1893_0_createTree_LE(x54, x55, x57, x58, x59) -> f1893_0_createTree_LE(x60, x61, x62, x63, x64) :|: x58 + 1 = x63 && x57 - 1 = x62 && 2 <= x61 - 1 && 2 <= x60 - 1 && 1 <= x55 - 1 && 2 <= x54 - 1 && 0 <= x57 - 1 && -1 <= x58 - 1
(8) f1893_0_createTree_LE(x65, x66, x67, x68, x69) -> f1893_0_createTree_LE(x70, x71, x72, x73, x74) :|: x68 + 1 = x73 && x67 - 1 = x72 && 4 <= x71 - 1 && 4 <= x70 - 1 && 2 <= x66 - 1 && 2 <= x65 - 1 && x71 - 2 <= x66 && x71 - 2 <= x65 && x70 - 2 <= x66 && x70 - 2 <= x65 && 0 <= x67 - 1 && -1 <= x68 - 1
(9) f1893_0_createTree_LE(x76, x77, x78, x79, x80) -> f1893_0_createTree_LE(x81, x82, x84, x85, x86) :|: 0 <= x78 - 1 && 0 <= x87 - 1 && -1 <= x79 - 1 && x81 - 2 <= x76 && x81 - 2 <= x77 && x82 - 2 <= x76 && x82 - 2 <= x77 && 2 <= x76 - 1 && 2 <= x77 - 1 && 4 <= x81 - 1 && 4 <= x82 - 1 && x78 - 1 = x84 && x79 + 1 = x85
(10) f1_0_main_Load(x88, x89, x91, x92, x93) -> f1821_0_duplicateRandomPath_NULL(x94, x95, x96, x97, x98) :|: 1 = x97 && x89 = x96 && -1 <= x95 - 1 && -1 <= x94 - 1 && 0 <= x88 - 1 && x95 + 1 <= x88 && 0 <= x89 - 1 && x94 + 1 <= x88
(11) f1938_0_main_InvokeMethod(x99, x100, x101, x102, x103) -> f1821_0_duplicateRandomPath_NULL(x104, x105, x106, x107, x108) :|: x101 = x107 && x102 + 2 <= x100 && 2 <= x105 - 1 && 2 <= x104 - 1 && 2 <= x100 - 1 && 0 <= x99 - 1 && x105 <= x100 && 0 <= x106 - 1 && x104 <= x100
(12) f1821_0_duplicateRandomPath_NULL(x109, x110, x111, x112, x113) -> f1989_0_duplicateRandomPath_NULL(x114, x115, x116, x117, x118) :|: -1 <= x111 - 1 && 41 <= x119 - 1 && -1 <= x112 - 1 && x114 <= x109 && x114 <= x110 && x115 + 1 <= x109 && x115 + 1 <= x110 && 0 <= x109 - 1 && 0 <= x110 - 1 && 0 <= x114 - 1 && -1 <= x115 - 1 && x118 + 2 <= x109 && x118 + 2 <= x110 && x111 = x116 && x112 + 1 = x117
(13) f1821_0_duplicateRandomPath_NULL(x120, x121, x122, x123, x124) -> f1989_0_duplicateRandomPath_NULL(x125, x126, x127, x128, x129) :|: -1 <= x122 - 1 && -1 <= x123 - 1 && x130 <= 41 && -1 <= x130 - 1 && x125 <= x120 && x125 <= x121 && x126 + 2 <= x120 && x126 + 2 <= x121 && 1 <= x120 - 1 && 1 <= x121 - 1 && 1 <= x125 - 1 && -1 <= x126 - 1 && x129 + 2 <= x120 && x129 + 2 <= x121 && x122 = x127 && x123 + 1 = x128
(14) f1821_0_duplicateRandomPath_NULL(x131, x132, x133, x134, x135) -> f1821_0_duplicateRandomPath_NULL(x136, x137, x138, x139, x140) :|: -1 <= x133 - 1 && -1 <= x134 - 1 && x141 <= 41 && -1 <= x141 - 1 && x136 + 2 <= x131 && x136 + 2 <= x132 && x137 + 2 <= x131 && x137 + 2 <= x132 && 2 <= x131 - 1 && 2 <= x132 - 1 && 0 <= x136 - 1 && 0 <= x137 - 1 && x133 = x138 && x134 + 1 = x139
(15) f1989_0_duplicateRandomPath_NULL(x142, x143, x144, x145, x146) -> f1821_0_duplicateRandomPath_NULL(x147, x148, x149, x150, x151) :|: x145 = x150 && x144 = x149 && x146 + 2 <= x142 && 0 <= x148 - 1 && 0 <= x147 - 1 && 0 <= x143 - 1 && 2 <= x142 - 1 && x148 <= x143 && x148 + 2 <= x142 && x147 <= x143 && x147 + 2 <= x142
(16) __init(x152, x153, x154, x155, x156) -> f1_0_main_Load(x157, x158, x159, x160, x161) :|: 0 <= 0

