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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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, 785 ms]
(4) AND
    (5) IRSwT
        (6) IntTRSCompressionProof [EQUIVALENT, 8 ms]
        (7) IRSwT
        (8) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms]
        (9) IRSwT
        (10) TempFilterProof [SOUND, 13 ms]
        (11) IntTRS
        (12) PolynomialOrderProcessor [EQUIVALENT, 0 ms]
        (13) YES
    (14) IRSwT
        (15) IntTRSCompressionProof [EQUIVALENT, 33 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) IntTRSPeriodicNontermProof [COMPLETE, 0 ms]
        (24) NO


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

(0)
Obligation:
Rules:
f1_0_main_New(arg1, arg2, arg3, arg4, arg5) -> f155_0_main_ArrayAccess(arg1P, arg2P, arg3P, arg4P, arg5P) :|: -1 <= x4 - 1 && 0 <= arg2 - 1 && arg2P <= arg1 && 0 <= arg1 - 1 && 2 <= arg1P - 1 && 0 <= arg2P - 1 && arg2 = arg3P
f1_0_main_New(x, x1, x2, x3, x5) -> f155_0_main_ArrayAccess(x6, x7, x8, x9, x10) :|: x1 = x8 && 0 <= x7 - 1 && 1 <= x6 - 1 && 0 <= x - 1 && x7 <= x && 0 <= x1 - 1 && x6 - 1 <= x
f155_0_main_ArrayAccess(x11, x12, x13, x14, x15) -> f204_0_main_InvokeMethod(x16, x17, x18, x19, x20) :|: x13 = x19 && x20 + 2 <= x11 && 1 <= x18 - 1 && 0 <= x17 - 1 && 0 <= x16 - 1 && 0 <= x12 - 1 && 0 <= x11 - 1 && x18 - 1 <= x12 && x18 - 1 <= x11 && x17 <= x11 && x16 <= x12 && 1 <= x13 - 1 && x16 <= x11
f155_0_main_ArrayAccess(x21, x22, x24, x25, x26) -> f204_0_main_InvokeMethod(x27, x28, x29, x30, x31) :|: -1 <= x32 - 1 && 1 <= x24 - 1 && x27 <= x21 && x27 <= x22 && x28 <= x21 && 0 <= x21 - 1 && 0 <= x22 - 1 && 0 <= x27 - 1 && 0 <= x28 - 1 && 2 <= x29 - 1 && x31 + 2 <= x21 && x24 = x30
f1_0_main_New(x33, x34, x35, x36, x37) -> f69_0__init__GT(x38, x39, x40, x41, x42) :|: 0 <= x33 - 1 && 0 <= x34 - 1 && -1 <= x38 - 1
f155_0_main_ArrayAccess(x43, x44, x45, x46, x47) -> f69_0__init__GT(x48, x49, x50, x51, x52) :|: 0 <= x44 - 1 && 0 <= x43 - 1 && 1 <= x45 - 1 && -1 <= x48 - 1
f69_0__init__GT(x53, x54, x55, x56, x57) -> f69_0__init__GT(x58, x59, x60, x61, x62) :|: x53 - 1 = x58 && x53 - 1 <= x53 - 1 && 0 <= x53 - 1
f204_0_main_InvokeMethod(x63, x64, x65, x66, x67) -> f292_0_isZero_NONNULL(x68, x69, x70, x71, x72) :|: x67 + 2 <= x64 && -1 <= x71 - 1 && 0 <= x70 - 1 && 0 <= x69 - 1 && 0 <= x68 - 1 && 0 <= x65 - 1 && 0 <= x64 - 1 && 0 <= x63 - 1 && x71 + 1 <= x65 && x70 <= x65 && x69 <= x65 && 1 <= x66 - 1 && x68 <= x64
f292_0_isZero_NONNULL(x73, x74, x75, x76, x77) -> f292_0_isZero_NONNULL(x78, x79, x80, x81, x82) :|: 0 <= x81 - 1 && 2 <= x80 - 1 && 2 <= x79 - 1 && 0 <= x78 - 1 && 0 <= x76 - 1 && 2 <= x75 - 1 && 1 <= x74 - 1 && 0 <= x73 - 1 && x81 <= x76 && x81 + 2 <= x75 && x80 - 2 <= x76 && x80 <= x75 && x79 - 2 <= x76 && x79 <= x75 && x78 <= x73
