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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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, 338 ms]
(4) IRSwT
(5) IntTRSCompressionProof [EQUIVALENT, 29 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_29HAT0, lt_10HAT0, lt_11HAT0, lt_12HAT0, px_8HAT0, py_6HAT0, q_9HAT0, x_7HAT0, y_5HAT0) -> l1(Result_4HATpost, cnt_29HATpost, lt_10HATpost, lt_11HATpost, lt_12HATpost, px_8HATpost, py_6HATpost, q_9HATpost, x_7HATpost, y_5HATpost) :|: lt_11HAT1 = x_7HAT0 && lt_12HAT1 = cnt_29HAT0 && 0 <= -1 + lt_12HAT1 && lt_11HATpost = lt_11HATpost && lt_12HATpost = lt_12HATpost && lt_10HAT1 = cnt_29HAT0 && lt_10HATpost = lt_10HATpost && Result_4HAT0 = Result_4HATpost && cnt_29HAT0 = cnt_29HATpost && px_8HAT0 = px_8HATpost && py_6HAT0 = py_6HATpost && q_9HAT0 = q_9HATpost && x_7HAT0 = x_7HATpost && y_5HAT0 = y_5HATpost
l1(x, x1, x2, x3, x4, x5, x6, x7, x8, x9) -> l0(x10, x11, x12, x13, x14, x15, x16, x17, x18, x19) :|: x9 = x19 && x8 = x18 && x7 = x17 && x6 = x16 && x5 = x15 && x4 = x14 && x3 = x13 && x2 = x12 && x1 = x11 && x = x10
l0(x20, x21, x22, x23, x24, x25, x26, x27, x28, x29) -> l2(x30, x31, x32, x33, x34, x35, x36, x37, x38, x39) :|: x40 = x28 && x41 = x21 && x41 <= 0 && x33 = x33 && x34 = x34 && x30 = x30 && x21 = x31 && x22 = x32 && x25 = x35 && x26 = x36 && x27 = x37 && x28 = x38 && x29 = x39
l3(x42, x43, x44, x45, x46, x47, x48, x49, x50, x51) -> l0(x52, x53, x54, x55, x56, x57, x58, x59, x60, x61) :|: x46 = x56 && x45 = x55 && x44 = x54 && x43 = x53 && x42 = x52 && x59 = x57 && x58 = x61 && x61 = x61 && x60 = x60 && x57 = x57
l4(x62, x63, x64, x65, x66, x67, x68, x69, x70, x71) -> l3(x72, x73, x74, x75, x76, x77, x78, x79, x80, x81) :|: x71 = x81 && x70 = x80 && x69 = x79 && x68 = x78 && x67 = x77 && x66 = x76 && x65 = x75 && x64 = x74 && x63 = x73 && x62 = x72
Start term: l4(Result_4HAT0, cnt_29HAT0, 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_29HAT0, lt_10HAT0, lt_11HAT0, lt_12HAT0, px_8HAT0, py_6HAT0, q_9HAT0, x_7HAT0, y_5HAT0) -> l1(Result_4HATpost, cnt_29HATpost, lt_10HATpost, lt_11HATpost, lt_12HATpost, px_8HATpost, py_6HATpost, q_9HATpost, x_7HATpost, y_5HATpost) :|: lt_11HAT1 = x_7HAT0 && lt_12HAT1 = cnt_29HAT0 && 0 <= -1 + lt_12HAT1 && lt_11HATpost = lt_11HATpost && lt_12HATpost = lt_12HATpost && lt_10HAT1 = cnt_29HAT0 && lt_10HATpost = lt_10HATpost && Result_4HAT0 = Result_4HATpost && cnt_29HAT0 = cnt_29HATpost && px_8HAT0 = px_8HATpost && py_6HAT0 = py_6HATpost && q_9HAT0 = q_9HATpost && x_7HAT0 = x_7HATpost && y_5HAT0 = y_5HATpost
l1(x, x1, x2, x3, x4, x5, x6, x7, x8, x9) -> l0(x10, x11, x12, x13, x14, x15, x16, x17, x18, x19) :|: x9 = x19 && x8 = x18 && x7 = x17 && x6 = x16 && x5 = x15 && x4 = x14 && x3 = x13 && x2 = x12 && x1 = x11 && x = x10
l0(x20, x21, x22, x23, x24, x25, x26, x27, x28, x29) -> l2(x30, x31, x32, x33, x34, x35, x36, x37, x38, x39) :|: x40 = x28 && x41 = x21 && x41 <= 0 && x33 = x33 && x34 = x34 && x30 = x30 && x21 = x31 && x22 = x32 && x25 = x35 && x26 = x36 && x27 = x37 && x28 = x38 && x29 = x39
l3(x42, x43, x44, x45, x46, x47, x48, x49, x50, x51) -> l0(x52, x53, x54, x55, x56, x57, x58, x59, x60, x61) :|: x46 = x56 && x45 = x55 && x44 = x54 && x43 = x53 && x42 = x52 && x59 = x57 && x58 = x61 && x61 = x61 && x60 = x60 && x57 = x57
l4(x62, x63, x64, x65, x66, x67, x68, x69, x70, x71) -> l3(x72, x73, x74, x75, x76, x77, x78, x79, x80, x81) :|: x71 = x81 && x70 = x80 && x69 = x79 && x68 = x78 && x67 = x77 && x66 = x76 && x65 = x75 && x64 = x74 && x63 = x73 && x62 = x72
Start term: l4(Result_4HAT0, cnt_29HAT0, 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_29HAT0, lt_10HAT0, lt_11HAT0, lt_12HAT0, px_8HAT0, py_6HAT0, q_9HAT0, x_7HAT0, y_5HAT0) -> l1(Result_4HATpost, cnt_29HATpost, lt_10HATpost, lt_11HATpost, lt_12HATpost, px_8HATpost, py_6HATpost, q_9HATpost, x_7HATpost, y_5HATpost) :|: lt_11HAT1 = x_7HAT0 && lt_12HAT1 = cnt_29HAT0 && 0 <= -1 + lt_12HAT1 && lt_11HATpost = lt_11HATpost && lt_12HATpost = lt_12HATpost && lt_10HAT1 = cnt_29HAT0 && lt_10HATpost = lt_10HATpost && Result_4HAT0 = Result_4HATpost && cnt_29HAT0 = cnt_29HATpost && px_8HAT0 = px_8HATpost && py_6HAT0 = py_6HATpost && q_9HAT0 = q_9HATpost && x_7HAT0 = x_7HATpost && y_5HAT0 = y_5HATpost
(2) l1(x, x1, x2, x3, x4, x5, x6, x7, x8, x9) -> l0(x10, x11, x12, x13, x14, x15, x16, x17, x18, x19) :|: x9 = x19 && x8 = x18 && x7 = x17 && x6 = x16 && x5 = x15 && x4 = x14 && x3 = x13 && x2 = x12 && x1 = x11 && x = x10
(3) l0(x20, x21, x22, x23, x24, x25, x26, x27, x28, x29) -> l2(x30, x31, x32, x33, x34, x35, x36, x37, x38, x39) :|: x40 = x28 && x41 = x21 && x41 <= 0 && x33 = x33 && x34 = x34 && x30 = x30 && x21 = x31 && x22 = x32 && x25 = x35 && x26 = x36 && x27 = x37 && x28 = x38 && x29 = x39
(4) l3(x42, x43, x44, x45, x46, x47, x48, x49, x50, x51) -> l0(x52, x53, x54, x55, x56, x57, x58, x59, x60, x61) :|: x46 = x56 && x45 = x55 && x44 = x54 && x43 = x53 && x42 = x52 && x59 = x57 && x58 = x61 && x61 = x61 && x60 = x60 && x57 = x57
(5) l4(x62, x63, x64, x65, x66, x67, x68, x69, x70, x71) -> l3(x72, x73, x74, x75, x76, x77, x78, x79, x80, x81) :|: x71 = x81 && x70 = x80 && x69 = x79 && x68 = x78 && x67 = x77 && x66 = x76 && x65 = x75 && x64 = x74 && x63 = x73 && x62 = x72

