YES Problem: a(a(x1)) -> a(b(a(b(a(x1))))) c(a(x1)) -> a(b(a(a(c(x1))))) b(b(b(x1))) -> a(b(x1)) c(b(x1)) -> a(a(c(x1))) c(b(x1)) -> b(a(d(x1))) d(d(x1)) -> d(b(d(b(d(x1))))) c(c(x1)) -> c(d(c(x1))) a(a(a(x1))) -> a(b(b(x1))) Proof: DP Processor: DPs: a#(a(x1)) -> b#(a(x1)) a#(a(x1)) -> a#(b(a(x1))) a#(a(x1)) -> b#(a(b(a(x1)))) a#(a(x1)) -> a#(b(a(b(a(x1))))) c#(a(x1)) -> c#(x1) c#(a(x1)) -> a#(c(x1)) c#(a(x1)) -> a#(a(c(x1))) c#(a(x1)) -> b#(a(a(c(x1)))) c#(a(x1)) -> a#(b(a(a(c(x1))))) b#(b(b(x1))) -> a#(b(x1)) c#(b(x1)) -> c#(x1) c#(b(x1)) -> a#(c(x1)) c#(b(x1)) -> a#(a(c(x1))) c#(b(x1)) -> d#(x1) c#(b(x1)) -> a#(d(x1)) c#(b(x1)) -> b#(a(d(x1))) d#(d(x1)) -> b#(d(x1)) d#(d(x1)) -> d#(b(d(x1))) d#(d(x1)) -> b#(d(b(d(x1)))) d#(d(x1)) -> d#(b(d(b(d(x1))))) c#(c(x1)) -> d#(c(x1)) c#(c(x1)) -> c#(d(c(x1))) a#(a(a(x1))) -> b#(x1) a#(a(a(x1))) -> b#(b(x1)) a#(a(a(x1))) -> a#(b(b(x1))) TRS: a(a(x1)) -> a(b(a(b(a(x1))))) c(a(x1)) -> a(b(a(a(c(x1))))) b(b(b(x1))) -> a(b(x1)) c(b(x1)) -> a(a(c(x1))) c(b(x1)) -> b(a(d(x1))) d(d(x1)) -> d(b(d(b(d(x1))))) c(c(x1)) -> c(d(c(x1))) a(a(a(x1))) -> a(b(b(x1))) TDG Processor: DPs: a#(a(x1)) -> b#(a(x1)) a#(a(x1)) -> a#(b(a(x1))) a#(a(x1)) -> b#(a(b(a(x1)))) a#(a(x1)) -> a#(b(a(b(a(x1))))) c#(a(x1)) -> c#(x1) c#(a(x1)) -> a#(c(x1)) c#(a(x1)) -> a#(a(c(x1))) c#(a(x1)) -> b#(a(a(c(x1)))) c#(a(x1)) -> a#(b(a(a(c(x1))))) b#(b(b(x1))) -> a#(b(x1)) c#(b(x1)) -> c#(x1) c#(b(x1)) -> a#(c(x1)) c#(b(x1)) -> a#(a(c(x1))) c#(b(x1)) -> d#(x1) c#(b(x1)) -> a#(d(x1)) c#(b(x1)) -> b#(a(d(x1))) d#(d(x1)) -> b#(d(x1)) d#(d(x1)) -> d#(b(d(x1))) d#(d(x1)) -> b#(d(b(d(x1)))) d#(d(x1)) -> d#(b(d(b(d(x1))))) c#(c(x1)) -> d#(c(x1)) c#(c(x1)) -> c#(d(c(x1))) a#(a(a(x1))) -> b#(x1) a#(a(a(x1))) -> b#(b(x1)) a#(a(a(x1))) -> a#(b(b(x1))) TRS: a(a(x1)) -> a(b(a(b(a(x1))))) c(a(x1)) -> a(b(a(a(c(x1))))) b(b(b(x1))) -> a(b(x1)) c(b(x1)) -> a(a(c(x1))) c(b(x1)) -> b(a(d(x1))) d(d(x1)) -> d(b(d(b(d(x1))))) c(c(x1)) -> c(d(c(x1))) a(a(a(x1))) -> a(b(b(x1))) graph: d#(d(x1)) -> d#(b(d(b(d(x1))))) -> d#(d(x1)) -> d#(b(d(b(d(x1))))) d#(d(x1)) -> d#(b(d(b(d(x1))))) -> d#(d(x1)) -> b#(d(b(d(x1)))) d#(d(x1)) -> d#(b(d(b(d(x1))))) -> d#(d(x1)) -> d#(b(d(x1))) d#(d(x1)) -> d#(b(d(b(d(x1))))) -> d#(d(x1)) -> b#(d(x1)) d#(d(x1)) -> d#(b(d(x1))) -> d#(d(x1)) -> d#(b(d(b(d(x1))))) d#(d(x1)) -> d#(b(d(x1))) -> d#(d(x1)) -> b#(d(b(d(x1)))) d#(d(x1)) -> d#(b(d(x1))) -> d#(d(x1)) -> d#(b(d(x1))) d#(d(x1)) -> d#(b(d(x1))) -> d#(d(x1)) -> b#(d(x1)) d#(d(x1)) -> b#(d(b(d(x1)))) -> b#(b(b(x1))) -> a#(b(x1)) d#(d(x1)) -> b#(d(x1)) -> b#(b(b(x1))) -> a#(b(x1)) c#(c(x1)) -> d#(c(x1)) -> d#(d(x1)) -> d#(b(d(b(d(x1))))) c#(c(x1)) -> d#(c(x1)) -> d#(d(x1)) -> b#(d(b(d(x1)))) c#(c(x1)) -> d#(c(x1)) -> d#(d(x1)) -> d#(b(d(x1))) c#(c(x1)) -> d#(c(x1)) -> d#(d(x1)) -> b#(d(x1)) c#(c(x1)) -> c#(d(c(x1))) -> c#(c(x1)) -> c#(d(c(x1))) c#(c(x1)) -> c#(d(c(x1))) -> c#(c(x1)) -> d#(c(x1)) c#(c(x1)) -> c#(d(c(x1))) -> c#(b(x1)) -> b#(a(d(x1))) c#(c(x1)) -> c#(d(c(x1))) -> c#(b(x1)) -> a#(d(x1)) c#(c(x1)) -> c#(d(c(x1))) -> c#(b(x1)) -> d#(x1) c#(c(x1)) -> c#(d(c(x1))) -> c#(b(x1)) -> a#(a(c(x1))) c#(c(x1)) -> c#(d(c(x1))) -> c#(b(x1)) -> a#(c(x1)) c#(c(x1)) -> c#(d(c(x1))) -> c#(b(x1)) -> c#(x1) c#(c(x1)) -> c#(d(c(x1))) -> c#(a(x1)) -> a#(b(a(a(c(x1))))) c#(c(x1)) -> c#(d(c(x1))) -> c#(a(x1)) -> b#(a(a(c(x1)))) c#(c(x1)) -> c#(d(c(x1))) -> c#(a(x1)) -> a#(a(c(x1))) c#(c(x1)) -> c#(d(c(x1))) -> c#(a(x1)) -> a#(c(x1)) c#(c(x1)) -> c#(d(c(x1))) -> c#(a(x1)) -> c#(x1) c#(b(x1)) -> d#(x1) -> d#(d(x1)) -> d#(b(d(b(d(x1))))) c#(b(x1)) -> d#(x1) -> d#(d(x1)) -> b#(d(b(d(x1)))) c#(b(x1)) -> d#(x1) -> d#(d(x1)) -> d#(b(d(x1))) c#(b(x1)) -> d#(x1) -> d#(d(x1)) -> b#(d(x1)) c#(b(x1)) -> c#(x1) -> c#(c(x1)) -> c#(d(c(x1))) c#(b(x1)) -> c#(x1) -> c#(c(x1)) -> d#(c(x1)) c#(b(x1)) -> c#(x1) -> c#(b(x1)) -> b#(a(d(x1))) c#(b(x1)) -> c#(x1) -> c#(b(x1)) -> a#(d(x1)) c#(b(x1)) -> c#(x1) -> c#(b(x1)) -> d#(x1) c#(b(x1)) -> c#(x1) -> c#(b(x1)) -> a#(a(c(x1))) c#(b(x1)) -> c#(x1) -> c#(b(x1)) -> a#(c(x1)) c#(b(x1)) -> c#(x1) -> c#(b(x1)) -> c#(x1) c#(b(x1)) -> c#(x1) -> c#(a(x1)) -> a#(b(a(a(c(x1))))) c#(b(x1)) -> c#(x1) -> c#(a(x1)) -> b#(a(a(c(x1)))) c#(b(x1)) -> c#(x1) -> c#(a(x1)) -> a#(a(c(x1))) c#(b(x1)) -> c#(x1) -> c#(a(x1)) -> a#(c(x1)) c#(b(x1)) -> c#(x1) -> c#(a(x1)) -> c#(x1) c#(b(x1)) -> b#(a(d(x1))) -> b#(b(b(x1))) -> a#(b(x1)) c#(b(x1)) -> a#(d(x1)) -> a#(a(a(x1))) -> a#(b(b(x1))) c#(b(x1)) -> a#(d(x1)) -> a#(a(a(x1))) -> b#(b(x1)) c#(b(x1)) -> a#(d(x1)) -> a#(a(a(x1))) -> b#(x1) c#(b(x1)) -> a#(d(x1)) -> a#(a(x1)) -> a#(b(a(b(a(x1))))) c#(b(x1)) -> a#(d(x1)) -> a#(a(x1)) -> b#(a(b(a(x1)))) c#(b(x1)) -> a#(d(x1)) -> a#(a(x1)) -> a#(b(a(x1))) c#(b(x1)) -> a#(d(x1)) -> a#(a(x1)) -> b#(a(x1)) c#(b(x1)) -> a#(c(x1)) -> a#(a(a(x1))) -> a#(b(b(x1))) c#(b(x1)) -> a#(c(x1)) -> a#(a(a(x1))) -> b#(b(x1)) c#(b(x1)) -> a#(c(x1)) -> a#(a(a(x1))) -> b#(x1) c#(b(x1)) -> a#(c(x1)) -> a#(a(x1)) -> a#(b(a(b(a(x1))))) c#(b(x1)) -> a#(c(x1)) -> a#(a(x1)) -> b#(a(b(a(x1)))) c#(b(x1)) -> a#(c(x1)) -> a#(a(x1)) -> a#(b(a(x1))) c#(b(x1)) -> a#(c(x1)) -> a#(a(x1)) -> b#(a(x1)) c#(b(x1)) -> a#(a(c(x1))) -> a#(a(a(x1))) -> a#(b(b(x1))) c#(b(x1)) -> a#(a(c(x1))) -> a#(a(a(x1))) -> b#(b(x1)) c#(b(x1)) -> a#(a(c(x1))) -> a#(a(a(x1))) -> b#(x1) c#(b(x1)) -> a#(a(c(x1))) -> a#(a(x1)) -> a#(b(a(b(a(x1))))) c#(b(x1)) -> a#(a(c(x1))) -> a#(a(x1)) -> b#(a(b(a(x1)))) c#(b(x1)) -> a#(a(c(x1))) -> a#(a(x1)) -> a#(b(a(x1))) c#(b(x1)) -> a#(a(c(x1))) -> a#(a(x1)) -> b#(a(x1)) c#(a(x1)) -> c#(x1) -> c#(c(x1)) -> c#(d(c(x1))) c#(a(x1)) -> c#(x1) -> c#(c(x1)) -> d#(c(x1)) c#(a(x1)) -> c#(x1) -> c#(b(x1)) -> b#(a(d(x1))) c#(a(x1)) -> c#(x1) -> c#(b(x1)) -> a#(d(x1)) c#(a(x1)) -> c#(x1) -> c#(b(x1)) -> d#(x1) c#(a(x1)) -> c#(x1) -> c#(b(x1)) -> a#(a(c(x1))) c#(a(x1)) -> c#(x1) -> c#(b(x1)) -> a#(c(x1)) c#(a(x1)) -> c#(x1) -> c#(b(x1)) -> c#(x1) c#(a(x1)) -> c#(x1) -> c#(a(x1)) -> a#(b(a(a(c(x1))))) c#(a(x1)) -> c#(x1) -> c#(a(x1)) -> b#(a(a(c(x1)))) c#(a(x1)) -> c#(x1) -> c#(a(x1)) -> a#(a(c(x1))) c#(a(x1)) -> c#(x1) -> c#(a(x1)) -> a#(c(x1)) c#(a(x1)) -> c#(x1) -> c#(a(x1)) -> c#(x1) c#(a(x1)) -> b#(a(a(c(x1)))) -> b#(b(b(x1))) -> a#(b(x1)) c#(a(x1)) -> a#(c(x1)) -> a#(a(a(x1))) -> a#(b(b(x1))) c#(a(x1)) -> a#(c(x1)) -> a#(a(a(x1))) -> b#(b(x1)) c#(a(x1)) -> a#(c(x1)) -> a#(a(a(x1))) -> b#(x1) c#(a(x1)) -> a#(c(x1)) -> a#(a(x1)) -> a#(b(a(b(a(x1))))) c#(a(x1)) -> a#(c(x1)) -> a#(a(x1)) -> b#(a(b(a(x1)))) c#(a(x1)) -> a#(c(x1)) -> a#(a(x1)) -> a#(b(a(x1))) c#(a(x1)) -> a#(c(x1)) -> a#(a(x1)) -> b#(a(x1)) c#(a(x1)) -> a#(b(a(a(c(x1))))) -> a#(a(a(x1))) -> a#(b(b(x1))) c#(a(x1)) -> a#(b(a(a(c(x1))))) -> a#(a(a(x1))) -> b#(b(x1)) c#(a(x1)) -> a#(b(a(a(c(x1))))) -> a#(a(a(x1))) -> b#(x1) c#(a(x1)) -> a#(b(a(a(c(x1))))) -> a#(a(x1)) -> a#(b(a(b(a(x1))))) c#(a(x1)) -> a#(b(a(a(c(x1))))) -> a#(a(x1)) -> b#(a(b(a(x1)))) c#(a(x1)) -> a#(b(a(a(c(x1))))) -> a#(a(x1)) -> a#(b(a(x1))) c#(a(x1)) -> a#(b(a(a(c(x1))))) -> a#(a(x1)) -> b#(a(x1)) c#(a(x1)) -> a#(a(c(x1))) -> a#(a(a(x1))) -> a#(b(b(x1))) c#(a(x1)) -> a#(a(c(x1))) -> a#(a(a(x1))) -> b#(b(x1)) c#(a(x1)) -> a#(a(c(x1))) -> a#(a(a(x1))) -> b#(x1) c#(a(x1)) -> a#(a(c(x1))) -> a#(a(x1)) -> a#(b(a(b(a(x1))))) c#(a(x1)) -> a#(a(c(x1))) -> a#(a(x1)) -> b#(a(b(a(x1)))) c#(a(x1)) -> a#(a(c(x1))) -> a#(a(x1)) -> a#(b(a(x1))) c#(a(x1)) -> a#(a(c(x1))) -> a#(a(x1)) -> b#(a(x1)) b#(b(b(x1))) -> a#(b(x1)) -> a#(a(a(x1))) -> a#(b(b(x1))) b#(b(b(x1))) -> a#(b(x1)) -> a#(a(a(x1))) -> b#(b(x1)) b#(b(b(x1))) -> a#(b(x1)) -> a#(a(a(x1))) -> b#(x1) b#(b(b(x1))) -> a#(b(x1)) -> a#(a(x1)) -> a#(b(a(b(a(x1))))) b#(b(b(x1))) -> a#(b(x1)) -> a#(a(x1)) -> b#(a(b(a(x1)))) b#(b(b(x1))) -> a#(b(x1)) -> a#(a(x1)) -> a#(b(a(x1))) b#(b(b(x1))) -> a#(b(x1)) -> a#(a(x1)) -> b#(a(x1)) a#(a(a(x1))) -> b#(b(x1)) -> b#(b(b(x1))) -> a#(b(x1)) a#(a(a(x1))) -> b#(x1) -> b#(b(b(x1))) -> a#(b(x1)) a#(a(a(x1))) -> a#(b(b(x1))) -> a#(a(a(x1))) -> a#(b(b(x1))) a#(a(a(x1))) -> a#(b(b(x1))) -> a#(a(a(x1))) -> b#(b(x1)) a#(a(a(x1))) -> a#(b(b(x1))) -> a#(a(a(x1))) -> b#(x1) a#(a(a(x1))) -> a#(b(b(x1))) -> a#(a(x1)) -> a#(b(a(b(a(x1))))) a#(a(a(x1))) -> a#(b(b(x1))) -> a#(a(x1)) -> b#(a(b(a(x1)))) a#(a(a(x1))) -> a#(b(b(x1))) -> a#(a(x1)) -> a#(b(a(x1))) a#(a(a(x1))) -> a#(b(b(x1))) -> a#(a(x1)) -> b#(a(x1)) a#(a(x1)) -> b#(a(b(a(x1)))) -> b#(b(b(x1))) -> a#(b(x1)) a#(a(x1)) -> b#(a(x1)) -> b#(b(b(x1))) -> a#(b(x1)) a#(a(x1)) -> a#(b(a(b(a(x1))))) -> a#(a(a(x1))) -> a#(b(b(x1))) a#(a(x1)) -> a#(b(a(b(a(x1))))) -> a#(a(a(x1))) -> b#(b(x1)) a#(a(x1)) -> a#(b(a(b(a(x1))))) -> a#(a(a(x1))) -> b#(x1) a#(a(x1)) -> a#(b(a(b(a(x1))))) -> a#(a(x1)) -> a#(b(a(b(a(x1))))) a#(a(x1)) -> a#(b(a(b(a(x1))))) -> a#(a(x1)) -> b#(a(b(a(x1)))) a#(a(x1)) -> a#(b(a(b(a(x1))))) -> a#(a(x1)) -> a#(b(a(x1))) a#(a(x1)) -> a#(b(a(b(a(x1))))) -> a#(a(x1)) -> b#(a(x1)) a#(a(x1)) -> a#(b(a(x1))) -> a#(a(a(x1))) -> a#(b(b(x1))) a#(a(x1)) -> a#(b(a(x1))) -> a#(a(a(x1))) -> b#(b(x1)) a#(a(x1)) -> a#(b(a(x1))) -> a#(a(a(x1))) -> b#(x1) a#(a(x1)) -> a#(b(a(x1))) -> a#(a(x1)) -> a#(b(a(b(a(x1))))) a#(a(x1)) -> a#(b(a(x1))) -> a#(a(x1)) -> b#(a(b(a(x1)))) a#(a(x1)) -> a#(b(a(x1))) -> a#(a(x1)) -> a#(b(a(x1))) a#(a(x1)) -> a#(b(a(x1))) -> a#(a(x1)) -> b#(a(x1)) SCC Processor: #sccs: 3 #rules: 13 #arcs: 133/625 DPs: c#(c(x1)) -> c#(d(c(x1))) c#(a(x1)) -> c#(x1) c#(b(x1)) -> c#(x1) TRS: a(a(x1)) -> a(b(a(b(a(x1))))) c(a(x1)) -> a(b(a(a(c(x1))))) b(b(b(x1))) -> a(b(x1)) c(b(x1)) -> a(a(c(x1))) c(b(x1)) -> b(a(d(x1))) d(d(x1)) -> d(b(d(b(d(x1))))) c(c(x1)) -> c(d(c(x1))) a(a(a(x1))) -> a(b(b(x1))) Polynomial Interpretation Processor: dimension: 1 interpretation: [b](x0) = x0, [d](x0) = x0, [a](x0) = x0, [c#](x0) = x0, [c](x0) = x0 + 1 orientation: c#(c(x1)) = x1 + 1 >= x1 + 1 = c#(d(c(x1))) c#(a(x1)) = x1 >= x1 = c#(x1) c#(b(x1)) = x1 >= x1 = c#(x1) a(a(x1)) = x1 >= x1 = a(b(a(b(a(x1))))) c(a(x1)) = x1 + 1 >= x1 + 1 = a(b(a(a(c(x1))))) b(b(b(x1))) = x1 >= x1 = a(b(x1)) c(b(x1)) = x1 + 1 >= x1 + 1 = a(a(c(x1))) c(b(x1)) = x1 + 1 >= x1 = b(a(d(x1))) d(d(x1)) = x1 >= x1 = d(b(d(b(d(x1))))) c(c(x1)) = x1 + 2 >= x1 + 2 = c(d(c(x1))) a(a(a(x1))) = x1 >= x1 = a(b(b(x1))) problem: DPs: c#(c(x1)) -> c#(d(c(x1))) c#(a(x1)) -> c#(x1) c#(b(x1)) -> c#(x1) TRS: a(a(x1)) -> a(b(a(b(a(x1))))) c(a(x1)) -> a(b(a(a(c(x1))))) b(b(b(x1))) -> a(b(x1)) c(b(x1)) -> a(a(c(x1))) d(d(x1)) -> d(b(d(b(d(x1))))) c(c(x1)) -> c(d(c(x1))) a(a(a(x1))) -> a(b(b(x1))) Polynomial Interpretation Processor: dimension: 1 usable rules: d(d(x1)) -> d(b(d(b(d(x1))))) interpretation: [b](x0) = x0 + 1, [d](x0) = 1, [a](x0) = x0 + 1, [c#](x0) = x0 + 1, [c](x0) = 1 orientation: c#(c(x1)) = 2 >= 2 = c#(d(c(x1))) c#(a(x1)) = x1 + 2 >= x1 + 1 = c#(x1) c#(b(x1)) = x1 + 2 >= x1 + 1 = c#(x1) a(a(x1)) = x1 + 2 >= x1 + 5 = a(b(a(b(a(x1))))) c(a(x1)) = 1 >= 5 = a(b(a(a(c(x1))))) b(b(b(x1))) = x1 + 3 >= x1 + 2 = a(b(x1)) c(b(x1)) = 1 >= 3 = a(a(c(x1))) d(d(x1)) = 1 >= 1 = d(b(d(b(d(x1))))) c(c(x1)) = 1 >= 1 = c(d(c(x1))) a(a(a(x1))) = x1 + 3 >= x1 + 3 = a(b(b(x1))) problem: DPs: c#(c(x1)) -> c#(d(c(x1))) TRS: a(a(x1)) -> a(b(a(b(a(x1))))) c(a(x1)) -> a(b(a(a(c(x1))))) b(b(b(x1))) -> a(b(x1)) c(b(x1)) -> a(a(c(x1))) d(d(x1)) -> d(b(d(b(d(x1))))) c(c(x1)) -> c(d(c(x1))) a(a(a(x1))) -> a(b(b(x1))) Polynomial