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 to remove from the DP problem
  pairs:
  
  a____#(__(X, Y), Z) -> a____#(mark(X), a____(mark(Y), mark(Z)))
  a____#(__(X, Y), Z) -> mark#(X)
  a____#(__(X, Y), Z) -> a____#(mark(Y), mark(Z))
  a____#(__(X, Y), Z) -> mark#(Y)
  a____#(__(X, Y), Z) -> mark#(Z)
  a____#(X, nil) -> mark#(X)
  a____#(nil, X) -> mark#(X)
  mark#(__(X1, X2)) -> a____#(mark(X1), mark(X2))
  mark#(__(X1, X2)) -> mark#(X1)
  mark#(__(X1, X2)) -> mark#(X2)
  mark#(U11(X1, X2)) -> mark#(X1)
  mark#(U12(X1, X2)) -> mark#(X1)
  mark#(U13(X)) -> mark#(X)
  mark#(U21(X1, X2, X3)) -> mark#(X1)
  mark#(U22(X1, X2, X3)) -> mark#(X1)
  mark#(U23(X1, X2, X3)) -> mark#(X1)
  mark#(U24(X1, X2, X3)) -> mark#(X1)
  mark#(U25(X1, X2)) -> mark#(X1)
  mark#(U26(X)) -> mark#(X)
  mark#(U31(X1, X2)) -> mark#(X1)
  mark#(U32(X1, X2)) -> mark#(X1)
  mark#(U33(X)) -> mark#(X)
  mark#(U41(X1, X2, X3)) -> mark#(X1)
  mark#(U42(X1, X2, X3)) -> mark#(X1)
  mark#(U43(X1, X2, X3)) -> mark#(X1)
  mark#(U44(X1, X2, X3)) -> mark#(X1)
  mark#(U45(X1, X2)) -> mark#(X1)
  mark#(U46(X)) -> mark#(X)
  mark#(U51(X1, X2, X3)) -> mark#(X1)
  mark#(U52(X1, X2, X3)) -> mark#(X1)
  mark#(U53(X1, X2, X3)) -> mark#(X1)
  mark#(U54(X1, X2, X3)) -> mark#(X1)
  mark#(U55(X1, X2)) -> mark#(X1)
  mark#(U56(X)) -> mark#(X)
  mark#(U61(X1, X2)) -> mark#(X1)
  mark#(U62(X1, X2)) -> mark#(X1)
  mark#(U63(X)) -> mark#(X)
  mark#(U71(X1, X2, X3)) -> mark#(X1)
  mark#(U72(X1, X2)) -> mark#(X1)
  mark#(U73(X1, X2)) -> mark#(X1)
  mark#(U74(X)) -> mark#(X)
  mark#(U81(X1, X2)) -> mark#(X1)
  mark#(U82(X1, X2)) -> mark#(X1)
  mark#(U83(X)) -> mark#(X)
  mark#(U91(X1, X2)) -> mark#(X1)
  mark#(U92(X)) -> mark#(X)
  rules:
  
  a__U11(tt, V) -> a__U12(a__isPalListKind(V), V)
  a__U11(X1, X2) -> U11(X1, X2)
  a__U12(tt, V) -> a__U13(a__isNeList(V))
  a__U12(X1, X2) -> U12(X1, X2)
  a__U13(tt) -> tt
  a__U13(X) -> U13(X)
  a__U21(tt, V1, V2) -> a__U22(a__isPalListKind(V1), V1, V2)
  a__U21(X1, X2, X3) -> U21(X1, X2, X3)
  a__U22(tt, V1, V2) -> a__U23(a__isPalListKind(V2), V1, V2)
  a__U22(X1, X2, X3) -> U22(X1, X2, X3)
  a__U23(tt, V1, V2) -> a__U24(a__isPalListKind(V2), V1, V2)
  a__U23(X1, X2, X3) -> U23(X1, X2, X3)
  a__U24(tt, V1, V2) -> a__U25(a__isList(V1), V2)
  a__U24(X1, X2, X3) -> U24(X1, X2, X3)
  a__U25(tt, V2) -> a__U26(a__isList(V2))
  a__U25(X1, X2) -> U25(X1, X2)
