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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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, 2099 ms]
(4) AND
    (5) IRSwT
        (6) IntTRSCompressionProof [EQUIVALENT, 0 ms]
        (7) IRSwT
        (8) TempFilterProof [SOUND, 34 ms]
        (9) IntTRS
        (10) PolynomialOrderProcessor [EQUIVALENT, 0 ms]
        (11) YES
    (12) IRSwT
        (13) IntTRSCompressionProof [EQUIVALENT, 0 ms]
        (14) IRSwT
        (15) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms]
        (16) IRSwT
        (17) FilterProof [EQUIVALENT, 0 ms]
        (18) IntTRS
        (19) IntTRSCompressionProof [EQUIVALENT, 0 ms]
        (20) IntTRS
        (21) IntTRSPeriodicNontermProof [COMPLETE, 7 ms]
        (22) NO
    (23) IRSwT
        (24) IntTRSCompressionProof [EQUIVALENT, 0 ms]
        (25) IRSwT
        (26) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms]
        (27) IRSwT
        (28) FilterProof [EQUIVALENT, 0 ms]
        (29) IntTRS
        (30) IntTRSCompressionProof [EQUIVALENT, 0 ms]
        (31) IntTRS
        (32) IntTRSPeriodicNontermProof [COMPLETE, 0 ms]
        (33) NO


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

(0)
Obligation:
Rules:
f1_0_main_Load(arg1, arg2, arg3, arg4) -> f1797_0_main_InvokeMethod(arg1P, arg2P, arg3P, arg4P) :|: 0 <= arg2P - 1 && 0 <= arg1P - 1 && 0 <= arg1 - 1 && arg1P <= arg1
f462_0_createTree_Return(x, x1, x2, x3) -> f1797_0_main_InvokeMethod(x4, x5, x6, x7) :|: x2 = x6 && x2 + 2 <= x1 && 1 <= x5 - 1 && 0 <= x4 - 1 && 1 <= x1 - 1 && 0 <= x - 1 && x5 <= x1 && x4 + 1 <= x1 && x4 <= x
f1_0_main_Load(x8, x9, x10, x11) -> f1770_0_createTree_LE(x12, x13, x14, x15) :|: 1 = x15 && 1 <= x13 - 1 && 1 <= x12 - 1 && 0 <= x8 - 1 && x13 - 1 <= x8 && x12 - 1 <= x8 && -1 <= x9 - 1 && 0 <= x14 - 1
f1770_0_createTree_LE(x16, x17, x18, x19) -> f1770_0_createTree_LE(x20, x21, x22, x23) :|: x19 + 1 = x23 && x18 - 1 = x22 && 0 <= x21 - 1 && 0 <= x20 - 1 && 2 <= x17 - 1 && 0 <= x16 - 1 && x21 + 2 <= x17 && x20 <= x16 && 0 <= x18 - 1 && -1 <= x19 - 1
f1770_0_createTree_LE(x24, x25, x26, x27) -> f1770_0_createTree_LE(x29, x30, x31, x32) :|: 0 <= x26 - 1 && 0 <= x33 - 1 && -1 <= x27 - 1 && x29 <= x24 && x30 + 2 <= x25 && 0 <= x24 - 1 && 2 <= x25 - 1 && 0 <= x29 - 1 && 0 <= x30 - 1 && x26 - 1 = x31 && x27 + 1 = x32
f1770_0_createTree_LE(x34, x36, x37, x38) -> f1770_0_createTree_LE(x39, x40, x41, x42) :|: 0 <= x37 - 1 && 0 <= x43 - 1 && -1 <= x38 - 1 && 0 <= x34 - 1 && 1 <= x36 - 1 && 0 <= x39 - 1 && 0 <= x40 - 1 && x37 - 1 = x41 && x38 + 1 = x42
f1770_0_createTree_LE(x44, x45, x46, x47) -> f1770_0_createTree_LE(x48, x49, x50, x51) :|: x47 + 1 = x51 && x46 - 1 = x50 && 0 <= x49 - 1 && 0 <= x48 - 1 && 1 <= x45 - 1 && 0 <= x44 - 1 && 0 <= x46 - 1 && -1 <= x47 - 1
f1770_0_createTree_LE(x52, x53, x55, x56) -> f1770_0_createTree_LE(x57, x58, x60, x61) :|: x56 + 1 = x61 && x55 - 1 = x60 && 3 <= x58 - 1 && 3 <= x57 - 1 && 1 <= x53 - 1 && 1 <= x52 - 1 && x58 - 2 <= x53 && x58 - 2 <= x52 && x57 - 2 <= x53 && x57 - 2 <= x52 && 0 <= x55 - 1 && -1 <= x56 - 1
f1770_0_createTree_LE(x62, x63, x64, x65) -> f1770_0_createTree_LE(x66, x67, x68, x69) :|: 0 <= x64 - 1 && 0 <= x70 - 1 && -1 <= x65 - 1 && x66 - 2 <= x62 && x66 - 2 <= x63 && x67 - 2 <= x62 && x67 - 2 <= x63 && 1 <= x62 - 1 && 1 <= x63 - 1 && 3 <= x66 - 1 && 3 <= x67 - 1 && x64 - 1 = x68 && x65 + 1 = x69
f1_0_main_Load(x71, x72, x73, x74) -> f1542_0_count_NULL(x75, x76, x77, x78) :|: -1 <= x76 - 1 && -1 <= x75 - 1 && 0 <= x71 - 1 && x76 + 1 <= x71 && 0 <= x72 - 1 && x75 + 1 <= x71
f1797_0_main_InvokeMethod(x79, x80, x81, x82) -> f1542_0_count_NULL(x83, x84, x85, x86) :|: x83 <= x80 && 0 <= x87 - 1 && x84 <= x80 && 0 <= x79 - 1 && 0 <= x80 - 1 && 0 <= x83 - 1 && 0 <= x84 - 1 && x81 + 2 <= x80
f1542_0_count_NULL(x88, x89, x90, x91) -> f1542_0_count_NULL(x92, x93, x94, x95) :|: -1 <= x93 - 1 && -1 <= x92 - 1 && 1 <= x89 - 1 && 1 <= x88 - 1 && x93 + 2 <= x89 && x93 + 2 <= x88 && x92 + 2 <= x89 && x92 + 2 <= x88
f1542_0_count_NULL(x96, x97, x98, x99) -> f1542_0_count_NULL(x100, x101, x102, x103) :|: -1 <= x101 - 1 && -1 <= x100 - 1 && 2 <= x97 - 1 && 2 <= x96 - 1
f1542_0_count_NULL(x104, x105, x106, x107) -> f2102_0_flatten_NULL(x108, x109, x110, x111) :|: 2 <= x108 - 1 && 2 <= x105 - 1 && 2 <= x104 - 1 && x108 <= x105 && x108 <= x104
f2102_0_flatten_NULL(x112, x113, x114, x115) -> f2102_0_flatten_NULL(x116, x117, x118, x119) :|: -1 <= x116 - 1 && 1 <= x112 - 1 && x116 + 2 <= x112
f2102_0_flatten_NULL(x120, x121, x122, x123) -> f2102_0_flatten_NULL(x124, x125, x126, x127) :|: 2 <= x124 - 1 && 2 <= x120 - 1 && x124 - 2 <= x120
__init(x128, x129, x130, x131) -> f1_0_main_Load(x132, x133, x134, x135) :|: 0 <= 0
Start term: __init(arg1, arg2, arg3, arg4)

