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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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, 1363 ms]
(4) AND
    (5) IRSwT
        (6) IntTRSCompressionProof [EQUIVALENT, 12 ms]
        (7) IRSwT
        (8) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms]
        (9) IRSwT
        (10) TempFilterProof [SOUND, 10 ms]
        (11) IntTRS
        (12) RankingReductionPairProof [EQUIVALENT, 3 ms]
        (13) YES
    (14) IRSwT
        (15) IntTRSCompressionProof [EQUIVALENT, 5 ms]
        (16) IRSwT
        (17) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms]
        (18) IRSwT
        (19) TempFilterProof [SOUND, 30 ms]
        (20) IntTRS
        (21) PolynomialOrderProcessor [EQUIVALENT, 10 ms]
        (22) YES
    (23) IRSwT
        (24) IntTRSCompressionProof [EQUIVALENT, 4 ms]
        (25) IRSwT
        (26) FilterProof [EQUIVALENT, 0 ms]
        (27) IntTRS
        (28) IntTRSCompressionProof [EQUIVALENT, 0 ms]
        (29) IntTRS
        (30) RankingReductionPairProof [EQUIVALENT, 0 ms]
        (31) YES
    (32) IRSwT
        (33) IntTRSCompressionProof [EQUIVALENT, 9 ms]
        (34) IRSwT
        (35) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms]
        (36) IRSwT
        (37) FilterProof [EQUIVALENT, 0 ms]
        (38) IntTRS
        (39) IntTRSCompressionProof [EQUIVALENT, 2 ms]
        (40) IntTRS
        (41) RankingReductionPairProof [EQUIVALENT, 0 ms]
        (42) YES


