Table 3: (a) Composition of binary relations in the -direction for the hybrid model (composed relations of {WE} and {WE,V,WW}). (b) Composition of binary relations in the -direction for the hybrid model (part 1: composed relations of {V} and {WE,V,WW}). (c) Composition of binary relations in the -direction for the hybrid model (part 2: composed relations of {V} and {WE,V,WW}). (d) Composition of binary relations in the -direction for the hybrid model (part 2: composed relations of {WW} and {WE,V,WW}).
(a)
 Composed relations of  {WE} and {WE,V,WW} WE(c,b) V(c,b) WW(c,b) NTPPx(c,WE(b)) TPPx(c,WE(b))  ∧ ECx(c,V(b)) TPPx(c,V(b))  ∧ ECx(c,WE(b)) TPPx(c,V(b))  ∧ ECx(c,WW(b)) NTPPx(c,V(b)) EQx(c,V(b)) NTPPx(c,WW(b)) TPPx(c,WW(b))  ∧ ECx(c,V(b)) WE(b,a) NTPPx(b,WE(a)) NTPPx(c,WE(a)) NTPPx(c,WE(a)) NTPPx(c,WE(a)) NTPPx(c,WE(a)) NTPPx(c,WE(a)) NTPPx(c,WE(a)) U-13 relations NTPPx(c,WE(a))  ∨  TPPx(c,WE(a)) ∧ ECx(c,V(a))  ∨  POx(c,WE(a)) ∧ POx(c,V(a)) ∧ DCy(c,WW(a))  ∨  POx(c,WE(a)) ∧ POx(c,V(a)) ∧ ECx(c,WW(a))  ∨  POx(c,WE(a)) ∧ POx(c,WW(a)) ∧ NTPPix(c,V(a)) TPPx(b,WE(a))  ∧ ECx(b,V(a)) NTPPx(c,WE(a)) NTPPx(c,WE(a)) NTPPx(c,WE(a)) TPPx(c,WE(a)) ∧ ECx(c,V(a)) NTPPx(c,WE(a)) TPPx(c,WE(a)) ∧ ECx(c,V(a)) NTPPx(c,V(a))  ∨  TPPx(c,V(a)) ∧ ECx(c,WW(a))  ∨  TPPx(c,WW(a))   ∧ ECx(c,V(a))  ∨  NTPPx(c,WW(a))    ∨  POx(c,WW(a))   ∧ POx(c,V(a)) ∧ DCy(c,WE(a)) TPPx(c,V(a)) ∧ ECx(c,WE(a))  ∨  EQx(c,V(a))  ∨  POx(c,WW(a)) ∧ POx(c,V(a)) ∧ ECx(c,WE(a)) WE(b,a) NTPPx(c,WE(a)) WE(c,a) WE(c,a) ∨ V(c,a) ∨ WW(c,a)
Note: the data in bold are the results of the composition of relations.
(b)
 Part 1 of composed relations of  {V} and {WE,V,WW} WE(c,b) V(c,b) WW(c,b) NTPPx(c,WE(b)) TPPx(c,WE(b))  ∧ ECx(c,V(b)) TPPx(c,V(b))  ∧ ECx(c,WE(b)) TPPx(c,V(b))  ∧ ECx(c,WW(b)) NTPPx(c,V(b)) EQx(c,V(b)) NTPPx(c,WW(b)) TPPx(c,WW(b))  ∧ ECx(c,V(b)) V(b,a) TPPx(b,V(a))  ∧ ECx(b,WE(a)) NTPPx(c,WE(a)) TPPx(c,WE(a)) ∧ ECx(c,V(a)) TPPx(c,V(a)) ∧ ECx(c,WE(a)) NTPPx(c,V(a)) NTPPx(c,V(a)) TPPx(c,V(a)) ∧ ECx(c,WE(a)) NTPPx(c,V(a))  ∨  TPPx(c,V(a)) ∧ ECx(c,WW(a))  ∨  TPPx(c,WW(a)) ∧ ECx(c,V(a))  ∨  NTPPx(c,WW(a))   ∨  POx(c,WW(a)) ∧ POx(c,V(a)) ∧ DCy(c,WE(a)) NTPPx(c,V(a))  ∨  TPPx(c,V(a)) ∧ ECx(c,WW(a))  ∨  POx(c,WW(a)) ∧ POx(c,V(a)) ∧ DCy(c,WE(a)) TPPx(b,V(a))  ∧ ECx(b,WW(a)) NTPPx(c,V(a))  ∨  TPPx(c,V(a)) ∧ ECx(c,WE(a))  ∨  TPPx(c,WE(a)) ∧ ECx(c,V(a))  ∨  NTPPx(c,WE(a))    ∨  POx(c,WE(a)) ∧ POx(c,V(a)) ∧ DCy(c,WW(a)) NTPPx(c,V(a))  ∨  TPPx(c,V(a)) ∧ ECx(c,WE(a))  ∨  POx(c,WE(a)) ∧ POx(c,V(a)) ∧ DCy(c,WW(a)) NTPPx(c,V(a)) TPPx(c,V(a)) ∧ ECx(c,WE(a)) NTPPx(c,V(a)) TPPx(c,V(a)) ∧ ECx(c,WE(a)) NTPPx(c,WW(a)) TPPx(c,WW(a)) ∧ ECx(c,V(a))
Note: the data in bold are the results of the composition of relations.
