YES Problem: a(b(x1)) -> C(x1) b(c(x1)) -> A(x1) c(a(x1)) -> B(x1) A(C(x1)) -> b(x1) C(B(x1)) -> a(x1) B(A(x1)) -> c(x1) a(a(a(a(a(x1))))) -> A(A(A(x1))) A(A(A(A(x1)))) -> a(a(a(a(x1)))) b(b(b(b(b(x1))))) -> B(B(B(x1))) B(B(B(B(x1)))) -> b(b(b(b(x1)))) c(c(c(c(c(x1))))) -> C(C(C(x1))) C(C(C(C(x1)))) -> c(c(c(c(x1)))) B(a(a(a(a(x1))))) -> c(A(A(A(x1)))) A(A(A(b(x1)))) -> a(a(a(a(C(x1))))) C(b(b(b(b(x1))))) -> a(B(B(B(x1)))) B(B(B(c(x1)))) -> b(b(b(b(A(x1))))) A(c(c(c(c(x1))))) -> b(C(C(C(x1)))) C(C(C(a(x1)))) -> c(c(c(c(B(x1))))) a(A(x1)) -> x1 A(a(x1)) -> x1 b(B(x1)) -> x1 B(b(x1)) -> x1 c(C(x1)) -> x1 C(c(x1)) -> x1 Proof: Arctic Interpretation Processor: dimension: 1 interpretation: [B](x0) = 3x0, [A](x0) = 3x0, [c](x0) = 2x0, [C](x0) = 3x0, [a](x0) = 2x0, [b](x0) = 2x0 orientation: a(b(x1)) = 4x1 >= 3x1 = C(x1) b(c(x1)) = 4x1 >= 3x1 = A(x1) c(a(x1)) = 4x1 >= 3x1 = B(x1) A(C(x1)) = 6x1 >= 2x1 = b(x1) C(B(x1)) = 6x1 >= 2x1 = a(x1) B(A(x1)) = 6x1 >= 2x1 = c(x1) a(a(a(a(a(x1))))) = 10x1 >= 9x1 = A(A(A(x1))) A(A(A(A(x1)))) = 12x1 >= 8x1 = a(a(a(a(x1)))) b(b(b(b(b(x1))))) = 10x1 >= 9x1 = B(B(B(x1))) B(B(B(B(x1)))) = 12x1 >= 8x1 = b(b(b(b(x1)))) c(c(c(c(c(x1))))) = 10x1 >= 9x1 = C(C(C(x1))) C(C(C(C(x1)))) = 12x1 >= 8x1 = c(c(c(c(x1)))) B(a(a(a(a(x1))))) = 11x1 >= 11x1 = c(A(A(A(x1)))) A(A(A(b(x1)))) = 11x1 >= 11x1 = a(a(a(a(C(x1))))) C(b(b(b(b(x1))))) = 11x1 >= 11x1 = a(B(B(B(x1)))) B(B(B(c(x1)))) = 11x1 >= 11x1 = b(b(b(b(A(x1))))) A(c(c(c(c(x1))))) = 11x1 >= 11x1 = b(C(C(C(x1)))) C(C(C(a(x1)))) = 11x1 >= 11x1 = c(c(c(c(B(x1))))) a(A(x1)) = 5x1 >= x1 = x1 A(a(x1)) = 5x1 >= x1 = x1 b(B(x1)) = 5x1 >= x1 = x1 B(b(x1)) = 5x1 >= x1 = x1 c(C(x1)) = 5x1 >= x1 = x1 C(c(x1)) = 5x1 >= x1 = x1 problem: B(a(a(a(a(x1))))) -> c(A(A(A(x1)))) A(A(A(b(x1)))) -> a(a(a(a(C(x1))))) C(b(b(b(b(x1))))) -> a(B(B(B(x1)))) B(B(B(c(x1)))) -> b(b(b(b(A(x1))))) A(c(c(c(c(x1))))) -> b(C(C(C(x1)))) C(C(C(a(x1)))) -> c(c(c(c(B(x1))))) String Reversal Processor: a(a(a(a(B(x1))))) -> A(A(A(c(x1)))) b(A(A(A(x1)))) -> C(a(a(a(a(x1))))) b(b(b(b(C(x1))))) -> B(B(B(a(x1)))) c(B(B(B(x1)))) -> A(b(b(b(b(x1))))) c(c(c(c(A(x1))))) -> C(C(C(b(x1)))) a(C(C(C(x1)))) -> B(c(c(c(c(x1))))) DP Processor: DPs: a#(a(a(a(B(x1))))) -> c#(x1) b#(A(A(A(x1)))) -> a#(x1) b#(A(A(A(x1)))) -> a#(a(x1)) b#(A(A(A(x1)))) -> a#(a(a(x1))) b#(A(A(A(x1)))) -> a#(a(a(a(x1)))) b#(b(b(b(C(x1))))) -> a#(x1) c#(B(B(B(x1)))) -> b#(x1) c#(B(B(B(x1)))) -> b#(b(x1)) c#(B(B(B(x1)))) -> b#(b(b(x1))) c#(B(B(B(x1)))) -> b#(b(b(b(x1)))) c#(c(c(c(A(x1))))) -> b#(x1) a#(C(C(C(x1)))) -> c#(x1) a#(C(C(C(x1)))) -> c#(c(x1)) a#(C(C(C(x1)))) -> c#(c(c(x1))) a#(C(C(C(x1)))) -> c#(c(c(c(x1)))) TRS: a(a(a(a(B(x1))))) -> A(A(A(c(x1)))) b(A(A(A(x1)))) -> C(a(a(a(a(x1))))) b(b(b(b(C(x1))))) -> B(B(B(a(x1)))) c(B(B(B(x1)))) -> A(b(b(b(b(x1))))) c(c(c(c(A(x1))))) -> C(C(C(b(x1)))) a(C(C(C(x1)))) -> B(c(c(c(c(x1))))) TDG Processor: DPs: a#(a(a(a(B(x1))))) -> c#(x1) b#(A(A(A(x1)))) -> a#(x1) b#(A(A(A(x1)))) -> a#(a(x1)) b#(A(A(A(x1)))) -> a#(a(a(x1))) b#(A(A(A(x1)))) -> a#(a(a(a(x1)))) b#(b(b(b(C(x1))))) -> a#(x1) c#(B(B(B(x1)))) -> b#(x1) c#(B(B(B(x1)))) -> b#(b(x1)) c#(B(B(B(x1)))) -> b#(b(b(x1))) c#(B(B(B(x1)))) -> b#(b(b(b(x1)))) c#(c(c(c(A(x1))))) -> b#(x1) a#(C(C(C(x1)))) -> c#(x1) a#(C(C(C(x1)))) -> c#(c(x1)) a#(C(C(C(x1)))) -> c#(c(c(x1))) a#(C(C(C(x1)))) -> c#(c(c(c(x1)))) TRS: a(a(a(a(B(x1))))) -> A(A(A(c(x1)))) b(A(A(A(x1)))) -> C(a(a(a(a(x1))))) b(b(b(b(C(x1))))) -> B(B(B(a(x1)))) c(B(B(B(x1)))) -> A(b(b(b(b(x1))))) c(c(c(c(A(x1))))) -> C(C(C(b(x1)))) a(C(C(C(x1)))) -> B(c(c(c(c(x1))))) graph: b#(A(A(A(x1)))) -> a#(a(a(a(x1)))) -> a#(C(C(C(x1)))) -> c#(c(c(c(x1)))) b#(A(A(A(x1)))) -> a#(a(a(a(x1)))) -> a#(C(C(C(x1)))) -> c#(c(c(x1))) b#(A(A(A(x1)))) -> a#(a(a(a(x1)))) -> a#(C(C(C(x1)))) -> c#(c(x1)) b#(A(A(A(x1)))) -> a#(a(a(a(x1)))) -> a#(C(C(C(x1)))) -> c#(x1) b#(A(A(A(x1)))) -> a#(a(a(a(x1)))) -> a#(a(a(a(B(x1))))) -> c#(x1) b#(A(A(A(x1)))) -> a#(a(a(x1))) -> a#(C(C(C(x1)))) -> c#(c(c(c(x1)))) b#(A(A(A(x1)))) -> a#(a(a(x1))) -> a#(C(C(C(x1)))) -> c#(c(c(x1))) b#(A(A(A(x1)))) -> a#(a(a(x1))) -> a#(C(C(C(x1)))) -> c#(c(x1)) b#(A(A(A(x1)))) -> a#(a(a(x1))) -> a#(C(C(C(x1)))) -> c#(x1) b#(A(A(A(x1)))) -> a#(a(a(x1))) -> a#(a(a(a(B(x1))))) -> c#(x1) b#(A(A(A(x1)))) -> a#(a(x1)) -> a#(C(C(C(x1)))) -> c#(c(c(c(x1)))) b#(A(A(A(x1)))) -> a#(a(x1)) -> a#(C(C(C(x1)))) -> c#(c(c(x1))) b#(A(A(A(x1)))) -> a#(a(x1)) -> a#(C(C(C(x1)))) -> c#(c(x1)) b#(A(A(A(x1)))) -> a#(a(x1)) -> a#(C(C(C(x1)))) -> c#(x1) b#(A(A(A(x1)))) -> a#(a(x1)) -> a#(a(a(a(B(x1))))) -> c#(x1) b#(A(A(A(x1)))) -> a#(x1) -> a#(C(C(C(x1)))) -> c#(c(c(c(x1)))) b#(A(A(A(x1)))) -> a#(x1) -> a#(C(C(C(x1)))) -> c#(c(c(x1))) b#(A(A(A(x1)))) -> a#(x1) -> a#(C(C(C(x1)))) -> c#(c(x1)) b#(A(A(A(x1)))) -> a#(x1) -> a#(C(C(C(x1)))) -> c#(x1) b#(A(A(A(x1)))) -> a#(x1) -> a#(a(a(a(B(x1))))) -> c#(x1) b#(b(b(b(C(x1))))) -> a#(x1) -> a#(C(C(C(x1)))) -> c#(c(c(c(x1)))) b#(b(b(b(C(x1))))) -> a#(x1) -> a#(C(C(C(x1)))) -> c#(c(c(x1))) b#(b(b(b(C(x1))))) -> a#(x1) -> a#(C(C(C(x1)))) -> c#(c(x1)) b#(b(b(b(C(x1))))) -> a#(x1) -> a#(C(C(C(x1)))) -> c#(x1) b#(b(b(b(C(x1))))) -> a#(x1) -> a#(a(a(a(B(x1))))) -> c#(x1) c#(B(B(B(x1)))) -> b#(b(b(b(x1)))) -> b#(b(b(b(C(x1))))) -> a#(x1) c#(B(B(B(x1)))) -> b#(b(b(b(x1)))) -> b#(A(A(A(x1)))) -> a#(a(a(a(x1)))) c#(B(B(B(x1)))) -> b#(b(b(b(x1)))) -> b#(A(A(A(x1)))) -> a#(a(a(x1))) c#(B(B(B(x1)))) -> b#(b(b(b(x1)))) -> b#(A(A(A(x1)))) -> a#(a(x1)) c#(B(B(B(x1)))) -> b#(b(b(b(x1)))) -> b#(A(A(A(x1)))) -> a#(x1) c#(B(B(B(x1)))) -> b#(b(b(x1))) -> b#(b(b(b(C(x1))))) -> a#(x1) c#(B(B(B(x1)))) -> b#(b(b(x1))) -> b#(A(A(A(x1)))) -> a#(a(a(a(x1)))) c#(B(B(B(x1)))) -> b#(b(b(x1))) -> b#(A(A(A(x1)))) -> a#(a(a(x1))) c#(B(B(B(x1)))) -> b#(b(b(x1))) -> b#(A(A(A(x1)))) -> a#(a(x1)) c#(B(B(B(x1)))) -> b#(b(b(x1))) -> b#(A(A(A(x1)))) -> a#(x1) c#(B(B(B(x1)))) -> b#(b(x1)) -> b#(b(b(b(C(x1))))) -> a#(x1) c#(B(B(B(x1)))) -> b#(b(x1)) -> b#(A(A(A(x1)))) -> a#(a(a(a(x1)))) c#(B(B(B(x1)))) -> b#(b(x1)) -> b#(A(A(A(x1)))) -> a#(a(a(x1))) c#(B(B