applyMarked_reneqMarked_eqconsifandMarked_andvarrentrueMarked_ifnillambdafalseZYKXpXSpSLpTpLTand(false,false)falseand(true,false)falseand(false,true)falseand(true,true)trueeq(nil,nil)trueeq(cons(T,L),nil)falseeq(nil,cons(T,L))falseeq(cons(T,L),cons(Tp,Lp))and(eq(T,Tp),eq(L,Lp))eq(var(L),var(Lp))eq(L,Lp)eq(var(L),apply(T,S))falseeq(var(L),lambda(X,T))falseeq(apply(T,S),var(L))falseeq(apply(T,S),apply(Tp,Sp))and(eq(T,Tp),eq(S,Sp))eq(apply(T,S),lambda(X,Tp))falseeq(lambda(X,T),var(L))falseeq(lambda(X,T),apply(Tp,Sp))falseeq(lambda(X,T),lambda(Xp,Tp))and(eq(T,Tp),eq(X,Xp))if(true,var(K),var(L))var(K)if(false,var(K),var(L))var(L)ren(var(L),var(K),var(Lp))if(eq(L,Lp),var(K),var(Lp))ren(X,Y,apply(T,S))apply(ren(X,Y,T),ren(X,Y,S))ren(X,Y,lambda(Z,T))lambda(var(cons(X,cons(Y,cons(lambda(Z,T),nil)))), ren(X,Y,ren(Z,var(cons(X,cons(Y,cons(lambda(Z,T),nil)))),T)))and(false,false)falseand(true,false)falseand(false,true)falseand(true,true)trueeq(nil,nil)trueeq(cons(T,L),nil)falseeq(nil,cons(T,L))falseeq(cons(T,L),cons(Tp,Lp))and(eq(T,Tp),eq(L,Lp))eq(var(L),var(Lp))eq(L,Lp)eq(var(L),apply(T,S))falseeq(var(L),lambda(X,T))falseeq(apply(T,S),var(L))falseeq(apply(T,S),apply(Tp,Sp))and(eq(T,Tp),eq(S,Sp))eq(apply(T,S),lambda(X,Tp))falseeq(lambda(X,T),var(L))falseeq(lambda(X,T),apply(Tp,Sp))falseeq(lambda(X,T),lambda(Xp,Tp))and(eq(T,Tp),eq(X,Xp))if(true,var(K),var(L))var(K)if(false,var(K),var(L))var(L)ren(var(L),var(K),var(Lp))if(eq(L,Lp),var(K),var(Lp))ren(X,Y,apply(T,S))apply(ren(X,Y,T),ren(X,Y,S))ren(X,Y,lambda(Z,T))lambda(var(cons(X,cons(Y,cons(lambda(Z,T),nil)))), ren(X,Y,ren(Z,var(cons(X,cons(Y,cons(lambda(Z,T),nil)))),T)))Marked_eq(cons(T,L),cons(Tp,Lp))Marked_and(eq(T,Tp),eq(L,Lp))Marked_eq(cons(T,L),cons(Tp,Lp))Marked_eq(T,Tp)Marked_eq(cons(T,L),cons(Tp,Lp))Marked_eq(L,Lp)Marked_eq(var(L),var(Lp))Marked_eq(L,Lp)Marked_eq(apply(T,S),apply(Tp,Sp))Marked_and(eq(T,Tp),eq(S,Sp))Marked_eq(apply(T,S),apply(Tp,Sp))Marked_eq(T,Tp)Marked_eq(apply(T,S),apply(Tp,Sp))Marked_eq(S,Sp)Marked_eq(lambda(X,T),lambda(Xp,Tp))Marked_and(eq(T,Tp),eq(X,Xp))Marked_eq(lambda(X,T),lambda(Xp,Tp))Marked_eq(T,Tp)Marked_eq(lambda(X,T),lambda(Xp,Tp))Marked_eq(X,Xp)Marked_ren(var(L),var(K),var(Lp))Marked_if(eq(L,Lp),var(K),var(Lp))Marked_ren(var(L),var(K),var(Lp))Marked_eq(L,Lp)Marked_ren(X,Y,apply(T,S))Marked_ren(X,Y,T)Marked_ren(X,Y,apply(T,S))Marked_ren(X,Y,S)Marked_ren(X,Y,lambda(Z,T))Marked_ren(X,Y,ren(Z,var(cons(X,cons(Y,cons(lambda(Z,T),nil)))),T))Marked_ren(X,Y,lambda(Z,T))Marked_ren(Z,var(cons(X,cons(Y,cons(lambda(Z,T),nil)))),T)and(false,false)falseand(true,false)falseand(false,true)falseand(true,true)trueeq(nil,nil)trueeq(cons