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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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, 309 ms]
(4) AND
    (5) IRSwT
        (6) IntTRSCompressionProof [EQUIVALENT, 7 ms]
        (7) IRSwT
        (8) TempFilterProof [SOUND, 7 ms]
        (9) IntTRS
        (10) PolynomialOrderProcessor [EQUIVALENT, 0 ms]
        (11) YES
    (12) IRSwT
        (13) IntTRSCompressionProof [EQUIVALENT, 25 ms]
        (14) IRSwT
        (15) TempFilterProof [SOUND, 73 ms]
        (16) IntTRS
        (17) PolynomialOrderProcessor [EQUIVALENT, 10 ms]
        (18) YES


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(0)
Obligation:
Rules:
f1_0_main_Load(arg1, arg2, arg3, arg4) -> f577_0_loop_LE(arg1P, arg2P, arg3P, arg4P) :|: 0 = arg4P && 0 = arg3P && 0 = arg2P && 0 = arg1P && 0 = arg2 && 0 <= arg1 - 1
f1_0_main_Load(x, x1, x2, x3) -> f577_0_loop_LE(x4, x5, x6, x7) :|: 1 = x7 && 1 = x6 && 0 = x5 && 1 = x1 && -1 <= x4 - 1 && 0 <= x - 1
f1_0_main_Load(x8, x9, x10, x11) -> f577_0_loop_LE(x12, x13, x14, x16) :|: 2 = x16 && x9 = x14 && 0 <= x8 - 1 && -1 <= x12 - 1 && 1 <= x9 - 1 && -1 <= x13 - 1
f577_0_loop_LE(x17, x18, x19, x20) -> f577_0_loop_LE(x21, x22, x23, x24) :|: x20 = x24 && x19 = x23 && x17 - 1 = x22 && x17 - 1 = x21 && 0 <= x18 - 1 && x19 <= x20 && x17 - 1 <= x17 - 1 && -1 <= x19 - 1
f577_0_loop_LE(x25, x26, x27, x28) -> f577_0_loop_LE(x29, x30, x31, x32) :|: 0 <= x26 - 1 && 0 <= x27 - 1 && -1 <= x28 - 1 && x28 <= x27 - 1 && x28 + 1 <= x27 && -1 <= x33 - 1 && x25 - 1 - x33 = x29 && x25 - 1 - x33 = x30 && x27 = x31 && x28 + 1 = x32
__init(x34, x35, x36, x37) -> f1_0_main_Load(x38, x39, x40, x41) :|: 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) -> f577_0_loop_LE(arg1P, arg2P, arg3P, arg4P) :|: 0 = arg4P && 0 = arg3P && 0 = arg2P && 0 = arg1P && 0 = arg2 && 0 <= arg1 - 1
f1_0_main_Load(x, x1, x2, x3) -> f577_0_loop_LE(x4, x5, x6, x7) :|: 1 = x7 && 1 = x6 && 0 = x5 && 1 = x1 && -1 <= x4 - 1 && 0 <= x - 1
f1_0_main_Load(x8, x9, x10, x11) -> f577_0_loop_LE(x12, x13, x14, x16) :|: 2 = x16 && x9 = x14 && 0 <= x8 - 1 && -1 <= x12 - 1 && 1 <= x9 - 1 && -1 <= x13 - 1
f577_0_loop_LE(x17, x18, x19, x20) -> f577_0_loop_LE(x21, x22, x23, x24) :|: x20 = x24 && x19 = x23 && x17 - 1 = x22 && x17 - 1 = x21 && 0 <= x18 - 1 && x19 <= x20 && x17 - 1 <= x17 - 1 && -1 <= x19 - 1
f577_0_loop_LE(x25, x26, x27, x28) -> f577_0_loop_LE(x29, x30, x31, x32) :|: 0 <= x26 - 1 && 0 <= x27 - 1 && -1 <= x28 - 1 && x28 <= x27 - 1 && x28 + 1 <= x27 && -1 <= x33 - 1 && x25 - 1 - x33 = x29 && x25 - 1 - x33 = x30 && x27 = x31 && x28 + 1 = x32
__init(x34, x35, x36, x37) -> f1_0_main_Load(x38, x39, x40, x41) :|: 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) -> f577_0_loop_LE(arg1P, arg2P, arg3P, arg4P) :|: 0 = arg4P && 0 = arg3P && 0 = arg2P && 0 = arg1P && 0 = arg2 && 0 <= arg1 - 1
(2) f1_0_main_Load(x, x1, x2, x3) -> f577_0_loop_LE(x4, x5, x6, x7) :|: 1 = x7 && 1 = x6 && 0 = x5 && 1 = x1 && -1 <= x4 - 1 && 0 <= x - 1
(3) f1_0_main_Load(x8, x9, x10, x11) -> f577_0_loop_LE(x12, x13, x14, x16) :|: 2 = x16 && x9 = x14 && 0 <= x8 - 1 && -1 <= x12 - 1 && 1 <= x9 - 1 && -1 <= x13 - 1
(4) f577_0_loop_LE(x17, x18, x19, x20) -> f577_0_loop_LE(x21, x22, x23, x24) :|: x20 = x24 && x19 = x23 && x17 - 1 = x22 && x17 - 1 = x21 && 0 <= x18 - 1 && x19 <= x20 && x17 - 1 <= x17 - 1 && -1 <= x19 - 1
(5) f577_0_loop_LE(x25, x26, x27, x28) -> f577_0_loop_LE(x29, x30, x31, x32) :|: 0 <= x26 - 1 && 0 <= x27 - 1 && -1 <= x28 - 1 && x28 <= x27 - 1 && x28 + 1 <= x27 && -1 <= x33 - 1 && x25 - 1 - x33 = x29 && x25 - 1 - x33 = x30 && x27 = x31 && x28 + 1 = x32
(6) __init(x34, x35, x36, x37) -> f1_0_main_Load(x38, x39, x40, x41) :|: 0 <= 0

