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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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, 335 ms]
(4) IRSwT
(5) IntTRSCompressionProof [EQUIVALENT, 45 ms]
(6) IRSwT
(7) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms]
(8) IRSwT
(9) FilterProof [EQUIVALENT, 0 ms]
(10) IntTRS
(11) IntTRSNonPeriodicNontermProof [COMPLETE, 0 ms]
(12) NO


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(0)
Obligation:
Rules:
l0(Result_4HAT0, ct_12HAT0, ct_13HAT0, ct_21HAT0, ct_27HAT0, lt_10HAT0, lt_11HAT0, lt_9HAT0, x_5HAT0, y_6HAT0) -> l1(Result_4HATpost, ct_12HATpost, ct_13HATpost, ct_21HATpost, ct_27HATpost, lt_10HATpost, lt_11HATpost, lt_9HATpost, x_5HATpost, y_6HATpost) :|: lt_10HAT1 = ct_21HAT0 && lt_11HAT1 = ct_27HAT0 && -1 * lt_10HAT1 + lt_11HAT1 <= 0 && lt_10HATpost = lt_10HATpost && lt_11HATpost = lt_11HATpost && Result_4HATpost = Result_4HATpost && ct_12HAT0 = ct_12HATpost && ct_13HAT0 = ct_13HATpost && ct_21HAT0 = ct_21HATpost && ct_27HAT0 = ct_27HATpost && lt_9HAT0 = lt_9HATpost && x_5HAT0 = x_5HATpost && y_6HAT0 = y_6HATpost
l0(x, x1, x2, x3, x4, x5, x6, x7, x8, x9) -> l2(x10, x11, x12, x13, x14, x15, x16, x17, x18, x19) :|: x20 = x3 && x21 = x4 && 0 <= -1 - x20 + x21 && x15 = x15 && x16 = x16 && x22 = x3 && x17 = x17 && x = x10 && x1 = x11 && x2 = x12 && x3 = x13 && x4 = x14 && x8 = x18 && x9 = x19
l2(x23, x24, x25, x26, x27, x28, x29, x30, x31, x32) -> l0(x33, x34, x35, x36, x37, x38, x39, x40, x41, x42) :|: x32 = x42 && x31 = x41 && x30 = x40 && x29 = x39 && x28 = x38 && x27 = x37 && x26 = x36 && x25 = x35 && x24 = x34 && x23 = x33
l3(x43, x44, x45, x46, x47, x48, x49, x50, x51, x52) -> l0(x53, x54, x55, x56, x57, x58, x59, x60, x61, x62) :|: x62 = x62 && x61 = x61 && x63 = x63 && x55 = x55 && x64 = x64 && x54 = x54 && x43 = x53 && x46 = x56 && x47 = x57 && x48 = x58 && x49 = x59 && x50 = x60
l4(x65, x66, x67, x68, x69, x70, x71, x72, x73, x74) -> l3(x75, x76, x77, x78, x79, x80, x81, x82, x83, x84) :|: x74 = x84 && x73 = x83 && x72 = x82 && x71 = x81 && x70 = x80 && x69 = x79 && x68 = x78 && x67 = x77 && x66 = x76 && x65 = x75
Start term: l4(Result_4HAT0, ct_12HAT0, ct_13HAT0, ct_21HAT0, ct_27HAT0, lt_10HAT0, lt_11HAT0, 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, ct_12HAT0, ct_13HAT0, ct_21HAT0, ct_27HAT0, lt_10HAT0, lt_11HAT0, lt_9HAT0, x_5HAT0, y_6HAT0) -> l1(Result_4HATpost, ct_12HATpost, ct_13HATpost, ct_21HATpost, ct_27HATpost, lt_10HATpost, lt_11HATpost, lt_9HATpost, x_5HATpost, y_6HATpost) :|: lt_10HAT1 = ct_21HAT0 && lt_11HAT1 = ct_27HAT0 && -1 * lt_10HAT1 + lt_11HAT1 <= 0 && lt_10HATpost = lt_10HATpost && lt_11HATpost = lt_11HATpost && Result_4HATpost = Result_4HATpost && ct_12HAT0 = ct_12HATpost && ct_13HAT0 = ct_13HATpost && ct_21HAT0 = ct_21HATpost && ct_27HAT0 = ct_27HATpost && lt_9HAT0 = lt_9HATpost && x_5HAT0 = x_5HATpost && y_6HAT0 = y_6HATpost
l0(x, x1, x2, x3, x4, x5, x6, x7, x8, x9) -> l2(x10, x11, x12, x13, x14, x15, x16, x17, x18, x19) :|: x20 = x3 && x21 = x4 && 0 <= -1 - x20 + x21 && x15 = x15 && x16 = x16 && x22 = x3 && x17 = x17 && x = x10 && x1 = x11 && x2 = x12 && x3 = x13 && x4 = x14 && x8 = x18 && x9 = x19
l2(x23, x24, x25, x26, x27, x28, x29, x30, x31, x32) -> l0(x33, x34, x35, x36, x37, x38, x39, x40, x41, x42) :|: x32 = x42 && x31 = x41 && x30 = x40 && x29 = x39 && x28 = x38 && x27 = x37 && x26 = x36 && x25 = x35 && x24 = x34 && x23 = x33
l3(x43, x44, x45, x46, x47, x48, x49, x50, x51, x52) -> l0(x53, x54, x55, x56, x57, x58, x59, x60, x61, x62) :|: x62 = x62 && x61 = x61 && x63 = x63 && x55 = x55 && x64 = x64 && x54 = x54 && x43 = x53 && x46 = x56 && x47 = x57 && x48 = x58 && x49 = x59 && x50 = x60
l4(x65, x66, x67, x68, x69, x70, x71, x72, x73, x74) -> l3(x75, x76, x77, x78, x79, x80, x81, x82, x83, x84) :|: x74 = x84 && x73 = x83 && x72 = x82 && x71 = x81 && x70 = x80 && x69 = x79 && x68 = x78 && x67 = x77 && x66 = x76 && x65 = x75
Start term: l4(Result_4HAT0, ct_12HAT0, ct_13HAT0, ct_21HAT0, ct_27HAT0, lt_10HAT0, lt_11HAT0, lt_9HAT0, x_5HAT0, y_6HAT0)