Arcs:
(1) -> (11)
(2) -> (11)
(3) -> (4), (5), (6), (7), (8), (9)
(4) -> (4), (5), (6), (7), (8), (9)
(5) -> (4), (5), (6), (7), (8), (9)
(6) -> (4), (5), (6), (7), (8), (9)
(7) -> (4), (5), (6), (7), (8), (9)
(8) -> (4), (5), (6), (7), (8), (9)
(9) -> (4), (5), (6), (7), (8), (9)
(10) -> (12), (13), (14)
(11) -> (12), (13), (14)
(12) -> (15)
(13) -> (15)
(14) -> (12), (13), (14)
(15) -> (12), (13), (14)
(16) -> (1), (3), (10)

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

(4)
Complex Obligation (AND)

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

(5)
Obligation:

Termination digraph:
Nodes:
(1) f1893_0_createTree_LE(x20, x21, x22, x23, x24) -> f1893_0_createTree_LE(x25, x26, x27, x28, x29) :|: x23 + 1 = x28 && x22 - 1 = x27 && 0 <= x26 - 1 && 2 <= x25 - 1 && 2 <= x21 - 1 && 2 <= x20 - 1 && x26 + 2 <= x21 && x25 <= x20 && 0 <= x22 - 1 && -1 <= x23 - 1
(2) f1893_0_createTree_LE(x31, x32, x33, x34, x35) -> f1893_0_createTree_LE(x36, x38, x39, x40, x41) :|: 0 <= x33 - 1 && 0 <= x42 - 1 && -1 <= x34 - 1 && x36 <= x31 && x38 + 2 <= x32 && 2 <= x31 - 1 && 2 <= x32 - 1 && 2 <= x36 - 1 && 0 <= x38 - 1 && x33 - 1 = x39 && x34 + 1 = x40
(3) f1893_0_createTree_LE(x43, x44, x45, x46, x47) -> f1893_0_createTree_LE(x48, x49, x50, x51, x52) :|: 0 <= x45 - 1 && 0 <= x53 - 1 && -1 <= x46 - 1 && 2 <= x43 - 1 && 1 <= x44 - 1 && 2 <= x48 - 1 && 2 <= x49 - 1 && x45 - 1 = x50 && x46 + 1 = x51
(4) f1893_0_createTree_LE(x54, x55, x57, x58, x59) -> f1893_0_createTree_LE(x60, x61, x62, x63, x64) :|: x58 + 1 = x63 && x57 - 1 = x62 && 2 <= x61 - 1 && 2 <= x60 - 1 && 1 <= x55 - 1 && 2 <= x54 - 1 && 0 <= x57 - 1 && -1 <= x58 - 1
(5) f1893_0_createTree_LE(x65, x66, x67, x68, x69) -> f1893_0_createTree_LE(x70, x71, x72, x73, x74) :|: x68 + 1 = x73 && x67 - 1 = x72 && 4 <= x71 - 1 && 4 <= x70 - 1 && 2 <= x66 - 1 && 2 <= x65 - 1 && x71 - 2 <= x66 && x71 - 2 <= x65 && x70 - 2 <= x66 && x70 - 2 <= x65 && 0 <= x67 - 1 && -1 <= x68 - 1
(6) f1893_0_createTree_LE(x76, x77, x78, x79, x80) -> f1893_0_createTree_LE(x81, x82, x84, x85, x86) :|: 0 <= x78 - 1 && 0 <= x87 - 1 && -1 <= x79 - 1 && x81 - 2 <= x76 && x81 - 2 <= x77 && x82 - 2 <= x76 && x82 - 2 <= x77 && 2 <= x76 - 1 && 2 <= x77 - 1 && 4 <= x81 - 1 && 4 <= x82 - 1 && x78 - 1 = x84 && x79 + 1 = x85

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

This digraph is fully evaluated!

