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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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, 909 ms]
(4) AND
    (5) IRSwT
        (6) IntTRSCompressionProof [EQUIVALENT, 0 ms]
        (7) IRSwT
        (8) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 2 ms]
        (9) IRSwT
        (10) TempFilterProof [SOUND, 25 ms]
        (11) IntTRS
        (12) RankingReductionPairProof [EQUIVALENT, 0 ms]
        (13) YES
    (14) IRSwT
        (15) IntTRSCompressionProof [EQUIVALENT, 0 ms]
        (16) IRSwT
        (17) FilterProof [EQUIVALENT, 0 ms]
        (18) IntTRS
        (19) IntTRSCompressionProof [EQUIVALENT, 0 ms]
        (20) IntTRS
        (21) RankingReductionPairProof [EQUIVALENT, 0 ms]
        (22) YES
    (23) IRSwT
        (24) IntTRSCompressionProof [EQUIVALENT, 15 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) RankingReductionPairProof [EQUIVALENT, 11 ms]
        (33) YES


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

(0)
Obligation:
Rules:
f1_0_main_Load(arg1, arg2, arg3, arg4) -> f172_0_createList_LE(arg1P, arg2P, arg3P, arg4P) :|: -1 <= x4 - 1 && 0 <= arg2 - 1 && arg1P - 1 <= arg1 && arg2P - 1 <= arg1 && 0 <= arg1 - 1 && 1 <= arg1P - 1 && 1 <= arg2P - 1 && x4 - 2 = arg3P
f172_0_createList_LE(x, x1, x2, x3) -> f172_0_createList_LE(x5, x6, x7, x8) :|: x2 - 1 = x7 && 2 <= x6 - 1 && 0 <= x5 - 1 && 0 <= x1 - 1 && 0 <= x - 1 && x6 - 2 <= x1 && 0 <= x2 - 1 && x5 <= x
f172_0_createList_LE(x9, x10, x11, x12) -> f355_0_reverse_NULL(x13, x14, x15, x16) :|: 1 <= x14 - 1 && 1 <= x13 - 1 && 1 <= x10 - 1 && 1 <= x9 - 1 && x14 <= x10 && x14 <= x9 && x13 <= x10 && x11 <= 0 && x13 <= x9
f172_0_createList_LE(x17, x18, x19, x20) -> f355_0_reverse_NULL(x21, x22, x23, x24) :|: -1 <= x22 - 1 && 1 <= x21 - 1 && 0 <= x18 - 1 && 1 <= x17 - 1 && x21 - 1 <= x18 && x19 <= 0 && x21 <= x17
f172_0_createList_LE(x25, x26, x27, x28) -> f355_0_reverse_NULL(x29, x30, x31, x32) :|: 0 <= x30 - 1 && 1 <= x29 - 1 && 0 <= x26 - 1 && 1 <= x25 - 1 && x29 - 1 <= x26 && x27 <= 0 && x29 <= x25
f172_0_createList_LE(x33, x34, x35, x36) -> f370_0_reverse_FieldAccess(x37, x38, x39, x40) :|: 0 <= x38 - 1 && 1 <= x37 - 1 && 0 <= x34 - 1 && 1 <= x33 - 1 && x37 - 1 <= x34 && x35 <= 0 && x37 <= x33
f355_0_reverse_NULL(x41, x42, x43, x44) -> f385_0_reverse_FieldAccess(x45, x46, x47, x48) :|: -1 <= x48 - 1 && 0 <= x47 - 1 && 0 <= x46 - 1 && -1 <= x45 - 1 && 0 <= x42 - 1 && 0 <= x41 - 1 && x48 + 1 <= x42 && x47 <= x41 && x46 <= x42 && x45 + 1 <= x42
