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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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, 286 ms]
(4) IRSwT
(5) IntTRSCompressionProof [EQUIVALENT, 29 ms]
(6) IRSwT
(7) TempFilterProof [SOUND, 104 ms]
(8) IntTRS
(9) RankingReductionPairProof [EQUIVALENT, 46 ms]
(10) IntTRS
(11) RankingReductionPairProof [EQUIVALENT, 0 ms]
(12) YES


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(0)
Obligation:
Rules:
f1_0_main_New(arg1, arg2, arg3, arg4, arg5, arg6) -> f83_0_doSum_NONNULL(arg1P, arg2P, arg3P, arg4P, arg5P, arg6P) :|: 3 <= arg1P - 1
f83_0_doSum_NONNULL(x, x1, x2, x3, x4, x5) -> f160_0_factorial_GT(x6, x7, x8, x9, x10, x11) :|: 1 = x9 && 1 = x8 && 1 = x7 && x10 + 2 <= x && -1 <= x11 - 1 && 0 <= x6 - 1 && 0 <= x - 1 && x11 + 1 <= x && x6 <= x
f160_0_factorial_GT(x12, x13, x14, x15, x16, x17) -> f83_0_doSum_NONNULL(x18, x19, x20, x21, x22, x23) :|: x14 = x15 && x16 + 2 <= x12 && -1 <= x18 - 1 && -1 <= x17 - 1 && 0 <= x12 - 1 && x18 <= x17 && x18 + 1 <= x12 && x16 <= x14 - 1 && 0 <= x13 - 1
f160_0_factorial_GT(x24, x25, x26, x27, x28, x29) -> f160_0_factorial_GT(x30, x31, x32, x33, x34, x35) :|: x28 = x34 && x26 + 1 = x33 && x26 + 1 = x32 && x25 * x26 = x31 && x26 = x27 && x28 + 2 <= x24 && -1 <= x35 - 1 && 0 <= x30 - 1 && -1 <= x29 - 1 && 0 <= x24 - 1 && x35 <= x29 && x35 + 1 <= x24 && x30 <= x24 && 0 <= x25 - 1 && 0 <= x26 - 1 && x26 <= x28
__init(x36, x37, x38, x39, x40, x41) -> f1_0_main_New(x42, x43, x44, x45, x46, x47) :|: 0 <= 0
Start term: __init(arg1, arg2, arg3, arg4, arg5, arg6)

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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_New(arg1, arg2, arg3, arg4, arg5, arg6) -> f83_0_doSum_NONNULL(arg1P, arg2P, arg3P, arg4P, arg5P, arg6P) :|: 3 <= arg1P - 1
f83_0_doSum_NONNULL(x, x1, x2, x3, x4, x5) -> f160_0_factorial_GT(x6, x7, x8, x9, x10, x11) :|: 1 = x9 && 1 = x8 && 1 = x7 && x10 + 2 <= x && -1 <= x11 - 1 && 0 <= x6 - 1 && 0 <= x - 1 && x11 + 1 <= x && x6 <= x
f160_0_factorial_GT(x12, x13, x14, x15, x16, x17) -> f83_0_doSum_NONNULL(x18, x19, x20, x21, x22, x23) :|: x14 = x15 && x16 + 2 <= x12 && -1 <= x18 - 1 && -1 <= x17 - 1 && 0 <= x12 - 1 && x18 <= x17 && x18 + 1 <= x12 && x16 <= x14 - 1 && 0 <= x13 - 1
f160_0_factorial_GT(x24, x25, x26, x27, x28, x29) -> f160_0_factorial_GT(x30, x31, x32, x33, x34, x35) :|: x28 = x34 && x26 + 1 = x33 && x26 + 1 = x32 && x25 * x26 = x31 && x26 = x27 && x28 + 2 <= x24 && -1 <= x35 - 1 && 0 <= x30 - 1 && -1 <= x29 - 1 && 0 <= x24 - 1 && x35 <= x29 && x35 + 1 <= x24 && x30 <= x24 && 0 <= x25 - 1 && 0 <= x26 - 1 && x26 <= x28
__init(x36, x37, x38, x39, x40, x41) -> f1_0_main_New(x42, x43, x44, x45, x46, x47) :|: 0 <= 0
Start term: __init(arg1, arg2, arg3, arg4, arg5, arg6)