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

(0)
Obligation:
Rules:
f1_0_main_Load(arg1, arg2, arg3, arg4) -> f231_0_createList_LE(arg1P, arg2P, arg3P, arg4P) :|: -1 <= arg1P - 1 && 1 <= arg2 - 1 && -1 <= x5 - 1 && arg2P - 1 <= arg1 && arg3P - 1 <= arg1 && 0 <= arg1 - 1 && 1 <= arg2P - 1 && 1 <= arg3P - 1 && x5 - 2 = arg4P
f231_0_createList_LE(x, x1, x2, x3) -> f266_0_createList_LE(x4, x6, x7, x8) :|: x - 1 = x6 && 0 <= x4 - 1 && 0 <= x2 - 1 && x3 <= 0 && 1 <= x1 - 1
f231_0_createList_LE(x9, x10, x11, x12) -> f231_0_createList_LE(x13, x14, x15, x16) :|: x12 - 1 = x16 && x9 = x13 && 2 <= x15 - 1 && 0 <= x14 - 1 && 0 <= x11 - 1 && 0 <= x10 - 1 && x15 - 2 <= x11 && 0 <= x12 - 1 && x14 <= x10
f266_0_createList_LE(x17, x18, x19, x20) -> f266_0_createList_LE(x21, x22, x23, x24) :|: x18 - 1 = x22 && 2 <= x21 - 1 && 0 <= x18 - 1 && 0 <= x17 - 1
f231_0_createList_LE(x25, x26, x27, x28) -> f266_0_createList_LE(x29, x30, x31, x32) :|: x25 - 2 = x30 && 4 <= x29 - 1 && 1 <= x27 - 1 && 1 <= x26 - 1 && x29 - 3 <= x27 && x29 - 3 <= x26 && x28 <= 0 && 1 <= x25 - 1
f231_0_createList_LE(x33, x34, x35, x36) -> f458_0_reverse_NULL(x37, x38, x39, x40) :|: 1 <= x38 - 1 && 1 <= x37 - 1 && 1 <= x35 - 1 && 1 <= x34 - 1 && x38 <= x35 && x38 <= x34 && x37 <= x35 && x37 <= x34 && x36 <= 0 && x33 <= 1
f266_0_createList_LE(x41, x42, x43, x44) -> f458_0_reverse_NULL(x45, x46, x47, x48) :|: -1 <= x46 - 1 && 1 <= x45 - 1 && 0 <= x41 - 1 && x42 <= 0 && x45 - 1 <= x41
f266_0_createList_LE(x49, x50, x51, x52) -> f458_0_reverse_NULL(x53, x54, x55, x56) :|: 0 <= x54 - 1 && 1 <= x53 - 1 && 2 <= x49 - 1 && x50 <= 0 && x53 + 1 <= x49
f266_0_createList_LE(x57, x58, x59, x60) -> f473_0_reverse_FieldAccess(x61, x62, x63, x64) :|: 0 <= x62 - 1 && 1 <= x61 - 1 && 2 <= x57 - 1 && x58 <= 0 && x61 + 1 <= x57
f458_0_reverse_NULL(x65, x66, x67, x68) -> f488_0_reverse_FieldAccess(x69, x70, x71, x72) :|: -1 <= x72 - 1 && 0 <= x71 - 1 && 0 <= x70 - 1 && -1 <= x69 - 1 && 0 <= x66 - 1 && 0 <= x65 - 1 && x72 + 1 <= x66 && x71 <= x65 && x70 <= x66 && x69 + 1 <= x66
f488_0_reverse_FieldAccess(x73, x74, x75, x76) -> f458_0_reverse_NULL(x77, x80, x81, x82) :|: -1 <= x80 - 1 && 2 <= x77 - 1 && -1 <= x76 - 1 && 0 <= x75 - 1 && 0 <= x74 - 1 && -1 <= x73 - 1 && x80 <= x76 && x80 + 1 <= x74 && x80 <= x73
f488_0_reverse_FieldAccess(x83, x84, x85, x88) -> f458_0_reverse_NULL(x89, x90, x91, x92) :|: -1 <= x90 - 1 && 2 <= x89 - 1 && -1 <= x88 - 1 && 0 <= x85 - 1 && 0 <= x84 - 1 && -1 <= x83 - 1 && x90 <= x88 && x90 + 1 <= x85 && x90 + 1 <= x84 && x90 <= x83 && x89 - 3 <= x88 && x89 - 2 <= x85 && x89 - 2 <= x84 && x89 - 3 <= x83
f473_0_reverse_FieldAccess(x93, x94, x95, x96) -> f473_0_reverse_FieldAccess(x97, x98, x99, x100) :|: x95 = x99 && 0 <= x98 - 1 && 2 <= x97 - 1 && 2 <= x94 - 1 && 0 <= x93 - 1 && x97 - 2 <= x93 && x100 <= x96 - 1 && 0 <= x96 - 1 && 0 <= x95 - 1
f473_0_reverse_FieldAccess(x101, x102, x103, x104) -> f488_0_reverse_FieldAccess(x105, x106, x107, x108) :|: 0 <= x109 - 1 && -1 <= x110 - 1 && x109 <= x110 - 1 && x107 - 2 <= x101 && 0 <= x101 - 1 && 2 <= x102 - 1 && -1 <= x105 - 1 && 0 <= x106 - 1 && 2 <= x107 - 1 && -1 <= x108 - 1
f473_0_reverse_FieldAccess(x111, x112, x113, x114) -> f458_0_reverse_NULL(x115, x116, x117, x118) :|: -1 <= x119 - 1 && x120 <= x119 - 1 && x115 - 2 <= x111 && x115 <= x112 && x116 <= x111 && 0 <= x111 - 1 && 2 <= x112 - 1 && 2 <= x115 - 1 && 0 <= x116 - 1
