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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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, 889 ms]
(4) AND
    (5) IRSwT
        (6) IntTRSCompressionProof [EQUIVALENT, 0 ms]
        (7) IRSwT
        (8) TempFilterProof [SOUND, 34 ms]
        (9) IntTRS
        (10) PolynomialOrderProcessor [EQUIVALENT, 0 ms]
        (11) YES
    (12) IRSwT
        (13) IntTRSCompressionProof [EQUIVALENT, 0 ms]
        (14) IRSwT
        (15) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms]
        (16) IRSwT
        (17) TempFilterProof [SOUND, 42 ms]
        (18) IntTRS
        (19) RankingReductionPairProof [EQUIVALENT, 24 ms]
        (20) YES
    (21) IRSwT
        (22) IntTRSCompressionProof [EQUIVALENT, 0 ms]
        (23) IRSwT
        (24) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms]
        (25) IRSwT
        (26) FilterProof [EQUIVALENT, 0 ms]
        (27) IntTRS
        (28) IntTRSCompressionProof [EQUIVALENT, 0 ms]
        (29) IntTRS
        (30) PolynomialOrderProcessor [EQUIVALENT, 0 ms]
        (31) YES


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

(0)
Obligation:
Rules:
f1_0_main_Load(arg1, arg2, arg3, arg4, arg5) -> f165_0_appendNewList_LE(arg1P, arg2P, arg3P, arg4P, arg5P) :|: 0 = arg5P && 3 <= arg3P - 1 && 5 <= arg2P - 1 && 0 <= arg1P - 1 && 0 <= arg1 - 1 && arg3P - 3 <= arg1 && arg2P - 5 <= arg1 && arg1P <= arg1 && -1 <= arg4P - 1 && 0 <= arg2 - 1
f165_0_appendNewList_LE(x, x1, x2, x3, x4) -> f200_0_random_ArrayAccess(x5, x6, x7, x8, x9) :|: x3 <= 1 && 0 <= x4 - 1 && x4 <= x10 - 1 && x4 <= x11 - 1 && 0 <= x - 1 && 4 <= x1 - 1 && 2 <= x2 - 1 && 4 <= x5 - 1
f165_0_appendNewList_LE(x12, x15, x16, x17, x18) -> f200_0_random_ArrayAccess(x19, x20, x21, x22, x23) :|: 6 <= x19 - 1 && 3 <= x16 - 1 && 5 <= x15 - 1 && 0 <= x12 - 1 && x19 - 3 <= x16 && x19 - 1 <= x15 && x17 <= 1 && x19 - 6 <= x12
f165_0_appendNewList_LE(x24, x25, x26, x27, x28) -> f165_0_appendNewList_LE(x29, x30, x31, x32, x33) :|: x27 - 1 = x32 && 2 <= x31 - 1 && 4 <= x30 - 1 && 0 <= x29 - 1 && 2 <= x26 - 1 && 4 <= x25 - 1 && 0 <= x24 - 1 && x29 + 2 <= x26 && x29 + 4 <= x25 && x29 <= x24 && 1 <= x27 - 1 && 0 <= x28 - 1 && x28 <= x33 - 1
f165_0_appendNewList_LE(x34, x35, x36, x37, x38) -> f165_0_appendNewList_LE(x39, x40, x41, x42, x43) :|: 1 = x43 && x37 - 1 = x42 && 5 <= x41 - 1 && 7 <= x40 - 1 && 0 <= x39 - 1 && 3 <= x36 - 1 && 5 <= x35 - 1 && 0 <= x34 - 1 && x41 - 2 <= x36 && x41 <= x35 && x41 - 5 <= x34 && x40 - 4 <= x36 && x40 - 2 <= x35 && x40 - 7 <= x34 && x39 + 3 <= x36 && x39 + 5 <= x35 && 1 <= x37 - 1 && x39 <= x34
f200_0_random_ArrayAccess(x44, x45, x46, x47, x48) -> f314_0_appendNewList_LE(x49, x50, x51, x52, x53) :|: 0 = x51 && 3 <= x49 - 1 && 4 <= x44 - 1 && x49 + 1 <= x44 && -1 <= x50 - 1 && 1 <= x45 - 1
f314_0_appendNewList_LE(x54, x55, x56, x57, x58) -> f314_0_appendNewList_LE(x59, x60, x61, x62, x63) :|: x55 - 1 = x60 && 2 <= x59 - 1 && 2 <= x54 - 1 && 1 <= x55 - 1 && 0 <= x56 - 1 && x56 <= x61 - 1
f314_0_appendNewList_LE(x64, x65, x66, x67, x68) -> f314_0_appendNewList_LE(x69, x70, x71, x72, x73) :|: 1 = x71 && x65 - 1 = x70 && 5 <= x69 - 1 && 3 <= x64 - 1 && 1 <= x65 - 1 && x69 - 2 <= x64
f314_0_appendNewList_LE(x74, x75, x76, x77, x78) -> f387_0_length_NULL(x79, x80, x81, x82, x83) :|: 0 <= x79 - 1 && 2 <= x74 - 1 && x75 <= 1 && x79 + 2 <= x74
f387_0_length_NULL(x84, x85, x86, x87, x88) -> f387_0_length_NULL(x89, x90, x91, x92, x93) :|: -1 <= x89 - 1 && 0 <= x84 - 1 && x89 + 1 <= x84
__init(x94, x95, x96, x97, x98) -> f1_0_main_Load(x99, x100, x101, x102, x103) :|: 0 <= 0
Start term: __init(arg1, arg2, arg3, arg4, arg5)

