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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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, 1022 ms]
(4) AND
    (5) IRSwT
        (6) IntTRSCompressionProof [EQUIVALENT, 5 ms]
        (7) IRSwT
        (8) TempFilterProof [SOUND, 28 ms]
        (9) IntTRS
        (10) RankingReductionPairProof [EQUIVALENT, 14 ms]
        (11) YES
    (12) IRSwT
        (13) IntTRSCompressionProof [EQUIVALENT, 5 ms]
        (14) IRSwT
        (15) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms]
        (16) IRSwT
        (17) FilterProof [EQUIVALENT, 0 ms]
        (18) IntTRS
        (19) IntTRSCompressionProof [EQUIVALENT, 0 ms]
        (20) IntTRS
        (21) RankingReductionPairProof [EQUIVALENT, 0 ms]
        (22) YES
    (23) IRSwT
        (24) IntTRSCompressionProof [EQUIVALENT, 16 ms]
        (25) IRSwT
        (26) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms]
        (27) IRSwT
        (28) TempFilterProof [SOUND, 38 ms]
        (29) IntTRS
        (30) PolynomialOrderProcessor [EQUIVALENT, 14 ms]
        (31) YES


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

(0)
Obligation:
Rules:
f1_0_main_Load(arg1, arg2, arg3, arg4, arg5, arg6) -> f908_0_main_InvokeMethod(arg1P, arg2P, arg3P, arg4P, arg5P, arg6P) :|: -1 <= x7 - 1 && 0 <= arg2 - 1 && arg1P <= arg1 && 0 <= arg1 - 1 && 0 <= arg1P - 1 && 0 <= arg2P - 1 && -1 <= arg3P - 1
f358_0_createTree_Return(x, x1, x2, x3, x4, x5) -> f908_0_main_InvokeMethod(x6, x8, x9, x10, x11, x12) :|: x4 = x11 && x3 = x10 && x4 + 2 <= x1 && x3 + 2 <= x1 && -1 <= x9 - 1 && 0 <= x8 - 1 && 0 <= x6 - 1 && -1 <= x2 - 1 && 0 <= x1 - 1 && 0 <= x - 1 && x9 <= x2 && x9 + 1 <= x1 && x8 <= x1 && x6 - 1 <= x2 && x6 <= x1 && x6 <= x
f1_0_main_Load(x13, x14, x15, x16, x17, x18) -> f880_0_createTree_GE(x19, x20, x21, x22, x23, x24) :|: 2 = x23 && x14 = x22 && 0 = x20 && 1 <= x19 - 1 && 0 <= x13 - 1 && -1 <= x21 - 1 && 1 <= x14 - 1 && -1 <= x24 - 1
