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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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, 1517 ms]
(4) AND
    (5) IRSwT
        (6) IntTRSCompressionProof [EQUIVALENT, 25 ms]
        (7) IRSwT
        (8) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms]
        (9) IRSwT
        (10) TempFilterProof [SOUND, 32 ms]
        (11) IntTRS
        (12) RankingReductionPairProof [EQUIVALENT, 18 ms]
        (13) YES
    (14) IRSwT
        (15) IntTRSCompressionProof [EQUIVALENT, 13 ms]
        (16) IRSwT
        (17) FilterProof [EQUIVALENT, 0 ms]
        (18) IntTRS
        (19) IntTRSCompressionProof [EQUIVALENT, 0 ms]
        (20) IntTRS
        (21) RankingReductionPairProof [EQUIVALENT, 10 ms]
        (22) YES


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

(0)
Obligation:
Rules:
f1_0_main_Load(arg1, arg2, arg3, arg4, arg5, arg6, arg7) -> f234_0_slide88_FieldAccess(arg1P, arg2P, arg3P, arg4P, arg5P, arg6P, arg7P) :|: -1 <= x4 - 1 && 1 <= arg2 - 1 && -1 <= arg1P - 1 && arg2P <= x5 - 1 && -1 <= x5 - 1 && 0 <= arg1 - 1
f1_0_main_Load(x, x1, x2, x3, x6, x7, x8) -> f234_0_slide88_FieldAccess(x9, x11, x12, x13, x14, x15, x16) :|: -1 <= x17 - 1 && 1 <= x1 - 1 && x11 <= 0 && -1 <= x9 - 1 && 0 <= x - 1
f234_0_slide88_FieldAccess(x18, x19, x20, x21, x22, x23, x24) -> f292_0_slide88_EQ(x25, x26, x27, x28, x29, x30, x31) :|: x19 = x31 && x19 = x30 && 0 = x29 && x19 = x28 && x19 = x27 && 0 = x26 && x18 = x25 && 0 <= x19 - 1
f292_0_slide88_EQ(x32, x33, x34, x35, x36, x37, x38) -> f292_0_slide88_EQ'(x39, x42, x43, x44, x45, x46, x47) :|: 0 <= x55 - 1 && 0 <= x35 - 1 && 0 <= x36 - 1 && -1 <= x37 - 1 && x37 <= x33 - 1 && x37 <= x56 - 1 && x37 <= x34 - 1 && x38 <= x55 - 1 && -1 <= x38 - 1 && x38 <= x36 - 1 && x57 <= x35 - 1 && x38 <= x35 - 1 && x32 - 2 * x58 = 0 && x59 <= x55 - 1 && 0 <= x56 - 1 && 0 <= x33 - 1 && x60 <= x32 && x61 <= x36 - 1 && x32 = x39 && x33 = x42 && x34 = x43 && x35 = x44 && x36 = x45 && x37 = x46 && x38 = x47
f292_0_slide88_EQ'(x62, x63, x64, x65, x66, x70, x71) -> f292_0_slide88_EQ(x72, x73, x74, x75, x76, x82, x83) :|: 0 <= x84 - 1 && 0 <= x65 - 1 && 0 <= x66 - 1 && -1 <= x70 - 1 && x70 <= x63 - 1 && x70 <= x85 - 1 && x70 <= x64 - 1 && x71 <= x84 - 1 && -1 <= x71 - 1 && x71 <= x66 - 1 && x75 <= x65 - 1 && x71 <= x65 - 1 && x62 - 2 * x86 = 0 && x83 <= x84 - 1 && 0 <= x85 - 1 && 0 <= x63 - 1 && x76 <= x66 - 1 && x72 <= x62 && 0 <= x62 - 2 * x86 && x62 - 2 * x86 <= 1 && x62 - 2 * x72 <= 1 && 0 <= x62 - 2 * x72 && x64 = x74 && x63 = x82
f292_0_slide88_EQ(x87, x88, x89, x90, x91, x92, x95) -> f292_0_slide88_EQ'(x96, x97, x98, x99, x100, x101, x102) :|: -1 <= x92 - 1 && 0 <= x89 - 1 && x92 <= x88 - 1 && x92 <= x103 - 1 && x92 <= x89 - 1 && x95 <= x103 - 1 && -1 <= x95 - 1 && x95 <= x91 - 1 && x95 <= x89 - 1 && x87 - 2 * x104 = 0 && x105 <= x89 - 1 && x106 <= x103 - 1 && -1 <= x103 - 1 && x107 <= x87 && x89 = x90 && x87 = x96 && x88 = x97 && x89 = x98 && x89 = x99 && x91 = x100 && x92 = x101 && x95 = x102
f292_0_slide88_EQ'(x108, x109, x110, x111, x112, x113, x114) -> f292_0_slide88_EQ(x115, x116, x117, x118, x119, x120, x121) :|: -1 <= x113 - 1 && 0 <= x110 - 1 && x113 <= x109 - 1 && x113 <= x122 - 1 && x113 <= x110 - 1 && x114 <= x122 - 1 && -1 <= x114 - 1 && x114 <= x112 - 1 && x114 <= x110 - 1 && x108 - 2 * x123 = 0 && x118 <= x110 - 1 && x119 <= x122 - 1 && x115 <= x108 && -1 <= x122 - 1 && 0 <= x108 - 2 * x123 && x108 - 2 * x123 <= 1 && x108 - 2 * x115 <= 1 && 0 <= x108 - 2 * x115 && x110 = x111 && 1 = x116 && 0 = x120 && x119 = x121
f1_0_main_Load(x124, x125, x126, x127, x128, x129, x130) -> f196_0_create_LE(x131, x132, x133, x134, x135, x136, x137) :|: -1 <= x138 - 1 && 1 <= x125 - 1 && -1 <= x139 - 1 && 0 <= x124 - 1 && x139 - 1 = x131
f196_0_create_LE(x140, x141, x142, x143, x144, x145, x146) -> f196_0_create_LE(x147, x148, x149, x150, x151, x152, x153) :|: x140 - 1 = x147 && 0 <= x140 - 1
__init(x154, x155, x156, x157, x158, x159, x160) -> f1_0_main_Load(x161, x162, x163, x164, x165, x166, x167) :|: 0 <= 0
Start term: __init(arg1, arg2, arg3, arg4, arg5, arg6, arg7)

