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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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, 87 ms]
(4) IRSwT
(5) IntTRSCompressionProof [EQUIVALENT, 24 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, 5 ms]
(14) IntTRS
(15) PolynomialOrderProcessor [EQUIVALENT, 0 ms]
(16) YES


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(0)
Obligation:
Rules:
f1_0_main_Load(arg1, arg2, arg3) -> f150_0_main_LT(arg1P, arg2P, arg3P) :|: arg1P + 1 = arg3P && 0 <= arg1 - 1 && -1 <= arg1P - 1 && -1 <= arg2 - 1 && -1 <= arg2P - 1
f150_0_main_LT(x, x1, x2) -> f150_0_main_LT(x3, x4, x5) :|: x + 2 = x5 && x1 = x4 && x + 1 = x3 && -2 <= x - 1 && x2 <= x1
__init(x6, x7, x8) -> f1_0_main_Load(x9, x10, x11) :|: 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) -> f150_0_main_LT(arg1P, arg2P, arg3P) :|: arg1P + 1 = arg3P && 0 <= arg1 - 1 && -1 <= arg1P - 1 && -1 <= arg2 - 1 && -1 <= arg2P - 1
f150_0_main_LT(x, x1, x2) -> f150_0_main_LT(x3, x4, x5) :|: x + 2 = x5 && x1 = x4 && x + 1 = x3 && -2 <= x - 1 && x2 <= x1
__init(x6, x7, x8) -> f1_0_main_Load(x9, x10, x11) :|: 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) -> f150_0_main_LT(arg1P, arg2P, arg3P) :|: arg1P + 1 = arg3P && 0 <= arg1 - 1 && -1 <= arg1P - 1 && -1 <= arg2 - 1 && -1 <= arg2P - 1
(2) f150_0_main_LT(x, x1, x2) -> f150_0_main_LT(x3, x4, x5) :|: x + 2 = x5 && x1 = x4 && x + 1 = x3 && -2 <= x - 1 && x2 <= x1
(3) __init(x6, x7, x8) -> f1_0_main_Load(x9, x10, x11) :|: 0 <= 0

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

This digraph is fully evaluated!
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(4)
Obligation:

Termination digraph:
Nodes:
(1) f150_0_main_LT(x, x1, x2) -> f150_0_main_LT(x3, x4, x5) :|: x + 2 = x5 && x1 = x4 && x + 1 = x3 && -2 <= x - 1 && x2 <= x1

Arcs:
(1) -> (1)

This digraph is fully evaluated!

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(5) IntTRSCompressionProof (EQUIVALENT)
Compressed rules.
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(6)
Obligation:
Rules:
f150_0_main_LT(x:0, x1:0, x2:0) -> f150_0_main_LT(x:0 + 1, x1:0, x:0 + 2) :|: x2:0 <= x1:0 && x:0 > -2

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(7) IRSwTChainingProof (EQUIVALENT)
Chaining!
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(8)
Obligation:
Rules:
f150_0_main_LT(x, x1, x2) -> f150_0_main_LT(x + 2, x1, x + 3) :|: TRUE && x2 + -1 * x1 <= 0 && x >= -1 && x + -1 * x1 <= -2

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(9) IRSwTTerminationDigraphProof (EQUIVALENT)
Constructed termination digraph!
Nodes:
(1) f150_0_main_LT(x, x1, x2) -> f150_0_main_LT(x + 2, x1, x + 3) :|: TRUE && x2 + -1 * x1 <= 0 && x >= -1 && x + -1 * x1 <= -2

Arcs:
(1) -> (1)

This digraph is fully evaluated!
----------------------------------------

(10)
Obligation:

Termination digraph:
Nodes:
(1) f150_0_main_LT(x, x1, x2) -> f150_0_main_LT(x + 2, x1, x + 3) :|: TRUE && x2 + -1 * x1 <= 0 && x >= -1 && x + -1 * x1 <= -2

Arcs:
(1) -> (1)

This digraph is fully evaluated!

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(11) IntTRSCompressionProof (EQUIVALENT)
Compressed rules.
----------------------------------------

(12)
Obligation:
Rules:
f150_0_main_LT(x:0, x1:0, x2:0) -> f150_0_main_LT(x:0 + 2, x1:0, x:0 + 3) :|: x:0 > -2 && x2:0 + -1 * x1:0 <= 0 && x:0 + -1 * x1:0 <= -2

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(13) TempFilterProof (SOUND)
Used the following sort dictionary for filtering: 
f150_0_main_LT(INTEGER, INTEGER, INTEGER)
Replaced non-predefined constructor symbols by 0.
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(14)
Obligation:
Rules:
f150_0_main_LT(x:0, x1:0, x2:0) -> f150_0_main_LT(c, x1:0, c1) :|: c1 = x:0 + 3 && c = x:0 + 2 && (x:0 > -2 && x2:0 + -1 * x1:0 <= 0 && x:0 + -1 * x1:0 <= -2)

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(15) PolynomialOrderProcessor (EQUIVALENT)
Found the following polynomial interpretation:
[f150_0_main_LT(x, x1, x2)] = -1 - x + x1

The following rules are decreasing:
f150_0_main_LT(x:0, x1:0, x2:0) -> f150_0_main_LT(c, x1:0, c1) :|: c1 = x:0 + 3 && c = x:0 + 2 && (x:0 > -2 && x2:0 + -1 * x1:0 <= 0 && x:0 + -1 * x1:0 <= -2)
The following rules are bounded:
f150_0_main_LT(x:0, x1:0, x2:0) -> f150_0_main_LT(c, x1:0, c1) :|: c1 = x:0 + 3 && c = x:0 + 2 && (x:0 > -2 && x2:0 + -1 * x1:0 <= 0 && x:0 + -1 * x1:0 <= -2)

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(16)
YES