f880_0_createTree_GE(x25, x26, x27, x28, x29, x31) -> f880_0_createTree_GE(x32, x33, x34, x35, x36, x37) :|: -1 <= x29 - 1 && x26 <= x27 - 1 && 0 <= x27 - 1 && 1 <= x28 - 1 && -1 <= x38 - 1 && x29 <= x28 - 1 && 0 <= x25 - 1 && 3 <= x32 - 1 && x31 + 2 <= x25 && x26 + 1 = x33 && x27 = x34 && x28 = x35 && x29 + 1 = x36
f880_0_createTree_GE(x39, x40, x41, x42, x43, x44) -> f880_0_createTree_GE(x45, x46, x47, x49, x50, x51) :|: -1 <= x43 - 1 && x40 <= x41 - 1 && 0 <= x41 - 1 && 1 <= x42 - 1 && -1 <= x52 - 1 && x43 <= x42 - 1 && 0 <= x39 - 1 && 2 <= x45 - 1 && x44 + 2 <= x39 && x40 + 1 = x46 && x41 = x47 && x42 = x49 && x43 + 1 = x50
f908_0_main_InvokeMethod(x53, x54, x55, x56, x57, x59) -> f940_0_gopher_NONNULL(x60, x61, x62, x63, x64, x65) :|: x60 <= x54 && 1 <= x66 - 1 && x61 + 1 <= x54 && x61 <= x55 && 0 <= x53 - 1 && 0 <= x54 - 1 && -1 <= x55 - 1 && 0 <= x60 - 1 && -1 <= x61 - 1 && x56 + 2 <= x54 && x57 + 2 <= x54 && x57 = x62
f940_0_gopher_NONNULL(x67, x68, x69, x70, x71, x72) -> f940_0_gopher_NONNULL(x73, x74, x75, x76, x77, x78) :|: 0 = x75 && x69 + 2 <= x67 && -1 <= x74 - 1 && 3 <= x73 - 1 && 0 <= x68 - 1 && 2 <= x67 - 1 && x74 + 1 <= x68 && x74 + 3 <= x67 && x73 - 2 <= x67
f880_0_createTree_GE(x79, x80, x81, x82, x83, x84) -> f1019_0_insert_GT(x85, x86, x87, x88, x89, x90) :|: x84 = x88 && x82 = x87 && x84 + 2 <= x79 && 0 <= x85 - 1 && 0 <= x79 - 1 && x85 <= x79 && x83 <= x82 - 1 && -1 <= x86 - 1 && 1 <= x82 - 1 && 0 <= x81 - 1 && x80 <= x81 - 1 && -1 <= x83 - 1
f1019_0_insert_GT(x91, x92, x93, x94, x95, x96) -> f1019_0_insert_GT(x97, x98, x99, x100, x101, x102) :|: x93 = x99 && x92 = x98 && x100 + 4 <= x91 && x94 + 2 <= x91 && 0 <= x97 - 1 && 2 <= x91 - 1 && x97 + 2 <= x91 && x94 <= x92 - 1 && 1 <= x93 - 1
f1019_0_insert_GT(x103, x104, x105, x106, x107, x108) -> f1019_0_insert_GT(x109, x110, x111, x112, x113, x114) :|: x105 = x111 && x104 = x110 && x112 + 4 <= x103 && x106 + 2 <= x103 && 0 <= x109 - 1 && 2 <= x103 - 1 && x109 + 2 <= x103 && x104 <= x106 && 1 <= x105 - 1
__init(x115, x116, x117, x118, x119, x120) -> f1_0_main_Load(x121, x122, x123, x124, x125, x126) :|: 0 <= 0
Start term: __init(arg1, arg2, arg3, arg4, arg5, arg6)