  a__U26(tt) -> tt
  a__U26(X) -> U26(X)
  a__U31(tt, V) -> a__U32(a__isPalListKind(V), V)
  a__U31(X1, X2) -> U31(X1, X2)
  a__U32(tt, V) -> a__U33(a__isQid(V))
  a__U32(X1, X2) -> U32(X1, X2)
  a__U33(tt) -> tt
  a__U33(X) -> U33(X)
  a__U41(tt, V1, V2) -> a__U42(a__isPalListKind(V1), V1, V2)
  a__U41(X1, X2, X3) -> U41(X1, X2, X3)
  a__U42(tt, V1, V2) -> a__U43(a__isPalListKind(V2), V1, V2)
  a__U42(X1, X2, X3) -> U42(X1, X2, X3)
  a__U43(tt, V1, V2) -> a__U44(a__isPalListKind(V2), V1, V2)
  a__U43(X1, X2, X3) -> U43(X1, X2, X3)
  a__U44(tt, V1, V2) -> a__U45(a__isList(V1), V2)
  a__U44(X1, X2, X3) -> U44(X1, X2, X3)
  a__U45(tt, V2) -> a__U46(a__isNeList(V2))
  a__U45(X1, X2) -> U45(X1, X2)
  a__U46(tt) -> tt
  a__U46(X) -> U46(X)
  a__U51(tt, V1, V2) -> a__U52(a__isPalListKind(V1), V1, V2)
  a__U51(X1, X2, X3) -> U51(X1, X2, X3)
  a__U52(tt, V1, V2) -> a__U53(a__isPalListKind(V2), V1, V2)
  a__U52(X1, X2, X3) -> U52(X1, X2, X3)
  a__U53(tt, V1, V2) -> a__U54(a__isPalListKind(V2), V1, V2)
  a__U53(X1, X2, X3) -> U53(X1, X2, X3)
  a__U54(tt, V1, V2) -> a__U55(a__isNeList(V1), V2)
  a__U54(X1, X2, X3) -> U54(X1, X2, X3)
  a__U55(tt, V2) -> a__U56(a__isList(V2))
  a__U55(X1, X2) -> U55(X1, X2)
  a__U56(tt) -> tt
  a__U56(X) -> U56(X)
  a__U61(tt, V) -> a__U62(a__isPalListKind(V), V)
  a__U61(X1, X2) -> U61(X1, X2)
  a__U62(tt, V) -> a__U63(a__isQid(V))
  a__U62(X1, X2) -> U62(X1, X2)
  a__U63(tt) -> tt
  a__U63(X) -> U63(X)
  a__U71(tt, I, P) -> a__U72(a__isPalListKind(I), P)
  a__U71(X1, X2, X3) -> U71(X1, X2, X3)
  a__U72(tt, P) -> a__U73(a__isPal(P), P)
  a__U72(X1, X2) -> U72(X1, X2)
  a__U73(tt, P) -> a__U74(a__isPalListKind(P))
  a__U73(X1, X2) -> U73(X1, X2)
  a__U74(tt) -> tt
  a__U74(X) -> U74(X)
  a__U81(tt, V) -> a__U82(a__isPalListKind(V), V)
  a__U81(X1, X2) -> U81(X1, X2)
  a__U82(tt, V) -> a__U83(a__isNePal(V))
  a__U82(X1, X2) -> U82(X1, X2)
  a__U83(tt) -> tt
  a__U83(X) -> U83(X)
  a__U91(tt, V2) -> a__U92(a__isPalListKind(V2))
  a__U91(X1, X2) -> U91(X1, X2)
  a__U92(tt) -> tt
  a__U92(X) -> U92(X)
  a____(__(X, Y), Z) -> a____(mark(X), a____(mark(Y), mark(Z)))
  a____(X, nil) -> mark(X)
  a____(nil, X) -> mark(X)
  a____(X1, X2) -> __(X1, X2)
  a__isList(V) -> a__U11(a__isPalListKind(V), V)
  a__isList(nil) -> tt
  a__isList(__(V1, V2)) -> a__U21(a__isPalListKind(V1), V1, V2)
  a__isList(X) -> isList(X)
  a__isNeList(V) -> a__U31(a__isPalListKind(V), V)
