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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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, 259 ms]
(4) AND
    (5) IRSwT
        (6) IntTRSCompressionProof [EQUIVALENT, 0 ms]
        (7) IRSwT
        (8) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms]
        (9) IRSwT
        (10) TempFilterProof [SOUND, 15 ms]
        (11) IntTRS
        (12) PolynomialOrderProcessor [EQUIVALENT, 0 ms]
        (13) YES
    (14) IRSwT
        (15) IntTRSCompressionProof [EQUIVALENT, 0 ms]
        (16) IRSwT
        (17) TempFilterProof [SOUND, 4 ms]
        (18) IntTRS
        (19) PolynomialOrderProcessor [EQUIVALENT, 0 ms]
        (20) YES


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(0)
Obligation:
Rules:
f1_0_main_Load(arg1, arg2, arg3) -> f213_0_main_GT(arg1P, arg2P, arg3P) :|: 0 <= arg1 - 1 && -1 <= arg1P - 1 && -1 <= arg3P - 1 && -1 <= arg2 - 1 && -1 <= arg2P - 1
f213_0_main_GT(x, x1, x2) -> f252_0_main_LE(x3, x4, x5) :|: x2 = x5 && x1 = x4 && x = x3 && x2 <= x1 - 1
f213_0_main_GT(x6, x7, x8) -> f252_0_main_LE(x9, x10, x11) :|: x8 = x11 && x7 = x10 && x6 = x9 && x8 <= x6 - 1 && x7 <= x8
f252_0_main_LE(x12, x13, x14) -> f213_0_main_GT(x15, x16, x17) :|: x14 = x17 && x13 - 1 = x16 && x12 = x15 && x14 <= x13 - 1
f252_0_main_LE(x18, x19, x20) -> f213_0_main_GT(x21, x22, x23) :|: x20 = x23 && x19 = x22 && x18 = x21 && x18 <= x20 && x19 <= x20
f252_0_main_LE(x24, x25, x26) -> f213_0_main_GT(x27, x28, x29) :|: x26 = x29 && x25 = x28 && x24 - 1 = x27 && x26 <= x24 - 1 && x25 <= x26
__init(x30, x31, x32) -> f1_0_main_Load(x33, x34, x35) :|: 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) -> f213_0_main_GT(arg1P, arg2P, arg3P) :|: 0 <= arg1 - 1 && -1 <= arg1P - 1 && -1 <= arg3P - 1 && -1 <= arg2 - 1 && -1 <= arg2P - 1
f213_0_main_GT(x, x1, x2) -> f252_0_main_LE(x3, x4, x5) :|: x2 = x5 && x1 = x4 && x = x3 && x2 <= x1 - 1
f213_0_main_GT(x6, x7, x8) -> f252_0_main_LE(x9, x10, x11) :|: x8 = x11 && x7 = x10 && x6 = x9 && x8 <= x6 - 1 && x7 <= x8
f252_0_main_LE(x12, x13, x14) -> f213_0_main_GT(x15, x16, x17) :|: x14 = x17 && x13 - 1 = x16 && x12 = x15 && x14 <= x13 - 1
f252_0_main_LE(x18, x19, x20) -> f213_0_main_GT(x21, x22, x23) :|: x20 = x23 && x19 = x22 && x18 = x21 && x18 <= x20 && x19 <= x20
f252_0_main_LE(x24, x25, x26) -> f213_0_main_GT(x27, x28, x29) :|: x26 = x29 && x25 = x28 && x24 - 1 = x27 && x26 <= x24 - 1 && x25 <= x26
__init(x30, x31, x32) -> f1_0_main_Load(x33, x34, x35) :|: 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) -> f213_0_main_GT(arg1P, arg2P, arg3P) :|: 0 <= arg1 - 1 && -1 <= arg1P - 1 && -1 <= arg3P - 1 && -1 <= arg2 - 1 && -1 <= arg2P - 1
(2) f213_0_main_GT(x, x1, x2) -> f252_0_main_LE(x3, x4, x5) :|: x2 = x5 && x1 = x4 && x = x3 && x2 <= x1 - 1
(3) f213_0_main_GT(x6, x7, x8) -> f252_0_main_LE(x9, x10, x11) :|: x8 = x11 && x7 = x10 && x6 = x9 && x8 <= x6 - 1 && x7 <= x8
(4) f252_0_main_LE(x12, x13, x14) -> f213_0_main_GT(x15, x16, x17) :|: x14 = x17 && x13 - 1 = x16 && x12 = x15 && x14 <= x13 - 1
(5) f252_0_main_LE(x18, x19, x20) -> f213_0_main_GT(x21, x22, x23) :|: x20 = x23 && x19 = x22 && x18 = x21 && x18 <= x20 && x19 <= x20
(6) f252_0_main_LE(x24, x25, x26) -> f213_0_main_GT(x27, x28, x29) :|: x26 = x29 && x25 = x28 && x24 - 1 = x27 && x26 <= x24 - 1 && x25 <= x26
(7) __init(x30, x31, x32) -> f1_0_main_Load(x33, x34, x35) :|: 0 <= 0

