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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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, 81 ms]
(4) IRSwT
(5) IntTRSCompressionProof [EQUIVALENT, 39 ms]
(6) IRSwT
(7) TempFilterProof [SOUND, 53 ms]
(8) IntTRS
(9) PolynomialOrderProcessor [EQUIVALENT, 0 ms]
(10) YES


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(0)
Obligation:
Rules:
f1_0_main_Load(arg1, arg2) -> f234_0_main_LE(arg1P, arg2P) :|: 0 <= arg1 - 1 && -1 <= arg1P - 1 && -1 <= arg2 - 1 && -1 <= arg2P - 1
f234_0_main_LE(x, x1) -> f234_0_main_LE(x2, x3) :|: x = x3 && x1 - 1 = x2 && 0 <= x1 - 1
__init(x4, x5) -> f1_0_main_Load(x6, x7) :|: 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) -> f234_0_main_LE(arg1P, arg2P) :|: 0 <= arg1 - 1 && -1 <= arg1P - 1 && -1 <= arg2 - 1 && -1 <= arg2P - 1
f234_0_main_LE(x, x1) -> f234_0_main_LE(x2, x3) :|: x = x3 && x1 - 1 = x2 && 0 <= x1 - 1
__init(x4, x5) -> f1_0_main_Load(x6, x7) :|: 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) -> f234_0_main_LE(arg1P, arg2P) :|: 0 <= arg1 - 1 && -1 <= arg1P - 1 && -1 <= arg2 - 1 && -1 <= arg2P - 1
(2) f234_0_main_LE(x, x1) -> f234_0_main_LE(x2, x3) :|: x = x3 && x1 - 1 = x2 && 0 <= x1 - 1
(3) __init(x4, x5) -> f1_0_main_Load(x6, x7) :|: 0 <= 0

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

This digraph is fully evaluated!
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(4)
Obligation:

Termination digraph:
Nodes:
(1) f234_0_main_LE(x, x1) -> f234_0_main_LE(x2, x3) :|: x = x3 && x1 - 1 = x2 && 0 <= x1 - 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:
f234_0_main_LE(x3:0, x1:0) -> f234_0_main_LE(x1:0 - 1, x3:0) :|: x1:0 > 0

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(7) TempFilterProof (SOUND)
Used the following sort dictionary for filtering: 
f234_0_main_LE(VARIABLE, VARIABLE)
Replaced non-predefined constructor symbols by 0.
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(8)
Obligation:
Rules:
f234_0_main_LE(x3:0, x1:0) -> f234_0_main_LE(c, x3:0) :|: c = x1:0 - 1 && x1:0 > 0

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(9) PolynomialOrderProcessor (EQUIVALENT)
Found the following polynomial interpretation:
[f234_0_main_LE(x, x1)] = x^2 + x1^2

The following rules are decreasing:
f234_0_main_LE(x3:0, x1:0) -> f234_0_main_LE(c, x3:0) :|: c = x1:0 - 1 && x1:0 > 0
The following rules are bounded:
f234_0_main_LE(x3:0, x1:0) -> f234_0_main_LE(c, x3:0) :|: c = x1:0 - 1 && x1:0 > 0

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(10)
YES