YES Problem: a(a(a(a(b(b(x1)))))) -> b(b(a(a(b(b(x1)))))) b(b(a(a(x1)))) -> a(a(b(b(b(b(x1)))))) b(b(c(c(a(a(x1)))))) -> c(c(c(c(a(a(a(a(b(b(x1)))))))))) Proof: DP Processor: DPs: a#(a(a(a(b(b(x1)))))) -> b#(a(a(b(b(x1))))) a#(a(a(a(b(b(x1)))))) -> b#(b(a(a(b(b(x1)))))) b#(b(a(a(x1)))) -> b#(x1) b#(b(a(a(x1)))) -> b#(b(x1)) b#(b(a(a(x1)))) -> b#(b(b(x1))) b#(b(a(a(x1)))) -> b#(b(b(b(x1)))) b#(b(a(a(x1)))) -> a#(b(b(b(b(x1))))) b#(b(a(a(x1)))) -> a#(a(b(b(b(b(x1)))))) b#(b(c(c(a(a(x1)))))) -> b#(x1) b#(b(c(c(a(a(x1)))))) -> b#(b(x1)) b#(b(c(c(a(a(x1)))))) -> a#(b(b(x1))) b#(b(c(c(a(a(x1)))))) -> a#(a(b(b(x1)))) b#(b(c(c(a(a(x1)))))) -> a#(a(a(b(b(x1))))) b#(b(c(c(a(a(x1)))))) -> a#(a(a(a(b(b(x1)))))) TRS: a(a(a(a(b(b(x1)))))) -> b(b(a(a(b(b(x1)))))) b(b(a(a(x1)))) -> a(a(b(b(b(b(x1)))))) b(b(c(c(a(a(x1)))))) -> c(c(c(c(a(a(a(a(b(b(x1)))))))))) TDG Processor: DPs: a#(a(a(a(b(b(x1)))))) -> b#(a(a(b(b(x1))))) a#(a(a(a(b(b(x1)))))) -> b#(b(a(a(b(b(x1)))))) b#(b(a(a(x1)))) -> b#(x1) b#(b(a(a(x1)))) -> b#(b(x1)) b#(b(a(a(x1)))) -> b#(b(b(x1))) b#(b(a(a(x1)))) -> b#(b(b(b(x1)))) b#(b(a(a(x1)))) -> a#(b(b(b(b(x1))))) b#(b(a(a(x1)))) -> a#(a(b(b(b(b(x1)))))) b#(b(c(c(a(a(x1)))))) -> b#(x1) b#(b(c(c(a(a(x1)))))) -> b#(b(x1)) b#(b(c(c(a(a(x1)))))) -> a#(b(b(x1))) b#(b(c(c(a(a(x1)))))) -> a#(a(b(b(x1)))) b#(b(c(c(a(a(x1)))))) -> a#(a(a(b(b(x1))))) b#(b(c(c(a(a(x1)))))) -> a#(a(a(a(b(b(x1)))))) TRS: a(a(a(a(b(b(x1)))))) -> b(b(a(a(b(b(x1)))))) b(b(a(a(x1)))) -> a(a(b(b(b(b(x1)))))) b(b(c(c(a(a(x1)))))) -> c(c(c(c(a(a(a(a(b(b(x1)))))))))) graph: b#(b(c(c(a(a(x1)))))) -> b#(b(x1)) -> b#(b(c(c(a(a(x1)))))) -> a#(a(a(a(b(b(x1)))))) b#(b(c(c(a(a(x1)))))) -> b#(b(x1)) -> b#(b(c(c(a(a(x1)))))) -> a#(a(a(b(b(x1))))) b#(b(c(c(a(a(x1)))))) -> b#(b(x1)) -> b#(b(c(c(a(a(x1)))))) -> a#(a(b(b(x1)))) b#(b(c(c(a(a(x1)))))) -> b#(b(x1)) -> b#(b(c(c(a(a(x1)))))) -> a#(b(b(x1))) b#(b(c(c(a(a(x1)))))) -> b#(b(x1)) -> b#(b(c(c(a(a(x1)))))) -> b#(b(x1)) b#(b(c(c(a(a(x1)))))) -> b#(b(x1)) -> b#(b(c(c(a(a(x1)))))) -> b#(x1) b#(b(c(c(a(a(x1)))))) -> b#(b(x1)) -> b#(b(a(a(x1)))) -> a#(a(b(b(b(b(x1)))))) b#(b(c(c(a(a(x1)))))) -> b#(b(x1)) -> b#(b(a(a(x1)))) -> a#(b(b(b(b(x1))))) b#(b(c(c(a(a(x1)))))) -> b#(b(x1)) -> b#(b(a(a(x1)))) -> b#(b(b(b(x1)))) b#(b(c(c(a(a(x1)))))) -> b#(b(x1)) -> b#(b(a(a(x1)))) -> b#(b(b(x1))) b#(b(c(c(a(a(x1)))))) -> b#(b(x1)) -> b#(b(a(a(x1)))) -> b#(b(x1)) b#(b(c(c(a(a(x1)))))) -> b#(b(x1)) -> b#(b(a(a(x1)))) -> b#(x1) b#(b(c(c(a(a(x1)))))) -> b#(x1) -> b#(b(c(c(a(a(x1)))))) -> a#(a(a(a(b(b(x1)))))) b#(b(c(c(a(a(x1)))))) -> b#(x1) -> b#(b(c(c(a(a(x1)))))) -> a#(a(a(b(b(x1))))) b#(b(c(c(a(a(x1)))))) -> b#(x1) -> b#(b(c(c(a(a(x1)))))) -> a#(a(b(b(x1)))) b#(b(c(c(a(a(x1)))))) -> b#(x1) -> b#(b(c(c(a(a(x1)))))) -> a#(b(b(x1))) b#(b(c(c(a(a(x1)))))) -> b#(x1) -> b#(b(c(c(a(a(x1)))))) -> b#(b(x1)) b#(b(c(c(a(a(x1)))))) -> b#(x1) -> b#(b(c(c(a(a(x1)))))) -> b#(x1) b#(b(c(c(a(a(x1)))))) -> b#(x1) -> b#(b(a(a(x1)))) -> a#(a(b(b(b(b(x1)))))) b#(b(c(c(a(a(x1)))))) -> b#(x1) -> b#(b(a(a(x1)))) -> a#(b(b(b(b(x1))))) b#(b(c(c(a(a(x1)))))) -> b#(x1) -> b#(b(a(a(x1)))) -> b#(b(b(b(x1)))) b#(b(c(c(a(a(x1)))))) -> b#(x1) -> b#(b(a(a(x1)))) -> b#(b(b(x1))) b#(b(c(c(a(a(x1)))))) -> b#(x1) -> b#(b(a(a(x1)))) -> b#(b(x1)) b#(b(c(c(a(a(x1)))))) -> b#(x1) -> b#(b(a(a(x1)))) -> b#(x1) b#(b(c(c(a(a(x1)))))) -> a#(a(a(a(b(b(x1)))))) -> a#(a(a(a(b(b(x1)))))) -> b#(b(a(a(b(b(x1)))))) b#(b(c(c(a(a(x1)))))) -> a#(a(a(a(b(b(x1)))))) -> a#(a(a(a(b(b(x1)))))) -> b#(a(a(b(b(x1))))) b#(b(c(c(a(a(x1)))))) -> a#(a(a(b(b(x1))))) -> a#(a(a(a(b(b(x1)))))) -> b#(b(a(a(b(b(x1)))))) b#(b(c(c(a(a(x1)))))) -> a#(a(a(b(b(x1))))) -> a#(a(a(a(b(b(x1)))))) -> b#(a(a(b(b(x1))))) b#(b(c(c(a(a(x1)))))) -> a#(a(b(b(x1)))) -> a#(a(a(a(b(b(x1)))))) -> b#(b(a(a(b(b(x1)))))) b#(b(c(c(a(a(x1)))))) -> a#(a(b(b(x1)))) -> a#(a(a(a(b(b(x1)))))) -> b#(a(a(b(b(x1))))) b#(b(c(c(a(a(x1)))))) -> a#(b(b(x1))) -> a#(a(a(a(b(b(x1)))))) -> b#(b(a(a(b(b(x1)))))) b#(b(c(c(a(a(x1)))))) -> a#(b(b(x1))) -> a#(a(a(a(b(b(x1)))))) -> b#(a(a(b(b(x1))))) b#(b(a(a(x1)))) -> b#(b(b(b(x1)))) -> b#(b(c(c(a(a(x1)))))) -> a#(a(a(a(b(b(x1)))))) b#(b(a(a(x1)))) -> b#(b(b(b(x1)))) -> b#(b(c(c(a(a(x1)))))) -> a#(a(a(b(b(x1))))) b#(b(a(a(x1)))) -> b#(b(b(b(x1)))) -> b#(b(c(c(a(a(x1)))))) -> a#(a(b(b(x1)))) b#(b(a(a(x1)))) -> b#(b(b(b(x1)))) -> b#(b(c(c(a(a(x1)))))) -> a#(b(b(x1))) b#(b(a(a(x1)))) -> b#(b(b(b(x1)))) -> b#(b(c(c(a(a(x1)))))) -> b#(b(x1)) b#(b(a(a(x1)))) -> b#(b(b(b(x1)))) -> b#(b(c(c(a(a(x1)))))) -> b#(x1) b#(b(a(a(x1)))) -> b#(b(b(b(x1)))) -> b#(b(a(a(x1)))) -> a#(a(b(b(b(b(x1)))))) b#(b(a(a(x1)))) -> b#(b(b(b(x1)))) -> b#(b(a(a(x1)))) -> a#(b(b(b(b(x1))))) b#(b(a(a(x1)))) -> b#(b(b(b(x1)))) -> b#(b(a(a(x1)))) -> b#(b(b(b(x1)))) b#(b(a(a(x1)))) -> b#(b(b(b(x1)))) -> b#(b(a(a(x1)))) -> b#(b(b(x1))) b#(b(a(a(x1)))) -> b#(b(b(b(x1)))) -> b#(b(a(a(x1)))) -> b#(b(x1)) b#(b(a(a(x1)))) -> b#(b(b(b(x1)))) -> b#(b(a(a(x1)))) -> b#(x1) b#(b(a(a(x1)))) -> b#(b(b(x1))) -> b#(b(c(c(a(a(x1)))))) -> a#(a(a(a(b(b(x1)))))) b#(b(a(a(x1)))) -> b#(b(b(x1))) -> b#(b(c(c(a(a(x1)))))) -> a#(a(a(b(b(x1))))) b#(b(a(a(x1)))) -> b#(b(b(x1))) -> b#(b(c(c(a(a(x1)))))) -> a#(a(b(b(x1)))) b#(b(a(a(x1)))) -> b#(b(b(x1))) -> b#(b(c(c(a(a(x1)))))) -> a#(b(b(x1))) b#(b(a(a(x1)))) -> b#(b(b(x1))) -> b#(b(c(c(a(a(x1)))))) -> b#(b(x1)) b#(b(a(a(x1)))) -> b#(b(b(x1))) -> b#(b(c(c(a(a(x1)))))) -> b#(x1) b#(b(a(a(x1)))) -> b#(b(b(x1))) -> b#(b(a(a(x1)))) -> a#(a(b(b(b(b(x1)))))) b#(b(a(a(x1)))) -> b#(b(b(x1))) -> b#(b(a(a(x1)))) -> a#(b(b(b(b(x1))))) b#(b(a(a(x1)))) -> b#(b(b(x1))) -> b#(b(a(a(x1)))) -> b#(b(b(b(x1)))) b#(b(a(a(x1)))) -> b#(b(b(x1))) -> b#(b(a(a(x1)))) -> b#(b(b(x1))) b#(b(a(a(x1)))) -> b#(b(b(x1))) -> b#(b(a(a(x1)))) -> b#(b(x1)) b#(b(a(a(x1)))) -> b#(b(b(x1))) -> b#(b(a(a(x1)))) -> b#(x1) b#(b(a(a(x1)))) -> b#(b(x1)) -> b#(b(c(c(a(a(x1)))))) -> a#(a(a(a(b(b(x1)))))) b#(b(a(a(x1)))) -> b#(b(x1)) -> b#(b(c(c(a(a(x1)))))) -> a#(a(a(b(b(x1))))) b#(b