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(3) IRSwTTerminationDigraphProof (EQUIVALENT)
Constructed termination digraph!
Nodes:
(1) f1_0_main_New(arg1, arg2, arg3, arg4, arg5, arg6) -> f83_0_doSum_NONNULL(arg1P, arg2P, arg3P, arg4P, arg5P, arg6P) :|: 3 <= arg1P - 1
(2) f83_0_doSum_NONNULL(x, x1, x2, x3, x4, x5) -> f160_0_factorial_GT(x6, x7, x8, x9, x10, x11) :|: 1 = x9 && 1 = x8 && 1 = x7 && x10 + 2 <= x && -1 <= x11 - 1 && 0 <= x6 - 1 && 0 <= x - 1 && x11 + 1 <= x && x6 <= x
(3) f160_0_factorial_GT(x12, x13, x14, x15, x16, x17) -> f83_0_doSum_NONNULL(x18, x19, x20, x21, x22, x23) :|: x14 = x15 && x16 + 2 <= x12 && -1 <= x18 - 1 && -1 <= x17 - 1 && 0 <= x12 - 1 && x18 <= x17 && x18 + 1 <= x12 && x16 <= x14 - 1 && 0 <= x13 - 1
(4) f160_0_factorial_GT(x24, x25, x26, x27, x28, x29) -> f160_0_factorial_GT(x30, x31, x32, x33, x34, x35) :|: x28 = x34 && x26 + 1 = x33 && x26 + 1 = x32 && x25 * x26 = x31 && x26 = x27 && x28 + 2 <= x24 && -1 <= x35 - 1 && 0 <= x30 - 1 && -1 <= x29 - 1 && 0 <= x24 - 1 && x35 <= x29 && x35 + 1 <= x24 && x30 <= x24 && 0 <= x25 - 1 && 0 <= x26 - 1 && x26 <= x28
(5) __init(x36, x37, x38, x39, x40, x41) -> f1_0_main_New(x42, x43, x44, x45, x46, x47) :|: 0 <= 0

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

This digraph is fully evaluated!
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(4)
Obligation:

Termination digraph:
Nodes:
(1) f83_0_doSum_NONNULL(x, x1, x2, x3, x4, x5) -> f160_0_factorial_GT(x6, x7, x8, x9, x10, x11) :|: 1 = x9 && 1 = x8 && 1 = x7 && x10 + 2 <= x && -1 <= x11 - 1 && 0 <= x6 - 1 && 0 <= x - 1 && x11 + 1 <= x && x6 <= x
(2) f160_0_factorial_GT(x12, x13, x14, x15, x16, x17) -> f83_0_doSum_NONNULL(x18, x19, x20, x21, x22, x23) :|: x14 = x15 && x16 + 2 <= x12 && -1 <= x18 - 1 && -1 <= x17 - 1 && 0 <= x12 - 1 && x18 <= x17 && x18 + 1 <= x12 && x16 <= x14 - 1 && 0 <= x13 - 1
(3) f160_0_factorial_GT(x24, x25, x26, x27, x28, x29) -> f160_0_factorial_GT(x30, x31, x32, x33, x34, x35) :|: x28 = x34 && x26 + 1 = x33 && x26 + 1 = x32 && x25 * x26 = x31 && x26 = x27 && x28 + 2 <= x24 && -1 <= x35 - 1 && 0 <= x30 - 1 && -1 <= x29 - 1 && 0 <= x24 - 1 && x35 <= x29 && x35 + 1 <= x24 && x30 <= x24 && 0 <= x25 - 1 && 0 <= x26 - 1 && x26 <= x28

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

This digraph is fully evaluated!

