/export/starexec/sandbox/solver/bin/starexec_run_ttt2-1.17+nonreach /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files -------------------------------------------------------------------------------- YES Problem: s(b(x1)) -> b(s(s(s(x1)))) s(b(s(x1))) -> b(t(x1)) t(b(x1)) -> b(s(x1)) t(b(s(x1))) -> u(t(b(x1))) b(u(x1)) -> b(s(x1)) t(s(x1)) -> t(t(x1)) t(u(x1)) -> u(t(x1)) s(u(x1)) -> s(s(x1)) Proof: DP Processor: DPs: s#(b(x1)) -> s#(x1) s#(b(x1)) -> s#(s(x1)) s#(b(x1)) -> s#(s(s(x1))) s#(b(x1)) -> b#(s(s(s(x1)))) s#(b(s(x1))) -> t#(x1) s#(b(s(x1))) -> b#(t(x1)) t#(b(x1)) -> s#(x1) t#(b(x1)) -> b#(s(x1)) t#(b(s(x1))) -> b#(x1) t#(b(s(x1))) -> t#(b(x1)) b#(u(x1)) -> s#(x1) b#(u(x1)) -> b#(s(x1)) t#(s(x1)) -> t#(x1) t#(s(x1)) -> t#(t(x1)) t#(u(x1)) -> t#(x1) s#(u(x1)) -> s#(x1) s#(u(x1)) -> s#(s(x1)) TRS: s(b(x1)) -> b(s(s(s(x1)))) s(b(s(x1))) -> b(t(x1)) t(b(x1)) -> b(s(x1)) t(b(s(x1))) -> u(t(b(x1))) b(u(x1)) -> b(s(x1)) t(s(x1)) -> t(t(x1)) t(u(x1)) -> u(t(x1)) s(u(x1)) -> s(s(x1)) TDG Processor: DPs: s#(b(x1)) -> s#(x1) s#(b(x1)) -> s#(s(x1)) s#(b(x1)) -> s#(s(s(x1))) s#(b(x1)) -> b#(s(s(s(x1)))) s#(b(s(x1))) -> t#(x1) s#(b(s(x1))) -> b#(t(x1)) t#(b(x1)) -> s#(x1) t#(b(x1)) -> b#(s(x1)) t#(b(s(x1))) -> b#(x1) t#(b(s(x1))) -> t#(b(x1)) b#(u(x1)) -> s#(x1) b#(u(x1)) -> b#(s(x1)) t#(s(x1)) -> t#(x1) t#(s(x1)) -> t#(t(x1)) t#(u(x1)) -> t#(x1) s#(u(x1)) -> s#(x1) s#(u(x1)) -> s#(s(x1)) TRS: s(b(x1)) -> b(s(s(s(x1)))) s(b(s(x1))) -> b(t(x1)) t(b(x1)) -> b(s(x1)) t(b(s(x1))) -> u(t(b(x1))) b(u(x1)) -> b(s(x1)) t(s(x1)) -> t(t(x1)) t(u(x1)) -> u(t(x1)) s(u(x1)) -> s(s(x1)) graph: t#(u(x1)) -> t#(x1) -> t#(u(x1)) -> t#(x1) t#(u(x1)) -> t#(x1) -> t#(s(x1)) -> t#(t(x1)) t#(u(x1)) -> t#(x1) -> t#(s(x1)) -> t#(x1) t#(u(x1)) -> t#(x1) -> t#(b(s(x1))) -> t#(b(x1)) t#(u(x1)) -> t#(x1) -> t#(b(s(x1))) -> b#(x1) t#(u(x1)) -> t#(x1) -> t#(b(x1)) -> b#(s(x1)) t#(u(x1)) -> t#(x1) -> t#(b(x1)) -> s#(x1) t#(s(x1)) -> t#(t(x1)) -> t#(u(x1)) -> t#(x1) t#(s(x1)) -> t#(t(x1)) -> t#(s(x1)) -> t#(t(x1)) t#(s(x1)) -> t#(t(x1)) -> t#(s(x1)) -> t#(x1) t#(s(x1)) -> t#(t(x1)) -> t#(b(s(x1))) -> t#(b(x1)) t#(s(x1)) -> t#(t(x1)) -> t#(b(s(x1))) -> b#(x1) t#(s(x1)) -> t#(t(x1)) -> t#(b(x1)) -> b#(s(x1)) t#(s(x1)) -> t#(t(x1)) -> t#(b(x1)) -> s#(x1) t#(s(x1)) -> t#(x1) -> t#(u(x1)) -> t#(x1) t#(s(x1)) -> t#(x1) -> t#(s(x1)) -> t#(t(x1)) t#(s(x1)) -> t#(x1) -> t#(s(x1)) -> t#(x1) t#(s(x1)) -> t#(x1) -> t#(b(s(x1))) -> t#(b(x1)) t#(s(x1)) -> t#(x1) -> t#(b(s(x1))) -> b#(x1) t#(s(x1)) -> t#(x1) -> t#(b(x1)) -> b#(s(x1)) t#(s(x1)) -> t#(x1) -> t#(b(x1)) -> s#(x1) t#(b(s(x1))) -> t#(b(x1)) -> t#(u(x1)) -> t#(x1) t#(b(s(x1))) -> t#(b(x1)) -> t#(s(x1)) -> t#(t(x1)) t#(b(s(x1))) -> t#(b(x1)) -> t#(s(x1)) -> t#(x1) t#(b(s(x1))) -> t#(b(x1)) -> t#(b(s(x1))) -> t#(b(x1)) t#(b(s(x1))) -> t#(b(x1)) -> t#(b(s(x1))) -> b#(x1) t#(b(s(x1))) -> t#(b(x1)) -> t#(b(x1)) -> b#(s(x1)) t#(b(s(x1))) -> t#(b(x1)) -> t#(b(x1)) -> s#(x1) t#(b(s(x1))) -> b#(x1) -> b#(u(x1)) -> b#(s(x1)) t#(b(s(x1))) -> b#(x1) -> b#(u(x1)) -> s#(x1) t#(b(x1)) -> b#(s(x1)) -> b#(u(x1)) -> b#(s(x1)) t#(b(x1)) -> b#(s(x1)) -> b#(u(x1)) -> s#(x1) t#(b(x1)) -> s#(x1) -> s#(u(x1)) -> s#(s(x1)) t#(b(x1)) -> s#(x1) -> s#(u(x1)) -> s#(x1) t#(b(x1)) -> s#(x1) -> s#(b(s(x1))) -> b#(t(x1)) t#(b(x1)) -> s#(x1) -> s#(b(s(x1))) -> t#(x1) t#(b(x1)) -> s#(x1) -> s#(b(x1)) -> b#(s(s(s(x1)))) t#(b(x1)) -> s#(x1) -> s#(b(x1)) -> s#(s(s(x1))) t#(b(x1)) -> s#(x1) -> s#(b(x1)) -> s#(s(x1)) t#(b(x1)) -> s#(x1) -> s#(b(x1)) -> s#(x1) b#(u(x1)) -> b#(s(x1)) -> b#(u(x1)) -> b#(s(x1)) b#(u(x1)) -> b#(s(x1)) -> b#(u(x1)) -> s#(x1) b#(u(x1)) -> s#(x1) -> s#(u(x1)) -> s#(s(x1)) b#(u(x1)) -> s#(x1) -> s#(u(x1)) -> s#(x1) b#(u(x1)) -> s#(x1) -> s#(b(s(x1))) -> b#(t(x1)) b#(u(x1)) -> s#(x1) -> s#(b(s(x1))) -> t#(x1) b#(u(x1)) -> s#(x1) -> s#(b(x1)) -> b#(s(s(s(x1)))) b#(u(x1)) -> s#(x1) -> s#(b(x1)) -> s#(s(s(x1))) b#(u(x1)) -> s#(x1) -> s#(b(x1)) -> s#(s(x1)) b#(u(x1)) -> s#(x1) -> s#(b(x1)) -> s#(x1) s#(u(x1)) -> s#(s(x1)) -> s#(u(x1)) -> s#(s(x1)) s#(u(x1)) -> s#(s(x1)) -> s#(u(x1)) -> s#(x1) s#(u(x1)) -> s#(s(x1)) -> s#(b(s(x1))) -> b#(t(x1)) s#(u(x1)) -> s#(s(x1)) -> s#(b(s(x1))) -> t#(x1) s#(u(x1)) -> s#(s(x1)) -> s#(b(x1)) -> b#(s(s(s(x1)))) s#(u(x1)) -> s#(s(x1)) -> s#(b(x1)) -> s#(s(s(x1))) s#(u(x1)) -> s#(s(x1)) -> s#(b(x1)) -> s#(s(x1)) s#(u(x1)) -> s#(s(x1)) -> s#(b(x1)) -> s#(x1) s#(u(x1)) -> s#(x1) -> s#(u(x1)) -> s#(s(x1)) s#(u(x1)) -> s#(x1) -> s#(u(x1)) -> s#(x1) s#(u(x1)) -> s#(x1) -> s#(b(s(x1))) -> b#(t(x1)) s#(u(x1)) -> s#(x1) -> s#(b(s(x1))) -> t#(x1) s#(u(x1)) -> s#(x1) -> s#(b(x1)) -> b#(s(s(s(x1)))) s#(u(x1)) -> s#(x1) -> s#(b(x1)) -> s#(s(s(x1))) s#(u(x1)) -> s#(x1) -> s#(b(x1)) -> s#(s(x1)) s#(u(x1)) -> s#(x1) -> s#(b(x1)) -> s#(x1) s#(b(s(x1))) -> t#(x1) -> t#(u(x1)) -> t#(x1) s#(b(s(x1))) -> t#(x1) -> t#(s(x1)) -> t#(t(x1)) s#(b(s(x1))) -> t#(x1) -> t#(s(x1)) -> t#(x1) s#(b(s(x1))) -> t#(x1) -> t#(b(s(x1))) -> t#(b(x1)) s#(b(s(x1))) -> t#(x1) -> t#(b(s(x1))) -> b#(x1) s#(b(s(x1))) -> t#(x1) -> t#(b(x1)) -> b#(s(x1)) s#(b(s(x1))) -> t#(x1) -> t#(b(x1)) -> s#(x1) s#(b(s(x1))) -> b#(t(x1)) -> b#(u(x1)) -> b#(s(x1)) s#(b(s(x1))) -> b#(t(x1)) -> b#(u(x1)) -> s#(x1) s#(b(x1)) -> b#(s(s(s(x1)))) -> b#(u(x1)) -> b#(s(x1)) s#(b(x1)) -> b#(s(s(s(x1)))) -> b#(u(x1)) -> s#(x1) s#(b(x1)) -> s#(s(s(x1))) -> s#(u(x1)) -> s#(s(x1)) s#(b(x1)) -> s#(s(s(x1))) -> s#(u(x1)) -> s#(x1) s#(b(x1)) -> s#(s(s(x1))) -> s#(b(s(x1))) -> b#(t(x1)) s#(b(x1)) -> s#(s(s(x1))) -> s#(b(s(x1))) -> t#(x1) s#(b(x1)) -> s#(s(s(x1))) -> s#(b(x1)) -> b#(s(s(s(x1)))) s#(b(x1)) -> s#(s(s(x1))) -> s#(b(x1)) -> s#(s(s(x1))) s#(b(x1)) -> s#(s(s(x1))) -> s#(b(x1)) -> s#(s(x1)) s#(b(x1)) -> s#(s(s(x1))) -> s#(b(x1)) -> s#(x1) s#(b(x1)) -> s#(s(x1)) -> s#(u(x1)) -> s#(s(x1)) s#(b(x1)) -> s#(s(x1)) -> s#(u(x1)) -> s#(x1) s#(b(x1)) -> s#(s(x1)) -> s#(b(s(x1))) -> b#(t(x1)) s#(b(x1)) -> s#(s(x1)) -> s#(b(s(x1))) -> t#(x1) s#(b(x1)) -> s#(s(x1)) -> s#(b(x1)) -> b#(s(s(s(x1)))) s#(b(x1)) -> s#(s(x1)) -> s#(b(x1)) -> s#(s(s(x1))) s#(b(x1)) -> s#(s(x1)) -> s#(b(x1)) -> s#(s(x1)) s#(b(x1)) -> s#(s(x1)) -> s#(b(x1)) -> s#(x1) s#(b(x1)) -> s#(x1) -> s#(u(x1)) -> s#(s(x1)) s#(b(x1)) -> s#(x1) -> s#(u(x1)) -> s#(x1) s#(b(x1)) -> s#(x1) -> s#(b(s(x1))) -> b#(t(x1)) s#(b(x1)) -> s#(x1) -> s#(b(s(x1))) -> t#(x1) s#(b(x1)) -> s#(x1) -> s#(b(x1)) -> b#(s(s(s(x1)))) s#(b(x1)) -> s#(x1) -> s#(b(x1)) -> s#(s(s(x1))) s#(b(x1)) -> s#(x1) -> s#(b(x1)) -> s#(s(x1)) s#(b(x1)) -> s#(x1) -> s#(b(x1)) -> s#(x1) Polynomial Interpretation Processor: dimension: 1 interpretation: [t#](x0) = x0, [b#](x0) = x0 + 1, [s#](x0) = x0, [u](x0) = x0, [t](x0) = x0, [s](x0) = x0, [b](x0) = x0 + 1 orientation: s#(b(x1)) = x1 + 1 >= x1 = s#(x1) s#(b(x1)) = x1 + 1 >= x1 = s#(s(x1)) s#(b(x1)) = x1 + 1 >= x1 = s#(s(s(x1))) s#(b(x1)) = x1 + 1 >= x1 + 1 = b#(s(s(s(x1)))) s#(b(s(x1))) = x1 + 1 >= x1 = t#(x1) s#(b(s(x1))) = x1 + 1 >= x1 + 1 = b#(t(x1)) t#(b(x1)) = x1 + 1 >= x1 = s#(x1) t#(b(x1)) = x1 + 1 >= x1 + 1 = b#(s(x1)) t#(b(s(x1))) = x1 + 1 >= x1 + 1 = b#(x1) t#(b(s(x1))) = x1 + 1 >= x1 + 1 = t#(b(x1)) b#(u(x1)) = x1 + 1 >= x1 = s#(x1) b#(u(x1)) = x1 + 1 >= x1 + 1 = b#(s(x1)) t#(s(x1)) = x1 >= x1 = t#(x1) t#(s(x1)) = x1 >= x1 = t#(t(x1)) t#(u(x1)) = x1 >= x1 = t#(x1) s#(u(x1)) = x1 >= x1 = s#(x1) s#(u(x1)) = x1 >= x1 = s#(s(x1)) s(b(x1)) = x1 + 1 >= x1 + 1 = b(s(s(s(x1)))) s(b(s(x1))) = x1 + 1 >= x1 + 1 = b(t(x1)) t(b(x1)) = x1 + 1 >= x1 + 1 = b(s(x1)) t(b(s(x1))) = x1 + 1 >= x1 + 1 = u(t(b(x1))) b(u(x1)) = x1 + 1 >= x1 + 1 = b(s(x1)) t(s(x1)) = x1 >= x1 = t(t(x1)) t(u(x1)) = x1 >= x1 = u(t(x1)) s(u(x1)) = x1 >= x1 = s(s(x1)) problem: DPs: s#(b(x1)) -> b#(s(s(s(x1)))) s#(b(s(x1))) -> b#(t(x1)) t#(b(x1)) -> b#(s(x1)) t#(b(s(x1))) -> b#(x1) t#(b(s(x1))) -> t#(b(x1)) b#(u(x1)) -> b#(s(x1)) t#(s(x1)) -> t#(x1) t#(s(x1)) -> t#(t(x1)) t#(u(x1)) -> t#(x1) s#(u(x1)) -> s#(x1) s#(u(x1)) -> s#(s(x1)) TRS: s(b(x1)) -> b(s(s(s(x1)))) s(b(s(x1))) -> b(t(x1)) t(b(x1)) -> b(s(x1)) t(b(s(x1))) -> u(t(b(x1))) b(u(x1)) -> b(s(x1)) t(s(x1)) -> t(t(x1)) t(u(x1)) -> u(t(x1)) s(u(x1)) -> s(s(x1)) SCC Processor: #sccs: 3 #rules: 7 #arcs: 101/121 DPs: s#(u(x1)) -> s#(s(x1)) s#(u(x1)) -> s#(x1) TRS: s(b(x1)) -> b(s(s(s(x1)))) s(b(s(x1))) -> b(t(x1)) t(b(x1)) -> b(s(x1)) t(b(s(x1))) -> u(t(b(x1))) b(u(x1)) -> b(s(x1)) t(s(x1)) -> t(t(x1)) t(u(x1)) -> u(t(x1)) s(u(x1)) -> s(s(x1)) Polynomial Interpretation Processor: dimension: 1 usable rules: s(b(x1)) -> b(s(s(s(x1)))) s(b(s(x1))) -> b(t(x1)) b(u(x1)) -> b(s(x1)) s(u(x1)) -> s(s(x1)) interpretation: [s#](x0) = x0, [u](x0) = x0 + 1, [t](x0) = 0, [s](x0) = 1, [b](x0) = 1 orientation: s#(u(x1)) = x1 + 1 >= 1 = s#(s(x1)) s#(u(x1)) = x1 + 1 >= x1 = s#(x1) s(b(x1)) = 1 >= 1 = b(s(s(s(x1)))) s(b(s(x1))) = 1 >= 1 = b(t(x1)) t(b(x1)) = 0 >= 1 = b(s(x1)) t(b(s(x1))) = 0 >= 1 = u(t(b(x1))) b(u(x1)) = 1 >= 1 = b(s(x1)) t(s(x1)) = 0 >= 0 = t(t(x1)) t(u(x1)) = 0 >= 1 = u(t(x1)) s(u(x1)) = 1 >= 1 = s(s(x1)) problem: DPs: s#(u(x1)) -> s#(s(x1)) TRS: s(b(x1)) -> b(s(s(s(x1)))) s(b(s(x1))) -> b(t(x1)) t(b(x1)) -> b(s(x1)) t(b(s(x1))) -> u(t(b(x1))) b(u(x1)) -> b(s(x1)) t(s(x1)) -> t(t(x1)) t(u(x1)) -> u(t(x1)) s(u(x1)) -> s(s(x1)) Polynomial Interpretation Processor: dimension: 1 usable rules: s(b(x1)) -> b(s(s(s(x1)))) s(b(s(x1))) -> b(t(x1)) b(u(x1)) -> b(s(x1)) s(u(x1)) -> s(s(x1)) interpretation: [s#](x0) = x0, [u](x0) = 1, [t](x0) = 0, [s](x0) = 0, [b](x0) = 0 orientation: s#(u(x1)) = 1 >= 0 = s#(s(x1)) s(b(x1)) = 0 >= 0 = b(s(s(s(x1)))) s(b(s(x1))) = 0 >= 0 = b(t(x1)) t(b(x1)) = 0 >= 0 = b(s(x1)) t(b(s(x1))) = 0 >= 1 = u(t(b(x1))) b(u(x1)) = 0 >= 0 = b(s(x1)) t(s(x1)) = 0 >= 0 = t(t(x1)) t(u(x1)) = 0 >= 1 = u(t(x1)) s(u(x1)) = 0 >= 0 = s(s(x1)) problem: DPs: TRS: s(b(x1)) -> b(s(s(s(x1)))) s(b(s(x1))) -> b(t(x1)) t(b(x1)) -> b(s(x1)) t(b(s(x1))) -> u(t(b(x1))) b(u(x1)) -> b(s(x1)) t(s(x1)) -> t(t(x1)) t(u(x1)) -> u(t(x1)) s(u(x1)) -> s(s(x1)) Qed DPs: t#(u(x1)) -> t#(x1) t#(b(s(x1))) -> t#(b(x1)) t#(s(x1)) -> t#(x1) t#(s(x1)) -> t#(t(x1)) TRS: s(b(x1)) -> b(s(s(s(x1)))) s(b(s(x1))) -> b(t(x1)) t(b(x1)) -> b(s(x1)) t(b(s(x1))) -> u(t(b(x1))) b(u(x1)) -> b(s(x1)) t(s(x1)) -> t(t(x1)) t(u(x1)) -> u(t(x1)) s(u(x1)) -> s(s(x1)) Polynomial Interpretation Processor: dimension: 1 usable rules: t(b(x1)) -> b(s(x1)) t(b(s(x1))) -> u(t(b(x1))) b(u(x1)) -> b(s(x1)) t(s(x1)) -> t(t(x1)) t(u(x1)) -> u(t(x1)) interpretation: [t#](x0) = x0, [u](x0) = x0, [t](x0) = 0, [s](x0) = x0 + 1, [b](x0) = 0 orientation: t#(u(x1)) = x1 >= x1 = t#(x1) t#(b(s(x1))) = 0 >= 0 = t#(b(x1)) t#(s(x1)) = x1 + 1 >= x1 = t#(x1) t#(s(x1)) = x1 + 1 >= 0 = t#(t(x1)) s(b(x1)) = 1 >= 0 = b(s(s(s(x1)))) s(b(s(x1))) = 1 >= 0 = b(t(x1)) t(b(x1)) = 0 >= 0 = b(s(x1)) t(b(s(x1))) = 0 >= 0 = u(t(b(x1))) b(u(x1)) = 0 >= 0 = b(s(x1)) t(s(x1)) = 0 >= 0 = t(t(x1)) t(u(x1)) = 0 >= 0 = u(t(x1)) s(u(x1)) = x1 + 1 >= x1 + 2 = s(s(x1)) problem: DPs: t#(u(x1)) -> t#(x1) t#(b(s(x1))) -> t#(b(x1)) TRS: s(b(x1)) -> b(s(s(s(x1)))) s(b(s(x1))) -> b(t(x1)) t(b(x1)) -> b(s(x1)) t(b(s(x1))) -> u(t(b(x1))) b(u(x1)) -> b(s(x1)) t(s(x1)) -> t(t(x1)) t(u(x1)) -> u(t(x1)) s(u(x1)) -> s(s(x1)) Polynomial Interpretation Processor: dimension: 1 usable rules: b(u(x1)) -> b(s(x1)) interpretation: [t#](x0) = x0, [u](x0) = x0 + 1, [t](x0) = 0, [s](x0) = 0, [b](x0) = 0 orientation: t#(u(x1)) = x1 + 1 >= x1 = t#(x1) t#(b(s(x1))) = 0 >= 0 = t#(b(x1)) s(b(x1)) = 0 >= 0 = b(s(s(s(x1)))) s(b(s(x1))) = 0 >= 0 = b(t(x1)) t(b(x1)) = 0 >= 0 = b(s(x1)) t(b(s(x1))) = 0 >= 1 = u(t(b(x1))) b(u(x1)) = 0 >= 0 = b(s(x1)) t(s(x1)) = 0 >= 0 = t(t(x1)) t(u(x1)) = 0 >= 1 = u(t(x1)) s(u(x1)) = 0 >= 0 = s(s(x1)) problem: DPs: t#(b(s(x1))) -> t#(b(x1)) TRS: s(b(x1)) -> b(s(s(s(x1)))) s(b(s(x1))) -> b(t(x1)) t(b(x1)) -> b(s(x1)) t(b(s(x1))) -> u(t(b(x1))) b(u(x1)) -> b(s(x1)) t(s(x1)) -> t(t(x1)) t(u(x1)) -> u(t(x1)) s(u(x1)) -> s(s(x1)) Root-Labeling