Interpretation Processor: dimension: 1 usable rules: d(d(x1)) -> d(b(d(b(d(x1))))) interpretation: [b](x0) = 0, [d](x0) = 0, [a](x0) = 0, [c#](x0) = x0, [c](x0) = 1 orientation: c#(c(x1)) = 1 >= 0 = c#(d(c(x1))) a(a(x1)) = 0 >= 0 = a(b(a(b(a(x1))))) c(a(x1)) = 1 >= 0 = a(b(a(a(c(x1))))) b(b(b(x1))) = 0 >= 0 = a(b(x1)) c(b(x1)) = 1 >= 0 = a(a(c(x1))) d(d(x1)) = 0 >= 0 = d(b(d(b(d(x1))))) c(c(x1)) = 1 >= 1 = c(d(c(x1))) a(a(a(x1))) = 0 >= 0 = a(b(b(x1))) problem: DPs: TRS: a(a(x1)) -> a(b(a(b(a(x1))))) c(a(x1)) -> a(b(a(a(c(x1))))) b(b(b(x1))) -> a(b(x1)) c(b(x1)) -> a(a(c(x1))) d(d(x1)) -> d(b(d(b(d(x1))))) c(c(x1)) -> c(d(c(x1))) a(a(a(x1))) -> a(b(b(x1))) Qed DPs: d#(d(x1)) -> d#(b(d(b(d(x1))))) d#(d(x1)) -> d#(b(d(x1))) TRS: a(a(x1)) -> a(b(a(b(a(x1))))) c(a(x1)) -> a(b(a(a(c(x1))))) b(b(b(x1))) -> a(b(x1)) c(b(x1)) -> a(a(c(x1))) c(b(x1)) -> b(a(d(x1))) d(d(x1)) -> d(b(d(b(d(x1))))) c(c(x1)) -> c(d(c(x1))) a(a(a(x1))) -> a(b(b(x1))) Usable Rule Processor: DPs: d#(d(x1)) -> d#(b(d(b(d(x1))))) d#(d(x1)) -> d#(b(d(x1))) TRS: d(d(x1)) -> d(b(d(b(d(x1))))) b(b(b(x1))) -> a(b(x1)) a(a(x1)) -> a(b(a(b(a(x1))))) a(a(a(x1))) -> a(b(b(x1))) Polynomial Interpretation Processor: dimension: 1 usable rules: b(b(b(x1))) -> a(b(x1)) a(a(x1)) -> a(b(a(b(a(x1))))) a(a(a(x1))) -> a(b(b(x1))) interpretation: [b](x0) = 0, [d](x0) = 1, [a](x0) = 0, [d#](x0) = x0 orientation: d#(d(x1)) = 1 >= 0 = d#(b(d(b(d(x1))))) d#(d(x1)) = 1 >= 0 = d#(b(d(x1))) d(d(x1)) = 1 >= 1 = d(b(d(b(d(x1))))) b(b(b(x1))) = 0 >= 0 = a(b(x1)) a(a(x1)) = 0 >= 0 = a(b(a(b(a(x1))))) a(a(a(x1))) = 0 >= 0 = a(b(b(x1))) problem: DPs: TRS: d(d(x1)) -> d(b(d(b(d(x1))))) b(b(b(x1))) -> a(b(x1)) a(a(x1)) -> a(b(a(b(a(x1))))) a(a(a(x1))) -> a(b(b(x1))) Qed DPs: b#(b(b(x1))) -> a#(b(x1)) a#(a(x1)) -> b#(a(x1)) a#(a(x1)) -> a#(b(a(x1))) a#(a(x1)) -> b#(a(b(a(x1)))) a#(a(x1)) -> a#(b(a(b(a(x1))))) a#(a(a(x1))) -> b#(x1) a#(a(a(x1))) -> b#(b(x1)) a#(a(a(x1))) -> a#(b(b(x1))) TRS: a(a(x1)) -> a(b(a(b(a(x1))))) c(a(x1)) -> a(b(a(a(c(x1))))) b(b(b(x1))) -> a(b(x1)) c(b(x1)) -> a(a(c(x1))) c(b(x1)) -> b(a(d(x1))) d(d(x1)) -> d(b(d(b(d(x1))))) c(c(x1)) -> c(d(c(x1))) a(a(a(x1))) -> a(b(b(x1))) Usable Rule Processor: DPs: b#(b(b(x1))) -> a#(b(x1)) a#(a(x1)) -> b#(a(x1)) a#(a(x1)) -> a#(b(a(x1))) a#(a(x1)) -> b#(a(b(a(x1)))) a#(a(x1)) -> a#(b(a(b(a(x1))))) a#(a(a(x1))) -> b#(x1) a#(a(a(x1))) -> b#(b(x1)) a#(a(a(x1))) -> a#(b(b(x1))) TRS: b(b(b(x1))) -> a(b(x1)) a(a(x1)) -> a(b(a(b(a(x1))))) a(a(a(x1))) -> a(b(b(x1))) Root-Labeling Processor: DPs: b{#,(f8)}(f8(b)(b(b)(b(f8)(x1)))) -> a{#,(f8)}(f8(b)(b(f8)(x1))) b{#,(f8)}(f8(b)(b(b)(b(b)(x1)))) -> a{#,(f8)}(f8(b)(b(b)(x1))) b{#,(f8)}(f8(b)(b(b)(b(a)(x1)))) -> a{#,(f8)}(f8(b)(b(a)(x1))) a{#,(f8)}(f8(a)(a(f8)(x1))) -> b{#,(f8)}(f8(a)(a(f8)(x1))) a{#,(f8)}(f8(a)(a(b)(x1))) -> b{#,(f8)}(f8(a)(a(b)(x1))) a{#,(f8)}(f8(a)(a(a)(x1))) -> b{#,(f8)}(f8(a)(a(a)(x1))) a{#,(f8)}(f8(a)(a(f8)(x1))) -> a{#,(f8)}(f8(b)(b(a)(a(f8)(x1)))) a{#,(f8)}(f8(a)(a(b)(x1))) -> a{#,(f8)}(f8(b)(b(a)(a(b)(x1)))) a{#,(f8)}(f8(a)(a(a)(x1))) -> a{#,(f8)}(f8(b)(b(a)(a(a)(x1)))) a{#,(f8)}(f8(a)(a(f8)(x1))) -> b{#,(f8)}(f8(a)(a(b)(b(a)(a(f8)(x1))))) a{#,(f8)}(f8(a)(a(b)(x1))) -> b{#,(f8)}(f8(a)(a(b)(b(a)(a(b)(x1))))) a{#,(f8)}(f8(a)(a(a)(x1))) -> b{#,(f8)}(f8(a)(a(b)(b(a)(a(a)(x1))))) a{#,(f8)}(f8(a)(a(f8)(x1))) -> a{#,(f8)}(f8(b)(b(a)(a(b)(b(a)(a(f8)(x1)))))) a{#,(f8)}(f8(a)(a(b)(x1))) -> a{#,(f8)}(f8(b)(b(a)(a(b)(b(a)(a(b)(x1)))))) a{#,(f8)}(f8(a)(a(a)(x1))) -> a{#,(f8)}(f8(b)(b(a)(a(b)(b(a)(a(a)(x1)))))) a{#,(f8)}(f8(a)(a(a)(a(f8)(x1)))) -> b{#,(f8)}(f8(f8)(x1)) a{#,(f8)}(f8(a)(a(a)(a(b)(x1)))) -> b{#,(f8)}(f8(b)(x1)) a{#,(f8)}(f8(a)(a(a)(a(a)(x1)))) -> b{#,(f8)}(f8(a)(x1)) a{#,(f8)}(f8(a)(a(a)(a(f8)(x1)))) -> b{#,(f8)}(f8(b)(b(f8)(x1))) a{#,(f8)}(f8(a)(a(a)(a(b)(x1)))) -> b{#,(f8)}(f8(b)(b(b)(x1))) a{#,(f8)}(f8(a)(a(a)(a(a)(x1)))) -> b{#,(f8)}(f8(b)(b(a)(x1))) a{#,(f8)}(f8(a)(a(a)(a(f8)(x1)))) -> a{#,(f8)}(f8(b)(b(b)(b(f8)(x1)))) a{#,(f8)}(f8(a)(a(a)(a(b)(x1)))) -> a{#,(f8)}(f8(b)(b(b)(b(b)(x1)))) a{#,(f8)}(f8(a)(a(a)(a(a)(x1)))) -> a{#,(f8)}(f8(b)(b(b)(b(a)(x1)))) TRS: f8(b)(b(b)(b(b)(b(f8)(x1)))) -> f8(a)(a(b)(b(f8)(x1))) f8(b)(b(b)(b(b)(b(b)(x1)))) -> f8(a)(a(b)(b(b)(x1))) f8(b)(b(b)(b(b)(b(a)(x1)))) -> f8(a)(a(b)(b(a)(x1))) b(b)(b(b)(b(b)(b(f8)(x1)))) -> b(a)(a(b)(b(f8)(x1))) b(b)(b(b)(b(b)(b(b)(x1)))) -> b(a)(a(b)(b(b)(x1))) b(b)(b(b)(b(b)(b(a)(x1)))) -> b(a)(a(b)(b(a)(x1))) a(b)(b(b)(b(b)(b(f8)(x1)))) -> a(a)(a(b)(b(f8)(x1))) a(b)(b(b)(b(b)(b(b)(x1)))) -> a(a)(a(b)(b(b)(x1))) a(b)(b(b)(b(b)(b(a)(x1)))) -> a(a)(a(b)(b(a)(x1))) a(a)(a(f8)(x1)) -> a(b)(b(a)(a(b)(b(a)(a(f8)(x1))))) a(a)(a(b)(x1)) -> a(b)(b(a)(a(b)(b(a)(a(b)(x1))))) a(a)(a(a)(x1)) -> a(b)(b(a)(a(b)(b(a)(a(a)(x1))))) a(a)(a(a)(a(f8)(x1))) -> a(b)(b(b)(b(f8)(x1))) a(a)(a(a)(a(b)(x1))) -> a(b)(b(b)(b(b)(x1))) a(a)(a(a)(a(a)(x1))) -> a(b)(b(b)(b(a)(x1))) TDG Processor: DPs: b{#,(f8)}(f8(b)(b(b)(b(f8)(x1)))) -> a{#,(f8)}(f8(b)(b(f8)(x1))) b{#,(f8)}(f8(b)(b(b)(b(b)(x1)))) -> a{#,(f8)}(f8(b)(b(b)(x1))) b{#,(f8)}(f8(b)(b(b)(b(a)(x1)))) -> a{#,(f8)}(f8(b)(b(a)(x1))) a{#,(f8)}(f8(a)(a(f8)(x1))) -> b{#,(f8)}(f8(a)(a(f8)(x1))) a{#,(f8)}(f8(a)(a(b)(x1))) -> b{#,(f8)}(f8(a)(a(b)(x1))) a{#,(f8)}(f8(a)(a(a)(x1))) -> b{#,(f8)}(f8(a)(a(a)(x1))) a{#,(f8)}(f8(a)(a(f8)(x1))) -> a{#,(f8)}(f8(b)(b(a)(a(f8)(x1)))) a{#,(f8)}(f8(a)(a(b)(x1))) -> a{#,(f8)}(f8(b)(b(a)(a(b)(x1)))) a{#,(f8)}(f8(a)(a(a)(x1))) -> a{#,(f8)}(f8(b)(b(a)(a(a)(x1)))) a{#,(f8)}(f8(a)(a(f8)(x1))) -> b{#,(f8)}(f8(a)(a(b)(b(a)(a(f8)(x1))))) a{#,(f8)}(f8(a)(a(b)(x1))) -> b{#,(f8)}(f8(a)(a(b)(b(a)(a(b)(x1))))) a{#,(f8)}(f8(a)(a(a)(x1))) -> b{#,(f8)}(f8(a)(a(b)(b(a)(a(a)(x1))))) a{#,(f8)}(f8(a)(a(f8)(x1))) -> a{#,(f8)}(f8(b)(b(a)(a(b)(b(a)(a(f8)(x1)))))) a{#,(f8)}(f8(a)(a(b)(x1))) -> a{#,(f8)}(f8(b)(b(a)(a(b)(b(a)(a(b)(x1)))))) a{#,(f8)}(f8(a)(a(a)(x1))) -> a{#,(f8)}(f8(b)(b(a)(a(b)(b(a)(a(a)(x1)))))) a{#,(f8)}(f8(a)(a(a)(a(f8)(x1)))) -> b{#,(f8)}(f8(f8)(x1)) a{#,(f8)}(f8(a)(a(a)(a(b)(x1)))) -> b{#,(f8)}(f8(b)(x1)) a{#,(f8)}(f8(a)(a(a)(a(a)(x1)))) -> b{#,(f8)}(f8(a)(x1)) a{#,(f8)}(f8(a)(a(a)(a(f8)(x1)))) -> b{#,(f8)}(f8(b)(b(f8)(x1))) a{#,(f8)}(f8(a)(a(a)(a(b)(x1)))) -> b{#,(f8)}(f8(b)(b(b)(x1))) a{#,(f8)}(f8(a)(a(a)(a(a)(x1)))) -> b{#,(f8)}(f8(b)(b(a)(x1))) a{#,(f8)}(f8(a)(a(a)(a(f8)(x1)))) -> a{#,(f8)}(f8(b)(b(b)(b(f8)(x1)))) a{#,(f8)}(f8(a)(a(a)(a(b)(x1)))) -> a{#,(f8)}(f8(b)(b(b)(b(b)(x1)))) a{#,(f8)}(f8(a)(a(a)(a(a)(x1)))) -> a{#,(f8)}(f8(b)(b(b)(b(a)(x1)))) TRS: f8(b)(b(b)(b(b)(b(f8)(x1)))) -> f8(a)(a(b)(b(f8)(x1))) f8(b)(b(b)(b(b)(b(b)(x1)))) -> f8(a)(a(b)(b(b)(x1))) f8(b)(b(b)(b(b)(b(a)(x1)))) -> f8(a)(a(b)(b(a)(x1))) b(b)(b(b)(b(b)(b(f8)(x1)))) -> b(a)(a(b)(b(f8)(x1))) b(b)(b(b)(b(b)(b(b)(x1)))) -> b(a)(a(b)(b(b)(x1))) b(b)(b(b)(b(b)(b(a)(x1)))) -> b(a)(a(b)(b(a)(x1))) a(b)(b(b)(b(b)(b(f8)(x1)))) -> a(a)(a(b)(b(f8)(x1))) a(b)(b(b)(b(b)(b(b)(x1)))) -> a(a)(a(b)(b(b)(x1))) a(b)(b(b)(b(b)(b(a)(x1)))) -> a(a)(a(b)(b(a)(x1))) a(a)(a(f8)(x1)) -> a(b)(b(a)(a(b)(b(a)(a(f8)(x1))))) a(a)(a(b)(x1)) -> a(b)(b(a)(a(b)(b(a)(a(b)(x1))))) a(a)(a(a)(x1)) -> a(b)(b(a)(a(b)(b(a)(a(a)(x1))))) a(a)(a(a)(a(f8)(x1))) -> a(b)(b(b)(b(f8)(x1))) a(a)(a(a)(a(b)(x1))) -> a(b)(b(b)(b(b)(x1))) a(a)(a(a)(a(a)(x1))) -> a(b)(b(b)(b(a)(x1))) graph: a{#,(f8)}(f8(a)(a(a)(a(a)(x1)))) -> a{#,(f8)}(f8(b)(b(b)(b(a)(x1)))) -> a{#,(f8)}(f8(a)(a(a)(a(a)(x1)))) -> a{#,(f8)}(f8(b)(b(b)(b(a)(x1)))) a{#,(f8)}(f8(a)(a(a)(a(a)(x1)))) -> a{#,(f8)}(f8(b)(b(b)(b(a)(x1)))) -> a{#,(f8)}(f8(a)(a(a)(a(b)(x1)))) -> a{#,(f8)}(f8(b)(b(b)(b(b)(x1)))) a{#,(f8)}(f8(a)(a(a)(a(a)(x1)))) -> a{#,(f8)}(f8(b)(b(b)(b(a)(x1)))) -> a{#,(f8)}(f8(a)(a(a)(a(f8)(x1)))) -> a{#,(f8)}(f8(b)(b(b)(b(f8)(x1)))) a{#,(f8)}(f8(a)(a(a)(a(a)(x1)))) -> a{#,(f8)}(f8(b)(b(b)(b(a)(x1)))) -> a{#,(f8)}(f8(a)(a(a)(a(a)(x1)))) -> b{#,(f8)}(f8(b)(b(a)(x1))) a{#,(f8)}(f8(a)(a(a)(a(a)(x1)))) -> a{#,(f8)}(f8(b)(b(b)(b(a)(x1)))) -> a{#,(f8)}(f8(a)(a(a)(a(b)(x1)))) -> b{#,(f8)}(f8(b)(b(b)(x1))) a{#,(f8)}(f8(a)(a(a)(a(a)(x1)))) -> a{#,(f8)}(f8(b)(b(b)(b(a)(x1)))) -> a{#,(f8)}(f8(a)(a(a)(a(f8)(x1)))) -> b{#,(f8)}(f8(b)(b(f8)(x1))) a{#,(f8)}(f8(a)(a(a)(a(a)(x1)))) -> a{#,(f8)}(f8(b)(b(b)(b(a)(x1)))) -> a{#,(f8)}(f8(a)(a(a)(a(a)(x1)))) -> b{#,(f8)}(f8(a)(x1)) a{#,(f8)}(f8(a)(a(a)(a(a)(x1)))) -> a{#,(f8)}(f8(b)(b(b)(b(a)(x1)))) -> a{#,(f8)}(f8(a)(a(a)(a(b)(x1)))) -> b{#,(f8)}(f8(b)(x1)) a{#,(f8)}(f8(a)(a(a)(a(a)(x1)))) -> a{#,(f8)}(f8(b)(b(b)(b(a)(x1)))) -> a{#,(f8)}(f8(a)(a(a)(a(f8)(x1)))) -> b{#,(f8)}(f8(f8)(x1)) a{#,(f8)}(f8(a)(a(a)(a(a)(x1)))) -> a{#,(f8)}(f8(b)(b(b)(b(a)(x1)))) -> a{#,(f8)}(f8(a)(a(a)(x1))) -> a{#,(f8)}(f8(b)(b(a)(a(b)(b(a)(a(a)(x1)))))) a{#,(f8)}(f8(a)(a(a)(a(a)(x1)))) -> a{#,(f8)}(f8(b)(b(b)(b(a)(x1)))) -> a{#,(f8)}(f8(a)(a(b)(x1))) -> a{#,(f8)}(f8(b)(b(a)(a(b)(b(a)(a(b)(x1)))))) a{#,(f8)}(f8(a)(a(a)(a(a)(x1)))) -> a{#,(f8)}(f8(b)(b(b)(b(a)(x1)))) -> a{#,(f8)}(f8(a)(a(f8)(x1))) -> a{#,(f8)}(f8(b)(b(a)(a(b)(b(a)(a(f8)(x1)))))) a{#,(f8)}(f8(a)(a(a)(a(a)(x1)))) -> a{#,(f8)}(f8(b)(b(b)(b(a)(x1)))) -> a{#,(f8)}(f8(a)(a(a)(x1))) -> b{#,(f8)}(f8(a)(a(b)(b(a)(a(a)(x1))))) a{#,(f8)}(f8(a)(a(a)(a(a)(x1)))) -> a{#,(f8)}(f8(b)(b(b)(b(a)(x1)))) -> a{#,(f8)}(f8(a)(a(b)(x1))) -> b{#,(f8)}(f8(a)(a(b)(b(a)(a(b)(x1))))) a{#,(f8)}(f8(a)(a(a)(a(a)(x1)))) -> a{#,(f8)}(f8(b)(b(b)(b(a)(x1)))) -> a{#,(f8)}(f8(a)(a(f8)(x1))) -> b{#,(f8)}(f8(a)(a(b)(b(a)(a(f8)(x1))))) a{#,(f8)}(f8(a)(a(a)(a(a)(x1)))) -> a{#,(f8)}(f8(b)(b(b)(b(a)(x1)))) -> a{#,(f8)}(f8(a)(a(a)(x1))) -> a{#,(f8)}(f8(b)(b(a)(a(a)(x1)))) a{#,(f8)}(f8(a)(a(a)(a(a)(x1)))) -> a{#,(f8)}(f8(b)(b(b)(b(a)(x1)))) -> a{#,(f8)}(f8(a)(a(b)(x1))) -> a{#,(f8)}(f8(b)(b(a)(a(b)(x1)))) a{#,(f8)}(f8(a)(a(a)(a(a)(x1)))) -> a{#,(f8)}(f8(b)(b(b)(b(a)(x1)))) -> a{#,(f8)}(f8(a)(a(f8)(x1))) -> a{#,(f8)}(f8(b)(b(a)(a(f8)(x1)))) a{#,(f8)}(f8(a)(a(a)(a(a)(x1)))) -> a{#,(f8)}(f8(b)(b(b)(b(a)(x1)))) -> a{#,(f8)}(f8(a)(a(a)(x1))) -> b{#,(f8)}(f8(a)(a(a)(x1))) a{#,(f8)}(f8(a)(a(a)(a(a)(x1)))) -> a{#,(f8)}(f8(b)(b(b)(b(a)(x1)))) -> a{#,(f8)}(f8(a)(a(b)(x1))) -> b{#,(f8)}(f8(a)(a(b)(x1))) a{#,(f8)}(f8(a)(a(a)(a(a)(x1)))) -> a{#,(f8)}(f8(b)(b(b)(b(a)(x1)))) -> a{#,(f8)}(f8(a)(a(f8)(x1))) -> b{#,(f8)}(f8(a)(a(f8)(x1))) a{#,(f8)}(f8(a)(a(a)(a(a)(x1)))) -> b{#,(f8)}(f8(a)(x1)) -> b{#,(f8)}(f8(b)(b(b)(b(a)(x1)))) -> a{#,(f8)}(f8(b)(b(a)(x1))) a{#,(f8)}(f8(a)(a(a)(a(a)(x1)))) -> b{#,(f8)}(f8(a)(x1)) -> b{#,(f8)}(f8(b)(b(b)(b(b)(x1)))) -> a{#,(f8)}(f8(b)(b(b)(x1))) a{#,(f8)}(f8(a)(a(a)(a(a)(x1)))) -> b{#,(f8)}(f8(a)(x1)) -> b{#,(f8)}(f8(b)(b(b)(b(f8)(x1)))) -> a{#,(f8)}(f8(b)(b(f8)(x1))) a{#,(f8)}(f8(a)(a(a)(a(a)(x1)))) -> b{#,(f8)}(f8(b)(b(a)(x1))) -> b{#,(f8)}(f8(b)(b(b)(b(a)(x1)))) -> a{#,(f8)}(f8(b)(b(a)(x1))) a{#,(f8)}(f8(a)(a(a)(a(a)(x1)))) -> b{#,(f8)}(f8(b)(b(a)(x1))) -> b{#,(f8)}(f8(b)(b(b)(b(b)(x1)))) -> a{#,(f8)}(f8(b)(b(b)(x1))) a{#,(f8)}(f8(a)(a(a)(a(a)(x1)))) -> b{#,(f8)}(f8(b)(b(a)(x1))) -> b{#,(f8)}(f8(b)(b(b)(b(f8)(x1)))) -> a{#,(f8)}(f8(b)(b(f8)(x1))) a{#,(f8)}(f8(a)(a(a)(a(b)(x1)))) -> a{#,(f8)}(f8(b)(b(b)(b(b)(x1)))) -> a{#,(f8)}(f8(a)(a(a)(a(a)(x1)))) -> a{#,(f8)}(f8(b)(b(b)(b(a)(x1)))) a{#,(f8)}(f8(a)(a(a)(a(b)(x1)))) -> a{#,(f8)}(f8(b)(b(b)(b(b)(x1)))) -> a{#,(f8)}(f8(a)(a(a)(a(b)(x1)))) -> a{#,(f8)}(f8(b)(b(b)(b(b)(x1)))) a{#,(f8