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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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, 732 ms]
(4) AND
    (5) IRSwT
        (6) IntTRSCompressionProof [EQUIVALENT, 0 ms]
        (7) IRSwT
        (8) TempFilterProof [SOUND, 18 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, 15 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, arg7) -> f671_0_main_LT(arg1P, arg2P, arg3P, arg4P, arg5P, arg6P, arg7P) :|: 0 = arg7P && 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, x6) -> f671_0_main_LT(x7, x8, x9, x10, x11, x12, x13) :|: 1 = x13 && 1 = x12 && 1 = x11 && 0 = x10 && 0 = x9 && 1 = x1 && 0 <= x7 - 1 && 0 <= x - 1 && -1 <= x8 - 1 && x7 <= x
f1_0_main_Load(x15, x16, x17, x18, x19, x20, x21) -> f671_0_main_LT(x22, x23, x24, x25, x26, x28, x29) :|: 2 = x29 && 2 = x28 && 2 = x26 && 0 = x24 && 2 = x16 && 0 <= x22 - 1 && 0 <= x15 - 1 && x22 <= x15 && -1 <= x25 - 1 && -1 <= x23 - 1
f1_0_main_Load(x30, x31, x32, x33, x34, x35, x36) -> f671_0_main_LT(x37, x38, x39, x40, x41, x42, x43) :|: -1 <= x38 - 1 && 2 <= x31 - 1 && -1 <= x44 - 1 && -1 <= x39 - 1 && x37 <= x30 && 0 <= x30 - 1 && 0 <= x37 - 1 && x44 - x39 = x40 && x31 = x41 && 3 = x42 && x31 = x43
f671_0_main_LT(x45, x46, x47, x48, x49, x50, x51) -> f671_0_main_LT(x52, x53, x54, x55, x56, x57, x58) :|: x49 = x58 && x50 = x57 && x49 = x56 && 10 - (x46 + 1) = x55 && x46 + 1 = x54 && x46 + 1 = x53 && x49 = x51 && x46 = x47 && 0 <= x52 - 1 && 0 <= x45 - 1 && x52 <= x45 && -1 <= x49 - 1 && x49 <= x50 && -1 <= x46 - 1 && 0 <= x48 - 1
f671_0_main_LT(x59, x60, x61, x62, x63, x64, x65) -> f671_0_main_LT(x66, x67, x68, x69, x70, x71, x72) :|: -1 <= x63 - 1 && 0 <= x62 - 1 && -1 <= x64 - 1 && x64 <= x63 - 1 && -1 <= x73 - 1 && -1 <= x60 - 1 && 0 <= x60 + 1 + x73 && x66 <= x59 && 0 <= x59 - 1 && 0 <= x66 - 1 && x60 = x61 && x63 = x65 && x60 + 1 + x73 = x67 && x60 + 1 + x73 = x68 && 10 - (x60 + 1 + x73) = x69 && x63 = x70 && x64 + 1 = x71 && x63 = x72
__init(x74, x75, x76, x77, x78, x79, x80) -> f1_0_main_Load(x81, x82, x83, x84, x85, x86, x87) :|: 0 <= 0
Start term: __init(arg1, arg2, arg3, arg4, arg5, arg6, arg7)

