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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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, 957 ms]
(4) IRSwT
(5) IntTRSCompressionProof [EQUIVALENT, 26 ms]
(6) IRSwT
(7) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms]
(8) IRSwT
(9) TempFilterProof [SOUND, 17 ms]
(10) IntTRS
(11) PolynomialOrderProcessor [EQUIVALENT, 0 ms]
(12) YES


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(0)
Obligation:
Rules:
l0(Result_4HAT0, __cil_tmp2_6HAT0, __cil_tmp6_12HAT0, __const_400HAT0, __disjvr_0HAT0, maxRetries_9HAT0, retryCount_10HAT0, selected_11HAT0, x_5HAT0) -> l1(Result_4HATpost, __cil_tmp2_6HATpost, __cil_tmp6_12HATpost, __const_400HATpost, __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 && __const_400HAT0 = __const_400HATpost && __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, x8) -> l3(x9, x10, x11, x12, x13, x14, x15, x16, x17) :|: x10 = x8 && x18 = x10 && x16 = x18 && x9 = x9 && x15 = 1 + x6 && x2 = x11 && x3 = x12 && x4 = x13 && x5 = x14 && x8 = x17
l3(x19, x20, x21, x22, x23, x24, x25, x26, x27) -> l5(x28, x29, x30, x31, x32, x33, x34, x35, x36) :|: x27 = x36 && x26 = x35 && x25 = x34 && x24 = x33 && x23 = x32 && x22 = x31 && x21 = x30 && x20 = x29 && x19 = x28 && x32 = x23
l5(x37, x38, x39, x40, x41, x42, x43, x44, x45) -> l4(x46, x47, x48, x49, x50, x51, x52, x53, x54) :|: x45 = x54 && x44 = x53 && x43 = x52 && x42 = x51 && x41 = x50 && x40 = x49 && x38 = x47 && x46 = x48 && x48 = x44
l3(x55, x56, x57, x58, x59, x60, x61, x62, x63) -> l6(x64, x65, x66, x67, x68, x69, x70, x71, x72) :|: x63 = x72 && x62 = x71 && x61 = x70 && x60 = x69 && x59 = x68 && x58 = x67 && x56 = x65 && x64 = x66 && x66 = x62 && x60 - x61 <= 0 && 0 <= x62 && x62 <= 0
l3(x73, x74, x75, x76, x77, x78, x79, x80, x81) -> l1(x82, x83, x84, x85, x86, x87, x88, x89, x90) :|: x80 <= 0 && 0 <= x80 && 0 <= -1 + x78 - x79 && x83 = x81 && x91 = x83 && x89 = x91 && x82 = x82 && x75 = x84 && x76 = x85 && x77 = x86 && x78 = x87 && x79 = x88 && x81 = x90
l1(x92, x93, x94, x95, x96, x97, x98, x99, x100) -> l3(x101, x102, x103, x104, x105, x106, x107, x108, x109) :|: x100 = x109 && x99 = x108 && x97 = x106 && x96 = x105 && x95 = x104 && x94 = x103 && x93 = x102 && x92 = x101 && x107 = 1 + x98
l7(x110, x111, x112, x113, x114, x115, x116, x117, x118) -> l3(x119, x120, x121, x122, x123, x124, x125, x126, x127) :|: x118 = x127 && x114 = x123 && x113 = x122 && x112 = x121 && x111 = x120 && x110 = x119 && x126 = 0 && x125 = 0 && x124 = x113
l8(x128, x129, x130, x131, x132, x133, x134, x135, x136) -> l7(x137, x138, x139, x140, x141, x142, x143, x144, x145) :|: x136 = x145 && x135 = x144 && x134 = x143 && x133 = x142 && x132 = x141 && x131 = x140 && x130 = x139 && x129 = x138 && x128 = x137
Start term: l8(Result_4HAT0, __cil_tmp2_6HAT0, __cil_tmp6_12HAT0, __const_400HAT0, __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, __const_400HAT0, __disjvr_0HAT0, maxRetries_9HAT0, retryCount_10HAT0, selected_11HAT0, x_5HAT0) -> l1(Result_4HATpost, __cil_tmp2_6HATpost, __cil_tmp6_12HATpost, __const_400HATpost, __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 && __const_400HAT0 = __const_400HATpost && __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, x8) -> l3(x9, x10, x11, x12, x13, x14, x15, x16, x17) :|: x10 = x8 && x18 = x10 && x16 = x18 && x9 = x9 && x15 = 1 + x6 && x2 = x11 && x3 = x12 && x4 = x13 && x5 = x14 && x8 = x17
l3(x19, x20, x21, x22, x23, x24, x25, x26, x27) -> l5(x28, x29, x30, x31, x32, x33, x34, x35, x36) :|: x27 = x36 && x26 = x35 && x25 = x34 && x24 = x33 && x23 = x32 && x22 = x31 && x21 = x30 && x20 = x29 && x19 = x28 && x32 = x23
l5(x37, x38, x39, x40, x41, x42, x43, x44, x45) -> l4(x46, x47, x48, x49, x50, x51, x52, x53, x54) :|: x45 = x54 && x44 = x53 && x43 = x52 && x42 = x51 && x41 = x50 && x40 = x49 && x38 = x47 && x46 = x48 && x48 = x44
