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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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, 84 ms]
(4) TRUE


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(0)
Obligation:
Rules:
l0(rt_11HAT0, st_14HAT0, x_13HAT0) -> l1(rt_11HATpost, st_14HATpost, x_13HATpost) :|: st_14HAT0 = st_14HATpost && rt_11HATpost = st_14HAT0 && x_13HATpost = -1 + x_13HAT0 && 0 <= x_13HAT0
l0(x, x1, x2) -> l1(x3, x4, x5) :|: x2 = x5 && x1 = x4 && x3 = x1 && 1 + x2 <= 0
l2(x6, x7, x8) -> l0(x9, x10, x11) :|: x8 = x11 && x7 = x10 && x6 = x9
Start term: l2(rt_11HAT0, st_14HAT0, x_13HAT0)

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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(rt_11HAT0, st_14HAT0, x_13HAT0) -> l1(rt_11HATpost, st_14HATpost, x_13HATpost) :|: st_14HAT0 = st_14HATpost && rt_11HATpost = st_14HAT0 && x_13HATpost = -1 + x_13HAT0 && 0 <= x_13HAT0
l0(x, x1, x2) -> l1(x3, x4, x5) :|: x2 = x5 && x1 = x4 && x3 = x1 && 1 + x2 <= 0
l2(x6, x7, x8) -> l0(x9, x10, x11) :|: x8 = x11 && x7 = x10 && x6 = x9
Start term: l2(rt_11HAT0, st_14HAT0, x_13HAT0)

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(3) IRSwTTerminationDigraphProof (EQUIVALENT)
Constructed termination digraph!
Nodes:
(1) l0(rt_11HAT0, st_14HAT0, x_13HAT0) -> l1(rt_11HATpost, st_14HATpost, x_13HATpost) :|: st_14HAT0 = st_14HATpost && rt_11HATpost = st_14HAT0 && x_13HATpost = -1 + x_13HAT0 && 0 <= x_13HAT0
(2) l0(x, x1, x2) -> l1(x3, x4, x5) :|: x2 = x5 && x1 = x4 && x3 = x1 && 1 + x2 <= 0
(3) l2(x6, x7, x8) -> l0(x9, x10, x11) :|: x8 = x11 && x7 = x10 && x6 = x9

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

This digraph is fully evaluated!
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(4)
TRUE