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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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, 339 ms]
(4) AND
    (5) IRSwT
        (6) IntTRSCompressionProof [EQUIVALENT, 25 ms]
        (7) IRSwT
        (8) TempFilterProof [SOUND, 14 ms]
        (9) IntTRS
        (10) PolynomialOrderProcessor [EQUIVALENT, 0 ms]
        (11) YES
    (12) IRSwT
        (13) IntTRSCompressionProof [EQUIVALENT, 8 ms]
        (14) IRSwT
        (15) TempFilterProof [SOUND, 51 ms]
        (16) IntTRS
        (17) PolynomialOrderProcessor [EQUIVALENT, 3 ms]
        (18) YES


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(0)
Obligation:
Rules:
f1_0_main_Load(arg1, arg2, arg3, arg4) -> f563_0_mk_LE(arg1P, arg2P, arg3P, arg4P) :|: 0 = arg4P && 0 = arg3P && 0 = arg2P && -1 = arg1P && 0 = arg2 && 0 <= arg1 - 1
f1_0_main_Load(x, x1, x2, x4) -> f563_0_mk_LE(x5, x6, x7, x8) :|: -1 <= x9 - 1 && 0 <= x1 - 1 && 0 <= x - 1 && 3 * x9 - 1 = x5 && 3 * x9 = x6 && x1 = x7 && 1 = x8
f563_0_mk_LE(x10, x11, x12, x13) -> f563_0_mk_LE(x14, x15, x16, x17) :|: x13 = x17 && x12 = x16 && x10 = x15 && x10 - 1 = x14 && -1 <= x12 - 1 && x12 <= x13 && 0 <= x11 - 1
f563_0_mk_LE(x18, x19, x20, x21) -> f563_0_mk_LE(x22, x23, x24, x25) :|: x21 + 1 = x25 && x20 = x24 && x18 = x23 && x18 - 1 = x22 && x21 <= x20 - 1 && -1 <= x21 - 1 && -1 <= x20 - 1 && 0 <= x19 - 1
__init(x26, x27, x28, x29) -> f1_0_main_Load(x30, x31, x32, x33) :|: 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:
f1_0_main_Load(arg1, arg2, arg3, arg4) -> f563_0_mk_LE(arg1P, arg2P, arg3P, arg4P) :|: 0 = arg4P && 0 = arg3P && 0 = arg2P && -1 = arg1P && 0 = arg2 && 0 <= arg1 - 1
f1_0_main_Load(x, x1, x2, x4) -> f563_0_mk_LE(x5, x6, x7, x8) :|: -1 <= x9 - 1 && 0 <= x1 - 1 && 0 <= x - 1 && 3 * x9 - 1 = x5 && 3 * x9 = x6 && x1 = x7 && 1 = x8
f563_0_mk_LE(x10, x11, x12, x13) -> f563_0_mk_LE(x14, x15, x16, x17) :|: x13 = x17 && x12 = x16 && x10 = x15 && x10 - 1 = x14 && -1 <= x12 - 1 && x12 <= x13 && 0 <= x11 - 1
f563_0_mk_LE(x18, x19, x20, x21) -> f563_0_mk_LE(x22, x23, x24, x25) :|: x21 + 1 = x25 && x20 = x24 && x18 = x23 && x18 - 1 = x22 && x21 <= x20 - 1 && -1 <= x21 - 1 && -1 <= x20 - 1 && 0 <= x19 - 1
__init(x26, x27, x28, x29) -> f1_0_main_Load(x30, x31, x32, x33) :|: 0 <= 0
Start term: __init(arg1, arg2, arg3, arg4)

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(3) IRSwTTerminationDigraphProof (EQUIVALENT)
Constructed termination digraph!
Nodes:
(1) f1_0_main_Load(arg1, arg2, arg3, arg4) -> f563_0_mk_LE(arg1P, arg2P, arg3P, arg4P) :|: 0 = arg4P && 0 = arg3P && 0 = arg2P && -1 = arg1P && 0 = arg2 && 0 <= arg1 - 1
(2) f1_0_main_Load(x, x1, x2, x4) -> f563_0_mk_LE(x5, x6, x7, x8) :|: -1 <= x9 - 1 && 0 <= x1 - 1 && 0 <= x - 1 && 3 * x9 - 1 = x5 && 3 * x9 = x6 && x1 = x7 && 1 = x8
(3) f563_0_mk_LE(x10, x11, x12, x13) -> f563_0_mk_LE(x14, x15, x16, x17) :|: x13 = x17 && x12 = x16 && x10 = x15 && x10 - 1 = x14 && -1 <= x12 - 1 && x12 <= x13 && 0 <= x11 - 1
(4) f563_0_mk_LE(x18, x19, x20, x21) -> f563_0_mk_LE(x22, x23, x24, x25) :|: x21 + 1 = x25 && x20 = x24 && x18 = x23 && x18 - 1 = x22 && x21 <= x20 - 1 && -1 <= x21 - 1 && -1 <= x20 - 1 && 0 <= x19 - 1
(5) __init(x26, x27, x28, x29) -> f1_0_main_Load(x30, x31, x32, x33) :|: 0 <= 0

