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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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, 74 ms]
(4) IRSwT
(5) IntTRSCompressionProof [EQUIVALENT, 9 ms]
(6) IRSwT
(7) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms]
(8) IRSwT
(9) FilterProof [EQUIVALENT, 0 ms]
(10) IntTRS
(11) IntTRSCompressionProof [EQUIVALENT, 0 ms]
(12) IntTRS
(13) PolynomialOrderProcessor [EQUIVALENT, 0 ms]
(14) YES


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(0)
Obligation:
Rules:
f1_0_main_Load(arg1, arg2) -> f157_0_log_LE(arg1P, arg2P) :|: 0 <= arg1 - 1 && -1 <= arg1P - 1 && -1 <= arg2 - 1
f157_0_log_LE(x, x1) -> f157_0_log_LE'(x2, x3) :|: 1 <= x - 1 && x4 <= x - 1 && x = x2
f157_0_log_LE'(x6, x7) -> f157_0_log_LE(x8, x9) :|: 0 <= x6 - 2 * x8 && x6 - 2 * x8 <= 1 && 1 <= x6 - 1 && x8 <= x6 - 1
__init(x10, x11) -> f1_0_main_Load(x12, x13) :|: 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) -> f157_0_log_LE(arg1P, arg2P) :|: 0 <= arg1 - 1 && -1 <= arg1P - 1 && -1 <= arg2 - 1
f157_0_log_LE(x, x1) -> f157_0_log_LE'(x2, x3) :|: 1 <= x - 1 && x4 <= x - 1 && x = x2
f157_0_log_LE'(x6, x7) -> f157_0_log_LE(x8, x9) :|: 0 <= x6 - 2 * x8 && x6 - 2 * x8 <= 1 && 1 <= x6 - 1 && x8 <= x6 - 1
__init(x10, x11) -> f1_0_main_Load(x12, x13) :|: 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) -> f157_0_log_LE(arg1P, arg2P) :|: 0 <= arg1 - 1 && -1 <= arg1P - 1 && -1 <= arg2 - 1
(2) f157_0_log_LE(x, x1) -> f157_0_log_LE'(x2, x3) :|: 1 <= x - 1 && x4 <= x - 1 && x = x2
(3) f157_0_log_LE'(x6, x7) -> f157_0_log_LE(x8, x9) :|: 0 <= x6 - 2 * x8 && x6 - 2 * x8 <= 1 && 1 <= x6 - 1 && x8 <= x6 - 1
(4) __init(x10, x11) -> f1_0_main_Load(x12, x13) :|: 0 <= 0

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

This digraph is fully evaluated!
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(4)
Obligation:

Termination digraph:
Nodes:
(1) f157_0_log_LE(x, x1) -> f157_0_log_LE'(x2, x3) :|: 1 <= x - 1 && x4 <= x - 1 && x = x2
(2) f157_0_log_LE'(x6, x7) -> f157_0_log_LE(x8, x9) :|: 0 <= x6 - 2 * x8 && x6 - 2 * x8 <= 1 && 1 <= x6 - 1 && x8 <= x6 - 1

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

This digraph is fully evaluated!

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(5) IntTRSCompressionProof (EQUIVALENT)
Compressed rules.
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(6)
Obligation:
Rules:
f157_0_log_LE(x2:0, x1:0) -> f157_0_log_LE(x8:0, x9:0) :|: x8:0 <= x2:0 - 1 && x4:0 <= x2:0 - 1 && x2:0 > 1 && x2:0 - 2 * x8:0 <= 1 && x2:0 - 2 * x8:0 >= 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:

   f157_0_log_LE(x1, x2) -> f157_0_log_LE(x1)

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(8)
Obligation:
Rules:
f157_0_log_LE(x2:0) -> f157_0_log_LE(x8:0) :|: x8:0 <= x2:0 - 1 && x4:0 <= x2:0 - 1 && x2:0 > 1 && x2:0 - 2 * x8:0 <= 1 && x2:0 - 2 * x8:0 >= 0

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(9) FilterProof (EQUIVALENT)
Used the following sort dictionary for filtering: 
f157_0_log_LE(INTEGER)
Replaced non-predefined constructor symbols by 0.
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(10)
Obligation:
Rules:
f157_0_log_LE(x2:0) -> f157_0_log_LE(x8:0) :|: x8:0 <= x2:0 - 1 && x4:0 <= x2:0 - 1 && x2:0 > 1 && x2:0 - 2 * x8:0 <= 1 && x2:0 - 2 * x8:0 >= 0

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(11) IntTRSCompressionProof (EQUIVALENT)
Compressed rules.
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(12)
Obligation:
Rules:
f157_0_log_LE(x2:0:0) -> f157_0_log_LE(x8:0:0) :|: x2:0:0 - 2 * x8:0:0 <= 1 && x2:0:0 - 2 * x8:0:0 >= 0 && x2:0:0 > 1 && x4:0:0 <= x2:0:0 - 1 && x8:0:0 <= x2:0:0 - 1

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(13) PolynomialOrderProcessor (EQUIVALENT)
Found the following polynomial interpretation:
[f157_0_log_LE(x)] = x

The following rules are decreasing:
f157_0_log_LE(x2:0:0) -> f157_0_log_LE(x8:0:0) :|: x2:0:0 - 2 * x8:0:0 <= 1 && x2:0:0 - 2 * x8:0:0 >= 0 && x2:0:0 > 1 && x4:0:0 <= x2:0:0 - 1 && x8:0:0 <= x2:0:0 - 1
The following rules are bounded:
f157_0_log_LE(x2:0:0) -> f157_0_log_LE(x8:0:0) :|: x2:0:0 - 2 * x8:0:0 <= 1 && x2:0:0 - 2 * x8:0:0 >= 0 && x2:0:0 > 1 && x4:0:0 <= x2:0:0 - 1 && x8:0:0 <= x2:0:0 - 1

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(14)
YES