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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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, 2660 ms]
(4) AND
    (5) IRSwT
        (6) IntTRSCompressionProof [EQUIVALENT, 0 ms]
        (7) IRSwT
        (8) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms]
        (9) IRSwT
        (10) TempFilterProof [SOUND, 18 ms]
        (11) IntTRS
        (12) PolynomialOrderProcessor [EQUIVALENT, 5 ms]
        (13) YES
    (14) IRSwT
        (15) IntTRSCompressionProof [EQUIVALENT, 0 ms]
        (16) IRSwT
        (17) FilterProof [EQUIVALENT, 0 ms]
        (18) IntTRS
        (19) IntTRSPeriodicNontermProof [COMPLETE, 0 ms]
        (20) NO
    (21) IRSwT
        (22) IntTRSCompressionProof [EQUIVALENT, 0 ms]
        (23) IRSwT
        (24) FilterProof [EQUIVALENT, 0 ms]
        (25) IntTRS
        (26) IntTRSNonPeriodicNontermProof [COMPLETE, 2 ms]
        (27) NO
    (28) IRSwT
        (29) IntTRSCompressionProof [EQUIVALENT, 0 ms]
        (30) IRSwT
        (31) FilterProof [EQUIVALENT, 0 ms]
        (32) IntTRS
        (33) IntTRSNonPeriodicNontermProof [COMPLETE, 3 ms]
        (34) NO


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

(0)
Obligation:
Rules:
l0(i6HAT0, length5HAT0, sHAT0, tmp15HAT0, tmpHAT0, tmp___09HAT0) -> l1(i6HATpost, length5HATpost, sHATpost, tmp15HATpost, tmpHATpost, tmp___09HATpost) :|: tmp___09HAT0 = tmp___09HATpost && tmp15HAT0 = tmp15HATpost && tmpHAT0 = tmpHATpost && sHAT0 = sHATpost && length5HAT0 = length5HATpost && i6HAT0 = i6HATpost
l2(x, x1, x2, x3, x4, x5) -> l0(x6, x7, x8, x9, x10, x11) :|: x5 = x11 && x3 = x9 && x4 = x10 && x2 = x8 && x1 = x7 && x = x6
l2(x12, x13, x14, x15, x16, x17) -> l3(x18, x19, x20, x21, x22, x23) :|: x17 = x23 && x15 = x21 && x16 = x22 && x14 = x20 && x13 = x19 && x12 = x18
l4(x24, x25, x26, x27, x28, x29) -> l5(x30, x31, x32, x33, x34, x35) :|: x29 = x35 && x27 = x33 && x28 = x34 && x26 = x32 && x25 = x31 && x24 = x30
l6(x36, x37, x38, x39, x40, x41) -> l7(x42, x43, x44, x45, x46, x47) :|: x41 = x47 && x39 = x45 && x40 = x46 && x38 = x44 && x37 = x43 && x36 = x42
