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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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, 303 ms]
(4) AND
    (5) IRSwT
        (6) IntTRSCompressionProof [EQUIVALENT, 0 ms]
        (7) IRSwT
        (8) FilterProof [EQUIVALENT, 0 ms]
        (9) IntTRS
        (10) IntTRSCompressionProof [EQUIVALENT, 0 ms]
        (11) IntTRS
        (12) RankingReductionPairProof [EQUIVALENT, 0 ms]
        (13) YES
    (14) IRSwT
        (15) IntTRSCompressionProof [EQUIVALENT, 0 ms]
        (16) IRSwT
        (17) TempFilterProof [SOUND, 27 ms]
        (18) IntTRS
        (19) RankingReductionPairProof [EQUIVALENT, 9 ms]
        (20) YES


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(0)
Obligation:
Rules:
f1_0_main_Load(arg1, arg2, arg3) -> f302_0_createList_GE(arg1P, arg2P, arg3P) :|: 1 = arg3P && arg2 = arg2P && 0 <= arg1 - 1 && 0 <= arg2 - 1 && -1 <= arg1P - 1
f1_0_main_Load(x, x1, x2) -> f502_0_main_InvokeMethod(x3, x4, x5) :|: -1 <= x6 - 1 && 0 <= x1 - 1 && x3 <= x && 0 <= x - 1 && 0 <= x3 - 1 && 2 <= x4 - 1
f1_0_main_Load(x7, x9, x10) -> f502_0_main_InvokeMethod(x11, x12, x13) :|: -1 <= x15 - 1 && 0 <= x9 - 1 && x11 <= x7 && x12 - 1 <= x7 && 0 <= x7 - 1 && 0 <= x11 - 1 && 1 <= x12 - 1
f302_0_createList_GE(x16, x17, x19) -> f302_0_createList_GE(x20, x21, x22) :|: x19 + 1 = x22 && x17 = x21 && x16 - 1 = x20 && x19 <= x17 - 1 && x16 - 1 <= x16 - 1 && 0 <= x19 - 1 && -1 <= x17 - 1 && -1 <= x16 - 1
f502_0_main_InvokeMethod(x23, x24, x25) -> f571_0_sumList_NONNULL(x26, x27, x28) :|: 0 <= x29 - 1 && 1 <= x25 - 1 && x26 <= x24 && x27 + 1 <= x24 && 0 <= x23 - 1 && 0 <= x24 - 1 && 0 <= x26 - 1 && -1 <= x27 - 1 && x25 = x28
f571_0_sumList_NONNULL(x30, x31, x32) -> f571_0_sumList_NONNULL(x33, x34, x35) :|: x32 = x35 && -1 <= x34 - 1 && 0 <= x33 - 1 && 0 <= x31 - 1 && 2 <= x30 - 1 && x34 + 1 <= x31 && x34 + 3 <= x30 && x33 <= x31 && 1 <= x32 - 1 && x33 + 2 <= x30
__init(x36, x37, x38) -> f1_0_main_Load(x39, x40, x41) :|: 0 <= 0
Start term: __init(arg1, arg2, arg3)

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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, arg3) -> f302_0_createList_GE(arg1P, arg2P, arg3P) :|: 1 = arg3P && arg2 = arg2P && 0 <= arg1 - 1 && 0 <= arg2 - 1 && -1 <= arg1P - 1
f1_0_main_Load(x, x1, x2) -> f502_0_main_InvokeMethod(x3, x4, x5) :|: -1 <= x6 - 1 && 0 <= x1 - 1 && x3 <= x && 0 <= x - 1 && 0 <= x3 - 1 && 2 <= x4 - 1
f1_0_main_Load(x7, x9, x10) -> f502_0_main_InvokeMethod(x11, x12, x13) :|: -1 <= x15 - 1 && 0 <= x9 - 1 && x11 <= x7 && x12 - 1 <= x7 && 0 <= x7 - 1 && 0 <= x11 - 1 && 1 <= x12 - 1
f302_0_createList_GE(x16, x17, x19) -> f302_0_createList_GE(x20, x21, x22) :|: x19 + 1 = x22 && x17 = x21 && x16 - 1 = x20 && x19 <= x17 - 1 && x16 - 1 <= x16 - 1 && 0 <= x19 - 1 && -1 <= x17 - 1 && -1 <= x16 - 1
f502_0_main_InvokeMethod(x23, x24, x25) -> f571_0_sumList_NONNULL(x26, x27, x28) :|: 0 <= x29 - 1 && 1 <= x25 - 1 && x26 <= x24 && x27 + 1 <= x24 && 0 <= x23 - 1 && 0 <= x24 - 1 && 0 <= x26 - 1 && -1 <= x27 - 1 && x25 = x28
f571_0_sumList_NONNULL(x30, x31, x32) -> f571_0_sumList_NONNULL(x33, x34, x35) :|: x32 = x35 && -1 <= x34 - 1 && 0 <= x33 - 1 && 0 <= x31 - 1 && 2 <= x30 - 1 && x34 + 1 <= x31 && x34 + 3 <= x30 && x33 <= x31 && 1 <= x32 - 1 && x33 + 2 <= x30
__init(x36, x37, x38) -> f1_0_main_Load(x39, x40, x41) :|: 0 <= 0
Start term: __init(arg1, arg2, arg3)

