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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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, 71 ms]
(4) IRSwT
(5) IntTRSCompressionProof [EQUIVALENT, 28 ms]
(6) IRSwT
(7) FilterProof [EQUIVALENT, 0 ms]
(8) IntTRS
(9) IntTRSCompressionProof [EQUIVALENT, 0 ms]
(10) IntTRS
(11) IntTRSPeriodicNontermProof [COMPLETE, 0 ms]
(12) NO


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(0)
Obligation:
Rules:
l0(xHAT0) -> l1(xHATpost) :|: xHAT1 = xHAT1 && 1 <= xHAT1 && 2 <= xHAT1 && xHATpost = xHATpost && -1 <= xHATpost && 1 + xHATpost <= 2
l1(x) -> l0(x1) :|: x = x1
l2(x2) -> l0(x3) :|: 2 <= x3 && x3 = x3
l3(x4) -> l2(x5) :|: x4 = x5
Start term: l3(xHAT0)

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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(xHAT0) -> l1(xHATpost) :|: xHAT1 = xHAT1 && 1 <= xHAT1 && 2 <= xHAT1 && xHATpost = xHATpost && -1 <= xHATpost && 1 + xHATpost <= 2
l1(x) -> l0(x1) :|: x = x1
l2(x2) -> l0(x3) :|: 2 <= x3 && x3 = x3
l3(x4) -> l2(x5) :|: x4 = x5
Start term: l3(xHAT0)

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(3) IRSwTTerminationDigraphProof (EQUIVALENT)
Constructed termination digraph!
Nodes:
(1) l0(xHAT0) -> l1(xHATpost) :|: xHAT1 = xHAT1 && 1 <= xHAT1 && 2 <= xHAT1 && xHATpost = xHATpost && -1 <= xHATpost && 1 + xHATpost <= 2
(2) l1(x) -> l0(x1) :|: x = x1
(3) l2(x2) -> l0(x3) :|: 2 <= x3 && x3 = x3
(4) l3(x4) -> l2(x5) :|: x4 = x5

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

This digraph is fully evaluated!
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(4)
Obligation:

Termination digraph:
Nodes:
(1) l0(xHAT0) -> l1(xHATpost) :|: xHAT1 = xHAT1 && 1 <= xHAT1 && 2 <= xHAT1 && xHATpost = xHATpost && -1 <= xHATpost && 1 + xHATpost <= 2
(2) l1(x) -> l0(x1) :|: x = x1

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(xHAT0:0) -> l0(x1:0) :|: x1:0 > -2 && xHAT1:0 > 1 && x1:0 < 2

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(7) FilterProof (EQUIVALENT)
Used the following sort dictionary for filtering: 
l0(VARIABLE)
Replaced non-predefined constructor symbols by 0.
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(8)
Obligation:
Rules:
l0(xHAT0:0) -> l0(x1:0) :|: x1:0 > -2 && xHAT1:0 > 1 && x1:0 < 2

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(9) IntTRSCompressionProof (EQUIVALENT)
Compressed rules.
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(10)
Obligation:
Rules:
l0(xHAT0:0:0) -> l0(x1:0:0) :|: x1:0:0 > -2 && xHAT1:0:0 > 1 && x1:0:0 < 2

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(11) IntTRSPeriodicNontermProof (COMPLETE)
Normalized system to the following form:
f(pc, xHAT0:0:0) -> f(1, x1:0:0) :|: pc = 1 && (x1:0:0 > -2 && xHAT1:0:0 > 1 && x1:0:0 < 2)
Witness term starting non-terminating reduction: f(1, -1)
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(12)
NO