(T,L),nil)falseeq(nil,cons(T,L))falseeq(cons(T,L),cons(Tp,Lp))and(eq(T,Tp),eq(L,Lp))eq(var(L),var(Lp))eq(L,Lp)eq(var(L),apply(T,S))falseeq(var(L),lambda(X,T))falseeq(apply(T,S),var(L))falseeq(apply(T,S),apply(Tp,Sp))and(eq(T,Tp),eq(S,Sp))eq(apply(T,S),lambda(X,Tp))falseeq(lambda(X,T),var(L))falseeq(lambda(X,T),apply(Tp,Sp))falseeq(lambda(X,T),lambda(Xp,Tp))and(eq(T,Tp),eq(X,Xp))if(true,var(K),var(L))var(K)if(false,var(K),var(L))var(L)ren(var(L),var(K),var(Lp))if(eq(L,Lp),var(K),var(Lp))ren(X,Y,apply(T,S))apply(ren(X,Y,T),ren(X,Y,S))ren(X,Y,lambda(Z,T))lambda(var(cons(X,cons(Y,cons(lambda(Z,T),nil)))), ren(X,Y,ren(Z,var(cons(X,cons(Y,cons(lambda(Z,T),nil)))),T)))Marked_ren(X,Y,apply(T,S))Marked_ren(X,Y,T)Marked_ren(X,Y,apply(T,S))Marked_ren(X,Y,S)Marked_ren(X,Y,lambda(Z,T))Marked_ren(X,Y,ren(Z,var(cons(X,cons(Y,cons(lambda(Z,T),nil)))),T))Marked_ren(X,Y,lambda(Z,T))Marked_ren(Z,var(cons(X,cons(Y,cons(lambda(Z,T),nil)))),T)false0lambda20nil0true0ren10var0and0if0cons0eq0Marked_ren10apply2220Marked_ren(X,Y,apply(T,S))Marked_ren(X,Y,T)Marked_ren(X,Y,apply(T,S))Marked_ren(X,Y,S)and(false,false)falseand(true,false)falseand(false,true)falseand(true,true)trueeq(nil,nil)trueeq(cons(T,L),nil)falseeq(nil,cons(T,L))falseeq(cons(T,L),cons(Tp,Lp))and(eq(T,Tp),eq(L,Lp))eq(var(L),var(Lp))eq(L,Lp)eq(var(L),apply(T,S))falseeq(var(L),lambda(X,T))falseeq(apply(T,S),var(L))falseeq(apply(T,S),apply(Tp,Sp))and(eq(T,Tp),eq(S,Sp))eq(apply(T,S),lambda(X,Tp))falseeq(lambda(X,T),var(L))falseeq(lambda(X,T),apply(Tp,Sp))falseeq(lambda(X,T),lambda(Xp,Tp))and(eq(T,Tp),eq(X,Xp))if(true,var(K),var(L))var(K)if(false,var(K),var(L))var(L)ren(var(L),var(K),var(Lp))if(eq(L,Lp),var(K),var(Lp))ren(X,Y,apply(T,S))apply(ren(X,Y,T),ren(X,Y,S))ren(X,Y,lambda(Z,T))lambda(var(cons(X,cons(Y,cons(lambda(Z,T),nil)))), ren(X,Y,ren(Z,var(cons(X,cons(Y,cons(lambda(Z,T),nil)))),T)))Marked_ren(X,Y,lambda(Z,T))Marked_ren(X,Y,ren(Z,var(cons(X,cons(Y,cons(lambda(Z,T),nil)))),T))Marked_ren(X,Y,lambda(Z,T))Marked_ren(Z,var(cons(X,cons(Y,cons(lambda(Z,T),nil)))),T)and(false,false)falseand(true,false)falseand(false,true)falseand(true,true)trueeq(nil,nil)trueeq(cons(T,L),nil)falseeq(nil,cons(T,L))falseeq(cons(T,L),cons(Tp,Lp))and(eq(T,Tp),eq(L,Lp))eq(var(L),var(Lp))eq(L,Lp)eq(var(L),apply(T,S))falseeq(var(L),lambda(X,T))falseeq(apply(T,S),var(L))falseeq(apply(T,S),apply(Tp,Sp))and(eq(T,Tp),eq(S,Sp))eq(apply(T,S),lambda(X,Tp))falseeq(lambda(X,T),var(L))falseeq(lambda(X,T),apply(Tp,Sp))falseeq(lambda(X,T),lambda(Xp,Tp))and(eq(T,Tp),eq(X,Xp))if(true,var(K),var(L))var(K)if(false,var(K),var(L))var(L)ren(var(L),var(K),var(Lp))if(eq(L,Lp),var(K),var(Lp))ren(X,