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(X1), X2) -> mark(U12(X1, X2))
  U12(ok(X1), ok(X2)) -> ok(U12(X1, X2))
  U13(mark(X)) -> mark(U13(X))
  U13(ok(X)) -> ok(U13(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, X3) -> mark(U22(X1, X2, X3))
  U22(ok(X1), ok(X2), ok(X3)) -> ok(U22(X1, X2, X3))
  U23(mark(X1), X2, X3) -> mark(U23(X1, X2, X3))
  U23(ok(X1), ok(X2), ok(X3)) -> ok(U23(X1, X2, X3))
  U24(mark(X1), X2, X3) -> mark(U24(X1, X2, X3))
  U24(ok(X1), ok(X2), ok(X3)) -> ok(U24(X1, X2, X3))
  U25(mark(X1), X2) -> mark(U25(X1, X2))
  U25(ok(X1), ok(X2)) -> ok(U25(X1, X2))
  U26(mark(X)) -> mark(U26(X))
  U26(ok(X)) -> ok(U26(X))
  U31(mark(X1), X2) -> mark(U31(X1, X2))
  U31(ok(X1), ok(X2)) -> ok(U31(X1, X2))
  U32(mark(X1), X2) -> mark(U32(X1, X2))
  U32(ok(X1), ok(X2)) -> ok(U32(X1, X2))
  U33(mark(X)) -> mark(U33(X))
  U33(ok(X)) -> ok(U33(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, X3) -> mark(U42(X1, X2, X3))
  U42(ok(X1), ok(X2), ok(X3)) -> ok(U42(X1, X2, X3))
  U43(mark(X1), X2, X3) -> mark(U43(X1, X2, X3))
  U43(ok(X1), ok(X2), ok(X3)) -> ok(U43(X1, X2, X3))
  U44(mark(X1), X2, X3) -> mark(U44(X1, X2, X3))
  U44(ok(X1), ok(X2), ok(X3)) -> ok(U44(X1, X2, X3))
  U45(mark(X1), X2) -> mark(U45(X1, X2))
  U45(ok(X1), ok(X2)) -> ok(U45(X1, X2))
  U46(mark(X)) -> mark(U46(X))
  U46(ok(X)) -> ok(U46(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, X3) -> mark(U52(X1, X2, X3))
  U52(ok(X1), ok(X2), ok(X3)) -> ok(U52(X1, X2, X3))
  U53(mark(X1), X2, X3) -> mark(U53(X1, X2, X3))
  U53(ok(X1), ok(X2), ok(X3)) -> ok(U53(X1, X2, X3))
  U54(mark(X1), X2, X3) -> mark(U54(X1, X2, X3))
  U54(ok(X1), ok(X2), ok(X3)) -> ok(U54(X1, X2, X3))
  U55(mark(X1), X2) -> mark(U55(X1, X2))
  U55(ok(X1), ok(X2)) -> ok(U55(X1, X2))
  U56(mark(X)) -> mark(U56(X))
  U56(ok(X)) -> ok(U56(X))
  U61(mark(X1), X2) -> mark(U61(X1, X2))
  U61(ok(X1), ok(X2)) -> ok(U61(X1, X2))
  U62(mark(X1), X2) -> mark(U62(X1, X2))
  U62(ok(X1), ok(X2)) -> ok(U62(X1, X2))
  U63(mark(X)) -> mark(U63(X))
  U63(ok(X)) -> ok(U63(X))
  U71(mark(X1), X2, X3) -> mark(U71(X1, X2, X3))
  U71(ok(X1), ok(X2), ok(X3)) -> ok(U71(X1, X2, X3))
  U72(mark(X1), X2) -> mark(U72(X1, X2))
  U72(ok(X1), ok(X2)) -> ok(U72(X1, X2))
  U73(mark(X1), X2) -> mark(U73(X1, X2))
  U73(ok(X1), ok(X2)) -> ok(U73(X1, X2))
  U74(mark(X)) -> mark(U74(X))
  U74(ok(X)) -> ok(U74(X))
  U81(mark(X1), X2) -> mark(U81(X1, X2))
  U81(ok(X1), ok(X2)) -> ok(U81(X1, X2))
  U82(mark(X1), X2) -> mark(U82(X1, X2))
  U82(ok(X1), ok(X2)) -> ok(U82(X1, X2))