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

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

(7)
Obligation:
Rules:
f1893_0_createTree_LE(x65:0, x66:0, x67:0, x68:0, x69:0) -> f1893_0_createTree_LE(x70:0, x71:0, x67:0 - 1, x68:0 + 1, x74:0) :|: x67:0 > 0 && x68:0 > -1 && x70:0 - 2 <= x65:0 && x70:0 - 2 <= x66:0 && x71:0 - 2 <= x65:0 && x71:0 - 2 <= x66:0 && x65:0 > 2 && x66:0 > 2 && x71:0 > 4 && x70:0 > 4
f1893_0_createTree_LE(x20:0, x21:0, x22:0, x23:0, x24:0) -> f1893_0_createTree_LE(x25:0, x26:0, x22:0 - 1, x23:0 + 1, x29:0) :|: x22:0 > 0 && x23:0 > -1 && x25:0 <= x20:0 && x26:0 + 2 <= x21:0 && x20:0 > 2 && x21:0 > 2 && x26:0 > 0 && x25:0 > 2
f1893_0_createTree_LE(x31:0, x32:0, x33:0, x34:0, x35:0) -> f1893_0_createTree_LE(x36:0, x38:0, x33:0 - 1, x34:0 + 1, x41:0) :|: x36:0 > 2 && x38:0 > 0 && x32:0 > 2 && x31:0 > 2 && x38:0 + 2 <= x32:0 && x36:0 <= x31:0 && x34:0 > -1 && x42:0 > 0 && x33:0 > 0
f1893_0_createTree_LE(x43:0, x44:0, x45:0, x46:0, x47:0) -> f1893_0_createTree_LE(x48:0, x49:0, x45:0 - 1, x46:0 + 1, x52:0) :|: x48:0 > 2 && x49:0 > 2 && x44:0 > 1 && x43:0 > 2 && x46:0 > -1 && x53:0 > 0 && x45:0 > 0
f1893_0_createTree_LE(x76:0, x77:0, x78:0, x79:0, x80:0) -> f1893_0_createTree_LE(x81:0, x82:0, x78:0 - 1, x79:0 + 1, x86:0) :|: x81:0 > 4 && x82:0 > 4 && x77:0 > 2 && x76:0 > 2 && x82:0 - 2 <= x77:0 && x82:0 - 2 <= x76:0 && x81:0 - 2 <= x77:0 && x81:0 - 2 <= x76:0 && x79:0 > -1 && x87:0 > 0 && x78:0 > 0
f1893_0_createTree_LE(x54:0, x55:0, x57:0, x58:0, x59:0) -> f1893_0_createTree_LE(x60:0, x61:0, x57:0 - 1, x58:0 + 1, x64:0) :|: x57:0 > 0 && x58:0 > -1 && x54:0 > 2 && x55:0 > 1 && x61:0 > 2 && x60:0 > 2

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

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

   f1893_0_createTree_LE(x1, x2, x3, x4, x5) -> f1893_0_createTree_LE(x1, x2, x3, x4)

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

(9)
Obligation:
Rules:
f1893_0_createTree_LE(x65:0, x66:0, x67:0, x68:0) -> f1893_0_createTree_LE(x70:0, x71:0, x67:0 - 1, x68:0 + 1) :|: x67:0 > 0 && x68:0 > -1 && x70:0 - 2 <= x65:0 && x70:0 - 2 <= x66:0 && x71:0 - 2 <= x65:0 && x71:0 - 2 <= x66:0 && x65:0 > 2 && x66:0 > 2 && x71:0 > 4 && x70:0 > 4
f1893_0_createTree_LE(x20:0, x21:0, x22:0, x23:0) -> f1893_0_createTree_LE(x25:0, x26:0, x22:0 - 1, x23:0 + 1) :|: x22:0 > 0 && x23:0 > -1 && x25:0 <= x20:0 && x26:0 + 2 <= x21:0 && x20:0 > 2 && x21:0 > 2 && x26:0 > 0 && x25:0 > 2
f1893_0_createTree_LE(x31:0, x32:0, x33:0, x34:0) -> f1893_0_createTree_LE(x36:0, x38:0, x33:0 - 1, x34:0 + 1) :|: x36:0 > 2 && x38:0 > 0 && x32:0 > 2 && x31:0 > 2 && x38:0 + 2 <= x32:0 && x36:0 <= x31:0 && x34:0 > -1 && x42:0 > 0 && x33:0 > 0
f1893_0_createTree_LE(x43:0, x44:0, x45:0, x46:0) -> f1893_0_createTree_LE(x48:0, x49:0, x45:0 - 1, x46:0 + 1) :|: x48:0 > 2 && x49:0 > 2 && x44:0 > 1 && x43:0 > 2 && x46:0 > -1 && x53:0 > 0 && x45:0 > 0
f1893_0_createTree_LE(x76:0, x77:0, x78:0, x79:0) -> f1893_0_createTree_LE(x81:0, x82:0, x78:0 - 1, x79:0 + 1) :|: x81:0 > 4 && x82:0 > 4 && x77:0 > 2 && x76:0 > 2 && x82:0 - 2 <= x77:0 && x82:0 - 2 <= x76:0 && x81:0 - 2 <= x77:0 && x81:0 - 2 <= x76:0 && x79:0 > -1 && x87:0 > 0 && x78:0 > 0
f1893_0_createTree_LE(x54:0, x55:0, x57:0, x58:0) -> f1893_0_createTree_LE(x60:0, x61:0, x57:0 - 1, x58:0 + 1) :|: x57:0 > 0 && x58:0 > -1 && x54:0 > 2 && x55:0 > 1 && x61:0 > 2 && x60:0 > 2

