YES Problem: b(b(d(d(b(b(x1)))))) -> c(c(d(d(b(b(x1)))))) b(b(a(a(c(c(x1)))))) -> b(b(c(c(x1)))) a(a(d(d(x1)))) -> d(d(c(c(x1)))) b(b(b(b(b(b(x1)))))) -> a(a(b(b(c(c(x1)))))) d(d(c(c(x1)))) -> b(b(d(d(x1)))) d(d(c(c(x1)))) -> d(d(b(b(d(d(x1)))))) d(d(a(a(c(c(x1)))))) -> b(b(b(b(x1)))) Proof: Arctic Interpretation Processor: dimension: 1 interpretation: [a](x0) = 1x0, [c](x0) = 1x0, [d](x0) = x0, [b](x0) = 1x0 orientation: b(b(d(d(b(b(x1)))))) = 4x1 >= 4x1 = c(c(d(d(b(b(x1)))))) b(b(a(a(c(c(x1)))))) = 6x1 >= 4x1 = b(b(c(c(x1)))) a(a(d(d(x1)))) = 2x1 >= 2x1 = d(d(c(c(x1)))) b(b(b(b(b(b(x1)))))) = 6x1 >= 6x1 = a(a(b(b(c(c(x1)))))) d(d(c(c(x1)))) = 2x1 >= 2x1 = b(b(d(d(x1)))) d(d(c(c(x1)))) = 2x1 >= 2x1 = d(d(b(b(d(d(x1)))))) d(d(a(a(c(c(x1)))))) = 4x1 >= 4x1 = b(b(b(b(x1)))) problem: b(b(d(d(b(b(x1)))))) -> c(c(d(d(b(b(x1)))))) a(a(d(d(x1)))) -> d(d(c(c(x1)))) b(b(b(b(b(b(x1)))))) -> a(a(b(b(c(c(x1)))))) d(d(c(c(x1)))) -> b(b(d(d(x1)))) d(d(c(c(x1)))) -> d(d(b(b(d(d(x1)))))) d(d(a(a(c(c(x1)))))) -> b(b(b(b(x1)))) String Reversal Processor: b(b(d(d(b(b(x1)))))) -> b(b(d(d(c(c(x1)))))) d(d(a(a(x1)))) -> c(c(d(d(x1)))) b(b(b(b(b(b(x1)))))) -> c(c(b(b(a(a(x1)))))) c(c(d(d(x1)))) -> d(d(b(b(x1)))) c(c(d(d(x1)))) -> d(d(b(b(d(d(x1)))))) c(c(a(a(d(d(x1)))))) -> b(b(b(b(x1)))) Matrix Interpretation Processor: dim=3 interpretation: [1 0 0] [0] [a](x0) = [1 1 1]x0 + [0] [0 1 0] [1], [1 0 0] [c](x0) = [0 0 0]x0 [0 0 0] , [1 1 0] [d](x0) = [0 0 0]x0 [0 0 0] , [1 0 0] [b](x0) = [0 0 0]x0 [0 0 0] orientation: [1 0 0] [1 0 0] b(b(d(d(b(b(x1)))))) = [0 0 0]x1 >= [0 0 0]x1 = b(b(d(d(c(c(x1)))))) [0 0 0] [0 0 0] [3 2 1] [1] [1 1 0] d(d(a(a(x1)))) = [0 0 0]x1 + [0] >= [0 0 0]x1 = c(c(d(d(x1)))) [0 0 0] [0] [0 0 0] [1 0 0] [1 0 0] b(b(b(b(b(b(x1)))))) = [0 0 0]x1 >= [0 0 0]x1 = c(c(b(b(a(a(x1)))))) [0 0 0] [0 0 0] [1 1 0] [1 0 0] c(c(d(d(x1)))) = [0 0 0]x1 >= [0 0 0]x1 = d(d(b(b(x1)))) [0 0 0] [0 0 0] [1 1 0] [1 1 0] c(c(d(d(x1)))) = [0 0 0]x1 >= [0 0 0]x1 = d(d(b(b(d(d(x1)))))) [0 0 0] [0 0 0] [1 1 0] [1 0 0] c(c(a(a(d(d(x1)))))) = [0 0 0]x1 >= [0 0 0]x1 = b(b(b(b(x1)))) [0 0 0] [0 0 0] problem: b(b(d(d(b(b(x1)))))) -> b(b(d(d(c(c(x1)))))) b(b(b(b(b(b(x1)))))) -> c(c(b(b(a(a(x1)))))) c(c(d(d(x1)))) -> d(d(b(b(x1)))) c(c(d(d(x1)))) -> d(d(b(b(d(d(x1)))))) c(c(a(a(d(d(x1)))))) -> b(b(b(b(x1)))) DP Processor: DPs: b#(b(d(d(b(b(x1)))))) -> c#(x1) b#(b(d(d(b(b(x1)))))) -> c#(c(x1)) b#(b(d(d(b(b(x1)))))) -> b#(d(d(c(c(x1))))) b#(b(d(d(b(b(x1)))))) -> b#(b(d(d(c(c(x1)))))) b#(b(b(b(b(b(x1)))))) -> b#(a(a(x1))) b#(b(b(b(b(b(x1)))))) -> b#(b(a(a(x1)))) b#(b(b(b(b(b(x1)))))) -> c#(b(b(a(a(x1))))) b#(b(b(b(b(b(x1)))))) -> c#(c(b(b(a(a(x1)))))) c#(c(d(d(x1)))) -> b#(x1) c#(c(d(d(x1)))) -> b#(b(x1)) c#(c(d(d(x1)))) -> b#(d(d(x1))) c#(c(d(d(x1)))) -> b#(b(d(d(x1)))) c#(c(a(a(d(d(x1)))))) -> b#(x1) c#(c(a(a(d(d(x1)))))) -> b#(b(x1)) c#(c(a(a(d(d(x1)))))) -> b#(b(b(x1))) c#(c(a(a(d(d(x1)))))) -> b#(b(b(b(x1)))) TRS: b(b(d(d(b(b(x1)))))) -> b(b(d(d(c(c(x1)))))) b(b(b(b(b(b(x1)))))) -> c(c(b(b(a(a(x1)))))) c(c(d(d(x1)))) -> d(d(b(b(x1)))) c(c(d(d(x1)))) -> d(d(b(b(d(d(x1)))))) c(c(a(a(d(d(x1)))))) -> b(b(b(b(x1)))) TDG Processor: DPs: b#(b(d(d(b(b(x1)))))) -> c#(x1) b#(b(d(d(b(b(x1)))))) -> c#(c(x1)) b#(b(d(d(b(b(x1)))))) -> b#(d(d(c(c(x1))))) b#(b(d(d(b(b(x1)))))) -> b#(b(d(d(c(c(x1)))))) b#(b(b(b(b(b(x1)))))) -> b#(a(a(x1))) b#(b(b(b(b(b(x1)))))) -> b#(b(a(a(x1)))) b#(b(b(b(b(b(x1)))))) -> c#(b(b(a(a(x1))))) b#(b(b(b(b(b(x1)))))) -> c#(c(b(b(a(a(x1)))))) c#(c(d(d(x1)))) -> b#(x1) c#(c(d(d(x1)))) -> b#(b(x1)) c#(c(d(d(x1)))) -> b#(d(d(x1))) c#(c(d(d(x1)))) -> b#(b(d(d(x1)))) c#(c(a(a(d(d(x1)))))) -> b#(x1) c#(c(a(a(d(d(x1)))))) -> b#(b(x1)) c#(c(a(a(d(d(x1)))))) -> b#(b(b(x1))) c#(c(a(a(d(d(x1)))))) -> b#(b(b(b(x1)))) TRS: b(b(d(d(b(b(x1)))))) -> b(b(d(d(c(c(x1)))))) b(b(b(b(b(b(x1)))))) -> c(c(b(b(a(a(x1)))))) c(c(d(d(x1)))) -> d(d(b(b(x1)))) c(c(d(d(x1)))) -> d(d(b(b(d(d(x1)))))) c(c(a(a(d(d(x1)))))) -> b(b(b(b(x1)))) graph: c#(c(a(a(d(d(x1)))))) -> b#(b(b(b(x1)))) -> b#(b(b(b(b(b(x1)))))) -> c#(c(b(b(a(a(x1)))))) c#(c(a(a(d(d(x1)))))) -> b#(b(b(b(x1)))) -> b#(b(b(b(b(b(x1)))))) -> c#(b(b(a(a(x1))))) c#(c(a(a(d(d(x1)))))) -> b#(b(b(b(x1)))) -> b#(b(b(b(b(b(x1)))))) -> b#(b(a(a(x1)))) c#(c(a(a(d(d(x1)))))) -> b#(b(b(b(x1)))) -> b#(b(b(b(b(b(x1)))))) -> b#(a(a(x1))) c#(c(a(a(d(d(x1)))))) -> b#(b(b(b(x1)))) -> b#(b(d(d(b(b(x1)))))) -> b#(b(d(d(c(c(x1)))))) c#(c(a(a(d(d(x1)))))) -> b#(b(b(b(x1)))) -> b#(b(d(d(b(b(x1)))))) -> b#(d(d(c(c(x1))))) c#(c(a(a(d(d(x1)))))) -> b#(b(b(b(x1)))) -> b#(b(d(d(b(b(x1)))))) -> c#(c(x1)) c#(c(a(a(d(d(x1)))))) -> b#(b(b(b(x1)))) -> b#(b(d(d(b(b(x1)))))) -> c#(x1) c#(c(a(a(d(d(x1)))))) -> b#(b(b(x1))) -> b#(b(b(b(b(b(x1)))))) -> c#(c(b(b(a(a(x1)))))) c#(c(a(a(d(d(x1)))))) -> b#(b(b(x1))) -> b#(b(b(b(b(b(x1)))))) -> c#(b(b(a(a(x1))))) c#(c(a(a(d(d(x1)))))) -> b#(b(b(x1))) -> b#(b(b(b(b(b(x1)))))) -> b#(b(a(a(x1)))) c#(c(a(a(d(d(x1)))))) -> b#(b(b(x1))) -> b#(b(b(b(b(b(x1)))))) -> b#(a(a(x1))) c#(c(a(a(d(d(x1)))))) -> b#(b(b(x1))) -> b#(b(d(d(b(b(x1)))))) -> b#(b(d(d(c(c(x1)))))) c#(c(a(a(d(d(x1)))))) -> b#(b(b(x1))) -> b#(b(d(d(b(b(x1)))))) -> b#(d(d(c(c(x1))))) c#(c(a(a(d(d(x1)))))) -> b#(b(b(x1))) -> b#(b(d(d(b(b(x1)))))) -> c#(c(x1)) c#(c(a(a(d(d(x1)))))) -> b#(b(b(x1))) -> b#(b(d(d(b(b(x1)))))) -> c#(x1) c#(c(a(a(d(d(x1)))))) -> b#(b(x1)) -> b#(b(b(b(b(b(x1)))))) -> c#(c(b(b(a(a(x1)))))) c#(c(a(a(d(d(x1)))))) -> b#(b(x1)) -> b#(b(b(b(b(b(x1)))))) -> c#(b(b(a(a(x1))))) c#(c(a(a(d(d(x1)))))) -> b#(b(x1)) -> b#(b(b(b(b(b(x1)))))) -> b#(b(a(a(x1)))) c#(c(a(a(d(d(x1)))))) -> b#(b(x1)) -> b#(b(b(b(b(b(x1)))))) -> b#(a(a(x1))) c#(c(a(a(d(d(x1)))))) -> b#(b(x1)) -> b#(b(d(d(b(b(x1)))))) -> b#(b(d(d(c(c(x1)))))) c#(c(a(a(d(d(x1)))))) -> b#(b(x1)) -> b#(b(d(d(b(b(x1)))))) -> b#(d(d(c(c(x1))))) c#(c(a(a(d(d(x1)))))) -> b#(b(x1)) -> b#(b(d(d(b(b(x1)))))) -> c#(c(x1)) c#(c(a(a(d(d(x1)))))) -> b#(b(x1)) -> b#(b(d(d(b(b(x1)))))) -> c#(x1) c#(c(a(a(d(d(x1)))))) -> b#(x1) -> b#(b(b(b(b(b(x1)))))) -> c#(c(b(b(a(a(x1)))))) c#(c(a(a(d(d(x1)))))) -> b#(x1) -> b#(b(b(b(b(b(x1)))))) -> c#(b(b(a(a(x1))))) c#(c(a(a(d(d(x1)))))) -> b#(x1) -> b#(b(b(b(b(b(x1)))))) -> b#(b(a(a(x1)))) c#(c(a(a(d(d(x1)))))) -> b#(x1) -> b#(b(b(b(b(b(x1)))))) -> b#(a(a(x1))) c#(c(a(a(d(d(x1)))))) -> b#(x1) -> b#(b(d(d(b(b