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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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, 232 ms]
(4) IRSwT
(5) IntTRSCompressionProof [EQUIVALENT, 44 ms]
(6) IRSwT
(7) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms]
(8) IRSwT
(9) TempFilterProof [SOUND, 14 ms]
(10) IntTRS
(11) PolynomialOrderProcessor [EQUIVALENT, 0 ms]
(12) YES


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(0)
Obligation:
Rules:
l0(Result_4HAT0, ___cil_tmp4_8HAT0, ___retres3_7HAT0, i_5HAT0, x_6HAT0) -> l1(Result_4HATpost, ___cil_tmp4_8HATpost, ___retres3_7HATpost, i_5HATpost, x_6HATpost) :|: x_6HAT0 = x_6HATpost && i_5HAT0 = i_5HATpost && Result_4HATpost = ___cil_tmp4_8HATpost && ___cil_tmp4_8HATpost = ___retres3_7HATpost && ___retres3_7HATpost = 0 && 10 - x_6HAT0 <= 0
l0(x, x1, x2, x3, x4) -> l1(x5, x6, x7, x8, x9) :|: x4 = x9 && x3 = x8 && x5 = x6 && x6 = x7 && x7 = 0 && -100 + x3 <= 0 && 0 <= 9 - x4
l0(x10, x11, x12, x13, x14) -> l2(x15, x16, x17, x18, x19) :|: x14 = x19 && x12 = x17 && x11 = x16 && x10 = x15 && x18 = -1 + x13 && 0 <= -101 + x13 && 0 <= 9 - x14
l2(x20, x21, x22, x23, x24) -> l0(x25, x26, x27, x28, x29) :|: x24 = x29 && x23 = x28 && x22 = x27 && x21 = x26 && x20 = x25
l3(x30, x31, x32, x33, x34) -> l0(x35, x36, x37, x38, x39) :|: x34 = x39 && x32 = x37 && x31 = x36 && x30 = x35 && x38 = 1000
l4(x40, x41, x42, x43, x44) -> l3(x45, x46, x47, x48, x49) :|: x44 = x49 && x43 = x48 && x42 = x47 && x41 = x46 && x40 = x45
Start term: l4(Result_4HAT0, ___cil_tmp4_8HAT0, ___retres3_7HAT0, i_5HAT0, x_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, ___cil_tmp4_8HAT0, ___retres3_7HAT0, i_5HAT0, x_6HAT0) -> l1(Result_4HATpost, ___cil_tmp4_8HATpost, ___retres3_7HATpost, i_5HATpost, x_6HATpost) :|: x_6HAT0 = x_6HATpost && i_5HAT0 = i_5HATpost && Result_4HATpost = ___cil_tmp4_8HATpost && ___cil_tmp4_8HATpost = ___retres3_7HATpost && ___retres3_7HATpost = 0 && 10 - x_6HAT0 <= 0
l0(x, x1, x2, x3, x4) -> l1(x5, x6, x7, x8, x9) :|: x4 = x9 && x3 = x8 && x5 = x6 && x6 = x7 && x7 = 0 && -100 + x3 <= 0 && 0 <= 9 - x4
l0(x10, x11, x12, x13, x14) -> l2(x15, x16, x17, x18, x19) :|: x14 = x19 && x12 = x17 && x11 = x16 && x10 = x15 && x18 = -1 + x13 && 0 <= -101 + x13 && 0 <= 9 - x14
l2(x20, x21, x22, x23, x24) -> l0(x25, x26, x27, x28, x29) :|: x24 = x29 && x23 = x28 && x22 = x27 && x21 = x26 && x20 = x25
l3(x30, x31, x32, x33, x34) -> l0(x35, x36, x37, x38, x39) :|: x34 = x39 && x32 = x37 && x31 = x36 && x30 = x35 && x38 = 1000
l4(x40, x41, x42, x43, x44) -> l3(x45, x46, x47, x48, x49) :|: x44 = x49 && x43 = x48 && x42 = x47 && x41 = x46 && x40 = x45
Start term: l4(Result_4HAT0, ___cil_tmp4_8HAT0, ___retres3_7HAT0, i_5HAT0, x_6HAT0)