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

(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) -> f908_0_main_InvokeMethod(arg1P, arg2P, arg3P, arg4P, arg5P, arg6P) :|: -1 <= x7 - 1 && 0 <= arg2 - 1 && arg1P <= arg1 && 0 <= arg1 - 1 && 0 <= arg1P - 1 && 0 <= arg2P - 1 && -1 <= arg3P - 1
f358_0_createTree_Return(x, x1, x2, x3, x4, x5) -> f908_0_main_InvokeMethod(x6, x8, x9, x10, x11, x12) :|: x4 = x11 && x3 = x10 && x4 + 2 <= x1 && x3 + 2 <= x1 && -1 <= x9 - 1 && 0 <= x8 - 1 && 0 <= x6 - 1 && -1 <= x2 - 1 && 0 <= x1 - 1 && 0 <= x - 1 && x9 <= x2 && x9 + 1 <= x1 && x8 <= x1 && x6 - 1 <= x2 && x6 <= x1 && x6 <= x
f1_0_main_Load(x13, x14, x15, x16, x17, x18) -> f880_0_createTree_GE(x19, x20, x21, x22, x23, x24) :|: 2 = x23 && x14 = x22 && 0 = x20 && 1 <= x19 - 1 && 0 <= x13 - 1 && -1 <= x21 - 1 && 1 <= x14 - 1 && -1 <= x24 - 1
f880_0_createTree_GE(x25, x26, x27, x28, x29, x31) -> f880_0_createTree_GE(x32, x33, x34, x35, x36, x37) :|: -1 <= x29 - 1 && x26 <= x27 - 1 && 0 <= x27 - 1 && 1 <= x28 - 1 && -1 <= x38 - 1 && x29 <= x28 - 1 && 0 <= x25 - 1 && 3 <= x32 - 1 && x31 + 2 <= x25 && x26 + 1 = x33 && x27 = x34 && x28 = x35 && x29 + 1 = x36
f880_0_createTree_GE(x39, x40, x41, x42, x43, x44) -> f880_0_createTree_GE(x45, x46, x47, x49, x50, x51) :|: -1 <= x43 - 1 && x40 <= x41 - 1 && 0 <= x41 - 1 && 1 <= x42 - 1 && -1 <= x52 - 1 && x43 <= x42 - 1 && 0 <= x39 - 1 && 2 <= x45 - 1 && x44 + 2 <= x39 && x40 + 1 = x46 && x41 = x47 && x42 = x49 && x43 + 1 = x50
f908_0_main_InvokeMethod(x53, x54, x55, x56, x57, x59) -> f940_0_gopher_NONNULL(x60, x61, x62, x63, x64, x65) :|: x60 <= x54 && 1 <= x66 - 1 && x61 + 1 <= x54 && x61 <= x55 && 0 <= x53 - 1 && 0 <= x54 - 1 && -1 <= x55 - 1 && 0 <= x60 - 1 && -1 <= x61 - 1 && x56 + 2 <= x54 && x57 + 2 <= x54 && x57 = x62
f940_0_gopher_NONNULL(x67, x68, x69, x70, x71, x72) -> f940_0_gopher_NONNULL(x73, x74, x75, x76, x77, x78) :|: 0 = x75 && x69 + 2 <= x67 && -1 <= x74 - 1 && 3 <= x73 - 1 && 0 <= x68 - 1 && 2 <= x67 - 1 && x74 + 1 <= x68 && x74 + 3 <= x67 && x73 - 2 <= x67
f880_0_createTree_GE(x79, x80, x81, x82, x83, x84) -> f1019_0_insert_GT(x85, x86, x87, x88, x89, x90) :|: x84 = x88 && x82 = x87 && x84 + 2 <= x79 && 0 <= x85 - 1 && 0 <= x79 - 1 && x85 <= x79 && x83 <= x82 - 1 && -1 <= x86 - 1 && 1 <= x82 - 1 && 0 <= x81 - 1 && x80 <= x81 - 1 && -1 <= x83 - 1
f1019_0_insert_GT(x91, x92, x93, x94, x95, x96) -> f1019_0_insert_GT(x97, x98, x99, x100, x101, x102) :|: x93 = x99 && x92 = x98 && x100 + 4 <= x91 && x94 + 2 <= x91 && 0 <= x97 - 1 && 2 <= x91 - 1 && x97 + 2 <= x91 && x94 <= x92 - 1 && 1 <= x93 - 1
f1019_0_insert_GT(x103, x104, x105, x106, x107, x108) -> f1019_0_insert_GT(x109, x110, x111, x112, x113, x114) :|: x105 = x111 && x104 = x110 && x112 + 4 <= x103 && x106 + 2 <= x103 && 0 <= x109 - 1 && 2 <= x103 - 1 && x109 + 2 <= x103 && x104 <= x106 && 1 <= x105 - 1
__init(x115, x116, x117, x118, x119, x120) -> f1_0_main_Load(x121, x122, x123, x124, x125, x126) :|: 0 <= 0
Start term: __init(arg1, arg2, arg3, arg4, arg5, arg6)

