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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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, 1139 ms]
(4) AND
    (5) IRSwT
        (6) IntTRSCompressionProof [EQUIVALENT, 28 ms]
        (7) IRSwT
        (8) FilterProof [EQUIVALENT, 0 ms]
        (9) IntTRS
        (10) IntTRSNonPeriodicNontermProof [COMPLETE, 0 ms]
        (11) NO
    (12) IRSwT
        (13) IntTRSCompressionProof [EQUIVALENT, 13 ms]
        (14) IRSwT
        (15) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms]
        (16) IRSwT
        (17) IRSwTChainingProof [EQUIVALENT, 0 ms]
        (18) IRSwT
        (19) IRSwTTerminationDigraphProof [EQUIVALENT, 92 ms]
        (20) AND
            (21) IRSwT
                (22) IntTRSCompressionProof [EQUIVALENT, 0 ms]
                (23) IRSwT
            (24) IRSwT
                (25) IntTRSCompressionProof [EQUIVALENT, 0 ms]
                (26) IRSwT
                (27) FilterProof [EQUIVALENT, 0 ms]
                (28) IntTRS
                (29) IntTRSPeriodicNontermProof [COMPLETE, 0 ms]
                (30) NO


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

(0)
Obligation:
Rules:
l0(WItemsNumHAT0, __const_5HAT0, tmp1HAT0) -> l1(WItemsNumHATpost, __const_5HATpost, tmp1HATpost) :|: tmp1HAT0 = tmp1HATpost && __const_5HAT0 = __const_5HATpost && WItemsNumHAT0 = WItemsNumHATpost && 1 + __const_5HAT0 <= WItemsNumHAT0
l0(x, x1, x2) -> l2(x3, x4, x5) :|: x1 = x4 && x = x3 && x5 = x5 && x <= x1
l3(x6, x7, x8) -> l4(x9, x10, x11) :|: x8 = x11 && x7 = x10 && x6 = x9
l4(x12, x13, x14) -> l0(x15, x16, x17) :|: x14 = x17 && x13 = x16 && x12 = x15
l5(x18, x19, x20) -> l6(x21, x22, x23) :|: x20 = x23 && x19 = x22 && x18 = x21
l7(x24, x25, x26) -> l8(x27, x28, x29) :|: x26 = x29 && x25 = x28 && x24 = x27
l9(x30, x31, x32) -> l10(x33, x34, x35) :|: x32 = x35 && x31 = x34 && x30 = x33
l6(x36, x37, x38) -> l3(x39, x40, x41) :|: x38 = x41 && x37 = x40 && x36 = x39 && x36 <= 2
l6(x42, x43, x44) -> l5(x45, x46, x47) :|: x44 = x47 && x43 = x46 && x45 = -1 + x42 && 3 <= x42
l10(x48, x49, x50) -> l11(x51, x52, x53) :|: x50 = x53 && x49 = x52 && x48 = x51
l11(x54, x55, x56) -> l10(x57, x58, x59) :|: x56 = x59 && x55 = x58 && x54 = x57
l1(x60, x61, x62) -> l5(x63, x64, x65) :|: x62 = x65 && x61 = x64 && x60 = x63
l12(x66, x67, x68) -> l4(x69, x70, x71) :|: x68 = x71 && x67 = x70 && x69 = 1 + x66 && 1 + x67 <= x66
l12(x72, x73, x74) -> l4(x75, x76, x77) :|: x74 = x77 && x73 = x76 && x75 = 1 + x72 && x72 <= x73
l2(x78, x79, x80) -> l1(x81, x82, x83) :|: x80 = x83 && x79 = x82 && x78 = x81 && 0 <= x80 && x80 <= 0
l2(x84, x85, x86) -> l12(x87, x88, x89) :|: x86 = x89 && x85 = x88 && x84 = x87 && 1 <= x86
l2(x90, x91, x92) -> l12(x93, x94, x95) :|: x92 = x95 && x91 = x94 && x90 = x93 && 1 + x92 <= 0
l13(x96, x97, x98) -> l3(x99, x100, x101) :|: x102 = x102 && x99 = x99 && x97 = x100 && x98 = x101
l14(x103, x104, x105) -> l13(x106, x107, x108) :|: x105 = x108 && x104 = x107 && x103 = x106
Start term: l14(WItemsNumHAT0, __const_5HAT0, tmp1HAT0)