(B(x1)))) -> b#(b(x1)) -> b#(A(A(A(x1)))) -> a#(a(x1)) c#(B(B(B(x1)))) -> b#(b(x1)) -> b#(A(A(A(x1)))) -> a#(x1) c#(B(B(B(x1)))) -> b#(x1) -> b#(b(b(b(C(x1))))) -> a#(x1) c#(B(B(B(x1)))) -> b#(x1) -> b#(A(A(A(x1)))) -> a#(a(a(a(x1)))) c#(B(B(B(x1)))) -> b#(x1) -> b#(A(A(A(x1)))) -> a#(a(a(x1))) c#(B(B(B(x1)))) -> b#(x1) -> b#(A(A(A(x1)))) -> a#(a(x1)) c#(B(B(B(x1)))) -> b#(x1) -> b#(A(A(A(x1)))) -> a#(x1) c#(c(c(c(A(x1))))) -> b#(x1) -> b#(b(b(b(C(x1))))) -> a#(x1) c#(c(c(c(A(x1))))) -> b#(x1) -> b#(A(A(A(x1)))) -> a#(a(a(a(x1)))) c#(c(c(c(A(x1))))) -> b#(x1) -> b#(A(A(A(x1)))) -> a#(a(a(x1))) c#(c(c(c(A(x1))))) -> b#(x1) -> b#(A(A(A(x1)))) -> a#(a(x1)) c#(c(c(c(A(x1))))) -> b#(x1) -> b#(A(A(A(x1)))) -> a#(x1) a#(C(C(C(x1)))) -> c#(c(c(c(x1)))) -> c#(c(c(c(A(x1))))) -> b#(x1) a#(C(C(C(x1)))) -> c#(c(c(c(x1)))) -> c#(B(B(B(x1)))) -> b#(b(b(b(x1)))) a#(C(C(C(x1)))) -> c#(c(c(c(x1)))) -> c#(B(B(B(x1)))) -> b#(b(b(x1))) a#(C(C(C(x1)))) -> c#(c(c(c(x1)))) -> c#(B(B(B(x1)))) -> b#(b(x1)) a#(C(C(C(x1)))) -> c#(c(c(c(x1)))) -> c#(B(B(B(x1)))) -> b#(x1) a#(C(C(C(x1)))) -> c#(c(c(x1))) -> c#(c(c(c(A(x1))))) -> b#(x1) a#(C(C(C(x1)))) -> c#(c(c(x1))) -> c#(B(B(B(x1)))) -> b#(b(b(b(x1)))) a#(C(C(C(x1)))) -> c#(c(c(x1))) -> c#(B(B(B(x1)))) -> b#(b(b(x1))) a#(C(C(C(x1)))) -> c#(c(c(x1))) -> c#(B(B(B(x1)))) -> b#(b(x1)) a#(C(C(C(x1)))) -> c#(c(c(x1))) -> c#(B(B(B(x1)))) -> b#(x1) a#(C(C(C(x1)))) -> c#(c(x1)) -> c#(c(c(c(A(x1))))) -> b#(x1) a#(C(C(C(x1)))) -> c#(c(x1)) -> c#(B(B(B(x1)))) -> b#(b(b(b(x1)))) a#(C(C(C(x1)))) -> c#(c(x1)) -> c#(B(B(B(x1)))) -> b#(b(b(x1))) a#(C(C(C(x1)))) -> c#(c(x1)) -> c#(B(B(B(x1)))) -> b#(b(x1)) a#(C(C(C(x1)))) -> c#(c(x1)) -> c#(B(B(B(x1)))) -> b#(x1) a#(C(C(C(x1)))) -> c#(x1) -> c#(c(c(c(A(x1))))) -> b#(x1) a#(C(C(C(x1)))) -> c#(x1) -> c#(B(B(B(x1)))) -> b#(b(b(b(x1)))) a#(C(C(C(x1)))) -> c#(x1) -> c#(B(B(B(x1)))) -> b#(b(b(x1))) a#(C(C(C(x1)))) -> c#(x1) -> c#(B(B(B(x1)))) -> b#(b(x1)) a#(C(C(C(x1)))) -> c#(x1) -> c#(B(B(B(x1)))) -> b#(x1) a#(a(a(a(B(x