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(3) IRSwTTerminationDigraphProof (EQUIVALENT)
Constructed termination digraph!
Nodes:
(1) f1_0_main_Load(arg1, arg2, arg3) -> f302_0_createList_GE(arg1P, arg2P, arg3P) :|: 1 = arg3P && arg2 = arg2P && 0 <= arg1 - 1 && 0 <= arg2 - 1 && -1 <= arg1P - 1
(2) f1_0_main_Load(x, x1, x2) -> f502_0_main_InvokeMethod(x3, x4, x5) :|: -1 <= x6 - 1 && 0 <= x1 - 1 && x3 <= x && 0 <= x - 1 && 0 <= x3 - 1 && 2 <= x4 - 1
(3) f1_0_main_Load(x7, x9, x10) -> f502_0_main_InvokeMethod(x11, x12, x13) :|: -1 <= x15 - 1 && 0 <= x9 - 1 && x11 <= x7 && x12 - 1 <= x7 && 0 <= x7 - 1 && 0 <= x11 - 1 && 1 <= x12 - 1
(4) f302_0_createList_GE(x16, x17, x19) -> f302_0_createList_GE(x20, x21, x22) :|: x19 + 1 = x22 && x17 = x21 && x16 - 1 = x20 && x19 <= x17 - 1 && x16 - 1 <= x16 - 1 && 0 <= x19 - 1 && -1 <= x17 - 1 && -1 <= x16 - 1
(5) f502_0_main_InvokeMethod(x23, x24, x25) -> f571_0_sumList_NONNULL(x26, x27, x28) :|: 0 <= x29 - 1 && 1 <= x25 - 1 && x26 <= x24 && x27 + 1 <= x24 && 0 <= x23 - 1 && 0 <= x24 - 1 && 0 <= x26 - 1 && -1 <= x27 - 1 && x25 = x28
(6) f571_0_sumList_NONNULL(x30, x31, x32) -> f571_0_sumList_NONNULL(x33, x34, x35) :|: x32 = x35 && -1 <= x34 - 1 && 0 <= x33 - 1 && 0 <= x31 - 1 && 2 <= x30 - 1 && x34 + 1 <= x31 && x34 + 3 <= x30 && x33 <= x31 && 1 <= x32 - 1 && x33 + 2 <= x30
(7) __init(x36, x37, x38) -> f1_0_main_Load(x39, x40, x41) :|: 0 <= 0

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

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

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(5)
Obligation:

Termination digraph:
Nodes:
(1) f571_0_sumList_NONNULL(x30, x31, x32) -> f571_0_sumList_NONNULL(x33, x34, x35) :|: x32 = x35 && -1 <= x34 - 1 && 0 <= x33 - 1 && 0 <= x31 - 1 && 2 <= x30 - 1 && x34 + 1 <= x31 && x34 + 3 <= x30 && x33 <= x31 && 1 <= x32 - 1 && x33 + 2 <= x30

Arcs:
(1) -> (1)

This digraph is fully evaluated!

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

(7)
Obligation:
Rules:
f571_0_sumList_NONNULL(x30:0, x31:0, x32:0) -> f571_0_sumList_NONNULL(x33:0, x34:0, x32:0) :|: x32:0 > 1 && x33:0 + 2 <= x30:0 && x33:0 <= x31:0 && x34:0 + 3 <= x30:0 && x34:0 + 1 <= x31:0 && x30:0 > 2 && x31:0 > 0 && x34:0 > -1 && x33:0 > 0

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(8) FilterProof (EQUIVALENT)
Used the following sort dictionary for filtering: 
f571_0_sumList_NONNULL(INTEGER, INTEGER, INTEGER)
Replaced non-predefined constructor symbols by 0.
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(9)
Obligation:
Rules:
f571_0_sumList_NONNULL(x30:0, x31:0, x32:0) -> f571_0_sumList_NONNULL(x33:0, x34:0, x32:0) :|: x32:0 > 1 && x33:0 + 2 <= x30:0 && x33:0 <= x31:0 && x34:0 + 3 <= x30:0 && x34:0 + 1 <= x31:0 && x30:0 > 2 && x31:0 > 0 && x34:0 > -1 && x33:0 > 0

