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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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, 1045 ms]
(4) AND
    (5) IRSwT
        (6) IntTRSCompressionProof [EQUIVALENT, 0 ms]
        (7) IRSwT
        (8) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms]
        (9) IRSwT
        (10) TempFilterProof [SOUND, 20 ms]
        (11) IntTRS
        (12) RankingReductionPairProof [EQUIVALENT, 0 ms]
        (13) YES
    (14) IRSwT
        (15) IntTRSCompressionProof [EQUIVALENT, 15 ms]
        (16) IRSwT
        (17) FilterProof [EQUIVALENT, 0 ms]
        (18) IntTRS
        (19) IntTRSCompressionProof [EQUIVALENT, 0 ms]
        (20) IntTRS
        (21) RankingReductionPairProof [EQUIVALENT, 17 ms]
        (22) YES


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

(0)
Obligation:
Rules:
f1_0_main_Load(arg1, arg2, arg3) -> f234_0_slide95_FieldAccess(arg1P, arg2P, arg3P) :|: -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) -> f234_0_slide95_FieldAccess(x3, x6, x7) :|: -1 <= x8 - 1 && 1 <= x1 - 1 && x6 <= 0 && -1 <= x3 - 1 && 0 <= x - 1
f234_0_slide95_FieldAccess(x9, x11, x12) -> f411_0_slide95_EQ(x13, x14, x15) :|: x11 = x15 && x11 = x14 && x9 = x13 && 0 <= x11 - 1
f411_0_slide95_EQ(x16, x17, x18) -> f411_0_slide95_EQ'(x19, x20, x21) :|: -1 <= x22 - 1 && 0 <= x17 - 1 && x22 <= x23 - 1 && -1 <= x18 - 1 && x22 <= x18 - 1 && x22 <= x24 - 1 && x25 <= x17 - 1 && x22 <= x25 - 1 && x22 <= x26 - 1 && x27 <= x16 && x16 - 2 * x28 = 0 && x16 = x19 && x17 = x20 && x18 = x21
f411_0_slide95_EQ'(x29, x30, x31) -> f411_0_slide95_EQ(x32, x33, x34) :|: -1 <= x35 - 1 && 0 <= x30 - 1 && x35 <= x34 - 1 && -1 <= x31 - 1 && x35 <= x31 - 1 && x35 <= x38 - 1 && x33 <= x30 - 1 && x35 <= x33 - 1 && x35 <= x46 - 1 && x29 - 2 * x47 = 0 && x32 <= x29 && 0 <= x29 - 2 * x47 && x29 - 2 * x47 <= 1 && x29 - 2 * x32 <= 1 && 0 <= x29 - 2 * x32
f411_0_slide95_EQ(x48, x49, x50) -> f411_0_slide95_EQ'(x51, x56, x57) :|: -1 <= x50 - 1 && 0 <= x49 - 1 && x58 <= x50 - 1 && x64 <= x49 - 1 && x48 - 2 * x65 = 1 && x66 <= x48 && -1 <= x64 - 1 && x67 <= x64 && 0 <= x58 - 1 && x48 = x51 && x49 = x56 && x50 = x57
f411_0_slide95_EQ'(x68, x69, x72) -> f411_0_slide95_EQ(x73, x74, x78) :|: -1 <= x72 - 1 && 0 <= x69 - 1 && x78 <= x72 - 1 && x79 <= x69 - 1 && x68 - 2 * x80 = 1 && x73 <= x68 && -1 <= x79 - 1 && 0 <= x78 - 1 && x74 <= x79 && 0 <= x68 - 2 * x80 && x68 - 2 * x80 <= 1 && x68 - 2 * x73 <= 1 && 0 <= x68 - 2 * x73
f411_0_slide95_EQ(x81, x82, x84) -> f411_0_slide95_EQ'(x85, x86, x87) :|: -1 <= x84 - 1 && 0 <= x82 - 1 && x88 <= x84 - 1 && x88 <= x82 - 1 && x81 - 2 * x89 = 1 && 0 <= x88 - 1 && x90 <= x81 && x81 = x85 && x82 = x86 && x84 = x87
f411_0_slide95_EQ'(x91, x92, x93) -> f411_0_slide95_EQ(x94, x95, x96) :|: -1 <= x93 - 1 && 0 <= x92 - 1 && x95 <= x93 - 1 && x95 <= x92 - 1 && x91 - 2 * x97 = 1 && x94 <= x91 && 0 <= x95 - 1 && 0 <= x91 - 2 * x97 && x91 - 2 * x97 <= 1 && x91 - 2 * x94 <= 1 && 0 <= x91 - 2 * x94 && x95 = x96
f1_0_main_Load(x98, x99, x100) -> f196_0_create_LE(x101, x102, x103) :|: -1 <= x104 - 1 && 1 <= x99 - 1 && -1 <= x105 - 1 && 0 <= x98 - 1 && x105 - 1 = x101
f196_0_create_LE(x106, x107, x108) -> f196_0_create_LE(x109, x110, x111) :|: x106 - 1 = x109 && 0 <= x106 - 1
__init(x112, x113, x114) -> f1_0_main_Load(x115, x116, x117) :|: 0 <= 0
Start term: __init(arg1, arg2, arg3)

