The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(1, n^1).

(0) Obligation:

The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(1, n^1).


The TRS R consists of the following rules:

active(__(__(X, Y), Z)) → mark(__(X, __(Y, Z)))
active(__(X, nil)) → mark(X)
active(__(nil, X)) → mark(X)
active(U11(tt, V)) → mark(U12(isNeList(V)))
active(U12(tt)) → mark(tt)
active(U21(tt, V1, V2)) → mark(U22(isList(V1), V2))
active(U22(tt, V2)) → mark(U23(isList(V2)))
active(U23(tt)) → mark(tt)
active(U31(tt, V)) → mark(U32(isQid(V)))
active(U32(tt)) → mark(tt)
active(U41(tt, V1, V2)) → mark(U42(isList(V1), V2))
active(U42(tt, V2)) → mark(U43(isNeList(V2)))
active(U43(tt)) → mark(tt)
active(U51(tt, V1, V2)) → mark(U52(isNeList(V1), V2))
active(U52(tt, V2)) → mark(U53(isList(V2)))
active(U53(tt)) → mark(tt)
active(U61(tt, V)) → mark(U62(isQid(V)))
active(U62(tt)) → mark(tt)
active(U71(tt, V)) → mark(U72(isNePal(V)))
active(U72(tt)) → mark(tt)
active(and(tt, X)) → mark(X)
active(isList(V)) → mark(U11(isPalListKind(V), V))
active(isList(nil)) → mark(tt)
active(isList(__(V1, V2))) → mark(U21(and(isPalListKind(V1), isPalListKind(V2)), V1, V2))
active(isNeList(V)) → mark(U31(isPalListKind(V), V))
active(isNeList(__(V1, V2))) → mark(U41(and(isPalListKind(V1), isPalListKind(V2)), V1, V2))
active(isNeList(__(V1, V2))) → mark(U51(and(isPalListKind(V1), isPalListKind(V2)), V1, V2))
active(isNePal(V)) → mark(U61(isPalListKind(V), V))
active(isNePal(__(I, __(P, I)))) → mark(and(and(isQid(I), isPalListKind(I)), and(isPal(P), isPalListKind(P))))
active(isPal(V)) → mark(U71(isPalListKind(V), V))
active(isPal(nil)) → mark(tt)
active(isPalListKind(a)) → mark(tt)
active(isPalListKind(e)) → mark(tt)
active(isPalListKind(i)) → mark(tt)
active(isPalListKind(nil)) → mark(tt)
active(isPalListKind(o)) → mark(tt)
active(isPalListKind(u)) → mark(tt)
active(isPalListKind(__(V1, V2))) → mark(and(isPalListKind(V1), isPalListKind(V2)))
active(isQid(a)) → mark(tt)
active(isQid(e)) → mark(tt)
active(isQid(i)) → mark(tt)
active(isQid(o)) → mark(tt)
active(isQid(u)) → mark(tt)
active(__(X1, X2)) → __(active(X1), X2)
active(__(X1, X2)) → __(X1, active(X2))
active(U11(X1, X2)) → U11(active(X1), X2)
active(U12(X)) → U12(active(X))
active(U21(X1, X2, X3)) → U21(active(X1), X2, X3)
active(U22(X1, X2)) → U22(active(X1), X2)
active(U23(X)) → U23(active(X))
active(U31(X1, X2)) → U31(active(X1), X2)
active(U32(X)) → U32(active(X))
active(U41(X1, X2, X3)) → U41(active(X1), X2, X3)
active(U42(X1, X2)) → U42(active(X1), X2)
active(U43(X)) → U43(active(X))
active(U51(X1, X2, X3)) → U51(active(X1), X2, X3)
active(U52(X1, X2)) → U52(active(X1), X2)
active(U53(X)) → U53(active(X))
active(U61(X1, X2)) → U61(active(X1), X2)
active(U62(X)) → U62(active(X))
active(U71(X1, X2)) → U71(active(X1), X2)
active(U72(X)) → U72(active(X))
active(and(X1, X2)) → and(active(X1), X2)
