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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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, 998 ms]
(4) IRSwT
(5) IntTRSCompressionProof [EQUIVALENT, 12 ms]
(6) IRSwT
(7) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms]
(8) IRSwT
(9) TempFilterProof [SOUND, 31 ms]
(10) IntTRS
(11) PolynomialOrderProcessor [EQUIVALENT, 13 ms]
(12) YES


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

(0)
Obligation:
Rules:
l0(__const_8HAT0, nI6HAT0, nX4HAT0, nX9HAT0, nXHAT0, res10HAT0, res5HAT0, ret_nBC18HAT0, ret_nBC211HAT0, tmp7HAT0, tmpHAT0, tmp___0HAT0) -> l1(__const_8HATpost, nI6HATpost, nX4HATpost, nX9HATpost, nXHATpost, res10HATpost, res5HATpost, ret_nBC18HATpost, ret_nBC211HATpost, tmp7HATpost, tmpHATpost, tmp___0HATpost) :|: tmp___0HAT0 = tmp___0HATpost && tmp7HAT0 = tmp7HATpost && tmpHAT0 = tmpHATpost && ret_nBC211HAT0 = ret_nBC211HATpost && ret_nBC18HAT0 = ret_nBC18HATpost && res10HAT0 = res10HATpost && nX9HAT0 = nX9HATpost && nX4HAT0 = nX4HATpost && nXHAT0 = nXHATpost && __const_8HAT0 = __const_8HATpost && nI6HATpost = 1 + nI6HAT0 && res5HATpost = res5HAT0 + tmp7HAT0
l2(x, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11) -> l0(x12, x13, x14, x15, x16, x17, x18, x19, x20, x21, x22, x23) :|: x11 = x23 && x10 = x22 && x8 = x20 && x7 = x19 && x6 = x18 && x5 = x17 && x3 = x15 && x2 = x14 && x4 = x16 && x1 = x13 && x = x12 && x21 = 0
l2(x24, x25, x26, x27, x28, x29, x30, x31, x32, x33, x34, x35) -> l0(x36, x37, x38, x39, x40, x41, x42, x43, x44, x45, x46, x47) :|: x35 = x47 && x34 = x46 && x32 = x44 && x31 = x43 && x30 = x42 && x29 = x41 && x27 = x39 && x26 = x38 && x28 = x40 && x25 = x37 && x24 = x36 && x45 = 1
l3(x48, x49, x50, x51, x52, x53, x54, x55, x56, x57, x58, x59) -> l4(x60, x61, x62, x63, x64, x65, x66, x67, x68, x69, x70, x71) :|: 2 * x48 <= x49 && x67 = x54 && x70 = x67 && x63 = x52 && x72 = x63 && x73 = x73 && x74 = x74 && x75 = x75 && x65 = x65 && x68 = x65 && x71 = x68 && x48 = x60 && x49 = x61 && x52 = x64 && x50 = x62 && x54 = x66 && x57 = x69
l3(x76, x77, x78, x79, x80, x81, x82, x83, x84, x85, x86, x87) -> l2(x88, x89, x90, x91, x92, x93, x94, x95, x96, x97, x98, x99) :|: x87 = x99 && x85 = x97 && x86 = x98 && x84 = x96 && x83 = x95 && x82 = x94 && x81 = x93 && x79 = x91 && x78 = x90 && x80 = x92 && x77 = x89 && x76 = x88 && 1 + x77 <= 2 * x76
l1(x100, x101, x102, x103, x104, x105, x106, x107, x108, x109, x110, x111) -> l3(x112, x113, x114, x115, x116, x117, x118, x119, x120, x121, x122, x123) :|: x111 = x123 && x109 = x121 && x110 = x122 && x108 = x120 && x107 = x119 && x106 = x118 && x105 = x117 && x103 = x115 && x102 = x114 && x104 = x116 && x101 = x113 && x100 = x112
l5(x124, x125, x126, x127, x128, x129, x130, x131, x132, x133, x134, x135) -> l1(x136, x137, x138, x139, x140, x141, x142, x143, x144, x145, x146, x147) :|: x135 = x147 && x133 = x145 && x134 = x146 && x132 = x144 && x131 = x143 && x129 = x141 && x127 = x139 && x128 = x140 && x124 = x136 && x137 = 0 && x142 = 0 && x138 = x128
l6(x148, x149, x150, x151, x152, x153, x154, x155, x156, x157, x158, x159) -> l5(x160, x161, x162, x163, x164, x165, x166, x167, x168, x169, x170, x171) :|: x159 = x171 && x157 = x169 && x158 = x170 && x156 = x168 && x155 = x167 && x154 = x166 && x153 = x165 && x151 = x163 && x150 = x162 && x152 = x164 && x149 = x161 && x148 = x160
Start term: l6(__const_8HAT0, nI6HAT0, nX4HAT0, nX9HAT0, nXHAT0, res10HAT0, res5HAT0, ret_nBC18HAT0, ret_nBC211HAT0, tmp7HAT0, tmpHAT0, tmp___0HAT0)

