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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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, 186 ms]
(4) AND
    (5) IRSwT
        (6) IntTRSCompressionProof [EQUIVALENT, 6 ms]
        (7) IRSwT
        (8) TempFilterProof [SOUND, 34 ms]
        (9) IntTRS
        (10) PolynomialOrderProcessor [EQUIVALENT, 7 ms]
        (11) IntTRS
        (12) PolynomialOrderProcessor [EQUIVALENT, 0 ms]
        (13) YES
    (14) IRSwT
        (15) IntTRSCompressionProof [EQUIVALENT, 7 ms]
        (16) IRSwT
        (17) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms]
        (18) IRSwT
        (19) TempFilterProof [SOUND, 28 ms]
        (20) IntTRS
        (21) RankingReductionPairProof [EQUIVALENT, 12 ms]
        (22) YES
    (23) IRSwT
        (24) IntTRSCompressionProof [EQUIVALENT, 29 ms]
        (25) IRSwT
        (26) FilterProof [EQUIVALENT, 0 ms]
        (27) IntTRS
        (28) IntTRSNonPeriodicNontermProof [COMPLETE, 0 ms]
        (29) NO


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(0)
Obligation:
Rules:
f1_0_main_ConstantStackPush(arg1, arg2) -> f142_0_main_GE(arg1P, arg2P) :|: 0 = arg1P
f142_0_main_GE(x, x1) -> f142_0_main_GE(x2, x3) :|: x + 1 = x2 && x <= 99 && 9 <= x - 1 && x <= 49
f181_0_main_Load(x4, x5) -> f181_0_main_Load(x6, x7) :|: x4 = x6
f142_0_main_GE(x8, x9) -> f181_0_main_Load(x10, x11) :|: x8 = x10 && 49 <= x8 - 1 && x8 <= 99
f142_0_main_GE(x12, x13) -> f191_0_main_GE(x14, x15) :|: 0 = x15 && x12 = x14 && x12 <= 99 && x12 <= 9
f191_0_main_GE(x16, x17) -> f191_0_main_GE(x18, x19) :|: x17 + 1 = x19 && x16 = x18 && x17 <= 14
f191_0_main_GE(x20, x21) -> f142_0_main_GE(x22, x23) :|: x20 + 1 = x22 && 14 <= x21 - 1
__init(x24, x25) -> f1_0_main_ConstantStackPush(x26, x27) :|: 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_ConstantStackPush(arg1, arg2) -> f142_0_main_GE(arg1P, arg2P) :|: 0 = arg1P
f142_0_main_GE(x, x1) -> f142_0_main_GE(x2, x3) :|: x + 1 = x2 && x <= 99 && 9 <= x - 1 && x <= 49
f181_0_main_Load(x4, x5) -> f181_0_main_Load(x6, x7) :|: x4 = x6
f142_0_main_GE(x8, x9) -> f181_0_main_Load(x10, x11) :|: x8 = x10 && 49 <= x8 - 1 && x8 <= 99
f142_0_main_GE(x12, x13) -> f191_0_main_GE(x14, x15) :|: 0 = x15 && x12 = x14 && x12 <= 99 && x12 <= 9
f191_0_main_GE(x16, x17) -> f191_0_main_GE(x18, x19) :|: x17 + 1 = x19 && x16 = x18 && x17 <= 14
f191_0_main_GE(x20, x21) -> f142_0_main_GE(x22, x23) :|: x20 + 1 = x22 && 14 <= x21 - 1
__init(x24, x25) -> f1_0_main_ConstantStackPush(x26, x27) :|: 0 <= 0
Start term: __init(arg1, arg2)