__init(x121, x122, x123, x124) -> f1_0_main_Load(x125, x126, x127, x128) :|: 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) -> f231_0_createList_LE(arg1P, arg2P, arg3P, arg4P) :|: -1 <= arg1P - 1 && 1 <= arg2 - 1 && -1 <= x5 - 1 && arg2P - 1 <= arg1 && arg3P - 1 <= arg1 && 0 <= arg1 - 1 && 1 <= arg2P - 1 && 1 <= arg3P - 1 && x5 - 2 = arg4P
f231_0_createList_LE(x, x1, x2, x3) -> f266_0_createList_LE(x4, x6, x7, x8) :|: x - 1 = x6 && 0 <= x4 - 1 && 0 <= x2 - 1 && x3 <= 0 && 1 <= x1 - 1
f231_0_createList_LE(x9, x10, x11, x12) -> f231_0_createList_LE(x13, x14, x15, x16) :|: x12 - 1 = x16 && x9 = x13 && 2 <= x15 - 1 && 0 <= x14 - 1 && 0 <= x11 - 1 && 0 <= x10 - 1 && x15 - 2 <= x11 && 0 <= x12 - 1 && x14 <= x10
f266_0_createList_LE(x17, x18, x19, x20) -> f266_0_createList_LE(x21, x22, x23, x24) :|: x18 - 1 = x22 && 2 <= x21 - 1 && 0 <= x18 - 1 && 0 <= x17 - 1
f231_0_createList_LE(x25, x26, x27, x28) -> f266_0_createList_LE(x29, x30, x31, x32) :|: x25 - 2 = x30 && 4 <= x29 - 1 && 1 <= x27 - 1 && 1 <= x26 - 1 && x29 - 3 <= x27 && x29 - 3 <= x26 && x28 <= 0 && 1 <= x25 - 1
f231_0_createList_LE(x33, x34, x35, x36) -> f458_0_reverse_NULL(x37, x38, x39, x40) :|: 1 <= x38 - 1 && 1 <= x37 - 1 && 1 <= x35 - 1 && 1 <= x34 - 1 && x38 <= x35 && x38 <= x34 && x37 <= x35 && x37 <= x34 && x36 <= 0 && x33 <= 1
f266_0_createList_LE(x41, x42, x43, x44) -> f458_0_reverse_NULL(x45, x46, x47, x48) :|: -1 <= x46 - 1 && 1 <= x45 - 1 && 0 <= x41 - 1 && x42 <= 0 && x45 - 1 <= x41
f266_0_createList_LE(x49, x50, x51, x52) -> f458_0_reverse_NULL(x53, x54, x55, x56) :|: 0 <= x54 - 1 && 1 <= x53 - 1 && 2 <= x49 - 1 && x50 <= 0 && x53 + 1 <= x49
f266_0_createList_LE(x57, x58, x59, x60) -> f473_0_reverse_FieldAccess(x61, x62, x63, x64) :|: 0 <= x62 - 1 && 1 <= x61 - 1 && 2 <= x57 - 1 && x58 <= 0 && x61 + 1 <= x57
f458_0_reverse_NULL(x65, x66, x67, x68) -> f488_0_reverse_FieldAccess(x69, x70, x71, x72) :|: -1 <= x72 - 1 && 0 <= x71 - 1 && 0 <= x70 - 1 && -1 <= x69 - 1 && 0 <= x66 - 1 && 0 <= x65 - 1 && x72 + 1 <= x66 && x71 <= x65 && x70 <= x66 && x69 + 1 <= x66
f488_0_reverse_FieldAccess(x73, x74, x75, x76) -> f458_0_reverse_NULL(x77, x80, x81, x82) :|: -1 <= x80 - 1 && 2 <= x77 - 1 && -1 <= x76 - 1 && 0 <= x75 - 1 && 0 <= x74 - 1 && -1 <= x73 - 1 && x80 <= x76 && x80 + 1 <= x74 && x80 <= x73
f488_0_reverse_FieldAccess(x83, x84, x85, x88) -> f458_0_reverse_NULL(x89, x90, x91, x92) :|: -1 <= x90 - 1 && 2 <= x89 - 1 && -1 <= x88 - 1 && 0 <= x85 - 1 && 0 <= x84 - 1 && -1 <= x83 - 1 && x90 <= x88 && x90 + 1 <= x85 && x90 + 1 <= x84 && x90 <= x83 && x89 - 3 <= x88 && x89 - 2 <= x85 && x89 - 2 <= x84 && x89 - 3 <= x83
f473_0_reverse_FieldAccess(x93, x94, x95, x96) -> f473_0_reverse_FieldAccess(x97, x98, x99, x100) :|: x95 = x99 && 0 <= x98 - 1 && 2 <= x97 - 1 && 2 <= x94 - 1 && 0 <= x93 - 1 && x97 - 2 <= x93 && x100 <= x96 - 1 && 0 <= x96 - 1 && 0 <= x95 - 1
f473_0_reverse_FieldAccess(x101, x102, x103, x104) -> f488_0_reverse_FieldAccess(x105, x106, x107, x108) :|: 0 <= x109 - 1 && -1 <= x110 - 1 && x109 <= x110 - 1 && x107 - 2 <= x101 && 0 <= x101 - 1 && 2 <= x102 - 1 && -1 <= x105 - 1 && 0 <= x106 - 1 && 2 <= x107 - 1 && -1 <= x108 - 1
f473_0_reverse_FieldAccess(x111, x112, x113, x114) -> f458_0_reverse_NULL(x115, x116, x117, x118) :|: -1 <= x119 - 1 && x120 <= x119 - 1 && x115 - 2 <= x111 && x115 <= x112 && x116 <= x111 && 0 <= x111 - 1 && 2 <= x112 - 1 && 2 <= x115 - 1 && 0 <= x116 - 1