__(mark(X1), X2) → mark(__(X1, X2))
__(X1, mark(X2)) → mark(__(X1, X2))
U11(mark(X1), X2) → mark(U11(X1, X2))
U12(mark(X)) → mark(U12(X))
U21(mark(X1), X2, X3) → mark(U21(X1, X2, X3))
U22(mark(X1), X2) → mark(U22(X1, X2))
U23(mark(X)) → mark(U23(X))
U31(mark(X1), X2) → mark(U31(X1, X2))
U32(mark(X)) → mark(U32(X))
U41(mark(X1), X2, X3) → mark(U41(X1, X2, X3))
U42(mark(X1), X2) → mark(U42(X1, X2))
U43(mark(X)) → mark(U43(X))
U51(mark(X1), X2, X3) → mark(U51(X1, X2, X3))
U52(mark(X1), X2) → mark(U52(X1, X2))
U53(mark(X)) → mark(U53(X))
U61(mark(X1), X2) → mark(U61(X1, X2))
U62(mark(X)) → mark(U62(X))
U71(mark(X1), X2) → mark(U71(X1, X2))
U72(mark(X)) → mark(U72(X))
and(mark(X1), X2) → mark(and(X1, X2))
proper(__(X1, X2)) → __(proper(X1), proper(X2))
proper(nil) → ok(nil)
proper(U11(X1, X2)) → U11(proper(X1), proper(X2))
proper(tt) → ok(tt)
proper(U12(X)) → U12(proper(X))
proper(isNeList(X)) → isNeList(proper(X))
proper(U21(X1, X2, X3)) → U21(proper(X1), proper(X2), proper(X3))
proper(U22(X1, X2)) → U22(proper(X1), proper(X2))
proper(isList(X)) → isList(proper(X))
proper(U23(X)) → U23(proper(X))
proper(U31(X1, X2)) → U31(proper(X1), proper(X2))
proper(U32(X)) → U32(proper(X))
proper(isQid(X)) → isQid(proper(X))
proper(U41(X1, X2, X3)) → U41(proper(X1), proper(X2), proper(X3))
proper(U42(X1, X2)) → U42(proper(X1), proper(X2))
proper(U43(X)) → U43(proper(X))
proper(U51(X1, X2, X3)) → U51(proper(X1), proper(X2), proper(X3))
proper(U52(X1, X2)) → U52(proper(X1), proper(X2))
proper(U53(X)) → U53(proper(X))
proper(U61(X1, X2)) → U61(proper(X1), proper(X2))
proper(U62(X)) → U62(proper(X))
proper(U71(X1, X2)) → U71(proper(X1), proper(X2))
proper(U72(X)) → U72(proper(X))
proper(isNePal(X)) → isNePal(proper(X))
proper(and(X1, X2)) → and(proper(X1), proper(X2))
proper(isPalListKind(X)) → isPalListKind(proper(X))
proper(isPal(X)) → isPal(proper(X))
proper(a) → ok(a)
proper(e) → ok(e)
proper(i) → ok(i)
proper(o) → ok(o)
proper(u) → ok(u)
__(ok(X1), ok(X2)) → ok(__(X1, X2))
U11(ok(X1), ok(X2)) → ok(U11(X1, X2))
U12(ok(X)) → ok(U12(X))
isNeList(ok(X)) → ok(isNeList(X))
U21(ok(X1), ok(X2), ok(X3)) → ok(U21(X1, X2, X3))
U22(ok(X1), ok(X2)) → ok(U22(X1, X2))
isList(ok(X)) → ok(isList(X))
U23(ok(X)) → ok(U23(X))
U31(ok(X1), ok(X2)) → ok(U31(X1, X2))
U32(ok(X)) → ok(U32(X))
isQid(ok(X)) → ok(isQid(X))
U41(ok(X1), ok(X2), ok(X3)) → ok(U41(X1, X2, X3))
U42(ok(X1), ok(X2)) → ok(U42(X1, X2))
U43(ok(X)) → ok(U43(X))
U51(ok(X1), ok(X2), ok(X3)) → ok(U51(X1, X2, X3))
U52(ok(X1), ok(X2)) → ok(U52(X1, X2))
U53(ok(X)) → ok(U53(X))
U61(ok(X1), ok(X2)) → ok(U61(X1, X2))
U62(ok(X)) → ok(U62(X))
U71(ok(X1), ok(X2)) → ok(U71(X1, X2))
U72(ok(X)) → ok(U72(X))
isNePal(ok(X)) → ok(isNePal(X))
and(ok(X1), ok(X2)) → ok(and(X1, X2))
isPalListKind(ok(X)) → ok(isPalListKind(X))
isPal(ok(X)) → ok(isPal(X))
top(mark(X)) → top(proper(X))
top(ok(X)) → top(active(X))

