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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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, 218 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, arg3, arg4) -> f278_0_main_NE(arg1P, arg2P, arg3P, arg4P) :|: 0 <= arg1 - 1 && -1 <= arg3P - 1 && -1 <= arg1P - 1 && -1 <= arg2 - 1 && -1 <= arg2P - 1
f278_0_main_NE(x, x1, x2, x3) -> f322_0_main_LE(x4, x5, x6, x7) :|: x = x7 && x1 = x6 && x1 = x5 && x1 = x4 && x1 = x2 && x <= x1 - 1
f322_0_main_LE(x8, x9, x10, x11) -> f278_0_main_NE(x12, x13, x14, x15) :|: x9 = x14 && x8 = x13 && x11 = x12 && x9 = x10 && x9 <= x11
f322_0_main_LE(x16, x17, x18, x19) -> f322_0_main_LE(x20, x21, x22, x23) :|: x19 = x23 && x17 - 1 = x22 && x17 - 1 = x21 && x16 - 1 = x20 && x17 = x18 && x19 <= x17 - 1
__init(x24, x25, x26, x27) -> f1_0_main_Load(x28, x29, x30, x31) :|: 0 <= 0
Start term: __init(arg1, arg2, arg3, arg4)

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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, arg4) -> f278_0_main_NE(arg1P, arg2P, arg3P, arg4P) :|: 0 <= arg1 - 1 && -1 <= arg3P - 1 && -1 <= arg1P - 1 && -1 <= arg2 - 1 && -1 <= arg2P - 1
f278_0_main_NE(x, x1, x2, x3) -> f322_0_main_LE(x4, x5, x6, x7) :|: x = x7 && x1 = x6 && x1 = x5 && x1 = x4 && x1 = x2 && x <= x1 - 1
f322_0_main_LE(x8, x9, x10, x11) -> f278_0_main_NE(x12, x13, x14, x15) :|: x9 = x14 && x8 = x13 && x11 = x12 && x9 = x10 && x9 <= x11
f322_0_main_LE(x16, x17, x18, x19) -> f322_0_main_LE(x20, x21, x22, x23) :|: x19 = x23 && x17 - 1 = x22 && x17 - 1 = x21 && x16 - 1 = x20 && x17 = x18 && x19 <= x17 - 1
__init(x24, x25, x26, x27) -> f1_0_main_Load(x28, x29, x30, x31) :|: 0 <= 0
Start term: __init(arg1, arg2, arg3, arg4)

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(3) IRSwTTerminationDigraphProof (EQUIVALENT)
Constructed termination digraph!
Nodes:
(1) f1_0_main_Load(arg1, arg2, arg3, arg4) -> f278_0_main_NE(arg1P, arg2P, arg3P, arg4P) :|: 0 <= arg1 - 1 && -1 <= arg3P - 1 && -1 <= arg1P - 1 && -1 <= arg2 - 1 && -1 <= arg2P - 1
(2) f278_0_main_NE(x, x1, x2, x3) -> f322_0_main_LE(x4, x5, x6, x7) :|: x = x7 && x1 = x6 && x1 = x5 && x1 = x4 && x1 = x2 && x <= x1 - 1
(3) f322_0_main_LE(x8, x9, x10, x11) -> f278_0_main_NE(x12, x13, x14, x15) :|: x9 = x14 && x8 = x13 && x11 = x12 && x9 = x10 && x9 <= x11
(4) f322_0_main_LE(x16, x17, x18, x19) -> f322_0_main_LE(x20, x21, x22, x23) :|: x19 = x23 && x17 - 1 = x22 && x17 - 1 = x21 && x16 - 1 = x20 && x17 = x18 && x19 <= x17 - 1
(5) __init(x24, x25, x26, x27) -> f1_0_main_Load(x28, x29, x30, x31) :|: 0 <= 0

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

This digraph is fully evaluated!
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(4)
Obligation:

Termination digraph:
Nodes:
(1) f322_0_main_LE(x16, x17, x18, x19) -> f322_0_main_LE(x20, x21, x22, x23) :|: x19 = x23 && x17 - 1 = x22 && x17 - 1 = x21 && x16 - 1 = x20 && x17 = x18 && x19 <= x17 - 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:
f322_0_main_LE(x16:0, x17:0, x17:0, x19:0) -> f322_0_main_LE(x16:0 - 1, x17:0 - 1, x17:0 - 1, x19:0) :|: x19:0 <= x17:0 - 1

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

   f322_0_main_LE(x1, x2, x3, x4) -> f322_0_main_LE(x2, x3, x4)

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(8)
Obligation:
Rules:
f322_0_main_LE(x17:0, x17:0, x19:0) -> f322_0_main_LE(x17:0 - 1, x17:0 - 1, x19:0) :|: x19:0 <= x17:0 - 1

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(9) TempFilterProof (SOUND)
Used the following sort dictionary for filtering: 
f322_0_main_LE(INTEGER, INTEGER, INTEGER)
Replaced non-predefined constructor symbols by 0.
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(10)
Obligation:
Rules:
f322_0_main_LE(x17:0, x17:0, x19:0) -> f322_0_main_LE(c, c1, x19:0) :|: c1 = x17:0 - 1 && c = x17:0 - 1 && x19:0 <= x17:0 - 1

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(11) PolynomialOrderProcessor (EQUIVALENT)
Found the following polynomial interpretation:
[f322_0_main_LE(x, x1, x2)] = x1 - x2

The following rules are decreasing:
f322_0_main_LE(x17:0, x17:0, x19:0) -> f322_0_main_LE(c, c1, x19:0) :|: c1 = x17:0 - 1 && c = x17:0 - 1 && x19:0 <= x17:0 - 1
The following rules are bounded:
f322_0_main_LE(x17:0, x17:0, x19:0) -> f322_0_main_LE(c, c1, x19:0) :|: c1 = x17:0 - 1 && c = x17:0 - 1 && x19:0 <= x17:0 - 1

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(12)
YES