f385_0_reverse_FieldAccess(x49, x50, x51, x52) -> f355_0_reverse_NULL(x53, x54, x55, x56) :|: -1 <= x54 - 1 && 2 <= x53 - 1 && -1 <= x52 - 1 && 0 <= x51 - 1 && 0 <= x50 - 1 && -1 <= x49 - 1 && x54 <= x52 && x54 + 1 <= x50 && x54 <= x49
f385_0_reverse_FieldAccess(x57, x58, x59, x60) -> f355_0_reverse_NULL(x61, x62, x63, x64) :|: -1 <= x62 - 1 && 2 <= x61 - 1 && -1 <= x60 - 1 && 0 <= x59 - 1 && 0 <= x58 - 1 && -1 <= x57 - 1 && x62 <= x60 && x62 + 1 <= x59 && x62 + 1 <= x58 && x62 <= x57 && x61 - 3 <= x60 && x61 - 2 <= x59 && x61 - 2 <= x58 && x61 - 3 <= x57
f370_0_reverse_FieldAccess(x67, x68, x69, x70) -> f370_0_reverse_FieldAccess(x71, x72, x75, x76) :|: x69 = x75 && 0 <= x72 - 1 && 2 <= x71 - 1 && 2 <= x68 - 1 && 0 <= x67 - 1 && x71 - 2 <= x67 && x76 <= x70 - 1 && 0 <= x70 - 1 && 0 <= x69 - 1
f370_0_reverse_FieldAccess(x77, x78, x79, x80) -> f385_0_reverse_FieldAccess(x81, x82, x83, x84) :|: 0 <= x85 - 1 && -1 <= x86 - 1 && x85 <= x86 - 1 && x83 - 2 <= x77 && 0 <= x77 - 1 && 2 <= x78 - 1 && -1 <= x81 - 1 && 0 <= x82 - 1 && 2 <= x83 - 1 && -1 <= x84 - 1
f370_0_reverse_FieldAccess(x87, x88, x89, x90) -> f355_0_reverse_NULL(x91, x92, x93, x94) :|: -1 <= x95 - 1 && x96 <= x95 - 1 && x91 - 2 <= x87 && x91 <= x88 && x92 <= x87 && 0 <= x87 - 1 && 2 <= x88 - 1 && 2 <= x91 - 1 && 0 <= x92 - 1
__init(x97, x98, x99, x100) -> f1_0_main_Load(x101, x102, x103, x104) :|: 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) -> f172_0_createList_LE(arg1P, arg2P, arg3P, arg4P) :|: -1 <= x4 - 1 && 0 <= arg2 - 1 && arg1P - 1 <= arg1 && arg2P - 1 <= arg1 && 0 <= arg1 - 1 && 1 <= arg1P - 1 && 1 <= arg2P - 1 && x4 - 2 = arg3P
f172_0_createList_LE(x, x1, x2, x3) -> f172_0_createList_LE(x5, x6, x7, x8) :|: x2 - 1 = x7 && 2 <= x6 - 1 && 0 <= x5 - 1 && 0 <= x1 - 1 && 0 <= x - 1 && x6 - 2 <= x1 && 0 <= x2 - 1 && x5 <= x
f172_0_createList_LE(x9, x10, x11, x12) -> f355_0_reverse_NULL(x13, x14, x15, x16) :|: 1 <= x14 - 1 && 1 <= x13 - 1 && 1 <= x10 - 1 && 1 <= x9 - 1 && x14 <= x10 && x14 <= x9 && x13 <= x10 && x11 <= 0 && x13 <= x9
f172_0_createList_LE(x17, x18, x19, x20) -> f355_0_reverse_NULL(x21, x22, x23, x24) :|: -1 <= x22 - 1 && 1 <= x21 - 1 && 0 <= x18 - 1 && 1 <= x17 - 1 && x21 - 1 <= x18 && x19 <= 0 && x21 <= x17
