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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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, 691 ms]
(4) IRSwT
(5) IntTRSCompressionProof [EQUIVALENT, 0 ms]
(6) IRSwT
(7) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms]
(8) IRSwT
(9) FilterProof [EQUIVALENT, 2 ms]
(10) IntTRS
(11) IntTRSPeriodicNontermProof [COMPLETE, 0 ms]
(12) NO


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(0)
Obligation:
Rules:
l0(Result_4HAT0, cnt_33HAT0, cnt_40HAT0, lt_10HAT0, lt_11HAT0, lt_12HAT0, px_8HAT0, py_6HAT0, q_9HAT0, x_7HAT0, y_5HAT0) -> l1(Result_4HATpost, cnt_33HATpost, cnt_40HATpost, lt_10HATpost, lt_11HATpost, lt_12HATpost, px_8HATpost, py_6HATpost, q_9HATpost, x_7HATpost, y_5HATpost) :|: lt_12HAT0 = lt_12HATpost && lt_11HAT0 = lt_11HATpost && lt_10HAT0 = lt_10HATpost && cnt_40HAT0 = cnt_40HATpost && cnt_33HAT0 = cnt_33HATpost && Result_4HAT0 = Result_4HATpost && q_9HATpost = py_6HATpost && y_5HATpost = y_5HATpost && py_6HATpost = py_6HATpost && x_7HATpost = x_7HATpost && px_8HATpost = px_8HATpost
l1(x, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10) -> l2(x11, x12, x13, x14, x15, x16, x17, x18, x19, x20, x21) :|: x22 = x10 && x23 = x1 && x23 <= 0 && x15 = x15 && x16 = x16 && x11 = x11 && x1 = x12 && x2 = x13 && x3 = x14 && x6 = x17 && x7 = x18 && x8 = x19 && x9 = x20 && x10 = x21
l1(x24, x25, x26, x27, x28, x29, x30, x31, x32, x33, x34) -> l3(x35, x36, x37, x38, x39, x40, x41, x42, x43, x44, x45) :|: x46 = x34 && x47 = x25 && 0 <= -1 + x47 && x39 = x39 && x40 = x40 && x48 = x26 && x38 = x38 && x43 = x30 && x24 = x35 && x25 = x36 && x26 = x37 && x30 = x41 && x31 = x42 && x33 = x44 && x34 = x45
l3(x49, x50, x51, x52, x53, x54, x55, x56, x57, x58, x59) -> l2(x60, x61, x62, x63, x64, x65, x66, x67, x68, x69, x70) :|: x71 = x58 && x72 = -1 + x51 && x72 <= 0 && x64 = x64 && x65 = x65 && x60 = x60 && x50 = x61 && x51 = x62 && x52 = x63 && x55 = x66 && x56 = x67 && x57 = x68 && x58 = x69 && x59 = x70
l3(x73, x74, x75, x76, x77, x78, x79, x80, x81, x82, x83) -> l4(x84, x85, x86, x87, x88, x89, x90, x91, x92, x93, x94) :|: x95 = x82 && x96 = -1 + x75 && 0 <= -1 + x96 && x88 = x88 && x89 = x89 && x97 = -1 + x75 && x87 = x87 && x92 = x79 && x73 = x84 && x74 = x85 && x75 = x86 && x79 = x90 && x80 = x91 && x82 = x93 && x83 = x94
l4(x98, x99, x100, x101, x102, x103, x104, x105, x106, x107, x108) -> l3(x109, x110, x111, x112, x113, x114, x115, x116, x117, x118, x119) :|: x108 = x119 && x107 = x118 && x106 = x117 && x105 = x116 && x104 = x115 && x103 = x114 && x102 = x113 && x101 = x112 && x100 = x111 && x99 = x110 && x98 = x109
l5(x120, x121, x122, x123, x124, x125, x126, x127, x128, x129, x130) -> l0(x131, x132, x133, x134, x135, x136, x137, x138, x139, x140, x141) :|: x130 = x141 && x129 = x140 && x128 = x139 && x127 = x138 && x126 = x137 && x125 = x136 && x124 = x135 && x123 = x134 && x122 = x133 && x121 = x132 && x120 = x131
Start term: l5(Result_4HAT0, cnt_33HAT0, cnt_40HAT0, lt_10HAT0, lt_11HAT0, lt_12HAT0, px_8HAT0, py_6HAT0, q_9HAT0, x_7HAT0, y_5HAT0)