Rewrite Strategy: FULL

(1) NestedDefinedSymbolProof (BOTH BOUNDS(ID, ID) transformation)

The following defined symbols can occur below the 0th argument of top: proper, active
The following defined symbols can occur below the 0th argument of proper: proper, active
The following defined symbols can occur below the 0th argument of active: proper, active

Hence, the left-hand sides of the following rules are not basic-reachable and can be removed:
active(__(__(X, Y), Z)) → mark(__(X, __(Y, Z)))
active(__(X, nil)) → mark(X)
active(__(nil, X)) → mark(X)
active(U11(tt, V)) → mark(U12(isNeList(V)))
active(U12(tt)) → mark(tt)
active(U21(tt, V1, V2)) → mark(U22(isList(V1), V2))
active(U22(tt, V2)) → mark(U23(isList(V2)))
active(U23(tt)) → mark(tt)
active(U31(tt, V)) → mark(U32(isQid(V)))
active(U32(tt)) → mark(tt)
active(U41(tt, V1, V2)) → mark(U42(isList(V1), V2))
active(U42(tt, V2)) → mark(U43(isNeList(V2)))
active(U43(tt)) → mark(tt)
active(U51(tt, V1, V2)) → mark(U52(isNeList(V1), V2))
active(U52(tt, V2)) → mark(U53(isList(V2)))
active(U53(tt)) → mark(tt)
active(U61(tt, V)) → mark(U62(isQid(V)))
active(U62(tt)) → mark(tt)
active(U71(tt, V)) → mark(U72(isNePal(V)))
active(U72(tt)) → mark(tt)
active(and(tt, X)) → mark(X)
active(isList(V)) → mark(U11(isPalListKind(V), V))
active(isList(nil)) → mark(tt)
active(isList(__(V1, V2))) → mark(U21(and(isPalListKind(V1), isPalListKind(V2)), V1, V2))
active(isNeList(V)) → mark(U31(isPalListKind(V), V))
active(isNeList(__(V1, V2))) → mark(U41(and(isPalListKind(V1), isPalListKind(V2)), V1, V2))
active(isNeList(__(V1, V2))) → mark(U51(and(isPalListKind(V1), isPalListKind(V2)), V1, V2))
active(isNePal(V)) → mark(U61(isPalListKind(V), V))
active(isNePal(__(I, __(P, I)))) → mark(and(and(isQid(I), isPalListKind(I)), and(isPal(P), isPalListKind(P))))
active(isPal(V)) → mark(U71(isPalListKind(V), V))
active(isPal(nil)) → mark(tt)
active(isPalListKind(a)) → mark(tt)
active(isPalListKind(e)) → mark(tt)
active(isPalListKind(i)) → mark(tt)
active(isPalListKind(nil)) → mark(tt)
active(isPalListKind(o)) → mark(tt)
active(isPalListKind(u)) → mark(tt)
active(isPalListKind(__(V1, V2))) → mark(and(isPalListKind(V1), isPalListKind(V2)))
active(isQid(a)) → mark(tt)
active(isQid(e)) → mark(tt)
active(isQid(i)) → mark(tt)
active(isQid(o)) → mark(tt)
active(isQid(u)) → mark(tt)
active(__(X1, X2)) → __(active(X1), X2)
active(__(X1, X2)) → __(X1, active(X2))
active(U11(X1, X2)) → U11(active(X1), X2)
active(U12(X)) → U12(active(X))
active(U21(X1, X2, X3)) → U21(active(X1), X2, X3)
active(U22(X1, X2)) → U22(active(X1), X2)
active(U23(X)) → U23(active(X))
active(U31(X1, X2)) → U31(active(X1), X2)
active(U32(X)) → U32(active(X))
active(U41(X1, X2, X3)) → U41(active(X1), X2, X3)
active(U42(X1, X2)) → U42(active(X1), X2)
active(U43(X)) → U43(active(X))
active(U51(X1, X2, X3)) → U51(active(X1), X2, X3)
active(U52(X1, X2)) → U52(active(X1), X2)
active(U53(X)) → U53(active(X))
active(U61(X1, X2)) → U61(active(X1), X2)
active(U62(X)) → U62(active(X))
active(U71(X1, X2)) → U71(active(X1), X2)
active(U72(X)) → U72(active(X))
active(and(X1, X2)) → and(active(X1), X2)
proper(__(X1, X2)) → __(proper(X1), proper(X2))
proper(U11(X1, X2)) → U11(proper(X1), proper(X2))
proper(U12(X)) → U12(proper(X))
proper(isNeList(X)) → isNeList(proper(X))
proper(U21(X1, X2, X3)) → U21(proper(X1), proper(X2), proper(X3))
proper(U22(X1, X2)) → U22(proper(X1), proper(X2))
proper(isList(X)) → isList(proper(X))
proper(U23(X)) → U23(proper(X))
proper(U31(X1, X2)) → U31(proper(X1), proper(X2))
proper(U32(X)) → U32(proper(X))
proper(isQid(X)) → isQid(proper(X))
proper(U41(X1, X2, X3)) → U41(proper(X1), proper(X2), proper(X3))
proper(U42(X1, X2)) → U42(proper(X1), proper(X2))
proper(U43(X)) → U43(proper(X))
proper(U51(X1, X2, X3)) → U51(proper(X1), proper(X2), proper(X3))
proper(U52(X1, X2)) → U52(proper(X1), proper(X2))
proper(U53(X)) → U53(proper(X))
proper(U61(X1, X2)) → U61(proper(X1), proper(X2))
proper(U62(X)) → U62(proper(X))
proper(U71(X1, X2)) → U71(proper(X1), proper(X2))
proper(U72(X)) → U72(proper(X))
proper(isNePal(X)) → isNePal(proper(X))
proper(and(X1, X2)) → and(proper(X1), proper(X2))
proper(isPalListKind(X)) → isPalListKind(proper(X))
proper(isPal(X)) → isPal(proper(X))

