YES Problem: a(b(c(x1))) -> c(b(a(x1))) C(B(A(x1))) -> A(B(C(x1))) b(a(C(x1))) -> C(a(b(x1))) c(A(B(x1))) -> B(A(c(x1))) A(c(b(x1))) -> b(c(A(x1))) B(C(a(x1))) -> a(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: DP Processor: DPs: a#(b(c(x1))) -> a#(x1) a#(b(c(x1))) -> b#(a(x1)) a#(b(c(x1))) -> c#(b(a(x1))) C#(B(A(x1))) -> C#(x1) C#(B(A(x1))) -> B#(C(x1)) C#(B(A(x1))) -> A#(B(C(x1))) b#(a(C(x1))) -> b#(x1) b#(a(C(x1))) -> a#(b(x1)) b#(a(C(x1))) -> C#(a(b(x1))) c#(A(B(x1))) -> c#(x1) c#(A(B(x1))) -> A#(c(x1)) c#(A(B(x1))) -> B#(A(c(x1))) A#(c(b(x1))) -> A#(x1) A#(c(b(x1))) -> c#(A(x1)) A#(c(b(x1))) -> b#(c(A(x1))) B#(C(a(x1))) -> B#(x1) B#(C(a(x1))) -> C#(B(x1)) B#(C(a(x1))) -> a#(C(B(x1))) TRS: a(b(c(x1))) -> c(b(a(x1))) C(B(A(x1))) -> A(B(C(x1))) b(a(C(x1))) -> C(a(b(x1))) c(A(B(x1))) -> B(A(c(x1))) A(c(b(x1))) -> b(c(A(x1))) B(C(a(x1))) -> a(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 TDG Processor: DPs: a#(b(c(x1))) -> a#(x1) a#(b(c(x1))) -> b#(a(x1)) a#(b(c(x1))) -> c#(b(a(x1))) C#(B(A(x1))) -> C#(x1) C#(B(A(x1))) -> B#(C(x1)) C#(B(A(x1))) -> A#(B(C(x1))) b#(a(C(x1))) -> b#(x1) b#(a(C(x1))) -> a#(b(x1)) b#(a(C(x1))) -> C#(a(b(x1))) c#(A(B(x1))) -> c#(x1) c#(A(B(x1))) -> A#(c(x1)) c#(A(B(x1))) -> B#(A(c(x1))) A#(c(b(x1))) -> A#(x1) A#(c(b(x1))) -> c#(A(x1)) A#(c(b(x1))) -> b#(c(A(x1))) B#(C(a(x1))) -> B#(x1) B#(C(a(x1))) -> C#(B(x1)) B#(C(a(x1))) -> a#(C(B(x1))) TRS: a(b(c(x1))) -> c(b(a(x1))) C(B(A(x1))) -> A(B(C(x1))) b(a(C(x1))) -> C(a(b(x1))) c(A(B(x1))) -> B(A(c(x1))) A(c(b(x1))) -> b(c(A(x1))) B(C(a(x1))) -> a(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 graph: A#(c(b(x1))) -> A#(x1) -> A#(c(b(x1))) -> b#(c(A(x1))) A#(c(b(x1))) -> A#(x1) -> A#(c(b(x1))) -> c#(A(x1)) A#(c(b(x1))) -> A#(x1) -> A#(c(b(x1))) -> A#(x1) A#(c(b(x1))) -> c#(A(x1)) -> c#(A(B(x1))) -> B#(A(c(x1))) A#(c(b(x1))) -> c#(A(x1)) -> c#(A(B(x1))) -> A#(c(x1)) A#(c(b(x1))) -> c#(A(x1)) -> c#(A(B(x1))) -> c#(x1) A#(c(b(x1))) -> b#(c(A(x1))) -> b#(a(C(x1))) -> C#(a(b(x1))) A#(c(b(x1))) -> b#(c(A(x1))) -> b#(a(C(x1))) -> a#(b(x1)) A#(c(b(