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

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

(2)
Obligation:
Rules:
l0(__const_8HAT0, nI6HAT0, nX4HAT0, nX9HAT0, nXHAT0, res10HAT0, res5HAT0, ret_nBC18HAT0, ret_nBC211HAT0, tmp7HAT0, tmpHAT0, tmp___0HAT0) -> l1(__const_8HATpost, nI6HATpost, nX4HATpost, nX9HATpost, nXHATpost, res10HATpost, res5HATpost, ret_nBC18HATpost, ret_nBC211HATpost, tmp7HATpost, tmpHATpost, tmp___0HATpost) :|: tmp___0HAT0 = tmp___0HATpost && tmp7HAT0 = tmp7HATpost && tmpHAT0 = tmpHATpost && ret_nBC211HAT0 = ret_nBC211HATpost && ret_nBC18HAT0 = ret_nBC18HATpost && res10HAT0 = res10HATpost && nX9HAT0 = nX9HATpost && nX4HAT0 = nX4HATpost && nXHAT0 = nXHATpost && __const_8HAT0 = __const_8HATpost && nI6HATpost = 1 + nI6HAT0 && res5HATpost = res5HAT0 + tmp7HAT0
l2(x, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11) -> l0(x12, x13, x14, x15, x16, x17, x18, x19, x20, x21, x22, x23) :|: x11 = x23 && x10 = x22 && x8 = x20 && x7 = x19 && x6 = x18 && x5 = x17 && x3 = x15 && x2 = x14 && x4 = x16 && x1 = x13 && x = x12 && x21 = 0
l2(x24, x25, x26, x27, x28, x29, x30, x31, x32, x33, x34, x35) -> l0(x36, x37, x38, x39, x40, x41, x42, x43, x44, x45, x46, x47) :|: x35 = x47 && x34 = x46 && x32 = x44 && x31 = x43 && x30 = x42 && x29 = x41 && x27 = x39 && x26 = x38 && x28 = x40 && x25 = x37 && x24 = x36 && x45 = 1
l3(x48, x49, x50, x51, x52, x53, x54, x55, x56, x57, x58, x59) -> l4(x60, x61, x62, x63, x64, x65, x66, x67, x68, x69, x70, x71) :|: 2 * x48 <= x49 && x67 = x54 && x70 = x67 && x63 = x52 && x72 = x63 && x73 = x73 && x74 = x74 && x75 = x75 && x65 = x65 && x68 = x65 && x71 = x68 && x48 = x60 && x49 = x61 && x52 = x64 && x50 = x62 && x54 = x66 && x57 = x69
l3(x76, x77, x78, x79, x80, x81, x82, x83, x84, x85, x86, x87) -> l2(x88, x89, x90, x91, x92, x93, x94, x95, x96, x97, x98, x99) :|: x87 = x99 && x85 = x97 && x86 = x98 && x84 = x96 && x83 = x95 && x82 = x94 && x81 = x93 && x79 = x91 && x78 = x90 && x80 = x92 && x77 = x89 && x76 = x88 && 1 + x77 <= 2 * x76
l1(x100, x101, x102, x103, x104, x105, x106, x107, x108, x109, x110, x111) -> l3(x112, x113, x114, x115, x116, x117, x118, x119, x120, x121, x122, x123) :|: x111 = x123 && x109 = x121 && x110 = x122 && x108 = x120 && x107 = x119 && x106 = x118 && x105 = x117 && x103 = x115 && x102 = x114 && x104 = x116 && x101 = x113 && x100 = x112
l5(x124, x125, x126, x127, x128, x129, x130, x131, x132, x133, x134, x135) -> l1(x136, x137, x138, x139, x140, x141, x142, x143, x144, x145, x146, x147) :|: x135 = x147 && x133 = x145 && x134 = x146 && x132 = x144 && x131 = x143 && x129 = x141 && x127 = x139 && x128 = x140 && x124 = x136 && x137 = 0 && x142 = 0 && x138 = x128
l6(x148, x149, x150, x151, x152, x153, x154, x155, x156, x157, x158, x159) -> l5(x160, x161, x162, x163, x164, x165, x166, x167, x168, x169, x170, x171) :|: x159 = x171 && x157 = x169 && x158 = x170 && x156 = x168 && x155 = x167 && x154 = x166 && x153 = x165 && x151 = x163 && x150 = x162 && x152 = x164 && x149 = x161 && x148 = x160
Start term: l6(__const_8HAT0, nI6HAT0, nX4HAT0, nX9HAT0, nXHAT0, res10HAT0, res5HAT0, ret_nBC18HAT0, ret_nBC211HAT0, tmp7HAT0, tmpHAT0, tmp___0HAT0)

