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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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, 717 ms]
(4) AND
    (5) IRSwT
        (6) IntTRSCompressionProof [EQUIVALENT, 10 ms]
        (7) IRSwT
        (8) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms]
        (9) IRSwT
        (10) TempFilterProof [SOUND, 52 ms]
        (11) IntTRS
        (12) PolynomialOrderProcessor [EQUIVALENT, 0 ms]
        (13) IntTRS
        (14) PolynomialOrderProcessor [EQUIVALENT, 0 ms]
        (15) YES
    (16) IRSwT
        (17) IntTRSCompressionProof [EQUIVALENT, 35 ms]
        (18) IRSwT
        (19) FilterProof [EQUIVALENT, 0 ms]
        (20) IntTRS
        (21) IntTRSPeriodicNontermProof [COMPLETE, 5 ms]
        (22) NO


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(0)
Obligation:
Rules:
l0(___rho_1_HAT0, cHAT0, curr_servHAT0, respHAT0, serversHAT0, serversdiv2HAT0, tmp1HAT0) -> l1(___rho_1_HATpost, cHATpost, curr_servHATpost, respHATpost, serversHATpost, serversdiv2HATpost, tmp1HATpost) :|: tmp1HAT0 = tmp1HATpost && serversdiv2HAT0 = serversdiv2HATpost && serversHAT0 = serversHATpost && respHAT0 = respHATpost && curr_servHAT0 = curr_servHATpost && cHAT0 = cHATpost && ___rho_1_HAT0 = ___rho_1_HATpost
l2(x, x1, x2, x3, x4, x5, x6) -> l3(x7, x8, x9, x10, x11, x12, x13) :|: x6 = x13 && x5 = x12 && x4 = x11 && x3 = x10 && x2 = x9 && x1 = x8 && x = x7
l4(x14, x15, x16, x17, x18, x19, x20) -> l5(x21, x22, x23, x24, x25, x26, x27) :|: x20 = x27 && x19 = x26 && x18 = x25 && x17 = x24 && x16 = x23 && x15 = x22 && x14 = x21
l5(x28, x29, x30, x31, x32, x33, x34) -> l4(x35, x36, x37, x38, x39, x40, x41) :|: x34 = x41 && x33 = x40 && x32 = x39 && x31 = x38 && x30 = x37 && x29 = x36 && x28 = x35
l6(x42, x43, x44, x45, x46, x47, x48) -> l0(x49, x50, x51, x52, x53, x54, x55) :|: x48 = x55 && x47 = x54 && x46 = x53 && x45 = x52 && x43 = x50 && x42 = x49 && x51 = -1 + x44 && 1 + x43 <= x44 && x42 <= 0
l6(x56, x57, x58, x59, x60, x61, x62) -> l0(x63, x64, x65, x66, x67, x68, x69) :|: x62 = x69 && x61 = x68 && x60 = x67 && x56 = x63 && x66 = 1 + x59 && x65 = -1 + x58 && x64 = -1 + x57 && 1 <= x56
l1(x70, x71, x72, x73, x74, x75, x76) -> l6(x77, x78, x79, x80, x81, x82, x83) :|: x76 = x83 && x75 = x82 && x74 = x81 && x73 = x80 && x72 = x79 && x71 = x78 && x77 = x77 && 1 <= x72
l1(x84, x85, x86, x87, x88, x89, x90) -> l4(x91, x92, x93, x94, x95, x96, x97) :|: x90 = x97 && x89 = x96 && x88 = x95 && x87 = x94 && x86 = x93 && x85 = x92 && x84 = x91 && x86 <= 0
l7(x98, x99, x100, x101, x102, x103, x104) -> l0(x105, x106, x107, x108, x109, x110, x111) :|: x98 = x105 && x107 = x109 && x108 = 0 && x109 <= 1 + 2 * x110 && 1 + 2 * x110 <= x109 && x110 = x110 && 1 <= x109 && x109 = x109 && 1 <= x106 && x106 = x111 && x111 = x111
l8(x112, x113, x114, x115, x116, x117, x118) -> l7(x119, x120, x121, x122, x123, x124, x125) :|: x118 = x125 && x117 = x124 && x116 = x123 && x115 = x122 && x114 = x121 && x113 = x120 && x112 = x119
Start term: l8(___rho_1_HAT0, cHAT0, curr_servHAT0, respHAT0, serversHAT0, serversdiv2HAT0, tmp1HAT0)