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(5) IntTRSCompressionProof (EQUIVALENT)
Compressed rules.
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(6)
Obligation:
Rules:
f160_0_factorial_GT(x24:0, x25:0, x26:0, x26:0, x28:0, x29:0) -> f160_0_factorial_GT(x30:0, x25:0 * x26:0, x26:0 + 1, x26:0 + 1, x28:0, x35:0) :|: x26:0 > 0 && x28:0 >= x26:0 && x25:0 > 0 && x30:0 <= x24:0 && x35:0 + 1 <= x24:0 && x35:0 <= x29:0 && x24:0 > 0 && x29:0 > -1 && x30:0 > 0 && x28:0 + 2 <= x24:0 && x35:0 > -1
f160_0_factorial_GT(x12:0, x13:0, x14:0, x14:0, x16:0, x17:0) -> f160_0_factorial_GT(x6:0, 1, 1, 1, x10:0, x11:0) :|: x6:0 <= x18:0 && x13:0 > 0 && x16:0 <= x14:0 - 1 && x18:0 >= x11:0 + 1 && x18:0 + 1 <= x12:0 && x18:0 <= x17:0 && x6:0 > 0 && x12:0 > 0 && x11:0 > -1 && x17:0 > -1 && x18:0 >= x10:0 + 2 && x18:0 > 0 && x16:0 + 2 <= x12:0

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(7) TempFilterProof (SOUND)
Used the following sort dictionary for filtering: 
f160_0_factorial_GT(INTEGER, VARIABLE, VARIABLE, VARIABLE, INTEGER, INTEGER)
Replaced non-predefined constructor symbols by 0.
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(8)
Obligation:
Rules:
f160_0_factorial_GT(x24:0, x25:0, x26:0, x26:0, x28:0, x29:0) -> f160_0_factorial_GT(x30:0, c, c1, c2, x28:0, x35:0) :|: c2 = x26:0 + 1 && (c1 = x26:0 + 1 && c = x25:0 * x26:0) && (x26:0 > 0 && x28:0 >= x26:0 && x25:0 > 0 && x30:0 <= x24:0 && x35:0 + 1 <= x24:0 && x35:0 <= x29:0 && x24:0 > 0 && x29:0 > -1 && x30:0 > 0 && x28:0 + 2 <= x24:0 && x35:0 > -1)
f160_0_factorial_GT(x12:0, x13:0, x14:0, x14:0, x16:0, x17:0) -> f160_0_factorial_GT(x6:0, c3, c4, c5, x10:0, x11:0) :|: c5 = 1 && (c4 = 1 && c3 = 1) && (x6:0 <= x18:0 && x13:0 > 0 && x16:0 <= x14:0 - 1 && x18:0 >= x11:0 + 1 && x18:0 + 1 <= x12:0 && x18:0 <= x17:0 && x6:0 > 0 && x12:0 > 0 && x11:0 > -1 && x17:0 > -1 && x18:0 >= x10:0 + 2 && x18:0 > 0 && x16:0 + 2 <= x12:0)

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(9) RankingReductionPairProof (EQUIVALENT)
Interpretation:
[ f160_0_factorial_GT ] = f160_0_factorial_GT_6

The following rules are decreasing:
f160_0_factorial_GT(x12:0, x13:0, x14:0, x14:0, x16:0, x17:0) -> f160_0_factorial_GT(x6:0, c3, c4, c5, x10:0, x11:0) :|: c5 = 1 && (c4 = 1 && c3 = 1) && (x6:0 <= x18:0 && x13:0 > 0 && x16:0 <= x14:0 - 1 && x18:0 >= x11:0 + 1 && x18:0 + 1 <= x12:0 && x18:0 <= x17:0 && x6:0 > 0 && x12:0 > 0 && x11:0 > -1 && x17:0 > -1 && x18:0 >= x10:0 + 2 && x18:0 > 0 && x16:0 + 2 <= x12:0)