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

(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) -> f234_0_slide88_FieldAccess(arg1P, arg2P, arg3P, arg4P, arg5P, arg6P, arg7P) :|: -1 <= x4 - 1 && 1 <= arg2 - 1 && -1 <= arg1P - 1 && arg2P <= x5 - 1 && -1 <= x5 - 1 && 0 <= arg1 - 1
f1_0_main_Load(x, x1, x2, x3, x6, x7, x8) -> f234_0_slide88_FieldAccess(x9, x11, x12, x13, x14, x15, x16) :|: -1 <= x17 - 1 && 1 <= x1 - 1 && x11 <= 0 && -1 <= x9 - 1 && 0 <= x - 1
f234_0_slide88_FieldAccess(x18, x19, x20, x21, x22, x23, x24) -> f292_0_slide88_EQ(x25, x26, x27, x28, x29, x30, x31) :|: x19 = x31 && x19 = x30 && 0 = x29 && x19 = x28 && x19 = x27 && 0 = x26 && x18 = x25 && 0 <= x19 - 1
f292_0_slide88_EQ(x32, x33, x34, x35, x36, x37, x38) -> f292_0_slide88_EQ'(x39, x42, x43, x44, x45, x46, x47) :|: 0 <= x55 - 1 && 0 <= x35 - 1 && 0 <= x36 - 1 && -1 <= x37 - 1 && x37 <= x33 - 1 && x37 <= x56 - 1 && x37 <= x34 - 1 && x38 <= x55 - 1 && -1 <= x38 - 1 && x38 <= x36 - 1 && x57 <= x35 - 1 && x38 <= x35 - 1 && x32 - 2 * x58 = 0 && x59 <= x55 - 1 && 0 <= x56 - 1 && 0 <= x33 - 1 && x60 <= x32 && x61 <= x36 - 1 && x32 = x39 && x33 = x42 && x34 = x43 && x35 = x44 && x36 = x45 && x37 = x46 && x38 = x47
f292_0_slide88_EQ'(x62, x63, x64, x65, x66, x70, x71) -> f292_0_slide88_EQ(x72, x73, x74, x75, x76, x82, x83) :|: 0 <= x84 - 1 && 0 <= x65 - 1 && 0 <= x66 - 1 && -1 <= x70 - 1 && x70 <= x63 - 1 && x70 <= x85 - 1 && x70 <= x64 - 1 && x71 <= x84 - 1 && -1 <= x71 - 1 && x71 <= x66 - 1 && x75 <= x65 - 1 && x71 <= x65 - 1 && x62 - 2 * x86 = 0 && x83 <= x84 - 1 && 0 <= x85 - 1 && 0 <= x63 - 1 && x76 <= x66 - 1 && x72 <= x62 && 0 <= x62 - 2 * x86 && x62 - 2 * x86 <= 1 && x62 - 2 * x72 <= 1 && 0 <= x62 - 2 * x72 && x64 = x74 && x63 = x82
f292_0_slide88_EQ(x87, x88, x89, x90, x91, x92, x95) -> f292_0_slide88_EQ'(x96, x97, x98, x99, x100, x101, x102) :|: -1 <= x92 - 1 && 0 <= x89 - 1 && x92 <= x88 - 1 && x92 <= x103 - 1 && x92 <= x89 - 1 && x95 <= x103 - 1 && -1 <= x95 - 1 && x95 <= x91 - 1 && x95 <= x89 - 1 && x87 - 2 * x104 = 0 && x105 <= x89 - 1 && x106 <= x103 - 1 && -1 <= x103 - 1 && x107 <= x87 && x89 = x90 && x87 = x96 && x88 = x97 && x89 = x98 && x89 = x99 && x91 = x100 && x92 = x101 && x95 = x102
f292_0_slide88_EQ'(x108, x109, x110, x111, x112, x113, x114) -> f292_0_slide88_EQ(x115, x116, x117, x118, x119, x120, x121) :|: -1 <= x113 - 1 && 0 <= x110 - 1 && x113 <= x109 - 1 && x113 <= x122 - 1 && x113 <= x110 - 1 && x114 <= x122 - 1 && -1 <= x114 - 1 && x114 <= x112 - 1 && x114 <= x110 - 1 && x108 - 2 * x123 = 0 && x118 <= x110 - 1 && x119 <= x122 - 1 && x115 <= x108 && -1 <= x122 - 1 && 0 <= x108 - 2 * x123 && x108 - 2 * x123 <= 1 && x108 - 2 * x115 <= 1 && 0 <= x108 - 2 * x115 && x110 = x111 && 1 = x116 && 0 = x120 && x119 = x121
f1_0_main_Load(x124, x125, x126, x127, x128, x129, x130) -> f196_0_create_LE(x131, x132, x133, x134, x135, x136, x137) :|: -1 <= x138 - 1 && 1 <= x125 - 1 && -1 <= x139 - 1 && 0 <= x124 - 1 && x139 - 1 = x131
f196_0_create_LE(x140, x141, x142, x143, x144, x145, x146) -> f196_0_create_LE(x147, x148, x149, x150, x151, x152, x153) :|: x140 - 1 = x147 && 0 <= x140 - 1
__init(x154, x155, x156, x157, x158, x159, x160) -> f1_0_main_Load(x161, x162, x163, x164, x165, x166, x167) :|: 0 <= 0
Start term: __init(arg1, arg2, arg3, arg4, arg5, arg6, arg7)

