YES Problem: c(b(a(a(x1)))) -> a(a(b(c(x1)))) b(a(a(a(x1)))) -> a(a(a(b(x1)))) a(b(c(x1))) -> c(b(a(x1))) c(c(b(b(x1)))) -> b(b(c(c(x1)))) Proof: DP Processor: DPs: c#(b(a(a(x1)))) -> c#(x1) c#(b(a(a(x1)))) -> b#(c(x1)) c#(b(a(a(x1)))) -> a#(b(c(x1))) c#(b(a(a(x1)))) -> a#(a(b(c(x1)))) b#(a(a(a(x1)))) -> b#(x1) b#(a(a(a(x1)))) -> a#(b(x1)) b#(a(a(a(x1)))) -> a#(a(b(x1))) b#(a(a(a(x1)))) -> a#(a(a(b(x1)))) a#(b(c(x1))) -> a#(x1) a#(b(c(x1))) -> b#(a(x1)) a#(b(c(x1))) -> c#(b(a(x1))) c#(c(b(b(x1)))) -> c#(x1) c#(c(b(b(x1)))) -> c#(c(x1)) c#(c(b(b(x1)))) -> b#(c(c(x1))) c#(c(b(b(x1)))) -> b#(b(c(c(x1)))) TRS: c(b(a(a(x1)))) -> a(a(b(c(x1)))) b(a(a(a(x1)))) -> a(a(a(b(x1)))) a(b(c(x1))) -> c(b(a(x1))) c(c(b(b(x1)))) -> b(b(c(c(x1)))) TDG Processor: DPs: c#(b(a(a(x1)))) -> c#(x1) c#(b(a(a(x1)))) -> b#(c(x1)) c#(b(a(a(x1)))) -> a#(b(c(x1))) c#(b(a(a(x1)))) -> a#(a(b(c(x1)))) b#(a(a(a(x1)))) -> b#(x1) b#(a(a(a(x1)))) -> a#(b(x1)) b#(a(a(a(x1)))) -> a#(a(b(x1))) b#(a(a(a(x1)))) -> a#(a(a(b(x1)))) a#(b(c(x1))) -> a#(x1) a#(b(c(x1))) -> b#(a(x1)) a#(b(c(x1))) -> c#(b(a(x1))) c#(c(b(b(x1)))) -> c#(x1) c#(c(b(b(x1)))) -> c#(c(x1)) c#(c(b(b(x1)))) -> b#(c(c(x1))) c#(c(b(b(x1)))) -> b#(b(c(c(x1)))) TRS: c(b(a(a(x1)))) -> a(a(b(c(x1)))) b(a(a(a(x1)))) -> a(a(a(b(x1)))) a(b(c(x1))) -> c(b(a(x1))) c(c(b(b(x1)))) -> b(b(c(c(x1)))) graph: 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) a#(b(c(x1))) -> b#(a(x1)) -> b#(a(a(a(x1)))) -> a#(a(a(b(x1)))) a#(b(c(x1))) -> b#(a(x1)) -> b#(a(a(a(x1)))) -> a#(a(b(x1))) a#(b(c(x1))) -> b#(a(x1)) -> b#(a(a(a(x1)))) -> a#(b(x1)) a#(b(c(x1))) -> b#(a(x1)) -> b#(a(a(a(x1)))) -> b#(x1) a#(b(c(x1))) -> c#(b(a(x1))) -> c#(c(b(b(x1)))) -> b#(b(c(c(x1)))) a#(b(c(x1))) -> c#(b(a(x1))) -> c#(c(b(b(x1)))) -> b#(c(c(x1))) a#(b(c(x1))) -> c#(b(a(x1))) -> c#(c(b(b(x1)))) -> c#(c(x1)) a#(b(c(x1))) -> c#(b(a(x1))) -> c#(c(b(b(x1)))) -> c#(x1) a#(b(c(x1))) -> c#(b(a(x1))) -> c#(b(a(a(x1)))) -> a#(a(b(c(x1)))) a#(b(c(x1))) -> c#(b(a(x1))) -> c#(b(a(a(x1)))) -> a#(b(c(x1))) a#(b(c(x1))) -> c#(b(a(x1))) -> c#(b(a(a(x1)))) -> b#(c(x1)) a#(b(c(x1))) -> c#(b(a(x1))) -> c#(b(a(a(x1)))) -> c#(x1) b#(a(a(a(x1)))) -> a#(b(x1)) -> a#(b(c(x1))) -> c#(b(a(x1))) b#(a(a(a(x1)))) -> a#(b(x1)) -> a#(b(c(x1))) -> b#(a(x1)) b#(a(a(a(x1)))) -> a#(b(x1)) -> a#(b(c(x1))) -> a#(x1) b#(a(a(a(x1)))) -> a#(a(b(x1))) -> a#(b(c(x1))) -> c#(b(a(x1))) b#(a(a(a(x1)))) -> a#(a(b(x1))) -> a#(b(c(x1))) -> b#(a(x1)) b#(a(a(a(x1)))) -> a#(a(b(x1))) -> a#(b(c(x1))) -> a#(x1) b#(a(a(a(x1)))) -> a#(a(a(b(x1)))) -> a#(b(c(x1))) -> c#(b(a(x1))) b#(a(a(a(x1)))) -> a#(a(a(b(x1)))) -> a#(b(c(x1))) -> b#(a(x1)) b#(a(a(a(x1)))) -> a#(a(a(b(x1)))) -> a#(b(c(x1))) -> a#(x1) b#(a(a(a(x1)))) -> b#(x1) -> b#(a(a(a(x1)))) -> a#(a(a(b(x1)))) b#(a(a(a(x1)))) -> b#(x1) -> b#(a(a(a(x1)))) -> a#(a(b(x1))) b#(a(a(a(x1)))) -> b#(x1) -> b#(a(a(a(x1)))) -> a#(b(x1)) b#(a(a(a(x1)))) -> b#(x1) -> b#(a(a(a(x1)))) -> b#(x1) c#(c(b(b(x1)))) -> b#(c(c(x1))) -> b#(a(a(a(x1)))) -> a#(a(a(b(x1)))) c#(c(b(b(x1)))) -> b#(c(c(x1))) -> b#(a(a(a(x1)))) -> a#(a(b(x1))) c#(c(b(b(x1)))) -> b#(c(c(x1))) -> b#(a(a(a(x1)))) -> a#(b(x1)) c#(c(b(b(x1)))) -> b#(c(c(x1))) -> b#(a(a(a(x1)))) -> b#(x1) c#(c(b(b(x1)))) -> b#(b(c(c(x1)))) -> b#(a(a(a(x1)))) -> a#(a(a(b(x1)))) c#(c(b(b(x1)))) -> b#(b(c(c(x1)))) -> b#(a(a(a(x1)))) -> a#(a(b(x1))) c#(c(b(b(x1)))) -> b#(b(c(c(x1)))) -> b#(a(a(a(x1)))) -> a#(b(x1)) c#(c(b(b(x1)))) -> b#(b(c(c(x1)))) -> b#(a(a(a(x1)))) -> b#(x1) c#(c(b(b(x1)))) -> c#(c(x1)) -> c#(c(b(b(x1)))) -> b#(b(c(c(x1)))) c#(c(b(b(x1)))) -> c#(c(x1)) -> c#(c(b(b(x1)))) -> b#(c(c(x1))) c#(c(b(b(x1)))) -> c#(c(x1)) -> c#(c(b(b(x1)))) -> c#(c(x1)) c#(c(b(b(x1)))) -> c#(c(x1)) -> c#(c(b(b(x1)))) -> c#(x1) c#(c(b(b(x1)))) -> c#(c(x1)) -> c#(b(a(a(x1)))) -> a#(a(b(c(x1)))) c#(c(b(b(x1)))) -> c#(c(x1)) -> c#(b(a(a(x1)))) -> a#(b(c(x1))) c#(c(b(b(x1)))) -> c#(c(x1)) -> c#(b(a(a(x1)))) -> b#(c(x1)) c#(c(b(b(x1)))) -> c#(c(x1)) -> c#(b(a(a(x1)))) -> c#(x1) c#(c(b(b(x1)))) -> c#(x1) -> c#(c(b(b(x1)))) -> b#(b(c(c(x1)))) c#(c(b(b(x1)))) -> c#(x1) -> c#(c(b(b(x1)))) -> b#(c(c(x1))) c#(c(b(b(x1)))) -> c#(x1) -> c#(c(b(b(x1)))) -> c#(c(x1)) c#(c(b(b(x1)))) -> c#(x1) -> c#(c(b(b(x1)))) -> c#(x1) c#(c(b(b(x1)))) -> c#(x1) -> c#(b(a(a(x1)))) -> a#(a(b(c(x1)))) c#(c(b(b(x1)))) -> c#(x1) -> c#(b(a(a(x1)))) -> a#(b(c(x1))) c#(c(b(b(x1)))) -> c#(x1) -> c#(b(a(a(x1)))) -> b#(c(x1)) c#(c(b(b(x1)))) -> c#(x1) -> c#(b(a(a(x1)))) -> c#(x1) c#(b(a(a(x1)))) -> a#(b(c(x1))) -> a#(b(c(x1))) -> c#(b(a(x1))) c#(b(a(a(x1)))) -> a#(b(c(x1))) -> a#(b(c(x1))) -> b#(a(x1)) c#(b(a(a(x1)))) -> a#(b(c(x1))) -> a#(b(c(x1))) -> a#(x1) c#(b(a(a(x1)))) -> a#(a(b(c(x1)))) -> a#(b(c(x1))) -> c#(b(a(x1))) c#(b(a(a(x1)))) -> a#(a(b(c(x1)))) -> a#(b(c(x1))) -> b#(a(x1)) c#(b(a(a(x1)))) -> a#(a(b(c(x1)))) -> a#(b(c(x1))) -> a#(x1) c#(b(a(a(x1)))) -> b#(c(x1)) -> b#(a(a(a(x1)))) -> a#(a(a(b(x1)))) c#(b(a(a(x1)))) -> b#(c(x1)) -> b#(a(a(a(x1)))) -> a#(a(b(x1))) c#(b(a(a(x1)))) -> b#(c(x1)) -> b#(a(a(a(x1)))) -> a#(b(x1)) c#(b(a(a(x1)))) -> b#(c(x1)) -> b#(a(a(a(x1)))) -> b#(x1) c#(b(a(a(x1)))) -> c#(x1) -> c#(c(b(b(x1)))) -> b#(b(c(c(x1)))) c#(b(a(a(x1)))) -> c#(x1) -> c#(c(b(b(x1)))) -> b#(c(c(x1))) c#(b(a(a(x1)))) -> c#(x1) -> c#(c(b(b(x1)))) -> c#(c(x1)) c#(b(a(a(x1)))) -> c#(x1) -> c#(c(b(b(x1)))) -> c#(x1) c#(b(a(a(x1)))) -> c#(x1) -> c#(b(a(a(x1)))) -> a#(a(b(c(x1)))) c#(b(a(a(x1)))) -> c#(x1) -> c#(b(a(a(x1)))) -> a#(b(c(x1))) c#(b(a(a(x1)))) -> c#(x1) -> c#(b(a(a(x1)))) -> b#(c(x1)) c#(b(a(a(x1)))) -> c#(x1) -> c#(b(a(a(x1)))) -> c#(x1) Arctic Interpretation Processor: dimension: 1 interpretation: [a#](x0) = 1x0 + 1, [b#](x0) = x0, [c#](x0) = x0, [c](x0) = x0, [b](x0) = x0, [a](x0) = 1x0 + 0 orientation: c#(b(a(a(x1)))) = 2x1 + 1 >= x1 = c#(x1) c#(b(a(a(x1)))) = 2x1 + 1 >= x1 = b#(c(x1)) c#(b(a(a(x1)))) = 2x1 + 1 >= 1x1 + 1 = a#(b(c(x1))) c#(b(a(a(x1)))) = 2x1 + 1 >= 2x1 + 1 = a#(a(b(c(x1)))) b#(a(a(a(x1)))) = 3x1 + 2 >= x1 = b#(x1) b#(a(a(a(x1)))) = 3x1 + 2 >= 1x1 + 1 = a#(b(x1)) b#(a(a(a(x1)))) = 3x1 + 2 >= 2x1 + 1 = a#(a(b(x1))) b#(a(a(a(x1)))) = 3x1 + 2 >= 3x1 + 2 = a#(a(a(b(x1)))) a#(b(c(x1))) = 1x1 + 1 >= 1x1 + 1 = a#(x1) a#(b(c(x1))) = 1x1 + 1 >= 1x1 + 0 = b#(a(x1)) a#(b(c(x1))) = 