NO
proof of prog.inttrs
# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty


Termination of the given IRSwT could be disproven:

(0) IRSwT
(1) IRSFormatTransformerProof [EQUIVALENT, 0 ms]
(2) IRSwT
(3) IRSwTTerminationDigraphProof [EQUIVALENT, 1138 ms]
(4) AND
    (5) IRSwT
        (6) IntTRSCompressionProof [EQUIVALENT, 0 ms]
        (7) IRSwT
        (8) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms]
        (9) IRSwT
        (10) FilterProof [EQUIVALENT, 0 ms]
        (11) IntTRS
        (12) IntTRSCompressionProof [EQUIVALENT, 0 ms]
        (13) IntTRS
        (14) PolynomialOrderProcessor [EQUIVALENT, 3 ms]
        (15) YES
    (16) IRSwT
        (17) IntTRSCompressionProof [EQUIVALENT, 0 ms]
        (18) IRSwT
        (19) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms]
        (20) IRSwT
        (21) FilterProof [EQUIVALENT, 0 ms]
        (22) IntTRS
        (23) IntTRSCompressionProof [EQUIVALENT, 0 ms]
        (24) IntTRS
        (25) PolynomialOrderProcessor [EQUIVALENT, 0 ms]
        (26) YES
    (27) IRSwT
        (28) IntTRSCompressionProof [EQUIVALENT, 0 ms]
        (29) IRSwT
        (30) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms]
        (31) IRSwT
        (32) FilterProof [EQUIVALENT, 0 ms]
        (33) IntTRS
        (34) IntTRSCompressionProof [EQUIVALENT, 0 ms]
        (35) IntTRS
        (36) RankingReductionPairProof [EQUIVALENT, 22 ms]
        (37) YES
    (38) IRSwT
        (39) IntTRSCompressionProof [EQUIVALENT, 0 ms]
        (40) IRSwT
        (41) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms]
        (42) IRSwT
        (43) FilterProof [EQUIVALENT, 0 ms]
        (44) IntTRS
        (45) IntTRSCompressionProof [EQUIVALENT, 0 ms]
        (46) IntTRS
        (47) IntTRSPeriodicNontermProof [COMPLETE, 6 ms]
        (48) NO
    (49) IRSwT
        (50) IntTRSCompressionProof [EQUIVALENT, 0 ms]
        (51) IRSwT
        (52) FilterProof [EQUIVALENT, 0 ms]
        (53) IntTRS
        (54) IntTRSCompressionProof [EQUIVALENT, 0 ms]
        (55) IntTRS
        (56) RankingReductionPairProof [EQUIVALENT, 0 ms]
        (57) YES


