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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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, 234 ms]
(4) IRSwT
(5) IntTRSCompressionProof [EQUIVALENT, 0 ms]
(6) IRSwT
(7) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms]
(8) IRSwT
(9) IRSwTChainingProof [EQUIVALENT, 0 ms]
(10) IRSwT
(11) IRSwTTerminationDigraphProof [EQUIVALENT, 38 ms]
(12) AND
    (13) IRSwT
        (14) IntTRSCompressionProof [EQUIVALENT, 0 ms]
        (15) IRSwT
    (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) -> f89_0_loop_LE(arg1P, arg2P) :|: arg2 = arg1P && -1 <= arg2 - 1 && 0 <= arg1 - 1
f89_0_loop_LE(x, x1) -> f131_0_loop_LE(x2, x3) :|: x = x2 && 19 <= x - 1 && x <= 49
f89_0_loop_LE(x4, x5) -> f131_0_loop_LE(x6, x7) :|: x4 - 1 = x6 && 0 <= x4 - 1 && x4 <= 49 && x4 <= 19
f131_0_loop_LE(x8, x9) -> f89_0_loop_LE(x10, x11) :|: x8 = x10 && x8 <= 10 && x8 <= 29
f131_0_loop_LE(x12, x13) -> f89_0_loop_LE(x14, x15) :|: x12 + 1 = x14 && 10 <= x12 - 1 && x12 <= 28
f131_0_loop_LE(x16, x17) -> f89_0_loop_LE(x18, x19) :|: x16 + 1 = x18 && 39 <= x16 - 1
f131_0_loop_LE(x20, x21) -> f89_0_loop_LE(x22, x23) :|: x20 = x22 && 28 <= x20 - 1 && x20 <= 39
__init(x24, x25) -> f1_0_main_Load(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_Load(arg1, arg2) -> f89_0_loop_LE(arg1P, arg2P) :|: arg2 = arg1P && -1 <= arg2 - 1 && 0 <= arg1 - 1
f89_0_loop_LE(x, x1) -> f131_0_loop_LE(x2, x3) :|: x = x2 && 19 <= x - 1 && x <= 49
f89_0_loop_LE(x4, x5) -> f131_0_loop_LE(x6, x7) :|: x4 - 1 = x6 && 0 <= x4 - 1 && x4 <= 49 && x4 <= 19
f131_0_loop_LE(x8, x9) -> f89_0_loop_LE(x10, x11) :|: x8 = x10 && x8 <= 10 && x8 <= 29
f131_0_loop_LE(x12, x13) -> f89_0_loop_LE(x14, x15) :|: x12 + 1 = x14 && 10 <= x12 - 1 && x12 <= 28
f131_0_loop_LE(x16, x17) -> f89_0_loop_LE(x18, x19) :|: x16 + 1 = x18 && 39 <= x16 - 1
f131_0_loop_LE(x20, x21) -> f89_0_loop_LE(x22, x23) :|: x20 = x22 && 28 <= x20 - 1 && x20 <= 39
__init(x24, x25) -> f1_0_main_Load(x26, x27) :|: 0 <= 0
Start term: __init(arg1, arg2)

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

(3) IRSwTTerminationDigraphProof (EQUIVALENT)
Constructed termination digraph!
Nodes:
(1) f1_0_main_Load(arg1, arg2) -> f89_0_loop_LE(arg1P, arg2P) :|: arg2 = arg1P && -1 <= arg2 - 1 && 0 <= arg1 - 1
(2) f89_0_loop_LE(x, x1) -> f131_0_loop_LE(x2, x3) :|: x = x2 && 19 <= x - 1 && x <= 49
(3) f89_0_loop_LE(x4, x5) -> f131_0_loop_LE(x6, x7) :|: x4 - 1 = x6 && 0 <= x4 - 1 && x4 <= 49 && x4 <= 19
(4) f131_0_loop_LE(x8, x9) -> f89_0_loop_LE(x10, x11) :|: x8 = x10 && x8 <= 10 && x8 <= 29
(5) f131_0_loop_LE(x12, x13) -> f89_0_loop_LE(x14, x15) :|: x12 + 1 = x14 && 10 <= x12 - 1 && x12 <= 28
(6) f131_0_loop_LE(x16, x17) -> f89_0_loop_LE(x18, x19) :|: x16 + 1 = x18 && 39 <= x16 - 1
(7) f131_0_loop_LE(x20, x21) -> f89_0_loop_LE(x22, x23) :|: x20 = x22 && 28 <= x20 - 1 && x20 <= 39
(8) __init(x24, x25) -> f1_0_main_Load(x26, x27) :|: 0 <= 0

