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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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, 1234 ms]
(4) IRSwT
(5) IntTRSCompressionProof [EQUIVALENT, 0 ms]
(6) IRSwT
(7) TempFilterProof [SOUND, 62 ms]
(8) IntTRS
(9) PolynomialOrderProcessor [EQUIVALENT, 21 ms]
(10) YES


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(0)
Obligation:
Rules:
f1_0_main_Load(arg1, arg2, arg3, arg4, arg5, arg6, arg7) -> f852_0_loop_LT(arg1P, arg2P, arg3P, arg4P, arg5P, arg6P, arg7P) :|: 0 = arg7P && 0 = arg6P && 0 = arg5P && 0 = arg4P && 0 = arg3P && 0 = arg2P && 0 = arg1P && 0 = arg2 && 0 <= arg1 - 1
f1_0_main_Load(x, x1, x2, x3, x4, x5, x6) -> f852_0_loop_LT(x7, x8, x9, x10, x11, x12, x13) :|: 1 = x13 && 1 = x12 && 0 = x11 && 0 = x10 && 0 = x9 && 0 = x7 && 1 = x1 && -1 <= x8 - 1 && 0 <= x - 1
f1_0_main_Load(x14, x15, x16, x17, x18, x19, x20) -> f852_0_loop_LT(x21, x22, x23, x24, x25, x26, x27) :|: 2 = x27 && 2 = x26 && 0 = x25 && 0 = x24 && 0 = x21 && 2 = x15 && 0 <= x14 - 1 && -1 <= x23 - 1 && -1 <= x22 - 1
f1_0_main_Load(x28, x29, x30, x31, x32, x33, x34) -> f852_0_loop_LT(x35, x36, x37, x38, x39, x40, x41) :|: 3 = x41 && x29 = x40 && x35 = x39 && x35 = x38 && 0 <= x28 - 1 && -1 <= x37 - 1 && -1 <= x35 - 1 && 2 <= x29 - 1 && -1 <= x36 - 1
f852_0_loop_LT(x42, x43, x44, x45, x46, x47, x48) -> f852_0_loop_LT(x49, x50, x51, x52, x53, x54, x55) :|: x48 = x55 && x47 = x54 && x42 = x53 && x42 = x52 && 0 = x51 && 0 = x50 && x42 = x49 && x42 = x46 && x42 = x45 && 0 <= 2 * x43 && 0 <= 2 * x43 - x44 - 1 && -1 <= x44 - 1 && x47 <= x48 && -1 <= x47 - 1 && -1 <= x42 - 1
f852_0_loop_LT(x56, x57, x58, x59, x60, x61, x62) -> f852_0_loop_LT(x63, x64, x65, x66, x67, x68, x69) :|: x62 + 1 = x69 && x61 = x68 && x56 + 2 * x64 = x67 && x56 + 2 * x64 = x66 && 0 = x65 && x56 + 2 * x64 = x63 && x56 = x60 && x56 = x59 && 2 * x64 <= 2 * x57 - x58 - 1 && 0 <= x56 + 2 * x64 && 0 <= 2 * x64 && 0 <= 2 * x57 && -1 <= x58 - 1 && x61 <= x62 + 1 && -1 <= x64 - 1 && x62 <= x61 - 1 && -1 <= x62 - 1 && -1 <= x61 - 1 && -1 <= x56 - 1
f852_0_loop_LT(x70, x71, x72, x73, x74, x75, x76) -> f852_0_loop_LT(x77, x78, x79, x80, x81, x82, x83) :|: x76 + 2 = x83 && x75 = x82 && x70 + 2 * x78 - x79 = x81 && x70 + 2 * x78 - x79 = x80 && x70 + 2 * x78 - x79 = x77 && x70 = x74 && x70 = x73 && x76 + 2 <= x75 && 0 <= x70 + 2 * x78 && 2 * x78 - x79 <= 2 * x71 - x72 - 1 && 0 <= 2 * x78 && 0 <= 2 * x71 && -1 <= x72 - 1 && -1 <= x79 - 1 && -1 <= x78 - 1 && -1 <= x76 - 1 && -1 <= x70 - 1 && x76 + 1 <= x75 - 1 && 1 <= x75 - 1