(a(a(x1)))) -> b#(b(x1)) -> b#(b(c(c(a(a(x1)))))) -> a#(a(b(b(x1)))) b#(b(a(a(x1)))) -> b#(b(x1)) -> b#(b(c(c(a(a(x1)))))) -> a#(b(b(x1))) b#(b(a(a(x1)))) -> b#(b(x1)) -> b#(b(c(c(a(a(x1)))))) -> b#(b(x1)) b#(b(a(a(x1)))) -> b#(b(x1)) -> b#(b(c(c(a(a(x1)))))) -> b#(x1) b#(b(a(a(x1)))) -> b#(b(x1)) -> b#(b(a(a(x1)))) -> a#(a(b(b(b(b(x1)))))) b#(b(a(a(x1)))) -> b#(b(x1)) -> b#(b(a(a(x1)))) -> a#(b(b(b(b(x1))))) b#(b(a(a(x1)))) -> b#(b(x1)) -> b#(b(a(a(x1)))) -> b#(b(b(b(x1)))) b#(b(a(a(x1)))) -> b#(b(x1)) -> b#(b(a(a(x1)))) -> b#(b(b(x1))) b#(b(a(a(x1)))) -> b#(b(x1)) -> b#(b(a(a(x1)))) -> b#(b(x1)) b#(b(a(a(x1)))) -> b#(b(x1)) -> b#(b(a(a(x1)))) -> b#(x1) b#(b(a(a(x1)))) -> b#(x1) -> b#(b(c(c(a(a(x1)))))) -> a#(a(a(a(b(b(x1)))))) b#(b(a(a(x1)))) -> b#(x1) -> b#(b(c(c(a(a(x1)))))) -> a#(a(a(b(b(x1))))) b#(b(a(a(x1)))) -> b#(x1) -> b#(b(c(c(a(a(x1)))))) -> a#(a(b(b(x1)))) b#(b(a(a(x1)))) -> b#(x1) -> b#(b(c(c(a(a(x1)))))) -> a#(b(b(x1))) b#(b(a(a(x1)))) -> b#(x1) -> b#(b(c(c(a(a(x1)))))) -> b#(b(x1)) b#(b(a(a(x1)))) -> b#(x1) -> b#(b(c(c(a(a(x1)))))) -> b#(x1) b#(b(a(a(x1)))) -> b#(x1) -> b#(b(a(a(x1)))) -> a#(a(b(b(b(b(x1)))))) b#(b(a(a(x1)))) -> b#(x1) -> b#(b(a(a(x1)))) -> a#(b(b(b(b(x1))))) b#(b(a(a(x1)))) -> b#(x1) -> b#(b(a(a(x1)))) -> b#(b(b(b(x1)))) b#(b(a(a(x1)))) -> b#(x1) -> b#(b(a(a(x1)))) -> b#(b(b(x1))) b#(b(a(a(x1)))) -> b#(x1) -> b#(b(a(a(x1)))) -> b#(b(x1)) b#(b(a(a(x1)))) -> b#(x1) -> b#(b(a(a(x1)))) -> b#(x1) b#(b(a(a(x1)))) -> a#(a(b(b(b(b(x1)))))) -> a#(a(a(a(b(b(x1)))))) -> b#(b(a(a(b(b(x1)))))) b#(b(a(a(x1)))) -> a#(a(b(b(b(b(x1)))))) -> a#(a(a(a(b(b(x1)))))) -> b#(a(a(b(b(x1))))) b#(b(a(a(x1)))) -> a#(b(b(b(b(x1))))) -> a#(a(a(a(b(b(x1)))))) -> b#(b(a(a(b(b(x1)))))) b#(b(a(a(x1)))) -> a#(b(b(b(b(x1))))) -> a#(a(a(a(b(b(x1)))))) -> b#(a(a(b(b(x1))))) a#(a(a(a(b(b(x1)))))) -> b#(a(a(b(b(x1))))) -> b#(b(c(c(a(a(x1)))))) -> a#(a(a(a(b(b(x1)))))) a#(a(a(a(b(b(x1)))))) -> b#(a(a(b(b(x1))))) -> b#(b(c(c(a(a(x1)))))) -> a#(a(a(b(b(x1))))) a#(a(a(a(b(b(x1)))))) -> b#(a(a(b(b(x1))))) -> b#(b(c(c(a(a(x1)))))) -> a#(a(b(b(x1)))) a#(a(a(a(b(b(x1)))))) -> b#(a(a(b(b(x1))))) -> b#(b(c(c(a(a(x1)))))) -> a#(b(b(x1))) a#(a(a(a(b(b(x1)))))) -> b#(a(a(b(b(x1))))) -> b#(b(c(c(a(a(x1)))))) -> b#(b(x1)) a#(a(a(a(b(b(x1)))))) -> b#(a(a(b(b(x1))))) -> b#(b(c(c(a(a(x1)))))) -> b#(x1) a#(a(a(a(b(b(x1)))))) -> b#(a(a(b(b(x1))))) -> b#(b(a(a(x1)))) -> a#(a(b(b(b(b(x1)))))) a#(a(a(a(b(b(x1)))))) -> b#(a(a(b(b(x1))))) -> b#(b(a(a(x1)))) -> a#(b(b(b(b(x1))))) a#(a(a(a(b(b(x1)))))) -> b#(a(a(b(b(x1))))) -> b#(b(a(a(x1)))) -> b#(b(b(b(x1)))) a#(a(a(a(b(b(x1)))))) -> b#(a(a(b(b(x1))))) -> b#(b(a(a(x1)))) -> b#(b(b(x1))) a#(a(a(a(b(b(x1)))))) -> b#(a(a(b(b(x1))))) -> b#(b(a(a(x1)))) -> b#(b(x1)) a#(a(a(a(b(b(x1)))))) -> b#(a(a(b(b(x1))))) -> b#(b(a(a(x1)))) -> b#(x1) a#(a(a(a(b(b(x1)))))) -> b#(b(a(a(b(b(x1)))))) -> b#(b(c(c(a(a(x1)))))) -> a#(a(a(a(b(b(x1)))))) a#(a(a(a(b(b(x1)))))) -> b#(b(a(a(b(b(x1)))))) -> b#(b(c(c(a(a(x1)))))) -