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

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

(2)
Obligation:
Rules:
l0(WItemsNumHAT0, __const_5HAT0, tmp1HAT0) -> l1(WItemsNumHATpost, __const_5HATpost, tmp1HATpost) :|: tmp1HAT0 = tmp1HATpost && __const_5HAT0 = __const_5HATpost && WItemsNumHAT0 = WItemsNumHATpost && 1 + __const_5HAT0 <= WItemsNumHAT0
l0(x, x1, x2) -> l2(x3, x4, x5) :|: x1 = x4 && x = x3 && x5 = x5 && x <= x1
l3(x6, x7, x8) -> l4(x9, x10, x11) :|: x8 = x11 && x7 = x10 && x6 = x9
l4(x12, x13, x14) -> l0(x15, x16, x17) :|: x14 = x17 && x13 = x16 && x12 = x15
l5(x18, x19, x20) -> l6(x21, x22, x23) :|: x20 = x23 && x19 = x22 && x18 = x21
l7(x24, x25, x26) -> l8(x27, x28, x29) :|: x26 = x29 && x25 = x28 && x24 = x27
l9(x30, x31, x32) -> l10(x33, x34, x35) :|: x32 = x35 && x31 = x34 && x30 = x33
l6(x36, x37, x38) -> l3(x39, x40, x41) :|: x38 = x41 && x37 = x40 && x36 = x39 && x36 <= 2
l6(x42, x43, x44) -> l5(x45, x46, x47) :|: x44 = x47 && x43 = x46 && x45 = -1 + x42 && 3 <= x42
l10(x48, x49, x50) -> l11(x51, x52, x53) :|: x50 = x53 && x49 = x52 && x48 = x51
l11(x54, x55, x56) -> l10(x57, x58, x59) :|: x56 = x59 && x55 = x58 && x54 = x57
l1(x60, x61, x62) -> l5(x63, x64, x65) :|: x62 = x65 && x61 = x64 && x60 = x63
l12(x66, x67, x68) -> l4(x69, x70, x71) :|: x68 = x71 && x67 = x70 && x69 = 1 + x66 && 1 + x67 <= x66
l12(x72, x73, x74) -> l4(x75, x76, x77) :|: x74 = x77 && x73 = x76 && x75 = 1 + x72 && x72 <= x73
l2(x78, x79, x80) -> l1(x81, x82, x83) :|: x80 = x83 && x79 = x82 && x78 = x81 && 0 <= x80 && x80 <= 0
l2(x84, x85, x86) -> l12(x87, x88, x89) :|: x86 = x89 && x85 = x88 && x84 = x87 && 1 <= x86
l2(x90, x91, x92) -> l12(x93, x94, x95) :|: x92 = x95 && x91 = x94 && x90 = x93 && 1 + x92 <= 0
l13(x96, x97, x98) -> l3(x99, x100, x101) :|: x102 = x102 && x99 = x99 && x97 = x100 && x98 = x101
l14(x103, x104, x105) -> l13(x106, x107, x108) :|: x105 = x108 && x104 = x107 && x103 = x106
Start term: l14(WItemsNumHAT0, __const_5HAT0, tmp1HAT0)