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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, arg7) -> f671_0_main_LT(arg1P, arg2P, arg3P, arg4P, arg5P, arg6P, arg7P) :|: 0 = arg7P && 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, x6) -> f671_0_main_LT(x7, x8, x9, x10, x11, x12, x13) :|: 1 = x13 && 1 = x12 && 1 = x11 && 0 = x10 && 0 = x9 && 1 = x1 && 0 <= x7 - 1 && 0 <= x - 1 && -1 <= x8 - 1 && x7 <= x
f1_0_main_Load(x15, x16, x17, x18, x19, x20, x21) -> f671_0_main_LT(x22, x23, x24, x25, x26, x28, x29) :|: 2 = x29 && 2 = x28 && 2 = x26 && 0 = x24 && 2 = x16 && 0 <= x22 - 1 && 0 <= x15 - 1 && x22 <= x15 && -1 <= x25 - 1 && -1 <= x23 - 1
f1_0_main_Load(x30, x31, x32, x33, x34, x35, x36) -> f671_0_main_LT(x37, x38, x39, x40, x41, x42, x43) :|: -1 <= x38 - 1 && 2 <= x31 - 1 && -1 <= x44 - 1 && -1 <= x39 - 1 && x37 <= x30 && 0 <= x30 - 1 && 0 <= x37 - 1 && x44 - x39 = x40 && x31 = x41 && 3 = x42 && x31 = x43
f671_0_main_LT(x45, x46, x47, x48, x49, x50, x51) -> f671_0_main_LT(x52, x53, x54, x55, x56, x57, x58) :|: x49 = x58 && x50 = x57 && x49 = x56 && 10 - (x46 + 1) = x55 && x46 + 1 = x54 && x46 + 1 = x53 && x49 = x51 && x46 = x47 && 0 <= x52 - 1 && 0 <= x45 - 1 && x52 <= x45 && -1 <= x49 - 1 && x49 <= x50 && -1 <= x46 - 1 && 0 <= x48 - 1
f671_0_main_LT(x59, x60, x61, x62, x63, x64, x65) -> f671_0_main_LT(x66, x67, x68, x69, x70, x71, x72) :|: -1 <= x63 - 1 && 0 <= x62 - 1 && -1 <= x64 - 1 && x64 <= x63 - 1 && -1 <= x73 - 1 && -1 <= x60 - 1 && 0 <= x60 + 1 + x73 && x66 <= x59 && 0 <= x59 - 1 && 0 <= x66 - 1 && x60 = x61 && x63 = x65 && x60 + 1 + x73 = x67 && x60 + 1 + x73 = x68 && 10 - (x60 + 1 + x73) = x69 && x63 = x70 && x64 + 1 = x71 && x63 = x72
__init(x74, x75, x76, x77, x78, x79, x80) -> f1_0_main_Load(x81, x82, x83, x84, x85, x86, x87) :|: 0 <= 0
Start term: __init(arg1, arg2, arg3, arg4, arg5, arg6, arg7)

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(3) IRSwTTerminationDigraphProof (EQUIVALENT)
Constructed termination digraph!
Nodes:
(1) f1_0_main_Load(arg1, arg2, arg3, arg4, arg5, arg6, arg7) -> f671_0_main_LT(arg1P, arg2P, arg3P, arg4P, arg5P, arg6P, arg7P) :|: 0 = arg7P && 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, x6) -> f671_0_main_LT(x7, x8, x9, x10, x11, x12, x13) :|: 1 = x13 && 1 = x12 && 1 = x11 && 0 = x10 && 0 = x9 && 1 = x1 && 0 <= x7 - 1 && 0 <= x - 1 && -1 <= x8 - 1 && x7 <= x
(3) f1_0_main_Load(x15, x16, x17, x18, x19, x20, x21) -> f671_0_main_LT(x22, x23, x24, x25, x26, x28, x29) :|: 2 = x29 && 2 = x28 && 2 = x26 && 0 = x24 && 2 = x16 && 0 <= x22 - 1 && 0 <= x15 - 1 && x22 <= x15 && -1 <= x25 - 1 && -1 <= x23 - 1
(4) f1_0_main_Load(x30, x31, x32, x33, x34, x35, x36) -> f671_0_main_LT(x37, x38, x39, x40, x41, x42, x43) :|: -1 <= x38 - 1 && 2 <= x31 - 1 && -1 <= x44 - 1 && -1 <= x39 - 1 && x37 <= x30 && 0 <= x30 - 1 && 0 <= x37 - 1 && x44 - x39 = x40 && x31 = x41 && 3 = x42 && x31 = x43
(5) f671_0_main_LT(x45, x46, x47, x48, x49, x50, x51) -> f671_0_main_LT(x52, x53, x54, x55, x56, x57, x58) :|: x49 = x58 && x50 = x57 && x49 = x56 && 10 - (x46 + 1) = x55 && x46 + 1 = x54 && x46 + 1 = x53 && x49 = x51 && x46 = x47 && 0 <= x52 - 1 && 0 <= x45 - 1 && x52 <= x45 && -1 <= x49 - 1 && x49 <= x50 && -1 <= x46 - 1 && 0 <= x48 - 1
(6) f671_0_main_LT(x59, x60, x61, x62, x63, x64, x65) -> f671_0_main_LT(x66, x67, x68, x69, x70, x71, x72) :|: -1 <= x63 - 1 && 0 <= x62 - 1 && -1 <= x64 - 1 && x64 <= x63 - 1 && -1 <= x73 - 1 && -1 <= x60 - 1 && 0 <= x60 + 1 + x73 && x66 <= x59 && 0 <= x59 - 1 && 0 <= x66 - 1 && x60 = x61 && x63 = x65 && x60 + 1 + x73 = x67 && x60 + 1 + x73 = x68 && 10 - (x60 + 1 + x73) = x69 && x63 = x70 && x64 + 1 = x71 && x63 = x72
(7) __init(x74, x75, x76, x77, x78, x79, x80) -> f1_0_main_Load(x81, x82, x83, x84, x85, x86, x87) :|: 0 <= 0