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

(3) IRSwTTerminationDigraphProof (EQUIVALENT)
Constructed termination digraph!
Nodes:
(1) f1_0_main_Load(arg1, arg2, arg3, arg4, arg5, arg6) -> f908_0_main_InvokeMethod(arg1P, arg2P, arg3P, arg4P, arg5P, arg6P) :|: -1 <= x7 - 1 && 0 <= arg2 - 1 && arg1P <= arg1 && 0 <= arg1 - 1 && 0 <= arg1P - 1 && 0 <= arg2P - 1 && -1 <= arg3P - 1
(2) f358_0_createTree_Return(x, x1, x2, x3, x4, x5) -> f908_0_main_InvokeMethod(x6, x8, x9, x10, x11, x12) :|: x4 = x11 && x3 = x10 && x4 + 2 <= x1 && x3 + 2 <= x1 && -1 <= x9 - 1 && 0 <= x8 - 1 && 0 <= x6 - 1 && -1 <= x2 - 1 && 0 <= x1 - 1 && 0 <= x - 1 && x9 <= x2 && x9 + 1 <= x1 && x8 <= x1 && x6 - 1 <= x2 && x6 <= x1 && x6 <= x
(3) f1_0_main_Load(x13, x14, x15, x16, x17, x18) -> f880_0_createTree_GE(x19, x20, x21, x22, x23, x24) :|: 2 = x23 && x14 = x22 && 0 = x20 && 1 <= x19 - 1 && 0 <= x13 - 1 && -1 <= x21 - 1 && 1 <= x14 - 1 && -1 <= x24 - 1
(4) f880_0_createTree_GE(x25, x26, x27, x28, x29, x31) -> f880_0_createTree_GE(x32, x33, x34, x35, x36, x37) :|: -1 <= x29 - 1 && x26 <= x27 - 1 && 0 <= x27 - 1 && 1 <= x28 - 1 && -1 <= x38 - 1 && x29 <= x28 - 1 && 0 <= x25 - 1 && 3 <= x32 - 1 && x31 + 2 <= x25 && x26 + 1 = x33 && x27 = x34 && x28 = x35 && x29 + 1 = x36
(5) f880_0_createTree_GE(x39, x40, x41, x42, x43, x44) -> f880_0_createTree_GE(x45, x46, x47, x49, x50, x51) :|: -1 <= x43 - 1 && x40 <= x41 - 1 && 0 <= x41 - 1 && 1 <= x42 - 1 && -1 <= x52 - 1 && x43 <= x42 - 1 && 0 <= x39 - 1 && 2 <= x45 - 1 && x44 + 2 <= x39 && x40 + 1 = x46 && x41 = x47 && x42 = x49 && x43 + 1 = x50
(6) f908_0_main_InvokeMethod(x53, x54, x55, x56, x57, x59) -> f940_0_gopher_NONNULL(x60, x61, x62, x63, x64, x65) :|: x60 <= x54 && 1 <= x66 - 1 && x61 + 1 <= x54 && x61 <= x55 && 0 <= x53 - 1 && 0 <= x54 - 1 && -1 <= x55 - 1 && 0 <= x60 - 1 && -1 <= x61 - 1 && x56 + 2 <= x54 && x57 + 2 <= x54 && x57 = x62
(7) f940_0_gopher_NONNULL(x67, x68, x69, x70, x71, x72) -> f940_0_gopher_NONNULL(x73, x74, x75, x76, x77, x78) :|: 0 = x75 && x69 + 2 <= x67 && -1 <= x74 - 1 && 3 <= x73 - 1 && 0 <= x68 - 1 && 2 <= x67 - 1 && x74 + 1 <= x68 && x74 + 3 <= x67 && x73 - 2 <= x67
(8) f880_0_createTree_GE(x79, x80, x81, x82, x83, x84) -> f1019_0_insert_GT(x85, x86, x87, x88, x89, x90) :|: x84 = x88 && x82 = x87 && x84 + 2 <= x79 && 0 <= x85 - 1 && 0 <= x79 - 1 && x85 <= x79 && x83 <= x82 - 1 && -1 <= x86 - 1 && 1 <= x82 - 1 && 0 <= x81 - 1 && x80 <= x81 - 1 && -1 <= x83 - 1
(9) f1019_0_insert_GT(x91, x92, x93, x94, x95, x96) -> f1019_0_insert_GT(x97, x98, x99, x100, x101, x102) :|: x93 = x99 && x92 = x98 && x100 + 4 <= x91 && x94 + 2 <= x91 && 0 <= x97 - 1 && 2 <= x91 - 1 && x97 + 2 <= x91 && x94 <= x92 - 1 && 1 <= x93 - 1
(10) f1019_0_insert_GT(x103, x104, x105, x106, x107, x108) -> f1019_0_insert_GT(x109, x110, x111, x112, x113, x114) :|: x105 = x111 && x104 = x110 && x112 + 4 <= x103 && x106 + 2 <= x103 && 0 <= x109 - 1 && 2 <= x103 - 1 && x109 + 2 <= x103 && x104 <= x106 && 1 <= x105 - 1
(11) __init(x115, x116, x117, x118, x119, x120) -> f1_0_main_Load(x121, x122, x123, x124, x125, x126) :|: 0 <= 0

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

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

(4)
Complex Obligation (AND)

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

(5)
Obligation:

Termination digraph:
Nodes:
(1) f880_0_createTree_GE(x25, x26, x27, x28, x29, x31) -> f880_0_createTree_GE(x32, x33, x34, x35, x36, x37) :|: -1 <= x29 - 1 && x26 <= x27 - 1 && 0 <= x27 - 1 && 1 <= x28 - 1 && -1 <= x38 - 1 && x29 <= x28 - 1 && 0 <= x25 - 1 && 3 <= x32 - 1 && x31 + 2 <= x25 && x26 + 1 = x33 && x27 = x34 && x28 = x35 && x29 + 1 = x36
(2) f880_0_createTree_GE(x39, x40, x41, x42, x43, x44) -> f880_0_createTree_GE(x45, x46, x47, x49, x50, x51) :|: -1 <= x43 - 1 && x40 <= x41 - 1 && 0 <= x41 - 1 && 1 <= x42 - 1 && -1 <= x52 - 1 && x43 <= x42 - 1 && 0 <= x39 - 1 && 2 <= x45 - 1 && x44 + 2 <= x39 && x40 + 1 = x46 && x41 = x47 && x42 = x49 && x43 + 1 = x50

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

This digraph is fully evaluated!

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

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

(7)
Obligation:
Rules:
f880_0_createTree_GE(x25:0, x26:0, x27:0, x28:0, x29:0, x31:0) -> f880_0_createTree_GE(x32:0, x26:0 + 1, x27:0, x28:0, x29:0 + 1, x37:0) :|: x32:0 > 3 && x31:0 + 2 <= x25:0 && x25:0 > 0 && x29:0 <= x28:0 - 1 && x38:0 > -1 && x28:0 > 1 && x27:0 > 0 && x27:0 - 1 >= x26:0 && x29:0 > -1
f880_0_createTree_GE(x39:0, x40:0, x41:0, x42:0, x43:0, x44:0) -> f880_0_createTree_GE(x45:0, x40:0 + 1, x41:0, x42:0, x43:0 + 1, x51:0) :|: x45:0 > 2 && x44:0 + 2 <= x39:0 && x39:0 > 0 && x43:0 <= x42:0 - 1 && x52:0 > -1 && x42:0 > 1 && x41:0 > 0 && x41:0 - 1 >= x40:0 && x43:0 > -1

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

(8) TempFilterProof (SOUND)
Used the following sort dictionary for filtering: 
f880_0_createTree_GE(INTEGER, INTEGER, INTEGER, INTEGER, INTEGER, VARIABLE)
Replaced non-predefined constructor symbols by 0.
----------------------------------------

(9)
Obligation:
Rules:
f880_0_createTree_GE(x25:0, x26:0, x27:0, x28:0, x29:0, x31:0) -> f880_0_createTree_GE(x32:0, c, x27:0, x28:0, c1, x37:0) :|: c1 = x29:0 + 1 && c = x26:0 + 1 && (x32:0 > 3 && x31:0 + 2 <= x25:0 && x25:0 > 0 && x29:0 <= x28:0 - 1 && x38:0 > -1 && x28:0 > 1 && x27:0 > 0 && x27:0 - 1 >= x26:0 && x29:0 > -1)
f880_0_createTree_GE(x39:0, x40:0, x41:0, x42:0, x43:0, x44:0) -> f880_0_createTree_GE(x45:0, c2, x41:0, x42:0, c3, x51:0) :|: c3 = x43:0 + 1 && c2 = x40:0 + 1 && (x45:0 > 2 && x44:0 + 2 <= x39:0 && x39:0 > 0 && x43:0 <= x42:0 - 1 && x52:0 > -1 && x42:0 > 1 && x41:0 > 0 && x41:0 - 1 >= x40:0 && x43:0 > -1)

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

(10) RankingReductionPairProof (EQUIVALENT)
Interpretation:
[ f880_0_createTree_GE ] = -1*f880_0_createTree_GE_5 + f880_0_createTree_GE_4

