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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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, 326 ms]
(4) IRSwT
(5) IntTRSCompressionProof [EQUIVALENT, 0 ms]
(6) IRSwT
(7) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms]
(8) IRSwT
(9) FilterProof [EQUIVALENT, 0 ms]
(10) IntTRS
(11) IntTRSPeriodicNontermProof [COMPLETE, 0 ms]
(12) NO


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(0)
Obligation:
Rules:
l0(Result_4HAT0, cnt_15HAT0, cnt_20HAT0, lt_7HAT0, lt_8HAT0, lt_9HAT0, x_5HAT0, y_6HAT0) -> l1(Result_4HATpost, cnt_15HATpost, cnt_20HATpost, lt_7HATpost, lt_8HATpost, lt_9HATpost, x_5HATpost, y_6HATpost) :|: lt_9HAT0 = lt_9HATpost && lt_8HAT0 = lt_8HATpost && lt_7HAT0 = lt_7HATpost && cnt_20HAT0 = cnt_20HATpost && cnt_15HAT0 = cnt_15HATpost && Result_4HAT0 = Result_4HATpost && x_5HATpost = x_5HATpost && y_6HATpost = y_6HATpost
l1(x, x1, x2, x3, x4, x5, x6, x7) -> l2(x8, x9, x10, x11, x12, x13, x14, x15) :|: x16 = x1 && x17 = x2 && -1 * x16 + x17 <= 0 && x12 = x12 && x13 = x13 && x8 = x8 && x1 = x9 && x2 = x10 && x3 = x11 && x6 = x14 && x7 = x15
l1(x18, x19, x20, x21, x22, x23, x24, x25) -> l3(x26, x27, x28, x29, x30, x31, x32, x33) :|: x34 = x19 && x35 = x20 && 0 <= -1 - x34 + x35 && x30 = x30 && x31 = x31 && x36 = x19 && x29 = x29 && x18 = x26 && x19 = x27 && x20 = x28 && x24 = x32 && x25 = x33
l3(x37, x38, x39, x40, x41, x42, x43, x44) -> l1(x45, x46, x47, x48, x49, x50, x51, x52) :|: x44 = x52 && x43 = x51 && x42 = x50 && x41 = x49 && x40 = x48 && x39 = x47 && x38 = x46 && x37 = x45
l4(x53, x54, x55, x56, x57, x58, x59, x60) -> l0(x61, x62, x63, x64, x65, x66, x67, x68) :|: x60 = x68 && x59 = x67 && x58 = x66 && x57 = x65 && x56 = x64 && x55 = x63 && x54 = x62 && x53 = x61
Start term: l4(Result_4HAT0, cnt_15HAT0, cnt_20HAT0, lt_7HAT0, lt_8HAT0, lt_9HAT0, x_5HAT0, y_6HAT0)

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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_15HAT0, cnt_20HAT0, lt_7HAT0, lt_8HAT0, lt_9HAT0, x_5HAT0, y_6HAT0) -> l1(Result_4HATpost, cnt_15HATpost, cnt_20HATpost, lt_7HATpost, lt_8HATpost, lt_9HATpost, x_5HATpost, y_6HATpost) :|: lt_9HAT0 = lt_9HATpost && lt_8HAT0 = lt_8HATpost && lt_7HAT0 = lt_7HATpost && cnt_20HAT0 = cnt_20HATpost && cnt_15HAT0 = cnt_15HATpost && Result_4HAT0 = Result_4HATpost && x_5HATpost = x_5HATpost && y_6HATpost = y_6HATpost
l1(x, x1, x2, x3, x4, x5, x6, x7) -> l2(x8, x9, x10, x11, x12, x13, x14, x15) :|: x16 = x1 && x17 = x2 && -1 * x16 + x17 <= 0 && x12 = x12 && x13 = x13 && x8 = x8 && x1 = x9 && x2 = x10 && x3 = x11 && x6 = x14 && x7 = x15
l1(x18, x19, x20, x21, x22, x23, x24, x25) -> l3(x26, x27, x28, x29, x30, x31, x32, x33) :|: x34 = x19 && x35 = x20 && 0 <= -1 - x34 + x35 && x30 = x30 && x31 = x31 && x36 = x19 && x29 = x29 && x18 = x26 && x19 = x27 && x20 = x28 && x24 = x32 && x25 = x33
l3(x37, x38, x39, x40, x41, x42, x43, x44) -> l1(x45, x46, x47, x48, x49, x50, x51, x52) :|: x44 = x52 && x43 = x51 && x42 = x50 && x41 = x49 && x40 = x48 && x39 = x47 && x38 = x46 && x37 = x45
l4(x53, x54, x55, x56, x57, x58, x59, x60) -> l0(x61, x62, x63, x64, x65, x66, x67, x68) :|: x60 = x68 && x59 = x67 && x58 = x66 && x57 = x65 && x56 = x64 && x55 = x63 && x54 = x62 && x53 = x61
Start term: l4(Result_4HAT0, cnt_15HAT0, cnt_20HAT0, lt_7HAT0, lt_8HAT0, lt_9HAT0, x_5HAT0, y_6HAT0)