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

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

(2)
Obligation:
Rules:
f1_0_main_Load(arg1, arg2, arg3, arg4) -> f1797_0_main_InvokeMethod(arg1P, arg2P, arg3P, arg4P) :|: 0 <= arg2P - 1 && 0 <= arg1P - 1 && 0 <= arg1 - 1 && arg1P <= arg1
f462_0_createTree_Return(x, x1, x2, x3) -> f1797_0_main_InvokeMethod(x4, x5, x6, x7) :|: x2 = x6 && x2 + 2 <= x1 && 1 <= x5 - 1 && 0 <= x4 - 1 && 1 <= x1 - 1 && 0 <= x - 1 && x5 <= x1 && x4 + 1 <= x1 && x4 <= x
f1_0_main_Load(x8, x9, x10, x11) -> f1770_0_createTree_LE(x12, x13, x14, x15) :|: 1 = x15 && 1 <= x13 - 1 && 1 <= x12 - 1 && 0 <= x8 - 1 && x13 - 1 <= x8 && x12 - 1 <= x8 && -1 <= x9 - 1 && 0 <= x14 - 1
f1770_0_createTree_LE(x16, x17, x18, x19) -> f1770_0_createTree_LE(x20, x21, x22, x23) :|: x19 + 1 = x23 && x18 - 1 = x22 && 0 <= x21 - 1 && 0 <= x20 - 1 && 2 <= x17 - 1 && 0 <= x16 - 1 && x21 + 2 <= x17 && x20 <= x16 && 0 <= x18 - 1 && -1 <= x19 - 1
f1770_0_createTree_LE(x24, x25, x26, x27) -> f1770_0_createTree_LE(x29, x30, x31, x32) :|: 0 <= x26 - 1 && 0 <= x33 - 1 && -1 <= x27 - 1 && x29 <= x24 && x30 + 2 <= x25 && 0 <= x24 - 1 && 2 <= x25 - 1 && 0 <= x29 - 1 && 0 <= x30 - 1 && x26 - 1 = x31 && x27 + 1 = x32
f1770_0_createTree_LE(x34, x36, x37, x38) -> f1770_0_createTree_LE(x39, x40, x41, x42) :|: 0 <= x37 - 1 && 0 <= x43 - 1 && -1 <= x38 - 1 && 0 <= x34 - 1 && 1 <= x36 - 1 && 0 <= x39 - 1 && 0 <= x40 - 1 && x37 - 1 = x41 && x38 + 1 = x42
f1770_0_createTree_LE(x44, x45, x46, x47) -> f1770_0_createTree_LE(x48, x49, x50, x51) :|: x47 + 1 = x51 && x46 - 1 = x50 && 0 <= x49 - 1 && 0 <= x48 - 1 && 1 <= x45 - 1 && 0 <= x44 - 1 && 0 <= x46 - 1 && -1 <= x47 - 1
f1770_0_createTree_LE(x52, x53, x55, x56) -> f1770_0_createTree_LE(x57, x58, x60, x61) :|: x56 + 1 = x61 && x55 - 1 = x60 && 3 <= x58 - 1 && 3 <= x57 - 1 && 1 <= x53 - 1 && 1 <= x52 - 1 && x58 - 2 <= x53 && x58 - 2 <= x52 && x57 - 2 <= x53 && x57 - 2 <= x52 && 0 <= x55 - 1 && -1 <= x56 - 1
f1770_0_createTree_LE(x62, x63, x64, x65) -> f1770_0_createTree_LE(x66, x67, x68, x69) :|: 0 <= x64 - 1 && 0 <= x70 - 1 && -1 <= x65 - 1 && x66 - 2 <= x62 && x66 - 2 <= x63 && x67 - 2 <= x62 && x67 - 2 <= x63 && 1 <= x62 - 1 && 1 <= x63 - 1 && 3 <= x66 - 1 && 3 <= x67 - 1 && x64 - 1 = x68 && x65 + 1 = x69
f1_0_main_Load(x71, x72, x73, x74) -> f1542_0_count_NULL(x75, x76, x77, x78) :|: -1 <= x76 - 1 && -1 <= x75 - 1 && 0 <= x71 - 1 && x76 + 1 <= x71 && 0 <= x72 - 1 && x75 + 1 <= x71
f1797_0_main_InvokeMethod(x79, x80, x81, x82) -> f1542_0_count_NULL(x83, x84, x85, x86) :|: x83 <= x80 && 0 <= x87 - 1 && x84 <= x80 && 0 <= x79 - 1 && 0 <= x80 - 1 && 0 <= x83 - 1 && 0 <= x84 - 1 && x81 + 2 <= x80
f1542_0_count_NULL(x88, x89, x90, x91) -> f1542_0_count_NULL(x92, x93, x94, x95) :|: -1 <= x93 - 1 && -1 <= x92 - 1 && 1 <= x89 - 1 && 1 <= x88 - 1 && x93 + 2 <= x89 && x93 + 2 <= x88 && x92 + 2 <= x89 && x92 + 2 <= x88
f1542_0_count_NULL(x96, x97, x98, x99) -> f1542_0_count_NULL(x100, x101, x102, x103) :|: -1 <= x101 - 1 && -1 <= x100 - 1 && 2 <= x97 - 1 && 2 <= x96 - 1
f1542_0_count_NULL(x104, x105, x106, x107) -> f2102_0_flatten_NULL(x108, x109, x110, x111) :|: 2 <= x108 - 1 && 2 <= x105 - 1 && 2 <= x104 - 1 && x108 <= x105 && x108 <= x104
f2102_0_flatten_NULL(x112, x113, x114, x115) -> f2102_0_flatten_NULL(x116, x117, x118, x119) :|: -1 <= x116 - 1 && 1 <= x112 - 1 && x116 + 2 <= x112
f2102_0_flatten_NULL(x120, x121, x122, x123) -> f2102_0_flatten_NULL(x124, x125, x126, x127) :|: 2 <= x124 - 1 && 2 <= x120 - 1 && x124 - 2 <= x120
__init(x128, x129, x130, x131) -> f1_0_main_Load(x132, x133, x134, x135) :|: 0 <= 0
Start term: __init(arg1, arg2, arg3, arg4)

