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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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, 311 ms]
(4) IRSwT
(5) IntTRSCompressionProof [EQUIVALENT, 26 ms]
(6) IRSwT
(7) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms]
(8) IRSwT
(9) TempFilterProof [SOUND, 15 ms]
(10) IntTRS
(11) PolynomialOrderProcessor [EQUIVALENT, 0 ms]
(12) YES


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(0)
Obligation:
Rules:
l0(Result_4HAT0, __cil_tmp4_8HAT0, __const_100HAT0, __retres3_7HAT0, i_5HAT0, x_6HAT0) -> l1(Result_4HATpost, __cil_tmp4_8HATpost, __const_100HATpost, __retres3_7HATpost, i_5HATpost, x_6HATpost) :|: x_6HAT0 = x_6HATpost && i_5HAT0 = i_5HATpost && __const_100HAT0 = __const_100HATpost && Result_4HATpost = __cil_tmp4_8HATpost && __cil_tmp4_8HATpost = __retres3_7HATpost && __retres3_7HATpost = 0 && 1 + __const_100HAT0 - i_5HAT0 <= 0
l0(x, x1, x2, x3, x4, x5) -> l2(x6, x7, x8, x9, x10, x11) :|: x5 = x11 && x3 = x9 && x2 = x8 && x1 = x7 && x = x6 && x10 = 1 + x4 && 0 <= -1 + x5 && 0 <= x2 - x4
l2(x12, x13, x14, x15, x16, x17) -> l0(x18, x19, x20, x21, x22, x23) :|: x17 = x23 && x16 = x22 && x15 = x21 && x14 = x20 && x13 = x19 && x12 = x18
l3(x24, x25, x26, x27, x28, x29) -> l4(x30, x31, x32, x33, x34, x35) :|: x29 = x35 && x27 = x33 && x26 = x32 && x25 = x31 && x24 = x30 && x34 = 0
l4(x36, x37, x38, x39, x40, x41) -> l1(x42, x43, x44, x45, x46, x47) :|: x41 = x47 && x40 = x46 && x38 = x44 && x42 = x43 && x43 = x45 && x45 = 0 && x41 <= 0 && 0 <= x38 - x40
l4(x48, x49, x50, x51, x52, x53) -> l0(x54, x55, x56, x57, x58, x59) :|: x53 = x59 && x51 = x57 && x50 = x56 && x49 = x55 && x48 = x54 && x58 = 1 + x52 && 0 <= -1 + x53 && 0 <= x50 - x52
l5(x60, x61, x62, x63, x64, x65) -> l3(x66, x67, x68, x69, x70, x71) :|: x65 = x71 && x64 = x70 && x63 = x69 && x62 = x68 && x61 = x67 && x60 = x66
Start term: l5(Result_4HAT0, __cil_tmp4_8HAT0, __const_100HAT0, __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, __const_100HAT0, __retres3_7HAT0, i_5HAT0, x_6HAT0) -> l1(Result_4HATpost, __cil_tmp4_8HATpost, __const_100HATpost, __retres3_7HATpost, i_5HATpost, x_6HATpost) :|: x_6HAT0 = x_6HATpost && i_5HAT0 = i_5HATpost && __const_100HAT0 = __const_100HATpost && Result_4HATpost = __cil_tmp4_8HATpost && __cil_tmp4_8HATpost = __retres3_7HATpost && __retres3_7HATpost = 0 && 1 + __const_100HAT0 - i_5HAT0 <= 0
l0(x, x1, x2, x3, x4, x5) -> l2(x6, x7, x8, x9, x10, x11) :|: x5 = x11 && x3 = x9 && x2 = x8 && x1 = x7 && x = x6 && x10 = 1 + x4 && 0 <= -1 + x5 && 0 <= x2 - x4
l2(x12, x13, x14, x15, x16, x17) -> l0(x18, x19, x20, x21, x22, x23) :|: x17 = x23 && x16 = x22 && x15 = x21 && x14 = x20 && x13 = x19 && x12 = x18
l3(x24, x25, x26, x27, x28, x29) -> l4(x30, x31, x32, x33, x34, x35) :|: x29 = x35 && x27 = x33 && x26 = x32 && x25 = x31 && x24 = x30 && x34 = 0
l4(x36, x37, x38, x39, x40, x41) -> l1(x42, x43, x44, x45, x46, x47) :|: x41 = x47 && x40 = x46 && x38 = x44 && x42 = x43 && x43 = x45 && x45 = 0 && x41 <= 0 && 0 <= x38 - x40
l4(x48, x49, x50, x51, x52, x53) -> l0(x54, x55, x56, x57, x58, x59) :|: x53 = x59 && x51 = x57 && x50 = x56 && x49 = x55 && x48 = x54 && x58 = 1 + x52 && 0 <= -1 + x53 && 0 <= x50 - x52
l5(x60, x61, x62, x63, x64, x65) -> l3(x66, x67, x68, x69, x70, x71) :|: x65 = x71 && x64 = x70 && x63 = x69 && x62 = x68 && x61 = x67 && x60 = x66
Start term: l5(Result_4HAT0, __cil_tmp4_8HAT0, __const_100HAT0, __retres3_7HAT0, i_5HAT0, x_6HAT0)

