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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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, 417 ms]
(4) IRSwT
(5) IntTRSCompressionProof [EQUIVALENT, 51 ms]
(6) IRSwT
(7) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms]
(8) IRSwT
(9) FilterProof [EQUIVALENT, 0 ms]
(10) IntTRS
(11) IntTRSNonPeriodicNontermProof [COMPLETE, 5 ms]
(12) NO


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(0)
Obligation:
Rules:
l0(Result_4HAT0, ct_10HAT0, ct_11HAT0, ct_19HAT0, ct_25HAT0, lt_7HAT0, lt_8HAT0, lt_9HAT0, x_5HAT0, y_6HAT0) -> l1(Result_4HATpost, ct_10HATpost, ct_11HATpost, ct_19HATpost, ct_25HATpost, lt_7HATpost, lt_8HATpost, lt_9HATpost, x_5HATpost, y_6HATpost) :|: y_6HATpost = y_6HATpost && x_5HATpost = x_5HATpost && ct_11HAT1 = ct_11HAT1 && ct_11HATpost = ct_11HATpost && ct_10HAT1 = ct_10HAT1 && ct_10HATpost = ct_10HATpost && Result_4HAT0 = Result_4HATpost && ct_19HAT0 = ct_19HATpost && ct_25HAT0 = ct_25HATpost && lt_7HAT0 = lt_7HATpost && lt_8HAT0 = lt_8HATpost && lt_9HAT0 = lt_9HATpost
l1(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 && -1 * x20 + x21 <= 0 && x16 = x16 && x17 = x17 && x10 = x10 && x1 = x11 && x2 = x12 && x3 = x13 && x4 = x14 && x5 = x15 && x8 = x18 && x9 = x19
l1(x22, x23, x24, x25, x26, x27, x28, x29, x30, x31) -> l3(x32, x33, x34, x35, x36, x37, x38, x39, x40, x41) :|: x42 = x25 && x43 = x26 && 0 <= -1 - x42 + x43 && x38 = x38 && x39 = x39 && x44 = x25 && x37 = x37 && x22 = x32 && x23 = x33 && x24 = x34 && x25 = x35 && x26 = x36 && x30 = x40 && x31 = x41
l3(x45, x46, x47, x48, x49, x50, x51, x52, x53, x54) -> l1(x55, x56, x57, x58, x59, x60, x61, x62, x63, x64) :|: x54 = x64 && x53 = x63 && x52 = x62 && x51 = x61 && x50 = x60 && x49 = x59 && x48 = x58 && x47 = x57 && x46 = x56 && x45 = x55
l4(x65, x66, x67, x68, x69, x70, x71, x72, x73, x74) -> l0(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_10HAT0, ct_11HAT0, ct_19HAT0, ct_25HAT0, 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, ct_10HAT0, ct_11HAT0, ct_19HAT0, ct_25HAT0, lt_7HAT0, lt_8HAT0, lt_9HAT0, x_5HAT0, y_6HAT0) -> l1(Result_4HATpost, ct_10HATpost, ct_11HATpost, ct_19HATpost, ct_25HATpost, lt_7HATpost, lt_8HATpost, lt_9HATpost, x_5HATpost, y_6HATpost) :|: y_6HATpost = y_6HATpost && x_5HATpost = x_5HATpost && ct_11HAT1 = ct_11HAT1 && ct_11HATpost = ct_11HATpost && ct_10HAT1 = ct_10HAT1 && ct_10HATpost = ct_10HATpost && Result_4HAT0 = Result_4HATpost && ct_19HAT0 = ct_19HATpost && ct_25HAT0 = ct_25HATpost && lt_7HAT0 = lt_7HATpost && lt_8HAT0 = lt_8HATpost && lt_9HAT0 = lt_9HATpost
l1(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 && -1 * x20 + x21 <= 0 && x16 = x16 && x17 = x17 && x10 = x10 && x1 = x11 && x2 = x12 && x3 = x13 && x4 = x14 && x5 = x15 && x8 = x18 && x9 = x19
l1(x22, x23, x24, x25, x26, x27, x28, x29, x30, x31) -> l3(x32, x33, x34, x35, x36, x37, x38, x39, x40, x41) :|: x42 = x25 && x43 = x26 && 0 <= -1 - x42 + x43 && x38 = x38 && x39 = x39 && x44 = x25 && x37 = x37 && x22 = x32 && x23 = x33 && x24 = x34 && x25 = x35 && x26 = x36 && x30 = x40 && x31 = x41
l3(x45, x46, x47, x48, x49, x50, x51, x52, x53, x54) -> l1(x55, x56, x57, x58, x59, x60, x61, x62, x63, x64) :|: x54 = x64 && x53 = x63 && x52 = x62 && x51 = x61 && x50 = x60 && x49 = x59 && x48 = x58 && x47 = x57 && x46 = x56 && x45 = x55
