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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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, 193 ms]
(4) AND
    (5) IRSwT
        (6) IntTRSCompressionProof [EQUIVALENT, 0 ms]
        (7) IRSwT
        (8) TempFilterProof [SOUND, 87 ms]
        (9) IntTRS
        (10) PolynomialOrderProcessor [EQUIVALENT, 11 ms]
        (11) YES
    (12) IRSwT
        (13) IntTRSCompressionProof [EQUIVALENT, 0 ms]
        (14) IRSwT
        (15) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 2 ms]
        (16) IRSwT
        (17) FilterProof [EQUIVALENT, 0 ms]
        (18) IntTRS
        (19) IntTRSCompressionProof [EQUIVALENT, 0 ms]
        (20) IntTRS
        (21) PolynomialOrderProcessor [EQUIVALENT, 0 ms]
        (22) YES


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(0)
Obligation:
Rules:
f1_0_main_Load(arg1, arg2, arg3) -> f191_0_main_LE(arg1P, arg2P, arg3P) :|: 0 = arg3P && arg2 = arg2P && arg2 - 1 = arg1P && -1 <= arg2 - 1 && 0 <= arg1 - 1
f191_0_main_LE(x, x1, x2) -> f191_0_main_LE(x3, x4, x5) :|: x = x4 && x - 1 = x3 && 0 <= x2 - 1 && 0 <= x1 - 1
f191_0_main_LE(x6, x7, x8) -> f191_0_main_LE(x9, x10, x11) :|: 1 = x11 && x6 = x10 && x6 - 1 = x9 && 0 <= x7 - 1
f191_0_main_LE(x12, x13, x14) -> f270_0_length_FieldAccess(x15, x16, x17) :|: 0 <= x15 - 1 && x13 <= 0
f270_0_length_FieldAccess(x18, x19, x20) -> f270_0_length_FieldAccess(x21, x22, x23) :|: -1 <= x21 - 1 && 0 <= x18 - 1 && x21 + 1 <= x18
__init(x24, x25, x26) -> f1_0_main_Load(x27, x28, x29) :|: 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) -> f191_0_main_LE(arg1P, arg2P, arg3P) :|: 0 = arg3P && arg2 = arg2P && arg2 - 1 = arg1P && -1 <= arg2 - 1 && 0 <= arg1 - 1
f191_0_main_LE(x, x1, x2) -> f191_0_main_LE(x3, x4, x5) :|: x = x4 && x - 1 = x3 && 0 <= x2 - 1 && 0 <= x1 - 1
f191_0_main_LE(x6, x7, x8) -> f191_0_main_LE(x9, x10, x11) :|: 1 = x11 && x6 = x10 && x6 - 1 = x9 && 0 <= x7 - 1
f191_0_main_LE(x12, x13, x14) -> f270_0_length_FieldAccess(x15, x16, x17) :|: 0 <= x15 - 1 && x13 <= 0
f270_0_length_FieldAccess(x18, x19, x20) -> f270_0_length_FieldAccess(x21, x22, x23) :|: -1 <= x21 - 1 && 0 <= x18 - 1 && x21 + 1 <= x18
__init(x24, x25, x26) -> f1_0_main_Load(x27, x28, x29) :|: 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) -> f191_0_main_LE(arg1P, arg2P, arg3P) :|: 0 = arg3P && arg2 = arg2P && arg2 - 1 = arg1P && -1 <= arg2 - 1 && 0 <= arg1 - 1
(2) f191_0_main_LE(x, x1, x2) -> f191_0_main_LE(x3, x4, x5) :|: x = x4 && x - 1 = x3 && 0 <= x2 - 1 && 0 <= x1 - 1
(3) f191_0_main_LE(x6, x7, x8) -> f191_0_main_LE(x9, x10, x11) :|: 1 = x11 && x6 = x10 && x6 - 1 = x9 && 0 <= x7 - 1
(4) f191_0_main_LE(x12, x13, x14) -> f270_0_length_FieldAccess(x15, x16, x17) :|: 0 <= x15 - 1 && x13 <= 0
(5) f270_0_length_FieldAccess(x18, x19, x20) -> f270_0_length_FieldAccess(x21, x22, x23) :|: -1 <= x21 - 1 && 0 <= x18 - 1 && x21 + 1 <= x18
(6) __init(x24, x25, x26) -> f1_0_main_Load(x27, x28, x29) :|: 0 <= 0

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

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

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(5)
Obligation:

Termination digraph:
Nodes:
(1) f191_0_main_LE(x6, x7, x8) -> f191_0_main_LE(x9, x10, x11) :|: 1 = x11 && x6 = x10 && x6 - 1 = x9 && 0 <= x7 - 1
(2) f191_0_main_LE(x, x1, x2) -> f191_0_main_LE(x3, x4, x5) :|: x = x4 && x - 1 = x3 && 0 <= x2 - 1 && 0 <= x1 - 1

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

This digraph is fully evaluated!