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(3) IRSwTTerminationDigraphProof (EQUIVALENT)
Constructed termination digraph!
Nodes:
(1) l0(Result_4HAT0, ct_12HAT0, ct_13HAT0, ct_21HAT0, ct_27HAT0, lt_10HAT0, lt_11HAT0, lt_9HAT0, x_5HAT0, y_6HAT0) -> l1(Result_4HATpost, ct_12HATpost, ct_13HATpost, ct_21HATpost, ct_27HATpost, lt_10HATpost, lt_11HATpost, lt_9HATpost, x_5HATpost, y_6HATpost) :|: lt_10HAT1 = ct_21HAT0 && lt_11HAT1 = ct_27HAT0 && -1 * lt_10HAT1 + lt_11HAT1 <= 0 && lt_10HATpost = lt_10HATpost && lt_11HATpost = lt_11HATpost && Result_4HATpost = Result_4HATpost && ct_12HAT0 = ct_12HATpost && ct_13HAT0 = ct_13HATpost && ct_21HAT0 = ct_21HATpost && ct_27HAT0 = ct_27HATpost && lt_9HAT0 = lt_9HATpost && x_5HAT0 = x_5HATpost && y_6HAT0 = y_6HATpost
(2) l0(x, x1, x2, x3, x4, x5, x6, x7, x8, x9) -> l2(x10, x11, x12, x13, x14, x15, x16, x17, x18, x19) :|: x20 = x3 && x21 = x4 && 0 <= -1 - x20 + x21 && x15 = x15 && x16 = x16 && x22 = x3 && x17 = x17 && x = x10 && x1 = x11 && x2 = x12 && x3 = x13 && x4 = x14 && x8 = x18 && x9 = x19
(3) l2(x23, x24, x25, x26, x27, x28, x29, x30, x31, x32) -> l0(x33, x34, x35, x36, x37, x38, x39, x40, x41, x42) :|: x32 = x42 && x31 = x41 && x30 = x40 && x29 = x39 && x28 = x38 && x27 = x37 && x26 = x36 && x25 = x35 && x24 = x34 && x23 = x33
(4) l3(x43, x44, x45, x46, x47, x48, x49, x50, x51, x52) -> l0(x53, x54, x55, x56, x57, x58, x59, x60, x61, x62) :|: x62 = x62 && x61 = x61 && x63 = x63 && x55 = x55 && x64 = x64 && x54 = x54 && x43 = x53 && x46 = x56 && x47 = x57 && x48 = x58 && x49 = x59 && x50 = x60
(5) l4(x65, x66, x67, x68, x69, x70, x71, x72, x73, x74) -> l3(x75, x76, x77, x78, x79, x80, x81, x82, x83, x84) :|: x74 = x84 && x73 = x83 && x72 = x82 && x71 = x81 && x70 = x80 && x69 = x79 && x68 = x78 && x67 = x77 && x66 = x76 && x65 = x75

