YES
proof of prog.inttrs
# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty


Termination of the given IRSwT could be proven:

(0) IRSwT
(1) IRSFormatTransformerProof [EQUIVALENT, 0 ms]
(2) IRSwT
(3) IRSwTTerminationDigraphProof [EQUIVALENT, 462 ms]
(4) AND
    (5) IRSwT
        (6) IntTRSCompressionProof [EQUIVALENT, 0 ms]
        (7) IRSwT
        (8) TempFilterProof [SOUND, 8 ms]
        (9) IntTRS
        (10) PolynomialOrderProcessor [EQUIVALENT, 0 ms]
        (11) YES
    (12) IRSwT
        (13) IntTRSCompressionProof [EQUIVALENT, 0 ms]
        (14) IRSwT
        (15) IRSwTChainingProof [EQUIVALENT, 0 ms]
        (16) IRSwT
        (17) IRSwTTerminationDigraphProof [EQUIVALENT, 0 ms]
        (18) IRSwT
        (19) IntTRSCompressionProof [EQUIVALENT, 0 ms]
        (20) IRSwT
        (21) TempFilterProof [SOUND, 14 ms]
        (22) IntTRS
        (23) RankingReductionPairProof [EQUIVALENT, 0 ms]
        (24) YES


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(0)
Obligation:
Rules:
f1_0_main_Load(arg1, arg2, arg3, arg4, arg5, arg6) -> f593_0_main_LE(arg1P, arg2P, arg3P, arg4P, arg5P, arg6P) :|: 0 = arg6P && 0 = arg5P && 0 = arg4P && 0 = arg3P && 0 = arg2P && 0 = arg2 && 0 <= arg1P - 1 && 0 <= arg1 - 1 && arg1P <= arg1
f1_0_main_Load(x, x1, x2, x3, x4, x5) -> f593_0_main_LE(x6, x7, x8, x9, x10, x11) :|: 1 = x11 && 1 = x10 && 1 = x9 && 0 = x8 && 1 = x1 && 0 <= x6 - 1 && 0 <= x - 1 && -1 <= x7 - 1 && x6 <= x
f1_0_main_Load(x12, x13, x14, x15, x16, x17) -> f593_0_main_LE(x18, x19, x20, x21, x23, x24) :|: x13 = x24 && 2 = x23 && x13 = x21 && 0 <= x18 - 1 && 0 <= x12 - 1 && x18 <= x12 && -1 <= x19 - 1 && 1 <= x13 - 1 && -1 <= x20 - 1
f593_0_main_LE(x25, x26, x27, x28, x29, x30) -> f593_0_main_LE(x31, x32, x33, x34, x35, x36) :|: x28 = x36 && x29 = x35 && x28 = x34 && x26 - 1 = x33 && x26 - 1 = x32 && x28 = x30 && 0 <= x31 - 1 && 0 <= x25 - 1 && x31 <= x25 && 0 <= x27 - 1 && -1 <= x28 - 1 && x28 <= x29
f593_0_main_LE(x37, x38, x39, x40, x41, x42) -> f593_0_main_LE(x43, x44, x45, x46, x47, x48) :|: 0 <= x39 - 1 && -1 <= x40 - 1 && -1 <= x41 - 1 && x41 <= x40 - 1 && -1 <= x49 - 1 && x43 <= x37 && 0 <= x37 - 1 && 0 <= x43 - 1 && x40 = x42 && x38 - 1 - x49 = x44 && x38 - 1 - x49 = x45 && x40 = x46 && x41 + 1 = x47 && x40 = x48
__init(x50, x51, x52, x53, x54, x55) -> f1_0_main_Load(x56, x57, x58, x59, x60, x61) :|: 0 <= 0
Start term: __init(arg1, arg2, arg3, arg4, arg5, arg6)