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

(3) IRSwTTerminationDigraphProof (EQUIVALENT)
Constructed termination digraph!
Nodes:
(1) l0(WItemsNumHAT0, __const_5HAT0, tmp1HAT0) -> l1(WItemsNumHATpost, __const_5HATpost, tmp1HATpost) :|: tmp1HAT0 = tmp1HATpost && __const_5HAT0 = __const_5HATpost && WItemsNumHAT0 = WItemsNumHATpost && 1 + __const_5HAT0 <= WItemsNumHAT0
(2) l0(x, x1, x2) -> l2(x3, x4, x5) :|: x1 = x4 && x = x3 && x5 = x5 && x <= x1
(3) l3(x6, x7, x8) -> l4(x9, x10, x11) :|: x8 = x11 && x7 = x10 && x6 = x9
(4) l4(x12, x13, x14) -> l0(x15, x16, x17) :|: x14 = x17 && x13 = x16 && x12 = x15
(5) l5(x18, x19, x20) -> l6(x21, x22, x23) :|: x20 = x23 && x19 = x22 && x18 = x21
(6) l7(x24, x25, x26) -> l8(x27, x28, x29) :|: x26 = x29 && x25 = x28 && x24 = x27
(7) l9(x30, x31, x32) -> l10(x33, x34, x35) :|: x32 = x35 && x31 = x34 && x30 = x33
(8) l6(x36, x37, x38) -> l3(x39, x40, x41) :|: x38 = x41 && x37 = x40 && x36 = x39 && x36 <= 2
(9) l6(x42, x43, x44) -> l5(x45, x46, x47) :|: x44 = x47 && x43 = x46 && x45 = -1 + x42 && 3 <= x42
(10) l10(x48, x49, x50) -> l11(x51, x52, x53) :|: x50 = x53 && x49 = x52 && x48 = x51
(11) l11(x54, x55, x56) -> l10(x57, x58, x59) :|: x56 = x59 && x55 = x58 && x54 = x57
(12) l1(x60, x61, x62) -> l5(x63, x64, x65) :|: x62 = x65 && x61 = x64 && x60 = x63
(13) l12(x66, x67, x68) -> l4(x69, x70, x71) :|: x68 = x71 && x67 = x70 && x69 = 1 + x66 && 1 + x67 <= x66
(14) l12(x72, x73, x74) -> l4(x75, x76, x77) :|: x74 = x77 && x73 = x76 && x75 = 1 + x72 && x72 <= x73
(15) l2(x78, x79, x80) -> l1(x81, x82, x83) :|: x80 = x83 && x79 = x82 && x78 = x81 && 0 <= x80 && x80 <= 0
(16) l2(x84, x85, x86) -> l12(x87, x88, x89) :|: x86 = x89 && x85 = x88 && x84 = x87 && 1 <= x86
(17) l2(x90, x91, x92) -> l12(x93, x94, x95) :|: x92 = x95 && x91 = x94 && x90 = x93 && 1 + x92 <= 0
(18) l13(x96, x97, x98) -> l3(x99, x100, x101) :|: x102 = x102 && x99 = x99 && x97 = x100 && x98 = x101
(19) l14(x103, x104, x105) -> l13(x106, x107, x108) :|: x105 = x108 && x104 = x107 && x103 = x106

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

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

(4)
Complex Obligation (AND)

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

(5)
Obligation:

Termination digraph:
Nodes:
(1) l10(x48, x49, x50) -> l11(x51, x52, x53) :|: x50 = x53 && x49 = x52 && x48 = x51
(2) l11(x54, x55, x56) -> l10(x57, x58, x59) :|: x56 = x59 && x55 = x58 && x54 = x57

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

This digraph is fully evaluated!

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

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

(7)
Obligation:
Rules:
l10(x48:0, x49:0, x50:0) -> l10(x48:0, x49:0, x50:0) :|: TRUE

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

(8) FilterProof (EQUIVALENT)
Used the following sort dictionary for filtering: 
l10(VARIABLE, VARIABLE, VARIABLE)
Replaced non-predefined constructor symbols by 0.
----------------------------------------

(9)
Obligation:
Rules:
l10(x48:0, x49:0, x50:0) -> l10(x48:0, x49:0, x50:0) :|: TRUE

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

(10) IntTRSNonPeriodicNontermProof (COMPLETE)
Normalized system to the following form:
f(pc, x48:0, x49:0, x50:0) -> f(1, x48:0, x49:0, x50:0) :|: pc = 1 && TRUE
Proved unsatisfiability of the following formula, indicating that the system is never left after entering:
(((run2_0 = ((1 * 1)) and run2_1 = ((run1_1 * 1)) and run2_2 = ((run1_2 * 1)) and run2_3 = ((run1_3 * 1))) and (((run1_0 * 1)) = ((1 * 1)) and T)) and !(((run2_0 * 1)) = ((1 * 1)) and T))
Proved satisfiability of the following formula, indicating that the system is entered at least once:
((run2_0 = ((1 * 1)) and run2_1 = ((run1_1 * 1)) and run2_2 = ((run1_2 * 1)) and run2_3 = ((run1_3 * 1))) and (((run1_0 * 1)) = ((1 * 1)) and T))