  U83(mark(X)) -> mark(U83(X))
  U83(ok(X)) -> ok(U83(X))
  U91(mark(X1), X2) -> mark(U91(X1, X2))
  U91(ok(X1), ok(X2)) -> ok(U91(X1, X2))
  U92(mark(X)) -> mark(U92(X))
  U92(ok(X)) -> ok(U92(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(isPalListKind(V), V))
  active(U12(tt, V)) -> mark(U13(isNeList(V)))
  active(U13(tt)) -> mark(tt)
  active(U21(tt, V1, V2)) -> mark(U22(isPalListKind(V1), V1, V2))
  active(U22(tt, V1, V2)) -> mark(U23(isPalListKind(V2), V1, V2))
  active(U23(tt, V1, V2)) -> mark(U24(isPalListKind(V2), V1, V2))
  active(U24(tt, V1, V2)) -> mark(U25(isList(V1), V2))
  active(U25(tt, V2)) -> mark(U26(isList(V2)))
  active(U26(tt)) -> mark(tt)
  active(U31(tt, V)) -> mark(U32(isPalListKind(V), V))
  active(U32(tt, V)) -> mark(U33(isQid(V)))
  active(U33(tt)) -> mark(tt)
  active(U41(tt, V1, V2)) -> mark(U42(isPalListKind(V1), V1, V2))
  active(U42(tt, V1, V2)) -> mark(U43(isPalListKind(V2), V1, V2))
  active(U43(tt, V1, V2)) -> mark(U44(isPalListKind(V2), V1, V2))
  active(U44(tt, V1, V2)) -> mark(U45(isList(V1), V2))
  active(U45(tt, V2)) -> mark(U46(isNeList(V2)))
  active(U46(tt)) -> mark(tt)
  active(U51(tt, V1, V2)) -> mark(U52(isPalListKind(V1), V1, V2))
  active(U52(tt, V1, V2)) -> mark(U53(isPalListKind(V2), V1, V2))
  active(U53(tt, V1, V2)) -> mark(U54(isPalListKind(V2), V1, V2))
  active(U54(tt, V1, V2)) -> mark(U55(isNeList(V1), V2))
  active(U55(tt, V2)) -> mark(U56(isList(V2)))
  active(U56(tt)) -> mark(tt)
  active(U61(tt, V)) -> mark(U62(isPalListKind(V), V))
  active(U62(tt, V)) -> mark(U63(isQid(V)))
  active(U63(tt)) -> mark(tt)
  active(U71(tt, I, P)) -> mark(U72(isPalListKind(I), P))
  active(U72(tt, P)) -> mark(U73(isPal(P), P))
  active(U73(tt, P)) -> mark(U74(isPalListKind(P)))
  active(U74(tt)) -> mark(tt)
  active(U81(tt, V)) -> mark(U82(isPalListKind(V), V))
  active(U82(tt, V)) -> mark(U83(isNePal(V)))
  active(U83(tt)) -> mark(tt)
  active(U91(tt, V2)) -> mark(U92(isPalListKind(V2)))
  active(U92(tt)) -> mark(tt)
  active(isList(V)) -> mark(U11(isPalListKind(V), V))
  active(isList(nil)) -> mark(tt)
  active(isList(__(V1, V2))) -> mark(U21(isPalListKind(V1), V1, V2))
  active(isNeList(V)) -> mark(U31(isPalListKind(V), V))
  active(isNeList(__(V1, V2))) -> mark(U41(isPalListKind(V1), V1, V2))
  active(isNeList(__(V1, V2))) -> mark(U51(isPalListKind(V1), V1, V2))
  active(isNePal(V)) -> mark(U61(isPalListKind(V), V))
  active(isNePal(__(I, __(P, I)))) -> mark(U71(isQid(I), I, P))