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

(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) -> f234_0_slide95_FieldAccess(arg1P, arg2P, arg3P) :|: -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) -> f234_0_slide95_FieldAccess(x3, x6, x7) :|: -1 <= x8 - 1 && 1 <= x1 - 1 && x6 <= 0 && -1 <= x3 - 1 && 0 <= x - 1
f234_0_slide95_FieldAccess(x9, x11, x12) -> f411_0_slide95_EQ(x13, x14, x15) :|: x11 = x15 && x11 = x14 && x9 = x13 && 0 <= x11 - 1
f411_0_slide95_EQ(x16, x17, x18) -> f411_0_slide95_EQ'(x19, x20, x21) :|: -1 <= x22 - 1 && 0 <= x17 - 1 && x22 <= x23 - 1 && -1 <= x18 - 1 && x22 <= x18 - 1 && x22 <= x24 - 1 && x25 <= x17 - 1 && x22 <= x25 - 1 && x22 <= x26 - 1 && x27 <= x16 && x16 - 2 * x28 = 0 && x16 = x19 && x17 = x20 && x18 = x21
f411_0_slide95_EQ'(x29, x30, x31) -> f411_0_slide95_EQ(x32, x33, x34) :|: -1 <= x35 - 1 && 0 <= x30 - 1 && x35 <= x34 - 1 && -1 <= x31 - 1 && x35 <= x31 - 1 && x35 <= x38 - 1 && x33 <= x30 - 1 && x35 <= x33 - 1 && x35 <= x46 - 1 && x29 - 2 * x47 = 0 && x32 <= x29 && 0 <= x29 - 2 * x47 && x29 - 2 * x47 <= 1 && x29 - 2 * x32 <= 1 && 0 <= x29 - 2 * x32
f411_0_slide95_EQ(x48, x49, x50) -> f411_0_slide95_EQ'(x51, x56, x57) :|: -1 <= x50 - 1 && 0 <= x49 - 1 && x58 <= x50 - 1 && x64 <= x49 - 1 && x48 - 2 * x65 = 1 && x66 <= x48 && -1 <= x64 - 1 && x67 <= x64 && 0 <= x58 - 1 && x48 = x51 && x49 = x56 && x50 = x57
f411_0_slide95_EQ'(x68, x69, x72) -> f411_0_slide95_EQ(x73, x74, x78) :|: -1 <= x72 - 1 && 0 <= x69 - 1 && x78 <= x72 - 1 && x79 <= x69 - 1 && x68 - 2 * x80 = 1 && x73 <= x68 && -1 <= x79 - 1 && 0 <= x78 - 1 && x74 <= x79 && 0 <= x68 - 2 * x80 && x68 - 2 * x80 <= 1 && x68 - 2 * x73 <= 1 && 0 <= x68 - 2 * x73
f411_0_slide95_EQ(x81, x82, x84) -> f411_0_slide95_EQ'(x85, x86, x87) :|: -1 <= x84 - 1 && 0 <= x82 - 1 && x88 <= x84 - 1 && x88 <= x82 - 1 && x81 - 2 * x89 = 1 && 0 <= x88 - 1 && x90 <= x81 && x81 = x85 && x82 = x86 && x84 = x87
f411_0_slide95_EQ'(x91, x92, x93) -> f411_0_slide95_EQ(x94, x95, x96) :|: -1 <= x93 - 1 && 0 <= x92 - 1 && x95 <= x93 - 1 && x95 <= x92 - 1 && x91 - 2 * x97 = 1 && x94 <= x91 && 0 <= x95 - 1 && 0 <= x91 - 2 * x97 && x91 - 2 * x97 <= 1 && x91 - 2 * x94 <= 1 && 0 <= x91 - 2 * x94 && x95 = x96
f1_0_main_Load(x98, x99, x100) -> f196_0_create_LE(x101, x102, x103) :|: -1 <= x104 - 1 && 1 <= x99 - 1 && -1 <= x105 - 1 && 0 <= x98 - 1 && x105 - 1 = x101
f196_0_create_LE(x106, x107, x108) -> f196_0_create_LE(x109, x110, x111) :|: x106 - 1 = x109 && 0 <= x106 - 1
__init(x112, x113, x114) -> f1_0_main_Load(x115, x116, x117) :|: 0 <= 0
Start term: __init(arg1, arg2, arg3)

