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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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, 131 ms]
(4) IRSwT
(5) IntTRSCompressionProof [EQUIVALENT, 0 ms]
(6) IRSwT
(7) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms]
(8) IRSwT
(9) TempFilterProof [SOUND, 35 ms]
(10) IntTRS
(11) PolynomialOrderProcessor [EQUIVALENT, 0 ms]
(12) YES


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(0)
Obligation:
Rules:
f1_0_main_Load(arg1, arg2) -> f1_0_main_Load'(arg1P, arg2P) :|: 0 <= arg2 - 1 && -1 <= x2 - 1 && 0 <= arg1 - 1 && arg1 = arg1P && arg2 = arg2P
f1_0_main_Load'(x, x1) -> f126_0_test_LE(x3, x4) :|: 0 <= x1 - 1 && -1 <= x5 - 1 && 0 <= x - 1 && x5 - 100 * x8 <= 99 && 0 <= x5 - 100 * x8 && x5 - 100 * x8 = x3
f126_0_test_LE(x9, x10) -> f126_0_test_LE(x11, x12) :|: x9 - 1 = x11 && 0 <= x9 - 1
__init(x13, x14) -> f1_0_main_Load(x15, x16) :|: 0 <= 0
Start term: __init(arg1, arg2)

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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) -> f1_0_main_Load'(arg1P, arg2P) :|: 0 <= arg2 - 1 && -1 <= x2 - 1 && 0 <= arg1 - 1 && arg1 = arg1P && arg2 = arg2P
f1_0_main_Load'(x, x1) -> f126_0_test_LE(x3, x4) :|: 0 <= x1 - 1 && -1 <= x5 - 1 && 0 <= x - 1 && x5 - 100 * x8 <= 99 && 0 <= x5 - 100 * x8 && x5 - 100 * x8 = x3
f126_0_test_LE(x9, x10) -> f126_0_test_LE(x11, x12) :|: x9 - 1 = x11 && 0 <= x9 - 1
__init(x13, x14) -> f1_0_main_Load(x15, x16) :|: 0 <= 0
Start term: __init(arg1, arg2)

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(3) IRSwTTerminationDigraphProof (EQUIVALENT)
Constructed termination digraph!
Nodes:
(1) f1_0_main_Load(arg1, arg2) -> f1_0_main_Load'(arg1P, arg2P) :|: 0 <= arg2 - 1 && -1 <= x2 - 1 && 0 <= arg1 - 1 && arg1 = arg1P && arg2 = arg2P
(2) f1_0_main_Load'(x, x1) -> f126_0_test_LE(x3, x4) :|: 0 <= x1 - 1 && -1 <= x5 - 1 && 0 <= x - 1 && x5 - 100 * x8 <= 99 && 0 <= x5 - 100 * x8 && x5 - 100 * x8 = x3
(3) f126_0_test_LE(x9, x10) -> f126_0_test_LE(x11, x12) :|: x9 - 1 = x11 && 0 <= x9 - 1
(4) __init(x13, x14) -> f1_0_main_Load(x15, x16) :|: 0 <= 0

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

This digraph is fully evaluated!
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(4)
Obligation:

Termination digraph:
Nodes:
(1) f126_0_test_LE(x9, x10) -> f126_0_test_LE(x11, x12) :|: x9 - 1 = x11 && 0 <= x9 - 1

Arcs:
(1) -> (1)

This digraph is fully evaluated!

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(5) IntTRSCompressionProof (EQUIVALENT)
Compressed rules.
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(6)
Obligation:
Rules:
f126_0_test_LE(x9:0, x10:0) -> f126_0_test_LE(x9:0 - 1, x12:0) :|: x9:0 > 0

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

   f126_0_test_LE(x1, x2) -> f126_0_test_LE(x1)

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(8)
Obligation:
Rules:
f126_0_test_LE(x9:0) -> f126_0_test_LE(x9:0 - 1) :|: x9:0 > 0

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(9) TempFilterProof (SOUND)
Used the following sort dictionary for filtering: 
f126_0_test_LE(INTEGER)
Replaced non-predefined constructor symbols by 0.
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(10)
Obligation:
Rules:
f126_0_test_LE(x9:0) -> f126_0_test_LE(c) :|: c = x9:0 - 1 && x9:0 > 0

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(11) PolynomialOrderProcessor (EQUIVALENT)
Found the following polynomial interpretation:
[f126_0_test_LE(x)] = x

The following rules are decreasing:
f126_0_test_LE(x9:0) -> f126_0_test_LE(c) :|: c = x9:0 - 1 && x9:0 > 0
The following rules are bounded:
f126_0_test_LE(x9:0) -> f126_0_test_LE(c) :|: c = x9:0 - 1 && x9:0 > 0

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(12)
YES