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

(3) IRSwTTerminationDigraphProof (EQUIVALENT)
Constructed termination digraph!
Nodes:
(1) f1_0_main_Load(arg1, arg2, arg3, arg4) -> f1797_0_main_InvokeMethod(arg1P, arg2P, arg3P, arg4P) :|: 0 <= arg2P - 1 && 0 <= arg1P - 1 && 0 <= arg1 - 1 && arg1P <= arg1
(2) f462_0_createTree_Return(x, x1, x2, x3) -> f1797_0_main_InvokeMethod(x4, x5, x6, x7) :|: x2 = x6 && x2 + 2 <= x1 && 1 <= x5 - 1 && 0 <= x4 - 1 && 1 <= x1 - 1 && 0 <= x - 1 && x5 <= x1 && x4 + 1 <= x1 && x4 <= x
(3) f1_0_main_Load(x8, x9, x10, x11) -> f1770_0_createTree_LE(x12, x13, x14, x15) :|: 1 = x15 && 1 <= x13 - 1 && 1 <= x12 - 1 && 0 <= x8 - 1 && x13 - 1 <= x8 && x12 - 1 <= x8 && -1 <= x9 - 1 && 0 <= x14 - 1
(4) f1770_0_createTree_LE(x16, x17, x18, x19) -> f1770_0_createTree_LE(x20, x21, x22, x23) :|: x19 + 1 = x23 && x18 - 1 = x22 && 0 <= x21 - 1 && 0 <= x20 - 1 && 2 <= x17 - 1 && 0 <= x16 - 1 && x21 + 2 <= x17 && x20 <= x16 && 0 <= x18 - 1 && -1 <= x19 - 1
(5) f1770_0_createTree_LE(x24, x25, x26, x27) -> f1770_0_createTree_LE(x29, x30, x31, x32) :|: 0 <= x26 - 1 && 0 <= x33 - 1 && -1 <= x27 - 1 && x29 <= x24 && x30 + 2 <= x25 && 0 <= x24 - 1 && 2 <= x25 - 1 && 0 <= x29 - 1 && 0 <= x30 - 1 && x26 - 1 = x31 && x27 + 1 = x32
(6) f1770_0_createTree_LE(x34, x36, x37, x38) -> f1770_0_createTree_LE(x39, x40, x41, x42) :|: 0 <= x37 - 1 && 0 <= x43 - 1 && -1 <= x38 - 1 && 0 <= x34 - 1 && 1 <= x36 - 1 && 0 <= x39 - 1 && 0 <= x40 - 1 && x37 - 1 = x41 && x38 + 1 = x42
(7) f1770_0_createTree_LE(x44, x45, x46, x47) -> f1770_0_createTree_LE(x48, x49, x50, x51) :|: x47 + 1 = x51 && x46 - 1 = x50 && 0 <= x49 - 1 && 0 <= x48 - 1 && 1 <= x45 - 1 && 0 <= x44 - 1 && 0 <= x46 - 1 && -1 <= x47 - 1
(8) f1770_0_createTree_LE(x52, x53, x55, x56) -> f1770_0_createTree_LE(x57, x58, x60, x61) :|: x56 + 1 = x61 && x55 - 1 = x60 && 3 <= x58 - 1 && 3 <= x57 - 1 && 1 <= x53 - 1 && 1 <= x52 - 1 && x58 - 2 <= x53 && x58 - 2 <= x52 && x57 - 2 <= x53 && x57 - 2 <= x52 && 0 <= x55 - 1 && -1 <= x56 - 1
(9) f1770_0_createTree_LE(x62, x63, x64, x65) -> f1770_0_createTree_LE(x66, x67, x68, x69) :|: 0 <= x64 - 1 && 0 <= x70 - 1 && -1 <= x65 - 1 && x66 - 2 <= x62 && x66 - 2 <= x63 && x67 - 2 <= x62 && x67 - 2 <= x63 && 1 <= x62 - 1 && 1 <= x63 - 1 && 3 <= x66 - 1 && 3 <= x67 - 1 && x64 - 1 = x68 && x65 + 1 = x69
(10) f1_0_main_Load(x71, x72, x73, x74) -> f1542_0_count_NULL(x75, x76, x77, x78) :|: -1 <= x76 - 1 && -1 <= x75 - 1 && 0 <= x71 - 1 && x76 + 1 <= x71 && 0 <= x72 - 1 && x75 + 1 <= x71
(11) f1797_0_main_InvokeMethod(x79, x80, x81, x82) -> f1542_0_count_NULL(x83, x84, x85, x86) :|: x83 <= x80 && 0 <= x87 - 1 && x84 <= x80 && 0 <= x79 - 1 && 0 <= x80 - 1 && 0 <= x83 - 1 && 0 <= x84 - 1 && x81 + 2 <= x80
(12) f1542_0_count_NULL(x88, x89, x90, x91) -> f1542_0_count_NULL(x92, x93, x94, x95) :|: -1 <= x93 - 1 && -1 <= x92 - 1 && 1 <= x89 - 1 && 1 <= x88 - 1 && x93 + 2 <= x89 && x93 + 2 <= x88 && x92 + 2 <= x89 && x92 + 2 <= x88
(13) f1542_0_count_NULL(x96, x97, x98, x99) -> f1542_0_count_NULL(x100, x101, x102, x103) :|: -1 <= x101 - 1 && -1 <= x100 - 1 && 2 <= x97 - 1 && 2 <= x96 - 1
(14) f1542_0_count_NULL(x104, x105, x106, x107) -> f2102_0_flatten_NULL(x108, x109, x110, x111) :|: 2 <= x108 - 1 && 2 <= x105 - 1 && 2 <= x104 - 1 && x108 <= x105 && x108 <= x104
(15) f2102_0_flatten_NULL(x112, x113, x114, x115) -> f2102_0_flatten_NULL(x116, x117, x118, x119) :|: -1 <= x116 - 1 && 1 <= x112 - 1 && x116 + 2 <= x112
(16) f2102_0_flatten_NULL(x120, x121, x122, x123) -> f2102_0_flatten_NULL(x124, x125, x126, x127) :|: 2 <= x124 - 1 && 2 <= x120 - 1 && x124 - 2 <= x120
(17) __init(x128, x129, x130, x131) -> f1_0_main_Load(x132, x133, x134, x135) :|: 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) -> (12), (13), (14)
(13) -> (12), (13), (14)
(14) -> (15), (16)
(15) -> (15), (16)
(16) -> (15), (16)
(17) -> (1), (3), (10)

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

(4)
Complex Obligation (AND)

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

(5)
Obligation:

Termination digraph:
Nodes:
(1) f1770_0_createTree_LE(x16, x17, x18, x19) -> f1770_0_createTree_LE(x20, x21, x22, x23) :|: x19 + 1 = x23 && x18 - 1 = x22 && 0 <= x21 - 1 && 0 <= x20 - 1 && 2 <= x17 - 1 && 0 <= x16 - 1 && x21 + 2 <= x17 && x20 <= x16 && 0 <= x18 - 1 && -1 <= x19 - 1
(2) f1770_0_createTree_LE(x24, x25, x26, x27) -> f1770_0_createTree_LE(x29, x30, x31, x32) :|: 0 <= x26 - 1 && 0 <= x33 - 1 && -1 <= x27 - 1 && x29 <= x24 && x30 + 2 <= x25 && 0 <= x24 - 1 && 2 <= x25 - 1 && 0 <= x29 - 1 && 0 <= x30 - 1 && x26 - 1 = x31 && x27 + 1 = x32
(3) f1770_0_createTree_LE(x34, x36, x37, x38) -> f1770_0_createTree_LE(x39, x40, x41, x42) :|: 0 <= x37 - 1 && 0 <= x43 - 1 && -1 <= x38 - 1 && 0 <= x34 - 1 && 1 <= x36 - 1 && 0 <= x39 - 1 && 0 <= x40 - 1 && x37 - 1 = x41 && x38 + 1 = x42
(4) f1770_0_createTree_LE(x44, x45, x46, x47) -> f1770_0_createTree_LE(x48, x49, x50, x51) :|: x47 + 1 = x51 && x46 - 1 = x50 && 0 <= x49 - 1 && 0 <= x48 - 1 && 1 <= x45 - 1 && 0 <= x44 - 1 && 0 <= x46 - 1 && -1 <= x47 - 1
(5) f1770_0_createTree_LE(x52, x53, x55, x56) -> f1770_0_createTree_LE(x57, x58, x60, x61) :|: x56 + 1 = x61 && x55 - 1 = x60 && 3 <= x58 - 1 && 3 <= x57 - 1 && 1 <= x53 - 1 && 1 <= x52 - 1 && x58 - 2 <= x53 && x58 - 2 <= x52 && x57 - 2 <= x53 && x57 - 2 <= x52 && 0 <= x55 - 1 && -1 <= x56 - 1
(6) f1770_0_createTree_LE(x62, x63, x64, x65) -> f1770_0_createTree_LE(x66, x67, x68, x69) :|: 0 <= x64 - 1 && 0 <= x70 - 1 && -1 <= x65 - 1 && x66 - 2 <= x62 && x66 - 2 <= x63 && x67 - 2 <= x62 && x67 - 2 <= x63 && 1 <= x62 - 1 && 1 <= x63 - 1 && 3 <= x66 - 1 && 3 <= x67 - 1 && x64 - 1 = x68 && x65 + 1 = x69

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:
f1770_0_createTree_LE(x34:0, x36:0, x37:0, x38:0) -> f1770_0_createTree_LE(x39:0, x40:0, x37:0 - 1, x38:0 + 1) :|: x39:0 > 0 && x40:0 > 0 && x36:0 > 1 && x34:0 > 0 && x38:0 > -1 && x43:0 > 0 && x37:0 > 0
f1770_0_createTree_LE(x62:0, x63:0, x64:0, x65:0) -> f1770_0_createTree_LE(x66:0, x67:0, x64:0 - 1, x65:0 + 1) :|: x66:0 > 3 && x67:0 > 3 && x63:0 > 1 && x62:0 > 1 && x67:0 - 2 <= x63:0 && x67:0 - 2 <= x62:0 && x66:0 - 2 <= x63:0 && x66:0 - 2 <= x62:0 && x65:0 > -1 && x70:0 > 0 && x64:0 > 0
f1770_0_createTree_LE(x16:0, x17:0, x18:0, x19:0) -> f1770_0_createTree_LE(x20:0, x21:0, x18:0 - 1, x19:0 + 1) :|: x18:0 > 0 && x19:0 > -1 && x20:0 <= x16:0 && x21:0 + 2 <= x17:0 && x16:0 > 0 && x17:0 > 2 && x21:0 > 0 && x20:0 > 0
f1770_0_createTree_LE(x44:0, x45:0, x46:0, x47:0) -> f1770_0_createTree_LE(x48:0, x49:0, x46:0 - 1, x47:0 + 1) :|: x46:0 > 0 && x47:0 > -1 && x44:0 > 0 && x45:0 > 1 && x49:0 > 0 && x48:0 > 0
f1770_0_createTree_LE(x24:0, x25:0, x26:0, x27:0) -> f1770_0_createTree_LE(x29:0, x30:0, x26:0 - 1, x27:0 + 1) :|: x29:0 > 0 && x30:0 > 0 && x25:0 > 2 && x24:0 > 0 && x30:0 + 2 <= x25:0 && x29:0 <= x24:0 && x27:0 > -1 && x33:0 > 0 && x26:0 > 0
f1770_0_createTree_LE(x52:0, x53:0, x55:0, x56:0) -> f1770_0_createTree_LE(x57:0, x58:0, x55:0 - 1, x56:0 + 1) :|: x55:0 > 0 && x56:0 > -1 && x57:0 - 2 <= x52:0 && x57:0 - 2 <= x53:0 && x58:0 - 2 <= x52:0 && x58:0 - 2 <= x53:0 && x52:0 > 1 && x53:0 > 1 && x58:0 > 3 && x57:0 > 3

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

(8) TempFilterProof (SOUND)
Used the following sort dictionary for filtering: 
f1770_0_createTree_LE(INTEGER, INTEGER, INTEGER, INTEGER)
Replaced non-predefined constructor symbols by 0.
----------------------------------------