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

(3) IRSwTTerminationDigraphProof (EQUIVALENT)
Constructed termination digraph!
Nodes:
(1) f1_0_main_Load(arg1, arg2, arg3) -> f234_0_slide95_FieldAccess(arg1P, arg2P, arg3P) :|: -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) -> f234_0_slide95_FieldAccess(x3, x6, x7) :|: -1 <= x8 - 1 && 1 <= x1 - 1 && x6 <= 0 && -1 <= x3 - 1 && 0 <= x - 1
(3) f234_0_slide95_FieldAccess(x9, x11, x12) -> f411_0_slide95_EQ(x13, x14, x15) :|: x11 = x15 && x11 = x14 && x9 = x13 && 0 <= x11 - 1
(4) f411_0_slide95_EQ(x16, x17, x18) -> f411_0_slide95_EQ'(x19, x20, x21) :|: -1 <= x22 - 1 && 0 <= x17 - 1 && x22 <= x23 - 1 && -1 <= x18 - 1 && x22 <= x18 - 1 && x22 <= x24 - 1 && x25 <= x17 - 1 && x22 <= x25 - 1 && x22 <= x26 - 1 && x27 <= x16 && x16 - 2 * x28 = 0 && x16 = x19 && x17 = x20 && x18 = x21
(5) f411_0_slide95_EQ'(x29, x30, x31) -> f411_0_slide95_EQ(x32, x33, x34) :|: -1 <= x35 - 1 && 0 <= x30 - 1 && x35 <= x34 - 1 && -1 <= x31 - 1 && x35 <= x31 - 1 && x35 <= x38 - 1 && x33 <= x30 - 1 && x35 <= x33 - 1 && x35 <= x46 - 1 && x29 - 2 * x47 = 0 && x32 <= x29 && 0 <= x29 - 2 * x47 && x29 - 2 * x47 <= 1 && x29 - 2 * x32 <= 1 && 0 <= x29 - 2 * x32
(6) f411_0_slide95_EQ(x48, x49, x50) -> f411_0_slide95_EQ'(x51, x56, x57) :|: -1 <= x50 - 1 && 0 <= x49 - 1 && x58 <= x50 - 1 && x64 <= x49 - 1 && x48 - 2 * x65 = 1 && x66 <= x48 && -1 <= x64 - 1 && x67 <= x64 && 0 <= x58 - 1 && x48 = x51 && x49 = x56 && x50 = x57
(7) f411_0_slide95_EQ'(x68, x69, x72) -> f411_0_slide95_EQ(x73, x74, x78) :|: -1 <= x72 - 1 && 0 <= x69 - 1 && x78 <= x72 - 1 && x79 <= x69 - 1 && x68 - 2 * x80 = 1 && x73 <= x68 && -1 <= x79 - 1 && 0 <= x78 - 1 && x74 <= x79 && 0 <= x68 - 2 * x80 && x68 - 2 * x80 <= 1 && x68 - 2 * x73 <= 1 && 0 <= x68 - 2 * x73
(8) f411_0_slide95_EQ(x81, x82, x84) -> f411_0_slide95_EQ'(x85, x86, x87) :|: -1 <= x84 - 1 && 0 <= x82 - 1 && x88 <= x84 - 1 && x88 <= x82 - 1 && x81 - 2 * x89 = 1 && 0 <= x88 - 1 && x90 <= x81 && x81 = x85 && x82 = x86 && x84 = x87
(9) f411_0_slide95_EQ'(x91, x92, x93) -> f411_0_slide95_EQ(x94, x95, x96) :|: -1 <= x93 - 1 && 0 <= x92 - 1 && x95 <= x93 - 1 && x95 <= x92 - 1 && x91 - 2 * x97 = 1 && x94 <= x91 && 0 <= x95 - 1 && 0 <= x91 - 2 * x97 && x91 - 2 * x97 <= 1 && x91 - 2 * x94 <= 1 && 0 <= x91 - 2 * x94 && x95 = x96
(10) f1_0_main_Load(x98, x99, x100) -> f196_0_create_LE(x101, x102, x103) :|: -1 <= x104 - 1 && 1 <= x99 - 1 && -1 <= x105 - 1 && 0 <= x98 - 1 && x105 - 1 = x101
(11) f196_0_create_LE(x106, x107, x108) -> f196_0_create_LE(x109, x110, x111) :|: x106 - 1 = x109 && 0 <= x106 - 1
(12) __init(x112, x113, x114) -> f1_0_main_Load(x115, x116, x117) :|: 0 <= 0

Arcs:
(1) -> (3)
(3) -> (4), (6), (8)
(4) -> (5)
(5) -> (4), (6), (8)
(6) -> (7), (9)
(7) -> (4), (6), (8)
(8) -> (7), (9)
(9) -> (4), (6), (8)
(10) -> (11)
(11) -> (11)
(12) -> (1), (2), (10)

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

(4)
Complex Obligation (AND)

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

(5)
Obligation:

Termination digraph:
Nodes:
(1) f196_0_create_LE(x106, x107, x108) -> f196_0_create_LE(x109, x110, x111) :|: x106 - 1 = x109 && 0 <= x106 - 1

Arcs:
(1) -> (1)

This digraph is fully evaluated!

