NO
proof of prog.inttrs
# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty


Termination of the given IRSwT could be disproven:

(0) IRSwT
(1) IRSFormatTransformerProof [EQUIVALENT, 0 ms]
(2) IRSwT
(3) IRSwTTerminationDigraphProof [EQUIVALENT, 126 ms]
(4) IRSwT
(5) IntTRSCompressionProof [EQUIVALENT, 0 ms]
(6) IRSwT
(7) IRSwTChainingProof [EQUIVALENT, 0 ms]
(8) IRSwT
(9) IRSwTTerminationDigraphProof [EQUIVALENT, 14 ms]
(10) AND
    (11) IRSwT
        (12) IntTRSCompressionProof [EQUIVALENT, 0 ms]
        (13) IRSwT
        (14) TempFilterProof [SOUND, 9 ms]
        (15) IntTRS
        (16) RankingReductionPairProof [EQUIVALENT, 0 ms]
        (17) YES
    (18) IRSwT
        (19) TempFilterProof [SOUND, 4 ms]
        (20) IntTRS
        (21) PolynomialOrderProcessor [EQUIVALENT, 0 ms]
        (22) YES
    (23) IRSwT
        (24) IntTRSCompressionProof [EQUIVALENT, 0 ms]
        (25) IRSwT
        (26) FilterProof [EQUIVALENT, 0 ms]
        (27) IntTRS
        (28) IntTRSPeriodicNontermProof [COMPLETE, 5 ms]
        (29) NO


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(0)
Obligation:
Rules:
f1_0_main_ConstantStackPush(arg1) -> f55_0_main_GE(arg1P) :|: 0 = arg1P
f55_0_main_GE(x) -> f55_0_main_GE(x1) :|: x + 1 = x1 && x <= 99 && x <= 49
f55_0_main_GE(x2) -> f55_0_main_GE(x3) :|: x2 - 1 = x3 && x2 <= 99 && 49 <= x2 - 1
__init(x4) -> f1_0_main_ConstantStackPush(x5) :|: 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) -> f55_0_main_GE(arg1P) :|: 0 = arg1P
f55_0_main_GE(x) -> f55_0_main_GE(x1) :|: x + 1 = x1 && x <= 99 && x <= 49
f55_0_main_GE(x2) -> f55_0_main_GE(x3) :|: x2 - 1 = x3 && x2 <= 99 && 49 <= x2 - 1
__init(x4) -> f1_0_main_ConstantStackPush(x5) :|: 0 <= 0
Start term: __init(arg1)

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(3) IRSwTTerminationDigraphProof (EQUIVALENT)
Constructed termination digraph!
Nodes:
(1) f1_0_main_ConstantStackPush(arg1) -> f55_0_main_GE(arg1P) :|: 0 = arg1P
(2) f55_0_main_GE(x) -> f55_0_main_GE(x1) :|: x + 1 = x1 && x <= 99 && x <= 49
(3) f55_0_main_GE(x2) -> f55_0_main_GE(x3) :|: x2 - 1 = x3 && x2 <= 99 && 49 <= x2 - 1
(4) __init(x4) -> f1_0_main_ConstantStackPush(x5) :|: 0 <= 0

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

This digraph is fully evaluated!
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(4)
Obligation:

Termination digraph:
Nodes:
(1) f55_0_main_GE(x) -> f55_0_main_GE(x1) :|: x + 1 = x1 && x <= 99 && x <= 49
(2) f55_0_main_GE(x2) -> f55_0_main_GE(x3) :|: x2 - 1 = x3 && x2 <= 99 && 49 <= x2 - 1

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

This digraph is fully evaluated!

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(5) IntTRSCompressionProof (EQUIVALENT)
Compressed rules.
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(6)
Obligation:
Rules:
f55_0_main_GE(x:0) -> f55_0_main_GE(x:0 + 1) :|: x:0 < 50 && x:0 < 100
f55_0_main_GE(x2:0) -> f55_0_main_GE(x2:0 - 1) :|: x2:0 > 49 && x2:0 < 100

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(7) IRSwTChainingProof (EQUIVALENT)
Chaining!
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(8)
Obligation:
Rules:
f55_0_main_GE(x) -> f55_0_main_GE(x + 2) :|: TRUE && x <= 48
f55_0_main_GE(x2:0) -> f55_0_main_GE(x2:0 - 1) :|: x2:0 > 49 && x2:0 < 100
f55_0_main_GE(x2) -> f55_0_main_GE(x2) :|: TRUE && x2 <= 49 && x2 >= 49

