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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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, 71 ms]
(4) TRUE


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

Arcs:
(4) -> (3)

This digraph is fully evaluated!
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(4)
TRUE