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

(3) IRSwTTerminationDigraphProof (EQUIVALENT)
Constructed termination digraph!
Nodes:
(1) f1_0_main_Load(arg1, arg2, arg3, arg4, arg5, arg6, arg7) -> f234_0_slide88_FieldAccess(arg1P, arg2P, arg3P, arg4P, arg5P, arg6P, arg7P) :|: -1 <= x4 - 1 && 1 <= arg2 - 1 && -1 <= arg1P - 1 && arg2P <= x5 - 1 && -1 <= x5 - 1 && 0 <= arg1 - 1
(2) f1_0_main_Load(x, x1, x2, x3, x6, x7, x8) -> f234_0_slide88_FieldAccess(x9, x11, x12, x13, x14, x15, x16) :|: -1 <= x17 - 1 && 1 <= x1 - 1 && x11 <= 0 && -1 <= x9 - 1 && 0 <= x - 1
(3) f234_0_slide88_FieldAccess(x18, x19, x20, x21, x22, x23, x24) -> f292_0_slide88_EQ(x25, x26, x27, x28, x29, x30, x31) :|: x19 = x31 && x19 = x30 && 0 = x29 && x19 = x28 && x19 = x27 && 0 = x26 && x18 = x25 && 0 <= x19 - 1
(4) f292_0_slide88_EQ(x32, x33, x34, x35, x36, x37, x38) -> f292_0_slide88_EQ'(x39, x42, x43, x44, x45, x46, x47) :|: 0 <= x55 - 1 && 0 <= x35 - 1 && 0 <= x36 - 1 && -1 <= x37 - 1 && x37 <= x33 - 1 && x37 <= x56 - 1 && x37 <= x34 - 1 && x38 <= x55 - 1 && -1 <= x38 - 1 && x38 <= x36 - 1 && x57 <= x35 - 1 && x38 <= x35 - 1 && x32 - 2 * x58 = 0 && x59 <= x55 - 1 && 0 <= x56 - 1 && 0 <= x33 - 1 && x60 <= x32 && x61 <= x36 - 1 && x32 = x39 && x33 = x42 && x34 = x43 && x35 = x44 && x36 = x45 && x37 = x46 && x38 = x47
(5) f292_0_slide88_EQ'(x62, x63, x64, x65, x66, x70, x71) -> f292_0_slide88_EQ(x72, x73, x74, x75, x76, x82, x83) :|: 0 <= x84 - 1 && 0 <= x65 - 1 && 0 <= x66 - 1 && -1 <= x70 - 1 && x70 <= x63 - 1 && x70 <= x85 - 1 && x70 <= x64 - 1 && x71 <= x84 - 1 && -1 <= x71 - 1 && x71 <= x66 - 1 && x75 <= x65 - 1 && x71 <= x65 - 1 && x62 - 2 * x86 = 0 && x83 <= x84 - 1 && 0 <= x85 - 1 && 0 <= x63 - 1 && x76 <= x66 - 1 && x72 <= x62 && 0 <= x62 - 2 * x86 && x62 - 2 * x86 <= 1 && x62 - 2 * x72 <= 1 && 0 <= x62 - 2 * x72 && x64 = x74 && x63 = x82
(6) f292_0_slide88_EQ(x87, x88, x89, x90, x91, x92, x95) -> f292_0_slide88_EQ'(x96, x97, x98, x99, x100, x101, x102) :|: -1 <= x92 - 1 && 0 <= x89 - 1 && x92 <= x88 - 1 && x92 <= x103 - 1 && x92 <= x89 - 1 && x95 <= x103 - 1 && -1 <= x95 - 1 && x95 <= x91 - 1 && x95 <= x89 - 1 && x87 - 2 * x104 = 0 && x105 <= x89 - 1 && x106 <= x103 - 1 && -1 <= x103 - 1 && x107 <= x87 && x89 = x90 && x87 = x96 && x88 = x97 && x89 = x98 && x89 = x99 && x91 = x100 && x92 = x101 && x95 = x102