x1))) -> b#(c(A(x1))) -> b#(a(C(x1))) -> b#(x1) B#(C(a(x1))) -> B#(x1) -> B#(C(a(x1))) -> a#(C(B(x1))) B#(C(a(x1))) -> B#(x1) -> B#(C(a(x1))) -> C#(B(x1)) B#(C(a(x1))) -> B#(x1) -> B#(C(a(x1))) -> B#(x1) B#(C(a(x1))) -> C#(B(x1)) -> C#(B(A(x1))) -> A#(B(C(x1))) B#(C(a(x1))) -> C#(B(x1)) -> C#(B(A(x1))) -> B#(C(x1)) B#(C(a(x1))) -> C#(B(x1)) -> C#(B(A(x1))) -> C#(x1) B#(C(a(x1))) -> a#(C(B(x1))) -> a#(b(c(x1))) -> c#(b(a(x1))) B#(C(a(x1))) -> a#(C(B(x1))) -> a#(b(c(x1))) -> b#(a(x1)) B#(C(a(x1))) -> a#(C(B(x1))) -> a#(b(c(x1))) -> a#(x1) C#(B(A(x1))) -> A#(B(C(x1))) -> A#(c(b(x1))) -> b#(c(A(x1))) C#(B(A(x1))) -> A#(B(C(x1))) -> A#(c(b(x1))) -> c#(A(x1)) C#(B(A(x1))) -> A#(B(C(x1))) -> A#(c(b(x1))) -> A#(x1) C#(B(A(x1))) -> B#(C(x1)) -> B#(C(a(x1))) -> a#(C(B(x1))) C#(B(A(x1))) -> B#(C(x1)) -> B#(C(a(x1))) -> C#(B(x1)) C#(B(A(x1))) -> B#(C(x1)) -> B#(C(a(x1))) -> B#(x1) C#(B(A(x1))) -> C#(x1) -> C#(B(A(x1))) -> A#(B(C(x1))) C#(B(A(x1))) -> C#(x1) -> C#(B(A(x1))) -> B#(C(x1)) C#(B(A(x1))) -> C#(x1) -> C#(B(A(x1))) -> C#(x1) c#(A(B(x1))) -> A#(c(x1)) -> A#(c(b(x1))) -> b#(c(A(x1))) c#(A(B(x1))) -> A#(c(x1)) -> A#(c(b(x1))) -> c#(A(x1)) c#(A(B(x1))) -> A#(c(x1)) -> A#(c(b(x1))) -> A#(x1) c#(A(B(x1))) -> B#(A(c(x1))) -> B#(C(a(x1))) -> a#(C(B(x1))) c#(A(B(x1))) -> B#(A(c(x1))) -> B#(C(a(x1))) -> C#(B(x1)) c#(A(B(x1))) -> B#(A(c(x1))) -> B#(C(a(x1))) -> B#(x1) c#(A(B(x1))) -> c#(x1) -> c#(A(B(x1))) -> B#(A(c(x1))) c#(A(B(x1))) -> c#(x1) -> c#(A(B(x1))) -> A#(c(x1)) c#(A(B(x1))) -> c#(x1) -> c#(A(B(x1))) -> c#(x1) b#(a(C(x1))) -> C#(a(b(x1))) -> C#(B(A(x1))) -> A#(B(C(x1))) b#(a(C(x1))) -> C#(a(b(x1))) -> C#(B(A(x1))) -> B#(C(x1)) b#(a(C(x1))) -> C#(a(b(x1))) -> C#(B(A(x1))) -> C#(x1) b#(a(C(x1))) -> b#(x1) -> b#(a(C(x1))) -> C#(a(b(x1))) b#(a(C(x1))) -> b#(x1) -> b#(a(C(x1))) -> a#(b(x1)) b#(a(C(x1))) -> b#(x1) -> b#(a(C(x1))) -> b#(x1) b#(a(C(x1))) -> a#(b(x1)) -> a#(b(c(x1))) -> c#(b(a(x1))) b#(a(C(x1))) -> a#(b(x1)) -> a#(b(c(x1))) -> b#(a(x1)) b#(a(C(x1))) -> a#(b(x1)) -> a#(b(c(x1))) -> a#(x1) a#(b(c(x1))) -> c#(b(a(x1))) -> c#(A(B(x1))