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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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, 374 ms]
(4) AND
    (5) IRSwT
        (6) IntTRSCompressionProof [EQUIVALENT, 16 ms]
        (7) IRSwT
        (8) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms]
        (9) IRSwT
        (10) TempFilterProof [SOUND, 35 ms]
        (11) IntTRS
        (12) RankingReductionPairProof [EQUIVALENT, 0 ms]
        (13) YES
    (14) IRSwT
        (15) IntTRSCompressionProof [EQUIVALENT, 7 ms]
        (16) IRSwT
        (17) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms]
        (18) IRSwT
        (19) FilterProof [EQUIVALENT, 0 ms]
        (20) IntTRS
        (21) IntTRSCompressionProof [EQUIVALENT, 0 ms]
        (22) IntTRS
        (23) PolynomialOrderProcessor [EQUIVALENT, 3 ms]
        (24) YES


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(0)
Obligation:
Rules:
f289_0_appendNewList_Return(arg1, arg2, arg3, arg4, arg5) -> f540_0_random_ArrayAccess(arg1P, arg2P, arg3P, arg4P, arg5P) :|: arg5 = arg4P && 0 = arg3P && 0 = arg4 && arg5 + 2 <= arg2 && 3 <= arg1P - 1 && 3 <= arg2 - 1 && 0 <= arg1 - 1 && arg1P <= arg2
f1_0_main_Load(x, x1, x2, x3, x4) -> f540_0_random_ArrayAccess(x5, x6, x7, x8, x9) :|: 0 = x7 && x1 = x6 && 3 <= x5 - 1 && 0 <= x - 1
f540_0_random_ArrayAccess(x10, x11, x12, x13, x14) -> f673_0_main_InvokeMethod(x15, x16, x17, x18, x19) :|: 0 <= x20 - 1 && x20 <= x11 - 1 && -1 <= x21 - 1 && x15 + 3 <= x10 && 3 <= x10 - 1 && 0 <= x15 - 1 && 3 <= x16 - 1 && x13 + 2 <= x10 && 0 = x12 && x13 = x19
f673_0_main_InvokeMethod(x22, x23, x24, x25, x26) -> f760_0_copy_NONNULL(x27, x28, x29, x30, x31) :|: x24 = x28 && x25 + 4 <= x23 && x26 + 2 <= x23 && 3 <= x27 - 1 && 3 <= x23 - 1 && 0 <= x22 - 1 && 0 <= x24 - 1 && x27 <= x23
f1_0_main_Load(x32, x33, x34, x35, x38) -> f422_0_random_ArrayAccess(x39, x40, x42, x43, x44) :|: 1 = x39 && 0 <= x40 - 1 && 0 <= x32 - 1 && -1 <= x33 - 1 && x40 <= x32
f540_0_random_ArrayAccess(x45, x46, x47, x48, x49) -> f422_0_random_ArrayAccess(x50, x53, x54, x55, x56) :|: 0 <= x57 - 1 && x57 <= x46 - 1 && -1 <= x50 - 1 && -1 <= x46 - 1 && x53 + 3 <= x45 && 3 <= x45 - 1 && 0 <= x53 - 1 && x48 + 2 <= x45 && 0 = x47
f422_0_random_ArrayAccess(x58, x60, x61, x62, x63) -> f422_0_random_ArrayAccess(x64, x65, x66, x67, x68) :|: x69 <= x70 - 1 && 1 <= x58 - 1 && -1 <= x69 - 1 && -1 <= x71 - 1 && -1 <= x70 - 1 && x58 - 1 <= x58 - 1 && x65 <= x60 && 0 <= x60 - 1 && 0 <= x65 - 1 && x58 - 1 = x64
f760_0_copy_NONNULL(x72, x73, x74, x75, x76) -> f760_0_copy_NONNULL(x77, x78, x79, x80, x81) :|: x73 = x78 && -1 <= x77 - 1 && 0 <= x72 - 1 && 0 <= x73 - 1 && x77 + 1 <= x72
__init(x82, x83, x84, x85, x86) -> f1_0_main_Load(x87, x88, x89, x90, x91) :|: 0 <= 0
Start term: __init(arg1, arg2, arg3, arg4, arg5)