l8(x48, x49, x50, x51, x52, x53) -> l6(x54, x55, x56, x57, x58, x59) :|: x53 = x59 && x51 = x57 && x52 = x58 && x50 = x56 && x49 = x55 && x48 = x54
l8(x60, x61, x62, x63, x64, x65) -> l1(x66, x67, x68, x69, x70, x71) :|: x65 = x71 && x63 = x69 && x64 = x70 && x62 = x68 && x61 = x67 && x60 = x66
l9(x72, x73, x74, x75, x76, x77) -> l10(x78, x79, x80, x81, x82, x83) :|: x77 = x83 && x75 = x81 && x76 = x82 && x74 = x80 && x73 = x79 && x72 = x78
l7(x84, x85, x86, x87, x88, x89) -> l8(x90, x91, x92, x93, x94, x95) :|: x89 = x95 && x87 = x93 && x88 = x94 && x86 = x92 && x85 = x91 && x84 = x90
l11(x96, x97, x98, x99, x100, x101) -> l9(x102, x103, x104, x105, x106, x107) :|: x101 = x107 && x100 = x106 && x98 = x104 && x97 = x103 && x96 = x102 && x105 = x105
l10(x108, x109, x110, x111, x112, x113) -> l11(x114, x115, x116, x117, x118, x119) :|: x113 = x119 && x111 = x117 && x112 = x118 && x110 = x116 && x109 = x115 && x108 = x114
l10(x120, x121, x122, x123, x124, x125) -> l7(x126, x127, x128, x129, x130, x131) :|: x125 = x131 && x123 = x129 && x124 = x130 && x122 = x128 && x121 = x127 && x120 = x126
l1(x132, x133, x134, x135, x136, x137) -> l2(x138, x139, x140, x141, x142, x143) :|: x137 = x143 && x135 = x141 && x136 = x142 && x134 = x140 && x133 = x139 && x132 = x138
l5(x144, x145, x146, x147, x148, x149) -> l9(x150, x151, x152, x153, x154, x155) :|: x149 = x155 && x147 = x153 && x148 = x154 && x146 = x152 && x145 = x151 && x144 = x150 && x145 <= x144
l5(x156, x157, x158, x159, x160, x161) -> l4(x162, x163, x164, x165, x166, x167) :|: x159 = x165 && x160 = x166 && x158 = x164 && x157 = x163 && x162 = 1 + x156 && x167 = x167 && 1 + x156 <= x157
l12(x168, x169, x170, x171, x172, x173) -> l4(x174, x175, x176, x177, x178, x179) :|: x173 = x179 && x171 = x177 && x174 = 0 && x175 = x176 && x176 = x178 && x178 = x178
l13(x180, x181, x182, x183, x184, x185) -> l12(x186, x187, x188, x189, x190, x191) :|: x185 = x191 && x183 = x189 && x184 = x190 && x182 = x188 && x181 = x187 && x180 = x186
Start term: l13(i6HAT0, length5HAT0, sHAT0, tmp15HAT0, tmpHAT0, tmp___09HAT0)