(2) Obligation:

The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(1, n^1).


The TRS R consists of the following rules:

U11(ok(X1), ok(X2)) → ok(U11(X1, X2))
top(ok(X)) → top(active(X))
isNeList(ok(X)) → ok(isNeList(X))
U12(mark(X)) → mark(U12(X))
U61(ok(X1), ok(X2)) → ok(U61(X1, X2))
proper(i) → ok(i)
and(ok(X1), ok(X2)) → ok(and(X1, X2))
U62(mark(X)) → mark(U62(X))
U43(ok(X)) → ok(U43(X))
U52(ok(X1), ok(X2)) → ok(U52(X1, X2))
U51(mark(X1), X2, X3) → mark(U51(X1, X2, X3))
__(X1, mark(X2)) → mark(__(X1, X2))
proper(u) → ok(u)
proper(nil) → ok(nil)
proper(tt) → ok(tt)
isPal(ok(X)) → ok(isPal(X))
U32(mark(X)) → mark(U32(X))
U53(mark(X)) → mark(U53(X))
U72(mark(X)) → mark(U72(X))
U31(ok(X1), ok(X2)) → ok(U31(X1, X2))
U61(mark(X1), X2) → mark(U61(X1, X2))
U23(ok(X)) → ok(U23(X))
U11(mark(X1), X2) → mark(U11(X1, X2))
U71(ok(X1), ok(X2)) → ok(U71(X1, X2))
U21(ok(X1), ok(X2), ok(X3)) → ok(U21(X1, X2, X3))
U42(ok(X1), ok(X2)) → ok(U42(X1, X2))
U21(mark(X1), X2, X3) → mark(U21(X1, X2, X3))
isQid(ok(X)) → ok(isQid(X))
isNePal(ok(X)) → ok(isNePal(X))
__(mark(X1), X2) → mark(__(X1, X2))
U22(mark(X1), X2) → mark(U22(X1, X2))
U43(mark(X)) → mark(U43(X))
U12(ok(X)) → ok(U12(X))
U42(mark(X1), X2) → mark(U42(X1, X2))
U62(ok(X)) → ok(U62(X))
proper(o) → ok(o)
proper(e) → ok(e)
isList(ok(X)) → ok(isList(X))
U52(mark(X1), X2) → mark(U52(X1, X2))
U51(ok(X1), ok(X2), ok(X3)) → ok(U51(X1, X2, X3))
U53(ok(X)) → ok(U53(X))
isPalListKind(ok(X)) → ok(isPalListKind(X))
U72(ok(X)) → ok(U72(X))
and(mark(X1), X2) → mark(and(X1, X2))
__(ok(X1), ok(X2)) → ok(__(X1, X2))
U71(mark(X1), X2) → mark(U71(X1, X2))
proper(a) → ok(a)
U23(mark(X)) → mark(U23(X))
U32(ok(X)) → ok(U32(X))
U41(mark(X1), X2, X3) → mark(U41(X1, X2, X3))
U22(ok(X1), ok(X2)) → ok(U22(X1, X2))
U31(mark(X1), X2) → mark(U31(X1, X2))
top(mark(X)) → top(proper(X))
U41(ok(X1), ok(X2), ok(X3)) → ok(U41(X1, X2, X3))

Rewrite Strategy: FULL

(3) RcToIrcProof (BOTH BOUNDS(ID, ID) transformation)

