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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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, 708 ms]
(4) IRSwT
(5) IntTRSCompressionProof [EQUIVALENT, 0 ms]
(6) IRSwT
(7) FilterProof [EQUIVALENT, 0 ms]
(8) IntTRS
(9) IntTRSPeriodicNontermProof [COMPLETE, 10 ms]
(10) NO


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(0)
Obligation:
Rules:
l0(StoredHAT0, tmp1HAT0, tmp___02HAT0) -> l1(StoredHATpost, tmp1HATpost, tmp___02HATpost) :|: tmp___02HAT0 = tmp___02HATpost && tmp1HAT0 = tmp1HATpost && StoredHATpost = 1 && 0 <= tmp1HAT0 && tmp1HAT0 <= 0
l0(x, x1, x2) -> l2(x3, x4, x5) :|: x2 = x5 && x1 = x4 && x = x3 && 1 <= x1
l0(x6, x7, x8) -> l2(x9, x10, x11) :|: x8 = x11 && x7 = x10 && x6 = x9 && 1 + x7 <= 0
l3(x12, x13, x14) -> l0(x15, x16, x17) :|: x14 = x17 && x12 = x15 && x16 = x16
l4(x18, x19, x20) -> l1(x21, x22, x23) :|: x20 = x23 && x19 = x22 && x18 = x21 && 0 <= x20 && x20 <= 0
l4(x24, x25, x26) -> l3(x27, x28, x29) :|: x26 = x29 && x25 = x28 && x24 = x27 && 1 <= x26
l4(x30, x31, x32) -> l3(x33, x34, x35) :|: x32 = x35 && x31 = x34 && x30 = x33 && 1 + x32 <= 0
l5(x36, x37, x38) -> l6(x39, x40, x41) :|: x38 = x41 && x37 = x40 && x36 = x39
l7(x42, x43, x44) -> l4(x45, x46, x47) :|: x43 = x46 && x42 = x45 && x47 = x47
l1(x48, x49, x50) -> l8(x51, x52, x53) :|: x50 = x53 && x49 = x52 && x48 = x51
l8(x54, x55, x56) -> l5(x57, x58, x59) :|: x56 = x59 && x55 = x58 && x54 = x57 && 2 <= x54
l8(x60, x61, x62) -> l5(x63, x64, x65) :|: x62 = x65 && x61 = x64 && x60 = x63 && 1 + x60 <= 1
l8(x66, x67, x68) -> l5(x69, x70, x71) :|: x68 = x71 && x67 = x70 && x69 = 0 && 1 <= x66 && x66 <= 1
l2(x72, x73, x74) -> l7(x75, x76, x77) :|: x74 = x77 && x73 = x76 && x72 = x75
l9(x78, x79, x80) -> l7(x81, x82, x83) :|: x80 = x83 && x79 = x82 && x81 = 0
l10(x84, x85, x86) -> l9(x87, x88, x89) :|: x86 = x89 && x85 = x88 && x84 = x87
Start term: l10(StoredHAT0, tmp1HAT0, tmp___02HAT0)