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

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

(7)
Obligation:
Rules:
f196_0_create_LE(x106:0, x107:0, x108:0) -> f196_0_create_LE(x106:0 - 1, x110:0, x111:0) :|: x106:0 > 0

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

(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) -> f196_0_create_LE(x1)

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

(9)
Obligation:
Rules:
f196_0_create_LE(x106:0) -> f196_0_create_LE(x106:0 - 1) :|: x106:0 > 0

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

(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(x106:0) -> f196_0_create_LE(c) :|: c = x106:0 - 1 && x106:0 > 0

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

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

The following rules are decreasing:
f196_0_create_LE(x106:0) -> f196_0_create_LE(c) :|: c = x106:0 - 1 && x106:0 > 0

The following rules are bounded:
f196_0_create_LE(x106:0) -> f196_0_create_LE(c) :|: c = x106:0 - 1 && x106:0 > 0


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

(13)
YES

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

(14)
Obligation:

Termination digraph:
Nodes:
(1) f411_0_slide95_EQ(x16, x17, x18) -> f411_0_slide95_EQ'(x19, x20, x21) :|: -1 <= x22 - 1 && 0 <= x17 - 1 && x22 <= x23 - 1 && -1 <= x18 - 1 && x22 <= x18 - 1 && x22 <= x24 - 1 && x25 <= x17 - 1 && x22 <= x25 - 1 && x22 <= x26 - 1 && x27 <= x16 && x16 - 2 * x28 = 0 && x16 = x19 && x17 = x20 && x18 = x21
(2) f411_0_slide95_EQ'(x68, x69, x72) -> f411_0_slide95_EQ(x73, x74, x78) :|: -1 <= x72 - 1 && 0 <= x69 - 1 && x78 <= x72 - 1 && x79 <= x69 - 1 && x68 - 2 * x80 = 1 && x73 <= x68 && -1 <= x79 - 1 && 0 <= x78 - 1 && x74 <= x79 && 0 <= x68 - 2 * x80 && x68 - 2 * x80 <= 1 && x68 - 2 * x73 <= 1 && 0 <= x68 - 2 * x73
(3) f411_0_slide95_EQ(x48, x49, x50) -> f411_0_slide95_EQ'(x51, x56, x57) :|: -1 <= x50 - 1 && 0 <= x49 - 1 && x58 <= x50 - 1 && x64 <= x49 - 1 && x48 - 2 * x65 = 1 && x66 <= x48 && -1 <= x64 - 1 && x67 <= x64 && 0 <= x58 - 1 && x48 = x51 && x49 = x56 && x50 = x57
(4) f411_0_slide95_EQ'(x91, x92, x93) -> f411_0_slide95_EQ(x94, x95, x96) :|: -1 <= x93 - 1 && 0 <= x92 - 1 && x95 <= x93 - 1 && x95 <= x92 - 1 && x91 - 2 * x97 = 1 && x94 <= x91 && 0 <= x95 - 1 && 0 <= x91 - 2 * x97 && x91 - 2 * x97 <= 1 && x91 - 2 * x94 <= 1 && 0 <= x91 - 2 * x94 && x95 = x96
(5) f411_0_slide95_EQ(x81, x82, x84) -> f411_0_slide95_EQ'(x85, x86, x87) :|: -1 <= x84 - 1 && 0 <= x82 - 1 && x88 <= x84 - 1 && x88 <= x82 - 1 && x81 - 2 * x89 = 1 && 0 <= x88 - 1 && x90 <= x81 && x81 = x85 && x82 = x86 && x84 = x87
(6) f411_0_slide95_EQ'(x29, x30, x31) -> f411_0_slide95_EQ(x32, x33, x34) :|: -1 <= x35 - 1 && 0 <= x30 - 1 && x35 <= x34 - 1 && -1 <= x31 - 1 && x35 <= x31 - 1 && x35 <= x38 - 1 && x33 <= x30 - 1 && x35 <= x33 - 1 && x35 <= x46 - 1 && x29 - 2 * x47 = 0 && x32 <= x29 && 0 <= x29 - 2 * x47 && x29 - 2 * x47 <= 1 && x29 - 2 * x32 <= 1 && 0 <= x29 - 2 * x32

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

This digraph is fully evaluated!