) -> B#(A(c(x1))) a#(b(c(x1))) -> c#(b(a(x1))) -> c#(A(B(x1))) -> A#(c(x1)) a#(b(c(x1))) -> c#(b(a(x1))) -> c#(A(B(x1))) -> c#(x1) a#(b(c(x1))) -> b#(a(x1)) -> b#(a(C(x1))) -> C#(a(b(x1))) a#(b(c(x1))) -> b#(a(x1)) -> b#(a(C(x1))) -> a#(b(x1)) a#(b(c(x1))) -> b#(a(x1)) -> b#(a(C(x1))) -> b#(x1) a#(b(c(x1))) -> a#(x1) -> a#(b(c(x1))) -> c#(b(a(x1))) a#(b(c(x1))) -> a#(x1) -> a#(b(c(x1))) -> b#(a(x1)) a#(b(c(x1))) -> a#(x1) -> a#(b(c(x1))) -> a#(x1) Arctic Interpretation Processor: dimension: 1 interpretation: [A#](x0) = 4x0 + 1, [B#](x0) = 3x0 + 4, [C#](x0) = x0 + 0, [c#](x0) = x0 + 0, [b#](x0) = x0 + 0, [a#](x0) = x0 + 0, [C](x0) = x0, [B](x0) = 3x0 + 0, [A](x0) = 4x0 + 1, [a](x0) = x0, [b](x0) = x0, [c](x0) = x0 orientation: a#(b(c(x1))) = x1 + 0 >= x1 + 0 = a#(x1) a#(b(c(x1))) = x1 + 0 >= x1 + 0 = b#(a(x1)) a#(b(c(x1))) = x1 + 0 >= x1 + 0 = c#(b(a(x1))) C#(B(A(x1))) = 7x1 + 4 >= x1 + 0 = C#(x1) C#(B(A(x1))) = 7x1 + 4 >= 3x1 + 4 = B#(C(x1)) C#(B(A(x1))) = 7x1 + 4 >= 7x1 + 4 = A#(B(C(x1))) b#(a(C(x1))) = x1 + 0 >= x1 + 0 = b#(x1) b#(a(C(x1))) = x1 + 0 >= x1 + 0 = a#(b(x1)) b#(a(C(x1))) = x1 + 0 >= x1 + 0 = C#(a(b(x1))) c#(A(B(x1))) = 7x1 + 4 >= x1 + 0 = c#(x1) c#(A(B(x1))) = 7x1 + 4 >= 4x1 + 1 = A#(c(x1)) c#(A(B(x1))) = 7x1 + 4 >= 7x1 + 4 = B#(A(c(x1))) A#(c(b(x1))) = 4x1 + 1 >= 4x1 + 1 = A#(x1) A#(c(b(x1))) = 4x1 + 1 >= 4x1 + 1 = c#(A(x1)) A#(c(b(x1))) = 4x1 + 1 >= 4x1 + 1 = b#(c(A(x1))) B#(C(a(x1))) = 3x1 + 4 >= 3x1 + 4 = B#(x1) B#(C(a(x1))) = 3x1 + 4 >= 3x1 + 0 = C#(B(x1)) B#(C(a(x1))) = 3x1 + 4 >= 3x1 + 0 = a#(C(B(x1))) a(b(c(x1))) = x1 >= x1 = c(b(a(x1))) C(B(A(x1))) = 7x1 + 4 >= 7x1 + 4 = A(B(C(x1))) b(a(C(x1))) = x1 >= x1 = C(a(b(x1))) c(A(B(x1))) = 7x1 + 4 >= 7x1 + 4 = B(A(c(x1))) A(c(b(x1))) = 4x1 + 1 >= 4x1 + 1 = b(c(A(x1))) B(C(a(x1))) = 3x1 + 0 >= 3x1 + 0 = a(C(B(x1))) a(A(x1)) = 4x1 + 1 >= x1 = x1 A(a(x1)) = 4x1 + 1 >= x1 = x1 b(B(x1)) = 3x1 + 0 >= x1 = x1 B(b(x1)) = 3x1 + 0 >= x1 = x1 c(C(x1)) = x1 >= x1 = x1 C(c(x1)) = x1 >= x1 = x1 problem: DPs: a#(b(c(x1))) -> a#(x1) a#(b(c(x1))) -> b#(a(x1)) a#(b(c(x1))) -> c#(b(a(x1))) C#(B(A(x1))) -> B#(C(x1)) C#(B(A(x1))) -> A#(B(C(x1))) b#(a(C(x1))) -> b#(x1) b#(a(C(x1))) -> a#(b(x1)) b#(a(C(x1))) -> C#(a(b(x1))) c#(A(B(x1))) -> B#(A(c(x1))) A#(c(b(x1))) -> A#(x1) A#(c(b(x1))) -> c#(A(x1)) A#(c(b(x1))) -> b#(c(A(x1))) B#(C(a(x1))) -> B#(x1) B#(C(a(x1))) -> C#(B(x1)) B#(C(a(x1))) -> a#(C(B(x1))) TRS: a(b(c(x1))) -> c(b(a(x1))) C(B(A(x1))) -> A(B(C(x1))) b(a(C(x1))) -> C(a(b(x1))) c(A(B(x1))) -> B(A(c(x1))) A(c(b(x1))) -> b(c(A(x1))) B(C(a(x1))) -> a(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 EDG Processor: DPs: a#(b(c(x1))) -> a#(x1) a#(b(c(x1))) -> b#(a(x1)) a#(b(c(x1))) -> c#(b(a(x1))) C#(B(A(x1))) -> B#(C(x1)) C#(B(A(x1))) -> A#(B(C(x1))) b#(a(C(x1))) -> b#(x1) b#(a(C(x1))) -> a#(b(x1)) b#(a(C(x1))) -> C#(a(b(x1))) c#(A(B(x1))) -> B#(A(c(x1))) A#(c(b(x1))) -> A#(x1) A#(c(b(x1))) -> c#(A(x1)) A#(c(b(x1))) -> b#(c(A(x1))) B#(C(a(x1))) -> B#(x1) B#(C(a(x1))) -> C#(B(x1)) B#(C(a(x1))) -> a#(C(B(x1))) TRS: a(b(c(x1))) -> c(b(a(x1))) C(B(A(x1))) -> A(B(C(x1))) b(a(C(x1))) -> C(a(b(x1))) c(A(B(x1))) -> B(A(c(x1))) A(c(b(x1))) -> b(c(A(x1))) B(C(a(x1))) -> a(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 graph: A#(c(b(x1))) -> A#(x1) -> A#(c(b(x1))) -> A#(x1) A#(c(b(x1))) -> A#(x1) -> A#(c(b(x1))) -> c#(A(x1)) A#(c(b(x1))) -> A#(x1) -> A#(c(b(x1))) -> b#(c(A(x1))) A#(c(b(x1))) -> c#(A(x1)) -> c#(A(B(x1))) -> B#(A(c(x1))) A#(c(b(x1))) -> b#(c(A(x1))) -> b#(a(C(x1))) -> b#(x1) A#(c(b(x1))) -> b#(c(A(x1))) -> b#(a(C(x1))) -> a#(b(x1)) A#(c(b(x1))) -> b#(c(A(x1))) -> b#(a(C(x1))) -> C#(a(b(x1))) B#(C(a(x1))) -> B#(x1) -> B#(C(a(x1))) -> B#(x1) B#(C(a(x1))) -> B#(x1) -> B#(C(a(x1))) -> C#(B(x1)) B#(C(a(x1))) -> B#(x1) -> B#(C(a(x1))) -> a#(C(B(x1))) B#(C(a(x1))) -> C#(B(x1)) -> C#(B(A(x1))) -> B#(C(x1)) B#(C(a(x1))) -> C#(B(x1)) -> C#(B(A(x1))) -> A#(B(C(x1))) B#(C(a(x1))) -> a#(C(B(x1))) -> a#(b(c(x1))) -> a#(x1) B#(C(a(x1))) -> a#(C(B(x1))) -> a#(b(c(x1))) -> b#(a(x1)) B#(C(a(x1))) -> a#(C(B(x1))) -> a#(b(c(x1))) -> c#(b(a(x1))) C#(B(A(x1))) -> A#(B(C(x1))) -> A#(c(b(x1))) -> A#(x1) C#(B(A(x1))) -> A#(B