  active(isPal(V)) -> mark(U81(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(U91(isPalListKind(V1), 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(X1, X2)) -> U12(active(X1), X2)
  active(U13(X)) -> U13(active(X))
  active(U21(X1, X2, X3)) -> U21(active(X1), X2, X3)
  active(U22(X1, X2, X3)) -> U22(active(X1), X2, X3)
  active(U23(X1, X2, X3)) -> U23(active(X1), X2, X3)
  active(U24(X1, X2, X3)) -> U24(active(X1), X2, X3)
  active(U25(X1, X2)) -> U25(active(X1), X2)
  active(U26(X)) -> U26(active(X))
  active(U31(X1, X2)) -> U31(active(X1), X2)
  active(U32(X1, X2)) -> U32(active(X1), X2)
  active(U33(X)) -> U33(active(X))
  active(U41(X1, X2, X3)) -> U41(active(X1), X2, X3)
  active(U42(X1, X2, X3)) -> U42(active(X1), X2, X3)
  active(U43(X1, X2, X3)) -> U43(active(X1), X2, X3)
  active(U44(X1, X2, X3)) -> U44(active(X1), X2, X3)
  active(U45(X1, X2)) -> U45(active(X1), X2)
  active(U46(X)) -> U46(active(X))
  active(U51(X1, X2, X3)) -> U51(active(X1), X2, X3)
  active(U52(X1, X2, X3)) -> U52(active(X1), X2, X3)
  active(U53(X1, X2, X3)) -> U53(active(X1), X2, X3)
  active(U54(X1, X2, X3)) -> U54(active(X1), X2, X3)
  active(U55(X1, X2)) -> U55(active(X1), X2)
  active(U56(X)) -> U56(active(X))
  active(U61(X1, X2)) -> U61(active(X1), X2)
  active(U62(X1, X2)) -> U62(active(X1), X2)
  active(U63(X)) -> U63(active(X))
  active(U71(X1, X2, X3)) -> U71(active(X1), X2, X3)
  active(U72(X1, X2)) -> U72(active(X1), X2)
  active(U73(X1, X2)) -> U73(active(X1), X2)
  active(U74(X)) -> U74(active(X))
  active(U81(X1, X2)) -> U81(active(X1), X2)
  active(U82(X1, X2)) -> U82(active(X1), X2)
  active(U83(X)) -> U83(active(X))
  active(U91(X1, X2)) -> U91(active(X1), X2)
  active(U92(X)) -> U92(active(X))
  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(X1, X2)) -> U12(proper(X1), proper(X2))
  proper(isPalListKind(X)) -> isPalListKind(proper(X))
  proper(U13(X)) -> U13(proper(X))
  proper(isNeList(X)) -> isNeList(proper(X))
  proper(U21(X1, X2, X3)) -> U21(proper(X1), proper(X2), proper(X3))
  proper(U22(X1, X2, X3)) -> U22(proper(X1), proper(X2), proper(X3))
  proper(U23(X1, X2, X3)) -> U23(proper(X1), proper(X2), proper(X3))
  proper(U24(X1, X2, X3)) -> U24(proper(X1), proper(X2), proper(X3))
  proper(U25(X1, X2)) -> U25(proper(X1), proper(X2))
  proper(isList(X)) -> isList(proper(X))
  proper(U26(X)) -> U26(proper(X))
  proper(U31(X1, X2)) -> U31(proper(X1), proper(X2))
  proper(U32(X1, X2)) -> U32(proper(X1), proper(X2))
  proper(U33(X)) -> U33(proper(X))
  proper(isQid(X)) -> isQid(proper(X))
  proper(U41(X1, X2, X3)) -> U41(proper(X1), proper(X2), proper(X3))