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

(10) TempFilterProof (SOUND)
Used the following sort dictionary for filtering: 
f1893_0_createTree_LE(INTEGER, INTEGER, INTEGER, INTEGER)
Replaced non-predefined constructor symbols by 0.
----------------------------------------

(11)
Obligation:
Rules:
f1893_0_createTree_LE(x65:0, x66:0, x67:0, x68:0) -> f1893_0_createTree_LE(x70:0, x71:0, c, c1) :|: c1 = x68:0 + 1 && c = x67:0 - 1 && (x67:0 > 0 && x68:0 > -1 && x70:0 - 2 <= x65:0 && x70:0 - 2 <= x66:0 && x71:0 - 2 <= x65:0 && x71:0 - 2 <= x66:0 && x65:0 > 2 && x66:0 > 2 && x71:0 > 4 && x70:0 > 4)
f1893_0_createTree_LE(x20:0, x21:0, x22:0, x23:0) -> f1893_0_createTree_LE(x25:0, x26:0, c2, c3) :|: c3 = x23:0 + 1 && c2 = x22:0 - 1 && (x22:0 > 0 && x23:0 > -1 && x25:0 <= x20:0 && x26:0 + 2 <= x21:0 && x20:0 > 2 && x21:0 > 2 && x26:0 > 0 && x25:0 > 2)
f1893_0_createTree_LE(x31:0, x32:0, x33:0, x34:0) -> f1893_0_createTree_LE(x36:0, x38:0, c4, c5) :|: c5 = x34:0 + 1 && c4 = x33:0 - 1 && (x36:0 > 2 && x38:0 > 0 && x32:0 > 2 && x31:0 > 2 && x38:0 + 2 <= x32:0 && x36:0 <= x31:0 && x34:0 > -1 && x42:0 > 0 && x33:0 > 0)
f1893_0_createTree_LE(x43:0, x44:0, x45:0, x46:0) -> f1893_0_createTree_LE(x48:0, x49:0, c6, c7) :|: c7 = x46:0 + 1 && c6 = x45:0 - 1 && (x48:0 > 2 && x49:0 > 2 && x44:0 > 1 && x43:0 > 2 && x46:0 > -1 && x53:0 > 0 && x45:0 > 0)
f1893_0_createTree_LE(x76:0, x77:0, x78:0, x79:0) -> f1893_0_createTree_LE(x81:0, x82:0, c8, c9) :|: c9 = x79:0 + 1 && c8 = x78:0 - 1 && (x81:0 > 4 && x82:0 > 4 && x77:0 > 2 && x76:0 > 2 && x82:0 - 2 <= x77:0 && x82:0 - 2 <= x76:0 && x81:0 - 2 <= x77:0 && x81:0 - 2 <= x76:0 && x79:0 > -1 && x87:0 > 0 && x78:0 > 0)
f1893_0_createTree_LE(x54:0, x55:0, x57:0, x58:0) -> f1893_0_createTree_LE(x60:0, x61:0, c10, c11) :|: c11 = x58:0 + 1 && c10 = x57:0 - 1 && (x57:0 > 0 && x58:0 > -1 && x54:0 > 2 && x55:0 > 1 && x61:0 > 2 && x60:0 > 2)

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

(12) PolynomialOrderProcessor (EQUIVALENT)
Found the following polynomial interpretation:
[f1893_0_createTree_LE(x, x1, x2, x3)] = x2