(9)
Obligation:
Rules:
f1770_0_createTree_LE(x34:0, x36:0, x37:0, x38:0) -> f1770_0_createTree_LE(x39:0, x40:0, c, c1) :|: c1 = x38:0 + 1 && c = x37:0 - 1 && (x39:0 > 0 && x40:0 > 0 && x36:0 > 1 && x34:0 > 0 && x38:0 > -1 && x43:0 > 0 && x37:0 > 0)
f1770_0_createTree_LE(x62:0, x63:0, x64:0, x65:0) -> f1770_0_createTree_LE(x66:0, x67:0, c2, c3) :|: c3 = x65:0 + 1 && c2 = x64:0 - 1 && (x66:0 > 3 && x67:0 > 3 && x63:0 > 1 && x62:0 > 1 && x67:0 - 2 <= x63:0 && x67:0 - 2 <= x62:0 && x66:0 - 2 <= x63:0 && x66:0 - 2 <= x62:0 && x65:0 > -1 && x70:0 > 0 && x64:0 > 0)
f1770_0_createTree_LE(x16:0, x17:0, x18:0, x19:0) -> f1770_0_createTree_LE(x20:0, x21:0, c4, c5) :|: c5 = x19:0 + 1 && c4 = x18:0 - 1 && (x18:0 > 0 && x19:0 > -1 && x20:0 <= x16:0 && x21:0 + 2 <= x17:0 && x16:0 > 0 && x17:0 > 2 && x21:0 > 0 && x20:0 > 0)
f1770_0_createTree_LE(x44:0, x45:0, x46:0, x47:0) -> f1770_0_createTree_LE(x48:0, x49:0, c6, c7) :|: c7 = x47:0 + 1 && c6 = x46:0 - 1 && (x46:0 > 0 && x47:0 > -1 && x44:0 > 0 && x45:0 > 1 && x49:0 > 0 && x48:0 > 0)
f1770_0_createTree_LE(x24:0, x25:0, x26:0, x27:0) -> f1770_0_createTree_LE(x29:0, x30:0, c8, c9) :|: c9 = x27:0 + 1 && c8 = x26:0 - 1 && (x29:0 > 0 && x30:0 > 0 && x25:0 > 2 && x24:0 > 0 && x30:0 + 2 <= x25:0 && x29:0 <= x24:0 && x27:0 > -1 && x33:0 > 0 && x26:0 > 0)
f1770_0_createTree_LE(x52:0, x53:0, x55:0, x56:0) -> f1770_0_createTree_LE(x57:0, x58:0, c10, c11) :|: c11 = x56:0 + 1 && c10 = x55:0 - 1 && (x55:0 > 0 && x56:0 > -1 && x57:0 - 2 <= x52:0 && x57:0 - 2 <= x53:0 && x58:0 - 2 <= x52:0 && x58:0 - 2 <= x53:0 && x52:0 > 1 && x53:0 > 1 && x58:0 > 3 && x57:0 > 3)

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(10) PolynomialOrderProcessor (EQUIVALENT)
Found the following polynomial interpretation:
[f1770_0_createTree_LE(x, x1, x2, x3)] = x2

The following rules are decreasing:
f1770_0_createTree_LE(x34:0, x36:0, x37:0, x38:0) -> f1770_0_createTree_LE(x39:0, x40:0, c, c1) :|: c1 = x38:0 + 1 && c = x37:0 - 1 && (x39:0 > 0 && x40:0 > 0 && x36:0 > 1 && x34:0 > 0 && x38:0 > -1 && x43:0 > 0 && x37:0 > 0)
f1770_0_createTree_LE(x62:0, x63:0, x64:0, x65:0) -> f1770_0_createTree_LE(x66:0, x67:0, c2, c3) :|: c3 = x65:0 + 1 && c2 = x64:0 - 1 && (x66:0 > 3 && x67:0 > 3 && x63:0 > 1 && x62:0 > 1 && x67:0 - 2 <= x63:0 && x67:0 - 2 <= x62:0 && x66:0 - 2 <= x63:0 && x66:0 - 2 <= x62:0 && x65:0 > -1 && x70:0 > 0 && x64:0 > 0)
f1770_0_createTree_LE(x16:0, x17:0, x18:0, x19:0) -> f1770_0_createTree_LE(x20:0, x21:0, c4, c5) :|: c5 = x19:0 + 1 && c4 = x18:0 - 1 && (x18:0 > 0 && x19:0 > -1 && x20:0 <= x16:0 && x21:0 + 2 <= x17:0 && x16:0 > 0 && x17:0 > 2 && x21:0 > 0 && x20:0 > 0)
