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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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, 376 ms]
(4) AND
    (5) IRSwT
        (6) IntTRSCompressionProof [EQUIVALENT, 0 ms]
        (7) IRSwT
        (8) TempFilterProof [SOUND, 47 ms]
        (9) IntTRS
        (10) PolynomialOrderProcessor [EQUIVALENT, 6 ms]
        (11) IntTRS
        (12) PolynomialOrderProcessor [EQUIVALENT, 0 ms]
        (13) YES
    (14) IRSwT
        (15) IntTRSCompressionProof [EQUIVALENT, 0 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) IntTRSPeriodicNontermProof [COMPLETE, 0 ms]
        (24) NO


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(0)
Obligation:
Rules:
f265_0_createMetaList_Return(arg1, arg2, arg3, arg4) -> f724_0_countMetaList_NULL(arg1P, arg2P, arg3P, arg4P) :|: -1 <= arg1P - 1 && -1 <= arg1 - 1 && arg1P <= arg1
f1_0_main_Load(x, x1, x2, x3) -> f724_0_countMetaList_NULL(x4, x5, x6, x7) :|: -1 <= x4 - 1 && 0 <= x - 1
f724_0_countMetaList_NULL(x8, x9, x10, x11) -> f724_0_countMetaList_NULL(x12, x13, x14, x15) :|: -1 <= x12 - 1 && 2 <= x8 - 1 && x12 + 2 <= x8
f724_0_countMetaList_NULL(x16, x17, x18, x19) -> f724_0_countMetaList_NULL(x20, x21, x22, x23) :|: -1 <= x20 - 1 && 1 <= x16 - 1 && x20 + 2 <= x16
f724_0_countMetaList_NULL(x24, x25, x26, x27) -> f724_0_countMetaList_NULL(x28, x29, x30, x31) :|: 0 <= x28 - 1 && 2 <= x24 - 1 && x28 <= x24
f1_0_main_Load(x32, x33, x34, x35) -> f693_0_createMetaList_GE(x36, x37, x38, x39) :|: 1 = x38 && 0 = x36 && 0 <= x32 - 1 && -1 <= x37 - 1 && -1 <= x33 - 1
f693_0_createMetaList_GE(x40, x41, x42, x43) -> f932_0_createMetaList_LE(x44, x45, x46, x47) :|: x42 + 1 = x47 && x40 = x45 && x41 = x44 && 0 <= x42 - 1 && x40 <= x41 - 1 && -1 <= x46 - 1
f932_0_createMetaList_LE(x48, x49, x50, x51) -> f693_0_createMetaList_GE(x52, x53, x54, x55) :|: x51 = x54 && x48 = x53 && x49 + 1 = x52 && 0 = x50
f932_0_createMetaList_LE(x56, x57, x58, x59) -> f932_0_createMetaList_LE(x60, x61, x62, x63) :|: x59 = x63 && x58 - 1 = x62 && x57 = x61 && x56 = x60 && 0 <= x58 - 1
__init(x64, x65, x66, x67) -> f1_0_main_Load(x68, x69, x70, x71) :|: 0 <= 0
Start term: __init(arg1, arg2, arg3, arg4)

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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:
f265_0_createMetaList_Return(arg1, arg2, arg3, arg4) -> f724_0_countMetaList_NULL(arg1P, arg2P, arg3P, arg4P) :|: -1 <= arg1P - 1 && -1 <= arg1 - 1 && arg1P <= arg1
f1_0_main_Load(x, x1, x2, x3) -> f724_0_countMetaList_NULL(x4, x5, x6, x7) :|: -1 <= x4 - 1 && 0 <= x - 1
f724_0_countMetaList_NULL(x8, x9, x10, x11) -> f724_0_countMetaList_NULL(x12, x13, x14, x15) :|: -1 <= x12 - 1 && 2 <= x8 - 1 && x12 + 2 <= x8
f724_0_countMetaList_NULL(x16, x17, x18, x19) -> f724_0_countMetaList_NULL(x20, x21, x22, x23) :|: -1 <= x20 - 1 && 1 <= x16 - 1 && x20 + 2 <= x16
f724_0_countMetaList_NULL(x24, x25, x26, x27) -> f724_0_countMetaList_NULL(x28, x29, x30, x31) :|: 0 <= x28 - 1 && 2 <= x24 - 1 && x28 <= x24
f1_0_main_Load(x32, x33, x34, x35) -> f693_0_createMetaList_GE(x36, x37, x38, x39) :|: 1 = x38 && 0 = x36 && 0 <= x32 - 1 && -1 <= x37 - 1 && -1 <= x33 - 1
f693_0_createMetaList_GE(x40, x41, x42, x43) -> f932_0_createMetaList_LE(x44, x45, x46, x47) :|: x42 + 1 = x47 && x40 = x45 && x41 = x44 && 0 <= x42 - 1 && x40 <= x41 - 1 && -1 <= x46 - 1
f932_0_createMetaList_LE(x48, x49, x50, x51) -> f693_0_createMetaList_GE(x52, x53, x54, x55) :|: x51 = x54 && x48 = x53 && x49 + 1 = x52 && 0 = x50
f932_0_createMetaList_LE(x56, x57, x58, x59) -> f932_0_createMetaList_LE(x60, x61, x62, x63) :|: x59 = x63 && x58 - 1 = x62 && x57 = x61 && x56 = x60 && 0 <= x58 - 1
__init(x64, x65, x66, x67) -> f1_0_main_Load(x68, x69, x70, x71) :|: 0 <= 0
Start term: __init(arg1, arg2, arg3, arg4)

