YES
proof of prog.inttrs
# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty


Termination of the given IRSwT could be proven:

(0) IRSwT
(1) IRSFormatTransformerProof [EQUIVALENT, 0 ms]
(2) IRSwT
(3) IRSwTTerminationDigraphProof [EQUIVALENT, 323 ms]
(4) IRSwT
(5) IntTRSCompressionProof [EQUIVALENT, 0 ms]
(6) IRSwT
(7) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms]
(8) IRSwT
(9) TempFilterProof [SOUND, 16 ms]
(10) IntTRS
(11) PolynomialOrderProcessor [EQUIVALENT, 0 ms]
(12) YES


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(0)
Obligation:
Rules:
l0(__const_10HAT0, iEXCL14HAT0, iEXCL22HAT0, resultEXCL12HAT0, temp0EXCL15HAT0) -> l1(__const_10HATpost, iEXCL14HATpost, iEXCL22HATpost, resultEXCL12HATpost, temp0EXCL15HATpost) :|: iEXCL14HAT1 = 0 && 0 <= iEXCL14HAT1 && iEXCL14HAT1 <= 0 && 0 <= iEXCL14HAT1 && iEXCL14HAT1 <= 0 && 1 + iEXCL14HAT1 <= __const_10HAT0 && iEXCL14HAT2 = 1 + iEXCL14HAT1 && 1 <= iEXCL14HAT2 && iEXCL14HAT2 <= 1 && 1 <= iEXCL14HAT2 && iEXCL14HAT2 <= 1 && 1 + iEXCL14HAT2 <= __const_10HAT0 && iEXCL14HATpost = 1 + iEXCL14HAT2 && 2 <= iEXCL14HATpost && iEXCL14HATpost <= 2 && __const_10HAT0 = __const_10HATpost && iEXCL22HAT0 = iEXCL22HATpost && resultEXCL12HAT0 = resultEXCL12HATpost && temp0EXCL15HAT0 = temp0EXCL15HATpost
l1(x, x1, x2, x3, x4) -> l2(x5, x6, x7, x8, x9) :|: x4 = x9 && x2 = x7 && x1 = x6 && x = x5 && x8 = x4 && x <= x1
l1(x10, x11, x12, x13, x14) -> l3(x15, x16, x17, x18, x19) :|: x14 = x19 && x13 = x18 && x12 = x17 && x10 = x15 && 1 + x12 <= x10 && 1 + x12 <= x16 && x16 <= 1 + x12 && x16 = 1 + x11 && 1 + x11 <= x10
l3(x20, x21, x22, x23, x24) -> l1(x25, x26, x27, x28, x29) :|: x24 = x29 && x23 = x28 && x22 = x27 && x21 = x26 && x20 = x25
l4(x30, x31, x32, x33, x34) -> l0(x35, x36, x37, x38, x39) :|: x34 = x39 && x33 = x38 && x32 = x37 && x31 = x36 && x30 = x35
Start term: l4(__const_10HAT0, iEXCL14HAT0, iEXCL22HAT0, resultEXCL12HAT0, temp0EXCL15HAT0)

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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(__const_10HAT0, iEXCL14HAT0, iEXCL22HAT0, resultEXCL12HAT0, temp0EXCL15HAT0) -> l1(__const_10HATpost, iEXCL14HATpost, iEXCL22HATpost, resultEXCL12HATpost, temp0EXCL15HATpost) :|: iEXCL14HAT1 = 0 && 0 <= iEXCL14HAT1 && iEXCL14HAT1 <= 0 && 0 <= iEXCL14HAT1 && iEXCL14HAT1 <= 0 && 1 + iEXCL14HAT1 <= __const_10HAT0 && iEXCL14HAT2 = 1 + iEXCL14HAT1 && 1 <= iEXCL14HAT2 && iEXCL14HAT2 <= 1 && 1 <= iEXCL14HAT2 && iEXCL14HAT2 <= 1 && 1 + iEXCL14HAT2 <= __const_10HAT0 && iEXCL14HATpost = 1 + iEXCL14HAT2 && 2 <= iEXCL14HATpost && iEXCL14HATpost <= 2 && __const_10HAT0 = __const_10HATpost && iEXCL22HAT0 = iEXCL22HATpost && resultEXCL12HAT0 = resultEXCL12HATpost && temp0EXCL15HAT0 = temp0EXCL15HATpost
l1(x, x1, x2, x3, x4) -> l2(x5, x6, x7, x8, x9) :|: x4 = x9 && x2 = x7 && x1 = x6 && x = x5 && x8 = x4 && x <= x1
l1(x10, x11, x12, x13, x14) -> l3(x15, x16, x17, x18, x19) :|: x14 = x19 && x13 = x18 && x12 = x17 && x10 = x15 && 1 + x12 <= x10 && 1 + x12 <= x16 && x16 <= 1 + x12 && x16 = 1 + x11 && 1 + x11 <= x10
l3(x20, x21, x22, x23, x24) -> l1(x25, x26, x27, x28, x29) :|: x24 = x29 && x23 = x28 && x22 = x27 && x21 = x26 && x20 = x25
l4(x30, x31, x32, x33, x34) -> l0(x35, x36, x37, x38, x39) :|: x34 = x39 && x33 = x38 && x32 = x37 && x31 = x36 && x30 = x35
Start term: l4(__const_10HAT0, iEXCL14HAT0, iEXCL22HAT0, resultEXCL12HAT0, temp0EXCL15HAT0)