The following rules are decreasing:
f880_0_createTree_GE(x25:0, x26:0, x27:0, x28:0, x29:0, x31:0) -> f880_0_createTree_GE(x32:0, c, x27:0, x28:0, c1, x37:0) :|: c1 = x29:0 + 1 && c = x26:0 + 1 && (x32:0 > 3 && x31:0 + 2 <= x25:0 && x25:0 > 0 && x29:0 <= x28:0 - 1 && x38:0 > -1 && x28:0 > 1 && x27:0 > 0 && x27:0 - 1 >= x26:0 && x29:0 > -1)
f880_0_createTree_GE(x39:0, x40:0, x41:0, x42:0, x43:0, x44:0) -> f880_0_createTree_GE(x45:0, c2, x41:0, x42:0, c3, x51:0) :|: c3 = x43:0 + 1 && c2 = x40:0 + 1 && (x45:0 > 2 && x44:0 + 2 <= x39:0 && x39:0 > 0 && x43:0 <= x42:0 - 1 && x52:0 > -1 && x42:0 > 1 && x41:0 > 0 && x41:0 - 1 >= x40:0 && x43:0 > -1)

The following rules are bounded:
f880_0_createTree_GE(x25:0, x26:0, x27:0, x28:0, x29:0, x31:0) -> f880_0_createTree_GE(x32:0, c, x27:0, x28:0, c1, x37:0) :|: c1 = x29:0 + 1 && c = x26:0 + 1 && (x32:0 > 3 && x31:0 + 2 <= x25:0 && x25:0 > 0 && x29:0 <= x28:0 - 1 && x38:0 > -1 && x28:0 > 1 && x27:0 > 0 && x27:0 - 1 >= x26:0 && x29:0 > -1)
f880_0_createTree_GE(x39:0, x40:0, x41:0, x42:0, x43:0, x44:0) -> f880_0_createTree_GE(x45:0, c2, x41:0, x42:0, c3, x51:0) :|: c3 = x43:0 + 1 && c2 = x40:0 + 1 && (x45:0 > 2 && x44:0 + 2 <= x39:0 && x39:0 > 0 && x43:0 <= x42:0 - 1 && x52:0 > -1 && x42:0 > 1 && x41:0 > 0 && x41:0 - 1 >= x40:0 && x43:0 > -1)


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

(11)
YES

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

(12)
Obligation:

Termination digraph:
Nodes:
(1) f1019_0_insert_GT(x91, x92, x93, x94, x95, x96) -> f1019_0_insert_GT(x97, x98, x99, x100, x101, x102) :|: x93 = x99 && x92 = x98 && x100 + 4 <= x91 && x94 + 2 <= x91 && 0 <= x97 - 1 && 2 <= x91 - 1 && x97 + 2 <= x91 && x94 <= x92 - 1 && 1 <= x93 - 1
(2) f1019_0_insert_GT(x103, x104, x105, x106, x107, x108) -> f1019_0_insert_GT(x109, x110, x111, x112, x113, x114) :|: x105 = x111 && x104 = x110 && x112 + 4 <= x103 && x106 + 2 <= x103 && 0 <= x109 - 1 && 2 <= x103 - 1 && x109 + 2 <= x103 && x104 <= x106 && 1 <= x105 - 1

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

This digraph is fully evaluated!

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

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

(14)
Obligation:
Rules:
f1019_0_insert_GT(x103:0, x104:0, x105:0, x106:0, x107:0, x108:0) -> f1019_0_insert_GT(x109:0, x104:0, x105:0, x112:0, x113:0, x114:0) :|: x106:0 >= x104:0 && x105:0 > 1 && x109:0 + 2 <= x103:0 && x103:0 > 2 && x109:0 > 0 && x112:0 + 4 <= x103:0 && x106:0 + 2 <= x103:0
f1019_0_insert_GT(x91:0, x92:0, x93:0, x94:0, x95:0, x96:0) -> f1019_0_insert_GT(x97:0, x92:0, x93:0, x100:0, x101:0, x102:0) :|: x94:0 <= x92:0 - 1 && x93:0 > 1 && x97:0 + 2 <= x91:0 && x91:0 > 2 && x97:0 > 0 && x91:0 >= x100:0 + 4 && x94:0 + 2 <= x91:0

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

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

   f1019_0_insert_GT(x1, x2, x3, x4, x5, x6) -> f1019_0_insert_GT(x1, x2, x3, x4)