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

(0)
Obligation:
Rules:
f1_0_main_New(arg1, arg2, arg3, arg4) -> f230_0_alternate_NONNULL(arg1P, arg2P, arg3P, arg4P) :|: 3 <= arg3P - 1 && 3 <= arg4P - 1 && 3 <= arg2P - 1 && 3 <= arg1P - 1
f230_0_alternate_NONNULL(x, x1, x2, x3) -> f230_0_alternate_NONNULL(x4, x5, x6, x7) :|: -1 <= x7 - 1 && -1 <= x6 - 1 && 0 <= x5 - 1 && -1 <= x4 - 1 && 0 <= x3 - 1 && 0 <= x2 - 1 && 0 <= x1 - 1 && 0 <= x - 1 && x7 + 1 <= x1 && x6 + 1 <= x1 && x5 <= x3 && x5 <= x2 && x5 <= x && x4 + 1 <= x1
f1_0_main_New(x8, x9, x10, x11) -> f1096_0_append_NONNULL(x12, x13, x14, x15) :|: 4 <= x13 - 1 && -1 <= x14 - 1 && 3 <= x12 - 1
f1096_0_append_NONNULL(x16, x17, x18, x19) -> f1096_0_append_NONNULL(x20, x21, x22, x23) :|: -1 <= x22 - 1 && 0 <= x21 - 1 && 0 <= x20 - 1 && 0 <= x18 - 1 && 0 <= x17 - 1 && 2 <= x16 - 1 && x21 <= x17
f1_0_main_New(x24, x25, x26, x27) -> f565_0_iter_NULL(x28, x29, x30, x31) :|: 3 <= x28 - 1 && 1 <= x29 - 1
f565_0_iter_NULL(x32, x33, x34, x35) -> f565_0_iter_NULL(x36, x37, x38, x39) :|: -1 <= x37 - 1 && 0 <= x36 - 1 && 0 <= x33 - 1 && 2 <= x32 - 1 && x37 + 1 <= x33 && x37 + 3 <= x32 && x36 <= x33 && x36 + 2 <= x32
f1_0_main_New(x40, x41, x42, x43) -> f717_0_reverseAcc_NONNULL(x44, x45, x46, x47) :|: 3 <= x44 - 1 && 1 <= x45 - 1
f717_0_reverseAcc_NONNULL(x48, x49, x50, x51) -> f717_0_reverseAcc_NONNULL(x52, x53, x54, x55) :|: -1 <= x53 - 1 && 0 <= x52 - 1 && 0 <= x49 - 1 && 2 <= x48 - 1 && x53 + 1 <= x49 && x53 + 3 <= x48 && x52 <= x49 && x52 + 2 <= x48
f1_0_main_New(x56, x57, x58, x59) -> f845_0_reverse_NONNULL(x60, x61, x62, x63) :|: 3 <= x60 - 1 && 1 <= x61 - 1
f845_0_reverse_NONNULL(x64, x65, x66, x67) -> f845_0_reverse_NONNULL(x68, x69, x70, x71) :|: -1 <= x69 - 1 && 0 <= x68 - 1 && 0 <= x65 - 1 && 2 <= x64 - 1 && x69 + 1 <= x65 && x69 + 3 <= x64 && x68 <= x65 && x68 + 2 <= x64
f845_0_reverse_NONNULL(x72, x73, x74, x75) -> f1096_0_append_NONNULL(x76, x77, x78, x79) :|: -1 <= x78 - 1 && 1 <= x77 - 1 && 1 <= x76 - 1 && 0 <= x73 - 1 && 2 <= x72 - 1 && x77 - 1 <= x73 && x77 + 1 <= x72 && x76 - 1 <= x73 && x76 + 1 <= x72
f845_0_reverse_NONNULL(x80, x81, x82, x83) -> f1225_0_reverse_InvokeMethod(x84, x85, x86, x87) :|: 4 <= x84 - 1 && 0 <= x81 - 1 && 2 <= x80 - 1
f845_0_reverse_NONNULL(x88, x89, x90, x91) -> f1225_0_reverse_InvokeMethod(x92, x93, x94, x95) :|: 2 <= x92 - 1 && 0 <= x89 - 1 && 2 <= x88 - 1
f991_0_reverse_Return(x96, x97, x98, x99) -> f1225_0_reverse_InvokeMethod(x100, x101, x102, x103) :|: x97 + 4 <= x96 && 2 <= x100 - 1 && 2 <= x96 - 1 && x100 <= x96
f1225_0_reverse_InvokeMethod(x104, x105, x106, x107) -> f1096_0_append_NONNULL(x108, x109, x110, x111) :|: -1 <= x110 - 1 && 1 <= x109 - 1 && 2 <= x108 - 1 && 2 <= x104 - 1 && x109 + 1 <= x104 && x108 <= x104
__init(x112, x113, x114, x115) -> f1_0_main_New(x116, x117, x118, x119) :|: 0 <= 0
Start term: __init(arg1, arg2, arg3, arg4)

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

(1) IRSFormatTransformerProof (EQUIVALENT)
Reformatted IRS to match normalized format (transformed away non-linear left-hand sides, !=, / and %).
----------------------------------------