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

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

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(5)
Obligation:

Termination digraph:
Nodes:
(1) f563_0_mk_LE(x18, x19, x20, x21) -> f563_0_mk_LE(x22, x23, x24, x25) :|: x21 + 1 = x25 && x20 = x24 && x18 = x23 && x18 - 1 = x22 && x21 <= x20 - 1 && -1 <= x21 - 1 && -1 <= x20 - 1 && 0 <= x19 - 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:
f563_0_mk_LE(x18:0, x19:0, x20:0, x21:0) -> f563_0_mk_LE(x18:0 - 1, x18:0, x20:0, x21:0 + 1) :|: x20:0 > -1 && x19:0 > 0 && x21:0 <= x20:0 - 1 && x21:0 > -1

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(8) TempFilterProof (SOUND)
Used the following sort dictionary for filtering: 
f563_0_mk_LE(VARIABLE, VARIABLE, INTEGER, INTEGER)
Replaced non-predefined constructor symbols by 0.
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(9)
Obligation:
Rules:
f563_0_mk_LE(x18:0, x19:0, x20:0, x21:0) -> f563_0_mk_LE(c, x18:0, x20:0, c1) :|: c1 = x21:0 + 1 && c = x18:0 - 1 && (x20:0 > -1 && x19:0 > 0 && x21:0 <= x20:0 - 1 && x21:0 > -1)

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(10) PolynomialOrderProcessor (EQUIVALENT)
Found the following polynomial interpretation:
[f563_0_mk_LE(x, x1, x2, x3)] = x2 - x3

The following rules are decreasing:
f563_0_mk_LE(x18:0, x19:0, x20:0, x21:0) -> f563_0_mk_LE(c, x18:0, x20:0, c1) :|: c1 = x21:0 + 1 && c = x18:0 - 1 && (x20:0 > -1 && x19:0 > 0 && x21:0 <= x20:0 - 1 && x21:0 > -1)
The following rules are bounded:
f563_0_mk_LE(x18:0, x19:0, x20:0, x21:0) -> f563_0_mk_LE(c, x18:0, x20:0, c1) :|: c1 = x21:0 + 1 && c = x18:0 - 1 && (x20:0 > -1 && x19:0 > 0 && x21:0 <= x20:0 - 1 && x21:0 > -1)

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(11)
YES

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(12)
Obligation:

Termination digraph:
Nodes:
(1) f563_0_mk_LE(x10, x11, x12, x13) -> f563_0_mk_LE(x14, x15, x16, x17) :|: x13 = x17 && x12 = x16 && x10 = x15 && x10 - 1 = x14 && -1 <= x12 - 1 && x12 <= x13 && 0 <= x11 - 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:
f563_0_mk_LE(x10:0, x11:0, x12:0, x13:0) -> f563_0_mk_LE(x10:0 - 1, x10:0, x12:0, x13:0) :|: x13:0 >= x12:0 && x12:0 > -1 && x11:0 > 0

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(15) TempFilterProof (SOUND)
Used the following sort dictionary for filtering: 
f563_0_mk_LE(VARIABLE, VARIABLE, INTEGER, INTEGER)
Replaced non-predefined constructor symbols by 0.
----------------------------------------

(16)
Obligation:
Rules:
f563_0_mk_LE(x10:0, x11:0, x12:0, x13:0) -> f563_0_mk_LE(c, x10:0, x12:0, x13:0) :|: c = x10:0 - 1 && (x13:0 >= x12:0 && x12:0 > -1 && x11:0 > 0)

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(17) PolynomialOrderProcessor (EQUIVALENT)
Found the following polynomial interpretation:
[f563_0_mk_LE(x, x1, x2, x3)] = x^2 + 2*x1

The following rules are decreasing:
f563_0_mk_LE(x10:0, x11:0, x12:0, x13:0) -> f563_0_mk_LE(c, x10:0, x12:0, x13:0) :|: c = x10:0 - 1 && (x13:0 >= x12:0 && x12:0 > -1 && x11:0 > 0)
The following rules are bounded:
f563_0_mk_LE(x10:0, x11:0, x12:0, x13:0) -> f563_0_mk_LE(c, x10:0, x12:0, x13:0) :|: c = x10:0 - 1 && (x13:0 >= x12:0 && x12:0 > -1 && x11:0 > 0)

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(18)
YES