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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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, 140 ms]
(4) IRSwT
(5) IntTRSCompressionProof [EQUIVALENT, 0 ms]
(6) IRSwT
(7) FilterProof [EQUIVALENT, 0 ms]
(8) IntTRS
(9) IntTRSPeriodicNontermProof [COMPLETE, 0 ms]
(10) NO


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(0)
Obligation:
Rules:
l0(hiHAT0, loHAT0) -> l1(hiHATpost, loHATpost) :|: loHAT0 = loHATpost && hiHATpost = hiHATpost
l0(x, x1) -> l1(x2, x3) :|: x = x2 && x3 = x3
l2(x4, x5) -> l3(x6, x7) :|: x5 = x7 && x4 = x6 && x5 <= x4
l2(x8, x9) -> l0(x10, x11) :|: x9 = x11 && x8 = x10 && 1 + x8 <= x9
l1(x12, x13) -> l2(x14, x15) :|: x13 = x15 && x12 = x14
l4(x16, x17) -> l1(x18, x19) :|: x19 = 99 && x18 = 0
l5(x20, x21) -> l4(x22, x23) :|: x21 = x23 && x20 = x22
Start term: l5(hiHAT0, loHAT0)

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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(hiHAT0, loHAT0) -> l1(hiHATpost, loHATpost) :|: loHAT0 = loHATpost && hiHATpost = hiHATpost
l0(x, x1) -> l1(x2, x3) :|: x = x2 && x3 = x3
l2(x4, x5) -> l3(x6, x7) :|: x5 = x7 && x4 = x6 && x5 <= x4
l2(x8, x9) -> l0(x10, x11) :|: x9 = x11 && x8 = x10 && 1 + x8 <= x9
l1(x12, x13) -> l2(x14, x15) :|: x13 = x15 && x12 = x14
l4(x16, x17) -> l1(x18, x19) :|: x19 = 99 && x18 = 0
l5(x20, x21) -> l4(x22, x23) :|: x21 = x23 && x20 = x22
Start term: l5(hiHAT0, loHAT0)

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(3) IRSwTTerminationDigraphProof (EQUIVALENT)
Constructed termination digraph!
Nodes:
(1) l0(hiHAT0, loHAT0) -> l1(hiHATpost, loHATpost) :|: loHAT0 = loHATpost && hiHATpost = hiHATpost
(2) l0(x, x1) -> l1(x2, x3) :|: x = x2 && x3 = x3
(3) l2(x4, x5) -> l3(x6, x7) :|: x5 = x7 && x4 = x6 && x5 <= x4
(4) l2(x8, x9) -> l0(x10, x11) :|: x9 = x11 && x8 = x10 && 1 + x8 <= x9
(5) l1(x12, x13) -> l2(x14, x15) :|: x13 = x15 && x12 = x14
(6) l4(x16, x17) -> l1(x18, x19) :|: x19 = 99 && x18 = 0
(7) l5(x20, x21) -> l4(x22, x23) :|: x21 = x23 && x20 = x22

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

This digraph is fully evaluated!
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(4)
Obligation:

Termination digraph:
Nodes:
(1) l0(hiHAT0, loHAT0) -> l1(hiHATpost, loHATpost) :|: loHAT0 = loHATpost && hiHATpost = hiHATpost
(2) l2(x8, x9) -> l0(x10, x11) :|: x9 = x11 && x8 = x10 && 1 + x8 <= x9
(3) l1(x12, x13) -> l2(x14, x15) :|: x13 = x15 && x12 = x14
(4) l0(x, x1) -> l1(x2, x3) :|: x = x2 && x3 = x3

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

This digraph is fully evaluated!

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(5) IntTRSCompressionProof (EQUIVALENT)
Compressed rules.
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(6)
Obligation:
Rules:
l2(x10:0, x11:0) -> l2(x10:0, x15:0) :|: x11:0 >= 1 + x10:0
l2(x, x1) -> l2(x2, x1) :|: x1 >= 1 + x

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(7) FilterProof (EQUIVALENT)
Used the following sort dictionary for filtering: 
l2(VARIABLE, VARIABLE)
Replaced non-predefined constructor symbols by 0.
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(8)
Obligation:
Rules:
l2(x10:0, x11:0) -> l2(x10:0, x15:0) :|: x11:0 >= 1 + x10:0
l2(x, x1) -> l2(x2, x1) :|: x1 >= 1 + x

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(9) IntTRSPeriodicNontermProof (COMPLETE)
Normalized system to the following form:
f(pc, x10:0, x11:0) -> f(1, x10:0, x15:0) :|: pc = 1 && x11:0 >= 1 + x10:0
f(pc, x, x1) -> f(1, x2, x1) :|: pc = 1 && x1 >= 1 + x
Witness term starting non-terminating reduction: f(1, -4, 0)
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(10)
NO