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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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, 411 ms]
(4) IRSwT
(5) IntTRSCompressionProof [EQUIVALENT, 0 ms]
(6) IRSwT
(7) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms]
(8) IRSwT
(9) TempFilterProof [SOUND, 39 ms]
(10) IntTRS
(11) PolynomialOrderProcessor [EQUIVALENT, 15 ms]
(12) YES


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(0)
Obligation:
Rules:
l0(result_11HAT0, t_16HAT0, t_22HAT0, temp0_14HAT0, x_13HAT0, y_15HAT0, y_21HAT0) -> l1(result_11HATpost, t_16HATpost, t_22HATpost, temp0_14HATpost, x_13HATpost, y_15HATpost, y_21HATpost) :|: y_21HAT0 = y_21HATpost && y_15HAT0 = y_15HATpost && x_13HAT0 = x_13HATpost && temp0_14HAT0 = temp0_14HATpost && t_22HAT0 = t_22HATpost && t_16HAT0 = t_16HATpost && result_11HAT0 = result_11HATpost
l1(x, x1, x2, x3, x4, x5, x6) -> l2(x7, x8, x9, x10, x11, x12, x13) :|: x6 = x13 && x5 = x12 && x4 = x11 && x3 = x10 && x2 = x9 && x1 = x8 && x7 = x3 && x5 <= 0 && 1 <= x4
l1(x14, x15, x16, x17, x18, x19, x20) -> l2(x21, x22, x23, x24, x25, x26, x27) :|: x20 = x27 && x19 = x26 && x17 = x24 && x16 = x23 && x15 = x22 && x25 <= 0 && x21 = x17 && x25 = x25 && x18 <= 0
l1(x28, x29, x30, x31, x32, x33, x34) -> l3(x35, x36, x37, x38, x39, x40, x41) :|: x41 = x41 && x37 = x37 && 1 <= x32 && 1 <= x33 && x42 = x32 && x43 = -2 + x33 && x44 = 1 + x42 && x36 = x43 && x39 = -2 + x44 && x40 = 1 + x36 && x39 <= -1 + x37 && -1 + x37 <= x39 && x40 <= 1 + x36 && 1 + x36 <= x40 && x36 <= -2 + x41 && -2 + x41 <= x36 && 1 <= x41 && 1 <= x37 && x28 = x35 && x31 = x38
l3(x45, x46, x47, x48, x49, x50, x51) -> l1(x52, x53, x54, x55, x56, x57, x58) :|: x51 = x58 && x50 = x57 && x49 = x56 && x48 = x55 && x47 = x54 && x46 = x53 && x45 = x52
l4(x59, x60, x61, x62, x63, x64, x65) -> l0(x66, x67, x68, x69, x70, x71, x72) :|: x65 = x72 && x64 = x71 && x63 = x70 && x62 = x69 && x61 = x68 && x60 = x67 && x59 = x66
Start term: l4(result_11HAT0, t_16HAT0, t_22HAT0, temp0_14HAT0, x_13HAT0, y_15HAT0, y_21HAT0)

