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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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, 158 ms]
(4) IRSwT
(5) IntTRSCompressionProof [EQUIVALENT, 0 ms]
(6) IRSwT
(7) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms]
(8) IRSwT
(9) FilterProof [EQUIVALENT, 0 ms]
(10) IntTRS
(11) IntTRSCompressionProof [EQUIVALENT, 0 ms]
(12) IntTRS
(13) IntTRSPeriodicNontermProof [COMPLETE, 0 ms]
(14) NO


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(0)
Obligation:
Rules:
l0(elem_13HAT0, l_11HAT0, len_98HAT0, x_12HAT0) -> l1(elem_13HATpost, l_11HATpost, len_98HATpost, x_12HATpost) :|: 1 <= 1 + len_98HAT0 && 1 <= len_98HAT0 && len_98HAT1 = len_98HAT1 && elem_13HATpost = l_11HAT0 && 1 <= 1 + len_98HAT1 && 1 <= len_98HAT1 && len_98HATpost = len_98HATpost && 0 <= -1 * elem_13HATpost && -1 * elem_13HATpost <= 0 && l_11HATpost = x_12HAT0 && x_12HAT0 = x_12HATpost
l1(x, x1, x2, x3) -> l0(x4, x5, x6, x7) :|: x3 = x7 && x2 = x6 && x1 = x5 && x = x4
l2(x8, x9, x10, x11) -> l0(x12, x13, x14, x15) :|: x11 = x15 && x10 = x14 && x9 = x13 && x8 = x12
l3(x16, x17, x18, x19) -> l2(x20, x21, x22, x23) :|: x19 = x23 && x18 = x22 && x17 = x21 && x16 = x20
Start term: l3(elem_13HAT0, l_11HAT0, len_98HAT0, x_12HAT0)

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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(elem_13HAT0, l_11HAT0, len_98HAT0, x_12HAT0) -> l1(elem_13HATpost, l_11HATpost, len_98HATpost, x_12HATpost) :|: 1 <= 1 + len_98HAT0 && 1 <= len_98HAT0 && len_98HAT1 = len_98HAT1 && elem_13HATpost = l_11HAT0 && 1 <= 1 + len_98HAT1 && 1 <= len_98HAT1 && len_98HATpost = len_98HATpost && 0 <= -1 * elem_13HATpost && -1 * elem_13HATpost <= 0 && l_11HATpost = x_12HAT0 && x_12HAT0 = x_12HATpost
l1(x, x1, x2, x3) -> l0(x4, x5, x6, x7) :|: x3 = x7 && x2 = x6 && x1 = x5 && x = x4
l2(x8, x9, x10, x11) -> l0(x12, x13, x14, x15) :|: x11 = x15 && x10 = x14 && x9 = x13 && x8 = x12
l3(x16, x17, x18, x19) -> l2(x20, x21, x22, x23) :|: x19 = x23 && x18 = x22 && x17 = x21 && x16 = x20
Start term: l3(elem_13HAT0, l_11HAT0, len_98HAT0, x_12HAT0)

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(3) IRSwTTerminationDigraphProof (EQUIVALENT)
Constructed termination digraph!
Nodes:
(1) l0(elem_13HAT0, l_11HAT0, len_98HAT0, x_12HAT0) -> l1(elem_13HATpost, l_11HATpost, len_98HATpost, x_12HATpost) :|: 1 <= 1 + len_98HAT0 && 1 <= len_98HAT0 && len_98HAT1 = len_98HAT1 && elem_13HATpost = l_11HAT0 && 1 <= 1 + len_98HAT1 && 1 <= len_98HAT1 && len_98HATpost = len_98HATpost && 0 <= -1 * elem_13HATpost && -1 * elem_13HATpost <= 0 && l_11HATpost = x_12HAT0 && x_12HAT0 = x_12HATpost
(2) l1(x, x1, x2, x3) -> l0(x4, x5, x6, x7) :|: x3 = x7 && x2 = x6 && x1 = x5 && x = x4
(3) l2(x8, x9, x10, x11) -> l0(x12, x13, x14, x15) :|: x11 = x15 && x10 = x14 && x9 = x13 && x8 = x12
(4) l3(x16, x17, x18, x19) -> l2(x20, x21, x22, x23) :|: x19 = x23 && x18 = x22 && x17 = x21 && x16 = x20

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

This digraph is fully evaluated!
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(4)
Obligation:

Termination digraph:
Nodes:
(1) l0(elem_13HAT0, l_11HAT0, len_98HAT0, x_12HAT0) -> l1(elem_13HATpost, l_11HATpost, len_98HATpost, x_12HATpost) :|: 1 <= 1 + len_98HAT0 && 1 <= len_98HAT0 && len_98HAT1 = len_98HAT1 && elem_13HATpost = l_11HAT0 && 1 <= 1 + len_98HAT1 && 1 <= len_98HAT1 && len_98HATpost = len_98HATpost && 0 <= -1 * elem_13HATpost && -1 * elem_13HATpost <= 0 && l_11HATpost = x_12HAT0 && x_12HAT0 = x_12HATpost
(2) l1(x, x1, x2, x3) -> l0(x4, x5, x6, x7) :|: x3 = x7 && x2 = x6 && x1 = x5 && x = x4

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(elem_13HAT0:0, elem_13HATpost:0, len_98HAT0:0, l_11HATpost:0) -> l0(elem_13HATpost:0, l_11HATpost:0, len_98HATpost:0, l_11HATpost:0) :|: 0 = -1 * elem_13HATpost:0 && len_98HAT0:0 > 0 && len_98HAT1:0 > 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) -> l0(x2, x3, x4)

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(8)
Obligation:
Rules:
l0(elem_13HATpost:0, len_98HAT0:0, l_11HATpost:0) -> l0(l_11HATpost:0, len_98HATpost:0, l_11HATpost:0) :|: 0 = -1 * elem_13HATpost:0 && len_98HAT0:0 > 0 && len_98HAT1:0 > 0

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(9) FilterProof (EQUIVALENT)
Used the following sort dictionary for filtering: 
l0(VARIABLE, VARIABLE, VARIABLE)
Replaced non-predefined constructor symbols by 0.
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(10)
Obligation:
Rules:
l0(elem_13HATpost:0, len_98HAT0:0, l_11HATpost:0) -> l0(l_11HATpost:0, len_98HATpost:0, l_11HATpost:0) :|: 0 = -1 * elem_13HATpost:0 && len_98HAT0:0 > 0 && len_98HAT1:0 > 0

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(11) IntTRSCompressionProof (EQUIVALENT)
Compressed rules.
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(12)
Obligation:
Rules:
l0(elem_13HATpost:0:0, len_98HAT0:0:0, l_11HATpost:0:0) -> l0(l_11HATpost:0:0, len_98HATpost:0:0, l_11HATpost:0:0) :|: 0 = -1 * elem_13HATpost:0:0 && len_98HAT0:0:0 > 0 && len_98HAT1:0:0 > 0

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(13) IntTRSPeriodicNontermProof (COMPLETE)
Normalized system to the following form:
f(pc, elem_13HATpost:0:0, len_98HAT0:0:0, l_11HATpost:0:0) -> f(1, l_11HATpost:0:0, len_98HATpost:0:0, l_11HATpost:0:0) :|: pc = 1 && (0 = -1 * elem_13HATpost:0:0 && len_98HAT0:0:0 > 0 && len_98HAT1:0:0 > 0)
Witness term starting non-terminating reduction: f(1, 0, 1, 0)
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(14)
NO