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

(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) -> f165_0_appendNewList_LE(arg1P, arg2P, arg3P, arg4P, arg5P) :|: 0 = arg5P && 3 <= arg3P - 1 && 5 <= arg2P - 1 && 0 <= arg1P - 1 && 0 <= arg1 - 1 && arg3P - 3 <= arg1 && arg2P - 5 <= arg1 && arg1P <= arg1 && -1 <= arg4P - 1 && 0 <= arg2 - 1
f165_0_appendNewList_LE(x, x1, x2, x3, x4) -> f200_0_random_ArrayAccess(x5, x6, x7, x8, x9) :|: x3 <= 1 && 0 <= x4 - 1 && x4 <= x10 - 1 && x4 <= x11 - 1 && 0 <= x - 1 && 4 <= x1 - 1 && 2 <= x2 - 1 && 4 <= x5 - 1
f165_0_appendNewList_LE(x12, x15, x16, x17, x18) -> f200_0_random_ArrayAccess(x19, x20, x21, x22, x23) :|: 6 <= x19 - 1 && 3 <= x16 - 1 && 5 <= x15 - 1 && 0 <= x12 - 1 && x19 - 3 <= x16 && x19 - 1 <= x15 && x17 <= 1 && x19 - 6 <= x12
f165_0_appendNewList_LE(x24, x25, x26, x27, x28) -> f165_0_appendNewList_LE(x29, x30, x31, x32, x33) :|: x27 - 1 = x32 && 2 <= x31 - 1 && 4 <= x30 - 1 && 0 <= x29 - 1 && 2 <= x26 - 1 && 4 <= x25 - 1 && 0 <= x24 - 1 && x29 + 2 <= x26 && x29 + 4 <= x25 && x29 <= x24 && 1 <= x27 - 1 && 0 <= x28 - 1 && x28 <= x33 - 1
f165_0_appendNewList_LE(x34, x35, x36, x37, x38) -> f165_0_appendNewList_LE(x39, x40, x41, x42, x43) :|: 1 = x43 && x37 - 1 = x42 && 5 <= x41 - 1 && 7 <= x40 - 1 && 0 <= x39 - 1 && 3 <= x36 - 1 && 5 <= x35 - 1 && 0 <= x34 - 1 && x41 - 2 <= x36 && x41 <= x35 && x41 - 5 <= x34 && x40 - 4 <= x36 && x40 - 2 <= x35 && x40 - 7 <= x34 && x39 + 3 <= x36 && x39 + 5 <= x35 && 1 <= x37 - 1 && x39 <= x34
f200_0_random_ArrayAccess(x44, x45, x46, x47, x48) -> f314_0_appendNewList_LE(x49, x50, x51, x52, x53) :|: 0 = x51 && 3 <= x49 - 1 && 4 <= x44 - 1 && x49 + 1 <= x44 && -1 <= x50 - 1 && 1 <= x45 - 1
f314_0_appendNewList_LE(x54, x55, x56, x57, x58) -> f314_0_appendNewList_LE(x59, x60, x61, x62, x63) :|: x55 - 1 = x60 && 2 <= x59 - 1 && 2 <= x54 - 1 && 1 <= x55 - 1 && 0 <= x56 - 1 && x56 <= x61 - 1
f314_0_appendNewList_LE(x64, x65, x66, x67, x68) -> f314_0_appendNewList_LE(x69, x70, x71, x72, x73) :|: 1 = x71 && x65 - 1 = x70 && 5 <= x69 - 1 && 3 <= x64 - 1 && 1 <= x65 - 1 && x69 - 2 <= x64
f314_0_appendNewList_LE(x74, x75, x76, x77, x78) -> f387_0_length_NULL(x79, x80, x81, x82, x83) :|: 0 <= x79 - 1 && 2 <= x74 - 1 && x75 <= 1 && x79 + 2 <= x74
f387_0_length_NULL(x84, x85, x86, x87, x88) -> f387_0_length_NULL(x89, x90, x91, x92, x93) :|: -1 <= x89 - 1 && 0 <= x84 - 1 && x89 + 1 <= x84
__init(x94, x95, x96, x97, x98) -> f1_0_main_Load(x99, x100, x101, x102, x103) :|: 0 <= 0
Start term: __init(arg1, arg2, arg3, arg4, arg5)

