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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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, 235 ms]
(4) IRSwT
(5) IntTRSCompressionProof [EQUIVALENT, 37 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, lt_8HAT0, lt_9HAT0, p_7HAT0, x_5HAT0, y_6HAT0) -> l1(Result_4HATpost, cnt_15HATpost, lt_8HATpost, lt_9HATpost, p_7HATpost, x_5HATpost, y_6HATpost) :|: y_6HAT0 = y_6HATpost && lt_9HAT0 = lt_9HATpost && lt_8HAT0 = lt_8HATpost && cnt_15HAT0 = cnt_15HATpost && Result_4HAT0 = Result_4HATpost && p_7HATpost = x_5HATpost && x_5HATpost = x_5HATpost
l1(x, x1, x2, x3, x4, x5, x6) -> l2(x7, x8, x9, x10, x11, x12, x13) :|: x14 = x1 && -1 * x14 + x6 <= 0 && x10 = x10 && x7 = x7 && x1 = x8 && x2 = x9 && x4 = x11 && x5 = x12 && x6 = x13
l1(x15, x16, x17, x18, x19, x20, x21) -> l3(x22, x23, x24, x25, x26, x27, x28) :|: x29 = x16 && 0 <= -1 - x29 + x21 && x25 = x25 && x30 = x16 && x24 = x24 && x15 = x22 && x16 = x23 && x19 = x26 && x20 = x27 && x21 = x28
l3(x31, x32, x33, x34, x35, x36, x37) -> l1(x38, x39, x40, x41, x42, x43, x44) :|: x37 = x44 && x36 = x43 && x35 = x42 && x34 = x41 && x33 = x40 && x32 = x39 && x31 = x38
l4(x45, x46, x47, x48, x49, x50, x51) -> l0(x52, x53, x54, x55, x56, x57, x58) :|: x51 = x58 && x50 = x57 && x49 = x56 && x48 = x55 && x47 = x54 && x46 = x53 && x45 = x52
Start term: l4(Result_4HAT0, cnt_15HAT0, lt_8HAT0, lt_9HAT0, p_7HAT0, 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, lt_8HAT0, lt_9HAT0, p_7HAT0, x_5HAT0, y_6HAT0) -> l1(Result_4HATpost, cnt_15HATpost, lt_8HATpost, lt_9HATpost, p_7HATpost, x_5HATpost, y_6HATpost) :|: y_6HAT0 = y_6HATpost && lt_9HAT0 = lt_9HATpost && lt_8HAT0 = lt_8HATpost && cnt_15HAT0 = cnt_15HATpost && Result_4HAT0 = Result_4HATpost && p_7HATpost = x_5HATpost && x_5HATpost = x_5HATpost
l1(x, x1, x2, x3, x4, x5, x6) -> l2(x7, x8, x9, x10, x11, x12, x13) :|: x14 = x1 && -1 * x14 + x6 <= 0 && x10 = x10 && x7 = x7 && x1 = x8 && x2 = x9 && x4 = x11 && x5 = x12 && x6 = x13
l1(x15, x16, x17, x18, x19, x20, x21) -> l3(x22, x23, x24, x25, x26, x27, x28) :|: x29 = x16 && 0 <= -1 - x29 + x21 && x25 = x25 && x30 = x16 && x24 = x24 && x15 = x22 && x16 = x23 && x19 = x26 && x20 = x27 && x21 = x28
l3(x31, x32, x33, x34, x35, x36, x37) -> l1(x38, x39, x40, x41, x42, x43, x44) :|: x37 = x44 && x36 = x43 && x35 = x42 && x34 = x41 && x33 = x40 && x32 = x39 && x31 = x38
l4(x45, x46, x47, x48, x49, x50, x51) -> l0(x52, x53, x54, x55, x56, x57, x58) :|: x51 = x58 && x50 = x57 && x49 = x56 && x48 = x55 && x47 = x54 && x46 = x53 && x45 = x52
Start term: l4(Result_4HAT0, cnt_15HAT0, lt_8HAT0, lt_9HAT0, p_7HAT0, x_5HAT0, y_6HAT0)

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(3) IRSwTTerminationDigraphProof (EQUIVALENT)
Constructed termination digraph!
Nodes:
(1) l0(Result_4HAT0, cnt_15HAT0, lt_8HAT0, lt_9HAT0, p_7HAT0, x_5HAT0, y_6HAT0) -> l1(Result_4HATpost, cnt_15HATpost, lt_8HATpost, lt_9HATpost, p_7HATpost, x_5HATpost, y_6HATpost) :|: y_6HAT0 = y_6HATpost && lt_9HAT0 = lt_9HATpost && lt_8HAT0 = lt_8HATpost && cnt_15HAT0 = cnt_15HATpost && Result_4HAT0 = Result_4HATpost && p_7HATpost = x_5HATpost && x_5HATpost = x_5HATpost
(2) l1(x, x1, x2, x3, x4, x5, x6) -> l2(x7, x8, x9, x10, x11, x12, x13) :|: x14 = x1 && -1 * x14 + x6 <= 0 && x10 = x10 && x7 = x7 && x1 = x8 && x2 = x9 && x4 = x11 && x5 = x12 && x6 = x13
(3) l1(x15, x16, x17, x18, x19, x20, x21) -> l3(x22, x23, x24, x25, x26, x27, x28) :|: x29 = x16 && 0 <= -1 - x29 + x21 && x25 = x25 && x30 = x16 && x24 = x24 && x15 = x22 && x16 = x23 && x19 = x26 && x20 = x27 && x21 = x28
(4) l3(x31, x32, x33, x34, x35, x36, x37) -> l1(x38, x39, x40, x41, x42, x43, x44) :|: x37 = x44 && x36 = x43 && x35 = x42 && x34 = x41 && x33 = x40 && x32 = x39 && x31 = x38
(5) l4(x45, x46, x47, x48, x49, x50, x51) -> l0(x52, x53, x54, x55, x56, x57, x58) :|: x51 = x58 && x50 = x57 && x49 = x56 && x48 = x55 && x47 = x54 && x46 = x53 && x45 = x52

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(x15, x16, x17, x18, x19, x20, x21) -> l3(x22, x23, x24, x25, x26, x27, x28) :|: x29 = x16 && 0 <= -1 - x29 + x21 && x25 = x25 && x30 = x16 && x24 = x24 && x15 = x22 && x16 = x23 && x19 = x26 && x20 = x27 && x21 = x28
(2) l3(x31, x32, x33, x34, x35, x36, x37) -> l1(x38, x39, x40, x41, x42, x43, x44) :|: x37 = x44 && x36 = x43 && x35 = x42 && x34 = x41 && x33 = x40 && x32 = x39 && x31 = x38

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(x15:0, x16:0, x17:0, x18:0, x19:0, x20:0, x21:0) -> l1(x15:0, x16:0, x24:0, x25:0, x19:0, x20:0, x21:0) :|: 0 <= -1 - x16:0 + x21:0

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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) -> l1(x2, x7)

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(8)
Obligation:
Rules:
l1(x16:0, x21:0) -> l1(x16:0, x21:0) :|: 0 <= -1 - x16:0 + x21:0

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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(x16:0, x21:0) -> l1(x16:0, x21:0) :|: 0 <= -1 - x16:0 + x21:0

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(11) IntTRSPeriodicNontermProof (COMPLETE)
Normalized system to the following form:
f(pc, x16:0, x21:0) -> f(1, x16:0, x21:0) :|: pc = 1 && 0 <= -1 - x16:0 + x21:0
Witness term starting non-terminating reduction: f(1, -6, 1)
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(12)
NO