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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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, 215 ms]
(4) IRSwT
(5) IntTRSCompressionProof [EQUIVALENT, 11 ms]
(6) IRSwT
(7) TempFilterProof [SOUND, 16 ms]
(8) IntTRS
(9) PolynomialOrderProcessor [EQUIVALENT, 0 ms]
(10) YES


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(0)
Obligation:
Rules:
f1_0_main_Load(arg1, arg2) -> f145_0_main_LE(arg1P, arg2P) :|: 0 <= arg1 - 1 && -1 <= arg1P - 1 && -1 <= arg2 - 1 && -1 <= arg2P - 1
f145_0_main_LE(x, x1) -> f145_0_main_LE'(x2, x3) :|: x1 + 1 - 2 * x4 = 0 && -1 <= x1 - 1 && x1 <= x - 1 && x = x2 && x1 = x3
f145_0_main_LE'(x5, x6) -> f145_0_main_LE(x7, x8) :|: x6 + 1 - 2 * x9 = 0 && x6 <= x5 - 1 && -1 <= x6 - 1 && x6 + 1 - 2 * x9 <= 1 && 0 <= x6 + 1 - 2 * x9 && x5 = x7 && x6 + 1 = x8
f145_0_main_LE(x11, x12) -> f145_0_main_LE'(x14, x15) :|: -1 <= x12 - 1 && x12 + 1 - 2 * x17 = 1 && x12 <= x11 - 1 && x11 = x14 && x12 = x15
f145_0_main_LE'(x18, x20) -> f145_0_main_LE(x21, x22) :|: -1 <= x20 - 1 && x20 <= x18 - 1 && x20 + 1 - 2 * x23 = 1 && x20 + 1 - 2 * x23 <= 1 && 0 <= x20 + 1 - 2 * x23 && x18 = x21 && x20 + 2 = x22
__init(x24, x25) -> f1_0_main_Load(x26, x27) :|: 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) -> f145_0_main_LE(arg1P, arg2P) :|: 0 <= arg1 - 1 && -1 <= arg1P - 1 && -1 <= arg2 - 1 && -1 <= arg2P - 1
f145_0_main_LE(x, x1) -> f145_0_main_LE'(x2, x3) :|: x1 + 1 - 2 * x4 = 0 && -1 <= x1 - 1 && x1 <= x - 1 && x = x2 && x1 = x3
f145_0_main_LE'(x5, x6) -> f145_0_main_LE(x7, x8) :|: x6 + 1 - 2 * x9 = 0 && x6 <= x5 - 1 && -1 <= x6 - 1 && x6 + 1 - 2 * x9 <= 1 && 0 <= x6 + 1 - 2 * x9 && x5 = x7 && x6 + 1 = x8
f145_0_main_LE(x11, x12) -> f145_0_main_LE'(x14, x15) :|: -1 <= x12 - 1 && x12 + 1 - 2 * x17 = 1 && x12 <= x11 - 1 && x11 = x14 && x12 = x15
f145_0_main_LE'(x18, x20) -> f145_0_main_LE(x21, x22) :|: -1 <= x20 - 1 && x20 <= x18 - 1 && x20 + 1 - 2 * x23 = 1 && x20 + 1 - 2 * x23 <= 1 && 0 <= x20 + 1 - 2 * x23 && x18 = x21 && x20 + 2 = x22
__init(x24, x25) -> f1_0_main_Load(x26, x27) :|: 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) -> f145_0_main_LE(arg1P, arg2P) :|: 0 <= arg1 - 1 && -1 <= arg1P - 1 && -1 <= arg2 - 1 && -1 <= arg2P - 1
(2) f145_0_main_LE(x, x1) -> f145_0_main_LE'(x2, x3) :|: x1 + 1 - 2 * x4 = 0 && -1 <= x1 - 1 && x1 <= x - 1 && x = x2 && x1 = x3
(3) f145_0_main_LE'(x5, x6) -> f145_0_main_LE(x7, x8) :|: x6 + 1 - 2 * x9 = 0 && x6 <= x5 - 1 && -1 <= x6 - 1 && x6 + 1 - 2 * x9 <= 1 && 0 <= x6 + 1 - 2 * x9 && x5 = x7 && x6 + 1 = x8
(4) f145_0_main_LE(x11, x12) -> f145_0_main_LE'(x14, x15) :|: -1 <= x12 - 1 && x12 + 1 - 2 * x17 = 1 && x12 <= x11 - 1 && x11 = x14 && x12 = x15
(5) f145_0_main_LE'(x18, x20) -> f145_0_main_LE(x21, x22) :|: -1 <= x20 - 1 && x20 <= x18 - 1 && x20 + 1 - 2 * x23 = 1 && x20 + 1 - 2 * x23 <= 1 && 0 <= x20 + 1 - 2 * x23 && x18 = x21 && x20 + 2 = x22
(6) __init(x24, x25) -> f1_0_main_Load(x26, x27) :|: 0 <= 0