__init(x121, x122, x123, x124) -> f1_0_main_Load(x125, x126, x127, x128) :|: 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) -> f231_0_createList_LE(arg1P, arg2P, arg3P, arg4P) :|: -1 <= arg1P - 1 && 1 <= arg2 - 1 && -1 <= x5 - 1 && arg2P - 1 <= arg1 && arg3P - 1 <= arg1 && 0 <= arg1 - 1 && 1 <= arg2P - 1 && 1 <= arg3P - 1 && x5 - 2 = arg4P
(2) f231_0_createList_LE(x, x1, x2, x3) -> f266_0_createList_LE(x4, x6, x7, x8) :|: x - 1 = x6 && 0 <= x4 - 1 && 0 <= x2 - 1 && x3 <= 0 && 1 <= x1 - 1
(3) f231_0_createList_LE(x9, x10, x11, x12) -> f231_0_createList_LE(x13, x14, x15, x16) :|: x12 - 1 = x16 && x9 = x13 && 2 <= x15 - 1 && 0 <= x14 - 1 && 0 <= x11 - 1 && 0 <= x10 - 1 && x15 - 2 <= x11 && 0 <= x12 - 1 && x14 <= x10
(4) f266_0_createList_LE(x17, x18, x19, x20) -> f266_0_createList_LE(x21, x22, x23, x24) :|: x18 - 1 = x22 && 2 <= x21 - 1 && 0 <= x18 - 1 && 0 <= x17 - 1
(5) f231_0_createList_LE(x25, x26, x27, x28) -> f266_0_createList_LE(x29, x30, x31, x32) :|: x25 - 2 = x30 && 4 <= x29 - 1 && 1 <= x27 - 1 && 1 <= x26 - 1 && x29 - 3 <= x27 && x29 - 3 <= x26 && x28 <= 0 && 1 <= x25 - 1
(6) f231_0_createList_LE(x33, x34, x35, x36) -> f458_0_reverse_NULL(x37, x38, x39, x40) :|: 1 <= x38 - 1 && 1 <= x37 - 1 && 1 <= x35 - 1 && 1 <= x34 - 1 && x38 <= x35 && x38 <= x34 && x37 <= x35 && x37 <= x34 && x36 <= 0 && x33 <= 1
(7) f266_0_createList_LE(x41, x42, x43, x44) -> f458_0_reverse_NULL(x45, x46, x47, x48) :|: -1 <= x46 - 1 && 1 <= x45 - 1 && 0 <= x41 - 1 && x42 <= 0 && x45 - 1 <= x41
(8) f266_0_createList_LE(x49, x50, x51, x52) -> f458_0_reverse_NULL(x53, x54, x55, x56) :|: 0 <= x54 - 1 && 1 <= x53 - 1 && 2 <= x49 - 1 && x50 <= 0 && x53 + 1 <= x49
(9) f266_0_createList_LE(x57, x58, x59, x60) -> f473_0_reverse_FieldAccess(x61, x62, x63, x64) :|: 0 <= x62 - 1 && 1 <= x61 - 1 && 2 <= x57 - 1 && x58 <= 0 && x61 + 1 <= x57
(10) f458_0_reverse_NULL(x65, x66, x67, x68) -> f488_0_reverse_FieldAccess(x69, x70, x71, x72) :|: -1 <= x72 - 1 && 0 <= x71 - 1 && 0 <= x70 - 1 && -1 <= x69 - 1 && 0 <= x66 - 1 && 0 <= x65 - 1 && x72 + 1 <= x66 && x71 <= x65 && x70 <= x66 && x69 + 1 <= x66
(11) f488_0_reverse_FieldAccess(x73, x74, x75, x76) -> f458_0_reverse_NULL(x77, x80, x81, x82) :|: -1 <= x80 - 1 && 2 <= x77 - 1 && -1 <= x76 - 1 && 0 <= x75 - 1 && 0 <= x74 - 1 && -1 <= x73 - 1 && x80 <= x76 && x80 + 1 <= x74 && x80 <= x73
(12) f488_0_reverse_FieldAccess(x83, x84, x85, x88) -> f458_0_reverse_NULL(x89, x90, x91, x92) :|: -1 <= x90 - 1 && 2 <= x89 - 1 && -1 <= x88 - 1 && 0 <= x85 - 1 && 0 <= x84 - 1 && -1 <= x83 - 1 && x90 <= x88 && x90 + 1 <= x85 && x90 + 1 <= x84 && x90 <= x83 && x89 - 3 <= x88 && x89 - 2 <= x85 && x89 - 2 <= x84 && x89 - 3 <= x83
(13) f473_0_reverse_FieldAccess(x93, x94, x95, x96) -> f473_0_reverse_FieldAccess(x97, x98, x99, x100) :|: x95 = x99 && 0 <= x98 - 1 && 2 <= x97 - 1 && 2 <= x94 - 1 && 0 <= x93 - 1 && x97 - 2 <= x93 && x100 <= x96 - 1 && 0 <= x96 - 1 && 0 <= x95 - 1
(14) f473_0_reverse_FieldAccess(x101, x102, x103, x104) -> f488_0_reverse_FieldAccess(x105, x106, x107, x108) :|: 0 <= x109 - 1 && -1 <= x110 - 1 && x109 <= x110 - 1 && x107 - 2 <= x101 && 0 <= x101 - 1 && 2 <= x102 - 1 && -1 <= x105 - 1 && 0 <= x106 - 1 && 2 <= x107 - 1 && -1 <= x108 - 1
(15) f473_0_reverse_FieldAccess(x111, x112, x113, x114) -> f458_0_reverse_NULL(x115, x116, x117, x118) :|: -1 <= x119 - 1 && x120 <= x119 - 1 && x115 - 2 <= x111 && x115 <= x112 && x116 <= x111 && 0 <= x111 - 1 && 2 <= x112 - 1 && 2 <= x115 - 1 && 0 <= x116 - 1
(16) __init(x121, x122, x123, x124) -> f1_0_main_Load(x125, x126, x127, x128) :|: 0 <= 0