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

(11)
NO

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

(12)
Obligation:

Termination digraph:
Nodes:
(1) l0(WItemsNumHAT0, __const_5HAT0, tmp1HAT0) -> l1(WItemsNumHATpost, __const_5HATpost, tmp1HATpost) :|: tmp1HAT0 = tmp1HATpost && __const_5HAT0 = __const_5HATpost && WItemsNumHAT0 = WItemsNumHATpost && 1 + __const_5HAT0 <= WItemsNumHAT0
(2) l4(x12, x13, x14) -> l0(x15, x16, x17) :|: x14 = x17 && x13 = x16 && x12 = x15
(3) l12(x72, x73, x74) -> l4(x75, x76, x77) :|: x74 = x77 && x73 = x76 && x75 = 1 + x72 && x72 <= x73
(4) l12(x66, x67, x68) -> l4(x69, x70, x71) :|: x68 = x71 && x67 = x70 && x69 = 1 + x66 && 1 + x67 <= x66
(5) l2(x90, x91, x92) -> l12(x93, x94, x95) :|: x92 = x95 && x91 = x94 && x90 = x93 && 1 + x92 <= 0
(6) l2(x84, x85, x86) -> l12(x87, x88, x89) :|: x86 = x89 && x85 = x88 && x84 = x87 && 1 <= x86
(7) l3(x6, x7, x8) -> l4(x9, x10, x11) :|: x8 = x11 && x7 = x10 && x6 = x9
(8) l6(x36, x37, x38) -> l3(x39, x40, x41) :|: x38 = x41 && x37 = x40 && x36 = x39 && x36 <= 2
(9) l5(x18, x19, x20) -> l6(x21, x22, x23) :|: x20 = x23 && x19 = x22 && x18 = x21
(10) l1(x60, x61, x62) -> l5(x63, x64, x65) :|: x62 = x65 && x61 = x64 && x60 = x63
(11) l2(x78, x79, x80) -> l1(x81, x82, x83) :|: x80 = x83 && x79 = x82 && x78 = x81 && 0 <= x80 && x80 <= 0
(12) l0(x, x1, x2) -> l2(x3, x4, x5) :|: x1 = x4 && x = x3 && x5 = x5 && x <= x1
(13) l6(x42, x43, x44) -> l5(x45, x46, x47) :|: x44 = x47 && x43 = x46 && x45 = -1 + x42 && 3 <= x42

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

This digraph is fully evaluated!

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

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

(14)
Obligation:
Rules:
l5(x18:0, x10:0, x11:0) -> l4(x18:0, x10:0, x11:0) :|: x18:0 < 3
l4(x12:0, x13:0, x14:0) -> l12(x12:0, x13:0, x5:0) :|: x5:0 < 0 && x13:0 >= x12:0
l4(x, x1, x2) -> l12(x, x1, x3) :|: x3 > 0 && x1 >= x
l12(x66:0, x67:0, x68:0) -> l4(1 + x66:0, x67:0, x68:0) :|: x66:0 >= 1 + x67:0
l12(x72:0, x73:0, x74:0) -> l4(1 + x72:0, x73:0, x74:0) :|: x73:0 >= x72:0
l4(WItemsNumHATpost:0, __const_5HATpost:0, tmp1HATpost:0) -> l5(WItemsNumHATpost:0, __const_5HATpost:0, tmp1HATpost:0) :|: WItemsNumHATpost:0 >= 1 + __const_5HATpost:0
l5(x4, x5, x6) -> l5(-1 + x4, x5, x6) :|: x4 > 2
l4(x7, x8, x9) -> l5(x7, x8, x10) :|: x10 < 1 && x10 > -1 && x8 >= x7

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

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

   l5(x1, x2, x3) -> l5(x1, x2)
   l4(x1, x2, x3) -> l4(x1, x2)
   l12(x1, x2, x3) -> l12(x1, x2)