(c)
 Part 2 of composed relations of  {V} and {WE,V,WW} WE(c,b) V(c,b) WW(c,b) NTPPx(c,WE(b)) TPPx(c,WE(b))  ∧ ECx(c,V(b)) TPPx(c,V(b))  ∧ ECx(c,WE(b)) TPPx(c,V(b))  ∧ ECx(c,WW(b)) NTPPx(c,V(b)) EQx(c,V(b)) NTPPx(c,WW(b)) TPPx(c,WW(b))  ∧ ECx(c,V(b)) V(b,a) NTPPx(b,V(a)) NTPPx(c,V(a))  ∨  TPPx(c,V(a)) ∧ ECx(c,WE(a))  ∨  TPPx(c,WE(a)) ∧ ECx(c,V(a))  ∨  NTPPx(c,WE(a))   ∨  POx(c,WE(a))  ∧ POx(c,V(a)) ∧ DCy(c,WW(a)) NTPPx(c,V(a))  ∨  TPPx(c,V(a)) ∧  ECx(c,WE(a))  ∨   POx(c,WE(a))  ∧POx(c,V(a)) ∧  DCy(c,WW(a)) NTPPx(c,V(a)) NTPPx(c,V(a)) NTPPx(c,V(a)) NTPPx(c,V(a)) NTPPx(c,V(a))  ∨  TPPx(c,V(a)) ∧  ECx(c,WW(a))  ∨  TPPx(c,WW(a)) ∧  ECx(c,V(a))  ∨  NTPPx(c,WW(a))    ∨  POx(c,WW(a)) ∧  POx(c,V(a)) ∧  DCy(c,WE(a)) NTPPx(c,V(a))  ∨  TPPx(c,V(a)) ∧ ECx(c,WW(a))  ∨  POx(c,WW(a)) ∧ POx(c,V(a)) ∧ DCy(c,WE(a)) EQx(b,V(a)) NTPPx(c,WE(a)) TPPx(c,WE(a)) ∧ ECx(c,V(a)) TPPx(c,V(a)) ∧ ECx(c,WE(a)) TPPx(c,V(a)) ∧ ECx(c,WW(a)) NTPPx(c,V(a)) EQx(c,V(a)) NTPPx(c,WW(a)) TPPx(c,WW(a)) ∧ ECx(c,V(a)) V(b,a) WE(c,a) ∨ V(c,a) V(c,a) V(c,a) ∨ WW(c,a)
Note: the data in bold are the results of the composition of relations.
(d)
 Composed relations of  {WW} and {WE,V,WW} WE V WW NTPPx(c,WE(b)) TPPx(c,WE(b))  ∧ ECx(c,V(b)) TPPx(c,V(b))  ∧ ECx(c,WE(b)) TPPx(c,V(b))  ∧ ECx(c,WW(b)) NTPPx(c,V(b)) EQx(c,V(b)) NTPPx(c,WW(b)) TPPx(c,WW(b))   ∧  ECx(c,V(b)) WW(b,a) NTPPx(b,WW(a)) U-13 relations NTPPx(c,WW(a))    ∨  TPPx(c,WW(a))  ∧ ECx(c,V(a))  ∨  POx(c,WW(a)) ∧ POx(c,V(a)) ∧ DCy(c,WE(a))  ∨  POx(c,WW(a)) ∧ POx(c,V(a)) ∧ ECx(c,WE(a))  ∨  POx(c,WW(a)) ∧ POx(c,WE(a)) ∧ NTPPix(c,V(a)) NTPPx(c,  WW(a)) NTPPx(c,  WW(a)) NTPPx(c,  WW(a)) NTPPx(c,  WW(a)) NTPPx(c,  WW(a)) NTPPx(c,  WW(a)) TPPx(b,WW(a))  ∧ ECx(b,V(a)) NTPPx(c,V(a))  ∨  TPPx(c,V(a)) ∧ ECx(c,WE(a))  ∨  TPPx(c,WE(a)) ∧ ECx(c,V(a))  ∨  NTPPx(c,WE(a))    ∨  POx(c,WE(a))  ∧ POx(c,V(a)) ∧ DCy(c,WW(a)) TPPx(c,V(a)) ∧ ECx(c,WW(a))  ∨  EQx(c,V(a))  ∨  POx(c,WE(a)) ∧ POx(c,V(a)) ∧ ECx(c,WW(a)) TPPx(c,WW(a))   ∧ ECx(c,V(a)) NTPPx(c,  WW(a)) NTPPx(c,  WW(a)) TPPx(c,WW(a))   ∧ ECx(c,V(a)) NTPPx(c,  WW(a)) NTPPx(c,  WW(a)) WW(b,a) WE(c,a) ∨ V(c,a) ∨ WW(c,a) WW(c,a) NTPPx(c,WW(a))
Note: the data in bold are the results of the composition of relations.