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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(StoredHAT0, tmp1HAT0, tmp___02HAT0) -> l1(StoredHATpost, tmp1HATpost, tmp___02HATpost) :|: tmp___02HAT0 = tmp___02HATpost && tmp1HAT0 = tmp1HATpost && StoredHATpost = 1 && 0 <= tmp1HAT0 && tmp1HAT0 <= 0
l0(x, x1, x2) -> l2(x3, x4, x5) :|: x2 = x5 && x1 = x4 && x = x3 && 1 <= x1
l0(x6, x7, x8) -> l2(x9, x10, x11) :|: x8 = x11 && x7 = x10 && x6 = x9 && 1 + x7 <= 0
l3(x12, x13, x14) -> l0(x15, x16, x17) :|: x14 = x17 && x12 = x15 && x16 = x16
l4(x18, x19, x20) -> l1(x21, x22, x23) :|: x20 = x23 && x19 = x22 && x18 = x21 && 0 <= x20 && x20 <= 0
l4(x24, x25, x26) -> l3(x27, x28, x29) :|: x26 = x29 && x25 = x28 && x24 = x27 && 1 <= x26
l4(x30, x31, x32) -> l3(x33, x34, x35) :|: x32 = x35 && x31 = x34 && x30 = x33 && 1 + x32 <= 0
l5(x36, x37, x38) -> l6(x39, x40, x41) :|: x38 = x41 && x37 = x40 && x36 = x39
l7(x42, x43, x44) -> l4(x45, x46, x47) :|: x43 = x46 && x42 = x45 && x47 = x47
l1(x48, x49, x50) -> l8(x51, x52, x53) :|: x50 = x53 && x49 = x52 && x48 = x51
l8(x54, x55, x56) -> l5(x57, x58, x59) :|: x56 = x59 && x55 = x58 && x54 = x57 && 2 <= x54
l8(x60, x61, x62) -> l5(x63, x64, x65) :|: x62 = x65 && x61 = x64 && x60 = x63 && 1 + x60 <= 1
l8(x66, x67, x68) -> l5(x69, x70, x71) :|: x68 = x71 && x67 = x70 && x69 = 0 && 1 <= x66 && x66 <= 1
l2(x72, x73, x74) -> l7(x75, x76, x77) :|: x74 = x77 && x73 = x76 && x72 = x75
l9(x78, x79, x80) -> l7(x81, x82, x83) :|: x80 = x83 && x79 = x82 && x81 = 0
l10(x84, x85, x86) -> l9(x87, x88, x89) :|: x86 = x89 && x85 = x88 && x84 = x87
Start term: l10(StoredHAT0, tmp1HAT0, tmp___02HAT0)

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(3) IRSwTTerminationDigraphProof (EQUIVALENT)
Constructed termination digraph!
Nodes:
(1) l0(StoredHAT0, tmp1HAT0, tmp___02HAT0) -> l1(StoredHATpost, tmp1HATpost, tmp___02HATpost) :|: tmp___02HAT0 = tmp___02HATpost && tmp1HAT0 = tmp1HATpost && StoredHATpost = 1 && 0 <= tmp1HAT0 && tmp1HAT0 <= 0
(2) l0(x, x1, x2) -> l2(x3, x4, x5) :|: x2 = x5 && x1 = x4 && x = x3 && 1 <= x1
(3) l0(x6, x7, x8) -> l2(x9, x10, x11) :|: x8 = x11 && x7 = x10 && x6 = x9 && 1 + x7 <= 0
(4) l3(x12, x13, x14) -> l0(x15, x16, x17) :|: x14 = x17 && x12 = x15 && x16 = x16
(5) l4(x18, x19, x20) -> l1(x21, x22, x23) :|: x20 = x23 && x19 = x22 && x18 = x21 && 0 <= x20 && x20 <= 0
(6) l4(x24, x25, x26) -> l3(x27, x28, x29) :|: x26 = x29 && x25 = x28 && x24 = x27 && 1 <= x26
(7) l4(x30, x31, x32) -> l3(x33, x34, x35) :|: x32 = x35 && x31 = x34 && x30 = x33 && 1 + x32 <= 0
(8) l5(x36, x37, x38) -> l6(x39, x40, x41) :|: x38 = x41 && x37 = x40 && x36 = x39
(9) l7(x42, x43, x44) -> l4(x45, x46, x47) :|: x43 = x46 && x42 = x45 && x47 = x47
(10) l1(x48, x49, x50) -> l8(x51, x52, x53) :|: x50 = x53 && x49 = x52 && x48 = x51
(11) l8(x54, x55, x56) -> l5(x57, x58, x59) :|: x56 = x59 && x55 = x58 && x54 = x57 && 2 <= x54
(12) l8(x60, x61, x62) -> l5(x63, x64, x65) :|: x62 = x65 && x61 = x64 && x60 = x63 && 1 + x60 <= 1
(13) l8(x66, x67, x68) -> l5(x69, x70, x71) :|: x68 = x71 && x67 = x70 && x69 = 0 && 1 <= x66 && x66 <= 1
(14) l2(x72, x73, x74) -> l7(x75, x76, x77) :|: x74 = x77 && x73 = x76 && x72 = x75
(15) l9(x78, x79, x80) -> l7(x81, x82, x83) :|: x80 = x83 && x79 = x82 && x81 = 0
(16) l10(x84, x85, x86) -> l9(x87, x88, x89) :|: x86 = x89 && x85 = x88 && x84 = x87