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(1) IRSFormatTransformerProof (EQUIVALENT)
Reformatted IRS to match normalized format (transformed away non-linear left-hand sides, !=, / and %).
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(2)
Obligation:
Rules:
l0(___rho_1_HAT0, cHAT0, curr_servHAT0, respHAT0, serversHAT0, serversdiv2HAT0, tmp1HAT0) -> l1(___rho_1_HATpost, cHATpost, curr_servHATpost, respHATpost, serversHATpost, serversdiv2HATpost, tmp1HATpost) :|: tmp1HAT0 = tmp1HATpost && serversdiv2HAT0 = serversdiv2HATpost && serversHAT0 = serversHATpost && respHAT0 = respHATpost && curr_servHAT0 = curr_servHATpost && cHAT0 = cHATpost && ___rho_1_HAT0 = ___rho_1_HATpost
l2(x, x1, x2, x3, x4, x5, x6) -> l3(x7, x8, x9, x10, x11, x12, x13) :|: x6 = x13 && x5 = x12 && x4 = x11 && x3 = x10 && x2 = x9 && x1 = x8 && x = x7
l4(x14, x15, x16, x17, x18, x19, x20) -> l5(x21, x22, x23, x24, x25, x26, x27) :|: x20 = x27 && x19 = x26 && x18 = x25 && x17 = x24 && x16 = x23 && x15 = x22 && x14 = x21
l5(x28, x29, x30, x31, x32, x33, x34) -> l4(x35, x36, x37, x38, x39, x40, x41) :|: x34 = x41 && x33 = x40 && x32 = x39 && x31 = x38 && x30 = x37 && x29 = x36 && x28 = x35
l6(x42, x43, x44, x45, x46, x47, x48) -> l0(x49, x50, x51, x52, x53, x54, x55) :|: x48 = x55 && x47 = x54 && x46 = x53 && x45 = x52 && x43 = x50 && x42 = x49 && x51 = -1 + x44 && 1 + x43 <= x44 && x42 <= 0
l6(x56, x57, x58, x59, x60, x61, x62) -> l0(x63, x64, x65, x66, x67, x68, x69) :|: x62 = x69 && x61 = x68 && x60 = x67 && x56 = x63 && x66 = 1 + x59 && x65 = -1 + x58 && x64 = -1 + x57 && 1 <= x56
l1(x70, x71, x72, x73, x74, x75, x76) -> l6(x77, x78, x79, x80, x81, x82, x83) :|: x76 = x83 && x75 = x82 && x74 = x81 && x73 = x80 && x72 = x79 && x71 = x78 && x77 = x77 && 1 <= x72
l1(x84, x85, x86, x87, x88, x89, x90) -> l4(x91, x92, x93, x94, x95, x96, x97) :|: x90 = x97 && x89 = x96 && x88 = x95 && x87 = x94 && x86 = x93 && x85 = x92 && x84 = x91 && x86 <= 0
l7(x98, x99, x100, x101, x102, x103, x104) -> l0(x105, x106, x107, x108, x109, x110, x111) :|: x98 = x105 && x107 = x109 && x108 = 0 && x109 <= 1 + 2 * x110 && 1 + 2 * x110 <= x109 && x110 = x110 && 1 <= x109 && x109 = x109 && 1 <= x106 && x106 = x111 && x111 = x111
l8(x112, x113, x114, x115, x116, x117, x118) -> l7(x119, x120, x121, x122, x123, x124, x125) :|: x118 = x125 && x117 = x124 && x116 = x123 && x115 = x122 && x114 = x121 && x113 = x120 && x112 = x119
Start term: l8(___rho_1_HAT0, cHAT0, curr_servHAT0, respHAT0, serversHAT0, serversdiv2HAT0, tmp1HAT0)