(x1)))))) -> b#(b(d(d(c(c(x1)))))) c#(c(a(a(d(d(x1)))))) -> b#(x1) -> b#(b(d(d(b(b(x1)))))) -> b#(d(d(c(c(x1))))) c#(c(a(a(d(d(x1)))))) -> b#(x1) -> b#(b(d(d(b(b(x1)))))) -> c#(c(x1)) c#(c(a(a(d(d(x1)))))) -> b#(x1) -> b#(b(d(d(b(b(x1)))))) -> c#(x1) c#(c(d(d(x1)))) -> b#(d(d(x1))) -> b#(b(b(b(b(b(x1)))))) -> c#(c(b(b(a(a(x1)))))) c#(c(d(d(x1)))) -> b#(d(d(x1))) -> b#(b(b(b(b(b(x1)))))) -> c#(b(b(a(a(x1))))) c#(c(d(d(x1)))) -> b#(d(d(x1))) -> b#(b(b(b(b(b(x1)))))) -> b#(b(a(a(x1)))) c#(c(d(d(x1)))) -> b#(d(d(x1))) -> b#(b(b(b(b(b(x1)))))) -> b#(a(a(x1))) c#(c(d(d(x1)))) -> b#(d(d(x1))) -> b#(b(d(d(b(b(x1)))))) -> b#(b(d(d(c(c(x1)))))) c#(c(d(d(x1)))) -> b#(d(d(x1))) -> b#(b(d(d(b(b(x1)))))) -> b#(d(d(c(c(x1))))) c#(c(d(d(x1)))) -> b#(d(d(x1))) -> b#(b(d(d(b(b(x1)))))) -> c#(c(x1)) c#(c(d(d(x1)))) -> b#(d(d(x1))) -> b#(b(d(d(b(b(x1)))))) -> c#(x1) c#(c(d(d(x1)))) -> b#(b(d(d(x1)))) -> b#(b(b(b(b(b(x1)))))) -> c#(c(b(b(a(a(x1)))))) c#(c(d(d(x1)))) -> b#(b(d(d(x1)))) -> b#(b(b(b(b(b(x1)))))) -> c#(b(b(a(a(x1))))) c#(c(d(d(x1)))) -> b#(b(d(d(x1)))) -> b#(b(b(b(b(b(x1)))))) -> b#(b(a(a(x1)))) c#(c(d(d(x1)))) -> b#(b(d(d(x1)))) -> b#(b(b(b(b(b(x1)))))) -> b#(a(a(x1))) c#(c(d(d(x1)))) -> b#(b(d(d(x1)))) -> b#(b(d(d(b(b(x1)))))) -> b#(b(d(d(c(c(x1)))))) c#(c(d(d(x1)))) -> b#(b(d(d(x1)))) -> b#(b(d(d(b(b(x1)))))) -> b#(d(d(c(c(x1))))) c#(c(d(d(x1)))) -> b#(b(d(d(x1)))) -> b#(b(d(d(b(b(x1)))))) -> c#(c(x1)) c#(c(d(d(x1)))) -> b#(b(d(d(x1)))) -> b#(b(d(d(b(b(x1)))))) -> c#(x1) c#(c(d(d(x1)))) -> b#(b(x1)) -> b#(b(b(b(b(b(x1)))))) -> c#(c(b(b(a(a(x1)))))) c#(c(d(d(x1)))) -> b#(b(x1)) -> b#(b(b(b(b(b(x1)))))) -> c#(b(b(a(a(x1))))) c#(c(d(d(x1)))) -> b#(b(x1)) -> b#(b(b(b(b(b(x1)))))) -> b#(b(a(a(x1)))) c#(c(d(d(x1)))) -> b#(b(x1)) -> b#(b(b(b(b(b(x1)))))) -> b#(a(a(x1))) c#(c(d(d(x1)))) -> b#(b(x1)) -> b#(b(d(d(b(b(x1)))))) -> b#(b(d(d(c(c(x1)))))) c#(c(d(d(x1)))) -> b#(b(x1)) -> b#(b(d(d(b(b(x1)))))) -> b#(d(d(c(c(x1))))) c#(c(d(d(x1)))) -> b#(b(x1)) -> b#(b(d(d(b(b(x1)))))) -> c#(c(x1)) c#(c(d(d(x1)))) -> b#(b(x1)) -> b#(b(d(d(b(b(x1)))))) -> c#(x1) c#(c(d(d(x1)))) -> b#(x1) -> b#(b(b(b(b(b(x1)))))) -> c#(c(b(b(a(a(x1)))))) c#(c(d(d(x1)))) -> b#(x1) -> b#(b(b(b(b(b(x1)))))) -> c#(b(b(a(a(x1))))) c#(c(d(d(x1)))) -> b#(x1) -> b#(b(b(b(b(b(x1)))))) -> b#(b(a(a(x1)))) c#(c(d(d(x1)))) -> b#(x1) -> b#(b(b(b(b(b(x1)))))) -> b#(a(a(x1))) c#(c(d(d(x1)))) -> b#(x1) -> b#(b(d(d(b(b(x1)))))) -> b#(b(d(d(c(c(x1)))))) c#(c(d(d(x1)))) -> b#(x1) -> b#(b(d(d(b(b(x1)))))) -> b#(d(d(c(c(x1))))) c#(c(d(d(x1)))) -> b#(x1) -> b#(b(d(d(b(b(x1)))))) -> c#(c(x1)) c#(c(d(d(x1)))) -> b#(x1) -> b#(b(d(d(b(b(x1)))))) -> c#(x1) b#(b(d(d(b(b(x1)))))) -> c#(c(x1)) -> c#(c(a(a(d(d(x1)))))) -> b#(b(b(b(x1)))) b#(b(d(d(b(b(x1)))))) -> c#(c(x1)) -> c#(c(a(a(d(d(x1)))))) -> b#(b(b(x1))) b#(b(d(d(b(b(x1)))))) -> c#(c(x1)) -> c#(c(a(a(d(d(x1)))))) -> b#(b(x1)) b#(b(d(d(b(b(x1)))))) -> c#(c(x1)) -> c#(c(a(a(d(d(x1)))))) -> b#(x1) b#(b(d(d(b(b(x1)))))) -> c#(c(x1)) -> c#(c(d(d(x1)))) -> b#(b(d(d(x1)))) b#(b(d(d(b(b(x1)))))) -> c#(c(x1)) -> c#(c(d(d(x1)))) -> b#(d(d(x1))) b#(b(d(d(b(b(x1)))))) -> c#(c(x1)) -> c#(c(d(d(x1)))) -> b#(b(x1)) b#(b(d(d(b(b(x1)))))) -> c#(c(x1)) -> c#(c(d(d(x1)))) -> b#(x1) b#(b(d(d(b(b(x1)))))) -> c#(x1) -> c#(c(a(a(d(d(x1)))))) -> b#(b(b(b(x1)))) b#(b(d(d(b(b(x1)))))) -> c#(x1) -> c#(c(a(a(d(d(x1)))))) -> b#(b(b(x1))) b#(b(d(d(b(b(x1)))))) -> c#(x1) -> c#(c(a(a(d(d(x1)))))) -> b#(b(x1)) b#(b(d(d(b(b(x1)))))) -> c#(x1) -> c#(c(a(a(d(d(x1)))))) -> b#(x1) b#(b(d(d(b(b(x1)))))) -> c#(x1) -> c#(c(d(d(x1)))) -> b#(b(d(d(x1)))) b#(b(d(d(b(b(x1)))))) -> c#(x1) -> c#(c(d(d(x1)))) -> b#(d(d(x1))) b#(b(d(d(b(b(x1)))))) -> c#(x1) -> c#(c(d(d(x1)))) -> b#(b(x1)) b#(b(d(d(b(b(x1)))))) -> c#(x1) -> c#(c(d(d(x1)))) -> b#(x1) b#(b(d(d(b(b(x1)))))) -> b#(d(d(c(c(x1))))) -> b#(b(b(b(b(b(x1)))))) -> c#(c(b(b(a(a(x1)))))) b#(b(d(d(b(b(x1)))))) -> b#(d(d(c(c(x1))))) -> b#(b(b(b(b(b(x1)))))) -> c#(b(b(a(a(x1))))) b#(b(d(d(b(b(x1)))))) -> b#(d(d(c(c(x1))))) -> b#(b(b(b(b(b(x1)))))) -> b#(b(a(a(x1)))) b#(b(d(d(b(b(x1)))))) -> b#(d(d(c(c(x1))))) -> b#(b(b(b(b(b(x1)))))) -> b#(a(a(x1))) b#(b(d(d(b(b(x1)))))) -> b#(d(d(c(c(x1))))) -> b#(b(d(d(b(b(x1)))))) -> b#(b(d(d(c(c(x1)))))) b#(b(d(d(b(b(x1)))))) -> b#(d(d(c(c(x1))))) -> b#(b(d(d(b(b(x1)))))) -> b#(d(d(c(c(x1))))) b#(b(d(d(b(b(x1)))))) -> b#(d(d(c(c(x1))))) -> b#(b(d(d(b(b(x1)))))) -> c#(c(x1)) b#(b(d(d(b(b(x1)))))) -> b#(d(d(c(c(x1))))) -> b#(b(d(d(b(b(x1)))))) -> c#(x1) b#(b(d(d(b(b(x1)))))) -> b#(b(d(d(c(c(x1)))))) -> b#(b(b(b(b(b(x1)))))) -> c#(c(b(b(a(a(x1)))))) b#(b(d(d(b(b(x1)))))) -> b#(b(d(d(c(c(x1)))))) -> b#(b(b(b(b(b(x1)))))) -> c#(b(b(a(a(x1))))) b#(b(d(d(b(b(x1)))))) -> b#(b(d(d(c(c(x1)))))) -> b#(b(b(b(b(b(x1)))))) -> b#(b(a(a(x1)))) b#(b(d(d(b(b(x1)))))) -> b#(b(d(d(c(c(x1)))))) -> b#(b(b(b(b(b(x1)))))) -> b#(a(a(x1))) b#(b(d(d(b(b(x1)))))) -> b#(b(d(d(c(c(x1)))))) -> b#(b(d(d(b(b(x1)))))) -> b#(b(d(d(c(c(x1)))))) b#(b(d(d(b(b(x1)))))) -> b#(b(d(d(c(c(x1)))))) -> b#(b(d(d(b(b(x1)))))) -> b#(d(d(c(c(x1))))) b#(b(d(d(b(b(x1)))))) -> b#(b(d(d(c(c(x1)))))) -> b#(b(d(d(b(b(x1)))))) -> c#(c(x1)) b#(b(d(d(b(b(x1)))))) -> b#(b(d(d(c(c(x1)))))) -> b#(b(d(d(b(b(x1)))))) -> c#(x1) b#(b(b(b(b(b(x1)))))) -> c#(c(b(b(a(a(x1)))))) -> c#(c(a(a(d(d(x1)))))) -> b#(b(b(b(x1)))) b#(b(b(b(b(b(x1)))))) -> c#(c(b(b(a(a(x1)))))) -> c#(c(a(a(d(d(x1)))))) -> b#(b(b(x1))) b#(b(b(b(b(b(x1)))))) -> c#(c(b(b(a(a(x1)))))) -> c#(c(a(a(d(d(x1)))))) -> b#(b(x1)) b#(b(b(b(b(b(x1)))))) -> c#(c(b(b(a(a(x1)))))) -> c#(c(a(a(d(d(x1)))))) -> b#(x1) b#(b(b(b(b(b(x1)))))) -> c#(c(b(b(a(a(x1)))))) -> c#(c(d(d(x1)))) -> b#(b(d(d(x1)))) b#(b(b(b(b(b(x1)))))) -> c#(c(b(b(a(a(x1)))))) -> c#(c(d(d(x1)))) -> b#(d(d(x1))) b#(b(b(b(b(b(x1)))))) -> c#(c(b(b(a(a(x1)))))) -> c#(c(d(d(x1)))) -> b#(b(x1)) b#(b(b(b(b(b(x1)))))) -> c#(c(b(b(a(a(x1)))))) -> c#(c(d(d(x1)))) -> b#(x1) b#(b(b(b(b(b(x1)))))) -> c#(b(b(a(a(x1))))) -> c#(c(a(a(d(d(x1)))))) -> b#(b(b(b(x1)))) b#(b(b(b(b(b(x1)))))) -> c#(b(b(a(a(x1))))) -> c#(c(a(a(d(d(x1)))))) -> b#(b(b(x1))) b#(b(b(b(b(b(x1)))))) -> c#(b(b(a(a(x1))))) -> c#(c(a(a(d(d(x1)))))) -> b#(b(x1)) b#(b(b(b(b(b(x1)))))) -> c#(b(b(a(a(x1))))) -> c#(c(a(a(d(d(x1)))))) -> b#(x1) b#(b(b(b(b(b(x1)))))) -> c#(b(b(a(a(x1))))) -> c#(c(d(d(x1)))) -> b#(b(d(d(x1)))) b#(b(b(b(b(b(x1)