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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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, 244 ms]
(4) IRSwT
(5) IntTRSCompressionProof [EQUIVALENT, 0 ms]
(6) IRSwT
(7) TempFilterProof [SOUND, 50 ms]
(8) IntTRS
(9) PolynomialOrderProcessor [EQUIVALENT, 9 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) -> f198_0_mod_LE(x2, x3) :|: x1 = x3 && x = x2 && 0 <= x1 - 1 && -1 <= x - 1 && x <= x1 - 1
f152_0_gcd_EQ(x4, x5) -> f198_0_mod_LE(x6, x7) :|: x5 = x7 && x4 = x6 && 0 <= x5 - 1 && -1 <= x4 - 1 && x5 <= x4 - 1
f198_0_mod_LE(x8, x9) -> f198_0_mod_LE(x10, x11) :|: x9 = x11 && x8 - x9 = x10 && 0 <= x9 - 1 && 0 <= x8 - 1 && x9 <= x8 - 1
f152_0_gcd_EQ(x12, x13) -> f152_0_gcd_EQ(x14, x15) :|: 0 = x15 && x12 = x14 && x12 = x13 && 0 <= x12 - 1
f198_0_mod_LE(x16, x17) -> f152_0_gcd_EQ(x18, x19) :|: x16 = x19 && x17 = x18 && x16 <= x17 - 1
__init(x20, x21) -> f1_0_main_Load(x22, x23) :|: 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) -> f198_0_mod_LE(x2, x3) :|: x1 = x3 && x = x2 && 0 <= x1 - 1 && -1 <= x - 1 && x <= x1 - 1
f152_0_gcd_EQ(x4, x5) -> f198_0_mod_LE(x6, x7) :|: x5 = x7 && x4 = x6 && 0 <= x5 - 1 && -1 <= x4 - 1 && x5 <= x4 - 1
f198_0_mod_LE(x8, x9) -> f198_0_mod_LE(x10, x11) :|: x9 = x11 && x8 - x9 = x10 && 0 <= x9 - 1 && 0 <= x8 - 1 && x9 <= x8 - 1
f152_0_gcd_EQ(x12, x13) -> f152_0_gcd_EQ(x14, x15) :|: 0 = x15 && x12 = x14 && x12 = x13 && 0 <= x12 - 1
f198_0_mod_LE(x16, x17) -> f152_0_gcd_EQ(x18, x19) :|: x16 = x19 && x17 = x18 && x16 <= x17 - 1
__init(x20, x21) -> f1_0_main_Load(x22, x23) :|: 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) -> f198_0_mod_LE(x2, x3) :|: x1 = x3 && x = x2 && 0 <= x1 - 1 && -1 <= x - 1 && x <= x1 - 1
(3) f152_0_gcd_EQ(x4, x5) -> f198_0_mod_LE(x6, x7) :|: x5 = x7 && x4 = x6 && 0 <= x5 - 1 && -1 <= x4 - 1 && x5 <= x4 - 1
(4) f198_0_mod_LE(x8, x9) -> f198_0_mod_LE(x10, x11) :|: x9 = x11 && x8 - x9 = x10 && 0 <= x9 - 1 && 0 <= x8 - 1 && x9 <= x8 - 1
(5) f152_0_gcd_EQ(x12, x13) -> f152_0_gcd_EQ(x14, x15) :|: 0 = x15 && x12 = x14 && x12 = x13 && 0 <= x12 - 1
(6) f198_0_mod_LE(x16, x17) -> f152_0_gcd_EQ(x18, x19) :|: x16 = x19 && x17 = x18 && x16 <= x17 - 1
(7) __init(x20, x21) -> f1_0_main_Load(x22, x23) :|: 0 <= 0

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

This digraph is fully evaluated!
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(4)
Obligation:

Termination digraph:
Nodes:
(1) f198_0_mod_LE(x16, x17) -> f152_0_gcd_EQ(x18, x19) :|: x16 = x19 && x17 = x18 && x16 <= x17 - 1
(2) f198_0_mod_LE(x8, x9) -> f198_0_mod_LE(x10, x11) :|: x9 = x11 && x8 - x9 = x10 && 0 <= x9 - 1 && 0 <= x8 - 1 && x9 <= x8 - 1
(3) f152_0_gcd_EQ(x4, x5) -> f198_0_mod_LE(x6, x7) :|: x5 = x7 && x4 = x6 && 0 <= x5 - 1 && -1 <= x4 - 1 && x5 <= x4 - 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:
f198_0_mod_LE(x8:0, x11:0) -> f198_0_mod_LE(x8:0 - x11:0, x11:0) :|: x8:0 > 0 && x11:0 > 0 && x8:0 - 1 >= x11:0
f198_0_mod_LE(x16:0, x17:0) -> f198_0_mod_LE(x17:0, x16:0) :|: x17:0 - 1 >= x16:0 && x16:0 > 0 && x17:0 > -1

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(7) TempFilterProof (SOUND)
Used the following sort dictionary for filtering: 
f198_0_mod_LE(INTEGER, INTEGER)
Replaced non-predefined constructor symbols by 0.
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(8)
Obligation:
Rules:
f198_0_mod_LE(x8:0, x11:0) -> f198_0_mod_LE(c, x11:0) :|: c = x8:0 - x11:0 && (x8:0 > 0 && x11:0 > 0 && x8:0 - 1 >= x11:0)
f198_0_mod_LE(x16:0, x17:0) -> f198_0_mod_LE(x17:0, x16:0) :|: x17:0 - 1 >= x16:0 && x16:0 > 0 && x17:0 > -1

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(9) PolynomialOrderProcessor (EQUIVALENT)
Found the following polynomial interpretation:
[f198_0_mod_LE(x, x1)] = x + x1

The following rules are decreasing:
f198_0_mod_LE(x8:0, x11:0) -> f198_0_mod_LE(c, x11:0) :|: c = x8:0 - x11:0 && (x8:0 > 0 && x11:0 > 0 && x8:0 - 1 >= x11:0)
The following rules are bounded:
f198_0_mod_LE(x8:0, x11:0) -> f198_0_mod_LE(c, x11:0) :|: c = x8:0 - x11:0 && (x8:0 > 0 && x11:0 > 0 && x8:0 - 1 >= x11:0)
f198_0_mod_LE(x16:0, x17:0) -> f198_0_mod_LE(x17:0, x16:0) :|: x17:0 - 1 >= x16:0 && x16:0 > 0 && x17:0 > -1

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(10)
Obligation:
Rules:
f198_0_mod_LE(x16:0, x17:0) -> f198_0_mod_LE(x17:0, x16:0) :|: x17:0 - 1 >= x16:0 && x16:0 > 0 && x17:0 > -1

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(11) RankingReductionPairProof (EQUIVALENT)
Interpretation:
[ f198_0_mod_LE ] = 1/2*f198_0_mod_LE_2 + -1/2*f198_0_mod_LE_1

The following rules are decreasing:
f198_0_mod_LE(x16:0, x17:0) -> f198_0_mod_LE(x17:0, x16:0) :|: x17:0 - 1 >= x16:0 && x16:0 > 0 && x17:0 > -1

The following rules are bounded:
f198_0_mod_LE(x16:0, x17:0) -> f198_0_mod_LE(x17:0, x16:0) :|: x17:0 - 1 >= x16:0 && x16:0 > 0 && x17:0 > -1


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(12)
YES