ceta_eq: termination proof not accepted
1: error below switch to dependency pairs
1.1: error below the dependency graph processor
 1.1.1: error when applying the reduction pair processor with usable rules to remove from the DP problem
  pairs:
  
  top#(mark(X)) -> top#(proper(X))
  top#(ok(X)) -> top#(active(X))
  rules:
  
  U11(mark(X1), X2) -> mark(U11(X1, X2))
  U11(ok(X1), ok(X2)) -> ok(U11(X1, X2))
  U12(mark(X)) -> mark(U12(X))
  U12(ok(X)) -> ok(U12(X))
  U21(mark(X1), X2, X3) -> mark(U21(X1, X2, X3))
  U21(ok(X1), ok(X2), ok(X3)) -> ok(U21(X1, X2, X3))
  U22(mark(X1), X2) -> mark(U22(X1, X2))
  U22(ok(X1), ok(X2)) -> ok(U22(X1, X2))
  U23(mark(X)) -> mark(U23(X))
  U23(ok(X)) -> ok(U23(X))
  U31(mark(X1), X2) -> mark(U31(X1, X2))
  U31(ok(X1), ok(X2)) -> ok(U31(X1, X2))
  U32(mark(X)) -> mark(U32(X))
  U32(ok(X)) -> ok(U32(X))
  U41(mark(X1), X2, X3) -> mark(U41(X1, X2, X3))
  U41(ok(X1), ok(X2), ok(X3)) -> ok(U41(X1, X2, X3))
  U42(mark(X1), X2) -> mark(U42(X1, X2))
  U42(ok(X1), ok(X2)) -> ok(U42(X1, X2))
  U43(mark(X)) -> mark(U43(X))
  U43(ok(X)) -> ok(U43(X))
  U51(mark(X1), X2, X3) -> mark(U51(X1, X2, X3))
  U51(ok(X1), ok(X2), ok(X3)) -> ok(U51(X1, X2, X3))
  U52(mark(X1), X2) -> mark(U52(X1, X2))
  U52(ok(X1), ok(X2)) -> ok(U52(X1, X2))
  U53(mark(X)) -> mark(U53(X))
  U53(ok(X)) -> ok(U53(X))
  U61(mark(X1), X2) -> mark(U61(X1, X2))
  U61(ok(X1), ok(X2)) -> ok(U61(X1, X2))
  U62(mark(X)) -> mark(U62(X))
  U62(ok(X)) -> ok(U62(X))
  U71(mark(X1), X2) -> mark(U71(X1, X2))
  U71(ok(X1), ok(X2)) -> ok(U71(X1, X2))
  U72(mark(X)) -> mark(U72(X))
  U72(ok(X)) -> ok(U72(X))
  __(mark(X1), X2) -> mark(__(X1, X2))
  __(X1, mark(X2)) -> mark(__(X1, X2))
  __(ok(X1), ok(X2)) -> ok(__(X1, X2))
  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)
  and(mark(X1), X2) -> mark(and(X1, X2))
  and(ok(X1), ok(X2)) -> ok(and(X1, X2))
  isList(ok(X)) -> ok(isList(X))
  isNeList(ok(X)) -> ok(isNeList(X))
  isNePal(ok(X)) -> ok(isNePal(X))
  isPal(ok(X)) -> ok(isPal(X))
  isPalListKind(ok(X)) -> ok(isPalListKind(X))
  isQid(ok(X)) -> ok(isQid(X))
  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)
  top(mark(X)) -> top(proper(X))
  top(ok(X)) -> top(active(X))
  
   the pairs 
  top#(mark(X)) -> top#(proper(X))
  