(C(x1))) -> A#(c(b(x1))) -> c#(A(x1)) C#(B(A(x1))) -> A#(B(C(x1))) -> A#(c(b(x1))) -> b#(c(A(x1))) C#(B(A(x1))) -> B#(C(x1)) -> B#(C(a(x1))) -> B#(x1) C#(B(A(x1))) -> B#(C(x1)) -> B#(C(a(x1))) -> C#(B(x1)) C#(B(A(x1))) -> B#(C(x1)) -> B#(C(a(x1))) -> a#(C(B(x1))) c#(A(B(x1))) -> B#(A(c(x1))) -> B#(C(a(x1))) -> B#(x1) c#(A(B(x1))) -> B#(A(c(x1))) -> B#(C(a(x1))) -> C#(B(x1)) c#(A(B(x1))) -> B#(A(c(x1))) -> B#(C(a(x1))) -> a#(C(B(x1))) b#(a(C(x1))) -> C#(a(b(x1))) -> C#(B(A(x1))) -> B#(C(x1)) b#(a(C(x1))) -> C#(a(b(x1))) -> C#(B(A(x1))) -> A#(B(C(x1))) b#(a(C(x1))) -> b#(x1) -> b#(a(C(x1))) -> b#(x1) b#(a(C(x1))) -> b#(x1) -> b#(a(C(x1))) -> a#(b(x1)) b#(a(C(x1))) -> b#(x1) -> b#(a(C(x1))) -> C#(a(b(x1))) b#(a(C(x1))) -> a#(b(x1)) -> a#(b(c(x1))) -> a#(x1) b#(a(C(x1))) -> a#(b(x1)) -> a#(b(c(x1))) -> b#(a(x1)) b#(a(C(x1))) -> a#(b(x1)) -> a#(b(c(x1))) -> c#(b(a(x1))) a#(b(c(x1))) -> c#(b(a(x1))) -> c#(A(B(x1))) -> B#(A(c(x1))) a#(b(c(x1))) -> b#(a(x1)) -> b#(a(C(x1))) -> b#(x1) a#(b(c(x1))) -> b#(a(x1)) -> b#(a(C(x1))) -> a#(b(x1)) a#(b(c(x1))) -> b#(a(x1)) -> b#(a(C(x1))) -> C#(a(b(x1))) a#(b(c(x1))) -> a#(x1) -> a#(b(c(x1))) -> a#(x1) a#(b(c(x1))) -> a#(x1) -> a#(b(c(x1))) -> b#(a(x1)) a#(b(c(x1))) -> a#(x1) -> a#(b(c(x1))) -> c#(b(a(x1))) KBO Processor: argument filtering: pi(c) = 0 pi(b) = 0 pi(a) = 0 pi(A) = [0] pi(B) = 0 pi(C) = [0] pi(a#) = 0 pi(b#) = 0 pi(c#) = 0 pi(C#) = [0] pi(B#) = 0 pi(A#) = [0] weight function: w0 = 1 w(A#) = w(B#) = w(C#) = w(C) = w(A) = 1 w(c#) = w(b#) = w(a#) = w(B) = w(a) = w(b) = w(c) = 0 precedence: C > C# > A# > B# ~ c# ~ b# ~ a# ~ B ~ A ~ a ~ b ~ c problem: DPs: a#(b(c(x1))) -> a#(x1) a#(b(c(x1))) -> b#(a(x1)) a#(b(c(x1))) -> c#(b(a(x1))) c#(A(B(x1))) -> B#(A(c(x1))) A#(c(b(x1))) -> A#(x1) B#(C(a(x1))) -> a#(C(B(x1))) TRS: a(b(c(x1))) -> c(b(a(x1))) C(B(A(x1))) -> A(B(C(x1))) b(a(C(x1))) -> C(a(b(x1))) c(A(B(x1))) -> B(A(c(x1))) A(c(b(x1))) -> b(c(A(x1))) B(C(a(x1))) -> a(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 EDG Processor: DPs: a#(b(c(x1))) -> a#(x1) a#(b(c(x1))) -> b#(a(x1)) a#(b(c(x1))) -> c#(b(a(x1))) c#(A(B(x1))) -> B#(A(c(x1))) A#(c(b(x1))) -> A#(x1) B#(C(a(x1))) -> a#(C(B(x1))) TRS: a(b(c(x1))) -> c(b(a(x1))) C(B(A(x1))) -> A(B(C(x1))) b(a(C(x1))) -> C(a(b(x1))) c(A(B(x1))) -> B(A(c(x1))) A(c(b(x1))) -> b(c(A(x1))) B(C(a(x1))) -> a(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 graph: A#(c(b(x1))) -> A#(x1) -> A#(c(b(x1))) -> A#(x1) B#(C(a(x1))) -> a#(C(B(x1))) -> a#(b(c(x1))) -> c#(b(a(x1))) B#(C(a(x1))) -> a#(C(B(x1))) -> a#(b(c(x1))) -> b#(a(x1)) B#(C(a(x1))) -> a#(C(B(x1))) -> a#(b(c(x1))) -> a#(x1) c#(A(B(x1))) -> B#(A(c(x1))) -> B#(C(a(x1))) -> a#(C(B(x1))) a#(b(c(x1))) -> c#(b(a(x1))) -> c#(A(B(x1))) -> B#(A(c(x1))) a#(b(c(x1))) -> a#(x1) -> a#(b(c(x1))) -> c#(b(a(x1))) a#(b(c(x1))) -> a#(x1) -> a#(b(c(x1))) -> b#(a(x1)) a#(b(c(x1))) -> a#(x1) -> a#(b(c(x1))) -> a#(x1) CDG Processor: DPs: a#(b(c(x1))) -> a#(x1) a#(b(c(x1))) -> b#(a(x1)) a#(b(c(x1))) -> c#(b(a(x1))) c#(A(B(x1))) -> B#(A(c(x1))) A#(c(b(x1))) -> A#(x1) B#(C(a(x1))) -> a#(C(B(x1))) TRS: a(b(c(x1))) -> c(b(a(x1))) C(B(A(x1))) -> A(B(C(x1))) b(a(C(x1))) -> C(a(b(x1))) c(A(B(x1))) -> B(A(c(x1))) A(c(b(x1))) -> b(c(A(x1))) B(C(a(x1))) -> a(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 graph: B#(C(a(x1))) -> a#(C(B(x1))) -> a#(b(c(x1))) -> a#(x1) B#(C(a(x1))) -> a#(C(B(x1))) -> a#(b(c(x1))) -> b#(a(x1)) B#(C(a(x1))) -> a#(C(B(x1))) -> a#(b(c(x1))) -> c#(b(a(x1))) c#(A(B(x1))) -> B#(A(c(x1))) -> B#(C(a(x1))) -> a#(C(B(x1))) a#(b(c(x1))) -> c#(b(a(x1))) -> c#(A(B(x1))) -> B#(A(c(x1))) a#(b(c(x1))) -> a#(x1) -> a#(b(c(x1))) -> a#(x1) a#(b(c(x1))) -> a#(x1) -> a#(b(c(x1))) -> b#(a(x1)) a#(b(c(x1))) -> a#(x1) -> a#(b(c(x1))) -> c#(b(a(x1))) SCC Processor: #sccs: 1 #rules: 4 #arcs: 8/36 DPs: B#(C(a(x1))) -> a#(C(B(x1))) a#(b(c(x1))) -> c#(b(a(x1))) c#(A(B(x1))) -> B#(A(c(x1))) a#(b(c(x1))) -> a#(x1) TRS: a(b(c(x1))) -> c(b(a(x1))) C(B(A(x1))) -> A(B(C(x1))) b(a(C(x1))) -> C(a(b(x1))) c(A(B(x1))) -> B(A(c(x1))) A(c(b(x1))) -> b(c(A(x1))) B(C(a(x1))) -> a(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 Arctic Interpretation Processor: dimension: 1 interpretation: [B#](x0) = 4x0, [c#](x0) = 13x0, [a#](x0) = 6x0, [C](x0) = 5x0, [B](x0) = x0, [A](x0) = 1x0, [a](x0) = 2x0, [b](x0) = x0, [c](x0) = 9x0 orientation: B#(C(a(x1))) = 11x1 >= 11x1 = a#(C(B(x1))) a#(b(c(x1))) = 15x1 >= 15x1 = c#(b(a(x1))) c#(A(B(x1))) = 14x1 >= 14x1 = B#(A(c(x1))) a#(b(c(x1))) = 15x1 >= 6x1 = a#(x1) a(b(c(x1))) = 11x1 >= 11x1 = c(b(a(x1))) C(B(A(x1))) = 6x1 >= 6x1 = A(B(C(x1))) b(a(C(x1))) = 7x1 >= 7x1 = C(a(b(x1))) c(A(B(x1))) = 10x1 >= 10x1 = B(A(c(x1))) A(c(b(x1))) = 10x1 >= 10x1 = b(c(A(x1))) B(C(a(x1))) = 7x1 >= 7x1 = a(C(B(x1))) a(A(x1)) = 3x1 >= x1 = x1 A(a(x1)) = 3x1 >= x1 = x1 b(B(x1)) = x1 >= x1 = x1 B(b(x1)) = x1 >= x1 = x1 c(C(x1)) = 14x1 >= x1 = x1 C(c(x1)) = 14x1 >= x1 = x1 problem: DPs: B#(C(a(x1))) -> a#(C(B(x1))) a#(b(c(x1))) -> c#(b(a(x1))) c#(A(B(x1))) -> B#(A(c(x1))) TRS: a(b(c(x1))) -> c(b(a(x1))) C(B(A(x1))) -> A(B(C(x1))) b(a(C(x1))) -> C(a(b(x1))) c(A(B(x1))) -> B(A(c(x1))) A(c(b(x1))) -> b(c(A(x1))) B(C(a(x1))) -> a(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 EDG Processor: DPs: B#(C(a(x1))) -> a#(C(B(x1))) a#(b(c(x1))) -> c#(b(a(x1))) c#(A(B(x1))) -> B#(A(c(x1))) TRS: a(b(c(x1))) -> c(b(a(x1))) C(B(A(x1))) -> A(B(C(x1))) b(a(C(x1))) -> C(a(b(x1))) c(A(B(x1))) -> B(A(c(x1))) A(c(b(x1))) -> b(c(A(x1))) B(C(a(x1))) -> a(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 graph: B#(C(a(x1))) -> a#(C(B(x1))) -> a#(b(c(x1))) -> c#(b(a(x1))) c#(A(B(x1))) -> B#(A(c(x1))) -> B#(C(a(x1))) -> a#(C(B(x1))) a#(b(c(x1))) -> c#(b(a(x1))) -> c#(A(B(x1))) -> B#(A(c(x1))) KBO Processor: argument filtering: pi(c) = [0] pi(b) = 0 pi(a) = [0] pi(A) = 0 pi(B) = 0 pi(C) = 0 pi(a#) = [0] pi(c#) = [0] pi(B#) = 0 weight function: w0 = 1 w(B#) = w(c#) = w(a#) = w(a) = w(c) = 1 w(C) = w(B) = w(A) = w(b) = 0 precedence: a > a# > c# > B# ~ C ~ B ~ A ~ b ~ c problem: DPs: TRS: a(b(c(x1))) -> c(b(a(x1))) C(B(A(x1))) -> A(B(C(x1))) b(a(C(x1))) -> C(a(b(x1))) c(A(B(x1))) -> B(A(c(x1))) A(c(b(x1))) -> b(c(A(x1))) B(C(a(x1))) -> a(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 Qed