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, x8, x9) -> l2(x10, x11, x12, x13, x14, x15, x16, x17, x18, x19) :|: x20 = x3 && x21 = x4 && 0 <= -1 - x20 + x21 && x15 = x15 && x16 = x16 && x22 = x3 && x17 = x17 && x = x10 && x1 = x11 && x2 = x12 && x3 = x13 && x4 = x14 && x8 = x18 && x9 = x19
(2) l2(x23, x24, x25, x26, x27, x28, x29, x30, x31, x32) -> l0(x33, x34, x35, x36, x37, x38, x39, x40, x41, x42) :|: x32 = x42 && x31 = x41 && x30 = x40 && x29 = x39 && x28 = x38 && x27 = x37 && x26 = x36 && x25 = x35 && x24 = x34 && x23 = x33

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(x10:0, x11:0, x12:0, x13:0, x14:0, x5:0, x6:0, x7:0, x18:0, x19:0) -> l0(x10:0, x11:0, x12:0, x13:0, x14:0, x15:0, x16:0, x17:0, x18:0, x19:0) :|: 0 <= -1 - x13:0 + x14:0

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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(x4, x5)

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(8)
Obligation:
Rules:
l0(x13:0, x14:0) -> l0(x13:0, x14:0) :|: 0 <= -1 - x13:0 + x14:0

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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(x13:0, x14:0) -> l0(x13:0, x14:0) :|: 0 <= -1 - x13:0 + x14:0

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(11) IntTRSNonPeriodicNontermProof (COMPLETE)
Normalized system to the following form:
f(pc, x13:0, x14:0) -> f(1, x13:0, x14:0) :|: pc = 1 && 0 <= -1 - x13:0 + x14:0
Proved unsatisfiability of the following formula, indicating that the system is never left after entering:
(((run2_0 = ((1 * 1)) and run2_1 = ((run1_1 * 1)) and run2_2 = ((run1_2 * 1))) and (((run1_0 * 1)) = ((1 * 1)) and 0 <= ((1 * -1) + (run1_1 * -1) + (run1_2 * 1)))) and !(((run2_0 * 1)) = ((1 * 1)) and 0 <= ((1 * -1) + (run2_1 * -1) + (run2_2 * 1))))
Proved satisfiability of the following formula, indicating that the system is entered at least once:
((run2_0 = ((1 * 1)) and run2_1 = ((run1_1 * 1)) and run2_2 = ((run1_2 * 1))) and (((run1_0 * 1)) = ((1 * 1)) and 0 <= ((1 * -1) + (run1_1 * -1) + (run1_2 * 1))))

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(12)
NO