(2)
Obligation:
Rules:
f1_0_main_New(arg1, arg2, arg3, arg4) -> f230_0_alternate_NONNULL(arg1P, arg2P, arg3P, arg4P) :|: 3 <= arg3P - 1 && 3 <= arg4P - 1 && 3 <= arg2P - 1 && 3 <= arg1P - 1
f230_0_alternate_NONNULL(x, x1, x2, x3) -> f230_0_alternate_NONNULL(x4, x5, x6, x7) :|: -1 <= x7 - 1 && -1 <= x6 - 1 && 0 <= x5 - 1 && -1 <= x4 - 1 && 0 <= x3 - 1 && 0 <= x2 - 1 && 0 <= x1 - 1 && 0 <= x - 1 && x7 + 1 <= x1 && x6 + 1 <= x1 && x5 <= x3 && x5 <= x2 && x5 <= x && x4 + 1 <= x1
f1_0_main_New(x8, x9, x10, x11) -> f1096_0_append_NONNULL(x12, x13, x14, x15) :|: 4 <= x13 - 1 && -1 <= x14 - 1 && 3 <= x12 - 1
f1096_0_append_NONNULL(x16, x17, x18, x19) -> f1096_0_append_NONNULL(x20, x21, x22, x23) :|: -1 <= x22 - 1 && 0 <= x21 - 1 && 0 <= x20 - 1 && 0 <= x18 - 1 && 0 <= x17 - 1 && 2 <= x16 - 1 && x21 <= x17
f1_0_main_New(x24, x25, x26, x27) -> f565_0_iter_NULL(x28, x29, x30, x31) :|: 3 <= x28 - 1 && 1 <= x29 - 1
f565_0_iter_NULL(x32, x33, x34, x35) -> f565_0_iter_NULL(x36, x37, x38, x39) :|: -1 <= x37 - 1 && 0 <= x36 - 1 && 0 <= x33 - 1 && 2 <= x32 - 1 && x37 + 1 <= x33 && x37 + 3 <= x32 && x36 <= x33 && x36 + 2 <= x32
f1_0_main_New(x40, x41, x42, x43) -> f717_0_reverseAcc_NONNULL(x44, x45, x46, x47) :|: 3 <= x44 - 1 && 1 <= x45 - 1
f717_0_reverseAcc_NONNULL(x48, x49, x50, x51) -> f717_0_reverseAcc_NONNULL(x52, x53, x54, x55) :|: -1 <= x53 - 1 && 0 <= x52 - 1 && 0 <= x49 - 1 && 2 <= x48 - 1 && x53 + 1 <= x49 && x53 + 3 <= x48 && x52 <= x49 && x52 + 2 <= x48
f1_0_main_New(x56, x57, x58, x59) -> f845_0_reverse_NONNULL(x60, x61, x62, x63) :|: 3 <= x60 - 1 && 1 <= x61 - 1
f845_0_reverse_NONNULL(x64, x65, x66, x67) -> f845_0_reverse_NONNULL(x68, x69, x70, x71) :|: -1 <= x69 - 1 && 0 <= x68 - 1 && 0 <= x65 - 1 && 2 <= x64 - 1 && x69 + 1 <= x65 && x69 + 3 <= x64 && x68 <= x65 && x68 + 2 <= x64
f845_0_reverse_NONNULL(x72, x73, x74, x75) -> f1096_0_append_NONNULL(x76, x77, x78, x79) :|: -1 <= x78 - 1 && 1 <= x77 - 1 && 1 <= x76 - 1 && 0 <= x73 - 1 && 2 <= x72 - 1 && x77 - 1 <= x73 && x77 + 1 <= x72 && x76 - 1 <= x73 && x76 + 1 <= x72
f845_0_reverse_NONNULL(x80, x81, x82, x83) -> f1225_0_reverse_InvokeMethod(x84, x85, x86, x87) :|: 4 <= x84 - 1 && 0 <= x81 - 1 && 2 <= x80 - 1
f845_0_reverse_NONNULL(x88, x89, x90, x91) -> f1225_0_reverse_InvokeMethod(x92, x93, x94, x95) :|: 2 <= x92 - 1 && 0 <= x89 - 1 && 2 <= x88 - 1
f991_0_reverse_Return(x96, x97, x98, x99) -> f1225_0_reverse_InvokeMethod(x100, x101, x102, x103) :|: x97 + 4 <= x96 && 2 <= x100 - 1 && 2 <= x96 - 1 && x100 <= x96
f1225_0_reverse_InvokeMethod(x104, x105, x106, x107) -> f1096_0_append_NONNULL(x108, x109, x110, x111) :|: -1 <= x110 - 1 && 1 <= x109 - 1 && 2 <= x108 - 1 && 2 <= x104 - 1 && x109 + 1 <= x104 && x108 <= x104
__init(x112, x113, x114, x115) -> f1_0_main_New(x116, x117, x118, x119) :|: 0 <= 0
Start term: __init(arg1, arg2, arg3, arg4)

