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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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, 246 ms]
(4) IRSwT
(5) IntTRSCompressionProof [EQUIVALENT, 1 ms]
(6) IRSwT
(7) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms]
(8) IRSwT
(9) FilterProof [EQUIVALENT, 0 ms]
(10) IntTRS
(11) IntTRSPeriodicNontermProof [COMPLETE, 5 ms]
(12) NO


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(0)
Obligation:
Rules:
l0(Result_4HAT0, cnt_25HAT0, lt_10HAT0, lt_8HAT0, lt_9HAT0, p_6HAT0, q_7HAT0, x_5HAT0) -> l1(Result_4HATpost, cnt_25HATpost, lt_10HATpost, lt_8HATpost, lt_9HATpost, p_6HATpost, q_7HATpost, x_5HATpost) :|: lt_9HAT1 = x_5HAT0 && lt_10HAT1 = cnt_25HAT0 && lt_10HAT1 <= 0 && lt_9HATpost = lt_9HATpost && lt_10HATpost = lt_10HATpost && Result_4HATpost = Result_4HATpost && cnt_25HAT0 = cnt_25HATpost && lt_8HAT0 = lt_8HATpost && p_6HAT0 = p_6HATpost && q_7HAT0 = q_7HATpost && x_5HAT0 = x_5HATpost
l0(x, x1, x2, x3, x4, x5, x6, x7) -> l2(x8, x9, x10, x11, x12, x13, x14, x15) :|: x16 = x7 && x17 = x1 && 0 <= -1 + x17 && x12 = x12 && x10 = x10 && x18 = x1 && x11 = x11 && x = x8 && x1 = x9 && x5 = x13 && x6 = x14 && x7 = x15
l2(x19, x20, x21, x22, x23, x24, x25, x26) -> l0(x27, x28, x29, x30, x31, x32, x33, x34) :|: x26 = x34 && x25 = x33 && x24 = x32 && x23 = x31 && x22 = x30 && x21 = x29 && x20 = x28 && x19 = x27
l3(x35, x36, x37, x38, x39, x40, x41, x42) -> l0(x43, x44, x45, x46, x47, x48, x49, x50) :|: x39 = x47 && x38 = x46 && x37 = x45 && x36 = x44 && x35 = x43 && x49 = x48 && x50 = x50 && x48 = x48
l4(x51, x52, x53, x54, x55, x56, x57, x58) -> l3(x59, x60, x61, x62, x63, x64, x65, x66) :|: x58 = x66 && x57 = x65 && x56 = x64 && x55 = x63 && x54 = x62 && x53 = x61 && x52 = x60 && x51 = x59
Start term: l4(Result_4HAT0, cnt_25HAT0, lt_10HAT0, lt_8HAT0, lt_9HAT0, p_6HAT0, q_7HAT0, x_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_25HAT0, lt_10HAT0, lt_8HAT0, lt_9HAT0, p_6HAT0, q_7HAT0, x_5HAT0) -> l1(Result_4HATpost, cnt_25HATpost, lt_10HATpost, lt_8HATpost, lt_9HATpost, p_6HATpost, q_7HATpost, x_5HATpost) :|: lt_9HAT1 = x_5HAT0 && lt_10HAT1 = cnt_25HAT0 && lt_10HAT1 <= 0 && lt_9HATpost = lt_9HATpost && lt_10HATpost = lt_10HATpost && Result_4HATpost = Result_4HATpost && cnt_25HAT0 = cnt_25HATpost && lt_8HAT0 = lt_8HATpost && p_6HAT0 = p_6HATpost && q_7HAT0 = q_7HATpost && x_5HAT0 = x_5HATpost
l0(x, x1, x2, x3, x4, x5, x6, x7) -> l2(x8, x9, x10, x11, x12, x13, x14, x15) :|: x16 = x7 && x17 = x1 && 0 <= -1 + x17 && x12 = x12 && x10 = x10 && x18 = x1 && x11 = x11 && x = x8 && x1 = x9 && x5 = x13 && x6 = x14 && x7 = x15
l2(x19, x20, x21, x22, x23, x24, x25, x26) -> l0(x27, x28, x29, x30, x31, x32, x33, x34) :|: x26 = x34 && x25 = x33 && x24 = x32 && x23 = x31 && x22 = x30 && x21 = x29 && x20 = x28 && x19 = x27
l3(x35, x36, x37, x38, x39, x40, x41, x42) -> l0(x43, x44, x45, x46, x47, x48, x49, x50) :|: x39 = x47 && x38 = x46 && x37 = x45 && x36 = x44 && x35 = x43 && x49 = x48 && x50 = x50 && x48 = x48
l4(x51, x52, x53, x54, x55, x56, x57, x58) -> l3(x59, x60, x61, x62, x63, x64, x65, x66) :|: x58 = x66 && x57 = x65 && x56 = x64 && x55 = x63 && x54 = x62 && x53 = x61 && x52 = x60 && x51 = x59
Start term: l4(Result_4HAT0, cnt_25HAT0, lt_10HAT0, lt_8HAT0, lt_9HAT0, p_6HAT0, q_7HAT0, x_5HAT0)

