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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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, 210 ms]
(4) AND
    (5) IRSwT
        (6) IntTRSCompressionProof [EQUIVALENT, 0 ms]
        (7) IRSwT
        (8) TempFilterProof [SOUND, 42 ms]
        (9) IntTRS
        (10) PolynomialOrderProcessor [EQUIVALENT, 15 ms]
        (11) YES
    (12) IRSwT
        (13) IntTRSCompressionProof [EQUIVALENT, 0 ms]
        (14) IRSwT
        (15) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms]
        (16) IRSwT
        (17) FilterProof [EQUIVALENT, 0 ms]
        (18) IntTRS
        (19) IntTRSPeriodicNontermProof [COMPLETE, 5 ms]
        (20) NO
    (21) IRSwT
        (22) IntTRSCompressionProof [EQUIVALENT, 0 ms]
        (23) IRSwT
        (24) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms]
        (25) IRSwT
        (26) FilterProof [EQUIVALENT, 0 ms]
        (27) IntTRS
        (28) IntTRSPeriodicNontermProof [COMPLETE, 0 ms]
        (29) NO


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(0)
Obligation:
Rules:
f1_0_main_New(arg1, arg2, arg3, arg4) -> f909_0_main_GE(arg1P, arg2P, arg3P, arg4P) :|: arg2 = arg4P && 1 = arg3P && 1 <= arg2P - 1 && 0 <= arg1P - 1 && 0 <= arg1 - 1 && arg2P - 1 <= arg1 && -1 <= arg2 - 1 && arg1P <= arg1
f909_0_main_GE(x, x1, x2, x3) -> f1058_0_size_NULL(x4, x5, x6, x7) :|: -1 <= x4 - 1 && 0 <= x1 - 1 && x3 <= x2 && 0 <= x - 1
f1058_0_size_NULL(x8, x9, x10, x11) -> f1097_0_outputList_NULL(x12, x13, x14, x15) :|: -1 <= x12 - 1 && -1 <= x8 - 1
f1058_0_size_NULL(x16, x17, x18, x19) -> f1058_0_size_NULL(x20, x21, x22, x23) :|: -1 <= x20 - 1 && 0 <= x16 - 1
f1097_0_outputList_NULL(x24, x25, x26, x27) -> f1097_0_outputList_NULL(x28, x29, x30, x31) :|: -1 <= x28 - 1 && 0 <= x24 - 1
f909_0_main_GE(x32, x33, x34, x35) -> f909_0_main_GE(x36, x37, x38, x39) :|: x35 = x39 && x34 + 4 = x38 && 6 <= x37 - 1 && 0 <= x36 - 1 && 0 <= x33 - 1 && 0 <= x32 - 1 && x36 <= x33 && x36 <= x32 && -1 <= x35 - 1 && x34 + 1 <= x35 - 1 && x34 + 2 <= x35 - 1
__init(x40, x41, x42, x43) -> f1_0_main_New(x44, x45, x46, x47) :|: 0 <= 0
Start term: __init(arg1, arg2, arg3, arg4)

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

(1) IRSFormatTransformerProof (EQUIVALENT)
Reformatted IRS to match normalized format (transformed away non-linear left-hand sides, !=, / and %).
----------------------------------------

(2)
Obligation:
Rules:
f1_0_main_New(arg1, arg2, arg3, arg4) -> f909_0_main_GE(arg1P, arg2P, arg3P, arg4P) :|: arg2 = arg4P && 1 = arg3P && 1 <= arg2P - 1 && 0 <= arg1P - 1 && 0 <= arg1 - 1 && arg2P - 1 <= arg1 && -1 <= arg2 - 1 && arg1P <= arg1
f909_0_main_GE(x, x1, x2, x3) -> f1058_0_size_NULL(x4, x5, x6, x7) :|: -1 <= x4 - 1 && 0 <= x1 - 1 && x3 <= x2 && 0 <= x - 1
f1058_0_size_NULL(x8, x9, x10, x11) -> f1097_0_outputList_NULL(x12, x13, x14, x15) :|: -1 <= x12 - 1 && -1 <= x8 - 1
f1058_0_size_NULL(x16, x17, x18, x19) -> f1058_0_size_NULL(x20, x21, x22, x23) :|: -1 <= x20 - 1 && 0 <= x16 - 1
f1097_0_outputList_NULL(x24, x25, x26, x27) -> f1097_0_outputList_NULL(x28, x29, x30, x31) :|: -1 <= x28 - 1 && 0 <= x24 - 1
f909_0_main_GE(x32, x33, x34, x35) -> f909_0_main_GE(x36, x37, x38, x39) :|: x35 = x39 && x34 + 4 = x38 && 6 <= x37 - 1 && 0 <= x36 - 1 && 0 <= x33 - 1 && 0 <= x32 - 1 && x36 <= x33 && x36 <= x32 && -1 <= x35 - 1 && x34 + 1 <= x35 - 1 && x34 + 2 <= x35 - 1
__init(x40, x41, x42, x43) -> f1_0_main_New(x44, x45, x46, x47) :|: 0 <= 0
Start term: __init(arg1, arg2, arg3, arg4)