Converted rc-obligation to irc-obligation.

As the TRS is a non-duplicating overlay system, we have rc = irc.

(4) Obligation:

The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(1, n^1).


The TRS R consists of the following rules:

U11(ok(X1), ok(X2)) → ok(U11(X1, X2))
top(ok(X)) → top(active(X))
isNeList(ok(X)) → ok(isNeList(X))
U12(mark(X)) → mark(U12(X))
U61(ok(X1), ok(X2)) → ok(U61(X1, X2))
proper(i) → ok(i)
and(ok(X1), ok(X2)) → ok(and(X1, X2))
U62(mark(X)) → mark(U62(X))
U43(ok(X)) → ok(U43(X))
U52(ok(X1), ok(X2)) → ok(U52(X1, X2))
U51(mark(X1), X2, X3) → mark(U51(X1, X2, X3))
__(X1, mark(X2)) → mark(__(X1, X2))
proper(u) → ok(u)
proper(nil) → ok(nil)
proper(tt) → ok(tt)
isPal(ok(X)) → ok(isPal(X))
U32(mark(X)) → mark(U32(X))
U53(mark(X)) → mark(U53(X))
U72(mark(X)) → mark(U72(X))
U31(ok(X1), ok(X2)) → ok(U31(X1, X2))
U61(mark(X1), X2) → mark(U61(X1, X2))
U23(ok(X)) → ok(U23(X))
U11(mark(X1), X2) → mark(U11(X1, X2))
U71(ok(X1), ok(X2)) → ok(U71(X1, X2))
U21(ok(X1), ok(X2), ok(X3)) → ok(U21(X1, X2, X3))
U42(ok(X1), ok(X2)) → ok(U42(X1, X2))
U21(mark(X1), X2, X3) → mark(U21(X1, X2, X3))
isQid(ok(X)) → ok(isQid(X))
isNePal(ok(X)) → ok(isNePal(X))
__(mark(X1), X2) → mark(__(X1, X2))
U22(mark(X1), X2) → mark(U22(X1, X2))
U43(mark(X)) → mark(U43(X))
U12(ok(X)) → ok(U12(X))
U42(mark(X1), X2) → mark(U42(X1, X2))
U62(ok(X)) → ok(U62(X))
proper(o) → ok(o)
proper(e) → ok(e)
isList(ok(X)) → ok(isList(X))
U52(mark(X1), X2) → mark(U52(X1, X2))
U51(ok(X1), ok(X2), ok(X3)) → ok(U51(X1, X2, X3))
U53(ok(X)) → ok(U53(X))
isPalListKind(ok(X)) → ok(isPalListKind(X))
U72(ok(X)) → ok(U72(X))
and(mark(X1), X2) → mark(and(X1, X2))
__(ok(X1), ok(X2)) → ok(__(X1, X2))
U71(mark(X1), X2) → mark(U71(X1, X2))
proper(a) → ok(a)
U23(mark(X)) → mark(U23(X))
U32(ok(X)) → ok(U32(X))
U41(mark(X1), X2, X3) → mark(U41(X1, X2, X3))
U22(ok(X1), ok(X2)) → ok(U22(X1, X2))
U31(mark(X1), X2) → mark(U31(X1, X2))
top(mark(X)) → top(proper(X))
U41(ok(X1), ok(X2), ok(X3)) → ok(U41(X1, X2, X3))