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

This digraph is fully evaluated!
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(4)
Obligation:

Termination digraph:
Nodes:
(1) f145_0_main_LE(x11, x12) -> f145_0_main_LE'(x14, x15) :|: -1 <= x12 - 1 && x12 + 1 - 2 * x17 = 1 && x12 <= x11 - 1 && x11 = x14 && x12 = x15
(2) f145_0_main_LE'(x18, x20) -> f145_0_main_LE(x21, x22) :|: -1 <= x20 - 1 && x20 <= x18 - 1 && x20 + 1 - 2 * x23 = 1 && x20 + 1 - 2 * x23 <= 1 && 0 <= x20 + 1 - 2 * x23 && x18 = x21 && x20 + 2 = x22

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:
f145_0_main_LE(x11:0, x12:0) -> f145_0_main_LE(x11:0, x12:0 + 2) :|: x12:0 + 1 - 2 * x23:0 >= 0 && x12:0 + 1 - 2 * x17:0 = 1 && x12:0 + 1 - 2 * x23:0 <= 1 && x12:0 + 1 - 2 * x23:0 = 1 && x12:0 <= x11:0 - 1 && x12:0 > -1

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(7) TempFilterProof (SOUND)
Used the following sort dictionary for filtering: 
f145_0_main_LE(INTEGER, INTEGER)
Replaced non-predefined constructor symbols by 0.
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(8)
Obligation:
Rules:
f145_0_main_LE(x11:0, x12:0) -> f145_0_main_LE(x11:0, c) :|: c = x12:0 + 2 && (x12:0 + 1 - 2 * x23:0 >= 0 && x12:0 + 1 - 2 * x17:0 = 1 && x12:0 + 1 - 2 * x23:0 <= 1 && x12:0 + 1 - 2 * x23:0 = 1 && x12:0 <= x11:0 - 1 && x12:0 > -1)

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(9) PolynomialOrderProcessor (EQUIVALENT)
Found the following polynomial interpretation:
[f145_0_main_LE(x, x1)] = x - x1

The following rules are decreasing:
f145_0_main_LE(x11:0, x12:0) -> f145_0_main_LE(x11:0, c) :|: c = x12:0 + 2 && (x12:0 + 1 - 2 * x23:0 >= 0 && x12:0 + 1 - 2 * x17:0 = 1 && x12:0 + 1 - 2 * x23:0 <= 1 && x12:0 + 1 - 2 * x23:0 = 1 && x12:0 <= x11:0 - 1 && x12:0 > -1)
The following rules are bounded:
f145_0_main_LE(x11:0, x12:0) -> f145_0_main_LE(x11:0, c) :|: c = x12:0 + 2 && (x12:0 + 1 - 2 * x23:0 >= 0 && x12:0 + 1 - 2 * x17:0 = 1 && x12:0 + 1 - 2 * x23:0 <= 1 && x12:0 + 1 - 2 * x23:0 = 1 && x12:0 <= x11:0 - 1 && x12:0 > -1)

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(10)
YES