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

(2)
Obligation:
Rules:
f1_0_main_Load(arg1, arg2, arg3, arg4, arg5, arg6) -> f593_0_main_LE(arg1P, arg2P, arg3P, arg4P, arg5P, arg6P) :|: 0 = arg6P && 0 = arg5P && 0 = arg4P && 0 = arg3P && 0 = arg2P && 0 = arg2 && 0 <= arg1P - 1 && 0 <= arg1 - 1 && arg1P <= arg1
f1_0_main_Load(x, x1, x2, x3, x4, x5) -> f593_0_main_LE(x6, x7, x8, x9, x10, x11) :|: 1 = x11 && 1 = x10 && 1 = x9 && 0 = x8 && 1 = x1 && 0 <= x6 - 1 && 0 <= x - 1 && -1 <= x7 - 1 && x6 <= x
f1_0_main_Load(x12, x13, x14, x15, x16, x17) -> f593_0_main_LE(x18, x19, x20, x21, x23, x24) :|: x13 = x24 && 2 = x23 && x13 = x21 && 0 <= x18 - 1 && 0 <= x12 - 1 && x18 <= x12 && -1 <= x19 - 1 && 1 <= x13 - 1 && -1 <= x20 - 1
f593_0_main_LE(x25, x26, x27, x28, x29, x30) -> f593_0_main_LE(x31, x32, x33, x34, x35, x36) :|: x28 = x36 && x29 = x35 && x28 = x34 && x26 - 1 = x33 && x26 - 1 = x32 && x28 = x30 && 0 <= x31 - 1 && 0 <= x25 - 1 && x31 <= x25 && 0 <= x27 - 1 && -1 <= x28 - 1 && x28 <= x29
f593_0_main_LE(x37, x38, x39, x40, x41, x42) -> f593_0_main_LE(x43, x44, x45, x46, x47, x48) :|: 0 <= x39 - 1 && -1 <= x40 - 1 && -1 <= x41 - 1 && x41 <= x40 - 1 && -1 <= x49 - 1 && x43 <= x37 && 0 <= x37 - 1 && 0 <= x43 - 1 && x40 = x42 && x38 - 1 - x49 = x44 && x38 - 1 - x49 = x45 && x40 = x46 && x41 + 1 = x47 && x40 = x48
__init(x50, x51, x52, x53, x54, x55) -> f1_0_main_Load(x56, x57, x58, x59, x60, x61) :|: 0 <= 0
Start term: __init(arg1, arg2, arg3, arg4, arg5, arg6)

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(3) IRSwTTerminationDigraphProof (EQUIVALENT)
Constructed termination digraph!
Nodes:
(1) f1_0_main_Load(arg1, arg2, arg3, arg4, arg5, arg6) -> f593_0_main_LE(arg1P, arg2P, arg3P, arg4P, arg5P, arg6P) :|: 0 = arg6P && 0 = arg5P && 0 = arg4P && 0 = arg3P && 0 = arg2P && 0 = arg2 && 0 <= arg1P - 1 && 0 <= arg1 - 1 && arg1P <= arg1
(2) f1_0_main_Load(x, x1, x2, x3, x4, x5) -> f593_0_main_LE(x6, x7, x8, x9, x10, x11) :|: 1 = x11 && 1 = x10 && 1 = x9 && 0 = x8 && 1 = x1 && 0 <= x6 - 1 && 0 <= x - 1 && -1 <= x7 - 1 && x6 <= x
(3) f1_0_main_Load(x12, x13, x14, x15, x16, x17) -> f593_0_main_LE(x18, x19, x20, x21, x23, x24) :|: x13 = x24 && 2 = x23 && x13 = x21 && 0 <= x18 - 1 && 0 <= x12 - 1 && x18 <= x12 && -1 <= x19 - 1 && 1 <= x13 - 1 && -1 <= x20 - 1
(4) f593_0_main_LE(x25, x26, x27, x28, x29, x30) -> f593_0_main_LE(x31, x32, x33, x34, x35, x36) :|: x28 = x36 && x29 = x35 && x28 = x34 && x26 - 1 = x33 && x26 - 1 = x32 && x28 = x30 && 0 <= x31 - 1 && 0 <= x25 - 1 && x31 <= x25 && 0 <= x27 - 1 && -1 <= x28 - 1 && x28 <= x29
(5) f593_0_main_LE(x37, x38, x39, x40, x41, x42) -> f593_0_main_LE(x43, x44, x45, x46, x47, x48) :|: 0 <= x39 - 1 && -1 <= x40 - 1 && -1 <= x41 - 1 && x41 <= x40 - 1 && -1 <= x49 - 1 && x43 <= x37 && 0 <= x37 - 1 && 0 <= x43 - 1 && x40 = x42 && x38 - 1 - x49 = x44 && x38 - 1 - x49 = x45 && x40 = x46 && x41 + 1 = x47 && x40 = x48
(6) __init(x50, x51, x52, x53, x54, x55) -> f1_0_main_Load(x56, x57, x58, x59, x60, x61) :|: 0 <= 0

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

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

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(5)
Obligation:

Termination digraph:
Nodes:
(1) f593_0_main_LE(x37, x38, x39, x40, x41, x42) -> f593_0_main_LE(x43, x44, x45, x46, x47, x48) :|: 0 <= x39 - 1 && -1 <= x40 - 1 && -1 <= x41 - 1 && x41 <= x40 - 1 && -1 <= x49 - 1 && x43 <= x37 && 0 <= x37 - 1 && 0 <= x43 - 1 && x40 = x42 && x38 - 1 - x49 = x44 && x38 - 1 - x49 = x45 && x40 = x46 && x41 + 1 = x47 && x40 = x48

Arcs:
(1) -> (1)

This digraph is fully evaluated!