(7) f292_0_slide88_EQ'(x108, x109, x110, x111, x112, x113, x114) -> f292_0_slide88_EQ(x115, x116, x117, x118, x119, x120, x121) :|: -1 <= x113 - 1 && 0 <= x110 - 1 && x113 <= x109 - 1 && x113 <= x122 - 1 && x113 <= x110 - 1 && x114 <= x122 - 1 && -1 <= x114 - 1 && x114 <= x112 - 1 && x114 <= x110 - 1 && x108 - 2 * x123 = 0 && x118 <= x110 - 1 && x119 <= x122 - 1 && x115 <= x108 && -1 <= x122 - 1 && 0 <= x108 - 2 * x123 && x108 - 2 * x123 <= 1 && x108 - 2 * x115 <= 1 && 0 <= x108 - 2 * x115 && x110 = x111 && 1 = x116 && 0 = x120 && x119 = x121
(8) f1_0_main_Load(x124, x125, x126, x127, x128, x129, x130) -> f196_0_create_LE(x131, x132, x133, x134, x135, x136, x137) :|: -1 <= x138 - 1 && 1 <= x125 - 1 && -1 <= x139 - 1 && 0 <= x124 - 1 && x139 - 1 = x131
(9) f196_0_create_LE(x140, x141, x142, x143, x144, x145, x146) -> f196_0_create_LE(x147, x148, x149, x150, x151, x152, x153) :|: x140 - 1 = x147 && 0 <= x140 - 1
(10) __init(x154, x155, x156, x157, x158, x159, x160) -> f1_0_main_Load(x161, x162, x163, x164, x165, x166, x167) :|: 0 <= 0

Arcs:
(1) -> (3)
(4) -> (5), (7)
(5) -> (4), (6)
(6) -> (5), (7)
(8) -> (9)
(9) -> (9)
(10) -> (1), (2), (8)

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

(4)
Complex Obligation (AND)

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

(5)
Obligation:

Termination digraph:
Nodes:
(1) f196_0_create_LE(x140, x141, x142, x143, x144, x145, x146) -> f196_0_create_LE(x147, x148, x149, x150, x151, x152, x153) :|: x140 - 1 = x147 && 0 <= x140 - 1

Arcs:
(1) -> (1)

This digraph is fully evaluated!

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

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

(7)
Obligation:
Rules:
f196_0_create_LE(x140:0, x141:0, x142:0, x143:0, x144:0, x145:0, x146:0) -> f196_0_create_LE(x140:0 - 1, x148:0, x149:0, x150:0, x151:0, x152:0, x153:0) :|: x140:0 > 0

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

   f196_0_create_LE(x1, x2, x3, x4, x5, x6, x7) -> f196_0_create_LE(x1)

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

(9)
Obligation:
Rules:
f196_0_create_LE(x140:0) -> f196_0_create_LE(x140:0 - 1) :|: x140:0 > 0

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(10) TempFilterProof (SOUND)
Used the following sort dictionary for filtering: 
f196_0_create_LE(INTEGER)
Replaced non-predefined constructor symbols by 0.
----------------------------------------