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

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

(2)
Obligation:
Rules:
l0(i6HAT0, length5HAT0, sHAT0, tmp15HAT0, tmpHAT0, tmp___09HAT0) -> l1(i6HATpost, length5HATpost, sHATpost, tmp15HATpost, tmpHATpost, tmp___09HATpost) :|: tmp___09HAT0 = tmp___09HATpost && tmp15HAT0 = tmp15HATpost && tmpHAT0 = tmpHATpost && sHAT0 = sHATpost && length5HAT0 = length5HATpost && i6HAT0 = i6HATpost
l2(x, x1, x2, x3, x4, x5) -> l0(x6, x7, x8, x9, x10, x11) :|: x5 = x11 && x3 = x9 && x4 = x10 && x2 = x8 && x1 = x7 && x = x6
l2(x12, x13, x14, x15, x16, x17) -> l3(x18, x19, x20, x21, x22, x23) :|: x17 = x23 && x15 = x21 && x16 = x22 && x14 = x20 && x13 = x19 && x12 = x18
l4(x24, x25, x26, x27, x28, x29) -> l5(x30, x31, x32, x33, x34, x35) :|: x29 = x35 && x27 = x33 && x28 = x34 && x26 = x32 && x25 = x31 && x24 = x30
l6(x36, x37, x38, x39, x40, x41) -> l7(x42, x43, x44, x45, x46, x47) :|: x41 = x47 && x39 = x45 && x40 = x46 && x38 = x44 && x37 = x43 && x36 = x42
l8(x48, x49, x50, x51, x52, x53) -> l6(x54, x55, x56, x57, x58, x59) :|: x53 = x59 && x51 = x57 && x52 = x58 && x50 = x56 && x49 = x55 && x48 = x54
l8(x60, x61, x62, x63, x64, x65) -> l1(x66, x67, x68, x69, x70, x71) :|: x65 = x71 && x63 = x69 && x64 = x70 && x62 = x68 && x61 = x67 && x60 = x66
l9(x72, x73, x74, x75, x76, x77) -> l10(x78, x79, x80, x81, x82, x83) :|: x77 = x83 && x75 = x81 && x76 = x82 && x74 = x80 && x73 = x79 && x72 = x78
l7(x84, x85, x86, x87, x88, x89) -> l8(x90, x91, x92, x93, x94, x95) :|: x89 = x95 && x87 = x93 && x88 = x94 && x86 = x92 && x85 = x91 && x84 = x90
l11(x96, x97, x98, x99, x100, x101) -> l9(x102, x103, x104, x105, x106, x107) :|: x101 = x107 && x100 = x106 && x98 = x104 && x97 = x103 && x96 = x102 && x105 = x105
l10(x108, x109, x110, x111, x112, x113) -> l11(x114, x115, x116, x117, x118, x119) :|: x113 = x119 && x111 = x117 && x112 = x118 && x110 = x116 && x109 = x115 && x108 = x114
l10(x120, x121, x122, x123, x124, x125) -> l7(x126, x127, x128, x129, x130, x131) :|: x125 = x131 && x123 = x129 && x124 = x130 && x122 = x128 && x121 = x127 && x120 = x126
l1(x132, x133, x134, x135, x136, x137) -> l2(x138, x139, x140, x141, x142, x143) :|: x137 = x143 && x135 = x141 && x136 = x142 && x134 = x140 && x133 = x139 && x132 = x138
l5(x144, x145, x146, x147, x148, x149) -> l9(x150, x151, x152, x153, x154, x155) :|: x149 = x155 && x147 = x153 && x148 = x154 && x146 = x152 && x145 = x151 && x144 = x150 && x145 <= x144
l5(x156, x157, x158, x159, x160, x161) -> l4(x162, x163, x164, x165, x166, x167) :|: x159 = x165 && x160 = x166 && x158 = x164 && x157 = x163 && x162 = 1 + x156 && x167 = x167 && 1 + x156 <= x157
l12(x168, x169, x170, x171, x172, x173) -> l4(x174, x175, x176, x177, x178, x179) :|: x173 = x179 && x171 = x177 && x174 = 0 && x175 = x176 && x176 = x178 && x178 = x178
l13(x180, x181, x182, x183, x184, x185) -> l12(x186, x187, x188, x189, x190, x191) :|: x185 = x191 && x183 = x189 && x184 = x190 && x182 = x188 && x181 = x187 && x180 = x186
Start term: l13(i6HAT0, length5HAT0, sHAT0, tmp15HAT0, tmpHAT0, tmp___09HAT0)

