NO
proof of prog.inttrs
# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty


Termination of the given IRSwT could be disproven:

(0) IRSwT
(1) IRSFormatTransformerProof [EQUIVALENT, 0 ms]
(2) IRSwT
(3) IRSwTTerminationDigraphProof [EQUIVALENT, 430 ms]
(4) IRSwT
(5) IntTRSCompressionProof [EQUIVALENT, 0 ms]
(6) IRSwT
(7) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms]
(8) IRSwT
(9) FilterProof [EQUIVALENT, 0 ms]
(10) IntTRS
(11) IntTRSPeriodicNontermProof [COMPLETE, 0 ms]
(12) NO


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(0)
Obligation:
Rules:
l0(Result_4HAT0, cnt_27HAT0, lt_10HAT0, lt_11HAT0, lt_12HAT0, lt_29HAT0, lt_8HAT0, lt_9HAT0, p_6HAT0, q_7HAT0, x_5HAT0) -> l1(Result_4HATpost, cnt_27HATpost, lt_10HATpost, lt_11HATpost, lt_12HATpost, lt_29HATpost, lt_8HATpost, lt_9HATpost, p_6HATpost, q_7HATpost, x_5HATpost) :|: lt_11HAT1 = x_5HAT0 && lt_12HAT1 = cnt_27HAT0 && lt_12HAT1 <= 0 && lt_11HATpost = lt_11HATpost && lt_12HATpost = lt_12HATpost && Result_4HATpost = Result_4HATpost && cnt_27HAT0 = cnt_27HATpost && lt_10HAT0 = lt_10HATpost && lt_29HAT0 = lt_29HATpost && lt_8HAT0 = lt_8HATpost && lt_9HAT0 = lt_9HATpost && p_6HAT0 = p_6HATpost && q_7HAT0 = q_7HATpost && x_5HAT0 = x_5HATpost
l0(x, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10) -> l2(x11, x12, x13, x14, x15, x16, x17, x18, x19, x20, x21) :|: x22 = x10 && x23 = x1 && 0 <= -1 + x23 && x14 = x14 && x15 = x15 && x24 = x5 && x25 = x1 && x26 = x5 && x17 = x17 && x18 = x18 && x13 = x13 && x = x11 && x1 = x12 && x5 = x16 && x8 = x19 && x9 = x20 && x10 = x21
l2(x27, x28, x29, x30, x31, x32, x33, x34, x35, x36, x37) -> l0(x38, x39, x40, x41, x42, x43, x44, x45, x46, x47, x48) :|: x37 = x48 && x36 = x47 && x35 = x46 && x34 = x45 && x33 = x44 && x32 = x43 && x31 = x42 && x30 = x41 && x29 = x40 && x28 = x39 && x27 = x38
l3(x49, x50, x51, x52, x53, x54, x55, x56, x57, x58, x59) -> l0(x60, x61, x62, x63, x64, x65, x66, x67, x68, x69, x70) :|: x56 = x67 && x55 = x66 && x54 = x65 && x53 = x64 && x52 = x63 && x51 = x62 && x50 = x61 && x49 = x60 && x69 = x68 && x70 = x70 && x68 = x68
l4(x71, x72, x73, x74, x75, x76, x77, x78, x79, x80, x81) -> l3(x82, x83, x84, x85, x86, x87, x88, x89, x90, x91, x92) :|: x81 = x92 && x80 = x91 && x79 = x90 && x78 = x89 && x77 = x88 && x76 = x87 && x75 = x86 && x74 = x85 && x73 = x84 && x72 = x83 && x71 = x82
Start term: l4(Result_4HAT0, cnt_27HAT0, lt_10HAT0, lt_11HAT0, lt_12HAT0, lt_29HAT0, lt_8HAT0, lt_9HAT0, p_6HAT0, q_7HAT0, x_5HAT0)