The following rules are decreasing:
f1893_0_createTree_LE(x65:0, x66:0, x67:0, x68:0) -> f1893_0_createTree_LE(x70:0, x71:0, c, c1) :|: c1 = x68:0 + 1 && c = x67:0 - 1 && (x67:0 > 0 && x68:0 > -1 && x70:0 - 2 <= x65:0 && x70:0 - 2 <= x66:0 && x71:0 - 2 <= x65:0 && x71:0 - 2 <= x66:0 && x65:0 > 2 && x66:0 > 2 && x71:0 > 4 && x70:0 > 4)
f1893_0_createTree_LE(x20:0, x21:0, x22:0, x23:0) -> f1893_0_createTree_LE(x25:0, x26:0, c2, c3) :|: c3 = x23:0 + 1 && c2 = x22:0 - 1 && (x22:0 > 0 && x23:0 > -1 && x25:0 <= x20:0 && x26:0 + 2 <= x21:0 && x20:0 > 2 && x21:0 > 2 && x26:0 > 0 && x25:0 > 2)
f1893_0_createTree_LE(x31:0, x32:0, x33:0, x34:0) -> f1893_0_createTree_LE(x36:0, x38:0, c4, c5) :|: c5 = x34:0 + 1 && c4 = x33:0 - 1 && (x36:0 > 2 && x38:0 > 0 && x32:0 > 2 && x31:0 > 2 && x38:0 + 2 <= x32:0 && x36:0 <= x31:0 && x34:0 > -1 && x42:0 > 0 && x33:0 > 0)
f1893_0_createTree_LE(x43:0, x44:0, x45:0, x46:0) -> f1893_0_createTree_LE(x48:0, x49:0, c6, c7) :|: c7 = x46:0 + 1 && c6 = x45:0 - 1 && (x48:0 > 2 && x49:0 > 2 && x44:0 > 1 && x43:0 > 2 && x46:0 > -1 && x53:0 > 0 && x45:0 > 0)
f1893_0_createTree_LE(x76:0, x77:0, x78:0, x79:0) -> f1893_0_createTree_LE(x81:0, x82:0, c8, c9) :|: c9 = x79:0 + 1 && c8 = x78:0 - 1 && (x81:0 > 4 && x82:0 > 4 && x77:0 > 2 && x76:0 > 2 && x82:0 - 2 <= x77:0 && x82:0 - 2 <= x76:0 && x81:0 - 2 <= x77:0 && x81:0 - 2 <= x76:0 && x79:0 > -1 && x87:0 > 0 && x78:0 > 0)
f1893_0_createTree_LE(x54:0, x55:0, x57:0, x58:0) -> f1893_0_createTree_LE(x60:0, x61:0, c10, c11) :|: c11 = x58:0 + 1 && c10 = x57:0 - 1 && (x57:0 > 0 && x58:0 > -1 && x54:0 > 2 && x55:0 > 1 && x61:0 > 2 && x60:0 > 2)
The following rules are bounded:
f1893_0_createTree_LE(x65:0, x66:0, x67:0, x68:0) -> f1893_0_createTree_LE(x70:0, x71:0, c, c1) :|: c1 = x68:0 + 1 && c = x67:0 - 1 && (x67:0 > 0 && x68:0 > -1 && x70:0 - 2 <= x65:0 && x70:0 - 2 <= x66:0 && x71:0 - 2 <= x65:0 && x71:0 - 2 <= x66:0 && x65:0 > 2 && x66:0 > 2 && x71:0 > 4 && x70:0 > 4)
f1893_0_createTree_LE(x20:0, x21:0, x22:0, x23:0) -> f1893_0_createTree_LE(x25:0, x26:0, c2, c3) :|: c3 = x23:0 + 1 && c2 = x22:0 - 1 && (x22:0 > 0 && x23:0 > -1 && x25:0 <= x20:0 && x26:0 + 2 <= x21:0 && x20:0 > 2 && x21:0 > 2 && x26:0 > 0 && x25:0 > 2)
f1893_0_createTree_LE(x31:0, x32:0, x33:0, x34:0) -> f1893_0_createTree_LE(x36:0, x38:0, c4, c5) :|: c5 = x34:0 + 1 && c4 = x33:0 - 1 && (x36:0 > 2 && x38:0 > 0 && x32:0 > 2 && x31:0 > 2 && x38:0 + 2 <= x32:0 && x36:0 <= x31:0 && x34:0 > -1 && x42:0 > 0 && x33:0 > 0)
f1893_0_createTree_LE(x43:0, x44:0, x45:0, x46:0) -> f1893_0_createTree_LE(x48:0, x49:0, c6, c7) :|: c7 = x46:0 + 1 && c6 = x45:0 - 1 && (x48:0 > 2 && x49:0 > 2 && x44:0 > 1 && x43:0 > 2 && x46:0 > -1 && x53:0 > 0 && x45:0 > 0)
f1893_0_createTree_LE(x76:0, x77:0, x78:0, x79:0) -> f1893_0_createTree_LE(x81:0, x82:0, c8, c9) :|: c9 = x79:0 + 1 && c8 = x78:0 - 1 && (x81:0 > 4 && x82:0 > 4 && x77:0 > 2 && x76:0 > 2 && x82:0 - 2 <= x77:0 && x82:0 - 2 <= x76:0 && x81:0 - 2 <= x77:0 && x81:0 - 2 <= x76:0 && x79:0 > -1 && x87:0 > 0 && x78:0 > 0)
f1893_0_createTree_LE(x54:0, x55:0, x57:0, x58:0) -> f1893_0_createTree_LE(x60:0, x61:0, c10, c11) :|: c11 = x58:0 + 1 && c10 = x57:0 - 1 && (x57:0 > 0 && x58:0 > -1 && x54:0 > 2 && x55:0 > 1 && x61:0 > 2 && x60:0 > 2)

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

(13)
YES

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

(14)
Obligation:

Termination digraph:
Nodes:
(1) f1821_0_duplicateRandomPath_NULL(x109, x110, x111, x112, x113) -> f1989_0_duplicateRandomPath_NULL(x114, x115, x116, x117, x118) :|: -1 <= x111 - 1 && 41 <= x119 - 1 && -1 <= x112 - 1 && x114 <= x109 && x114 <= x110 && x115 + 1 <= x109 && x115 + 1 <= x110 && 0 <= x109 - 1 && 0 <= x110 - 1 && 0 <= x114 - 1 && -1 <= x115 - 1 && x118 + 2 <= x109 && x118 + 2 <= x110 && x111 = x116 && x112 + 1 = x117
(2) f1821_0_duplicateRandomPath_NULL(x131, x132, x133, x134, x135) -> f1821_0_duplicateRandomPath_NULL(x136, x137, x138, x139, x140) :|: -1 <= x133 - 1 && -1 <= x134 - 1 && x141 <= 41 && -1 <= x141 - 1 && x136 + 2 <= x131 && x136 + 2 <= x132 && x137 + 2 <= x131 && x137 + 2 <= x132 && 2 <= x131 - 1 && 2 <= x132 - 1 && 0 <= x136 - 1 && 0 <= x137 - 1 && x133 = x138 && x134 + 1 = x139
(3) f1989_0_duplicateRandomPath_NULL(x142, x143, x144, x145, x146) -> f1821_0_duplicateRandomPath_NULL(x147, x148, x149, x150, x151) :|: x145 = x150 && x144 = x149 && x146 + 2 <= x142 && 0 <= x148 - 1 && 0 <= x147 - 1 && 0 <= x143 - 1 && 2 <= x142 - 1 && x148 <= x143 && x148 + 2 <= x142 && x147 <= x143 && x147 + 2 <= x142
(4) f1821_0_duplicateRandomPath_NULL(x120, x121, x122, x123, x124) -> f1989_0_duplicateRandomPath_NULL(x125, x126, x127, x128, x129) :|: -1 <= x122 - 1 && -1 <= x123 - 1 && x130 <= 41 && -1 <= x130 - 1 && x125 <= x120 && x125 <= x121 && x126 + 2 <= x120 && x126 + 2 <= x121 && 1 <= x120 - 1 && 1 <= x121 - 1 && 1 <= x125 - 1 && -1 <= x126 - 1 && x129 + 2 <= x120 && x129 + 2 <= x121 && x122 = x127 && x123 + 1 = x128

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

This digraph is fully evaluated!

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

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

(16)
Obligation:
Rules:
f1821_0_duplicateRandomPath_NULL(x131:0, x132:0, x133:0, x134:0, x135:0) -> f1821_0_duplicateRandomPath_NULL(x136:0, x137:0, x133:0, x134:0 + 1, x140:0) :|: x136:0 > 0 && x137:0 > 0 && x132:0 > 2 && x131:0 > 2 && x137:0 + 2 <= x132:0 && x137:0 + 2 <= x131:0 && x136:0 + 2 <= x132:0 && x136:0 + 2 <= x131:0 && x141:0 > -1 && x141:0 < 42 && x134:0 > -1 && x133:0 > -1
f1821_0_duplicateRandomPath_NULL(x109:0, x110:0, x111:0, x112:0, x113:0) -> f1821_0_duplicateRandomPath_NULL(x147:0, x148:0, x111:0, x112:0 + 1, x151:0) :|: x147:0 <= x115:0 && x147:0 + 2 <= x114:0 && x118:0 + 2 <= x110:0 && x148:0 + 2 <= x114:0 && x118:0 + 2 <= x109:0 && x148:0 <= x115:0 && x110:0 > 0 && x147:0 > 0 && x109:0 > 0 && x148:0 > 0 && x115:0 + 1 <= x110:0 && x118:0 + 2 <= x114:0 && x115:0 + 1 <= x109:0 && x114:0 <= x110:0 && x114:0 <= x109:0 && x112:0 > -1 && x111:0 > -1 && x119:0 > 41 && x115:0 > 0 && x114:0 > 2
f1821_0_duplicateRandomPath_NULL(x, x1, x2, x3, x4) -> f1821_0_duplicateRandomPath_NULL(x5, x6, x2, x3 + 1, x7) :|: x5 <= x8 && x5 + 2 <= x9 && x10 + 2 <= x1 && x6 + 2 <= x9 && x10 + 2 <= x && x6 <= x8 && x1 > 1 && x5 > 0 && x > 1 && x6 > 0 && x8 + 2 <= x1 && x10 + 2 <= x9 && x8 + 2 <= x && x9 <= x1 && x9 <= x && x11 > -1 && x11 < 42 && x2 > -1 && x3 > -1 && x8 > 0 && x9 > 2