> a#(a(a(b(b(x1))))) a#(a(a(a(b(b(x1)))))) -> b#(b(a(a(b(b(x1)))))) -> b#(b(c(c(a(a(x1)))))) -> a#(a(b(b(x1)))) a#(a(a(a(b(b(x1)))))) -> b#(b(a(a(b(b(x1)))))) -> b#(b(c(c(a(a(x1)))))) -> a#(b(b(x1))) a#(a(a(a(b(b(x1)))))) -> b#(b(a(a(b(b(x1)))))) -> b#(b(c(c(a(a(x1)))))) -> b#(b(x1)) a#(a(a(a(b(b(x1)))))) -> b#(b(a(a(b(b(x1)))))) -> b#(b(c(c(a(a(x1)))))) -> b#(x1) a#(a(a(a(b(b(x1)))))) -> b#(b(a(a(b(b(x1)))))) -> b#(b(a(a(x1)))) -> a#(a(b(b(b(b(x1)))))) a#(a(a(a(b(b(x1)))))) -> b#(b(a(a(b(b(x1)))))) -> b#(b(a(a(x1)))) -> a#(b(b(b(b(x1))))) a#(a(a(a(b(b(x1)))))) -> b#(b(a(a(b(b(x1)))))) -> b#(b(a(a(x1)))) -> b#(b(b(b(x1)))) a#(a(a(a(b(b(x1)))))) -> b#(b(a(a(b(b(x1)))))) -> b#(b(a(a(x1)))) -> b#(b(b(x1))) a#(a(a(a(b(b(x1)))))) -> b#(b(a(a(b(b(x1)))))) -> b#(b(a(a(x1)))) -> b#(b(x1)) a#(a(a(a(b(b(x1)))))) -> b#(b(a(a(b(b(x1)))))) -> b#(b(a(a(x1)))) -> b#(x1) Matrix Interpretation Processor: dim=4 interpretation: [b#](x0) = [1], [a#](x0) = [0 0 1 0]x0, [0 0 0 1] [0 0 0 1] [c](x0) = [0 0 0 0]x0 [0 1 1 0] , [0 0 1 0] [0 0 0 0] [a](x0) = [1 0 0 0]x0 [0 0 1 0] , [0 0 0 1] [0] [0 0 0 0] [0] [b](x0) = [0 0 0 0]x0 + [0] [0 0 0 0] [1] orientation: a#(a(a(a(b(b(x1)))))) = [1] >= [1] = b#(a(a(b(b(x1))))) a#(a(a(a(b(b(x1)))))) = [1] >= [1] = b#(b(a(a(b(b(x1)))))) b#(b(a(a(x1)))) = [1] >= [1] = b#(x1) b#(b(a(a(x1)))) = [1] >= [1] = b#(b(x1)) b#(b(a(a(x1)))) = [1] >= [1] = b#(b(b(x1))) b#(b(a(a(x1)))) = [1] >= [1] = b#(b(b(b(x1)))) b#(b(a(a(x1)))) = [1] >= [0] = a#(b(b(b(b(x1))))) b#(b(a(a(x1)))) = [1] >= [1] = a#(a(b(b(b(b(x1)))))) b#(b(c(c(a(a(x1)))))) = [1] >= [1] = b#(x1) b#(b(c(c(a(a(x1)))))) = [1] >= [1] = b#(b(x1)) b#(b(c(c(a(a(x1)))))) = [1] >= [0] = a#(b(b(x1))) b#(b(c(c(a(a(x1)))))) = [1] >= [1] = a#(a(b(b(x1)))) b#(b(c(c(a(a(x1)))))) = [1] >= [0] = a#(a(a(b(b(x1))))) b#(b(c(c(a(a(x1)))))) = [1] >= [1] = a#(a(a(a(b(b(x1)))))) [1] [1] [0] [0] a(a(a(a(b(b(x1)))))) = [0] >= [0] = b(b(a(a(b(b(x1)))))) [1] [1] [1] [1] [0] [0] b(b(a(a(x1)))) = [0] >= [0] = a(a(b(b(b(b(x1)))))) [1] [1] [1] [0] [0] [0] b(b(c(c(a(a(x1)))))) = [0] >= [0] = c(c(c(c(a(a(a(a(b(b(x1)))))))))) [1] [1] problem: DPs: a#(a(a(a(b(b(x1)))))) -> b#(a(a(b(b(x1))))) a#(a(a(a(b(b(x1)))))) -> b#(b(a(a(b(b(x1)))))) b#(b(a(a(x1)))) -> b#(x1) b#(b(a(a(x1)))) -> b#(b(x1)) b#(b(a(a(x1)))) -> b#(b(b(x1))) b#(b(a(a(x1)))) -> b#(b(b(b(x1)))) b#(b(a(a(x1)))) -> a#(a(b(b(b(b(x1)))))) b#(b(c(c(a(a(x1)))))) -> b#(x1) b#(b(c(c(a(a(x1)))))) -> b#(b(x1)) b#(b(c(c(a(a(x1)))))) -> a#(a(b(b(x1)))) b#(b(c(c(a(a(x1)))))) -> a#(a(a(a(b(b(x1)))))) TRS: a(a(a(a(b(b(x1)))))) -> b(b(a(a(b(b(x1)))))) b(b(a(a(x1)))) -> a(a(b(b(b(b(x1)))))) b(b(c(c(a(a(x1)))))) -> c(c(c(c(a(a(a(a(b(b(x1)))))))))) EDG Processor: DPs: a#(a(a(a(b(b(x1)))))) -> b#(a(a(b(b(x1))))) a#(a(a(a(b(b(x1)))))) -> b#(b(a(a(b(b(x1)))))) b#(b(a(a(x1)))) -> b#(x1) b#(b(a(a(x1)))) -> b#(b(x1)) b#(b(a(a(x1)))) -> b#(b(b(x1))) b#(b(a(a(x1)))) -> b#(b(b(b(x1)))) b#(b(a(a(x1)))) -> a#(a(b(b(b(b(x1)))))) b#(b(c(c(a(a(x1)))))) -> b#(x1) b#(b(c(c(a(a(x1)))))) -> b#(b(x1)) b#(b(c(c(a(a(x1)))))) -> a#(a(b(b(x1)))) b#(b(c(c(a(a(x1)))))) -> a#(a(a(a(b(b(x1)))))) TRS: a(a(a(a(b(b(x1)))))) -> b(b(a(a(b(b(x1)))))) b(b(a(a(x1)))) -> a(a(b(b(b(b(x1)))))) b(b(c(c(a(a(x1)))))) -> c(c(c(c(a(a(a(a(b(b(x1)))))))))) graph: b#(b(c(c(a(a(x1)))))) -> b#(b(x1)) -> b#(b(a(a(x1)))) -> b#(x1) b#(b(c(c(a(a(x1)))))) -> b#(b(x1)) -> b#(b(a(a(x1)))) -> b#(b(x1)) b#(b(c(c(a(a(x1)))))) -> b#(b(x1)) -> b#(b(a(a(x1)))) -> b#(b(b(x1))) b#(b(c(c(a(a(x1)))))) -> b#(b(x1)) -> b#(b(a(a(x1)))) -> b#(b(b(b(x1)))) b#(b(c(c(a(a(x1)))))) -> b#(b(x1)) -> b#(b(a(a(x1)))) -> a#(a(b(b(b(b(x1)))))) b#(b(c(c(a(a(x1)))))) -> b#(b(x1)) -> b#(b(c(c(a(a(x1)))))) -> b#(x1) b#(b(c(c(a(a(x1)))))) -> b#(b(x1)) -> b#(b(c(c(a(a(x1)))))) -> b#(b(x1)) b#(b(c(c(a(a(x1)))))) -> b#(b(x1)) -> b#(b(c(c(a(a(x1)))))) -> a#(a(b(b(x1)))) b#(b(c(c(a(a(x1)))))) -> b#(b(x1)) -> b#(b(c(c(a(a(x1)))))) -> a#(a(a(a(b(b(x1)))))) b#(b(c(c(a(a(x1)))))) -> b#(x1) -> b#(b(a(a(x1)))) -> b#(x1) b#(b(c(c(a(a(x1)))))) -> b#(x1) -> b#(b(a(a(x1)))) -> b#(b(x1)) b#(b(c(c(a(a(x1)))))) -> b#(x1) -> b#(b(a(a(x1)))) -> b#(b(b(x1))) b#(b(c(c(a(a(x1)))))) -> b#(x1) -> b#(b(a(a(x1)))) -> b#(b(b(b(x1)))) b#(b(c(c(a(a(x1)))))) -> b#(x1) -> b#(b(a(a(x1)))) -> a#(a(b(b(b(b(x1)))))) b#(b(c(c(a(a(x1)))))) -> b#(x1) -> b#(b(c(c(a(a(x1)))))) -> b#(x1) b#(b(c(c(a(a(x1)))))) -> b#(x1) -> b#(b(c(c(a(a(x1)))))) -> b#(b(x1)) b#(b(c(c(a(a(x1)))))) -> b#(x1) -> b#(b(c(c(a(a(x1)))))) -> a#(a(b(b(x1)))) b#(b(c(c(a(a(x1)))))) -> b#(x1) -> b#(b(c(c(a(a(x1)))))) -> a#(a(a(a(b(b(x1)))))) b#(b(c(c(a(a(x1)))))) -> a#(a(a(a(b(b(x1)))))) -> a#(a(a(a(b(b(x1)))))) -> b#(a(a(b(b(x1))))) b#(b(c(c(a(a(x1)))))) -> a#(a(a(a(b(b(x1)))))) -> a#(a(a(a(b(b(x1)))))) -> b#(b(a(a(b(b(x1)))))) b#(b(c(c(a(a(x1)))))) -> a#(a(b(b(x1)))) -> a#(a(a(a(b(b(x1)))))) -> b#(a(a(b(b(x1))))) b#(b(c(c(a(a(x1)))))) -> a#(a(b(b(x1)))) -> a#(a(a(a(b(b(x1)))))) -> b#(b(a(a(b(b(x1)))))) b#(b(a(a(x1)))) -> b#(b(b(b(x1)))) -> b#(b(a(a(x1)))) -> b#(x1) b#(b(a(a(x1)))) -> b#(b(b(b(x1)))) -> b#(b(a(a(x1)))) -> b#(b(x1)) b#(b(a(a(x1)))) -> b#(b(b(b(x1)))) -> b#(b(a(a(x1)))) -> b#(b(b(x1))) b#(b(a(a(x1)))) -> b#(b(b(b(x1)))) -> b#(b(a(a(x1)))) -> b#(b(b(b(x1)))) b#(b(a(a(x1)))) -> b#(b(b(b(x1)))) -> b#(b(a(a(x1)))) -> a#(a(b(b(b(b(x1)))))) b#(b(a(a(x1)))) -> b#(b(b(b(x1)))) -> b#(b(c(c(a(a(x1)))))) -> b#(x1) b#(b(a(a(x1)))) -> b#(b(b(b(x1)))) -> b#(b(c(c(a(a(x1)))))) -> b#(b(x1)) b#(b(a(a(x1)))) -> b#(b(b(b(x1)))) -> b#(b(c(c(a(a(x1)))))) -> a#(a(b(b(x1)))) b#(b(a(a(x1)))) -> b#(b(b(b(x1)))) -> b#(b(c(c(a(a(x1)))))) -> a#(a(a(a(b(b(x1)))))) b#(b(a(a(x1)))) -> b#(b(b(x1))) -> b#(b(a(a(x1)))) -> b#(x1) b#(b(a(a(x1)))) -> b#(b(b(x1))) -> b#(b(a(a(x1)))) -> b#(b(x1)) b#(b(a(a(x1)))) -> b#(b(b(x1))) -> b#(b(a(a(x1)))) -> b#(b(b(x1))) b#(b(a(a(x1)))) -> b#(b(b(x1))) -> b#(b(a(a(x1)))) -> b#(b(b(b(x1)))) b#(b(a(a(x1)))) -> b#(b(b(x1))) -> b#(b(a(a(x1)))) -> a#(a(b(b(b(b(x1)))))) b#(b(a(a(x1)))) -> b#(b(b(x1))) -> b