f292_0_isZero_NONNULL(x83, x84, x85, x86, x87) -> f292_0_isZero_NONNULL(x88, x89, x90, x91, x92) :|: 0 <= x91 - 1 && 2 <= x90 - 1 && 0 <= x89 - 1 && 0 <= x88 - 1 && 0 <= x86 - 1 && 2 <= x85 - 1 && 2 <= x84 - 1 && 2 <= x83 - 1 && x91 <= x86 && x91 + 2 <= x85 && x90 - 2 <= x86 && x90 <= x85 && x89 + 2 <= x84 && x88 + 2 <= x83
__init(x93, x94, x95, x96, x97) -> f1_0_main_New(x98, x99, x100, x101, x102) :|: 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_New(arg1, arg2, arg3, arg4, arg5) -> f155_0_main_ArrayAccess(arg1P, arg2P, arg3P, arg4P, arg5P) :|: -1 <= x4 - 1 && 0 <= arg2 - 1 && arg2P <= arg1 && 0 <= arg1 - 1 && 2 <= arg1P - 1 && 0 <= arg2P - 1 && arg2 = arg3P
f1_0_main_New(x, x1, x2, x3, x5) -> f155_0_main_ArrayAccess(x6, x7, x8, x9, x10) :|: x1 = x8 && 0 <= x7 - 1 && 1 <= x6 - 1 && 0 <= x - 1 && x7 <= x && 0 <= x1 - 1 && x6 - 1 <= x
f155_0_main_ArrayAccess(x11, x12, x13, x14, x15) -> f204_0_main_InvokeMethod(x16, x17, x18, x19, x20) :|: x13 = x19 && x20 + 2 <= x11 && 1 <= x18 - 1 && 0 <= x17 - 1 && 0 <= x16 - 1 && 0 <= x12 - 1 && 0 <= x11 - 1 && x18 - 1 <= x12 && x18 - 1 <= x11 && x17 <= x11 && x16 <= x12 && 1 <= x13 - 1 && x16 <= x11
f155_0_main_ArrayAccess(x21, x22, x24, x25, x26) -> f204_0_main_InvokeMethod(x27, x28, x29, x30, x31) :|: -1 <= x32 - 1 && 1 <= x24 - 1 && x27 <= x21 && x27 <= x22 && x28 <= x21 && 0 <= x21 - 1 && 0 <= x22 - 1 && 0 <= x27 - 1 && 0 <= x28 - 1 && 2 <= x29 - 1 && x31 + 2 <= x21 && x24 = x30
f1_0_main_New(x33, x34, x35, x36, x37) -> f69_0__init__GT(x38, x39, x40, x41, x42) :|: 0 <= x33 - 1 && 0 <= x34 - 1 && -1 <= x38 - 1
f155_0_main_ArrayAccess(x43, x44, x45, x46, x47) -> f69_0__init__GT(x48, x49, x50, x51, x52) :|: 0 <= x44 - 1 && 0 <= x43 - 1 && 1 <= x45 - 1 && -1 <= x48 - 1
f69_0__init__GT(x53, x54, x55, x56, x57) -> f69_0__init__GT(x58, x59, x60, x61, x62) :|: x53 - 1 = x58 && x53 - 1 <= x53 - 1 && 0 <= x53 - 1
f204_0_main_InvokeMethod(x63, x64, x65, x66, x67) -> f292_0_isZero_NONNULL(x68, x69, x70, x71, x72) :|: x67 + 2 <= x64 && -1 <= x71 - 1 && 0 <= x70 - 1 && 0 <= x69 - 1 && 0 <= x68 - 1 && 0 <= x65 - 1 && 0 <= x64 - 1 && 0 <= x63 - 1 && x71 + 1 <= x65 && x70 <= x65 && x69 <= x65 && 1 <= x66 - 1 && x68 <= x64
f292_0_isZero_NONNULL(x73, x74, x75, x76, x77) -> f292_0_isZero_NONNULL(x78, x79, x80, x81, x82) :|: 0 <= x81 - 1 && 2 <= x80 - 1 && 2 <= x79 - 1 && 0 <= x78 - 1 && 0 <= x76 - 1 && 2 <= x75 - 1 && 1 <= x74 - 1 && 0 <= x73 - 1 && x81 <= x76 && x81 + 2 <= x75 && x80 - 2 <= x76 && x80 <= x75 && x79 - 2 <= x76 && x79 <= x75 && x78 <= x73
f292_0_isZero_NONNULL(x83, x84, x85, x86, x87) -> f292_0_isZero_NONNULL(x88, x89, x90, x91, x92) :|: 0 <= x91 - 1 && 2 <= x90 - 1 && 0 <= x89 - 1 && 0 <= x88 - 1 && 0 <= x86 - 1 && 2 <= x85 - 1 && 2 <= x84 - 1 && 2 <= x83 - 1 && x91 <= x86 && x91 + 2 <= x85 && x90 - 2 <= x86 && x90 <= x85 && x89 + 2 <= x84 && x88 + 2 <= x83
__init(x93, x94, x95, x96, x97) -> f1_0_main_New(x98, x99, x100, x101, x102) :|: 0 <= 0
Start term: __init(arg1, arg2, arg3, arg4, arg5)