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

(3) IRSwTTerminationDigraphProof (EQUIVALENT)
Constructed termination digraph!
Nodes:
(1) f1_0_main_Load(arg1, arg2, arg3, arg4, arg5) -> f165_0_appendNewList_LE(arg1P, arg2P, arg3P, arg4P, arg5P) :|: 0 = arg5P && 3 <= arg3P - 1 && 5 <= arg2P - 1 && 0 <= arg1P - 1 && 0 <= arg1 - 1 && arg3P - 3 <= arg1 && arg2P - 5 <= arg1 && arg1P <= arg1 && -1 <= arg4P - 1 && 0 <= arg2 - 1
(2) f165_0_appendNewList_LE(x, x1, x2, x3, x4) -> f200_0_random_ArrayAccess(x5, x6, x7, x8, x9) :|: x3 <= 1 && 0 <= x4 - 1 && x4 <= x10 - 1 && x4 <= x11 - 1 && 0 <= x - 1 && 4 <= x1 - 1 && 2 <= x2 - 1 && 4 <= x5 - 1
(3) f165_0_appendNewList_LE(x12, x15, x16, x17, x18) -> f200_0_random_ArrayAccess(x19, x20, x21, x22, x23) :|: 6 <= x19 - 1 && 3 <= x16 - 1 && 5 <= x15 - 1 && 0 <= x12 - 1 && x19 - 3 <= x16 && x19 - 1 <= x15 && x17 <= 1 && x19 - 6 <= x12
(4) f165_0_appendNewList_LE(x24, x25, x26, x27, x28) -> f165_0_appendNewList_LE(x29, x30, x31, x32, x33) :|: x27 - 1 = x32 && 2 <= x31 - 1 && 4 <= x30 - 1 && 0 <= x29 - 1 && 2 <= x26 - 1 && 4 <= x25 - 1 && 0 <= x24 - 1 && x29 + 2 <= x26 && x29 + 4 <= x25 && x29 <= x24 && 1 <= x27 - 1 && 0 <= x28 - 1 && x28 <= x33 - 1
(5) f165_0_appendNewList_LE(x34, x35, x36, x37, x38) -> f165_0_appendNewList_LE(x39, x40, x41, x42, x43) :|: 1 = x43 && x37 - 1 = x42 && 5 <= x41 - 1 && 7 <= x40 - 1 && 0 <= x39 - 1 && 3 <= x36 - 1 && 5 <= x35 - 1 && 0 <= x34 - 1 && x41 - 2 <= x36 && x41 <= x35 && x41 - 5 <= x34 && x40 - 4 <= x36 && x40 - 2 <= x35 && x40 - 7 <= x34 && x39 + 3 <= x36 && x39 + 5 <= x35 && 1 <= x37 - 1 && x39 <= x34
(6) f200_0_random_ArrayAccess(x44, x45, x46, x47, x48) -> f314_0_appendNewList_LE(x49, x50, x51, x52, x53) :|: 0 = x51 && 3 <= x49 - 1 && 4 <= x44 - 1 && x49 + 1 <= x44 && -1 <= x50 - 1 && 1 <= x45 - 1
(7) f314_0_appendNewList_LE(x54, x55, x56, x57, x58) -> f314_0_appendNewList_LE(x59, x60, x61, x62, x63) :|: x55 - 1 = x60 && 2 <= x59 - 1 && 2 <= x54 - 1 && 1 <= x55 - 1 && 0 <= x56 - 1 && x56 <= x61 - 1
(8) f314_0_appendNewList_LE(x64, x65, x66, x67, x68) -> f314_0_appendNewList_LE(x69, x70, x71, x72, x73) :|: 1 = x71 && x65 - 1 = x70 && 5 <= x69 - 1 && 3 <= x64 - 1 && 1 <= x65 - 1 && x69 - 2 <= x64
(9) f314_0_appendNewList_LE(x74, x75, x76, x77, x78) -> f387_0_length_NULL(x79, x80, x81, x82, x83) :|: 0 <= x79 - 1 && 2 <= x74 - 1 && x75 <= 1 && x79 + 2 <= x74
(10) f387_0_length_NULL(x84, x85, x86, x87, x88) -> f387_0_length_NULL(x89, x90, x91, x92, x93) :|: -1 <= x89 - 1 && 0 <= x84 - 1 && x89 + 1 <= x84
(11) __init(x94, x95, x96, x97, x98) -> f1_0_main_Load(x99, x100, x101, x102, x103) :|: 0 <= 0