f172_0_createList_LE(x25, x26, x27, x28) -> f355_0_reverse_NULL(x29, x30, x31, x32) :|: 0 <= x30 - 1 && 1 <= x29 - 1 && 0 <= x26 - 1 && 1 <= x25 - 1 && x29 - 1 <= x26 && x27 <= 0 && x29 <= x25
f172_0_createList_LE(x33, x34, x35, x36) -> f370_0_reverse_FieldAccess(x37, x38, x39, x40) :|: 0 <= x38 - 1 && 1 <= x37 - 1 && 0 <= x34 - 1 && 1 <= x33 - 1 && x37 - 1 <= x34 && x35 <= 0 && x37 <= x33
f355_0_reverse_NULL(x41, x42, x43, x44) -> f385_0_reverse_FieldAccess(x45, x46, x47, x48) :|: -1 <= x48 - 1 && 0 <= x47 - 1 && 0 <= x46 - 1 && -1 <= x45 - 1 && 0 <= x42 - 1 && 0 <= x41 - 1 && x48 + 1 <= x42 && x47 <= x41 && x46 <= x42 && x45 + 1 <= x42
f385_0_reverse_FieldAccess(x49, x50, x51, x52) -> f355_0_reverse_NULL(x53, x54, x55, x56) :|: -1 <= x54 - 1 && 2 <= x53 - 1 && -1 <= x52 - 1 && 0 <= x51 - 1 && 0 <= x50 - 1 && -1 <= x49 - 1 && x54 <= x52 && x54 + 1 <= x50 && x54 <= x49
f385_0_reverse_FieldAccess(x57, x58, x59, x60) -> f355_0_reverse_NULL(x61, x62, x63, x64) :|: -1 <= x62 - 1 && 2 <= x61 - 1 && -1 <= x60 - 1 && 0 <= x59 - 1 && 0 <= x58 - 1 && -1 <= x57 - 1 && x62 <= x60 && x62 + 1 <= x59 && x62 + 1 <= x58 && x62 <= x57 && x61 - 3 <= x60 && x61 - 2 <= x59 && x61 - 2 <= x58 && x61 - 3 <= x57
f370_0_reverse_FieldAccess(x67, x68, x69, x70) -> f370_0_reverse_FieldAccess(x71, x72, x75, x76) :|: x69 = x75 && 0 <= x72 - 1 && 2 <= x71 - 1 && 2 <= x68 - 1 && 0 <= x67 - 1 && x71 - 2 <= x67 && x76 <= x70 - 1 && 0 <= x70 - 1 && 0 <= x69 - 1
f370_0_reverse_FieldAccess(x77, x78, x79, x80) -> f385_0_reverse_FieldAccess(x81, x82, x83, x84) :|: 0 <= x85 - 1 && -1 <= x86 - 1 && x85 <= x86 - 1 && x83 - 2 <= x77 && 0 <= x77 - 1 && 2 <= x78 - 1 && -1 <= x81 - 1 && 0 <= x82 - 1 && 2 <= x83 - 1 && -1 <= x84 - 1
f370_0_reverse_FieldAccess(x87, x88, x89, x90) -> f355_0_reverse_NULL(x91, x92, x93, x94) :|: -1 <= x95 - 1 && x96 <= x95 - 1 && x91 - 2 <= x87 && x91 <= x88 && x92 <= x87 && 0 <= x87 - 1 && 2 <= x88 - 1 && 2 <= x91 - 1 && 0 <= x92 - 1
__init(x97, x98, x99, x100) -> f1_0_main_Load(x101, x102, x103, x104) :|: 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) -> f172_0_createList_LE(arg1P, arg2P, arg3P, arg4P) :|: -1 <= x4 - 1 && 0 <= arg2 - 1 && arg1P - 1 <= arg1 && arg2P - 1 <= arg1 && 0 <= arg1 - 1 && 1 <= arg1P - 1 && 1 <= arg2P - 1 && x4 - 2 = arg3P
(2) f172_0_createList_LE(x, x1, x2, x3) -> f172_0_createList_LE(x5, x6, x7, x8) :|: x2 - 1 = x7 && 2 <= x6 - 1 && 0 <= x5 - 1 && 0 <= x1 - 1 && 0 <= x - 1 && x6 - 2 <= x1 && 0 <= x2 - 1 && x5 <= x