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

(2)
Obligation:
Rules:
f289_0_appendNewList_Return(arg1, arg2, arg3, arg4, arg5) -> f540_0_random_ArrayAccess(arg1P, arg2P, arg3P, arg4P, arg5P) :|: arg5 = arg4P && 0 = arg3P && 0 = arg4 && arg5 + 2 <= arg2 && 3 <= arg1P - 1 && 3 <= arg2 - 1 && 0 <= arg1 - 1 && arg1P <= arg2
f1_0_main_Load(x, x1, x2, x3, x4) -> f540_0_random_ArrayAccess(x5, x6, x7, x8, x9) :|: 0 = x7 && x1 = x6 && 3 <= x5 - 1 && 0 <= x - 1
f540_0_random_ArrayAccess(x10, x11, x12, x13, x14) -> f673_0_main_InvokeMethod(x15, x16, x17, x18, x19) :|: 0 <= x20 - 1 && x20 <= x11 - 1 && -1 <= x21 - 1 && x15 + 3 <= x10 && 3 <= x10 - 1 && 0 <= x15 - 1 && 3 <= x16 - 1 && x13 + 2 <= x10 && 0 = x12 && x13 = x19
f673_0_main_InvokeMethod(x22, x23, x24, x25, x26) -> f760_0_copy_NONNULL(x27, x28, x29, x30, x31) :|: x24 = x28 && x25 + 4 <= x23 && x26 + 2 <= x23 && 3 <= x27 - 1 && 3 <= x23 - 1 && 0 <= x22 - 1 && 0 <= x24 - 1 && x27 <= x23
f1_0_main_Load(x32, x33, x34, x35, x38) -> f422_0_random_ArrayAccess(x39, x40, x42, x43, x44) :|: 1 = x39 && 0 <= x40 - 1 && 0 <= x32 - 1 && -1 <= x33 - 1 && x40 <= x32
f540_0_random_ArrayAccess(x45, x46, x47, x48, x49) -> f422_0_random_ArrayAccess(x50, x53, x54, x55, x56) :|: 0 <= x57 - 1 && x57 <= x46 - 1 && -1 <= x50 - 1 && -1 <= x46 - 1 && x53 + 3 <= x45 && 3 <= x45 - 1 && 0 <= x53 - 1 && x48 + 2 <= x45 && 0 = x47
f422_0_random_ArrayAccess(x58, x60, x61, x62, x63) -> f422_0_random_ArrayAccess(x64, x65, x66, x67, x68) :|: x69 <= x70 - 1 && 1 <= x58 - 1 && -1 <= x69 - 1 && -1 <= x71 - 1 && -1 <= x70 - 1 && x58 - 1 <= x58 - 1 && x65 <= x60 && 0 <= x60 - 1 && 0 <= x65 - 1 && x58 - 1 = x64
f760_0_copy_NONNULL(x72, x73, x74, x75, x76) -> f760_0_copy_NONNULL(x77, x78, x79, x80, x81) :|: x73 = x78 && -1 <= x77 - 1 && 0 <= x72 - 1 && 0 <= x73 - 1 && x77 + 1 <= x72
__init(x82, x83, x84, x85, x86) -> f1_0_main_Load(x87, x88, x89, x90, x91) :|: 0 <= 0
Start term: __init(arg1, arg2, arg3, arg4, arg5)