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(3) IRSwTTerminationDigraphProof (EQUIVALENT)
Constructed termination digraph!
Nodes:
(1) l0(Result_4HAT0, ___cil_tmp4_8HAT0, ___retres3_7HAT0, i_5HAT0, x_6HAT0) -> l1(Result_4HATpost, ___cil_tmp4_8HATpost, ___retres3_7HATpost, i_5HATpost, x_6HATpost) :|: x_6HAT0 = x_6HATpost && i_5HAT0 = i_5HATpost && Result_4HATpost = ___cil_tmp4_8HATpost && ___cil_tmp4_8HATpost = ___retres3_7HATpost && ___retres3_7HATpost = 0 && 10 - x_6HAT0 <= 0
(2) l0(x, x1, x2, x3, x4) -> l1(x5, x6, x7, x8, x9) :|: x4 = x9 && x3 = x8 && x5 = x6 && x6 = x7 && x7 = 0 && -100 + x3 <= 0 && 0 <= 9 - x4
(3) l0(x10, x11, x12, x13, x14) -> l2(x15, x16, x17, x18, x19) :|: x14 = x19 && x12 = x17 && x11 = x16 && x10 = x15 && x18 = -1 + x13 && 0 <= -101 + x13 && 0 <= 9 - x14
(4) l2(x20, x21, x22, x23, x24) -> l0(x25, x26, x27, x28, x29) :|: x24 = x29 && x23 = x28 && x22 = x27 && x21 = x26 && x20 = x25
(5) l3(x30, x31, x32, x33, x34) -> l0(x35, x36, x37, x38, x39) :|: x34 = x39 && x32 = x37 && x31 = x36 && x30 = x35 && x38 = 1000
(6) l4(x40, x41, x42, x43, x44) -> l3(x45, x46, x47, x48, x49) :|: x44 = x49 && x43 = x48 && x42 = x47 && x41 = x46 && x40 = x45

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

This digraph is fully evaluated!
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(4)
Obligation:

Termination digraph:
Nodes:
(1) l0(x10, x11, x12, x13, x14) -> l2(x15, x16, x17, x18, x19) :|: x14 = x19 && x12 = x17 && x11 = x16 && x10 = x15 && x18 = -1 + x13 && 0 <= -101 + x13 && 0 <= 9 - x14
(2) l2(x20, x21, x22, x23, x24) -> l0(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:
l0(x10:0, x11:0, x12:0, x13:0, x14:0) -> l0(x10:0, x11:0, x12:0, -1 + x13:0, x14:0) :|: x14:0 < 10 && x13:0 > 100

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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, x5) -> l0(x4, x5)

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(8)
Obligation:
Rules:
l0(x13:0, x14:0) -> l0(-1 + x13:0, x14:0) :|: x14:0 < 10 && x13:0 > 100

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(9) TempFilterProof (SOUND)
Used the following sort dictionary for filtering: 
l0(INTEGER, INTEGER)
Replaced non-predefined constructor symbols by 0.
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(10)
Obligation:
Rules:
l0(x13:0, x14:0) -> l0(c, x14:0) :|: c = -1 + x13:0 && (x14:0 < 10 && x13:0 > 100)

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(11) PolynomialOrderProcessor (EQUIVALENT)
Found the following polynomial interpretation:
[l0(x, x1)] = x

The following rules are decreasing:
l0(x13:0, x14:0) -> l0(c, x14:0) :|: c = -1 + x13:0 && (x14:0 < 10 && x13:0 > 100)
The following rules are bounded:
l0(x13:0, x14:0) -> l0(c, x14:0) :|: c = -1 + x13:0 && (x14:0 < 10 && x13:0 > 100)

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(12)
YES