(3) f172_0_createList_LE(x9, x10, x11, x12) -> f355_0_reverse_NULL(x13, x14, x15, x16) :|: 1 <= x14 - 1 && 1 <= x13 - 1 && 1 <= x10 - 1 && 1 <= x9 - 1 && x14 <= x10 && x14 <= x9 && x13 <= x10 && x11 <= 0 && x13 <= x9
(4) f172_0_createList_LE(x17, x18, x19, x20) -> f355_0_reverse_NULL(x21, x22, x23, x24) :|: -1 <= x22 - 1 && 1 <= x21 - 1 && 0 <= x18 - 1 && 1 <= x17 - 1 && x21 - 1 <= x18 && x19 <= 0 && x21 <= x17
(5) f172_0_createList_LE(x25, x26, x27, x28) -> f355_0_reverse_NULL(x29, x30, x31, x32) :|: 0 <= x30 - 1 && 1 <= x29 - 1 && 0 <= x26 - 1 && 1 <= x25 - 1 && x29 - 1 <= x26 && x27 <= 0 && x29 <= x25
(6) f172_0_createList_LE(x33, x34, x35, x36) -> f370_0_reverse_FieldAccess(x37, x38, x39, x40) :|: 0 <= x38 - 1 && 1 <= x37 - 1 && 0 <= x34 - 1 && 1 <= x33 - 1 && x37 - 1 <= x34 && x35 <= 0 && x37 <= x33
(7) f355_0_reverse_NULL(x41, x42, x43, x44) -> f385_0_reverse_FieldAccess(x45, x46, x47, x48) :|: -1 <= x48 - 1 && 0 <= x47 - 1 && 0 <= x46 - 1 && -1 <= x45 - 1 && 0 <= x42 - 1 && 0 <= x41 - 1 && x48 + 1 <= x42 && x47 <= x41 && x46 <= x42 && x45 + 1 <= x42
(8) f385_0_reverse_FieldAccess(x49, x50, x51, x52) -> f355_0_reverse_NULL(x53, x54, x55, x56) :|: -1 <= x54 - 1 && 2 <= x53 - 1 && -1 <= x52 - 1 && 0 <= x51 - 1 && 0 <= x50 - 1 && -1 <= x49 - 1 && x54 <= x52 && x54 + 1 <= x50 && x54 <= x49
(9) f385_0_reverse_FieldAccess(x57, x58, x59, x60) -> f355_0_reverse_NULL(x61, x62, x63, x64) :|: -1 <= x62 - 1 && 2 <= x61 - 1 && -1 <= x60 - 1 && 0 <= x59 - 1 && 0 <= x58 - 1 && -1 <= x57 - 1 && x62 <= x60 && x62 + 1 <= x59 && x62 + 1 <= x58 && x62 <= x57 && x61 - 3 <= x60 && x61 - 2 <= x59 && x61 - 2 <= x58 && x61 - 3 <= x57
(10) f370_0_reverse_FieldAccess(x67, x68, x69, x70) -> f370_0_reverse_FieldAccess(x71, x72, x75, x76) :|: x69 = x75 && 0 <= x72 - 1 && 2 <= x71 - 1 && 2 <= x68 - 1 && 0 <= x67 - 1 && x71 - 2 <= x67 && x76 <= x70 - 1 && 0 <= x70 - 1 && 0 <= x69 - 1
(11) f370_0_reverse_FieldAccess(x77, x78, x79, x80) -> f385_0_reverse_FieldAccess(x81, x82, x83, x84) :|: 0 <= x85 - 1 && -1 <= x86 - 1 && x85 <= x86 - 1 && x83 - 2 <= x77 && 0 <= x77 - 1 && 2 <= x78 - 1 && -1 <= x81 - 1 && 0 <= x82 - 1 && 2 <= x83 - 1 && -1 <= x84 - 1
(12) f370_0_reverse_FieldAccess(x87, x88, x89, x90) -> f355_0_reverse_NULL(x91, x92, x93, x94) :|: -1 <= x95 - 1 && x96 <= x95 - 1 && x91 - 2 <= x87 && x91 <= x88 && x92 <= x87 && 0 <= x87 - 1 && 2 <= x88 - 1 && 2 <= x91 - 1 && 0 <= x92 - 1
(13) __init(x97, x98, x99, x100) -> f1_0_main_Load(x101, x102, x103, x104) :|: 0 <= 0