Processor: DPs: t{#,(f7)}(f7(b)(b(s)(s(f7)(x1)))) -> t{#,(f7)}(f7(b)(b(f7)(x1))) t{#,(f7)}(f7(b)(b(s)(s(s)(x1)))) -> t{#,(f7)}(f7(b)(b(s)(x1))) t{#,(f7)}(f7(b)(b(s)(s(b)(x1)))) -> t{#,(f7)}(f7(b)(b(b)(x1))) t{#,(f7)}(f7(b)(b(s)(s(t)(x1)))) -> t{#,(f7)}(f7(b)(b(t)(x1))) t{#,(f7)}(f7(b)(b(s)(s(u)(x1)))) -> t{#,(f7)}(f7(b)(b(u)(x1))) TRS: f7(s)(s(b)(b(f7)(x1))) -> f7(b)(b(s)(s(s)(s(s)(s(f7)(x1))))) f7(s)(s(b)(b(s)(x1))) -> f7(b)(b(s)(s(s)(s(s)(s(s)(x1))))) f7(s)(s(b)(b(b)(x1))) -> f7(b)(b(s)(s(s)(s(s)(s(b)(x1))))) f7(s)(s(b)(b(t)(x1))) -> f7(b)(b(s)(s(s)(s(s)(s(t)(x1))))) f7(s)(s(b)(b(u)(x1))) -> f7(b)(b(s)(s(s)(s(s)(s(u)(x1))))) s(s)(s(b)(b(f7)(x1))) -> s(b)(b(s)(s(s)(s(s)(s(f7)(x1))))) s(s)(s(b)(b(s)(x1))) -> s(b)(b(s)(s(s)(s(s)(s(s)(x1))))) s(s)(s(b)(b(b)(x1))) -> s(b)(b(s)(s(s)(s(s)(s(b)(x1))))) s(s)(s(b)(b(t)(x1))) -> s(b)(b(s)(s(s)(s(s)(s(t)(x1))))) s(s)(s(b)(b(u)(x1))) -> s(b)(b(s)(s(s)(s(s)(s(u)(x1))))) b(s)(s(b)(b(f7)(x1))) -> b(b)(b(s)(s(s)(s(s)(s(f7)(x1))))) b(s)(s(b)(b(s)(x1))) -> b(b)(b(s)(s(s)(s(s)(s(s)(x1))))) b(s)(s(b)(b(b)(x1))) -> b(b)(b(s)(s(s)(s(s)(s(b)(x1))))) b(s)(s(b)(b(t)(x1))) -> b(b)(b(s)(s(s)(s(s)(s(t)(x1))))) b(s)(s(b)(b(u)(x1))) -> b(b)(b(s)(s(s)(s(s)(s(u)(x1))))) t(s)(s(b)(b(f7)(x1))) -> t(b)(b(s)(s(s)(s(s)(s(f7)(x1))))) t(s)(s(b)(b(s)(x1))) -> t(b)(b(s)(s(s)(s(s)(s(s)(x1))))) t(s)(s(b)(b(b)(x1))) -> t(b)(b(s)(s(s)(s(s)(s(b)(x1))))) t(s)(s(b)(b(t)(x1))) -> t(b)(b(s)(s(s)(s(s)(s(t)(x1))))) t(s)(s(b)(b(u)(x1))) -> t(b)(b(s)(s(s)(s(s)(s(u)(x1))))) u(s)(s(b)(b(f7)(x1))) -> u(b)(b(s)(s(s)(s(s)(s(f7)(x1))))) u(s)(s(b)(b(s)(x1))) -> u(b)(b(s)(s(s)(s(s)(s(s)(x1))))) u(s)(s(b)(b(b)(x1))) -> u(b)(b(s)(s(s)(s(s)(s(b)(x1))))) u(s)(s(b)(b(t)(x1))) -> u(b)(b(s)(s(s)(s(s)(s(t)(x1))))) u(s)(s(b)(b(u)(x1))) -> u(b)(b(s)(s(s)(s(s)(s(u)(x1))))) f7(s)(s(b)(b(s)(s(f7)(x1)))) -> f7(b)(b(t)(t(f7)(x1))) f7(s)(s(b)(b(s)(s(s)(x1)))) -> f7(b)(b(t)(t(s)(x1))) f7(s)(s(b)(b(s)(s(b)(x1)))) -> f7(b)(b(t)(t(b)(x1))) f7(s)(s(b)(b(s)(s(t)(x1)))) -> f7(b)(b(t)(t(t)(x1))) f7(s)(s(b)(b(s)(s(u)(x1)))) -> f7(b)(b(t)(t(u)(x1))) s(s)(s(b)(b(s)(s(f7)(x1)))) -> s(b)(b(t)(t(f7)(x1))) s(s)(s(b)(b(s)(s(s)(x1)))) -> s(b)(b(t)(t(s)(x1))) s(s)(s(b)(b(s)(s(b)(x1)))) -> s(b)(b(t)(t(b)(x1))) s(s)(s(b)(b(s)(s(t)(x1)))) -> s(b)(b(t)(t(t)(x1))) s(s)(s(b)(b(s)(s(u)(x1)))) -> s(b)(b(t)(t(u)(x1))) b(s)(s(b)(b(s)(s(f7)(x1)))) -> b(b)(b(t)(t(f7)(x1))) b(s)(s(b)(b(s)(s(s)(x1)))) -> b(b)(b(t)(t(s)(x1))) b(s)(s(b)(b(s)(s(b)(x1)))) -> b(b)(b(t)(t(b)(x1))) b(s)(s(b)(b(s)(s(t)(x1)))) -> b(b)(b(t)(t(t)(x1))) b(s)(s(b)(b(s)(s(u)(x1)))) -> b(b)(b(t)(t(u)(x1))) t(s)(s(b)(b(s)(s(f7)(x1)))) -> t(b)(b(t)(t(f7)(x1))) t(s)(s(b)(b(s)(s(s)(x1)))) -> t(b)(b(t)(t(s)(x1))) t(s)(s(b)(b(s)(s(b)(x1)))) -> t(b)(b(t)(t(b)(x1))) t(s)(s(b)(b(s)(s(t)(x1)))) -> t(b)(b(t)(t(t)(x1))) t(s)(s(b)(b(s)(s(u)(x1)))) -> t(b)(b(t)(t(u)(x1))) u(s)(s(b)(b(s)(s(f7)(x1)))) -> u(b)(b(t)(t(f7)(x1))) u(s)(s(b)(b(s)(s(s)(x1)))) -> u(b)(b(t)(t(s)(x1))) u(s)(s(b)(b(s)(s(b)(x1)))) -> u(b)(b(t)(t(b)(x1))) u(s)(s(b)(b(s)(s(t)(x1)))) -> u(b)(b(t)(t(t)(x1))) u(s)(s(b)(b(s)(s(u)(x1)))) -> u(b)(b(t)(t(u)(x1))) f7(t)(t(b)(b(f7)(x1))) -> f7(b)(b(s)(s(f7)(x1))) f7(t)(t(b)(b(s)(x1))) -> f7(b)(b(s)(s(s)(x1))) f7(t)(t(b)(b(b)(x1))) -> f7(b)(b(s)(s(b)(x1))) f7(t)(t(b)(b(t)(x1))) -> f7(b)(b(s)(s(t)(x1))) f7(t)(t(b)(b(u)(x1))) -> f7(b)(b(s)(s(u)(x1))) s(t)(t(b)(b(f7)(x1))) -> s(b)(b(s)(s(f7)(x1))) s(t)(t(b)(b(s)(x1))) -> s(b)(b(s)(s(s)(x1))) s(t)(t(b)(b(b)(x1))) -> s(b)(b(s)(s(b)(x1))) s(t)(t(b)(b(t)(x1))) -> s(b)(b(s)(s(t)(x1))) s(t)(t(b)(b(u)(x1))) -> s(b)(b(s)(s(u)(x1))) b(t)(t(b)(b(f7)(x1))) -> b(b)(b(s)(s(f7)(x1))) b(t)(t(b)(b(s)(x1))) -> b(b)(b(s)(s(s)(x1))) b(t)(t(b)(b(b)(x1))) -> b(b)(b(s)(s(b)(x1))) b(t)(t(b)(b(t)(x1))) -> b(b)(b(s)(s(t)(x1))) b(t)(t(b)(b(u)(x1))) -> b(b)(b(s)(s(u)(x1))) t(t)(t(b)(b(f7)(x1))) -> t(b)(b(s)(s(f7)(x1))) t(t)(t(b)(b(s)(x1))) -> t(b)(b