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(3) IRSwTTerminationDigraphProof (EQUIVALENT)
Constructed termination digraph!
Nodes:
(1) l0(Result_4HAT0, __cil_tmp4_8HAT0, __const_100HAT0, __retres3_7HAT0, i_5HAT0, x_6HAT0) -> l1(Result_4HATpost, __cil_tmp4_8HATpost, __const_100HATpost, __retres3_7HATpost, i_5HATpost, x_6HATpost) :|: x_6HAT0 = x_6HATpost && i_5HAT0 = i_5HATpost && __const_100HAT0 = __const_100HATpost && Result_4HATpost = __cil_tmp4_8HATpost && __cil_tmp4_8HATpost = __retres3_7HATpost && __retres3_7HATpost = 0 && 1 + __const_100HAT0 - i_5HAT0 <= 0
(2) l0(x, x1, x2, x3, x4, x5) -> l2(x6, x7, x8, x9, x10, x11) :|: x5 = x11 && x3 = x9 && x2 = x8 && x1 = x7 && x = x6 && x10 = 1 + x4 && 0 <= -1 + x5 && 0 <= x2 - x4
(3) l2(x12, x13, x14, x15, x16, x17) -> l0(x18, x19, x20, x21, x22, x23) :|: x17 = x23 && x16 = x22 && x15 = x21 && x14 = x20 && x13 = x19 && x12 = x18
(4) l3(x24, x25, x26, x27, x28, x29) -> l4(x30, x31, x32, x33, x34, x35) :|: x29 = x35 && x27 = x33 && x26 = x32 && x25 = x31 && x24 = x30 && x34 = 0
(5) l4(x36, x37, x38, x39, x40, x41) -> l1(x42, x43, x44, x45, x46, x47) :|: x41 = x47 && x40 = x46 && x38 = x44 && x42 = x43 && x43 = x45 && x45 = 0 && x41 <= 0 && 0 <= x38 - x40
(6) l4(x48, x49, x50, x51, x52, x53) -> l0(x54, x55, x56, x57, x58, x59) :|: x53 = x59 && x51 = x57 && x50 = x56 && x49 = x55 && x48 = x54 && x58 = 1 + x52 && 0 <= -1 + x53 && 0 <= x50 - x52
(7) l5(x60, x61, x62, x63, x64, x65) -> l3(x66, x67, x68, x69, x70, x71) :|: x65 = x71 && x64 = x70 && x63 = x69 && x62 = x68 && x61 = x67 && x60 = x66

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

This digraph is fully evaluated!
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(4)
Obligation:

Termination digraph:
Nodes:
(1) l0(x, x1, x2, x3, x4, x5) -> l2(x6, x7, x8, x9, x10, x11) :|: x5 = x11 && x3 = x9 && x2 = x8 && x1 = x7 && x = x6 && x10 = 1 + x4 && 0 <= -1 + x5 && 0 <= x2 - x4
(2) l2(x12, x13, x14, x15, x16, x17) -> l0(x18, x19, x20, x21, x22, x23) :|: x17 = x23 && x16 = x22 && x15 = x21 && x14 = x20 && x13 = x19 && x12 = x18

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(x18:0, x19:0, x20:0, x21:0, x4:0, x11:0) -> l0(x18:0, x19:0, x20:0, x21:0, 1 + x4:0, x11:0) :|: x20:0 - x4:0 >= 0 && x11:0 > 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, x5, x6) -> l0(x3, x5, x6)

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(8)
Obligation:
Rules:
l0(x20:0, x4:0, x11:0) -> l0(x20:0, 1 + x4:0, x11:0) :|: x20:0 - x4:0 >= 0 && x11:0 > 0

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(9) TempFilterProof (SOUND)
Used the following sort dictionary for filtering: 
l0(INTEGER, INTEGER, INTEGER)
Replaced non-predefined constructor symbols by 0.
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(10)
Obligation:
Rules:
l0(x20:0, x4:0, x11:0) -> l0(x20:0, c, x11:0) :|: c = 1 + x4:0 && (x20:0 - x4:0 >= 0 && x11:0 > 0)

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(11) PolynomialOrderProcessor (EQUIVALENT)
Found the following polynomial interpretation:
[l0(x, x1, x2)] = x - x1

The following rules are decreasing:
l0(x20:0, x4:0, x11:0) -> l0(x20:0, c, x11:0) :|: c = 1 + x4:0 && (x20:0 - x4:0 >= 0 && x11:0 > 0)
The following rules are bounded:
l0(x20:0, x4:0, x11:0) -> l0(x20:0, c, x11:0) :|: c = 1 + x4:0 && (x20:0 - x4:0 >= 0 && x11:0 > 0)

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(12)
YES