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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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, 1372 ms]
(4) AND
    (5) IRSwT
        (6) IntTRSCompressionProof [EQUIVALENT, 7 ms]
        (7) IRSwT
        (8) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms]
        (9) IRSwT
        (10) TempFilterProof [SOUND, 12 ms]
        (11) IntTRS
        (12) PolynomialOrderProcessor [EQUIVALENT, 0 ms]
        (13) YES
    (14) IRSwT
        (15) IntTRSCompressionProof [EQUIVALENT, 25 ms]
        (16) IRSwT
        (17) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms]
        (18) IRSwT
        (19) FilterProof [EQUIVALENT, 0 ms]
        (20) IntTRS
        (21) IntTRSCompressionProof [EQUIVALENT, 0 ms]
        (22) IntTRS
        (23) RankingReductionPairProof [EQUIVALENT, 0 ms]
        (24) YES


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

(0)
Obligation:
Rules:
f1_0_main_Load(arg1, arg2, arg3) -> f480_0_main_InvokeMethod(arg1P, arg2P, arg3P) :|: 0 = arg2 && 2 <= arg1P - 1 && 0 <= arg1 - 1
f1_0_main_Load(x, x1, x2) -> f480_0_main_InvokeMethod(x3, x4, x5) :|: 0 = x1 && 1 <= x3 - 1 && 0 <= x - 1 && x3 - 1 <= x
f1_0_main_Load(x7, x8, x9) -> f481_0_main_InvokeMethod(x10, x11, x12) :|: 0 <= x7 - 1 && -1 <= x13 - 1 && 2 <= x10 - 1 && 1 = x8
f1_0_main_Load(x16, x17, x18) -> f481_0_main_InvokeMethod(x19, x22, x23) :|: x19 - 1 <= x16 && -1 <= x24 - 1 && 0 <= x16 - 1 && 1 <= x19 - 1 && 1 = x17
f1_0_main_Load(x25, x26, x29) -> f482_0_main_InvokeMethod(x30, x31, x32) :|: 0 <= x33 * x34 && 1 <= x26 - 1 && -1 <= x34 - 1 && -1 <= x33 - 1 && x30 <= x25 && 0 <= x25 - 1 && 0 <= x30 - 1 && 2 <= x31 - 1
f1_0_main_Load(x35, x36, x37) -> f482_0_main_InvokeMethod(x38, x39, x40) :|: 0 <= x41 * x42 && 1 <= x36 - 1 && -1 <= x42 - 1 && -1 <= x41 - 1 && x38 <= x35 && x39 - 1 <= x35 && 0 <= x35 - 1 && 0 <= x38 - 1 && 1 <= x39 - 1
f1_0_main_Load(x43, x44, x45) -> f193_0__init__LE(x47, x48, x49) :|: 10 = x47 && 0 = x44 && 0 <= x43 - 1
f1_0_main_Load(x50, x51, x52) -> f193_0__init__LE(x53, x54, x55) :|: 0 <= x50 - 1 && -1 <= x56 - 1 && 1 = x51 && 10 = x53
f1_0_main_Load(x57, x58, x59) -> f193_0__init__LE(x60, x61, x62) :|: 0 <= x63 * x65 && 1 <= x58 - 1 && -1 <= x65 - 1 && -1 <= x63 - 1 && 0 <= x57 - 1 && x63 * x65 + 10 = x60