l4(x65, x66, x67, x68, x69, x70, x71, x72, x73, x74) -> l0(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_10HAT0, ct_11HAT0, ct_19HAT0, ct_25HAT0, 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, ct_10HAT0, ct_11HAT0, ct_19HAT0, ct_25HAT0, lt_7HAT0, lt_8HAT0, lt_9HAT0, x_5HAT0, y_6HAT0) -> l1(Result_4HATpost, ct_10HATpost, ct_11HATpost, ct_19HATpost, ct_25HATpost, lt_7HATpost, lt_8HATpost, lt_9HATpost, x_5HATpost, y_6HATpost) :|: y_6HATpost = y_6HATpost && x_5HATpost = x_5HATpost && ct_11HAT1 = ct_11HAT1 && ct_11HATpost = ct_11HATpost && ct_10HAT1 = ct_10HAT1 && ct_10HATpost = ct_10HATpost && Result_4HAT0 = Result_4HATpost && ct_19HAT0 = ct_19HATpost && ct_25HAT0 = ct_25HATpost && lt_7HAT0 = lt_7HATpost && lt_8HAT0 = lt_8HATpost && lt_9HAT0 = lt_9HATpost
(2) l1(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 && -1 * x20 + x21 <= 0 && x16 = x16 && x17 = x17 && x10 = x10 && x1 = x11 && x2 = x12 && x3 = x13 && x4 = x14 && x5 = x15 && x8 = x18 && x9 = x19
(3) l1(x22, x23, x24, x25, x26, x27, x28, x29, x30, x31) -> l3(x32, x33, x34, x35, x36, x37, x38, x39, x40, x41) :|: x42 = x25 && x43 = x26 && 0 <= -1 - x42 + x43 && x38 = x38 && x39 = x39 && x44 = x25 && x37 = x37 && x22 = x32 && x23 = x33 && x24 = x34 && x25 = x35 && x26 = x36 && x30 = x40 && x31 = x41
(4) l3(x45, x46, x47, x48, x49, x50, x51, x52, x53, x54) -> l1(x55, x56, x57, x58, x59, x60, x61, x62, x63, x64) :|: x54 = x64 && x53 = x63 && x52 = x62 && x51 = x61 && x50 = x60 && x49 = x59 && x48 = x58 && x47 = x57 && x46 = x56 && x45 = x55
(5) l4(x65, x66, x67, x68, x69, x70, x71, x72, x73, x74) -> l0(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:
(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(x22, x23, x24, x25, x26, x27, x28, x29, x30, x31) -> l3(x32, x33, x34, x35, x36, x37, x38, x39, x40, x41) :|: x42 = x25 && x43 = x26 && 0 <= -1 - x42 + x43 && x38 = x38 && x39 = x39 && x44 = x25 && x37 = x37 && x22 = x32 && x23 = x33 && x24 = x34 && x25 = x35 && x26 = x36 && x30 = x40 && x31 = x41
(2) l3(x45, x46, x47, x48, x49, x50, x51, x52, x53, x54) -> l1(x55, x56, x57, x58, x59, x60, x61, x62, x63, x64) :|: x54 = x64 && x53 = x63 && x52 = x62 && x51 = x61 && x50 = x60 && x49 = x59 && x48 = x58 && x47 = x57 && x46 = x56 && x45 = x55

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(x22:0, x23:0, x24:0, x25:0, x26:0, x27:0, x28:0, x29:0, x30:0, x31:0) -> l1(x22:0, x23:0, x24:0, x25:0, x26:0, x37:0, x38:0, x39:0, x30:0, x31:0) :|: 0 <= -1 - x25:0 + x26:0

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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, x9, x10) -> l1(x4, x5)

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(8)
Obligation:
Rules:
l1(x25:0, x26:0) -> l1(x25:0, x26:0) :|: 0 <= -1 - x25:0 + x26:0

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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(x25:0, x26:0) -> l1(x25:0, x26:0) :|: 0 <= -1 - x25:0 + x26:0

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(11) IntTRSNonPeriodicNontermProof (COMPLETE)
Normalized system to the following form:
f(pc, x25:0, x26:0) -> f(1, x25:0, x26:0) :|: pc = 1 && 0 <= -1 - x25:0 + x26:0
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