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__U31#(tt, N) -> mark#(N)
  a__U41#(tt, M, N) -> a__U42#(a__isNat(N), M, N)
  a__U42#(tt, M, N) -> a__plus#(mark(N), mark(M))
  a__U42#(tt, M, N) -> mark#(N)
  a__U42#(tt, M, N) -> mark#(M)
  a__plus#(N, 0) -> a__U31#(a__isNat(N), N)
  a__plus#(N, s(M)) -> a__U41#(a__isNat(M), M, N)
  mark#(U11(X1, X2)) -> mark#(X1)
  mark#(U12(X)) -> mark#(X)
  mark#(U21(X)) -> mark#(X)
  mark#(U31(X1, X2)) -> a__U31#(mark(X1), X2)
  mark#(U31(X1, X2)) -> mark#(X1)
  mark#(U41(X1, X2, X3)) -> a__U41#(mark(X1), X2, X3)
  mark#(U41(X1, X2, X3)) -> mark#(X1)
  mark#(U42(X1, X2, X3)) -> a__U42#(mark(X1), X2, X3)
  mark#(U42(X1, X2, X3)) -> mark#(X1)
  mark#(plus(X1, X2)) -> a__plus#(mark(X1), mark(X2))
  mark#(plus(X1, X2)) -> mark#(X1)
  mark#(plus(X1, X2)) -> mark#(X2)
  mark#(s(X)) -> mark#(X)
  rules:
  
  a__U11(tt, V2) -> a__U12(a__isNat(V2))
  a__U11(X1, X2) -> U11(X1, X2)
  a__U12(tt) -> tt
  a__U12(X) -> U12(X)
  a__U21(tt) -> tt
  a__U21(X) -> U21(X)
  a__U31(tt, N) -> mark(N)
  a__U31(X1, X2) -> U31(X1, X2)
  a__U41(tt, M, N) -> a__U42(a__isNat(N), M, N)
  a__U41(X1, X2, X3) -> U41(X1, X2, X3)
  a__U42(tt, M, N) -> s(a__plus(mark(N), mark(M)))
  a__U42(X1, X2, X3) -> U42(X1, X2, X3)
  a__isNat(0) -> tt
  a__isNat(plus(V1, V2)) -> a__U11(a__isNat(V1), V2)
  a__isNat(s(V1)) -> a__U21(a__isNat(V1))
  a__isNat(X) -> isNat(X)
  a__plus(N, 0) -> a__U31(a__isNat(N), N)
  a__plus(N, s(M)) -> a__U41(a__isNat(M), M, N)
  a__plus(X1, X2) -> plus(X1, X2)
  mark(U11(X1, X2)) -> a__U11(mark(X1), X2)
  mark(U12(X)) -> a__U12(mark(X))
  mark(isNat(X)) -> a__isNat(X)
  mark(U21(X)) -> a__U21(mark(X))
  mark(U31(X1, X2)) -> a__U31(mark(X1), X2)
  mark(U41(X1, X2, X3)) -> a__U41(mark(X1), X2, X3)
  mark(U42(X1, X2, X3)) -> a__U42(mark(X1), X2, X3)
  mark(plus(X1, X2)) -> a__plus(mark(X1), mark(X2))
  mark(tt) -> tt
  mark(s(X)) -> s(mark(X))
  mark(0) -> 0
  
   the pairs 
  a__U42#(tt, M, N) -> a__plus#(mark(N), mark(M))
  a__U42#(tt, M, N) -> mark#(N)
  a__U42#(tt, M, N) -> mark#(M)
  a__plus#(N, 0) -> a__U31#(a__isNat(N), N)
  a__plus#(N, s(M)) -> a__U41#(a__isNat(M), M, N)
  mark#(U31(X1, X2)) -> a__U31#(mark(X1), X2)
  mark#(U31(X1, X2)) -> mark#(X1)
  mark#(U41(X1, X2, X3)) -> a__U41#(mark(X1), X2, X3)
  mark#(U41(X1, X2, X3)) -> mark#(X1)
  mark#(U42(X1, X2, X3)) -> a__U42#(mark(X1), X2, X3)
  mark#(U42(X1, X2, X3)) -> mark#(X1)
  mark#(plus(X1, X2)) -> a__plus#(mark(X1), mark(X2))
  mark#(plus(X1, X2)) -> mark#(X1)
  mark#(plus(X1, X2)) -> mark#(X2)
  mark#(s(X)) -> mark#(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(mark#) = [(1,9)]
  pi(a__U31#) = [(2,9)]
  pi(a__U41#) = [(epsilon,0)]
  pi(a__U42#) = [(epsilon,0),(1,13),(3,0)]
  pi(a__plus#) = [(epsilon,0)]
  Argument Filter: 
  pi(mark#/1) = []
  pi(U11/2) = 1
  pi(U12/1) = 1
  pi(U21/1) = 1
  pi(U31/2) = [1,2]
  pi(a__U31#/2) = [1]
  pi(mark/1) = 1
  pi(tt/0) = []
  pi(U41/3) = [3,2,1]
  pi(a__U41#/3) = [1,2,3]
  pi(a__U42#/3) = [1,2,3]
  pi(a__isNat/1) = []
  pi(a__plus#/2) = [1,2]
  pi(0/0) = []
  pi(s/1) = [1]
  pi(U42/3) = [3,2,1]
  pi(plus/2) = [1,2]
  pi(a__U11/2) = 1
  pi(a__U12/1) = 1
  pi(isNat/1) = []
  pi(a__U21/1) = 1
  pi(a__U31/2) = [1,2]
  pi(a__plus/2) = [1,2]
  pi(a__U41/3) = [3,2,1]
  pi(a__U42/3) = [3,2,1]
  
  RPO with the following precedence
  precedence(mark#[1]) = 2
  precedence(U31[2]) = 3
  precedence(a__U31#[2]) = 0
  precedence(tt[0]) = 2
  precedence(U41[3]) = 5
  precedence(a__U41#[3]) = 1
  precedence(a__U42#[3]) = 1
  precedence(a__isNat[1]) = 2
  precedence(a__plus#[2]) = 1
  precedence(0[0]) = 6
  precedence(s[1]) = 4
  precedence(U42[3]) = 5
  precedence(plus[2]) = 5
  precedence(isNat[1]) = 2
  precedence(a__U31[2]) = 3
  precedence(a__plus[2]) = 5
  precedence(a__U41[3]) = 5
  precedence(a__U42[3]) = 5
  
  precedence(_) = 0
  and the following status
  status(mark#[1]) = mul
  status(U31[2]) = mul
  status(a__U31#[2]) = mul
  status(tt[0]) = mul
  status(U41[3]) = lex
  status(a__U41#[3]) = mul
  status(a__U42#[3]) = mul
  status(a__isNat[1]) = lex
  status(a__plus#[2]) = mul
  status(0[0]) = mul
  status(s[1]) = mul
  status(U42[3]) = lex
  status(plus[2]) = lex
  status(isNat[1]) = lex
  status(a__U31[2]) = mul
  status(a__plus[2]) = lex
  status(a__U41[3]) = lex
  status(a__U42[3]) = lex
  
  status(_) = lex
  
  problem when orienting DPs
  cannot orient pair a__U41#(tt, M, N) -> a__U42#(a__isNat(N), M, N) weakly:
  [(a__U41#(tt, M, N),0)] >=mu [(a__U42#(a__isNat(N), M, N),0),(a__isNat(N),13),(N,0)] could not be ensured