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

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

(4)
Complex Obligation (AND)

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

(5)
Obligation:

Termination digraph:
Nodes:
(1) f165_0_appendNewList_LE(x34, x35, x36, x37, x38) -> f165_0_appendNewList_LE(x39, x40, x41, x42, x43) :|: 1 = x43 && x37 - 1 = x42 && 5 <= x41 - 1 && 7 <= x40 - 1 && 0 <= x39 - 1 && 3 <= x36 - 1 && 5 <= x35 - 1 && 0 <= x34 - 1 && x41 - 2 <= x36 && x41 <= x35 && x41 - 5 <= x34 && x40 - 4 <= x36 && x40 - 2 <= x35 && x40 - 7 <= x34 && x39 + 3 <= x36 && x39 + 5 <= x35 && 1 <= x37 - 1 && x39 <= x34
(2) f165_0_appendNewList_LE(x24, x25, x26, x27, x28) -> f165_0_appendNewList_LE(x29, x30, x31, x32, x33) :|: x27 - 1 = x32 && 2 <= x31 - 1 && 4 <= x30 - 1 && 0 <= x29 - 1 && 2 <= x26 - 1 && 4 <= x25 - 1 && 0 <= x24 - 1 && x29 + 2 <= x26 && x29 + 4 <= x25 && x29 <= x24 && 1 <= x27 - 1 && 0 <= x28 - 1 && x28 <= x33 - 1

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

This digraph is fully evaluated!

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

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

(7)
Obligation:
Rules:
f165_0_appendNewList_LE(x34:0, x35:0, x36:0, x37:0, x38:0) -> f165_0_appendNewList_LE(x39:0, x40:0, x41:0, x37:0 - 1, 1) :|: x37:0 > 1 && x39:0 <= x34:0 && x39:0 + 5 <= x35:0 && x39:0 + 3 <= x36:0 && x40:0 - 7 <= x34:0 && x40:0 - 2 <= x35:0 && x40:0 - 4 <= x36:0 && x41:0 - 5 <= x34:0 && x41:0 <= x35:0 && x41:0 - 2 <= x36:0 && x34:0 > 0 && x35:0 > 5 && x36:0 > 3 && x39:0 > 0 && x41:0 > 5 && x40:0 > 7
f165_0_appendNewList_LE(x24:0, x25:0, x26:0, x27:0, x28:0) -> f165_0_appendNewList_LE(x29:0, x30:0, x31:0, x27:0 - 1, x33:0) :|: x28:0 > 0 && x33:0 - 1 >= x28:0 && x27:0 > 1 && x29:0 <= x24:0 && x29:0 + 4 <= x25:0 && x29:0 + 2 <= x26:0 && x24:0 > 0 && x25:0 > 4 && x26:0 > 2 && x29:0 > 0 && x31:0 > 2 && x30:0 > 4

