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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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, 83 ms]
(4) TRUE


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(0)
Obligation:
Rules:
l0(aHAT0, ret_incr3HAT0, x2HAT0) -> l1(aHATpost, ret_incr3HATpost, x2HATpost) :|: aHAT1 = -1 && x2HATpost = aHAT1 && ret_incr3HATpost = x2HATpost && aHATpost = ret_incr3HATpost
l2(x, x1, x2) -> l0(x3, x4, x5) :|: x2 = x5 && x1 = x4 && x = x3
Start term: l2(aHAT0, ret_incr3HAT0, x2HAT0)

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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(aHAT0, ret_incr3HAT0, x2HAT0) -> l1(aHATpost, ret_incr3HATpost, x2HATpost) :|: aHAT1 = -1 && x2HATpost = aHAT1 && ret_incr3HATpost = x2HATpost && aHATpost = ret_incr3HATpost
l2(x, x1, x2) -> l0(x3, x4, x5) :|: x2 = x5 && x1 = x4 && x = x3
Start term: l2(aHAT0, ret_incr3HAT0, x2HAT0)

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(3) IRSwTTerminationDigraphProof (EQUIVALENT)
Constructed termination digraph!
Nodes:
(1) l0(aHAT0, ret_incr3HAT0, x2HAT0) -> l1(aHATpost, ret_incr3HATpost, x2HATpost) :|: aHAT1 = -1 && x2HATpost = aHAT1 && ret_incr3HATpost = x2HATpost && aHATpost = ret_incr3HATpost
(2) l2(x, x1, x2) -> l0(x3, x4, x5) :|: x2 = x5 && x1 = x4 && x = x3

Arcs:
(2) -> (1)

This digraph is fully evaluated!
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(4)
TRUE