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

(11)
Obligation:
Rules:
f571_0_sumList_NONNULL(x30:0:0, x31:0:0, x32:0:0) -> f571_0_sumList_NONNULL(x33:0:0, x34:0:0, x32:0:0) :|: x34:0:0 > -1 && x33:0:0 > 0 && x31:0:0 > 0 && x30:0:0 > 2 && x34:0:0 + 1 <= x31:0:0 && x34:0:0 + 3 <= x30:0:0 && x33:0:0 <= x31:0:0 && x33:0:0 + 2 <= x30:0:0 && x32:0:0 > 1

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(12) RankingReductionPairProof (EQUIVALENT)
Interpretation:
[ f571_0_sumList_NONNULL ] = 1/2*f571_0_sumList_NONNULL_1

The following rules are decreasing:
f571_0_sumList_NONNULL(x30:0:0, x31:0:0, x32:0:0) -> f571_0_sumList_NONNULL(x33:0:0, x34:0:0, x32:0:0) :|: x34:0:0 > -1 && x33:0:0 > 0 && x31:0:0 > 0 && x30:0:0 > 2 && x34:0:0 + 1 <= x31:0:0 && x34:0:0 + 3 <= x30:0:0 && x33:0:0 <= x31:0:0 && x33:0:0 + 2 <= x30:0:0 && x32:0:0 > 1

The following rules are bounded:
f571_0_sumList_NONNULL(x30:0:0, x31:0:0, x32:0:0) -> f571_0_sumList_NONNULL(x33:0:0, x34:0:0, x32:0:0) :|: x34:0:0 > -1 && x33:0:0 > 0 && x31:0:0 > 0 && x30:0:0 > 2 && x34:0:0 + 1 <= x31:0:0 && x34:0:0 + 3 <= x30:0:0 && x33:0:0 <= x31:0:0 && x33:0:0 + 2 <= x30:0:0 && x32:0:0 > 1


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(13)
YES

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(14)
Obligation:

Termination digraph:
Nodes:
(1) f302_0_createList_GE(x16, x17, x19) -> f302_0_createList_GE(x20, x21, x22) :|: x19 + 1 = x22 && x17 = x21 && x16 - 1 = x20 && x19 <= x17 - 1 && x16 - 1 <= x16 - 1 && 0 <= x19 - 1 && -1 <= x17 - 1 && -1 <= x16 - 1

Arcs:
(1) -> (1)

This digraph is fully evaluated!

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

(16)
Obligation:
Rules:
f302_0_createList_GE(x16:0, x17:0, x19:0) -> f302_0_createList_GE(x16:0 - 1, x17:0, x19:0 + 1) :|: x17:0 > -1 && x16:0 > -1 && x19:0 <= x17:0 - 1 && x19:0 > 0

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(17) TempFilterProof (SOUND)
Used the following sort dictionary for filtering: 
f302_0_createList_GE(INTEGER, INTEGER, INTEGER)
Replaced non-predefined constructor symbols by 0.
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(18)
Obligation:
Rules:
f302_0_createList_GE(x16:0, x17:0, x19:0) -> f302_0_createList_GE(c, x17:0, c1) :|: c1 = x19:0 + 1 && c = x16:0 - 1 && (x17:0 > -1 && x16:0 > -1 && x19:0 <= x17:0 - 1 && x19:0 > 0)

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(19) RankingReductionPairProof (EQUIVALENT)
Interpretation:
[ f302_0_createList_GE ] = f302_0_createList_GE_2 + -1*f302_0_createList_GE_3

The following rules are decreasing:
f302_0_createList_GE(x16:0, x17:0, x19:0) -> f302_0_createList_GE(c, x17:0, c1) :|: c1 = x19:0 + 1 && c = x16:0 - 1 && (x17:0 > -1 && x16:0 > -1 && x19:0 <= x17:0 - 1 && x19:0 > 0)

The following rules are bounded:
f302_0_createList_GE(x16:0, x17:0, x19:0) -> f302_0_createList_GE(c, x17:0, c1) :|: c1 = x19:0 + 1 && c = x16:0 - 1 && (x17:0 > -1 && x16:0 > -1 && x19:0 <= x17:0 - 1 && x19:0 > 0)


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(20)
YES