1))))) -> c#(x1) -> c#(c(c(c(A(x1))))) -> b#(x1) a#(a(a(a(B(x1))))) -> c#(x1) -> c#(B(B(B(x1)))) -> b#(b(b(b(x1)))) a#(a(a(a(B(x1))))) -> c#(x1) -> c#(B(B(B(x1)))) -> b#(b(b(x1))) a#(a(a(a(B(x1))))) -> c#(x1) -> c#(B(B(B(x1)))) -> b#(b(x1)) a#(a(a(a(B(x1))))) -> c#(x1) -> c#(B(B(B(x1)))) -> b#(x1) Arctic Interpretation Processor: dimension: 1 interpretation: [b#](x0) = 2x0, [c#](x0) = 3x0, [a#](x0) = x0, [B](x0) = 3x0, [A](x0) = 3x0, [c](x0) = 2x0, [C](x0) = 3x0, [a](x0) = 2x0, [b](x0) = 2x0 orientation: a#(a(a(a(B(x1))))) = 9x1 >= 3x1 = c#(x1) b#(A(A(A(x1)))) = 11x1 >= x1 = a#(x1) b#(A(A(A(x1)))) = 11x1 >= 2x1 = a#(a(x1)) b#(A(A(A(x1)))) = 11x1 >= 4x1 = a#(a(a(x1))) b#(A(A(A(x1)))) = 11x1 >= 6x1 = a#(a(a(a(x1)))) b#(b(b(b(C(x1))))) = 11x1 >= x1 = a#(x1) c#(B(B(B(x1)))) = 12x1 >= 2x1 = b#(x1) c#(B(B(B(x1)))) = 12x1 >= 4x1 = b#(b(x1)) c#(B(B(B(x1)))) = 12x1 >= 6x1 = b#(b(b(x1))) c#(B(B(B(x1)))) = 12x1 >= 8x1 = b#(b(b(b(x1)))) c#(c(c(c(A(x1))))) = 12x1 >= 2x1 = b#(x1) a#(C(C(C(x1)))) = 9x1 >= 3x1 = c#(x1) a#(C(C(C(x1)))) = 9x1 >= 5x1 = c#(c(x1)) a#(C(C(C(x1)))) = 9x1 >= 7x1 = c#(c(c(x1))) a#(C(C(C(x1)))) = 9x1 >= 9x1 = c#(c(c(c(x1)))) a(a(a(a(B(x1))))) = 11x1 >= 11x1 = A(A(A(c(x1)))) b(A(A(A(x1)))) = 11x1 >= 11x1 = C(a(a(a(a(x1))))) b(b(b(b(C(x1))))) = 11x1 >= 11x1 = B(B(B(a(x1)))) c(B(B(B(x1)))) = 11x1 >= 11x1 = A(b(b(b(b(x1))))) c(c(c(c(A(x1))))) = 11x1 >= 11x1 = C(C(C(b(x1)))) a(C(C(C(x1)))) = 11x1 >= 11x1 = B(c(c(c(c(x1))))) problem: DPs: a#(C(C(C(x1)))) -> c#(c(c(c(x1)))) TRS: a(a(a(a(B(x1))))) -> A(A(A(c(x1)))) b(A(A(A(x1)))) -> C(a(a(a(a(x1))))) b(b(b(b(C(x1))))) -> B(B(B(a(x1)))) c(B(B(B(x1)))) -> A(b(b(b(b(x1))))) c(c(c(c(A(x1))))) -> C(C(C(b(x1)))) a(C(C(C(x1)))) -> B(c(c(c(c(x1))))) EDG Processor: DPs: a#(C(C(C(x1)))) -> c#(c(c(c(x1)))) TRS: a(a(a(a(B(x1))))) -> A(A(A(c(x1)))) b(A(A(A(x1)))) -> C(a(a(a(a(x1))))) b(b(b(b(C(x1))))) -> B(B(B(a(x1)))) c(B(B(B(x1)))) -> A(b(b(b(b(x1))))) c(c(c(c(A(x1))))) -> C(C(C(b(x1)))) a(C(C(C(x1)))) -> B(c(c(c(c(x1))))) graph: Qed