Rewrite Strategy: INNERMOST

(5) CpxTrsMatchBoundsTAProof (EQUIVALENT transformation)

A linear upper bound on the runtime complexity of the TRS R could be shown with a Match-Bound[TAB_LEFTLINEAR,TAB_NONLEFTLINEAR] (for contructor-based start-terms) of 2.

The compatible tree automaton used to show the Match-Boundedness (for constructor-based start-terms) is represented by:
final states : [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27]
transitions:
ok0(0) → 0
active0(0) → 0
mark0(0) → 0
i0() → 0
u0() → 0
nil0() → 0
tt0() → 0
o0() → 0
e0() → 0
a0() → 0
U110(0, 0) → 1
top0(0) → 2
isNeList0(0) → 3
U120(0) → 4
U610(0, 0) → 5
proper0(0) → 6
and0(0, 0) → 7
U620(0) → 8
U430(0) → 9
U520(0, 0) → 10
U510(0, 0, 0) → 11
__0(0, 0) → 12
isPal0(0) → 13
U320(0) → 14
U530(0) → 15
U720(0) → 16
U310(0, 0) → 17
U230(0) → 18
U710(0, 0) → 19
U210(0, 0, 0) → 20
U420(0, 0) → 21
isQid0(0) → 22
isNePal0(0) → 23
U220(0, 0) → 24
isList0(0) → 25
isPalListKind0(0) → 26
U410(0, 0, 0) → 27
U111(0, 0) → 28
ok1(28) → 1
active1(0) → 29
top1(29) → 2
isNeList1(0) → 30
ok1(30) → 3
U121(0) → 31
mark1(31) → 4
U611(0, 0) → 32
ok1(32) → 5
i1() → 33
ok1(33) → 6
and1(0, 0) → 34
ok1(34) → 7
U621(0) → 35
mark1(35) → 8
U431(0) → 36
ok1(36) → 9
U521(0, 0) → 37
ok1(37) → 10
U511(0, 0, 0) → 38
mark1(38) → 11
__1(0, 0) → 39
mark1(39) → 12
u1() → 40
ok1(40) → 6
nil1() → 41
ok1(41) → 6
tt1() → 42
ok1(42) → 6
isPal1(0) → 43
ok1(43) → 13
U321(0) → 44
mark1(44) → 14
U531(0) → 45
mark1(45) → 15
U721(0) → 46
mark1(46) → 16
U311(0, 0) → 47
ok1(47) → 17
U611(0, 0) → 48
mark1(48) → 5
U231(0) → 49
ok1(49) → 18
U111(0, 0) → 50
mark1(50) → 1
U711(0, 0) → 51
ok1(51) → 19
U211(0, 0, 0) → 52
ok1(52) → 20
U421(0, 0) → 53
ok1(53) → 21
U211(0, 0, 0) → 54
mark1(54) → 20
isQid1(0) → 55
ok1(55) → 22
isNePal1(0) → 56
ok1(56) → 23
U221(0, 0) → 57
mark1(57) → 24
U431(0) → 58
mark1(58) → 9
U121(0) → 59
ok1(59) → 4
U421(0, 0) → 60
mark1(60) → 21
U621(0) → 61
ok1(61) → 8