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

(16)
Obligation:
Rules:
f1019_0_insert_GT(x103:0, x104:0, x105:0, x106:0) -> f1019_0_insert_GT(x109:0, x104:0, x105:0, x112:0) :|: x106:0 >= x104:0 && x105:0 > 1 && x109:0 + 2 <= x103:0 && x103:0 > 2 && x109:0 > 0 && x112:0 + 4 <= x103:0 && x106:0 + 2 <= x103:0
f1019_0_insert_GT(x91:0, x92:0, x93:0, x94:0) -> f1019_0_insert_GT(x97:0, x92:0, x93:0, x100:0) :|: x94:0 <= x92:0 - 1 && x93:0 > 1 && x97:0 + 2 <= x91:0 && x91:0 > 2 && x97:0 > 0 && x91:0 >= x100:0 + 4 && x94:0 + 2 <= x91:0

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(17) FilterProof (EQUIVALENT)
Used the following sort dictionary for filtering: 
f1019_0_insert_GT(INTEGER, INTEGER, INTEGER, INTEGER)
Replaced non-predefined constructor symbols by 0.
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(18)
Obligation:
Rules:
f1019_0_insert_GT(x103:0, x104:0, x105:0, x106:0) -> f1019_0_insert_GT(x109:0, x104:0, x105:0, x112:0) :|: x106:0 >= x104:0 && x105:0 > 1 && x109:0 + 2 <= x103:0 && x103:0 > 2 && x109:0 > 0 && x112:0 + 4 <= x103:0 && x106:0 + 2 <= x103:0
f1019_0_insert_GT(x91:0, x92:0, x93:0, x94:0) -> f1019_0_insert_GT(x97:0, x92:0, x93:0, x100:0) :|: x94:0 <= x92:0 - 1 && x93:0 > 1 && x97:0 + 2 <= x91:0 && x91:0 > 2 && x97:0 > 0 && x91:0 >= x100:0 + 4 && x94:0 + 2 <= x91:0

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

(20)
Obligation:
Rules:
f1019_0_insert_GT(x103:0:0, x104:0:0, x105:0:0, x106:0:0) -> f1019_0_insert_GT(x109:0:0, x104:0:0, x105:0:0, x112:0:0) :|: x112:0:0 + 4 <= x103:0:0 && x106:0:0 + 2 <= x103:0:0 && x109:0:0 > 0 && x103:0:0 > 2 && x109:0:0 + 2 <= x103:0:0 && x105:0:0 > 1 && x106:0:0 >= x104:0:0
f1019_0_insert_GT(x91:0:0, x92:0:0, x93:0:0, x94:0:0) -> f1019_0_insert_GT(x97:0:0, x92:0:0, x93:0:0, x100:0:0) :|: x91:0:0 >= x100:0:0 + 4 && x94:0:0 + 2 <= x91:0:0 && x97:0:0 > 0 && x91:0:0 > 2 && x97:0:0 + 2 <= x91:0:0 && x93:0:0 > 1 && x94:0:0 <= x92:0:0 - 1

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(21) RankingReductionPairProof (EQUIVALENT)
Interpretation:
[ f1019_0_insert_GT ] = 1/2*f1019_0_insert_GT_1

The following rules are decreasing:
f1019_0_insert_GT(x103:0:0, x104:0:0, x105:0:0, x106:0:0) -> f1019_0_insert_GT(x109:0:0, x104:0:0, x105:0:0, x112:0:0) :|: x112:0:0 + 4 <= x103:0:0 && x106:0:0 + 2 <= x103:0:0 && x109:0:0 > 0 && x103:0:0 > 2 && x109:0:0 + 2 <= x103:0:0 && x105:0:0 > 1 && x106:0:0 >= x104:0:0
f1019_0_insert_GT(x91:0:0, x92:0:0, x93:0:0, x94:0:0) -> f1019_0_insert_GT(x97:0:0, x92:0:0, x93:0:0, x100:0:0) :|: x91:0:0 >= x100:0:0 + 4 && x94:0:0 + 2 <= x91:0:0 && x97:0:0 > 0 && x91:0:0 > 2 && x97:0:0 + 2 <= x91:0:0 && x93:0:0 > 1 && x94:0:0 <= x92:0:0 - 1