f193_0__init__LE(x66, x67, x68) -> f193_0__init__LE(x70, x71, x72) :|: x66 - 1 = x70 && x66 - 1 <= x66 - 1 && 1 <= x66 - 1
f193_0__init__LE(x73, x74, x75) -> f518_0__init__InvokeMethod(x76, x77, x78) :|: x73 - 1 = x77 && 1 <= x73 - 1 && 4 <= x76 - 1 && x73 - 1 <= x73 - 1
f193_0__init__LE(x79, x80, x81) -> f518_0__init__InvokeMethod(x82, x83, x84) :|: x79 - 1 = x83 && 1 <= x79 - 1 && 3 <= x82 - 1 && x79 - 1 <= x79 - 1
f518_0__init__InvokeMethod(x85, x86, x87) -> f193_0__init__LE(x88, x89, x90) :|: x86 = x88 && 0 <= x86 - 1 && 2 <= x85 - 1
f480_0_main_InvokeMethod(x91, x92, x93) -> f388_0_height_NONNULL(x94, x95, x96) :|: -1 <= x95 - 1 && 0 <= x94 - 1 && 0 <= x91 - 1 && x95 + 1 <= x91 && x94 <= x91
f481_0_main_InvokeMethod(x97, x98, x99) -> f388_0_height_NONNULL(x100, x101, x102) :|: -1 <= x101 - 1 && 0 <= x100 - 1 && 0 <= x97 - 1 && x101 + 1 <= x97 && x100 <= x97
f482_0_main_InvokeMethod(x103, x104, x105) -> f388_0_height_NONNULL(x106, x107, x108) :|: x106 <= x104 && 1 <= x109 - 1 && x107 + 1 <= x104 && 0 <= x103 - 1 && 0 <= x104 - 1 && 0 <= x106 - 1 && -1 <= x107 - 1
f388_0_height_NONNULL(x110, x111, x112) -> f388_0_height_NONNULL(x113, x114, x115) :|: -1 <= x114 - 1 && 0 <= x113 - 1 && 0 <= x111 - 1 && 2 <= x110 - 1 && x114 + 1 <= x111 && x114 + 3 <= x110 && x113 <= x111 && x113 + 2 <= x110
f388_0_height_NONNULL(x116, x117, x118) -> f388_0_height_NONNULL(x119, x120, x121) :|: -1 <= x120 - 1 && 0 <= x119 - 1 && -1 <= x117 - 1 && 2 <= x116 - 1 && x120 + 3 <= x116 && x119 + 2 <= x116
__init(x122, x123, x124) -> f1_0_main_Load(x125, x126, x127) :|: 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) -> f480_0_main_InvokeMethod(arg1P, arg2P, arg3P) :|: 0 = arg2 && 2 <= arg1P - 1 && 0 <= arg1 - 1
f1_0_main_Load(x, x1, x2) -> f480_0_main_InvokeMethod(x3, x4, x5) :|: 0 = x1 && 1 <= x3 - 1 && 0 <= x - 1 && x3 - 1 <= x
f1_0_main_Load(x7, x8, x9) -> f481_0_main_InvokeMethod(x10, x11, x12) :|: 0 <= x7 - 1 && -1 <= x13 - 1 && 2 <= x10 - 1 && 1 = x8
f1_0_main_Load(x16, x17, x18) -> f481_0_main_InvokeMethod(x19, x22, x23) :|: x19 - 1 <= x16 && -1 <= x24 - 1 && 0 <= x16 - 1 && 1 <= x19 - 1 && 1 = x17
f1_0_main_Load(x25, x26, x29) -> f482_0_main_InvokeMethod(x30, x31, x32) :|: 0 <= x33 * x34 && 1 <= x26 - 1 && -1 <= x34 - 1 && -1 <= x33 - 1 && x30 <= x25 && 0 <= x25 - 1 && 0 <= x30 - 1 && 2 <= x31 - 1