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

(3) IRSwTTerminationDigraphProof (EQUIVALENT)
Constructed termination digraph!
Nodes:
(1) l0(i6HAT0, length5HAT0, sHAT0, tmp15HAT0, tmpHAT0, tmp___09HAT0) -> l1(i6HATpost, length5HATpost, sHATpost, tmp15HATpost, tmpHATpost, tmp___09HATpost) :|: tmp___09HAT0 = tmp___09HATpost && tmp15HAT0 = tmp15HATpost && tmpHAT0 = tmpHATpost && sHAT0 = sHATpost && length5HAT0 = length5HATpost && i6HAT0 = i6HATpost
(2) l2(x, x1, x2, x3, x4, x5) -> l0(x6, x7, x8, x9, x10, x11) :|: x5 = x11 && x3 = x9 && x4 = x10 && x2 = x8 && x1 = x7 && x = x6
(3) l2(x12, x13, x14, x15, x16, x17) -> l3(x18, x19, x20, x21, x22, x23) :|: x17 = x23 && x15 = x21 && x16 = x22 && x14 = x20 && x13 = x19 && x12 = x18
(4) l4(x24, x25, x26, x27, x28, x29) -> l5(x30, x31, x32, x33, x34, x35) :|: x29 = x35 && x27 = x33 && x28 = x34 && x26 = x32 && x25 = x31 && x24 = x30
(5) l6(x36, x37, x38, x39, x40, x41) -> l7(x42, x43, x44, x45, x46, x47) :|: x41 = x47 && x39 = x45 && x40 = x46 && x38 = x44 && x37 = x43 && x36 = x42
(6) l8(x48, x49, x50, x51, x52, x53) -> l6(x54, x55, x56, x57, x58, x59) :|: x53 = x59 && x51 = x57 && x52 = x58 && x50 = x56 && x49 = x55 && x48 = x54
(7) l8(x60, x61, x62, x63, x64, x65) -> l1(x66, x67, x68, x69, x70, x71) :|: x65 = x71 && x63 = x69 && x64 = x70 && x62 = x68 && x61 = x67 && x60 = x66
(8) l9(x72, x73, x74, x75, x76, x77) -> l10(x78, x79, x80, x81, x82, x83) :|: x77 = x83 && x75 = x81 && x76 = x82 && x74 = x80 && x73 = x79 && x72 = x78
(9) l7(x84, x85, x86, x87, x88, x89) -> l8(x90, x91, x92, x93, x94, x95) :|: x89 = x95 && x87 = x93 && x88 = x94 && x86 = x92 && x85 = x91 && x84 = x90
(10) l11(x96, x97, x98, x99, x100, x101) -> l9(x102, x103, x104, x105, x106, x107) :|: x101 = x107 && x100 = x106 && x98 = x104 && x97 = x103 && x96 = x102 && x105 = x105
(11) l10(x108, x109, x110, x111, x112, x113) -> l11(x114, x115, x116, x117, x118, x119) :|: x113 = x119 && x111 = x117 && x112 = x118 && x110 = x116 && x109 = x115 && x108 = x114
(12) l10(x120, x121, x122, x123, x124, x125) -> l7(x126, x127, x128, x129, x130, x131) :|: x125 = x131 && x123 = x129 && x124 = x130 && x122 = x128 && x121 = x127 && x120 = x126
(13) l1(x132, x133, x134, x135, x136, x137) -> l2(x138, x139, x140, x141, x142, x143) :|: x137 = x143 && x135 = x141 && x136 = x142 && x134 = x140 && x133 = x139 && x132 = x138
(14) l5(x144, x145, x146, x147, x148, x149) -> l9(x150, x151, x152, x153, x154, x155) :|: x149 = x155 && x147 = x153 && x148 = x154 && x146 = x152 && x145 = x151 && x144 = x150 && x145 <= x144
(15) l5(x156, x157, x158, x159, x160, x161) -> l4(x162, x163, x164, x165, x166, x167) :|: x159 = x165 && x160 = x166 && x158 = x164 && x157 = x163 && x162 = 1 + x156 && x167 = x167 && 1 + x156 <= x157
(16) l12(x168, x169, x170, x171, x172, x173) -> l4(x174, x175, x176, x177, x178, x179) :|: x173 = x179 && x171 = x177 && x174 = 0 && x175 = x176 && x176 = x178 && x178 = x178
(17) l13(x180, x181, x182, x183, x184, x185) -> l12(x186, x187, x188, x189, x190, x191) :|: x185 = x191 && x183 = x189 && x184 = x190 && x182 = x188 && x181 = x187 && x180 = x186

Arcs:
(1) -> (13)
(2) -> (1)
(4) -> (14), (15)
(5) -> (9)
(6) -> (5)
(7) -> (13)
(8) -> (11), (12)
(9) -> (6), (7)
(10) -> (8)
(11) -> (10)
(12) -> (9)
(13) -> (2), (3)
(14) -> (8)
(15) -> (4)
(16) -> (4)
(17) -> (16)

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

(4)
Complex Obligation (AND)

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

(5)
Obligation:

Termination digraph:
Nodes:
(1) l4(x24, x25, x26, x27, x28, x29) -> l5(x30, x31, x32, x33, x34, x35) :|: x29 = x35 && x27 = x33 && x28 = x34 && x26 = x32 && x25 = x31 && x24 = x30
(2) l5(x156, x157, x158, x159, x160, x161) -> l4(x162, x163, x164, x165, x166, x167) :|: x159 = x165 && x160 = x166 && x158 = x164 && x157 = x163 && x162 = 1 + x156 && x167 = x167 && 1 + x156 <= x157

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

This digraph is fully evaluated!