  proper(U42(X1, X2, X3)) -> U42(proper(X1), proper(X2), proper(X3))
  proper(U43(X1, X2, X3)) -> U43(proper(X1), proper(X2), proper(X3))
  proper(U44(X1, X2, X3)) -> U44(proper(X1), proper(X2), proper(X3))
  proper(U45(X1, X2)) -> U45(proper(X1), proper(X2))
  proper(U46(X)) -> U46(proper(X))
  proper(U51(X1, X2, X3)) -> U51(proper(X1), proper(X2), proper(X3))
  proper(U52(X1, X2, X3)) -> U52(proper(X1), proper(X2), proper(X3))
  proper(U53(X1, X2, X3)) -> U53(proper(X1), proper(X2), proper(X3))
  proper(U54(X1, X2, X3)) -> U54(proper(X1), proper(X2), proper(X3))
  proper(U55(X1, X2)) -> U55(proper(X1), proper(X2))
  proper(U56(X)) -> U56(proper(X))
  proper(U61(X1, X2)) -> U61(proper(X1), proper(X2))
  proper(U62(X1, X2)) -> U62(proper(X1), proper(X2))
  proper(U63(X)) -> U63(proper(X))
  proper(U71(X1, X2, X3)) -> U71(proper(X1), proper(X2), proper(X3))
  proper(U72(X1, X2)) -> U72(proper(X1), proper(X2))
  proper(U73(X1, X2)) -> U73(proper(X1), proper(X2))
  proper(isPal(X)) -> isPal(proper(X))
  proper(U74(X)) -> U74(proper(X))
  proper(U81(X1, X2)) -> U81(proper(X1), proper(X2))
  proper(U82(X1, X2)) -> U82(proper(X1), proper(X2))
  proper(U83(X)) -> U83(proper(X))
  proper(isNePal(X)) -> isNePal(proper(X))
  proper(U91(X1, X2)) -> U91(proper(X1), proper(X2))
  proper(U92(X)) -> U92(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#) = [(epsilon,0),(1,0)]
  Argument Filter: 
  pi(top#/1) = []
  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(U12/2) = [2,1]
  pi(isPalListKind/1) = [1]
  pi(U13/1) = [1]
  pi(isNeList/1) = [1]
  pi(U21/3) = [1,2,3]
  pi(U22/3) = [1,3,2]
  pi(U23/3) = [1,2,3]
  pi(U24/3) = [1,3,2]
  pi(U25/2) = [1,2]
  pi(isList/1) = [1]
  pi(U26/1) = [1]
  pi(U31/2) = [2,1]
  pi(U32/2) = [2,1]
  pi(U33/1) = [1]
  pi(isQid/1) = 1
  pi(U41/3) = [1,2,3]
  pi(U42/3) = [3,2,1]
  pi(U43/3) = [1,2,3]
  pi(U44/3) = [2,3,1]
  pi(U45/2) = [2,1]
  pi(U46/1) = [1]
  pi(U51/3) = [1,3,2]
  pi(U52/3) = [2,1,3]
  pi(U53/3) = [2,1,3]
  pi(U54/3) = [3,1,2]
  pi(U55/2) = [1,2]
  pi(U56/1) = [1]
  pi(U61/2) = [2,1]
  pi(U62/2) = [2,1]
  pi(U63/1) = [1]
  pi(U71/3) = [1,2,3]
  pi(U72/2) = [1,2]
  pi(U73/2) = [1,2]
  pi(isPal/1) = [1]
  pi(U74/1) = [1]
  pi(U81/2) = [1,2]
  pi(U82/2) = [2,1]
  pi(U83/1) = [1]
  pi(isNePal/1) = [1]
  pi(U91/2) = [2,1]
  pi(U92/1) = [1]
  pi(a/0) = []
  pi(e/0) = []
  pi(i/0) = []
  pi(o/0) = []
  pi(u/0) = []
  
  RPO with the following precedence
  precedence(top#[1]) = 0
  precedence(mark[1]) = 1
  precedence(__[2]) = 35
  precedence(nil[0]) = 36
