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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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, 295 ms]
(4) IRSwT
(5) IntTRSCompressionProof [EQUIVALENT, 27 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(i_13HAT0, j_15HAT0, rt_11HAT0, s_16HAT0, s_17HAT0, st_14HAT0) -> l1(i_13HATpost, j_15HATpost, rt_11HATpost, s_16HATpost, s_17HATpost, st_14HATpost) :|: i_13HAT1 = s_17HAT0 && j_15HATpost = s_16HAT0 && i_13HATpost = j_15HATpost && rt_11HAT0 = rt_11HATpost && s_16HAT0 = s_16HATpost && s_17HAT0 = s_17HATpost && st_14HAT0 = st_14HATpost
l2(x, x1, x2, x3, x4, x5) -> l3(x6, x7, x8, x9, x10, x11) :|: x5 = x11 && x4 = x10 && x3 = x9 && x1 = x7 && x = x6 && x8 = x5 && 500 <= x
l2(x12, x13, x14, x15, x16, x17) -> l4(x18, x19, x20, x21, x22, x23) :|: x17 = x23 && x16 = x22 && x15 = x21 && x14 = x20 && x13 = x19 && x18 = 1 + x12 && 1 + x12 <= 500
l4(x24, x25, x26, x27, x28, x29) -> l2(x30, x31, x32, x33, x34, x35) :|: x29 = x35 && x28 = x34 && x27 = x33 && x26 = x32 && x25 = x31 && x24 = x30
l1(x36, x37, x38, x39, x40, x41) -> l3(x42, x43, x44, x45, x46, x47) :|: x41 = x47 && x40 = x46 && x39 = x45 && x37 = x43 && x36 = x42 && x44 = x41 && 500 <= x36
l1(x48, x49, x50, x51, x52, x53) -> l2(x54, x55, x56, x57, x58, x59) :|: x53 = x59 && x52 = x58 && x51 = x57 && x50 = x56 && x49 = x55 && x54 = 1 + x48 && 1 + x48 <= 500
l5(x60, x61, x62, x63, x64, x65) -> l0(x66, x67, x68, x69, x70, x71) :|: x65 = x71 && x64 = x70 && x63 = x69 && x62 = x68 && x61 = x67 && x60 = x66
Start term: l5(i_13HAT0, j_15HAT0, rt_11HAT0, s_16HAT0, s_17HAT0, st_14HAT0)

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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(i_13HAT0, j_15HAT0, rt_11HAT0, s_16HAT0, s_17HAT0, st_14HAT0) -> l1(i_13HATpost, j_15HATpost, rt_11HATpost, s_16HATpost, s_17HATpost, st_14HATpost) :|: i_13HAT1 = s_17HAT0 && j_15HATpost = s_16HAT0 && i_13HATpost = j_15HATpost && rt_11HAT0 = rt_11HATpost && s_16HAT0 = s_16HATpost && s_17HAT0 = s_17HATpost && st_14HAT0 = st_14HATpost
l2(x, x1, x2, x3, x4, x5) -> l3(x6, x7, x8, x9, x10, x11) :|: x5 = x11 && x4 = x10 && x3 = x9 && x1 = x7 && x = x6 && x8 = x5 && 500 <= x
l2(x12, x13, x14, x15, x16, x17) -> l4(x18, x19, x20, x21, x22, x23) :|: x17 = x23 && x16 = x22 && x15 = x21 && x14 = x20 && x13 = x19 && x18 = 1 + x12 && 1 + x12 <= 500
l4(x24, x25, x26, x27, x28, x29) -> l2(x30, x31, x32, x33, x34, x35) :|: x29 = x35 && x28 = x34 && x27 = x33 && x26 = x32 && x25 = x31 && x24 = x30
l1(x36, x37, x38, x39, x40, x41) -> l3(x42, x43, x44, x45, x46, x47) :|: x41 = x47 && x40 = x46 && x39 = x45 && x37 = x43 && x36 = x42 && x44 = x41 && 500 <= x36
l1(x48, x49, x50, x51, x52, x53) -> l2(x54, x55, x56, x57, x58, x59) :|: x53 = x59 && x52 = x58 && x51 = x57 && x50 = x56 && x49 = x55 && x54 = 1 + x48 && 1 + x48 <= 500
l5(x60, x61, x62, x63, x64, x65) -> l0(x66, x67, x68, x69, x70, x71) :|: x65 = x71 && x64 = x70 && x63 = x69 && x62 = x68 && x61 = x67 && x60 = x66
Start term: l5(i_13HAT0, j_15HAT0, rt_11HAT0, s_16HAT0, s_17HAT0, st_14HAT0)