  could not apply the generic root reduction pair processor with the following
  SCNP-version with mu = MAX and the level mapping defined by 
  pi(top#) = [(1,0)]
  Argument Filter: 
  pi(ok/1) = 1
  pi(active/1) = 1
  pi(mark/1) = [1]
  pi(proper/1) = 1
  pi(__/2) = [1,2]
  pi(nil/0) = []
  pi(U11/2) = [1,2]
  pi(tt/0) = []
  pi(U12/1) = [1]
  pi(isNeList/1) = [1]
  pi(U21/3) = [1,2,3]
  pi(U22/2) = [1,2]
  pi(isList/1) = [1]
  pi(U23/1) = [1]
  pi(U31/2) = [1,2]
  pi(U32/1) = [1]
  pi(isQid/1) = [1]
  pi(U41/3) = [1,2,3]
  pi(U42/2) = [1,2]
  pi(U43/1) = [1]
  pi(U51/3) = [1,2,3]
  pi(U52/2) = [2,1]
  pi(U53/1) = [1]
  pi(U61/2) = [2,1]
  pi(U62/1) = [1]
  pi(U71/2) = [2,1]
  pi(U72/1) = [1]
  pi(isNePal/1) = [1]
  pi(and/2) = [1,2]
  pi(isPalListKind/1) = 1
  pi(isPal/1) = [1]
  pi(a/0) = []
  pi(e/0) = []
  pi(i/0) = []
  pi(o/0) = []
  pi(u/0) = []
  
  RPO with the following precedence
  precedence(mark[1]) = 1
  precedence(__[2]) = 16
  precedence(nil[0]) = 17
  precedence(U11[2]) = 5
  precedence(tt[0]) = 1
  precedence(U12[1]) = 2
  precedence(isNeList[1]) = 4
  precedence(U21[3]) = 9
  precedence(U22[2]) = 8
  precedence(isList[1]) = 7
  precedence(U23[1]) = 1
  precedence(U31[2]) = 3
  precedence(U32[1]) = 1
  precedence(isQid[1]) = 0
  precedence(U41[3]) = 10
  precedence(U42[2]) = 4
  precedence(U43[1]) = 1
  precedence(U51[3]) = 11
  precedence(U52[2]) = 7
  precedence(U53[1]) = 6
  precedence(U61[2]) = 12
  precedence(U62[1]) = 1
  precedence(U71[2]) = 15
  precedence(U72[1]) = 13
  precedence(isNePal[1]) = 14
  precedence(and[2]) = 7
  precedence(isPal[1]) = 16
  precedence(a[0]) = 18
  precedence(e[0]) = 19
  precedence(i[0]) = 20
  precedence(o[0]) = 21
  precedence(u[0]) = 22
  
  precedence(_) = 0
  and the following status
  status(mark[1]) = mul
  status(__[2]) = lex
  status(nil[0]) = mul
  status(U11[2]) = lex
  status(tt[0]) = mul
  status(U12[1]) = mul
  status(isNeList[1]) = mul
  status(U21[3]) = mul
  status(U22[2]) = mul
  status(isList[1]) = lex
  status(U23[1]) = mul
  status(U31[2]) = mul
  status(U32[1]) = mul
  status(isQid[1]) = lex
  status(U41[3]) = mul
  status(U42[2]) = mul
  status(U43[1]) = mul
  status(U51[3]) = lex
  status(U52[2]) = lex
  status(U53[1]) = lex
  status(U61[2]) = lex
  status(U62[1]) = mul
  status(U71[2]) = lex
  status(U72[1]) = lex
  status(isNePal[1]) = lex
  status(and[2]) = mul
  status(isPal[1]) = lex
  status(a[0]) = mul
  status(e[0]) = mul
  status(i[0]) = mul
  status(o[0]) = mul
  status(u[0]) = mul
  
  status(_) = lex
  
  problem when orienting (usable) rules
  could not orient U23(mark(X)) >= mark(U23(X))
  pi( U23(mark(X)) ) = U23(mark(X))
  pi( mark(U23(X)) ) = mark(U23(X))
  could not orient U23(mark(X)) >=RPO mark(U23(X))