o1() → 62
ok1(62) → 6
e1() → 63
ok1(63) → 6
isList1(0) → 64
ok1(64) → 25
U521(0, 0) → 65
mark1(65) → 10
U511(0, 0, 0) → 66
ok1(66) → 11
U531(0) → 67
ok1(67) → 15
isPalListKind1(0) → 68
ok1(68) → 26
U721(0) → 69
ok1(69) → 16
and1(0, 0) → 70
mark1(70) → 7
__1(0, 0) → 71
ok1(71) → 12
U711(0, 0) → 72
mark1(72) → 19
a1() → 73
ok1(73) → 6
U231(0) → 74
mark1(74) → 18
U321(0) → 75
ok1(75) → 14
U411(0, 0, 0) → 76
mark1(76) → 27
U221(0, 0) → 77
ok1(77) → 24
U311(0, 0) → 78
mark1(78) → 17
proper1(0) → 79
top1(79) → 2
U411(0, 0, 0) → 80
ok1(80) → 27
ok1(28) → 28
ok1(28) → 50
ok1(30) → 30
mark1(31) → 31
mark1(31) → 59
ok1(32) → 32
ok1(32) → 48
ok1(33) → 79
ok1(34) → 34
ok1(34) → 70
mark1(35) → 35
mark1(35) → 61
ok1(36) → 36
ok1(36) → 58
ok1(37) → 37
ok1(37) → 65
mark1(38) → 38
mark1(38) → 66
mark1(39) → 39
mark1(39) → 71
ok1(40) → 79
ok1(41) → 79
ok1(42) → 79
ok1(43) → 43
mark1(44) → 44
mark1(44) → 75
mark1(45) → 45
mark1(45) → 67
mark1(46) → 46
mark1(46) → 69
ok1(47) → 47
ok1(47) → 78
mark1(48) → 32
mark1(48) → 48
ok1(49) → 49
ok1(49) → 74
mark1(50) → 28
mark1(50) → 50
ok1(51) → 51
ok1(51) → 72
ok1(52) → 52
ok1(52) → 54
ok1(53) → 53
ok1(53) → 60
mark1(54) → 52
mark1(54) → 54
ok1(55) → 55
ok1(56) → 56
mark1(57) → 57
mark1(57) → 77
mark1(58) → 36
mark1(58) → 58
ok1(59) → 31
ok1(59) → 59
mark1(60) → 53
mark1(60) → 60
ok1(61) → 35
ok1(61) → 61
ok1(62) → 79
ok1(63) → 79
ok1(64) → 64
mark1(65) → 37
mark1(65) → 65
ok1(66) → 38
ok1(66) → 66
ok1(67) → 45
ok1(67) → 67
ok1(68) → 68
ok1(69) → 46
ok1(69) → 69
mark1(70) → 34
mark1(70) → 70
ok1(71) → 39
ok1(71) → 71
mark1(72) → 51
mark1(72) → 72
ok1(73) → 79
mark1(74) → 49
mark1(74) → 74
ok1(75) → 44
ok1(75) → 75
mark1(76) → 76
mark1(76) → 80
ok1(77) → 57
ok1(77) → 77
mark1(78) → 47
mark1(78) → 78
ok1(80) → 76
ok1(80) → 80
active2(33) → 81
top2(81) → 2
active2(40) → 81
active2(41) → 81
active2(42) → 81
active2(62) → 81
active2(63) → 81
active2(73) → 81

(6) BOUNDS(1, n^1)