f1770_0_createTree_LE(x44:0, x45:0, x46:0, x47:0) -> f1770_0_createTree_LE(x48:0, x49:0, c6, c7) :|: c7 = x47:0 + 1 && c6 = x46:0 - 1 && (x46:0 > 0 && x47:0 > -1 && x44:0 > 0 && x45:0 > 1 && x49:0 > 0 && x48:0 > 0)
f1770_0_createTree_LE(x24:0, x25:0, x26:0, x27:0) -> f1770_0_createTree_LE(x29:0, x30:0, c8, c9) :|: c9 = x27:0 + 1 && c8 = x26:0 - 1 && (x29:0 > 0 && x30:0 > 0 && x25:0 > 2 && x24:0 > 0 && x30:0 + 2 <= x25:0 && x29:0 <= x24:0 && x27:0 > -1 && x33:0 > 0 && x26:0 > 0)
f1770_0_createTree_LE(x52:0, x53:0, x55:0, x56:0) -> f1770_0_createTree_LE(x57:0, x58:0, c10, c11) :|: c11 = x56:0 + 1 && c10 = x55:0 - 1 && (x55:0 > 0 && x56:0 > -1 && x57:0 - 2 <= x52:0 && x57:0 - 2 <= x53:0 && x58:0 - 2 <= x52:0 && x58:0 - 2 <= x53:0 && x52:0 > 1 && x53:0 > 1 && x58:0 > 3 && x57:0 > 3)
The following rules are bounded:
f1770_0_createTree_LE(x34:0, x36:0, x37:0, x38:0) -> f1770_0_createTree_LE(x39:0, x40:0, c, c1) :|: c1 = x38:0 + 1 && c = x37:0 - 1 && (x39:0 > 0 && x40:0 > 0 && x36:0 > 1 && x34:0 > 0 && x38:0 > -1 && x43:0 > 0 && x37:0 > 0)
f1770_0_createTree_LE(x62:0, x63:0, x64:0, x65:0) -> f1770_0_createTree_LE(x66:0, x67:0, c2, c3) :|: c3 = x65:0 + 1 && c2 = x64:0 - 1 && (x66:0 > 3 && x67:0 > 3 && x63:0 > 1 && x62:0 > 1 && x67:0 - 2 <= x63:0 && x67:0 - 2 <= x62:0 && x66:0 - 2 <= x63:0 && x66:0 - 2 <= x62:0 && x65:0 > -1 && x70:0 > 0 && x64:0 > 0)
f1770_0_createTree_LE(x16:0, x17:0, x18:0, x19:0) -> f1770_0_createTree_LE(x20:0, x21:0, c4, c5) :|: c5 = x19:0 + 1 && c4 = x18:0 - 1 && (x18:0 > 0 && x19:0 > -1 && x20:0 <= x16:0 && x21:0 + 2 <= x17:0 && x16:0 > 0 && x17:0 > 2 && x21:0 > 0 && x20:0 > 0)
f1770_0_createTree_LE(x44:0, x45:0, x46:0, x47:0) -> f1770_0_createTree_LE(x48:0, x49:0, c6, c7) :|: c7 = x47:0 + 1 && c6 = x46:0 - 1 && (x46:0 > 0 && x47:0 > -1 && x44:0 > 0 && x45:0 > 1 && x49:0 > 0 && x48:0 > 0)
f1770_0_createTree_LE(x24:0, x25:0, x26:0, x27:0) -> f1770_0_createTree_LE(x29:0, x30:0, c8, c9) :|: c9 = x27:0 + 1 && c8 = x26:0 - 1 && (x29:0 > 0 && x30:0 > 0 && x25:0 > 2 && x24:0 > 0 && x30:0 + 2 <= x25:0 && x29:0 <= x24:0 && x27:0 > -1 && x33:0 > 0 && x26:0 > 0)
f1770_0_createTree_LE(x52:0, x53:0, x55:0, x56:0) -> f1770_0_createTree_LE(x57:0, x58:0, c10, c11) :|: c11 = x56:0 + 1 && c10 = x55:0 - 1 && (x55:0 > 0 && x56:0 > -1 && x57:0 - 2 <= x52:0 && x57:0 - 2 <= x53:0 && x58:0 - 2 <= x52:0 && x58:0 - 2 <= x53:0 && x52:0 > 1 && x53:0 > 1 && x58:0 > 3 && x57:0 > 3)