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

(3) IRSwTTerminationDigraphProof (EQUIVALENT)
Constructed termination digraph!
Nodes:
(1) l0(__const_8HAT0, nI6HAT0, nX4HAT0, nX9HAT0, nXHAT0, res10HAT0, res5HAT0, ret_nBC18HAT0, ret_nBC211HAT0, tmp7HAT0, tmpHAT0, tmp___0HAT0) -> l1(__const_8HATpost, nI6HATpost, nX4HATpost, nX9HATpost, nXHATpost, res10HATpost, res5HATpost, ret_nBC18HATpost, ret_nBC211HATpost, tmp7HATpost, tmpHATpost, tmp___0HATpost) :|: tmp___0HAT0 = tmp___0HATpost && tmp7HAT0 = tmp7HATpost && tmpHAT0 = tmpHATpost && ret_nBC211HAT0 = ret_nBC211HATpost && ret_nBC18HAT0 = ret_nBC18HATpost && res10HAT0 = res10HATpost && nX9HAT0 = nX9HATpost && nX4HAT0 = nX4HATpost && nXHAT0 = nXHATpost && __const_8HAT0 = __const_8HATpost && nI6HATpost = 1 + nI6HAT0 && res5HATpost = res5HAT0 + tmp7HAT0
(2) l2(x, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11) -> l0(x12, x13, x14, x15, x16, x17, x18, x19, x20, x21, x22, x23) :|: x11 = x23 && x10 = x22 && x8 = x20 && x7 = x19 && x6 = x18 && x5 = x17 && x3 = x15 && x2 = x14 && x4 = x16 && x1 = x13 && x = x12 && x21 = 0
(3) l2(x24, x25, x26, x27, x28, x29, x30, x31, x32, x33, x34, x35) -> l0(x36, x37, x38, x39, x40, x41, x42, x43, x44, x45, x46, x47) :|: x35 = x47 && x34 = x46 && x32 = x44 && x31 = x43 && x30 = x42 && x29 = x41 && x27 = x39 && x26 = x38 && x28 = x40 && x25 = x37 && x24 = x36 && x45 = 1
(4) l3(x48, x49, x50, x51, x52, x53, x54, x55, x56, x57, x58, x59) -> l4(x60, x61, x62, x63, x64, x65, x66, x67, x68, x69, x70, x71) :|: 2 * x48 <= x49 && x67 = x54 && x70 = x67 && x63 = x52 && x72 = x63 && x73 = x73 && x74 = x74 && x75 = x75 && x65 = x65 && x68 = x65 && x71 = x68 && x48 = x60 && x49 = x61 && x52 = x64 && x50 = x62 && x54 = x66 && x57 = x69
(5) l3(x76, x77, x78, x79, x80, x81, x82, x83, x84, x85, x86, x87) -> l2(x88, x89, x90, x91, x92, x93, x94, x95, x96, x97, x98, x99) :|: x87 = x99 && x85 = x97 && x86 = x98 && x84 = x96 && x83 = x95 && x82 = x94 && x81 = x93 && x79 = x91 && x78 = x90 && x80 = x92 && x77 = x89 && x76 = x88 && 1 + x77 <= 2 * x76
(6) l1(x100, x101, x102, x103, x104, x105, x106, x107, x108, x109, x110, x111) -> l3(x112, x113, x114, x115, x116, x117, x118, x119, x120, x121, x122, x123) :|: x111 = x123 && x109 = x121 && x110 = x122 && x108 = x120 && x107 = x119 && x106 = x118 && x105 = x117 && x103 = x115 && x102 = x114 && x104 = x116 && x101 = x113 && x100 = x112
(7) l5(x124, x125, x126, x127, x128, x129, x130, x131, x132, x133, x134, x135) -> l1(x136, x137, x138, x139, x140, x141, x142, x143, x144, x145, x146, x147) :|: x135 = x147 && x133 = x145 && x134 = x146 && x132 = x144 && x131 = x143 && x129 = x141 && x127 = x139 && x128 = x140 && x124 = x136 && x137 = 0 && x142 = 0 && x138 = x128
(8) l6(x148, x149, x150, x151, x152, x153, x154, x155, x156, x157, x158, x159) -> l5(x160, x161, x162, x163, x164, x165, x166, x167, x168, x169, x170, x171) :|: x159 = x171 && x157 = x169 && x158 = x170 && x156 = x168 && x155 = x167 && x154 = x166 && x153 = x165 && x151 = x163 && x150 = x162 && x152 = x164 && x149 = x161 && x148 = x160

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

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

(4)
Obligation:

Termination digraph:
Nodes:
(1) l0(__const_8HAT0, nI6HAT0, nX4HAT0, nX9HAT0, nXHAT0, res10HAT0, res5HAT0, ret_nBC18HAT0, ret_nBC211HAT0, tmp7HAT0, tmpHAT0, tmp___0HAT0) -> l1(__const_8HATpost, nI6HATpost, nX4HATpost, nX9HATpost, nXHATpost, res10HATpost, res5HATpost, ret_nBC18HATpost, ret_nBC211HATpost, tmp7HATpost, tmpHATpost, tmp___0HATpost) :|: tmp___0HAT0 = tmp___0HATpost && tmp7HAT0 = tmp7HATpost && tmpHAT0 = tmpHATpost && ret_nBC211HAT0 = ret_nBC211HATpost && ret_nBC18HAT0 = ret_nBC18HATpost && res10HAT0 = res10HATpost && nX9HAT0 = nX9HATpost && nX4HAT0 = nX4HATpost && nXHAT0 = nXHATpost && __const_8HAT0 = __const_8HATpost && nI6HATpost = 1 + nI6HAT0 && res5HATpost = res5HAT0 + tmp7HAT0
(2) l2(x24, x25, x26, x27, x28, x29, x30, x31, x32, x33, x34, x35) -> l0(x36, x37, x38, x39, x40, x41, x42, x43, x44, x45, x46, x47) :|: x35 = x47 && x34 = x46 && x32 = x44 && x31 = x43 && x30 = x42 && x29 = x41 && x27 = x39 && x26 = x38 && x28 = x40 && x25 = x37 && x24 = x36 && x45 = 1
(3) l2(x, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11) -> l0(x12, x13, x14, x15, x16, x17, x18, x19, x20, x21, x22, x23) :|: x11 = x23 && x10 = x22 && x8 = x20 && x7 = x19 && x6 = x18 && x5 = x17 && x3 = x15 && x2 = x14 && x4 = x16 && x1 = x13 && x = x12 && x21 = 0
(4) l3(x76, x77, x78, x79, x80, x81, x82, x83, x84, x85, x86, x87) -> l2(x88, x89, x90, x91, x92, x93, x94, x95, x96, x97, x98, x99) :|: x87 = x99 && x85 = x97 && x86 = x98 && x84 = x96 && x83 = x95 && x82 = x94 && x81 = x93 && x79 = x91 && x78 = x90 && x80 = x92 && x77 = x89 && x76 = x88 && 1 + x77 <= 2 * x76
(5) l1(x100, x101, x102, x103, x104, x105, x106, x107, x108, x109, x110, x111) -> l3(x112, x113, x114, x115, x116, x117, x118, x119, x120, x121, x122, x123) :|: x111 = x123 && x109 = x121 && x110 = x122 && x108 = x120 && x107 = x119 && x106 = x118 && x105 = x117 && x103 = x115 && x102 = x114 && x104 = x116 && x101 = x113 && x100 = x112

Arcs:
(1) -> (5)
(2) -> (1)
(3) -> (1)
(4) -> (2), (3)
(5) -> (4)

