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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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, 359 ms]
(4) IRSwT
(5) IntTRSCompressionProof [EQUIVALENT, 17 ms]
(6) IRSwT
(7) FilterProof [EQUIVALENT, 0 ms]
(8) IntTRS
(9) IntTRSCompressionProof [EQUIVALENT, 0 ms]
(10) IntTRS
(11) RankingReductionPairProof [EQUIVALENT, 22 ms]
(12) YES


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(0)
Obligation:
Rules:
f1_0_main_Load(arg1, arg2, arg3) -> f96_0_random_GT(arg1P, arg2P, arg3P) :|: 0 = arg2P && 0 <= arg1P - 1 && 0 <= arg1 - 1 && 0 <= arg2 - 1 && arg1P <= arg1
f1_0_main_Load(x, x1, x2) -> f96_0_random_GT(x3, x4, x5) :|: 0 <= x3 - 1 && 0 <= x - 1 && x3 <= x && 0 <= x1 - 1 && -1 <= x4 - 1
f96_0_random_GT(x6, x8, x9) -> f154_0_main_InvokeMethod(x10, x12, x13) :|: x10 <= x6 && 1 <= x14 - 1 && 0 <= x6 - 1 && 0 <= x10 - 1 && x8 = x12 && 0 = x13
f96_0_random_GT(x15, x16, x17) -> f154_0_main_InvokeMethod(x18, x20, x21) :|: 1 <= x22 - 1 && -1 <= x21 - 1 && x18 <= x15 && 0 <= x15 - 1 && 0 <= x18 - 1 && x16 = x20
f1_0_main_Load(x23, x24, x25) -> f167_0_log_LT(x26, x27, x29) :|: 0 = x29 && 0 = x27 && 0 = x26 && 0 = x24 && 0 <= x23 - 1
f96_0_random_GT(x30, x31, x32) -> f167_0_log_LT(x33, x34, x35) :|: 0 = x35 && x31 = x34 && 0 = x33 && 0 <= x30 - 1
f154_0_main_InvokeMethod(x36, x37, x38) -> f167_0_log_LT(x39, x40, x41) :|: 0 <= x36 - 1 && 1 <= x42 - 1 && x38 = x39 && x37 = x40 && x38 = x41
f167_0_log_LT(x43, x44, x45) -> f167_0_log_LT'(x46, x47, x48) :|: 1 <= x44 - 1 && 1 <= x43 - 1 && x49 <= x44 - 1 && x43 <= x44 && x43 = x45 && x43 = x46 && x44 = x47 && x43 = x48
f167_0_log_LT'(x50, x51, x52) -> f167_0_log_LT(x53, x54, x55) :|: x50 = x55 && x50 = x53 && x50 = x52 && 0 <= x51 - x50 * x54 && x51 - x50 * x54 <= x50 - 1 && x54 <= x51 - 1 && x50 <= x51 && 1 <= x50 - 1 && 1 <= x51 - 1
__init(x56, x57, x58) -> f1_0_main_Load(x59, x60, x61) :|: 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) -> f96_0_random_GT(arg1P, arg2P, arg3P) :|: 0 = arg2P && 0 <= arg1P - 1 && 0 <= arg1 - 1 && 0 <= arg2 - 1 && arg1P <= arg1
f1_0_main_Load(x, x1, x2) -> f96_0_random_GT(x3, x4, x5) :|: 0 <= x3 - 1 && 0 <= x - 1 && x3 <= x && 0 <= x1 - 1 && -1 <= x4 - 1
f96_0_random_GT(x6, x8, x9) -> f154_0_main_InvokeMethod(x10, x12, x13) :|: x10 <= x6 && 1 <= x14 - 1 && 0 <= x6 - 1 && 0 <= x10 - 1 && x8 = x12 && 0 = x13
f96_0_random_GT(x15, x16, x17) -> f154_0_main_InvokeMethod(x18, x20, x21) :|: 1 <= x22 - 1 && -1 <= x21 - 1 && x18 <= x15 && 0 <= x15 - 1 && 0 <= x18 - 1 && x16 = x20