  a__isNeList(__(V1, V2)) -> a__U41(a__isPalListKind(V1), V1, V2)
  a__isNeList(__(V1, V2)) -> a__U51(a__isPalListKind(V1), V1, V2)
  a__isNeList(X) -> isNeList(X)
  a__isNePal(V) -> a__U61(a__isPalListKind(V), V)
  a__isNePal(__(I, __(P, I))) -> a__U71(a__isQid(I), I, P)
  a__isNePal(X) -> isNePal(X)
  a__isPal(V) -> a__U81(a__isPalListKind(V), V)
  a__isPal(nil) -> tt
  a__isPal(X) -> isPal(X)
  a__isPalListKind(a) -> tt
  a__isPalListKind(e) -> tt
  a__isPalListKind(i) -> tt
  a__isPalListKind(nil) -> tt
  a__isPalListKind(o) -> tt
  a__isPalListKind(u) -> tt
  a__isPalListKind(__(V1, V2)) -> a__U91(a__isPalListKind(V1), V2)
  a__isPalListKind(X) -> isPalListKind(X)
  a__isQid(a) -> tt
  a__isQid(e) -> tt
  a__isQid(i) -> tt
  a__isQid(o) -> tt
  a__isQid(u) -> tt
  a__isQid(X) -> isQid(X)
  mark(__(X1, X2)) -> a____(mark(X1), mark(X2))
  mark(U11(X1, X2)) -> a__U11(mark(X1), X2)
  mark(U12(X1, X2)) -> a__U12(mark(X1), X2)
  mark(isPalListKind(X)) -> a__isPalListKind(X)
  mark(U13(X)) -> a__U13(mark(X))
  mark(isNeList(X)) -> a__isNeList(X)
  mark(U21(X1, X2, X3)) -> a__U21(mark(X1), X2, X3)
  mark(U22(X1, X2, X3)) -> a__U22(mark(X1), X2, X3)
  mark(U23(X1, X2, X3)) -> a__U23(mark(X1), X2, X3)
  mark(U24(X1, X2, X3)) -> a__U24(mark(X1), X2, X3)
  mark(U25(X1, X2)) -> a__U25(mark(X1), X2)
  mark(isList(X)) -> a__isList(X)
  mark(U26(X)) -> a__U26(mark(X))
  mark(U31(X1, X2)) -> a__U31(mark(X1), X2)
  mark(U32(X1, X2)) -> a__U32(mark(X1), X2)
  mark(U33(X)) -> a__U33(mark(X))
  mark(isQid(X)) -> a__isQid(X)
  mark(U41(X1, X2, X3)) -> a__U41(mark(X1), X2, X3)
  mark(U42(X1, X2, X3)) -> a__U42(mark(X1), X2, X3)
  mark(U43(X1, X2, X3)) -> a__U43(mark(X1), X2, X3)
  mark(U44(X1, X2, X3)) -> a__U44(mark(X1), X2, X3)
  mark(U45(X1, X2)) -> a__U45(mark(X1), X2)
  mark(U46(X)) -> a__U46(mark(X))
  mark(U51(X1, X2, X3)) -> a__U51(mark(X1), X2, X3)
  mark(U52(X1, X2, X3)) -> a__U52(mark(X1), X2, X3)
  mark(U53(X1, X2, X3)) -> a__U53(mark(X1), X2, X3)
  mark(U54(X1, X2, X3)) -> a__U54(mark(X1), X2, X3)
  mark(U55(X1, X2)) -> a__U55(mark(X1), X2)
  mark(U56(X)) -> a__U56(mark(X))
  mark(U61(X1, X2)) -> a__U61(mark(X1), X2)
  mark(U62(X1, X2)) -> a__U62(mark(X1), X2)
  mark(U63(X)) -> a__U63(mark(X))
  mark(U71(X1, X2, X3)) -> a__U71(mark(X1), X2, X3)
  mark(U72(X1, X2)) -> a__U72(mark(X1), X2)
  mark(U73(X1, X2)) -> a__U73(mark(X1), X2)
