YES
proof of prog.inttrs
# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty


Termination of the given IRSwT could be proven:

(0) IRSwT
(1) IRSFormatTransformerProof [EQUIVALENT, 0 ms]
(2) IRSwT
(3) IRSwTTerminationDigraphProof [EQUIVALENT, 846 ms]
(4) IRSwT
(5) IntTRSCompressionProof [EQUIVALENT, 0 ms]
(6) IRSwT
(7) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms]
(8) IRSwT
(9) TempFilterProof [SOUND, 41 ms]
(10) IntTRS
(11) PolynomialOrderProcessor [EQUIVALENT, 15 ms]
(12) YES


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(0)
Obligation:
Rules:
l0(Result_4HAT0, __cil_tmp2_6HAT0, __cil_tmp6_12HAT0, __disjvr_0HAT0, maxRetries_9HAT0, retryCount_10HAT0, selected_11HAT0, x_5HAT0) -> l1(Result_4HATpost, __cil_tmp2_6HATpost, __cil_tmp6_12HATpost, __disjvr_0HATpost, maxRetries_9HATpost, retryCount_10HATpost, selected_11HATpost, x_5HATpost) :|: __cil_tmp2_6HATpost = x_5HAT0 && Result_4HAT1 = __cil_tmp2_6HATpost && selected_11HATpost = Result_4HAT1 && Result_4HATpost = Result_4HATpost && __cil_tmp6_12HAT0 = __cil_tmp6_12HATpost && __disjvr_0HAT0 = __disjvr_0HATpost && maxRetries_9HAT0 = maxRetries_9HATpost && retryCount_10HAT0 = retryCount_10HATpost && x_5HAT0 = x_5HATpost
l2(x, x1, x2, x3, x4, x5, x6, x7) -> l3(x8, x9, x10, x11, x12, x13, x14, x15) :|: x9 = x7 && x16 = x9 && x14 = x16 && x8 = x8 && x13 = 1 + x5 && x2 = x10 && x3 = x11 && x4 = x12 && x7 = x15
l3(x17, x18, x19, x20, x21, x22, x23, x24) -> l5(x25, x26, x27, x28, x29, x30, x31, x32) :|: x24 = x32 && x23 = x31 && x22 = x30 && x21 = x29 && x20 = x28 && x19 = x27 && x18 = x26 && x17 = x25 && x28 = x20
l5(x33, x34, x35, x36, x37, x38, x39, x40) -> l4(x41, x42, x43, x44, x45, x46, x47, x48) :|: x40 = x48 && x39 = x47 && x38 = x46 && x37 = x45 && x36 = x44 && x34 = x42 && x41 = x43 && x43 = x39
l3(x49, x50, x51, x52, x53, x54, x55, x56) -> l6(x57, x58, x59, x60, x61, x62, x63, x64) :|: x56 = x64 && x55 = x63 && x54 = x62 && x53 = x61 && x52 = x60 && x50 = x58 && x57 = x59 && x59 = x55 && x53 - x54 <= 0 && 0 <= x55 && x55 <= 0
l3(x65, x66, x67, x68, x69, x70, x71, x72) -> l1(x73, x74, x75, x76, x77, x78, x79, x80) :|: x71 <= 0 && 0 <= x71 && 0 <= -1 + x69 - x70 && x74 = x72 && x81 = x74 && x79 = x81 && x73 = x73 && x67 = x75 && x68 = x76 && x69 = x77 && x70 = x78 && x72 = x80
l1(x82, x83, x84, x85, x86, x87, x88, x89) -> l3(x90, x91, x92, x93, x94, x95, x96, x97) :|: x89 = x97 && x88 = x96 && x86 = x94 && x85 = x93 && x84 = x92 && x83 = x91 && x82 = x90 && x95 = 1 + x87
l7(x98, x99, x100, x101, x102, x103, x104, x105) -> l3(x106, x107, x108, x109, x110, x111, x112, x113) :|: x105 = x113 && x101 = x109 && x100 = x108 && x99 = x107 && x98 = x106 && x112 = 0 && x111 = 0 && x110 = 4
l8(x114, x115, x116, x117, x118, x119, x120, x121) -> l7(x122, x123, x124, x125, x126, x127, x128, x129) :|: x121 = x129 && x120 = x128 && x119 = x127 && x118 = x126 && x117 = x125 && x116 = x124 && x115 = x123 && x114 = x122
Start term: l8(Result_4HAT0, __cil_tmp2_6HAT0, __cil_tmp6_12HAT0, __disjvr_0HAT0, maxRetries_9HAT0, retryCount_10HAT0, selected_11HAT0, x_5HAT0)