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

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

(4)
Complex Obligation (AND)

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

(5)
Obligation:

Termination digraph:
Nodes:
(1) f172_0_createList_LE(x, x1, x2, x3) -> f172_0_createList_LE(x5, x6, x7, x8) :|: x2 - 1 = x7 && 2 <= x6 - 1 && 0 <= x5 - 1 && 0 <= x1 - 1 && 0 <= x - 1 && x6 - 2 <= x1 && 0 <= x2 - 1 && x5 <= x

Arcs:
(1) -> (1)

This digraph is fully evaluated!

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

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

(7)
Obligation:
Rules:
f172_0_createList_LE(x:0, x1:0, x2:0, x3:0) -> f172_0_createList_LE(x5:0, x6:0, x2:0 - 1, x8:0) :|: x2:0 > 0 && x:0 >= x5:0 && x6:0 - 2 <= x1:0 && x:0 > 0 && x1:0 > 0 && x6:0 > 2 && x5:0 > 0

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

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

   f172_0_createList_LE(x1, x2, x3, x4) -> f172_0_createList_LE(x1, x2, x3)

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

(9)
Obligation:
Rules:
f172_0_createList_LE(x:0, x1:0, x2:0) -> f172_0_createList_LE(x5:0, x6:0, x2:0 - 1) :|: x2:0 > 0 && x:0 >= x5:0 && x6:0 - 2 <= x1:0 && x:0 > 0 && x1:0 > 0 && x6:0 > 2 && x5:0 > 0

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

(10) TempFilterProof (SOUND)
Used the following sort dictionary for filtering: 
f172_0_createList_LE(INTEGER, INTEGER, INTEGER)
Replaced non-predefined constructor symbols by 0.
----------------------------------------

(11)
Obligation:
Rules:
f172_0_createList_LE(x:0, x1:0, x2:0) -> f172_0_createList_LE(x5:0, x6:0, c) :|: c = x2:0 - 1 && (x2:0 > 0 && x:0 >= x5:0 && x6:0 - 2 <= x1:0 && x:0 > 0 && x1:0 > 0 && x6:0 > 2 && x5:0 > 0)

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

(12) RankingReductionPairProof (EQUIVALENT)
Interpretation:
[ f172_0_createList_LE ] = f172_0_createList_LE_3

The following rules are decreasing:
f172_0_createList_LE(x:0, x1:0, x2:0) -> f172_0_createList_LE(x5:0, x6:0, c) :|: c = x2:0 - 1 && (x2:0 > 0 && x:0 >= x5:0 && x6:0 - 2 <= x1:0 && x:0 > 0 && x1:0 > 0 && x6:0 > 2 && x5:0 > 0)

The following rules are bounded:
f172_0_createList_LE(x:0, x1:0, x2:0) -> f172_0_createList_LE(x5:0, x6:0, c) :|: c = x2:0 - 1 && (x2:0 > 0 && x:0 >= x5:0 && x6:0 - 2 <= x1:0 && x:0 > 0 && x1:0 > 0 && x6:0 > 2 && x5:0 > 0)


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

(13)
YES

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

(14)
Obligation:

Termination digraph:
Nodes:
(1) f370_0_reverse_FieldAccess(x67, x68, x69, x70) -> f370_0_reverse_FieldAccess(x71, x72, x75, x76) :|: x69 = x75 && 0 <= x72 - 1 && 2 <= x71 - 1 && 2 <= x68 - 1 && 0 <= x67 - 1 && x71 - 2 <= x67 && x76 <= x70 - 1 && 0 <= x70 - 1 && 0 <= x69 - 1

Arcs:
(1) -> (1)

This digraph is fully evaluated!

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

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

(16)
Obligation:
Rules:
f370_0_reverse_FieldAccess(x67:0, x68:0, x69:0, x70:0) -> f370_0_reverse_FieldAccess(x71:0, x72:0, x69:0, x76:0) :|: x70:0 > 0 && x69:0 > 0 && x76:0 <= x70:0 - 1 && x71:0 - 2 <= x67:0 && x67:0 > 0 && x68:0 > 2 && x72:0 > 0 && x71:0 > 2

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

(17) FilterProof (EQUIVALENT)
Used the following sort dictionary for filtering: 
f370_0_reverse_FieldAccess(INTEGER, INTEGER, INTEGER, INTEGER)
Replaced non-predefined constructor symbols by 0.
----------------------------------------

(18)
Obligation:
Rules:
f370_0_reverse_FieldAccess(x67:0, x68:0, x69:0, x70:0) -> f370_0_reverse_FieldAccess(x71:0, x72:0, x69:0, x76:0) :|: x70:0 > 0 && x69:0 > 0 && x76:0 <= x70:0 - 1 && x71:0 - 2 <= x67:0 && x67:0 > 0 && x68:0 > 2 && x72:0 > 0 && x71:0 > 2

