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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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, 205 ms]
(4) IRSwT
(5) IntTRSCompressionProof [EQUIVALENT, 37 ms]
(6) IRSwT
(7) IRSwTChainingProof [EQUIVALENT, 0 ms]
(8) IRSwT
(9) IRSwTTerminationDigraphProof [EQUIVALENT, 13 ms]
(10) IRSwT
(11) IntTRSCompressionProof [EQUIVALENT, 0 ms]
(12) IRSwT
(13) IRSwTChainingProof [EQUIVALENT, 1 ms]
(14) IRSwT
(15) IRSwTTerminationDigraphProof [EQUIVALENT, 0 ms]
(16) IRSwT
(17) IntTRSCompressionProof [EQUIVALENT, 0 ms]
(18) IRSwT
(19) FilterProof [EQUIVALENT, 0 ms]
(20) IntTRS
(21) IntTRSNonPeriodicNontermProof [COMPLETE, 4 ms]
(22) NO


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(0)
Obligation:
Rules:
f1_0_main_Load(arg1, arg2) -> f116_0_flip_LE(arg1P, arg2P) :|: 0 <= arg1 - 1 && -1 <= arg2P - 1 && 1 <= arg2 - 1 && -1 <= arg1P - 1
f116_0_flip_LE(x, x1) -> f116_0_flip_LE(x2, x3) :|: x - 1 = x3 && x = x2 && x = x1 && 0 <= x - 1
f116_0_flip_LE(x4, x5) -> f116_0_flip_LE(x6, x7) :|: x5 = x7 && x5 = x6 && x4 <= x5 - 1 && 0 <= x4 - 1 && 0 <= x5 - 1
f116_0_flip_LE(x8, x9) -> f116_0_flip_LE(x10, x11) :|: x8 = x11 && x9 = x10 && 0 <= x8 - 1 && 0 <= x9 - 1 && x9 <= x8 - 1
__init(x12, x13) -> f1_0_main_Load(x14, x15) :|: 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) -> f116_0_flip_LE(arg1P, arg2P) :|: 0 <= arg1 - 1 && -1 <= arg2P - 1 && 1 <= arg2 - 1 && -1 <= arg1P - 1
f116_0_flip_LE(x, x1) -> f116_0_flip_LE(x2, x3) :|: x - 1 = x3 && x = x2 && x = x1 && 0 <= x - 1
f116_0_flip_LE(x4, x5) -> f116_0_flip_LE(x6, x7) :|: x5 = x7 && x5 = x6 && x4 <= x5 - 1 && 0 <= x4 - 1 && 0 <= x5 - 1
f116_0_flip_LE(x8, x9) -> f116_0_flip_LE(x10, x11) :|: x8 = x11 && x9 = x10 && 0 <= x8 - 1 && 0 <= x9 - 1 && x9 <= x8 - 1
__init(x12, x13) -> f1_0_main_Load(x14, x15) :|: 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) -> f116_0_flip_LE(arg1P, arg2P) :|: 0 <= arg1 - 1 && -1 <= arg2P - 1 && 1 <= arg2 - 1 && -1 <= arg1P - 1
(2) f116_0_flip_LE(x, x1) -> f116_0_flip_LE(x2, x3) :|: x - 1 = x3 && x = x2 && x = x1 && 0 <= x - 1
(3) f116_0_flip_LE(x4, x5) -> f116_0_flip_LE(x6, x7) :|: x5 = x7 && x5 = x6 && x4 <= x5 - 1 && 0 <= x4 - 1 && 0 <= x5 - 1
(4) f116_0_flip_LE(x8, x9) -> f116_0_flip_LE(x10, x11) :|: x8 = x11 && x9 = x10 && 0 <= x8 - 1 && 0 <= x9 - 1 && x9 <= x8 - 1
(5) __init(x12, x13) -> f1_0_main_Load(x14, x15) :|: 0 <= 0

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

This digraph is fully evaluated!
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(4)
Obligation:

Termination digraph:
Nodes:
(1) f116_0_flip_LE(x, x1) -> f116_0_flip_LE(x2, x3) :|: x - 1 = x3 && x = x2 && x = x1 && 0 <= x - 1
(2) f116_0_flip_LE(x4, x5) -> f116_0_flip_LE(x6, x7) :|: x5 = x7 && x5 = x6 && x4 <= x5 - 1 && 0 <= x4 - 1 && 0 <= x5 - 1
(3) f116_0_flip_LE(x8, x9) -> f116_0_flip_LE(x10, x11) :|: x8 = x11 && x9 = x10 && 0 <= x8 - 1 && 0 <= x9 - 1 && x9 <= x8 - 1

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

This digraph is fully evaluated!