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

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

(7)
Obligation:
Rules:
l4(x24:0, x163:0, x164:0, x165:0, x166:0, x29:0) -> l4(1 + x24:0, x163:0, x164:0, x165:0, x166:0, x167:0) :|: x163:0 >= 1 + x24:0

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

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

   l4(x1, x2, x3, x4, x5, x6) -> l4(x1, x2)

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

(9)
Obligation:
Rules:
l4(x24:0, x163:0) -> l4(1 + x24:0, x163:0) :|: x163:0 >= 1 + x24:0

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

(10) TempFilterProof (SOUND)
Used the following sort dictionary for filtering: 
l4(INTEGER, INTEGER)
Replaced non-predefined constructor symbols by 0.
----------------------------------------

(11)
Obligation:
Rules:
l4(x24:0, x163:0) -> l4(c, x163:0) :|: c = 1 + x24:0 && x163:0 >= 1 + x24:0

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

(12) PolynomialOrderProcessor (EQUIVALENT)
Found the following polynomial interpretation:
[l4(x, x1)] = -x + x1

The following rules are decreasing:
l4(x24:0, x163:0) -> l4(c, x163:0) :|: c = 1 + x24:0 && x163:0 >= 1 + x24:0
The following rules are bounded:
l4(x24:0, x163:0) -> l4(c, x163:0) :|: c = 1 + x24:0 && x163:0 >= 1 + x24:0

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

(13)
YES

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

(14)
Obligation:

Termination digraph:
Nodes:
(1) l9(x72, x73, x74, x75, x76, x77) -> l10(x78, x79, x80, x81, x82, x83) :|: x77 = x83 && x75 = x81 && x76 = x82 && x74 = x80 && x73 = x79 && x72 = x78
(2) l11(x96, x97, x98, x99, x100, x101) -> l9(x102, x103, x104, x105, x106, x107) :|: x101 = x107 && x100 = x106 && x98 = x104 && x97 = x103 && x96 = x102 && x105 = x105
(3) l10(x108, x109, x110, x111, x112, x113) -> l11(x114, x115, x116, x117, x118, x119) :|: x113 = x119 && x111 = x117 && x112 = x118 && x110 = x116 && x109 = x115 && x108 = x114

Arcs:
(1) -> (3)
(2) -> (1)
(3) -> (2)

This digraph is fully evaluated!

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

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

(16)
Obligation:
Rules:
l11(x102:0, x103:0, x104:0, x99:0, x100:0, x101:0) -> l11(x102:0, x103:0, x104:0, x105:0, x100:0, x101:0) :|: TRUE

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

(17) FilterProof (EQUIVALENT)
Used the following sort dictionary for filtering: 
l11(VARIABLE, VARIABLE, VARIABLE, VARIABLE, VARIABLE, VARIABLE)
Replaced non-predefined constructor symbols by 0.
----------------------------------------

(18)
Obligation:
Rules:
l11(x102:0, x103:0, x104:0, x99:0, x100:0, x101:0) -> l11(x102:0, x103:0, x104:0, x105:0, x100:0, x101:0) :|: TRUE

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

(19) IntTRSPeriodicNontermProof (COMPLETE)
Normalized system to the following form:
f(pc, x102:0, x103:0, x104:0, x99:0, x100:0, x101:0) -> f(1, x102:0, x103:0, x104:0, x105:0, x100:0, x101:0) :|: pc = 1 && TRUE
Witness term starting non-terminating reduction: f(1, -8, -8, -8, 0, -8, -8)
----------------------------------------

(20)
NO

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

(21)
Obligation:

Termination digraph:
Nodes:
(1) l7(x84, x85, x86, x87, x88, x89) -> l8(x90, x91, x92, x93, x94, x95) :|: x89 = x95 && x87 = x93 && x88 = x94 && x86 = x92 && x85 = x91 && x84 = x90
(2) l6(x36, x37, x38, x39, x40, x41) -> l7(x42, x43, x44, x45, x46, x47) :|: x41 = x47 && x39 = x45 && x40 = x46 && x38 = x44 && x37 = x43 && x36 = x42
(3) l8(x48, x49, x50, x51, x52, x53) -> l6(x54, x55, x56, x57, x58, x59) :|: x53 = x59 && x51 = x57 && x52 = x58 && x50 = x56 && x49 = x55 && x48 = x54

Arcs:
(1) -> (3)
(2) -> (1)
(3) -> (2)

This digraph is fully evaluated!