  precedence(U11[2]) = 11
  precedence(tt[0]) = 9
  precedence(U12[2]) = 10
  precedence(isPalListKind[1]) = 9
  precedence(U13[1]) = 2
  precedence(isNeList[1]) = 10
  precedence(U21[3]) = 18
  precedence(U22[3]) = 17
  precedence(U23[3]) = 16
  precedence(U24[3]) = 15
  precedence(U25[2]) = 14
  precedence(isList[1]) = 13
  precedence(U26[1]) = 3
  precedence(U31[2]) = 9
  precedence(U32[2]) = 5
  precedence(U33[1]) = 4
  precedence(U41[3]) = 22
  precedence(U42[3]) = 21
  precedence(U43[3]) = 20
  precedence(U44[3]) = 19
  precedence(U45[2]) = 10
  precedence(U46[1]) = 6
  precedence(U51[3]) = 26
  precedence(U52[3]) = 25
  precedence(U53[3]) = 24
  precedence(U54[3]) = 23
  precedence(U55[2]) = 13
  precedence(U56[1]) = 12
  precedence(U61[2]) = 27
  precedence(U62[2]) = 7
  precedence(U63[1]) = 7
  precedence(U71[3]) = 33
  precedence(U72[2]) = 32
  precedence(U73[2]) = 28
  precedence(isPal[1]) = 32
  precedence(U74[1]) = 1
  precedence(U81[2]) = 31
  precedence(U82[2]) = 30
  precedence(U83[1]) = 29
  precedence(isNePal[1]) = 30
  precedence(U91[2]) = 34
  precedence(U92[1]) = 8
  precedence(a[0]) = 37
  precedence(e[0]) = 38
  precedence(i[0]) = 39
  precedence(o[0]) = 40
  precedence(u[0]) = 41
  
  precedence(_) = 0
  and the following status
  status(top#[1]) = mul
  status(mark[1]) = mul
  status(__[2]) = lex
  status(nil[0]) = mul
  status(U11[2]) = mul
  status(tt[0]) = mul
  status(U12[2]) = lex
  status(isPalListKind[1]) = lex
  status(U13[1]) = lex
  status(isNeList[1]) = lex
  status(U21[3]) = mul
  status(U22[3]) = lex
  status(U23[3]) = mul
  status(U24[3]) = lex
  status(U25[2]) = lex
  status(isList[1]) = mul
  status(U26[1]) = lex
  status(U31[2]) = lex
  status(U32[2]) = lex
  status(U33[1]) = lex
  status(U41[3]) = mul
  status(U42[3]) = lex
  status(U43[3]) = mul
  status(U44[3]) = lex
  status(U45[2]) = lex
  status(U46[1]) = lex
  status(U51[3]) = lex
  status(U52[3]) = lex
  status(U53[3]) = lex
  status(U54[3]) = lex
  status(U55[2]) = mul
  status(U56[1]) = lex
  status(U61[2]) = lex
  status(U62[2]) = lex
  status(U63[1]) = lex
  status(U71[3]) = mul
  status(U72[2]) = mul
  status(U73[2]) = lex
  status(isPal[1]) = mul
  status(U74[1]) = mul
  status(U81[2]) = mul
  status(U82[2]) = lex
  status(U83[1]) = lex
  status(isNePal[1]) = lex
  status(U91[2]) = lex
  status(U92[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 U74(mark(X)) >= mark(U74(X))
  pi( U74(mark(X)) ) = U74(mark(X))
  pi( mark(U74(X)) ) = mark(U74(X))
  could not orient U74(mark(X)) >=RPO mark(U74(X))