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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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, 507 ms]
(4) IRSwT
(5) IntTRSCompressionProof [EQUIVALENT, 0 ms]
(6) IRSwT
(7) FilterProof [EQUIVALENT, 1 ms]
(8) IntTRS
(9) IntTRSNonPeriodicNontermProof [COMPLETE, 0 ms]
(10) NO


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(0)
Obligation:
Rules:
l0(Result_4HAT0, __disjvr_0HAT0, cnt_15HAT0, cnt_20HAT0, lt_7HAT0, lt_8HAT0, lt_9HAT0, x_5HAT0, y_6HAT0) -> l1(Result_4HATpost, __disjvr_0HATpost, cnt_15HATpost, cnt_20HATpost, lt_7HATpost, lt_8HATpost, lt_9HATpost, x_5HATpost, y_6HATpost) :|: lt_9HAT0 = lt_9HATpost && lt_8HAT0 = lt_8HATpost && lt_7HAT0 = lt_7HATpost && cnt_20HAT0 = cnt_20HATpost && cnt_15HAT0 = cnt_15HATpost && __disjvr_0HAT0 = __disjvr_0HATpost && Result_4HAT0 = Result_4HATpost && x_5HATpost = x_5HATpost && y_6HATpost = y_6HATpost
l1(x, x1, x2, x3, x4, x5, x6, x7, x8) -> l2(x9, x10, x11, x12, x13, x14, x15, x16, x17) :|: x18 = x2 && x19 = x3 && x18 <= x19 && x19 <= x18 && x14 = x14 && x15 = x15 && x9 = x9 && x1 = x10 && x2 = x11 && x3 = x12 && x4 = x13 && x7 = x16 && x8 = x17
l1(x20, x21, x22, x23, x24, x25, x26, x27, x28) -> l4(x29, x30, x31, x32, x33, x34, x35, x36, x37) :|: x28 = x37 && x27 = x36 && x24 = x33 && x23 = x32 && x22 = x31 && x21 = x30 && x20 = x29 && x35 = x23 && x34 = x22
l4(x38, x39, x40, x41, x42, x43, x44, x45, x46) -> l5(x47, x48, x49, x50, x51, x52, x53, x54, x55) :|: x46 = x55 && x45 = x54 && x44 = x53 && x43 = x52 && x42 = x51 && x41 = x50 && x40 = x49 && x39 = x48 && x38 = x47 && x48 = x39
l5(x56, x57, x58, x59, x60, x61, x62, x63, x64) -> l3(x65, x66, x67, x68, x69, x70, x71, x72, x73) :|: x70 = x70 && x71 = x71 && x74 = x58 && x69 = x69 && x56 = x65 && x57 = x66 && x58 = x67 && x59 = x68 && x63 = x72 && x64 = x73
l3(x75, x76, x77, x78, x79, x80, x81, x82, x83) -> l1(x84, x85, x86, x87, x88, x89, x90, x91, x92) :|: x83 = x92 && x82 = x91 && x81 = x90 && x80 = x89 && x79 = x88 && x78 = x87 && x77 = x86 && x76 = x85 && x75 = x84
l6(x93, x94, x95, x96, x97, x98, x99, x100, x101) -> l0(x102, x103, x104, x105, x106, x107, x108, x109, x110) :|: x101 = x110 && x100 = x109 && x99 = x108 && x98 = x107 && x97 = x106 && x96 = x105 && x95 = x104 && x94 = x103 && x93 = x102
Start term: l6(Result_4HAT0, __disjvr_0HAT0, cnt_15HAT0, cnt_20HAT0, 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, __disjvr_0HAT0, cnt_15HAT0, cnt_20HAT0, lt_7HAT0, lt_8HAT0, lt_9HAT0, x_5HAT0, y_6HAT0) -> l1(Result_4HATpost, __disjvr_0HATpost, cnt_15HATpost, cnt_20HATpost, lt_7HATpost, lt_8HATpost, lt_9HATpost, x_5HATpost, y_6HATpost) :|: lt_9HAT0 = lt_9HATpost && lt_8HAT0 = lt_8HATpost && lt_7HAT0 = lt_7HATpost && cnt_20HAT0 = cnt_20HATpost && cnt_15HAT0 = cnt_15HATpost && __disjvr_0HAT0 = __disjvr_0HATpost && Result_4HAT0 = Result_4HATpost && x_5HATpost = x_5HATpost && y_6HATpost = y_6HATpost
l1(x, x1, x2, x3, x4, x5, x6, x7, x8) -> l2(x9, x10, x11, x12, x13, x14, x15, x16, x17) :|: x18 = x2 && x19 = x3 && x18 <= x19 && x19 <= x18 && x14 = x14 && x15 = x15 && x9 = x9 && x1 = x10 && x2 = x11 && x3 = x12 && x4 = x13 && x7 = x16 && x8 = x17
