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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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, 236 ms]
(4) IRSwT
(5) IntTRSCompressionProof [EQUIVALENT, 0 ms]
(6) IRSwT
(7) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms]
(8) IRSwT
(9) FilterProof [EQUIVALENT, 3 ms]
(10) IntTRS
(11) IntTRSPeriodicNontermProof [COMPLETE, 0 ms]
(12) NO


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(0)
Obligation:
Rules:
l0(Result_4HAT0, cnt_15HAT0, lt_9HAT0, p_8HAT0, x_5HAT0, y_6HAT0, z_7HAT0) -> l1(Result_4HATpost, cnt_15HATpost, lt_9HATpost, p_8HATpost, x_5HATpost, y_6HATpost, z_7HATpost) :|: z_7HAT0 = z_7HATpost && y_6HAT0 = y_6HATpost && x_5HAT0 = x_5HATpost && p_8HAT0 = p_8HATpost && lt_9HAT0 = lt_9HATpost && cnt_15HAT0 = cnt_15HATpost && Result_4HATpost = Result_4HATpost && -1 * x_5HAT0 + y_6HAT0 <= 0
l0(x, x1, x2, x3, x4, x5, x6) -> l2(x7, x8, x9, x10, x11, x12, x13) :|: 0 <= -1 - x4 + x5 && x14 = x1 && x9 = x9 && x = x7 && x1 = x8 && x3 = x10 && x4 = x11 && x5 = x12 && x6 = x13
l2(x15, x16, x17, x18, x19, x20, x21) -> l0(x22, x23, x24, x25, x26, x27, x28) :|: x21 = x28 && x20 = x27 && x19 = x26 && x18 = x25 && x17 = x24 && x16 = x23 && x15 = x22
l3(x29, x30, x31, x32, x33, x34, x35) -> l0(x36, x37, x38, x39, x40, x41, x42) :|: x34 = x41 && x33 = x40 && x31 = x38 && x30 = x37 && x29 = x36 && x39 = x42 && x42 = x42
l4(x43, x44, x45, x46, x47, x48, x49) -> l3(x50, x51, x52, x53, x54, x55, x56) :|: x49 = x56 && x48 = x55 && x47 = x54 && x46 = x53 && x45 = x52 && x44 = x51 && x43 = x50
Start term: l4(Result_4HAT0, cnt_15HAT0, lt_9HAT0, p_8HAT0, x_5HAT0, y_6HAT0, z_7HAT0)

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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_9HAT0, p_8HAT0, x_5HAT0, y_6HAT0, z_7HAT0) -> l1(Result_4HATpost, cnt_15HATpost, lt_9HATpost, p_8HATpost, x_5HATpost, y_6HATpost, z_7HATpost) :|: z_7HAT0 = z_7HATpost && y_6HAT0 = y_6HATpost && x_5HAT0 = x_5HATpost && p_8HAT0 = p_8HATpost && lt_9HAT0 = lt_9HATpost && cnt_15HAT0 = cnt_15HATpost && Result_4HATpost = Result_4HATpost && -1 * x_5HAT0 + y_6HAT0 <= 0
l0(x, x1, x2, x3, x4, x5, x6) -> l2(x7, x8, x9, x10, x11, x12, x13) :|: 0 <= -1 - x4 + x5 && x14 = x1 && x9 = x9 && x = x7 && x1 = x8 && x3 = x10 && x4 = x11 && x5 = x12 && x6 = x13
l2(x15, x16, x17, x18, x19, x20, x21) -> l0(x22, x23, x24, x25, x26, x27, x28) :|: x21 = x28 && x20 = x27 && x19 = x26 && x18 = x25 && x17 = x24 && x16 = x23 && x15 = x22
l3(x29, x30, x31, x32, x33, x34, x35) -> l0(x36, x37, x38, x39, x40, x41, x42) :|: x34 = x41 && x33 = x40 && x31 = x38 && x30 = x37 && x29 = x36 && x39 = x42 && x42 = x42
l4(x43, x44, x45, x46, x47, x48, x49) -> l3(x50, x51, x52, x53, x54, x55, x56) :|: x49 = x56 && x48 = x55 && x47 = x54 && x46 = x53 && x45 = x52 && x44 = x51 && x43 = x50
Start term: l4(Result_4HAT0, cnt_15HAT0, lt_9HAT0, p_8HAT0, x_5HAT0, y_6HAT0, z_7HAT0)

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(3) IRSwTTerminationDigraphProof (EQUIVALENT)
Constructed termination digraph!
Nodes:
(1) l0(Result_4HAT0, cnt_15HAT0, lt_9HAT0, p_8HAT0, x_5HAT0, y_6HAT0, z_7HAT0) -> l1(Result_4HATpost, cnt_15HATpost, lt_9HATpost, p_8HATpost, x_5HATpost, y_6HATpost, z_7HATpost) :|: z_7HAT0 = z_7HATpost && y_6HAT0 = y_6HATpost && x_5HAT0 = x_5HATpost && p_8HAT0 = p_8HATpost && lt_9HAT0 = lt_9HATpost && cnt_15HAT0 = cnt_15HATpost && Result_4HATpost = Result_4HATpost && -1 * x_5HAT0 + y_6HAT0 <= 0
(2) l0(x, x1, x2, x3, x4, x5, x6) -> l2(x7, x8, x9, x10, x11, x12, x13) :|: 0 <= -1 - x4 + x5 && x14 = x1 && x9 = x9 && x = x7 && x1 = x8 && x3 = x10 && x4 = x11 && x5 = x12 && x6 = x13
(3) l2(x15, x16, x17, x18, x19, x20, x21) -> l0(x22, x23, x24, x25, x26, x27, x28) :|: x21 = x28 && x20 = x27 && x19 = x26 && x18 = x25 && x17 = x24 && x16 = x23 && x15 = x22
(4) l3(x29, x30, x31, x32, x33, x34, x35) -> l0(x36, x37, x38, x39, x40, x41, x42) :|: x34 = x41 && x33 = x40 && x31 = x38 && x30 = x37 && x29 = x36 && x39 = x42 && x42 = x42
(5) l4(x43, x44, x45, x46, x47, x48, x49) -> l3(x50, x51, x52, x53, x54, x55, x56) :|: x49 = x56 && x48 = x55 && x47 = x54 && x46 = x53 && x45 = x52 && x44 = x51 && x43 = x50

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

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(x22:0, x14:0, x2:0, x10:0, x11:0, x12:0, x13:0) -> l0(x22:0, x14:0, x24:0, x10:0, x11:0, x12:0, x13:0) :|: 0 <= -1 - x11:0 + x12:0

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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) -> l0(x5, x6)

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(8)
Obligation:
Rules:
l0(x11:0, x12:0) -> l0(x11:0, x12:0) :|: 0 <= -1 - x11:0 + x12:0

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(9) FilterProof (EQUIVALENT)
Used the following sort dictionary for filtering: 
l0(INTEGER, INTEGER)
Replaced non-predefined constructor symbols by 0.
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(10)
Obligation:
Rules:
l0(x11:0, x12:0) -> l0(x11:0, x12:0) :|: 0 <= -1 - x11:0 + x12:0

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(11) IntTRSPeriodicNontermProof (COMPLETE)
Normalized system to the following form:
f(pc, x11:0, x12:0) -> f(1, x11:0, x12:0) :|: pc = 1 && 0 <= -1 - x11:0 + x12:0
Witness term starting non-terminating reduction: f(1, -6, 1)
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(12)
NO