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(3) IRSwTTerminationDigraphProof (EQUIVALENT)
Constructed termination digraph!
Nodes:
(1) l0(Result_4HAT0, cnt_15HAT0, cnt_20HAT0, lt_7HAT0, lt_8HAT0, lt_9HAT0, x_5HAT0, y_6HAT0) -> l1(Result_4HATpost, cnt_15HATpost, cnt_20HATpost, lt_7HATpost, lt_8HATpost, lt_9HATpost, x_5HATpost, y_6HATpost) :|: lt_9HAT0 = lt_9HATpost && lt_8HAT0 = lt_8HATpost && lt_7HAT0 = lt_7HATpost && cnt_20HAT0 = cnt_20HATpost && cnt_15HAT0 = cnt_15HATpost && Result_4HAT0 = Result_4HATpost && x_5HATpost = x_5HATpost && y_6HATpost = y_6HATpost
(2) l1(x, x1, x2, x3, x4, x5, x6, x7) -> l2(x8, x9, x10, x11, x12, x13, x14, x15) :|: x16 = x1 && x17 = x2 && -1 * x16 + x17 <= 0 && x12 = x12 && x13 = x13 && x8 = x8 && x1 = x9 && x2 = x10 && x3 = x11 && x6 = x14 && x7 = x15
(3) l1(x18, x19, x20, x21, x22, x23, x24, x25) -> l3(x26, x27, x28, x29, x30, x31, x32, x33) :|: x34 = x19 && x35 = x20 && 0 <= -1 - x34 + x35 && x30 = x30 && x31 = x31 && x36 = x19 && x29 = x29 && x18 = x26 && x19 = x27 && x20 = x28 && x24 = x32 && x25 = x33
(4) l3(x37, x38, x39, x40, x41, x42, x43, x44) -> l1(x45, x46, x47, x48, x49, x50, x51, x52) :|: x44 = x52 && x43 = x51 && x42 = x50 && x41 = x49 && x40 = x48 && x39 = x47 && x38 = x46 && x37 = x45
(5) l4(x53, x54, x55, x56, x57, x58, x59, x60) -> l0(x61, x62, x63, x64, x65, x66, x67, x68) :|: x60 = x68 && x59 = x67 && x58 = x66 && x57 = x65 && x56 = x64 && x55 = x63 && x54 = x62 && x53 = x61

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

This digraph is fully evaluated!
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(4)
Obligation:

Termination digraph:
Nodes:
(1) l1(x18, x19, x20, x21, x22, x23, x24, x25) -> l3(x26, x27, x28, x29, x30, x31, x32, x33) :|: x34 = x19 && x35 = x20 && 0 <= -1 - x34 + x35 && x30 = x30 && x31 = x31 && x36 = x19 && x29 = x29 && x18 = x26 && x19 = x27 && x20 = x28 && x24 = x32 && x25 = x33
(2) l3(x37, x38, x39, x40, x41, x42, x43, x44) -> l1(x45, x46, x47, x48, x49, x50, x51, x52) :|: x44 = x52 && x43 = x51 && x42 = x50 && x41 = x49 && x40 = x48 && x39 = x47 && x38 = x46 && x37 = x45

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(x18:0, x19:0, x20:0, x21:0, x22:0, x23:0, x24:0, x25:0) -> l1(x18:0, x19:0, x20:0, x29:0, x30:0, x31:0, x24:0, x25:0) :|: 0 <= -1 - x19:0 + x20:0

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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(x2, x3)

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(8)
Obligation:
Rules:
l1(x19:0, x20:0) -> l1(x19:0, x20:0) :|: 0 <= -1 - x19:0 + x20:0

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(9) FilterProof (EQUIVALENT)
Used the following sort dictionary for filtering: 
l1(INTEGER, INTEGER)
Replaced non-predefined constructor symbols by 0.
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(10)
Obligation:
Rules:
l1(x19:0, x20:0) -> l1(x19:0, x20:0) :|: 0 <= -1 - x19:0 + x20:0

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(11) IntTRSPeriodicNontermProof (COMPLETE)
Normalized system to the following form:
f(pc, x19:0, x20:0) -> f(1, x19:0, x20:0) :|: pc = 1 && 0 <= -1 - x19:0 + x20:0
Witness term starting non-terminating reduction: f(1, -6, 1)
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(12)
NO