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

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

(4)
Complex Obligation (AND)

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

(5)
Obligation:

Termination digraph:
Nodes:
(1) f231_0_createList_LE(x9, x10, x11, x12) -> f231_0_createList_LE(x13, x14, x15, x16) :|: x12 - 1 = x16 && x9 = x13 && 2 <= x15 - 1 && 0 <= x14 - 1 && 0 <= x11 - 1 && 0 <= x10 - 1 && x15 - 2 <= x11 && 0 <= x12 - 1 && x14 <= x10

Arcs:
(1) -> (1)

This digraph is fully evaluated!

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

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

(7)
Obligation:
Rules:
f231_0_createList_LE(x13:0, x10:0, x11:0, x12:0) -> f231_0_createList_LE(x13:0, x14:0, x15:0, x12:0 - 1) :|: x12:0 > 0 && x14:0 <= x10:0 && x15:0 - 2 <= x11:0 && x10:0 > 0 && x11:0 > 0 && x15:0 > 2 && x14:0 > 0

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

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

   f231_0_createList_LE(x1, x2, x3, x4) -> f231_0_createList_LE(x2, x3, x4)

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

(9)
Obligation:
Rules:
f231_0_createList_LE(x10:0, x11:0, x12:0) -> f231_0_createList_LE(x14:0, x15:0, x12:0 - 1) :|: x12:0 > 0 && x14:0 <= x10:0 && x15:0 - 2 <= x11:0 && x10:0 > 0 && x11:0 > 0 && x15:0 > 2 && x14:0 > 0

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

(10) TempFilterProof (SOUND)
Used the following sort dictionary for filtering: 
f231_0_createList_LE(INTEGER, INTEGER, INTEGER)
Replaced non-predefined constructor symbols by 0.
----------------------------------------

(11)
Obligation:
Rules:
f231_0_createList_LE(x10:0, x11:0, x12:0) -> f231_0_createList_LE(x14:0, x15:0, c) :|: c = x12:0 - 1 && (x12:0 > 0 && x14:0 <= x10:0 && x15:0 - 2 <= x11:0 && x10:0 > 0 && x11:0 > 0 && x15:0 > 2 && x14:0 > 0)

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

(12) RankingReductionPairProof (EQUIVALENT)
Interpretation:
[ f231_0_createList_LE ] = f231_0_createList_LE_3

The following rules are decreasing:
f231_0_createList_LE(x10:0, x11:0, x12:0) -> f231_0_createList_LE(x14:0, x15:0, c) :|: c = x12:0 - 1 && (x12:0 > 0 && x14:0 <= x10:0 && x15:0 - 2 <= x11:0 && x10:0 > 0 && x11:0 > 0 && x15:0 > 2 && x14:0 > 0)

The following rules are bounded:
f231_0_createList_LE(x10:0, x11:0, x12:0) -> f231_0_createList_LE(x14:0, x15:0, c) :|: c = x12:0 - 1 && (x12:0 > 0 && x14:0 <= x10:0 && x15:0 - 2 <= x11:0 && x10:0 > 0 && x11:0 > 0 && x15:0 > 2 && x14:0 > 0)


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

(13)
YES

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

(14)
Obligation:

Termination digraph:
Nodes:
(1) f266_0_createList_LE(x17, x18, x19, x20) -> f266_0_createList_LE(x21, x22, x23, x24) :|: x18 - 1 = x22 && 2 <= x21 - 1 && 0 <= x18 - 1 && 0 <= x17 - 1

Arcs:
(1) -> (1)

This digraph is fully evaluated!

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

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

(16)
Obligation:
Rules:
f266_0_createList_LE(x17:0, x18:0, x19:0, x20:0) -> f266_0_createList_LE(x21:0, x18:0 - 1, x23:0, x24:0) :|: x18:0 > 0 && x21:0 > 2 && x17:0 > 0

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

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

   f266_0_createList_LE(x1, x2, x3, x4) -> f266_0_createList_LE(x1, x2)

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

(18)
Obligation:
Rules:
f266_0_createList_LE(x17:0, x18:0) -> f266_0_createList_LE(x21:0, x18:0 - 1) :|: x18:0 > 0 && x21:0 > 2 && x17:0 > 0

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

(19) TempFilterProof (SOUND)
Used the following sort dictionary for filtering: 
f266_0_createList_LE(INTEGER, INTEGER)
Replaced non-predefined constructor symbols by 0.
----------------------------------------

(20)
Obligation:
Rules:
f266_0_createList_LE(x17:0, x18:0) -> f266_0_createList_LE(x21:0, c) :|: c = x18:0 - 1 && (x18:0 > 0 && x21:0 > 2 && x17:0 > 0)

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

(21) PolynomialOrderProcessor (EQUIVALENT)
Found the following polynomial interpretation:
[f266_0_createList_LE(x, x1)] = x1