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

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

(16)
Obligation:
Rules:
f411_0_slide95_EQ'(x29:0, x30:0, x31:0) -> f411_0_slide95_EQ(x32:0, x33:0, x34:0) :|: x29:0 - 2 * x32:0 <= 1 && x29:0 - 2 * x32:0 >= 0 && x29:0 - 2 * x47:0 <= 1 && x29:0 - 2 * x47:0 >= 0 && x32:0 <= x29:0 && x29:0 - 2 * x47:0 = 0 && x46:0 - 1 >= x35:0 && x35:0 <= x33:0 - 1 && x33:0 <= x30:0 - 1 && x38:0 - 1 >= x35:0 && x35:0 <= x31:0 - 1 && x31:0 > -1 && x35:0 <= x34:0 - 1 && x30:0 > 0 && x35:0 > -1
f411_0_slide95_EQ(x16:0, x17:0, x18:0) -> f411_0_slide95_EQ'(x16:0, x17:0, x18:0) :|: x27:0 <= x16:0 && x16:0 - 2 * x28:0 = 0 && x26:0 - 1 >= x22:0 && x25:0 - 1 >= x22:0 && x25:0 <= x17:0 - 1 && x24:0 - 1 >= x22:0 && x22:0 <= x18:0 - 1 && x18:0 > -1 && x23:0 - 1 >= x22:0 && x17:0 > 0 && x22:0 > -1
f411_0_slide95_EQ(x48:0, x49:0, x50:0) -> f411_0_slide95_EQ'(x48:0, x49:0, x50:0) :|: x67:0 <= x64:0 && x58:0 > 0 && x64:0 > -1 && x66:0 <= x48:0 && x48:0 - 2 * x65:0 = 1 && x64:0 <= x49:0 - 1 && x58:0 <= x50:0 - 1 && x49:0 > 0 && x50:0 > -1
f411_0_slide95_EQ'(x91:0, x92:0, x93:0) -> f411_0_slide95_EQ(x94:0, x95:0, x95:0) :|: x91:0 - 2 * x94:0 <= 1 && x91:0 - 2 * x94:0 >= 0 && x91:0 - 2 * x97:0 <= 1 && x91:0 - 2 * x97:0 >= 0 && x95:0 > 0 && x94:0 <= x91:0 && x91:0 - 2 * x97:0 = 1 && x95:0 <= x92:0 - 1 && x95:0 <= x93:0 - 1 && x92:0 > 0 && x93:0 > -1
f411_0_slide95_EQ(x81:0, x82:0, x84:0) -> f411_0_slide95_EQ'(x81:0, x82:0, x84:0) :|: x88:0 > 0 && x90:0 <= x81:0 && x81:0 - 2 * x89:0 = 1 && x88:0 <= x82:0 - 1 && x88:0 <= x84:0 - 1 && x82:0 > 0 && x84:0 > -1
f411_0_slide95_EQ'(x68:0, x69:0, x72:0) -> f411_0_slide95_EQ(x73:0, x74:0, x78:0) :|: x68:0 - 2 * x73:0 <= 1 && x68:0 - 2 * x73:0 >= 0 && x68:0 - 2 * x80:0 <= 1 && x68:0 - 2 * x80:0 >= 0 && x79:0 >= x74:0 && x78:0 > 0 && x79:0 > -1 && x73:0 <= x68:0 && x68:0 - 2 * x80:0 = 1 && x79:0 <= x69:0 - 1 && x78:0 <= x72:0 - 1 && x69:0 > 0 && x72:0 > -1

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

(17) FilterProof (EQUIVALENT)
Used the following sort dictionary for filtering: 
f411_0_slide95_EQ'(INTEGER, INTEGER, INTEGER)
f411_0_slide95_EQ(INTEGER, INTEGER, INTEGER)
Replaced non-predefined constructor symbols by 0.
----------------------------------------

(18)
Obligation:
Rules:
f411_0_slide95_EQ'(x29:0, x30:0, x31:0) -> f411_0_slide95_EQ(x32:0, x33:0, x34:0) :|: x29:0 - 2 * x32:0 <= 1 && x29:0 - 2 * x32:0 >= 0 && x29:0 - 2 * x47:0 <= 1 && x29:0 - 2 * x47:0 >= 0 && x32:0 <= x29:0 && x29:0 - 2 * x47:0 = 0 && x46:0 - 1 >= x35:0 && x35:0 <= x33:0 - 1 && x33:0 <= x30:0 - 1 && x38:0 - 1 >= x35:0 && x35:0 <= x31:0 - 1 && x31:0 > -1 && x35:0 <= x34:0 - 1 && x30:0 > 0 && x35:0 > -1
f411_0_slide95_EQ(x16:0, x17:0, x18:0) -> f411_0_slide95_EQ'(x16:0, x17:0, x18:0) :|: x27:0 <= x16:0 && x16:0 - 2 * x28:0 = 0 && x26:0 - 1 >= x22:0 && x25:0 - 1 >= x22:0 && x25:0 <= x17:0 - 1 && x24:0 - 1 >= x22:0 && x22:0 <= x18:0 - 1 && x18:0 > -1 && x23:0 - 1 >= x22:0 && x17:0 > 0 && x22:0 > -1
f411_0_slide95_EQ(x48:0, x49:0, x50:0) -> f411_0_slide95_EQ'(x48:0, x49:0, x50:0) :|: x67:0 <= x64:0 && x58:0 > 0 && x64:0 > -1 && x66:0 <= x48:0 && x48:0 - 2 * x65:0 = 1 && x64:0 <= x49:0 - 1 && x58:0 <= x50:0 - 1 && x49:0 > 0 && x50:0 > -1
f411_0_slide95_EQ'(x91:0, x92:0, x93:0) -> f411_0_slide95_EQ(x94:0, x95:0, x95:0) :|: x91:0 - 2 * x94:0 <= 1 && x91:0 - 2 * x94:0 >= 0 && x91:0 - 2 * x97:0 <= 1 && x91:0 - 2 * x97:0 >= 0 && x95:0 > 0 && x94:0 <= x91:0 && x91:0 - 2 * x97:0 = 1 && x95:0 <= x92:0 - 1 && x95:0 <= x93:0 - 1 && x92:0 > 0 && x93:0 > -1
f411_0_slide95_EQ(x81:0, x82:0, x84:0) -> f411_0_slide95_EQ'(x81:0, x82:0, x84:0) :|: x88:0 > 0 && x90:0 <= x81:0 && x81:0 - 2 * x89:0 = 1 && x88:0 <= x82:0 - 1 && x88:0 <= x84:0 - 1 && x82:0 > 0 && x84:0 > -1
f411_0_slide95_EQ'(x68:0, x69:0, x72:0) -> f411_0_slide95_EQ(x73:0, x74:0, x78:0) :|: x68:0 - 2 * x73:0 <= 1 && x68:0 - 2 * x73:0 >= 0 && x68:0 - 2 * x80:0 <= 1 && x68:0 - 2 * x80:0 >= 0 && x79:0 >= x74:0 && x78:0 > 0 && x79:0 > -1 && x73:0 <= x68:0 && x68:0 - 2 * x80:0 = 1 && x79:0 <= x69:0 - 1 && x78:0 <= x72:0 - 1 && x69:0 > 0 && x72:0 > -1