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(3) IRSwTTerminationDigraphProof (EQUIVALENT)
Constructed termination digraph!
Nodes:
(1) f265_0_createMetaList_Return(arg1, arg2, arg3, arg4) -> f724_0_countMetaList_NULL(arg1P, arg2P, arg3P, arg4P) :|: -1 <= arg1P - 1 && -1 <= arg1 - 1 && arg1P <= arg1
(2) f1_0_main_Load(x, x1, x2, x3) -> f724_0_countMetaList_NULL(x4, x5, x6, x7) :|: -1 <= x4 - 1 && 0 <= x - 1
(3) f724_0_countMetaList_NULL(x8, x9, x10, x11) -> f724_0_countMetaList_NULL(x12, x13, x14, x15) :|: -1 <= x12 - 1 && 2 <= x8 - 1 && x12 + 2 <= x8
(4) f724_0_countMetaList_NULL(x16, x17, x18, x19) -> f724_0_countMetaList_NULL(x20, x21, x22, x23) :|: -1 <= x20 - 1 && 1 <= x16 - 1 && x20 + 2 <= x16
(5) f724_0_countMetaList_NULL(x24, x25, x26, x27) -> f724_0_countMetaList_NULL(x28, x29, x30, x31) :|: 0 <= x28 - 1 && 2 <= x24 - 1 && x28 <= x24
(6) f1_0_main_Load(x32, x33, x34, x35) -> f693_0_createMetaList_GE(x36, x37, x38, x39) :|: 1 = x38 && 0 = x36 && 0 <= x32 - 1 && -1 <= x37 - 1 && -1 <= x33 - 1
(7) f693_0_createMetaList_GE(x40, x41, x42, x43) -> f932_0_createMetaList_LE(x44, x45, x46, x47) :|: x42 + 1 = x47 && x40 = x45 && x41 = x44 && 0 <= x42 - 1 && x40 <= x41 - 1 && -1 <= x46 - 1
(8) f932_0_createMetaList_LE(x48, x49, x50, x51) -> f693_0_createMetaList_GE(x52, x53, x54, x55) :|: x51 = x54 && x48 = x53 && x49 + 1 = x52 && 0 = x50
(9) f932_0_createMetaList_LE(x56, x57, x58, x59) -> f932_0_createMetaList_LE(x60, x61, x62, x63) :|: x59 = x63 && x58 - 1 = x62 && x57 = x61 && x56 = x60 && 0 <= x58 - 1
(10) __init(x64, x65, x66, x67) -> f1_0_main_Load(x68, x69, x70, x71) :|: 0 <= 0

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

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

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(5)
Obligation:

Termination digraph:
Nodes:
(1) f693_0_createMetaList_GE(x40, x41, x42, x43) -> f932_0_createMetaList_LE(x44, x45, x46, x47) :|: x42 + 1 = x47 && x40 = x45 && x41 = x44 && 0 <= x42 - 1 && x40 <= x41 - 1 && -1 <= x46 - 1
(2) f932_0_createMetaList_LE(x48, x49, x50, x51) -> f693_0_createMetaList_GE(x52, x53, x54, x55) :|: x51 = x54 && x48 = x53 && x49 + 1 = x52 && 0 = x50
(3) f932_0_createMetaList_LE(x56, x57, x58, x59) -> f932_0_createMetaList_LE(x60, x61, x62, x63) :|: x59 = x63 && x58 - 1 = x62 && x57 = x61 && x56 = x60 && 0 <= x58 - 1

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

This digraph is fully evaluated!