f1_0_main_Load(x35, x36, x37) -> f482_0_main_InvokeMethod(x38, x39, x40) :|: 0 <= x41 * x42 && 1 <= x36 - 1 && -1 <= x42 - 1 && -1 <= x41 - 1 && x38 <= x35 && x39 - 1 <= x35 && 0 <= x35 - 1 && 0 <= x38 - 1 && 1 <= x39 - 1
f1_0_main_Load(x43, x44, x45) -> f193_0__init__LE(x47, x48, x49) :|: 10 = x47 && 0 = x44 && 0 <= x43 - 1
f1_0_main_Load(x50, x51, x52) -> f193_0__init__LE(x53, x54, x55) :|: 0 <= x50 - 1 && -1 <= x56 - 1 && 1 = x51 && 10 = x53
f1_0_main_Load(x57, x58, x59) -> f193_0__init__LE(x60, x61, x62) :|: 0 <= x63 * x65 && 1 <= x58 - 1 && -1 <= x65 - 1 && -1 <= x63 - 1 && 0 <= x57 - 1 && x63 * x65 + 10 = x60
f193_0__init__LE(x66, x67, x68) -> f193_0__init__LE(x70, x71, x72) :|: x66 - 1 = x70 && x66 - 1 <= x66 - 1 && 1 <= x66 - 1
f193_0__init__LE(x73, x74, x75) -> f518_0__init__InvokeMethod(x76, x77, x78) :|: x73 - 1 = x77 && 1 <= x73 - 1 && 4 <= x76 - 1 && x73 - 1 <= x73 - 1
f193_0__init__LE(x79, x80, x81) -> f518_0__init__InvokeMethod(x82, x83, x84) :|: x79 - 1 = x83 && 1 <= x79 - 1 && 3 <= x82 - 1 && x79 - 1 <= x79 - 1
f518_0__init__InvokeMethod(x85, x86, x87) -> f193_0__init__LE(x88, x89, x90) :|: x86 = x88 && 0 <= x86 - 1 && 2 <= x85 - 1
f480_0_main_InvokeMethod(x91, x92, x93) -> f388_0_height_NONNULL(x94, x95, x96) :|: -1 <= x95 - 1 && 0 <= x94 - 1 && 0 <= x91 - 1 && x95 + 1 <= x91 && x94 <= x91
f481_0_main_InvokeMethod(x97, x98, x99) -> f388_0_height_NONNULL(x100, x101, x102) :|: -1 <= x101 - 1 && 0 <= x100 - 1 && 0 <= x97 - 1 && x101 + 1 <= x97 && x100 <= x97
f482_0_main_InvokeMethod(x103, x104, x105) -> f388_0_height_NONNULL(x106, x107, x108) :|: x106 <= x104 && 1 <= x109 - 1 && x107 + 1 <= x104 && 0 <= x103 - 1 && 0 <= x104 - 1 && 0 <= x106 - 1 && -1 <= x107 - 1
f388_0_height_NONNULL(x110, x111, x112) -> f388_0_height_NONNULL(x113, x114, x115) :|: -1 <= x114 - 1 && 0 <= x113 - 1 && 0 <= x111 - 1 && 2 <= x110 - 1 && x114 + 1 <= x111 && x114 + 3 <= x110 && x113 <= x111 && x113 + 2 <= x110
f388_0_height_NONNULL(x116, x117, x118) -> f388_0_height_NONNULL(x119, x120, x121) :|: -1 <= x120 - 1 && 0 <= x119 - 1 && -1 <= x117 - 1 && 2 <= x116 - 1 && x120 + 3 <= x116 && x119 + 2 <= x116
__init(x122, x123, x124) -> f1_0_main_Load(x125, x126, x127) :|: 0 <= 0
Start term: __init(arg1, arg2, arg3)