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

(16)
Obligation:
Rules:
l5(x18:0, x10:0) -> l4(x18:0, x10:0) :|: x18:0 < 3
l4(x12:0, x13:0) -> l12(x12:0, x13:0) :|: x5:0 < 0 && x13:0 >= x12:0
l4(x, x1) -> l12(x, x1) :|: x3 > 0 && x1 >= x
l12(x66:0, x67:0) -> l4(1 + x66:0, x67:0) :|: x66:0 >= 1 + x67:0
l12(x72:0, x73:0) -> l4(1 + x72:0, x73:0) :|: x73:0 >= x72:0
l4(WItemsNumHATpost:0, __const_5HATpost:0) -> l5(WItemsNumHATpost:0, __const_5HATpost:0) :|: WItemsNumHATpost:0 >= 1 + __const_5HATpost:0
l5(x4, x5) -> l5(-1 + x4, x5) :|: x4 > 2
l4(x7, x8) -> l5(x7, x8) :|: x10 < 1 && x10 > -1 && x8 >= x7

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

(17) IRSwTChainingProof (EQUIVALENT)
Chaining!
----------------------------------------

(18)
Obligation:
Rules:
l4(x12:0, x13:0) -> l12(x12:0, x13:0) :|: x5:0 < 0 && x13:0 >= x12:0
l5(x12, x13) -> l12(x12, x13) :|: TRUE && x12 <= 2 && x16 <= -1 && x13 + -1 * x12 >= 0
l4(x, x1) -> l12(x, x1) :|: x3 > 0 && x1 >= x
l5(x17, x18) -> l12(x17, x18) :|: TRUE && x17 <= 2 && x21 >= 1 && x18 + -1 * x17 >= 0
l12(x66:0, x67:0) -> l4(1 + x66:0, x67:0) :|: x66:0 >= 1 + x67:0
l12(x72:0, x73:0) -> l4(1 + x72:0, x73:0) :|: x73:0 >= x72:0
l4(WItemsNumHATpost:0, __const_5HATpost:0) -> l5(WItemsNumHATpost:0, __const_5HATpost:0) :|: WItemsNumHATpost:0 >= 1 + __const_5HATpost:0
l5(x30, x31) -> l5(x30, x31) :|: TRUE && x30 <= 2 && x30 + -1 * x31 >= 1
l5(x4, x5) -> l5(-1 + x4, x5) :|: x4 > 2
l4(x7, x8) -> l5(x7, x8) :|: x10 < 1 && x10 > -1 && x8 >= x7
l5(x38, x39) -> l5(x38, x39) :|: TRUE && x38 <= 2 && x42 <= 0 && x42 >= 0 && x39 + -1 * x38 >= 0

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

(19) IRSwTTerminationDigraphProof (EQUIVALENT)
Constructed termination digraph!
Nodes:
(1) l4(x12:0, x13:0) -> l12(x12:0, x13:0) :|: x5:0 < 0 && x13:0 >= x12:0
(2) l5(x12, x13) -> l12(x12, x13) :|: TRUE && x12 <= 2 && x16 <= -1 && x13 + -1 * x12 >= 0
(3) l4(x, x1) -> l12(x, x1) :|: x3 > 0 && x1 >= x
(4) l5(x17, x18) -> l12(x17, x18) :|: TRUE && x17 <= 2 && x21 >= 1 && x18 + -1 * x17 >= 0
(5) l12(x66:0, x67:0) -> l4(1 + x66:0, x67:0) :|: x66:0 >= 1 + x67:0
(6) l12(x72:0, x73:0) -> l4(1 + x72:0, x73:0) :|: x73:0 >= x72:0
(7) l4(WItemsNumHATpost:0, __const_5HATpost:0) -> l5(WItemsNumHATpost:0, __const_5HATpost:0) :|: WItemsNumHATpost:0 >= 1 + __const_5HATpost:0
(8) l5(x30, x31) -> l5(x30, x31) :|: TRUE && x30 <= 2 && x30 + -1 * x31 >= 1
(9) l5(x4, x5) -> l5(-1 + x4, x5) :|: x4 > 2
(10) l4(x7, x8) -> l5(x7, x8) :|: x10 < 1 && x10 > -1 && x8 >= x7
(11) l5(x38, x39) -> l5(x38, x39) :|: TRUE && x38 <= 2 && x42 <= 0 && x42 >= 0 && x39 + -1 * x38 >= 0

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

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

(20)
Complex Obligation (AND)