))))) -> c#(b(b(a(a(x1))))) -> c#(c(d(d(x1)))) -> b#(d(d(x1))) b#(b(b(b(b(b(x1)))))) -> c#(b(b(a(a(x1))))) -> c#(c(d(d(x1)))) -> b#(b(x1)) b#(b(b(b(b(b(x1)))))) -> c#(b(b(a(a(x1))))) -> c#(c(d(d(x1)))) -> b#(x1) b#(b(b(b(b(b(x1)))))) -> b#(a(a(x1))) -> b#(b(b(b(b(b(x1)))))) -> c#(c(b(b(a(a(x1)))))) b#(b(b(b(b(b(x1)))))) -> b#(a(a(x1))) -> b#(b(b(b(b(b(x1)))))) -> c#(b(b(a(a(x1))))) b#(b(b(b(b(b(x1)))))) -> b#(a(a(x1))) -> b#(b(b(b(b(b(x1)))))) -> b#(b(a(a(x1)))) b#(b(b(b(b(b(x1)))))) -> b#(a(a(x1))) -> b#(b(b(b(b(b(x1)))))) -> b#(a(a(x1))) b#(b(b(b(b(b(x1)))))) -> b#(a(a(x1))) -> b#(b(d(d(b(b(x1)))))) -> b#(b(d(d(c(c(x1)))))) b#(b(b(b(b(b(x1)))))) -> b#(a(a(x1))) -> b#(b(d(d(b(b(x1)))))) -> b#(d(d(c(c(x1))))) b#(b(b(b(b(b(x1)))))) -> b#(a(a(x1))) -> b#(b(d(d(b(b(x1)))))) -> c#(c(x1)) b#(b(b(b(b(b(x1)))))) -> b#(a(a(x1))) -> b#(b(d(d(b(b(x1)))))) -> c#(x1) b#(b(b(b(b(b(x1)))))) -> b#(b(a(a(x1)))) -> b#(b(b(b(b(b(x1)))))) -> c#(c(b(b(a(a(x1)))))) b#(b(b(b(b(b(x1)))))) -> b#(b(a(a(x1)))) -> b#(b(b(b(b(b(x1)))))) -> c#(b(b(a(a(x1))))) b#(b(b(b(b(b(x1)))))) -> b#(b(a(a(x1)))) -> b#(b(b(b(b(b(x1)))))) -> b#(b(a(a(x1)))) b#(b(b(b(b(b(x1)))))) -> b#(b(a(a(x1)))) -> b#(b(b(b(b(b(x1)))))) -> b#(a(a(x1))) b#(b(b(b(b(b(x1)))))) -> b#(b(a(a(x1)))) -> b#(b(d(d(b(b(x1)))))) -> b#(b(d(d(c(c(x1)))))) b#(b(b(b(b(b(x1)))))) -> b#(b(a(a(x1)))) -> b#(b(d(d(b(b(x1)))))) -> b#(d(d(c(c(x1))))) b#(b(b(b(b(b(x1)))))) -> b#(b(a(a(x1)))) -> b#(b(d(d(b(b(x1)))))) -> c#(c(x1)) b#(b(b(b(b(b(x1)))))) -> b#(b(a(a(x1)))) -> b#(b(d(d(b(b(x1)))))) -> c#(x1) EDG Processor: DPs: b#(b(d(d(b(b(x1)))))) -> c#(x1) b#(b(d(d(b(b(x1)))))) -> c#(c(x1)) b#(b(d(d(b(b(x1)))))) -> b#(d(d(c(c(x1))))) b#(b(d(d(b(b(x1)))))) -> b#(b(d(d(c(c(x1)))))) b#(b(b(b(b(b(x1)))))) -> b#(a(a(x1))) b#(b(b(b(b(b(x1)))))) -> b#(b(a(a(x1)))) b#(b(b(b(b(b(x1)))))) -> c#(b(b(a(a(x1))))) b#(b(b(b(b(b(x1)))))) -> c#(c(b(b(a(a(x1)))))) c#(c(d(d(x1)))) -> b#(x1) c#(c(d(d(x1)))) -> b#(b(x1)) c#(c(d(d(x1)))) -> b#(d(d(x1))) c#(c(d(d(x1)))) -> b#(b(d(d(x1)))) c#(c(a(a(d(d(x1)))))) -> b#(x1) c#(c(a(a(d(d(x1)))))) -> b#(b(x1)) c#(c(a(a(d(d(x1)))))) -> b#(b(b(x1))) c#(c(a(a(d(d(x1)))))) -> b#(b(b(b(x1)))) TRS: b(b(d(d(b(b(x1)))))) -> b(b(d(d(c(c(x1)))))) b(b(b(b(b(b(x1)))))) -> c(c(b(b(a(a(x1)))))) c(c(d(d(x1)))) -> d(d(b(b(x1)))) c(c(d(d(x1)))) -> d(d(b(b(d(d(x1)))))) c(c(a(a(d(d(x1)))))) -> b(b(b(b(x1)))) graph: c#(c(a(a(d(d(x1)))))) -> b#(b(b(b(x1)))) -> b#(b(d(d(b(b(x1)))))) -> c#(x1) c#(c(a(a(d(d(x1)))))) -> b#(b(b(b(x1)))) -> b#(b(d(d(b(b(x1)))))) -> c#(c(x1)) c#(c(a(a(d(d(x1)))))) -> b#(b(b(b(x1)))) -> b#(b(d(d(b(b(x1)))))) -> b#(d(d(c(c(x1))))) c#(c(a(a(d(d(x1)))))) -> b#(b(b(b(x1)))) -> b#(b(d(d(b(b(x1)))))) -> b#(b(d(d(c(c(x1)))))) c#(c(a(a(d(d(x1)))))) -> b#(b(b(b(x1)))) -> b#(b(b(b(b(b(x1)))))) -> b#(a(a(x1))) c#(c(a(a(d(d(x1)))))) -> b#(b(b(b(x1)))) -> b#(b(b(b(b(b(x1)))))) -> b#(b(a(a(x1)))) c#(c(a(a(d(d(x1)))))) -> b#(b(b(b(x1)))) -> b#(b(b(b(b(b(x1)))))) -> c#(b(b(a(a(x1))))) c#(c(a(a(d(d(x1)))))) -> b#(b(b(b(x1)))) -> b#(b(b(b(b(b(x1)))))) -> c#(c(b(b(a(a(x1)))))) c#(c(a(a(d(d(x1)))))) -> b#(b(b(x1))) -> b#(b(d(d(b(b(x1)))))) -> c#(x1) c#(c(a(a(d(d(x