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

(2)
Obligation:
Rules:
l0(Result_4HAT0, __cil_tmp2_6HAT0, __cil_tmp6_12HAT0, __disjvr_0HAT0, maxRetries_9HAT0, retryCount_10HAT0, selected_11HAT0, x_5HAT0) -> l1(Result_4HATpost, __cil_tmp2_6HATpost, __cil_tmp6_12HATpost, __disjvr_0HATpost, maxRetries_9HATpost, retryCount_10HATpost, selected_11HATpost, x_5HATpost) :|: __cil_tmp2_6HATpost = x_5HAT0 && Result_4HAT1 = __cil_tmp2_6HATpost && selected_11HATpost = Result_4HAT1 && Result_4HATpost = Result_4HATpost && __cil_tmp6_12HAT0 = __cil_tmp6_12HATpost && __disjvr_0HAT0 = __disjvr_0HATpost && maxRetries_9HAT0 = maxRetries_9HATpost && retryCount_10HAT0 = retryCount_10HATpost && x_5HAT0 = x_5HATpost
l2(x, x1, x2, x3, x4, x5, x6, x7) -> l3(x8, x9, x10, x11, x12, x13, x14, x15) :|: x9 = x7 && x16 = x9 && x14 = x16 && x8 = x8 && x13 = 1 + x5 && x2 = x10 && x3 = x11 && x4 = x12 && x7 = x15
l3(x17, x18, x19, x20, x21, x22, x23, x24) -> l5(x25, x26, x27, x28, x29, x30, x31, x32) :|: x24 = x32 && x23 = x31 && x22 = x30 && x21 = x29 && x20 = x28 && x19 = x27 && x18 = x26 && x17 = x25 && x28 = x20
l5(x33, x34, x35, x36, x37, x38, x39, x40) -> l4(x41, x42, x43, x44, x45, x46, x47, x48) :|: x40 = x48 && x39 = x47 && x38 = x46 && x37 = x45 && x36 = x44 && x34 = x42 && x41 = x43 && x43 = x39
l3(x49, x50, x51, x52, x53, x54, x55, x56) -> l6(x57, x58, x59, x60, x61, x62, x63, x64) :|: x56 = x64 && x55 = x63 && x54 = x62 && x53 = x61 && x52 = x60 && x50 = x58 && x57 = x59 && x59 = x55 && x53 - x54 <= 0 && 0 <= x55 && x55 <= 0
l3(x65, x66, x67, x68, x69, x70, x71, x72) -> l1(x73, x74, x75, x76, x77, x78, x79, x80) :|: x71 <= 0 && 0 <= x71 && 0 <= -1 + x69 - x70 && x74 = x72 && x81 = x74 && x79 = x81 && x73 = x73 && x67 = x75 && x68 = x76 && x69 = x77 && x70 = x78 && x72 = x80
l1(x82, x83, x84, x85, x86, x87, x88, x89) -> l3(x90, x91, x92, x93, x94, x95, x96, x97) :|: x89 = x97 && x88 = x96 && x86 = x94 && x85 = x93 && x84 = x92 && x83 = x91 && x82 = x90 && x95 = 1 + x87
l7(x98, x99, x100, x101, x102, x103, x104, x105) -> l3(x106, x107, x108, x109, x110, x111, x112, x113) :|: x105 = x113 && x101 = x109 && x100 = x108 && x99 = x107 && x98 = x106 && x112 = 0 && x111 = 0 && x110 = 4
l8(x114, x115, x116, x117, x118, x119, x120, x121) -> l7(x122, x123, x124, x125, x126, x127, x128, x129) :|: x121 = x129 && x120 = x128 && x119 = x127 && x118 = x126 && x117 = x125 && x116 = x124 && x115 = x123 && x114 = x122
Start term: l8(Result_4HAT0, __cil_tmp2_6HAT0, __cil_tmp6_12HAT0, __disjvr_0HAT0, maxRetries_9HAT0, retryCount_10HAT0, selected_11HAT0, x_5HAT0)