l1(x20, x21, x22, x23, x24, x25, x26, x27, x28) -> l4(x29, x30, x31, x32, x33, x34, x35, x36, x37) :|: x28 = x37 && x27 = x36 && x24 = x33 && x23 = x32 && x22 = x31 && x21 = x30 && x20 = x29 && x35 = x23 && x34 = x22
l4(x38, x39, x40, x41, x42, x43, x44, x45, x46) -> l5(x47, x48, x49, x50, x51, x52, x53, x54, x55) :|: x46 = x55 && x45 = x54 && x44 = x53 && x43 = x52 && x42 = x51 && x41 = x50 && x40 = x49 && x39 = x48 && x38 = x47 && x48 = x39
l5(x56, x57, x58, x59, x60, x61, x62, x63, x64) -> l3(x65, x66, x67, x68, x69, x70, x71, x72, x73) :|: x70 = x70 && x71 = x71 && x74 = x58 && x69 = x69 && x56 = x65 && x57 = x66 && x58 = x67 && x59 = x68 && x63 = x72 && x64 = x73
l3(x75, x76, x77, x78, x79, x80, x81, x82, x83) -> l1(x84, x85, x86, x87, x88, x89, x90, x91, x92) :|: x83 = x92 && x82 = x91 && x81 = x90 && x80 = x89 && x79 = x88 && x78 = x87 && x77 = x86 && x76 = x85 && x75 = x84
l6(x93, x94, x95, x96, x97, x98, x99, x100, x101) -> l0(x102, x103, x104, x105, x106, x107, x108, x109, x110) :|: x101 = x110 && x100 = x109 && x99 = x108 && x98 = x107 && x97 = x106 && x96 = x105 && x95 = x104 && x94 = x103 && x93 = x102
Start term: l6(Result_4HAT0, __disjvr_0HAT0, cnt_15HAT0, cnt_20HAT0, 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, __disjvr_0HAT0, cnt_15HAT0, cnt_20HAT0, lt_7HAT0, lt_8HAT0, lt_9HAT0, x_5HAT0, y_6HAT0) -> l1(Result_4HATpost, __disjvr_0HATpost, cnt_15HATpost, cnt_20HATpost, lt_7HATpost, lt_8HATpost, lt_9HATpost, x_5HATpost, y_6HATpost) :|: lt_9HAT0 = lt_9HATpost && lt_8HAT0 = lt_8HATpost && lt_7HAT0 = lt_7HATpost && cnt_20HAT0 = cnt_20HATpost && cnt_15HAT0 = cnt_15HATpost && __disjvr_0HAT0 = __disjvr_0HATpost && Result_4HAT0 = Result_4HATpost && x_5HATpost = x_5HATpost && y_6HATpost = y_6HATpost
(2) l1(x, x1, x2, x3, x4, x5, x6, x7, x8) -> l2(x9, x10, x11, x12, x13, x14, x15, x16, x17) :|: x18 = x2 && x19 = x3 && x18 <= x19 && x19 <= x18 && x14 = x14 && x15 = x15 && x9 = x9 && x1 = x10 && x2 = x11 && x3 = x12 && x4 = x13 && x7 = x16 && x8 = x17
(3) l1(x20, x21, x22, x23, x24, x25, x26, x27, x28) -> l4(x29, x30, x31, x32, x33, x34, x35, x36, x37) :|: x28 = x37 && x27 = x36 && x24 = x33 && x23 = x32 && x22 = x31 && x21 = x30 && x20 = x29 && x35 = x23 && x34 = x22
(4) l4(x38, x39, x40, x41, x42, x43, x44, x45, x46) -> l5(x47, x48, x49, x50, x51, x52, x53, x54, x55) :|: x46 = x55 && x45 = x54 && x44 = x53 && x43 = x52 && x42 = x51 && x41 = x50 && x40 = x49 && x39 = x48 && x38 = x47 && x48 = x39
(5) l5(x56, x57, x58, x59, x60, x61, x62, x63, x64) -> l3(x65, x66, x67, x68, x69, x70, x71, x72, x73) :|: x70 = x70 && x71 = x71 && x74 = x58 && x69 = x69 && x56 = x65 && x57 = x66 && x58 = x67 && x59 = x68 && x63 = x72 && x64 = x73
(6) l3(x75, x76, x77, x78, x79, x80, x81, x82, x83) -> l1(x84, x85, x86, x87, x88, x89, x90, x91, x92) :|: x83 = x92 && x82 = x91 && x81 = x90 && x80 = x89 && x79 = x88 && x78 = x87 && x77 = x86 && x76 = x85 && x75 = x84
(7) l6(x93, x94, x95, x96, x97, x98, x99, x100, x101) -> l0(x102, x103, x104, x105, x106, x107, x108, x109, x110) :|: x101 = x110 && x100 = x109 && x99 = x108 && x98 = x107 && x97 = x106 && x96 = x105 && x95 = x104 && x94 = x103 && x93 = x102

