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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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, 87 ms]
(4) TRUE


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(0)
Obligation:
Rules:
l0(iHAT0, tmp10HAT0, tmp13HAT0, tmp___011HAT0, tmp___014HAT0) -> l1(iHATpost, tmp10HATpost, tmp13HATpost, tmp___011HATpost, tmp___014HATpost) :|: iHAT1 = 0 && tmp10HATpost = iHAT1 && iHAT2 = 1 + iHAT1 && tmp___011HATpost = iHAT2 && iHAT3 = 1 + iHAT2 && tmp13HATpost = iHAT3 && iHAT4 = 1 + iHAT3 && tmp___014HATpost = iHAT4 && iHATpost = 1 + iHAT4
l2(x, x1, x2, x3, x4) -> l0(x5, x6, x7, x8, x9) :|: x4 = x9 && x3 = x8 && x2 = x7 && x1 = x6 && x = x5
Start term: l2(iHAT0, tmp10HAT0, tmp13HAT0, tmp___011HAT0, tmp___014HAT0)

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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, tmp10HAT0, tmp13HAT0, tmp___011HAT0, tmp___014HAT0) -> l1(iHATpost, tmp10HATpost, tmp13HATpost, tmp___011HATpost, tmp___014HATpost) :|: iHAT1 = 0 && tmp10HATpost = iHAT1 && iHAT2 = 1 + iHAT1 && tmp___011HATpost = iHAT2 && iHAT3 = 1 + iHAT2 && tmp13HATpost = iHAT3 && iHAT4 = 1 + iHAT3 && tmp___014HATpost = iHAT4 && iHATpost = 1 + iHAT4
l2(x, x1, x2, x3, x4) -> l0(x5, x6, x7, x8, x9) :|: x4 = x9 && x3 = x8 && x2 = x7 && x1 = x6 && x = x5
Start term: l2(iHAT0, tmp10HAT0, tmp13HAT0, tmp___011HAT0, tmp___014HAT0)

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(3) IRSwTTerminationDigraphProof (EQUIVALENT)
Constructed termination digraph!
Nodes:
(1) l0(iHAT0, tmp10HAT0, tmp13HAT0, tmp___011HAT0, tmp___014HAT0) -> l1(iHATpost, tmp10HATpost, tmp13HATpost, tmp___011HATpost, tmp___014HATpost) :|: iHAT1 = 0 && tmp10HATpost = iHAT1 && iHAT2 = 1 + iHAT1 && tmp___011HATpost = iHAT2 && iHAT3 = 1 + iHAT2 && tmp13HATpost = iHAT3 && iHAT4 = 1 + iHAT3 && tmp___014HATpost = iHAT4 && iHATpost = 1 + iHAT4
(2) l2(x, x1, x2, x3, x4) -> l0(x5, x6, x7, x8, x9) :|: x4 = x9 && x3 = x8 && x2 = x7 && x1 = x6 && x = x5

Arcs:
(2) -> (1)

This digraph is fully evaluated!
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(4)
TRUE