This digraph is fully evaluated!

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

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

(6)
Obligation:
Rules:
l3(__const_8HATpost:0, x37:0, nX4HATpost:0, nX9HATpost:0, nXHATpost:0, res10HATpost:0, x42:0, ret_nBC18HATpost:0, ret_nBC211HATpost:0, x85:0, tmpHATpost:0, tmp___0HATpost:0) -> l3(__const_8HATpost:0, 1 + x37:0, nX4HATpost:0, nX9HATpost:0, nXHATpost:0, res10HATpost:0, x42:0 + 1, ret_nBC18HATpost:0, ret_nBC211HATpost:0, 1, tmpHATpost:0, tmp___0HATpost:0) :|: 2 * __const_8HATpost:0 >= 1 + x37:0
l3(x, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11) -> l3(x, 1 + x1, x2, x3, x4, x5, x6, x7, x8, 0, x10, x11) :|: 2 * x >= 1 + x1

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

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

   l3(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12) -> l3(x1, x2)

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

(8)
Obligation:
Rules:
l3(__const_8HATpost:0, x37:0) -> l3(__const_8HATpost:0, 1 + x37:0) :|: 2 * __const_8HATpost:0 >= 1 + x37:0

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

(9) TempFilterProof (SOUND)
Used the following sort dictionary for filtering: 
l3(INTEGER, INTEGER)
Replaced non-predefined constructor symbols by 0.
----------------------------------------

(10)
Obligation:
Rules:
l3(__const_8HATpost:0, x37:0) -> l3(__const_8HATpost:0, c) :|: c = 1 + x37:0 && 2 * __const_8HATpost:0 >= 1 + x37:0

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

(11) PolynomialOrderProcessor (EQUIVALENT)
Found the following polynomial interpretation:
[l3(x, x1)] = 2*x - x1

The following rules are decreasing:
l3(__const_8HATpost:0, x37:0) -> l3(__const_8HATpost:0, c) :|: c = 1 + x37:0 && 2 * __const_8HATpost:0 >= 1 + x37:0
The following rules are bounded:
l3(__const_8HATpost:0, x37:0) -> l3(__const_8HATpost:0, c) :|: c = 1 + x37:0 && 2 * __const_8HATpost:0 >= 1 + x37:0

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

(12)
YES