Arcs:
(3) -> (4), (5)
(4) -> (4)
(5) -> (4), (5)
(6) -> (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) f577_0_loop_LE(x25, x26, x27, x28) -> f577_0_loop_LE(x29, x30, x31, x32) :|: 0 <= x26 - 1 && 0 <= x27 - 1 && -1 <= x28 - 1 && x28 <= x27 - 1 && x28 + 1 <= x27 && -1 <= x33 - 1 && x25 - 1 - x33 = x29 && x25 - 1 - x33 = x30 && x27 = x31 && x28 + 1 = x32

Arcs:
(1) -> (1)

This digraph is fully evaluated!

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(6) IntTRSCompressionProof (EQUIVALENT)
Compressed rules.
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(7)
Obligation:
Rules:
f577_0_loop_LE(x25:0, x26:0, x27:0, x28:0) -> f577_0_loop_LE(x25:0 - 1 - x33:0, x25:0 - 1 - x33:0, x27:0, x28:0 + 1) :|: x28:0 + 1 <= x27:0 && x33:0 > -1 && x28:0 <= x27:0 - 1 && x28:0 > -1 && x27:0 > 0 && x26:0 > 0

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(8) TempFilterProof (SOUND)
Used the following sort dictionary for filtering: 
f577_0_loop_LE(VARIABLE, INTEGER, INTEGER, INTEGER)
Replaced non-predefined constructor symbols by 0.
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(9)
Obligation:
Rules:
f577_0_loop_LE(x25:0, x26:0, x27:0, x28:0) -> f577_0_loop_LE(c, c1, x27:0, c2) :|: c2 = x28:0 + 1 && (c1 = x25:0 - 1 - x33:0 && c = x25:0 - 1 - x33:0) && (x28:0 + 1 <= x27:0 && x33:0 > -1 && x28:0 <= x27:0 - 1 && x28:0 > -1 && x27:0 > 0 && x26:0 > 0)

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(10) PolynomialOrderProcessor (EQUIVALENT)
Found the following polynomial interpretation:
[f577_0_loop_LE(x, x1, x2, x3)] = x2 - x3

The following rules are decreasing:
f577_0_loop_LE(x25:0, x26:0, x27:0, x28:0) -> f577_0_loop_LE(c, c1, x27:0, c2) :|: c2 = x28:0 + 1 && (c1 = x25:0 - 1 - x33:0 && c = x25:0 - 1 - x33:0) && (x28:0 + 1 <= x27:0 && x33:0 > -1 && x28:0 <= x27:0 - 1 && x28:0 > -1 && x27:0 > 0 && x26:0 > 0)
The following rules are bounded:
f577_0_loop_LE(x25:0, x26:0, x27:0, x28:0) -> f577_0_loop_LE(c, c1, x27:0, c2) :|: c2 = x28:0 + 1 && (c1 = x25:0 - 1 - x33:0 && c = x25:0 - 1 - x33:0) && (x28:0 + 1 <= x27:0 && x33:0 > -1 && x28:0 <= x27:0 - 1 && x28:0 > -1 && x27:0 > 0 && x26:0 > 0)

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(11)
YES

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(12)
Obligation:

Termination digraph:
Nodes:
(1) f577_0_loop_LE(x17, x18, x19, x20) -> f577_0_loop_LE(x21, x22, x23, x24) :|: x20 = x24 && x19 = x23 && x17 - 1 = x22 && x17 - 1 = x21 && 0 <= x18 - 1 && x19 <= x20 && x17 - 1 <= x17 - 1 && -1 <= x19 - 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:
f577_0_loop_LE(x17:0, x18:0, x19:0, x20:0) -> f577_0_loop_LE(x17:0 - 1, x17:0 - 1, x19:0, x20:0) :|: x20:0 >= x19:0 && x18:0 > 0 && x19:0 > -1

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(15) TempFilterProof (SOUND)
Used the following sort dictionary for filtering: 
f577_0_loop_LE(VARIABLE, INTEGER, INTEGER, INTEGER)
Replaced non-predefined constructor symbols by 0.
----------------------------------------

(16)
Obligation:
Rules:
f577_0_loop_LE(x17:0, x18:0, x19:0, x20:0) -> f577_0_loop_LE(c, c1, x19:0, x20:0) :|: c1 = x17:0 - 1 && c = x17:0 - 1 && (x20:0 >= x19:0 && x18:0 > 0 && x19:0 > -1)

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(17) PolynomialOrderProcessor (EQUIVALENT)
Found the following polynomial interpretation:
[f577_0_loop_LE(x, x1, x2, x3)] = -2 + x^2 + 2*x1

The following rules are decreasing:
f577_0_loop_LE(x17:0, x18:0, x19:0, x20:0) -> f577_0_loop_LE(c, c1, x19:0, x20:0) :|: c1 = x17:0 - 1 && c = x17:0 - 1 && (x20:0 >= x19:0 && x18:0 > 0 && x19:0 > -1)
The following rules are bounded:
f577_0_loop_LE(x17:0, x18:0, x19:0, x20:0) -> f577_0_loop_LE(c, c1, x19:0, x20:0) :|: c1 = x17:0 - 1 && c = x17:0 - 1 && (x20:0 >= x19:0 && x18:0 > 0 && x19:0 > -1)

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(18)
YES