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

(3) IRSwTTerminationDigraphProof (EQUIVALENT)
Constructed termination digraph!
Nodes:
(1) f1_0_main_New(arg1, arg2, arg3, arg4, arg5) -> f155_0_main_ArrayAccess(arg1P, arg2P, arg3P, arg4P, arg5P) :|: -1 <= x4 - 1 && 0 <= arg2 - 1 && arg2P <= arg1 && 0 <= arg1 - 1 && 2 <= arg1P - 1 && 0 <= arg2P - 1 && arg2 = arg3P
(2) f1_0_main_New(x, x1, x2, x3, x5) -> f155_0_main_ArrayAccess(x6, x7, x8, x9, x10) :|: x1 = x8 && 0 <= x7 - 1 && 1 <= x6 - 1 && 0 <= x - 1 && x7 <= x && 0 <= x1 - 1 && x6 - 1 <= x
(3) f155_0_main_ArrayAccess(x11, x12, x13, x14, x15) -> f204_0_main_InvokeMethod(x16, x17, x18, x19, x20) :|: x13 = x19 && x20 + 2 <= x11 && 1 <= x18 - 1 && 0 <= x17 - 1 && 0 <= x16 - 1 && 0 <= x12 - 1 && 0 <= x11 - 1 && x18 - 1 <= x12 && x18 - 1 <= x11 && x17 <= x11 && x16 <= x12 && 1 <= x13 - 1 && x16 <= x11
(4) f155_0_main_ArrayAccess(x21, x22, x24, x25, x26) -> f204_0_main_InvokeMethod(x27, x28, x29, x30, x31) :|: -1 <= x32 - 1 && 1 <= x24 - 1 && x27 <= x21 && x27 <= x22 && x28 <= x21 && 0 <= x21 - 1 && 0 <= x22 - 1 && 0 <= x27 - 1 && 0 <= x28 - 1 && 2 <= x29 - 1 && x31 + 2 <= x21 && x24 = x30
(5) f1_0_main_New(x33, x34, x35, x36, x37) -> f69_0__init__GT(x38, x39, x40, x41, x42) :|: 0 <= x33 - 1 && 0 <= x34 - 1 && -1 <= x38 - 1
(6) f155_0_main_ArrayAccess(x43, x44, x45, x46, x47) -> f69_0__init__GT(x48, x49, x50, x51, x52) :|: 0 <= x44 - 1 && 0 <= x43 - 1 && 1 <= x45 - 1 && -1 <= x48 - 1
(7) f69_0__init__GT(x53, x54, x55, x56, x57) -> f69_0__init__GT(x58, x59, x60, x61, x62) :|: x53 - 1 = x58 && x53 - 1 <= x53 - 1 && 0 <= x53 - 1
(8) f204_0_main_InvokeMethod(x63, x64, x65, x66, x67) -> f292_0_isZero_NONNULL(x68, x69, x70, x71, x72) :|: x67 + 2 <= x64 && -1 <= x71 - 1 && 0 <= x70 - 1 && 0 <= x69 - 1 && 0 <= x68 - 1 && 0 <= x65 - 1 && 0 <= x64 - 1 && 0 <= x63 - 1 && x71 + 1 <= x65 && x70 <= x65 && x69 <= x65 && 1 <= x66 - 1 && x68 <= x64
(9) f292_0_isZero_NONNULL(x73, x74, x75, x76, x77) -> f292_0_isZero_NONNULL(x78, x79, x80, x81, x82) :|: 0 <= x81 - 1 && 2 <= x80 - 1 && 2 <= x79 - 1 && 0 <= x78 - 1 && 0 <= x76 - 1 && 2 <= x75 - 1 && 1 <= x74 - 1 && 0 <= x73 - 1 && x81 <= x76 && x81 + 2 <= x75 && x80 - 2 <= x76 && x80 <= x75 && x79 - 2 <= x76 && x79 <= x75 && x78 <= x73
(10) f292_0_isZero_NONNULL(x83, x84, x85, x86, x87) -> f292_0_isZero_NONNULL(x88, x89, x90, x91, x92) :|: 0 <= x91 - 1 && 2 <= x90 - 1 && 0 <= x89 - 1 && 0 <= x88 - 1 && 0 <= x86 - 1 && 2 <= x85 - 1 && 2 <= x84 - 1 && 2 <= x83 - 1 && x91 <= x86 && x91 + 2 <= x85 && x90 - 2 <= x86 && x90 <= x85 && x89 + 2 <= x84 && x88 + 2 <= x83
(11) __init(x93, x94, x95, x96, x97) -> f1_0_main_New(x98, x99, x100, x101, x102) :|: 0 <= 0