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(3) IRSwTTerminationDigraphProof (EQUIVALENT)
Constructed termination digraph!
Nodes:
(1) l0(i_13HAT0, j_15HAT0, rt_11HAT0, s_16HAT0, s_17HAT0, st_14HAT0) -> l1(i_13HATpost, j_15HATpost, rt_11HATpost, s_16HATpost, s_17HATpost, st_14HATpost) :|: i_13HAT1 = s_17HAT0 && j_15HATpost = s_16HAT0 && i_13HATpost = j_15HATpost && rt_11HAT0 = rt_11HATpost && s_16HAT0 = s_16HATpost && s_17HAT0 = s_17HATpost && st_14HAT0 = st_14HATpost
(2) l2(x, x1, x2, x3, x4, x5) -> l3(x6, x7, x8, x9, x10, x11) :|: x5 = x11 && x4 = x10 && x3 = x9 && x1 = x7 && x = x6 && x8 = x5 && 500 <= x
(3) l2(x12, x13, x14, x15, x16, x17) -> l4(x18, x19, x20, x21, x22, x23) :|: x17 = x23 && x16 = x22 && x15 = x21 && x14 = x20 && x13 = x19 && x18 = 1 + x12 && 1 + x12 <= 500
(4) l4(x24, x25, x26, x27, x28, x29) -> l2(x30, x31, x32, x33, x34, x35) :|: x29 = x35 && x28 = x34 && x27 = x33 && x26 = x32 && x25 = x31 && x24 = x30
(5) l1(x36, x37, x38, x39, x40, x41) -> l3(x42, x43, x44, x45, x46, x47) :|: x41 = x47 && x40 = x46 && x39 = x45 && x37 = x43 && x36 = x42 && x44 = x41 && 500 <= x36
(6) l1(x48, x49, x50, x51, x52, x53) -> l2(x54, x55, x56, x57, x58, x59) :|: x53 = x59 && x52 = x58 && x51 = x57 && x50 = x56 && x49 = x55 && x54 = 1 + x48 && 1 + x48 <= 500
(7) l5(x60, x61, x62, x63, x64, x65) -> l0(x66, x67, x68, x69, x70, x71) :|: x65 = x71 && x64 = x70 && x63 = x69 && x62 = x68 && x61 = x67 && x60 = x66

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

This digraph is fully evaluated!
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(4)
Obligation:

Termination digraph:
Nodes:
(1) l2(x12, x13, x14, x15, x16, x17) -> l4(x18, x19, x20, x21, x22, x23) :|: x17 = x23 && x16 = x22 && x15 = x21 && x14 = x20 && x13 = x19 && x18 = 1 + x12 && 1 + x12 <= 500
(2) l4(x24, x25, x26, x27, x28, x29) -> l2(x30, x31, x32, x33, x34, x35) :|: x29 = x35 && x28 = x34 && x27 = x33 && x26 = x32 && x25 = x31 && x24 = x30

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:
l2(x12:0, x13:0, x14:0, x15:0, x16:0, x17:0) -> l2(1 + x12:0, x13:0, x14:0, x15:0, x16:0, x17:0) :|: x12:0 < 500

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(7) IntTRSUnneededArgumentFilterProof (EQUIVALENT)
Some arguments are removed because they cannot influence termination. We removed arguments according to the following replacements:

   l2(x1, x2, x3, x4, x5, x6) -> l2(x1)

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(8)
Obligation:
Rules:
l2(x12:0) -> l2(1 + x12:0) :|: x12:0 < 500

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(9) TempFilterProof (SOUND)
Used the following sort dictionary for filtering: 
l2(INTEGER)
Replaced non-predefined constructor symbols by 0.
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(10)
Obligation:
Rules:
l2(x12:0) -> l2(c) :|: c = 1 + x12:0 && x12:0 < 500

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(11) PolynomialOrderProcessor (EQUIVALENT)
Found the following polynomial interpretation:
[l2(x)] = 499 - x

The following rules are decreasing:
l2(x12:0) -> l2(c) :|: c = 1 + x12:0 && x12:0 < 500
The following rules are bounded:
l2(x12:0) -> l2(c) :|: c = 1 + x12:0 && x12:0 < 500

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(12)
YES