  mark(isPal(X)) -> a__isPal(X)
  mark(U74(X)) -> a__U74(mark(X))
  mark(U81(X1, X2)) -> a__U81(mark(X1), X2)
  mark(U82(X1, X2)) -> a__U82(mark(X1), X2)
  mark(U83(X)) -> a__U83(mark(X))
  mark(isNePal(X)) -> a__isNePal(X)
  mark(U91(X1, X2)) -> a__U91(mark(X1), X2)
  mark(U92(X)) -> a__U92(mark(X))
  mark(nil) -> nil
  mark(tt) -> tt
  mark(a) -> a
  mark(e) -> e
  mark(i) -> i
  mark(o) -> o
  mark(u) -> u
  
   the pairs 
  a____#(__(X, Y), Z) -> a____#(mark(X), a____(mark(Y), mark(Z)))
  a____#(__(X, Y), Z) -> mark#(X)
  a____#(__(X, Y), Z) -> a____#(mark(Y), mark(Z))
  a____#(__(X, Y), Z) -> mark#(Y)
  a____#(__(X, Y), Z) -> mark#(Z)
  a____#(X, nil) -> mark#(X)
  a____#(nil, X) -> mark#(X)
  mark#(__(X1, X2)) -> mark#(X1)
  mark#(__(X1, X2)) -> mark#(X2)
  mark#(U71(X1, X2, X3)) -> mark#(X1)
  mark#(U72(X1, X2)) -> mark#(X1)
  mark#(U73(X1, X2)) -> mark#(X1)
  mark#(U81(X1, X2)) -> mark#(X1)
  mark#(U82(X1, X2)) -> mark#(X1)
  mark#(U83(X)) -> mark#(X)
  
  could not apply the generic reduction pair processor with the following
  Argument Filter: 
  pi(a____#/2) = [1,2]
  pi(__/2) = [1,2]
  pi(mark#/1) = 1
  pi(mark/1) = 1
  pi(a____/2) = [1,2]
  pi(U11/2) = 1
  pi(U12/2) = 1
  pi(U13/1) = 1
  pi(U21/3) = 1
  pi(U22/3) = 1
  pi(U23/3) = 1
  pi(U24/3) = 1
  pi(U25/2) = 1
  pi(U26/1) = 1
  pi(U31/2) = 1
  pi(U32/2) = 1
  pi(U33/1) = 1
  pi(U41/3) = 1
  pi(U42/3) = 1
  pi(U43/3) = 1
  pi(U44/3) = 1
  pi(U45/2) = 1
  pi(U46/1) = 1
  pi(U51/3) = 1
  pi(U52/3) = 1
  pi(U53/3) = 1
  pi(U54/3) = 1
  pi(U55/2) = 1
  pi(U56/1) = 1
  pi(U61/2) = 1
  pi(U62/2) = 1
  pi(U63/1) = 1
  pi(U71/3) = [3,1]
  pi(U72/2) = [2,1]
  pi(U73/2) = [1,2]
  pi(U74/1) = 1
  pi(U81/2) = [1,2]
  pi(U82/2) = [1,2]
  pi(U83/1) = [1]
  pi(U91/2) = 1
  pi(U92/1) = 1
  pi(nil/0) = []
  pi(a__U11/2) = 1
  pi(a__U12/2) = 1
  pi(isPalListKind/1) = []
  pi(a__isPalListKind/1) = []
  pi(a__U13/1) = 1
  pi(isNeList/1) = []
  pi(a__isNeList/1) = []
  pi(a__U21/3) = 1
  pi(a__U22/3) = 1
  pi(a__U23/3) = 1
  pi(a__U24/3) = 1
  pi(a__U25/2) = 1
  pi(isList/1) = []
  pi(a__isList/1) = []
  pi(a__U26/1) = 1
  pi(a__U31/2) = 1
  pi(a__U32/2) = 1
  pi(a__U33/1) = 1
  pi(isQid/1) = []
  pi(a__isQid/1) = []
  pi(a__U41/3) = 1
  pi(a__U42/3) = 1
  pi(a__U43/3) = 1
  pi(a__U44/3) = 1
  pi(a__U45/2) = 1
  pi(a__U46/1) = 1
  pi(a__U51/3) = 1
  pi(a__U52/3) = 1
  pi(a__U53/3) = 1
  pi(a__U54/3) = 1