The following rules are decreasing:
f266_0_createList_LE(x17:0, x18:0) -> f266_0_createList_LE(x21:0, c) :|: c = x18:0 - 1 && (x18:0 > 0 && x21:0 > 2 && x17:0 > 0)
The following rules are bounded:
f266_0_createList_LE(x17:0, x18:0) -> f266_0_createList_LE(x21:0, c) :|: c = x18:0 - 1 && (x18:0 > 0 && x21:0 > 2 && x17:0 > 0)

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

(22)
YES

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

(23)
Obligation:

Termination digraph:
Nodes:
(1) f473_0_reverse_FieldAccess(x93, x94, x95, x96) -> f473_0_reverse_FieldAccess(x97, x98, x99, x100) :|: x95 = x99 && 0 <= x98 - 1 && 2 <= x97 - 1 && 2 <= x94 - 1 && 0 <= x93 - 1 && x97 - 2 <= x93 && x100 <= x96 - 1 && 0 <= x96 - 1 && 0 <= x95 - 1

Arcs:
(1) -> (1)

This digraph is fully evaluated!

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

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

(25)
Obligation:
Rules:
f473_0_reverse_FieldAccess(x93:0, x94:0, x95:0, x96:0) -> f473_0_reverse_FieldAccess(x97:0, x98:0, x95:0, x100:0) :|: x96:0 > 0 && x95:0 > 0 && x96:0 - 1 >= x100:0 && x97:0 - 2 <= x93:0 && x93:0 > 0 && x94:0 > 2 && x98:0 > 0 && x97:0 > 2

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(26) FilterProof (EQUIVALENT)
Used the following sort dictionary for filtering: 
f473_0_reverse_FieldAccess(INTEGER, INTEGER, INTEGER, INTEGER)
Replaced non-predefined constructor symbols by 0.
----------------------------------------

(27)
Obligation:
Rules:
f473_0_reverse_FieldAccess(x93:0, x94:0, x95:0, x96:0) -> f473_0_reverse_FieldAccess(x97:0, x98:0, x95:0, x100:0) :|: x96:0 > 0 && x95:0 > 0 && x96:0 - 1 >= x100:0 && x97:0 - 2 <= x93:0 && x93:0 > 0 && x94:0 > 2 && x98:0 > 0 && x97:0 > 2

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

(29)
Obligation:
Rules:
f473_0_reverse_FieldAccess(x93:0:0, x94:0:0, x95:0:0, x96:0:0) -> f473_0_reverse_FieldAccess(x97:0:0, x98:0:0, x95:0:0, x100:0:0) :|: x98:0:0 > 0 && x97:0:0 > 2 && x94:0:0 > 2 && x93:0:0 > 0 && x97:0:0 - 2 <= x93:0:0 && x96:0:0 - 1 >= x100:0:0 && x95:0:0 > 0 && x96:0:0 > 0

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(30) RankingReductionPairProof (EQUIVALENT)
Interpretation:
[ f473_0_reverse_FieldAccess ] = f473_0_reverse_FieldAccess_4

The following rules are decreasing:
f473_0_reverse_FieldAccess(x93:0:0, x94:0:0, x95:0:0, x96:0:0) -> f473_0_reverse_FieldAccess(x97:0:0, x98:0:0, x95:0:0, x100:0:0) :|: x98:0:0 > 0 && x97:0:0 > 2 && x94:0:0 > 2 && x93:0:0 > 0 && x97:0:0 - 2 <= x93:0:0 && x96:0:0 - 1 >= x100:0:0 && x95:0:0 > 0 && x96:0:0 > 0

The following rules are bounded:
f473_0_reverse_FieldAccess(x93:0:0, x94:0:0, x95:0:0, x96:0:0) -> f473_0_reverse_FieldAccess(x97:0:0, x98:0:0, x95:0:0, x100:0:0) :|: x98:0:0 > 0 && x97:0:0 > 2 && x94:0:0 > 2 && x93:0:0 > 0 && x97:0:0 - 2 <= x93:0:0 && x96:0:0 - 1 >= x100:0:0 && x95:0:0 > 0 && x96:0:0 > 0


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(31)
YES

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(32)
Obligation:

Termination digraph:
Nodes:
(1) f458_0_reverse_NULL(x65, x66, x67, x68) -> f488_0_reverse_FieldAccess(x69, x70, x71, x72) :|: -1 <= x72 - 1 && 0 <= x71 - 1 && 0 <= x70 - 1 && -1 <= x69 - 1 && 0 <= x66 - 1 && 0 <= x65 - 1 && x72 + 1 <= x66 && x71 <= x65 && x70 <= x66 && x69 + 1 <= x66
(2) f488_0_reverse_FieldAccess(x83, x84, x85, x88) -> f458_0_reverse_NULL(x89, x90, x91, x92) :|: -1 <= x90 - 1 && 2 <= x89 - 1 && -1 <= x88 - 1 && 0 <= x85 - 1 && 0 <= x84 - 1 && -1 <= x83 - 1 && x90 <= x88 && x90 + 1 <= x85 && x90 + 1 <= x84 && x90 <= x83 && x89 - 3 <= x88 && x89 - 2 <= x85 && x89 - 2 <= x84 && x89 - 3 <= x83
(3) f488_0_reverse_FieldAccess(x73, x74, x75, x76) -> f458_0_reverse_NULL(x77, x80, x81, x82) :|: -1 <= x80 - 1 && 2 <= x77 - 1 && -1 <= x76 - 1 && 0 <= x75 - 1 && 0 <= x74 - 1 && -1 <= x73 - 1 && x80 <= x76 && x80 + 1 <= x74 && x80 <= x73

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

This digraph is fully evaluated!

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

(34)
Obligation:
Rules:
f458_0_reverse_NULL(x65:0, x66:0, x67:0, x68:0) -> f458_0_reverse_NULL(x77:0, x80:0, x81:0, x82:0) :|: x80:0 <= x69:0 && x69:0 + 1 <= x66:0 && x70:0 <= x66:0 && x80:0 + 1 <= x70:0 && x71:0 <= x65:0 && x80:0 <= x72:0 && x72:0 + 1 <= x66:0 && x65:0 > 0 && x66:0 > 0 && x69:0 > -1 && x70:0 > 0 && x80:0 > -1 && x77:0 > 2 && x71:0 > 0 && x72:0 > -1
f458_0_reverse_NULL(x, x1, x2, x3) -> f458_0_reverse_NULL(x4, x5, x6, x7) :|: x4 - 3 <= x8 && x8 + 1 <= x1 && x9 <= x1 && x4 - 2 <= x9 && x10 <= x && x4 - 2 <= x10 && x11 + 1 <= x1 && x4 - 3 <= x11 && x > 0 && x5 <= x8 && x1 > 0 && x5 + 1 <= x9 && x5 + 1 <= x10 && x5 <= x11 && x8 > -1 && x9 > 0 && x10 > 0 && x11 > -1 && x4 > 2 && x5 > -1

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

   f458_0_reverse_NULL(x1, x2, x3, x4) -> f458_0_reverse_NULL(x1, x2)

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

(36)
Obligation:
Rules:
f458_0_reverse_NULL(x65:0, x66:0) -> f458_0_reverse_NULL(x77:0, x80:0) :|: x80:0 <= x69:0 && x69:0 + 1 <= x66:0 && x70:0 <= x66:0 && x80:0 + 1 <= x70:0 && x71:0 <= x65:0 && x80:0 <= x72:0 && x72:0 + 1 <= x66:0 && x65:0 > 0 && x66:0 > 0 && x69:0 > -1 && x70:0 > 0 && x80:0 > -1 && x77:0 > 2 && x71:0 > 0 && x72:0 > -1
f458_0_reverse_NULL(x, x1) -> f458_0_reverse_NULL(x4, x5) :|: x4 - 3 <= x8 && x8 + 1 <= x1 && x9 <= x1 && x4 - 2 <= x9 && x10 <= x && x4 - 2 <= x10 && x11 + 1 <= x1 && x4 - 3 <= x11 && x > 0 && x5 <= x8 && x1 > 0 && x5 + 1 <= x9 && x5 + 1 <= x10 && x5 <= x11 && x8 > -1 && x9 > 0 && x10 > 0 && x11 > -1 && x4 > 2 && x5 > -1

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(37) FilterProof (EQUIVALENT)
Used the following sort dictionary for filtering: 
f458_0_reverse_NULL(INTEGER, INTEGER)
Replaced non-predefined constructor symbols by 0.
----------------------------------------

(38)
Obligation:
Rules:
f458_0_reverse_NULL(x65:0, x66:0) -> f458_0_reverse_NULL(x77:0, x80:0) :|: x80:0 <= x69:0 && x69:0 + 1 <= x66:0 && x70:0 <= x66:0 && x80:0 + 1 <= x70:0 && x71:0 <= x65:0 && x80:0 <= x72:0 && x72:0 + 1 <= x66:0 && x65:0 > 0 && x66:0 > 0 && x69:0 > -1 && x70:0 > 0 && x80:0 > -1 && x77:0 > 2 && x71:0 > 0 && x72:0 > -1
f458_0_reverse_NULL(x, x1) -> f458_0_reverse_NULL(x4, x5) :|: x4 - 3 <= x8 && x8 + 1 <= x1 && x9 <= x1 && x4 - 2 <= x9 && x10 <= x && x4 - 2 <= x10 && x11 + 1 <= x1 && x4 - 3 <= x11 && x > 0 && x5 <= x8 && x1 > 0 && x5 + 1 <= x9 && x5 + 1 <= x10 && x5 <= x11 && x8 > -1 && x9 > 0 && x10 > 0 && x11 > -1 && x4 > 2 && x5 > -1