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(9) IRSwTTerminationDigraphProof (EQUIVALENT)
Constructed termination digraph!
Nodes:
(1) f55_0_main_GE(x) -> f55_0_main_GE(x + 2) :|: TRUE && x <= 48
(2) f55_0_main_GE(x2:0) -> f55_0_main_GE(x2:0 - 1) :|: x2:0 > 49 && x2:0 < 100
(3) f55_0_main_GE(x2) -> f55_0_main_GE(x2) :|: TRUE && x2 <= 49 && x2 >= 49

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

This digraph is fully evaluated!
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(10)
Complex Obligation (AND)

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(11)
Obligation:

Termination digraph:
Nodes:
(1) f55_0_main_GE(x) -> f55_0_main_GE(x + 2) :|: TRUE && x <= 48

Arcs:
(1) -> (1)

This digraph is fully evaluated!

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(12) IntTRSCompressionProof (EQUIVALENT)
Compressed rules.
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(13)
Obligation:
Rules:
f55_0_main_GE(x:0) -> f55_0_main_GE(x:0 + 2) :|: x:0 < 49

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(14) TempFilterProof (SOUND)
Used the following sort dictionary for filtering: 
f55_0_main_GE(INTEGER)
Replaced non-predefined constructor symbols by 0.
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(15)
Obligation:
Rules:
f55_0_main_GE(x:0) -> f55_0_main_GE(c) :|: c = x:0 + 2 && x:0 < 49

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(16) RankingReductionPairProof (EQUIVALENT)
Interpretation:
[ f55_0_main_GE ] = -1/2*f55_0_main_GE_1

The following rules are decreasing:
f55_0_main_GE(x:0) -> f55_0_main_GE(c) :|: c = x:0 + 2 && x:0 < 49

The following rules are bounded:
f55_0_main_GE(x:0) -> f55_0_main_GE(c) :|: c = x:0 + 2 && x:0 < 49


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(17)
YES

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(18)
Obligation:

Termination digraph:
Nodes:
(1) f55_0_main_GE(x2:0) -> f55_0_main_GE(x2:0 - 1) :|: x2:0 > 49 && x2:0 < 100

Arcs:
(1) -> (1)

This digraph is fully evaluated!

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(19) TempFilterProof (SOUND)
Used the following sort dictionary for filtering: 
f55_0_main_GE(INTEGER)
Replaced non-predefined constructor symbols by 0.
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(20)
Obligation:
Rules:
f55_0_main_GE(x2:0) -> f55_0_main_GE(c) :|: c = x2:0 - 1 && (x2:0 > 49 && x2:0 < 100)

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(21) PolynomialOrderProcessor (EQUIVALENT)
Found the following polynomial interpretation:
[f55_0_main_GE(x)] = x

The following rules are decreasing:
f55_0_main_GE(x2:0) -> f55_0_main_GE(c) :|: c = x2:0 - 1 && (x2:0 > 49 && x2:0 < 100)
The following rules are bounded:
f55_0_main_GE(x2:0) -> f55_0_main_GE(c) :|: c = x2:0 - 1 && (x2:0 > 49 && x2:0 < 100)

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(22)
YES

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(23)
Obligation:

Termination digraph:
Nodes:
(1) f55_0_main_GE(x2) -> f55_0_main_GE(x2) :|: TRUE && x2 <= 49 && x2 >= 49

Arcs:
(1) -> (1)

This digraph is fully evaluated!

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

(25)
Obligation:
Rules:
f55_0_main_GE(x2:0) -> f55_0_main_GE(x2:0) :|: x2:0 > 48 && x2:0 < 50

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(26) FilterProof (EQUIVALENT)
Used the following sort dictionary for filtering: 
f55_0_main_GE(INTEGER)
Replaced non-predefined constructor symbols by 0.
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(27)
Obligation:
Rules:
f55_0_main_GE(x2:0) -> f55_0_main_GE(x2:0) :|: x2:0 > 48 && x2:0 < 50

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(28) IntTRSPeriodicNontermProof (COMPLETE)
Normalized system to the following form:
f(pc, x2:0) -> f(1, x2:0) :|: pc = 1 && (x2:0 > 48 && x2:0 < 50)
Witness term starting non-terminating reduction: f(1, 49)
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(29)
NO