)}(f8(a)(a(a)(a(b)(x1)))) -> a{#,(f8)}(f8(b)(b(b)(b(b)(x1)))) -> a{#,(f8)}(f8(a)(a(a)(a(f8)(x1)))) -> a{#,(f8)}(f8(b)(b(b)(b(f8)(x1)))) a{#,(f8)}(f8(a)(a(a)(a(b)(x1)))) -> a{#,(f8)}(f8(b)(b(b)(b(b)(x1)))) -> a{#,(f8)}(f8(a)(a(a)(a(a)(x1)))) -> b{#,(f8)}(f8(b)(b(a)(x1))) a{#,(f8)}(f8(a)(a(a)(a(b)(x1)))) -> a{#,(f8)}(f8(b)(b(b)(b(b)(x1)))) -> a{#,(f8)}(f8(a)(a(a)(a(b)(x1)))) -> b{#,(f8)}(f8(b)(b(b)(x1))) a{#,(f8)}(f8(a)(a(a)(a(b)(x1)))) -> a{#,(f8)}(f8(b)(b(b)(b(b)(x1)))) -> a{#,(f8)}(f8(a)(a(a)(a(f8)(x1)))) -> b{#,(f8)}(f8(b)(b(f8)(x1))) a{#,(f8)}(f8(a)(a(a)(a(b)(x1)))) -> a{#,(f8)}(f8(b)(b(b)(b(b)(x1)))) -> a{#,(f8)}(f8(a)(a(a)(a(a)(x1)))) -> b{#,(f8)}(f8(a)(x1)) a{#,(f8)}(f8(a)(a(a)(a(b)(x1)))) -> a{#,(f8)}(f8(b)(b(b)(b(b)(x1)))) -> a{#,(f8)}(f8(a)(a(a)(a(b)(x1)))) -> b{#,(f8)}(f8(b)(x1)) a{#,(f8)}(f8(a)(a(a)(a(b)(x1)))) -> a{#,(f8)}(f8(b)(b(b)(b(b)(x1)))) -> a{#,(f8)}(f8(a)(a(a)(a(f8)(x1)))) -> b{#,(f8)}(f8(f8)(x1)) a{#,(f8)}(f8(a)(a(a)(a(b)(x1)))) -> a{#,(f8)}(f8(b)(b(b)(b(b)(x1)))) -> a{#,(f8)}(f8(a)(a(a)(x1))) -> a{#,(f8)}(f8(b)(b(a)(a(b)(b(a)(a(a)(x1)))))) a{#,(f8)}(f8(a)(a(a)(a(b)(x1)))) -> a{#,(f8)}(f8(b)(b(b)(b(b)(x1)))) -> a{#,(f8)}(f8(a)(a(b)(x1))) -> a{#,(f8)}(f8(b)(b(a)(a(b)(b(a)(a(b)(x1)))))) a{#,(f8)}(f8(a)(a(a)(a(b)(x1)))) -> a{#,(f8)}(f8(b)(b(b)(b(b)(x1)))) -> a{#,(f8)}(f8(a)(a(f8)(x1))) -> a{#,(f8)}(f8(b)(b(a)(a(b)(b(a)(a(f8)(x1)))))) a{#,(f8)}(f8(a)(a(a)(a(b)(x1)))) -> a{#,(f8)}(f8(b)(b(b)(b(b)(x1)))) -> a{#,(f8)}(f8(a)(a(a)(x1))) -> b{#,(f8)}(f8(a)(a(b)(b(a)(a(a)(x1))))) a{#,(f8)}(f8(a)(a(a)(a(b)(x1)))) -> a{#,(f8)}(f8(b)(b(b)(b(b)(x1)))) -> a{#,(f8)}(f8(a)(a(b)(x1))) -> b{#,(f8)}(f8(a)(a(b)(b(a)(a(b)(x1))))) a{#,(f8)}(f8(a)(a(a)(a(b)(x1)))) -> a{#,(f8)}(f8(b)(b(b)(b(b)(x1)))) -> a{#,(f8)}(f8(a)(a(f8)(x1))) -> b{#,(f8)}(f8(a)(a(b)(b(a)(a(f8)(x1))))) a{#,(f8)}(f8(a)(a(a)(a(b)(x1)))) -> a{#,(f8)}(f8(b)(b(b)(b(b)(x1)))) -> a{#,(f8)}(f8(a)(a(a)(x1))) -> a{#,(f8)}(f8(b)(b(a)(a(a)(x1)))) a{#,(f8)}(f8(a)(a(a)(a(b)(x1)))) -> a{#,(f8)}(f8(b)(b(b)(b(b)(x1)))) -> a{#,(f8)}(f8(a)(a(b)(x1))) -> a{#,(f8)}(f8(b)(b(a)(a(b)(x1)))) a{#,(f8)}(f8(a)(a(a)(a(b)(x1)))) -> a{#,(f8)}(f8(b)(b(b)(b(b)(x1)))) -> a{#,(f8)}(f8(a)(a(f8)(x1))) -> a{#,(f8)}(f8(b)(b(a)(a(f8)(x1)))) a{#,(f8)}(f8(a)(a(a)(a(b)(x1)))) -> a{#,(f8)}(f8(b)(b(b)(b(b)(x1)))) -> a{#,(f8)}(f8(a)(a(a)(x1))) -> b{#,(f8)}(f8(a)(a(a)(x1))) a{#,(f8)}(f8(a)(a(a)(a(b)(x1)))) -> a{#,(f8)}(f8(b)(b(b)(b(b)(x1)))) -> a{#,(f8)}(f8(a)(a(b)(x1))) -> b{#,(f8)}(f8(a)(a(b)(x1))) a{#,(f8)}(f8(a)(a(a)(a(b)(x1)))) -> a{#,(f8)}(f8(b)(b(b)(b(b)(x1)))) -> a{#,(f8)}(f8(a)(a(f8)(x1))) -> b{#,(f8)}(f8(a)(a(f8)(x1))) a{#,(f8)}(f8(a)(a(a)(a(b)(x1)))) -> b{#,(f8)}(f8(b)(b(b)(x1))) -> b{#,(f8)}(f8(b)(b(b)(b(a)(x1)))) -> a{#,(f8)}(f8(b)(b(a)(x1))) a{#,(f8)}(f8(a)(a(a)(a(b)(x1)))) -> b{#,(f8)}(f8(b)(b(b)(x1))) -> b{#,(f8)}(f8(b)(b(b)(b(b)(x1)))) -> a{#,(f8)}(f8(b)(b(b)(x1))) a{#,(f8)}(f8(a)(a(a)(a(b)(x1)))) -> b{#,(f8)}(f8(b)(b(b)(x1))) -> b{#,(f8)}(f8(b)(b(b)(b(f8)(x1)))) -> a{#,(f8)}(f8(b)(b(f8)(x1))) a{#,(f8)}(f8(a)(a(a)(a(b)(x1)))) -> b{#,(f8)}(f8(b)(x1)) -> b{#,(f8)}(f8(b)(b(b)(b(a)(x1)))) -> a{#,(f8)}(f8(b)(b(a)(x1))) a{#,(f8)}(f8(a)(a(a)(a(b)(x1)))) -> b{#,(f8)}(f8(b)(x1)) -> b{#,(f8)}(f8(b)(b(b)(b(b)(x1)))) -> a{#,(f8)}(f8(b)(b(b)(x1))) a{#,(f8)}(f8(a)(a(a)(a(b)(x1)))) -> b{#,(f8)}(f8(b)(x1)) -> b{#,(f8)}(f8(b)(b(b)(b(f8)(x1)))) -> a{#,(f8)}(f8(b)(b(f8)(x1))) a{#,(f8)}(f8(a)(a(a)(a(f8)(x1)))) -> a{#,(f8)}(f8(b)(b(b)(b(f8)(x1)))) -> a{#,(f8)}(f8(a)(a(a)(a(a)(x1)))) -> a{#,(f8)}(f8(b)(b(b)(b(a)(x1)))) a{#,(f8)}(f8(a)(a(a)(a(f8)(x1)))) -> a{#,(f8)}(f8(b)(b(b)(b(f8)(x1)))) -> a{#,(f8)}(f8(a)(a(a)(a(b)(x1)))) -> a{#,(f8)}(f8(b)(b(b)(b(b)(x1)))) a{#,(f8)}(f8(a)(a(a)(a(f8)(x1)))) -> a{#,(f8)}(f8(b)(b(b)(b(f8)(x1)))) -> a{#,(f8)}(f8(a)(a(a)(a(f8)(x1)))) -> a{#,(f8)}(f8(b)(b(b)(b(f8)(x1)))) a{#,(f8)}(f8(a)(a(a)(a(f8)(x1)))) -> a{#,(f8)}(f8(b)(b(b)(b(f8)(x1)))) -> a{#,(f8)}(f8(a)(a(a)(a(a)(x1)))) -> b{#,(f8)}(f8(b)(b(a)(x1))) a{#,(f8)}(f8(a)(a(a)(a(f8)(x1)))) -> a{#,(f8)}(f8(b)(b(b)(b(f8)(x1)))) -> a{#,(f8)}(f8(a)(a(a)(a(b)(x1)))) -> b{#,(f8)}(f8(b)(b(b)(x1))) a{#,(f8)}(f8(a)(a(a)(a(f8)(x1)))) -> a{#,(f8)}(f8(b)(b(b)(b(f8)(x1)))) -> a{#,(f8)}(f8(a)(a(a)(a(f8)(x1)))) -> b{#,(f8)}(f8(b)(b(f8)(x1))) a{#,(f8)}(f8(a)(a(a)(a(f8)(x1)))) -> a{#,(f8)}(f8(b)(b(b)(b(f8)(x1)))) -> a{#,(f8)}(f8(a)(a(a)(a(a)(x1)))) -> b{#,(f8)}(f8(a)(x1)) a{#,(f8)}(f8(a)(a(a)(a(f8)(x1)))) -> a{#,(f8)}(f8(b)(b(b)(b(f8)(x1)))) -> a{#,(f8)}(f8(a)(a(a)(a(b)(x1)))) -> b{#,(f8)}(f8(b)(x1)) a{#,(f8)}(f8(a)(a(a)(a(f8)(x1)))) -> a{#,(f8)}(f8(b)(b(b)(b(f8)(x1)))) -> a{#,(f8)}(f8(a)(a(a)(a(f8)(x1)))) -> b{#,(f8)}(f8(f8)(x1)) a{#,(f8)}(f8(a)(a(a)(a(f8)(x1)))) -> a{#,(f8)}(f8(b)(b(b)(b(f8)(x1)))) -> a{#,(f8)}(f8(a)(a(a)(x1))) -> a{#,(f8)}(f8(b)(b(a)(a(b)(b(a)(a(a)(x1)))))) a{#,(f8)}(f8(a)(a(a)(a(f8)(x1)))) -> a{#,(f8)}(f8(b)(b(b)(b(f8)(x1)))) -> a{#,(f8)}(f8(a)(a(b)(x1))) -> a{#,(f8)}(f8(b)(b(a)(a(b)(b(a)(a(b)(x1)))))) a{#,(f8)}(f8(a)(a(a)(a(f8)(x1)))) -> a{#,(f8)}(f8(b)(b(b)(b(f8)(x1)))) -> a{#,(f8)}(f8(a)(a(f8)(x1))) -> a{#,(f8)}(f8(b)(b(a)(a(b)(b(a)(a(f8)(x1)))))) a{#,(f8)}(f8(a)(a(a)(a(f8)(x1)))) -> a{#,(f8)}(f8(b)(b(b)(b(f8)(x1)))) -> a{#,(f8)}(f8(a)(a(a)(x1))) -> b{#,(f8)}(f8(a)(a(b)(b(a)(a(a)(x1))))) a{#,(f8)}(f8(a)(a(a)(a(f8)(x1)))) -> a{#,(f8)}(f8(b)(b(b)(b(f8)(x1)))) -> a{#,(f8)}(f8(a)(a(b)(x1))) -> b{#,(f8)}(f8(a)(a(b)(b(a)(a(b)(x1))))) a{#,(f8)}(f8(a)(a(a)(a(f8)(x1)))) -> a{#,(f8)}(f8(b)(b(b)(b(f8)(x1)))) -> a{#,(f8)}(f8(a)(a(f8)(x1))) -> b{#,(f8)}(f8(a)(a(b)(b(a)(a(f8)(x1))))) a{#,(f8)}(f8(a)(a(a)(a(f8)(x1)))) -> a{#,(f8)}(f8(b)(b(b)(b(f8)(x1)))) -> a{#,(f8)}(f8(a)(a(a)(x1))) -> a{#,(f8)}(f8(b)(b(a)(a(a)(x1)))) a{#,(f8)}(f8(a)(a(a)(a(f8)(x1)))) -> a{#,(f8)}(f8(b)(b(b)(b(f8)(x1)))) -> a{#,(f8)}(f8(a)(a(b)(x1))) -> a{#,(f8)}(f8(b)(b(a)(a(b)(x1)))) a{#,(f8)}(f8(a)(a(a)(a(f8)(x1)))) -> a{#,(f8)}(f8(b)(b(b)(b(f8)(x1)))) -> a{#,(f8)}(f8(a)(a(f8)(x1))) -> a{#,(f8)}(f8(b)(b(a)(a(f8)(x1)))) a{#,(f8)}(f8(a)(a(a)(a(f8)(x1)))) -> a{#,(f8)}(f8(b)(b(b)(b(f8)(x1)))) -> a{#,(f8)}(f8(a)(a(a)(x1))) -> b{#,(f8)}(f8(a)(a(a)(x1))) a{#,(f8)}(f8(a)(a(a)(a(f8)(x1)))) -> a{#,(f8)}(f8(b)(b(b)(b(f8)(x1)))) -> a{#,(f8)}(f8(a)(a(b)(x1))) -> b{#,(f8)}(f8(a)(a(b)(x1))) a{#,(f8)}(f8(a)(a(a)(a(f8)(x1)))) -> a{#,(f8)}(f8(b)(b(b)(b(f8)(x1)))) -> a{#,(f8)}(f8(a)(a(f8)(x1))) -> b{#,(f8)}(f8(a)(a(f8)(x1))) a{#,(f8)}(f8(a)(a(a)(a(f8)(x1)))) -> b{#,(f8)}(f8(f8)(x1)) -> b{#,(f8)}(f8(b)(b(b)(b(a)(x1)))) -> a{#,(f8)}(f8(b)(b(a)(x1))) a{#,(f8)}(f8(a)(a(a)(a(f8)(x1)))) -> b{#,(f8)}(f8(f8)(x1)) -> b{#,(f8)}(f8(b)(b(b)(b(b)(x1)))) -> a{#,(f8)}(f8(b)(b(b)(x1))) a{#,(f8)}(f8(a)(a(a)(a(f8)(x1)))) -> b{#,(f8)}(f8(f8)(x1)) -> b{#,(f8)}(f8(b)(b(b)(b(f8)(x1)))) -> a{#,(f8)}(f8(b)(b(f8)(x1))) a{#,(f8)}(f8(a)(a(a)(a(f8)(x1)))) -> b{#,(f8)}(f8(b)(b(f8)(x1))) -> b{#,(f8)}(f8(b)(b(b)(b(a)(x1)))) -> a{#,(f8)}(f8(b)(b(a)(x1))) a{#,(f8)}(f8(a)(a(a)(a(f8)(x1)))) -> b{#,(f8)}(f8(b)(b(f8)(x1))) -> b{#,(f8)}(f8(b)(b(b)(b(b)(x1)))) -> a{#,(f8)}(f8(b)(b(b)(x1))) a{#,(f8)}(f8(a)(a(a)(a(f8)(x1)))) -> b{#,(f8)}(f8(b)(b(f8)(x1))) -> b{#,(f8)}(f8(b)(b(b)(b(f8)(x1)))) -> a{#,(f8)}(f8(b)(b(f8)(x1))) a{#,(f8)}(f8(a)(a(a)(x1))) -> a{#,(f8)}(f8(b)(b(a)(a(a)(x1)))) -> a{#,(f8)}(f8(a)(a(a)(a(a)(x1)))) -> a{#,(f8)}(f8(b)(b(b)(b(a)(x1)))) a{#,(f8)}(f8(a)(a(a)(x1))) -> a{#,(f8)}(f8(b)(b(a)(a(a)(x1)))) -> a{#,(f8)}(f8(a)(a(a)(a(b)(x1)))) -> a{#,(f8)}(f8(b)(b(b)(b(b)(x1)))) a{#,(f8)}(f8(a)(a(a)(x1))) -> a{#,(f8)}(f8(b)(b(a)(a(a)(x1)))) -> a{#,(f8)}(f8(a)(a(a)(a(f8)(x1)))) -> a{#,(f8)}(f8(b)(b(b)(b(f8)(x1)))) a{#,(f8)}(f8(a)(a(a)(x1))) -> a{#,(f8)}(f8(b)(b(a)(a(a)(x1)))) -> a{#,(f8)}(f8(a)(a(a)(a(a)(x1)))) -> b{#,(f8)}(f8(b)(b(a)(x1))) a{#,(f8)}(f8(a)(a(a)(x1))) -> a{#,(f8)}(f8(b)(b(a)(a(a)(x1)))) -> a{#,(f8)}(f8(a)(a(a)(a(b)(x1)))) -> b{#,(f8)}(f8(b)(b(b)(x1))) a{#,(f8)}(f8(a)(a(a)(x1))) -> a{#,(f8)}(f8(b)(b(a)(a(a)(x1)))) -> a{#,(f8)}(f8(a)(a(a)(a(f8)(x1)))) -> b{#,(f8)}(f8(b)(b(f8)(x1))) a{#,(f8)}(f8(a)(a(a)(x1))) -> a{#,(f8)}(f8(b)(b(a)(a(a)(x1)))) -> a{#,(f8)}(f8(a)(a(a)(a(a)(x1)))) -> b{#,(f8)}(f8(a)(x1)) a{#,(f8)}(f8(a)(a(a)(x1))) -> a{#,(f8)}(f8(b)(b(a)(a(a)(x1)))) -> a{#,(f8)}(f8(a)(a(a)(a(b)(x1)))) -> b{#,(f8)}(f8(b)(x1)) a{#,(f8)}(f8(a)(a(a)(x1))) -> a{#,(f8)}(f8(b)(b(a)(a(a)(x1)))) -> a{#,(f8)}(f8(a)(a(a)(a(f8)(x1)))) -> b{#,(f8)}(f8(f8)(x1)) a{#,(f8)}(f8(a)(a(a)(x1))) -> a{#,(f8)}(f8(b)(b(a)(a(a)(x1)))) -> a{#,(f8)}(f8(a)(a(a)(x1))) -> a{#,(f8)}(f8(b)(b(a)(a(b)(b(a)(a(a)(x1)))))) a{#,(f8)}(f8(a)(a(a)(x1))) -> a{#,(f8)}(f8(b)(b(a)(a(a)(x1)))) -> a{#,(f8)}(f8(a)(a(b)(x1))) -> a{#,(f8)}(f8(b)(b(a)(a(b)(b(a)(a(b)(x1)))))) a{#,(f8)}(f8(a)(a(a)(x1))) -> a{#,(f8)}(f8(b)(b(a)(a(a)(x1)))) -> a{#,(f8)}(f8(a)(a(f8)(x1))) -> a{#,(f8)}(f8(b)(b(a)(a(b)(b(a)(a(f8)(x1)))))) a{#,(f8)}(f8(a)(a(a)(x1))) -> a{#,(f8)}(f8(b)(b(a)(a(a)(x1)))) -> a{#,(f8)}(f8(a)(a(a)(x1))) -> b{#,(f8)}(f8(a)(a(b)(b(a)(a(a)(x1))))) a{#,(f8)}(f8(a)(a(a)(x1))) -> a{#,(f8)}(f8(b)(b(a)(a(a)(x1)))) -> a{#,(f8)}(f8(a)(a(b)(x1))) -> b{#,(f8)}(f8(a)(a(b)(b(a)(a(b)(x1))))) a{#,(f8)}(f8(a)(a(a)(x1))) -> a{#,(f8)}(f8(b)(b(a)(a(a)(x1)))) -> a{#,(f8)}(f8(a)(a(f8)(x1))) -> b{#,(f8)}(f8(a)(a(b)(b(a)(a(f8)(x1))))) a{#,(f8)}(f8(a)(a(a)(x1))) -> a{#,(f8)}(f8(b)(b(a)(a(a)(x1)))) -> a{#,(f8)}(f8(a)(a(a)(x1))) -> a{#,(f8)}(f8(b)(b(a)(a(a)(x1)))) a{#,(f8)}(f8(a)(a(a)(x1))) -> a{#,(f8)}(f8(b)(b(a)(a(a)(x1)))) -> a{#,(f8)}(f8(a)(a(b)(x1))) -> a{#,(f8)}(f8(b)(b(a)(a(b)(x1)))) a{#,(f8)}(f8(a)(a(a)(x1))) -> a{#,(f8)}(f8(b)(b(a)(a(a)(x1)))) -> a{#,(f8)}(f8(a)(a(f8)(x1))) -> a{#,(f8)}(f8(b)(b(a)(a(f8)(x1)))) a{#,(f8)}(f8(a)(a(a)(x1))) -> a{#,(f8)}(f8(b)(b(a)(a(a)(x1)))) -> a{#,(f8)}(f8(a)(a(a)(x1))) -> b{#,(f8)}(f8(a)(a(a)(x1))) a{#,(f8)}(f8(a)(a(a)(x1))) -> a{#,(f8)}(f8(b)(b(a)(a(a)(x1)))) -> a{#,(f8)}(f8(a)(a(b)(x1))) -> b{#,(f8)}(f8(a)(a(b)(x1))) a{#,(f8)}(f8(a)(a(a)(x1))) -> a{#,(f8)}(f8(b)(b(a)(a(a)(x1)))) -> a{#,(f8)}(f8(a)(a(f8)(x1))) -> b{#,(f8)}(f8(a)(a(f8)(x1))) a{#,(f8)}(f8(a)(a(a)(x1))) -> a{#,(f8)}(f8(b)(b(a)(a(b)(b(a)(a(a)(x1)))))) -> a{#,(f8)}(f8(a)(a(a)(a(a)(x1)))) -> a{#,(f8)}(f8(b)(b(b)(b(a)(x1)))) a{#,(f8)}(f8(a)(a(a)(x1))) -> a{#,(f8)}(f8(b)(b(a)(a(b)(b(a)(a(a)(x1)))))) -> a{#,(f8)}(f8(a)(a(a)(a(b)(x1)))) -> a{#,(f8)}(f8(b)(b(b)(b(b)(x1)))) a{#,(f8)}(f8(a)(a(a)(x1))) -> a{#,(f8)}(f8(b)(b(a)(a(b)(b(a)(a(a)(x1)))))) -> a{#,(f8)}(f8(a)(a(a)(a(f8)(x1)))) -> a{#,(f8)}(f8(b)(b(b)(b(f8)(x1)))) a{#,(f8)}(f8(a)(a(a)(x1))) -> a{#,(f8)}(f8(b)(b(a)(a(b)(b(a)(a(a)(x1)))))) -> a{#,(f8)}(f8(a)(a(a)(a(a)(x1)))) -> b{#,(f8)}(f8(b)(b(a)(x1))) a{#,(f8)}(f8(a)(a(a)(x1))) -> a{#,(f8)}(f8(b)(b(a)(a(b)(b(a)(a(a)(x1)))))) -> a{#,(f8)}(f8(a)(a(a)(a(b)(x1)))) -> b{#,(f8)}(f8(b)(b(b)(x1))) a{#,(f8)}(f8(a)(a(a)(x1))) -> a{#,(f8)}(f8(b)(b(a)(a(b)(b(a)(a(a)(x1)))))) -> a{#,(f8)}(f8(a)(a(a)(a(f8)(x1)))) -> b{#,(f8)}(f8(b)(b(f8)(x1))) a{#,(f8)}(f8(a)(a(a)(x1))) -> a{#,(f8)}(f8(b)(b(a)(a(b)(b(a)(a(a)(x1)))))) -> a{#,(f8)}(f8(a)(a(a)(a(a)(x1)))) -> b{#,(f8)}(f8(a)(x1)) a{#,(f8)}(f8(a)(a(a)(x1))) -> a{#,(f8)}(f8(b)(b(a)(a(b)(b(a)(a(a)(x1)))))) -> a{#,(f8)}(f8(a)(a(a)(a(b)(x1)))) -> b{#,(f8)}(f8(b)(x1)) a{#,(f8)}(f8(a)(a(a)(x1))) -> a{#,(f8)}(f8(b)(b(a)(a(b)(b(a)(a(a)(x1)))))) -> a{#,(f8)}(f8(a)(a(a)(a(f8)(x1)))) -> b{#,(f8)}(f8(f8)(x1)) a{#,(f8)}(f8(a)(a(a)(x1))) -> a{#,(f8)}(f8(b)(b(a)(a(b)(b(a)(a(a)(x1)))))) -> a{#,(f8)}(f8(a)(a(a)(x1))