(11)
Obligation:
Rules:
f196_0_create_LE(x140:0) -> f196_0_create_LE(c) :|: c = x140:0 - 1 && x140:0 > 0

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

(12) RankingReductionPairProof (EQUIVALENT)
Interpretation:
[ f196_0_create_LE ] = f196_0_create_LE_1

The following rules are decreasing:
f196_0_create_LE(x140:0) -> f196_0_create_LE(c) :|: c = x140:0 - 1 && x140:0 > 0

The following rules are bounded:
f196_0_create_LE(x140:0) -> f196_0_create_LE(c) :|: c = x140:0 - 1 && x140:0 > 0


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

(13)
YES

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

(14)
Obligation:

Termination digraph:
Nodes:
(1) f292_0_slide88_EQ(x32, x33, x34, x35, x36, x37, x38) -> f292_0_slide88_EQ'(x39, x42, x43, x44, x45, x46, x47) :|: 0 <= x55 - 1 && 0 <= x35 - 1 && 0 <= x36 - 1 && -1 <= x37 - 1 && x37 <= x33 - 1 && x37 <= x56 - 1 && x37 <= x34 - 1 && x38 <= x55 - 1 && -1 <= x38 - 1 && x38 <= x36 - 1 && x57 <= x35 - 1 && x38 <= x35 - 1 && x32 - 2 * x58 = 0 && x59 <= x55 - 1 && 0 <= x56 - 1 && 0 <= x33 - 1 && x60 <= x32 && x61 <= x36 - 1 && x32 = x39 && x33 = x42 && x34 = x43 && x35 = x44 && x36 = x45 && x37 = x46 && x38 = x47
(2) f292_0_slide88_EQ'(x62, x63, x64, x65, x66, x70, x71) -> f292_0_slide88_EQ(x72, x73, x74, x75, x76, x82, x83) :|: 0 <= x84 - 1 && 0 <= x65 - 1 && 0 <= x66 - 1 && -1 <= x70 - 1 && x70 <= x63 - 1 && x70 <= x85 - 1 && x70 <= x64 - 1 && x71 <= x84 - 1 && -1 <= x71 - 1 && x71 <= x66 - 1 && x75 <= x65 - 1 && x71 <= x65 - 1 && x62 - 2 * x86 = 0 && x83 <= x84 - 1 && 0 <= x85 - 1 && 0 <= x63 - 1 && x76 <= x66 - 1 && x72 <= x62 && 0 <= x62 - 2 * x86 && x62 - 2 * x86 <= 1 && x62 - 2 * x72 <= 1 && 0 <= x62 - 2 * x72 && x64 = x74 && x63 = x82
(3) f292_0_slide88_EQ(x87, x88, x89, x90, x91, x92, x95) -> f292_0_slide88_EQ'(x96, x97, x98, x99, x100, x101, x102) :|: -1 <= x92 - 1 && 0 <= x89 - 1 && x92 <= x88 - 1 && x92 <= x103 - 1 && x92 <= x89 - 1 && x95 <= x103 - 1 && -1 <= x95 - 1 && x95 <= x91 - 1 && x95 <= x89 - 1 && x87 - 2 * x104 = 0 && x105 <= x89 - 1 && x106 <= x103 - 1 && -1 <= x103 - 1 && x107 <= x87 && x89 = x90 && x87 = x96 && x88 = x97 && x89 = x98 && x89 = x99 && x91 = x100 && x92 = x101 && x95 = x102

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

This digraph is fully evaluated!

