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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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, 78 ms]
(4) TRUE


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(0)
Obligation:
Rules:
l0(iHAT0, jHAT0, tmpHAT0) -> l1(iHATpost, jHATpost, tmpHATpost) :|: tmpHAT0 = tmpHATpost && jHAT0 = jHATpost && iHAT0 = iHATpost
l1(x, x1, x2) -> l2(x3, x4, x5) :|: x2 = x5 && x1 = x4 && x = x3
l3(x6, x7, x8) -> l0(x9, x10, x11) :|: x11 = x11 && x10 = 1 && x9 = 0
l4(x12, x13, x14) -> l3(x15, x16, x17) :|: x14 = x17 && x13 = x16 && x12 = x15
Start term: l4(iHAT0, jHAT0, tmpHAT0)

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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(iHAT0, jHAT0, tmpHAT0) -> l1(iHATpost, jHATpost, tmpHATpost) :|: tmpHAT0 = tmpHATpost && jHAT0 = jHATpost && iHAT0 = iHATpost
l1(x, x1, x2) -> l2(x3, x4, x5) :|: x2 = x5 && x1 = x4 && x = x3
l3(x6, x7, x8) -> l0(x9, x10, x11) :|: x11 = x11 && x10 = 1 && x9 = 0
l4(x12, x13, x14) -> l3(x15, x16, x17) :|: x14 = x17 && x13 = x16 && x12 = x15
Start term: l4(iHAT0, jHAT0, tmpHAT0)

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(3) IRSwTTerminationDigraphProof (EQUIVALENT)
Constructed termination digraph!
Nodes:
(1) l0(iHAT0, jHAT0, tmpHAT0) -> l1(iHATpost, jHATpost, tmpHATpost) :|: tmpHAT0 = tmpHATpost && jHAT0 = jHATpost && iHAT0 = iHATpost
(2) l1(x, x1, x2) -> l2(x3, x4, x5) :|: x2 = x5 && x1 = x4 && x = x3
(3) l3(x6, x7, x8) -> l0(x9, x10, x11) :|: x11 = x11 && x10 = 1 && x9 = 0
(4) l4(x12, x13, x14) -> l3(x15, x16, x17) :|: x14 = x17 && x13 = x16 && x12 = x15

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

This digraph is fully evaluated!
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(4)
TRUE