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(3) IRSwTTerminationDigraphProof (EQUIVALENT)
Constructed termination digraph!
Nodes:
(1) l0(___rho_1_HAT0, cHAT0, curr_servHAT0, respHAT0, serversHAT0, serversdiv2HAT0, tmp1HAT0) -> l1(___rho_1_HATpost, cHATpost, curr_servHATpost, respHATpost, serversHATpost, serversdiv2HATpost, tmp1HATpost) :|: tmp1HAT0 = tmp1HATpost && serversdiv2HAT0 = serversdiv2HATpost && serversHAT0 = serversHATpost && respHAT0 = respHATpost && curr_servHAT0 = curr_servHATpost && cHAT0 = cHATpost && ___rho_1_HAT0 = ___rho_1_HATpost
(2) l2(x, x1, x2, x3, x4, x5, x6) -> l3(x7, x8, x9, x10, x11, x12, x13) :|: x6 = x13 && x5 = x12 && x4 = x11 && x3 = x10 && x2 = x9 && x1 = x8 && x = x7
(3) l4(x14, x15, x16, x17, x18, x19, x20) -> l5(x21, x22, x23, x24, x25, x26, x27) :|: x20 = x27 && x19 = x26 && x18 = x25 && x17 = x24 && x16 = x23 && x15 = x22 && x14 = x21
(4) l5(x28, x29, x30, x31, x32, x33, x34) -> l4(x35, x36, x37, x38, x39, x40, x41) :|: x34 = x41 && x33 = x40 && x32 = x39 && x31 = x38 && x30 = x37 && x29 = x36 && x28 = x35
(5) l6(x42, x43, x44, x45, x46, x47, x48) -> l0(x49, x50, x51, x52, x53, x54, x55) :|: x48 = x55 && x47 = x54 && x46 = x53 && x45 = x52 && x43 = x50 && x42 = x49 && x51 = -1 + x44 && 1 + x43 <= x44 && x42 <= 0
(6) l6(x56, x57, x58, x59, x60, x61, x62) -> l0(x63, x64, x65, x66, x67, x68, x69) :|: x62 = x69 && x61 = x68 && x60 = x67 && x56 = x63 && x66 = 1 + x59 && x65 = -1 + x58 && x64 = -1 + x57 && 1 <= x56
(7) l1(x70, x71, x72, x73, x74, x75, x76) -> l6(x77, x78, x79, x80, x81, x82, x83) :|: x76 = x83 && x75 = x82 && x74 = x81 && x73 = x80 && x72 = x79 && x71 = x78 && x77 = x77 && 1 <= x72
(8) l1(x84, x85, x86, x87, x88, x89, x90) -> l4(x91, x92, x93, x94, x95, x96, x97) :|: x90 = x97 && x89 = x96 && x88 = x95 && x87 = x94 && x86 = x93 && x85 = x92 && x84 = x91 && x86 <= 0
(9) l7(x98, x99, x100, x101, x102, x103, x104) -> l0(x105, x106, x107, x108, x109, x110, x111) :|: x98 = x105 && x107 = x109 && x108 = 0 && x109 <= 1 + 2 * x110 && 1 + 2 * x110 <= x109 && x110 = x110 && 1 <= x109 && x109 = x109 && 1 <= x106 && x106 = x111 && x111 = x111
(10) l8(x112, x113, x114, x115, x116, x117, x118) -> l7(x119, x120, x121, x122, x123, x124, x125) :|: x118 = x125 && x117 = x124 && x116 = x123 && x115 = x122 && x114 = x121 && x113 = x120 && x112 = x119

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

This digraph is fully evaluated!
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(4)
Complex Obligation (AND)

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(5)
Obligation:

Termination digraph:
Nodes:
(1) l0(___rho_1_HAT0, cHAT0, curr_servHAT0, respHAT0, serversHAT0, serversdiv2HAT0, tmp1HAT0) -> l1(___rho_1_HATpost, cHATpost, curr_servHATpost, respHATpost, serversHATpost, serversdiv2HATpost, tmp1HATpost) :|: tmp1HAT0 = tmp1HATpost && serversdiv2HAT0 = serversdiv2HATpost && serversHAT0 = serversHATpost && respHAT0 = respHATpost && curr_servHAT0 = curr_servHATpost && cHAT0 = cHATpost && ___rho_1_HAT0 = ___rho_1_HATpost
(2) l6(x56, x57, x58, x59, x60, x61, x62) -> l0(x63, x64, x65, x66, x67, x68, x69) :|: x62 = x69 && x61 = x68 && x60 = x67 && x56 = x63 && x66 = 1 + x59 && x65 = -1 + x58 && x64 = -1 + x57 && 1 <= x56
(3) l6(x42, x43, x44, x45, x46, x47, x48) -> l0(x49, x50, x51, x52, x53, x54, x55) :|: x48 = x55 && x47 = x54 && x46 = x53 && x45 = x52 && x43 = x50 && x42 = x49 && x51 = -1 + x44 && 1 + x43 <= x44 && x42 <= 0
(4) l1(x70, x71, x72, x73, x74, x75, x76) -> l6(x77, x78, x79, x80, x81, x82, x83) :|: x76 = x83 && x75 = x82 && x74 = x81 && x73 = x80 && x72 = x79 && x71 = x78 && x77 = x77 && 1 <= x72

Arcs:
(1) -> (4)
(2) -> (1)
(3) -> (1)
(4) -> (2), (3)

This digraph is fully evaluated!

