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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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, 224 ms]
(4) IRSwT
(5) IntTRSCompressionProof [EQUIVALENT, 0 ms]
(6) IRSwT
(7) TempFilterProof [SOUND, 59 ms]
(8) IntTRS
(9) PolynomialOrderProcessor [EQUIVALENT, 10 ms]
(10) IntTRS
(11) RankingReductionPairProof [EQUIVALENT, 0 ms]
(12) YES


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(0)
Obligation:
Rules:
f1_0_main_Load(arg1, arg2, arg3) -> f368_0_main_LE(arg1P, arg2P, arg3P) :|: 2 = arg3P && 0 <= arg1 - 1 && -1 <= arg2P - 1 && -1 <= arg2 - 1 && -1 <= arg1P - 1
f368_0_main_LE(x, x1, x2) -> f368_0_main_LE(x3, x4, x5) :|: -1 <= x2 - 1 && 41 <= x6 - 1 && 0 <= x - 1 && 0 <= x1 - 1 && x - 1 = x3 && x1 = x4 && x2 + 1 = x5
f368_0_main_LE(x8, x9, x10) -> f368_0_main_LE(x11, x13, x14) :|: 0 <= x8 - 1 && -1 <= x10 - 1 && 0 <= x9 - 1 && -1 <= x15 - 1 && -1 <= x11 - 1 && x15 <= 41 && x9 - 1 = x13 && x10 + 2 = x14
__init(x16, x17, x18) -> f1_0_main_Load(x19, x20, x21) :|: 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) -> f368_0_main_LE(arg1P, arg2P, arg3P) :|: 2 = arg3P && 0 <= arg1 - 1 && -1 <= arg2P - 1 && -1 <= arg2 - 1 && -1 <= arg1P - 1
f368_0_main_LE(x, x1, x2) -> f368_0_main_LE(x3, x4, x5) :|: -1 <= x2 - 1 && 41 <= x6 - 1 && 0 <= x - 1 && 0 <= x1 - 1 && x - 1 = x3 && x1 = x4 && x2 + 1 = x5
f368_0_main_LE(x8, x9, x10) -> f368_0_main_LE(x11, x13, x14) :|: 0 <= x8 - 1 && -1 <= x10 - 1 && 0 <= x9 - 1 && -1 <= x15 - 1 && -1 <= x11 - 1 && x15 <= 41 && x9 - 1 = x13 && x10 + 2 = x14
__init(x16, x17, x18) -> f1_0_main_Load(x19, x20, x21) :|: 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) -> f368_0_main_LE(arg1P, arg2P, arg3P) :|: 2 = arg3P && 0 <= arg1 - 1 && -1 <= arg2P - 1 && -1 <= arg2 - 1 && -1 <= arg1P - 1
(2) f368_0_main_LE(x, x1, x2) -> f368_0_main_LE(x3, x4, x5) :|: -1 <= x2 - 1 && 41 <= x6 - 1 && 0 <= x - 1 && 0 <= x1 - 1 && x - 1 = x3 && x1 = x4 && x2 + 1 = x5
(3) f368_0_main_LE(x8, x9, x10) -> f368_0_main_LE(x11, x13, x14) :|: 0 <= x8 - 1 && -1 <= x10 - 1 && 0 <= x9 - 1 && -1 <= x15 - 1 && -1 <= x11 - 1 && x15 <= 41 && x9 - 1 = x13 && x10 + 2 = x14
(4) __init(x16, x17, x18) -> f1_0_main_Load(x19, x20, x21) :|: 0 <= 0

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

This digraph is fully evaluated!
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(4)
Obligation:

Termination digraph:
Nodes:
(1) f368_0_main_LE(x, x1, x2) -> f368_0_main_LE(x3, x4, x5) :|: -1 <= x2 - 1 && 41 <= x6 - 1 && 0 <= x - 1 && 0 <= x1 - 1 && x - 1 = x3 && x1 = x4 && x2 + 1 = x5
(2) f368_0_main_LE(x8, x9, x10) -> f368_0_main_LE(x11, x13, x14) :|: 0 <= x8 - 1 && -1 <= x10 - 1 && 0 <= x9 - 1 && -1 <= x15 - 1 && -1 <= x11 - 1 && x15 <= 41 && x9 - 1 = x13 && x10 + 2 = x14

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

This digraph is fully evaluated!