(s)(s(s)(x1))) t(t)(t(b)(b(b)(x1))) -> t(b)(b(s)(s(b)(x1))) t(t)(t(b)(b(t)(x1))) -> t(b)(b(s)(s(t)(x1))) t(t)(t(b)(b(u)(x1))) -> t(b)(b(s)(s(u)(x1))) u(t)(t(b)(b(f7)(x1))) -> u(b)(b(s)(s(f7)(x1))) u(t)(t(b)(b(s)(x1))) -> u(b)(b(s)(s(s)(x1))) u(t)(t(b)(b(b)(x1))) -> u(b)(b(s)(s(b)(x1))) u(t)(t(b)(b(t)(x1))) -> u(b)(b(s)(s(t)(x1))) u(t)(t(b)(b(u)(x1))) -> u(b)(b(s)(s(u)(x1))) f7(t)(t(b)(b(s)(s(f7)(x1)))) -> f7(u)(u(t)(t(b)(b(f7)(x1)))) f7(t)(t(b)(b(s)(s(s)(x1)))) -> f7(u)(u(t)(t(b)(b(s)(x1)))) f7(t)(t(b)(b(s)(s(b)(x1)))) -> f7(u)(u(t)(t(b)(b(b)(x1)))) f7(t)(t(b)(b(s)(s(t)(x1)))) -> f7(u)(u(t)(t(b)(b(t)(x1)))) f7(t)(t(b)(b(s)(s(u)(x1)))) -> f7(u)(u(t)(t(b)(b(u)(x1)))) s(t)(t(b)(b(s)(s(f7)(x1)))) -> s(u)(u(t)(t(b)(b(f7)(x1)))) s(t)(t(b)(b(s)(s(s)(x1)))) -> s(u)(u(t)(t(b)(b(s)(x1)))) s(t)(t(b)(b(s)(s(b)(x1)))) -> s(u)(u(t)(t(b)(b(b)(x1)))) s(t)(t(b)(b(s)(s(t)(x1)))) -> s(u)(u(t)(t(b)(b(t)(x1)))) s(t)(t(b)(b(s)(s(u)(x1)))) -> s(u)(u(t)(t(b)(b(u)(x1)))) b(t)(t(b)(b(s)(s(f7)(x1)))) -> b(u)(u(t)(t(b)(b(f7)(x1)))) b(t)(t(b)(b(s)(s(s)(x1)))) -> b(u)(u(t)(t(b)(b(s)(x1)))) b(t)(t(b)(b(s)(s(b)(x1)))) -> b(u)(u(t)(t(b)(b(b)(x1)))) b(t)(t(b)(b(s)(s(t)(x1)))) -> b(u)(u(t)(t(b)(b(t)(x1)))) b(t)(t(b)(b(s)(s(u)(x1)))) -> b(u)(u(t)(t(b)(b(u)(x1)))) t(t)(t(b)(b(s)(s(f7)(x1)))) -> t(u)(u(t)(t(b)(b(f7)(x1)))) t(t)(t(b)(b(s)(s(s)(x1)))) -> t(u)(u(t)(t(b)(b(s)(x1)))) t(t)(t(b)(b(s)(s(b)(x1)))) -> t(u)(u(t)(t(b)(b(b)(x1)))) t(t)(t(b)(b(s)(s(t)(x1)))) -> t(u)(u(t)(t(b)(b(t)(x1)))) t(t)(t(b)(b(s)(s(u)(x1)))) -> t(u)(u(t)(t(b)(b(u)(x1)))) u(t)(t(b)(b(s)(s(f7)(x1)))) -> u(u)(u(t)(t(b)(b(f7)(x1)))) u(t)(t(b)(b(s)(s(s)(x1)))) -> u(u)(u(t)(t(b)(b(s)(x1)))) u(t)(t(b)(b(s)(s(b)(x1)))) -> u(u)(u(t)(t(b)(b(b)(x1)))) u(t)(t(b)(b(s)(s(t)(x1)))) -> u(u)(u(t)(t(b)(b(t)(x1)))) u(t)(t(b)(b(s)(s(u)(x1)))) -> u(u)(u(t)(t(b)(b(u)(x1)))) b(u)(u(f7)(x1)) -> b(s)(s(f7)(x1)) b(u)(u(s)(x1)) -> b(s)(s(s)(x1)) b(u)(u(b)(x1)) -> b(s)(s(b)(x1)) b(u)(u(t)(x1)) -> b(s)(s(t)(x1)) b(u)(u(u)(x1)) -> b(s)(s(u)(x1)) t(s)(s(f7)(x1)) -> t(t)(t(f7)(x1)) t(s)(s(s)(x1)) -> t(t)(t(s)(x1)) t(s)(s(b)(x1)) -> t(t)(t(b)(x1)) t(s)(s(t)(x1)) -> t(t)(t(t)(x1)) t(s)(s(u)(x1)) -> t(t)(t(u)(x1)) f7(t)(t(u)(u(f7)(x1))) -> f7(u)(u(t)(t(f7)(x1))) f7(t)(t(u)(u(s)(x1))) -> f7(u)(u(t)(t(s)(x1))) f7(t)(t(u)(u(b)(x1))) -> f7(u)(u(t)(t(b)(x1))) f7(t)(t(u)(u(t)(x1))) -> f7(u)(u(t)(t(t)(x1))) f7(t)(t(u)(u(u)(x1))) -> f7(u)(u(t)(t(u)(x1))) s(t)(t(u)(u(f7)(x1))) -> s(u)(u(t)(t(f7)(x1))) s(t)(t(u)(u(s)(x1))) -> s(u)(u(t)(t(s)(x1))) s(t)(t(u)(u(b)(x1))) -> s(u)(u(t)(t(b)(x1))) s(t)(t(u)(u(t)(x1))) -> s(u)(u(t)(t(t)(x1))) s(t)(t(u)(u(u)(x1))) -> s(u)(u(t)(t(u)(x1))) b(t)(t(u)(u(f7)(x1))) -> b(u)(u(t)(t(f7)(x1))) b(t)(t(u)(u(s)(x1))) -> b(u)(u(t)(t(s)(x1))) b(t)(t(u)(u(b)(x1))) -> b(u)(u(t)(t(b)(x1))) b(t)(t(u)(u(t)(x1))) -> b(u)(u(t)(t(t)(x1))) b(t)(t(u)(u(u)(x1))) -> b(u)(u(t)(t(u)(x1))) t(t)(t(u)(u(f7)(x1))) -> t(u)(u(t)(t(f7)(x1))) t(t)(t(u)(u(s)(x1))) -> t(u)(u(t)(t(s)(x1))) t(t)(t(u)(u(b)(x1))) -> t(u)(u(t)(t(b)(x1))) t(t)(t(u)(u(t)(x1))) -> t(u)(u(t)(t(t)(x1))) t(t)(t(u)(u(u)(x1))) -> t(u)(u(t)(t(u)(x1))) u(t)(t(u)(u(f7)(x1))) -> u(u)(u(t)(t(f7)(x1))) u(t)(t(u)(u(s)(x1))) -> u(u)(u(t)(t(s)(x1))) u(t)(t(u)(u(b)(x1))) -> u(u)(u(t)(t(b)(x1))) u(t)(t(u)(u(t)(x1))) -> u(u)(u(t)(t(t)(x1))) u(t)(t(u)(u(u)(x1))) -> u(u)(u(t)(t(u)(x1))) s(u)(u(f7)(x1)) -> s(s)(s(f7)(x1)) s(u)(u(s)(x1)) -> s(s)(s(s)(x1)) s(u)(u(b)(x1)) -> s(s)(s(b)(x1)) s(u)(u(t)(x1)) -> s(s)(s(t)(x1)) s(u)(u(u)(x1)) -> s(s)(s(u)(x1)) Usable Rule Processor: DPs: t{#,(f7)}(f7(b)(b(s)(s(f7)(x1)))) -> t{#,(f7)}(f7(b)(b(f7)(x1))) t{#,(f7)}(f7(b)(b(s)(s(s)(x1)))) -> t{#,(f7)}(f7(b)(b(s)(x1))) t{#,(f7)}(f7(b)(b(s)(s(b)(x1)))) -> t{#,(f7)}(f7(b)(b(b)(x1))) t{#,(f7)}(f7(b)(b(s)(s(t)(x1)))) -> t{#,(f7)}(f7(b)(b(t)(x1))) t{#,(f7)}(f7(b)(b(s)(s(u)(x1)))) -> t{#,(f7)}(f7(b)(b(u)(x1))) TRS: b(s)(s(b)(b(f7)(x1))) -> b(b)(b(s)(s(s)(s(s)(s(f7)(x1))))) b(s)(s(b)(b(s)(x1))) -> b(b)(b(s)(s(s)(s(s)(s(s)(x1))))) b(s)(s(b)(b(b)(x1))) -> b(b)(b(s)(s(s)(s(s)(s(b)(x1))))) b(s)(s(b)(b(t)(x1))) -> b(b)(b(s)(s(s)(s(s)(s(t)(x1))))) b(s)(s(b)(b(u)(x1))) -> b(b)(b(s)(s(s)(s(s)(s(u)(x1))))) b(s)(s(b)(b(s)(s(f7)(x1)))) -> b(b)(b(t)(t(f7)(x1))) b(s)(s(b)(b(s)(s(s)(x1)))) -> b(b)(b(t)(t(s)(x1))) b(s)(s(b)(b(s)(s(b)(x1)))) -> b(b)(b(t)(t(b)(x1))) b(s)(s(b)(b(s)(s(t)(x1)))) -> b(b)(b(t)(t(t)(x1))) b(s)(s(b)(b(s)(s(u)(x1)))) -> b(b)(b(t)(t(u)(x1))) s(s)(s(b)(b(f7)(x1))) -> s(b)(b(s)(s(s)(s(s)(s(f7)(x1))))) s(s)(s(b)(b(s)(x1))) -> s(b)(b(s)(s(s)(s(s)(s(s)(x1))))) s(s)(s(b)(b(b)(x1))) -> s(b)(b(s)(s(s)(s(s)(s(b)(x1))))) s(s)(s(b)(b(t)(x1))) -> s(b)(b(s)(s(s)(s(s)(s(t)(x1))))) s(s)(s(b)(b(u)(x1))) -> s(b)(b(s)(s(s)(s(s)(s(u)(x1))))) s(s)(s(b)(b(s)(s(f7)(x1)))) -> s(b)(b(t)(t(f7)(x1))) s(s)(s(b)(b(s)(s(s)(x1)))) -> s(b)(b(t)(t(s)(x1))) s(s)(s(b)(b(s)(s(b)(x1)))) -> s(b)(b(t)(t(b)(x1))) s(s)(s(b)(b(s)(s(t)(x1)))) -> s(b)(b(t)(t(t)(x1))) s(s)(s(b)(b(s)(s(u)(x1)))) -> s(b)(b(t)(t(u)(x1))) s(t)(t(b)(b(f7)(x1))) -> s(b)(b(s)(s(f7)(x1))) s(t)(t(b)(b(s)(x1))) -> s(b)(b(s)(s(s)(x1))) s(t)(t(b)(b(b)(x1))) -> s(b)(b(s)(s(b)(x1))) s(t)(t(b)(b(t)(x1))) -> s(b)(b(s)(s(t)(x1))) s(t)(t(b)(b(u)(x1))) -> s(b)(b(s)(s(u)(x1))) s(t)(t(b)(b(s)(s(f7)(x1)))) -> s(u)(u(t)(t(b)(b(f7)(x1)))) s(t)(t(b)(b(s)(s(s)(x1)))) -> s(u)(u(t)(t(b)(b(s)(x1)))) s(t)(t(b)(b(s)(s(b)(x1)))) -> s(u)(u(t)(t(b)(b(b)(x1)))) s(t)(t(b)(b(s)(s(t)(x1)))) -> s(u)(u(t)(t(b)(b(t)(x1)))) s(t)(t(b)(b(s)(s(u)(x1)))) -> s(u)(u(t)(t(b)(b(u)(x1)))) s(t)(t(u)(u(f7)(x1))) -> s(u)(u(t)(t(f7)(x1))) s(t)(t(u)(u(s)(x1))) -> s(u)(u(t)(t(s)(x1))) s(t)(t(u)(u(b)(x1))) -> s(u)(u(t)(t(b)(x1))) s(t)(t(u)(u(t)(x1))) -> s(u)(u(t)(t(t)(x1))) s(t)(t(u)(u(u)(x1))) -> s(u)(u(t)(t(u)(x1))) s(u)(u(f7)(x1)) -> s(s)(s(f7)(x1)) s(u)(u(s)(x1)) -> s(s)(s(s)(x1)) s(u)(u(b)(x1)) -> s(s)(s(b)(x1)) s(u)(u(t)(x1)) -> s(s)(s(t)(x1)) s(u)(u(u)(x1)) -> s(s)(s(u)(x1)) t(s)(s(b)(b(f7)(x1))) -> t(b)(b(s)(s(s)(s(s)(s(f7)(x1))))) t(s)(s(b)(b(s)(x1))) -> t(b)(b(s)(s(s)(s(s)(s(s)(x1))))) t(s)(s(b)(b(b)(x1))) -> t(b)(b(s)(s(s)(s(s)(s(b)(x1))))) t(s)(s(b)(b(t)(x1))) -> t(b)(b(s)(s(s)(s(s)(s(t)(x1))))) t(s)(s(b)(b(u)(x1))) -> t(b)(b(s)(s(s)(s(s)(s(u)(x1))))) t(s)(s(b)(b(s)(s(f7)(x1)))) -> t(b)(b(t)(t(f7)(x1))) t(s)(s(b)(b(s)(s(s)(x1)))) -> t(b)(b(t)(t(s)(x1))) t(s)(s(b)(b(s)(s(b)(x1)))) -> t(b)(b(t)(t(b)(x1))) t(s)(s(b)(b(s)(s(t)(x1)))) -> t(b)(b(t)(t(t)(x1))) t(s)(s(b)(b(s)(s(u)(x1)))) -> t(b)(b(t)(t(u)(x1))) t(s)(s(f7)(x1)) -> t(t)(t(f7)(x1)) t(s)(s(s)(x1)) -> t(t)(t(s)(x1)) t(s)(s(b)(x1)) -> t(t)(t(b)(x1)) t(s)(s(t)(x1)) -> t(t)(t(t)(x1)) t(s)(s(u)(x1)) -> t(t)(t(u)(x1)) b(t)(t(b)(b(f7)(x1))) -> b(b)(b(s)(s(f7)(x1))) b(t)(t(b)(b(s)(x1))) -> b(b)(b(s)(s(s)(x1))) b(t)(t(b)(b(b)(x1))) -> b(b)(b(s)(s(b)(x1))) b(t)(t(b)(b(t)(x1))) -> b(b)(b(s)(s(t)(x1))) b(t)(t(b)(b(u)(x1))) -> b(b)(b(s)(s(u)(x1))) b(t)(t(b)(b(s)(s(f7)(x1)))) -> b(u)(u(t)(t(b)(b(f7)(x1)))) b(t)(t(b)(b(s)(s(s)(x1)))) -> b(u)(u(t)(t(b)(b(s)(x1)))) b(t)(t(b)(b(s)(s(b)(x1)))) -> b(u)(u(t)(t(b)(b(b)(x1)))) b(t)(t(b)(b(s)(s(t)(x1)))) -> b(u)(u(t)(t(b)(b(t)(x1)))) b(t)(t(b)(b(s)(s(u)(x1)))) -> b(u)(u(t)(t(b)(b(u)(x1)))) t(t)(t(b)(b(f7)(x1))) -> t(b)(b(s)(s(f7)(x1))) t(t)(t(b)(b(s)(x1))) -> t(b)(b(s)(s(s)(x1))) t(t)(t(b)(b(b)(x1))) -> t(b)(b(s)(s(b)(x1))) t(t)(t(b)(b(t)(x1))) -> t(b)(b(s)(s(t)(x1))) t(t)(t(b)(b(u)(x1))) -> t(b)(b(s)(s(u)(x1))) t(t)(t(b)(b(s)(s(f7)(x1)))) -> t(u)(u(t)(t(b)(b(f7)(x1)))) t(t)(t(b)(b(s)(s(s)(x1)))) -> t(u)(u(t)(t(b)(b(s)(x1)))) t(t)(t(b)(b(s)(s(b)(x1)))) -> t(u)(u(t)(t(b)(b(b)(x1)))) t(t)(t(b)(b(s)(s(t)(x1)))) -> t(u)(u(t)(t(b)(b(t)(x1)))) t(t)(t(b)(b(s)(s(u)(x1)))) -> t(u)(u(t)(t(b)(b(u)(x1)))) t(t)(t(u)(u(f7)(x1))) -> t(u)(u(t)(t(f7)(x1))) t(t)(t(u)(u(s)(x1))) -> t(u)(u(t)(t(s)(x1))) t(t)(t(u)(u(b)(x1))) -> t(u)(u(t)(t(b)(x1))) t(t)(t(u)(u(t)(x1))) -> t(u)(u(t)(t(t)(x1))) t(t)(t(u)(u(u)(x1))) -> t(u)(u(t)(t(u)(x1))) b(t)(t(u)(u(f7)(x1))) -> b(u)(u(t)(t(f7)(x1))) b(t)(t