l3(x55, x56, x57, x58, x59, x60, x61, x62, x63) -> l6(x64, x65, x66, x67, x68, x69, x70, x71, x72) :|: x63 = x72 && x62 = x71 && x61 = x70 && x60 = x69 && x59 = x68 && x58 = x67 && x56 = x65 && x64 = x66 && x66 = x62 && x60 - x61 <= 0 && 0 <= x62 && x62 <= 0
l3(x73, x74, x75, x76, x77, x78, x79, x80, x81) -> l1(x82, x83, x84, x85, x86, x87, x88, x89, x90) :|: x80 <= 0 && 0 <= x80 && 0 <= -1 + x78 - x79 && x83 = x81 && x91 = x83 && x89 = x91 && x82 = x82 && x75 = x84 && x76 = x85 && x77 = x86 && x78 = x87 && x79 = x88 && x81 = x90
l1(x92, x93, x94, x95, x96, x97, x98, x99, x100) -> l3(x101, x102, x103, x104, x105, x106, x107, x108, x109) :|: x100 = x109 && x99 = x108 && x97 = x106 && x96 = x105 && x95 = x104 && x94 = x103 && x93 = x102 && x92 = x101 && x107 = 1 + x98
l7(x110, x111, x112, x113, x114, x115, x116, x117, x118) -> l3(x119, x120, x121, x122, x123, x124, x125, x126, x127) :|: x118 = x127 && x114 = x123 && x113 = x122 && x112 = x121 && x111 = x120 && x110 = x119 && x126 = 0 && x125 = 0 && x124 = x113
l8(x128, x129, x130, x131, x132, x133, x134, x135, x136) -> l7(x137, x138, x139, x140, x141, x142, x143, x144, x145) :|: x136 = x145 && x135 = x144 && x134 = x143 && x133 = x142 && x132 = x141 && x131 = x140 && x130 = x139 && x129 = x138 && x128 = x137
Start term: l8(Result_4HAT0, __cil_tmp2_6HAT0, __cil_tmp6_12HAT0, __const_400HAT0, __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, __const_400HAT0, __disjvr_0HAT0, maxRetries_9HAT0, retryCount_10HAT0, selected_11HAT0, x_5HAT0) -> l1(Result_4HATpost, __cil_tmp2_6HATpost, __cil_tmp6_12HATpost, __const_400HATpost, __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 && __const_400HAT0 = __const_400HATpost && __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, x8) -> l3(x9, x10, x11, x12, x13, x14, x15, x16, x17) :|: x10 = x8 && x18 = x10 && x16 = x18 && x9 = x9 && x15 = 1 + x6 && x2 = x11 && x3 = x12 && x4 = x13 && x5 = x14 && x8 = x17
(3) l3(x19, x20, x21, x22, x23, x24, x25, x26, x27) -> l5(x28, x29, x30, x31, x32, x33, x34, x35, x36) :|: x27 = x36 && x26 = x35 && x25 = x34 && x24 = x33 && x23 = x32 && x22 = x31 && x21 = x30 && x20 = x29 && x19 = x28 && x32 = x23
(4) l5(x37, x38, x39, x40, x41, x42, x43, x44, x45) -> l4(x46, x47, x48, x49, x50, x51, x52, x53, x54) :|: x45 = x54 && x44 = x53 && x43 = x52 && x42 = x51 && x41 = x50 && x40 = x49 && x38 = x47 && x46 = x48 && x48 = x44
(5) l3(x55, x56, x57, x58, x59, x60, x61, x62, x63) -> l6(x64, x65, x66, x67, x68, x69, x70, x71, x72) :|: x63 = x72 && x62 = x71 && x61 = x70 && x60 = x69 && x59 = x68 && x58 = x67 && x56 = x65 && x64 = x66 && x66 = x62 && x60 - x61 <= 0 && 0 <= x62 && x62 <= 0
(6) l3(x73, x74, x75, x76, x77, x78, x79, x80, x81) -> l1(x82, x83, x84, x85, x86, x87, x88, x89, x90) :|: x80 <= 0 && 0 <= x80 && 0 <= -1 + x78 - x79 && x83 = x81 && x91 = x83 && x89 = x91 && x82 = x82 && x75 = x84 && x76 = x85 && x77 = x86 && x78 = x87 && x79 = x88 && x81 = x90
(7) l1(x92, x93, x94, x95, x96, x97, x98, x99, x100) -> l3(x101, x102, x103, x104, x105, x106, x107, x108, x109) :|: x100 = x109 && x99 = x108 && x97 = x106 && x96 = x105 && x95 = x104 && x94 = x103 && x93 = x102 && x92 = x101 && x107 = 1 + x98
(8) l7(x110, x111, x112, x113, x114, x115, x116, x117, x118) -> l3(x119, x120, x121, x122, x123, x124, x125, x126, x127) :|: x118 = x127 && x114 = x123 && x113 = x122 && x112 = x121 && x111 = x120 && x110 = x119 && x126 = 0 && x125 = 0 && x124 = x113
(9) l8(x128, x129, x130, x131, x132, x133, x134, x135, x136) -> l7(x137, x138, x139, x140, x141, x142, x143, x144, x145) :|: x136 = x145 && x135 = x144 && x134 = x143 && x133 = x142 && x132 = x141 && x131 = x140 && x130 = x139 && x129 = x138 && x128 = x137