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(19) IntTRSCompressionProof (EQUIVALENT)
Compressed rules.
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(20)
Obligation:
Rules:
f411_0_slide95_EQ(x48:0:0, x49:0:0, x50:0:0) -> f411_0_slide95_EQ'(x48:0:0, x49:0:0, x50:0:0) :|: x49:0:0 > 0 && x50:0:0 > -1 && x58:0:0 <= x50:0:0 - 1 && x64:0:0 <= x49:0:0 - 1 && x48:0:0 - 2 * x65:0:0 = 1 && x66:0:0 <= x48:0:0 && x64:0:0 > -1 && x58:0:0 > 0 && x67:0:0 <= x64:0:0
f411_0_slide95_EQ'(x29:0:0, x30:0:0, x31:0:0) -> f411_0_slide95_EQ(x32:0:0, x33:0:0, x34:0:0) :|: x30:0:0 > 0 && x35:0:0 > -1 && x35:0:0 <= x34:0:0 - 1 && x31:0:0 > -1 && x35:0:0 <= x31:0:0 - 1 && x38:0:0 - 1 >= x35:0:0 && x33:0:0 <= x30:0:0 - 1 && x35:0:0 <= x33:0:0 - 1 && x46:0:0 - 1 >= x35:0:0 && x29:0:0 - 2 * x47:0:0 = 0 && x32:0:0 <= x29:0:0 && x29:0:0 - 2 * x47:0:0 >= 0 && x29:0:0 - 2 * x47:0:0 <= 1 && x29:0:0 - 2 * x32:0:0 >= 0 && x29:0:0 - 2 * x32:0:0 <= 1
f411_0_slide95_EQ(x16:0:0, x17:0:0, x18:0:0) -> f411_0_slide95_EQ'(x16:0:0, x17:0:0, x18:0:0) :|: x17:0:0 > 0 && x22:0:0 > -1 && x23:0:0 - 1 >= x22:0:0 && x18:0:0 > -1 && x22:0:0 <= x18:0:0 - 1 && x24:0:0 - 1 >= x22:0:0 && x25:0:0 <= x17:0:0 - 1 && x25:0:0 - 1 >= x22:0:0 && x26:0:0 - 1 >= x22:0:0 && x16:0:0 - 2 * x28:0:0 = 0 && x27:0:0 <= x16:0:0
f411_0_slide95_EQ'(x91:0:0, x92:0:0, x93:0:0) -> f411_0_slide95_EQ(x94:0:0, x95:0:0, x95:0:0) :|: x92:0:0 > 0 && x93:0:0 > -1 && x95:0:0 <= x93:0:0 - 1 && x95:0:0 <= x92:0:0 - 1 && x91:0:0 - 2 * x97:0:0 = 1 && x94:0:0 <= x91:0:0 && x95:0:0 > 0 && x91:0:0 - 2 * x97:0:0 >= 0 && x91:0:0 - 2 * x97:0:0 <= 1 && x91:0:0 - 2 * x94:0:0 >= 0 && x91:0:0 - 2 * x94:0:0 <= 1
f411_0_slide95_EQ'(x68:0:0, x69:0:0, x72:0:0) -> f411_0_slide95_EQ(x73:0:0, x74:0:0, x78:0:0) :|: x69:0:0 > 0 && x72:0:0 > -1 && x78:0:0 <= x72:0:0 - 1 && x79:0:0 <= x69:0:0 - 1 && x68:0:0 - 2 * x80:0:0 = 1 && x73:0:0 <= x68:0:0 && x79:0:0 > -1 && x78:0:0 > 0 && x79:0:0 >= x74:0:0 && x68:0:0 - 2 * x80:0:0 >= 0 && x68:0:0 - 2 * x80:0:0 <= 1 && x68:0:0 - 2 * x73:0:0 >= 0 && x68:0:0 - 2 * x73:0:0 <= 1
f411_0_slide95_EQ(x81:0:0, x82:0:0, x84:0:0) -> f411_0_slide95_EQ'(x81:0:0, x82:0:0, x84:0:0) :|: x82:0:0 > 0 && x84:0:0 > -1 && x88:0:0 <= x84:0:0 - 1 && x88:0:0 <= x82:0:0 - 1 && x81:0:0 - 2 * x89:0:0 = 1 && x90:0:0 <= x81:0:0 && x88:0:0 > 0