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

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

(4)
Complex Obligation (AND)

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

(5)
Obligation:

Termination digraph:
Nodes:
(1) f69_0__init__GT(x53, x54, x55, x56, x57) -> f69_0__init__GT(x58, x59, x60, x61, x62) :|: x53 - 1 = x58 && x53 - 1 <= x53 - 1 && 0 <= x53 - 1

Arcs:
(1) -> (1)

This digraph is fully evaluated!

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

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

(7)
Obligation:
Rules:
f69_0__init__GT(x53:0, x54:0, x55:0, x56:0, x57:0) -> f69_0__init__GT(x53:0 - 1, x59:0, x60:0, x61:0, x62:0) :|: x53:0 > 0

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

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

   f69_0__init__GT(x1, x2, x3, x4, x5) -> f69_0__init__GT(x1)

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

(9)
Obligation:
Rules:
f69_0__init__GT(x53:0) -> f69_0__init__GT(x53:0 - 1) :|: x53:0 > 0

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

(10) TempFilterProof (SOUND)
Used the following sort dictionary for filtering: 
f69_0__init__GT(INTEGER)
Replaced non-predefined constructor symbols by 0.
----------------------------------------

(11)
Obligation:
Rules:
f69_0__init__GT(x53:0) -> f69_0__init__GT(c) :|: c = x53:0 - 1 && x53:0 > 0

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(12) PolynomialOrderProcessor (EQUIVALENT)
Found the following polynomial interpretation:
[f69_0__init__GT(x)] = x

The following rules are decreasing:
f69_0__init__GT(x53:0) -> f69_0__init__GT(c) :|: c = x53:0 - 1 && x53:0 > 0
The following rules are bounded:
f69_0__init__GT(x53:0) -> f69_0__init__GT(c) :|: c = x53:0 - 1 && x53:0 > 0

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

(13)
YES

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

(14)
Obligation:

Termination digraph:
Nodes:
(1) f292_0_isZero_NONNULL(x73, x74, x75, x76, x77) -> f292_0_isZero_NONNULL(x78, x79, x80, x81, x82) :|: 0 <= x81 - 1 && 2 <= x80 - 1 && 2 <= x79 - 1 && 0 <= x78 - 1 && 0 <= x76 - 1 && 2 <= x75 - 1 && 1 <= x74 - 1 && 0 <= x73 - 1 && x81 <= x76 && x81 + 2 <= x75 && x80 - 2 <= x76 && x80 <= x75 && x79 - 2 <= x76 && x79 <= x75 && x78 <= x73
(2) f292_0_isZero_NONNULL(x83, x84, x85, x86, x87) -> f292_0_isZero_NONNULL(x88, x89, x90, x91, x92) :|: 0 <= x91 - 1 && 2 <= x90 - 1 && 0 <= x89 - 1 && 0 <= x88 - 1 && 0 <= x86 - 1 && 2 <= x85 - 1 && 2 <= x84 - 1 && 2 <= x83 - 1 && x91 <= x86 && x91 + 2 <= x85 && x90 - 2 <= x86 && x90 <= x85 && x89 + 2 <= x84 && x88 + 2 <= x83