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

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

   f1821_0_duplicateRandomPath_NULL(x1, x2, x3, x4, x5) -> f1821_0_duplicateRandomPath_NULL(x1, x2, x3, x4)

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

(18)
Obligation:
Rules:
f1821_0_duplicateRandomPath_NULL(x131:0, x132:0, x133:0, x134:0) -> f1821_0_duplicateRandomPath_NULL(x136:0, x137:0, x133:0, x134:0 + 1) :|: x136:0 > 0 && x137:0 > 0 && x132:0 > 2 && x131:0 > 2 && x137:0 + 2 <= x132:0 && x137:0 + 2 <= x131:0 && x136:0 + 2 <= x132:0 && x136:0 + 2 <= x131:0 && x141:0 > -1 && x141:0 < 42 && x134:0 > -1 && x133:0 > -1
f1821_0_duplicateRandomPath_NULL(x109:0, x110:0, x111:0, x112:0) -> f1821_0_duplicateRandomPath_NULL(x147:0, x148:0, x111:0, x112:0 + 1) :|: x147:0 <= x115:0 && x147:0 + 2 <= x114:0 && x118:0 + 2 <= x110:0 && x148:0 + 2 <= x114:0 && x118:0 + 2 <= x109:0 && x148:0 <= x115:0 && x110:0 > 0 && x147:0 > 0 && x109:0 > 0 && x148:0 > 0 && x115:0 + 1 <= x110:0 && x118:0 + 2 <= x114:0 && x115:0 + 1 <= x109:0 && x114:0 <= x110:0 && x114:0 <= x109:0 && x112:0 > -1 && x111:0 > -1 && x119:0 > 41 && x115:0 > 0 && x114:0 > 2
f1821_0_duplicateRandomPath_NULL(x, x1, x2, x3) -> f1821_0_duplicateRandomPath_NULL(x5, x6, x2, x3 + 1) :|: x5 <= x8 && x5 + 2 <= x9 && x10 + 2 <= x1 && x6 + 2 <= x9 && x10 + 2 <= x && x6 <= x8 && x1 > 1 && x5 > 0 && x > 1 && x6 > 0 && x8 + 2 <= x1 && x10 + 2 <= x9 && x8 + 2 <= x && x9 <= x1 && x9 <= x && x11 > -1 && x11 < 42 && x2 > -1 && x3 > -1 && x8 > 0 && x9 > 2

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

(19) TempFilterProof (SOUND)
Used the following sort dictionary for filtering: 
f1821_0_duplicateRandomPath_NULL(INTEGER, INTEGER, INTEGER, INTEGER)
Replaced non-predefined constructor symbols by 0.
----------------------------------------

(20)
Obligation:
Rules:
f1821_0_duplicateRandomPath_NULL(x131:0, x132:0, x133:0, x134:0) -> f1821_0_duplicateRandomPath_NULL(x136:0, x137:0, x133:0, c) :|: c = x134:0 + 1 && (x136:0 > 0 && x137:0 > 0 && x132:0 > 2 && x131:0 > 2 && x137:0 + 2 <= x132:0 && x137:0 + 2 <= x131:0 && x136:0 + 2 <= x132:0 && x136:0 + 2 <= x131:0 && x141:0 > -1 && x141:0 < 42 && x134:0 > -1 && x133:0 > -1)
f1821_0_duplicateRandomPath_NULL(x109:0, x110:0, x111:0, x112:0) -> f1821_0_duplicateRandomPath_NULL(x147:0, x148:0, x111:0, c1) :|: c1 = x112:0 + 1 && (x147:0 <= x115:0 && x147:0 + 2 <= x114:0 && x118:0 + 2 <= x110:0 && x148:0 + 2 <= x114:0 && x118:0 + 2 <= x109:0 && x148:0 <= x115:0 && x110:0 > 0 && x147:0 > 0 && x109:0 > 0 && x148:0 > 0 && x115:0 + 1 <= x110:0 && x118:0 + 2 <= x114:0 && x115:0 + 1 <= x109:0 && x114:0 <= x110:0 && x114:0 <= x109:0 && x112:0 > -1 && x111:0 > -1 && x119:0 > 41 && x115:0 > 0 && x114:0 > 2)
f1821_0_duplicateRandomPath_NULL(x, x1, x2, x3) -> f1821_0_duplicateRandomPath_NULL(x5, x6, x2, c2) :|: c2 = x3 + 1 && (x5 <= x8 && x5 + 2 <= x9 && x10 + 2 <= x1 && x6 + 2 <= x9 && x10 + 2 <= x && x6 <= x8 && x1 > 1 && x5 > 0 && x > 1 && x6 > 0 && x8 + 2 <= x1 && x10 + 2 <= x9 && x8 + 2 <= x && x9 <= x1 && x9 <= x && x11 > -1 && x11 < 42 && x2 > -1 && x3 > -1 && x8 > 0 && x9 > 2)