) -> a{#,(f8)}(f8(b)(b(a)(a(b)(b(a)(a(a)(x1)))))) a{#,(f8)}(f8(a)(a(a)(x1))) -> a{#,(f8)}(f8(b)(b(a)(a(b)(b(a)(a(a)(x1)))))) -> a{#,(f8)}(f8(a)(a(b)(x1))) -> a{#,(f8)}(f8(b)(b(a)(a(b)(b(a)(a(b)(x1)))))) a{#,(f8)}(f8(a)(a(a)(x1))) -> a{#,(f8)}(f8(b)(b(a)(a(b)(b(a)(a(a)(x1)))))) -> a{#,(f8)}(f8(a)(a(f8)(x1))) -> a{#,(f8)}(f8(b)(b(a)(a(b)(b(a)(a(f8)(x1)))))) a{#,(f8)}(f8(a)(a(a)(x1))) -> a{#,(f8)}(f8(b)(b(a)(a(b)(b(a)(a(a)(x1)))))) -> a{#,(f8)}(f8(a)(a(a)(x1))) -> b{#,(f8)}(f8(a)(a(b)(b(a)(a(a)(x1))))) a{#,(f8)}(f8(a)(a(a)(x1))) -> a{#,(f8)}(f8(b)(b(a)(a(b)(b(a)(a(a)(x1)))))) -> a{#,(f8)}(f8(a)(a(b)(x1))) -> b{#,(f8)}(f8(a)(a(b)(b(a)(a(b)(x1))))) a{#,(f8)}(f8(a)(a(a)(x1))) -> a{#,(f8)}(f8(b)(b(a)(a(b)(b(a)(a(a)(x1)))))) -> a{#,(f8)}(f8(a)(a(f8)(x1))) -> b{#,(f8)}(f8(a)(a(b)(b(a)(a(f8)(x1))))) a{#,(f8)}(f8(a)(a(a)(x1))) -> a{#,(f8)}(f8(b)(b(a)(a(b)(b(a)(a(a)(x1)))))) -> a{#,(f8)}(f8(a)(a(a)(x1))) -> a{#,(f8)}(f8(b)(b(a)(a(a)(x1)))) a{#,(f8)}(f8(a)(a(a)(x1))) -> a{#,(f8)}(f8(b)(b(a)(a(b)(b(a)(a(a)(x1)))))) -> a{#,(f8)}(f8(a)(a(b)(x1))) -> a{#,(f8)}(f8(b)(b(a)(a(b)(x1)))) a{#,(f8)}(f8(a)(a(a)(x1))) -> a{#,(f8)}(f8(b)(b(a)(a(b)(b(a)(a(a)(x1)))))) -> a{#,(f8)}(f8(a)(a(f8)(x1))) -> a{#,(f8)}(f8(b)(b(a)(a(f8)(x1)))) a{#,(f8)}(f8(a)(a(a)(x1))) -> a{#,(f8)}(f8(b)(b(a)(a(b)(b(a)(a(a)(x1)))))) -> a{#,(f8)}(f8(a)(a(a)(x1))) -> b{#,(f8)}(f8(a)(a(a)(x1))) a{#,(f8)}(f8(a)(a(a)(x1))) -> a{#,(f8)}(f8(b)(b(a)(a(b)(b(a)(a(a)(x1)))))) -> a{#,(f8)}(f8(a)(a(b)(x1))) -> b{#,(f8)}(f8(a)(a(b)(x1))) a{#,(f8)}(f8(a)(a(a)(x1))) -> a{#,(f8)}(f8(b)(b(a)(a(b)(b(a)(a(a)(x1)))))) -> a{#,(f8)}(f8(a)(a(f8)(x1))) -> b{#,(f8)}(f8(a)(a(f8)(x1))) a{#,(f8)}(f8(a)(a(a)(x1))) -> b{#,(f8)}(f8(a)(a(a)(x1))) -> b{#,(f8)}(f8(b)(b(b)(b(a)(x1)))) -> a{#,(f8)}(f8(b)(b(a)(x1))) a{#,(f8)}(f8(a)(a(a)(x1))) -> b{#,(f8)}(f8(a)(a(a)(x1))) -> b{#,(f8)}(f8(b)(b(b)(b(b)(x1)))) -> a{#,(f8)}(f8(b)(b(b)(x1))) a{#,(f8)}(f8(a)(a(a)(x1))) -> b{#,(f8)}(f8(a)(a(a)(x1))) -> b{#,(f8)}(f8(b)(b(b)(b(f8)(x1)))) -> a{#,(f8)}(f8(b)(b(f8)(x1))) a{#,(f8)}(f8(a)(a(a)(x1))) -> b{#,(f8)}(f8(a)(a(b)(b(a)(a(a)(x1))))) -> b{#,(f8)}(f8(b)(b(b)(b(a)(x1)))) -> a{#,(f8)}(f8(b)(b(a)(x1))) a{#,(f8)}(f8(a)(a(a)(x1))) -> b{#,(f8)}(f8(a)(a(b)(b(a)(a(a)(x1))))) -> b{#,(f8)}(f8(b)(b(b)(b(b)(x1)))) -> a{#,(f8)}(f8(b)(b(b)(x1))) a{#,(f8)}(f8(a)(a(a)(x1))) -> b{#,(f8)}(f8(a)(a(b)(b(a)(a(a)(x1))))) -> b{#,(f8)}(f8(b)(b(b)(b(f8)(x1)))) -> a{#,(f8)}(f8(b)(b(f8)(x1))) a{#,(f8)}(f8(a)(a(b)(x1))) -> a{#,(f8)}(f8(b)(b(a)(a(b)(b(a)(a(b)(x1)))))) -> a{#,(f8)}(f8(a)(a(a)(a(a)(x1)))) -> a{#,(f8)}(f8(b)(b(b)(b(a)(x1)))) a{#,(f8)}(f8(a)(a(b)(x1))) -> a{#,(f8)}(f8(b)(b(a)(a(b)(b(a)(a(b)(x1)))))) -> a{#,(f8)}(f8(a)(a(a)(a(b)(x1)))) -> a{#,(f8)}(f8(b)(b(b)(b(b)(x1)))) a{#,(f8)}(f8(a)(a(b)(x1))) -> a{#,(f8)}(f8(b)(b(a)(a(b)(b(a)(a(b)(x1)))))) -> a{#,(f8)}(f8(a)(a(a)(a(f8)(x1)))) -> a{#,(f8)}(f8(b)(b(b)(b(f8)(x1)))) a{#,(f8)}(f8(a)(a(b)(x1))) -> a{#,(f8)}(f8(b)(b(a)(a(b)(b(a)(a(b)(x1)))))) -> a{#,(f8)}(f8(a)(a(a)(a(a)(x1)))) -> b{#,(f8)}(f8(b)(b(a)(x1))) a{#,(f8)}(f8(a)(a(b)(x1))) -> a{#,(f8)}(f8(b)(b(a)(a(b)(b(a)(a(b)(x1)))))) -> a{#,(f8)}(f8(a)(a(a)(a(b)(x1)))) -> b{#,(f8)}(f8(b)(b(b)(x1))) a{#,(f8)}(f8(a)(a(b)(x1))) -> a{#,(f8)}(f8(b)(b(a)(a(b)(b(a)(a(b)(x1)))))) -> a{#,(f8)}(f8(a)(a(a)(a(f8)(x1)))) -> b{#,(f8)}(f8(b)(b(f8)(x1))) a{#,(f8)}(f8(a)(a(b)(x1))) -> a{#,(f8)}(f8(b)(b(a)(a(b)(b(a)(a(b)(x1)))))) -> a{#,(f8)}(f8(a)(a(a)(a(a)(x1)))) -> b{#,(f8)}(f8(a)(x1)) a{#,(f8)}(f8(a)(a(b)(x1))) -> a{#,(f8)}(f8(b)(b(a)(a(b)(b(a)(a(b)(x1)))))) -> a{#,(f8)}(f8(a)(a(a)(a(b)(x1)))) -> b{#,(f8)}(f8(b)(x1)) a{#,(f8)}(f8(a)(a(b)(x1))) -> a{#,(f8)}(f8(b)(b(a)(a(b)(b(a)(a(b)(x1)))))) -> a{#,(f8)}(f8(a)(a(a)(a(f8)(x1)))) -> b{#,(f8)}(f8(f8)(x1)) a{#,(f8)}(f8(a)(a(b)(x1))) -> a{#,(f8)}(f8(b)(b(a)(a(b)(b(a)(a(b)(x1)))))) -> a{#,(f8)}(f8(a)(a(a)(x1))) -> a{#,(f8)}(f8(b)(b(a)(a(b)(b(a)(a(a)(x1)))))) a{#,(f8)}(f8(a)(a(b)(x1))) -> a{#,(f8)}(f8(b)(b(a)(a(b)(b(a)(a(b)(x1)))))) -> a{#,(f8)}(f8(a)(a(b)(x1))) -> a{#,(f8)}(f8(b)(b(a)(a(b)(b(a)(a(b)(x1)))))) a{#,(f8)}(f8(a)(a(b)(x1))) -> a{#,(f8)}(f8(b)(b(a)(a(b)(b(a)(a(b)(x1)))))) -> a{#,(f8)}(f8(a)(a(f8)(x1))) -> a{#,(f8)}(f8(b)(b(a)(a(b)(b(a)(a(f8)(x1)))))) a{#,(f8)}(f8(a)(a(b)(x1))) -> a{#,(f8)}(f8(b)(b(a)(a(b)(b(a)(a(b)(x1)))))) -> a{#,(f8)}(f8(a)(a(a)(x1))) -> b{#,(f8)}(f8(a)(a(b)(b(a)(a(a)(x1))))) a{#,(f8)}(f8(a)(a(b)(x1))) -> a{#,(f8)}(f8(b)(b(a)(a(b)(b(a)(a(b)(x1)))))) -> a{#,(f8)}(f8(a)(a(b)(x1))) -> b{#,(f8)}(f8(a)(a(b)(b(a)(a(b)(x1))))) a{#,(f8)}(f8(a)(a(b)(x1))) -> a{#,(f8)}(f8(b)(b(a)(a(b)(b(a)(a(b)(x1)))))) -> a{#,(f8)}(f8(a)(a(f8)(x1))) -> b{#,(f8)}(f8(a)(a(b)(b(a)(a(f8)(x1))))) a{#,(f8)}(f8(a)(a(b)(x1))) -> a{#,(f8)}(f8(b)(b(a)(a(b)(b(a)(a(b)(x1)))))) -> a{#,(f8)}(f8(a)(a(a)(x1))) -> a{#,(f8)}(f8(b)(b(a)(a(a)(x1)))) a{#,(f8)}(f8(a)(a(b)(x1))) -> a{#,(f8)}(f8(b)(b(a)(a(b)(b(a)(a(b)(x1)))))) -> a{#,(f8)}(f8(a)(a(b)(x1))) -> a{#,(f8)}(f8(b)(b(a)(a(b)(x1)))) a{#,(f8)}(f8(a)(a(b)(x1))) -> a{#,(f8)}(f8(b)(b(a)(a(b)(b(a)(a(b)(x1)))))) -> a{#,(f8)}(f8(a)(a(f8)(x1))) -> a{#,(f8)}(f8(b)(b(a)(a(f8)(x1)))) a{#,(f8)}(f8(a)(a(b)(x1))) -> a{#,(f8)}(f8(b)(b(a)(a(b)(b(a)(a(b)(x1)))))) -> a{#,(f8)}(f8(a)(a(a)(x1))) -> b{#,(f8)}(f8(a)(a(a)(x1))) a{#,(f8)}(f8(a)(a(b)(x1))) -> a{#,(f8)}(f8(b)(b(a)(a(b)(b(a)(a(b)(x1)))))) -> a{#,(f8)}(f8(a)(a(b)(x1))) -> b{#,(f8)}(f8(a)(a(b)(x1))) a{#,(f8)}(f8(a)(a(b)(x1))) -> a{#,(f8)}(f8(b)(b(a)(a(b)(b(a)(a(b)(x1)))))) -> a{#,(f8)}(f8(a)(a(f8)(x1))) -> b{#,(f8)}(f8(a)(a(f8)(x1))) a{#,(f8)}(f8(a)(a(b)(x1))) -> a{#,(f8)}(f8(b)(b(a)(a(b)(x1)))) -> a{#,(f8)}(f8(a)(a(a)(a(a)(x1)))) -> a{#,(f8)}(f8(b)(b(b)(b(a)(x1)))) a{#,(f8)}(f8(a)(a(b)(x1))) -> a{#,(f8)}(f8(b)(b(a)(a(b)(x1)))) -> a{#,(f8)}(f8(a)(a(a)(a(b)(x1)))) -> a{#,(f8)}(f8(b)(b(b)(b(b)(x1)))) a{#,(f8)}(f8(a)(a(b)(x1))) -> a{#,(f8)}(f8(b)(b(a)(a(b)(x1)))) -> a{#,(f8)}(f8(a)(a(a)(a(f8)(x1)))) -> a{#,(f8)}(f8(b)(b(b)(b(f8)(x1)))) a{#,(f8)}(f8(a)(a(b)(x1))) -> a{#,(f8)}(f8(b)(b(a)(a(b)(x1)))) -> a{#,(f8)}(f8(a)(a(a)(a(a)(x1)))) -> b{#,(f8)}(f8(b)(b(a)(x1))) a{#,(f8)}(f8(a)(a(b)(x1))) -> a{#,(f8)}(f8(b)(b(a)(a(b)(x1)))) -> a{#,(f8)}(f8(a)(a(a)(a(b)(x1)))) -> b{#,(f8)}(f8(b)(b(b)(x1))) a{#,(f8)}(f8(a)(a(b)(x1))) -> a{#,(f8)}(f8(b)(b(a)(a(b)(x1)))) -> a{#,(f8)}(f8(a)(a(a)(a(f8)(x1)))) -> b{#,(f8)}(f8(b)(b(f8)(x1))) a{#,(f8)}(f8(a)(a(b)(x1))) -> a{#,(f8)}(f8(b)(b(a)(a(b)(x1)))) -> a{#,(f8)}(f8(a)(a(a)(a(a)(x1)))) -> b{#,(f8)}(f8(a)(x1)) a{#,(f8)}(f8(a)(a(b)(x1))) -> a{#,(f8)}(f8(b)(b(a)(a(b)(x1)))) -> a{#,(f8)}(f8(a)(a(a)(a(b)(x1)))) -> b{#,(f8)}(f8(b)(x1)) a{#,(f8)}(f8(a)(a(b)(x1))) -> a{#,(f8)}(f8(b)(b(a)(a(b)(x1)))) -> a{#,(f8)}(f8(a)(a(a)(a(f8)(x1)))) -> b{#,(f8)}(f8(f8)(x1)) a{#,(f8)}(f8(a)(a(b)(x1))) -> a{#,(f8)}(f8(b)(b(a)(a(b)(x1)))) -> a{#,(f8)}(f8(a)(a(a)(x1))) -> a{#,(f8)}(f8(b)(b(a)(a(b)(b(a)(a(a)(x1)))))) a{#,(f8)}(f8(a)(a(b)(x1))) -> a{#,(f8)}(f8(b)(b(a)(a(b)(x1)))) -> a{#,(f8)}(f8(a)(a(b)(x1))) -> a{#,(f8)}(f8(b)(b(a)(a(b)(b(a)(a(b)(x1)))))) a{#,(f8)}(f8(a)(a(b)(x1))) -> a{#,(f8)}(f8(b)(b(a)(a(b)(x1)))) -> a{#,(f8)}(f8(a)(a(f8)(x1))) -> a{#,(f8)}(f8(b)(b(a)(a(b)(b(a)(a(f8)(x1)))))) a{#,(f8)}(f8(a)(a(b)(x1))) -> a{#,(f8)}(f8(b)(b(a)(a(b)(x1)))) -> a{#,(f8)}(f8(a)(a(a)(x1))) -> b{#,(f8)}(f8(a)(a(b)(b(a)(a(a)(x1))))) a{#,(f8)}(f8(a)(a(b)(x1))) -> a{#,(f8)}(f8(b)(b(a)(a(b)(x1)))) -> a{#,(f8)}(f8(a)(a(b)(x1))) -> b{#,(f8)}(f8(a)(a(b)(b(a)(a(b)(x1))))) a{#,(f8)}(f8(a)(a(b)(x1))) -> a{#,(f8)}(f8(b)(b(a)(a(b)(x1)))) -> a{#,(f8)}(f8(a)(a(f8)(x1))) -> b{#,(f8)}(f8(a)(a(b)(b(a)(a(f8)(x1))))) a{#,(f8)}(f8(a)(a(b)(x1))) -> a{#,(f8)}(f8(b)(b(a)(a(b)(x1)))) -> a{#,(f8)}(f8(a)(a(a)(x1))) -> a{#,(f8)}(f8(b)(b(a)(a(a)(x1)))) a{#,(f8)}(f8(a)(a(b)(x1))) -> a{#,(f8)}(f8(b)(b(a)(a(b)(x1)))) -> a{#,(f8)}(f8(a)(a(b)(x1))) -> a{#,(f8)}(f8(b)(b(a)(a(b)(x1)))) a{#,(f8)}(f8(a)(a(b)(x1))) -> a{#,(f8)}(f8(b)(b(a)(a(b)(x1)))) -> a{#,(f8)}(f8(a)(a(f8)(x1))) -> a{#,(f8)}(f8(b)(b(a)(a(f8)(x1)))) a{#,(f8)}(f8(a)(a(b)(x1))) -> a{#,(f8)}(f8(b)(b(a)(a(b)(x1)))) -> a{#,(f8)}(f8(a)(a(a)(x1))) -> b{#,(f8)}(f8(a)(a(a)(x1))) a{#,(f8)}(f8(a)(a(b)(x1))) -> a{#,(f8)}(f8(b)(b(a)(a(b)(x1)))) -> a{#,(f8)}(f8(a)(a(b)(x1))) -> b{#,(f8)}(f8(a)(a(b)(x1))) a{#,(f8)}(f8(a)(a(b)(x1))) -> a{#,(f8)}(f8(b)(b(a)(a(b)(x1)))) -> a{#,(f8)}(f8(a)(a(f8)(x1))) -> b{#,(f8)}(f8(a)(a(f8)(x1))) a{#,(f8)}(f8(a)(a(b)(x1))) -> b{#,(f8)}(f8(a)(a(b)(b(a)(a(b)(x1))))) -> b{#,(f8)}(f8(b)(b(b)(b(a)(x1)))) -> a{#,(f8)}(f8(b)(b(a)(x1))) a{#,(f8)}(f8(a)(a(b)(x1))) -> b{#,(f8)}(f8(a)(a(b)(b(a)(a(b)(x1))))) -> b{#,(f8)}(f8(b)(b(b)(b(b)(x1)))) -> a{#,(f8)}(f8(b)(b(b)(x1))) a{#,(f8)}(f8(a)(a(b)(x1))) -> b{#,(f8)}(f8(a)(a(b)(b(a)(a(b)(x1))))) -> b{#,(f8)}(f8(b)(b(b)(b(f8)(x1)))) -> a{#,(f8)}(f8(b)(b(f8)(x1))) a{#,(f8)}(f8(a)(a(b)(x1))) -> b{#,(f8)}(f8(a)(a(b)(x1))) -> b{#,(f8)}(f8(b)(b(b)(b(a)(x1)))) -> a{#,(f8)}(f8(b)(b(a)(x1))) a{#,(f8)}(f8(a)(a(b)(x1))) -> b{#,(f8)}(f8(a)(a(b)(x1))) -> b{#,(f8)}(f8(b)(b(b)(b(b)(x1)))) -> a{#,(f8)}(f8(b)(b(b)(x1))) a{#,(f8)}(f8(a)(a(b)(x1))) -> b{#,(f8)}(f8(a)(a(b)(x1))) -> b{#,(f8)}(f8(b)(b(b)(b(f8)(x1)))) -> a{#,(f8)}(f8(b)(b(f8)(x1))) a{#,(f8)}(f8(a)(a(f8)(x1))) -> a{#,(f8)}(f8(b)(b(a)(a(b)(b(a)(a(f8)(x1)))))) -> a{#,(f8)}(f8(a)(a(a)(a(a)(x1)))) -> a{#,(f8)}(f8(b)(b(b)(b(a)(x1)))) a{#,(f8)}(f8(a)(a(f8)(x1))) -> a{#,(f8)}(f8(b)(b(a)(a(b)(b(a)(a(f8)(x1)))))) -> a{#,(f8)}(f8(a)(a(a)(a(b)(x1)))) -> a{#,(f8)}(f8(b)(b(b)(b(b)(x1)))) a{#,(f8)}(f8(a)(a(f8)(x1))) -> a{#,(f8)}(f8(b)(b(a)(a(b)(b(a)(a(f8)(x1)))))) -> a{#,(f8)}(f8(a)(a(a)(a(f8)(x1)))) -> a{#,(f8)}(f8(b)(b(b)(b(f8)(x1)))) a{#,(f8)}(f8(a)(a(f8)(x1))) -> a{#,(f8)}(f8(b)(b(a)(a(b)(b(a)(a(f8)(x1)))))) -> a{#,(f8)}(f8(a)(a(a)(a(a)(x1)))) -> b{#,(f8)}(f8(b)(b(a)(x1))) a{#,(f8)}(f8(a)(a(f8)(x1))) -> a{#,(f8)}(f8(b)(b(a)(a(b)(b(a)(a(f8)(x1)))))) -> a{#,(f8)}(f8(a)(a(a)(a(b)(x1)))) -> b{#,(f8)}(f8(b)(b(b)(x1))) a{#,(f8)}(f8(a)(a(f8)(x1))) -> a{#,(f8)}(f8(b)(b(a)(a(b)(b(a)(a(f8)(x1)))))) -> a{#,(f8)}(f8(a)(a(a)(a(f8)(x1)))) -> b{#,(f8)}(f8(b)(b(f8)(x1))) a{#,(f8)}(f8(a)(a(f8)(x1))) -> a{#,(f8)}(f8(b)(b(a)(a(b)(b(a)(a(f8)(x1)))))) -> a{#,(f8)}(f8(a)(a(a)(a(a)(x1)))) -> b{#,(f8)}(f8(a)(x1)) a{#,(f8)}(f8(a)(a(f8)(x1))) -> a{#,(f8)}(f8(b)(b(a)(a(b)(b(a)(a(f8)(x1)))))) -> a{#,(f8)}(f8(a)(a(a)(a(b)(x1)))) -> b{#,(f8)}(f8(b)(x1)) a{#,(f8)}(f8(a)(a(f8)(x1))) -> a{#,(f8)}(f8(b)(b(a)(a(b)(b(a)(a(f8)(x1)))))) -> a{#,(f8)}(f8(a)(a(a)(a(f8)(x1)))) -> b{#,(f8)}(f8(f8)(x1)) a{#,(f8)}(f8(a)(a(f8)(x1))) -> a{#,(f8)}(f8(b)(b(a)(a(b)(b(a)(a(f8)(x1)))))) -> a{#,(f8)}(f8(a)(a(a)(x1))) -> a{#,(f8)}(f8(b)(b(a)(a(b)(b(a)(a(a)(x1)))))) a{#,(f8)}(f8(a)(a(f8)(x1))) -> a{#,(f8)}(f8(b)(b(a)(a(b)(b(a)(a(f8)(x1)))))) -> a{#,(f8)}(f8(a)(a(b)(x1))) -> a{#,(f8)}(f8(b)(b(a)(a(b)(b(a)(a(b)(x1)))))) a{#,(f8)}(f8(a)(a(f8)(x1))) -> a{#,(f8)}(f8(b)(b(a)(a(b)(b(a)(a(f8)(x1)))))) -> a{#,(f8)}(f8(a)(a(f8)(x1))) -> a{#,(f8)}(f8(b)(b(a)(a(b)(b(a)(a(f8)(x1)))))) a{#,(f8)}(f8(a)(a(f8)(x1))) -> a{#,(f8)}(f8(b)(b(a)(a(b)(b(a)(a(f8)(x1)))))) -> a{#,(f8)}(f8(a)(a(a)(x1))) -> b{#,(f8)}(f8(a)(a(b)(b(a)(a(a)(x1))))) a{#,(f8)}(f8(a)(a(f8)(x1))) -> a{#,(f8)}(f8(b)(b(a)(a(b)(b(a)(a(f8)(x1)))))) -> a{#,(f8)}(f8(a)(a(b)(x1))) -> b{#,(f8)}(f8(a)(a(b)(b(a)(a(b)(x1))))) a{#,(f8)}(f8(a)(a(f8)(x1))) -> a{#,(f8)}(f8(b)(b(a)(a(b)(b(a)(a(f8)(x1)))))) -> a{#,(f8)}(f8(a)(a(f8)(x1))) -> b{#,(f8)}(f8(a)(a(b)(b(a)(a(f8)(x1))))) a{#,(f8)}(f8(a)(a(f8)