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

(3) IRSwTTerminationDigraphProof (EQUIVALENT)
Constructed termination digraph!
Nodes:
(1) f1_0_main_Load(arg1, arg2, arg3) -> f480_0_main_InvokeMethod(arg1P, arg2P, arg3P) :|: 0 = arg2 && 2 <= arg1P - 1 && 0 <= arg1 - 1
(2) f1_0_main_Load(x, x1, x2) -> f480_0_main_InvokeMethod(x3, x4, x5) :|: 0 = x1 && 1 <= x3 - 1 && 0 <= x - 1 && x3 - 1 <= x
(3) f1_0_main_Load(x7, x8, x9) -> f481_0_main_InvokeMethod(x10, x11, x12) :|: 0 <= x7 - 1 && -1 <= x13 - 1 && 2 <= x10 - 1 && 1 = x8
(4) f1_0_main_Load(x16, x17, x18) -> f481_0_main_InvokeMethod(x19, x22, x23) :|: x19 - 1 <= x16 && -1 <= x24 - 1 && 0 <= x16 - 1 && 1 <= x19 - 1 && 1 = x17
(5) f1_0_main_Load(x25, x26, x29) -> f482_0_main_InvokeMethod(x30, x31, x32) :|: 0 <= x33 * x34 && 1 <= x26 - 1 && -1 <= x34 - 1 && -1 <= x33 - 1 && x30 <= x25 && 0 <= x25 - 1 && 0 <= x30 - 1 && 2 <= x31 - 1
(6) f1_0_main_Load(x35, x36, x37) -> f482_0_main_InvokeMethod(x38, x39, x40) :|: 0 <= x41 * x42 && 1 <= x36 - 1 && -1 <= x42 - 1 && -1 <= x41 - 1 && x38 <= x35 && x39 - 1 <= x35 && 0 <= x35 - 1 && 0 <= x38 - 1 && 1 <= x39 - 1
(7) f1_0_main_Load(x43, x44, x45) -> f193_0__init__LE(x47, x48, x49) :|: 10 = x47 && 0 = x44 && 0 <= x43 - 1
(8) f1_0_main_Load(x50, x51, x52) -> f193_0__init__LE(x53, x54, x55) :|: 0 <= x50 - 1 && -1 <= x56 - 1 && 1 = x51 && 10 = x53
(9) f1_0_main_Load(x57, x58, x59) -> f193_0__init__LE(x60, x61, x62) :|: 0 <= x63 * x65 && 1 <= x58 - 1 && -1 <= x65 - 1 && -1 <= x63 - 1 && 0 <= x57 - 1 && x63 * x65 + 10 = x60
(10) f193_0__init__LE(x66, x67, x68) -> f193_0__init__LE(x70, x71, x72) :|: x66 - 1 = x70 && x66 - 1 <= x66 - 1 && 1 <= x66 - 1
(11) f193_0__init__LE(x73, x74, x75) -> f518_0__init__InvokeMethod(x76, x77, x78) :|: x73 - 1 = x77 && 1 <= x73 - 1 && 4 <= x76 - 1 && x73 - 1 <= x73 - 1
(12) f193_0__init__LE(x79, x80, x81) -> f518_0__init__InvokeMethod(x82, x83, x84) :|: x79 - 1 = x83 && 1 <= x79 - 1 && 3 <= x82 - 1 && x79 - 1 <= x79 - 1
(13) f518_0__init__InvokeMethod(x85, x86, x87) -> f193_0__init__LE(x88, x89, x90) :|: x86 = x88 && 0 <= x86 - 1 && 2 <= x85 - 1
(14) f480_0_main_InvokeMethod(x91, x92, x93) -> f388_0_height_NONNULL(x94, x95, x96) :|: -1 <= x95 - 1 && 0 <= x94 - 1 && 0 <= x91 - 1 && x95 + 1 <= x91 && x94 <= x91
(15) f481_0_main_InvokeMethod(x97, x98, x99) -> f388_0_height_NONNULL(x100, x101, x102) :|: -1 <= x101 - 1 && 0 <= x100 - 1 && 0 <= x97 - 1 && x101 + 1 <= x97 && x100 <= x97
(16) f482_0_main_InvokeMethod(x103, x104, x105) -> f388_0_height_NONNULL(x106, x107, x108) :|: x106 <= x104 && 1 <= x109 - 1 && x107 + 1 <= x104 && 0 <= x103 - 1 && 0 <= x104 - 1 && 0 <= x106 - 1 && -1 <= x107 - 1
(17) f388_0_height_NONNULL(x110, x111, x112) -> f388_0_height_NONNULL(x113, x114, x115) :|: -1 <= x114 - 1 && 0 <= x113 - 1 && 0 <= x111 - 1 && 2 <= x110 - 1 && x114 + 1 <= x111 && x114 + 3 <= x110 && x113 <= x111 && x113 + 2 <= x110
(18) f388_0_height_NONNULL(x116, x117, x118) -> f388_0_height_NONNULL(x119, x120, x121) :|: -1 <= x120 - 1 && 0 <= x119 - 1 && -1 <= x117 - 1 && 2 <= x116 - 1 && x120 + 3 <= x116 && x119 + 2 <= x116
(19) __init(x122, x123, x124) -> f1_0_main_Load(x125, x126, x127) :|: 0 <= 0