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

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

(16)
Obligation:
Rules:
f292_0_slide88_EQ(x32:0, x33:0, x34:0, x35:0, x36:0, x37:0, x38:0) -> f292_0_slide88_EQ(x72:0, x73:0, x34:0, x75:0, x76:0, x33:0, x83:0) :|: x32:0 - 2 * x72:0 <= 1 && x32:0 - 2 * x72:0 >= 0 && x32:0 - 2 * x86:0 <= 1 && x32:0 - 2 * x86:0 >= 0 && x72:0 <= x32:0 && x61:0 <= x36:0 - 1 && x76:0 <= x36:0 - 1 && x60:0 <= x32:0 && x33:0 > 0 && x85:0 > 0 && x56:0 > 0 && x84:0 - 1 >= x83:0 && x59:0 <= x55:0 - 1 && x32:0 - 2 * x86:0 = 0 && x32:0 - 2 * x58:0 = 0 && x38:0 <= x35:0 - 1 && x75:0 <= x35:0 - 1 && x57:0 <= x35:0 - 1 && x38:0 <= x36:0 - 1 && x38:0 > -1 && x84:0 - 1 >= x38:0 && x55:0 - 1 >= x38:0 && x37:0 <= x34:0 - 1 && x85:0 - 1 >= x37:0 && x56:0 - 1 >= x37:0 && x37:0 <= x33:0 - 1 && x37:0 > -1 && x36:0 > 0 && x84:0 > 0 && x35:0 > 0 && x55:0 > 0
f292_0_slide88_EQ(x, x1, x2, x2, x3, x4, x5) -> f292_0_slide88_EQ(x6, x7, x2, x8, x9, x1, x10) :|: x - 2 * x6 <= 1 && x - 2 * x6 >= 0 && x - 2 * x11 <= 1 && x - 2 * x11 >= 0 && x >= x6 && x9 <= x3 - 1 && x >= x12 && x1 > 0 && x13 > -1 && x14 > 0 && x15 <= x13 - 1 && x16 - 1 >= x10 && x2 - 1 >= x17 && x - 2 * x11 = 0 && x - 2 * x18 = 0 && x2 - 1 >= x5 && x8 <= x2 - 1 && x5 <= x3 - 1 && x5 > -1 && x13 - 1 >= x5 && x16 - 1 >= x5 && x2 - 1 >= x4 && x13 - 1 >= x4 && x14 - 1 >= x4 && x1 - 1 >= x4 && x4 > -1 && x3 > 0 && x2 > 0 && x16 > 0

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

(17) FilterProof (EQUIVALENT)
Used the following sort dictionary for filtering: 
f292_0_slide88_EQ(INTEGER, VARIABLE, INTEGER, INTEGER, INTEGER, INTEGER, INTEGER)
Replaced non-predefined constructor symbols by 0.
----------------------------------------

(18)
Obligation:
Rules:
f292_0_slide88_EQ(x32:0, x33:0, x34:0, x35:0, x36:0, x37:0, x38:0) -> f292_0_slide88_EQ(x72:0, x73:0, x34:0, x75:0, x76:0, x33:0, x83:0) :|: x32:0 - 2 * x72:0 <= 1 && x32:0 - 2 * x72:0 >= 0 && x32:0 - 2 * x86:0 <= 1 && x32:0 - 2 * x86:0 >= 0 && x72:0 <= x32:0 && x61:0 <= x36:0 - 1 && x76:0 <= x36:0 - 1 && x60:0 <= x32:0 && x33:0 > 0 && x85:0 > 0 && x56:0 > 0 && x84:0 - 1 >= x83:0 && x59:0 <= x55:0 - 1 && x32:0 - 2 * x86:0 = 0 && x32:0 - 2 * x58:0 = 0 && x38:0 <= x35:0 - 1 && x75:0 <= x35:0 - 1 && x57:0 <= x35:0 - 1 && x38:0 <= x36:0 - 1 && x38:0 > -1 && x84:0 - 1 >= x38:0 && x55:0 - 1 >= x38:0 && x37:0 <= x34:0 - 1 && x85:0 - 1 >= x37:0 && x56:0 - 1 >= x37:0 && x37:0 <= x33:0 - 1 && x37:0 > -1 && x36:0 > 0 && x84:0 > 0 && x35:0 > 0 && x55:0 > 0
f292_0_slide88_EQ(x, x1, x2, x2, x3, x4, x5) -> f292_0_slide88_EQ(x6, x7, x2, x8, x9, x1, x10) :|: x - 2 * x6 <= 1 && x - 2 * x6 >= 0 && x - 2 * x11 <= 1 && x - 2 * x11 >= 0 && x >= x6 && x9 <= x3 - 1 && x >= x12 && x1 > 0 && x13 > -1 && x14 > 0 && x15 <= x13 - 1 && x16 - 1 >= x10 && x2 - 1 >= x17 && x - 2 * x11 = 0 && x - 2 * x18 = 0 && x2 - 1 >= x5 && x8 <= x2 - 1 && x5 <= x3 - 1 && x5 > -1 && x13 - 1 >= x5 && x16 - 1 >= x5 && x2 - 1 >= x4 && x13 - 1 >= x4 && x14 - 1 >= x4 && x1 - 1 >= x4 && x4 > -1 && x3 > 0 && x2 > 0 && x16 > 0