(x1))) -> a{#,(f8)}(f8(b)(b(a)(a(b)(b(a)(a(f8)(x1)))))) -> a{#,(f8)}(f8(a)(a(a)(x1))) -> a{#,(f8)}(f8(b)(b(a)(a(a)(x1)))) a{#,(f8)}(f8(a)(a(f8)(x1))) -> a{#,(f8)}(f8(b)(b(a)(a(b)(b(a)(a(f8)(x1)))))) -> a{#,(f8)}(f8(a)(a(b)(x1))) -> a{#,(f8)}(f8(b)(b(a)(a(b)(x1)))) a{#,(f8)}(f8(a)(a(f8)(x1))) -> a{#,(f8)}(f8(b)(b(a)(a(b)(b(a)(a(f8)(x1)))))) -> a{#,(f8)}(f8(a)(a(f8)(x1))) -> a{#,(f8)}(f8(b)(b(a)(a(f8)(x1)))) a{#,(f8)}(f8(a)(a(f8)(x1))) -> a{#,(f8)}(f8(b)(b(a)(a(b)(b(a)(a(f8)(x1)))))) -> a{#,(f8)}(f8(a)(a(a)(x1))) -> b{#,(f8)}(f8(a)(a(a)(x1))) a{#,(f8)}(f8(a)(a(f8)(x1))) -> a{#,(f8)}(f8(b)(b(a)(a(b)(b(a)(a(f8)(x1)))))) -> a{#,(f8)}(f8(a)(a(b)(x1))) -> b{#,(f8)}(f8(a)(a(b)(x1))) a{#,(f8)}(f8(a)(a(f8)(x1))) -> a{#,(f8)}(f8(b)(b(a)(a(b)(b(a)(a(f8)(x1)))))) -> a{#,(f8)}(f8(a)(a(f8)(x1))) -> b{#,(f8)}(f8(a)(a(f8)(x1))) a{#,(f8)}(f8(a)(a(f8)(x1))) -> a{#,(f8)}(f8(b)(b(a)(a(f8)(x1)))) -> a{#,(f8)}(f8(a)(a(a)(a(a)(x1)))) -> a{#,(f8)}(f8(b)(b(b)(b(a)(x1)))) a{#,(f8)}(f8(a)(a(f8)(x1))) -> a{#,(f8)}(f8(b)(b(a)(a(f8)(x1)))) -> a{#,(f8)}(f8(a)(a(a)(a(b)(x1)))) -> a{#,(f8)}(f8(b)(b(b)(b(b)(x1)))) a{#,(f8)}(f8(a)(a(f8)(x1))) -> a{#,(f8)}(f8(b)(b(a)(a(f8)(x1)))) -> a{#,(f8)}(f8(a)(a(a)(a(f8)(x1)))) -> a{#,(f8)}(f8(b)(b(b)(b(f8)(x1)))) a{#,(f8)}(f8(a)(a(f8)(x1))) -> a{#,(f8)}(f8(b)(b(a)(a(f8)(x1)))) -> a{#,(f8)}(f8(a)(a(a)(a(a)(x1)))) -> b{#,(f8)}(f8(b)(b(a)(x1))) a{#,(f8)}(f8(a)(a(f8)(x1))) -> a{#,(f8)}(f8(b)(b(a)(a(f8)(x1)))) -> a{#,(f8)}(f8(a)(a(a)(a(b)(x1)))) -> b{#,(f8)}(f8(b)(b(b)(x1))) a{#,(f8)}(f8(a)(a(f8)(x1))) -> a{#,(f8)}(f8(b)(b(a)(a(f8)(x1)))) -> a{#,(f8)}(f8(a)(a(a)(a(f8)(x1)))) -> b{#,(f8)}(f8(b)(b(f8)(x1))) a{#,(f8)}(f8(a)(a(f8)(x1))) -> a{#,(f8)}(f8(b)(b(a)(a(f8)(x1)))) -> a{#,(f8)}(f8(a)(a(a)(a(a)(x1)))) -> b{#,(f8)}(f8(a)(x1)) a{#,(f8)}(f8(a)(a(f8)(x1))) -> a{#,(f8)}(f8(b)(b(a)(a(f8)(x1)))) -> a{#,(f8)}(f8(a)(a(a)(a(b)(x1)))) -> b{#,(f8)}(f8(b)(x1)) a{#,(f8)}(f8(a)(a(f8)(x1))) -> a{#,(f8)}(f8(b)(b(a)(a(f8)(x1)))) -> a{#,(f8)}(f8(a)(a(a)(a(f8)(x1)))) -> b{#,(f8)}(f8(f8)(x1)) a{#,(f8)}(f8(a)(a(f8)(x1))) -> a{#,(f8)}(f8(b)(b(a)(a(f8)(x1)))) -> a{#,(f8)}(f8(a)(a(a)(x1))) -> a{#,(f8)}(f8(b)(b(a)(a(b)(b(a)(a(a)(x1)))))) a{#,(f8)}(f8(a)(a(f8)(x1))) -> a{#,(f8)}(f8(b)(b(a)(a(f8)(x1)))) -> a{#,(f8)}(f8(a)(a(b)(x1))) -> a{#,(f8)}(f8(b)(b(a)(a(b)(b(a)(a(b)(x1)))))) a{#,(f8)}(f8(a)(a(f8)(x1))) -> a{#,(f8)}(f8(b)(b(a)(a(f8)(x1)))) -> a{#,(f8)}(f8(a)(a(f8)(x1))) -> a{#,(f8)}(f8(b)(b(a)(a(b)(b(a)(a(f8)(x1)))))) a{#,(f8)}(f8(a)(a(f8)(x1))) -> a{#,(f8)}(f8(b)(b(a)(a(f8)(x1)))) -> a{#,(f8)}(f8(a)(a(a)(x1))) -> b{#,(f8)}(f8(a)(a(b)(b(a)(a(a)(x1))))) a{#,(f8)}(f8(a)(a(f8)(x1))) -> a{#,(f8)}(f8(b)(b(a)(a(f8)(x1)))) -> a{#,(f8)}(f8(a)(a(b)(x1))) -> b{#,(f8)}(f8(a)(a(b)(b(a)(a(b)(x1))))) a{#,(f8)}(f8(a)(a(f8)(x1))) -> a{#,(f8)}(f8(b)(b(a)(a(f8)(x1)))) -> a{#,(f8)}(f8(a)(a(f8)(x1))) -> b{#,(f8)}(f8(a)(a(b)(b(a)(a(f8)(x1))))) a{#,(f8)}(f8(a)(a(f8)(x1))) -> a{#,(f8)}(f8(b)(b(a)(a(f8)(x1)))) -> a{#,(f8)}(f8(a)(a(a)(x1))) -> a{#,(f8)}(f8(b)(b(a)(a(a)(x1)))) a{#,(f8)}(f8(a)(a(f8)(x1))) -> a{#,(f8)}(f8(b)(b(a)(a(f8)(x1)))) -> a{#,(f8)}(f8(a)(a(b)(x1))) -> a{#,(f8)}(f8(b)(b(a)(a(b)(x1)))) a{#,(f8)}(f8(a)(a(f8)(x1))) -> a{#,(f8)}(f8(b)(b(a)(a(f8)(x1)))) -> a{#,(f8)}(f8(a)(a(f8)(x1))) -> a{#,(f8)}(f8(b)(b(a)(a(f8)(x1)))) a{#,(f8)}(f8(a)(a(f8)(x1))) -> a{#,(f8)}(f8(b)(b(a)(a(f8)(x1)))) -> a{#,(f8)}(f8(a)(a(a)(x1))) -> b{#,(f8)}(f8(a)(a(a)(x1))) a{#,(f8)}(f8(a)(a(f8)(x1))) -> a{#,(f8)}(f8(b)(b(a)(a(f8)(x1)))) -> a{#,(f8)}(f8(a)(a(b)(x1))) -> b{#,(f8)}(f8(a)(a(b)(x1))) a{#,(f8)}(f8(a)(a(f8)(x1))) -> a{#,(f8)}(f8(b)(b(a)(a(f8)(x1)))) -> a{#,(f8)}(f8(a)(a(f8)(x1))) -> b{#,(f8)}(f8(a)(a(f8)(x1))) a{#,(f8)}(f8(a)(a(f8)(x1))) -> b{#,(f8)}(f8(a)(a(b)(b(a)(a(f8)(x1))))) -> b{#,(f8)}(f8(b)(b(b)(b(a)(x1)))) -> a{#,(f8)}(f8(b)(b(a)(x1))) a{#,(f8)}(f8(a)(a(f8)(x1))) -> b{#,(f8)}(f8(a)(a(b)(b(a)(a(f8)(x1))))) -> b{#,(f8)}(f8(b)(b(b)(b(b)(x1)))) -> a{#,(f8)}(f8(b)(b(b)(x1))) a{#,(f8)}(f8(a)(a(f8)(x1))) -> b{#,(f8)}(f8(a)(a(b)(b(a)(a(f8)(x1))))) -> b{#,(f8)}(f8(b)(b(b)(b(f8)(x1)))) -> a{#,(f8)}(f8(b)(b(f8)(x1))) a{#,(f8)}(f8(a)(a(f8)(x1))) -> b{#,(f8)}(f8(a)(a(f8)(x1))) -> b{#,(f8)}(f8(b)(b(b)(b(a)(x1)))) -> a{#,(f8)}(f8(b)(b(a)(x1))) a{#,(f8)}(f8(a)(a(f8)(x1))) -> b{#,(f8)}(f8(a)(a(f8)(x1))) -> b{#,(f8)}(f8(b)(b(b)(b(b)(x1)))) -> a{#,(f8)}(f8(b)(b(b)(x1))) a{#,(f8)}(f8(a)(a(f8)(x1))) -> b{#,(f8)}(f8(a)(a(f8)(x1))) -> b{#,(f8)}(f8(b)(b(b)(b(f8)(x1)))) -> a{#,(f8)}(f8(b)(b(f8)(x1))) b{#,(f8)}(f8(b)(b(b)(b(a)(x1)))) -> a{#,(f8)}(f8(b)(b(a)(x1))) -> a{#,(f8)}(f8(a)(a(a)(a(a)(x1)))) -> a{#,(f8)}(f8(b)(b(b)(b(a)(x1)))) b{#,(f8)}(f8(b)(b(b)(b(a)(x1)))) -> a{#,(f8)}(f8(b)(b(a)(x1))) -> a{#,(f8)}(f8(a)(a(a)(a(b)(x1)))) -> a{#,(f8)}(f8(b)(b(b)(b(b)(x1)))) b{#,(f8)}(f8(b)(b(b)(b(a)(x1)))) -> a{#,(f8)}(f8(b)(b(a)(x1))) -> a{#,(f8)}(f8(a)(a(a)(a(f8)(x1)))) -> a{#,(f8)}(f8(b)(b(b)(b(f8)(x1)))) b{#,(f8)}(f8(b)(b(b)(b(a)(x1)))) -> a{#,(f8)}(f8(b)(b(a)(x1))) -> a{#,(f8)}(f8(a)(a(a)(a(a)(x1)))) -> b{#,(f8)}(f8(b)(b(a)(x1))) b{#,(f8)}(f8(b)(b(b)(b(a)(x1)))) -> a{#,(f8)}(f8(b)(b(a)(x1))) -> a{#,(f8)}(f8(a)(a(a)(a(b)(x1)))) -> b{#,(f8)}(f8(b)(b(b)(x1))) b{#,(f8)}(f8(b)(b(b)(b(a)(x1)))) -> a{#,(f8)}(f8(b)(b(a)(x1))) -> a{#,(f8)}(f8(a)(a(a)(a(f8)(x1)))) -> b{#,(f8)}(f8(b)(b(f8)(x1))) b{#,(f8)}(f8(b)(b(b)(b(a)(x1)))) -> a{#,(f8)}(f8(b)(b(a)(x1))) -> a{#,(f8)}(f8(a)(a(a)(a(a)(x1)))) -> b{#,(f8)}(f8(a)(x1)) b{#,(f8)}(f8(b)(b(b)(b(a)(x1)))) -> a{#,(f8)}(f8(b)(b(a)(x1))) -> a{#,(f8)}(f8(a)(a(a)(a(b)(x1)))) -> b{#,(f8)}(f8(b)(x1)) b{#,(f8)}(f8(b)(b(b)(b(a)(x1)))) -> a{#,(f8)}(f8(b)(b(a)(x1))) -> a{#,(f8)}(f8(a)(a(a)(a(f8)(x1)))) -> b{#,(f8)}(f8(f8)(x1)) b{#,(f8)}(f8(b)(b(b)(b(a)(x1)))) -> a{#,(f8)}(f8(b)(b(a)(x1))) -> a{#,(f8)}(f8(a)(a(a)(x1))) -> a{#,(f8)}(f8(b)(b(a)(a(b)(b(a)(a(a)(x1)))))) b{#,(f8)}(f8(b)(b(b)(b(a)(x1)))) -> a{#,(f8)}(f8(b)(b(a)(x1))) -> a{#,(f8)}(f8(a)(a(b)(x1))) -> a{#,(f8)}(f8(b)(b(a)(a(b)(b(a)(a(b)(x1)))))) b{#,(f8)}(f8(b)(b(b)(b(a)(x1)))) -> a{#,(f8)}(f8(b)(b(a)(x1))) -> a{#,(f8)}(f8(a)(a(f8)(x1))) -> a{#,(f8)}(f8(b)(b(a)(a(b)(b(a)(a(f8)(x1)))))) b{#,(f8)}(f8(b)(b(b)(b(a)(x1)))) -> a{#,(f8)}(f8(b)(b(a)(x1))) -> a{#,(f8)}(f8(a)(a(a)(x1))) -> b{#,(f8)}(f8(a)(a(b)(b(a)(a(a)(x1))))) b{#,(f8)}(f8(b)(b(b)(b(a)(x1)))) -> a{#,(f8)}(f8(b)(b(a)(x1))) -> a{#,(f8)}(f8(a)(a(b)(x1))) -> b{#,(f8)}(f8(a)(a(b)(b(a)(a(b)(x1))))) b{#,(f8)}(f8(b)(b(b)(b(a)(x1)))) -> a{#,(f8)}(f8(b)(b(a)(x1))) -> a{#,(f8)}(f8(a)(a(f8)(x1))) -> b{#,(f8)}(f8(a)(a(b)(b(a)(a(f8)(x1))))) b{#,(f8)}(f8(b)(b(b)(b(a)(x1)))) -> a{#,(f8)}(f8(b)(b(a)(x1))) -> a{#,(f8)}(f8(a)(a(a)(x1))) -> a{#,(f8)}(f8(b)(b(a)(a(a)(x1)))) b{#,(f8)}(f8(b)(b(b)(b(a)(x1)))) -> a{#,(f8)}(f8(b)(b(a)(x1))) -> a{#,(f8)}(f8(a)(a(b)(x1))) -> a{#,(f8)}(f8(b)(b(a)(a(b)(x1)))) b{#,(f8)}(f8(b)(b(b)(b(a)(x1)))) -> a{#,(f8)}(f8(b)(b(a)(x1))) -> a{#,(f8)}(f8(a)(a(f8)(x1))) -> a{#,(f8)}(f8(b)(b(a)(a(f8)(x1)))) b{#,(f8)}(f8(b)(b(b)(b(a)(x1)))) -> a{#,(f8)}(f8(b)(b(a)(x1))) -> a{#,(f8)}(f8(a)(a(a)(x1))) -> b{#,(f8)}(f8(a)(a(a)(x1))) b{#,(f8)}(f8(b)(b(b)(b(a)(x1)))) -> a{#,(f8)}(f8(b)(b(a)(x1))) -> a{#,(f8)}(f8(a)(a(b)(x1))) -> b{#,(f8)}(f8(a)(a(b)(x1))) b{#,(f8)}(f8(b)(b(b)(b(a)(x1)))) -> a{#,(f8)}(f8(b)(b(a)(x1))) -> a{#,(f8)}(f8(a)(a(f8)(x1))) -> b{#,(f8)}(f8(a)(a(f8)(x1))) b{#,(f8)}(f8(b)(b(b)(b(f8)(x1)))) -> a{#,(f8)}(f8(b)(b(f8)(x1))) -> a{#,(f8)}(f8(a)(a(a)(a(a)(x1)))) -> a{#,(f8)}(f8(b)(b(b)(b(a)(x1)))) b{#,(f8)}(f8(b)(b(b)(b(f8)(x1)))) -> a{#,(f8)}(f8(b)(b(f8)(x1))) -> a{#,(f8)}(f8(a)(a(a)(a(b)(x1)))) -> a{#,(f8)}(f8(b)(b(b)(b(b)(x1)))) b{#,(f8)}(f8(b)(b(b)(b(f8)(x1)))) -> a{#,(f8)}(f8(b)(b(f8)(x1))) -> a{#,(f8)}(f8(a)(a(a)(a(f8)(x1)))) -> a{#,(f8)}(f8(b)(b(b)(b(f8)(x1)))) b{#,(f8)}(f8(b)(b(b)(b(f8)(x1)))) -> a{#,(f8)}(f8(b)(b(f8)(x1))) -> a{#,(f8)}(f8(a)(a(a)(a(a)(x1)))) -> b{#,(f8)}(f8(b)(b(a)(x1))) b{#,(f8)}(f8(b)(b(b)(b(f8)(x1)))) -> a{#,(f8)}(f8(b)(b(f8)(x1))) -> a{#,(f8)}(f8(a)(a(a)(a(b)(x1)))) -> b{#,(f8)}(f8(b)(b(b)(x1))) b{#,(f8)}(f8(b)(b(b)(b(f8)(x1)))) -> a{#,(f8)}(f8(b)(b(f8)(x1))) -> a{#,(f8)}(f8(a)(a(a)(a(f8)(x1)))) -> b{#,(f8)}(f8(b)(b(f8)(x1))) b{#,(f8)}(f8(b)(b(b)(b(f8)(x1)))) -> a{#,(f8)}(f8(b)(b(f8)(x1))) -> a{#,(f8)}(f8(a)(a(a)(a(a)(x1)))) -> b{#,(f8)}(f8(a)(x1)) b{#,(f8)}(f8(b)(b(b)(b(f8)(x1)))) -> a{#,(f8)}(f8(b)(b(f8)(x1))) -> a{#,(f8)}(f8(a)(a(a)(a(b)(x1)))) -> b{#,(f8)}(f8(b)(x1)) b{#,(f8)}(f8(b)(b(b)(b(f8)(x1)))) -> a{#,(f8)}(f8(b)(b(f8)(x1))) -> a{#,(f8)}(f8(a)(a(a)(a(f8)(x1)))) -> b{#,(f8)}(f8(f8)(x1)) b{#,(f8)}(f8(b)(b(b)(b(f8)(x1)))) -> a{#,(f8)}(f8(b)(b(f8)(x1))) -> a{#,(f8)}(f8(a)(a(a)(x1))) -> a{#,(f8)}(f8(b)(b(a)(a(b)(b(a)(a(a)(x1)))))) b{#,(f8)}(f8(b)(b(b)(b(f8)(x1)))) -> a{#,(f8)}(f8(b)(b(f8)(x1))) -> a{#,(f8)}(f8(a)(a(b)(x1))) -> a{#,(f8)}(f8(b)(b(a)(a(b)(b(a)(a(b)(x1)))))) b{#,(f8)}(f8(b)(b(b)(b(f8)(x1)))) -> a{#,(f8)}(f8(b)(b(f8)(x1))) -> a{#,(f8)}(f8(a)(a(f8)(x1))) -> a{#,(f8)}(f8(b)(b(a)(a(b)(b(a)(a(f8)(x1)))))) b{#,(f8)}(f8(b)(b(b)(b(f8)(x1)))) -> a{#,(f8)}(f8(b)(b(f8)(x1))) -> a{#,(f8)}(f8(a)(a(a)(x1))) -> b{#,(f8)}(f8(a)(a(b)(b(a)(a(a)(x1))))) b{#,(f8)}(f8(b)(b(b)(b(f8)(x1)))) -> a{#,(f8)}(f8(b)(b(f8)(x1))) -> a{#,(f8)}(f8(a)(a(b)(x1))) -> b{#,(f8)}(f8(a)(a(b)(b(a)(a(b)(x1))))) b{#,(f8)}(f8(b)(b(b)(b(f8)(x1)))) -> a{#,(f8)}(f8(b)(b(f8)(x1))) -> a{#,(f8)}(f8(a)(a(f8)(x1))) -> b{#,(f8)}(f8(a)(a(b)(b(a)(a(f8)(x1))))) b{#,(f8)}(f8(b)(b(b)(b(f8)(x1)))) -> a{#,(f8)}(f8(b)(b(f8)(x1))) -> a{#,(f8)}(f8(a)(a(a)(x1))) -> a{#,(f8)}(f8(b)(b(a)(a(a)(x1)))) b{#,(f8)}(f8(b)(b(b)(b(f8)(x1)))) -> a{#,(f8)}(f8(b)(b(f8)(x1))) -> a{#,(f8)}(f8(a)(a(b)(x1))) -> a{#,(f8)}(f8(b)(b(a)(a(b)(x1)))) b{#,(f8)}(f8(b)(b(b)(b(f8)(x1)))) -> a{#,(f8)}(f8(b)(b(f8)(x1))) -> a{#,(f8)}(f8(a)(a(f8)(x1))) -> a{#,(f8)}(f8(b)(b(a)(a(f8)(x1)))) b{#,(f8)}(f8(b)(b(b)(b(f8)(x1)))) -> a{#,(f8)}(f8(b)(b(f8)(x1))) -> a{#,(f8)}(f8(a)(a(a)(x1))) -> b{#,(f8)}(f8(a)(a(a)(x1))) b{#,(f8)}(f8(b)(b(b)(b(f8)(x1)))) -> a{#,(f8)}(f8(b)(b(f8)(x1))) -> a{#,(f8)}(f8(a)(a(b)(x1))) -> b{#,(f8)}(f8(a)(a(b)(x1))) b{#,(f8)}(f8(b)(b(b)(b(f8)(x1)))) -> a{#,(f8)}(f8(b)(b(f8)(x1))) -> a{#,(f8)}(f8(a)(a(f8)(x1))) -> b{#,(f8)}(f8(a)(a(f8)(x1))) b{#,(f8)}(f8(b)(b(b)(b(b)(x1)))) -> a{#,(f8)}(f8(b)(b(b)(x1))) -> a{#,(f8)}(f8(a)(a(a)(a(a)(x1)))) -> a{#,(f8)}(f8(b)(b(b)(b(a)(x1)))) b{#,(f8)}(f8(b)(b(b)(b(b)(x1)))) -> a{#,(f8)}(f8(b)(b(b)(x1))) -> a{#,(f8)}(f8(a)(a(a)(a(b)(x1)))) -> a{#,(f8)}(f8(b)(b(b)(b(b)(x1)))) b{#,(f8)}(f8(b)(b(b)(b(b)(x1)))) -> a{#,(f8)}(f8(b)(b(b)(x1))) -> a{#,(f8)}(f8(a)(a(a)(a(f8)(x1)))) -> a{#,(f8)}(f8(b)(b(b)(b(f8)(x1)))) b{#,(f8)}(f8(b)(b(b)(b(b)(x1)))) -> a{#,(f8)}(f8(b)(b(b)(x1))) -> a{#,(f8)}(f8(a)(a(a)(a(a)(x1)))) -> b{#,(f8)}(f8(b)(b(a)(x1))) b{#,(f8)}(f8(b)(b(b)(b(b)(x1)))) -> a{#,(f8)}(f8(b)(b(b)(x1))) -> a{#,(f8)}(f8(a)(a(a)(a(b)(x1)))) -> b{#,(f8)}(f8(b)(b(b)(x1))) b{#,(f8)}(f8(b)(b(b)(b(b)(x1)))) -> a{#,(f8)}(f8(b)(b(b)(x1))) -> a{#,(f8)}(f8(a)(a(a)(a(f8)(x1)))) -> b{#,(f8)}(f8(b)(b(f8)(x1))) b{#,(f8)}(f8(b)(b(b)(b(b)(x1)))) -> a{#,(f8)}(f8(b)(b(b)(x1))) -> a{#,(f8)}(f8(a)(a(a)(a(a)(x1)))) -> b{#,(f8)}(f8(a)(x1)) b{#,(f8)}(f8(b)(b(b)(b(b)(x1)))) -> a{#,(f8)}(f8(b)(b(b)(x1))) -> a{#,(f8)}(f8(a)(a(a)(a(b)(x1)))) -> b{#,(f8)}(f8(b)(x1)) b{#,(f8)}(f8(b)(b(b)(b(b)(x1)))) -> a{#,(f8)}(f8(b)(b(b)(x1))) -> a{#,(f8)}(f8(a)(a(a)(a(f8)(x1)))) -> b{#,(f8)}(f8(f8)(x1)) b{#,(f8)}(f8(b)(b(b)(b(b)(x1)))) -> a{#,(f8)}(f8(b)(b(b)(x1))) -> a{#,(f8)}(f8(a)(a(a)(x1))) -> a{#,(f8)}(f8(b)(b(a)(a(b)(b(a)(a(a)(x1)))))) b{#,(f8)}(f8(b)(b(b)(b(b)(x1)))) -> a{#,(f8)}(f8(b)(b(b)(x1))) -> a{#,(f8)}(f8(a)(a(b)(x1))) -> a{#,(f8)}(f8(b)(b(a)(a(b)(b(a)(a(b)(x1)))))) b{#,(f8)}(f8(b)(b(b)(b(b)(x1)))) -> a{#,(f8)}(f8(b)(b(b)(x1))) -> a{#,(f8)}(f8(a)(a(f8)(x1))) -> a{#,(f8)}(f8(b)(b(a)(a(b)(b(a)(a(f8)(x1)))))) b{#,(f8)}(f8(b)(b(b)(b(b)(x1)))) -> a{#,(f8)}(f8(b)(b(b)(x1))) -> a{#,(f8)}(f8(a)(a(a)(x1))) -> b{#,(f8)}(f8(a)(a(b)(b(a)(a(a)(x1))))) b{#,(f8)}(f8(b)(b(b)(b(b)(x1)))) -> a{#,(f8)}(f8(b)(b(b)(x1))) -> a{#,(f8)}(f8(a)(a(b)(x1))) -> b{#,(f8)}(f8(a)(a(b)(b(a)(a(b)(x1))))) b{#,(f8)}(f8(b)(b(b)(b(b)(x1)))) -> a{#,(f8)}(f8(b)(b(b)(x1))) -> a{#,(f8)}(f8(a)(a(f8)(x1))) -> b{#,(f8)}(f8(a)(a(b)(b(a)(a(f8)(x1))))) b{#,(f8)}(f8(b)(b(b)(b(b)(x1)))) -> a{#,(f8)}(f8(b)(b(b)(x1))) -> a{#,(f8)}(f8(a)(a(a)(x1))) -> a{#,(f8)}(f8(b)(b(a)(a(a)(x1)))) b{#,(f8)}(f8(b)(b(b)(b(b)(x1)))) -> a{#,(f8)}(f8(b)(b(b)(x1))) -> a{#,(f8)}(f8(a)(a(b)(x1))) -> a{#,(f8)}(f8(b)(b(a)(a(b)(x1)))) b{#,(f8)}(f8(b)(b(b)(b(b)(x1)))) -> a{#,(f8)}(f8(b)(b(b)(x1))) -> a{#,(f8)}(f8(a)(a(f8)(x1))) -> a{#,(f8)}(f8(b)(b(a)(a(f8)(x1)))) b{#,(f8)}(f8(b)(b(b)(b(b)(x1)))) -> a{#,(f8)}(f8(b)(b(b)(x1))) -> a{#,(f8)}(f8(a)(a(a)(x1))) -> b{#,(f8)}(f8(a)(a(a)(x1))) b{#,(f8)}(f8(b)(b(b)(b(b)(x1)))) -> a{#,(f8)}(f8(b)(b(b)(x1))) -> a{#,(f8)}(f8(a)(a(b)(x1))) -> b{#,(f8)}(f8(a)(a(b)(x1))) b{#,(f8)}(f8(b)(b(b)(b(b)(x1)))) -> a{#,(f8)}(f8(b)(b(b)(x1))) -> a{#,(f8)}(f8(a)(a(f8)(x1))) -> b{#,(f8)}(f8(a)(a(f8)(x1))) Polynomial