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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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, 159 ms]
(4) IRSwT
(5) IntTRSCompressionProof [EQUIVALENT, 9 ms]
(6) IRSwT
(7) IRSwTChainingProof [EQUIVALENT, 0 ms]
(8) IRSwT
(9) IRSwTTerminationDigraphProof [EQUIVALENT, 0 ms]
(10) IRSwT
(11) IntTRSCompressionProof [EQUIVALENT, 0 ms]
(12) IRSwT
(13) TempFilterProof [SOUND, 38 ms]
(14) IntTRS
(15) PolynomialOrderProcessor [EQUIVALENT, 0 ms]
(16) YES


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(0)
Obligation:
Rules:
f1_0_main_Load(arg1, arg2, arg3) -> f260_0_loop_LE(arg1P, arg2P, arg3P) :|: 0 = arg3P && 0 = arg2P && 0 = arg1P && 0 = arg2 && 0 <= arg1 - 1
f1_0_main_Load(x, x1, x3) -> f260_0_loop_LE(x4, x7, x8) :|: 0 <= x - 1 && -1 <= x9 - 1 && 1 = x1 && 0 = x4 && 0 - x9 = x7 && 0 = x8
f1_0_main_Load(x10, x11, x12) -> f260_0_loop_LE(x13, x14, x15) :|: -1 <= x16 - 1 && 1 <= x11 - 1 && -1 <= x17 - 1 && 0 <= x10 - 1 && 0 - x17 = x13 && 0 - x16 = x14 && 0 - x17 = x15
f260_0_loop_LE(x18, x19, x20) -> f260_0_loop_LE(x21, x22, x23) :|: x18 + x19 = x23 && x19 + 1 = x22 && x18 + x19 = x21 && x18 = x20 && x18 <= x19 + 1 - 1 && x19 <= x19 + 1 - 1 && x18 <= x19 - 1
__init(x24, x25, x26) -> f1_0_main_Load(x27, x28, x29) :|: 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) -> f260_0_loop_LE(arg1P, arg2P, arg3P) :|: 0 = arg3P && 0 = arg2P && 0 = arg1P && 0 = arg2 && 0 <= arg1 - 1
f1_0_main_Load(x, x1, x3) -> f260_0_loop_LE(x4, x7, x8) :|: 0 <= x - 1 && -1 <= x9 - 1 && 1 = x1 && 0 = x4 && 0 - x9 = x7 && 0 = x8
f1_0_main_Load(x10, x11, x12) -> f260_0_loop_LE(x13, x14, x15) :|: -1 <= x16 - 1 && 1 <= x11 - 1 && -1 <= x17 - 1 && 0 <= x10 - 1 && 0 - x17 = x13 && 0 - x16 = x14 && 0 - x17 = x15
f260_0_loop_LE(x18, x19, x20) -> f260_0_loop_LE(x21, x22, x23) :|: x18 + x19 = x23 && x19 + 1 = x22 && x18 + x19 = x21 && x18 = x20 && x18 <= x19 + 1 - 1 && x19 <= x19 + 1 - 1 && x18 <= x19 - 1
__init(x24, x25, x26) -> f1_0_main_Load(x27, x28, x29) :|: 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) -> f260_0_loop_LE(arg1P, arg2P, arg3P) :|: 0 = arg3P && 0 = arg2P && 0 = arg1P && 0 = arg2 && 0 <= arg1 - 1
(2) f1_0_main_Load(x, x1, x3) -> f260_0_loop_LE(x4, x7, x8) :|: 0 <= x - 1 && -1 <= x9 - 1 && 1 = x1 && 0 = x4 && 0 - x9 = x7 && 0 = x8
(3) f1_0_main_Load(x10, x11, x12) -> f260_0_loop_LE(x13, x14, x15) :|: -1 <= x16 - 1 && 1 <= x11 - 1 && -1 <= x17 - 1 && 0 <= x10 - 1 && 0 - x17 = x13 && 0 - x16 = x14 && 0 - x17 = x15
(4) f260_0_loop_LE(x18, x19, x20) -> f260_0_loop_LE(x21, x22, x23) :|: x18 + x19 = x23 && x19 + 1 = x22 && x18 + x19 = x21 && x18 = x20 && x18 <= x19 + 1 - 1 && x19 <= x19 + 1 - 1 && x18 <= x19 - 1
(5) __init(x24, x25, x26) -> f1_0_main_Load(x27, x28, x29) :|: 0 <= 0