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(3) IRSwTTerminationDigraphProof (EQUIVALENT)
Constructed termination digraph!
Nodes:
(1) f289_0_appendNewList_Return(arg1, arg2, arg3, arg4, arg5) -> f540_0_random_ArrayAccess(arg1P, arg2P, arg3P, arg4P, arg5P) :|: arg5 = arg4P && 0 = arg3P && 0 = arg4 && arg5 + 2 <= arg2 && 3 <= arg1P - 1 && 3 <= arg2 - 1 && 0 <= arg1 - 1 && arg1P <= arg2
(2) f1_0_main_Load(x, x1, x2, x3, x4) -> f540_0_random_ArrayAccess(x5, x6, x7, x8, x9) :|: 0 = x7 && x1 = x6 && 3 <= x5 - 1 && 0 <= x - 1
(3) f540_0_random_ArrayAccess(x10, x11, x12, x13, x14) -> f673_0_main_InvokeMethod(x15, x16, x17, x18, x19) :|: 0 <= x20 - 1 && x20 <= x11 - 1 && -1 <= x21 - 1 && x15 + 3 <= x10 && 3 <= x10 - 1 && 0 <= x15 - 1 && 3 <= x16 - 1 && x13 + 2 <= x10 && 0 = x12 && x13 = x19
(4) f673_0_main_InvokeMethod(x22, x23, x24, x25, x26) -> f760_0_copy_NONNULL(x27, x28, x29, x30, x31) :|: x24 = x28 && x25 + 4 <= x23 && x26 + 2 <= x23 && 3 <= x27 - 1 && 3 <= x23 - 1 && 0 <= x22 - 1 && 0 <= x24 - 1 && x27 <= x23
(5) f1_0_main_Load(x32, x33, x34, x35, x38) -> f422_0_random_ArrayAccess(x39, x40, x42, x43, x44) :|: 1 = x39 && 0 <= x40 - 1 && 0 <= x32 - 1 && -1 <= x33 - 1 && x40 <= x32
(6) f540_0_random_ArrayAccess(x45, x46, x47, x48, x49) -> f422_0_random_ArrayAccess(x50, x53, x54, x55, x56) :|: 0 <= x57 - 1 && x57 <= x46 - 1 && -1 <= x50 - 1 && -1 <= x46 - 1 && x53 + 3 <= x45 && 3 <= x45 - 1 && 0 <= x53 - 1 && x48 + 2 <= x45 && 0 = x47
(7) f422_0_random_ArrayAccess(x58, x60, x61, x62, x63) -> f422_0_random_ArrayAccess(x64, x65, x66, x67, x68) :|: x69 <= x70 - 1 && 1 <= x58 - 1 && -1 <= x69 - 1 && -1 <= x71 - 1 && -1 <= x70 - 1 && x58 - 1 <= x58 - 1 && x65 <= x60 && 0 <= x60 - 1 && 0 <= x65 - 1 && x58 - 1 = x64
(8) f760_0_copy_NONNULL(x72, x73, x74, x75, x76) -> f760_0_copy_NONNULL(x77, x78, x79, x80, x81) :|: x73 = x78 && -1 <= x77 - 1 && 0 <= x72 - 1 && 0 <= x73 - 1 && x77 + 1 <= x72
(9) __init(x82, x83, x84, x85, x86) -> f1_0_main_Load(x87, x88, x89, x90, x91) :|: 0 <= 0

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

This digraph is fully evaluated!
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(4)
Complex Obligation (AND)

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(5)
Obligation:

Termination digraph:
Nodes:
(1) f422_0_random_ArrayAccess(x58, x60, x61, x62, x63) -> f422_0_random_ArrayAccess(x64, x65, x66, x67, x68) :|: x69 <= x70 - 1 && 1 <= x58 - 1 && -1 <= x69 - 1 && -1 <= x71 - 1 && -1 <= x70 - 1 && x58 - 1 <= x58 - 1 && x65 <= x60 && 0 <= x60 - 1 && 0 <= x65 - 1 && x58 - 1 = x64

Arcs:
(1) -> (1)

This digraph is fully evaluated!

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(6) IntTRSCompressionProof (EQUIVALENT)
Compressed rules.
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(7)
Obligation:
Rules:
f422_0_random_ArrayAccess(x58:0, x60:0, x61:0, x62:0, x63:0) -> f422_0_random_ArrayAccess(x58:0 - 1, x65:0, x66:0, x67:0, x68:0) :|: x60:0 > 0 && x65:0 > 0 && x65:0 <= x60:0 && x70:0 > -1 && x71:0 > -1 && x69:0 > -1 && x58:0 > 1 && x70:0 - 1 >= x69:0

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

   f422_0_random_ArrayAccess(x1, x2, x3, x4, x5) -> f422_0_random_ArrayAccess(x1, x2)

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(9)
Obligation:
Rules:
f422_0_random_ArrayAccess(x58:0, x60:0) -> f422_0_random_ArrayAccess(x58:0 - 1, x65:0) :|: x60:0 > 0 && x65:0 > 0 && x65:0 <= x60:0 && x70:0 > -1 && x71:0 > -1 && x69:0 > -1 && x58:0 > 1 && x70:0 - 1 >= x69:0