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

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

(20)
Obligation:
Rules:
f370_0_reverse_FieldAccess(x67:0:0, x68:0:0, x69:0:0, x70:0:0) -> f370_0_reverse_FieldAccess(x71:0:0, x72:0:0, x69:0:0, x76:0:0) :|: x72:0:0 > 0 && x71:0:0 > 2 && x68:0:0 > 2 && x67:0:0 > 0 && x71:0:0 - 2 <= x67:0:0 && x76:0:0 <= x70:0:0 - 1 && x69:0:0 > 0 && x70:0:0 > 0

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

(21) RankingReductionPairProof (EQUIVALENT)
Interpretation:
[ f370_0_reverse_FieldAccess ] = f370_0_reverse_FieldAccess_4

The following rules are decreasing:
f370_0_reverse_FieldAccess(x67:0:0, x68:0:0, x69:0:0, x70:0:0) -> f370_0_reverse_FieldAccess(x71:0:0, x72:0:0, x69:0:0, x76:0:0) :|: x72:0:0 > 0 && x71:0:0 > 2 && x68:0:0 > 2 && x67:0:0 > 0 && x71:0:0 - 2 <= x67:0:0 && x76:0:0 <= x70:0:0 - 1 && x69:0:0 > 0 && x70:0:0 > 0

The following rules are bounded:
f370_0_reverse_FieldAccess(x67:0:0, x68:0:0, x69:0:0, x70:0:0) -> f370_0_reverse_FieldAccess(x71:0:0, x72:0:0, x69:0:0, x76:0:0) :|: x72:0:0 > 0 && x71:0:0 > 2 && x68:0:0 > 2 && x67:0:0 > 0 && x71:0:0 - 2 <= x67:0:0 && x76:0:0 <= x70:0:0 - 1 && x69:0:0 > 0 && x70:0:0 > 0


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

(22)
YES

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

(23)
Obligation:

Termination digraph:
Nodes:
(1) f355_0_reverse_NULL(x41, x42, x43, x44) -> f385_0_reverse_FieldAccess(x45, x46, x47, x48) :|: -1 <= x48 - 1 && 0 <= x47 - 1 && 0 <= x46 - 1 && -1 <= x45 - 1 && 0 <= x42 - 1 && 0 <= x41 - 1 && x48 + 1 <= x42 && x47 <= x41 && x46 <= x42 && x45 + 1 <= x42
(2) f385_0_reverse_FieldAccess(x57, x58, x59, x60) -> f355_0_reverse_NULL(x61, x62, x63, x64) :|: -1 <= x62 - 1 && 2 <= x61 - 1 && -1 <= x60 - 1 && 0 <= x59 - 1 && 0 <= x58 - 1 && -1 <= x57 - 1 && x62 <= x60 && x62 + 1 <= x59 && x62 + 1 <= x58 && x62 <= x57 && x61 - 3 <= x60 && x61 - 2 <= x59 && x61 - 2 <= x58 && x61 - 3 <= x57
(3) f385_0_reverse_FieldAccess(x49, x50, x51, x52) -> f355_0_reverse_NULL(x53, x54, x55, x56) :|: -1 <= x54 - 1 && 2 <= x53 - 1 && -1 <= x52 - 1 && 0 <= x51 - 1 && 0 <= x50 - 1 && -1 <= x49 - 1 && x54 <= x52 && x54 + 1 <= x50 && x54 <= x49

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

This digraph is fully evaluated!

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

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

(25)
Obligation:
Rules:
f355_0_reverse_NULL(x41:0, x42:0, x43:0, x44:0) -> f355_0_reverse_NULL(x61:0, x62:0, x63:0, x64:0) :|: x61:0 - 3 <= x45:0 && x45:0 + 1 <= x42:0 && x46:0 <= x42:0 && x61:0 - 2 <= x46:0 && x47:0 <= x41:0 && x61:0 - 2 <= x47:0 && x48:0 + 1 <= x42:0 && x61:0 - 3 <= x48:0 && x41:0 > 0 && x62:0 <= x45:0 && x42:0 > 0 && x62:0 + 1 <= x46:0 && x62:0 + 1 <= x47:0 && x62:0 <= x48:0 && x45:0 > -1 && x46:0 > 0 && x47:0 > 0 && x48:0 > -1 && x61:0 > 2 && x62:0 > -1
f355_0_reverse_NULL(x, x1, x2, x3) -> f355_0_reverse_NULL(x4, x5, x6, x7) :|: x5 <= x8 && x8 + 1 <= x1 && x9 <= x1 && x5 + 1 <= x9 && x10 <= x && x5 <= x11 && x11 + 1 <= x1 && x > 0 && x1 > 0 && x8 > -1 && x9 > 0 && x5 > -1 && x4 > 2 && x10 > 0 && x11 > -1

