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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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, 144 ms]
(4) AND
    (5) IRSwT
        (6) IntTRSCompressionProof [EQUIVALENT, 0 ms]
        (7) IRSwT
        (8) TempFilterProof [SOUND, 36 ms]
        (9) IntTRS
        (10) PolynomialOrderProcessor [EQUIVALENT, 0 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:
f238_0_createIntList_Return(arg1, arg2) -> f376_0_main_FieldAccess(arg1P, arg2P) :|: -1 <= arg1P - 1 && -1 <= arg1 - 1 && arg1P <= arg1
f1_0_main_Load(x, x1) -> f376_0_main_FieldAccess(x2, x3) :|: -1 <= x2 - 1 && 0 <= x - 1
f376_0_main_FieldAccess(x4, x5) -> f376_0_main_FieldAccess(x6, x8) :|: x6 <= x4 && 0 <= x9 - 1 && 0 <= x4 - 1 && 0 <= x6 - 1
f1_0_main_Load(x10, x11) -> f491_0_createIntList_LE(x12, x13) :|: 1 = x13 && 0 <= x10 - 1 && -1 <= x12 - 1 && -1 <= x11 - 1
f491_0_createIntList_LE(x14, x15) -> f491_0_createIntList_LE(x16, x17) :|: x15 + 1 = x17 && x14 - 1 = x16 && 0 <= x15 - 1 && 0 <= x14 - 1
__init(x18, x19) -> f1_0_main_Load(x20, x21) :|: 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:
f238_0_createIntList_Return(arg1, arg2) -> f376_0_main_FieldAccess(arg1P, arg2P) :|: -1 <= arg1P - 1 && -1 <= arg1 - 1 && arg1P <= arg1
f1_0_main_Load(x, x1) -> f376_0_main_FieldAccess(x2, x3) :|: -1 <= x2 - 1 && 0 <= x - 1
f376_0_main_FieldAccess(x4, x5) -> f376_0_main_FieldAccess(x6, x8) :|: x6 <= x4 && 0 <= x9 - 1 && 0 <= x4 - 1 && 0 <= x6 - 1
f1_0_main_Load(x10, x11) -> f491_0_createIntList_LE(x12, x13) :|: 1 = x13 && 0 <= x10 - 1 && -1 <= x12 - 1 && -1 <= x11 - 1
f491_0_createIntList_LE(x14, x15) -> f491_0_createIntList_LE(x16, x17) :|: x15 + 1 = x17 && x14 - 1 = x16 && 0 <= x15 - 1 && 0 <= x14 - 1
__init(x18, x19) -> f1_0_main_Load(x20, x21) :|: 0 <= 0
Start term: __init(arg1, arg2)

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(3) IRSwTTerminationDigraphProof (EQUIVALENT)
Constructed termination digraph!
Nodes:
(1) f238_0_createIntList_Return(arg1, arg2) -> f376_0_main_FieldAccess(arg1P, arg2P) :|: -1 <= arg1P - 1 && -1 <= arg1 - 1 && arg1P <= arg1
(2) f1_0_main_Load(x, x1) -> f376_0_main_FieldAccess(x2, x3) :|: -1 <= x2 - 1 && 0 <= x - 1
(3) f376_0_main_FieldAccess(x4, x5) -> f376_0_main_FieldAccess(x6, x8) :|: x6 <= x4 && 0 <= x9 - 1 && 0 <= x4 - 1 && 0 <= x6 - 1
(4) f1_0_main_Load(x10, x11) -> f491_0_createIntList_LE(x12, x13) :|: 1 = x13 && 0 <= x10 - 1 && -1 <= x12 - 1 && -1 <= x11 - 1
(5) f491_0_createIntList_LE(x14, x15) -> f491_0_createIntList_LE(x16, x17) :|: x15 + 1 = x17 && x14 - 1 = x16 && 0 <= x15 - 1 && 0 <= x14 - 1
(6) __init(x18, x19) -> f1_0_main_Load(x20, x21) :|: 0 <= 0