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(6) IntTRSCompressionProof (EQUIVALENT)
Compressed rules.
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(7)
Obligation:
Rules:
f593_0_main_LE(x37:0, x38:0, x39:0, x40:0, x41:0, x40:0) -> f593_0_main_LE(x43:0, x38:0 - 1 - x49:0, x38:0 - 1 - x49:0, x40:0, x41:0 + 1, x40:0) :|: x37:0 > 0 && x43:0 > 0 && x43:0 <= x37:0 && x49:0 > -1 && x41:0 <= x40:0 - 1 && x41:0 > -1 && x40:0 > -1 && x39:0 > 0

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(8) TempFilterProof (SOUND)
Used the following sort dictionary for filtering: 
f593_0_main_LE(INTEGER, VARIABLE, INTEGER, INTEGER, INTEGER, INTEGER)
Replaced non-predefined constructor symbols by 0.
----------------------------------------

(9)
Obligation:
Rules:
f593_0_main_LE(x37:0, x38:0, x39:0, x40:0, x41:0, x40:0) -> f593_0_main_LE(x43:0, c, c1, x40:0, c2, x40:0) :|: c2 = x41:0 + 1 && (c1 = x38:0 - 1 - x49:0 && c = x38:0 - 1 - x49:0) && (x37:0 > 0 && x43:0 > 0 && x43:0 <= x37:0 && x49:0 > -1 && x41:0 <= x40:0 - 1 && x41:0 > -1 && x40:0 > -1 && x39:0 > 0)

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(10) PolynomialOrderProcessor (EQUIVALENT)
Found the following polynomial interpretation:
[f593_0_main_LE(x, x1, x2, x3, x4, x5)] = -x4 + x5

The following rules are decreasing:
f593_0_main_LE(x37:0, x38:0, x39:0, x40:0, x41:0, x40:0) -> f593_0_main_LE(x43:0, c, c1, x40:0, c2, x40:0) :|: c2 = x41:0 + 1 && (c1 = x38:0 - 1 - x49:0 && c = x38:0 - 1 - x49:0) && (x37:0 > 0 && x43:0 > 0 && x43:0 <= x37:0 && x49:0 > -1 && x41:0 <= x40:0 - 1 && x41:0 > -1 && x40:0 > -1 && x39:0 > 0)
The following rules are bounded:
f593_0_main_LE(x37:0, x38:0, x39:0, x40:0, x41:0, x40:0) -> f593_0_main_LE(x43:0, c, c1, x40:0, c2, x40:0) :|: c2 = x41:0 + 1 && (c1 = x38:0 - 1 - x49:0 && c = x38:0 - 1 - x49:0) && (x37:0 > 0 && x43:0 > 0 && x43:0 <= x37:0 && x49:0 > -1 && x41:0 <= x40:0 - 1 && x41:0 > -1 && x40:0 > -1 && x39:0 > 0)

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(11)
YES

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(12)
Obligation:

Termination digraph:
Nodes:
(1) f593_0_main_LE(x25, x26, x27, x28, x29, x30) -> f593_0_main_LE(x31, x32, x33, x34, x35, x36) :|: x28 = x36 && x29 = x35 && x28 = x34 && x26 - 1 = x33 && x26 - 1 = x32 && x28 = x30 && 0 <= x31 - 1 && 0 <= x25 - 1 && x31 <= x25 && 0 <= x27 - 1 && -1 <= x28 - 1 && x28 <= x29

Arcs:
(1) -> (1)

This digraph is fully evaluated!