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

(11)
YES

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

(12)
Obligation:

Termination digraph:
Nodes:
(1) f1542_0_count_NULL(x88, x89, x90, x91) -> f1542_0_count_NULL(x92, x93, x94, x95) :|: -1 <= x93 - 1 && -1 <= x92 - 1 && 1 <= x89 - 1 && 1 <= x88 - 1 && x93 + 2 <= x89 && x93 + 2 <= x88 && x92 + 2 <= x89 && x92 + 2 <= x88
(2) f1542_0_count_NULL(x96, x97, x98, x99) -> f1542_0_count_NULL(x100, x101, x102, x103) :|: -1 <= x101 - 1 && -1 <= x100 - 1 && 2 <= x97 - 1 && 2 <= x96 - 1

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

This digraph is fully evaluated!

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

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

(14)
Obligation:
Rules:
f1542_0_count_NULL(x88:0, x89:0, x90:0, x91:0) -> f1542_0_count_NULL(x92:0, x93:0, x94:0, x95:0) :|: x92:0 + 2 <= x89:0 && x92:0 + 2 <= x88:0 && x93:0 + 2 <= x88:0 && x93:0 + 2 <= x89:0 && x88:0 > 1 && x89:0 > 1 && x92:0 > -1 && x93:0 > -1
f1542_0_count_NULL(x96:0, x97:0, x98:0, x99:0) -> f1542_0_count_NULL(x100:0, x101:0, x102:0, x103:0) :|: x97:0 > 2 && x96:0 > 2 && x100:0 > -1 && x101:0 > -1

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

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

   f1542_0_count_NULL(x1, x2, x3, x4) -> f1542_0_count_NULL(x1, x2)

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

(16)
Obligation:
Rules:
f1542_0_count_NULL(x88:0, x89:0) -> f1542_0_count_NULL(x92:0, x93:0) :|: x92:0 + 2 <= x89:0 && x92:0 + 2 <= x88:0 && x93:0 + 2 <= x88:0 && x93:0 + 2 <= x89:0 && x88:0 > 1 && x89:0 > 1 && x92:0 > -1 && x93:0 > -1
f1542_0_count_NULL(x96:0, x97:0) -> f1542_0_count_NULL(x100:0, x101:0) :|: x97:0 > 2 && x96:0 > 2 && x100:0 > -1 && x101:0 > -1

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

(17) FilterProof (EQUIVALENT)
Used the following sort dictionary for filtering: 
f1542_0_count_NULL(INTEGER, INTEGER)
Replaced non-predefined constructor symbols by 0.
----------------------------------------

(18)
Obligation:
Rules:
f1542_0_count_NULL(x88:0, x89:0) -> f1542_0_count_NULL(x92:0, x93:0) :|: x92:0 + 2 <= x89:0 && x92:0 + 2 <= x88:0 && x93:0 + 2 <= x88:0 && x93:0 + 2 <= x89:0 && x88:0 > 1 && x89:0 > 1 && x92:0 > -1 && x93:0 > -1
f1542_0_count_NULL(x96:0, x97:0) -> f1542_0_count_NULL(x100:0, x101:0) :|: x97:0 > 2 && x96:0 > 2 && x100:0 > -1 && x101:0 > -1