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

This digraph is fully evaluated!

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

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

(16)
Obligation:
Rules:
f292_0_isZero_NONNULL(x73:0, x74:0, x75:0, x76:0, x77:0) -> f292_0_isZero_NONNULL(x78:0, x79:0, x80:0, x81:0, x82:0) :|: x79:0 <= x75:0 && x78:0 <= x73:0 && x79:0 - 2 <= x76:0 && x80:0 <= x75:0 && x80:0 - 2 <= x76:0 && x81:0 + 2 <= x75:0 && x81:0 <= x76:0 && x73:0 > 0 && x74:0 > 1 && x75:0 > 2 && x76:0 > 0 && x78:0 > 0 && x79:0 > 2 && x80:0 > 2 && x81:0 > 0
f292_0_isZero_NONNULL(x83:0, x84:0, x85:0, x86:0, x87:0) -> f292_0_isZero_NONNULL(x88:0, x89:0, x90:0, x91:0, x92:0) :|: x89:0 + 2 <= x84:0 && x88:0 + 2 <= x83:0 && x90:0 <= x85:0 && x90:0 - 2 <= x86:0 && x91:0 + 2 <= x85:0 && x91:0 <= x86:0 && x83:0 > 2 && x84:0 > 2 && x85:0 > 2 && x86:0 > 0 && x88:0 > 0 && x89:0 > 0 && x90:0 > 2 && x91:0 > 0

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

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

   f292_0_isZero_NONNULL(x1, x2, x3, x4, x5) -> f292_0_isZero_NONNULL(x1, x2, x3, x4)

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

(18)
Obligation:
Rules:
f292_0_isZero_NONNULL(x73:0, x74:0, x75:0, x76:0) -> f292_0_isZero_NONNULL(x78:0, x79:0, x80:0, x81:0) :|: x79:0 <= x75:0 && x78:0 <= x73:0 && x79:0 - 2 <= x76:0 && x80:0 <= x75:0 && x80:0 - 2 <= x76:0 && x81:0 + 2 <= x75:0 && x81:0 <= x76:0 && x73:0 > 0 && x74:0 > 1 && x75:0 > 2 && x76:0 > 0 && x78:0 > 0 && x79:0 > 2 && x80:0 > 2 && x81:0 > 0
f292_0_isZero_NONNULL(x83:0, x84:0, x85:0, x86:0) -> f292_0_isZero_NONNULL(x88:0, x89:0, x90:0, x91:0) :|: x89:0 + 2 <= x84:0 && x88:0 + 2 <= x83:0 && x90:0 <= x85:0 && x90:0 - 2 <= x86:0 && x91:0 + 2 <= x85:0 && x91:0 <= x86:0 && x83:0 > 2 && x84:0 > 2 && x85:0 > 2 && x86:0 > 0 && x88:0 > 0 && x89:0 > 0 && x90:0 > 2 && x91:0 > 0

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

(19) FilterProof (EQUIVALENT)
Used the following sort dictionary for filtering: 
f292_0_isZero_NONNULL(INTEGER, INTEGER, INTEGER, INTEGER)
Replaced non-predefined constructor symbols by 0.
----------------------------------------

