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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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, 137 ms]
(4) TRUE


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(0)
Obligation:
Rules:
l0(iHAT0, jHAT0, tmp1HAT0, tmp2HAT0, tmp3HAT0) -> l1(iHATpost, jHATpost, tmp1HATpost, tmp2HATpost, tmp3HATpost) :|: tmp3HAT0 = tmp3HATpost && tmp2HAT0 = tmp2HATpost && tmp1HAT0 = tmp1HATpost && jHAT0 = jHATpost && iHAT0 = iHATpost
l2(x, x1, x2, x3, x4) -> l0(x5, x6, x7, x8, x9) :|: x4 = x9 && x3 = x8 && x2 = x7 && x1 = x6 && x = x5
l3(x10, x11, x12, x13, x14) -> l2(x15, x16, x17, x18, x19) :|: x19 = x19 && x18 = x18 && x17 = x17 && x16 = 1 && x15 = 0
l4(x20, x21, x22, x23, x24) -> l3(x25, x26, x27, x28, x29) :|: x24 = x29 && x23 = x28 && x22 = x27 && x21 = x26 && x20 = x25
Start term: l4(iHAT0, jHAT0, tmp1HAT0, tmp2HAT0, tmp3HAT0)

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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, jHAT0, tmp1HAT0, tmp2HAT0, tmp3HAT0) -> l1(iHATpost, jHATpost, tmp1HATpost, tmp2HATpost, tmp3HATpost) :|: tmp3HAT0 = tmp3HATpost && tmp2HAT0 = tmp2HATpost && tmp1HAT0 = tmp1HATpost && jHAT0 = jHATpost && iHAT0 = iHATpost
l2(x, x1, x2, x3, x4) -> l0(x5, x6, x7, x8, x9) :|: x4 = x9 && x3 = x8 && x2 = x7 && x1 = x6 && x = x5
l3(x10, x11, x12, x13, x14) -> l2(x15, x16, x17, x18, x19) :|: x19 = x19 && x18 = x18 && x17 = x17 && x16 = 1 && x15 = 0
l4(x20, x21, x22, x23, x24) -> l3(x25, x26, x27, x28, x29) :|: x24 = x29 && x23 = x28 && x22 = x27 && x21 = x26 && x20 = x25
Start term: l4(iHAT0, jHAT0, tmp1HAT0, tmp2HAT0, tmp3HAT0)

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(3) IRSwTTerminationDigraphProof (EQUIVALENT)
Constructed termination digraph!
Nodes:
(1) l0(iHAT0, jHAT0, tmp1HAT0, tmp2HAT0, tmp3HAT0) -> l1(iHATpost, jHATpost, tmp1HATpost, tmp2HATpost, tmp3HATpost) :|: tmp3HAT0 = tmp3HATpost && tmp2HAT0 = tmp2HATpost && tmp1HAT0 = tmp1HATpost && jHAT0 = jHATpost && iHAT0 = iHATpost
(2) l2(x, x1, x2, x3, x4) -> l0(x5, x6, x7, x8, x9) :|: x4 = x9 && x3 = x8 && x2 = x7 && x1 = x6 && x = x5
(3) l3(x10, x11, x12, x13, x14) -> l2(x15, x16, x17, x18, x19) :|: x19 = x19 && x18 = x18 && x17 = x17 && x16 = 1 && x15 = 0
(4) l4(x20, x21, x22, x23, x24) -> l3(x25, x26, x27, x28, x29) :|: x24 = x29 && x23 = x28 && x22 = x27 && x21 = x26 && x20 = x25

Arcs:
(2) -> (1)
(3) -> (2)
(4) -> (3)

This digraph is fully evaluated!
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(4)
TRUE