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(3) IRSwTTerminationDigraphProof (EQUIVALENT)
Constructed termination digraph!
Nodes:
(1) l0(Result_4HAT0, cnt_25HAT0, lt_10HAT0, lt_8HAT0, lt_9HAT0, p_6HAT0, q_7HAT0, x_5HAT0) -> l1(Result_4HATpost, cnt_25HATpost, lt_10HATpost, lt_8HATpost, lt_9HATpost, p_6HATpost, q_7HATpost, x_5HATpost) :|: lt_9HAT1 = x_5HAT0 && lt_10HAT1 = cnt_25HAT0 && lt_10HAT1 <= 0 && lt_9HATpost = lt_9HATpost && lt_10HATpost = lt_10HATpost && Result_4HATpost = Result_4HATpost && cnt_25HAT0 = cnt_25HATpost && lt_8HAT0 = lt_8HATpost && p_6HAT0 = p_6HATpost && q_7HAT0 = q_7HATpost && x_5HAT0 = x_5HATpost
(2) l0(x, x1, x2, x3, x4, x5, x6, x7) -> l2(x8, x9, x10, x11, x12, x13, x14, x15) :|: x16 = x7 && x17 = x1 && 0 <= -1 + x17 && x12 = x12 && x10 = x10 && x18 = x1 && x11 = x11 && x = x8 && x1 = x9 && x5 = x13 && x6 = x14 && x7 = x15
(3) l2(x19, x20, x21, x22, x23, x24, x25, x26) -> l0(x27, x28, x29, x30, x31, x32, x33, x34) :|: x26 = x34 && x25 = x33 && x24 = x32 && x23 = x31 && x22 = x30 && x21 = x29 && x20 = x28 && x19 = x27
(4) l3(x35, x36, x37, x38, x39, x40, x41, x42) -> l0(x43, x44, x45, x46, x47, x48, x49, x50) :|: x39 = x47 && x38 = x46 && x37 = x45 && x36 = x44 && x35 = x43 && x49 = x48 && x50 = x50 && x48 = x48
(5) l4(x51, x52, x53, x54, x55, x56, x57, x58) -> l3(x59, x60, x61, x62, x63, x64, x65, x66) :|: x58 = x66 && x57 = x65 && x56 = x64 && x55 = x63 && x54 = x62 && x53 = x61 && x52 = x60 && x51 = x59

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

This digraph is fully evaluated!
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(4)
Obligation:

Termination digraph:
Nodes:
(1) l0(x, x1, x2, x3, x4, x5, x6, x7) -> l2(x8, x9, x10, x11, x12, x13, x14, x15) :|: x16 = x7 && x17 = x1 && 0 <= -1 + x17 && x12 = x12 && x10 = x10 && x18 = x1 && x11 = x11 && x = x8 && x1 = x9 && x5 = x13 && x6 = x14 && x7 = x15
(2) l2(x19, x20, x21, x22, x23, x24, x25, x26) -> l0(x27, x28, x29, x30, x31, x32, x33, x34) :|: x26 = x34 && x25 = x33 && x24 = x32 && x23 = x31 && x22 = x30 && x21 = x29 && x20 = x28 && x19 = x27

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:
l0(x27:0, x17:0, x2:0, x3:0, x4:0, x13:0, x14:0, x15:0) -> l0(x27:0, x17:0, x10:0, x11:0, x12:0, x13:0, x14:0, x15:0) :|: x17:0 > 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:

   l0(x1, x2, x3, x4, x5, x6, x7, x8) -> l0(x2)

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(8)
Obligation:
Rules:
l0(x17:0) -> l0(x17:0) :|: x17:0 > 0

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(9) FilterProof (EQUIVALENT)
Used the following sort dictionary for filtering: 
l0(INTEGER)
Replaced non-predefined constructor symbols by 0.
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(10)
Obligation:
Rules:
l0(x17:0) -> l0(x17:0) :|: x17:0 > 0

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(11) IntTRSPeriodicNontermProof (COMPLETE)
Normalized system to the following form:
f(pc, x17:0) -> f(1, x17:0) :|: pc = 1 && x17:0 > 0
Witness term starting non-terminating reduction: f(1, 1)
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(12)
NO