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

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

(20)
Obligation:
Rules:
f1542_0_count_NULL(x96:0:0, x97:0:0) -> f1542_0_count_NULL(x100:0:0, x101:0:0) :|: x100:0:0 > -1 && x101:0:0 > -1 && x96:0:0 > 2 && x97:0:0 > 2
f1542_0_count_NULL(x88:0:0, x89:0:0) -> f1542_0_count_NULL(x92:0:0, x93:0:0) :|: x92:0:0 > -1 && x93:0:0 > -1 && x89:0:0 > 1 && x88:0:0 > 1 && x93:0:0 + 2 <= x89:0:0 && x93:0:0 + 2 <= x88:0:0 && x92:0:0 + 2 <= x88:0:0 && x92:0:0 + 2 <= x89:0:0

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

(21) IntTRSPeriodicNontermProof (COMPLETE)
Normalized system to the following form:
f(pc, x96:0:0, x97:0:0) -> f(1, x100:0:0, x101:0:0) :|: pc = 1 && (x100:0:0 > -1 && x101:0:0 > -1 && x96:0:0 > 2 && x97:0:0 > 2)
f(pc, x88:0:0, x89:0:0) -> f(1, x92:0:0, x93:0:0) :|: pc = 1 && (x92:0:0 > -1 && x93:0:0 > -1 && x89:0:0 > 1 && x88:0:0 > 1 && x93:0:0 + 2 <= x89:0:0 && x93:0:0 + 2 <= x88:0:0 && x92:0:0 + 2 <= x88:0:0 && x92:0:0 + 2 <= x89:0:0)
Witness term starting non-terminating reduction: f(1, 7, 7)
----------------------------------------

(22)
NO

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

(23)
Obligation:

Termination digraph:
Nodes:
(1) f2102_0_flatten_NULL(x112, x113, x114, x115) -> f2102_0_flatten_NULL(x116, x117, x118, x119) :|: -1 <= x116 - 1 && 1 <= x112 - 1 && x116 + 2 <= x112
(2) f2102_0_flatten_NULL(x120, x121, x122, x123) -> f2102_0_flatten_NULL(x124, x125, x126, x127) :|: 2 <= x124 - 1 && 2 <= x120 - 1 && x124 - 2 <= x120

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

This digraph is fully evaluated!

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

(25)
Obligation:
Rules:
f2102_0_flatten_NULL(x112:0, x113:0, x114:0, x115:0) -> f2102_0_flatten_NULL(x116:0, x117:0, x118:0, x119:0) :|: x116:0 > -1 && x112:0 > 1 && x116:0 + 2 <= x112:0
f2102_0_flatten_NULL(x120:0, x121:0, x122:0, x123:0) -> f2102_0_flatten_NULL(x124:0, x125:0, x126:0, x127:0) :|: x124:0 > 2 && x120:0 > 2 && x124:0 - 2 <= x120:0

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

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

   f2102_0_flatten_NULL(x1, x2, x3, x4) -> f2102_0_flatten_NULL(x1)

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

(27)
Obligation:
Rules:
f2102_0_flatten_NULL(x112:0) -> f2102_0_flatten_NULL(x116:0) :|: x116:0 > -1 && x112:0 > 1 && x116:0 + 2 <= x112:0
f2102_0_flatten_NULL(x120:0) -> f2102_0_flatten_NULL(x124:0) :|: x124:0 > 2 && x120:0 > 2 && x124:0 - 2 <= x120:0

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

(28) FilterProof (EQUIVALENT)
Used the following sort dictionary for filtering: 
f2102_0_flatten_NULL(INTEGER)
Replaced non-predefined constructor symbols by 0.
----------------------------------------

(29)
Obligation:
Rules:
f2102_0_flatten_NULL(x112:0) -> f2102_0_flatten_NULL(x116:0) :|: x116:0 > -1 && x112:0 > 1 && x116:0 + 2 <= x112:0
f2102_0_flatten_NULL(x120:0) -> f2102_0_flatten_NULL(x124:0) :|: x124:0 > 2 && x120:0 > 2 && x124:0 - 2 <= x120:0

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

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

(31)
Obligation:
Rules:
f2102_0_flatten_NULL(x112:0:0) -> f2102_0_flatten_NULL(x116:0:0) :|: x116:0:0 > -1 && x112:0:0 > 1 && x116:0:0 + 2 <= x112:0:0
f2102_0_flatten_NULL(x120:0:0) -> f2102_0_flatten_NULL(x124:0:0) :|: x124:0:0 > 2 && x120:0:0 > 2 && x124:0:0 - 2 <= x120:0:0

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

(32) IntTRSPeriodicNontermProof (COMPLETE)
Normalized system to the following form:
f(pc, x112:0:0) -> f(1, x116:0:0) :|: pc = 1 && (x116:0:0 > -1 && x112:0:0 > 1 && x116:0:0 + 2 <= x112:0:0)
f(pc, x120:0:0) -> f(1, x124:0:0) :|: pc = 1 && (x124:0:0 > 2 && x120:0:0 > 2 && x124:0:0 - 2 <= x120:0:0)
Witness term starting non-terminating reduction: f(1, 7)
----------------------------------------

(33)
NO