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

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

(23)
Obligation:
Rules:
l6(x36:0, x37:0, x38:0, x39:0, x40:0, x41:0) -> l6(x36:0, x37:0, x38:0, x39:0, x40:0, x41:0) :|: TRUE

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

(24) FilterProof (EQUIVALENT)
Used the following sort dictionary for filtering: 
l6(VARIABLE, VARIABLE, VARIABLE, VARIABLE, VARIABLE, VARIABLE)
Replaced non-predefined constructor symbols by 0.
----------------------------------------

(25)
Obligation:
Rules:
l6(x36:0, x37:0, x38:0, x39:0, x40:0, x41:0) -> l6(x36:0, x37:0, x38:0, x39:0, x40:0, x41:0) :|: TRUE

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

(26) IntTRSNonPeriodicNontermProof (COMPLETE)
Normalized system to the following form:
f(pc, x36:0, x37:0, x38:0, x39:0, x40:0, x41:0) -> f(1, x36:0, x37:0, x38:0, x39:0, x40:0, x41:0) :|: 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 run2_4 = ((run1_4 * 1)) and run2_5 = ((run1_5 * 1)) and run2_6 = ((run1_6 * 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 run2_4 = ((run1_4 * 1)) and run2_5 = ((run1_5 * 1)) and run2_6 = ((run1_6 * 1))) and (((run1_0 * 1)) = ((1 * 1)) and T))

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(27)
NO

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

(28)
Obligation:

Termination digraph:
Nodes:
(1) l0(i6HAT0, length5HAT0, sHAT0, tmp15HAT0, tmpHAT0, tmp___09HAT0) -> l1(i6HATpost, length5HATpost, sHATpost, tmp15HATpost, tmpHATpost, tmp___09HATpost) :|: tmp___09HAT0 = tmp___09HATpost && tmp15HAT0 = tmp15HATpost && tmpHAT0 = tmpHATpost && sHAT0 = sHATpost && length5HAT0 = length5HATpost && i6HAT0 = i6HATpost
(2) l2(x, x1, x2, x3, x4, x5) -> l0(x6, x7, x8, x9, x10, x11) :|: x5 = x11 && x3 = x9 && x4 = x10 && x2 = x8 && x1 = x7 && x = x6
(3) l1(x132, x133, x134, x135, x136, x137) -> l2(x138, x139, x140, x141, x142, x143) :|: x137 = x143 && x135 = x141 && x136 = x142 && x134 = x140 && x133 = x139 && x132 = x138

Arcs:
(1) -> (3)
(2) -> (1)
(3) -> (2)

This digraph is fully evaluated!

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(29) IntTRSCompressionProof (EQUIVALENT)
Compressed rules.
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(30)
Obligation:
Rules:
l2(i6HATpost:0, length5HATpost:0, sHATpost:0, tmp15HATpost:0, tmpHATpost:0, tmp___09HATpost:0) -> l2(i6HATpost:0, length5HATpost:0, sHATpost:0, tmp15HATpost:0, tmpHATpost:0, tmp___09HATpost:0) :|: TRUE

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(31) FilterProof (EQUIVALENT)
Used the following sort dictionary for filtering: 
l2(VARIABLE, VARIABLE, VARIABLE, VARIABLE, VARIABLE, VARIABLE)
Replaced non-predefined constructor symbols by 0.
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(32)
Obligation:
Rules:
l2(i6HATpost:0, length5HATpost:0, sHATpost:0, tmp15HATpost:0, tmpHATpost:0, tmp___09HATpost:0) -> l2(i6HATpost:0, length5HATpost:0, sHATpost:0, tmp15HATpost:0, tmpHATpost:0, tmp___09HATpost:0) :|: TRUE

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(33) IntTRSNonPeriodicNontermProof (COMPLETE)
Normalized system to the following form:
f(pc, i6HATpost:0, length5HATpost:0, sHATpost:0, tmp15HATpost:0, tmpHATpost:0, tmp___09HATpost:0) -> f(1, i6HATpost:0, length5HATpost:0, sHATpost:0, tmp15HATpost:0, tmpHATpost:0, tmp___09HATpost: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 run2_4 = ((run1_4 * 1)) and run2_5 = ((run1_5 * 1)) and run2_6 = ((run1_6 * 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 run2_4 = ((run1_4 * 1)) and run2_5 = ((run1_5 * 1)) and run2_6 = ((run1_6 * 1))) and (((run1_0 * 1)) = ((1 * 1)) and T))

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(34)
NO