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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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, 373 ms]
(4) IRSwT
(5) IntTRSCompressionProof [EQUIVALENT, 25 ms]
(6) IRSwT
(7) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms]
(8) IRSwT
(9) TempFilterProof [SOUND, 56 ms]
(10) IntTRS
(11) PolynomialOrderProcessor [EQUIVALENT, 0 ms]
(12) IntTRS
(13) PolynomialOrderProcessor [EQUIVALENT, 0 ms]
(14) YES


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(0)
Obligation:
Rules:
l0(x_13HAT0, x_27HAT0, x_32HAT0, y_16HAT0, y_28HAT0, y_33HAT0) -> l1(x_13HATpost, x_27HATpost, x_32HATpost, y_16HATpost, y_28HATpost, y_33HATpost) :|: y_33HAT0 = y_33HATpost && y_28HAT0 = y_28HATpost && x_32HAT0 = x_32HATpost && x_27HAT0 = x_27HATpost && y_16HATpost = y_16HATpost && x_13HATpost = x_13HATpost
l1(x, x1, x2, x3, x4, x5) -> l2(x6, x7, x8, x9, x10, x11) :|: x5 = x11 && x4 = x10 && x2 = x8 && x1 = x7 && x = x6 && 1 <= x && 1 <= x9 && x9 = 5000 && 1 <= x
l3(x12, x13, x14, x15, x16, x17) -> l2(x18, x19, x20, x21, x22, x23) :|: x17 = x23 && x14 = x20 && 1 <= x22 && 1 <= x19 && -1 + x22 <= x21 && x21 <= -1 + x22 && -1 + x19 <= x18 && x18 <= -1 + x19 && x21 = -1 + x15 && x18 = -1 + x12 && 1 <= x15 && x22 = x22 && x19 = x19
l2(x24, x25, x26, x27, x28, x29) -> l1(x30, x31, x32, x33, x34, x35) :|: x29 = x35 && x28 = x34 && x27 = x33 && x26 = x32 && x25 = x31 && x24 = x30 && x27 <= 0 && x27 <= 0
l2(x36, x37, x38, x39, x40, x41) -> l4(x42, x43, x44, x45, x46, x47) :|: x40 = x46 && x37 = x43 && 1 <= x47 && -1 + x47 <= x45 && x45 <= -1 + x47 && -1 + x44 <= x42 && x42 <= -1 + x44 && x45 = -1 + x39 && x42 = -1 + x36 && 1 <= x39 && x47 = x47 && x44 = x44
l4(x48, x49, x50, x51, x52, x53) -> l2(x54, x55, x56, x57, x58, x59) :|: x53 = x59 && x52 = x58 && x51 = x57 && x50 = x56 && x49 = x55 && x48 = x54
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(x_13HAT0, x_27HAT0, x_32HAT0, y_16HAT0, y_28HAT0, y_33HAT0)

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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(x_13HAT0, x_27HAT0, x_32HAT0, y_16HAT0, y_28HAT0, y_33HAT0) -> l1(x_13HATpost, x_27HATpost, x_32HATpost, y_16HATpost, y_28HATpost, y_33HATpost) :|: y_33HAT0 = y_33HATpost && y_28HAT0 = y_28HATpost && x_32HAT0 = x_32HATpost && x_27HAT0 = x_27HATpost && y_16HATpost = y_16HATpost && x_13HATpost = x_13HATpost
l1(x, x1, x2, x3, x4, x5) -> l2(x6, x7, x8, x9, x10, x11) :|: x5 = x11 && x4 = x10 && x2 = x8 && x1 = x7 && x = x6 && 1 <= x && 1 <= x9 && x9 = 5000 && 1 <= x
l3(x12, x13, x14, x15, x16, x17) -> l2(x18, x19, x20, x21, x22, x23) :|: x17 = x23 && x14 = x20 && 1 <= x22 && 1 <= x19 && -1 + x22 <= x21 && x21 <= -1 + x22 && -1 + x19 <= x18 && x18 <= -1 + x19 && x21 = -1 + x15 && x18 = -1 + x12 && 1 <= x15 && x22 = x22 && x19 = x19
l2(x24, x25, x26, x27, x28, x29) -> l1(x30, x31, x32, x33, x34, x35) :|: x29 = x35 && x28 = x34 && x27 = x33 && x26 = x32 && x25 = x31 && x24 = x30 && x27 <= 0 && x27 <= 0
l2(x36, x37, x38, x39, x40, x41) -> l4(x42, x43, x44, x45, x46, x47) :|: x40 = x46 && x37 = x43 && 1 <= x47 && -1 + x47 <= x45 && x45 <= -1 + x47 && -1 + x44 <= x42 && x42 <= -1 + x44 && x45 = -1 + x39 && x42 = -1 + x36 && 1 <= x39 && x47 = x47 && x44 = x44
l4(x48, x49, x50, x51, x52, x53) -> l2(x54, x55, x56, x57, x58, x59) :|: x53 = x59 && x52 = x58 && x51 = x57 && x50 = x56 && x49 = x55 && x48 = x54
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(x_13HAT0, x_27HAT0, x_32HAT0, y_16HAT0, y_28HAT0, y_33HAT0)