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

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

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(5)
Obligation:

Termination digraph:
Nodes:
(1) f671_0_main_LT(x59, x60, x61, x62, x63, x64, x65) -> f671_0_main_LT(x66, x67, x68, x69, x70, x71, x72) :|: -1 <= x63 - 1 && 0 <= x62 - 1 && -1 <= x64 - 1 && x64 <= x63 - 1 && -1 <= x73 - 1 && -1 <= x60 - 1 && 0 <= x60 + 1 + x73 && x66 <= x59 && 0 <= x59 - 1 && 0 <= x66 - 1 && x60 = x61 && x63 = x65 && x60 + 1 + x73 = x67 && x60 + 1 + x73 = x68 && 10 - (x60 + 1 + x73) = x69 && x63 = x70 && x64 + 1 = x71 && x63 = x72

Arcs:
(1) -> (1)

This digraph is fully evaluated!

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

(7)
Obligation:
Rules:
f671_0_main_LT(x59:0, x60:0, x60:0, x62:0, x63:0, x64:0, x63:0) -> f671_0_main_LT(x66:0, x60:0 + 1 + x73:0, x60:0 + 1 + x73:0, 10 - (x60:0 + 1 + x73:0), x63:0, x64:0 + 1, x63:0) :|: x59:0 > 0 && x66:0 > 0 && x66:0 <= x59:0 && x60:0 + 1 + x73:0 >= 0 && x60:0 > -1 && x73:0 > -1 && x64:0 <= x63:0 - 1 && x64:0 > -1 && x62:0 > 0 && x63:0 > -1

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(8) TempFilterProof (SOUND)
Used the following sort dictionary for filtering: 
f671_0_main_LT(INTEGER, INTEGER, INTEGER, INTEGER, INTEGER, INTEGER, INTEGER)
Replaced non-predefined constructor symbols by 0.
----------------------------------------

(9)
Obligation:
Rules:
f671_0_main_LT(x59:0, x60:0, x60:0, x62:0, x63:0, x64:0, x63:0) -> f671_0_main_LT(x66:0, c, c1, c2, x63:0, c3, x63:0) :|: c3 = x64:0 + 1 && (c2 = 10 - (x60:0 + 1 + x73:0) && (c1 = x60:0 + 1 + x73:0 && c = x60:0 + 1 + x73:0)) && (x59:0 > 0 && x66:0 > 0 && x66:0 <= x59:0 && x60:0 + 1 + x73:0 >= 0 && x60:0 > -1 && x73:0 > -1 && x64:0 <= x63:0 - 1 && x64:0 > -1 && x62:0 > 0 && x63:0 > -1)