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

(3) IRSwTTerminationDigraphProof (EQUIVALENT)
Constructed termination digraph!
Nodes:
(1) f1_0_main_New(arg1, arg2, arg3, arg4) -> f230_0_alternate_NONNULL(arg1P, arg2P, arg3P, arg4P) :|: 3 <= arg3P - 1 && 3 <= arg4P - 1 && 3 <= arg2P - 1 && 3 <= arg1P - 1
(2) f230_0_alternate_NONNULL(x, x1, x2, x3) -> f230_0_alternate_NONNULL(x4, x5, x6, x7) :|: -1 <= x7 - 1 && -1 <= x6 - 1 && 0 <= x5 - 1 && -1 <= x4 - 1 && 0 <= x3 - 1 && 0 <= x2 - 1 && 0 <= x1 - 1 && 0 <= x - 1 && x7 + 1 <= x1 && x6 + 1 <= x1 && x5 <= x3 && x5 <= x2 && x5 <= x && x4 + 1 <= x1
(3) f1_0_main_New(x8, x9, x10, x11) -> f1096_0_append_NONNULL(x12, x13, x14, x15) :|: 4 <= x13 - 1 && -1 <= x14 - 1 && 3 <= x12 - 1
(4) f1096_0_append_NONNULL(x16, x17, x18, x19) -> f1096_0_append_NONNULL(x20, x21, x22, x23) :|: -1 <= x22 - 1 && 0 <= x21 - 1 && 0 <= x20 - 1 && 0 <= x18 - 1 && 0 <= x17 - 1 && 2 <= x16 - 1 && x21 <= x17
(5) f1_0_main_New(x24, x25, x26, x27) -> f565_0_iter_NULL(x28, x29, x30, x31) :|: 3 <= x28 - 1 && 1 <= x29 - 1
(6) f565_0_iter_NULL(x32, x33, x34, x35) -> f565_0_iter_NULL(x36, x37, x38, x39) :|: -1 <= x37 - 1 && 0 <= x36 - 1 && 0 <= x33 - 1 && 2 <= x32 - 1 && x37 + 1 <= x33 && x37 + 3 <= x32 && x36 <= x33 && x36 + 2 <= x32
(7) f1_0_main_New(x40, x41, x42, x43) -> f717_0_reverseAcc_NONNULL(x44, x45, x46, x47) :|: 3 <= x44 - 1 && 1 <= x45 - 1
(8) f717_0_reverseAcc_NONNULL(x48, x49, x50, x51) -> f717_0_reverseAcc_NONNULL(x52, x53, x54, x55) :|: -1 <= x53 - 1 && 0 <= x52 - 1 && 0 <= x49 - 1 && 2 <= x48 - 1 && x53 + 1 <= x49 && x53 + 3 <= x48 && x52 <= x49 && x52 + 2 <= x48
(9) f1_0_main_New(x56, x57, x58, x59) -> f845_0_reverse_NONNULL(x60, x61, x62, x63) :|: 3 <= x60 - 1 && 1 <= x61 - 1
(10) f845_0_reverse_NONNULL(x64, x65, x66, x67) -> f845_0_reverse_NONNULL(x68, x69, x70, x71) :|: -1 <= x69 - 1 && 0 <= x68 - 1 && 0 <= x65 - 1 && 2 <= x64 - 1 && x69 + 1 <= x65 && x69 + 3 <= x64 && x68 <= x65 && x68 + 2 <= x64
(11) f845_0_reverse_NONNULL(x72, x73, x74, x75) -> f1096_0_append_NONNULL(x76, x77, x78, x79) :|: -1 <= x78 - 1 && 1 <= x77 - 1 && 1 <= x76 - 1 && 0 <= x73 - 1 && 2 <= x72 - 1 && x77 - 1 <= x73 && x77 + 1 <= x72 && x76 - 1 <= x73 && x76 + 1 <= x72
(12) f845_0_reverse_NONNULL(x80, x81, x82, x83) -> f1225_0_reverse_InvokeMethod(x84, x85, x86, x87) :|: 4 <= x84 - 1 && 0 <= x81 - 1 && 2 <= x80 - 1
(13) f845_0_reverse_NONNULL(x88, x89, x90, x91) -> f1225_0_reverse_InvokeMethod(x92, x93, x94, x95) :|: 2 <= x92 - 1 && 0 <= x89 - 1 && 2 <= x88 - 1
(14) f991_0_reverse_Return(x96, x97, x98, x99) -> f1225_0_reverse_InvokeMethod(x100, x101, x102, x103) :|: x97 + 4 <= x96 && 2 <= x100 - 1 && 2 <= x96 - 1 && x100 <= x96
(15) f1225_0_reverse_InvokeMethod(x104, x105, x106, x107) -> f1096_0_append_NONNULL(x108, x109, x110, x111) :|: -1 <= x110 - 1 && 1 <= x109 - 1 && 2 <= x108 - 1 && 2 <= x104 - 1 && x109 + 1 <= x104 && x108 <= x104
(16) __init(x112, x113, x114, x115) -> f1_0_main_New(x116, x117, x118, x119) :|: 0 <= 0

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

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

(4)
Complex Obligation (AND)

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

(5)
Obligation:

Termination digraph:
Nodes:
(1) f845_0_reverse_NONNULL(x64, x65, x66, x67) -> f845_0_reverse_NONNULL(x68, x69, x70, x71) :|: -1 <= x69 - 1 && 0 <= x68 - 1 && 0 <= x65 - 1 && 2 <= x64 - 1 && x69 + 1 <= x65 && x69 + 3 <= x64 && x68 <= x65 && x68 + 2 <= x64

Arcs:
(1) -> (1)

This digraph is fully evaluated!