f1_0_main_Load(x23, x24, x25) -> f167_0_log_LT(x26, x27, x29) :|: 0 = x29 && 0 = x27 && 0 = x26 && 0 = x24 && 0 <= x23 - 1
f96_0_random_GT(x30, x31, x32) -> f167_0_log_LT(x33, x34, x35) :|: 0 = x35 && x31 = x34 && 0 = x33 && 0 <= x30 - 1
f154_0_main_InvokeMethod(x36, x37, x38) -> f167_0_log_LT(x39, x40, x41) :|: 0 <= x36 - 1 && 1 <= x42 - 1 && x38 = x39 && x37 = x40 && x38 = x41
f167_0_log_LT(x43, x44, x45) -> f167_0_log_LT'(x46, x47, x48) :|: 1 <= x44 - 1 && 1 <= x43 - 1 && x49 <= x44 - 1 && x43 <= x44 && x43 = x45 && x43 = x46 && x44 = x47 && x43 = x48
f167_0_log_LT'(x50, x51, x52) -> f167_0_log_LT(x53, x54, x55) :|: x50 = x55 && x50 = x53 && x50 = x52 && 0 <= x51 - x50 * x54 && x51 - x50 * x54 <= x50 - 1 && x54 <= x51 - 1 && x50 <= x51 && 1 <= x50 - 1 && 1 <= x51 - 1
__init(x56, x57, x58) -> f1_0_main_Load(x59, x60, x61) :|: 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) -> f96_0_random_GT(arg1P, arg2P, arg3P) :|: 0 = arg2P && 0 <= arg1P - 1 && 0 <= arg1 - 1 && 0 <= arg2 - 1 && arg1P <= arg1
(2) f1_0_main_Load(x, x1, x2) -> f96_0_random_GT(x3, x4, x5) :|: 0 <= x3 - 1 && 0 <= x - 1 && x3 <= x && 0 <= x1 - 1 && -1 <= x4 - 1
(3) f96_0_random_GT(x6, x8, x9) -> f154_0_main_InvokeMethod(x10, x12, x13) :|: x10 <= x6 && 1 <= x14 - 1 && 0 <= x6 - 1 && 0 <= x10 - 1 && x8 = x12 && 0 = x13
(4) f96_0_random_GT(x15, x16, x17) -> f154_0_main_InvokeMethod(x18, x20, x21) :|: 1 <= x22 - 1 && -1 <= x21 - 1 && x18 <= x15 && 0 <= x15 - 1 && 0 <= x18 - 1 && x16 = x20
(5) f1_0_main_Load(x23, x24, x25) -> f167_0_log_LT(x26, x27, x29) :|: 0 = x29 && 0 = x27 && 0 = x26 && 0 = x24 && 0 <= x23 - 1
(6) f96_0_random_GT(x30, x31, x32) -> f167_0_log_LT(x33, x34, x35) :|: 0 = x35 && x31 = x34 && 0 = x33 && 0 <= x30 - 1
(7) f154_0_main_InvokeMethod(x36, x37, x38) -> f167_0_log_LT(x39, x40, x41) :|: 0 <= x36 - 1 && 1 <= x42 - 1 && x38 = x39 && x37 = x40 && x38 = x41
(8) f167_0_log_LT(x43, x44, x45) -> f167_0_log_LT'(x46, x47, x48) :|: 1 <= x44 - 1 && 1 <= x43 - 1 && x49 <= x44 - 1 && x43 <= x44 && x43 = x45 && x43 = x46 && x44 = x47 && x43 = x48
(9) f167_0_log_LT'(x50, x51, x52) -> f167_0_log_LT(x53, x54, x55) :|: x50 = x55 && x50 = x53 && x50 = x52 && 0 <= x51 - x50 * x54 && x51 - x50 * x54 <= x50 - 1 && x54 <= x51 - 1 && x50 <= x51 && 1 <= x50 - 1 && 1 <= x51 - 1
(10) __init(x56, x57, x58) -> f1_0_main_Load(x59, x60, x61) :|: 0 <= 0

Arcs:
(1) -> (3), (4), (6)
(2) -> (3), (4), (6)
(3) -> (7)
(4) -> (7)
(7) -> (8)
(8) -> (9)
(9) -> (8)
(10) -> (1), (2), (5)

