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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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, 151 ms]
(4) IRSwT
(5) IntTRSCompressionProof [EQUIVALENT, 0 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) -> f256_0_log_LT(arg1P, arg2P) :|: 0 <= arg1 - 1 && -1 <= arg1P - 1 && -1 <= arg2 - 1 && -1 <= arg2P - 1
f256_0_log_LT(x, x1) -> f256_0_log_LT'(x2, x3) :|: 1 <= x - 1 && 1 <= x1 - 1 && x1 <= x && x4 <= x - 1 && x = x2 && x1 = x3
f256_0_log_LT'(x5, x6) -> f256_0_log_LT(x7, x9) :|: x6 = x9 && 0 <= x5 - x6 * x7 && x5 - x6 * x7 <= x6 - 1 && x6 <= x5 && x7 <= x5 - 1 && 1 <= x6 - 1 && 1 <= x5 - 1
__init(x10, x11) -> f1_0_main_Load(x12, x13) :|: 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) -> f256_0_log_LT(arg1P, arg2P) :|: 0 <= arg1 - 1 && -1 <= arg1P - 1 && -1 <= arg2 - 1 && -1 <= arg2P - 1
f256_0_log_LT(x, x1) -> f256_0_log_LT'(x2, x3) :|: 1 <= x - 1 && 1 <= x1 - 1 && x1 <= x && x4 <= x - 1 && x = x2 && x1 = x3
f256_0_log_LT'(x5, x6) -> f256_0_log_LT(x7, x9) :|: x6 = x9 && 0 <= x5 - x6 * x7 && x5 - x6 * x7 <= x6 - 1 && x6 <= x5 && x7 <= x5 - 1 && 1 <= x6 - 1 && 1 <= x5 - 1
__init(x10, x11) -> f1_0_main_Load(x12, x13) :|: 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) -> f256_0_log_LT(arg1P, arg2P) :|: 0 <= arg1 - 1 && -1 <= arg1P - 1 && -1 <= arg2 - 1 && -1 <= arg2P - 1
(2) f256_0_log_LT(x, x1) -> f256_0_log_LT'(x2, x3) :|: 1 <= x - 1 && 1 <= x1 - 1 && x1 <= x && x4 <= x - 1 && x = x2 && x1 = x3
(3) f256_0_log_LT'(x5, x6) -> f256_0_log_LT(x7, x9) :|: x6 = x9 && 0 <= x5 - x6 * x7 && x5 - x6 * x7 <= x6 - 1 && x6 <= x5 && x7 <= x5 - 1 && 1 <= x6 - 1 && 1 <= x5 - 1
(4) __init(x10, x11) -> f1_0_main_Load(x12, x13) :|: 0 <= 0

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

This digraph is fully evaluated!
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(4)
Obligation:

Termination digraph:
Nodes:
(1) f256_0_log_LT(x, x1) -> f256_0_log_LT'(x2, x3) :|: 1 <= x - 1 && 1 <= x1 - 1 && x1 <= x && x4 <= x - 1 && x = x2 && x1 = x3
(2) f256_0_log_LT'(x5, x6) -> f256_0_log_LT(x7, x9) :|: x6 = x9 && 0 <= x5 - x6 * x7 && x5 - x6 * x7 <= x6 - 1 && x6 <= x5 && x7 <= x5 - 1 && 1 <= x6 - 1 && 1 <= x5 - 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:
f256_0_log_LT(x2:0, x1:0) -> f256_0_log_LT(x7:0, x1:0) :|: x4:0 <= x2:0 - 1 && x7:0 <= x2:0 - 1 && x2:0 >= x1:0 && x2:0 > 1 && x1:0 > 1 && x2:0 - x1:0 * x7:0 >= 0 && x2:0 - x1:0 * x7:0 <= x1:0 - 1

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(7) FilterProof (EQUIVALENT)
Used the following sort dictionary for filtering: 
f256_0_log_LT(INTEGER, INTEGER)
Replaced non-predefined constructor symbols by 0.
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(8)
Obligation:
Rules:
f256_0_log_LT(x2:0, x1:0) -> f256_0_log_LT(x7:0, x1:0) :|: x4:0 <= x2:0 - 1 && x7:0 <= x2:0 - 1 && x2:0 >= x1:0 && x2:0 > 1 && x1:0 > 1 && x2:0 - x1:0 * x7:0 >= 0 && x2:0 - x1:0 * x7:0 <= x1:0 - 1

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(9) IntTRSCompressionProof (EQUIVALENT)
Compressed rules.
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(10)
Obligation:
Rules:
f256_0_log_LT(x2:0:0, x1:0:0) -> f256_0_log_LT(x7:0:0, x1:0:0) :|: x2:0:0 - x1:0:0 * x7:0:0 >= 0 && x2:0:0 - x1:0:0 * x7:0:0 <= x1:0:0 - 1 && x1:0:0 > 1 && x2:0:0 > 1 && x2:0:0 >= x1:0:0 && x7:0:0 <= x2:0:0 - 1 && x4:0:0 <= x2:0:0 - 1

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(11) RankingReductionPairProof (EQUIVALENT)
Interpretation:
[ f256_0_log_LT ] = f256_0_log_LT_1

The following rules are decreasing:
f256_0_log_LT(x2:0:0, x1:0:0) -> f256_0_log_LT(x7:0:0, x1:0:0) :|: x2:0:0 - x1:0:0 * x7:0:0 >= 0 && x2:0:0 - x1:0:0 * x7:0:0 <= x1:0:0 - 1 && x1:0:0 > 1 && x2:0:0 > 1 && x2:0:0 >= x1:0:0 && x7:0:0 <= x2:0:0 - 1 && x4:0:0 <= x2:0:0 - 1

The following rules are bounded:
f256_0_log_LT(x2:0:0, x1:0:0) -> f256_0_log_LT(x7:0:0, x1:0:0) :|: x2:0:0 - x1:0:0 * x7:0:0 >= 0 && x2:0:0 - x1:0:0 * x7:0:0 <= x1:0:0 - 1 && x1:0:0 > 1 && x2:0:0 > 1 && x2:0:0 >= x1:0:0 && x7:0:0 <= x2:0:0 - 1 && x4:0:0 <= x2:0:0 - 1


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(12)
YES