Arcs:
(1) -> (2), (3)
(3) -> (4)
(4) -> (5)
(5) -> (6)
(6) -> (2), (3)
(7) -> (1)

This digraph is fully evaluated!
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(4)
Obligation:

Termination digraph:
Nodes:
(1) l1(x20, x21, x22, x23, x24, x25, x26, x27, x28) -> l4(x29, x30, x31, x32, x33, x34, x35, x36, x37) :|: x28 = x37 && x27 = x36 && x24 = x33 && x23 = x32 && x22 = x31 && x21 = x30 && x20 = x29 && x35 = x23 && x34 = x22
(2) l3(x75, x76, x77, x78, x79, x80, x81, x82, x83) -> l1(x84, x85, x86, x87, x88, x89, x90, x91, x92) :|: x83 = x92 && x82 = x91 && x81 = x90 && x80 = x89 && x79 = x88 && x78 = x87 && x77 = x86 && x76 = x85 && x75 = x84
(3) l5(x56, x57, x58, x59, x60, x61, x62, x63, x64) -> l3(x65, x66, x67, x68, x69, x70, x71, x72, x73) :|: x70 = x70 && x71 = x71 && x74 = x58 && x69 = x69 && x56 = x65 && x57 = x66 && x58 = x67 && x59 = x68 && x63 = x72 && x64 = x73
(4) l4(x38, x39, x40, x41, x42, x43, x44, x45, x46) -> l5(x47, x48, x49, x50, x51, x52, x53, x54, x55) :|: x46 = x55 && x45 = x54 && x44 = x53 && x43 = x52 && x42 = x51 && x41 = x50 && x40 = x49 && x39 = x48 && x38 = x47 && x48 = x39

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

This digraph is fully evaluated!

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(5) IntTRSCompressionProof (EQUIVALENT)
Compressed rules.
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(6)
Obligation:
Rules:
l5(x29:0, x30:0, x31:0, x32:0, x60:0, x61:0, x62:0, x36:0, x37:0) -> l5(x29:0, x30:0, x31:0, x32:0, x33:0, x31:0, x32:0, x36:0, x37:0) :|: TRUE

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(7) FilterProof (EQUIVALENT)
Used the following sort dictionary for filtering: 
l5(VARIABLE, VARIABLE, VARIABLE, VARIABLE, VARIABLE, VARIABLE, VARIABLE, VARIABLE, VARIABLE)
Replaced non-predefined constructor symbols by 0.
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(8)
Obligation:
Rules:
l5(x29:0, x30:0, x31:0, x32:0, x60:0, x61:0, x62:0, x36:0, x37:0) -> l5(x29:0, x30:0, x31:0, x32:0, x33:0, x31:0, x32:0, x36:0, x37:0) :|: TRUE

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(9) IntTRSNonPeriodicNontermProof (COMPLETE)
Normalized system to the following form:
f(pc, x29:0, x30:0, x31:0, x32:0, x60:0, x61:0, x62:0, x36:0, x37:0) -> f(1, x29:0, x30:0, x31:0, x32:0, x33:0, x31:0, x32:0, x36:0, x37:0) :|: pc = 1 && TRUE
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 run2_3 = ((run1_3 * 1)) and run2_4 = ((run1_4 * 1)) and run2_5 = ((run1_10 * 1)) and run2_6 = ((run1_3 * 1)) and run2_7 = ((run1_4 * 1)) and run2_8 = ((run1_8 * 1)) and run2_9 = ((run1_9 * 1))) and (((run1_0 * 1)) = ((1 * 1)) and T)) and !(((run2_0 * 1)) = ((1 * 1)) and T))
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 run2_3 = ((run1_3 * 1)) and run2_4 = ((run1_4 * 1)) and run2_5 = ((run1_10 * 1)) and run2_6 = ((run1_3 * 1)) and run2_7 = ((run1_4 * 1)) and run2_8 = ((run1_8 * 1)) and run2_9 = ((run1_9 * 1))) and (((run1_0 * 1)) = ((1 * 1)) and T))

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(10)
NO