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

This digraph is fully evaluated!
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(4)
Obligation:

Termination digraph:
Nodes:
(1) l1(x92, x93, x94, x95, x96, x97, x98, x99, x100) -> l3(x101, x102, x103, x104, x105, x106, x107, x108, x109) :|: x100 = x109 && x99 = x108 && x97 = x106 && x96 = x105 && x95 = x104 && x94 = x103 && x93 = x102 && x92 = x101 && x107 = 1 + x98
(2) l3(x73, x74, x75, x76, x77, x78, x79, x80, x81) -> l1(x82, x83, x84, x85, x86, x87, x88, x89, x90) :|: x80 <= 0 && 0 <= x80 && 0 <= -1 + x78 - x79 && x83 = x81 && x91 = x83 && x89 = x91 && x82 = x82 && x75 = x84 && x76 = x85 && x77 = x86 && x78 = x87 && x79 = x88 && x81 = x90

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

This digraph is fully evaluated!

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

(6)
Obligation:
Rules:
l1(x101:0, x102:0, x103:0, x104:0, x105:0, x106:0, x98:0, x108:0, x100:0) -> l1(x82:0, x100:0, x103:0, x104:0, x105:0, x106:0, 1 + x98:0, x100:0, x100:0) :|: x108:0 < 1 && x108:0 > -1 && 0 <= -1 + x106:0 - (1 + x98:0)

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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, x9) -> l1(x6, x7, x8, x9)

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(8)
Obligation:
Rules:
l1(x106:0, x98:0, x108:0, x100:0) -> l1(x106:0, 1 + x98:0, x100:0, x100:0) :|: x108:0 < 1 && x108:0 > -1 && 0 <= -1 + x106:0 - (1 + x98:0)

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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(x106:0, x98:0, x108:0, x100:0) -> l1(x106:0, c, x100:0, x100:0) :|: c = 1 + x98:0 && (x108:0 < 1 && x108:0 > -1 && 0 <= -1 + x106:0 - (1 + x98:0))

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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(x106:0, x98:0, x108:0, x100:0) -> l1(x106:0, c, x100:0, x100:0) :|: c = 1 + x98:0 && (x108:0 < 1 && x108:0 > -1 && 0 <= -1 + x106:0 - (1 + x98:0))
The following rules are bounded:
l1(x106:0, x98:0, x108:0, x100:0) -> l1(x106:0, c, x100:0, x100:0) :|: c = 1 + x98:0 && (x108:0 < 1 && x108:0 > -1 && 0 <= -1 + x106:0 - (1 + x98:0))

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(12)
YES