1x1 + 1 >= 1x1 + 0 = c#(b(a(x1))) c#(c(b(b(x1)))) = x1 >= x1 = c#(x1) c#(c(b(b(x1)))) = x1 >= x1 = c#(c(x1)) c#(c(b(b(x1)))) = x1 >= x1 = b#(c(c(x1))) c#(c(b(b(x1)))) = x1 >= x1 = b#(b(c(c(x1)))) c(b(a(a(x1)))) = 2x1 + 1 >= 2x1 + 1 = a(a(b(c(x1)))) b(a(a(a(x1)))) = 3x1 + 2 >= 3x1 + 2 = a(a(a(b(x1)))) a(b(c(x1))) = 1x1 + 0 >= 1x1 + 0 = c(b(a(x1))) c(c(b(b(x1)))) = x1 >= x1 = b(b(c(c(x1)))) problem: DPs: c#(b(a(a(x1)))) -> a#(b(c(x1))) c#(b(a(a(x1)))) -> a#(a(b(c(x1)))) b#(a(a(a(x1)))) -> a#(a(a(b(x1)))) a#(b(c(x1))) -> a#(x1) a#(b(c(x1))) -> b#(a(x1)) a#(b(c(x1))) -> c#(b(a(x1))) c#(c(b(b(x1)))) -> c#(x1) c#(c(b(b(x1)))) -> c#(c(x1)) c#(c(b(b(x1)))) -> b#(c(c(x1))) c#(c(b(b(x1)))) -> b#(b(c(c(x1)))) TRS: c(b(a(a(x1)))) -> a(a(b(c(x1)))) b(a(a(a(x1)))) -> a(a(a(b(x1)))) a(b(c(x1))) -> c(b(a(x1))) c(c(b(b(x1)))) -> b(b(c(c(x1)))) EDG Processor: DPs: c#(b(a(a(x1)))) -> a#(b(c(x1))) c#(b(a(a(x1)))) -> a#(a(b(c(x1)))) b#(a(a(a(x1)))) -> a#(a(a(b(x1)))) a#(b(c(x1))) -> a#(x1) a#(b(c(x1))) -> b#(a(x1)) a#(b(c(x1))) -> c#(b(a(x1))) c#(c(b(b(x1)))) -> c#(x1) c#(c(b(b(x1)))) -> c#(c(x1)) c#(c(b(b(x1)))) -> b#(c(c(x1))) c#(c(b(b(x1)))) -> b#(b(c(c(x1)))) TRS: c(b(a(a(x1)))) -> a(a(b(c(x1)))) b(a(a(a(x1)))) -> a(a(a(b(x1)))) a(b(c(x1))) -> c(b(a(x1))) c(c(b(b(x1)))) -> b(b(c(c(x1)))) graph: 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))) a#(b(c(x1))) -> b#(a(x1)) -> b#(a(a(a(x1)))) -> a#(a(a(b(x1)))) a#(b(c(x1))) -> c#(b(a(x1))) -> c#(b(a(a(x1)))) -> a#(b(c(x1))) a#(b(c(x1))) -> c#(b(a(x1))) -> c#(b(a(a(x1)))) -> a#(a(b(c(x1)))) a#(b(c(x1))) -> c#(b(a(x1))) -> c#(c(b(b(x1)))) -> c#(x1) a#(b(c(x1))) -> c#(b(a(x1))) -> c#(c(b(b(x1)))) -> c#(c(x1)) a#(b(c(x1))) -> c#(b(a(x1))) -> c#(c(b(b(x1)))) -> b#(c(c(x1))) a#(b(c(x1))) -> c#(b(a(x1))) -> c#(c(b(b(x1)))) -> b#(b(c(c(x1)))) b#(a(a(a(x1)))) -> a#(a(a(b(x1)))) -> a#(b(c(x1))) -> a#(x1) b#(a(a(a(x1)))) -> a#(a(a(b(x1)))) -> a#(b(c(x1))) -> b#(a(x1)) b#(a(a(a(x1)))) -> a#(a(a(b(x1)))) -> a#(b(c(x1))) -> c#(b(a(x1))) c#(c(b(b(x1)))) -> b#(c(c(x1))) -> b#(a(a(a(x1)))) -> a#(a(a(b