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

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

(7)
Obligation:
Rules:
f845_0_reverse_NONNULL(x64:0, x65:0, x66:0, x67:0) -> f845_0_reverse_NONNULL(x68:0, x69:0, x70:0, x71:0) :|: x68:0 <= x65:0 && x68:0 + 2 <= x64:0 && x69:0 + 3 <= x64:0 && x69:0 + 1 <= x65:0 && x64:0 > 2 && x65:0 > 0 && x68:0 > 0 && x69:0 > -1

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

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

   f845_0_reverse_NONNULL(x1, x2, x3, x4) -> f845_0_reverse_NONNULL(x1, x2)

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

(9)
Obligation:
Rules:
f845_0_reverse_NONNULL(x64:0, x65:0) -> f845_0_reverse_NONNULL(x68:0, x69:0) :|: x68:0 <= x65:0 && x68:0 + 2 <= x64:0 && x69:0 + 3 <= x64:0 && x69:0 + 1 <= x65:0 && x64:0 > 2 && x65:0 > 0 && x68:0 > 0 && x69:0 > -1

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

(10) FilterProof (EQUIVALENT)
Used the following sort dictionary for filtering: 
f845_0_reverse_NONNULL(INTEGER, INTEGER)
Replaced non-predefined constructor symbols by 0.
----------------------------------------

(11)
Obligation:
Rules:
f845_0_reverse_NONNULL(x64:0, x65:0) -> f845_0_reverse_NONNULL(x68:0, x69:0) :|: x68:0 <= x65:0 && x68:0 + 2 <= x64:0 && x69:0 + 3 <= x64:0 && x69:0 + 1 <= x65:0 && x64:0 > 2 && x65:0 > 0 && x68:0 > 0 && x69:0 > -1

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

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

(13)
Obligation:
Rules:
f845_0_reverse_NONNULL(x64:0:0, x65:0:0) -> f845_0_reverse_NONNULL(x68:0:0, x69:0:0) :|: x68:0:0 > 0 && x69:0:0 > -1 && x65:0:0 > 0 && x64:0:0 > 2 && x69:0:0 + 1 <= x65:0:0 && x69:0:0 + 3 <= x64:0:0 && x68:0:0 + 2 <= x64:0:0 && x68:0:0 <= x65:0:0

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

(14) PolynomialOrderProcessor (EQUIVALENT)
Found the following polynomial interpretation:
[f845_0_reverse_NONNULL(x, x1)] = -3 + x + x1

The following rules are decreasing:
f845_0_reverse_NONNULL(x64:0:0, x65:0:0) -> f845_0_reverse_NONNULL(x68:0:0, x69:0:0) :|: x68:0:0 > 0 && x69:0:0 > -1 && x65:0:0 > 0 && x64:0:0 > 2 && x69:0:0 + 1 <= x65:0:0 && x69:0:0 + 3 <= x64:0:0 && x68:0:0 + 2 <= x64:0:0 && x68:0:0 <= x65:0:0
The following rules are bounded:
f845_0_reverse_NONNULL(x64:0:0, x65:0:0) -> f845_0_reverse_NONNULL(x68:0:0, x69:0:0) :|: x68:0:0 > 0 && x69:0:0 > -1 && x65:0:0 > 0 && x64:0:0 > 2 && x69:0:0 + 1 <= x65:0:0 && x69:0:0 + 3 <= x64:0:0 && x68:0:0 + 2 <= x64:0:0 && x68:0:0 <= x65:0:0

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

(15)
YES

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

(16)
Obligation:

Termination digraph:
Nodes:
(1) f717_0_reverseAcc_NONNULL(x48, x49, x50, x51) -> f717_0_reverseAcc_NONNULL(x52, x53, x54, x55) :|: -1 <= x53 - 1 && 0 <= x52 - 1 && 0 <= x49 - 1 && 2 <= x48 - 1 && x53 + 1 <= x49 && x53 + 3 <= x48 && x52 <= x49 && x52 + 2 <= x48

Arcs:
(1) -> (1)

This digraph is fully evaluated!

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

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

(18)
Obligation:
Rules:
f717_0_reverseAcc_NONNULL(x48:0, x49:0, x50:0, x51:0) -> f717_0_reverseAcc_NONNULL(x52:0, x53:0, x54:0, x55:0) :|: x52:0 <= x49:0 && x52:0 + 2 <= x48:0 && x53:0 + 3 <= x48:0 && x53:0 + 1 <= x49:0 && x48:0 > 2 && x49:0 > 0 && x52:0 > 0 && x53:0 > -1

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

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

   f717_0_reverseAcc_NONNULL(x1, x2, x3, x4) -> f717_0_reverseAcc_NONNULL(x1, x2)

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

(20)
Obligation:
Rules:
f717_0_reverseAcc_NONNULL(x48:0, x49:0) -> f717_0_reverseAcc_NONNULL(x52:0, x53:0) :|: x52:0 <= x49:0 && x52:0 + 2 <= x48:0 && x53:0 + 3 <= x48:0 && x53:0 + 1 <= x49:0 && x48:0 > 2 && x49:0 > 0 && x52:0 > 0 && x53:0 > -1

