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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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, 125 ms]
(4) AND
    (5) IRSwT
        (6) IntTRSCompressionProof [EQUIVALENT, 1 ms]
        (7) IRSwT
        (8) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms]
        (9) IRSwT
        (10) TempFilterProof [SOUND, 11 ms]
        (11) IntTRS
        (12) PolynomialOrderProcessor [EQUIVALENT, 0 ms]
        (13) YES
    (14) IRSwT
        (15) IntTRSCompressionProof [EQUIVALENT, 1 ms]
        (16) IRSwT
        (17) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms]
        (18) IRSwT
        (19) TempFilterProof [SOUND, 9 ms]
        (20) IntTRS
        (21) PolynomialOrderProcessor [EQUIVALENT, 0 ms]
        (22) YES


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(0)
Obligation:
Rules:
f171_0_createList_Return(arg1, arg2) -> f231_0_random_ArrayAccess(arg1P, arg2P) :|: 0 <= arg1 - 1
f1_0_main_Load(x, x1) -> f231_0_random_ArrayAccess(x2, x3) :|: x1 = x2 && 0 <= x - 1
f1_0_main_Load(x4, x5) -> f197_0_createList_LE(x6, x7) :|: 0 <= x4 - 1 && -1 <= x6 - 1 && -1 <= x5 - 1
f197_0_createList_LE(x8, x9) -> f197_0_createList_LE(x10, x11) :|: x8 - 1 = x10 && 0 <= x8 - 1
f231_0_random_ArrayAccess(x12, x13) -> f352_0_appE_GT(x14, x15) :|: 1 <= x12 - 1 && 0 <= x14 - 1
f352_0_appE_GT(x16, x17) -> f352_0_appE_GT(x18, x19) :|: x16 - 1 = x18 && 0 <= x16 - 1
__init(x20, x21) -> f1_0_main_Load(x22, x23) :|: 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:
f171_0_createList_Return(arg1, arg2) -> f231_0_random_ArrayAccess(arg1P, arg2P) :|: 0 <= arg1 - 1
f1_0_main_Load(x, x1) -> f231_0_random_ArrayAccess(x2, x3) :|: x1 = x2 && 0 <= x - 1
f1_0_main_Load(x4, x5) -> f197_0_createList_LE(x6, x7) :|: 0 <= x4 - 1 && -1 <= x6 - 1 && -1 <= x5 - 1
f197_0_createList_LE(x8, x9) -> f197_0_createList_LE(x10, x11) :|: x8 - 1 = x10 && 0 <= x8 - 1
f231_0_random_ArrayAccess(x12, x13) -> f352_0_appE_GT(x14, x15) :|: 1 <= x12 - 1 && 0 <= x14 - 1
f352_0_appE_GT(x16, x17) -> f352_0_appE_GT(x18, x19) :|: x16 - 1 = x18 && 0 <= x16 - 1
__init(x20, x21) -> f1_0_main_Load(x22, x23) :|: 0 <= 0
Start term: __init(arg1, arg2)

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(3) IRSwTTerminationDigraphProof (EQUIVALENT)
Constructed termination digraph!
Nodes:
(1) f171_0_createList_Return(arg1, arg2) -> f231_0_random_ArrayAccess(arg1P, arg2P) :|: 0 <= arg1 - 1
(2) f1_0_main_Load(x, x1) -> f231_0_random_ArrayAccess(x2, x3) :|: x1 = x2 && 0 <= x - 1
(3) f1_0_main_Load(x4, x5) -> f197_0_createList_LE(x6, x7) :|: 0 <= x4 - 1 && -1 <= x6 - 1 && -1 <= x5 - 1
(4) f197_0_createList_LE(x8, x9) -> f197_0_createList_LE(x10, x11) :|: x8 - 1 = x10 && 0 <= x8 - 1
(5) f231_0_random_ArrayAccess(x12, x13) -> f352_0_appE_GT(x14, x15) :|: 1 <= x12 - 1 && 0 <= x14 - 1
(6) f352_0_appE_GT(x16, x17) -> f352_0_appE_GT(x18, x19) :|: x16 - 1 = x18 && 0 <= x16 - 1
(7) __init(x20, x21) -> f1_0_main_Load(x22, x23) :|: 0 <= 0

Arcs:
(1) -> (5)
(2) -> (5)
(3) -> (4)
(4) -> (4)
(5) -> (6)
(6) -> (6)
(7) -> (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) f197_0_createList_LE(x8, x9) -> f197_0_createList_LE(x10, x11) :|: x8 - 1 = x10 && 0 <= x8 - 1

Arcs:
(1) -> (1)

This digraph is fully evaluated!

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

(7)
Obligation:
Rules:
f197_0_createList_LE(x8:0, x9:0) -> f197_0_createList_LE(x8:0 - 1, x11:0) :|: x8:0 > 0

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

   f197_0_createList_LE(x1, x2) -> f197_0_createList_LE(x1)

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(9)
Obligation:
Rules:
f197_0_createList_LE(x8:0) -> f197_0_createList_LE(x8:0 - 1) :|: x8:0 > 0

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(10) TempFilterProof (SOUND)
Used the following sort dictionary for filtering: 
f197_0_createList_LE(INTEGER)
Replaced non-predefined constructor symbols by 0.
----------------------------------------

(11)
Obligation:
Rules:
f197_0_createList_LE(x8:0) -> f197_0_createList_LE(c) :|: c = x8:0 - 1 && x8:0 > 0

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(12) PolynomialOrderProcessor (EQUIVALENT)
Found the following polynomial interpretation:
[f197_0_createList_LE(x)] = x

The following rules are decreasing:
f197_0_createList_LE(x8:0) -> f197_0_createList_LE(c) :|: c = x8:0 - 1 && x8:0 > 0
The following rules are bounded:
f197_0_createList_LE(x8:0) -> f197_0_createList_LE(c) :|: c = x8:0 - 1 && x8:0 > 0

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(13)
YES

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(14)
Obligation:

Termination digraph:
Nodes:
(1) f352_0_appE_GT(x16, x17) -> f352_0_appE_GT(x18, x19) :|: x16 - 1 = x18 && 0 <= x16 - 1

Arcs:
(1) -> (1)

This digraph is fully evaluated!

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

(16)
Obligation:
Rules:
f352_0_appE_GT(x16:0, x17:0) -> f352_0_appE_GT(x16:0 - 1, x19:0) :|: x16:0 > 0

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

   f352_0_appE_GT(x1, x2) -> f352_0_appE_GT(x1)

----------------------------------------

(18)
Obligation:
Rules:
f352_0_appE_GT(x16:0) -> f352_0_appE_GT(x16:0 - 1) :|: x16:0 > 0

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(19) TempFilterProof (SOUND)
Used the following sort dictionary for filtering: 
f352_0_appE_GT(INTEGER)
Replaced non-predefined constructor symbols by 0.
----------------------------------------

(20)
Obligation:
Rules:
f352_0_appE_GT(x16:0) -> f352_0_appE_GT(c) :|: c = x16:0 - 1 && x16:0 > 0

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(21) PolynomialOrderProcessor (EQUIVALENT)
Found the following polynomial interpretation:
[f352_0_appE_GT(x)] = x

The following rules are decreasing:
f352_0_appE_GT(x16:0) -> f352_0_appE_GT(c) :|: c = x16:0 - 1 && x16:0 > 0
The following rules are bounded:
f352_0_appE_GT(x16:0) -> f352_0_appE_GT(c) :|: c = x16:0 - 1 && x16:0 > 0

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(22)
YES