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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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, 284 ms]
(4) IRSwT
(5) IntTRSCompressionProof [EQUIVALENT, 0 ms]
(6) IRSwT
(7) TempFilterProof [SOUND, 57 ms]
(8) IntTRS
(9) PolynomialOrderProcessor [EQUIVALENT, 15 ms]
(10) IntTRS
(11) RankingReductionPairProof [EQUIVALENT, 0 ms]
(12) YES


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(0)
Obligation:
Rules:
f1_0_main_Load(arg1, arg2) -> f152_0_gcd_EQ(arg1P, arg2P) :|: 0 <= arg1 - 1 && -1 <= arg1P - 1 && -1 <= arg2 - 1 && -1 <= arg2P - 1
f152_0_gcd_EQ(x, x1) -> f207_0_mod_LE(x2, x3) :|: x1 = x3 && x = x2 && 0 <= x - 1 && x <= x1 - 1 && 0 <= x1 - 1
f152_0_gcd_EQ(x4, x5) -> f207_0_mod_LE(x6, x7) :|: x5 = x7 && x4 = x6 && 0 <= x4 - 1 && x5 <= x4 - 1 && 0 <= x5 - 1
f152_0_gcd_EQ(x8, x9) -> f152_0_gcd_EQ(x10, x11) :|: 0 = x11 && x9 = x10 && 0 = x8 && 0 <= x9 - 1
f152_0_gcd_EQ(x12, x13) -> f152_0_gcd_EQ(x14, x15) :|: 0 = x15 && x12 = x14 && x12 = x13 && 0 <= x12 - 1
f207_0_mod_LE(x16, x17) -> f207_0_mod_LE(x18, x19) :|: x17 = x19 && x16 - x17 = x18 && 0 <= x17 - 1 && 0 <= x16 - 1 && x17 <= x16 - 1
f207_0_mod_LE(x20, x21) -> f152_0_gcd_EQ(x22, x23) :|: x20 = x23 && x21 = x22 && x20 <= x21 - 1
__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) -> f152_0_gcd_EQ(arg1P, arg2P) :|: 0 <= arg1 - 1 && -1 <= arg1P - 1 && -1 <= arg2 - 1 && -1 <= arg2P - 1
f152_0_gcd_EQ(x, x1) -> f207_0_mod_LE(x2, x3) :|: x1 = x3 && x = x2 && 0 <= x - 1 && x <= x1 - 1 && 0 <= x1 - 1
f152_0_gcd_EQ(x4, x5) -> f207_0_mod_LE(x6, x7) :|: x5 = x7 && x4 = x6 && 0 <= x4 - 1 && x5 <= x4 - 1 && 0 <= x5 - 1
f152_0_gcd_EQ(x8, x9) -> f152_0_gcd_EQ(x10, x11) :|: 0 = x11 && x9 = x10 && 0 = x8 && 0 <= x9 - 1
f152_0_gcd_EQ(x12, x13) -> f152_0_gcd_EQ(x14, x15) :|: 0 = x15 && x12 = x14 && x12 = x13 && 0 <= x12 - 1
f207_0_mod_LE(x16, x17) -> f207_0_mod_LE(x18, x19) :|: x17 = x19 && x16 - x17 = x18 && 0 <= x17 - 1 && 0 <= x16 - 1 && x17 <= x16 - 1
f207_0_mod_LE(x20, x21) -> f152_0_gcd_EQ(x22, x23) :|: x20 = x23 && x21 = x22 && x20 <= x21 - 1
__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) -> f152_0_gcd_EQ(arg1P, arg2P) :|: 0 <= arg1 - 1 && -1 <= arg1P - 1 && -1 <= arg2 - 1 && -1 <= arg2P - 1
(2) f152_0_gcd_EQ(x, x1) -> f207_0_mod_LE(x2, x3) :|: x1 = x3 && x = x2 && 0 <= x - 1 && x <= x1 - 1 && 0 <= x1 - 1
(3) f152_0_gcd_EQ(x4, x5) -> f207_0_mod_LE(x6, x7) :|: x5 = x7 && x4 = x6 && 0 <= x4 - 1 && x5 <= x4 - 1 && 0 <= x5 - 1
(4) f152_0_gcd_EQ(x8, x9) -> f152_0_gcd_EQ(x10, x11) :|: 0 = x11 && x9 = x10 && 0 = x8 && 0 <= x9 - 1
(5) f152_0_gcd_EQ(x12, x13) -> f152_0_gcd_EQ(x14, x15) :|: 0 = x15 && x12 = x14 && x12 = x13 && 0 <= x12 - 1
(6) f207_0_mod_LE(x16, x17) -> f207_0_mod_LE(x18, x19) :|: x17 = x19 && x16 - x17 = x18 && 0 <= x17 - 1 && 0 <= x16 - 1 && x17 <= x16 - 1
(7) f207_0_mod_LE(x20, x21) -> f152_0_gcd_EQ(x22, x23) :|: x20 = x23 && x21 = x22 && x20 <= x21 - 1
(8) __init(x24, x25) -> f1_0_main_Load(x26, x27) :|: 0 <= 0