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

(21) FilterProof (EQUIVALENT)
Used the following sort dictionary for filtering: 
f717_0_reverseAcc_NONNULL(INTEGER, INTEGER)
Replaced non-predefined constructor symbols by 0.
----------------------------------------

(22)
Obligation:
Rules:
f717_0_reverseAcc_NONNULL(x48:0, x49:0) -> f717_0_reverseAcc_NONNULL(x52:0, x53:0) :|: x52:0 <= x49:0 && x52:0 + 2 <= x48:0 && x53:0 + 3 <= x48:0 && x53:0 + 1 <= x49:0 && x48:0 > 2 && x49:0 > 0 && x52:0 > 0 && x53:0 > -1

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

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

(24)
Obligation:
Rules:
f717_0_reverseAcc_NONNULL(x48:0:0, x49:0:0) -> f717_0_reverseAcc_NONNULL(x52:0:0, x53:0:0) :|: x52:0:0 > 0 && x53:0:0 > -1 && x49:0:0 > 0 && x48:0:0 > 2 && x53:0:0 + 1 <= x49:0:0 && x53:0:0 + 3 <= x48:0:0 && x52:0:0 + 2 <= x48:0:0 && x52:0:0 <= x49:0:0

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

(25) PolynomialOrderProcessor (EQUIVALENT)
Found the following polynomial interpretation:
[f717_0_reverseAcc_NONNULL(x, x1)] = -3 + x + x1

The following rules are decreasing:
f717_0_reverseAcc_NONNULL(x48:0:0, x49:0:0) -> f717_0_reverseAcc_NONNULL(x52:0:0, x53:0:0) :|: x52:0:0 > 0 && x53:0:0 > -1 && x49:0:0 > 0 && x48:0:0 > 2 && x53:0:0 + 1 <= x49:0:0 && x53:0:0 + 3 <= x48:0:0 && x52:0:0 + 2 <= x48:0:0 && x52:0:0 <= x49:0:0
The following rules are bounded:
f717_0_reverseAcc_NONNULL(x48:0:0, x49:0:0) -> f717_0_reverseAcc_NONNULL(x52:0:0, x53:0:0) :|: x52:0:0 > 0 && x53:0:0 > -1 && x49:0:0 > 0 && x48:0:0 > 2 && x53:0:0 + 1 <= x49:0:0 && x53:0:0 + 3 <= x48:0:0 && x52:0:0 + 2 <= x48:0:0 && x52:0:0 <= x49:0:0

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(26)
YES

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(27)
Obligation:

Termination digraph:
Nodes:
(1) f565_0_iter_NULL(x32, x33, x34, x35) -> f565_0_iter_NULL(x36, x37, x38, x39) :|: -1 <= x37 - 1 && 0 <= x36 - 1 && 0 <= x33 - 1 && 2 <= x32 - 1 && x37 + 1 <= x33 && x37 + 3 <= x32 && x36 <= x33 && x36 + 2 <= x32

Arcs:
(1) -> (1)

This digraph is fully evaluated!

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

(29)
Obligation:
Rules:
f565_0_iter_NULL(x32:0, x33:0, x34:0, x35:0) -> f565_0_iter_NULL(x36:0, x37:0, x38:0, x39:0) :|: x36:0 <= x33:0 && x36:0 + 2 <= x32:0 && x37:0 + 3 <= x32:0 && x37:0 + 1 <= x33:0 && x32:0 > 2 && x33:0 > 0 && x36:0 > 0 && x37:0 > -1

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

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

   f565_0_iter_NULL(x1, x2, x3, x4) -> f565_0_iter_NULL(x1, x2)

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

(31)
Obligation:
Rules:
f565_0_iter_NULL(x32:0, x33:0) -> f565_0_iter_NULL(x36:0, x37:0) :|: x36:0 <= x33:0 && x36:0 + 2 <= x32:0 && x37:0 + 3 <= x32:0 && x37:0 + 1 <= x33:0 && x32:0 > 2 && x33:0 > 0 && x36:0 > 0 && x37:0 > -1

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(32) FilterProof (EQUIVALENT)
Used the following sort dictionary for filtering: 
f565_0_iter_NULL(INTEGER, INTEGER)
Replaced non-predefined constructor symbols by 0.
----------------------------------------

(33)
Obligation:
Rules:
f565_0_iter_NULL(x32:0, x33:0) -> f565_0_iter_NULL(x36:0, x37:0) :|: x36:0 <= x33:0 && x36:0 + 2 <= x32:0 && x37:0 + 3 <= x32:0 && x37:0 + 1 <= x33:0 && x32:0 > 2 && x33:0 > 0 && x36:0 > 0 && x37:0 > -1