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(10) PolynomialOrderProcessor (EQUIVALENT)
Found the following polynomial interpretation:
[f671_0_main_LT(x, x1, x2, x3, x4, x5, x6)] = x4 - x5

The following rules are decreasing:
f671_0_main_LT(x59:0, x60:0, x60:0, x62:0, x63:0, x64:0, x63:0) -> f671_0_main_LT(x66:0, c, c1, c2, x63:0, c3, x63:0) :|: c3 = x64:0 + 1 && (c2 = 10 - (x60:0 + 1 + x73:0) && (c1 = x60:0 + 1 + x73:0 && c = x60:0 + 1 + x73:0)) && (x59:0 > 0 && x66:0 > 0 && x66:0 <= x59:0 && x60:0 + 1 + x73:0 >= 0 && x60:0 > -1 && x73:0 > -1 && x64:0 <= x63:0 - 1 && x64:0 > -1 && x62:0 > 0 && x63:0 > -1)
The following rules are bounded:
f671_0_main_LT(x59:0, x60:0, x60:0, x62:0, x63:0, x64:0, x63:0) -> f671_0_main_LT(x66:0, c, c1, c2, x63:0, c3, x63:0) :|: c3 = x64:0 + 1 && (c2 = 10 - (x60:0 + 1 + x73:0) && (c1 = x60:0 + 1 + x73:0 && c = x60:0 + 1 + x73:0)) && (x59:0 > 0 && x66:0 > 0 && x66:0 <= x59:0 && x60:0 + 1 + x73:0 >= 0 && x60:0 > -1 && x73:0 > -1 && x64:0 <= x63:0 - 1 && x64:0 > -1 && x62:0 > 0 && x63:0 > -1)

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(11)
YES

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(12)
Obligation:

Termination digraph:
Nodes:
(1) f671_0_main_LT(x45, x46, x47, x48, x49, x50, x51) -> f671_0_main_LT(x52, x53, x54, x55, x56, x57, x58) :|: x49 = x58 && x50 = x57 && x49 = x56 && 10 - (x46 + 1) = x55 && x46 + 1 = x54 && x46 + 1 = x53 && x49 = x51 && x46 = x47 && 0 <= x52 - 1 && 0 <= x45 - 1 && x52 <= x45 && -1 <= x49 - 1 && x49 <= x50 && -1 <= x46 - 1 && 0 <= x48 - 1

Arcs:
(1) -> (1)

This digraph is fully evaluated!

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

(14)
Obligation:
Rules:
f671_0_main_LT(x45:0, x46:0, x46:0, x48:0, x49:0, x50:0, x49:0) -> f671_0_main_LT(x52:0, x46:0 + 1, x46:0 + 1, 10 - (x46:0 + 1), x49:0, x50:0, x49:0) :|: x46:0 > -1 && x48:0 > 0 && x50:0 >= x49:0 && x49:0 > -1 && x52:0 <= x45:0 && x52:0 > 0 && x45:0 > 0

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(15) IRSwTChainingProof (EQUIVALENT)
Chaining!
----------------------------------------

(16)
Obligation:
Rules:
f671_0_main_LT(x, x1, x1, x2, x3, x4, x3) -> f671_0_main_LT(x11, x1 + 2, x1 + 2, 8 + -1 * x1, x3, x4, x3) :|: TRUE && x1 >= 0 && x2 >= 1 && x4 + -1 * x3 >= 0 && x3 >= 0 && x5 + -1 * x <= 0 && x5 >= 1 && x >= 1 && -1 * x1 >= -8 && x11 + -1 * x5 <= 0 && x11 >= 1

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(17) IRSwTTerminationDigraphProof (EQUIVALENT)
Constructed termination digraph!
Nodes:
(1) f671_0_main_LT(x, x1, x1, x2, x3, x4, x3) -> f671_0_main_LT(x11, x1 + 2, x1 + 2, 8 + -1 * x1, x3, x4, x3) :|: TRUE && x1 >= 0 && x2 >= 1 && x4 + -1 * x3 >= 0 && x3 >= 0 && x5 + -1 * x <= 0 && x5 >= 1 && x >= 1 && -1 * x1 >= -8 && x11 + -1 * x5 <= 0 && x11 >= 1