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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, cnt_27HAT0, lt_10HAT0, lt_11HAT0, lt_12HAT0, lt_29HAT0, lt_8HAT0, lt_9HAT0, p_6HAT0, q_7HAT0, x_5HAT0) -> l1(Result_4HATpost, cnt_27HATpost, lt_10HATpost, lt_11HATpost, lt_12HATpost, lt_29HATpost, lt_8HATpost, lt_9HATpost, p_6HATpost, q_7HATpost, x_5HATpost) :|: lt_11HAT1 = x_5HAT0 && lt_12HAT1 = cnt_27HAT0 && lt_12HAT1 <= 0 && lt_11HATpost = lt_11HATpost && lt_12HATpost = lt_12HATpost && Result_4HATpost = Result_4HATpost && cnt_27HAT0 = cnt_27HATpost && lt_10HAT0 = lt_10HATpost && lt_29HAT0 = lt_29HATpost && lt_8HAT0 = lt_8HATpost && lt_9HAT0 = lt_9HATpost && p_6HAT0 = p_6HATpost && q_7HAT0 = q_7HATpost && x_5HAT0 = x_5HATpost
l0(x, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10) -> l2(x11, x12, x13, x14, x15, x16, x17, x18, x19, x20, x21) :|: x22 = x10 && x23 = x1 && 0 <= -1 + x23 && x14 = x14 && x15 = x15 && x24 = x5 && x25 = x1 && x26 = x5 && x17 = x17 && x18 = x18 && x13 = x13 && x = x11 && x1 = x12 && x5 = x16 && x8 = x19 && x9 = x20 && x10 = x21
l2(x27, x28, x29, x30, x31, x32, x33, x34, x35, x36, x37) -> l0(x38, x39, x40, x41, x42, x43, x44, x45, x46, x47, x48) :|: x37 = x48 && x36 = x47 && x35 = x46 && x34 = x45 && x33 = x44 && x32 = x43 && x31 = x42 && x30 = x41 && x29 = x40 && x28 = x39 && x27 = x38
l3(x49, x50, x51, x52, x53, x54, x55, x56, x57, x58, x59) -> l0(x60, x61, x62, x63, x64, x65, x66, x67, x68, x69, x70) :|: x56 = x67 && x55 = x66 && x54 = x65 && x53 = x64 && x52 = x63 && x51 = x62 && x50 = x61 && x49 = x60 && x69 = x68 && x70 = x70 && x68 = x68
l4(x71, x72, x73, x74, x75, x76, x77, x78, x79, x80, x81) -> l3(x82, x83, x84, x85, x86, x87, x88, x89, x90, x91, x92) :|: x81 = x92 && x80 = x91 && x79 = x90 && x78 = x89 && x77 = x88 && x76 = x87 && x75 = x86 && x74 = x85 && x73 = x84 && x72 = x83 && x71 = x82
Start term: l4(Result_4HAT0, cnt_27HAT0, lt_10HAT0, lt_11HAT0, lt_12HAT0, lt_29HAT0, lt_8HAT0, lt_9HAT0, p_6HAT0, q_7HAT0, x_5HAT0)