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

This digraph is fully evaluated!
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(4)
Obligation:

Termination digraph:
Nodes:
(1) f260_0_loop_LE(x18, x19, x20) -> f260_0_loop_LE(x21, x22, x23) :|: x18 + x19 = x23 && x19 + 1 = x22 && x18 + x19 = x21 && x18 = x20 && x18 <= x19 + 1 - 1 && x19 <= x19 + 1 - 1 && x18 <= x19 - 1

Arcs:
(1) -> (1)

This digraph is fully evaluated!

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(5) IntTRSCompressionProof (EQUIVALENT)
Compressed rules.
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(6)
Obligation:
Rules:
f260_0_loop_LE(x18:0, x19:0, x18:0) -> f260_0_loop_LE(x18:0 + x19:0, x19:0 + 1, x18:0 + x19:0) :|: x19:0 - 1 >= x18:0 && x19:0 >= x18:0

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(7) IRSwTChainingProof (EQUIVALENT)
Chaining!
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(8)
Obligation:
Rules:
f260_0_loop_LE(x, x1, x) -> f260_0_loop_LE(x + 2 * x1 + 1, x1 + 2, x + 2 * x1 + 1) :|: TRUE && x1 + -1 * x >= 1 && -1 * x >= 0

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(9) IRSwTTerminationDigraphProof (EQUIVALENT)
Constructed termination digraph!
Nodes:
(1) f260_0_loop_LE(x, x1, x) -> f260_0_loop_LE(x + 2 * x1 + 1, x1 + 2, x + 2 * x1 + 1) :|: TRUE && x1 + -1 * x >= 1 && -1 * x >= 0

Arcs:
(1) -> (1)

This digraph is fully evaluated!
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(10)
Obligation:

Termination digraph:
Nodes:
(1) f260_0_loop_LE(x, x1, x) -> f260_0_loop_LE(x + 2 * x1 + 1, x1 + 2, x + 2 * x1 + 1) :|: TRUE && x1 + -1 * x >= 1 && -1 * x >= 0

Arcs:
(1) -> (1)

This digraph is fully evaluated!

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(11) IntTRSCompressionProof (EQUIVALENT)
Compressed rules.
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(12)
Obligation:
Rules:
f260_0_loop_LE(x:0, x1:0, x:0) -> f260_0_loop_LE(x:0 + 2 * x1:0 + 1, x1:0 + 2, x:0 + 2 * x1:0 + 1) :|: 0 <= -1 * x:0 && x1:0 + -1 * x:0 >= 1

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(13) TempFilterProof (SOUND)
Used the following sort dictionary for filtering: 
f260_0_loop_LE(INTEGER, INTEGER, INTEGER)
Replaced non-predefined constructor symbols by 0.
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(14)
Obligation:
Rules:
f260_0_loop_LE(x:0, x1:0, x:0) -> f260_0_loop_LE(c, c1, c2) :|: c2 = x:0 + 2 * x1:0 + 1 && (c1 = x1:0 + 2 && c = x:0 + 2 * x1:0 + 1) && (0 <= -1 * x:0 && x1:0 + -1 * x:0 >= 1)

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(15) PolynomialOrderProcessor (EQUIVALENT)
Found the following polynomial interpretation:
[f260_0_loop_LE(x, x1, x2)] = 1 - 2*x - 2*x1 + x1^2

The following rules are decreasing:
f260_0_loop_LE(x:0, x1:0, x:0) -> f260_0_loop_LE(c, c1, c2) :|: c2 = x:0 + 2 * x1:0 + 1 && (c1 = x1:0 + 2 && c = x:0 + 2 * x1:0 + 1) && (0 <= -1 * x:0 && x1:0 + -1 * x:0 >= 1)
The following rules are bounded:
f260_0_loop_LE(x:0, x1:0, x:0) -> f260_0_loop_LE(c, c1, c2) :|: c2 = x:0 + 2 * x1:0 + 1 && (c1 = x1:0 + 2 && c = x:0 + 2 * x1:0 + 1) && (0 <= -1 * x:0 && x1:0 + -1 * x:0 >= 1)

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(16)
YES