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(6) IntTRSCompressionProof (EQUIVALENT)
Compressed rules.
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(7)
Obligation:
Rules:
f932_0_createMetaList_LE(x44:0, x49:0, cons_0, x51:0) -> f932_0_createMetaList_LE(x44:0, x49:0 + 1, x46:0, x51:0 + 1) :|: x49:0 + 1 <= x44:0 - 1 && x51:0 > 0 && x46:0 > -1 && cons_0 = 0
f932_0_createMetaList_LE(x56:0, x57:0, x58:0, x59:0) -> f932_0_createMetaList_LE(x56:0, x57:0, x58:0 - 1, x59:0) :|: x58:0 > 0

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(8) TempFilterProof (SOUND)
Used the following sort dictionary for filtering: 
f932_0_createMetaList_LE(VARIABLE, VARIABLE, INTEGER, VARIABLE)
Replaced non-predefined constructor symbols by 0.
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(9)
Obligation:
Rules:
f932_0_createMetaList_LE(x44:0, x49:0, c, x51:0) -> f932_0_createMetaList_LE(x44:0, c1, x46:0, c2) :|: c2 = x51:0 + 1 && (c1 = x49:0 + 1 && c = 0) && (x49:0 + 1 <= x44:0 - 1 && x51:0 > 0 && x46:0 > -1 && cons_0 = 0)
f932_0_createMetaList_LE(x56:0, x57:0, x58:0, x59:0) -> f932_0_createMetaList_LE(x56:0, x57:0, c3, x59:0) :|: c3 = x58:0 - 1 && x58:0 > 0

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(10) PolynomialOrderProcessor (EQUIVALENT)
Found the following polynomial interpretation:
[f932_0_createMetaList_LE(x, x1, x2, x3)] = -1 + 2*x - 2*x1 + x3

The following rules are decreasing:
f932_0_createMetaList_LE(x44:0, x49:0, c, x51:0) -> f932_0_createMetaList_LE(x44:0, c1, x46:0, c2) :|: c2 = x51:0 + 1 && (c1 = x49:0 + 1 && c = 0) && (x49:0 + 1 <= x44:0 - 1 && x51:0 > 0 && x46:0 > -1 && cons_0 = 0)
The following rules are bounded:
f932_0_createMetaList_LE(x44:0, x49:0, c, x51:0) -> f932_0_createMetaList_LE(x44:0, c1, x46:0, c2) :|: c2 = x51:0 + 1 && (c1 = x49:0 + 1 && c = 0) && (x49:0 + 1 <= x44:0 - 1 && x51:0 > 0 && x46:0 > -1 && cons_0 = 0)

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(11)
Obligation:
Rules:
f932_0_createMetaList_LE(x56:0, x57:0, x58:0, x59:0) -> f932_0_createMetaList_LE(x56:0, x57:0, c3, x59:0) :|: c3 = x58:0 - 1 && x58:0 > 0

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(12) PolynomialOrderProcessor (EQUIVALENT)
Found the following polynomial interpretation:
[f932_0_createMetaList_LE(x, x1, x2, x3)] = x2

The following rules are decreasing:
f932_0_createMetaList_LE(x56:0, x57:0, x58:0, x59:0) -> f932_0_createMetaList_LE(x56:0, x57:0, c3, x59:0) :|: c3 = x58:0 - 1 && x58:0 > 0
The following rules are bounded:
f932_0_createMetaList_LE(x56:0, x57:0, x58:0, x59:0) -> f932_0_createMetaList_LE(x56:0, x57:0, c3, x59:0) :|: c3 = x58:0 - 1 && x58:0 > 0

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(13)
YES

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(14)
Obligation:

Termination digraph:
Nodes:
(1) f724_0_countMetaList_NULL(x8, x9, x10, x11) -> f724_0_countMetaList_NULL(x12, x13, x14, x15) :|: -1 <= x12 - 1 && 2 <= x8 - 1 && x12 + 2 <= x8
(2) f724_0_countMetaList_NULL(x16, x17, x18, x19) -> f724_0_countMetaList_NULL(x20, x21, x22, x23) :|: -1 <= x20 - 1 && 1 <= x16 - 1 && x20 + 2 <= x16
(3) f724_0_countMetaList_NULL(x24, x25, x26, x27) -> f724_0_countMetaList_NULL(x28, x29, x30, x31) :|: 0 <= x28 - 1 && 2 <= x24 - 1 && x28 <= x24

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

This digraph is fully evaluated!