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(3) IRSwTTerminationDigraphProof (EQUIVALENT)
Constructed termination digraph!
Nodes:
(1) l0(__const_10HAT0, iEXCL14HAT0, iEXCL22HAT0, resultEXCL12HAT0, temp0EXCL15HAT0) -> l1(__const_10HATpost, iEXCL14HATpost, iEXCL22HATpost, resultEXCL12HATpost, temp0EXCL15HATpost) :|: iEXCL14HAT1 = 0 && 0 <= iEXCL14HAT1 && iEXCL14HAT1 <= 0 && 0 <= iEXCL14HAT1 && iEXCL14HAT1 <= 0 && 1 + iEXCL14HAT1 <= __const_10HAT0 && iEXCL14HAT2 = 1 + iEXCL14HAT1 && 1 <= iEXCL14HAT2 && iEXCL14HAT2 <= 1 && 1 <= iEXCL14HAT2 && iEXCL14HAT2 <= 1 && 1 + iEXCL14HAT2 <= __const_10HAT0 && iEXCL14HATpost = 1 + iEXCL14HAT2 && 2 <= iEXCL14HATpost && iEXCL14HATpost <= 2 && __const_10HAT0 = __const_10HATpost && iEXCL22HAT0 = iEXCL22HATpost && resultEXCL12HAT0 = resultEXCL12HATpost && temp0EXCL15HAT0 = temp0EXCL15HATpost
(2) l1(x, x1, x2, x3, x4) -> l2(x5, x6, x7, x8, x9) :|: x4 = x9 && x2 = x7 && x1 = x6 && x = x5 && x8 = x4 && x <= x1
(3) l1(x10, x11, x12, x13, x14) -> l3(x15, x16, x17, x18, x19) :|: x14 = x19 && x13 = x18 && x12 = x17 && x10 = x15 && 1 + x12 <= x10 && 1 + x12 <= x16 && x16 <= 1 + x12 && x16 = 1 + x11 && 1 + x11 <= x10
(4) l3(x20, x21, x22, x23, x24) -> l1(x25, x26, x27, x28, x29) :|: x24 = x29 && x23 = x28 && x22 = x27 && x21 = x26 && x20 = x25
(5) l4(x30, x31, x32, x33, x34) -> l0(x35, x36, x37, x38, x39) :|: x34 = x39 && x33 = x38 && x32 = x37 && x31 = x36 && x30 = x35

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(x10, x11, x12, x13, x14) -> l3(x15, x16, x17, x18, x19) :|: x14 = x19 && x13 = x18 && x12 = x17 && x10 = x15 && 1 + x12 <= x10 && 1 + x12 <= x16 && x16 <= 1 + x12 && x16 = 1 + x11 && 1 + x11 <= x10
(2) l3(x20, x21, x22, x23, x24) -> l1(x25, x26, x27, x28, x29) :|: x24 = x29 && x23 = x28 && x22 = x27 && x21 = x26 && x20 = x25

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(x10:0, x11:0, x12:0, x13:0, x14:0) -> l1(x10:0, 1 + x11:0, x12:0, x13:0, x14:0) :|: x10:0 >= 1 + x12:0 && 1 + x12:0 = 1 + x11:0 && x10:0 >= 1 + x11:0

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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) -> l1(x1, x2, x3)

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(8)
Obligation:
Rules:
l1(x10:0, x11:0, x12:0) -> l1(x10:0, 1 + x11:0, x12:0) :|: x10:0 >= 1 + x12:0 && 1 + x12:0 = 1 + x11:0 && x10:0 >= 1 + x11:0

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(9) TempFilterProof (SOUND)
Used the following sort dictionary for filtering: 
l1(INTEGER, INTEGER, INTEGER)
Replaced non-predefined constructor symbols by 0.
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(10)
Obligation:
Rules:
l1(x10:0, x11:0, x12:0) -> l1(x10:0, c, x12:0) :|: c = 1 + x11:0 && (x10:0 >= 1 + x12:0 && 1 + x12:0 = 1 + x11:0 && x10:0 >= 1 + x11:0)

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(11) PolynomialOrderProcessor (EQUIVALENT)
Found the following polynomial interpretation:
[l1(x, x1, x2)] = -x1 + x2

The following rules are decreasing:
l1(x10:0, x11:0, x12:0) -> l1(x10:0, c, x12:0) :|: c = 1 + x11:0 && (x10:0 >= 1 + x12:0 && 1 + x12:0 = 1 + x11:0 && x10:0 >= 1 + x11:0)
The following rules are bounded:
l1(x10:0, x11:0, x12:0) -> l1(x10:0, c, x12:0) :|: c = 1 + x11:0 && (x10:0 >= 1 + x12:0 && 1 + x12:0 = 1 + x11:0 && x10:0 >= 1 + x11:0)

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(12)
YES