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

(8) TempFilterProof (SOUND)
Used the following sort dictionary for filtering: 
f165_0_appendNewList_LE(INTEGER, INTEGER, INTEGER, INTEGER, VARIABLE)
Replaced non-predefined constructor symbols by 0.
----------------------------------------

(9)
Obligation:
Rules:
f165_0_appendNewList_LE(x34:0, x35:0, x36:0, x37:0, x38:0) -> f165_0_appendNewList_LE(x39:0, x40:0, x41:0, c, c1) :|: c1 = 1 && c = x37:0 - 1 && (x37:0 > 1 && x39:0 <= x34:0 && x39:0 + 5 <= x35:0 && x39:0 + 3 <= x36:0 && x40:0 - 7 <= x34:0 && x40:0 - 2 <= x35:0 && x40:0 - 4 <= x36:0 && x41:0 - 5 <= x34:0 && x41:0 <= x35:0 && x41:0 - 2 <= x36:0 && x34:0 > 0 && x35:0 > 5 && x36:0 > 3 && x39:0 > 0 && x41:0 > 5 && x40:0 > 7)
f165_0_appendNewList_LE(x24:0, x25:0, x26:0, x27:0, x28:0) -> f165_0_appendNewList_LE(x29:0, x30:0, x31:0, c2, x33:0) :|: c2 = x27:0 - 1 && (x28:0 > 0 && x33:0 - 1 >= x28:0 && x27:0 > 1 && x29:0 <= x24:0 && x29:0 + 4 <= x25:0 && x29:0 + 2 <= x26:0 && x24:0 > 0 && x25:0 > 4 && x26:0 > 2 && x29:0 > 0 && x31:0 > 2 && x30:0 > 4)

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

(10) PolynomialOrderProcessor (EQUIVALENT)
Found the following polynomial interpretation:
[f165_0_appendNewList_LE(x, x1, x2, x3, x4)] = x3

The following rules are decreasing:
f165_0_appendNewList_LE(x34:0, x35:0, x36:0, x37:0, x38:0) -> f165_0_appendNewList_LE(x39:0, x40:0, x41:0, c, c1) :|: c1 = 1 && c = x37:0 - 1 && (x37:0 > 1 && x39:0 <= x34:0 && x39:0 + 5 <= x35:0 && x39:0 + 3 <= x36:0 && x40:0 - 7 <= x34:0 && x40:0 - 2 <= x35:0 && x40:0 - 4 <= x36:0 && x41:0 - 5 <= x34:0 && x41:0 <= x35:0 && x41:0 - 2 <= x36:0 && x34:0 > 0 && x35:0 > 5 && x36:0 > 3 && x39:0 > 0 && x41:0 > 5 && x40:0 > 7)
f165_0_appendNewList_LE(x24:0, x25:0, x26:0, x27:0, x28:0) -> f165_0_appendNewList_LE(x29:0, x30:0, x31:0, c2, x33:0) :|: c2 = x27:0 - 1 && (x28:0 > 0 && x33:0 - 1 >= x28:0 && x27:0 > 1 && x29:0 <= x24:0 && x29:0 + 4 <= x25:0 && x29:0 + 2 <= x26:0 && x24:0 > 0 && x25:0 > 4 && x26:0 > 2 && x29:0 > 0 && x31:0 > 2 && x30:0 > 4)
The following rules are bounded:
f165_0_appendNewList_LE(x34:0, x35:0, x36:0, x37:0, x38:0) -> f165_0_appendNewList_LE(x39:0, x40:0, x41:0, c, c1) :|: c1 = 1 && c = x37:0 - 1 && (x37:0 > 1 && x39:0 <= x34:0 && x39:0 + 5 <= x35:0 && x39:0 + 3 <= x36:0 && x40:0 - 7 <= x34:0 && x40:0 - 2 <= x35:0 && x40:0 - 4 <= x36:0 && x41:0 - 5 <= x34:0 && x41:0 <= x35:0 && x41:0 - 2 <= x36:0 && x34:0 > 0 && x35:0 > 5 && x36:0 > 3 && x39:0 > 0 && x41:0 > 5 && x40:0 > 7)
f165_0_appendNewList_LE(x24:0, x25:0, x26:0, x27:0, x28:0) -> f165_0_appendNewList_LE(x29:0, x30:0, x31:0, c2, x33:0) :|: c2 = x27:0 - 1 && (x28:0 > 0 && x33:0 - 1 >= x28:0 && x27:0 > 1 && x29:0 <= x24:0 && x29:0 + 4 <= x25:0 && x29:0 + 2 <= x26:0 && x24:0 > 0 && x25:0 > 4 && x26:0 > 2 && x29:0 > 0 && x31:0 > 2 && x30:0 > 4)