Arcs:
(1) -> (1)

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

(18)
Obligation:

Termination digraph:
Nodes:
(1) f671_0_main_LT(x, x1, x1, x2, x3, x4, x3) -> f671_0_main_LT(x11, x1 + 2, x1 + 2, 8 + -1 * x1, x3, x4, x3) :|: TRUE && x1 >= 0 && x2 >= 1 && x4 + -1 * x3 >= 0 && x3 >= 0 && x5 + -1 * x <= 0 && x5 >= 1 && x >= 1 && -1 * x1 >= -8 && 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:
f671_0_main_LT(x:0, x1:0, x1:0, x2:0, x3:0, x4:0, x3:0) -> f671_0_main_LT(x11:0, x1:0 + 2, x1:0 + 2, 8 + -1 * x1:0, x3:0, x4:0, x3:0) :|: x11:0 + -1 * x5:0 <= 0 && x11:0 > 0 && -8 <= -1 * x1:0 && x:0 > 0 && x5:0 > 0 && x5:0 + -1 * x:0 <= 0 && x3:0 > -1 && x4:0 + -1 * x3:0 >= 0 && x1:0 > -1 && x2:0 > 0

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(21) TempFilterProof (SOUND)
Used the following sort dictionary for filtering: 
f671_0_main_LT(INTEGER, INTEGER, INTEGER, INTEGER, INTEGER, INTEGER, INTEGER)
Replaced non-predefined constructor symbols by 0.
----------------------------------------

(22)
Obligation:
Rules:
f671_0_main_LT(x:0, x1:0, x1:0, x2:0, x3:0, x4:0, x3:0) -> f671_0_main_LT(x11:0, c, c1, c2, x3:0, x4:0, x3:0) :|: c2 = 8 + -1 * x1:0 && (c1 = x1:0 + 2 && c = x1:0 + 2) && (x11:0 + -1 * x5:0 <= 0 && x11:0 > 0 && -8 <= -1 * x1:0 && x:0 > 0 && x5:0 > 0 && x5:0 + -1 * x:0 <= 0 && x3:0 > -1 && x4:0 + -1 * x3:0 >= 0 && x1:0 > -1 && x2:0 > 0)

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(23) RankingReductionPairProof (EQUIVALENT)
Interpretation:
[ f671_0_main_LT ] = -1/2*f671_0_main_LT_3

The following rules are decreasing:
f671_0_main_LT(x:0, x1:0, x1:0, x2:0, x3:0, x4:0, x3:0) -> f671_0_main_LT(x11:0, c, c1, c2, x3:0, x4:0, x3:0) :|: c2 = 8 + -1 * x1:0 && (c1 = x1:0 + 2 && c = x1:0 + 2) && (x11:0 + -1 * x5:0 <= 0 && x11:0 > 0 && -8 <= -1 * x1:0 && x:0 > 0 && x5:0 > 0 && x5:0 + -1 * x:0 <= 0 && x3:0 > -1 && x4:0 + -1 * x3:0 >= 0 && x1:0 > -1 && x2:0 > 0)

The following rules are bounded:
f671_0_main_LT(x:0, x1:0, x1:0, x2:0, x3:0, x4:0, x3:0) -> f671_0_main_LT(x11:0, c, c1, c2, x3:0, x4:0, x3:0) :|: c2 = 8 + -1 * x1:0 && (c1 = x1:0 + 2 && c = x1:0 + 2) && (x11:0 + -1 * x5:0 <= 0 && x11:0 > 0 && -8 <= -1 * x1:0 && x:0 > 0 && x5:0 > 0 && x5:0 + -1 * x:0 <= 0 && x3:0 > -1 && x4:0 + -1 * x3:0 >= 0 && x1:0 > -1 && x2:0 > 0)


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(24)
YES