The following rules are bounded:
f160_0_factorial_GT(x24:0, x25:0, x26:0, x26:0, x28:0, x29:0) -> f160_0_factorial_GT(x30:0, c, c1, c2, x28:0, x35:0) :|: c2 = x26:0 + 1 && (c1 = x26:0 + 1 && c = x25:0 * x26:0) && (x26:0 > 0 && x28:0 >= x26:0 && x25:0 > 0 && x30:0 <= x24:0 && x35:0 + 1 <= x24:0 && x35:0 <= x29:0 && x24:0 > 0 && x29:0 > -1 && x30:0 > 0 && x28:0 + 2 <= x24:0 && x35:0 > -1)
f160_0_factorial_GT(x12:0, x13:0, x14:0, x14:0, x16:0, x17:0) -> f160_0_factorial_GT(x6:0, c3, c4, c5, x10:0, x11:0) :|: c5 = 1 && (c4 = 1 && c3 = 1) && (x6:0 <= x18:0 && x13:0 > 0 && x16:0 <= x14:0 - 1 && x18:0 >= x11:0 + 1 && x18:0 + 1 <= x12:0 && x18:0 <= x17:0 && x6:0 > 0 && x12:0 > 0 && x11:0 > -1 && x17:0 > -1 && x18:0 >= x10:0 + 2 && x18:0 > 0 && x16:0 + 2 <= x12:0)


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(10)
Obligation:
Rules:
f160_0_factorial_GT(x24:0, x25:0, x26:0, x26:0, x28:0, x29:0) -> f160_0_factorial_GT(x30:0, c, c1, c2, x28:0, x35:0) :|: c2 = x26:0 + 1 && (c1 = x26:0 + 1 && c = x25:0 * x26:0) && (x26:0 > 0 && x28:0 >= x26:0 && x25:0 > 0 && x30:0 <= x24:0 && x35:0 + 1 <= x24:0 && x35:0 <= x29:0 && x24:0 > 0 && x29:0 > -1 && x30:0 > 0 && x28:0 + 2 <= x24:0 && x35:0 > -1)

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(11) RankingReductionPairProof (EQUIVALENT)
Interpretation:
[ f160_0_factorial_GT ] = -1*f160_0_factorial_GT_4 + f160_0_factorial_GT_5

The following rules are decreasing:
f160_0_factorial_GT(x24:0, x25:0, x26:0, x26:0, x28:0, x29:0) -> f160_0_factorial_GT(x30:0, c, c1, c2, x28:0, x35:0) :|: c2 = x26:0 + 1 && (c1 = x26:0 + 1 && c = x25:0 * x26:0) && (x26:0 > 0 && x28:0 >= x26:0 && x25:0 > 0 && x30:0 <= x24:0 && x35:0 + 1 <= x24:0 && x35:0 <= x29:0 && x24:0 > 0 && x29:0 > -1 && x30:0 > 0 && x28:0 + 2 <= x24:0 && x35:0 > -1)

The following rules are bounded:
f160_0_factorial_GT(x24:0, x25:0, x26:0, x26:0, x28:0, x29:0) -> f160_0_factorial_GT(x30:0, c, c1, c2, x28:0, x35:0) :|: c2 = x26:0 + 1 && (c1 = x26:0 + 1 && c = x25:0 * x26:0) && (x26:0 > 0 && x28:0 >= x26:0 && x25:0 > 0 && x30:0 <= x24:0 && x35:0 + 1 <= x24:0 && x35:0 <= x29:0 && x24:0 > 0 && x29:0 > -1 && x30:0 > 0 && x28:0 + 2 <= x24:0 && x35:0 > -1)


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(12)
YES