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

(21) RankingReductionPairProof (EQUIVALENT)
Interpretation:
[ f1821_0_duplicateRandomPath_NULL ] = 1/2*f1821_0_duplicateRandomPath_NULL_2

The following rules are decreasing:
f1821_0_duplicateRandomPath_NULL(x131:0, x132:0, x133:0, x134:0) -> f1821_0_duplicateRandomPath_NULL(x136:0, x137:0, x133:0, c) :|: c = x134:0 + 1 && (x136:0 > 0 && x137:0 > 0 && x132:0 > 2 && x131:0 > 2 && x137:0 + 2 <= x132:0 && x137:0 + 2 <= x131:0 && x136:0 + 2 <= x132:0 && x136:0 + 2 <= x131:0 && x141:0 > -1 && x141:0 < 42 && x134:0 > -1 && x133:0 > -1)
f1821_0_duplicateRandomPath_NULL(x109:0, x110:0, x111:0, x112:0) -> f1821_0_duplicateRandomPath_NULL(x147:0, x148:0, x111:0, c1) :|: c1 = x112:0 + 1 && (x147:0 <= x115:0 && x147:0 + 2 <= x114:0 && x118:0 + 2 <= x110:0 && x148:0 + 2 <= x114:0 && x118:0 + 2 <= x109:0 && x148:0 <= x115:0 && x110:0 > 0 && x147:0 > 0 && x109:0 > 0 && x148:0 > 0 && x115:0 + 1 <= x110:0 && x118:0 + 2 <= x114:0 && x115:0 + 1 <= x109:0 && x114:0 <= x110:0 && x114:0 <= x109:0 && x112:0 > -1 && x111:0 > -1 && x119:0 > 41 && x115:0 > 0 && x114:0 > 2)
f1821_0_duplicateRandomPath_NULL(x, x1, x2, x3) -> f1821_0_duplicateRandomPath_NULL(x5, x6, x2, c2) :|: c2 = x3 + 1 && (x5 <= x8 && x5 + 2 <= x9 && x10 + 2 <= x1 && x6 + 2 <= x9 && x10 + 2 <= x && x6 <= x8 && x1 > 1 && x5 > 0 && x > 1 && x6 > 0 && x8 + 2 <= x1 && x10 + 2 <= x9 && x8 + 2 <= x && x9 <= x1 && x9 <= x && x11 > -1 && x11 < 42 && x2 > -1 && x3 > -1 && x8 > 0 && x9 > 2)

The following rules are bounded:
f1821_0_duplicateRandomPath_NULL(x131:0, x132:0, x133:0, x134:0) -> f1821_0_duplicateRandomPath_NULL(x136:0, x137:0, x133:0, c) :|: c = x134:0 + 1 && (x136:0 > 0 && x137:0 > 0 && x132:0 > 2 && x131:0 > 2 && x137:0 + 2 <= x132:0 && x137:0 + 2 <= x131:0 && x136:0 + 2 <= x132:0 && x136:0 + 2 <= x131:0 && x141:0 > -1 && x141:0 < 42 && x134:0 > -1 && x133:0 > -1)
f1821_0_duplicateRandomPath_NULL(x109:0, x110:0, x111:0, x112:0) -> f1821_0_duplicateRandomPath_NULL(x147:0, x148:0, x111:0, c1) :|: c1 = x112:0 + 1 && (x147:0 <= x115:0 && x147:0 + 2 <= x114:0 && x118:0 + 2 <= x110:0 && x148:0 + 2 <= x114:0 && x118:0 + 2 <= x109:0 && x148:0 <= x115:0 && x110:0 > 0 && x147:0 > 0 && x109:0 > 0 && x148:0 > 0 && x115:0 + 1 <= x110:0 && x118:0 + 2 <= x114:0 && x115:0 + 1 <= x109:0 && x114:0 <= x110:0 && x114:0 <= x109:0 && x112:0 > -1 && x111:0 > -1 && x119:0 > 41 && x115:0 > 0 && x114:0 > 2)
f1821_0_duplicateRandomPath_NULL(x, x1, x2, x3) -> f1821_0_duplicateRandomPath_NULL(x5, x6, x2, c2) :|: c2 = x3 + 1 && (x5 <= x8 && x5 + 2 <= x9 && x10 + 2 <= x1 && x6 + 2 <= x9 && x10 + 2 <= x && x6 <= x8 && x1 > 1 && x5 > 0 && x > 1 && x6 > 0 && x8 + 2 <= x1 && x10 + 2 <= x9 && x8 + 2 <= x && x9 <= x1 && x9 <= x && x11 > -1 && x11 < 42 && x2 > -1 && x3 > -1 && x8 > 0 && x9 > 2)


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(22)
YES