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(19) IntTRSCompressionProof (EQUIVALENT)
Compressed rules.
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(20)
Obligation:
Rules:
f292_0_slide88_EQ(x32:0:0, x33:0:0, x34:0:0, x35:0:0, x36:0:0, x37:0:0, x38:0:0) -> f292_0_slide88_EQ(x72:0:0, x73:0:0, x34:0:0, x75:0:0, x76:0:0, x33:0:0, x83:0:0) :|: x35:0:0 > 0 && x55:0:0 > 0 && x84:0:0 > 0 && x36:0:0 > 0 && x37:0:0 > -1 && x37:0:0 <= x33:0:0 - 1 && x56:0:0 - 1 >= x37:0:0 && x85:0:0 - 1 >= x37:0:0 && x37:0:0 <= x34:0:0 - 1 && x55:0:0 - 1 >= x38:0:0 && x84:0:0 - 1 >= x38:0:0 && x38:0:0 > -1 && x38:0:0 <= x36:0:0 - 1 && x57:0:0 <= x35:0:0 - 1 && x75:0:0 <= x35:0:0 - 1 && x38:0:0 <= x35:0:0 - 1 && x32:0:0 - 2 * x58:0:0 = 0 && x32:0:0 - 2 * x86:0:0 = 0 && x59:0:0 <= x55:0:0 - 1 && x84:0:0 - 1 >= x83:0:0 && x56:0:0 > 0 && x85:0:0 > 0 && x33:0:0 > 0 && x60:0:0 <= x32:0:0 && x76:0:0 <= x36:0:0 - 1 && x61:0:0 <= x36:0:0 - 1 && x72:0:0 <= x32:0:0 && x32:0:0 - 2 * x86:0:0 >= 0 && x32:0:0 - 2 * x86:0:0 <= 1 && x32:0:0 - 2 * x72:0:0 >= 0 && x32:0:0 - 2 * x72:0:0 <= 1
f292_0_slide88_EQ(x:0, x1:0, x2:0, x2:01, x3:0, x4:0, x5:0) -> f292_0_slide88_EQ(x6:0, x7:0, x2:0, x8:0, x9:0, x1:0, x10:0) :|: x2:0 > 0 && x16:0 > 0 && x3:0 > 0 && x4:0 > -1 && x4:0 <= x1:0 - 1 && x4:0 <= x14:0 - 1 && x4:0 <= x13:0 - 1 && x4:0 <= x2:0 - 1 && x5:0 <= x16:0 - 1 && x5:0 <= x13:0 - 1 && x5:0 > -1 && x5:0 <= x3:0 - 1 && x8:0 <= x2:0 - 1 && x5:0 <= x2:0 - 1 && x:0 - 2 * x18:0 = 0 && x:0 - 2 * x11:0 = 0 && x2:0 - 1 >= x17:0 && x16:0 - 1 >= x10:0 && x15:0 <= x13:0 - 1 && x14:0 > 0 && x13:0 > -1 && x1:0 > 0 && x:0 >= x12:0 && x9:0 <= x3:0 - 1 && x:0 >= x6:0 && x:0 - 2 * x11:0 >= 0 && x:0 - 2 * x11:0 <= 1 && x:0 - 2 * x6:0 >= 0 && x:0 - 2 * x6:0 <= 1 && x2:0 = x2:01

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(21) RankingReductionPairProof (EQUIVALENT)
Interpretation:
[ f292_0_slide88_EQ ] = f292_0_slide88_EQ_5

The following rules are decreasing:
f292_0_slide88_EQ(x32:0:0, x33:0:0, x34:0:0, x35:0:0, x36:0:0, x37:0:0, x38:0:0) -> f292_0_slide88_EQ(x72:0:0, x73:0:0, x34:0:0, x75:0:0, x76:0:0, x33:0:0, x83:0:0) :|: x35:0:0 > 0 && x55:0:0 > 0 && x84:0:0 > 0 && x36:0:0 > 0 && x37:0:0 > -1 && x37:0:0 <= x33:0:0 - 1 && x56:0:0 - 1 >= x37:0:0 && x85:0:0 - 1 >= x37:0:0 && x37:0:0 <= x34:0:0 - 1 && x55:0:0 - 1 >= x38:0:0 && x84:0:0 - 1 >= x38:0:0 && x38:0:0 > -1 && x38:0:0 <= x36:0:0 - 1 && x57:0:0 <= x35:0:0 - 1 && x75:0:0 <= x35:0:0 - 1 && x38:0:0 <= x35:0:0 - 1 && x32:0:0 - 2 * x58:0:0 = 0 && x32:0:0 - 2 * x86:0:0 = 0 && x59:0:0 <= x55:0:0 - 1 && x84:0:0 - 1 >= x83:0:0 && x56:0:0 > 0 && x85:0:0 > 0 && x33:0:0 > 0 && x60:0:0 <= x32:0:0 && x76:0:0 <= x36:0:0 - 1 && x61:0:0 <= x36:0:0 - 1 && x72:0:0 <= x32:0:0 && x32:0:0 - 2 * x86:0:0 >= 0 && x32:0:0 - 2 * x86:0:0 <= 1 && x32:0:0 - 2 * x72:0:0 >= 0 && x32:0:0 - 2 * x72:0:0 <= 1
f292_0_slide88_EQ(x:0, x1:0, x2:0, x2:01, x3:0, x4:0, x5:0) -> f292_0_slide88_EQ(x6:0, x7:0, x2:0, x8:0, x9:0, x1:0, x10:0) :|: x2:0 > 0 && x16:0 > 0 && x3:0 > 0 && x4:0 > -1 && x4:0 <= x1:0 - 1 && x4:0 <= x14:0 - 1 && x4:0 <= x13:0 - 1 && x4:0 <= x2:0 - 1 && x5:0 <= x16:0 - 1 && x5:0 <= x13:0 - 1 && x5:0 > -1 && x5:0 <= x3:0 - 1 && x8:0 <= x2:0 - 1 && x5:0 <= x2:0 - 1 && x:0 - 2 * x18:0 = 0 && x:0 - 2 * x11:0 = 0 && x2:0 - 1 >= x17:0 && x16:0 - 1 >= x10:0 && x15:0 <= x13:0 - 1 && x14:0 > 0 && x13:0 > -1 && x1:0 > 0 && x:0 >= x12:0 && x9:0 <= x3:0 - 1 && x:0 >= x6:0 && x:0 - 2 * x11:0 >= 0 && x:0 - 2 * x11:0 <= 1 && x:0 - 2 * x6:0 >= 0 && x:0 - 2 * x6:0 <= 1 && x2:0 = x2:01