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

(11)
YES

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

(12)
Obligation:

Termination digraph:
Nodes:
(1) f314_0_appendNewList_LE(x64, x65, x66, x67, x68) -> f314_0_appendNewList_LE(x69, x70, x71, x72, x73) :|: 1 = x71 && x65 - 1 = x70 && 5 <= x69 - 1 && 3 <= x64 - 1 && 1 <= x65 - 1 && x69 - 2 <= x64
(2) f314_0_appendNewList_LE(x54, x55, x56, x57, x58) -> f314_0_appendNewList_LE(x59, x60, x61, x62, x63) :|: x55 - 1 = x60 && 2 <= x59 - 1 && 2 <= x54 - 1 && 1 <= x55 - 1 && 0 <= x56 - 1 && x56 <= x61 - 1

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

This digraph is fully evaluated!

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

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

(14)
Obligation:
Rules:
f314_0_appendNewList_LE(x54:0, x55:0, x56:0, x57:0, x58:0) -> f314_0_appendNewList_LE(x59:0, x55:0 - 1, x61:0, x62:0, x63:0) :|: x56:0 > 0 && x61:0 - 1 >= x56:0 && x55:0 > 1 && x59:0 > 2 && x54:0 > 2
f314_0_appendNewList_LE(x64:0, x65:0, x66:0, x67:0, x68:0) -> f314_0_appendNewList_LE(x69:0, x65:0 - 1, 1, x72:0, x73:0) :|: x65:0 > 1 && x69:0 - 2 <= x64:0 && x69:0 > 5 && x64:0 > 3

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

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

   f314_0_appendNewList_LE(x1, x2, x3, x4, x5) -> f314_0_appendNewList_LE(x1, x2, x3)

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

(16)
Obligation:
Rules:
f314_0_appendNewList_LE(x54:0, x55:0, x56:0) -> f314_0_appendNewList_LE(x59:0, x55:0 - 1, x61:0) :|: x56:0 > 0 && x61:0 - 1 >= x56:0 && x55:0 > 1 && x59:0 > 2 && x54:0 > 2
f314_0_appendNewList_LE(x64:0, x65:0, x66:0) -> f314_0_appendNewList_LE(x69:0, x65:0 - 1, 1) :|: x65:0 > 1 && x69:0 - 2 <= x64:0 && x69:0 > 5 && x64:0 > 3

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

(17) TempFilterProof (SOUND)
Used the following sort dictionary for filtering: 
f314_0_appendNewList_LE(INTEGER, INTEGER, VARIABLE)
Replaced non-predefined constructor symbols by 0.
----------------------------------------

(18)
Obligation:
Rules:
f314_0_appendNewList_LE(x54:0, x55:0, x56:0) -> f314_0_appendNewList_LE(x59:0, c, x61:0) :|: c = x55:0 - 1 && (x56:0 > 0 && x61:0 - 1 >= x56:0 && x55:0 > 1 && x59:0 > 2 && x54:0 > 2)
f314_0_appendNewList_LE(x64:0, x65:0, x66:0) -> f314_0_appendNewList_LE(x69:0, c1, c2) :|: c2 = 1 && c1 = x65:0 - 1 && (x65:0 > 1 && x69:0 - 2 <= x64:0 && x69:0 > 5 && x64:0 > 3)

