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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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, 196 ms]
(4) IRSwT
(5) IntTRSCompressionProof [EQUIVALENT, 2 ms]
(6) IRSwT
(7) IRSwTChainingProof [EQUIVALENT, 0 ms]
(8) IRSwT
(9) IRSwTTerminationDigraphProof [EQUIVALENT, 12 ms]
(10) IRSwT
(11) IntTRSCompressionProof [EQUIVALENT, 0 ms]
(12) IRSwT
(13) IRSwTChainingProof [EQUIVALENT, 0 ms]
(14) IRSwT
(15) IRSwTTerminationDigraphProof [EQUIVALENT, 8 ms]
(16) IRSwT
(17) IntTRSCompressionProof [EQUIVALENT, 0 ms]
(18) IRSwT
(19) FilterProof [EQUIVALENT, 0 ms]
(20) IntTRS
(21) IntTRSPeriodicNontermProof [COMPLETE, 0 ms]
(22) NO


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(0)
Obligation:
Rules:
f1_0_main_Load(arg1, arg2) -> f87_0_flip_LE(arg1P, arg2P) :|: arg2 = arg2P && arg2 + 5 = arg1P && 0 <= arg1 - 1 && -1 <= arg2 - 1 && arg2 <= arg2 + 5 - 1
f87_0_flip_LE(x, x1) -> f87_0_flip_LE(x2, x3) :|: x - 1 = x3 && x = x2 && x = x1 && x - 1 <= x - 1 && 0 <= x - 1
f87_0_flip_LE(x4, x5) -> f87_0_flip_LE(x6, x7) :|: x5 = x7 && x5 = x6 && 1 <= x5 - 1 && 0 <= x4 - 1 && x4 <= x5 - 1
f87_0_flip_LE(x8, x9) -> f87_0_flip_LE(x10, x11) :|: x8 = x11 && x9 = x10 && 1 <= x8 - 1 && x9 <= x8 - 1 && 0 <= x9 - 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) -> f87_0_flip_LE(arg1P, arg2P) :|: arg2 = arg2P && arg2 + 5 = arg1P && 0 <= arg1 - 1 && -1 <= arg2 - 1 && arg2 <= arg2 + 5 - 1
f87_0_flip_LE(x, x1) -> f87_0_flip_LE(x2, x3) :|: x - 1 = x3 && x = x2 && x = x1 && x - 1 <= x - 1 && 0 <= x - 1
f87_0_flip_LE(x4, x5) -> f87_0_flip_LE(x6, x7) :|: x5 = x7 && x5 = x6 && 1 <= x5 - 1 && 0 <= x4 - 1 && x4 <= x5 - 1
f87_0_flip_LE(x8, x9) -> f87_0_flip_LE(x10, x11) :|: x8 = x11 && x9 = x10 && 1 <= x8 - 1 && x9 <= x8 - 1 && 0 <= x9 - 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) -> f87_0_flip_LE(arg1P, arg2P) :|: arg2 = arg2P && arg2 + 5 = arg1P && 0 <= arg1 - 1 && -1 <= arg2 - 1 && arg2 <= arg2 + 5 - 1
(2) f87_0_flip_LE(x, x1) -> f87_0_flip_LE(x2, x3) :|: x - 1 = x3 && x = x2 && x = x1 && x - 1 <= x - 1 && 0 <= x - 1
(3) f87_0_flip_LE(x4, x5) -> f87_0_flip_LE(x6, x7) :|: x5 = x7 && x5 = x6 && 1 <= x5 - 1 && 0 <= x4 - 1 && x4 <= x5 - 1
(4) f87_0_flip_LE(x8, x9) -> f87_0_flip_LE(x10, x11) :|: x8 = x11 && x9 = x10 && 1 <= x8 - 1 && x9 <= x8 - 1 && 0 <= x9 - 1
(5) __init(x12, x13) -> f1_0_main_Load(x14, x15) :|: 0 <= 0

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

This digraph is fully evaluated!
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(4)
Obligation:

Termination digraph:
Nodes:
(1) f87_0_flip_LE(x8, x9) -> f87_0_flip_LE(x10, x11) :|: x8 = x11 && x9 = x10 && 1 <= x8 - 1 && x9 <= x8 - 1 && 0 <= x9 - 1
(2) f87_0_flip_LE(x, x1) -> f87_0_flip_LE(x2, x3) :|: x - 1 = x3 && x = x2 && x = x1 && x - 1 <= x - 1 && 0 <= x - 1
(3) f87_0_flip_LE(x4, x5) -> f87_0_flip_LE(x6, x7) :|: x5 = x7 && x5 = x6 && 1 <= x5 - 1 && 0 <= x4 - 1 && x4 <= x5 - 1

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

This digraph is fully evaluated!