Interpretation Processor: dimension: 1 interpretation: [a(a)](x0) = x0, [f8(a)](x0) = x0, [a(f8)](x0) = x0 + 1, [f8(f8)](x0) = x0 + 1, [a(b)](x0) = x0, [f8(b)](x0) = x0, [b(a)](x0) = x0, [b(f8)](x0) = x0, [b(b)](x0) = x0, [b{#,(f8)}](x0) = x0, [a{#,(f8)}](x0) = x0 orientation: b{#,(f8)}(f8(b)(b(b)(b(f8)(x1)))) = x1 >= x1 = a{#,(f8)}(f8(b)(b(f8)(x1))) b{#,(f8)}(f8(b)(b(b)(b(b)(x1)))) = x1 >= x1 = a{#,(f8)}(f8(b)(b(b)(x1))) b{#,(f8)}(f8(b)(b(b)(b(a)(x1)))) = x1 >= x1 = a{#,(f8)}(f8(b)(b(a)(x1))) a{#,(f8)}(f8(a)(a(f8)(x1))) = x1 + 1 >= x1 + 1 = b{#,(f8)}(f8(a)(a(f8)(x1))) a{#,(f8)}(f8(a)(a(b)(x1))) = x1 >= x1 = b{#,(f8)}(f8(a)(a(b)(x1))) a{#,(f8)}(f8(a)(a(a)(x1))) = x1 >= x1 = b{#,(f8)}(f8(a)(a(a)(x1))) a{#,(f8)}(f8(a)(a(f8)(x1))) = x1 + 1 >= x1 + 1 = a{#,(f8)}(f8(b)(b(a)(a(f8)(x1)))) a{#,(f8)}(f8(a)(a(b)(x1))) = x1 >= x1 = a{#,(f8)}(f8(b)(b(a)(a(b)(x1)))) a{#,(f8)}(f8(a)(a(a)(x1))) = x1 >= x1 = a{#,(f8)}(f8(b)(b(a)(a(a)(x1)))) a{#,(f8)}(f8(a)(a(f8)(x1))) = x1 + 1 >= x1 + 1 = b{#,(f8)}(f8(a)(a(b)(b(a)(a(f8)(x1))))) a{#,(f8)}(f8(a)(a(b)(x1))) = x1 >= x1 = b{#,(f8)}(f8(a)(a(b)(b(a)(a(b)(x1))))) a{#,(f8)}(f8(a)(a(a)(x1))) = x1 >= x1 = b{#,(f8)}(f8(a)(a(b)(b(a)(a(a)(x1))))) a{#,(f8)}(f8(a)(a(f8)(x1))) = x1 + 1 >= x1 + 1 = a{#,(f8)}(f8(b)(b(a)(a(b)(b(a)(a(f8)(x1)))))) a{#,(f8)}(f8(a)(a(b)(x1))) = x1 >= x1 = a{#,(f8)}(f8(b)(b(a)(a(b)(b(a)(a(b)(x1)))))) a{#,(f8)}(f8(a)(a(a)(x1))) = x1 >= x1 = a{#,(f8)}(f8(b)(b(a)(a(b)(b(a)(a(a)(x1)))))) a{#,(f8)}(f8(a)(a(a)(a(f8)(x1)))) = x1 + 1 >= x1 + 1 = b{#,(f8)}(f8(f8)(x1)) a{#,(f8)}(f8(a)(a(a)(a(b)(x1)))) = x1 >= x1 = b{#,(f8)}(f8(b)(x1)) a{#,(f8)}(f8(a)(a(a)(a(a)(x1)))) = x1 >= x1 = b{#,(f8)}(f8(a)(x1)) a{#,(f8)}(f8(a)(a(a)(a(f8)(x1)))) = x1 + 1 >= x1 = b{#,(f8)}(f8(b)(b(f8)(x1))) a{#,(f8)}(f8(a)(a(a)(a(b)(x1)))) = x1 >= x1 = b{#,(f8)}(f8(b)(b(b)(x1))) a{#,(f8)}(f8(a)(a(a)(a(a)(x1)))) = x1 >= x1 = b{#,(f8)}(f8(b)(b(a)(x1))) a{#,(f8)}(f8(a)(a(a)(a(f8)(x1)))) = x1 + 1 >= x1 = a{#,(f8)}(f8(b)(b(b)(b(f8)(x1)))) a{#,(f8)}(f8(a)(a(a)(a(b)(x1)))) = x1 >= x1 = a{#,(f8)}(f8(b)(b(b)(b(b)(x1)))) a{#,(f8)}(f8(a)(a(a)(a(a)(x1)))) = x1 >= x1 = a{#,(f8)}(f8(b)(b(b)(b(a)(x1)))) f8(b)(b(b)(b(b)(b(f8)(x1)))) = x1 >= x1 = f8(a)(a(b)(b(f8)(x1))) f8(b)(b(b)(b(b)(b(b)(x1)))) = x1 >= x1 = f8(a)(a(b)(b(b)(x1))) f8(b)(b(b)(b(b)(b(a)(x1)))) = x1 >= x1 = f8(a)(a(b)(b(a)(x1))) b(b)(b(b)(b(b)(b(f8)(x1)))) = x1 >= x1 = b(a)(a(b)(b(f8)(x1))) b(b)(b(b)(b(b)(b(b)(x1)))) = x1 >= x1 = b(a)(a(b)(b(b)(x1))) b(b)(b(b)(b(b)(b(a)(x1)))) = x1 >= x1 = b(a)(a(b)(b(a)(x1))) a(b)(b(b)(b(b)(b(f8)(x1)))) = x1 >= x1 = a(a)(a(b)(b(f8)(x1))) a(b)(b(b)(b(b)(b(b)(x1)))) = x1 >= x1 = a(a)(a(b)(b(b)(x1))) a(b)(b(b)(b(b)(b(a)(x1)))) = x1 >= x1 = a(a)(a(b)(b(a)(x1))) a(a)(a(f8)(x1)) = x1 + 1 >= x1 + 1 = a(b)(b(a)(a(b)(b(a)(a(f8)(x1))))) a(a)(a(b)(x1)) = x1 >= x1 = a(b)(b(a)(a(b)(b(a)(a(b)(x1))))) a(a)(a(a)(x1)) = x1 >= x1 = a(b)(b(a)(a(b)(b(a)(a(a)(x1))))) a(a)(a(a)(a(f8)(x1))) = x1 + 1 >= x1 = a(b)(b(b)(b(f8)(x1))) a(a)(a(a)(a(b)(x1))) = x1 >= x1 = a(b)(b(b)(b(b)(x1))) a(a)(a(a)(a(a)(x1))) = x1 >= x1 = a(b)(b(b)(b(a)(x1))) problem: DPs: b{#,(f8)}(f8(b)(b(b)(b(f8)(x1)))) -> a{#,(f8)}(f8(b)(b(f8)(x1))) b{#,(f8)}(f8(b)(b(b)(b(b)(x1)))) -> a{#,(f8)}(f8(b)(b(b)(x1))) b{#,(f8)}(f8(b)(b(b)(b(a)(x1)))) -> a{#,(f8)}(f8(b)(b(a)(x1))) a{#,(f8)}(f8(a)(a(f8)(x1))) -> b{#,(f8)}(f8(a)(a(f8)(x1))) a{#,(f8)}(f8(a)(a(b)(x1))) -> b{#,(f8)}(f8(a)(a(b)(x1))) a{#,(f8)}(f8(a)(a(a)(x1))) -> b{#,(f8)}(f8(a)(a(a)(x1))) a{#,(f8)}(f8(a)(a(f8)(x1))) -> a{#,(f8)}(f8(b)(b(a)(a(f8)(x1)))) a{#,(f8)}(f8(a)(a(b)(x1))) -> a{#,(f8)}(f8(b)(b(a)(a(b)(x1)))) a{#,(f8)}(f8(a)(a(a)(x1))) -> a{#,(f8)}(f8(b)(b(a)(a(a)(x1)))) a{#,(f8)}(f8(a)(a(f8)(x1))) -> b{#,(f8)}(f8(a)(a(b)(b(a)(a(f8)(x1))))) a{#,(f8)}(f8(a)(a(b)(x1))) -> b{#,(f8)}(f8(a)(a(b)(b(a)(a(b)(x1))))) a{#,(f8)}(f8(a)(a(a)(x1))) -> b{#,(f8)}(f8(a)(a(b)(b(a)(a(a)(x1))))) a{#,(f8)}(f8(a)(a(f8)(x1))) -> a{#,(f8)}(f8(b)(b(a)(a(b)(b(a)(a(f8)(x1)))))) a{#,(f8)}(f8(a)(a(b)(x1))) -> a{#,(f8)}(f8(b)(b(a)(a(b)(b(a)(a(b)(x1)))))) a{#,(f8)}(f8(a)(a(a)(x1))) -> a{#,(f8)}(f8(b)(b(a)(a(b)(b(a)(a(a)(x1)))))) a{#,(f8)}(f8(a)(a(a)(a(f8)(x1)))) -> b{#,(f8)}(f8(f8)(x1)) a{#,(f8)}(f8(a)(a(a)(a(b)(x1)))) -> b{#,(f8)}(f8(b)(x1)) a{#,(f8)}(f8(a)(a(a)(a(a)(x1)))) -> b{#,(f8)}(f8(a)(x1)) a{#,(f8)}(f8(a)(a(a)(a(b)(x1)))) -> b{#,(f8)}(f8(b)(b(b)(x1))) a{#,(f8)}(f8(a)(a(a)(a(a)(x1)))) -> b{#,(f8)}(f8(b)(b(a)(x1))) a{#,(f8)}(f8(a)(a(a)(a(b)(x1)))) -> a{#,(f8)}(f8(b)(b(b)(b(b)(x1)))) a{#,(f8)}(f8(a)(a(a)(a(a)(x1)))) -> a{#,(f8)}(f8(b)(b(b)(b(a)(x1)))) TRS: f8(b)(b(b)(b(b)(b(f8)(x1)))) -> f8(a)(a(b)(b(f8)(x1))) f8(b)(b(b)(b(b)(b(b)(x1)))) -> f8(a)(a(b)(b(b)(x1))) f8(b)(b(b)(b(b)(b(a)(x1)))) -> f8(a)(a(b)(b(a)(x1))) b(b)(b(b)(b(b)(b(f8)(x1)))) -> b(a)(a(b)(b(f8)(x1))) b(b)(b(b)(b(b)(b(b)(x1)))) -> b(a)(a(b)(b(b)(x1))) b(b)(b(b)(b(b)(b(a)(x1)))) -> b(a)(a(b)(b(a)(x1))) a(b)(b(b)(b(b)(b(f8)(x1)))) -> a(a)(a(b)(b(f8)(x1))) a(b)(b(b)(b(b)(b(b)(x1)))) -> a(a)(a(b)(b(b)(x1))) a(b)(b(b)(b(b)(b(a)(x1)))) -> a(a)(a(b)(b(a)(x1))) a(a)(a(f8)(x1)) -> a(b)(b(a)(a(b)(b(a)(a(f8)(x1))))) a(a)(a(b)(x1)) -> a(b)(b(a)(a(b)(b(a)(a(b)(x1))))) a(a)(a(a)(x1)) -> a(b)(b(a)(a(b)(b(a)(a(a)(x1))))) a(a)(a(a)(a(b)(x1))) -> a(b)(b(b)(b(b)(x1))) a(a)(a(a)(a(a)(x1))) -> a(b)(b(b)(b(a)(x1))) Polynomial Interpretation Processor: dimension: 1 interpretation: [a(a)](x0) = x0, [f8(a)](x0) = x0, [a(f8)](x0) = x0 + 1, [f8(f8)](x0) = x0, [a(b)](x0) = x0, [f8(b)](x0) = x0, [b(a)](x0) = x0, [b(f8)](x0) = x0 + 1, [b(b)](x0) = x0, [b{#,(f8)}](x0) = x0 + 1, [a{#,(f8)}](x0) = x0 + 1 orientation: b{#,(f8)}(f8(b)(b(b)(b(f8)(x1)))) = x1 + 2 >= x1 + 2 = a{#,(f8)}(f8(b)(b(f8)(x1))) b{#,(f8)}(f8(b)(b(b)(b(b)(x1)))) = x1 + 1 >= x1 + 1 = a{#,(f8)}(f8(b)(b(b)(x1))) b{#,(f8)}(f8(b)(b(b)(b(a)(x1)))) = x1 + 1 >= x1 + 1 = a{#,(f8)}(f8(b)(b(a)(x1))) a{#,(f8)}(f8(a)(a(f8)(x1))) = x1 + 2 >= x1 + 2 = b{#,(f8)}(f8(a)(a(f8)(x1))) a{#,(f8)}(f8(a)(a(b)(x1))) = x1 + 1 >= x1 + 1 = b{#,(f8)}(f8(a)(a(b)(x1))) a{#,(f8)}(f8(a)(a(a)(x1))) = x1 + 1 >= x1 + 1 = b{#,(f8)}(f8(a)(a(a)(x1))) a{#,(f8)}(f8(a)(a(f8)(x1))) = x1 + 2 >= x1 + 2 = a{#,(f8)}(f8(b)(b(a)(a(f8)(x1)))) a{#,(f8)}(f8(a)(a(b)(x1))) = x1 + 1 >= x1 + 1 = a{#,(f8)}(f8(b)(b(a)(a(b)(x1)))) a{#,(f8)}(f8(a)(a(a)(x1))) = x1 + 1 >= x1 + 1 = a{#,(f8)}(f8(b)(b(a)(a(a)(x1)))) a{#,(f8)}(f8(a)(a(f8)(x1))) = x1 + 2 >= x1 + 2 = b{#,(f8)}(f8(a)(a(b)(b(a)(a(f8)(x1))))) a{#,(f8)}(f8(a)(a(b)(x1))) = x1 + 1 >= x1 + 1 = b{#,(f8)}(f8(a)(a(b)(b(a)(a(b)(x1))))) a{#,(f8)}(f8(a)(a(a)(x1))) = x1 + 1 >= x1 + 1 = b{#,(f8)}(f8(a)(a(b)(b(a)(a(a)(x1))))) a{#,(f8)}(f8(a)(a(f8)(x1))) = x1 + 2 >= x1 + 2 = a{#,(f8)}(f8(b)(b(a)(a(b)(b(a)(a(f8)(x1)))))) a{#,(f8)}(f8(a)(a(b)(x1))) = x1 + 1 >= x1 + 1 = a{#,(f8)}(f8(b)(b(a)(a(b)(b(a)(a(b)(x1)))))) a{#,(f8)}(f8(a)(a(a)(x1))) = x1 + 1 >= x1 + 1 = a{#,(f8)}(f8(b)(b(a)(a(b)(b(a)(a(a)(x1)))))) a{#,(f8)}(f8(a)(a(a)(a(f8)(x1)))) = x1 + 2 >= x1 + 1 = b{#,(f8)}(f8(f8)(x1)) a{#,(f8)}(f8(a)(a(a)(a(b)(x1)))) = x1 + 1 >= x1 + 1 = b{#,(f8)}(f8(b)(x1)) a{#,(f8)}(f8(a)(a(a)(a(a)(x1)))) = x1 + 1 >= x1 + 1 = b{#,(f8)}(f8(a)(x1)) a{#,(f8)}(f8(a)(a(a)(a(b)(x1)))) = x1 + 1 >= x1 + 1 = b{#,(f8)}(f8(b)(b(b)(x1))) a{#,(f8)}(f8(a)(a(a)(a(a)(x1)))) = x1 + 1 >= x1 + 1 = b{#,(f8)}(f8(b)(b(a)(x1))) a{#,(f8)}(f8(a)(a(a)(a(b)(x1)))) = x1 + 1 >= x1 + 1 = a{#,(f8)}(f8(b)(b(b)(b(b)(x1)))) a{#,(f8)}(f8(a)(a(a)(a(a)(x1)))) = x1 + 1 >= x1 + 1 = a{#,(f8)}(f8(b)(b(b)(b(a)(x1)))) f8(b)(b(b)(b(b)(b(f8)(x1)))) = x1 + 1 >= x1 + 1 = f8(a)(a(b)(b(f8)(x1))) f8(b)(b(b)(b(b)(b(b)(x1)))) = x1 >= x1 = f8(a)(a(b)(b(b)(x1))) f8(b)(b(b)(b(b)(b(a)(x1)))) = x1 >= x1 = f8(a)(a(b)(b(a)(x1))) b(b)(b(b)(b(b)(b(f8)(x1)))) = x1 + 1 >= x1 + 1 = b(a)(a(b)(b(f8)(x1))) b(b)(b(b)(b(b)(b(b)(x1)))) = x1 >= x1 = b(a)(a(b)(b(b)(x1))) b(b)(b(b)(b(b)(b(a)(x1)))) = x1 >= x1 = b(a)(a(b)(b(a)(x1))) a(b)(b(b)(b(b)(b(f8)(x1)))) = x1 + 1 >= x1 + 1 = a(a)(a(b)(b(f8)(x1))) a(b)(b(b)(b(b)(b(b)(x1)))) = x1 >= x1 = a(a)(a(b)(b(b)(x1))) a(b)(b(b)(b(b)(b(a)(x1)))) = x1 >= x1 = a(a)(a(b)(b(a)(x1))) a(a)(a(f8)(x1)) = x1 + 1 >= x1 + 1 = a(b)(b(a)(a(b)(b(a)(a(f8)(x1))))) a(a)(a(b)(x1)) = x1 >= x1 = a(b)(b(a)(a(b)(b(a)(a(b)(x1))))) a(a)(a(a)(x1)) = x1 >= x1 = a(b)(b(a)(a(b)(b(a)(a(a)(x1))))) a(a)(a(a)(a(b)(x1))) = x1 >= x1 = a(b)(b(b)(b(b)(x1))) a(a)(a(a)(a(a)(x1))) = x1 >= x1 = a(b)(b(b)(b(a)(x1))) problem: DPs: b{#,(f8)}(f8(b)(b(b)(b(f8)(x1)))) -> a{#,(f8)}(f8(b)(b(f8)(x1))) b{#,(f8)}(f8(b)(b(b)(b(b)(x1)))) -> a{#,(f8)}(f8(b)(b(b)(x1))) b{#,(f8)}(f8(b)(b(b)(b(a)(x1)))) -> a{#,(f8)}(f8(b)(b(a)(x1))) a{#,(f8)}(f8(a)(a(f8)(x1))) -> b{#,(f8)}(f8(a)(a(f8)(x1))) a{#,(f8)}(f8(a)(a(b)(x1))) -> b{#,(f8)}(f8(a)(a(b)(x1))) a{#,(f8)}(f8(a)(a(a)(x1))) -> b{#,(f8)}(f8(a)(a(a)(x1))) a{#,(f8)}(f8(a)(a(f8)(x1))) -> a{#,(f8)}(f8(b)(b(a)(a(f8)(x1)))) a{#,(f8)}(f8(a)(a(b)(x1))) -> a{#,(f8)}(f8(b)(b(a)(a(b)(x1)))) a{#,(f8)}(f8(a)(a(a)(x1))) -> a{#,(f8)}(f8(b)(b(a)(a(a)(x1)))) a{#,(f8)}(f8(a)(a(f8)(x1))) -> b{#,(f8)}(f8(a)(a(b)(b(a)(a(f8)(x1))))) a{#,(f8)}(f8(a)(a(b)(x1))) -> b{#,(f8)}(f8(a)(a(b)(b(a)(a(b)(x1))))) a{#,(f8)}(f8(a)(a(a)(x1))) -> b{#,(f8)}(f8(a)(a(b)(b(a)(a(a)(x1))))) a{#,(f8)}(f8(a)(a(f8)(x1))) -> a{#,(f8)}(f8(b)(b(a)(a(b)(b(a)(a(f8)(x1)))))) a{#,(f8)}(f8(a)(a(b)(x1))) -> a{#,(f8)}(f8(b)(b(a)(a(b)(b(a)(a(b)(x1)))))) a{#,(f8)}(f8(a)(a(a)(x1))) -> a{#,(f8)}(f8(b)(b(a)(a(b)(b(a)(a(a)(x1)))))) a{#,(f8)}(f8(a)(a(a)(a(b)(x1)))) -> b{#,(f8)}(f8(b)(x1)) a{#,(f8)}(f8(a)(a(a)(a(a)(x1)))) -> b{#,(f8)}(f8(a)(x1)) a{#,(f8)}(f8(a)(a(a)(a(b)(x1)))) -> b{#,(f8)}(f8(b)(b(b)(x1))) a{#,(f8)}(f8(a)(a(a)(a(a)(x1)))) -> b{#,(f8)}(f8(b)(b(a)(x1))) a{#,(f8)}(f8(a)(a(a)(a(b)(x1)))) -> a{#,(f8)}(f8(b)(b(b)(b(b)(x1)))) a{#,(f8)}(f8(a)(a(a)(a(a)(x1)))) -> a{#,(f8)}(f8(b)(b(b)(b(a)(x1)))) TRS: f8(b)(b(b)(b(b)(b(f8)(x1)))) -> f8(a)(a(b)(b(f8)(x1))) f8(b)(b(b)(b(b)(b(b)(x1)))) -> f8(a)(a(b)(b(b)(x1))) f8(b)(b(b)(b(b)(b(a)(x1)))) -> f8(a)(a(b)(b(a)(x1))) b(b)(b(b)(b(b)(b(f8)(x1)))) -> b(a)(a(b)(b(f8)(x1))) b(b)(b(b)(b(b)(b(b)(x1)))) -> b(a)(a(b)(b(b)(x1))) b(b)(b(b)(b(b)(b(a)(x1)))) -> b(a)(a(b)(b(a)(x1))) a(b)(b(b)(b(b)(b(f8)(x1)))) -> a(a)(a(b)(b(f8)(x1))) a(b)(b(b)(b(b)(b(b)(x1)))) -> a(a)(a(b)(b(b)(x1))) a(b)(b(b)(b(b)(b(a)(x1)))) -> a(a)(a(b)(b(a)(x1))) a(a)(a(f8)(x1)) -> a(b)(b(a)(a(b)(b(a)(a(f8)(x1))))) a(a)(a(b)(x1)) -> a(b)(b(a)(a(b)(b(a)(a(b)(x1))))) a(a)(a(a)(x1)) -> a(b)(b(a)(a(b)(b(a)(a(a)(x1))))) a(a)(a(a)(a(b)(x1))) -> a(b)(b(b)(b(b)(x1))) a(a)(a(a)(a(a)(x1))) -> a(b)(b(b)(b(a)(x1))) Polynomial Interpretation Processor: dimension: 1 usable rules: f8(b)(b(b)(b(b)(b(f8)(x1)))) -> f8(a)(a(b)(b(f8)(x1))) f8(b)(b(b)(b(b)(b(b)(x1)))) -> f8(a)(a(b)(b(b)(x1))) f8(b)(b(b)(b(b)(b(a)(x1)))) -> f8(a)(a(b)(b(a)(x1))) a(b)(b(b)(b(b)(b(f8)(x1)))) -> a(a)(a(b)(b(f8)(x1))) a(b)(b(b)(b(b)(b(b)(x1)))) -> a(a)(a(b)(b(b)(x1))) a(b)(b(b)(b(b)(b(a)(x1)))) -> a(a)(a(b)(b(a)(x1))) a(a)(a(f8)(x1)) -> a(b)(b(a)(a(b)(b(a)(a(f8)(x1))))) a(a)(a(b)(x1)) -> a(b)(b(a)(a(b)(b(a)(a(b)(x1))))) a(a)(a(a)(x1)) -> a(b)(b(a)(a(b)(b(a)(a(a)(x1))))) a(a)(a(a)(a(b)(x1))) -> a(b)(b(b)(b(b)(x1))) a(a)(a(a)(a(a)(x1))) -> a(b)(b(b)(b(a)(x1))) interpretation: [a(a)](x0) = x0, [f8(a)](x0) = x0, [a(f8)](x0) = 1, [a(b)](x0) = 0, [f8(b)](x0) = 0, [b(a)](x0) = 0, [b(f8)](x0) = 0, [b(b)](x0) = 0, [b{#,(f8)}](x0) = x0, [a{#,(f8)}](x0) = x0 orientation: b{#,(f8)}(f8(b)(b(b)(b(f8)(x1)))) = 0 >= 0 = a{#,(f8)}(f8(b)(b(f8)(x1))) b{#,(f8)}(f8(b)(b(b)(b(b)(x1)))) = 0 >= 0 = a{#,(f8)}(f8(b)(b(b)(x1))) b{#,(f8)}(f8(b)(b(b)(b(a)(x1)))) = 0 >= 0 = a{#,(f8)}(f8(b)(b(a)(x1))) a{#,(f8)}(f8(a)(a(f8)(x1))) = 1 >= 1 = b{#,(f8)}(f8(a)(a(f8)(x1))) a{#,(f8)}(f8(a)(a(b)(x1))) = 0 >= 0 = b{#,(f8)}(f8(a)(a(b)(x1))) a{#,(f8)}(f8(a)(a(a)(x1))) = x1 >= x1 = b{#,(f8)}(f8(a)(a(a)(x1))) a{#,(f8)}(f8(a)(a(f8)(x1))) = 1 >= 0 = a{#,(f8)}(f8(b)(b(a)(a(f8)(x1)))) a{#,(f8)}(f8(a)(a(b)(x1))) = 0 >= 0 = a{#,(f8)}(f8(b)(b(a)(a(b)(x1)))) a{#,(f8)}(f8(a)(a(a)(x1))) = x1 >= 0 = a{#,(f8)}(f8(b)(b(a)(a(a)(x1)))) a{#,(f8)}(f8(a)(a(f8)(x1))) = 1 >= 0 = b{#,(f8)}(f8(a)(a(b)(b(a)(a(f8)(x1))))) a{#,(f8)}(f8(a)(a(b)(x1))) = 0 >= 0 = b{#,(f8)}(f8(a)(a(b)(b(a)(a(b)(x1))))) a{#,(f8)}(f8(a)(a(a)(x1))) = x1 >= 0 = b{#,(f8)}(f8(a)(a(b)(b(a)(a(a)(x1))))) a{#,(f8)}(f8(a)(a(f8)(x1))) = 1 >= 0 = a{#,(f8)}(f8(b)(b(a)(a(b)(b(a)(a(f8)(x1)))))) a{#,(f8)}(f8(a)(a(b)(x1))) = 0 >= 0 = a{#,(f8)}(f8(b)(b(a)(a(b)(b(a)(a(b)(x1)))))) a{#,(f8)}(f8(a)(a(a)(x1))) = x1 >= 0 = a{#,(f8)}(f8(b)(b(a)(a(b)(b(a)(a(a)(x1)))))) a{#,(f8)}(f8(a)(a(a)(a(b)(x1)))) = 0 >= 0 = b{#,(f8)}(f8(b)(x1)) a{#,(f8)}(f8(a)(a(a)(a(a)(x1)))) = x1 >= x1 = b{#,(f8)}(f8(a)(x1)) a{#,(f8)}(f8(a)(a(a)(a(b)(x1)))) = 0 >= 0 = b{#,(f8)}(f8(b)(b(b)(x1))) a{#,(f8)}(f8(a)(a(a)(a(a)(x1)))) = x1 >= 0 = b{#,(f8)}(f8(b)(b(a)(x1))) a{#,(f8)}(f8(a)(a(a)(a(b)(x1)))) = 0 >= 0 = a{#,(f8)}(f8(b)(b(b)(b(b)(x1)))) a{#,(f8)}(f8(a)(a(a)(a(a)(x1)))) = x1 >= 0 = a{#,(f8)}(f8(b)(b(b)(b(a)(x1)))) f8(b)(b(b)(b(b)(b(f8)(x1)))) = 0 >= 0 = f8(a)(a(b)(b(f8)(x1))) f8(b)(b(b)(b(b)(b(b)(x1)))) = 0 >= 0 = f8(a)(a(b)(b(b)(x1))) f8(b)(b(b)(b(b)(b(a)(x1)))) = 0 >= 0 = f8(a)(a(b)(b(a)(x1))) b(b)(b(b)(b(b)(b(f8)(x1)))) = 0 >= 0 = b(a)(a(b)(b(f8)(x1))) b(b)(b(b)(b(b)(b(b)(x1)))) = 0 >= 0 = b(a)(a(b)(b(b)(x1))) b(b)(b(b)(b(b)(b(a)(x1)))) = 0 >= 0 = b(a)(a(b)(b(a)(x1))) a(b)(b(b)(b(b)(b(f8)(x1)))) = 0 >= 0 = a(a)(a(b)(b(f8)(x1))) a(b)(b(b)(b(b)(b(b)(x1)))) = 0 >= 0 = a(a)(a(b)(b(b)(x1))) a(b)(b(b)(b(b)(b(a)(x1)))) = 0 >= 0 = a(a)(a(b)(b(a)(x1))) a(a)(a(f8)(x1)) = 1 >= 0 = a(b)(b(a)(a(b)(b(a)(a(f8)(x1))))) a(a)(a(b)(x1)) = 0 >= 0 = a(b)(b(a)(a(b)(b(a)(a(b)(x1))))) a(a)(a(a)(x1)) = x1 >= 0 = a(b)(b(a)(a(b)(b(a)(a(a)(x1))))) a(a)(a(a)(a(b)(x1))) = 0 >= 0 = a(b)(b(b)(b(b)(x1))) a(a)(a(a)(a(a)(x1))) = x1 >= 0 = a(b)(b(b)(b(a)(x1))) problem: DPs: b{#,(f8)}(f8(b)(b(b)(b(f8)(x1)))) -> a{#,(f8)}(f8(b)(b(f8)(x1))) b{#,(f8)}(f8(b)(b(b)(b(b)(x1)))) -> a{#,(f8)}(f8(b)(b(b)(x1))) b{#,(f8)}(f8(b)(b(b)(b(a)(x1)))) -> a{#,(f8)}(f8(b)(b(a)(x1))) a{#,(f8)}(f8(a)(a(f8)(x1))) -> b{#,(f8)}(f8(a)(a(f8)(x1))) a{#,(f8)}(f8(a)(a(b)(x1))) -> b{#,(f8)}(f8(a)(a(b)(x1))) a{#,(f8)}(f8(a)(a(a)(x1))) -> b{#,(f8)}(f8(a)(a(a)(x1))) a{#,(f8)}(f8(a)(a(b)(x1))) -> a{#,(f8)}(f8(b)(b(a)(a(b)(x1)))) a{#,(f8)}(f8(a)(a(a)(x1))) -> a{#,(f8)}(f8(b)(b(a)(a(a)(x1)))) a{#,(f8)}(f8(a)(a(b)(x1))) -> b{#,(f8)}(f8(a)(a(b)(b(a)(a(b)(x1))))) a{#,(f8)}(f8(a)(a(a)(x1))) -> b{#,(f8)}(f8(a)(a(b)(b(a)(a(a)(x1))))) a{#,(f8)}(f8(a)(a(b)(x1))) -> a{#,(f8)}(f8(b)(b(a)(a(b)(b(a)(a(b)(x1)))))) a{#,(f8)}(f8(a)(a(a)(x1))) -> a{#,(f8)}(f8(b)(b(a)(a(b)(b(a)(a(a)(x1)))))) a{#,(f8)}(f8(a)(a(a)(a(b)(x1)))) -> b{#,(f8)}(f8(b)(x1)) a{#,(f8)}(f8(a)(a(a)(a(a)(x1)))) -> b{#,(f8)}(f8(a)(x1)) a{#,(f8)}(f8(a)(a(a)(a(b)(x1)))) -> b{#,(f8)}(f8(b)(b(b)(x1))) a{#,(f8)}(f8(a)(a(a)(a(a)(x1)))) -> b{#,(f8)}(f8(b)(b(a)(x1))) a{#,(f8)}(f8(a)(a(a)(a(b)(x1)))) -> a{#,(f8)}(f8(b)(b(b)(b(b)(x1)))) a{#,(f8)}(f8(a)(a(a)(a(a)(x1)))) -> a{#,(f8)}(f8(b)(b(b)(b(a)(x1)))) TRS: f8(b)(b(b)(b(b)(b(f8)(x1)))) -> f8(a)(a(b)(b(f8)(x1))) f8(b)(b(b)(b(b)(b(b)(x1)))) -> f8(a)(a(b)(b(b)(x1))) f8(b)(b(b)(b(b)(b(a)(x1)))) -> f8(a)(a(b)(b(a)(x1))) b(b)(b(b)(b(b)(b(f8)(x1)))) -> b(a)(a(b)(b(f8)(x1))) b(b)(b(b)(b(b)(b(b)(x1)))) -> b(a)(a(b)(b(b)(x1))) b(b)(b(b)(b(b)(b(a)(x1)))) -> b(a)(a(b)(b(a)(x1))) a(b)(b(b)(b(b)(b(f8)(x1)))) -> a(a)(a(b)(b(f8)(x1))) a(b)(b(b)(b(b)(b(b)(x1)))) -> a(a)(a(b)(b(b)(x1))) a(b)(b(b)(b(b)(b(a)(x1)))) -> a(a)(a(b)(b(a)(x1))) a(a)(a(f8)(x1)) -> a(b)(b(a)(a(b)(b(a)(a(f8)(x1))))) a(a)(a(b)(x1)) -> a(b)(b(a)(a(b)(b(a)(a(b)(x1))))) a(a)(a(a)(x1)) -> a(b)(b(a)(a(b)(b(a)(a(a)(x1))))) a(a)(a(a)(a(b)(x1))) -> a(b)(b(b)(b(b)(x1))) a(a)(a(a)(a(a)(x1))) -> a(b)(b(b)(b(a)(x1))) Polynomial Interpretation Processor: dimension: 1 usable rules: f8(b)(b(b)(b(b)(b(f8)(x1)))) -> f8(a)(a(b)(b(f8)(x1))) f8(b)(b(b)(b(b)(b(b)(x1)))) -> f8(a)(a(b)(b(b)(x1))) f8(b)(b(b)(b(b)(b(a)(x1)))) -> f8(a)(a(b)(b(a)(x1))) a(b)(b(b)(b(b)(b(f8)(x1)))) -> a(a)(a(b)(b(f8)(x1))) a(b)(b(b)(b(b)(b(b)(x1)))) -> a(a)(a(b)(b(b)(x1))) a(b)(b(b)(b(b)(b(a)(x1)))) -> a(a)(a(b)(b(a)(x1))) a(a)(a(f8)(x1)) -> a(b)(b(a)(a(b)(b(a)(a(f8)(x1))))) a(a)(a(b)(x1)) -> a(b)(b(a)(a(b)(b(a)(a(b)(x1))))) a(a)(a(a)(x1)) -> a(b)(b(a)(a(b)(b(a)(a(a)(x1))))) a(a)(a(a)(a(b)(x1))) -> a(b)(b(b)(b(b)(x1))) a(a)(a(a)(a(a)(x1))) -> a(b)(b(b)(b(a)(x1))) interpretation: [a(a)](x0) = 0, [f8(a)](x0) = x0, [a(f8)](x0) = 1, [a(b)](x0) = 0, [f8(b)](x0) = 0, [b(a)](x0) = 0, [b(f8)](x0) = 0, [b(b)](x0) = 0, [b{#,(f8)}](x0) = 0, [a{#,(f8)}](x0) = x0 orientation: b{#,(f8)}(f8(b)(b(b)(b(f8)(x1)))) = 0 >= 0 = a{#,(f8)}(f8(b)(b(f8)(x1))) b{#,(f8)}(f8(b)(b(b)(b(b)(x1)))) = 0 >= 0 = a{#,(f8)}(f8(b)(b(b)(x1))) b{#,(f8)}(f8(b)(b(b)(b(a)(x1)))) = 0 >= 0 = a{#,(f8)}(f8(b)(b(a)(x1))) a{#,(f8)}(f8(a)(a(f8)(x1))) = 1 >= 0 = b{#,(f8)}(f8(a)(a(f8)(x1))) a{#,(f8)}(f8(a)(a(b)(x1))) = 0 >= 0 = b{#,(f8)}(f8(a)(a(b)(x1))) a{#,(f8)}(f8(a)(a(a)(x1))) = 0 >= 0 = b{#,(f8)}(f8(a)(a(a)(x1))) a{#,(f8)}(f8(a)(a(b)(x1))) = 0 >= 0 = a{#,(f8)}(f8(b)(b(a)(a(b)(x1)))) a{#,(f8)}(f8(a)(a(a)(x1))) = 0 >= 0 = a{#,(f8)}(f8(b)(b(a)(a(a)(x1)))) a{#,(f8)}(f8(a)(a(b)(x1))) = 0 >= 0 = b{#,(f8)}(f8(a)(a(b)(b(a)(a(b)(x1))))) a{#,(f8)}(f8(a)(a(a)(x1))) = 0 >= 0 = b{#,(f8)}(f8(a)(a(b)(b(a)(a(a)(x1))))) a{#,(f8)}(f8(a)(a(b)(x1))) = 0 >= 0 = a{#,(f8)}(f8(b)(b(a)(a(b)(b(a)(a(b)(x1)))))) a{#,(f8)}(f8(a)(a(a)(x1))) = 0 >= 0 = a{#,(f8)}(f8(b)(b(a)(a(b)(b(a)(a(a)(x1)))))) a{#,(f8)}(f8(a)(a(a)(a(b)(x1)))) = 0 >= 0 = b{#,(f8)}(f8(b)(x1)) a{#,(f8)}(f8(a)(a(a)(a(a)(x1)))) = 0 >= 0 = b{#,(f8)}(f8(a)(x1)) a{#,(f8)}(f8(a)(a(a)(a(b)(x1)))) = 0 >= 0 = b{#,(f8)}(f8(b)(b(b)(x1))) a{#,(f8)}(f8(a)(a(a)(a(a)(x1)))) = 0 >= 0 = b{#,(f8)}(f8(b)(b(a)(x1))) a{#,(f8)}(f8(a)(a(a)(a(b)(x1)))) = 0 >= 0 = a{#,(f8)}(f8(b)(b(b)(b(b)(x1)))) a{#,(f8)}(f8(a)(a(a)(a(a)(x1)))) = 0 >= 0 = a{#,(f8)}(f8(b)(b(b)(b(a)(x1)))) f8(b)(b(b)(b(b)(b(f8)(x1)))) = 0 >= 0 = f8(a)(a(b)(b(f8)(x1))) f8(b)(b(b)(b(b)(b(b)(x1)))) = 0 >= 0 = f8(a)(a(b)(b(b)(x1))) f8(b)(b(b)(b(b)(b(a)(x1)))) = 0 >= 0 = f8(a)(a(b)(b(a)(x1))) b(b)(b(b)(b(b)(b(f8)(x1)))) = 0 >= 0 = b(a)(a(b)(b(f8)(x1))) b(b)(b(b)(b(b)(b(b)(x1)))) = 0 >= 0 = b(a)(a(b)(b(b)(x1))) b(b)(b(b)(b(b)(b(a)(x1)))) = 0 >= 0 = b(a)(a(b)(b(a)(x1))) a(b)(b(b)(b(b)(b(f8)(x1)))) = 0 >= 0 = a(a)(a(b)(b(f8)(x1))) a(b)(b(b)(b(b)(b(b)(x1)))) = 0 >= 0 = a(a)(a(b)(b(b)(x1))) a(b)(b(b)(b(b)(b(a)(x1)))) = 0 >= 0 = a(a)(a(b)(b(a)(x1))) a(a)(a(f8)(x1)) = 0 >= 0 = a(b)(b(a)(a(b)(b(a)(a(f8)(x1))))) a(a)(a(b)(x1)) = 0 >= 0 = a(b)(b(a)(a(b)(b(a)(a(b)(x1))))) a(a)(a(a)(x1)) = 0 >= 0 = a(b)(b(a)(a(b)(b(a)(a(a)(x1))))) a(a)(a(a)(a(b)(x1))) = 0 >= 0 = a(b)(b(b)(b(b)(x1))) a(a)(a(a)(a(a)(x1))) = 0 >= 0 = a(b)(b(b)(b(a)(x1))) problem: DPs: b{#,(f8)}(f8(b)(b(b)(b(f8)(x1)))) -> a{#,(f8)}(f8(b)(b(f8)(x1))) b{#,(f8)}(f8(b)(b(b)(b(b)(x1)))) -> a{#,(f8)}(f8(b)(b(b)(x1))) b{#,(f8)}(f8(b)(b(b)(b(a)(x1)))) -> a{#,(f8)}(f8(b)(b(a)(x1))) a{#,(f8)}(f8(a)(a(b)(x1))) -> b{#,(f8)}(f8(a)(a(b)(x1))) a{#,(f8)}(f8(a)(a(a)(x1))) -> b{#,(f8)}(f8(a)(a(a)(x1))) a{#,(f8)}(f8(a)(a(b)(x1))) -> a{#,(f8)}(f8(b)(b(a)(a(b)(x1)))) a{#,(f8)}(f8(a)(a(a)(x1))) -> a{#,(f8)}(f8(b)(b(a)(a(a)(x1)))) a{#,(f8)}(f8(a)(a(b)(x1))) -> b{#,(f8)}(f8(a)(a(b)(b(a)(a(b)(x1))))) a{#,(f8)}(f8(a)(a(a)(x1))) -> b{#,(f8)}(f8(a)(a(b)(b(a)(a(a)(x1))))) a{#,(f8)}(f8(a)(a(b)(x1))) -> a{#,(f8)}(f8(b)(b(a)(a(b)(b(a)(a(b)(x1)))))) a{#,(f8)}(f8(a)(a(a)(x1))) -> a{#,(f8)}(f8(b)(b(a)(a(b)(b(a)(a(a)(x1)))))) a{#,(f8)}(f8(a)(a(a)(a(b)(x1)))) -> b{#,(f8)}(f8(b)(x1)) a{#,(f8)}(f8(a)(a(a)(a(a)(x1)))) -> b{#,(f8)}(f8(a)(x1)) a{#,(f8)}(f8(a)(a(a)(a(b)(x1)))) -> b{#,(f8)}(f8(b)(b(b)(x1))) a{#,(f8)}(f8(a)(a(a)(a(a)(x1)))) -> b{#,(f8)}(f8(b)(b(a)(x1))) a{#,(f8)}(f8(a)(a(a)(a(b)(x1)))) -> a{#,(f8)}(f8(b)(b(b)(b(b)(x1)))) a{#,(f8)}(f8(a)(a(a)(a(a)(x1)))) -> a{#,(f8)}(f8(b)(b(b)(b(a)(x1)))) TRS: f8(b)(b(b)(b(b)(b(f8)(x1)))) -> f8(a)(a(b)(b(f8)(x1))) f8(b)(b(b)(b(b)(b(b)(x1)))) -> f8(a)(a(b)(b(b)(x1))) f8(b)(b(b)(b(b)(b(a)(x1)))) -> f8(a)(a(b)(b(a)(x1))) b(b)(b(b)(b(b)(b(f8)(x1)))) -> b(a)(a(b)(b(f8)(x1))) b(b)(b(b)(b(b)(b(b)(x1)))) -> b(a)(a(b)(b(b)(x1))) b(b)(b(b)(b(b)(b(a)(x1)))) -> b(a)(a(b)(b(a)(x1))) a(b)(b(b)(b(b)(b(f8)(x1)))) -> a(a)(a(b)(b(f8)(x1))) a(b)(b(b)(b(b)(b(b)(x1)))) -> a(a)(a(b)(b(b)(x1))) a(b)(b(b)(b(b)(b(a)(x1)))) -> a(a)(a(b)(b(a)(x1))) a(a)(a(f8)(x1)) -> a(b)(b(a)(a(b)(b(a)(a(f8)(x1))))) a(a)(a(b)(x1)) -> a(b)(b(a)(a(b)(b(a)(a(b)(x1))))) a(a)(a(a)(x1)) -> a(b)(b(a)(a(b)(b(a)(a(a)(x1))))) a(a)(a(a)(a(b)(x1))) -> a(b)(b(b)(b(b)(x1))) a(a)(a(a)(a(a)(x1))) -> a(b)(b(b)(b(a)(x1))) Polynomial Interpretation Processor: dimension: 1 usable rules: f8(b)(b(b)(b(b)(b(f8)(x1)))) -> f8(a)(a(b)(b(f8)(x1))) f8(b)(b(b)(b(b)(b(b)(x1)))) -> f8(a)(a(b)(b(b)(x1))) f8(b)(b(b)(b(b)(b(a)(x1)))) -> f8(a)(a(b)(b(a)(x1))) b(b)(b(b)(b(b)(b(f8)(x1)))) -> b(a)(a(b)(b(f8)(x1))) b(b)(b(b)(b(b)(b(b)(x1)))) -> b(a)(a(b)(b(b)(x1))) b(b)(b(b)(b(b)(b(a)(x1)))) -> b(a)(a(b)(b(a)(x1))) a(b)(b(b)(b(b)(b(f8)(x1)))) -> a(a)(a(b)(b(f8)(x1))) a(b)(b(b)(b(b)(b(b)(x1)))) -> a(a)(a(b)(b(b)(x1))) a(b)(b(b)(b(b)(b(a)(x1)))) -> a(a)(a(b)(b(a)(x1))) a(a)(a(f8)(x1)) -> a(b)(b(a)(a(b)(b(a)(a(f8)(x1))))) a(a)(a(b)(x1)) -> a(b)(b(a)(a(b)(b(a)(a(b)(x1))))) a(a)(a(a)(x1)) -> a(b)(b(a)(a(b)(b(a)(a(a)(x1))))) a(a)(a(a)(a(b)(x1))) -> a(b)(b(b)(b(b)(x1))) a(a)(a(a)(a(a)(x1))) -> a(b)(b(b)(b(a)(x1))) interpretation: [a(a)](x0) = 1, [f8(a)](x0) = x0, [a(f8)](x0) = 0, [a(b)](x0) = 1, [f8(b)](x0) = x0, [b(a)](x0) = 0, [b(f8)](x0) = 0, [b(b)](x0) = 1, [b{#,(f8)}](x0) = 1, [a{#,(f8)}](x0) = x0 orientation: b{#,(f8)}(f8(b)(b(b)(b(f8)(x1)))) = 1 >= 0 = a{#,(f8)}(f8(b)(b(f8)(x1))) b{#,(f8)}(f8(b)(b(b)(b(b)(x1)))) = 1 >= 1 = a{#,(f8)}(f8(b)(b(b)(x1))) b{#,(f8)}(f8(b)(b(b)(b(a)(x1)))) = 1 >= 0 = a{#,(f8)}(f8(b)(b(a)(x1))) a{#,(f8)}(f8(a)(a(b)(x1))) = 1 >= 1 = b{#,(f8)}(f8(a)(a(b)(x1))) a{#,(f8)}(f8(a)(a(a)(x1))) = 1 >= 1 = b{#,(f8)}(f8(a)(a(a)(x1))) a{#,(f8)}(f8(a)(a(b)(x1))) = 1 >= 0 = a{#,(f8)}(f8(b)(b(a)(a(b)(x1)))) a{#,(f8)}(f8(a)(a(a)(x1))) = 1 >= 0 = a{#,(f8)}(f8(b)(b(a)(a(a)(x1)))) a{#,(f8)}(f8(a)(a(b)(x1))) = 1 >= 1 = b{#,(f8)}(f8(a)(a(b)(b(a)(a(b)(x1))))) a{#,(f8)}(f8(a)(a(a)(x1))) = 1 >= 1 = b{#,(f8)}(f8(a)(a(b)(b(a)(a(a)(x1))))) a{#,(f8)}(f8(a)(a(b)(x1))) = 1 >= 0 = a{#,(f8)}(f8(b)(b(a)(a(b)(b(a)(a(b)(x1)))))) a{#,(f8)}(f8(a)(a(a)(x1))) = 1 >= 0 = a{#,(f8)}(f8(b)(b(a)(a(b)(b(a)(a(a)(x1)))))) a{#,(f8)}(f8(a)(a(a)(a(b)(x1)))) = 1 >= 1 = b{#,(f8)}(f8(b)(x1)) a{#,(f8)}(f8(a)(a(a)(a(a)(x1)))) = 1 >= 1 = b{#,(f8)}(f8(a)(x1)) a{#,(f8)}(f8(a)(a(a)(a(b)(x1)))) = 1 >= 1 = b{#,(f8)}(f8(b)(b(b)(x1))) a{#,(f8)}(f8(a)(a(a)(a(a)(x1)))) = 1 >= 1 = b{#,(f8)}(f8(b)(b(a)(x1))) a{#,(f8)}(f8(a)(a(a)(a(b)(x1)))) = 1 >= 1 = a{#,(f8)}(f8(b)(b(b)(b(b)(x1)))) a{#,(f8)}(f8(a)(a(a)(a(a)(x1)))) = 1 >= 1 = a{#,(f8)}(f8(b)(b(b)(b(a)(x1)))) f8(b)(b(b)(b(b)(b(f8)(x1)))) = 1 >= 1 = f8(a)(a(b)(b(f8)(x1))) f8(b)(b(b)(b(b)(b(b)(x1)))) = 1 >= 1 = f8(a)(a(b)(b(b)(x1))) f8(b)(b(b)(b(b)(b(a)(x1)))) = 1 >= 1 = f8(a)(a(b)(b(a)(x1))) b(b)(b(b)(b(b)(b(f8)(x1)))) = 1 >= 0 = b(a)(a(b)(b(f8)(x1))) b(b)(b(b)(b(b)(b(b)(x1)))) = 1 >= 0 = b(a)(a(b)(b(b)(x1))) b(b)(b(b)(b(b)(b(a)(x1)))) = 1 >= 0 = b(a)(a(b)(b(a)(x1))) a(b)(b(b)(b(b)(b(f8)(x1)))) = 1 >= 1 = a(a)(a(b)(b(f8)(x1))) a(b)(b(b)(b(b)(b(b)(x1)))) = 1 >= 1 = a(a)(a(b)(b(b)(x1))) a(b)(b(b)(b(b)(b(a)(x1)))) = 1 >= 1 = a(a)(a(b)(b(a)(x1))) a(a)(a(f8)(x1)) = 1 >= 1 = a(b)(b(a)(a(b)(b(a)(a(f8)(x1))))) a(a)(a(b)(x1)) = 1 >= 1 = a(b)(b(a)(a(b)(b(a)(a(b)(x1))))) a(a)(a(a)(x1)) = 1 >= 1 = a(b)(b(a)(a(b)(b(a)(a(a)(x1))))) a(a)(a(a)(a(b)(x1))) = 1 >= 1 = a(b)(b(b)(b(b)(x1))) a(a)(a(a)(a(a)(x1))) = 1 >= 1 = a(b)(b(b)(b(a)(x1))) problem: DPs: b{#,(f8)}(f8(b)(b(b)(b(b)(x1)))) -> a{#,(f8)}(f8(b)(b(b)(x1))) a{#,(f8)}(f8(a)(a(b)(x1))) -> b{#,(f8)}(f8(a)(a(b)(x1))) a{#,(f8)}(f8(a)(a(a)(x1))) -> b{#,(f8)}(f8(a)(a(a)(x1))) a{#,(f8)}(f8(a)(a(b)(x1))) -> b{#,(f8)}(f8(a)(a(b)(b(a)(a(b)(x1))))) a{#,(f8)}(f8(a)(a(a)(x1))) -> b{#,(f8)}(f8(a)(a(b)(b(a)(a(a)(x1))))) a{#,(f8)}(f8(a)(a(a)(a(b)(x1)))) -> b{#,(f8)}(f8(b)(x1)) a{#,(f8)}(f8(a)(a(a)(a(a)(x1)))) -> b{#,(f8)}(f8(a)(x1)) a{#,(f8)}(f8(a)(a(a)(a(b)(x1)))) -> b{#,(f8)}(f8(b)(b(b)(x1))) a{#,(f8)}(f8(a)(a(a)(a(a)(x1)))) -> b{#,(f8)}(f8(b)(b(a)(x1))) a{#,(f8)}(f8(a)(a(a)(a(b)(x1)))) -> a{#,(f8)}(f8(b)(b(b)(b(b)(x1)))) a{#,(f8)}(f8(a)(a(a)(a(a)(x1)))) -> a{#,(f8)}(f8(b)(b(b)(b(a)(x1)))) TRS: f8(b)(b(b)(b(b)(b(f8)(x1)))) -> f8(a)(a(b)(b(f8)(x1))) f8(b)(b(b)(b(b)(b(b)(x1)))) -> f8(a)(a(b)(b(b)(x1))) f8(b)(b(b)(b(b)(b(a)(x1)))) -> f8(a)(a(b)(b(a)(x1))) b(b)(b(b)(b(b)(b(f8)(x1)))) -> b(a)(a(b)(b(f8)(x1))) b(b)(b(b)(b(b)(b(b)(x1)))) -> b(a)(a(b)(b(b)(x1))) b(b)(b(b)(b(b)(b(a)(x1)))) -> b(a)(a(b)(b(a)(x1))) a(b)(b(b)(b(b)(b(f8)(x1)))) -> a(a)(a(b)(b(f8)(x1))) a(b)(b(b)(b(b)(b(b)(x1)))) -> a(a)(a(b)(b(b)(x1))) a(b)(b(b)(b(b)(b(a)(x1)))) -> a(a)(a(b)(b(a)(x1))) a(a)(a(f8)(x1)) -> a(b)(b(a)(a(b)(b(a)(a(f8)(x1))))) a(a)(a(b)(x1)) -> a(b)(b(a)(a(b)(b(a)(a(b)(x1))))) a(a)(a(a)(x1)) -> a(b)(b(a)(a(b)(b(a)(a(a)(x1))))) a(a)(a(a)(a(b)(x1))) -> a(b)(b(b)(b(b)(x1))) a(a)(a(a)(a(a)(x1))) -> a(b)(b(b)(b(a)(x1))) Polynomial Interpretation Processor: dimension: 1 usable rules: f8(b)(b(b)(b(b)(b(f8)(x1)))) -> f8(a)(a(b)(b(f8)(x1))) f8(b)(b(b)(b(b)(b(b)(x1)))) -> f8(a)(a(b)(b(b)(x1))) f8(b)(b(b)(b(b)(b(a)(x1)))) -> f8(a)(a(b)(b(a)(x1))) b(b)(b(b)(b(b)(b(f8)(x1)))) -> b(a)(a(b)(b(f8)(x1))) b(b)(b(b)(b(b)(b(b)(x1)))) -> b(a)(a(b)(b(b)(x1))) b(b)(b(b)(b(b)(b(a)(x1)))) -> b(a)(a(b)(b(a)(x1))) a(b)(b(b)(b(b)(b(f8)(x1)))) -> a(a)(a(b)(b(f8)(x1))) a(b)(b(b)(b(b)(b(b)(x1)))) -> a(a)(a(b)(b(b)(x1))) a(b)(b(b)(b(b)(b(a)(x1)))) -> a(a)(a(b)(b(a)(x1))) a(a)(a(f8)(x1)) -> a(b)(b(a)(a(b)(b(a)(a(f8)(x1))))) a(a)(a(b)(x1)) -> a(b)(b(a)(a(b)(b(a)(a(b)(x1))))) a(a)(a(a)(x1)) -> a(b)(b(a)(a(b)(b(a)(a(a)(x1))))) a(a)(a(a)(a(b)(x1))) -> a(b)(b(b)(b(b)(x1))) a(a)(a(a)(a(a)(x1))) -> a(b)(b(b)(b(a)(x1))) interpretation: [a(a)](x0) = x0 + 1, [f8(a)](x0) = x0, [a(f8)](x0) = 0, [a(b)](x0) = x0 + 1, [f8(b)](x0) = x0, [b(a)](x0) = 0, [b(f8)](x0) = 0, [b(b)](x0) = x0 + 1, [b{#,(f8)}](x0) = x0, [a{#,(f8)}](x0) = x0 orientation: b{#,(f8)}(f8(b)(b(b)(b(b)(x1)))) = x1 + 2 >= x1 + 1 = a{#,(f8)}(f8(b)(b(b)(x1))) a{#,(f8)}(f8(a)(a(b)(x1))) = x1 + 1 >= x1 + 1 = b{#,(f8)}(f8(a)(a(b)(x1))) a{#,(f8)}(f8(a)(a(a)(x1))) = x1 + 1 >= x1 + 1 = b{#,(f8)}(f8(a)(a(a)(x1))) a{#,(f8)}(f8(a)(a(b)(x1))) = x1 + 1 >= 1 = b{#,(f8)}(f8(a)(a(b)(b(a)(a(b)(x1))))) a{#,(f8)}(f8(a)(a(a)(x1))) = x1 + 1 >= 1 = b{#,(f8)}(f8(a)(a(b)(b(a)(a(a)(x1))))) a{#,(f8)}(f8(a)(a(a)(a(b)(x1)))) = x1 + 2 >= x1 = b{#,(f8)}(f8(b)(x1)) a{#,(f8)}(f8(a)(a(a)(a(a)(x1)))) = x1 + 2 >= x1 = b{#,(f8)}(f8(a)(x1)) a{#,(f8)}(f8(a)(a(a)(a(b)(x1)))) = x1 + 2 >= x1 + 1 = b{#,(f8)}(f8(b)(b(b)(x1))) a{#,(f8)}(f8(a)(a(a)(a(a)(x1)))) = x1 + 2 >= 0 = b{#,(f8)}(f8(b)(b(a)(x1))) a{#,(f8)}(f8(a)(a(a)(a(b)(x1)))) = x1 + 2 >= x1 + 2 = a{#,(f8)}(f8(b)(b(b)(b(b)(x1)))) a{#,(f8)}(f8(a)(a(a)(a(a)(x1)))) = x1 + 2 >= 1 = a{#,(f8)}(f8(b)(b(b)(b(a)(x1)))) f8(b)(b(b)(b(b)(b(f8)(x1)))) = 2 >= 1 = f8(a)(a(b)(b(f8)(x1))) f8(b)(b(b)(b(b)(b(b)(x1)))) = x1 + 3 >= x1 + 2 = f8(a)(a(b)(b(b)(x1))) f8(b)(b(b)(b(b)(b(a)(x1)))) = 2 >= 1 = f8(a)(a(b)(b(a)(x1))) b(b)(b(b)(b(b)(b(f8)(x1)))) = 3 >= 0 = b(a)(a(b)(b(f8)(x1))) b(b)(b(b)(b(b)(b(b)(x1)))) = x1 + 4 >= 0 = b(a)(a(b)(b(b)(x1))) b(b)(b(b)(b(b)(b(a)(x1)))) = 3 >= 0 = b(a)(a(b)(b(a)(x1))) a(b)(b(b)(b(b)(b(f8)(x1)))) = 3 >= 2 = a(a)(a(b)(b(f8)(x1))) a(b)(b(b)(b(b)(b(b)(x1)))) = x1 + 4 >= x1 + 3 = a(a)(a(b)(b(b)(x1))) a(b)(b(b)(b(b)(b(a)(x1)))) = 3 >= 2 = a(a)(a(b)(b(a)(x1))) a(a)(a(f8)(x1)) = 1 >= 1 = a(b)(b(a)(a(b)(b(a)(a(f8)(x1))))) a(a)(a(b)(x1)) = x1 + 2 >= 1 = a(b)(b(a)(a(b)(b(a)(a(b)(x1))))) a(a)(a(a)(x1)) = x1 + 2 >= 1 = a(b)(b(a)(a(b)(b(a)(a(a)(x1))))) a(a)(a(a)(a(b)(x1))) = x1 + 3 >= x1 + 3 = a(b)(b(b)(b(b)(x1))) a(a)(a(a)(a(a)(x1))) = x1 + 3 >= 2 = a(b)(b(b)(b(a)(x1))) problem: DPs: a{#,(f8)}(f8(a)(a(b)(x1))) -> b{#,(f8)}(f8(a)(a(b)(x1))) a{#,(f8)}(f8(a)(a(a)(x1))) -> b{#,(f8)}(f8(a)(a(a)(x1))) a{#,(f8)}(f8(a)(a(b)(x1))) -> b{#,(f8)}(f8(a)(a(b)(b(a)(a(b)(x1))))) a{#,(f8)}(f8(a)(a(a)(x1))) -> b{#,(f8)}(f8(a)(a(b)(b(a)(a(a)(x1))))) a{#,(f8)}(f8(a)(a(a)(a(b)(x1)))) -> a{#,(f8)}(f8(b)(b(b)(b(b)(x1)))) TRS: f8(b)(b(b)(b(b)(b(f8)(x1)))) -> f8(a)(a(b)(b(f8)(x1))) f8(b)(b(b)(b(b)(b(b)(x1)))) -> f8(a)(a(b)(b(b)(x1))) f8(b)(b(b)(b(b)(b(a)(x1)))) -> f8(a)(a(b)(b(a)(x1))) b(b)(b(b)(b(b)(b(f8)(x1)))) -> b(a)(a(b)(b(f8)(x1))) b(b)(b(b)(b(b)(b(b)(x1)))) -> b(a)(a(b)(b(b)(x1))) b(b)(b(b)(b(b)(b(a)(x1)))) -> b(a)(a(b)(b(a)(x1))) a(b)(b(b)(b(b)(b(f8)(x1)))) -> a(a)(a(b)(b(f8)(x1))) a(b)(b(b)(b(b)(b(b)(x1)))) -> a(a)(a(b)(b(b)(x1))) a(b)(b(b)(b(b)(b(a)(x1)))) -> a(a)(a(b)(b(a)(x1))) a(a)(a(f8)(x1)) -> a(b)(b(a)(a(b)(b(a)(a(f8)(x1))))) a(a)(a(b)(x1)) -> a(b)(b(a)(a(b)(b(a)(a(b)(x1))))) a(a)(a(a)(x1)) -> a(b)(b(a)(a(b)(b(a)(a(a)(x1))))) a(a)(a(a)(a(b)(x1))) -> a(b)(b(b)(b(b)(x1))) a(a)(a(a)(a(a)(x1))) -> a(b)(b(b)(b(a)(x1))) SCC Processor: #sccs: 1 #rules: 1 #arcs: 288/25 DPs: a{#,(f8)}(f8(a)(a(a)(a(b)(x1)))) -> a{#,(f8)}(f8(b)(b(b)(b(b)(x1)))) TRS: f8(b)(b(b)(b(b)(b(f8)(x1)))) -> f8(a)(a(b)(b(f8)(x1))) f8(b)(b(b)(b(b)(b(b)(x1)))) -> f8(a)(a(b)(b(b)(x1))) f8(b)(b(b)(b(b)(b(a)(x1)))) -> f8(a)(a(b)(b(a)(x1))) b(b)(b(b)(b(b)(b(f8)(x1)))) -> b(a)(a(b)(b(f8)(x1))) b(b)(b(b)(b(b)(b(b)(x1)))) -> b(a)(a(b)(b(b)(x1))) b(b)(b(b)(b(b)(b(a)(x1)))) -> b(a)(a(b)(b(a)(x1))) a(b)(b(b)(b(b)(b(f8)(x1)))) -> a(a)(a(b)(b(f8)(x1))) a(b)(b(b)(b(b)(b(b)(x1)))) -> a(a)(a(b)(b(b)(x1))) a(b)(b(b)(b(b)(b(a)(x1)))) -> a(a)(a(b)(b(a)(x1))) a(a)(a(f8)(x1)) -> a(b)(b(a)(a(b)(b(a)(a(f8)(x1))))) a(a)(a(b)(x1)) -> a(b)(b(a)(a(b)(b(a)(a(b)(x1))))) a(a)(a(a)(x1)) -> a(b)(b(a)(a(b)(b(a)(a(a)(x1))))) a(a)(a(a)(a(b)(x1))) -> a(b)(b(b)(b(b)(x1))) a(a)(a(a)(a(a)(x1))) -> a(b)(b(b)(b(a)(x1))) Polynomial Interpretation Processor: dimension: 1 usable rules: f8(b)(b(b)(b(b)(b(f8)(x1)))) -> f8(a)(a(b)(b(f8)(x1))) f8(b)(b(b)(b(b)(b(b)(x1)))) -> f8(a)(a(b)(b(b)(x1))) f8(b)(b(b)(b(b)(b(a)(x1)))) -> f8(a)(a(b)(b(a)(x1))) b(b)(b(b)(b(b)(b(f8)(x1)))) -> b(a)(a(b)(b(f8)(x1))) b(b)(b(b)(b(b)(b(b)(x1)))) -> b(a)(a(b)(b(b)(x1))) b(b)(b(b)(b(b)(b(a)(x1)))) -> b(a)(a(b)(b(a)(x1))) a(b)(b(b)(b(b)(b(f8)(x1)))) -> a(a)(a(b)(b(f8)(x1))) a(b)(b(b)(b(b)(b(b)(x1)))) -> a(a)(a(b)(b(b)(x1))) a(b)(b(b)(b(b)(b(a)(x1)))) -> a(a)(a(b)(b(a)(x1))) a(a)(a(f8)(x1)) -> a(b)(b(a)(a(b)(b(a)(a(f8)(x1))))) a(a)(a(b)(x1)) -> a(b)(b(a)(a(b)(b(a)(a(b)(x1))))) a(a)(a(a)(x1)) -> a(b)(b(a)(a(b)(b(a)(a(a)(x1))))) a(a)(a(a)(a(b)(x1))) -> a(b)(b(b)(b(b)(x1))) a(a)(a(a)(a(a)(x1))) -> a(b)(b(b)(b(a)(x1))) interpretation: [a(a)](x0) = x0 + 1, [f8(a)](x0) = x0 + 1, [a(f8)](x0) = 0, [a(b)](x0) = x0 + 1, [f8(b)](x0) = x0, [b(a)](x0) = 0, [b(f8)](x0) = 1, [b(b)](x0) = x0 + 1, [a{#,(f8)}](x0) = x0 orientation: a{#,(f8)}(f8(a)(a(a)(a(b)(x1)))) = x1 + 3 >= x1 + 2 = a{#,(f8)}(f8(b)(b(b)(b(b)(x1)))) f8(b)(b(b)(b(b)(b(f8)(x1)))) = 3 >= 3 = f8(a)(a(b)(b(f8)(x1))) f8(b)(b(b)(b(b)(b(b)(x1)))) = x1 + 3 >= x1 + 3 = f8(a)(a(b)(b(b)(x1))) f8(b)(b(b)(b(b)(b(a)(x1)))) = 2 >= 2 = f8(a)(a(b)(b(a)(x1))) b(b)(b(b)(b(b)(b(f8)(x1)))) = 4 >= 0 = b(a)(a(b)(b(f8)(x1))) b(b)(b(b)(b(b)(b(b)(x1)))) = x1 + 4 >= 0 = b(a)(a(b)(b(b)(x1))) b(b)(b(b)(b(b)(b(a)(x1)))) = 3 >= 0 = b(a)(a(b)(b(a)(x1))) a(b)(b(b)(b(b)(b(f8)(x1)))) = 4 >= 3 = a(a)(a(b)(b(f8)(x1))) a(b)(b(b)(b(b)(b(b)(x1)))) = x1 + 4 >= x1 + 3 = a(a)(a(b)(b(b)(x1))) a(b)(b(b)(b(b)(b(a)(x1)))) = 3 >= 2 = a(a)(a(b)(b(a)(x1))) a(a)(a(f8)(x1)) = 1 >= 1 = a(b)(b(a)(a(b)(b(a)(a(f8)(x1))))) a(a)(a(b)(x1)) = x1 + 2 >= 1 = a(b)(b(a)(a(b)(b(a)(a(b)(x1))))) a(a)(a(a)(x1)) = x1 + 2 >= 1 = a(b)(b(a)(a(b)(b(a)(a(a)(x1))))) a(a)(a(a)(a(b)(x1))) = x1 + 3 >= x1 + 3 = a(b)(b(b)(b(b)(x1))) a(a)(a(a)(a(a)(x1))) = x1 + 3 >= 2 = a(b)(b(b)(b(a)(x1))) problem: DPs: TRS: f8(b)(b(b)(b(b)(b(f8)(x1)))) -> f8(a)(a(b)(b(f8)(x1))) f8(b)(b(b)(b(b)(b(b)(x1)))) -> f8(a)(a(b)(b(b)(x1))) f8(b)(b(b)(b(b)(b(a)(x1)))) -> f8(a)(a(b)(b(a)(x1))) b(b)(b(b)(b(b)(b(f8)(x1)))) -> b(a)(a(b)(b(f8)(x1))) b(b)(b(b)(b(b)(b(b)(x1)))) -> b(a)(a(b)(b(b)(x1))) b(b)(b(b)(b(b)(b(a)(x1)))) -> b(a)(a(b)(b(a)(x1))) a(b)(b(b)(b(b)(b(f8)(x1)))) -> a(a)(a(b)(b(f8)(x1))) a(b)(b(b)(b(b)(b(b)(x1)))) -> a(a)(a(b)(b(b)(x1))) a(b)(b(b)(b(b)(b(a)(x1)))) -> a(a)(a(b)(b(a)(x1))) a(a)(a(f8)(x1)) -> a(b)(b(a)(a(b)(b(a)(a(f8)(x1))))) a(a)(a(b)(x1)) -> a(b)(b(a)(a(b)(b(a)(a(b)(x1))))) a(a)(a(a)(x1)) -> a(b)(b(a)(a(b)(b(a)(a(a)(x1))))) a(a)(a(a)(a(b)(x1))) -> a(b)(b(b)(b(b)(x1))) a(a)(a(a)(a(a)(x1))) -> a(b)(b(b)(b(a)(x1))) Qed