#(b(c(c(a(a(x1)))))) -> b#(x1) b#(b(a(a(x1)))) -> b#(b(b(x1))) -> b#(b(c(c(a(a(x1)))))) -> b#(b(x1)) b#(b(a(a(x1)))) -> b#(b(b(x1))) -> b#(b(c(c(a(a(x1)))))) -> a#(a(b(b(x1)))) b#(b(a(a(x1)))) -> b#(b(b(x1))) -> b#(b(c(c(a(a(x1)))))) -> a#(a(a(a(b(b(x1)))))) b#(b(a(a(x1)))) -> b#(b(x1)) -> b#(b(a(a(x1)))) -> b#(x1) b#(b(a(a(x1)))) -> b#(b(x1)) -> b#(b(a(a(x1)))) -> b#(b(x1)) b#(b(a(a(x1)))) -> b#(b(x1)) -> b#(b(a(a(x1)))) -> b#(b(b(x1))) b#(b(a(a(x1)))) -> b#(b(x1)) -> b#(b(a(a(x1)))) -> b#(b(b(b(x1)))) b#(b(a(a(x1)))) -> b#(b(x1)) -> b#(b(a(a(x1)))) -> a#(a(b(b(b(b(x1)))))) b#(b(a(a(x1)))) -> b#(b(x1)) -> b#(b(c(c(a(a(x1)))))) -> b#(x1) b#(b(a(a(x1)))) -> b#(b(x1)) -> b#(b(c(c(a(a(x1)))))) -> b#(b(x1)) b#(b(a(a(x1)))) -> b#(b(x1)) -> b#(b(c(c(a(a(x1)))))) -> a#(a(b(b(x1)))) b#(b(a(a(x1)))) -> b#(b(x1)) -> b#(b(c(c(a(a(x1)))))) -> a#(a(a(a(b(b(x1)))))) b#(b(a(a(x1)))) -> b#(x1) -> b#(b(a(a(x1)))) -> b#(x1) b#(b(a(a(x1)))) -> b#(x1) -> b#(b(a(a(x1)))) -> b#(b(x1)) b#(b(a(a(x1)))) -> b#(x1) -> b#(b(a(a(x1)))) -> b#(b(b(x1))) b#(b(a(a(x1)))) -> b#(x1) -> b#(b(a(a(x1)))) -> b#(b(b(b(x1)))) b#(b(a(a(x1)))) -> b#(x1) -> b#(b(a(a(x1)))) -> a#(a(b(b(b(b(x1)))))) b#(b(a(a(x1)))) -> b#(x1) -> b#(b(c(c(a(a(x1)))))) -> b#(x1) b#(b(a(a(x1)))) -> b#(x1) -> b#(b(c(c(a(a(x1)))))) -> b#(b(x1)) b#(b(a(a(x1)))) -> b#(x1) -> b#(b(c(c(a(a(x1)))))) -> a#(a(b(b(x1)))) b#(b(a(a(x1)))) -> b#(x1) -> b#(b(c(c(a(a(x1)))))) -> a#(a(a(a(b(b(x1)))))) b#(b(a(a(x1)))) -> a#(a(b(b(b(b(x1)))))) -> a#(a(a(a(b(b(x1)))))) -> b#(a(a(b(b(x1))))) b#(b(a(a(x1)))) -> a#(a(b(b(b(b(x1)))))) -> a#(a(a(a(b(b(x1)))))) -> b#(b(a(a(b(b(x1)))))) a#(a(a(a(b(b(x1)))))) -> b#(a(a(b(b(x1))))) -> b#(b(a(a(x1)))) -> b#(x1) a#(a(a(a(b(b(x1)))))) -> b#(a(a(b(b(x1))))) -> b#(b(a(a(x1)))) -> b#(b(x1)) a#(a(a(a(b(b(x1)))))) -> b#(a(a(b(b(x1))))) -> b#(b(a(a(x1)))) -> b#(b(b(x1))) a#(a(a(a(b(b(x1)))))) -> b#(a(a(b(b(x1))))) -> b#(b(a(a(x1)))) -> b#(b(b(b(x1)))) a#(a(a(a(b(b(x1)))))) -> b#(a(a(b(b(x1))))) -> b#(b(a(a(x1)))) -> a#(a(b(b(b(b(x1)))))) a#(a(a(a(b(b(x1)))))) -> b#(a(a(b(b(x1))))) -> b#(b(c(c(a(a(x1)))))) -> b#(x1) a#(a(a(a(b(b(x1)))))) -> b#(a(a(b(b(x1))))) -> b#(b(c(c(a(a(x1)))))) -> b#(b(x1)) a#(a(a(a(b(b(x1)))))) -> b#(a(a(b(b(x1))))) -> b#(b(c(c(a(a(x1)))))) -> a#(a(b(b(x1)))) a#(a(a(a(b(b(x1)))))) -> b#(a(a(b(b(x1))))) -> b#(b(c(c(a(a(x1)))))) -> a#(a(a(a(b(b(x1)))))) a#(a(a(a(b(b(x1)))))) -> b#(b(a(a(b(b(x1)))))) -> b#(b(a(a(x1)))) -> b#(x1) a#(a(a(a(b(b(x1)))))) -> b#(b(a(a(b(b(x1)))))) -> b#(b(a(a(x1)))) -> b#(b(x1)) a#(a(a(a(b(b(x1)))))) -> b#(b(a(a(b(b(x1)))))) -> b#(b(a(a(x1)))) -> b#(b(b(x1))) a#(a(a(a(b(b(x1)))))) -> b#(b(a(a(b(b(x1)))))) -> b#(b(a(a(x1)))) -> b#(b(b(b(x1)))) a#(a(a(a(b(b(x1)))))) -> b#(b(a(a(b(b(x1)))))) -> b#(b(a(a(x1)))) -> a#(a(b(b(b(b(x1)))))) a#(a(a(a(b(b(x1)))))) -> b#(b(a(a(b(b(x1)))))) -> b#(b(c(c(a(a(x1)))))) -> b#(x1) a#(a(a(a(b(b(x1)))))) -> b#(b(a(a(b(b(x1)))))) -> b#(b(c(c(a(a(x1)))))) -> b#(b(x1)) a#(a(a(a(b(b(x1)))))) -> b#(b(a(a(b(b(x1)))))) -> b#(b(c(c(a(a(x1)))))) -> a#(a(b(b(x1)))) a#(a(a(a(b(b(x1)))))) -> b#(b(a(a(b(b(x1)))))) -> b#(b(c(c(a(a(x1)))))) -> a#(a(a(a(b(b(x1)))))) Matrix