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(21) RankingReductionPairProof (EQUIVALENT)
Interpretation:
[ f411_0_slide95_EQ ] = 2*f411_0_slide95_EQ_2 + 1
[ f411_0_slide95_EQ' ] = 2*f411_0_slide95_EQ'_2

The following rules are decreasing:
f411_0_slide95_EQ(x48:0:0, x49:0:0, x50:0:0) -> f411_0_slide95_EQ'(x48:0:0, x49:0:0, x50:0:0) :|: x49:0:0 > 0 && x50:0:0 > -1 && x58:0:0 <= x50:0:0 - 1 && x64:0:0 <= x49:0:0 - 1 && x48:0:0 - 2 * x65:0:0 = 1 && x66:0:0 <= x48:0:0 && x64:0:0 > -1 && x58:0:0 > 0 && x67:0:0 <= x64:0:0
f411_0_slide95_EQ'(x29:0:0, x30:0:0, x31:0:0) -> f411_0_slide95_EQ(x32:0:0, x33:0:0, x34:0:0) :|: x30:0:0 > 0 && x35:0:0 > -1 && x35:0:0 <= x34:0:0 - 1 && x31:0:0 > -1 && x35:0:0 <= x31:0:0 - 1 && x38:0:0 - 1 >= x35:0:0 && x33:0:0 <= x30:0:0 - 1 && x35:0:0 <= x33:0:0 - 1 && x46:0:0 - 1 >= x35:0:0 && x29:0:0 - 2 * x47:0:0 = 0 && x32:0:0 <= x29:0:0 && x29:0:0 - 2 * x47:0:0 >= 0 && x29:0:0 - 2 * x47:0:0 <= 1 && x29:0:0 - 2 * x32:0:0 >= 0 && x29:0:0 - 2 * x32:0:0 <= 1
f411_0_slide95_EQ(x16:0:0, x17:0:0, x18:0:0) -> f411_0_slide95_EQ'(x16:0:0, x17:0:0, x18:0:0) :|: x17:0:0 > 0 && x22:0:0 > -1 && x23:0:0 - 1 >= x22:0:0 && x18:0:0 > -1 && x22:0:0 <= x18:0:0 - 1 && x24:0:0 - 1 >= x22:0:0 && x25:0:0 <= x17:0:0 - 1 && x25:0:0 - 1 >= x22:0:0 && x26:0:0 - 1 >= x22:0:0 && x16:0:0 - 2 * x28:0:0 = 0 && x27:0:0 <= x16:0:0
f411_0_slide95_EQ'(x91:0:0, x92:0:0, x93:0:0) -> f411_0_slide95_EQ(x94:0:0, x95:0:0, x95:0:0) :|: x92:0:0 > 0 && x93:0:0 > -1 && x95:0:0 <= x93:0:0 - 1 && x95:0:0 <= x92:0:0 - 1 && x91:0:0 - 2 * x97:0:0 = 1 && x94:0:0 <= x91:0:0 && x95:0:0 > 0 && x91:0:0 - 2 * x97:0:0 >= 0 && x91:0:0 - 2 * x97:0:0 <= 1 && x91:0:0 - 2 * x94:0:0 >= 0 && x91:0:0 - 2 * x94:0:0 <= 1
f411_0_slide95_EQ'(x68:0:0, x69:0:0, x72:0:0) -> f411_0_slide95_EQ(x73:0:0, x74:0:0, x78:0:0) :|: x69:0:0 > 0 && x72:0:0 > -1 && x78:0:0 <= x72:0:0 - 1 && x79:0:0 <= x69:0:0 - 1 && x68:0:0 - 2 * x80:0:0 = 1 && x73:0:0 <= x68:0:0 && x79:0:0 > -1 && x78:0:0 > 0 && x79:0:0 >= x74:0:0 && x68:0:0 - 2 * x80:0:0 >= 0 && x68:0:0 - 2 * x80:0:0 <= 1 && x68:0:0 - 2 * x73:0:0 >= 0 && x68:0:0 - 2 * x73:0:0 <= 1
f411_0_slide95_EQ(x81:0:0, x82:0:0, x84:0:0) -> f411_0_slide95_EQ'(x81:0:0, x82:0:0, x84:0:0) :|: x82:0:0 > 0 && x84:0:0 > -1 && x88:0:0 <= x84:0:0 - 1 && x88:0:0 <= x82:0:0 - 1 && x81:0:0 - 2 * x89:0:0 = 1 && x90:0:0 <= x81:0:0 && x88:0:0 > 0