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(3) IRSwTTerminationDigraphProof (EQUIVALENT)
Constructed termination digraph!
Nodes:
(1) l0(x_13HAT0, x_27HAT0, x_32HAT0, y_16HAT0, y_28HAT0, y_33HAT0) -> l1(x_13HATpost, x_27HATpost, x_32HATpost, y_16HATpost, y_28HATpost, y_33HATpost) :|: y_33HAT0 = y_33HATpost && y_28HAT0 = y_28HATpost && x_32HAT0 = x_32HATpost && x_27HAT0 = x_27HATpost && y_16HATpost = y_16HATpost && x_13HATpost = x_13HATpost
(2) l1(x, x1, x2, x3, x4, x5) -> l2(x6, x7, x8, x9, x10, x11) :|: x5 = x11 && x4 = x10 && x2 = x8 && x1 = x7 && x = x6 && 1 <= x && 1 <= x9 && x9 = 5000 && 1 <= x
(3) l3(x12, x13, x14, x15, x16, x17) -> l2(x18, x19, x20, x21, x22, x23) :|: x17 = x23 && x14 = x20 && 1 <= x22 && 1 <= x19 && -1 + x22 <= x21 && x21 <= -1 + x22 && -1 + x19 <= x18 && x18 <= -1 + x19 && x21 = -1 + x15 && x18 = -1 + x12 && 1 <= x15 && x22 = x22 && x19 = x19
(4) l2(x24, x25, x26, x27, x28, x29) -> l1(x30, x31, x32, x33, x34, x35) :|: x29 = x35 && x28 = x34 && x27 = x33 && x26 = x32 && x25 = x31 && x24 = x30 && x27 <= 0 && x27 <= 0
(5) l2(x36, x37, x38, x39, x40, x41) -> l4(x42, x43, x44, x45, x46, x47) :|: x40 = x46 && x37 = x43 && 1 <= x47 && -1 + x47 <= x45 && x45 <= -1 + x47 && -1 + x44 <= x42 && x42 <= -1 + x44 && x45 = -1 + x39 && x42 = -1 + x36 && 1 <= x39 && x47 = x47 && x44 = x44
(6) l4(x48, x49, x50, x51, x52, x53) -> l2(x54, x55, x56, x57, x58, x59) :|: x53 = x59 && x52 = x58 && x51 = x57 && x50 = x56 && x49 = x55 && x48 = x54
(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) -> (2)
(2) -> (5)
(3) -> (4), (5)
(4) -> (2)
(5) -> (6)
(6) -> (4), (5)
(7) -> (1)

This digraph is fully evaluated!
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(4)
Obligation:

Termination digraph:
Nodes:
(1) l1(x, x1, x2, x3, x4, x5) -> l2(x6, x7, x8, x9, x10, x11) :|: x5 = x11 && x4 = x10 && x2 = x8 && x1 = x7 && x = x6 && 1 <= x && 1 <= x9 && x9 = 5000 && 1 <= x
(2) l2(x24, x25, x26, x27, x28, x29) -> l1(x30, x31, x32, x33, x34, x35) :|: x29 = x35 && x28 = x34 && x27 = x33 && x26 = x32 && x25 = x31 && x24 = x30 && x27 <= 0 && x27 <= 0
(3) l4(x48, x49, x50, x51, x52, x53) -> l2(x54, x55, x56, x57, x58, x59) :|: x53 = x59 && x52 = x58 && x51 = x57 && x50 = x56 && x49 = x55 && x48 = x54
(4) l2(x36, x37, x38, x39, x40, x41) -> l4(x42, x43, x44, x45, x46, x47) :|: x40 = x46 && x37 = x43 && 1 <= x47 && -1 + x47 <= x45 && x45 <= -1 + x47 && -1 + x44 <= x42 && x42 <= -1 + x44 && x45 = -1 + x39 && x42 = -1 + x36 && 1 <= x39 && x47 = x47 && x44 = x44

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

This digraph is fully evaluated!