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

(6)
Obligation:
Rules:
f87_0_flip_LE(x11:0, x10:0) -> f87_0_flip_LE(x10:0, x11:0) :|: x11:0 - 1 >= x10:0 && x11:0 > 1 && x10:0 > 0
f87_0_flip_LE(x1:0, x1:0) -> f87_0_flip_LE(x1:0, x1:0 - 1) :|: x1:0 > 0
f87_0_flip_LE(x4:0, x5:0) -> f87_0_flip_LE(x5:0, x5:0) :|: x4:0 > 0 && x5:0 > 1 && x5:0 - 1 >= x4:0

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(7) IRSwTChainingProof (EQUIVALENT)
Chaining!
----------------------------------------

(8)
Obligation:
Rules:
f87_0_flip_LE(x1:0, x1:0) -> f87_0_flip_LE(x1:0, x1:0 - 1) :|: x1:0 > 0
f87_0_flip_LE(x5, x5) -> f87_0_flip_LE(x5, x5 + -1) :|: TRUE && 0 >= 1 && x5 >= 2
f87_0_flip_LE(x4:0, x5:0) -> f87_0_flip_LE(x5:0, x5:0) :|: x4:0 > 0 && x5:0 > 1 && x5:0 - 1 >= x4:0
f87_0_flip_LE(x7, x8) -> f87_0_flip_LE(x7, x7) :|: TRUE && x7 + -1 * x8 >= 1 && x7 >= 2 && x8 >= 1

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(9) IRSwTTerminationDigraphProof (EQUIVALENT)
Constructed termination digraph!
Nodes:
(1) f87_0_flip_LE(x1:0, x1:0) -> f87_0_flip_LE(x1:0, x1:0 - 1) :|: x1:0 > 0
(2) f87_0_flip_LE(x5, x5) -> f87_0_flip_LE(x5, x5 + -1) :|: TRUE && 0 >= 1 && x5 >= 2
(3) f87_0_flip_LE(x4:0, x5:0) -> f87_0_flip_LE(x5:0, x5:0) :|: x4:0 > 0 && x5:0 > 1 && x5:0 - 1 >= x4:0
(4) f87_0_flip_LE(x7, x8) -> f87_0_flip_LE(x7, x7) :|: TRUE && x7 + -1 * x8 >= 1 && x7 >= 2 && x8 >= 1

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

This digraph is fully evaluated!
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(10)
Obligation:

Termination digraph:
Nodes:
(1) f87_0_flip_LE(x1:0, x1:0) -> f87_0_flip_LE(x1:0, x1:0 - 1) :|: x1:0 > 0
(2) f87_0_flip_LE(x7, x8) -> f87_0_flip_LE(x7, x7) :|: TRUE && x7 + -1 * x8 >= 1 && x7 >= 2 && x8 >= 1

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

This digraph is fully evaluated!

----------------------------------------

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

(12)
Obligation:
Rules:
f87_0_flip_LE(x1:0:0, x1:0:0) -> f87_0_flip_LE(x1:0:0, x1:0:0 - 1) :|: x1:0:0 > 0
f87_0_flip_LE(x7:0, x8:0) -> f87_0_flip_LE(x7:0, x7:0) :|: x7:0 > 1 && x7:0 + -1 * x8:0 >= 1 && x8:0 > 0

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(13) IRSwTChainingProof (EQUIVALENT)
Chaining!
----------------------------------------

(14)
Obligation:
Rules:
f87_0_flip_LE(x7:0, x8:0) -> f87_0_flip_LE(x7:0, x7:0) :|: x7:0 > 1 && x7:0 + -1 * x8:0 >= 1 && x8:0 > 0
f87_0_flip_LE(x2, x2) -> f87_0_flip_LE(x2, x2) :|: TRUE && x2 >= 2

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(15) IRSwTTerminationDigraphProof (EQUIVALENT)
Constructed termination digraph!
Nodes:
(1) f87_0_flip_LE(x7:0, x8:0) -> f87_0_flip_LE(x7:0, x7:0) :|: x7:0 > 1 && x7:0 + -1 * x8:0 >= 1 && x8:0 > 0
(2) f87_0_flip_LE(x2, x2) -> f87_0_flip_LE(x2, x2) :|: TRUE && x2 >= 2

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

This digraph is fully evaluated!
----------------------------------------

(16)
Obligation:

Termination digraph:
Nodes:
(1) f87_0_flip_LE(x2, x2) -> f87_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.
----------------------------------------

(18)
Obligation:
Rules:
f87_0_flip_LE(x2:0, x2:0) -> f87_0_flip_LE(x2:0, x2:0) :|: x2:0 > 1

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(19) FilterProof (EQUIVALENT)
Used the following sort dictionary for filtering: 
f87_0_flip_LE(INTEGER, INTEGER)
Replaced non-predefined constructor symbols by 0.
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(20)
Obligation:
Rules:
f87_0_flip_LE(x2:0, x2:0) -> f87_0_flip_LE(x2:0, x2:0) :|: x2:0 > 1

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(21) IntTRSPeriodicNontermProof (COMPLETE)
Normalized system to the following form:
f(pc, x2:0, x2:0) -> f(1, x2:0, x2:0) :|: pc = 1 && x2:0 > 1
Witness term starting non-terminating reduction: f(1, 16, 16)
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(22)
NO