  pi(a__U55/2) = 1
  pi(a__U56/1) = 1
  pi(a__U61/2) = 1
  pi(a__U62/2) = 1
  pi(a__U63/1) = 1
  pi(a__U71/3) = [3,1]
  pi(a__U72/2) = [2,1]
  pi(a__U73/2) = [1,2]
  pi(isPal/1) = [1]
  pi(a__isPal/1) = [1]
  pi(a__U74/1) = 1
  pi(a__U81/2) = [1,2]
  pi(a__U82/2) = [1,2]
  pi(a__U83/1) = [1]
  pi(isNePal/1) = 1
  pi(a__isNePal/1) = 1
  pi(a__U91/2) = 1
  pi(a__U92/1) = 1
  pi(tt/0) = []
  pi(a/0) = []
  pi(e/0) = []
  pi(i/0) = []
  pi(o/0) = []
  pi(u/0) = []
  
  RPO with the following precedence
  precedence(a____#[2]) = 5
  precedence(__[2]) = 5
  precedence(a____[2]) = 5
  precedence(U71[3]) = 4
  precedence(U72[2]) = 4
  precedence(U73[2]) = 1
  precedence(U81[2]) = 3
  precedence(U82[2]) = 3
  precedence(U83[1]) = 2
  precedence(nil[0]) = 0
  precedence(isPalListKind[1]) = 0
  precedence(a__isPalListKind[1]) = 0
  precedence(isNeList[1]) = 0
  precedence(a__isNeList[1]) = 0
  precedence(isList[1]) = 0
  precedence(a__isList[1]) = 0
  precedence(isQid[1]) = 0
  precedence(a__isQid[1]) = 0
  precedence(a__U71[3]) = 4
  precedence(a__U72[2]) = 4
  precedence(a__U73[2]) = 1
  precedence(isPal[1]) = 4
  precedence(a__isPal[1]) = 4
  precedence(a__U81[2]) = 3
  precedence(a__U82[2]) = 3
  precedence(a__U83[1]) = 2
  precedence(tt[0]) = 0
  precedence(a[0]) = 0
  precedence(e[0]) = 6
  precedence(i[0]) = 7
  precedence(o[0]) = 8
  precedence(u[0]) = 0
  
  precedence(_) = 0
  and the following status
  status(a____#[2]) = lex
  status(__[2]) = lex
  status(a____[2]) = lex
  status(U71[3]) = lex
  status(U72[2]) = lex
  status(U73[2]) = mul
  status(U81[2]) = mul
  status(U82[2]) = mul
  status(U83[1]) = mul
  status(nil[0]) = mul
  status(isPalListKind[1]) = mul
  status(a__isPalListKind[1]) = mul
  status(isNeList[1]) = mul
  status(a__isNeList[1]) = mul
  status(isList[1]) = mul
  status(a__isList[1]) = mul
  status(isQid[1]) = mul
  status(a__isQid[1]) = mul
  status(a__U71[3]) = lex
  status(a__U72[2]) = lex
  status(a__U73[2]) = mul
  status(isPal[1]) = lex
  status(a__isPal[1]) = lex
  status(a__U81[2]) = mul
  status(a__U82[2]) = mul
  status(a__U83[1]) = mul
  status(tt[0]) = mul
  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 a__U81(tt, V) >= a__U82(a__isPalListKind(V), V)
  pi( a__U81(tt, V) ) = a__U81(tt, V)
  pi( a__U82(a__isPalListKind(V), V) ) = a__U82(a__isPalListKind, V)
  could not orient a__U81(tt, V) >=RPO a__U82(a__isPalListKind, V)