The following rules are bounded:
f292_0_slide88_EQ(x32:0:0, x33:0:0, x34:0:0, x35:0:0, x36:0:0, x37:0:0, x38:0:0) -> f292_0_slide88_EQ(x72:0:0, x73:0:0, x34:0:0, x75:0:0, x76:0:0, x33:0:0, x83:0:0) :|: x35:0:0 > 0 && x55:0:0 > 0 && x84:0:0 > 0 && x36:0:0 > 0 && x37:0:0 > -1 && x37:0:0 <= x33:0:0 - 1 && x56:0:0 - 1 >= x37:0:0 && x85:0:0 - 1 >= x37:0:0 && x37:0:0 <= x34:0:0 - 1 && x55:0:0 - 1 >= x38:0:0 && x84:0:0 - 1 >= x38:0:0 && x38:0:0 > -1 && x38:0:0 <= x36:0:0 - 1 && x57:0:0 <= x35:0:0 - 1 && x75:0:0 <= x35:0:0 - 1 && x38:0:0 <= x35:0:0 - 1 && x32:0:0 - 2 * x58:0:0 = 0 && x32:0:0 - 2 * x86:0:0 = 0 && x59:0:0 <= x55:0:0 - 1 && x84:0:0 - 1 >= x83:0:0 && x56:0:0 > 0 && x85:0:0 > 0 && x33:0:0 > 0 && x60:0:0 <= x32:0:0 && x76:0:0 <= x36:0:0 - 1 && x61:0:0 <= x36:0:0 - 1 && x72:0:0 <= x32:0:0 && x32:0:0 - 2 * x86:0:0 >= 0 && x32:0:0 - 2 * x86:0:0 <= 1 && x32:0:0 - 2 * x72:0:0 >= 0 && x32:0:0 - 2 * x72:0:0 <= 1
f292_0_slide88_EQ(x:0, x1:0, x2:0, x2:01, x3:0, x4:0, x5:0) -> f292_0_slide88_EQ(x6:0, x7:0, x2:0, x8:0, x9:0, x1:0, x10:0) :|: x2:0 > 0 && x16:0 > 0 && x3:0 > 0 && x4:0 > -1 && x4:0 <= x1:0 - 1 && x4:0 <= x14:0 - 1 && x4:0 <= x13:0 - 1 && x4:0 <= x2:0 - 1 && x5:0 <= x16:0 - 1 && x5:0 <= x13:0 - 1 && x5:0 > -1 && x5:0 <= x3:0 - 1 && x8:0 <= x2:0 - 1 && x5:0 <= x2:0 - 1 && x:0 - 2 * x18:0 = 0 && x:0 - 2 * x11:0 = 0 && x2:0 - 1 >= x17:0 && x16:0 - 1 >= x10:0 && x15:0 <= x13:0 - 1 && x14:0 > 0 && x13:0 > -1 && x1:0 > 0 && x:0 >= x12:0 && x9:0 <= x3:0 - 1 && x:0 >= x6:0 && x:0 - 2 * x11:0 >= 0 && x:0 - 2 * x11:0 <= 1 && x:0 - 2 * x6:0 >= 0 && x:0 - 2 * x6:0 <= 1 && x2:0 = x2:01


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(22)
YES