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(3) IRSwTTerminationDigraphProof (EQUIVALENT)
Constructed termination digraph!
Nodes:
(1) l0(Result_4HAT0, __cil_tmp2_6HAT0, __cil_tmp6_12HAT0, __disjvr_0HAT0, maxRetries_9HAT0, retryCount_10HAT0, selected_11HAT0, x_5HAT0) -> l1(Result_4HATpost, __cil_tmp2_6HATpost, __cil_tmp6_12HATpost, __disjvr_0HATpost, maxRetries_9HATpost, retryCount_10HATpost, selected_11HATpost, x_5HATpost) :|: __cil_tmp2_6HATpost = x_5HAT0 && Result_4HAT1 = __cil_tmp2_6HATpost && selected_11HATpost = Result_4HAT1 && Result_4HATpost = Result_4HATpost && __cil_tmp6_12HAT0 = __cil_tmp6_12HATpost && __disjvr_0HAT0 = __disjvr_0HATpost && maxRetries_9HAT0 = maxRetries_9HATpost && retryCount_10HAT0 = retryCount_10HATpost && x_5HAT0 = x_5HATpost
(2) l2(x, x1, x2, x3, x4, x5, x6, x7) -> l3(x8, x9, x10, x11, x12, x13, x14, x15) :|: x9 = x7 && x16 = x9 && x14 = x16 && x8 = x8 && x13 = 1 + x5 && x2 = x10 && x3 = x11 && x4 = x12 && x7 = x15
(3) l3(x17, x18, x19, x20, x21, x22, x23, x24) -> l5(x25, x26, x27, x28, x29, x30, x31, x32) :|: x24 = x32 && x23 = x31 && x22 = x30 && x21 = x29 && x20 = x28 && x19 = x27 && x18 = x26 && x17 = x25 && x28 = x20
(4) l5(x33, x34, x35, x36, x37, x38, x39, x40) -> l4(x41, x42, x43, x44, x45, x46, x47, x48) :|: x40 = x48 && x39 = x47 && x38 = x46 && x37 = x45 && x36 = x44 && x34 = x42 && x41 = x43 && x43 = x39
(5) l3(x49, x50, x51, x52, x53, x54, x55, x56) -> l6(x57, x58, x59, x60, x61, x62, x63, x64) :|: x56 = x64 && x55 = x63 && x54 = x62 && x53 = x61 && x52 = x60 && x50 = x58 && x57 = x59 && x59 = x55 && x53 - x54 <= 0 && 0 <= x55 && x55 <= 0
(6) l3(x65, x66, x67, x68, x69, x70, x71, x72) -> l1(x73, x74, x75, x76, x77, x78, x79, x80) :|: x71 <= 0 && 0 <= x71 && 0 <= -1 + x69 - x70 && x74 = x72 && x81 = x74 && x79 = x81 && x73 = x73 && x67 = x75 && x68 = x76 && x69 = x77 && x70 = x78 && x72 = x80
(7) l1(x82, x83, x84, x85, x86, x87, x88, x89) -> l3(x90, x91, x92, x93, x94, x95, x96, x97) :|: x89 = x97 && x88 = x96 && x86 = x94 && x85 = x93 && x84 = x92 && x83 = x91 && x82 = x90 && x95 = 1 + x87
(8) l7(x98, x99, x100, x101, x102, x103, x104, x105) -> l3(x106, x107, x108, x109, x110, x111, x112, x113) :|: x105 = x113 && x101 = x109 && x100 = x108 && x99 = x107 && x98 = x106 && x112 = 0 && x111 = 0 && x110 = 4
(9) l8(x114, x115, x116, x117, x118, x119, x120, x121) -> l7(x122, x123, x124, x125, x126, x127, x128, x129) :|: x121 = x129 && x120 = x128 && x119 = x127 && x118 = x126 && x117 = x125 && x116 = x124 && x115 = x123 && x114 = x122