Arcs:
(1) -> (14)
(2) -> (14)
(3) -> (15)
(4) -> (15)
(5) -> (16)
(6) -> (16)
(7) -> (10), (11), (12)
(8) -> (10), (11), (12)
(9) -> (10), (11), (12)
(10) -> (10), (11), (12)
(11) -> (13)
(12) -> (13)
(13) -> (10), (11), (12)
(14) -> (17), (18)
(15) -> (17), (18)
(16) -> (17), (18)
(17) -> (17), (18)
(18) -> (17), (18)
(19) -> (1), (2), (3), (4), (5), (6), (7), (8), (9)

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

(4)
Complex Obligation (AND)

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

(5)
Obligation:

Termination digraph:
Nodes:
(1) f193_0__init__LE(x66, x67, x68) -> f193_0__init__LE(x70, x71, x72) :|: x66 - 1 = x70 && x66 - 1 <= x66 - 1 && 1 <= x66 - 1
(2) f518_0__init__InvokeMethod(x85, x86, x87) -> f193_0__init__LE(x88, x89, x90) :|: x86 = x88 && 0 <= x86 - 1 && 2 <= x85 - 1
(3) f193_0__init__LE(x79, x80, x81) -> f518_0__init__InvokeMethod(x82, x83, x84) :|: x79 - 1 = x83 && 1 <= x79 - 1 && 3 <= x82 - 1 && x79 - 1 <= x79 - 1
(4) f193_0__init__LE(x73, x74, x75) -> f518_0__init__InvokeMethod(x76, x77, x78) :|: x73 - 1 = x77 && 1 <= x73 - 1 && 4 <= x76 - 1 && x73 - 1 <= x73 - 1

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

This digraph is fully evaluated!

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

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

(7)
Obligation:
Rules:
f193_0__init__LE(x79:0, x80:0, x81:0) -> f193_0__init__LE(x79:0 - 1, x89:0, x90:0) :|: x82:0 > 3 && x79:0 > 1
f193_0__init__LE(x66:0, x67:0, x68:0) -> f193_0__init__LE(x66:0 - 1, x71:0, x72:0) :|: x66:0 > 1
f193_0__init__LE(x, x1, x2) -> f193_0__init__LE(x - 1, x3, x4) :|: x5 > 4 && x > 1

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

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

   f193_0__init__LE(x1, x2, x3) -> f193_0__init__LE(x1)

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

(9)
Obligation:
Rules:
f193_0__init__LE(x79:0) -> f193_0__init__LE(x79:0 - 1) :|: x82:0 > 3 && x79:0 > 1
f193_0__init__LE(x66:0) -> f193_0__init__LE(x66:0 - 1) :|: x66:0 > 1
f193_0__init__LE(x) -> f193_0__init__LE(x - 1) :|: x5 > 4 && x > 1

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

(10) TempFilterProof (SOUND)
Used the following sort dictionary for filtering: 
f193_0__init__LE(INTEGER)
Replaced non-predefined constructor symbols by 0.
----------------------------------------