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(3) IRSwTTerminationDigraphProof (EQUIVALENT)
Constructed termination digraph!
Nodes:
(1) l0(Result_4HAT0, cnt_27HAT0, lt_10HAT0, lt_11HAT0, lt_12HAT0, lt_29HAT0, lt_8HAT0, lt_9HAT0, p_6HAT0, q_7HAT0, x_5HAT0) -> l1(Result_4HATpost, cnt_27HATpost, lt_10HATpost, lt_11HATpost, lt_12HATpost, lt_29HATpost, lt_8HATpost, lt_9HATpost, p_6HATpost, q_7HATpost, x_5HATpost) :|: lt_11HAT1 = x_5HAT0 && lt_12HAT1 = cnt_27HAT0 && lt_12HAT1 <= 0 && lt_11HATpost = lt_11HATpost && lt_12HATpost = lt_12HATpost && Result_4HATpost = Result_4HATpost && cnt_27HAT0 = cnt_27HATpost && lt_10HAT0 = lt_10HATpost && lt_29HAT0 = lt_29HATpost && lt_8HAT0 = lt_8HATpost && lt_9HAT0 = lt_9HATpost && p_6HAT0 = p_6HATpost && q_7HAT0 = q_7HATpost && x_5HAT0 = x_5HATpost
(2) l0(x, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10) -> l2(x11, x12, x13, x14, x15, x16, x17, x18, x19, x20, x21) :|: x22 = x10 && x23 = x1 && 0 <= -1 + x23 && x14 = x14 && x15 = x15 && x24 = x5 && x25 = x1 && x26 = x5 && x17 = x17 && x18 = x18 && x13 = x13 && x = x11 && x1 = x12 && x5 = x16 && x8 = x19 && x9 = x20 && x10 = x21
(3) l2(x27, x28, x29, x30, x31, x32, x33, x34, x35, x36, x37) -> l0(x38, x39, x40, x41, x42, x43, x44, x45, x46, x47, x48) :|: x37 = x48 && x36 = x47 && x35 = x46 && x34 = x45 && x33 = x44 && x32 = x43 && x31 = x42 && x30 = x41 && x29 = x40 && x28 = x39 && x27 = x38
(4) l3(x49, x50, x51, x52, x53, x54, x55, x56, x57, x58, x59) -> l0(x60, x61, x62, x63, x64, x65, x66, x67, x68, x69, x70) :|: x56 = x67 && x55 = x66 && x54 = x65 && x53 = x64 && x52 = x63 && x51 = x62 && x50 = x61 && x49 = x60 && x69 = x68 && x70 = x70 && x68 = x68
(5) l4(x71, x72, x73, x74, x75, x76, x77, x78, x79, x80, x81) -> l3(x82, x83, x84, x85, x86, x87, x88, x89, x90, x91, x92) :|: x81 = x92 && x80 = x91 && x79 = x90 && x78 = x89 && x77 = x88 && x76 = x87 && x75 = x86 && x74 = x85 && x73 = x84 && x72 = x83 && x71 = x82

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

This digraph is fully evaluated!
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(4)
Obligation:

Termination digraph:
Nodes:
(1) l0(x, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10) -> l2(x11, x12, x13, x14, x15, x16, x17, x18, x19, x20, x21) :|: x22 = x10 && x23 = x1 && 0 <= -1 + x23 && x14 = x14 && x15 = x15 && x24 = x5 && x25 = x1 && x26 = x5 && x17 = x17 && x18 = x18 && x13 = x13 && x = x11 && x1 = x12 && x5 = x16 && x8 = x19 && x9 = x20 && x10 = x21
(2) l2(x27, x28, x29, x30, x31, x32, x33, x34, x35, x36, x37) -> l0(x38, x39, x40, x41, x42, x43, x44, x45, x46, x47, x48) :|: x37 = x48 && x36 = x47 && x35 = x46 && x34 = x45 && x33 = x44 && x32 = x43 && x31 = x42 && x30 = x41 && x29 = x40 && x28 = x39 && x27 = x38

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(x11:0, x12:0, x2:0, x3:0, x4:0, x16:0, x6:0, x7:0, x19:0, x20:0, x10:0) -> l0(x11:0, x12:0, x13:0, x14:0, x15:0, x16:0, x17:0, x18:0, x19:0, x20:0, x10:0) :|: x12:0 > 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, x7, x8, x9, x10, x11) -> l0(x2)

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(8)
Obligation:
Rules:
l0(x12:0) -> l0(x12:0) :|: x12:0 > 0

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(9) FilterProof (EQUIVALENT)
Used the following sort dictionary for filtering: 
l0(INTEGER)
Replaced non-predefined constructor symbols by 0.
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(10)
Obligation:
Rules:
l0(x12:0) -> l0(x12:0) :|: x12:0 > 0

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(11) IntTRSPeriodicNontermProof (COMPLETE)
Normalized system to the following form:
f(pc, x12:0) -> f(1, x12:0) :|: pc = 1 && x12:0 > 0
Witness term starting non-terminating reduction: f(1, 1)
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(12)
NO