1)))))) -> b#(b(b(x1))) -> b#(b(d(d(b(b(x1)))))) -> c#(c(x1)) c#(c(a(a(d(d(x1)))))) -> b#(b(b(x1))) -> b#(b(d(d(b(b(x1)))))) -> b#(d(d(c(c(x1))))) c#(c(a(a(d(d(x1)))))) -> b#(b(b(x1))) -> b#(b(d(d(b(b(x1)))))) -> b#(b(d(d(c(c(x1)))))) c#(c(a(a(d(d(x1)))))) -> b#(b(b(x1))) -> b#(b(b(b(b(b(x1)))))) -> b#(a(a(x1))) c#(c(a(a(d(d(x1)))))) -> b#(b(b(x1))) -> b#(b(b(b(b(b(x1)))))) -> b#(b(a(a(x1)))) c#(c(a(a(d(d(x1)))))) -> b#(b(b(x1))) -> b#(b(b(b(b(b(x1)))))) -> c#(b(b(a(a(x1))))) c#(c(a(a(d(d(x1)))))) -> b#(b(b(x1))) -> b#(b(b(b(b(b(x1)))))) -> c#(c(b(b(a(a(x1)))))) c#(c(a(a(d(d(x1)))))) -> b#(b(x1)) -> b#(b(d(d(b(b(x1)))))) -> c#(x1) c#(c(a(a(d(d(x1)))))) -> b#(b(x1)) -> b#(b(d(d(b(b(x1)))))) -> c#(c(x1)) c#(c(a(a(d(d(x1)))))) -> b#(b(x1)) -> b#(b(d(d(b(b(x1)))))) -> b#(d(d(c(c(x1))))) c#(c(a(a(d(d(x1)))))) -> b#(b(x1)) -> b#(b(d(d(b(b(x1)))))) -> b#(b(d(d(c(c(x1)))))) c#(c(a(a(d(d(x1)))))) -> b#(b(x1)) -> b#(b(b(b(b(b(x1)))))) -> b#(a(a(x1))) c#(c(a(a(d(d(x1)))))) -> b#(b(x1)) -> b#(b(b(b(b(b(x1)))))) -> b#(b(a(a(x1)))) c#(c(a(a(d(d(x1)))))) -> b#(b(x1)) -> b#(b(b(b(b(b(x1)))))) -> c#(b(b(a(a(x1))))) c#(c(a(a(d(d(x1)))))) -> b#(b(x1)) -> b#(b(b(b(b(b(x1)))))) -> c#(c(b(b(a(a(x1)))))) c#(c(a(a(d(d(x1)))))) -> b#(x1) -> b#(b(d(d(b(b(x1)))))) -> c#(x1) c#(c(a(a(d(d(x1)))))) -> b#(x1) -> b#(b(d(d(b(b(x1)))))) -> c#(c(x1)) c#(c(a(a(d(d(x1)))))) -> b#(x1) -> b#(b(d(d(b(b(x1)))))) -> b#(d(d(c(c(x1))))) c#(c(a(a(d(d(x1)))))) -> b#(x1) -> b#(b(d(d(b(b(x1)))))) -> b#(b(d(d(c(c(x1)))))) c#(c(a(a(d(d(x1)))))) -> b#(x1) -> b#(b(b(b(b(b(x1)))))) -> b#(a(a(x1))) c#(c(a(a(d(d(x1)))))) -> b#(x1) -> b#(b(b(b(b(b(x1)))))) -> b#(b(a(a(x1)))) c#(c(a(a(d(d(x1)))))) -> b#(x1) -> b#(b(b(b(b(b(x1)))))) -> c#(b(b(a(a(x1))))) c#(c(a(a(d(d(x1)))))) -> b#(x1) -> b#(b(b(b(b(b(x1)))))) -> c#(c(b(b(a(a(x1)))))) c#(c(d(d(x1)))) -> b#(b(d(d(x1)))) -> b#(b(d(d(b(b(x1)))))) -> c#(x1) c#(c(d(d(x1)))) -> b#(b(d(d(x1)))) -> b#(b(d(d(b(b(x1)))))) -> c#(c(x1)) c#(c(d(d(x1)))) -> b#(b(d(d(x1)))) -> b#(b(d(d(b(b(x1)))))) -> b#(d(d(c(c(x1))))) c#(c(d(d(x1)))) -> b#(b(d(d(x1)))) -> b#(b(d(d(b(b(x1)))))) -> b#(b(d(d(c(c(x1)))))) c#(c(d(d(x1)))) -> b#(b(x1)) -> b#(b(d(d(b(b(x1)))))) -> c#(x1) c#(c(d(d(x1)))) -> b#(b(x1)) -> b#(b(d(d(b(b(x1)))))) -> c#(c(x1)) c#(c(d(d(x1)))) -> b#(b(x1)) -> b#(b(d(d(b(b(x1)))))) -> b#(d(d(c(c(x1))))) c#(c(d(d(x1)))) -> b#(b(x1)) -> b#(b(d(d(b(b(x1)))))) -> b#(b(d(d(c(c(x1)))))) c#(c(d(d(x1)))) -> b#(b(x1)) -> b#(b(b(b(b(b(x1)))))) -> b#(a(a(x1))) c#(c(d(d(x1)))) -> b#(b(x1)) -> b#(b(b(b(b(b(x1)))))) -> b#(b(a(a(x1)))) c#(c(d(d(x1)))) -> b#(b(x1)) -> b#(b(b(b(b(b(x1)))))) -> c#(b(b(a(a(x1))))) c#(c(d(d(x1)))) -> b#(b(x1)) -> b#(b(b(b(b(b(x1)))))) -> c#(c(b(b(a(a(x1)))))) c#(c(d(d(x1)))) -> b#(x1) -> b#(b(d(d(b(b(x1)))))) -> c#(x1) c#(c(d(d(x1)))) -> b#(x1) -> b#(b(d(d(b(b(x1)))))) -> c#(c(x1)) c#(c(d(d(x1)))) -> b#(x1) -> b#(b(d(d(b(b(x1)))))) -> b#(d(d(c(c(x1))))) c#(c(d(d(x1)))) -> b#(x1) -> b#(b(d(d(b(b(x1)))))) -> b#(b(d(d(c(c(x1)))))) c#(c(d(d(x1)))) -> b#(x1) -> b#(b(b(b(b(b(x1)))))) -> b#(a(a(x1))) c#(c(d(d(x1)))) -> b#(x1) -> b#(b(b(b(b(b(x1)))))) -> b#(b(a(a(x1)))) c#(c(d(d(x1)))) -> b#(x1) -> b#(b(b(b(b(b(x1)))))) -> c#(b(b(a(a(x1))))) c#(c(d(d(x1)))) -> b#(x1) -> b#(b(b(b(b(b(x1)))))) -> c#(c(b(b(a(a(x1)))))) b#(b(d(d(b(b(x1)))))) -> c#(c(x1)) -> c#(c(d(d(x1)))) -> b#(x1) b#(b(d(d(b(b(x1)))))) -> c#(c(x1)) -> c#(c(d(d(x1)))) -> b#(b(x1)) b#(b(d(d(b(b(x1)))))) -> c#(c(x1)) -> c#(c(d(d(x1)))) -> b#(d(d(x1))) b#(b(d(d(b(b(x1)))))) -> c#(c(x1)) -> c#(c(d(d(x1)))) -> b#(b(d(d(x1)))) b#(b(d(d(b(b(x1)))))) -> c#(c(x1)) -> c#(c(a(a(d(d(x1)))))) -> b#(x1) b#(b(d(d(b(b(x1)))))) -> c#(c(x1)) -> c#(c(a(a(d(d(x1)))))) -> b#(b(x1)) b#(b(d(d(b(b(x1)))))) -> c#(c(x1)) -> c#(c(a(a(d(d(x1)))))) -> b#(b(b(x1))) b#(b(d(d(b(b(x1)))))) -> c#(c(x1)) -> c#(c(a(a(d(d(x1)))))) -> b#(b(b(b(x1)))) b#(b(d(d(b(b(x1)))))) -> c#(x1) -> c#(c(d(d(x1)))) -> b#(x1) b#(b(d(d(b(b(x1)))))) -> c#(x1) -> c#(c(d(d(x1)))) -> b#(b(x1)) b#(b(d(d(b(b(x1)))))) -> c#(x1) -> c#(c(d(d(x1)))) -> b#(d(d(x1))) b#(b(d(d(b(b(x1)))))) -> c#(x1) -> c#(c(d(d(x1)))) -> b#(b(d(d(x1)))) b#(b(d(d(b(b(x1)))))) -> c#(x1) -> c#(c(a(a(d(d(x1)))))) -> b#(x1) b#(b(d(d(b(b(x1)))))) -> c#(x1) -> c#(c(a(a(d(d(x1)))))) -> b#(b(x1)) b#(b(d(d(b(b(x1)))))) -> c#(x1) -> c#(c(a(a(d(d(x1)))))) -> b#(b(b(x1))) b#(b(d(d(b(b(x1)))))) -> c#(x1) -> c#(c(a(a(d(d(x1)))))) -> b#(b(b(b(x1)))) b#(b(d(d(b(b(x1)))))) -> b#(b(d(d(c(c(x1)))))) -> b#(b(d(d(b(b(x1)))))) -> c#(x1) b#(b(d(d(b(b(x1)))))) -> b#(b(d(d(c(c(x1)))))) -> b#(b(d(d(b(b(x1)))))) -> c#(c(x1)) b#(b(d(d(b(b(x1)))))) -> b#(b(d(d(c(c(x1)))))) -> b#(b(d(d(b(b(x1)))))) -> b#(d(d(c(c(x1))))) b#(b(d(d(b(b(x1)))))) -> b#(b(d(d(c(c(x1)))))) -> b#(b(d(d(b(b(x1)))))) -> b#(b(d(d(c(c(x1)))))) SCC Processor: #sccs: 1 #rules: 10 #arcs: 72/256 DPs: c#(c(a(a(d(d(x1)))))) -> b#(b(b(b(x1)))) b#(b(d(d(b(b(x1)))))) -> b#(b(d(d(c(c(x1)))))) b#(b(d(d(b(b(x1)))))) -> c#(c(x1)) c#(c(a(a(d(d(x1)))))) -> b#(b(b(x1))) b#(b(d(d(b(b(x1)))))) -> c#(x1) c#(c(a(a(d(d(x1)))))) -> b#(b(x1)) c#(c(a(a(d(d(x1)))))) -> b#(x1) c#(c(d(d(x1)))) -> b#(b(d(d(x1)))) c#(c(d(d(x1)))) -> b#(b(x1)) c#(c(d(d(x1)))) -> b#(x1) TRS: b(b(d(d(b(b(x1)))))) -> b(b(d(d(c(c(x1)))))) b(b(b(b(b(b(x1)))))) -> c(c(b(b(a(a(x1)))))) c(c(d(d(x1)))) -> d(d(b(b(x1)))) c(c(d(d(x1)))) -> d(d(b(b(d(d(x1)))))) c(c(a(a(d(d(x1)))))) -> b(b(b(b(x1)))) Arctic Interpretation Processor: dimension: 1 interpretation: [c#](x0) = x0, [b#](x0) = x0, [a](x0) = 1x0, [c](x0) = 1x0, [d](x0) = x0, [b](x0) = 1x0 orientation: c#(c(a(a(d(d(x1)))))) = 3x1 >= 3x1 = b#(b(b(b(x1)))) b#(b(d(d(b(b(x1)))))) = 3x1 >= 3x1 = b#(b(d(d(c(c(x1)))))) b#(b(d(d(b(b(x1)))))) = 3x1 >= 1x1 = c#(c(x1)) c#(c(a(a(d(d(x1)))))) = 3x1 >= 2x1 = b#(b(b(x1))) b#(b(d(d(b(b(x1)))))) = 3x1 >= x1 = c#(x1) c#(c(a(a(d(d(x1)))))) = 3x1 >= 1x1 = b#(b(x1)) c#(c(a(a(d(d(x1)))))) = 3x1 >= x1 = b#(x1) c#(c(d(d(x1)))) = 1x1 >= 1x1 = b#(b(d(d(x1)))) c#(c(d(d(x1)))) = 1x1 >= 1x1 = b#(b(x1)) c#(c(d(d(x1)))) = 1x1 >= x1 = b#(x1) b(b(d(d(b(b(x1)))))) = 4x1 >= 4x1 = b(b(d(d(c(c(x1)))))) b(b(b(b(b(b(x1)))))) = 6x1 >= 6x1 = c(c(b(b(a(a(x1)))))) c(c(d(d(x1)))) = 2x1 >= 2x1 = d(d(b(b(x1)))) c(c(d(d(x1)))) = 2x1 >= 2x1 = d(d(b(b(d(d(x1)))))) c(c(a(a(d(d(x1)))))) = 4x1 >= 4x1 = b(b(b(b(x1)))) problem: DPs: c#(c(a(a(d(d(x1)))))) -> b#(b(b(b(x1)))) b#(b(d(d(b(b(x1)))))) -> b#(b(d(d(c(c(x1)))))) c#(c(d(d(x1)))) -> b#(b(d(d(x1)))) c#(c(d(d(x1)))) -> b#(b(x1)) TRS: b(b(d(d(b(b(x1)))))) -> b(b(d(d(c(c(x1)))))) b(b(b(b(b(b(x1)))))) -> c(c(b(b(a(a(x1)))))) c(c(d(d(x1)))) -> d(d(b(b(x1)))) c(c(d(d(x1)))) -> d(d(b(b(d(d(x1)))))) c(c(a(a(d(d(x1)))))) -> b(b(b(b(x1)))) EDG Processor: DPs: c#(c(a(a(d(d(x1)))))) -> b#(b(b(b(x1)))) b#(b(d(d(b(b(x1)))))) -> b#(b(d(d(c(c(x1)))))) c#(c(d(d(x1)))) -> b#(b(d(d(x1)))) c#(c(d(d(x1)))) -> b#(b(x1)) TRS: b(b(d(d(b(b(x1)))))) -> b(b(d(d(c(c(x1)))))) b(b(b(b(b(b(x1)))))) -> c(c(b(b(a(a(x1)))))) c(c(d(d(x1)))) -> d(d(b(b(x1)))) c(c(d(d(x1)))) -> d(d(b(b(d(d(x1)))))) c(c(a(a(d(d(x1)))))) -> b(b(b(b(x1)))) graph: c#(c(a(a(d(d(x1)))))) -> b#(b(b(b(x1)))) -> b#(b(d(d(b(b(x1)))))) -> b#(b(d(d(c(c(x1)))))) c#(c(d(d(x1)))) -> b#(b(d(d(x1)))) -> b#(b(d(d(b(b(x1)))))) -> b#(b(d(d(c(c(x1)))))) c#(c(d(d(x1)))) -> b#(b(x1)) -> b#(b(d(d(b(b(x1)))))) -> b#(b(d(d(c(c(x1)))))) b#(b(d(d(b(b(x1)))))) -> b#(b(d(d(c(c(x1)))))) -> b#(b(d(d(b(b(x1)))))) -> b#(b(d(d(c(c(x1)))))) CDG Processor: DPs: c#(c(a(a(d(d(x1)))))) -> b#(b(b(b(x1)))) b#(b(d(d(b(b(x1)))))) -> b#(b(d(d(c(c(x1)))))) c#(c(d(d(x1)))) -> b#(b(d(d(x1)))) c#(c(d(d(x1)))) -> b#(b(x1)) TRS: b(b(d(d(b(b(x1)))))) -> b(b(d(d(c(c(x1)))))) b(b(b(b(b(b(x1)))))) -> c(c(b(b(a(a(x1)))))) c(c(d(d(x1)))) -> d(d(b(b(x1)))) c(c(d(d(x1)))) -> d(d(b(b(d(d(x1)))))) c(c(a(a(d(d(x1)))))) -> b(b(b(b(x1)))) graph: c#(c(d(d(x1)))) -> b#(b(d(d(x1)))) -> b#(b(d(d(b(b(x1)))))) -> b#(b(d(d(c(c(x1)))))) c#(c(d(d(x1)))) -> b#(b(x1)) -> b#(b(d(d(b(b(x1)))))) -> b#(b(d(d(c(c(x1)))))) b#(b(d(d(b(b(x1)))))) -> b#(b(d(d(c(c(x1)))))) -> b#(b(d(d(b(b(x1)))))) -> b#(b(d(d(c(c(x1)))))) SCC Processor: #sccs: 1 #rules: 1 #arcs: 3/16 DPs: b#(b(d(d(b(b(x1)))))) -> b#(b(d(d(c(c(x1)))))) TRS: b(b(d(d(b(b(x1)))))) -> b(b(d(d(c(c(x1)))))) b(b(b(b(b(b(x1)))))) -> c(c(b(b(a(a(x1)))))) c(c(d(d(x1)))) -> d(d(b(b(x1)))) c(c(d(d(x1)))) -> d(d(b(b(d(d(x1)))))) c(c(a(a(d(d(x1)))))) -> b(b(b(b(x1)))) Matrix Interpretation Processor: dim=3 interpretation: [b#](x0) = [0 0 1]x0 + [1], [0 0 0] [1] [a](x0) = [0 1 0]x0 + [0] [0 1 0] [1], [1 0 1] [c](x0) = [0 0 1]x0 [1 0 0] , [0 0 1] [0] [d](x0) = [1 0 0]x0 + [0] [0 1 0] [1], [0 0 0] [0] [b](x0) = [0 0 1]x0 + [1] [1 0 0] [0] orientation: b#(b(d(d(b(b(x1)))))) = [1 0 0]x1 + [3] >= [1 0 0]x1 + [2] = b#(b(d(d(c(c(x1)))))) [0 0 0] [0] [0 0 0] [0] b(b(d(d(b(b(x1)))))) = [1 0 0]x1 + [3] >= [1 0 0]x1 + [2] = b(b(d(d(c(c(x1)))))) [0 0 0] [0] [0 0 0] [0] [0] [0] b(b(b(b(b(b(x1)))))) = [1] >= [0] = c(c(b(b(a(a(x1)))))) [0] [0] [1 2 0] [3] [1 0 0] [2] c(c(d(d(x1)))) = [0 1 0]x1 + [1] >= [0 0 0]x1 + [0] = d(d(b(b(x1)))) [1 1 0] [2] [0 0 0] [1] [1 2 0] [3] [0 1 0] [3] c(c(d(d(x1)))) = [0 1 0]x1 + [1] >= [0 0 0]x1 + [0] = d(d(b(b(d(d(x1)))))) [1 1 0] [2] [0 0 0] [1] [0 0 1] [3] [0] c(c(a(a(d(d(x1)))))) = [0 0 0]x1 + [1] >= [1] = b(b(b(b(x1)))) [0 0 1] [2] [0] problem: DPs: TRS: b(b(d(d(b(b(x1)))))) -> b(b(d(d(c(c(x1)))))) b(b(b(b(b(b(x1)))))) -> c(c(b(b(a(a(x1)))))) c(c(d(d(x1)))) -> d(d(b(b(x1)))) c(c(d(d(x1)))) -> d(d(b(b(d(d(x1)))))) c(c(a(a(d(d(x1)))))) -> b(b(b(b(x1)))) Qed