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

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

(4)
Obligation:

Termination digraph:
Nodes:
(1) l1(x82, x83, x84, x85, x86, x87, x88, x89) -> l3(x90, x91, x92, x93, x94, x95, x96, x97) :|: x89 = x97 && x88 = x96 && x86 = x94 && x85 = x93 && x84 = x92 && x83 = x91 && x82 = x90 && x95 = 1 + x87
(2) l3(x65, x66, x67, x68, x69, x70, x71, x72) -> l1(x73, x74, x75, x76, x77, x78, x79, x80) :|: x71 <= 0 && 0 <= x71 && 0 <= -1 + x69 - x70 && x74 = x72 && x81 = x74 && x79 = x81 && x73 = x73 && x67 = x75 && x68 = x76 && x69 = x77 && x70 = x78 && x72 = x80

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

This digraph is fully evaluated!

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(5) IntTRSCompressionProof (EQUIVALENT)
Compressed rules.
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(6)
Obligation:
Rules:
l1(x82:0, x83:0, x75:0, x76:0, x77:0, x87:0, x88:0, x74:0) -> l1(x73:0, x74:0, x75:0, x76:0, x77:0, 1 + x87:0, x74:0, x74:0) :|: x88:0 < 1 && x88:0 > -1 && 0 <= -1 + x77:0 - (1 + x87:0)

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

   l1(x1, x2, x3, x4, x5, x6, x7, x8) -> l1(x5, x6, x7, x8)

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(8)
Obligation:
Rules:
l1(x77:0, x87:0, x88:0, x74:0) -> l1(x77:0, 1 + x87:0, x74:0, x74:0) :|: x88:0 < 1 && x88:0 > -1 && 0 <= -1 + x77:0 - (1 + x87:0)

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(9) TempFilterProof (SOUND)
Used the following sort dictionary for filtering: 
l1(INTEGER, INTEGER, VARIABLE, VARIABLE)
Replaced non-predefined constructor symbols by 0.
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(10)
Obligation:
Rules:
l1(x77:0, x87:0, x88:0, x74:0) -> l1(x77:0, c, x74:0, x74:0) :|: c = 1 + x87:0 && (x88:0 < 1 && x88:0 > -1 && 0 <= -1 + x77:0 - (1 + x87:0))

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(11) PolynomialOrderProcessor (EQUIVALENT)
Found the following polynomial interpretation:
[l1(x, x1, x2, x3)] = x - x1

The following rules are decreasing:
l1(x77:0, x87:0, x88:0, x74:0) -> l1(x77:0, c, x74:0, x74:0) :|: c = 1 + x87:0 && (x88:0 < 1 && x88:0 > -1 && 0 <= -1 + x77:0 - (1 + x87:0))
The following rules are bounded:
l1(x77:0, x87:0, x88:0, x74:0) -> l1(x77:0, c, x74:0, x74:0) :|: c = 1 + x87:0 && (x88:0 < 1 && x88:0 > -1 && 0 <= -1 + x77:0 - (1 + x87:0))

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(12)
YES