constituent of BSithat was first reached on a planning graph and now we do not commit to any one constituent. Our rationale is that we were possibly using different constituents in each of the multiple graphs, and in this condensed version of the multiple graphs we still want to be able to support different constituents of the BSiin different worlds. We could also use the constituent representation of BSiin defining the layers of the relaxed plan, but choose the clausal representation of BSiinstead because we know that we have to support each clause. However with constituents we know we only need to support one (but we don't need to know which one).

The relaxed plan, shown in bold in Figure 7, for BSI to reach BSG in CBTC is listed as follows:
ARP
0 = {inP1p, inP2p, Flush},
ℓ RP
0(inP1p**) = (**arm ∧ ¬clog ∧ inP1 ∧ ¬inP2),
ℓ RP
0(inP2p**) = (**arm ∧ ¬clog ∧ ¬inP1 ∧ inP2),
ℓ RP
0(Flush) = BSP ,
E
RP
0 = {ϕ 0(inP1p), ϕ0(inP2p), ϕ0(Flush)},
ℓ RP
0(ϕ 0(inP1p**)) = (**arm ∧ ¬clog ∧ inP1 ∧ ¬inP2),
ℓ RP
0(ϕ 0(inP2p**)) = (**arm ∧ ¬clog ∧ ¬inP1 ∧ inP2),
ℓ RP
0(ϕ 0(Flush**)) =** BSP ,
L
RP
1 = {inP1, inP2,¬clog},
ℓ RP
1(inP1**) = (**arm ∧ ¬clog ∧ inP1 ∧ ¬inP2),
ℓ RP
1(inP2**) = (**arm ∧ ¬clog ∧ ¬inP1 ∧ inP2),
ℓ RP
1(¬clog) = BSP ,
ARP
1 = {DunkP1, DunkP2,¬clogp
},
ℓ RP
1(DunkP1**) = (**arm ∧ ¬clog ∧ inP1 ∧ ¬inP2),
ℓ RP
1(DunkP2**) = (**arm ∧ ¬clog ∧ ¬inP1 ∧ inP2),
ℓ RP
1(¬clogp
) = BSP ,
E
RP
1 = {ϕ 1(DunkP1), ϕ1(DunkP2), ϕ0(¬clogp
)},
ℓ RP
1(ϕ 1(DunkP1**)) = (**arm ∧ ¬clog ∧ inP1 ∧ ¬inP2),
ℓ RP
1(ϕ 1(DunkP2**)) = (**arm ∧ ¬clog ∧ ¬inP1 ∧ inP2),
ℓ RP
1(ϕ 0(¬clogp
)) = BSP ,
L
RP
2 = {¬arm,¬clog},
ℓ RP
2(¬arm) = BSP ,
ℓ RP
2(¬clog) = BSP
We start by forming L
RP
2 with the clauses in κ(BSG), namely ¬arm and ¬clog; we label the clauses with BSP because they need to be supported by all states in our belief state. Next, we support each clause in L
RP
2 with the relevant effects from E1 to form E
RP
1. For ¬clog we use persistence because it supports ¬clog in all worlds described by BSP (this is an example of positive interaction of worlds). For ¬arm the relevant effects are the respective ϕ 1from each Dunk action.

We choose both effects to support ¬arm because we need to support ¬arm in all worlds of BSP , and each effect gives support in only one world (this is an example of independence of worlds). We then insert the actions associated with each chosen effect into ARP
1 with the appropriate label indicating