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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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, 274 ms]
(4) AND
    (5) IRSwT
        (6) IntTRSCompressionProof [EQUIVALENT, 39 ms]
        (7) IRSwT
        (8) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms]
        (9) IRSwT
        (10) TempFilterProof [SOUND, 36 ms]
        (11) IntTRS
        (12) PolynomialOrderProcessor [EQUIVALENT, 0 ms]
        (13) YES
    (14) IRSwT
        (15) IntTRSCompressionProof [EQUIVALENT, 12 ms]
        (16) IRSwT
        (17) TempFilterProof [SOUND, 129 ms]
        (18) IntTRS
        (19) PolynomialOrderProcessor [EQUIVALENT, 0 ms]
        (20) IntTRS
        (21) PolynomialOrderProcessor [EQUIVALENT, 0 ms]
        (22) IntTRS
        (23) PolynomialOrderProcessor [EQUIVALENT, 0 ms]
        (24) YES


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(0)
Obligation:
Rules:
f1_0_main_Load(arg1, arg2) -> f180_0_main_InvokeMethod(arg1P, arg2P) :|: -1 <= x4 - 1 && 0 <= arg2 - 1 && arg1P <= arg1 && 0 <= arg1 - 1 && 0 <= arg1P - 1 && 2 <= arg2P - 1
f1_0_main_Load(x, x1) -> f180_0_main_InvokeMethod(x2, x3) :|: -1 <= x5 - 1 && 0 <= x1 - 1 && x2 <= x && x3 - 1 <= x && 0 <= x - 1 && 0 <= x2 - 1 && 1 <= x3 - 1
f180_0_main_InvokeMethod(x6, x7) -> f370_0_growReduce_NONNULL(x8, x11) :|: x11 <= x7 && 0 <= x12 - 1 && 0 <= x6 - 1 && 0 <= x7 - 1 && 0 <= x11 - 1 && 0 = x8
f1_0_main_Load(x13, x14) -> f117_0_createList_LE(x15, x16) :|: 0 <= x13 - 1 && 0 <= x14 - 1 && -1 <= x15 - 1
f117_0_createList_LE(x17, x18) -> f117_0_createList_LE(x19, x20) :|: x17 - 1 = x19 && x17 - 1 <= x17 - 1 && 1 <= x17 - 1
f370_0_growReduce_NONNULL(x21, x22) -> f370_0_growReduce_NONNULL(x23, x24) :|: 1 = x23 && 0 = x21 && -1 <= x24 - 1 && 6 <= x22 - 1 && x24 + 7 <= x22
f370_0_growReduce_NONNULL(x25, x26) -> f370_0_growReduce_NONNULL(x27, x28) :|: 2 = x27 && 1 = x25 && 2 <= x28 - 1 && 0 <= x26 - 1 && x28 - 2 <= x26
f370_0_growReduce_NONNULL(x29, x30) -> f370_0_growReduce_NONNULL(x31, x32) :|: 0 = x31 && 2 = x29 && 4 <= x32 - 1 && 0 <= x30 - 1 && x32 - 4 <= x30
__init(x33, x34) -> f1_0_main_Load(x35, x36) :|: 0 <= 0
Start term: __init(arg1, arg2)