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

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

(35)
Obligation:
Rules:
f565_0_iter_NULL(x32:0:0, x33:0:0) -> f565_0_iter_NULL(x36:0:0, x37:0:0) :|: x36:0:0 > 0 && x37:0:0 > -1 && x33:0:0 > 0 && x32:0:0 > 2 && x37:0:0 + 1 <= x33:0:0 && x37:0:0 + 3 <= x32:0:0 && x36:0:0 + 2 <= x32:0:0 && x36:0:0 <= x33:0:0

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

(36) RankingReductionPairProof (EQUIVALENT)
Interpretation:
[ f565_0_iter_NULL ] = 1/2*f565_0_iter_NULL_1

The following rules are decreasing:
f565_0_iter_NULL(x32:0:0, x33:0:0) -> f565_0_iter_NULL(x36:0:0, x37:0:0) :|: x36:0:0 > 0 && x37:0:0 > -1 && x33:0:0 > 0 && x32:0:0 > 2 && x37:0:0 + 1 <= x33:0:0 && x37:0:0 + 3 <= x32:0:0 && x36:0:0 + 2 <= x32:0:0 && x36:0:0 <= x33:0:0

The following rules are bounded:
f565_0_iter_NULL(x32:0:0, x33:0:0) -> f565_0_iter_NULL(x36:0:0, x37:0:0) :|: x36:0:0 > 0 && x37:0:0 > -1 && x33:0:0 > 0 && x32:0:0 > 2 && x37:0:0 + 1 <= x33:0:0 && x37:0:0 + 3 <= x32:0:0 && x36:0:0 + 2 <= x32:0:0 && x36:0:0 <= x33:0:0


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

(37)
YES

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

(38)
Obligation:

Termination digraph:
Nodes:
(1) f1096_0_append_NONNULL(x16, x17, x18, x19) -> f1096_0_append_NONNULL(x20, x21, x22, x23) :|: -1 <= x22 - 1 && 0 <= x21 - 1 && 0 <= x20 - 1 && 0 <= x18 - 1 && 0 <= x17 - 1 && 2 <= x16 - 1 && x21 <= x17

Arcs:
(1) -> (1)

This digraph is fully evaluated!

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

(40)
Obligation:
Rules:
f1096_0_append_NONNULL(x16:0, x17:0, x18:0, x19:0) -> f1096_0_append_NONNULL(x20:0, x21:0, x22:0, x23:0) :|: x16:0 > 2 && x21:0 <= x17:0 && x17:0 > 0 && x18:0 > 0 && x20:0 > 0 && x21:0 > 0 && x22:0 > -1

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

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

   f1096_0_append_NONNULL(x1, x2, x3, x4) -> f1096_0_append_NONNULL(x1, x2, x3)

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

(42)
Obligation:
Rules:
f1096_0_append_NONNULL(x16:0, x17:0, x18:0) -> f1096_0_append_NONNULL(x20:0, x21:0, x22:0) :|: x16:0 > 2 && x21:0 <= x17:0 && x17:0 > 0 && x18:0 > 0 && x20:0 > 0 && x21:0 > 0 && x22:0 > -1

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

(43) FilterProof (EQUIVALENT)
Used the following sort dictionary for filtering: 
f1096_0_append_NONNULL(INTEGER, INTEGER, INTEGER)
Replaced non-predefined constructor symbols by 0.
----------------------------------------

(44)
Obligation:
Rules:
f1096_0_append_NONNULL(x16:0, x17:0, x18:0) -> f1096_0_append_NONNULL(x20:0, x21:0, x22:0) :|: x16:0 > 2 && x21:0 <= x17:0 && x17:0 > 0 && x18:0 > 0 && x20:0 > 0 && x21:0 > 0 && x22:0 > -1

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

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

(46)
Obligation:
Rules:
f1096_0_append_NONNULL(x16:0:0, x17:0:0, x18:0:0) -> f1096_0_append_NONNULL(x20:0:0, x21:0:0, x22:0:0) :|: x21:0:0 > 0 && x22:0:0 > -1 && x20:0:0 > 0 && x18:0:0 > 0 && x17:0:0 > 0 && x21:0:0 <= x17:0:0 && x16:0:0 > 2

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(47) IntTRSPeriodicNontermProof (COMPLETE)
Normalized system to the following form:
f(pc, x16:0:0, x17:0:0, x18:0:0) -> f(1, x20:0:0, x21:0:0, x22:0:0) :|: pc = 1 && (x21:0:0 > 0 && x22:0:0 > -1 && x20:0:0 > 0 && x18:0:0 > 0 && x17:0:0 > 0 && x21:0:0 <= x17:0:0 && x16:0:0 > 2)
Witness term starting non-terminating reduction: f(1, 11, 10, 1)
----------------------------------------

(48)
NO

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(49)
Obligation:

Termination digraph:
Nodes:
(1) f230_0_alternate_NONNULL(x, x1, x2, x3) -> f230_0_alternate_NONNULL(x4, x5, x6, x7) :|: -1 <= x7 - 1 && -1 <= x6 - 1 && 0 <= x5 - 1 && -1 <= x4 - 1 && 0 <= x3 - 1 && 0 <= x2 - 1 && 0 <= x1 - 1 && 0 <= x - 1 && x7 + 1 <= x1 && x6 + 1 <= x1 && x5 <= x3 && x5 <= x2 && x5 <= x && x4 + 1 <= x1

Arcs:
(1) -> (1)

This digraph is fully evaluated!