Arcs:
(1) -> (2), (3), (4), (5)
(2) -> (7)
(3) -> (6)
(6) -> (6), (7)
(7) -> (3)
(8) -> (1)

This digraph is fully evaluated!
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(4)
Obligation:

Termination digraph:
Nodes:
(1) f207_0_mod_LE(x20, x21) -> f152_0_gcd_EQ(x22, x23) :|: x20 = x23 && x21 = x22 && x20 <= x21 - 1
(2) f207_0_mod_LE(x16, x17) -> f207_0_mod_LE(x18, x19) :|: x17 = x19 && x16 - x17 = x18 && 0 <= x17 - 1 && 0 <= x16 - 1 && x17 <= x16 - 1
(3) f152_0_gcd_EQ(x4, x5) -> f207_0_mod_LE(x6, x7) :|: x5 = x7 && x4 = x6 && 0 <= x4 - 1 && x5 <= x4 - 1 && 0 <= x5 - 1

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

This digraph is fully evaluated!

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(5) IntTRSCompressionProof (EQUIVALENT)
Compressed rules.
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(6)
Obligation:
Rules:
f207_0_mod_LE(x20:0, x21:0) -> f207_0_mod_LE(x21:0, x20:0) :|: x20:0 > 0 && x21:0 > 0 && x21:0 - 1 >= x20:0
f207_0_mod_LE(x16:0, x17:0) -> f207_0_mod_LE(x16:0 - x17:0, x17:0) :|: x16:0 > 0 && x17:0 > 0 && x17:0 <= x16:0 - 1

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(7) TempFilterProof (SOUND)
Used the following sort dictionary for filtering: 
f207_0_mod_LE(INTEGER, INTEGER)
Replaced non-predefined constructor symbols by 0.
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(8)
Obligation:
Rules:
f207_0_mod_LE(x20:0, x21:0) -> f207_0_mod_LE(x21:0, x20:0) :|: x20:0 > 0 && x21:0 > 0 && x21:0 - 1 >= x20:0
f207_0_mod_LE(x16:0, x17:0) -> f207_0_mod_LE(c, x17:0) :|: c = x16:0 - x17:0 && (x16:0 > 0 && x17:0 > 0 && x17:0 <= x16:0 - 1)

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(9) PolynomialOrderProcessor (EQUIVALENT)
Found the following polynomial interpretation:
[f207_0_mod_LE(x, x1)] = -2 + x1

The following rules are decreasing:
f207_0_mod_LE(x20:0, x21:0) -> f207_0_mod_LE(x21:0, x20:0) :|: x20:0 > 0 && x21:0 > 0 && x21:0 - 1 >= x20:0
The following rules are bounded:
f207_0_mod_LE(x20:0, x21:0) -> f207_0_mod_LE(x21:0, x20:0) :|: x20:0 > 0 && x21:0 > 0 && x21:0 - 1 >= x20:0

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(10)
Obligation:
Rules:
f207_0_mod_LE(x16:0, x17:0) -> f207_0_mod_LE(c, x17:0) :|: c = x16:0 - x17:0 && (x16:0 > 0 && x17:0 > 0 && x17:0 <= x16:0 - 1)

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(11) RankingReductionPairProof (EQUIVALENT)
Interpretation:
[ f207_0_mod_LE ] = f207_0_mod_LE_1

The following rules are decreasing:
f207_0_mod_LE(x16:0, x17:0) -> f207_0_mod_LE(c, x17:0) :|: c = x16:0 - x17:0 && (x16:0 > 0 && x17:0 > 0 && x17:0 <= x16:0 - 1)

The following rules are bounded:
f207_0_mod_LE(x16:0, x17:0) -> f207_0_mod_LE(c, x17:0) :|: c = x16:0 - x17:0 && (x16:0 > 0 && x17:0 > 0 && x17:0 <= x16:0 - 1)


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(12)
YES