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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(Result_4HAT0, cnt_33HAT0, cnt_40HAT0, lt_10HAT0, lt_11HAT0, lt_12HAT0, px_8HAT0, py_6HAT0, q_9HAT0, x_7HAT0, y_5HAT0) -> l1(Result_4HATpost, cnt_33HATpost, cnt_40HATpost, lt_10HATpost, lt_11HATpost, lt_12HATpost, px_8HATpost, py_6HATpost, q_9HATpost, x_7HATpost, y_5HATpost) :|: lt_12HAT0 = lt_12HATpost && lt_11HAT0 = lt_11HATpost && lt_10HAT0 = lt_10HATpost && cnt_40HAT0 = cnt_40HATpost && cnt_33HAT0 = cnt_33HATpost && Result_4HAT0 = Result_4HATpost && q_9HATpost = py_6HATpost && y_5HATpost = y_5HATpost && py_6HATpost = py_6HATpost && x_7HATpost = x_7HATpost && px_8HATpost = px_8HATpost
l1(x, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10) -> l2(x11, x12, x13, x14, x15, x16, x17, x18, x19, x20, x21) :|: x22 = x10 && x23 = x1 && x23 <= 0 && x15 = x15 && x16 = x16 && x11 = x11 && x1 = x12 && x2 = x13 && x3 = x14 && x6 = x17 && x7 = x18 && x8 = x19 && x9 = x20 && x10 = x21
l1(x24, x25, x26, x27, x28, x29, x30, x31, x32, x33, x34) -> l3(x35, x36, x37, x38, x39, x40, x41, x42, x43, x44, x45) :|: x46 = x34 && x47 = x25 && 0 <= -1 + x47 && x39 = x39 && x40 = x40 && x48 = x26 && x38 = x38 && x43 = x30 && x24 = x35 && x25 = x36 && x26 = x37 && x30 = x41 && x31 = x42 && x33 = x44 && x34 = x45
l3(x49, x50, x51, x52, x53, x54, x55, x56, x57, x58, x59) -> l2(x60, x61, x62, x63, x64, x65, x66, x67, x68, x69, x70) :|: x71 = x58 && x72 = -1 + x51 && x72 <= 0 && x64 = x64 && x65 = x65 && x60 = x60 && x50 = x61 && x51 = x62 && x52 = x63 && x55 = x66 && x56 = x67 && x57 = x68 && x58 = x69 && x59 = x70
l3(x73, x74, x75, x76, x77, x78, x79, x80, x81, x82, x83) -> l4(x84, x85, x86, x87, x88, x89, x90, x91, x92, x93, x94) :|: x95 = x82 && x96 = -1 + x75 && 0 <= -1 + x96 && x88 = x88 && x89 = x89 && x97 = -1 + x75 && x87 = x87 && x92 = x79 && x73 = x84 && x74 = x85 && x75 = x86 && x79 = x90 && x80 = x91 && x82 = x93 && x83 = x94
l4(x98, x99, x100, x101, x102, x103, x104, x105, x106, x107, x108) -> l3(x109, x110, x111, x112, x113, x114, x115, x116, x117, x118, x119) :|: x108 = x119 && x107 = x118 && x106 = x117 && x105 = x116 && x104 = x115 && x103 = x114 && x102 = x113 && x101 = x112 && x100 = x111 && x99 = x110 && x98 = x109
l5(x120, x121, x122, x123, x124, x125, x126, x127, x128, x129, x130) -> l0(x131, x132, x133, x134, x135, x136, x137, x138, x139, x140, x141) :|: x130 = x141 && x129 = x140 && x128 = x139 && x127 = x138 && x126 = x137 && x125 = x136 && x124 = x135 && x123 = x134 && x122 = x133 && x121 = x132 && x120 = x131
Start term: l5(Result_4HAT0, cnt_33HAT0, cnt_40HAT0, lt_10HAT0, lt_11HAT0, lt_12HAT0, px_8HAT0, py_6HAT0, q_9HAT0, x_7HAT0, y_5HAT0)