__init(x84, x85, x86, x87, x88, x89, x90) -> f1_0_main_Load(x91, x92, x93, x94, x95, x96, x97) :|: 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 %).
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(2)
Obligation:
Rules:
f1_0_main_Load(arg1, arg2, arg3, arg4, arg5, arg6, arg7) -> f852_0_loop_LT(arg1P, arg2P, arg3P, arg4P, arg5P, arg6P, arg7P) :|: 0 = arg7P && 0 = arg6P && 0 = arg5P && 0 = arg4P && 0 = arg3P && 0 = arg2P && 0 = arg1P && 0 = arg2 && 0 <= arg1 - 1
f1_0_main_Load(x, x1, x2, x3, x4, x5, x6) -> f852_0_loop_LT(x7, x8, x9, x10, x11, x12, x13) :|: 1 = x13 && 1 = x12 && 0 = x11 && 0 = x10 && 0 = x9 && 0 = x7 && 1 = x1 && -1 <= x8 - 1 && 0 <= x - 1
f1_0_main_Load(x14, x15, x16, x17, x18, x19, x20) -> f852_0_loop_LT(x21, x22, x23, x24, x25, x26, x27) :|: 2 = x27 && 2 = x26 && 0 = x25 && 0 = x24 && 0 = x21 && 2 = x15 && 0 <= x14 - 1 && -1 <= x23 - 1 && -1 <= x22 - 1
f1_0_main_Load(x28, x29, x30, x31, x32, x33, x34) -> f852_0_loop_LT(x35, x36, x37, x38, x39, x40, x41) :|: 3 = x41 && x29 = x40 && x35 = x39 && x35 = x38 && 0 <= x28 - 1 && -1 <= x37 - 1 && -1 <= x35 - 1 && 2 <= x29 - 1 && -1 <= x36 - 1
f852_0_loop_LT(x42, x43, x44, x45, x46, x47, x48) -> f852_0_loop_LT(x49, x50, x51, x52, x53, x54, x55) :|: x48 = x55 && x47 = x54 && x42 = x53 && x42 = x52 && 0 = x51 && 0 = x50 && x42 = x49 && x42 = x46 && x42 = x45 && 0 <= 2 * x43 && 0 <= 2 * x43 - x44 - 1 && -1 <= x44 - 1 && x47 <= x48 && -1 <= x47 - 1 && -1 <= x42 - 1
f852_0_loop_LT(x56, x57, x58, x59, x60, x61, x62) -> f852_0_loop_LT(x63, x64, x65, x66, x67, x68, x69) :|: x62 + 1 = x69 && x61 = x68 && x56 + 2 * x64 = x67 && x56 + 2 * x64 = x66 && 0 = x65 && x56 + 2 * x64 = x63 && x56 = x60 && x56 = x59 && 2 * x64 <= 2 * x57 - x58 - 1 && 0 <= x56 + 2 * x64 && 0 <= 2 * x64 && 0 <= 2 * x57 && -1 <= x58 - 1 && x61 <= x62 + 1 && -1 <= x64 - 1 && x62 <= x61 - 1 && -1 <= x62 - 1 && -1 <= x61 - 1 && -1 <= x56 - 1
f852_0_loop_LT(x70, x71, x72, x73, x74, x75, x76) -> f852_0_loop_LT(x77, x78, x79, x80, x81, x82, x83) :|: x76 + 2 = x83 && x75 = x82 && x70 + 2 * x78 - x79 = x81 && x70 + 2 * x78 - x79 = x80 && x70 + 2 * x78 - x79 = x77 && x70 = x74 && x70 = x73 && x76 + 2 <= x75 && 0 <= x70 + 2 * x78 && 2 * x78 - x79 <= 2 * x71 - x72 - 1 && 0 <= 2 * x78 && 0 <= 2 * x71 && -1 <= x72 - 1 && -1 <= x79 - 1 && -1 <= x78 - 1 && -1 <= x76 - 1 && -1 <= x70 - 1 && x76 + 1 <= x75 - 1 && 1 <= x75 - 1