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

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

(4)
Obligation:

Termination digraph:
Nodes:
(1) f89_0_loop_LE(x, x1) -> f131_0_loop_LE(x2, x3) :|: x = x2 && 19 <= x - 1 && x <= 49
(2) f131_0_loop_LE(x20, x21) -> f89_0_loop_LE(x22, x23) :|: x20 = x22 && 28 <= x20 - 1 && x20 <= 39
(3) f131_0_loop_LE(x16, x17) -> f89_0_loop_LE(x18, x19) :|: x16 + 1 = x18 && 39 <= x16 - 1
(4) f131_0_loop_LE(x12, x13) -> f89_0_loop_LE(x14, x15) :|: x12 + 1 = x14 && 10 <= x12 - 1 && x12 <= 28
(5) f89_0_loop_LE(x4, x5) -> f131_0_loop_LE(x6, x7) :|: x4 - 1 = x6 && 0 <= x4 - 1 && x4 <= 49 && x4 <= 19
(6) f131_0_loop_LE(x8, x9) -> f89_0_loop_LE(x10, x11) :|: x8 = x10 && x8 <= 10 && x8 <= 29

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

This digraph is fully evaluated!

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

(6)
Obligation:
Rules:
f131_0_loop_LE(x20:0, x21:0) -> f89_0_loop_LE(x20:0, x23:0) :|: x20:0 < 40 && x20:0 > 28
f131_0_loop_LE(x16:0, x17:0) -> f89_0_loop_LE(x16:0 + 1, x19:0) :|: x16:0 > 39
f89_0_loop_LE(x2:0, x1:0) -> f131_0_loop_LE(x2:0, x3:0) :|: x2:0 < 50 && x2:0 > 19
f131_0_loop_LE(x12:0, x13:0) -> f89_0_loop_LE(x12:0 + 1, x15:0) :|: x12:0 < 29 && x12:0 > 10
f89_0_loop_LE(x4:0, x5:0) -> f131_0_loop_LE(x4:0 - 1, x7:0) :|: x4:0 < 50 && x4:0 > 0 && x4:0 < 20
f131_0_loop_LE(x10:0, x9:0) -> f89_0_loop_LE(x10:0, x11:0) :|: x10:0 < 30 && x10:0 < 11

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

   f131_0_loop_LE(x1, x2) -> f131_0_loop_LE(x1)
   f89_0_loop_LE(x1, x2) -> f89_0_loop_LE(x1)

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(8)
Obligation:
Rules:
f131_0_loop_LE(x20:0) -> f89_0_loop_LE(x20:0) :|: x20:0 < 40 && x20:0 > 28
f131_0_loop_LE(x16:0) -> f89_0_loop_LE(x16:0 + 1) :|: x16:0 > 39
f89_0_loop_LE(x2:0) -> f131_0_loop_LE(x2:0) :|: x2:0 < 50 && x2:0 > 19
f131_0_loop_LE(x12:0) -> f89_0_loop_LE(x12:0 + 1) :|: x12:0 < 29 && x12:0 > 10
f89_0_loop_LE(x4:0) -> f131_0_loop_LE(x4:0 - 1) :|: x4:0 < 50 && x4:0 > 0 && x4:0 < 20
f131_0_loop_LE(x10:0) -> f89_0_loop_LE(x10:0) :|: x10:0 < 30 && x10:0 < 11

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(9) IRSwTChainingProof (EQUIVALENT)
Chaining!
----------------------------------------

(10)
Obligation:
Rules:
f131_0_loop_LE(x16:0) -> f89_0_loop_LE(x16:0 + 1) :|: x16:0 > 39
f89_0_loop_LE(x2:0) -> f131_0_loop_LE(x2:0) :|: x2:0 < 50 && x2:0 > 19
f131_0_loop_LE(x4) -> f131_0_loop_LE(x4) :|: TRUE && x4 <= 39 && x4 >= 29
f131_0_loop_LE(x12:0) -> f89_0_loop_LE(x12:0 + 1) :|: x12:0 < 29 && x12:0 > 10
f89_0_loop_LE(x4:0) -> f131_0_loop_LE(x4:0 - 1) :|: x4:0 < 50 && x4:0 > 0 && x4:0 < 20
f131_0_loop_LE(x10:0) -> f89_0_loop_LE(x10:0) :|: x10:0 < 30 && x10:0 < 11

