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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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, 242 ms]
(4) IRSwT
(5) IntTRSCompressionProof [EQUIVALENT, 0 ms]
(6) IRSwT
(7) TempFilterProof [SOUND, 54 ms]
(8) IntTRS
(9) PolynomialOrderProcessor [EQUIVALENT, 0 ms]
(10) IntTRS
(11) RankingReductionPairProof [EQUIVALENT, 0 ms]
(12) YES


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(0)
Obligation:
Rules:
f1_0_main_Load(arg1, arg2, arg3, arg4) -> f278_0_main_LE(arg1P, arg2P, arg3P, arg4P) :|: arg2P = arg4P && arg2P = arg3P && 0 <= arg1 - 1 && -1 <= arg1P - 1 && -1 <= arg2 - 1 && -1 <= arg2P - 1
f278_0_main_LE(x, x1, x2, x3) -> f278_0_main_LE(x4, x5, x6, x7) :|: x2 = x7 && x2 = x6 && x2 = x5 && x = x4 && x2 = x3 && 0 = x1 && 0 <= x2 - 1
f278_0_main_LE(x8, x9, x10, x11) -> f278_0_main_LE(x12, x13, x14, x15) :|: x10 = x15 && x10 = x14 && x9 - 1 = x13 && x8 - 1 = x12 && x10 = x11 && 0 <= x9 - 1 && 0 <= x10 - 1 && 0 <= x8 - 1
__init(x16, x17, x18, x19) -> f1_0_main_Load(x20, x21, x22, x23) :|: 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_LE(arg1P, arg2P, arg3P, arg4P) :|: arg2P = arg4P && arg2P = arg3P && 0 <= arg1 - 1 && -1 <= arg1P - 1 && -1 <= arg2 - 1 && -1 <= arg2P - 1
f278_0_main_LE(x, x1, x2, x3) -> f278_0_main_LE(x4, x5, x6, x7) :|: x2 = x7 && x2 = x6 && x2 = x5 && x = x4 && x2 = x3 && 0 = x1 && 0 <= x2 - 1
f278_0_main_LE(x8, x9, x10, x11) -> f278_0_main_LE(x12, x13, x14, x15) :|: x10 = x15 && x10 = x14 && x9 - 1 = x13 && x8 - 1 = x12 && x10 = x11 && 0 <= x9 - 1 && 0 <= x10 - 1 && 0 <= x8 - 1
__init(x16, x17, x18, x19) -> f1_0_main_Load(x20, x21, x22, x23) :|: 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_LE(arg1P, arg2P, arg3P, arg4P) :|: arg2P = arg4P && arg2P = arg3P && 0 <= arg1 - 1 && -1 <= arg1P - 1 && -1 <= arg2 - 1 && -1 <= arg2P - 1
(2) f278_0_main_LE(x, x1, x2, x3) -> f278_0_main_LE(x4, x5, x6, x7) :|: x2 = x7 && x2 = x6 && x2 = x5 && x = x4 && x2 = x3 && 0 = x1 && 0 <= x2 - 1
(3) f278_0_main_LE(x8, x9, x10, x11) -> f278_0_main_LE(x12, x13, x14, x15) :|: x10 = x15 && x10 = x14 && x9 - 1 = x13 && x8 - 1 = x12 && x10 = x11 && 0 <= x9 - 1 && 0 <= x10 - 1 && 0 <= x8 - 1
(4) __init(x16, x17, x18, x19) -> f1_0_main_Load(x20, x21, x22, x23) :|: 0 <= 0

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

This digraph is fully evaluated!
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(4)
Obligation:

Termination digraph:
Nodes:
(1) f278_0_main_LE(x8, x9, x10, x11) -> f278_0_main_LE(x12, x13, x14, x15) :|: x10 = x15 && x10 = x14 && x9 - 1 = x13 && x8 - 1 = x12 && x10 = x11 && 0 <= x9 - 1 && 0 <= x10 - 1 && 0 <= x8 - 1
(2) f278_0_main_LE(x, x1, x2, x3) -> f278_0_main_LE(x4, x5, x6, x7) :|: x2 = x7 && x2 = x6 && x2 = x5 && x = x4 && x2 = x3 && 0 = x1 && 0 <= x2 - 1

Arcs:
(1) -> (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:
f278_0_main_LE(x8:0, x9:0, x10:0, x10:0) -> f278_0_main_LE(x8:0 - 1, x9:0 - 1, x10:0, x10:0) :|: x10:0 > 0 && x9:0 > 0 && x8:0 > 0
f278_0_main_LE(x4:0, cons_0, x2:0, x2:0) -> f278_0_main_LE(x4:0, x2:0, x2:0, x2:0) :|: x2:0 > 0 && cons_0 = 0

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(7) TempFilterProof (SOUND)
Used the following sort dictionary for filtering: 
f278_0_main_LE(VARIABLE, INTEGER, INTEGER, INTEGER)
Replaced non-predefined constructor symbols by 0.
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(8)
Obligation:
Rules:
f278_0_main_LE(x8:0, x9:0, x10:0, x10:0) -> f278_0_main_LE(c, c1, x10:0, x10:0) :|: c1 = x9:0 - 1 && c = x8:0 - 1 && (x10:0 > 0 && x9:0 > 0 && x8:0 > 0)
f278_0_main_LE(x4:0, c2, x2:0, x2:0) -> f278_0_main_LE(x4:0, x2:0, x2:0, x2:0) :|: c2 = 0 && (x2:0 > 0 && cons_0 = 0)

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(9) PolynomialOrderProcessor (EQUIVALENT)
Found the following polynomial interpretation:
[f278_0_main_LE(x, x1, x2, x3)] = -1 + x

The following rules are decreasing:
f278_0_main_LE(x8:0, x9:0, x10:0, x10:0) -> f278_0_main_LE(c, c1, x10:0, x10:0) :|: c1 = x9:0 - 1 && c = x8:0 - 1 && (x10:0 > 0 && x9:0 > 0 && x8:0 > 0)
The following rules are bounded:
f278_0_main_LE(x8:0, x9:0, x10:0, x10:0) -> f278_0_main_LE(c, c1, x10:0, x10:0) :|: c1 = x9:0 - 1 && c = x8:0 - 1 && (x10:0 > 0 && x9:0 > 0 && x8:0 > 0)

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(10)
Obligation:
Rules:
f278_0_main_LE(x4:0, c2, x2:0, x2:0) -> f278_0_main_LE(x4:0, x2:0, x2:0, x2:0) :|: c2 = 0 && (x2:0 > 0 && cons_0 = 0)

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(11) RankingReductionPairProof (EQUIVALENT)
Interpretation:
[ f278_0_main_LE ] = -1*f278_0_main_LE_2

The following rules are decreasing:
f278_0_main_LE(x4:0, c2, x2:0, x2:0) -> f278_0_main_LE(x4:0, x2:0, x2:0, x2:0) :|: c2 = 0 && (x2:0 > 0 && cons_0 = 0)

The following rules are bounded:
f278_0_main_LE(x4:0, c2, x2:0, x2:0) -> f278_0_main_LE(x4:0, x2:0, x2:0, x2:0) :|: c2 = 0 && (x2:0 > 0 && cons_0 = 0)


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(12)
YES