Interpretation Processor: dim=4 interpretation: [b#](x0) = [0 1 0 0]x0, [a#](x0) = [0 1 0 0]x0, [0 0 1 0] [0 1 0 1] [c](x0) = [0 0 0 0]x0 [0 0 1 0] , [0 0 1 0] [0] [0 1 0 0] [0] [a](x0) = [0 0 0 0]x0 + [1] [0 0 0 0] [0], [0 0 1 0] [0 1 0 0] [b](x0) = [0 0 1 0]x0 [0 0 0 0] orientation: a#(a(a(a(b(b(x1)))))) = [0 1 0 0]x1 >= [0 1 0 0]x1 = b#(a(a(b(b(x1))))) a#(a(a(a(b(b(x1)))))) = [0 1 0 0]x1 >= [0 1 0 0]x1 = b#(b(a(a(b(b(x1)))))) b#(b(a(a(x1)))) = [0 1 0 0]x1 >= [0 1 0 0]x1 = b#(x1) b#(b(a(a(x1)))) = [0 1 0 0]x1 >= [0 1 0 0]x1 = b#(b(x1)) b#(b(a(a(x1)))) = [0 1 0 0]x1 >= [0 1 0 0]x1 = b#(b(b(x1))) b#(b(a(a(x1)))) = [0 1 0 0]x1 >= [0 1 0 0]x1 = b#(b(b(b(x1)))) b#(b(a(a(x1)))) = [0 1 0 0]x1 >= [0 1 0 0]x1 = a#(a(b(b(b(b(x1)))))) b#(b(c(c(a(a(x1)))))) = [0 1 0 0]x1 + [1] >= [0 1 0 0]x1 = b#(x1) b#(b(c(c(a(a(x1)))))) = [0 1 0 0]x1 + [1] >= [0 1 0 0]x1 = b#(b(x1)) b#(b(c(c(a(a(x1)))))) = [0 1 0 0]x1 + [1] >= [0 1 0 0]x1 = a#(a(b(b(x1)))) b#(b(c(c(a(a(x1)))))) = [0 1 0 0]x1 + [1] >= [0 1 0 0]x1 = a#(a(a(a(b(b(x1)))))) [0 0 0 0] [1] [0 0 0 0] [1] [0 1 0 0] [0] [0 1 0 0] [0] a(a(a(a(b(b(x1)))))) = [0 0 0 0]x1 + [1] >= [0 0 0 0]x1 + [1] = b(b(a(a(b(b(x1)))))) [0 0 0 0] [0] [0 0 0 0] [0] [0 0 0 0] [1] [0 0 0 0] [1] [0 1 0 0] [0] [0 1 0 0] [0] b(b(a(a(x1)))) = [0 0 0 0]x1 + [1] >= [0 0 0 0]x1 + [1] = a(a(b(b(b(b(x1)))))) [0 0 0 0] [0] [0 0 0 0] [0] [0 0 0 0] [0] [0 0 0 0] [0] [0 1 0 0] [1] [0 1 0 0] [1] b(b(c(c(a(a(x1)))))) = [0 0 0 0]x1 + [0] >= [0 0 0 0]x1 + [0] = c(c(c(c(a(a(a(a(b(b(x1)))))))))) [0 0 0 0] [0] [0 0 0 0] [0] problem: DPs: a#(a(a(a(b(b(x1)))))) -> b#(a(a(b(b(x1))))) a#(a(a(a(b(b(x1)))))) -> b#(b(a(a(b(b(x1)))))) b#(b(a(a(x1)))) -> b#(x1) b#(b(a(a(x1)))) -> b#(b(x1)) b#(b(a(a(x1)))) -> b#(b(b(x1))) b#(b(a(a(x1)))) -> b#(b(b(b(x1)))) b#(b(a(a(x1)))) -> a#(a(b(b(b(b(x1)))))) TRS: a(a(a(a(b(b(x1)))))) -> b(b(a(a(b(b(x1)))))) b(b(a(a(x1)))) -> a(a(b(b(b(b(x1)))))) b(b(c(c(a(a(x1)))))) -> c(c(c(c(a(a(a(a(b(b(x1)))))))))) EDG Processor: DPs: a#(a(a(a(b(b(x1)))))) -> b#(a(a(b(b(x1))))) a#(a(a(a(b(b(x1)))))) -> b#(b(a(a(b(b(x1)))))) b#(b(a(a(x1)))) -> b#(x1) b#(b(a(a(x1)))) -> b#(b(x1)) b#(b(a(a(x1)))) -> b#(b(b(x1))) b#(b(a(a(x1)))) -> b#(b(b(b(x1)))) b#(b(a(a(x1)))) -> a#(a(b(b(b(b(x1)))))) TRS: a(a(a(a(b(b(x1)))))) -> b(b(a(a(b(b(x1)))))) b(b(a(a(x1)))) -> a(a(b(b(b(b(x1)))))) b(b(c(c(a(a(x1)))))) -> c(c(c(c(a(a(a(a(b(b(x1)))))))))) graph: b#(b(a(a(x1)))) -> b#(b(b(b(x1)))) -> b#(b(a(a(x1)))) -> a#(a(b(b(b(b(x1)))))) b#(b(a(a(x1)))) -> b#(b(b(b(x1)))) -> b#(b(a(a(x1)))) -> b#(b(b(b(x1)))) b#(b(a(a(x1)))) -> b#(b(b(b(x1)))) -> b#(b(a(a(x1)))) -> b#(b(b(x1))) b#(b(a(a(x1)))) -> b#(b(b(b(x1)))) -> b#(b(a(a(x1)))) -> b#(b(x1)) b#(b(a(a(x1)))) -> b#(b(b(b(x1)))) -> b#(b(a(a(x1)))) -> b#(x1) b#(b(a(a(x1)))) -> b#(b(b(x1))) -> b#(b(a(a(x1)))) -> a#(a(b(b(b(b(x1)))))) b#(b(a(a(x1)))) -> b#(b(b(x1))) -> b#(b(a(a(x1)))) -> b#(b(b(b(x1)))) b#(b(a(a(x1)))) -> b#(b(b(x1))) -> b#(b(a(a(x1)))) -> b#(b(b(x1))) b#(b(a(a(x1)))) -> b#(b(b(x1))) -> b#(b(a(a(x1)))) -> b#(b(x1)) b#(b(a(a(x1)))) -> b#(b(b(x1))) -> b#(b(a(a(x1)))) -> b#(x1) b#(b(a(a(x1)))) -> b#(b(x1)) -> b#(b(a(a(x1)))) -> a#(a(b(b(b(b(x1)))))) b#(b(a(a(x1)))) -> b#(b(x1)) -> b#(b(a(a(x1)))) -> b#(b(b(b(x1)))) b#(b(a(a(x1)))) -> b#(b(x1)) -> b#(b(a(a(x1)))) -> b#(b(b(x1))) b#(b(a(a(x1)))) -> b#(b(x1)) -> b#(b(a(a(x1)))) -> b#(b(x1)) b#(b(a(a(x1)))) -> b#(b(x1)) -> b#(b(a(a(x1)))) -> b#(x1) b#(b(a(a(x1)))) -> b#(x1) -> b#(b(a(a(x1)))) -> a#(a(b(b(b(b(x1)))))) b#(b(a(a(x1)))) -> b#(x1) -> b#(b(a(a(x1)))) -> b#(b(b(b(x1)))) b#(b(a(a(x1)))) -> b#(x1) -> b#(b(a(a(x1)))) -> b#(b(b(x1))) b#(b(a(a(x1)))) -> b#(x1) -> b#(b(a(a(x1)))) -> b#(b(x1)) b#(b(a(a(x1)))) -> b#(x1) -> b#(b(a(a(x1)))) -> b#(x1) b#(b(a(a(x1)))) -> a#(a(b(b(b(b(x1)))))) -> a#(a(a(a(b(b(x1)))))) -> b#(b(a(a(b(b(x1)))))) b#(b(a(a(x1)))) -> a#(a(b(b(b(b(x1)))))) -> a#(a(a(a(b(b(x1)))))) -> b#(a(a(b(b(x1))))) a#(a(a(a(b(b(x1)))))) -> b#(a(a(b(b(x1))))) -> b#(b(a(a(x1)))) -> a#(a(b(b(b(b(x1)))))) a#(a(a(a(b(b(x1)))))) -> b#(a(a(b(b(x1))))) -> b#(b(a(a(x1)))) -> b#(b(b(b(x1)))) a#(a(a(a(b(b(x1)))))) -> b#(a(a(b(b(x1))))) -> b#(b(a(a(x1)))) -> b#(b(b(x1))) a#(a(a(a(b(b(x1)))))) -> b#(a(a(b(b(x1))))) -> b#(b(a(a(x1)))) -> b#(b(x1)) a#(a(a(a(b(b(x1)))))) -> b#(a(a(b(b(x1))))) -> b#(b(a(a(x1)))) -> b#(x1) a#(a(a(a(b(b(x1)))))) -> b#(b(a(a(b(b(x1)))))) -> b#(b(a(a(x1)))) -> a#(a(b(b(b(b(x1)))))) a#(a(a(a(b(b(x1)))))) -> b#(b(a(a(b(b(x1)))))) -> b#(b(a(a(x1)))) -> b#(b(b(b(x1)))) a#(a(a(a(b(b(x1)))))) -> b#(b(a(a(b(b(x1)))))) -> b#(b(a(a(x1)))) -> b#(b(b(x1))) a#(a(a(a(b(b(x1)))))) -> b#(b(a(a(b(b(x1)))))) -> b#(b(a(a(x1)))) -> b#(b(x1)) a#(a(a(a(b(b(x1)))))) -> b#(b(a(a(b(b(x1)))))) -> b#(b(a(a(x1)))) -> b#(x1) Arctic Interpretation Processor: dimension: 1 interpretation: [b#](x0) = 8x0, [a#](x0) = 12x0, [c](x0) = 0, [a](x0) = 4x0, [b](x0) = x0 orientation: a#(a(a(a(b(b(x1)))))) = 24x1 >= 16x1 = b#(a(a(b(b(x1))))) a#(a(a(a(b(b(x1)))))) = 24x1 >= 16x1 = b#(b(a(a(b(b(x1)))))) b#(b(a(a(x1)))) = 16x1 >= 8x1 = b#(x1) b#(b(a(a(x1)))) = 16x1 >= 8x1 = b#(b(x1)) b#(b(a(a(x1)))) = 16x1 >= 8x1 = b#(b(b(x1))) b#(b(a(a(x1)))) = 16x1 >= 8x1 = b#(b(b(b(x1)))) b#(b(a(a(x1)))) = 16x1 >= 16x1 = a#(a(b(b(b(b(x1)))))) a(a(a(a(b(b(x1)))))) = 16x1 >= 8x1 = b(b(a(a(b(b(x1)))))) b(b(a(a(x1)))) = 8x1 >= 8x1 = a(a(b(b(b(b(x1)))))) b(b(c(c(a(a(x1)))))) = 0 >= 0 = c(c(c(c(a(a(a(a(b(b(x1)))))))))) problem: DPs: b#(b(a(a(x1)))) -> a#(a(b(b(b(b(x1)))))) TRS: a(a(a(a(b(b(x1)))))) -> b(b(a(a(b(b(x1)))))) b(b(a(a(x1)))) -> a(a(b(b(b(b(x1)))))) b(b(c(c(a(a(x1)))))) -> c(c(c(c(a(a(a(a(b(b(x1)))))))))) EDG Processor: DPs: b#(b(a(a(x1)))) -> a#(a(b(b(b(b(x1)))))) TRS: a(a(a(a(b(b(x1)))))) -> b(b(a(a(b(b(x1)))))) b(b(a(a(x1)))) -> a(a(b(b(b(b(x1)))))) b(b(c(c(a(a(x1)))))) -> c(c(c(c(a(a(a(a(b(b(x1)))))))))) graph: Qed