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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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, 264 ms]
(4) AND
    (5) IRSwT
        (6) IntTRSCompressionProof [EQUIVALENT, 0 ms]
        (7) IRSwT
        (8) TempFilterProof [SOUND, 36 ms]
        (9) IntTRS
        (10) RankingReductionPairProof [EQUIVALENT, 21 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, 0 ms]
        (22) NO


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(0)
Obligation:
Rules:
f289_0_createIntList_Return(arg1, arg2) -> f491_0_random_ArrayAccess(arg1P, arg2P) :|: -1 <= arg1P - 1 && -1 <= arg1 - 1 && arg1P <= arg1
f1_0_main_Load(x, x1) -> f491_0_random_ArrayAccess(x2, x3) :|: -1 <= x2 - 1 && 0 <= x - 1
f491_0_random_ArrayAccess(x4, x5) -> f815_0_main_NULL(x6, x8) :|: x6 <= x4 && 0 <= x9 - 1 && -1 <= x4 - 1 && -1 <= x6 - 1
f815_0_main_NULL(x10, x11) -> f815_0_main_NULL(x13, x14) :|: x13 + 2 <= x10 && x16 <= 0 && 1 <= x10 - 1 && -1 <= x13 - 1
f815_0_main_NULL(x17, x19) -> f815_0_main_NULL(x20, x21) :|: x20 <= x17 && 0 <= x22 - 1 && 0 <= x17 - 1 && 0 <= x20 - 1
f815_0_main_NULL(x23, x24) -> f815_0_main_NULL(x25, x26) :|: x25 + 2 <= x23 && x27 <= 0 && 2 <= x23 - 1 && 0 <= x25 - 1
f1_0_main_Load(x28, x29) -> f639_0_createIntList_LE(x30, x31) :|: 1 = x31 && 0 <= x28 - 1 && -1 <= x30 - 1 && -1 <= x29 - 1
f639_0_createIntList_LE(x32, x33) -> f639_0_createIntList_LE(x34, x35) :|: x33 + 1 = x35 && x32 - 1 = x34 && 0 <= x33 - 1 && 0 <= x32 - 1
__init(x36, x37) -> f1_0_main_Load(x38, x39) :|: 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:
f289_0_createIntList_Return(arg1, arg2) -> f491_0_random_ArrayAccess(arg1P, arg2P) :|: -1 <= arg1P - 1 && -1 <= arg1 - 1 && arg1P <= arg1
f1_0_main_Load(x, x1) -> f491_0_random_ArrayAccess(x2, x3) :|: -1 <= x2 - 1 && 0 <= x - 1
f491_0_random_ArrayAccess(x4, x5) -> f815_0_main_NULL(x6, x8) :|: x6 <= x4 && 0 <= x9 - 1 && -1 <= x4 - 1 && -1 <= x6 - 1
f815_0_main_NULL(x10, x11) -> f815_0_main_NULL(x13, x14) :|: x13 + 2 <= x10 && x16 <= 0 && 1 <= x10 - 1 && -1 <= x13 - 1
f815_0_main_NULL(x17, x19) -> f815_0_main_NULL(x20, x21) :|: x20 <= x17 && 0 <= x22 - 1 && 0 <= x17 - 1 && 0 <= x20 - 1
f815_0_main_NULL(x23, x24) -> f815_0_main_NULL(x25, x26) :|: x25 + 2 <= x23 && x27 <= 0 && 2 <= x23 - 1 && 0 <= x25 - 1
f1_0_main_Load(x28, x29) -> f639_0_createIntList_LE(x30, x31) :|: 1 = x31 && 0 <= x28 - 1 && -1 <= x30 - 1 && -1 <= x29 - 1
f639_0_createIntList_LE(x32, x33) -> f639_0_createIntList_LE(x34, x35) :|: x33 + 1 = x35 && x32 - 1 = x34 && 0 <= x33 - 1 && 0 <= x32 - 1
__init(x36, x37) -> f1_0_main_Load(x38, x39) :|: 0 <= 0
Start term: __init(arg1, arg2)