Arcs:
(1) -> (3)
(2) -> (3)
(3) -> (3)
(4) -> (5)
(5) -> (5)
(6) -> (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) f491_0_createIntList_LE(x14, x15) -> f491_0_createIntList_LE(x16, x17) :|: x15 + 1 = x17 && x14 - 1 = x16 && 0 <= x15 - 1 && 0 <= x14 - 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:
f491_0_createIntList_LE(x14:0, x15:0) -> f491_0_createIntList_LE(x14:0 - 1, x15:0 + 1) :|: x14:0 > 0 && x15:0 > 0

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(8) TempFilterProof (SOUND)
Used the following sort dictionary for filtering: 
f491_0_createIntList_LE(INTEGER, INTEGER)
Replaced non-predefined constructor symbols by 0.
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(9)
Obligation:
Rules:
f491_0_createIntList_LE(x14:0, x15:0) -> f491_0_createIntList_LE(c, c1) :|: c1 = x15:0 + 1 && c = x14:0 - 1 && (x14:0 > 0 && x15:0 > 0)

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(10) PolynomialOrderProcessor (EQUIVALENT)
Found the following polynomial interpretation:
[f491_0_createIntList_LE(x, x1)] = x

The following rules are decreasing:
f491_0_createIntList_LE(x14:0, x15:0) -> f491_0_createIntList_LE(c, c1) :|: c1 = x15:0 + 1 && c = x14:0 - 1 && (x14:0 > 0 && x15:0 > 0)
The following rules are bounded:
f491_0_createIntList_LE(x14:0, x15:0) -> f491_0_createIntList_LE(c, c1) :|: c1 = x15:0 + 1 && c = x14:0 - 1 && (x14:0 > 0 && x15:0 > 0)

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(11)
YES

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(12)
Obligation:

Termination digraph:
Nodes:
(1) f376_0_main_FieldAccess(x4, x5) -> f376_0_main_FieldAccess(x6, x8) :|: x6 <= x4 && 0 <= x9 - 1 && 0 <= x4 - 1 && 0 <= x6 - 1

Arcs:
(1) -> (1)

This digraph is fully evaluated!

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(13) IntTRSCompressionProof (EQUIVALENT)
Compressed rules.
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(14)
Obligation:
Rules:
f376_0_main_FieldAccess(x4:0, x5:0) -> f376_0_main_FieldAccess(x6:0, x8:0) :|: x4:0 > 0 && x6:0 > 0 && x9:0 > 0 && x6:0 <= x4:0

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

   f376_0_main_FieldAccess(x1, x2) -> f376_0_main_FieldAccess(x1)

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(16)
Obligation:
Rules:
f376_0_main_FieldAccess(x4:0) -> f376_0_main_FieldAccess(x6:0) :|: x4:0 > 0 && x6:0 > 0 && x9:0 > 0 && x6:0 <= x4:0

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(17) FilterProof (EQUIVALENT)
Used the following sort dictionary for filtering: 
f376_0_main_FieldAccess(INTEGER)
Replaced non-predefined constructor symbols by 0.
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(18)
Obligation:
Rules:
f376_0_main_FieldAccess(x4:0) -> f376_0_main_FieldAccess(x6:0) :|: x4:0 > 0 && x6:0 > 0 && x9:0 > 0 && x6:0 <= x4:0

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(19) IntTRSCompressionProof (EQUIVALENT)
Compressed rules.
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(20)
Obligation:
Rules:
f376_0_main_FieldAccess(x4:0:0) -> f376_0_main_FieldAccess(x6:0:0) :|: x9:0:0 > 0 && x6:0:0 <= x4:0:0 && x6:0:0 > 0 && x4:0:0 > 0

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(21) IntTRSPeriodicNontermProof (COMPLETE)
Normalized system to the following form:
f(pc, x4:0:0) -> f(1, x6:0:0) :|: pc = 1 && (x9:0:0 > 0 && x6:0:0 <= x4:0:0 && x6:0:0 > 0 && x4:0:0 > 0)
Witness term starting non-terminating reduction: f(1, 13)
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(22)
NO