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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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, 72 ms]
(4) AND
    (5) IRSwT
        (6) IntTRSCompressionProof [EQUIVALENT, 7 ms]
        (7) IRSwT
        (8) TempFilterProof [SOUND, 34 ms]
        (9) IntTRS
        (10) PolynomialOrderProcessor [EQUIVALENT, 13 ms]
        (11) YES
    (12) IRSwT
        (13) IntTRSCompressionProof [EQUIVALENT, 12 ms]
        (14) IRSwT
        (15) TempFilterProof [SOUND, 12 ms]
        (16) IntTRS
        (17) PolynomialOrderProcessor [EQUIVALENT, 0 ms]
        (18) YES


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(0)
Obligation:
Rules:
f1_0_main_ConstantStackPush(arg1) -> f46_0_main_GE(arg1P) :|: 0 = arg1P
f46_0_main_GE(x) -> f46_0_main_GE(x1) :|: x + 1 = x1 && x <= 99
f46_0_main_GE(x2) -> f74_0_main_GE(x3) :|: 5 = x3 && 99 <= x2 - 1
f74_0_main_GE(x4) -> f74_0_main_GE(x5) :|: x4 + 3 = x5 && x4 <= 20
__init(x6) -> f1_0_main_ConstantStackPush(x7) :|: 0 <= 0
Start term: __init(arg1)

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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_ConstantStackPush(arg1) -> f46_0_main_GE(arg1P) :|: 0 = arg1P
f46_0_main_GE(x) -> f46_0_main_GE(x1) :|: x + 1 = x1 && x <= 99
f46_0_main_GE(x2) -> f74_0_main_GE(x3) :|: 5 = x3 && 99 <= x2 - 1
f74_0_main_GE(x4) -> f74_0_main_GE(x5) :|: x4 + 3 = x5 && x4 <= 20
__init(x6) -> f1_0_main_ConstantStackPush(x7) :|: 0 <= 0
Start term: __init(arg1)

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(3) IRSwTTerminationDigraphProof (EQUIVALENT)
Constructed termination digraph!
Nodes:
(1) f1_0_main_ConstantStackPush(arg1) -> f46_0_main_GE(arg1P) :|: 0 = arg1P
(2) f46_0_main_GE(x) -> f46_0_main_GE(x1) :|: x + 1 = x1 && x <= 99
(3) f46_0_main_GE(x2) -> f74_0_main_GE(x3) :|: 5 = x3 && 99 <= x2 - 1
(4) f74_0_main_GE(x4) -> f74_0_main_GE(x5) :|: x4 + 3 = x5 && x4 <= 20
(5) __init(x6) -> f1_0_main_ConstantStackPush(x7) :|: 0 <= 0

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

This digraph is fully evaluated!
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(4)
Complex Obligation (AND)

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(5)
Obligation:

Termination digraph:
Nodes:
(1) f46_0_main_GE(x) -> f46_0_main_GE(x1) :|: x + 1 = x1 && x <= 99

Arcs:
(1) -> (1)

This digraph is fully evaluated!

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(6) IntTRSCompressionProof (EQUIVALENT)
Compressed rules.
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(7)
Obligation:
Rules:
f46_0_main_GE(x:0) -> f46_0_main_GE(x:0 + 1) :|: x:0 < 100

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(8) TempFilterProof (SOUND)
Used the following sort dictionary for filtering: 
f46_0_main_GE(INTEGER)
Replaced non-predefined constructor symbols by 0.
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(9)
Obligation:
Rules:
f46_0_main_GE(x:0) -> f46_0_main_GE(c) :|: c = x:0 + 1 && x:0 < 100

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(10) PolynomialOrderProcessor (EQUIVALENT)
Found the following polynomial interpretation:
[f46_0_main_GE(x)] = 99 - x

The following rules are decreasing:
f46_0_main_GE(x:0) -> f46_0_main_GE(c) :|: c = x:0 + 1 && x:0 < 100
The following rules are bounded:
f46_0_main_GE(x:0) -> f46_0_main_GE(c) :|: c = x:0 + 1 && x:0 < 100

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(11)
YES

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(12)
Obligation:

Termination digraph:
Nodes:
(1) f74_0_main_GE(x4) -> f74_0_main_GE(x5) :|: x4 + 3 = x5 && x4 <= 20

Arcs:
(1) -> (1)

This digraph is fully evaluated!

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

(14)
Obligation:
Rules:
f74_0_main_GE(x4:0) -> f74_0_main_GE(x4:0 + 3) :|: x4:0 < 21

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(15) TempFilterProof (SOUND)
Used the following sort dictionary for filtering: 
f74_0_main_GE(INTEGER)
Replaced non-predefined constructor symbols by 0.
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(16)
Obligation:
Rules:
f74_0_main_GE(x4:0) -> f74_0_main_GE(c) :|: c = x4:0 + 3 && x4:0 < 21

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(17) PolynomialOrderProcessor (EQUIVALENT)
Found the following polynomial interpretation:
[f74_0_main_GE(x)] = 20 - x

The following rules are decreasing:
f74_0_main_GE(x4:0) -> f74_0_main_GE(c) :|: c = x4:0 + 3 && x4:0 < 21
The following rules are bounded:
f74_0_main_GE(x4:0) -> f74_0_main_GE(c) :|: c = x4:0 + 3 && x4:0 < 21

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(18)
YES