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

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

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(5)
Obligation:

Termination digraph:
Nodes:
(1) f213_0_main_GT(x, x1, x2) -> f252_0_main_LE(x3, x4, x5) :|: x2 = x5 && x1 = x4 && x = x3 && x2 <= x1 - 1
(2) f252_0_main_LE(x12, x13, x14) -> f213_0_main_GT(x15, x16, x17) :|: x14 = x17 && x13 - 1 = x16 && x12 = x15 && x14 <= x13 - 1

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

This digraph is fully evaluated!

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(6) IntTRSCompressionProof (EQUIVALENT)
Compressed rules.
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(7)
Obligation:
Rules:
f213_0_main_GT(x15:0, x1:0, x17:0) -> f213_0_main_GT(x15:0, x1:0 - 1, x17:0) :|: x1:0 - 1 >= x17:0

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

   f213_0_main_GT(x1, x2, x3) -> f213_0_main_GT(x2, x3)

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(9)
Obligation:
Rules:
f213_0_main_GT(x1:0, x17:0) -> f213_0_main_GT(x1:0 - 1, x17:0) :|: x1:0 - 1 >= x17:0

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(10) TempFilterProof (SOUND)
Used the following sort dictionary for filtering: 
f213_0_main_GT(INTEGER, INTEGER)
Replaced non-predefined constructor symbols by 0.
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(11)
Obligation:
Rules:
f213_0_main_GT(x1:0, x17:0) -> f213_0_main_GT(c, x17:0) :|: c = x1:0 - 1 && x1:0 - 1 >= x17:0

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(12) PolynomialOrderProcessor (EQUIVALENT)
Found the following polynomial interpretation:
[f213_0_main_GT(x, x1)] = x - x1

The following rules are decreasing:
f213_0_main_GT(x1:0, x17:0) -> f213_0_main_GT(c, x17:0) :|: c = x1:0 - 1 && x1:0 - 1 >= x17:0
The following rules are bounded:
f213_0_main_GT(x1:0, x17:0) -> f213_0_main_GT(c, x17:0) :|: c = x1:0 - 1 && x1:0 - 1 >= x17:0

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(13)
YES

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(14)
Obligation:

Termination digraph:
Nodes:
(1) f213_0_main_GT(x6, x7, x8) -> f252_0_main_LE(x9, x10, x11) :|: x8 = x11 && x7 = x10 && x6 = x9 && x8 <= x6 - 1 && x7 <= x8
(2) f252_0_main_LE(x24, x25, x26) -> f213_0_main_GT(x27, x28, x29) :|: x26 = x29 && x25 = x28 && x24 - 1 = x27 && x26 <= x24 - 1 && x25 <= x26

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

This digraph is fully evaluated!

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

(16)
Obligation:
Rules:
f213_0_main_GT(x6:0, x10:0, x11:0) -> f213_0_main_GT(x6:0 - 1, x10:0, x11:0) :|: x6:0 - 1 >= x11:0 && x11:0 >= x10:0

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(17) TempFilterProof (SOUND)
Used the following sort dictionary for filtering: 
f213_0_main_GT(INTEGER, INTEGER, INTEGER)
Replaced non-predefined constructor symbols by 0.
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(18)
Obligation:
Rules:
f213_0_main_GT(x6:0, x10:0, x11:0) -> f213_0_main_GT(c, x10:0, x11:0) :|: c = x6:0 - 1 && (x6:0 - 1 >= x11:0 && x11:0 >= x10:0)

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(19) PolynomialOrderProcessor (EQUIVALENT)
Found the following polynomial interpretation:
[f213_0_main_GT(x, x1, x2)] = x - x1

The following rules are decreasing:
f213_0_main_GT(x6:0, x10:0, x11:0) -> f213_0_main_GT(c, x10:0, x11:0) :|: c = x6:0 - 1 && (x6:0 - 1 >= x11:0 && x11:0 >= x10:0)
The following rules are bounded:
f213_0_main_GT(x6:0, x10:0, x11:0) -> f213_0_main_GT(c, x10:0, x11:0) :|: c = x6:0 - 1 && (x6:0 - 1 >= x11:0 && x11:0 >= x10:0)

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(20)
YES