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(5) IntTRSCompressionProof (EQUIVALENT)
Compressed rules.
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(6)
Obligation:
Rules:
f116_0_flip_LE(x11:0, x10:0) -> f116_0_flip_LE(x10:0, x11:0) :|: x10:0 > 0 && x11:0 > 0 && x11:0 - 1 >= x10:0
f116_0_flip_LE(x4:0, x5:0) -> f116_0_flip_LE(x5:0, x5:0) :|: x4:0 > 0 && x5:0 - 1 >= x4:0 && x5:0 > 0
f116_0_flip_LE(x1:0, x1:0) -> f116_0_flip_LE(x1:0, x1:0 - 1) :|: x1:0 > 0

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(7) IRSwTChainingProof (EQUIVALENT)
Chaining!
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(8)
Obligation:
Rules:
f116_0_flip_LE(x4:0, x5:0) -> f116_0_flip_LE(x5:0, x5:0) :|: x4:0 > 0 && x5:0 - 1 >= x4:0 && x5:0 > 0
f116_0_flip_LE(x4, x5) -> f116_0_flip_LE(x4, x4) :|: TRUE && x5 >= 1 && x4 >= 1 && x4 + -1 * x5 >= 1
f116_0_flip_LE(x1:0, x1:0) -> f116_0_flip_LE(x1:0, x1:0 - 1) :|: x1:0 > 0
f116_0_flip_LE(x9, x9) -> f116_0_flip_LE(x9, x9 + -1) :|: TRUE && x9 >= 1 && 0 >= 1

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(9) IRSwTTerminationDigraphProof (EQUIVALENT)
Constructed termination digraph!
Nodes:
(1) f116_0_flip_LE(x4:0, x5:0) -> f116_0_flip_LE(x5:0, x5:0) :|: x4:0 > 0 && x5:0 - 1 >= x4:0 && x5:0 > 0
(2) f116_0_flip_LE(x4, x5) -> f116_0_flip_LE(x4, x4) :|: TRUE && x5 >= 1 && x4 >= 1 && x4 + -1 * x5 >= 1
(3) f116_0_flip_LE(x1:0, x1:0) -> f116_0_flip_LE(x1:0, x1:0 - 1) :|: x1:0 > 0
(4) f116_0_flip_LE(x9, x9) -> f116_0_flip_LE(x9, x9 + -1) :|: TRUE && x9 >= 1 && 0 >= 1

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

This digraph is fully evaluated!
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(10)
Obligation:

Termination digraph:
Nodes:
(1) f116_0_flip_LE(x1:0, x1:0) -> f116_0_flip_LE(x1:0, x1:0 - 1) :|: x1:0 > 0
(2) f116_0_flip_LE(x4, x5) -> f116_0_flip_LE(x4, x4) :|: TRUE && x5 >= 1 && x4 >= 1 && x4 + -1 * x5 >= 1

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

This digraph is fully evaluated!

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(11) IntTRSCompressionProof (EQUIVALENT)
Compressed rules.
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(12)
Obligation:
Rules:
f116_0_flip_LE(x1:0:0, x1:0:0) -> f116_0_flip_LE(x1:0:0, x1:0:0 - 1) :|: x1:0:0 > 0
f116_0_flip_LE(x4:0, x5:0) -> f116_0_flip_LE(x4:0, x4:0) :|: x4:0 > 0 && x5:0 > 0 && x4:0 + -1 * x5:0 >= 1

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(13) IRSwTChainingProof (EQUIVALENT)
Chaining!
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(14)
Obligation:
Rules:
f116_0_flip_LE(x4:0, x5:0) -> f116_0_flip_LE(x4:0, x4:0) :|: x4:0 > 0 && x5:0 > 0 && x4:0 + -1 * x5:0 >= 1
f116_0_flip_LE(x2, x2) -> f116_0_flip_LE(x2, x2) :|: TRUE && x2 >= 2

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(15) IRSwTTerminationDigraphProof (EQUIVALENT)
Constructed termination digraph!
Nodes:
(1) f116_0_flip_LE(x4:0, x5:0) -> f116_0_flip_LE(x4:0, x4:0) :|: x4:0 > 0 && x5:0 > 0 && x4:0 + -1 * x5:0 >= 1
(2) f116_0_flip_LE(x2, x2) -> f116_0_flip_LE(x2, x2) :|: TRUE && x2 >= 2

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

This digraph is fully evaluated!
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(16)
Obligation:

Termination digraph:
Nodes:
(1) f116_0_flip_LE(x2, x2) -> f116_0_flip_LE(x2, x2) :|: TRUE && x2 >= 2

Arcs:
(1) -> (1)

This digraph is fully evaluated!

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(17) IntTRSCompressionProof (EQUIVALENT)
Compressed rules.
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(18)
Obligation:
Rules:
f116_0_flip_LE(x2:0, x2:0) -> f116_0_flip_LE(x2:0, x2:0) :|: x2:0 > 1

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(19) FilterProof (EQUIVALENT)
Used the following sort dictionary for filtering: 
f116_0_flip_LE(INTEGER, INTEGER)
Replaced non-predefined constructor symbols by 0.
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(20)
Obligation:
Rules:
f116_0_flip_LE(x2:0, x2:0) -> f116_0_flip_LE(x2:0, x2:0) :|: x2:0 > 1

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(21) IntTRSNonPeriodicNontermProof (COMPLETE)
Normalized system to the following form:
f(pc, x2:0, x2:0) -> f(1, x2:0, x2:0) :|: pc = 1 && x2:0 > 1
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_1 = ((run1_1 * 1))) and (((run1_0 * 1)) = ((1 * 1)) and ((run1_1 * 1)) > ((1 * 1)))) and !(((run2_0 * 1)) = ((1 * 1)) and ((run2_1 * 1)) > ((1 * 1))))
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_1 = ((run1_1 * 1))) and (((run1_0 * 1)) = ((1 * 1)) and ((run1_1 * 1)) > ((1 * 1))))

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(22)
NO