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(15) IntTRSCompressionProof (EQUIVALENT)
Compressed rules.
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(16)
Obligation:
Rules:
f724_0_countMetaList_NULL(x24:0, x25:0, x26:0, x27:0) -> f724_0_countMetaList_NULL(x28:0, x29:0, x30:0, x31:0) :|: x28:0 > 0 && x24:0 > 2 && x28:0 <= x24:0
f724_0_countMetaList_NULL(x16:0, x17:0, x18:0, x19:0) -> f724_0_countMetaList_NULL(x20:0, x21:0, x22:0, x23:0) :|: x20:0 > -1 && x16:0 > 1 && x20:0 + 2 <= x16:0
f724_0_countMetaList_NULL(x8:0, x9:0, x10:0, x11:0) -> f724_0_countMetaList_NULL(x12:0, x13:0, x14:0, x15:0) :|: x12:0 > -1 && x8:0 > 2 && x8:0 >= x12:0 + 2

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

   f724_0_countMetaList_NULL(x1, x2, x3, x4) -> f724_0_countMetaList_NULL(x1)

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(18)
Obligation:
Rules:
f724_0_countMetaList_NULL(x24:0) -> f724_0_countMetaList_NULL(x28:0) :|: x28:0 > 0 && x24:0 > 2 && x28:0 <= x24:0
f724_0_countMetaList_NULL(x16:0) -> f724_0_countMetaList_NULL(x20:0) :|: x20:0 > -1 && x16:0 > 1 && x20:0 + 2 <= x16:0
f724_0_countMetaList_NULL(x8:0) -> f724_0_countMetaList_NULL(x12:0) :|: x12:0 > -1 && x8:0 > 2 && x8:0 >= x12:0 + 2

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(19) FilterProof (EQUIVALENT)
Used the following sort dictionary for filtering: 
f724_0_countMetaList_NULL(INTEGER)
Replaced non-predefined constructor symbols by 0.
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(20)
Obligation:
Rules:
f724_0_countMetaList_NULL(x24:0) -> f724_0_countMetaList_NULL(x28:0) :|: x28:0 > 0 && x24:0 > 2 && x28:0 <= x24:0
f724_0_countMetaList_NULL(x16:0) -> f724_0_countMetaList_NULL(x20:0) :|: x20:0 > -1 && x16:0 > 1 && x20:0 + 2 <= x16:0
f724_0_countMetaList_NULL(x8:0) -> f724_0_countMetaList_NULL(x12:0) :|: x12:0 > -1 && x8:0 > 2 && x8:0 >= x12:0 + 2

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

(22)
Obligation:
Rules:
f724_0_countMetaList_NULL(x24:0:0) -> f724_0_countMetaList_NULL(x28:0:0) :|: x28:0:0 > 0 && x24:0:0 > 2 && x28:0:0 <= x24:0:0
f724_0_countMetaList_NULL(x8:0:0) -> f724_0_countMetaList_NULL(x12:0:0) :|: x12:0:0 > -1 && x8:0:0 > 2 && x8:0:0 >= x12:0:0 + 2
f724_0_countMetaList_NULL(x16:0:0) -> f724_0_countMetaList_NULL(x20:0:0) :|: x20:0:0 > -1 && x16:0:0 > 1 && x20:0:0 + 2 <= x16:0:0

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(23) IntTRSPeriodicNontermProof (COMPLETE)
Normalized system to the following form:
f(pc, x24:0:0) -> f(1, x28:0:0) :|: pc = 1 && (x28:0:0 > 0 && x24:0:0 > 2 && x28:0:0 <= x24:0:0)
f(pc, x8:0:0) -> f(1, x12:0:0) :|: pc = 1 && (x12:0:0 > -1 && x8:0:0 > 2 && x8:0:0 >= x12:0:0 + 2)
f(pc, x16:0:0) -> f(1, x20:0:0) :|: pc = 1 && (x20:0:0 > -1 && x16:0:0 > 1 && x20:0:0 + 2 <= x16:0:0)
Witness term starting non-terminating reduction: f(1, 7)
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(24)
NO