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

This digraph is fully evaluated!
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(4)
Obligation:

Termination digraph:
Nodes:
(1) l0(Result_4HAT0, cnt_29HAT0, lt_10HAT0, lt_11HAT0, lt_12HAT0, px_8HAT0, py_6HAT0, q_9HAT0, x_7HAT0, y_5HAT0) -> l1(Result_4HATpost, cnt_29HATpost, lt_10HATpost, lt_11HATpost, lt_12HATpost, px_8HATpost, py_6HATpost, q_9HATpost, x_7HATpost, y_5HATpost) :|: lt_11HAT1 = x_7HAT0 && lt_12HAT1 = cnt_29HAT0 && 0 <= -1 + lt_12HAT1 && lt_11HATpost = lt_11HATpost && lt_12HATpost = lt_12HATpost && lt_10HAT1 = cnt_29HAT0 && lt_10HATpost = lt_10HATpost && Result_4HAT0 = Result_4HATpost && cnt_29HAT0 = cnt_29HATpost && px_8HAT0 = px_8HATpost && py_6HAT0 = py_6HATpost && q_9HAT0 = q_9HATpost && x_7HAT0 = x_7HATpost && y_5HAT0 = y_5HATpost
(2) l1(x, x1, x2, x3, x4, x5, x6, x7, x8, x9) -> l0(x10, x11, x12, x13, x14, x15, x16, x17, x18, x19) :|: x9 = x19 && x8 = x18 && x7 = x17 && x6 = x16 && x5 = x15 && x4 = x14 && x3 = x13 && x2 = x12 && x1 = x11 && x = x10

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(Result_4HAT0:0, cnt_29HAT0:0, lt_10HAT0:0, lt_11HAT0:0, lt_12HAT0:0, px_8HAT0:0, py_6HAT0:0, q_9HAT0:0, lt_11HAT1:0, x19:0) -> l0(Result_4HAT0:0, cnt_29HAT0:0, lt_10HATpost:0, lt_11HATpost:0, lt_12HATpost:0, px_8HAT0:0, py_6HAT0:0, q_9HAT0:0, lt_11HAT1:0, x19:0) :|: cnt_29HAT0:0 > 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, x9, x10) -> l0(x2)

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(8)
Obligation:
Rules:
l0(cnt_29HAT0:0) -> l0(cnt_29HAT0:0) :|: cnt_29HAT0:0 > 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(cnt_29HAT0:0) -> l0(cnt_29HAT0:0) :|: cnt_29HAT0:0 > 0

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(11) IntTRSPeriodicNontermProof (COMPLETE)
Normalized system to the following form:
f(pc, cnt_29HAT0:0) -> f(1, cnt_29HAT0:0) :|: pc = 1 && cnt_29HAT0:0 > 0
Witness term starting non-terminating reduction: f(1, 1)
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(12)
NO