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

(19) RankingReductionPairProof (EQUIVALENT)
Interpretation:
[ f314_0_appendNewList_LE ] = f314_0_appendNewList_LE_2

The following rules are decreasing:
f314_0_appendNewList_LE(x54:0, x55:0, x56:0) -> f314_0_appendNewList_LE(x59:0, c, x61:0) :|: c = x55:0 - 1 && (x56:0 > 0 && x61:0 - 1 >= x56:0 && x55:0 > 1 && x59:0 > 2 && x54:0 > 2)
f314_0_appendNewList_LE(x64:0, x65:0, x66:0) -> f314_0_appendNewList_LE(x69:0, c1, c2) :|: c2 = 1 && c1 = x65:0 - 1 && (x65:0 > 1 && x69:0 - 2 <= x64:0 && x69:0 > 5 && x64:0 > 3)

The following rules are bounded:
f314_0_appendNewList_LE(x54:0, x55:0, x56:0) -> f314_0_appendNewList_LE(x59:0, c, x61:0) :|: c = x55:0 - 1 && (x56:0 > 0 && x61:0 - 1 >= x56:0 && x55:0 > 1 && x59:0 > 2 && x54:0 > 2)
f314_0_appendNewList_LE(x64:0, x65:0, x66:0) -> f314_0_appendNewList_LE(x69:0, c1, c2) :|: c2 = 1 && c1 = x65:0 - 1 && (x65:0 > 1 && x69:0 - 2 <= x64:0 && x69:0 > 5 && x64:0 > 3)


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

(20)
YES

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

(21)
Obligation:

Termination digraph:
Nodes:
(1) f387_0_length_NULL(x84, x85, x86, x87, x88) -> f387_0_length_NULL(x89, x90, x91, x92, x93) :|: -1 <= x89 - 1 && 0 <= x84 - 1 && x89 + 1 <= x84

Arcs:
(1) -> (1)

This digraph is fully evaluated!

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

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

(23)
Obligation:
Rules:
f387_0_length_NULL(x84:0, x85:0, x86:0, x87:0, x88:0) -> f387_0_length_NULL(x89:0, x90:0, x91:0, x92:0, x93:0) :|: x89:0 > -1 && x84:0 > 0 && x89:0 + 1 <= x84:0

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

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

   f387_0_length_NULL(x1, x2, x3, x4, x5) -> f387_0_length_NULL(x1)

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

(25)
Obligation:
Rules:
f387_0_length_NULL(x84:0) -> f387_0_length_NULL(x89:0) :|: x89:0 > -1 && x84:0 > 0 && x89:0 + 1 <= x84:0

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

(26) FilterProof (EQUIVALENT)
Used the following sort dictionary for filtering: 
f387_0_length_NULL(INTEGER)
Replaced non-predefined constructor symbols by 0.
----------------------------------------

(27)
Obligation:
Rules:
f387_0_length_NULL(x84:0) -> f387_0_length_NULL(x89:0) :|: x89:0 > -1 && x84:0 > 0 && x89:0 + 1 <= x84:0

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

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

(29)
Obligation:
Rules:
f387_0_length_NULL(x84:0:0) -> f387_0_length_NULL(x89:0:0) :|: x89:0:0 > -1 && x84:0:0 > 0 && x89:0:0 + 1 <= x84:0:0

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

(30) PolynomialOrderProcessor (EQUIVALENT)
Found the following polynomial interpretation:
[f387_0_length_NULL(x)] = x

The following rules are decreasing:
f387_0_length_NULL(x84:0:0) -> f387_0_length_NULL(x89:0:0) :|: x89:0:0 > -1 && x84:0:0 > 0 && x89:0:0 + 1 <= x84:0:0
The following rules are bounded:
f387_0_length_NULL(x84:0:0) -> f387_0_length_NULL(x89:0:0) :|: x89:0:0 > -1 && x84:0:0 > 0 && x89:0:0 + 1 <= x84:0:0

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

(31)
YES