(20)
Obligation:
Rules:
f292_0_isZero_NONNULL(x73:0, x74:0, x75:0, x76:0) -> f292_0_isZero_NONNULL(x78:0, x79:0, x80:0, x81:0) :|: x79:0 <= x75:0 && x78:0 <= x73:0 && x79:0 - 2 <= x76:0 && x80:0 <= x75:0 && x80:0 - 2 <= x76:0 && x81:0 + 2 <= x75:0 && x81:0 <= x76:0 && x73:0 > 0 && x74:0 > 1 && x75:0 > 2 && x76:0 > 0 && x78:0 > 0 && x79:0 > 2 && x80:0 > 2 && x81:0 > 0
f292_0_isZero_NONNULL(x83:0, x84:0, x85:0, x86:0) -> f292_0_isZero_NONNULL(x88:0, x89:0, x90:0, x91:0) :|: x89:0 + 2 <= x84:0 && x88:0 + 2 <= x83:0 && x90:0 <= x85:0 && x90:0 - 2 <= x86:0 && x91:0 + 2 <= x85:0 && x91:0 <= x86:0 && x83:0 > 2 && x84:0 > 2 && x85:0 > 2 && x86:0 > 0 && x88:0 > 0 && x89:0 > 0 && x90:0 > 2 && x91:0 > 0

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

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

(22)
Obligation:
Rules:
f292_0_isZero_NONNULL(x73:0:0, x74:0:0, x75:0:0, x76:0:0) -> f292_0_isZero_NONNULL(x78:0:0, x79:0:0, x80:0:0, x81:0:0) :|: x80:0:0 > 2 && x81:0:0 > 0 && x79:0:0 > 2 && x78:0:0 > 0 && x76:0:0 > 0 && x75:0:0 > 2 && x74:0:0 > 1 && x73:0:0 > 0 && x81:0:0 <= x76:0:0 && x81:0:0 + 2 <= x75:0:0 && x80:0:0 - 2 <= x76:0:0 && x80:0:0 <= x75:0:0 && x79:0:0 - 2 <= x76:0:0 && x78:0:0 <= x73:0:0 && x79:0:0 <= x75:0:0
f292_0_isZero_NONNULL(x83:0:0, x84:0:0, x85:0:0, x86:0:0) -> f292_0_isZero_NONNULL(x88:0:0, x89:0:0, x90:0:0, x91:0:0) :|: x90:0:0 > 2 && x91:0:0 > 0 && x89:0:0 > 0 && x88:0:0 > 0 && x86:0:0 > 0 && x85:0:0 > 2 && x84:0:0 > 2 && x83:0:0 > 2 && x91:0:0 <= x86:0:0 && x91:0:0 + 2 <= x85:0:0 && x90:0:0 - 2 <= x86:0:0 && x90:0:0 <= x85:0:0 && x88:0:0 + 2 <= x83:0:0 && x89:0:0 + 2 <= x84:0:0

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(23) IntTRSPeriodicNontermProof (COMPLETE)
Normalized system to the following form:
f(pc, x73:0:0, x74:0:0, x75:0:0, x76:0:0) -> f(1, x78:0:0, x79:0:0, x80:0:0, x81:0:0) :|: pc = 1 && (x80:0:0 > 2 && x81:0:0 > 0 && x79:0:0 > 2 && x78:0:0 > 0 && x76:0:0 > 0 && x75:0:0 > 2 && x74:0:0 > 1 && x73:0:0 > 0 && x81:0:0 <= x76:0:0 && x81:0:0 + 2 <= x75:0:0 && x80:0:0 - 2 <= x76:0:0 && x80:0:0 <= x75:0:0 && x79:0:0 - 2 <= x76:0:0 && x78:0:0 <= x73:0:0 && x79:0:0 <= x75:0:0)
f(pc, x83:0:0, x84:0:0, x85:0:0, x86:0:0) -> f(1, x88:0:0, x89:0:0, x90:0:0, x91:0:0) :|: pc = 1 && (x90:0:0 > 2 && x91:0:0 > 0 && x89:0:0 > 0 && x88:0:0 > 0 && x86:0:0 > 0 && x85:0:0 > 2 && x84:0:0 > 2 && x83:0:0 > 2 && x91:0:0 <= x86:0:0 && x91:0:0 + 2 <= x85:0:0 && x90:0:0 - 2 <= x86:0:0 && x90:0:0 <= x85:0:0 && x88:0:0 + 2 <= x83:0:0 && x89:0:0 + 2 <= x84:0:0)
Witness term starting non-terminating reduction: f(1, 1, 4, 4, 2)
----------------------------------------

(24)
NO