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(1) IRSFormatTransformerProof (EQUIVALENT)
Reformatted IRS to match normalized format (transformed away non-linear left-hand sides, !=, / and %).
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(2)
Obligation:
Rules:
f1_0_main_Load(arg1, arg2) -> f180_0_main_InvokeMethod(arg1P, arg2P) :|: -1 <= x4 - 1 && 0 <= arg2 - 1 && arg1P <= arg1 && 0 <= arg1 - 1 && 0 <= arg1P - 1 && 2 <= arg2P - 1
f1_0_main_Load(x, x1) -> f180_0_main_InvokeMethod(x2, x3) :|: -1 <= x5 - 1 && 0 <= x1 - 1 && x2 <= x && x3 - 1 <= x && 0 <= x - 1 && 0 <= x2 - 1 && 1 <= x3 - 1
f180_0_main_InvokeMethod(x6, x7) -> f370_0_growReduce_NONNULL(x8, x11) :|: x11 <= x7 && 0 <= x12 - 1 && 0 <= x6 - 1 && 0 <= x7 - 1 && 0 <= x11 - 1 && 0 = x8
f1_0_main_Load(x13, x14) -> f117_0_createList_LE(x15, x16) :|: 0 <= x13 - 1 && 0 <= x14 - 1 && -1 <= x15 - 1
f117_0_createList_LE(x17, x18) -> f117_0_createList_LE(x19, x20) :|: x17 - 1 = x19 && x17 - 1 <= x17 - 1 && 1 <= x17 - 1
f370_0_growReduce_NONNULL(x21, x22) -> f370_0_growReduce_NONNULL(x23, x24) :|: 1 = x23 && 0 = x21 && -1 <= x24 - 1 && 6 <= x22 - 1 && x24 + 7 <= x22
f370_0_growReduce_NONNULL(x25, x26) -> f370_0_growReduce_NONNULL(x27, x28) :|: 2 = x27 && 1 = x25 && 2 <= x28 - 1 && 0 <= x26 - 1 && x28 - 2 <= x26
f370_0_growReduce_NONNULL(x29, x30) -> f370_0_growReduce_NONNULL(x31, x32) :|: 0 = x31 && 2 = x29 && 4 <= x32 - 1 && 0 <= x30 - 1 && x32 - 4 <= x30
__init(x33, x34) -> f1_0_main_Load(x35, x36) :|: 0 <= 0
Start term: __init(arg1, arg2)

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(3) IRSwTTerminationDigraphProof (EQUIVALENT)
Constructed termination digraph!
Nodes:
(1) f1_0_main_Load(arg1, arg2) -> f180_0_main_InvokeMethod(arg1P, arg2P) :|: -1 <= x4 - 1 && 0 <= arg2 - 1 && arg1P <= arg1 && 0 <= arg1 - 1 && 0 <= arg1P - 1 && 2 <= arg2P - 1
(2) f1_0_main_Load(x, x1) -> f180_0_main_InvokeMethod(x2, x3) :|: -1 <= x5 - 1 && 0 <= x1 - 1 && x2 <= x && x3 - 1 <= x && 0 <= x - 1 && 0 <= x2 - 1 && 1 <= x3 - 1
(3) f180_0_main_InvokeMethod(x6, x7) -> f370_0_growReduce_NONNULL(x8, x11) :|: x11 <= x7 && 0 <= x12 - 1 && 0 <= x6 - 1 && 0 <= x7 - 1 && 0 <= x11 - 1 && 0 = x8
(4) f1_0_main_Load(x13, x14) -> f117_0_createList_LE(x15, x16) :|: 0 <= x13 - 1 && 0 <= x14 - 1 && -1 <= x15 - 1
(5) f117_0_createList_LE(x17, x18) -> f117_0_createList_LE(x19, x20) :|: x17 - 1 = x19 && x17 - 1 <= x17 - 1 && 1 <= x17 - 1
(6) f370_0_growReduce_NONNULL(x21, x22) -> f370_0_growReduce_NONNULL(x23, x24) :|: 1 = x23 && 0 = x21 && -1 <= x24 - 1 && 6 <= x22 - 1 && x24 + 7 <= x22
(7) f370_0_growReduce_NONNULL(x25, x26) -> f370_0_growReduce_NONNULL(x27, x28) :|: 2 = x27 && 1 = x25 && 2 <= x28 - 1 && 0 <= x26 - 1 && x28 - 2 <= x26
(8) f370_0_growReduce_NONNULL(x29, x30) -> f370_0_growReduce_NONNULL(x31, x32) :|: 0 = x31 && 2 = x29 && 4 <= x32 - 1 && 0 <= x30 - 1 && x32 - 4 <= x30
(9) __init(x33, x34) -> f1_0_main_Load(x35, x36) :|: 0 <= 0

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

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

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(5)
Obligation:

Termination digraph:
Nodes:
(1) f117_0_createList_LE(x17, x18) -> f117_0_createList_LE(x19, x20) :|: x17 - 1 = x19 && x17 - 1 <= x17 - 1 && 1 <= x17 - 1

Arcs:
(1) -> (1)

This digraph is fully evaluated!