(11)
Obligation:
Rules:
f193_0__init__LE(x79:0) -> f193_0__init__LE(c) :|: c = x79:0 - 1 && (x82:0 > 3 && x79:0 > 1)
f193_0__init__LE(x66:0) -> f193_0__init__LE(c1) :|: c1 = x66:0 - 1 && x66:0 > 1
f193_0__init__LE(x) -> f193_0__init__LE(c2) :|: c2 = x - 1 && (x5 > 4 && x > 1)

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

(12) PolynomialOrderProcessor (EQUIVALENT)
Found the following polynomial interpretation:
[f193_0__init__LE(x)] = x

The following rules are decreasing:
f193_0__init__LE(x79:0) -> f193_0__init__LE(c) :|: c = x79:0 - 1 && (x82:0 > 3 && x79:0 > 1)
f193_0__init__LE(x66:0) -> f193_0__init__LE(c1) :|: c1 = x66:0 - 1 && x66:0 > 1
f193_0__init__LE(x) -> f193_0__init__LE(c2) :|: c2 = x - 1 && (x5 > 4 && x > 1)
The following rules are bounded:
f193_0__init__LE(x79:0) -> f193_0__init__LE(c) :|: c = x79:0 - 1 && (x82:0 > 3 && x79:0 > 1)
f193_0__init__LE(x66:0) -> f193_0__init__LE(c1) :|: c1 = x66:0 - 1 && x66:0 > 1
f193_0__init__LE(x) -> f193_0__init__LE(c2) :|: c2 = x - 1 && (x5 > 4 && x > 1)

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

(13)
YES

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

(14)
Obligation:

Termination digraph:
Nodes:
(1) f388_0_height_NONNULL(x110, x111, x112) -> f388_0_height_NONNULL(x113, x114, x115) :|: -1 <= x114 - 1 && 0 <= x113 - 1 && 0 <= x111 - 1 && 2 <= x110 - 1 && x114 + 1 <= x111 && x114 + 3 <= x110 && x113 <= x111 && x113 + 2 <= x110
(2) f388_0_height_NONNULL(x116, x117, x118) -> f388_0_height_NONNULL(x119, x120, x121) :|: -1 <= x120 - 1 && 0 <= x119 - 1 && -1 <= x117 - 1 && 2 <= x116 - 1 && x120 + 3 <= x116 && x119 + 2 <= x116

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

This digraph is fully evaluated!

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

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

(16)
Obligation:
Rules:
f388_0_height_NONNULL(x110:0, x111:0, x112:0) -> f388_0_height_NONNULL(x113:0, x114:0, x115:0) :|: x113:0 <= x111:0 && x113:0 + 2 <= x110:0 && x114:0 + 3 <= x110:0 && x114:0 + 1 <= x111:0 && x110:0 > 2 && x111:0 > 0 && x113:0 > 0 && x114:0 > -1
f388_0_height_NONNULL(x116:0, x117:0, x118:0) -> f388_0_height_NONNULL(x119:0, x120:0, x121:0) :|: x120:0 + 3 <= x116:0 && x119:0 + 2 <= x116:0 && x116:0 > 2 && x117:0 > -1 && x119:0 > 0 && x120:0 > -1

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

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

   f388_0_height_NONNULL(x1, x2, x3) -> f388_0_height_NONNULL(x1, x2)

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

(18)
Obligation:
Rules:
f388_0_height_NONNULL(x110:0, x111:0) -> f388_0_height_NONNULL(x113:0, x114:0) :|: x113:0 <= x111:0 && x113:0 + 2 <= x110:0 && x114:0 + 3 <= x110:0 && x114:0 + 1 <= x111:0 && x110:0 > 2 && x111:0 > 0 && x113:0 > 0 && x114:0 > -1
f388_0_height_NONNULL(x116:0, x117:0) -> f388_0_height_NONNULL(x119:0, x120:0) :|: x120:0 + 3 <= x116:0 && x119:0 + 2 <= x116:0 && x116:0 > 2 && x117:0 > -1 && x119:0 > 0 && x120:0 > -1