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(11) IRSwTTerminationDigraphProof (EQUIVALENT)
Constructed termination digraph!
Nodes:
(1) f131_0_loop_LE(x16:0) -> f89_0_loop_LE(x16:0 + 1) :|: x16:0 > 39
(2) f89_0_loop_LE(x2:0) -> f131_0_loop_LE(x2:0) :|: x2:0 < 50 && x2:0 > 19
(3) f131_0_loop_LE(x4) -> f131_0_loop_LE(x4) :|: TRUE && x4 <= 39 && x4 >= 29
(4) f131_0_loop_LE(x12:0) -> f89_0_loop_LE(x12:0 + 1) :|: x12:0 < 29 && x12:0 > 10
(5) f89_0_loop_LE(x4:0) -> f131_0_loop_LE(x4:0 - 1) :|: x4:0 < 50 && x4:0 > 0 && x4:0 < 20
(6) f131_0_loop_LE(x10:0) -> f89_0_loop_LE(x10:0) :|: x10:0 < 30 && x10:0 < 11

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

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

(12)
Complex Obligation (AND)

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

(13)
Obligation:

Termination digraph:
Nodes:
(1) f131_0_loop_LE(x16:0) -> f89_0_loop_LE(x16:0 + 1) :|: x16:0 > 39
(2) f89_0_loop_LE(x2:0) -> f131_0_loop_LE(x2:0) :|: x2:0 < 50 && x2:0 > 19
(3) f131_0_loop_LE(x12:0) -> f89_0_loop_LE(x12:0 + 1) :|: x12:0 < 29 && x12:0 > 10
(4) f89_0_loop_LE(x4:0) -> f131_0_loop_LE(x4:0 - 1) :|: x4:0 < 50 && x4:0 > 0 && x4:0 < 20
(5) f131_0_loop_LE(x10:0) -> f89_0_loop_LE(x10:0) :|: x10:0 < 30 && x10:0 < 11

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

This digraph is fully evaluated!

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

(15)
Obligation:
Rules:
f89_0_loop_LE(x4:0:0) -> f131_0_loop_LE(x4:0:0 - 1) :|: x4:0:0 < 50 && x4:0:0 > 0 && x4:0:0 < 20
f89_0_loop_LE(x2:0:0) -> f131_0_loop_LE(x2:0:0) :|: x2:0:0 < 50 && x2:0:0 > 19
f131_0_loop_LE(x12:0:0) -> f89_0_loop_LE(x12:0:0 + 1) :|: x12:0:0 < 29 && x12:0:0 > 10
f131_0_loop_LE(x16:0:0) -> f89_0_loop_LE(x16:0:0 + 1) :|: x16:0:0 > 39
f131_0_loop_LE(x10:0:0) -> f89_0_loop_LE(x10:0:0) :|: x10:0:0 < 30 && x10:0:0 < 11

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

(16)
Obligation:

Termination digraph:
Nodes:
(1) f131_0_loop_LE(x4) -> f131_0_loop_LE(x4) :|: TRUE && x4 <= 39 && x4 >= 29

Arcs:
(1) -> (1)

This digraph is fully evaluated!

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

(18)
Obligation:
Rules:
f131_0_loop_LE(x4:0) -> f131_0_loop_LE(x4:0) :|: x4:0 > 28 && x4:0 < 40

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(19) FilterProof (EQUIVALENT)
Used the following sort dictionary for filtering: 
f131_0_loop_LE(INTEGER)
Replaced non-predefined constructor symbols by 0.
----------------------------------------

(20)
Obligation:
Rules:
f131_0_loop_LE(x4:0) -> f131_0_loop_LE(x4:0) :|: x4:0 > 28 && x4:0 < 40

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

(21) IntTRSPeriodicNontermProof (COMPLETE)
Normalized system to the following form:
f(pc, x4:0) -> f(1, x4:0) :|: pc = 1 && (x4:0 > 28 && x4:0 < 40)
Witness term starting non-terminating reduction: f(1, 32)
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(22)
NO