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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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, 80 ms]
(4) TRUE


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(0)
Obligation:
Rules:
l0(xHAT0, yHAT0) -> l1(xHATpost, yHATpost) :|: 1 <= xHAT0 && yHAT1 = xHAT0 && yHAT1 <= 0 && yHATpost = 1 + yHAT1 && xHAT0 = xHATpost
l1(x, x1) -> l0(x2, x3) :|: x1 = x3 && x = x2
l2(x4, x5) -> l0(x6, x7) :|: x5 = x7 && x4 = x6
l3(x8, x9) -> l2(x10, x11) :|: x9 = x11 && x8 = x10
Start term: l3(xHAT0, yHAT0)

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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, yHAT0) -> l1(xHATpost, yHATpost) :|: 1 <= xHAT0 && yHAT1 = xHAT0 && yHAT1 <= 0 && yHATpost = 1 + yHAT1 && xHAT0 = xHATpost
l1(x, x1) -> l0(x2, x3) :|: x1 = x3 && x = x2
l2(x4, x5) -> l0(x6, x7) :|: x5 = x7 && x4 = x6
l3(x8, x9) -> l2(x10, x11) :|: x9 = x11 && x8 = x10
Start term: l3(xHAT0, yHAT0)

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(3) IRSwTTerminationDigraphProof (EQUIVALENT)
Constructed termination digraph!
Nodes:
(1) l0(xHAT0, yHAT0) -> l1(xHATpost, yHATpost) :|: 1 <= xHAT0 && yHAT1 = xHAT0 && yHAT1 <= 0 && yHATpost = 1 + yHAT1 && xHAT0 = xHATpost
(2) l1(x, x1) -> l0(x2, x3) :|: x1 = x3 && x = x2
(3) l2(x4, x5) -> l0(x6, x7) :|: x5 = x7 && x4 = x6
(4) l3(x8, x9) -> l2(x10, x11) :|: x9 = x11 && x8 = x10

Arcs:
(4) -> (3)

This digraph is fully evaluated!
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(4)
TRUE