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(10) TempFilterProof (SOUND)
Used the following sort dictionary for filtering: 
f422_0_random_ArrayAccess(INTEGER, INTEGER)
Replaced non-predefined constructor symbols by 0.
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(11)
Obligation:
Rules:
f422_0_random_ArrayAccess(x58:0, x60:0) -> f422_0_random_ArrayAccess(c, x65:0) :|: c = x58:0 - 1 && (x60:0 > 0 && x65:0 > 0 && x65:0 <= x60:0 && x70:0 > -1 && x71:0 > -1 && x69:0 > -1 && x58:0 > 1 && x70:0 - 1 >= x69:0)

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(12) RankingReductionPairProof (EQUIVALENT)
Interpretation:
[ f422_0_random_ArrayAccess ] = f422_0_random_ArrayAccess_1

The following rules are decreasing:
f422_0_random_ArrayAccess(x58:0, x60:0) -> f422_0_random_ArrayAccess(c, x65:0) :|: c = x58:0 - 1 && (x60:0 > 0 && x65:0 > 0 && x65:0 <= x60:0 && x70:0 > -1 && x71:0 > -1 && x69:0 > -1 && x58:0 > 1 && x70:0 - 1 >= x69:0)

The following rules are bounded:
f422_0_random_ArrayAccess(x58:0, x60:0) -> f422_0_random_ArrayAccess(c, x65:0) :|: c = x58:0 - 1 && (x60:0 > 0 && x65:0 > 0 && x65:0 <= x60:0 && x70:0 > -1 && x71:0 > -1 && x69:0 > -1 && x58:0 > 1 && x70:0 - 1 >= x69:0)


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(13)
YES

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(14)
Obligation:

Termination digraph:
Nodes:
(1) f760_0_copy_NONNULL(x72, x73, x74, x75, x76) -> f760_0_copy_NONNULL(x77, x78, x79, x80, x81) :|: x73 = x78 && -1 <= x77 - 1 && 0 <= x72 - 1 && 0 <= x73 - 1 && x77 + 1 <= x72

Arcs:
(1) -> (1)

This digraph is fully evaluated!

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

(16)
Obligation:
Rules:
f760_0_copy_NONNULL(x72:0, x73:0, x74:0, x75:0, x76:0) -> f760_0_copy_NONNULL(x77:0, x73:0, x79:0, x80:0, x81:0) :|: x73:0 > 0 && x77:0 + 1 <= x72:0 && x77:0 > -1 && x72:0 > 0

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

   f760_0_copy_NONNULL(x1, x2, x3, x4, x5) -> f760_0_copy_NONNULL(x1, x2)

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(18)
Obligation:
Rules:
f760_0_copy_NONNULL(x72:0, x73:0) -> f760_0_copy_NONNULL(x77:0, x73:0) :|: x73:0 > 0 && x77:0 + 1 <= x72:0 && x77:0 > -1 && x72:0 > 0

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(19) FilterProof (EQUIVALENT)
Used the following sort dictionary for filtering: 
f760_0_copy_NONNULL(INTEGER, INTEGER)
Replaced non-predefined constructor symbols by 0.
----------------------------------------

(20)
Obligation:
Rules:
f760_0_copy_NONNULL(x72:0, x73:0) -> f760_0_copy_NONNULL(x77:0, x73:0) :|: x73:0 > 0 && x77:0 + 1 <= x72:0 && x77:0 > -1 && x72:0 > 0

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

(22)
Obligation:
Rules:
f760_0_copy_NONNULL(x72:0:0, x73:0:0) -> f760_0_copy_NONNULL(x77:0:0, x73:0:0) :|: x77:0:0 > -1 && x72:0:0 > 0 && x77:0:0 + 1 <= x72:0:0 && x73:0:0 > 0

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(23) PolynomialOrderProcessor (EQUIVALENT)
Found the following polynomial interpretation:
[f760_0_copy_NONNULL(x, x1)] = x

The following rules are decreasing:
f760_0_copy_NONNULL(x72:0:0, x73:0:0) -> f760_0_copy_NONNULL(x77:0:0, x73:0:0) :|: x77:0:0 > -1 && x72:0:0 > 0 && x77:0:0 + 1 <= x72:0:0 && x73:0:0 > 0
The following rules are bounded:
f760_0_copy_NONNULL(x72:0:0, x73:0:0) -> f760_0_copy_NONNULL(x77:0:0, x73:0:0) :|: x77:0:0 > -1 && x72:0:0 > 0 && x77:0:0 + 1 <= x72:0:0 && x73:0:0 > 0

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(24)
YES