The following rules are bounded:
f1019_0_insert_GT(x103:0:0, x104:0:0, x105:0:0, x106:0:0) -> f1019_0_insert_GT(x109:0:0, x104:0:0, x105:0:0, x112:0:0) :|: x112:0:0 + 4 <= x103:0:0 && x106:0:0 + 2 <= x103:0:0 && x109:0:0 > 0 && x103:0:0 > 2 && x109:0:0 + 2 <= x103:0:0 && x105:0:0 > 1 && x106:0:0 >= x104:0:0
f1019_0_insert_GT(x91:0:0, x92:0:0, x93:0:0, x94:0:0) -> f1019_0_insert_GT(x97:0:0, x92:0:0, x93:0:0, x100:0:0) :|: x91:0:0 >= x100:0:0 + 4 && x94:0:0 + 2 <= x91:0:0 && x97:0:0 > 0 && x91:0:0 > 2 && x97:0:0 + 2 <= x91:0:0 && x93:0:0 > 1 && x94:0:0 <= x92:0:0 - 1


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(22)
YES

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(23)
Obligation:

Termination digraph:
Nodes:
(1) f940_0_gopher_NONNULL(x67, x68, x69, x70, x71, x72) -> f940_0_gopher_NONNULL(x73, x74, x75, x76, x77, x78) :|: 0 = x75 && x69 + 2 <= x67 && -1 <= x74 - 1 && 3 <= x73 - 1 && 0 <= x68 - 1 && 2 <= x67 - 1 && x74 + 1 <= x68 && x74 + 3 <= x67 && x73 - 2 <= x67

Arcs:
(1) -> (1)

This digraph is fully evaluated!

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

(25)
Obligation:
Rules:
f940_0_gopher_NONNULL(x67:0, x68:0, x69:0, x70:0, x71:0, x72:0) -> f940_0_gopher_NONNULL(x73:0, x74:0, 0, x76:0, x77:0, x78:0) :|: x74:0 + 3 <= x67:0 && x73:0 - 2 <= x67:0 && x74:0 + 1 <= x68:0 && x67:0 > 2 && x68:0 > 0 && x73:0 > 3 && x69:0 + 2 <= x67:0 && x74:0 > -1

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

   f940_0_gopher_NONNULL(x1, x2, x3, x4, x5, x6) -> f940_0_gopher_NONNULL(x1, x2, x3)

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(27)
Obligation:
Rules:
f940_0_gopher_NONNULL(x67:0, x68:0, x69:0) -> f940_0_gopher_NONNULL(x73:0, x74:0, 0) :|: x74:0 + 3 <= x67:0 && x73:0 - 2 <= x67:0 && x74:0 + 1 <= x68:0 && x67:0 > 2 && x68:0 > 0 && x73:0 > 3 && x69:0 + 2 <= x67:0 && x74:0 > -1

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(28) TempFilterProof (SOUND)
Used the following sort dictionary for filtering: 
f940_0_gopher_NONNULL(INTEGER, INTEGER, VARIABLE)
Replaced non-predefined constructor symbols by 0.
----------------------------------------

(29)
Obligation:
Rules:
f940_0_gopher_NONNULL(x67:0, x68:0, x69:0) -> f940_0_gopher_NONNULL(x73:0, x74:0, c) :|: c = 0 && (x74:0 + 3 <= x67:0 && x73:0 - 2 <= x67:0 && x74:0 + 1 <= x68:0 && x67:0 > 2 && x68:0 > 0 && x73:0 > 3 && x69:0 + 2 <= x67:0 && x74:0 > -1)

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(30) PolynomialOrderProcessor (EQUIVALENT)
Found the following polynomial interpretation:
[f940_0_gopher_NONNULL(x, x1, x2)] = x1

The following rules are decreasing:
f940_0_gopher_NONNULL(x67:0, x68:0, x69:0) -> f940_0_gopher_NONNULL(x73:0, x74:0, c) :|: c = 0 && (x74:0 + 3 <= x67:0 && x73:0 - 2 <= x67:0 && x74:0 + 1 <= x68:0 && x67:0 > 2 && x68:0 > 0 && x73:0 > 3 && x69:0 + 2 <= x67:0 && x74:0 > -1)
The following rules are bounded:
f940_0_gopher_NONNULL(x67:0, x68:0, x69:0) -> f940_0_gopher_NONNULL(x73:0, x74:0, c) :|: c = 0 && (x74:0 + 3 <= x67:0 && x73:0 - 2 <= x67:0 && x74:0 + 1 <= x68:0 && x67:0 > 2 && x68:0 > 0 && x73:0 > 3 && x69:0 + 2 <= x67:0 && x74:0 > -1)

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(31)
YES