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(5) IntTRSCompressionProof (EQUIVALENT)
Compressed rules.
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(6)
Obligation:
Rules:
l2(x24:0, x25:0, x26:0, x27:0, x10:0, x11:0) -> l2(x24:0, x25:0, x26:0, 5000, x10:0, x11:0) :|: x24:0 > 0 && x27:0 < 1
l2(x36:0, x37:0, x38:0, x39:0, x40:0, x41:0) -> l2(-1 + x36:0, x37:0, x44:0, -1 + x39:0, x40:0, x47:0) :|: x47:0 > 0 && x39:0 > 0 && -1 + x47:0 = -1 + x39:0 && -1 + x44:0 = -1 + x36:0

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

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

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(8)
Obligation:
Rules:
l2(x24:0, x26:0, x27:0, x11:0) -> l2(x24:0, x26:0, 5000, x11:0) :|: x24:0 > 0 && x27:0 < 1
l2(x36:0, x38:0, x39:0, x41:0) -> l2(-1 + x36:0, x44:0, -1 + x39:0, x47:0) :|: x47:0 > 0 && x39:0 > 0 && -1 + x47:0 = -1 + x39:0 && -1 + x44:0 = -1 + x36:0

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(9) TempFilterProof (SOUND)
Used the following sort dictionary for filtering: 
l2(INTEGER, VARIABLE, VARIABLE, VARIABLE)
Replaced non-predefined constructor symbols by 0.
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(10)
Obligation:
Rules:
l2(x24:0, x26:0, x27:0, x11:0) -> l2(x24:0, x26:0, c, x11:0) :|: c = 5000 && (x24:0 > 0 && x27:0 < 1)
l2(x36:0, x38:0, x39:0, x41:0) -> l2(c1, x44:0, c2, x47:0) :|: c2 = -1 + x39:0 && c1 = -1 + x36:0 && (x47:0 > 0 && x39:0 > 0 && -1 + x47:0 = -1 + x39:0 && -1 + x44:0 = -1 + x36:0)

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(11) PolynomialOrderProcessor (EQUIVALENT)
Found the following polynomial interpretation:
[l2(x, x1, x2, x3)] = x - x2

The following rules are decreasing:
l2(x24:0, x26:0, x27:0, x11:0) -> l2(x24:0, x26:0, c, x11:0) :|: c = 5000 && (x24:0 > 0 && x27:0 < 1)
The following rules are bounded:
l2(x24:0, x26:0, x27:0, x11:0) -> l2(x24:0, x26:0, c, x11:0) :|: c = 5000 && (x24:0 > 0 && x27:0 < 1)

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(12)
Obligation:
Rules:
l2(x36:0, x38:0, x39:0, x41:0) -> l2(c1, x44:0, c2, x47:0) :|: c2 = -1 + x39:0 && c1 = -1 + x36:0 && (x47:0 > 0 && x39:0 > 0 && -1 + x47:0 = -1 + x39:0 && -1 + x44:0 = -1 + x36:0)

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(13) PolynomialOrderProcessor (EQUIVALENT)
Found the following polynomial interpretation:
[l2(x, x1, x2, x3)] = x2

The following rules are decreasing:
l2(x36:0, x38:0, x39:0, x41:0) -> l2(c1, x44:0, c2, x47:0) :|: c2 = -1 + x39:0 && c1 = -1 + x36:0 && (x47:0 > 0 && x39:0 > 0 && -1 + x47:0 = -1 + x39:0 && -1 + x44:0 = -1 + x36:0)
The following rules are bounded:
l2(x36:0, x38:0, x39:0, x41:0) -> l2(c1, x44:0, c2, x47:0) :|: c2 = -1 + x39:0 && c1 = -1 + x36:0 && (x47:0 > 0 && x39:0 > 0 && -1 + x47:0 = -1 + x39:0 && -1 + x44:0 = -1 + x36:0)

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(14)
YES