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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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, 70 ms]
(4) AND
    (5) IRSwT
        (6) IntTRSCompressionProof [EQUIVALENT, 10 ms]
        (7) IRSwT
        (8) TempFilterProof [SOUND, 11 ms]
        (9) IntTRS
        (10) PolynomialOrderProcessor [EQUIVALENT, 0 ms]
        (11) YES
    (12) IRSwT
        (13) IntTRSCompressionProof [EQUIVALENT, 7 ms]
        (14) IRSwT
        (15) FilterProof [EQUIVALENT, 0 ms]
        (16) IntTRS
        (17) IntTRSNonPeriodicNontermProof [COMPLETE, 5 ms]
        (18) NO


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(0)
Obligation:
Rules:
f1_0_main_ConstantStackPush(arg1) -> f46_0_main_LE(arg1P) :|: 0 = arg1P
f46_0_main_LE(x) -> f46_0_main_LE(x1) :|: x + 1 = x1 && x <= 10
f46_0_main_LE(x2) -> f46_0_main_LE(x3) :|: x2 = x3 && 10 <= 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) -> f46_0_main_LE(arg1P) :|: 0 = arg1P
f46_0_main_LE(x) -> f46_0_main_LE(x1) :|: x + 1 = x1 && x <= 10
f46_0_main_LE(x2) -> f46_0_main_LE(x3) :|: x2 = x3 && 10 <= 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) -> f46_0_main_LE(arg1P) :|: 0 = arg1P
(2) f46_0_main_LE(x) -> f46_0_main_LE(x1) :|: x + 1 = x1 && x <= 10
(3) f46_0_main_LE(x2) -> f46_0_main_LE(x3) :|: x2 = x3 && 10 <= x2 - 1
(4) __init(x4) -> f1_0_main_ConstantStackPush(x5) :|: 0 <= 0

Arcs:
(1) -> (2)
(2) -> (2), (3)
(3) -> (3)
(4) -> (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_LE(x) -> f46_0_main_LE(x1) :|: x + 1 = x1 && x <= 10

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_LE(x:0) -> f46_0_main_LE(x:0 + 1) :|: x:0 < 11

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(8) TempFilterProof (SOUND)
Used the following sort dictionary for filtering: 
f46_0_main_LE(INTEGER)
Replaced non-predefined constructor symbols by 0.
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(9)
Obligation:
Rules:
f46_0_main_LE(x:0) -> f46_0_main_LE(c) :|: c = x:0 + 1 && x:0 < 11

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(10) PolynomialOrderProcessor (EQUIVALENT)
Found the following polynomial interpretation:
[f46_0_main_LE(x)] = 10 - x

The following rules are decreasing:
f46_0_main_LE(x:0) -> f46_0_main_LE(c) :|: c = x:0 + 1 && x:0 < 11
The following rules are bounded:
f46_0_main_LE(x:0) -> f46_0_main_LE(c) :|: c = x:0 + 1 && x:0 < 11

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(11)
YES

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(12)
Obligation:

Termination digraph:
Nodes:
(1) f46_0_main_LE(x2) -> f46_0_main_LE(x3) :|: x2 = x3 && 10 <= x2 - 1

Arcs:
(1) -> (1)

This digraph is fully evaluated!

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(13) IntTRSCompressionProof (EQUIVALENT)
Compressed rules.
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(14)
Obligation:
Rules:
f46_0_main_LE(x2:0) -> f46_0_main_LE(x2:0) :|: x2:0 > 10

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(15) FilterProof (EQUIVALENT)
Used the following sort dictionary for filtering: 
f46_0_main_LE(INTEGER)
Replaced non-predefined constructor symbols by 0.
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(16)
Obligation:
Rules:
f46_0_main_LE(x2:0) -> f46_0_main_LE(x2:0) :|: x2:0 > 10

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(17) IntTRSNonPeriodicNontermProof (COMPLETE)
Normalized system to the following form:
f(pc, x2:0) -> f(1, x2:0) :|: pc = 1 && x2:0 > 10
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 (((run1_0 * 1)) = ((1 * 1)) and ((run1_1 * 1)) > ((1 * 10)))) and !(((run2_0 * 1)) = ((1 * 1)) and ((run2_1 * 1)) > ((1 * 10))))
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 (((run1_0 * 1)) = ((1 * 1)) and ((run1_1 * 1)) > ((1 * 10))))

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(18)
NO