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

(51)
Obligation:
Rules:
f230_0_alternate_NONNULL(x:0, x1:0, x2:0, x3:0) -> f230_0_alternate_NONNULL(x4:0, x5:0, x6:0, x7:0) :|: x:0 >= x5:0 && x4:0 + 1 <= x1:0 && x5:0 <= x2:0 && x5:0 <= x3:0 && x6:0 + 1 <= x1:0 && x7:0 + 1 <= x1:0 && x:0 > 0 && x1:0 > 0 && x2:0 > 0 && x3:0 > 0 && x4:0 > -1 && x5:0 > 0 && x6:0 > -1 && x7:0 > -1

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

(52) FilterProof (EQUIVALENT)
Used the following sort dictionary for filtering: 
f230_0_alternate_NONNULL(INTEGER, INTEGER, INTEGER, INTEGER)
Replaced non-predefined constructor symbols by 0.
----------------------------------------

(53)
Obligation:
Rules:
f230_0_alternate_NONNULL(x:0, x1:0, x2:0, x3:0) -> f230_0_alternate_NONNULL(x4:0, x5:0, x6:0, x7:0) :|: x:0 >= x5:0 && x4:0 + 1 <= x1:0 && x5:0 <= x2:0 && x5:0 <= x3:0 && x6:0 + 1 <= x1:0 && x7:0 + 1 <= x1:0 && x:0 > 0 && x1:0 > 0 && x2:0 > 0 && x3:0 > 0 && x4:0 > -1 && x5:0 > 0 && x6:0 > -1 && x7:0 > -1

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

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

(55)
Obligation:
Rules:
f230_0_alternate_NONNULL(x:0:0, x1:0:0, x2:0:0, x3:0:0) -> f230_0_alternate_NONNULL(x4:0:0, x5:0:0, x6:0:0, x7:0:0) :|: x6:0:0 > -1 && x7:0:0 > -1 && x5:0:0 > 0 && x4:0:0 > -1 && x3:0:0 > 0 && x2:0:0 > 0 && x1:0:0 > 0 && x:0:0 > 0 && x7:0:0 + 1 <= x1:0:0 && x6:0:0 + 1 <= x1:0:0 && x5:0:0 <= x3:0:0 && x5:0:0 <= x2:0:0 && x4:0:0 + 1 <= x1:0:0 && x:0:0 >= x5:0:0

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

(56) RankingReductionPairProof (EQUIVALENT)
Interpretation:
[ f230_0_alternate_NONNULL ] = f230_0_alternate_NONNULL_4 + f230_0_alternate_NONNULL_2

The following rules are decreasing:
f230_0_alternate_NONNULL(x:0:0, x1:0:0, x2:0:0, x3:0:0) -> f230_0_alternate_NONNULL(x4:0:0, x5:0:0, x6:0:0, x7:0:0) :|: x6:0:0 > -1 && x7:0:0 > -1 && x5:0:0 > 0 && x4:0:0 > -1 && x3:0:0 > 0 && x2:0:0 > 0 && x1:0:0 > 0 && x:0:0 > 0 && x7:0:0 + 1 <= x1:0:0 && x6:0:0 + 1 <= x1:0:0 && x5:0:0 <= x3:0:0 && x5:0:0 <= x2:0:0 && x4:0:0 + 1 <= x1:0:0 && x:0:0 >= x5:0:0

The following rules are bounded:
f230_0_alternate_NONNULL(x:0:0, x1:0:0, x2:0:0, x3:0:0) -> f230_0_alternate_NONNULL(x4:0:0, x5:0:0, x6:0:0, x7:0:0) :|: x6:0:0 > -1 && x7:0:0 > -1 && x5:0:0 > 0 && x4:0:0 > -1 && x3:0:0 > 0 && x2:0:0 > 0 && x1:0:0 > 0 && x:0:0 > 0 && x7:0:0 + 1 <= x1:0:0 && x6:0:0 + 1 <= x1:0:0 && x5:0:0 <= x3:0:0 && x5:0:0 <= x2:0:0 && x4:0:0 + 1 <= x1:0:0 && x:0:0 >= x5:0:0


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

(57)
YES