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

(21)
Obligation:

Termination digraph:
Nodes:
(1) l4(x12:0, x13:0) -> l12(x12:0, x13:0) :|: x5:0 < 0 && x13:0 >= x12:0
(2) l12(x72:0, x73:0) -> l4(1 + x72:0, x73:0) :|: x73:0 >= x72:0
(3) l5(x17, x18) -> l12(x17, x18) :|: TRUE && x17 <= 2 && x21 >= 1 && x18 + -1 * x17 >= 0
(4) l4(x, x1) -> l12(x, x1) :|: x3 > 0 && x1 >= x
(5) l5(x12, x13) -> l12(x12, x13) :|: TRUE && x12 <= 2 && x16 <= -1 && x13 + -1 * x12 >= 0
(6) l5(x38, x39) -> l5(x38, x39) :|: TRUE && x38 <= 2 && x42 <= 0 && x42 >= 0 && x39 + -1 * x38 >= 0
(7) l5(x4, x5) -> l5(-1 + x4, x5) :|: x4 > 2
(8) l4(x7, x8) -> l5(x7, x8) :|: x10 < 1 && x10 > -1 && x8 >= x7
(9) l4(WItemsNumHATpost:0, __const_5HATpost:0) -> l5(WItemsNumHATpost:0, __const_5HATpost:0) :|: WItemsNumHATpost:0 >= 1 + __const_5HATpost:0

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

This digraph is fully evaluated!

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

(23)
Obligation:
Rules:
l5(x4:0, x5:0) -> l5(-1 + x4:0, x5:0) :|: x4:0 > 2
l5(x17:0, x18:0) -> l4(1 + x17:0, x18:0) :|: x18:0 + -1 * x17:0 >= 0 && x18:0 >= x17:0 && x17:0 < 3 && x21:0 > 0
l5(x38:0, x39:0) -> l5(x38:0, x39:0) :|: x42:0 > -1 && x39:0 + -1 * x38:0 >= 0 && x38:0 < 3 && x42:0 < 1
l4(WItemsNumHATpost:0:0, __const_5HATpost:0:0) -> l5(WItemsNumHATpost:0:0, __const_5HATpost:0:0) :|: WItemsNumHATpost:0:0 >= 1 + __const_5HATpost:0:0
l4(x7:0, x8:0) -> l5(x7:0, x8:0) :|: x10:0 < 1 && x10:0 > -1 && x8:0 >= x7:0
l4(x:0, x1:0) -> l4(1 + x:0, x1:0) :|: x:0 <= x1:0 && x3:0 > 0
l4(x12:0:0, x13:0:0) -> l4(1 + x12:0:0, x13:0:0) :|: x13:0:0 >= x12:0:0 && x5:0:0 < 0
l5(x12:0, x13:0) -> l4(1 + x12:0, x13:0) :|: x13:0 + -1 * x12:0 >= 0 && x13:0 >= x12:0 && x12:0 < 3 && x16:0 < 0

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

(24)
Obligation:

Termination digraph:
Nodes:
(1) l5(x30, x31) -> l5(x30, x31) :|: TRUE && x30 <= 2 && x30 + -1 * x31 >= 1

Arcs:
(1) -> (1)

This digraph is fully evaluated!

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

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

(26)
Obligation:
Rules:
l5(x30:0, x31:0) -> l5(x30:0, x31:0) :|: x30:0 + -1 * x31:0 >= 1 && x30:0 < 3

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

(27) FilterProof (EQUIVALENT)
Used the following sort dictionary for filtering: 
l5(INTEGER, INTEGER)
Replaced non-predefined constructor symbols by 0.
----------------------------------------

(28)
Obligation:
Rules:
l5(x30:0, x31:0) -> l5(x30:0, x31:0) :|: x30:0 + -1 * x31:0 >= 1 && x30:0 < 3

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

(29) IntTRSPeriodicNontermProof (COMPLETE)
Normalized system to the following form:
f(pc, x30:0, x31:0) -> f(1, x30:0, x31:0) :|: pc = 1 && (x30:0 + -1 * x31:0 >= 1 && x30:0 < 3)
Witness term starting non-terminating reduction: f(1, 0, -4)
----------------------------------------

(30)
NO