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

   f355_0_reverse_NULL(x1, x2, x3, x4) -> f355_0_reverse_NULL(x1, x2)

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(27)
Obligation:
Rules:
f355_0_reverse_NULL(x41:0, x42:0) -> f355_0_reverse_NULL(x61:0, x62:0) :|: x61:0 - 3 <= x45:0 && x45:0 + 1 <= x42:0 && x46:0 <= x42:0 && x61:0 - 2 <= x46:0 && x47:0 <= x41:0 && x61:0 - 2 <= x47:0 && x48:0 + 1 <= x42:0 && x61:0 - 3 <= x48:0 && x41:0 > 0 && x62:0 <= x45:0 && x42:0 > 0 && x62:0 + 1 <= x46:0 && x62:0 + 1 <= x47:0 && x62:0 <= x48:0 && x45:0 > -1 && x46:0 > 0 && x47:0 > 0 && x48:0 > -1 && x61:0 > 2 && x62:0 > -1
f355_0_reverse_NULL(x, x1) -> f355_0_reverse_NULL(x4, x5) :|: x5 <= x8 && x8 + 1 <= x1 && x9 <= x1 && x5 + 1 <= x9 && x10 <= x && x5 <= x11 && x11 + 1 <= x1 && x > 0 && x1 > 0 && x8 > -1 && x9 > 0 && x5 > -1 && x4 > 2 && x10 > 0 && x11 > -1

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(28) FilterProof (EQUIVALENT)
Used the following sort dictionary for filtering: 
f355_0_reverse_NULL(INTEGER, INTEGER)
Replaced non-predefined constructor symbols by 0.
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(29)
Obligation:
Rules:
f355_0_reverse_NULL(x41:0, x42:0) -> f355_0_reverse_NULL(x61:0, x62:0) :|: x61:0 - 3 <= x45:0 && x45:0 + 1 <= x42:0 && x46:0 <= x42:0 && x61:0 - 2 <= x46:0 && x47:0 <= x41:0 && x61:0 - 2 <= x47:0 && x48:0 + 1 <= x42:0 && x61:0 - 3 <= x48:0 && x41:0 > 0 && x62:0 <= x45:0 && x42:0 > 0 && x62:0 + 1 <= x46:0 && x62:0 + 1 <= x47:0 && x62:0 <= x48:0 && x45:0 > -1 && x46:0 > 0 && x47:0 > 0 && x48:0 > -1 && x61:0 > 2 && x62:0 > -1
f355_0_reverse_NULL(x, x1) -> f355_0_reverse_NULL(x4, x5) :|: x5 <= x8 && x8 + 1 <= x1 && x9 <= x1 && x5 + 1 <= x9 && x10 <= x && x5 <= x11 && x11 + 1 <= x1 && x > 0 && x1 > 0 && x8 > -1 && x9 > 0 && x5 > -1 && x4 > 2 && x10 > 0 && x11 > -1