This digraph is fully evaluated!
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(4)
Obligation:

Termination digraph:
Nodes:
(1) f167_0_log_LT(x43, x44, x45) -> f167_0_log_LT'(x46, x47, x48) :|: 1 <= x44 - 1 && 1 <= x43 - 1 && x49 <= x44 - 1 && x43 <= x44 && x43 = x45 && x43 = x46 && x44 = x47 && x43 = x48
(2) f167_0_log_LT'(x50, x51, x52) -> f167_0_log_LT(x53, x54, x55) :|: x50 = x55 && x50 = x53 && x50 = x52 && 0 <= x51 - x50 * x54 && x51 - x50 * x54 <= x50 - 1 && x54 <= x51 - 1 && x50 <= x51 && 1 <= x50 - 1 && 1 <= x51 - 1

Arcs:
(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:
f167_0_log_LT(x43:0, x44:0, x43:0) -> f167_0_log_LT(x43:0, x54:0, x43:0) :|: x54:0 <= x44:0 - 1 && x44:0 >= x43:0 && x44:0 - x43:0 * x54:0 <= x43:0 - 1 && x49:0 <= x44:0 - 1 && x44:0 - x43:0 * x54:0 >= 0 && x43:0 > 1 && x44:0 > 1

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(7) FilterProof (EQUIVALENT)
Used the following sort dictionary for filtering: 
f167_0_log_LT(INTEGER, INTEGER, INTEGER)
Replaced non-predefined constructor symbols by 0.
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(8)
Obligation:
Rules:
f167_0_log_LT(x43:0, x44:0, x43:0) -> f167_0_log_LT(x43:0, x54:0, x43:0) :|: x54:0 <= x44:0 - 1 && x44:0 >= x43:0 && x44:0 - x43:0 * x54:0 <= x43:0 - 1 && x49:0 <= x44:0 - 1 && x44:0 - x43:0 * x54:0 >= 0 && x43:0 > 1 && x44:0 > 1

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(9) IntTRSCompressionProof (EQUIVALENT)
Compressed rules.
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(10)
Obligation:
Rules:
f167_0_log_LT(x43:0:0, x44:0:0, x43:0:01) -> f167_0_log_LT(x43:0:0, x54:0:0, x43:0:0) :|: x43:0:0 > 1 && x44:0:0 > 1 && x44:0:0 - x43:0:0 * x54:0:0 >= 0 && x49:0:0 <= x44:0:0 - 1 && x44:0:0 - x43:0:0 * x54:0:0 <= x43:0:0 - 1 && x44:0:0 >= x43:0:0 && x54:0:0 <= x44:0:0 - 1 && x43:0:0 = x43:0:01

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(11) RankingReductionPairProof (EQUIVALENT)
Interpretation:
[ f167_0_log_LT ] = f167_0_log_LT_2

The following rules are decreasing:
f167_0_log_LT(x43:0:0, x44:0:0, x43:0:01) -> f167_0_log_LT(x43:0:0, x54:0:0, x43:0:0) :|: x43:0:0 > 1 && x44:0:0 > 1 && x44:0:0 - x43:0:0 * x54:0:0 >= 0 && x49:0:0 <= x44:0:0 - 1 && x44:0:0 - x43:0:0 * x54:0:0 <= x43:0:0 - 1 && x44:0:0 >= x43:0:0 && x54:0:0 <= x44:0:0 - 1 && x43:0:0 = x43:0:01

The following rules are bounded:
f167_0_log_LT(x43:0:0, x44:0:0, x43:0:01) -> f167_0_log_LT(x43:0:0, x54:0:0, x43:0:0) :|: x43:0:0 > 1 && x44:0:0 > 1 && x44:0:0 - x43:0:0 * x54:0:0 >= 0 && x49:0:0 <= x44:0:0 - 1 && x44:0:0 - x43:0:0 * x54:0:0 <= x43:0:0 - 1 && x44:0:0 >= x43:0:0 && x54:0:0 <= x44:0:0 - 1 && x43:0:0 = x43:0:01


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(12)
YES