(x1)))) c#(c(b(b(x1)))) -> b#(b(c(c(x1)))) -> b#(a(a(a(x1)))) -> a#(a(a(b(x1)))) c#(c(b(b(x1)))) -> c#(c(x1)) -> c#(b(a(a(x1)))) -> a#(b(c(x1))) c#(c(b(b(x1)))) -> c#(c(x1)) -> c#(b(a(a(x1)))) -> a#(a(b(c(x1)))) c#(c(b(b(x1)))) -> c#(c(x1)) -> c#(c(b(b(x1)))) -> c#(x1) c#(c(b(b(x1)))) -> c#(c(x1)) -> c#(c(b(b(x1)))) -> c#(c(x1)) c#(c(b(b(x1)))) -> c#(c(x1)) -> c#(c(b(b(x1)))) -> b#(c(c(x1))) c#(c(b(b(x1)))) -> c#(c(x1)) -> c#(c(b(b(x1)))) -> b#(b(c(c(x1)))) c#(c(b(b(x1)))) -> c#(x1) -> c#(b(a(a(x1)))) -> a#(b(c(x1))) c#(c(b(b(x1)))) -> c#(x1) -> c#(b(a(a(x1)))) -> a#(a(b(c(x1)))) c#(c(b(b(x1)))) -> c#(x1) -> c#(c(b(b(x1)))) -> c#(x1) c#(c(b(b(x1)))) -> c#(x1) -> c#(c(b(b(x1)))) -> c#(c(x1)) c#(c(b(b(x1)))) -> c#(x1) -> c#(c(b(b(x1)))) -> b#(c(c(x1))) c#(c(b(b(x1)))) -> c#(x1) -> c#(c(b(b(x1)))) -> b#(b(c(c(x1)))) c#(b(a(a(x1)))) -> a#(b(c(x1))) -> a#(b(c(x1))) -> a#(x1) c#(b(a(a(x1)))) -> a#(b(c(x1))) -> a#(b(c(x1))) -> b#(a(x1)) c#(b(a(a(x1)))) -> a#(b(c(x1))) -> a#(b(c(x1))) -> c#(b(a(x1))) c#(b(a(a(x1)))) -> a#(a(b(c(x1)))) -> a#(b(c(x1))) -> a#(x1) c#(b(a(a(x1)))) -> a#(a(b(c(x1)))) -> a#(b(c(x1))) -> b#(a(x1)) c#(b(a(a(x1)))) -> a#(a(b(c(x1)))) -> a#(b(c(x1))) -> c#(b(a(x1))) Arctic Interpretation Processor: dimension: 1 interpretation: [a#](x0) = x0, [b#](x0) = 8x0, [c#](x0) = x0, [c](x0) = x0, [b](x0) = 8x0, [a](x0) = x0 orientation: c#(b(a(a(x1)))) = 8x1 >= 8x1 = a#(b(c(x1))) c#(b(a(a(x1)))) = 8x1 >= 8x1 = a#(a(b(c(x1)))) b#(a(a(a(x1)))) = 8x1 >= 8x1 = a#(a(a(b(x1)))) a#(b(c(x1))) = 8x1 >= x1 = a#(x1) a#(b(c(x1))) = 8x1 >= 8x1 = b#(a(x1)) a#(b(c(x1))) = 8x1 >= 8x1 = c#(b(a(x1))) c#(c(b(b(x1)))) = 16x1 >= x1 = c#(x1) c#(c(b(b(x1)))) = 16x1 >= x1 = c#(c(x1)) c#(c(b(b(x1)))) = 16x1 >= 8x1 = b#(c(c(x1))) c#(c(b(b(x1)))) = 16x1 >= 16x1 = b#(b(c(c(x1)))) c(b(a(a(x1)))) = 8x1 >= 8x1 = a(a(b(c(x1)))) b(a(a(a(x1)))) = 8x1 >= 8x1 = a(a(a(b(x1)))) a(b(c(x1))) = 8x1 >= 8x1 = c(b(a(x1))) c(c(b(b(x1)))) = 16x1 >= 16x1 = b(b(c(c(x1)))) problem: DPs: c#(b(a(a(x1)))) -> a#(b(c(x1))) c#(b(a(a(x1)))) -> a#(a(b(c(x1)))) b#(a(a(a(x1)))) -> a#(a(a(b(x1)))) a#(b(c(x1))) -> b#(a(x1)) a#(b(c(x1))) -> c#(b(a(x1))) c#(c(b(b(x1)))) -> b#(b(c(c(x1)))) TRS: c(b(a(a(x1)))) -> a(a(b(c(x1)))) b(a(a(a(x1)))) -> a(a(a(b(x1)))) a(b(c(x1))) -> c(b(a(x1))) c(c(b(b(x1)))) -> b(b(c(c(x1)))) EDG Processor: DPs: c#(b(a(a(x1)))) -> a#(b(c(x1))) c#(b(a(a(x1)))) -> a#(a(b(c(x1)))) b#(a(a(a(x1)))) -> a#(a(a(b(x1)))) a#(b(c(x1))) -> b#(a(x1)) a#(b(c(x1))) -> c#(b(a(x1))) c#(c(b(b(x1)))) -> b#(b(c(c(x1)))) TRS: c(b(a(a(x1)))) -> a(a(b(c(x1)))) b(a(a(a(x1)))) -> a(a(a(b(x1)))) a(b(c(x1))) -> c(b(a(x1))) c(c(b(b(x1)))) -> b(b(c(c(x1)))) graph: a#(b(c(x1))) -> b#(a(x1)) -> b#(a(a(a(x1)))) -> a#(a(a(b(x1)))) a#(b(c(x1))) -> c#(b(a(x1))) -> c#(c(b(b(x1)))) -> b#(b(c(c(x1)))) a#(b(c(x1))) -> c#(b(a(x1))) -> c#(b(a(a(x1)))) -> a#(a(b(c(x1)))) a#(b(c(x1))) -> c#(b(a(x1))) -> c#(b(a(a(x1)))) -> a#(b(c(x1))) b#(a(a(a(x1)))) -> a#(a(a(b(x1)))) -> a#(b(c(x1))) -> c#(b(a(x1))) b#(a(a(a(x1)))) -> a#(a(a(b(x1)))) -> a#(b(c(x1))) -> b#(a(x1)) c#(c(b(b(x1)))) -> b#(b(c(c(x1)))) -> b#(a(a(a(x1)))) -> a#(a(a(b(x1)))) c#(b(a(a(x1)))) -> a#(b(c(x1))) -> a#(b(c(x1))) -> c#(b(a(x1))) c#(b(a(a(x1)))) -> a#(b(c(x1))) -> a#(b(c(x1))) -> b#(a(x1)) c#(b(a(a(x1)))) -> a#(a(b(c(x1)))) -> a#(b(c(x1))) -> c#(b(a(x1))) c#(b(a(a(x1)))) -> a#(a(b(c(x1)))) -> a#(b(c(x1))) -> b#(a(x1)) Arctic Interpretation Processor: dimension: 1 interpretation: [a#](x0) = 4x0, [b#](x0) = x0, [c#](x0) = x0, [c](x0) = x0, [b](x0) = x0, [a](x0) = 4x0 orientation: c#(b(a(a(x1)))) = 8x1 >= 4x1 = a#(b(c(x1))) c#(b(a(a(x1)))) = 8x1 >= 8x1 = a#(a(b(c(x1)))) b#(a(a(a(x1)))) = 12x1 >= 12x1 = a#(a(a(b(x1)))) a#(b(c(x1))) = 4x1 >= 4x1 = b#(a(x1)) a#(b(c(x1))) = 4x1 >= 4x1 = c#(b(a(x1))) c#(c(b(b(x1)))) = x1 >= x1 = b#(b(c(c(x1)))) c(b(a(a(x1)))) = 8x1 >= 8x1 = a(a(b(c(x1)))) b(a(a(a(x1)))) = 12x1 >= 12x1 = a(a(a(b(x1)))) a(b(c(x1))) = 4x1 >= 4x1 = c(b(a(x1))) c(c(b(b(x1)))) = x1 >= x1 = b(b(c(c(x1)))) problem: DPs: c#(b(a(a(x1)))) -> a#(a(b(c(x1)))) b#(a(a(a(x1)))) -> a#(a(a(b(x1)))) a#(b(c(x1))) -> b#(a(x1)) a#(b(c(x1))) -> c#(b(a(x1))) c#(c(b(b(x1)))) -> b#(b(c(c(x1)))) TRS: c(b(a(a(x1)))) -> a(a(b(c(x1)))) b(a(a(a(x1)))) -> a(a(a(b(x1)))) a(b(c(x1))) -> c(b(a(x1))) c(c(b(b(x1)))) -> b(b(c(c(x1)))) EDG Processor: DPs: c#(b(a(a(x1)))) -> a#(a(b(c(x1)))) b#(a(a(a(x1)))) -> a#(a(a(b(x1)))) a#(b(c(x1))) -> b#(a(x1)) a#(b(c(x1))) -> c#(b(a(x1))) c#(c(b(b(x1)))) -> b#(b(c(c(x1)))) TRS: c(b(a(a(x1)))) -> a(a(b(c(x1)))) b(a(a(a(x1)))) -> a(a(a(b(x1)))) a(b(c(x1))) -> c(b(a(x1))) c(c(b(b(x1)))) -> b(b(c(c(x1)))) graph: a#(b(c(x1))) -> b#(a(x1)) -> b#(a(a(a(x1)))) -> a#(a(a(b(x1)))) a#(b(c(x1))) -> c#(b(a(x1))) -> c#(b(a(a(x1)))) -> a#(a(b(c(x1)))) a#(b(c(x1))) -> c#(b(a(x1))) -> c#(c(b(b(x1)))) -> b#(b(c(c(x1)))) b#(a(a(a(x1)))) -> a#(a(a(b(x1)))) -> a#(b(c(x1))) -> b#(a(x1)) b#(a(a(a(x1)))) -> a#(a(a(b(x1)))) -> a#(b(c(x1))) -> c#(b(a(x1))) c#(c(b(b(x1)))) -> b#(b(c(c(x1)))) -> b#(a(a(a(x1)))) -> a#(a(a(b(x1)))) c#(b(a(a(x1)))) -> a#(a(b(c(x1)))) -> a#(b(c(x1))) -> b#(a(x1)) c#(b(a(a(x1)))) -> a#(a(b(c(x1)))) -> a#(b(c(x1))) -> c#(b(a(x1))) Arctic Interpretation Processor: dimension: 1 interpretation: [a#](x0) = 2x0, [b#](x0) = x0, [c#](x0) = 4x0, [c](x0) = 4x0, [b](x0) = x0, [a](x0) = 2x0 orientation: c#(b(a(a(x1)))) = 8x1 >= 8x1 = a#(a(b(c(x1)))) b#(a(a(a(x1)))) = 6x1 >= 6x1 = a#(a(a(b(x1)))) a#(b(c(x1))) = 6x1 >= 2x1 = b#(a(x1)) a#(b(c(x1))) = 6x1 >= 6x1 = c#(b(a(x1))) c#(c(b(b(x1)))) = 8x1 >= 8x1 = b#(b(c(c(x1)))) c(b(a(a(x1)))) = 8x1 >= 8x1 = a(a(b(c(x1)))) b(a(a(a(x1)))) = 6x1 >= 6x1 = a(a(a(b(x1)))) a(b(c(x1))) = 6x1 >= 6x1 = c(b(a(x1))) c(c(b(b(x1)))) = 8x1 >= 8x1 = b(b(c(c(x1)))) problem: DPs: c#(b(a(a(x1)))) -> a#(a(b(c(x1)))) b#(a(a(a(x1)))) -> a#(a(a(b(x1)))) a#(b(c(x1))) -> c#(b(a(x1))) c#(c(b(b(x1)))) -> b#(b(c(c(x1)))) TRS: c(b(a(a(x1)))) -> a(a(b(c(x1)))) b(a(a(a(x1)))) -> a(a(a(b(x1)))) a(b(c(x1))) -> c(b(a(x1))) c(c(b(b(x1)))) -> b(b(c(c(x1)))) EDG Processor: DPs: c#(b(a(a(x1)))) -> a#(a(b(c(x1)))) b#(a(a(a(x1)))) -> a#(a(a(b(x1)))) a#(b(c(x1))) -> c#(b(a(x1))) c#(c(b(b(x1)))) -> b#(b(c(c(x1)))) TRS: c(b(a(a(x1)))) -> a(a(b(c(x1)))) b(a(a(a(x1)))) -> a(a(a(b(x1)))) a(b(c(x1))) -> c(b(a(x1))) c(c(b(b(x1)))) -> b(b(c(c(x1)))) graph: a#(b(c(x1))) -> c#(b(a(x1))) -> c#(c(b(b(x1)))) -> b#(b(c(c(x1)))) a#(b(c(x1))) -> c#(b(a(x1))) -> c#(b(a(a(x1)))) -> a#(a(b(c(x1)))) b#(a(a(a(x1)))) -> a#(a(a(b(x1)))) -> a#(b(c(x1))) -> c#(b(a(x1))) c#(c(b(b(x1)))) -> b#(b(c(c(x1)))) -> b#(a(a(a(x1)))) -> a#(a(a(b(x1)))) c#(b(a(a(x1)))) -> a#(a(b(c(x1)))) -> a#(b(c(x1))) -> c#(b(a(x1))) Matrix Interpretation Processor: dim=4 interpretation: [a#](x0) = [0 0 1 0]x0, [b#](x0) = [1], [c#](x0) = [1 0 1 0]x0, [0 0 1 0] [0] [0 0 0 1] [0] [c](x0) = [1 0 0 0]x0 + [0] [0 1 0 0] [1], [0 0 0 0] [0] [0 1 0 0] [0] [b](x0) = [0 0 0 0]x0 + [1] [0 0 0 1] [0], [0 0 1 0] [0 1 0 0] [a](x0) = [0 0 0 0]x0 [0 0 0 1] orientation: c#(b(a(a(x1)))) = [1] >= [0] = a#(a(b(c(x1)))) b#(a(a(a(x1)))) = [1] >= [0] = a#(a(a(b(x1)))) a#(b(c(x1))) = [1] >= [1] = c#(b(a(x1))) c#(c(b(b(x1)))) = [1] >= [1] = b#(b(c(c(x1)))) [0 0 0 0] [1] [0 0 0 0] [0] [0 0 0 1] [0] [0 0 0 1] [0] c(b(a(a(x1)))) = [0 0 0 0]x1 + [0] >= [0 0 0 0]x1 + [0] = a(a(b(c(x1)))) [0 1 0 0] [1] [0 1 0 0] [1] [0 0 0 0] [0] [0 0 0 0] [0 1 0 0] [0] [0 1 0 0] b(a(a(a(x1)))) = [0 0 0 0]x1 + [1] >= [0 0 0 0]x1 = a(a(a(b(x1)))) [0 0 0 1] [0] [0 0 0 1] [0 0 0 0] [1] [0 0 0 0] [1] [0 0 0 1] [0] [0 0 0 1] [0] a(b(c(x1))) = [0 0 0 0]x1 + [0] >= [0 0 0 0]x1 + [0] = c(b(a(x1))) [0 1 0 0] [1] [0 1 0 0] [1] [0 0 0 0] [0] [0 0 0 0] [0] [0 1 0 0] [1] [0 1 0 0] [1] c(c(b(b(x1)))) = [0 0 0 0]x1 + [1] >= [0 0 0 0]x1 + [1] = b(b(c(c(x1)))) [0 0 0 1] [1] [0 0 0 1] [1] problem: DPs: a#(b(c(x1))) -> c#(b(a(x1))) c#(c(b(b(x1)))) -> b#(b(c(c(x1)))) TRS: c(b(a(a(x1)))) -> a(a(b(c(x1)))) b(a(a(a(x1)))) -> a(a(a(b(x1)))) a(b(c(x1))) -> c(b(a(x1))) c(c(b(b(x1)))) -> b(b(c(c(x1)))) EDG Processor: DPs: a#(b(c(x1))) -> c#(b(a(x1))) c#(c(b(b(x1)))) -> b#(b(c(c(x1)))) TRS: c(b(a(a(x1)))) -> a(a(b(c(x1)))) b(a(a(a(x1)))) -> a(a(a(b(x1)))) a(b(c(x1))) -> c(b(a(x1))) c(c(b(b(x1)))) -> b(b(c(c(x1)))) graph: a#(b(c(x1))) -> c#(b(a(x1))) -> c#(c(b(b(x1)))) -> b#(b(c(c(x1)))) SCC Processor: #sccs: 0 #rules: 0 #arcs: 1/4