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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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, 143 ms]
(4) AND
    (5) IRSwT
        (6) IntTRSCompressionProof [EQUIVALENT, 0 ms]
        (7) IRSwT
        (8) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms]
        (9) IRSwT
        (10) TempFilterProof [SOUND, 12 ms]
        (11) IntTRS
        (12) PolynomialOrderProcessor [EQUIVALENT, 0 ms]
        (13) YES
    (14) IRSwT
        (15) IntTRSCompressionProof [EQUIVALENT, 0 ms]
        (16) IRSwT
        (17) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 2 ms]
        (18) IRSwT
        (19) TempFilterProof [SOUND, 39 ms]
        (20) IntTRS
        (21) PolynomialOrderProcessor [EQUIVALENT, 0 ms]
        (22) YES


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(0)
Obligation:
Rules:
f1_0_main_Load(arg1, arg2, arg3) -> f339_0_main_LT(arg1P, arg2P, arg3P) :|: 2 = arg3P && 0 <= arg1 - 1 && -1 <= arg2P - 1 && -1 <= arg2 - 1 && -1 <= arg1P - 1
f339_0_main_LT(x, x1, x2) -> f339_0_main_LT(x3, x4, x5) :|: x2 = x5 && -1 = x4 && x - 1 = x3 && -1 = x1 && -1 <= x - 1
f339_0_main_LT(x6, x7, x8) -> f339_0_main_LT(x9, x10, x11) :|: x8 + 1 = x11 && x7 - 1 = x10 && -1 <= x8 - 1 && -1 <= x7 - 1 && -1 <= x9 - 1
__init(x12, x13, x14) -> f1_0_main_Load(x15, x16, x17) :|: 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) -> f339_0_main_LT(arg1P, arg2P, arg3P) :|: 2 = arg3P && 0 <= arg1 - 1 && -1 <= arg2P - 1 && -1 <= arg2 - 1 && -1 <= arg1P - 1
f339_0_main_LT(x, x1, x2) -> f339_0_main_LT(x3, x4, x5) :|: x2 = x5 && -1 = x4 && x - 1 = x3 && -1 = x1 && -1 <= x - 1
f339_0_main_LT(x6, x7, x8) -> f339_0_main_LT(x9, x10, x11) :|: x8 + 1 = x11 && x7 - 1 = x10 && -1 <= x8 - 1 && -1 <= x7 - 1 && -1 <= x9 - 1
__init(x12, x13, x14) -> f1_0_main_Load(x15, x16, x17) :|: 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) -> f339_0_main_LT(arg1P, arg2P, arg3P) :|: 2 = arg3P && 0 <= arg1 - 1 && -1 <= arg2P - 1 && -1 <= arg2 - 1 && -1 <= arg1P - 1
(2) f339_0_main_LT(x, x1, x2) -> f339_0_main_LT(x3, x4, x5) :|: x2 = x5 && -1 = x4 && x - 1 = x3 && -1 = x1 && -1 <= x - 1
(3) f339_0_main_LT(x6, x7, x8) -> f339_0_main_LT(x9, x10, x11) :|: x8 + 1 = x11 && x7 - 1 = x10 && -1 <= x8 - 1 && -1 <= x7 - 1 && -1 <= x9 - 1
(4) __init(x12, x13, x14) -> f1_0_main_Load(x15, x16, x17) :|: 0 <= 0

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

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

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(5)
Obligation:

Termination digraph:
Nodes:
(1) f339_0_main_LT(x6, x7, x8) -> f339_0_main_LT(x9, x10, x11) :|: x8 + 1 = x11 && x7 - 1 = x10 && -1 <= x8 - 1 && -1 <= x7 - 1 && -1 <= x9 - 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:
f339_0_main_LT(x6:0, x7:0, x8:0) -> f339_0_main_LT(x9:0, x7:0 - 1, x8:0 + 1) :|: x7:0 > -1 && x8:0 > -1 && x9:0 > -1

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

   f339_0_main_LT(x1, x2, x3) -> f339_0_main_LT(x2, x3)

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(9)
Obligation:
Rules:
f339_0_main_LT(x7:0, x8:0) -> f339_0_main_LT(x7:0 - 1, x8:0 + 1) :|: x7:0 > -1 && x8:0 > -1 && x9:0 > -1

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(10) TempFilterProof (SOUND)
Used the following sort dictionary for filtering: 
f339_0_main_LT(INTEGER, INTEGER)
Replaced non-predefined constructor symbols by 0.
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(11)
Obligation:
Rules:
f339_0_main_LT(x7:0, x8:0) -> f339_0_main_LT(c, c1) :|: c1 = x8:0 + 1 && c = x7:0 - 1 && (x7:0 > -1 && x8:0 > -1 && x9:0 > -1)

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(12) PolynomialOrderProcessor (EQUIVALENT)
Found the following polynomial interpretation:
[f339_0_main_LT(x, x1)] = x

The following rules are decreasing:
f339_0_main_LT(x7:0, x8:0) -> f339_0_main_LT(c, c1) :|: c1 = x8:0 + 1 && c = x7:0 - 1 && (x7:0 > -1 && x8:0 > -1 && x9:0 > -1)
The following rules are bounded:
f339_0_main_LT(x7:0, x8:0) -> f339_0_main_LT(c, c1) :|: c1 = x8:0 + 1 && c = x7:0 - 1 && (x7:0 > -1 && x8:0 > -1 && x9:0 > -1)

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(13)
YES

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(14)
Obligation:

Termination digraph:
Nodes:
(1) f339_0_main_LT(x, x1, x2) -> f339_0_main_LT(x3, x4, x5) :|: x2 = x5 && -1 = x4 && x - 1 = x3 && -1 = x1 && -1 <= x - 1

Arcs:
(1) -> (1)

This digraph is fully evaluated!

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(15) IntTRSCompressionProof (EQUIVALENT)
Compressed rules.
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(16)
Obligation:
Rules:
f339_0_main_LT(x:0, cons_-1, x2:0) -> f339_0_main_LT(x:0 - 1, -1, x2:0) :|: x:0 > -1 && cons_-1 = -1

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

   f339_0_main_LT(x1, x2, x3) -> f339_0_main_LT(x1, x2)

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(18)
Obligation:
Rules:
f339_0_main_LT(x:0, cons_-1) -> f339_0_main_LT(x:0 - 1, -1) :|: x:0 > -1 && cons_-1 = -1

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(19) TempFilterProof (SOUND)
Used the following sort dictionary for filtering: 
f339_0_main_LT(INTEGER, VARIABLE)
Replaced non-predefined constructor symbols by 0.
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(20)
Obligation:
Rules:
f339_0_main_LT(x:0, c) -> f339_0_main_LT(c1, c2) :|: c2 = -1 && (c1 = x:0 - 1 && c = -1) && (x:0 > -1 && cons_-1 = -1)

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(21) PolynomialOrderProcessor (EQUIVALENT)
Found the following polynomial interpretation:
[f339_0_main_LT(x, x1)] = x

The following rules are decreasing:
f339_0_main_LT(x:0, c) -> f339_0_main_LT(c1, c2) :|: c2 = -1 && (c1 = x:0 - 1 && c = -1) && (x:0 > -1 && cons_-1 = -1)
The following rules are bounded:
f339_0_main_LT(x:0, c) -> f339_0_main_LT(c1, c2) :|: c2 = -1 && (c1 = x:0 - 1 && c = -1) && (x:0 > -1 && cons_-1 = -1)

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(22)
YES