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(3) IRSwTTerminationDigraphProof (EQUIVALENT)
Constructed termination digraph!
Nodes:
(1) l0(Result_4HAT0, cnt_33HAT0, cnt_40HAT0, lt_10HAT0, lt_11HAT0, lt_12HAT0, px_8HAT0, py_6HAT0, q_9HAT0, x_7HAT0, y_5HAT0) -> l1(Result_4HATpost, cnt_33HATpost, cnt_40HATpost, lt_10HATpost, lt_11HATpost, lt_12HATpost, px_8HATpost, py_6HATpost, q_9HATpost, x_7HATpost, y_5HATpost) :|: lt_12HAT0 = lt_12HATpost && lt_11HAT0 = lt_11HATpost && lt_10HAT0 = lt_10HATpost && cnt_40HAT0 = cnt_40HATpost && cnt_33HAT0 = cnt_33HATpost && Result_4HAT0 = Result_4HATpost && q_9HATpost = py_6HATpost && y_5HATpost = y_5HATpost && py_6HATpost = py_6HATpost && x_7HATpost = x_7HATpost && px_8HATpost = px_8HATpost
(2) l1(x, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10) -> l2(x11, x12, x13, x14, x15, x16, x17, x18, x19, x20, x21) :|: x22 = x10 && x23 = x1 && x23 <= 0 && x15 = x15 && x16 = x16 && x11 = x11 && x1 = x12 && x2 = x13 && x3 = x14 && x6 = x17 && x7 = x18 && x8 = x19 && x9 = x20 && x10 = x21
(3) l1(x24, x25, x26, x27, x28, x29, x30, x31, x32, x33, x34) -> l3(x35, x36, x37, x38, x39, x40, x41, x42, x43, x44, x45) :|: x46 = x34 && x47 = x25 && 0 <= -1 + x47 && x39 = x39 && x40 = x40 && x48 = x26 && x38 = x38 && x43 = x30 && x24 = x35 && x25 = x36 && x26 = x37 && x30 = x41 && x31 = x42 && x33 = x44 && x34 = x45
(4) l3(x49, x50, x51, x52, x53, x54, x55, x56, x57, x58, x59) -> l2(x60, x61, x62, x63, x64, x65, x66, x67, x68, x69, x70) :|: x71 = x58 && x72 = -1 + x51 && x72 <= 0 && x64 = x64 && x65 = x65 && x60 = x60 && x50 = x61 && x51 = x62 && x52 = x63 && x55 = x66 && x56 = x67 && x57 = x68 && x58 = x69 && x59 = x70
(5) l3(x73, x74, x75, x76, x77, x78, x79, x80, x81, x82, x83) -> l4(x84, x85, x86, x87, x88, x89, x90, x91, x92, x93, x94) :|: x95 = x82 && x96 = -1 + x75 && 0 <= -1 + x96 && x88 = x88 && x89 = x89 && x97 = -1 + x75 && x87 = x87 && x92 = x79 && x73 = x84 && x74 = x85 && x75 = x86 && x79 = x90 && x80 = x91 && x82 = x93 && x83 = x94
(6) l4(x98, x99, x100, x101, x102, x103, x104, x105, x106, x107, x108) -> l3(x109, x110, x111, x112, x113, x114, x115, x116, x117, x118, x119) :|: x108 = x119 && x107 = x118 && x106 = x117 && x105 = x116 && x104 = x115 && x103 = x114 && x102 = x113 && x101 = x112 && x100 = x111 && x99 = x110 && x98 = x109
(7) l5(x120, x121, x122, x123, x124, x125, x126, x127, x128, x129, x130) -> l0(x131, x132, x133, x134, x135, x136, x137, x138, x139, x140, x141) :|: x130 = x141 && x129 = x140 && x128 = x139 && x127 = x138 && x126 = x137 && x125 = x136 && x124 = x135 && x123 = x134 && x122 = x133 && x121 = x132 && x120 = x131

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

This digraph is fully evaluated!
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(4)
Obligation:

Termination digraph:
Nodes:
(1) l3(x73, x74, x75, x76, x77, x78, x79, x80, x81, x82, x83) -> l4(x84, x85, x86, x87, x88, x89, x90, x91, x92, x93, x94) :|: x95 = x82 && x96 = -1 + x75 && 0 <= -1 + x96 && x88 = x88 && x89 = x89 && x97 = -1 + x75 && x87 = x87 && x92 = x79 && x73 = x84 && x74 = x85 && x75 = x86 && x79 = x90 && x80 = x91 && x82 = x93 && x83 = x94
(2) l4(x98, x99, x100, x101, x102, x103, x104, x105, x106, x107, x108) -> l3(x109, x110, x111, x112, x113, x114, x115, x116, x117, x118, x119) :|: x108 = x119 && x107 = x118 && x106 = x117 && x105 = x116 && x104 = x115 && x103 = x114 && x102 = x113 && x101 = x112 && x100 = x111 && x99 = x110 && x98 = x109

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:
l3(x109:0, x110:0, x111:0, x76:0, x77:0, x78:0, x115:0, x116:0, x81:0, x118:0, x119:0) -> l3(x109:0, x110:0, x111:0, x112:0, x113:0, x114:0, x115:0, x116:0, x115:0, x118:0, x119:0) :|: x111:0 > 1

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(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) -> l3(x3)

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(8)
Obligation:
Rules:
l3(x111:0) -> l3(x111:0) :|: x111:0 > 1

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(9) FilterProof (EQUIVALENT)
Used the following sort dictionary for filtering: 
l3(INTEGER)
Replaced non-predefined constructor symbols by 0.
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(10)
Obligation:
Rules:
l3(x111:0) -> l3(x111:0) :|: x111:0 > 1

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(11) IntTRSPeriodicNontermProof (COMPLETE)
Normalized system to the following form:
f(pc, x111:0) -> f(1, x111:0) :|: pc = 1 && x111:0 > 1
Witness term starting non-terminating reduction: f(1, 16)
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(12)
NO