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(5) IntTRSCompressionProof (EQUIVALENT)
Compressed rules.
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(6)
Obligation:
Rules:
f368_0_main_LE(x:0, x1:0, x2:0) -> f368_0_main_LE(x:0 - 1, x1:0, x2:0 + 1) :|: x:0 > 0 && x1:0 > 0 && x6:0 > 41 && x2:0 > -1
f368_0_main_LE(x8:0, x9:0, x10:0) -> f368_0_main_LE(x11:0, x9:0 - 1, x10:0 + 2) :|: x11:0 > -1 && x15:0 < 42 && x15:0 > -1 && x9:0 > 0 && x10:0 > -1 && x8:0 > 0

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(7) TempFilterProof (SOUND)
Used the following sort dictionary for filtering: 
f368_0_main_LE(INTEGER, INTEGER, INTEGER)
Replaced non-predefined constructor symbols by 0.
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(8)
Obligation:
Rules:
f368_0_main_LE(x:0, x1:0, x2:0) -> f368_0_main_LE(c, x1:0, c1) :|: c1 = x2:0 + 1 && c = x:0 - 1 && (x:0 > 0 && x1:0 > 0 && x6:0 > 41 && x2:0 > -1)
f368_0_main_LE(x8:0, x9:0, x10:0) -> f368_0_main_LE(x11:0, c2, c3) :|: c3 = x10:0 + 2 && c2 = x9:0 - 1 && (x11:0 > -1 && x15:0 < 42 && x15:0 > -1 && x9:0 > 0 && x10:0 > -1 && x8:0 > 0)

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(9) PolynomialOrderProcessor (EQUIVALENT)
Found the following polynomial interpretation:
[f368_0_main_LE(x, x1, x2)] = x1

The following rules are decreasing:
f368_0_main_LE(x8:0, x9:0, x10:0) -> f368_0_main_LE(x11:0, c2, c3) :|: c3 = x10:0 + 2 && c2 = x9:0 - 1 && (x11:0 > -1 && x15:0 < 42 && x15:0 > -1 && x9:0 > 0 && x10:0 > -1 && x8:0 > 0)
The following rules are bounded:
f368_0_main_LE(x:0, x1:0, x2:0) -> f368_0_main_LE(c, x1:0, c1) :|: c1 = x2:0 + 1 && c = x:0 - 1 && (x:0 > 0 && x1:0 > 0 && x6:0 > 41 && x2:0 > -1)
f368_0_main_LE(x8:0, x9:0, x10:0) -> f368_0_main_LE(x11:0, c2, c3) :|: c3 = x10:0 + 2 && c2 = x9:0 - 1 && (x11:0 > -1 && x15:0 < 42 && x15:0 > -1 && x9:0 > 0 && x10:0 > -1 && x8:0 > 0)

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(10)
Obligation:
Rules:
f368_0_main_LE(x:0, x1:0, x2:0) -> f368_0_main_LE(c, x1:0, c1) :|: c1 = x2:0 + 1 && c = x:0 - 1 && (x:0 > 0 && x1:0 > 0 && x6:0 > 41 && x2:0 > -1)

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(11) RankingReductionPairProof (EQUIVALENT)
Interpretation:
[ f368_0_main_LE ] = f368_0_main_LE_1

The following rules are decreasing:
f368_0_main_LE(x:0, x1:0, x2:0) -> f368_0_main_LE(c, x1:0, c1) :|: c1 = x2:0 + 1 && c = x:0 - 1 && (x:0 > 0 && x1:0 > 0 && x6:0 > 41 && x2:0 > -1)

The following rules are bounded:
f368_0_main_LE(x:0, x1:0, x2:0) -> f368_0_main_LE(c, x1:0, c1) :|: c1 = x2:0 + 1 && c = x:0 - 1 && (x:0 > 0 && x1:0 > 0 && x6:0 > 41 && x2:0 > -1)


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(12)
YES