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(6) IntTRSCompressionProof (EQUIVALENT)
Compressed rules.
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(7)
Obligation:
Rules:
f117_0_createList_LE(x17:0, x18:0) -> f117_0_createList_LE(x17:0 - 1, x20:0) :|: x17:0 > 1

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

   f117_0_createList_LE(x1, x2) -> f117_0_createList_LE(x1)

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(9)
Obligation:
Rules:
f117_0_createList_LE(x17:0) -> f117_0_createList_LE(x17:0 - 1) :|: x17:0 > 1

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(10) TempFilterProof (SOUND)
Used the following sort dictionary for filtering: 
f117_0_createList_LE(INTEGER)
Replaced non-predefined constructor symbols by 0.
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(11)
Obligation:
Rules:
f117_0_createList_LE(x17:0) -> f117_0_createList_LE(c) :|: c = x17:0 - 1 && x17:0 > 1

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(12) PolynomialOrderProcessor (EQUIVALENT)
Found the following polynomial interpretation:
[f117_0_createList_LE(x)] = x

The following rules are decreasing:
f117_0_createList_LE(x17:0) -> f117_0_createList_LE(c) :|: c = x17:0 - 1 && x17:0 > 1
The following rules are bounded:
f117_0_createList_LE(x17:0) -> f117_0_createList_LE(c) :|: c = x17:0 - 1 && x17:0 > 1

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(13)
YES

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(14)
Obligation:

Termination digraph:
Nodes:
(1) f370_0_growReduce_NONNULL(x21, x22) -> f370_0_growReduce_NONNULL(x23, x24) :|: 1 = x23 && 0 = x21 && -1 <= x24 - 1 && 6 <= x22 - 1 && x24 + 7 <= x22
(2) f370_0_growReduce_NONNULL(x29, x30) -> f370_0_growReduce_NONNULL(x31, x32) :|: 0 = x31 && 2 = x29 && 4 <= x32 - 1 && 0 <= x30 - 1 && x32 - 4 <= x30
(3) f370_0_growReduce_NONNULL(x25, x26) -> f370_0_growReduce_NONNULL(x27, x28) :|: 2 = x27 && 1 = x25 && 2 <= x28 - 1 && 0 <= x26 - 1 && x28 - 2 <= x26

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

This digraph is fully evaluated!

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

(16)
Obligation:
Rules:
f370_0_growReduce_NONNULL(cons_0, x22:0) -> f370_0_growReduce_NONNULL(1, x24:0) :|: x22:0 > 6 && x24:0 > -1 && x24:0 + 7 <= x22:0 && cons_0 = 0
f370_0_growReduce_NONNULL(cons_2, x30:0) -> f370_0_growReduce_NONNULL(0, x32:0) :|: x30:0 > 0 && x32:0 > 4 && x32:0 - 4 <= x30:0 && cons_2 = 2
f370_0_growReduce_NONNULL(cons_1, x26:0) -> f370_0_growReduce_NONNULL(2, x28:0) :|: x26:0 > 0 && x28:0 > 2 && x28:0 - 2 <= x26:0 && cons_1 = 1

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(17) TempFilterProof (SOUND)
Used the following sort dictionary for filtering: 
f370_0_growReduce_NONNULL(VARIABLE, INTEGER)
Replaced non-predefined constructor symbols by 0.
----------------------------------------

(18)
Obligation:
Rules:
f370_0_growReduce_NONNULL(c, x22:0) -> f370_0_growReduce_NONNULL(c1, x24:0) :|: c1 = 1 && c = 0 && (x22:0 > 6 && x24:0 > -1 && x24:0 + 7 <= x22:0 && cons_0 = 0)
f370_0_growReduce_NONNULL(c2, x30:0) -> f370_0_growReduce_NONNULL(c3, x32:0) :|: c3 = 0 && c2 = 2 && (x30:0 > 0 && x32:0 > 4 && x32:0 - 4 <= x30:0 && cons_2 = 2)
f370_0_growReduce_NONNULL(c4, x26:0) -> f370_0_growReduce_NONNULL(c5, x28:0) :|: c5 = 2 && c4 = 1 && (x26:0 > 0 && x28:0 > 2 && x28:0 - 2 <= x26:0 && cons_1 = 1)

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(19) PolynomialOrderProcessor (EQUIVALENT)
Found the following polynomial interpretation:
[f370_0_growReduce_NONNULL(x, x1)] = 10*x - 4*x^2 + x1