__init(x84, x85, x86, x87, x88, x89, x90) -> f1_0_main_Load(x91, x92, x93, x94, x95, x96, x97) :|: 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) -> f852_0_loop_LT(arg1P, arg2P, arg3P, arg4P, arg5P, arg6P, arg7P) :|: 0 = arg7P && 0 = arg6P && 0 = arg5P && 0 = arg4P && 0 = arg3P && 0 = arg2P && 0 = arg1P && 0 = arg2 && 0 <= arg1 - 1
(2) f1_0_main_Load(x, x1, x2, x3, x4, x5, x6) -> f852_0_loop_LT(x7, x8, x9, x10, x11, x12, x13) :|: 1 = x13 && 1 = x12 && 0 = x11 && 0 = x10 && 0 = x9 && 0 = x7 && 1 = x1 && -1 <= x8 - 1 && 0 <= x - 1
(3) f1_0_main_Load(x14, x15, x16, x17, x18, x19, x20) -> f852_0_loop_LT(x21, x22, x23, x24, x25, x26, x27) :|: 2 = x27 && 2 = x26 && 0 = x25 && 0 = x24 && 0 = x21 && 2 = x15 && 0 <= x14 - 1 && -1 <= x23 - 1 && -1 <= x22 - 1
(4) f1_0_main_Load(x28, x29, x30, x31, x32, x33, x34) -> f852_0_loop_LT(x35, x36, x37, x38, x39, x40, x41) :|: 3 = x41 && x29 = x40 && x35 = x39 && x35 = x38 && 0 <= x28 - 1 && -1 <= x37 - 1 && -1 <= x35 - 1 && 2 <= x29 - 1 && -1 <= x36 - 1
(5) f852_0_loop_LT(x42, x43, x44, x45, x46, x47, x48) -> f852_0_loop_LT(x49, x50, x51, x52, x53, x54, x55) :|: x48 = x55 && x47 = x54 && x42 = x53 && x42 = x52 && 0 = x51 && 0 = x50 && x42 = x49 && x42 = x46 && x42 = x45 && 0 <= 2 * x43 && 0 <= 2 * x43 - x44 - 1 && -1 <= x44 - 1 && x47 <= x48 && -1 <= x47 - 1 && -1 <= x42 - 1
(6) f852_0_loop_LT(x56, x57, x58, x59, x60, x61, x62) -> f852_0_loop_LT(x63, x64, x65, x66, x67, x68, x69) :|: x62 + 1 = x69 && x61 = x68 && x56 + 2 * x64 = x67 && x56 + 2 * x64 = x66 && 0 = x65 && x56 + 2 * x64 = x63 && x56 = x60 && x56 = x59 && 2 * x64 <= 2 * x57 - x58 - 1 && 0 <= x56 + 2 * x64 && 0 <= 2 * x64 && 0 <= 2 * x57 && -1 <= x58 - 1 && x61 <= x62 + 1 && -1 <= x64 - 1 && x62 <= x61 - 1 && -1 <= x62 - 1 && -1 <= x61 - 1 && -1 <= x56 - 1
(7) f852_0_loop_LT(x70, x71, x72, x73, x74, x75, x76) -> f852_0_loop_LT(x77, x78, x79, x80, x81, x82, x83) :|: x76 + 2 = x83 && x75 = x82 && x70 + 2 * x78 - x79 = x81 && x70 + 2 * x78 - x79 = x80 && x70 + 2 * x78 - x79 = x77 && x70 = x74 && x70 = x73 && x76 + 2 <= x75 && 0 <= x70 + 2 * x78 && 2 * x78 - x79 <= 2 * x71 - x72 - 1 && 0 <= 2 * x78 && 0 <= 2 * x71 && -1 <= x72 - 1 && -1 <= x79 - 1 && -1 <= x78 - 1 && -1 <= x76 - 1 && -1 <= x70 - 1 && x76 + 1 <= x75 - 1 && 1 <= x75 - 1
(8) __init(x84, x85, x86, x87, x88, x89, x90) -> f1_0_main_Load(x91, x92, x93, x94, x95, x96, x97) :|: 0 <= 0