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(13) IntTRSCompressionProof (EQUIVALENT)
Compressed rules.
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(14)
Obligation:
Rules:
f593_0_main_LE(x25:0, x26:0, x27:0, x28:0, x29:0, x28:0) -> f593_0_main_LE(x31:0, x26:0 - 1, x26:0 - 1, x28:0, x29:0, x28:0) :|: x28:0 > -1 && x29:0 >= x28:0 && x27:0 > 0 && x31:0 <= x25:0 && x31:0 > 0 && x25:0 > 0

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(15) IRSwTChainingProof (EQUIVALENT)
Chaining!
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(16)
Obligation:
Rules:
f593_0_main_LE(x, x1, x2, x3, x4, x3) -> f593_0_main_LE(x11, x1 + -2, x1 + -2, x3, x4, x3) :|: TRUE && x3 >= 0 && x4 + -1 * x3 >= 0 && x2 >= 1 && x5 + -1 * x <= 0 && x5 >= 1 && x >= 1 && x1 >= 2 && x11 + -1 * x5 <= 0 && x11 >= 1

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(17) IRSwTTerminationDigraphProof (EQUIVALENT)
Constructed termination digraph!
Nodes:
(1) f593_0_main_LE(x, x1, x2, x3, x4, x3) -> f593_0_main_LE(x11, x1 + -2, x1 + -2, x3, x4, x3) :|: TRUE && x3 >= 0 && x4 + -1 * x3 >= 0 && x2 >= 1 && x5 + -1 * x <= 0 && x5 >= 1 && x >= 1 && x1 >= 2 && x11 + -1 * x5 <= 0 && x11 >= 1

Arcs:
(1) -> (1)

This digraph is fully evaluated!
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(18)
Obligation:

Termination digraph:
Nodes:
(1) f593_0_main_LE(x, x1, x2, x3, x4, x3) -> f593_0_main_LE(x11, x1 + -2, x1 + -2, x3, x4, x3) :|: TRUE && x3 >= 0 && x4 + -1 * x3 >= 0 && x2 >= 1 && x5 + -1 * x <= 0 && x5 >= 1 && x >= 1 && x1 >= 2 && x11 + -1 * x5 <= 0 && x11 >= 1

Arcs:
(1) -> (1)

This digraph is fully evaluated!

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

(20)
Obligation:
Rules:
f593_0_main_LE(x:0, x1:0, x2:0, x3:0, x4:0, x3:0) -> f593_0_main_LE(x11:0, x1:0 - 2, x1:0 - 2, x3:0, x4:0, x3:0) :|: x11:0 + -1 * x5:0 <= 0 && x11:0 > 0 && x1:0 > 1 && x:0 > 0 && x5:0 > 0 && x5:0 + -1 * x:0 <= 0 && x2:0 > 0 && x3:0 > -1 && x4:0 + -1 * x3:0 >= 0

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(21) TempFilterProof (SOUND)
Used the following sort dictionary for filtering: 
f593_0_main_LE(INTEGER, INTEGER, INTEGER, INTEGER, INTEGER, INTEGER)
Replaced non-predefined constructor symbols by 0.
----------------------------------------

(22)
Obligation:
Rules:
f593_0_main_LE(x:0, x1:0, x2:0, x3:0, x4:0, x3:0) -> f593_0_main_LE(x11:0, c, c1, x3:0, x4:0, x3:0) :|: c1 = x1:0 - 2 && c = x1:0 - 2 && (x11:0 + -1 * x5:0 <= 0 && x11:0 > 0 && x1:0 > 1 && x:0 > 0 && x5:0 > 0 && x5:0 + -1 * x:0 <= 0 && x2:0 > 0 && x3:0 > -1 && x4:0 + -1 * x3:0 >= 0)

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(23) RankingReductionPairProof (EQUIVALENT)
Interpretation:
[ f593_0_main_LE ] = 1/2*f593_0_main_LE_2

The following rules are decreasing:
f593_0_main_LE(x:0, x1:0, x2:0, x3:0, x4:0, x3:0) -> f593_0_main_LE(x11:0, c, c1, x3:0, x4:0, x3:0) :|: c1 = x1:0 - 2 && c = x1:0 - 2 && (x11:0 + -1 * x5:0 <= 0 && x11:0 > 0 && x1:0 > 1 && x:0 > 0 && x5:0 > 0 && x5:0 + -1 * x:0 <= 0 && x2:0 > 0 && x3:0 > -1 && x4:0 + -1 * x3:0 >= 0)

The following rules are bounded:
f593_0_main_LE(x:0, x1:0, x2:0, x3:0, x4:0, x3:0) -> f593_0_main_LE(x11:0, c, c1, x3:0, x4:0, x3:0) :|: c1 = x1:0 - 2 && c = x1:0 - 2 && (x11:0 + -1 * x5:0 <= 0 && x11:0 > 0 && x1:0 > 1 && x:0 > 0 && x5:0 > 0 && x5:0 + -1 * x:0 <= 0 && x2:0 > 0 && x3:0 > -1 && x4:0 + -1 * x3:0 >= 0)


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(24)
YES