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

(3) IRSwTTerminationDigraphProof (EQUIVALENT)
Constructed termination digraph!
Nodes:
(1) f1_0_main_New(arg1, arg2, arg3, arg4) -> f909_0_main_GE(arg1P, arg2P, arg3P, arg4P) :|: arg2 = arg4P && 1 = arg3P && 1 <= arg2P - 1 && 0 <= arg1P - 1 && 0 <= arg1 - 1 && arg2P - 1 <= arg1 && -1 <= arg2 - 1 && arg1P <= arg1
(2) f909_0_main_GE(x, x1, x2, x3) -> f1058_0_size_NULL(x4, x5, x6, x7) :|: -1 <= x4 - 1 && 0 <= x1 - 1 && x3 <= x2 && 0 <= x - 1
(3) f1058_0_size_NULL(x8, x9, x10, x11) -> f1097_0_outputList_NULL(x12, x13, x14, x15) :|: -1 <= x12 - 1 && -1 <= x8 - 1
(4) f1058_0_size_NULL(x16, x17, x18, x19) -> f1058_0_size_NULL(x20, x21, x22, x23) :|: -1 <= x20 - 1 && 0 <= x16 - 1
(5) f1097_0_outputList_NULL(x24, x25, x26, x27) -> f1097_0_outputList_NULL(x28, x29, x30, x31) :|: -1 <= x28 - 1 && 0 <= x24 - 1
(6) f909_0_main_GE(x32, x33, x34, x35) -> f909_0_main_GE(x36, x37, x38, x39) :|: x35 = x39 && x34 + 4 = x38 && 6 <= x37 - 1 && 0 <= x36 - 1 && 0 <= x33 - 1 && 0 <= x32 - 1 && x36 <= x33 && x36 <= x32 && -1 <= x35 - 1 && x34 + 1 <= x35 - 1 && x34 + 2 <= x35 - 1
(7) __init(x40, x41, x42, x43) -> f1_0_main_New(x44, x45, x46, x47) :|: 0 <= 0

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

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

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(5)
Obligation:

Termination digraph:
Nodes:
(1) f909_0_main_GE(x32, x33, x34, x35) -> f909_0_main_GE(x36, x37, x38, x39) :|: x35 = x39 && x34 + 4 = x38 && 6 <= x37 - 1 && 0 <= x36 - 1 && 0 <= x33 - 1 && 0 <= x32 - 1 && x36 <= x33 && x36 <= x32 && -1 <= x35 - 1 && x34 + 1 <= x35 - 1 && x34 + 2 <= x35 - 1

Arcs:
(1) -> (1)

This digraph is fully evaluated!

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

(7)
Obligation:
Rules:
f909_0_main_GE(x32:0, x33:0, x34:0, x35:0) -> f909_0_main_GE(x36:0, x37:0, x34:0 + 4, x35:0) :|: x35:0 - 1 >= x34:0 + 1 && x35:0 - 1 >= x34:0 + 2 && x35:0 > -1 && x36:0 <= x32:0 && x36:0 <= x33:0 && x32:0 > 0 && x33:0 > 0 && x37:0 > 6 && x36:0 > 0

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(8) TempFilterProof (SOUND)
Used the following sort dictionary for filtering: 
f909_0_main_GE(INTEGER, INTEGER, INTEGER, INTEGER)
Replaced non-predefined constructor symbols by 0.
----------------------------------------

(9)
Obligation:
Rules:
f909_0_main_GE(x32:0, x33:0, x34:0, x35:0) -> f909_0_main_GE(x36:0, x37:0, c, x35:0) :|: c = x34:0 + 4 && (x35:0 - 1 >= x34:0 + 1 && x35:0 - 1 >= x34:0 + 2 && x35:0 > -1 && x36:0 <= x32:0 && x36:0 <= x33:0 && x32:0 > 0 && x33:0 > 0 && x37:0 > 6 && x36:0 > 0)