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

(19) FilterProof (EQUIVALENT)
Used the following sort dictionary for filtering: 
f388_0_height_NONNULL(INTEGER, INTEGER)
Replaced non-predefined constructor symbols by 0.
----------------------------------------

(20)
Obligation:
Rules:
f388_0_height_NONNULL(x110:0, x111:0) -> f388_0_height_NONNULL(x113:0, x114:0) :|: x113:0 <= x111:0 && x113:0 + 2 <= x110:0 && x114:0 + 3 <= x110:0 && x114:0 + 1 <= x111:0 && x110:0 > 2 && x111:0 > 0 && x113:0 > 0 && x114:0 > -1
f388_0_height_NONNULL(x116:0, x117:0) -> f388_0_height_NONNULL(x119:0, x120:0) :|: x120:0 + 3 <= x116:0 && x119:0 + 2 <= x116:0 && x116:0 > 2 && x117:0 > -1 && x119:0 > 0 && x120:0 > -1

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

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

(22)
Obligation:
Rules:
f388_0_height_NONNULL(x110:0:0, x111:0:0) -> f388_0_height_NONNULL(x113:0:0, x114:0:0) :|: x113:0:0 > 0 && x114:0:0 > -1 && x111:0:0 > 0 && x110:0:0 > 2 && x114:0:0 + 1 <= x111:0:0 && x114:0:0 + 3 <= x110:0:0 && x113:0:0 + 2 <= x110:0:0 && x113:0:0 <= x111:0:0
f388_0_height_NONNULL(x116:0:0, x117:0:0) -> f388_0_height_NONNULL(x119:0:0, x120:0:0) :|: x119:0:0 > 0 && x120:0:0 > -1 && x117:0:0 > -1 && x116:0:0 > 2 && x119:0:0 + 2 <= x116:0:0 && x120:0:0 + 3 <= x116:0:0

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

(23) RankingReductionPairProof (EQUIVALENT)
Interpretation:
[ f388_0_height_NONNULL ] = 1/2*f388_0_height_NONNULL_1

The following rules are decreasing:
f388_0_height_NONNULL(x110:0:0, x111:0:0) -> f388_0_height_NONNULL(x113:0:0, x114:0:0) :|: x113:0:0 > 0 && x114:0:0 > -1 && x111:0:0 > 0 && x110:0:0 > 2 && x114:0:0 + 1 <= x111:0:0 && x114:0:0 + 3 <= x110:0:0 && x113:0:0 + 2 <= x110:0:0 && x113:0:0 <= x111:0:0
f388_0_height_NONNULL(x116:0:0, x117:0:0) -> f388_0_height_NONNULL(x119:0:0, x120:0:0) :|: x119:0:0 > 0 && x120:0:0 > -1 && x117:0:0 > -1 && x116:0:0 > 2 && x119:0:0 + 2 <= x116:0:0 && x120:0:0 + 3 <= x116:0:0

The following rules are bounded:
f388_0_height_NONNULL(x110:0:0, x111:0:0) -> f388_0_height_NONNULL(x113:0:0, x114:0:0) :|: x113:0:0 > 0 && x114:0:0 > -1 && x111:0:0 > 0 && x110:0:0 > 2 && x114:0:0 + 1 <= x111:0:0 && x114:0:0 + 3 <= x110:0:0 && x113:0:0 + 2 <= x110:0:0 && x113:0:0 <= x111:0:0
f388_0_height_NONNULL(x116:0:0, x117:0:0) -> f388_0_height_NONNULL(x119:0:0, x120:0:0) :|: x119:0:0 > 0 && x120:0:0 > -1 && x117:0:0 > -1 && x116:0:0 > 2 && x119:0:0 + 2 <= x116:0:0 && x120:0:0 + 3 <= x116:0:0


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(24)
YES