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(3) IRSwTTerminationDigraphProof (EQUIVALENT)
Constructed termination digraph!
Nodes:
(1) f289_0_createIntList_Return(arg1, arg2) -> f491_0_random_ArrayAccess(arg1P, arg2P) :|: -1 <= arg1P - 1 && -1 <= arg1 - 1 && arg1P <= arg1
(2) f1_0_main_Load(x, x1) -> f491_0_random_ArrayAccess(x2, x3) :|: -1 <= x2 - 1 && 0 <= x - 1
(3) f491_0_random_ArrayAccess(x4, x5) -> f815_0_main_NULL(x6, x8) :|: x6 <= x4 && 0 <= x9 - 1 && -1 <= x4 - 1 && -1 <= x6 - 1
(4) f815_0_main_NULL(x10, x11) -> f815_0_main_NULL(x13, x14) :|: x13 + 2 <= x10 && x16 <= 0 && 1 <= x10 - 1 && -1 <= x13 - 1
(5) f815_0_main_NULL(x17, x19) -> f815_0_main_NULL(x20, x21) :|: x20 <= x17 && 0 <= x22 - 1 && 0 <= x17 - 1 && 0 <= x20 - 1
(6) f815_0_main_NULL(x23, x24) -> f815_0_main_NULL(x25, x26) :|: x25 + 2 <= x23 && x27 <= 0 && 2 <= x23 - 1 && 0 <= x25 - 1
(7) f1_0_main_Load(x28, x29) -> f639_0_createIntList_LE(x30, x31) :|: 1 = x31 && 0 <= x28 - 1 && -1 <= x30 - 1 && -1 <= x29 - 1
(8) f639_0_createIntList_LE(x32, x33) -> f639_0_createIntList_LE(x34, x35) :|: x33 + 1 = x35 && x32 - 1 = x34 && 0 <= x33 - 1 && 0 <= x32 - 1
(9) __init(x36, x37) -> f1_0_main_Load(x38, x39) :|: 0 <= 0

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

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

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(5)
Obligation:

Termination digraph:
Nodes:
(1) f639_0_createIntList_LE(x32, x33) -> f639_0_createIntList_LE(x34, x35) :|: x33 + 1 = x35 && x32 - 1 = x34 && 0 <= x33 - 1 && 0 <= x32 - 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:
f639_0_createIntList_LE(x32:0, x33:0) -> f639_0_createIntList_LE(x32:0 - 1, x33:0 + 1) :|: x32:0 > 0 && x33:0 > 0

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(8) TempFilterProof (SOUND)
Used the following sort dictionary for filtering: 
f639_0_createIntList_LE(INTEGER, INTEGER)
Replaced non-predefined constructor symbols by 0.
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(9)
Obligation:
Rules:
f639_0_createIntList_LE(x32:0, x33:0) -> f639_0_createIntList_LE(c, c1) :|: c1 = x33:0 + 1 && c = x32:0 - 1 && (x32:0 > 0 && x33:0 > 0)

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(10) RankingReductionPairProof (EQUIVALENT)
Interpretation:
[ f639_0_createIntList_LE ] = f639_0_createIntList_LE_1

The following rules are decreasing:
f639_0_createIntList_LE(x32:0, x33:0) -> f639_0_createIntList_LE(c, c1) :|: c1 = x33:0 + 1 && c = x32:0 - 1 && (x32:0 > 0 && x33:0 > 0)

The following rules are bounded:
f639_0_createIntList_LE(x32:0, x33:0) -> f639_0_createIntList_LE(c, c1) :|: c1 = x33:0 + 1 && c = x32:0 - 1 && (x32:0 > 0 && x33:0 > 0)


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(11)
YES

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(12)
Obligation:

Termination digraph:
Nodes:
(1) f815_0_main_NULL(x10, x11) -> f815_0_main_NULL(x13, x14) :|: x13 + 2 <= x10 && x16 <= 0 && 1 <= x10 - 1 && -1 <= x13 - 1
(2) f815_0_main_NULL(x17, x19) -> f815_0_main_NULL(x20, x21) :|: x20 <= x17 && 0 <= x22 - 1 && 0 <= x17 - 1 && 0 <= x20 - 1
(3) f815_0_main_NULL(x23, x24) -> f815_0_main_NULL(x25, x26) :|: x25 + 2 <= x23 && x27 <= 0 && 2 <= x23 - 1 && 0 <= x25 - 1

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

This digraph is fully evaluated!