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

This digraph is fully evaluated!
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(4)
Obligation:

Termination digraph:
Nodes:
(1) f852_0_loop_LT(x70, x71, x72, x73, x74, x75, x76) -> f852_0_loop_LT(x77, x78, x79, x80, x81, x82, x83) :|: x76 + 2 = x83 && x75 = x82 && x70 + 2 * x78 - x79 = x81 && x70 + 2 * x78 - x79 = x80 && x70 + 2 * x78 - x79 = x77 && x70 = x74 && x70 = x73 && x76 + 2 <= x75 && 0 <= x70 + 2 * x78 && 2 * x78 - x79 <= 2 * x71 - x72 - 1 && 0 <= 2 * x78 && 0 <= 2 * x71 && -1 <= x72 - 1 && -1 <= x79 - 1 && -1 <= x78 - 1 && -1 <= x76 - 1 && -1 <= x70 - 1 && x76 + 1 <= x75 - 1 && 1 <= x75 - 1

Arcs:
(1) -> (1)

This digraph is fully evaluated!

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(5) IntTRSCompressionProof (EQUIVALENT)
Compressed rules.
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(6)
Obligation:
Rules:
f852_0_loop_LT(x70:0, x71:0, x72:0, x70:0, x70:0, x75:0, x76:0) -> f852_0_loop_LT(x70:0 + 2 * x78:0 - x79:0, x78:0, x79:0, x70:0 + 2 * x78:0 - x79:0, x70:0 + 2 * x78:0 - x79:0, x75:0, x76:0 + 2) :|: x76:0 + 1 <= x75:0 - 1 && x75:0 > 1 && x70:0 > -1 && x76:0 > -1 && x78:0 > -1 && x79:0 > -1 && x72:0 > -1 && 2 * x71:0 >= 0 && 2 * x78:0 >= 0 && 2 * x78:0 - x79:0 <= 2 * x71:0 - x72:0 - 1 && x76:0 + 2 <= x75:0 && x70:0 + 2 * x78:0 >= 0

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(7) TempFilterProof (SOUND)
Used the following sort dictionary for filtering: 
f852_0_loop_LT(INTEGER, INTEGER, INTEGER, INTEGER, INTEGER, INTEGER, INTEGER)
Replaced non-predefined constructor symbols by 0.
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(8)
Obligation:
Rules:
f852_0_loop_LT(x70:0, x71:0, x72:0, x70:0, x70:0, x75:0, x76:0) -> f852_0_loop_LT(c, x78:0, x79:0, c1, c2, x75:0, c3) :|: c3 = x76:0 + 2 && (c2 = x70:0 + 2 * x78:0 - x79:0 && (c1 = x70:0 + 2 * x78:0 - x79:0 && c = x70:0 + 2 * x78:0 - x79:0)) && (x76:0 + 1 <= x75:0 - 1 && x75:0 > 1 && x70:0 > -1 && x76:0 > -1 && x78:0 > -1 && x79:0 > -1 && x72:0 > -1 && 2 * x71:0 >= 0 && 2 * x78:0 >= 0 && 2 * x78:0 - x79:0 <= 2 * x71:0 - x72:0 - 1 && x76:0 + 2 <= x75:0 && x70:0 + 2 * x78:0 >= 0)

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(9) PolynomialOrderProcessor (EQUIVALENT)
Found the following polynomial interpretation:
[f852_0_loop_LT(x, x1, x2, x3, x4, x5, x6)] = -1 + x5 - x6

The following rules are decreasing:
f852_0_loop_LT(x70:0, x71:0, x72:0, x70:0, x70:0, x75:0, x76:0) -> f852_0_loop_LT(c, x78:0, x79:0, c1, c2, x75:0, c3) :|: c3 = x76:0 + 2 && (c2 = x70:0 + 2 * x78:0 - x79:0 && (c1 = x70:0 + 2 * x78:0 - x79:0 && c = x70:0 + 2 * x78:0 - x79:0)) && (x76:0 + 1 <= x75:0 - 1 && x75:0 > 1 && x70:0 > -1 && x76:0 > -1 && x78:0 > -1 && x79:0 > -1 && x72:0 > -1 && 2 * x71:0 >= 0 && 2 * x78:0 >= 0 && 2 * x78:0 - x79:0 <= 2 * x71:0 - x72:0 - 1 && x76:0 + 2 <= x75:0 && x70:0 + 2 * x78:0 >= 0)
The following rules are bounded:
f852_0_loop_LT(x70:0, x71:0, x72:0, x70:0, x70:0, x75:0, x76:0) -> f852_0_loop_LT(c, x78:0, x79:0, c1, c2, x75:0, c3) :|: c3 = x76:0 + 2 && (c2 = x70:0 + 2 * x78:0 - x79:0 && (c1 = x70:0 + 2 * x78:0 - x79:0 && c = x70:0 + 2 * x78:0 - x79:0)) && (x76:0 + 1 <= x75:0 - 1 && x75:0 > 1 && x70:0 > -1 && x76:0 > -1 && x78:0 > -1 && x79:0 > -1 && x72:0 > -1 && 2 * x71:0 >= 0 && 2 * x78:0 >= 0 && 2 * x78:0 - x79:0 <= 2 * x71:0 - x72:0 - 1 && x76:0 + 2 <= x75:0 && x70:0 + 2 * x78:0 >= 0)

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(10)
YES