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

(40)
Obligation:
Rules:
f458_0_reverse_NULL(x65:0:0, x66:0:0) -> f458_0_reverse_NULL(x77:0:0, x80:0:0) :|: x71:0:0 > 0 && x72:0:0 > -1 && x77:0:0 > 2 && x80:0:0 > -1 && x70:0:0 > 0 && x69:0:0 > -1 && x66:0:0 > 0 && x65:0:0 > 0 && x72:0:0 + 1 <= x66:0:0 && x80:0:0 <= x72:0:0 && x71:0:0 <= x65:0:0 && x80:0:0 + 1 <= x70:0:0 && x70:0:0 <= x66:0:0 && x69:0:0 + 1 <= x66:0:0 && x80:0:0 <= x69:0:0
f458_0_reverse_NULL(x:0, x1:0) -> f458_0_reverse_NULL(x4:0, x5:0) :|: x4:0 > 2 && x5:0 > -1 && x11:0 > -1 && x10:0 > 0 && x9:0 > 0 && x8:0 > -1 && x5:0 <= x11:0 && x5:0 + 1 <= x10:0 && x9:0 >= x5:0 + 1 && x1:0 > 0 && x8:0 >= x5:0 && x:0 > 0 && x4:0 - 3 <= x11:0 && x1:0 >= x11:0 + 1 && x4:0 - 2 <= x10:0 && x:0 >= x10:0 && x9:0 >= x4:0 - 2 && x9:0 <= x1:0 && x8:0 + 1 <= x1:0 && x8:0 >= x4:0 - 3

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(41) RankingReductionPairProof (EQUIVALENT)
Interpretation:
[ f458_0_reverse_NULL ] = f458_0_reverse_NULL_2

The following rules are decreasing:
f458_0_reverse_NULL(x65:0:0, x66:0:0) -> f458_0_reverse_NULL(x77:0:0, x80:0:0) :|: x71:0:0 > 0 && x72:0:0 > -1 && x77:0:0 > 2 && x80:0:0 > -1 && x70:0:0 > 0 && x69:0:0 > -1 && x66:0:0 > 0 && x65:0:0 > 0 && x72:0:0 + 1 <= x66:0:0 && x80:0:0 <= x72:0:0 && x71:0:0 <= x65:0:0 && x80:0:0 + 1 <= x70:0:0 && x70:0:0 <= x66:0:0 && x69:0:0 + 1 <= x66:0:0 && x80:0:0 <= x69:0:0
f458_0_reverse_NULL(x:0, x1:0) -> f458_0_reverse_NULL(x4:0, x5:0) :|: x4:0 > 2 && x5:0 > -1 && x11:0 > -1 && x10:0 > 0 && x9:0 > 0 && x8:0 > -1 && x5:0 <= x11:0 && x5:0 + 1 <= x10:0 && x9:0 >= x5:0 + 1 && x1:0 > 0 && x8:0 >= x5:0 && x:0 > 0 && x4:0 - 3 <= x11:0 && x1:0 >= x11:0 + 1 && x4:0 - 2 <= x10:0 && x:0 >= x10:0 && x9:0 >= x4:0 - 2 && x9:0 <= x1:0 && x8:0 + 1 <= x1:0 && x8:0 >= x4:0 - 3

The following rules are bounded:
f458_0_reverse_NULL(x65:0:0, x66:0:0) -> f458_0_reverse_NULL(x77:0:0, x80:0:0) :|: x71:0:0 > 0 && x72:0:0 > -1 && x77:0:0 > 2 && x80:0:0 > -1 && x70:0:0 > 0 && x69:0:0 > -1 && x66:0:0 > 0 && x65:0:0 > 0 && x72:0:0 + 1 <= x66:0:0 && x80:0:0 <= x72:0:0 && x71:0:0 <= x65:0:0 && x80:0:0 + 1 <= x70:0:0 && x70:0:0 <= x66:0:0 && x69:0:0 + 1 <= x66:0:0 && x80:0:0 <= x69:0:0
f458_0_reverse_NULL(x:0, x1:0) -> f458_0_reverse_NULL(x4:0, x5:0) :|: x4:0 > 2 && x5:0 > -1 && x11:0 > -1 && x10:0 > 0 && x9:0 > 0 && x8:0 > -1 && x5:0 <= x11:0 && x5:0 + 1 <= x10:0 && x9:0 >= x5:0 + 1 && x1:0 > 0 && x8:0 >= x5:0 && x:0 > 0 && x4:0 - 3 <= x11:0 && x1:0 >= x11:0 + 1 && x4:0 - 2 <= x10:0 && x:0 >= x10:0 && x9:0 >= x4:0 - 2 && x9:0 <= x1:0 && x8:0 + 1 <= x1:0 && x8:0 >= x4:0 - 3


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(42)
YES