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(6) IntTRSCompressionProof (EQUIVALENT)
Compressed rules.
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(7)
Obligation:
Rules:
l6(___rho_1_HATpost:0, x57:0, x58:0, x59:0, serversHATpost:0, serversdiv2HATpost:0, tmp1HATpost:0) -> l6(x77:0, -1 + x57:0, -1 + x58:0, 1 + x59:0, serversHATpost:0, serversdiv2HATpost:0, tmp1HATpost:0) :|: ___rho_1_HATpost:0 > 0 && x58:0 > 1
l6(x, x1, x2, x3, x4, x5, x6) -> l6(x7, x1, -1 + x2, x3, x4, x5, x6) :|: x2 >= 1 + x1 && x2 > 1 && x < 1

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

   l6(x1, x2, x3, x4, x5, x6, x7) -> l6(x1, x2, x3)

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(9)
Obligation:
Rules:
l6(___rho_1_HATpost:0, x57:0, x58:0) -> l6(x77:0, -1 + x57:0, -1 + x58:0) :|: ___rho_1_HATpost:0 > 0 && x58:0 > 1
l6(x, x1, x2) -> l6(x7, x1, -1 + x2) :|: x2 >= 1 + x1 && x2 > 1 && x < 1

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(10) TempFilterProof (SOUND)
Used the following sort dictionary for filtering: 
l6(VARIABLE, VARIABLE, INTEGER)
Replaced non-predefined constructor symbols by 0.
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(11)
Obligation:
Rules:
l6(___rho_1_HATpost:0, x57:0, x58:0) -> l6(x77:0, c, c1) :|: c1 = -1 + x58:0 && c = -1 + x57:0 && (___rho_1_HATpost:0 > 0 && x58:0 > 1)
l6(x, x1, x2) -> l6(x7, x1, c2) :|: c2 = -1 + x2 && (x2 >= 1 + x1 && x2 > 1 && x < 1)

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(12) PolynomialOrderProcessor (EQUIVALENT)
Found the following polynomial interpretation:
[l6(x, x1, x2)] = -x1 + x2

The following rules are decreasing:
l6(x, x1, x2) -> l6(x7, x1, c2) :|: c2 = -1 + x2 && (x2 >= 1 + x1 && x2 > 1 && x < 1)
The following rules are bounded:
l6(x, x1, x2) -> l6(x7, x1, c2) :|: c2 = -1 + x2 && (x2 >= 1 + x1 && x2 > 1 && x < 1)

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(13)
Obligation:
Rules:
l6(___rho_1_HATpost:0, x57:0, x58:0) -> l6(x77:0, c, c1) :|: c1 = -1 + x58:0 && c = -1 + x57:0 && (___rho_1_HATpost:0 > 0 && x58:0 > 1)

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(14) PolynomialOrderProcessor (EQUIVALENT)
Found the following polynomial interpretation:
[l6(x, x1, x2)] = x2

The following rules are decreasing:
l6(___rho_1_HATpost:0, x57:0, x58:0) -> l6(x77:0, c, c1) :|: c1 = -1 + x58:0 && c = -1 + x57:0 && (___rho_1_HATpost:0 > 0 && x58:0 > 1)
The following rules are bounded:
l6(___rho_1_HATpost:0, x57:0, x58:0) -> l6(x77:0, c, c1) :|: c1 = -1 + x58:0 && c = -1 + x57:0 && (___rho_1_HATpost:0 > 0 && x58:0 > 1)

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(15)
YES

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(16)
Obligation:

Termination digraph:
Nodes:
(1) l4(x14, x15, x16, x17, x18, x19, x20) -> l5(x21, x22, x23, x24, x25, x26, x27) :|: x20 = x27 && x19 = x26 && x18 = x25 && x17 = x24 && x16 = x23 && x15 = x22 && x14 = x21
(2) l5(x28, x29, x30, x31, x32, x33, x34) -> l4(x35, x36, x37, x38, x39, x40, x41) :|: x34 = x41 && x33 = x40 && x32 = x39 && x31 = x38 && x30 = x37 && x29 = x36 && x28 = x35

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

This digraph is fully evaluated!

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

(18)
Obligation:
Rules:
l4(x14:0, x15:0, x16:0, x17:0, x18:0, x19:0, x20:0) -> l4(x14:0, x15:0, x16:0, x17:0, x18:0, x19:0, x20:0) :|: TRUE

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(19) FilterProof (EQUIVALENT)
Used the following sort dictionary for filtering: 
l4(VARIABLE, VARIABLE, VARIABLE, VARIABLE, VARIABLE, VARIABLE, VARIABLE)
Replaced non-predefined constructor symbols by 0.
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(20)
Obligation:
Rules:
l4(x14:0, x15:0, x16:0, x17:0, x18:0, x19:0, x20:0) -> l4(x14:0, x15:0, x16:0, x17:0, x18:0, x19:0, x20:0) :|: TRUE

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(21) IntTRSPeriodicNontermProof (COMPLETE)
Normalized system to the following form:
f(pc, x14:0, x15:0, x16:0, x17:0, x18:0, x19:0, x20:0) -> f(1, x14:0, x15:0, x16:0, x17:0, x18:0, x19:0, x20:0) :|: pc = 1 && TRUE
Witness term starting non-terminating reduction: f(1, -8, -8, -8, -8, -8, -8, -8)
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(22)
NO