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(13) IntTRSCompressionProof (EQUIVALENT)
Compressed rules.
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(14)
Obligation:
Rules:
f815_0_main_NULL(x23:0, x24:0) -> f815_0_main_NULL(x25:0, x26:0) :|: x23:0 > 2 && x25:0 > 0 && x27:0 < 1 && x25:0 + 2 <= x23:0
f815_0_main_NULL(x17:0, x19:0) -> f815_0_main_NULL(x20:0, x21:0) :|: x17:0 > 0 && x20:0 > 0 && x22:0 > 0 && x20:0 <= x17:0
f815_0_main_NULL(x10:0, x11:0) -> f815_0_main_NULL(x13:0, x14:0) :|: x10:0 > 1 && x13:0 > -1 && x16:0 < 1 && x13:0 + 2 <= x10:0

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

   f815_0_main_NULL(x1, x2) -> f815_0_main_NULL(x1)

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(16)
Obligation:
Rules:
f815_0_main_NULL(x23:0) -> f815_0_main_NULL(x25:0) :|: x23:0 > 2 && x25:0 > 0 && x27:0 < 1 && x25:0 + 2 <= x23:0
f815_0_main_NULL(x17:0) -> f815_0_main_NULL(x20:0) :|: x17:0 > 0 && x20:0 > 0 && x22:0 > 0 && x20:0 <= x17:0
f815_0_main_NULL(x10:0) -> f815_0_main_NULL(x13:0) :|: x10:0 > 1 && x13:0 > -1 && x16:0 < 1 && x13:0 + 2 <= x10:0

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(17) FilterProof (EQUIVALENT)
Used the following sort dictionary for filtering: 
f815_0_main_NULL(INTEGER)
Replaced non-predefined constructor symbols by 0.
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(18)
Obligation:
Rules:
f815_0_main_NULL(x23:0) -> f815_0_main_NULL(x25:0) :|: x23:0 > 2 && x25:0 > 0 && x27:0 < 1 && x25:0 + 2 <= x23:0
f815_0_main_NULL(x17:0) -> f815_0_main_NULL(x20:0) :|: x17:0 > 0 && x20:0 > 0 && x22:0 > 0 && x20:0 <= x17:0
f815_0_main_NULL(x10:0) -> f815_0_main_NULL(x13:0) :|: x10:0 > 1 && x13:0 > -1 && x16:0 < 1 && x13:0 + 2 <= x10:0

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

(20)
Obligation:
Rules:
f815_0_main_NULL(x23:0:0) -> f815_0_main_NULL(x25:0:0) :|: x27:0:0 < 1 && x25:0:0 + 2 <= x23:0:0 && x25:0:0 > 0 && x23:0:0 > 2
f815_0_main_NULL(x17:0:0) -> f815_0_main_NULL(x20:0:0) :|: x22:0:0 > 0 && x20:0:0 <= x17:0:0 && x20:0:0 > 0 && x17:0:0 > 0
f815_0_main_NULL(x10:0:0) -> f815_0_main_NULL(x13:0:0) :|: x16:0:0 < 1 && x13:0:0 + 2 <= x10:0:0 && x13:0:0 > -1 && x10:0:0 > 1

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(21) IntTRSPeriodicNontermProof (COMPLETE)
Normalized system to the following form:
f(pc, x23:0:0) -> f(1, x25:0:0) :|: pc = 1 && (x27:0:0 < 1 && x25:0:0 + 2 <= x23:0:0 && x25:0:0 > 0 && x23:0:0 > 2)
f(pc, x17:0:0) -> f(1, x20:0:0) :|: pc = 1 && (x22:0:0 > 0 && x20:0:0 <= x17:0:0 && x20:0:0 > 0 && x17:0:0 > 0)
f(pc, x10:0:0) -> f(1, x13:0:0) :|: pc = 1 && (x16:0:0 < 1 && x13:0:0 + 2 <= x10:0:0 && x13:0:0 > -1 && x10:0:0 > 1)
Witness term starting non-terminating reduction: f(1, 3)
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(22)
NO