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(3) IRSwTTerminationDigraphProof (EQUIVALENT)
Constructed termination digraph!
Nodes:
(1) f1_0_main_ConstantStackPush(arg1, arg2) -> f142_0_main_GE(arg1P, arg2P) :|: 0 = arg1P
(2) f142_0_main_GE(x, x1) -> f142_0_main_GE(x2, x3) :|: x + 1 = x2 && x <= 99 && 9 <= x - 1 && x <= 49
(3) f181_0_main_Load(x4, x5) -> f181_0_main_Load(x6, x7) :|: x4 = x6
(4) f142_0_main_GE(x8, x9) -> f181_0_main_Load(x10, x11) :|: x8 = x10 && 49 <= x8 - 1 && x8 <= 99
(5) f142_0_main_GE(x12, x13) -> f191_0_main_GE(x14, x15) :|: 0 = x15 && x12 = x14 && x12 <= 99 && x12 <= 9
(6) f191_0_main_GE(x16, x17) -> f191_0_main_GE(x18, x19) :|: x17 + 1 = x19 && x16 = x18 && x17 <= 14
(7) f191_0_main_GE(x20, x21) -> f142_0_main_GE(x22, x23) :|: x20 + 1 = x22 && 14 <= x21 - 1
(8) __init(x24, x25) -> f1_0_main_ConstantStackPush(x26, x27) :|: 0 <= 0

Arcs:
(1) -> (5)
(2) -> (2), (4)
(3) -> (3)
(4) -> (3)
(5) -> (6)
(6) -> (6), (7)
(7) -> (2), (4), (5)
(8) -> (1)

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

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(5)
Obligation:

Termination digraph:
Nodes:
(1) f142_0_main_GE(x12, x13) -> f191_0_main_GE(x14, x15) :|: 0 = x15 && x12 = x14 && x12 <= 99 && x12 <= 9
(2) f191_0_main_GE(x20, x21) -> f142_0_main_GE(x22, x23) :|: x20 + 1 = x22 && 14 <= x21 - 1
(3) f191_0_main_GE(x16, x17) -> f191_0_main_GE(x18, x19) :|: x17 + 1 = x19 && x16 = x18 && x17 <= 14

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

This digraph is fully evaluated!

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(6) IntTRSCompressionProof (EQUIVALENT)
Compressed rules.
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(7)
Obligation:
Rules:
f191_0_main_GE(x20:0, x21:0) -> f191_0_main_GE(x20:0 + 1, 0) :|: x20:0 < 9 && x20:0 < 99 && x21:0 > 14
f191_0_main_GE(x16:0, x17:0) -> f191_0_main_GE(x16:0, x17:0 + 1) :|: x17:0 < 15

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(8) TempFilterProof (SOUND)
Used the following sort dictionary for filtering: 
f191_0_main_GE(VARIABLE, VARIABLE)
Replaced non-predefined constructor symbols by 0.
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(9)
Obligation:
Rules:
f191_0_main_GE(x20:0, x21:0) -> f191_0_main_GE(c, c1) :|: c1 = 0 && c = x20:0 + 1 && (x20:0 < 9 && x20:0 < 99 && x21:0 > 14)
f191_0_main_GE(x16:0, x17:0) -> f191_0_main_GE(x16:0, c2) :|: c2 = x17:0 + 1 && x17:0 < 15

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(10) PolynomialOrderProcessor (EQUIVALENT)
Found the following polynomial interpretation:
[f191_0_main_GE(x, x1)] = 8 - x

The following rules are decreasing:
f191_0_main_GE(x20:0, x21:0) -> f191_0_main_GE(c, c1) :|: c1 = 0 && c = x20:0 + 1 && (x20:0 < 9 && x20:0 < 99 && x21:0 > 14)
The following rules are bounded:
f191_0_main_GE(x20:0, x21:0) -> f191_0_main_GE(c, c1) :|: c1 = 0 && c = x20:0 + 1 && (x20:0 < 9 && x20:0 < 99 && x21:0 > 14)

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(11)
Obligation:
Rules:
f191_0_main_GE(x16:0, x17:0) -> f191_0_main_GE(x16:0, c2) :|: c2 = x17:0 + 1 && x17:0 < 15

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(12) PolynomialOrderProcessor (EQUIVALENT)
Found the following polynomial interpretation:
[f191_0_main_GE(x, x1)] = 14 - x1

The following rules are decreasing:
f191_0_main_GE(x16:0, x17:0) -> f191_0_main_GE(x16:0, c2) :|: c2 = x17:0 + 1 && x17:0 < 15
The following rules are bounded:
f191_0_main_GE(x16:0, x17:0) -> f191_0_main_GE(x16:0, c2) :|: c2 = x17:0 + 1 && x17:0 < 15

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(13)
YES

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(14)
Obligation:

Termination digraph:
Nodes:
(1) f142_0_main_GE(x, x1) -> f142_0_main_GE(x2, x3) :|: x + 1 = x2 && x <= 99 && 9 <= x - 1 && x <= 49

Arcs:
(1) -> (1)

This digraph is fully evaluated!