The following rules are decreasing:
f370_0_growReduce_NONNULL(c, x22:0) -> f370_0_growReduce_NONNULL(c1, x24:0) :|: c1 = 1 && c = 0 && (x22:0 > 6 && x24:0 > -1 && x24:0 + 7 <= x22:0 && cons_0 = 0)
The following rules are bounded:
f370_0_growReduce_NONNULL(c, x22:0) -> f370_0_growReduce_NONNULL(c1, x24:0) :|: c1 = 1 && c = 0 && (x22:0 > 6 && x24:0 > -1 && x24:0 + 7 <= x22:0 && cons_0 = 0)
f370_0_growReduce_NONNULL(c2, x30:0) -> f370_0_growReduce_NONNULL(c3, x32:0) :|: c3 = 0 && c2 = 2 && (x30:0 > 0 && x32:0 > 4 && x32:0 - 4 <= x30:0 && cons_2 = 2)
f370_0_growReduce_NONNULL(c4, x26:0) -> f370_0_growReduce_NONNULL(c5, x28:0) :|: c5 = 2 && c4 = 1 && (x26:0 > 0 && x28:0 > 2 && x28:0 - 2 <= x26:0 && cons_1 = 1)

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(20)
Obligation:
Rules:
f370_0_growReduce_NONNULL(c2, x30:0) -> f370_0_growReduce_NONNULL(c3, x32:0) :|: c3 = 0 && c2 = 2 && (x30:0 > 0 && x32:0 > 4 && x32:0 - 4 <= x30:0 && cons_2 = 2)
f370_0_growReduce_NONNULL(c4, x26:0) -> f370_0_growReduce_NONNULL(c5, x28:0) :|: c5 = 2 && c4 = 1 && (x26:0 > 0 && x28:0 > 2 && x28:0 - 2 <= x26:0 && cons_1 = 1)

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(21) PolynomialOrderProcessor (EQUIVALENT)
Found the following polynomial interpretation:
[f370_0_growReduce_NONNULL(x, x1)] = -1 + 3*x - x^2

The following rules are decreasing:
f370_0_growReduce_NONNULL(c2, x30:0) -> f370_0_growReduce_NONNULL(c3, x32:0) :|: c3 = 0 && c2 = 2 && (x30:0 > 0 && x32:0 > 4 && x32:0 - 4 <= x30:0 && cons_2 = 2)
The following rules are bounded:
f370_0_growReduce_NONNULL(c2, x30:0) -> f370_0_growReduce_NONNULL(c3, x32:0) :|: c3 = 0 && c2 = 2 && (x30:0 > 0 && x32:0 > 4 && x32:0 - 4 <= x30:0 && cons_2 = 2)
f370_0_growReduce_NONNULL(c4, x26:0) -> f370_0_growReduce_NONNULL(c5, x28:0) :|: c5 = 2 && c4 = 1 && (x26:0 > 0 && x28:0 > 2 && x28:0 - 2 <= x26:0 && cons_1 = 1)

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(22)
Obligation:
Rules:
f370_0_growReduce_NONNULL(c4, x26:0) -> f370_0_growReduce_NONNULL(c5, x28:0) :|: c5 = 2 && c4 = 1 && (x26:0 > 0 && x28:0 > 2 && x28:0 - 2 <= x26:0 && cons_1 = 1)

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(23) PolynomialOrderProcessor (EQUIVALENT)
Found the following polynomial interpretation:
[f370_0_growReduce_NONNULL(x, x1)] = 1 - x

The following rules are decreasing:
f370_0_growReduce_NONNULL(c4, x26:0) -> f370_0_growReduce_NONNULL(c5, x28:0) :|: c5 = 2 && c4 = 1 && (x26:0 > 0 && x28:0 > 2 && x28:0 - 2 <= x26:0 && cons_1 = 1)
The following rules are bounded:
f370_0_growReduce_NONNULL(c4, x26:0) -> f370_0_growReduce_NONNULL(c5, x28:0) :|: c5 = 2 && c4 = 1 && (x26:0 > 0 && x28:0 > 2 && x28:0 - 2 <= x26:0 && cons_1 = 1)

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(24)
YES