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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_11HAT0, t_16HAT0, t_22HAT0, temp0_14HAT0, x_13HAT0, y_15HAT0, y_21HAT0) -> l1(result_11HATpost, t_16HATpost, t_22HATpost, temp0_14HATpost, x_13HATpost, y_15HATpost, y_21HATpost) :|: y_21HAT0 = y_21HATpost && y_15HAT0 = y_15HATpost && x_13HAT0 = x_13HATpost && temp0_14HAT0 = temp0_14HATpost && t_22HAT0 = t_22HATpost && t_16HAT0 = t_16HATpost && result_11HAT0 = result_11HATpost
l1(x, x1, x2, x3, x4, x5, x6) -> l2(x7, x8, x9, x10, x11, x12, x13) :|: x6 = x13 && x5 = x12 && x4 = x11 && x3 = x10 && x2 = x9 && x1 = x8 && x7 = x3 && x5 <= 0 && 1 <= x4
l1(x14, x15, x16, x17, x18, x19, x20) -> l2(x21, x22, x23, x24, x25, x26, x27) :|: x20 = x27 && x19 = x26 && x17 = x24 && x16 = x23 && x15 = x22 && x25 <= 0 && x21 = x17 && x25 = x25 && x18 <= 0
l1(x28, x29, x30, x31, x32, x33, x34) -> l3(x35, x36, x37, x38, x39, x40, x41) :|: x41 = x41 && x37 = x37 && 1 <= x32 && 1 <= x33 && x42 = x32 && x43 = -2 + x33 && x44 = 1 + x42 && x36 = x43 && x39 = -2 + x44 && x40 = 1 + x36 && x39 <= -1 + x37 && -1 + x37 <= x39 && x40 <= 1 + x36 && 1 + x36 <= x40 && x36 <= -2 + x41 && -2 + x41 <= x36 && 1 <= x41 && 1 <= x37 && x28 = x35 && x31 = x38
l3(x45, x46, x47, x48, x49, x50, x51) -> l1(x52, x53, x54, x55, x56, x57, x58) :|: x51 = x58 && x50 = x57 && x49 = x56 && x48 = x55 && x47 = x54 && x46 = x53 && x45 = x52
l4(x59, x60, x61, x62, x63, x64, x65) -> l0(x66, x67, x68, x69, x70, x71, x72) :|: x65 = x72 && x64 = x71 && x63 = x70 && x62 = x69 && x61 = x68 && x60 = x67 && x59 = x66
Start term: l4(result_11HAT0, t_16HAT0, t_22HAT0, temp0_14HAT0, x_13HAT0, y_15HAT0, y_21HAT0)

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(3) IRSwTTerminationDigraphProof (EQUIVALENT)
Constructed termination digraph!
Nodes:
(1) l0(result_11HAT0, t_16HAT0, t_22HAT0, temp0_14HAT0, x_13HAT0, y_15HAT0, y_21HAT0) -> l1(result_11HATpost, t_16HATpost, t_22HATpost, temp0_14HATpost, x_13HATpost, y_15HATpost, y_21HATpost) :|: y_21HAT0 = y_21HATpost && y_15HAT0 = y_15HATpost && x_13HAT0 = x_13HATpost && temp0_14HAT0 = temp0_14HATpost && t_22HAT0 = t_22HATpost && t_16HAT0 = t_16HATpost && result_11HAT0 = result_11HATpost
(2) l1(x, x1, x2, x3, x4, x5, x6) -> l2(x7, x8, x9, x10, x11, x12, x13) :|: x6 = x13 && x5 = x12 && x4 = x11 && x3 = x10 && x2 = x9 && x1 = x8 && x7 = x3 && x5 <= 0 && 1 <= x4
(3) l1(x14, x15, x16, x17, x18, x19, x20) -> l2(x21, x22, x23, x24, x25, x26, x27) :|: x20 = x27 && x19 = x26 && x17 = x24 && x16 = x23 && x15 = x22 && x25 <= 0 && x21 = x17 && x25 = x25 && x18 <= 0
(4) l1(x28, x29, x30, x31, x32, x33, x34) -> l3(x35, x36, x37, x38, x39, x40, x41) :|: x41 = x41 && x37 = x37 && 1 <= x32 && 1 <= x33 && x42 = x32 && x43 = -2 + x33 && x44 = 1 + x42 && x36 = x43 && x39 = -2 + x44 && x40 = 1 + x36 && x39 <= -1 + x37 && -1 + x37 <= x39 && x40 <= 1 + x36 && 1 + x36 <= x40 && x36 <= -2 + x41 && -2 + x41 <= x36 && 1 <= x41 && 1 <= x37 && x28 = x35 && x31 = x38
(5) l3(x45, x46, x47, x48, x49, x50, x51) -> l1(x52, x53, x54, x55, x56, x57, x58) :|: x51 = x58 && x50 = x57 && x49 = x56 && x48 = x55 && x47 = x54 && x46 = x53 && x45 = x52
(6) l4(x59, x60, x61, x62, x63, x64, x65) -> l0(x66, x67, x68, x69, x70, x71, x72) :|: x65 = x72 && x64 = x71 && x63 = x70 && x62 = x69 && x61 = x68 && x60 = x67 && x59 = x66