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(30) IntTRSCompressionProof (EQUIVALENT)
Compressed rules.
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(31)
Obligation:
Rules:
f355_0_reverse_NULL(x:0, x1:0) -> f355_0_reverse_NULL(x4:0, x5:0) :|: x10:0 > 0 && x11:0 > -1 && x4:0 > 2 && x5:0 > -1 && x9:0 > 0 && x8:0 > -1 && x1:0 > 0 && x:0 > 0 && x1:0 >= x11:0 + 1 && x5:0 <= x11:0 && x:0 >= x10:0 && x9:0 >= x5:0 + 1 && x9:0 <= x1:0 && x8:0 + 1 <= x1:0 && x8:0 >= x5:0
f355_0_reverse_NULL(x41:0:0, x42:0:0) -> f355_0_reverse_NULL(x61:0:0, x62:0:0) :|: x61:0:0 > 2 && x62:0:0 > -1 && x48:0:0 > -1 && x47:0:0 > 0 && x46:0:0 > 0 && x45:0:0 > -1 && x62:0:0 <= x48:0:0 && x62:0:0 + 1 <= x47:0:0 && x62:0:0 + 1 <= x46:0:0 && x42:0:0 > 0 && x62:0:0 <= x45:0:0 && x41:0:0 > 0 && x61:0:0 - 3 <= x48:0:0 && x48:0:0 + 1 <= x42:0:0 && x61:0:0 - 2 <= x47:0:0 && x47:0:0 <= x41:0:0 && x61:0:0 - 2 <= x46:0:0 && x46:0:0 <= x42:0:0 && x45:0:0 + 1 <= x42:0:0 && x61:0:0 - 3 <= x45:0:0

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(32) RankingReductionPairProof (EQUIVALENT)
Interpretation:
[ f355_0_reverse_NULL ] = f355_0_reverse_NULL_2

The following rules are decreasing:
f355_0_reverse_NULL(x:0, x1:0) -> f355_0_reverse_NULL(x4:0, x5:0) :|: x10:0 > 0 && x11:0 > -1 && x4:0 > 2 && x5:0 > -1 && x9:0 > 0 && x8:0 > -1 && x1:0 > 0 && x:0 > 0 && x1:0 >= x11:0 + 1 && x5:0 <= x11:0 && x:0 >= x10:0 && x9:0 >= x5:0 + 1 && x9:0 <= x1:0 && x8:0 + 1 <= x1:0 && x8:0 >= x5:0
f355_0_reverse_NULL(x41:0:0, x42:0:0) -> f355_0_reverse_NULL(x61:0:0, x62:0:0) :|: x61:0:0 > 2 && x62:0:0 > -1 && x48:0:0 > -1 && x47:0:0 > 0 && x46:0:0 > 0 && x45:0:0 > -1 && x62:0:0 <= x48:0:0 && x62:0:0 + 1 <= x47:0:0 && x62:0:0 + 1 <= x46:0:0 && x42:0:0 > 0 && x62:0:0 <= x45:0:0 && x41:0:0 > 0 && x61:0:0 - 3 <= x48:0:0 && x48:0:0 + 1 <= x42:0:0 && x61:0:0 - 2 <= x47:0:0 && x47:0:0 <= x41:0:0 && x61:0:0 - 2 <= x46:0:0 && x46:0:0 <= x42:0:0 && x45:0:0 + 1 <= x42:0:0 && x61:0:0 - 3 <= x45:0:0

The following rules are bounded:
f355_0_reverse_NULL(x:0, x1:0) -> f355_0_reverse_NULL(x4:0, x5:0) :|: x10:0 > 0 && x11:0 > -1 && x4:0 > 2 && x5:0 > -1 && x9:0 > 0 && x8:0 > -1 && x1:0 > 0 && x:0 > 0 && x1:0 >= x11:0 + 1 && x5:0 <= x11:0 && x:0 >= x10:0 && x9:0 >= x5:0 + 1 && x9:0 <= x1:0 && x8:0 + 1 <= x1:0 && x8:0 >= x5:0
f355_0_reverse_NULL(x41:0:0, x42:0:0) -> f355_0_reverse_NULL(x61:0:0, x62:0:0) :|: x61:0:0 > 2 && x62:0:0 > -1 && x48:0:0 > -1 && x47:0:0 > 0 && x46:0:0 > 0 && x45:0:0 > -1 && x62:0:0 <= x48:0:0 && x62:0:0 + 1 <= x47:0:0 && x62:0:0 + 1 <= x46:0:0 && x42:0:0 > 0 && x62:0:0 <= x45:0:0 && x41:0:0 > 0 && x61:0:0 - 3 <= x48:0:0 && x48:0:0 + 1 <= x42:0:0 && x61:0:0 - 2 <= x47:0:0 && x47:0:0 <= x41:0:0 && x61:0:0 - 2 <= x46:0:0 && x46:0:0 <= x42:0:0 && x45:0:0 + 1 <= x42:0:0 && x61:0:0 - 3 <= x45:0:0


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(33)
YES