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(6) IntTRSCompressionProof (EQUIVALENT)
Compressed rules.
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(7)
Obligation:
Rules:
f191_0_main_LE(x4:0, x1:0, x2:0) -> f191_0_main_LE(x4:0 - 1, x4:0, x5:0) :|: x1:0 > 0 && x2:0 > 0
f191_0_main_LE(x10:0, x7:0, x8:0) -> f191_0_main_LE(x10:0 - 1, x10:0, 1) :|: x7:0 > 0

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(8) TempFilterProof (SOUND)
Used the following sort dictionary for filtering: 
f191_0_main_LE(VARIABLE, VARIABLE, VARIABLE)
Replaced non-predefined constructor symbols by 0.
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(9)
Obligation:
Rules:
f191_0_main_LE(x4:0, x1:0, x2:0) -> f191_0_main_LE(c, x4:0, x5:0) :|: c = x4:0 - 1 && (x1:0 > 0 && x2:0 > 0)
f191_0_main_LE(x10:0, x7:0, x8:0) -> f191_0_main_LE(c1, x10:0, c2) :|: c2 = 1 && c1 = x10:0 - 1 && x7:0 > 0

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(10) PolynomialOrderProcessor (EQUIVALENT)
Found the following polynomial interpretation:
[f191_0_main_LE(x, x1, x2)] = -2 + x^2 + 2*x1

The following rules are decreasing:
f191_0_main_LE(x4:0, x1:0, x2:0) -> f191_0_main_LE(c, x4:0, x5:0) :|: c = x4:0 - 1 && (x1:0 > 0 && x2:0 > 0)
f191_0_main_LE(x10:0, x7:0, x8:0) -> f191_0_main_LE(c1, x10:0, c2) :|: c2 = 1 && c1 = x10:0 - 1 && x7:0 > 0
The following rules are bounded:
f191_0_main_LE(x4:0, x1:0, x2:0) -> f191_0_main_LE(c, x4:0, x5:0) :|: c = x4:0 - 1 && (x1:0 > 0 && x2:0 > 0)
f191_0_main_LE(x10:0, x7:0, x8:0) -> f191_0_main_LE(c1, x10:0, c2) :|: c2 = 1 && c1 = x10:0 - 1 && x7:0 > 0

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(11)
YES

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(12)
Obligation:

Termination digraph:
Nodes:
(1) f270_0_length_FieldAccess(x18, x19, x20) -> f270_0_length_FieldAccess(x21, x22, x23) :|: -1 <= x21 - 1 && 0 <= x18 - 1 && x21 + 1 <= x18

Arcs:
(1) -> (1)

This digraph is fully evaluated!

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

(14)
Obligation:
Rules:
f270_0_length_FieldAccess(x18:0, x19:0, x20:0) -> f270_0_length_FieldAccess(x21:0, x22:0, x23:0) :|: x21:0 > -1 && x18:0 > 0 && x21:0 + 1 <= x18:0

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

   f270_0_length_FieldAccess(x1, x2, x3) -> f270_0_length_FieldAccess(x1)

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(16)
Obligation:
Rules:
f270_0_length_FieldAccess(x18:0) -> f270_0_length_FieldAccess(x21:0) :|: x21:0 > -1 && x18:0 > 0 && x21:0 + 1 <= x18:0

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(17) FilterProof (EQUIVALENT)
Used the following sort dictionary for filtering: 
f270_0_length_FieldAccess(INTEGER)
Replaced non-predefined constructor symbols by 0.
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(18)
Obligation:
Rules:
f270_0_length_FieldAccess(x18:0) -> f270_0_length_FieldAccess(x21:0) :|: x21:0 > -1 && x18:0 > 0 && x21:0 + 1 <= x18:0

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(19) IntTRSCompressionProof (EQUIVALENT)
Compressed rules.
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(20)
Obligation:
Rules:
f270_0_length_FieldAccess(x18:0:0) -> f270_0_length_FieldAccess(x21:0:0) :|: x21:0:0 > -1 && x18:0:0 > 0 && x21:0:0 + 1 <= x18:0:0

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(21) PolynomialOrderProcessor (EQUIVALENT)
Found the following polynomial interpretation:
[f270_0_length_FieldAccess(x)] = x

The following rules are decreasing:
f270_0_length_FieldAccess(x18:0:0) -> f270_0_length_FieldAccess(x21:0:0) :|: x21:0:0 > -1 && x18:0:0 > 0 && x21:0:0 + 1 <= x18:0:0
The following rules are bounded:
f270_0_length_FieldAccess(x18:0:0) -> f270_0_length_FieldAccess(x21:0:0) :|: x21:0:0 > -1 && x18:0:0 > 0 && x21:0:0 + 1 <= x18:0:0

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(22)
YES