Y,apply(T,S))apply(ren(X,Y,T),ren(X,Y,S))ren(X,Y,lambda(Z,T))lambda(var(cons(X,cons(Y,cons(lambda(Z,T),nil)))), ren(X,Y,ren(Z,var(cons(X,cons(Y,cons(lambda(Z,T),nil)))),T)))Marked_ren(X,Y,lambda(Z,T))Marked_ren(X,Y,ren(Z,var(cons(X,cons(Y,cons(lambda(Z,T),nil)))),T))Marked_ren(X,Y,lambda(Z,T))Marked_ren(Z,var(cons(X,cons(Y,cons(lambda(Z,T),nil)))),T)false0lambda210nil0true0ren10var0and0if0cons0eq0Marked_ren20apply0and(false,false)falseand(true,false)falseand(false,true)falseand(true,true)trueeq(nil,nil)trueeq(cons(T,L),nil)falseeq(nil,cons(T,L))falseeq(cons(T,L),cons(Tp,Lp))and(eq(T,Tp),eq(L,Lp))eq(var(L),var(Lp))eq(L,Lp)eq(var(L),apply(T,S))falseeq(var(L),lambda(X,T))falseeq(apply(T,S),var(L))falseeq(apply(T,S),apply(Tp,Sp))and(eq(T,Tp),eq(S,Sp))eq(apply(T,S),lambda(X,Tp))falseeq(lambda(X,T),var(L))falseeq(lambda(X,T),apply(Tp,Sp))falseeq(lambda(X,T),lambda(Xp,Tp))and(eq(T,Tp),eq(X,Xp))if(true,var(K),var(L))var(K)if(false,var(K),var(L))var(L)ren(var(L),var(K),var(Lp))if(eq(L,Lp),var(K),var(Lp))ren(X,Y,apply(T,S))apply(ren(X,Y,T),ren(X,Y,S))ren(X,Y,lambda(Z,T))lambda(var(cons(X,cons(Y,cons(lambda(Z,T),nil)))), ren(X,Y,ren(Z,var(cons(X,cons(Y,cons(lambda(Z,T),nil)))),T)))Marked_eq(cons(T,L),cons(Tp,Lp))Marked_eq(T,Tp)Marked_eq(cons(T,L),cons(Tp,Lp))Marked_eq(L,Lp)Marked_eq(var(L),var(Lp))Marked_eq(L,Lp)Marked_eq(apply(T,S),apply(Tp,Sp))Marked_eq(T,Tp)Marked_eq(apply(T,S),apply(Tp,Sp))Marked_eq(S,Sp)Marked_eq(lambda(X,T),lambda(Xp,Tp))Marked_eq(T,Tp)Marked_eq(lambda(X,T),lambda(Xp,Tp))Marked_eq(X,Xp)Marked_eq2Marked_eq(lambda(X,T),lambda(Xp,Tp))Marked_eq(X,Xp)Marked_eq(lambda(X,T),lambda(Xp,Tp))Marked_eq(T,Tp)Marked_eq(apply(T,S),apply(Tp,Sp))Marked_eq(S,Sp)Marked_eq(apply(T,S),apply(Tp,Sp))Marked_eq(T,Tp)Marked_eq(var(L),var(Lp))Marked_eq(L,Lp)Marked_eq(cons(T,L),cons(Tp,Lp))Marked_eq(L,Lp)Marked_eq(cons(T,L),cons(Tp,Lp))Marked_eq(T,Tp)and(false,false)falseand(true,false)falseand(false,true)falseand(true,true)trueeq(nil,nil)trueeq(cons(T,L),nil)falseeq(nil,cons(T,L))falseeq(cons(T,L),cons(Tp,Lp))and(eq(T,Tp),eq(L,Lp))eq(var(L),var(Lp))eq(L,Lp)eq(var(L),apply(T,S))falseeq(var(L),lambda(X,T))falseeq(apply(T,S),var(L))falseeq(apply(T,S),apply(Tp,Sp))and(eq(T,Tp),eq(S,Sp))eq(apply(T,S),lambda(X,Tp))falseeq(lambda(X,T),var(L))falseeq(lambda(X,T),apply(Tp,Sp))falseeq(lambda(X,T),lambda(Xp,Tp))and(eq(T,Tp),eq(X,Xp))if(true,var(K),var(L))var(K)if(false,var(K),var(L))var(L)ren(var(L),var(K),var(Lp))if(eq(L,Lp),var(K),var(Lp))ren(X,Y,apply(T,S))apply(ren(X,Y,T),ren(X,Y,S))ren(X,Y,lambda(Z,T))lambda(var(cons(X,cons(Y,cons(lambda(Z,T),nil)))), ren(X,Y,ren(Z,var(cons(X,cons(Y,cons(lambda(Z,T),nil)))),T)))