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(15) IntTRSCompressionProof (EQUIVALENT)
Compressed rules.
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(16)
Obligation:
Rules:
f142_0_main_GE(x:0, x1:0) -> f142_0_main_GE(x:0 + 1, x3:0) :|: x:0 > 9 && x:0 < 100 && x:0 < 50

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(17) IntTRSUnneededArgumentFilterProof (EQUIVALENT)
Some arguments are removed because they cannot influence termination. We removed arguments according to the following replacements:

   f142_0_main_GE(x1, x2) -> f142_0_main_GE(x1)

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(18)
Obligation:
Rules:
f142_0_main_GE(x:0) -> f142_0_main_GE(x:0 + 1) :|: x:0 > 9 && x:0 < 100 && x:0 < 50

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(19) TempFilterProof (SOUND)
Used the following sort dictionary for filtering: 
f142_0_main_GE(INTEGER)
Replaced non-predefined constructor symbols by 0.
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(20)
Obligation:
Rules:
f142_0_main_GE(x:0) -> f142_0_main_GE(c) :|: c = x:0 + 1 && (x:0 > 9 && x:0 < 100 && x:0 < 50)

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(21) RankingReductionPairProof (EQUIVALENT)
Interpretation:
[ f142_0_main_GE ] = -1*f142_0_main_GE_1

The following rules are decreasing:
f142_0_main_GE(x:0) -> f142_0_main_GE(c) :|: c = x:0 + 1 && (x:0 > 9 && x:0 < 100 && x:0 < 50)

The following rules are bounded:
f142_0_main_GE(x:0) -> f142_0_main_GE(c) :|: c = x:0 + 1 && (x:0 > 9 && x:0 < 100 && x:0 < 50)


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(22)
YES

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(23)
Obligation:

Termination digraph:
Nodes:
(1) f181_0_main_Load(x4, x5) -> f181_0_main_Load(x6, x7) :|: x4 = x6

Arcs:
(1) -> (1)

This digraph is fully evaluated!

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(24) IntTRSCompressionProof (EQUIVALENT)
Compressed rules.
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(25)
Obligation:
Rules:
f181_0_main_Load(x4:0, x5:0) -> f181_0_main_Load(x4:0, x7:0) :|: TRUE

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(26) FilterProof (EQUIVALENT)
Used the following sort dictionary for filtering: 
f181_0_main_Load(VARIABLE, VARIABLE)
Replaced non-predefined constructor symbols by 0.
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(27)
Obligation:
Rules:
f181_0_main_Load(x4:0, x5:0) -> f181_0_main_Load(x4:0, x7:0) :|: TRUE

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(28) IntTRSNonPeriodicNontermProof (COMPLETE)
Normalized system to the following form:
f(pc, x4:0, x5:0) -> f(1, x4:0, x7:0) :|: pc = 1 && TRUE
Proved unsatisfiability of the following formula, indicating that the system is never left after entering:
(((run2_0 = ((1 * 1)) and run2_1 = ((run1_1 * 1)) and run2_2 = ((run1_3 * 1))) and (((run1_0 * 1)) = ((1 * 1)) and T)) and !(((run2_0 * 1)) = ((1 * 1)) and T))
Proved satisfiability of the following formula, indicating that the system is entered at least once:
((run2_0 = ((1 * 1)) and run2_1 = ((run1_1 * 1)) and run2_2 = ((run1_3 * 1))) and (((run1_0 * 1)) = ((1 * 1)) and T))

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(29)
NO