Problem Transformed CSR 04 PALINDROME complete C

Tool CaT

Execution Time	Unknown
Answer	MAYBE
Input	Transformed CSR 04 PALINDROME complete C

stdout:

MAYBE

Problem:
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))

Proof:
Open

Tool IRC1

Execution Time	Unknown
Answer	MAYBE
Input	Transformed CSR 04 PALINDROME complete C

stdout:

MAYBE

Tool IRC2

Execution Time	Unknown
Answer	TIMEOUT
Input	Transformed CSR 04 PALINDROME complete C

stdout:

TIMEOUT

'Fastest (timeout of 60.0 seconds)'
-----------------------------------
Answer:           TIMEOUT
Input Problem:    innermost runtime-complexity with respect to
  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))}

Proof Output:
  Computation stopped due to timeout after 60.0 seconds

Tool RC1

Execution Time	Unknown
Answer	MAYBE
Input	Transformed CSR 04 PALINDROME complete C

stdout:

MAYBE

Tool RC2

Execution Time	Unknown
Answer	TIMEOUT
Input	Transformed CSR 04 PALINDROME complete C

stdout:

TIMEOUT

'Fastest (timeout of 60.0 seconds)'
-----------------------------------
Answer:           TIMEOUT
Input Problem:    runtime-complexity with respect to
  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))}

Proof Output:
  Computation stopped due to timeout after 60.0 seconds