The following rules are bounded:
f411_0_slide95_EQ(x48:0:0, x49:0:0, x50:0:0) -> f411_0_slide95_EQ'(x48:0:0, x49:0:0, x50:0:0) :|: x49:0:0 > 0 && x50:0:0 > -1 && x58:0:0 <= x50:0:0 - 1 && x64:0:0 <= x49:0:0 - 1 && x48:0:0 - 2 * x65:0:0 = 1 && x66:0:0 <= x48:0:0 && x64:0:0 > -1 && x58:0:0 > 0 && x67:0:0 <= x64:0:0
f411_0_slide95_EQ'(x29:0:0, x30:0:0, x31:0:0) -> f411_0_slide95_EQ(x32:0:0, x33:0:0, x34:0:0) :|: x30:0:0 > 0 && x35:0:0 > -1 && x35:0:0 <= x34:0:0 - 1 && x31:0:0 > -1 && x35:0:0 <= x31:0:0 - 1 && x38:0:0 - 1 >= x35:0:0 && x33:0:0 <= x30:0:0 - 1 && x35:0:0 <= x33:0:0 - 1 && x46:0:0 - 1 >= x35:0:0 && x29:0:0 - 2 * x47:0:0 = 0 && x32:0:0 <= x29:0:0 && x29:0:0 - 2 * x47:0:0 >= 0 && x29:0:0 - 2 * x47:0:0 <= 1 && x29:0:0 - 2 * x32:0:0 >= 0 && x29:0:0 - 2 * x32:0:0 <= 1
f411_0_slide95_EQ(x16:0:0, x17:0:0, x18:0:0) -> f411_0_slide95_EQ'(x16:0:0, x17:0:0, x18:0:0) :|: x17:0:0 > 0 && x22:0:0 > -1 && x23:0:0 - 1 >= x22:0:0 && x18:0:0 > -1 && x22:0:0 <= x18:0:0 - 1 && x24:0:0 - 1 >= x22:0:0 && x25:0:0 <= x17:0:0 - 1 && x25:0:0 - 1 >= x22:0:0 && x26:0:0 - 1 >= x22:0:0 && x16:0:0 - 2 * x28:0:0 = 0 && x27:0:0 <= x16:0:0
f411_0_slide95_EQ'(x91:0:0, x92:0:0, x93:0:0) -> f411_0_slide95_EQ(x94:0:0, x95:0:0, x95:0:0) :|: x92:0:0 > 0 && x93:0:0 > -1 && x95:0:0 <= x93:0:0 - 1 && x95:0:0 <= x92:0:0 - 1 && x91:0:0 - 2 * x97:0:0 = 1 && x94:0:0 <= x91:0:0 && x95:0:0 > 0 && x91:0:0 - 2 * x97:0:0 >= 0 && x91:0:0 - 2 * x97:0:0 <= 1 && x91:0:0 - 2 * x94:0:0 >= 0 && x91:0:0 - 2 * x94:0:0 <= 1
f411_0_slide95_EQ'(x68:0:0, x69:0:0, x72:0:0) -> f411_0_slide95_EQ(x73:0:0, x74:0:0, x78:0:0) :|: x69:0:0 > 0 && x72:0:0 > -1 && x78:0:0 <= x72:0:0 - 1 && x79:0:0 <= x69:0:0 - 1 && x68:0:0 - 2 * x80:0:0 = 1 && x73:0:0 <= x68:0:0 && x79:0:0 > -1 && x78:0:0 > 0 && x79:0:0 >= x74:0:0 && x68:0:0 - 2 * x80:0:0 >= 0 && x68:0:0 - 2 * x80:0:0 <= 1 && x68:0:0 - 2 * x73:0:0 >= 0 && x68:0:0 - 2 * x73:0:0 <= 1
f411_0_slide95_EQ(x81:0:0, x82:0:0, x84:0:0) -> f411_0_slide95_EQ'(x81:0:0, x82:0:0, x84:0:0) :|: x82:0:0 > 0 && x84:0:0 > -1 && x88:0:0 <= x84:0:0 - 1 && x88:0:0 <= x82:0:0 - 1 && x81:0:0 - 2 * x89:0:0 = 1 && x90:0:0 <= x81:0:0 && x88:0:0 > 0


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(22)
YES