Arcs:
(1) -> (10)
(2) -> (14)
(3) -> (14)
(4) -> (1), (2), (3)
(5) -> (10)
(6) -> (4)
(7) -> (4)
(9) -> (5), (6), (7)
(10) -> (11), (12), (13)
(11) -> (8)
(12) -> (8)
(13) -> (8)
(14) -> (9)
(15) -> (9)
(16) -> (15)

This digraph is fully evaluated!
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(4)
Obligation:

Termination digraph:
Nodes:
(1) l0(x, x1, x2) -> l2(x3, x4, x5) :|: x2 = x5 && x1 = x4 && x = x3 && 1 <= x1
(2) l3(x12, x13, x14) -> l0(x15, x16, x17) :|: x14 = x17 && x12 = x15 && x16 = x16
(3) l4(x30, x31, x32) -> l3(x33, x34, x35) :|: x32 = x35 && x31 = x34 && x30 = x33 && 1 + x32 <= 0
(4) l4(x24, x25, x26) -> l3(x27, x28, x29) :|: x26 = x29 && x25 = x28 && x24 = x27 && 1 <= x26
(5) l7(x42, x43, x44) -> l4(x45, x46, x47) :|: x43 = x46 && x42 = x45 && x47 = x47
(6) l2(x72, x73, x74) -> l7(x75, x76, x77) :|: x74 = x77 && x73 = x76 && x72 = x75
(7) l0(x6, x7, x8) -> l2(x9, x10, x11) :|: x8 = x11 && x7 = x10 && x6 = x9 && 1 + x7 <= 0

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

This digraph is fully evaluated!

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(5) IntTRSCompressionProof (EQUIVALENT)
Compressed rules.
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(6)
Obligation:
Rules:
l7(x27:0, x28:0, x44:0) -> l3(x27:0, x28:0, x29:0) :|: x29:0 > 0
l7(x, x1, x2) -> l3(x, x1, x3) :|: x3 < 0
l3(x12:0, x13:0, x14:0) -> l7(x12:0, x16:0, x14:0) :|: x16:0 > 0
l3(x4, x5, x6) -> l7(x4, x7, x6) :|: x7 < 0

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(7) FilterProof (EQUIVALENT)
Used the following sort dictionary for filtering: 
l7(VARIABLE, VARIABLE, VARIABLE)
l3(VARIABLE, VARIABLE, VARIABLE)
Replaced non-predefined constructor symbols by 0.
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(8)
Obligation:
Rules:
l7(x27:0, x28:0, x44:0) -> l3(x27:0, x28:0, x29:0) :|: x29:0 > 0
l7(x, x1, x2) -> l3(x, x1, x3) :|: x3 < 0
l3(x12:0, x13:0, x14:0) -> l7(x12:0, x16:0, x14:0) :|: x16:0 > 0
l3(x4, x5, x6) -> l7(x4, x7, x6) :|: x7 < 0

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(9) IntTRSPeriodicNontermProof (COMPLETE)
Normalized system to the following form:
f(pc, x27:0, x28:0, x44:0) -> f(2, x27:0, x28:0, x29:0) :|: pc = 1 && x29:0 > 0
f(pc, x, x1, x2) -> f(2, x, x1, x3) :|: pc = 1 && x3 < 0
f(pc, x12:0, x13:0, x14:0) -> f(1, x12:0, x16:0, x14:0) :|: pc = 2 && x16:0 > 0
f(pc, x4, x5, x6) -> f(1, x4, x7, x6) :|: pc = 2 && x7 < 0
Witness term starting non-terminating reduction: f(1, -8, -8, -8)
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(10)
NO