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

This digraph is fully evaluated!
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(4)
Obligation:

Termination digraph:
Nodes:
(1) l1(x28, x29, x30, x31, x32, x33, x34) -> l3(x35, x36, x37, x38, x39, x40, x41) :|: x41 = x41 && x37 = x37 && 1 <= x32 && 1 <= x33 && x42 = x32 && x43 = -2 + x33 && x44 = 1 + x42 && x36 = x43 && x39 = -2 + x44 && x40 = 1 + x36 && x39 <= -1 + x37 && -1 + x37 <= x39 && x40 <= 1 + x36 && 1 + x36 <= x40 && x36 <= -2 + x41 && -2 + x41 <= x36 && 1 <= x41 && 1 <= x37 && x28 = x35 && x31 = x38
(2) l3(x45, x46, x47, x48, x49, x50, x51) -> l1(x52, x53, x54, x55, x56, x57, x58) :|: x51 = x58 && x50 = x57 && x49 = x56 && x48 = x55 && x47 = x54 && x46 = x53 && x45 = x52

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(x28:0, x29:0, x30:0, x31:0, x32:0, x33:0, x34:0) -> l1(x28:0, -2 + x33:0, x37:0, x31:0, -2 + (1 + x32:0), 1 + (-2 + x33:0), x41:0) :|: x41:0 > 0 && x37:0 > 0 && x33:0 > 0 && x32:0 > 0 && -2 + (1 + x32:0) = -1 + x37:0 && -2 + x41:0 = -2 + x33:0

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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, x6, x7) -> l1(x2, x3, x5, x6, x7)

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(8)
Obligation:
Rules:
l1(x29:0, x30:0, x32:0, x33:0, x34:0) -> l1(-2 + x33:0, x37:0, -2 + (1 + x32:0), 1 + (-2 + x33:0), x41:0) :|: x41:0 > 0 && x37:0 > 0 && x33:0 > 0 && x32:0 > 0 && -2 + (1 + x32:0) = -1 + x37:0 && -2 + x41:0 = -2 + x33:0

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(9) TempFilterProof (SOUND)
Used the following sort dictionary for filtering: 
l1(VARIABLE, VARIABLE, INTEGER, INTEGER, VARIABLE)
Replaced non-predefined constructor symbols by 0.
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(10)
Obligation:
Rules:
l1(x29:0, x30:0, x32:0, x33:0, x34:0) -> l1(c, x37:0, c1, c2, x41:0) :|: c2 = 1 + (-2 + x33:0) && (c1 = -2 + (1 + x32:0) && c = -2 + x33:0) && (x41:0 > 0 && x37:0 > 0 && x33:0 > 0 && x32:0 > 0 && -2 + (1 + x32:0) = -1 + x37:0 && -2 + x41:0 = -2 + x33:0)

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(11) PolynomialOrderProcessor (EQUIVALENT)
Found the following polynomial interpretation:
[l1(x, x1, x2, x3, x4)] = x2

The following rules are decreasing:
l1(x29:0, x30:0, x32:0, x33:0, x34:0) -> l1(c, x37:0, c1, c2, x41:0) :|: c2 = 1 + (-2 + x33:0) && (c1 = -2 + (1 + x32:0) && c = -2 + x33:0) && (x41:0 > 0 && x37:0 > 0 && x33:0 > 0 && x32:0 > 0 && -2 + (1 + x32:0) = -1 + x37:0 && -2 + x41:0 = -2 + x33:0)
The following rules are bounded:
l1(x29:0, x30:0, x32:0, x33:0, x34:0) -> l1(c, x37:0, c1, c2, x41:0) :|: c2 = 1 + (-2 + x33:0) && (c1 = -2 + (1 + x32:0) && c = -2 + x33:0) && (x41:0 > 0 && x37:0 > 0 && x33:0 > 0 && x32:0 > 0 && -2 + (1 + x32:0) = -1 + x37:0 && -2 + x41:0 = -2 + x33:0)

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(12)
YES