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(10) PolynomialOrderProcessor (EQUIVALENT)
Found the following polynomial interpretation:
[f909_0_main_GE(x, x1, x2, x3)] = -x2 + x3

The following rules are decreasing:
f909_0_main_GE(x32:0, x33:0, x34:0, x35:0) -> f909_0_main_GE(x36:0, x37:0, c, x35:0) :|: c = x34:0 + 4 && (x35:0 - 1 >= x34:0 + 1 && x35:0 - 1 >= x34:0 + 2 && x35:0 > -1 && x36:0 <= x32:0 && x36:0 <= x33:0 && x32:0 > 0 && x33:0 > 0 && x37:0 > 6 && x36:0 > 0)
The following rules are bounded:
f909_0_main_GE(x32:0, x33:0, x34:0, x35:0) -> f909_0_main_GE(x36:0, x37:0, c, x35:0) :|: c = x34:0 + 4 && (x35:0 - 1 >= x34:0 + 1 && x35:0 - 1 >= x34:0 + 2 && x35:0 > -1 && x36:0 <= x32:0 && x36:0 <= x33:0 && x32:0 > 0 && x33:0 > 0 && x37:0 > 6 && x36:0 > 0)

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(11)
YES

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(12)
Obligation:

Termination digraph:
Nodes:
(1) f1058_0_size_NULL(x16, x17, x18, x19) -> f1058_0_size_NULL(x20, x21, x22, x23) :|: -1 <= x20 - 1 && 0 <= x16 - 1

Arcs:
(1) -> (1)

This digraph is fully evaluated!

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

(14)
Obligation:
Rules:
f1058_0_size_NULL(x16:0, x17:0, x18:0, x19:0) -> f1058_0_size_NULL(x20:0, x21:0, x22:0, x23:0) :|: x20:0 > -1 && x16:0 > 0

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

   f1058_0_size_NULL(x1, x2, x3, x4) -> f1058_0_size_NULL(x1)

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

(16)
Obligation:
Rules:
f1058_0_size_NULL(x16:0) -> f1058_0_size_NULL(x20:0) :|: x20:0 > -1 && x16:0 > 0

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

(17) FilterProof (EQUIVALENT)
Used the following sort dictionary for filtering: 
f1058_0_size_NULL(INTEGER)
Replaced non-predefined constructor symbols by 0.
----------------------------------------

(18)
Obligation:
Rules:
f1058_0_size_NULL(x16:0) -> f1058_0_size_NULL(x20:0) :|: x20:0 > -1 && x16:0 > 0

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(19) IntTRSPeriodicNontermProof (COMPLETE)
Normalized system to the following form:
f(pc, x16:0) -> f(1, x20:0) :|: pc = 1 && (x20:0 > -1 && x16:0 > 0)
Witness term starting non-terminating reduction: f(1, 15)
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(20)
NO

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(21)
Obligation:

Termination digraph:
Nodes:
(1) f1097_0_outputList_NULL(x24, x25, x26, x27) -> f1097_0_outputList_NULL(x28, x29, x30, x31) :|: -1 <= x28 - 1 && 0 <= x24 - 1

Arcs:
(1) -> (1)

This digraph is fully evaluated!

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

(23)
Obligation:
Rules:
f1097_0_outputList_NULL(x24:0, x25:0, x26:0, x27:0) -> f1097_0_outputList_NULL(x28:0, x29:0, x30:0, x31:0) :|: x28:0 > -1 && x24:0 > 0

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

   f1097_0_outputList_NULL(x1, x2, x3, x4) -> f1097_0_outputList_NULL(x1)

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

(25)
Obligation:
Rules:
f1097_0_outputList_NULL(x24:0) -> f1097_0_outputList_NULL(x28:0) :|: x28:0 > -1 && x24:0 > 0

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(26) FilterProof (EQUIVALENT)
Used the following sort dictionary for filtering: 
f1097_0_outputList_NULL(INTEGER)
Replaced non-predefined constructor symbols by 0.
----------------------------------------

(27)
Obligation:
Rules:
f1097_0_outputList_NULL(x24:0) -> f1097_0_outputList_NULL(x28:0) :|: x28:0 > -1 && x24:0 > 0

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(28) IntTRSPeriodicNontermProof (COMPLETE)
Normalized system to the following form:
f(pc, x24:0) -> f(1, x28:0) :|: pc = 1 && (x28:0 > -1 && x24:0 > 0)
Witness term starting non-terminating reduction: f(1, 15)
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(29)
NO