(u)(u(s)(x1))) -> b(u)(u(t)(t(s)(x1))) b(t)(t(u)(u(b)(x1))) -> b(u)(u(t)(t(b)(x1))) b(t)(t(u)(u(t)(x1))) -> b(u)(u(t)(t(t)(x1))) b(t)(t(u)(u(u)(x1))) -> b(u)(u(t)(t(u)(x1))) b(u)(u(t)(x1)) -> b(s)(s(t)(x1)) b(u)(u(f7)(x1)) -> b(s)(s(f7)(x1)) b(u)(u(s)(x1)) -> b(s)(s(s)(x1)) b(u)(u(b)(x1)) -> b(s)(s(b)(x1)) b(u)(u(u)(x1)) -> b(s)(s(u)(x1)) u(t)(t(b)(b(f7)(x1))) -> u(b)(b(s)(s(f7)(x1))) u(t)(t(b)(b(s)(x1))) -> u(b)(b(s)(s(s)(x1))) u(t)(t(b)(b(b)(x1))) -> u(b)(b(s)(s(b)(x1))) u(t)(t(b)(b(t)(x1))) -> u(b)(b(s)(s(t)(x1))) u(t)(t(b)(b(u)(x1))) -> u(b)(b(s)(s(u)(x1))) u(t)(t(b)(b(s)(s(f7)(x1)))) -> u(u)(u(t)(t(b)(b(f7)(x1)))) u(t)(t(b)(b(s)(s(s)(x1)))) -> u(u)(u(t)(t(b)(b(s)(x1)))) u(t)(t(b)(b(s)(s(b)(x1)))) -> u(u)(u(t)(t(b)(b(b)(x1)))) u(t)(t(b)(b(s)(s(t)(x1)))) -> u(u)(u(t)(t(b)(b(t)(x1)))) u(t)(t(b)(b(s)(s(u)(x1)))) -> u(u)(u(t)(t(b)(b(u)(x1)))) u(t)(t(u)(u(f7)(x1))) -> u(u)(u(t)(t(f7)(x1))) u(t)(t(u)(u(s)(x1))) -> u(u)(u(t)(t(s)(x1))) u(t)(t(u)(u(b)(x1))) -> u(u)(u(t)(t(b)(x1))) u(t)(t(u)(u(t)(x1))) -> u(u)(u(t)(t(t)(x1))) u(t)(t(u)(u(u)(x1))) -> u(u)(u(t)(t(u)(x1))) Polynomial Interpretation Processor: dimension: 1 interpretation: [u(f7)](x0) = x0 + 1, [u(u)](x0) = x0, [u(t)](x0) = x0, [t(u)](x0) = x0, [t(t)](x0) = x0, [t(f7)](x0) = x0 + 1, [u(b)](x0) = x0, [u(s)](x0) = x0 + 1, [t(b)](x0) = x0, [t(s)](x0) = x0, [b(u)](x0) = x0, [s(u)](x0) = x0, [b(t)](x0) = x0, [s(t)](x0) = x0, [b(b)](x0) = x0, [s(b)](x0) = x0, [s(s)](x0) = x0, [b(f7)](x0) = x0 + 1, [s(f7)](x0) = x0 + 1, [b(s)](x0) = x0, [f7(b)](x0) = x0, [t{#,(f7)}](x0) = x0 orientation: t{#,(f7)}(f7(b)(b(s)(s(f7)(x1)))) = x1 + 1 >= x1 + 1 = t{#,(f7)}(f7(b)(b(f7)(x1))) t{#,(f7)}(f7(b)(b(s)(s(s)(x1)))) = x1 >= x1 = t{#,(f7)}(f7(b)(b(s)(x1))) t{#,(f7)}(f7(b)(b(s)(s(b)(x1)))) = x1 >= x1 = t{#,(f7)}(f7(b)(b(b)(x1))) t{#,(f7)}(f7(b)(b(s)(s(t)(x1)))) = x1 >= x1 = t{#,(f7)}(f7(b)(b(t)(x1))) t{#,(f7)}(f7(b)(b(s)(s(u)(x1)))) = x1 >= x1 = t{#,(f7)}(f7(b)(b(u)(x1))) b(s)(s(b)(b(f7)(x1))) = x1 + 1 >= x1 + 1 = b(b)(b(s)(s(s)(s(s)(s(f7)(x1))))) b(s)(s(b)(b(s)(x1))) = x1 >= x1 = b(b)(b(s)(s(s)(s(s)(s(s)(x1))))) b(s)(s(b)(b(b)(x1))) = x1 >= x1 = b(b)(b(s)(s(s)(s(s)(s(b)(x1))))) b(s)(s(b)(b(t)(x1))) = x1 >= x1 = b(b)(b(s)(s(s)(s(s)(s(t)(x1))))) b(s)(s(b)(b(u)(x1))) = x1 >= x1 = b(b)(b(s)(s(s)(s(s)(s(u)(x1))))) b(s)(s(b)(b(s)(s(f7)(x1)))) = x1 + 1 >= x1 + 1 = b(b)(b(t)(t(f7)(x1))) b(s)(s(b)(b(s)(s(s)(x1)))) = x1 >= x1 = b(b)(b(t)(t(s)(x1))) b(s)(s(b)(b(s)(s(b)(x1)))) = x1 >= x1 = b(b)(b(t)(t(b)(x1))) b(s)(s(b)(b(s)(s(t)(x1)))) = x1 >= x1 = b(b)(b(t)(t(t)(x1))) b(s)(s(b)(b(s)(s(u)(x1)))) = x1 >= x1 = b(b)(b(t)(t(u)(x1))) s(s)(s(b)(b(f7)(x1))) = x1 + 1 >= x1 + 1 = s(b)(b(s)(s(s)(s(s)(s(f7)(x1))))) s(s)(s(b)(b(s)(x1))) = x1 >= x1 = s(b)(b(s)(s(s)(s(s)(s(s)(x1))))) s(s)(s(b)(b(b)(x1))) = x1 >= x1 = s(b)(b(s)(s(s)(s(s)(s(b)(x1))))) s(s)(s(b)(b(t)(x1))) = x1 >= x1 = s(b)(b(s)(s(s)(s(s)(s(t)(x1))))) s(s)(s(b)(b(u)(x1))) = x1 >= x1 = s(b)(b(s)(s(s)(s(s)(s(u)(x1))))) s(s)(s(b)(b(s)(s(f7)(x1)))) = x1 + 1 >= x1 + 1 = s(b)(b(t)(t(f7)(x1))) s(s)(s(b)(b(s)(s(s)(x1)))) = x1 >= x1 = s(b)(b(t)(t(s)(x1))) s(s)(s(b)(b(s)(s(b)(x1)))) = x1 >= x1 = s(b)(b(t)(t(b)(x1))) s(s)(s(b)(b(s)(s(t)(x1)))) = x1 >= x1 = s(b)(b(t)(t(t)(x1))) s(s)(s(b)(b(s)(s(u)(x1)))) = x1 >= x1 = s(b)(b(t)(t(u)(x1))) s(t)(t(b)(b(f7)(x1))) = x1 + 1 >= x1 + 1 = s(b)(b(s)(s(f7)(x1))) s(t)(t(b)(b(s)(x1))) = x1 >= x1 = s(b)(b(s)(s(s)(x1))) s(t)(t(b)(b(b)(x1))) = x1 >= x1 = s(b)(b(s)(s(b)(x1))) s(t)(t(b)(b(t)(x1))) = x1 >= x1 = s(b)(b(s)(s(t)(x1))) s(t)(t(b)(b(u)(x1))) = x1 >= x1 = s(b)(b(s)(s(u)(x1))) s(t)(t(b)(b(s)(s(f7)(x1)))) = x1 + 1 >= x1 + 1 = s(u)(u(t)(t(b)(b(f7)(x1)))) s(t)(t(b)(b(s)(s(s)(x1)))) = x1 >= x1 = s(u)(u(t)(t(b)(b(s)(x1)))) s(t)(t(b)(b(s)(s(b)(x1)))) = x1 >= x1 = s(u)(u(t)(t(b)(b(b)(x1)))) s(t)(t(b)(b(s)(s(t)(x1)))) = x1 >= x1 = s(u)(u(t)(t(b)(b(t)(x1)))) s(t)(t(b)(b(s)(s(u)(x1)))) = x1 >= x1 = s(u)(u(t)(t(b)(b(u)(x1)))) s(t)(t(u)(u(f7)(x1))) = x1 + 1 >= x1 + 1 = s(u)(u(t)(t(f7)(x1))) s(t)(t(u)(u(s)(x1))) = x1 + 1 >= x1 = s(u)(u(t)(t(s)(x1))) s(t)(t(u)(u(b)(x1))) = x1 >= x1 = s(u)(u(t)(t(b)(x1))) s(t)(t(u)(u(t)(x1))) = x1 >= x1 = s(u)(u(t)(t(t)(x1))) s(t)(t(u)(u(u)(x1))) = x1 >= x1 = s(u)(u(t)(t(u)(x1))) s(u)(u(f7)(x1)) = x1 + 1 >= x1 + 1 = s(s)(s(f7)(x1)) s(u)(u(s)(x1)) = x1 + 1 >= x1 = s(s)(s(s)(x1)) s(u)(u(b)(x1)) = x1 >= x1 = s(s)(s(b)(x1)) s(u)(u(t)(x1)) = x1 >= x1 = s(s)(s(t)(x1)) s(u)(u(u)(x1)) = x1 >= x1 = s(s)(s(u)(x1)) t(s)(s(b)(b(f7)(x1))) = x1 + 1 >= x1 + 1 = t(b)(b(s)(s(s)(s(s)(s(f7)(x1))))) t(s)(s(b)(b(s)(x1))) = x1 >= x1 = t(b)(b(s)(s(s)(s(s)(s(s)(x1))))) t(s)(s(b)(b(b)(x1))) = x1 >= x1 = t(b)(b(s)(s(s)(s(s)(s(b)(x1))))) t(s)(s(b)(b(t)(x1))) = x1 >= x1 = t(b)(b(s)(s(s)(s(s)(s(t)(x1))))) t(s)(s(b)(b(u)(x1))) = x1 >= x1 = t(b)(b(s)(s(s)(s(s)(s(u)(x1))))) t(s)(s(b)(b(s)(s(f7)(x1)))) = x1 + 1 >= x1 + 1 = t(b)(b(t)(t(f7)(x1))) t(s)(s(b)(b(s)(s(s)(x1)))) = x1 >= x1 = t(b)(b(t)(t(s)(x1))) t(s)(s(b)(b(s)(s(b)(x1)))) = x1 >= x1 = t(b)(b(t)(t(b)(x1))) t(s)(s(b)(b(s)(s(t)(x1)))) = x1 >= x1 = t(b)(b(t)(t(t)(x1))) t(s)(s(b)(b(s)(s(u)(x1)))) = x1 >= x1 = t(b)(b(t)(t(u)(x1))) t(s)(s(f7)(x1)) = x1 + 1 >= x1 + 1 = t(t)(t(f7)(x1)) t(s)(s(s)(x1)) = x1 >= x1 = t(t)(t(s)(x1)) t(s)(s(b)(x1)) = x1 >= x1 = t(t)(t(b)(x1)) t(s)(s(t)(x1)) = x1 >= x1 = t(t)(t(t)(x1)) t(s)(s(u)(x1)) = x1 >= x1 = t(t)(t(u)(x1)) b(t)(t(b)(b(f7)(x1))) = x1 + 1 >= x1 + 1 = b(b)(b(s)(s(f7)(x1))) b(t)(t(b)(b(s)(x1))) = x1 >= x1 = b(b)(b(s)(s(s)(x1))) b(t)(t(b)(b(b)(x1))) = x1 >= x1 = b(b)(b(s)(s(b)(x1))) b(t)(t(b)(b(t)(x1))) = x1 >= x1 = b(b)(b(s)(s(t)(x1))) b(t)(t(b)(b(u)(x1))) = x1 >= x1 = b(b)(b(s)(s(u)(x1))) b(t)(t(b)(b(s)(s(f7)(x1)))) = x1 + 1 >= x1 + 1 = b(u)(u(t)(t(b)(b(f7)(x1)))) b(t)(t(b)(b(s)(s(s)(x1)))) = x1 >= x1 = b(u)(u(t)(t(b)(b(s)(x1)))) b(t)(t(b)(b(s)(s(b)(x1)))) = x1 >= x1 = b(u)(u(t)(t(b)(b(b)(x1)))) b(t)(t(b)(b(s)(s(t)(x1)))) = x1 >= x1 = b(u)(u(t)(t(b)(b(t)(x1)))) b(t)(t(b)(b(s)(s(u)(x1)))) = x1 >= x1 = b(u)(u(t)(t(b)(b(u)(x1)))) t(t)(t(b)(b(f7)(x1))) = x1 + 1 >= x1 + 1 = t(b)(b(s)(s(f7)(x1))) t(t)(t(b)(b(s)(x1))) = x1 >= x1 = t(b)(b(s)(s(s)(x1))) t(t)(t(b)(b(b)(x1))) = x1 >= x1 = t(b)(b(s)(s(b)(x1))) t(t)(t(b)(b(t)(x1))) = x1 >= x1 = t(b)(b(s)(s(t)(x1))) t(t)(t(b)(b(u)(x1))) = x1 >= x1 = t(b)(b(s)(s(u)(x1))) t(t)(t(b)(b(s)(s(f7)(x1)))) = x1 + 1 >= x1 + 1 = t(u)(u(t)(t(b)(b(f7)(x1)))) t(t)(t(b)(b(s)(s(s)(x1)))) = x1 >= x1 = t(u)(u(t)(t(b)(b(s)(x1)))) t(t)(t(b)(b(s)(s(b)(x1)))) = x1 >= x1 = t(u)(u(t)(t(b)(b(b)(x1)))) t(t)(t(b)(b(s)(s(t)(x1)))) = x1 >= x1 = t(u)(u(t)(t(b)(b(t)(x1)))) t(t)(t(b)(b(s)(s(u)(x1)))) = x1 >= x1 = t(u)(u(t)(t(b)(b(u)(x1)))) t(t)(t(u)(u(f7)(x1))) = x1 + 1 >= x1 + 1 = t(u)(u(t)(t(f7)(x1))) t(t)(t(u)(u(s)(x1))) = x1 + 1 >= x1 = t(u)(u(t)(t(s)(x1))) t(t)(t(u)(u(b)(x1))) = x1 >= x1 = t(u)(u(t)(t(b)(x1))) t(t)(t(u)(u(t)(x1))) = x1 >= x1 = t(u)(u(t)(t(t)(x1))) t(t)(t(u)(u(u)(x1))) = x1 >= x1 = t(u)(u(t)(t(u)(x1))) b(t)(t(u)(u(f7)(x1))) = x1 + 1 >= x1 + 1 = b(u)(u(t)(t(f7)(x1))) b(t)(t(u)(u(s)(x1))) = x1 + 1 >= x1 = b(u)(u(t)(t(s)(x1))) b(t)(t(u)(u(b)(x1))) = x1 >= x1 = b(u)(u(t)(t(b)(x1))) b(t)(t(u)(u(t)(x1))) = x1 >= x1 = b(u)(u(t)(t(t)(x1))) b(t)(t(u)(u(u)(x1))) = x1 >= x1 = b(u)(u(t)(t(u)(x1))) b(u)(u(t)(x1)) = x1 >= x1 = b(s)(s(t)(x1)) b(u)(u(f7)(x1)) = x1 + 1 >= x1 + 1 = b(s)(s(f7)(x1)) b(u)(u(s)(x1)) = x1 + 1 >= x1 = b(s)(s(s)(x1)) b(u)(u(b)(x1)) = x1 >= x1 = b(s)(s(b)(x1)) b(u)(u(u)(x1)) = x1 >= x1 = b(s)(s(u)(x1)) u(t)(t(b)(b(f7)(x1))) = x1 + 1 >= x1 + 1 = u(b)(b(s)(s(f7)(x1))) u(t)(t(b)(b(s)(x1))) = x1 >= x1 = u(b)(b(s)(s(s)(x1))) u(t)(t(b)(b(b)(x1))) = x1 >= x1 = u(b)(b(s)(s(b)(x1))) u(t)(t(b)(b(t)(x1))) = x1 >= x1 = u(b)(b(s)(s(t)(x1))) u(t)(t(b)(b(u)(x1))) = x1 >= x1 = u(b)(b(s)(s(u)(x1))) u(t)(t(b)(b(s)(s(f7)(x1)))) = x1 + 1 >= x1 + 1 = u(u)(u(t)(t(b)(b(f7)(x1)))) u(t)(t(b)(b(s)(s(s)(x1)))) = x1 >= x1 = u(u)(u(t)(t(b)(b(s)(x1)))) u(t)(t(b)(b(s)(s(b)(x1)))) = x1 >= x1 = u(u)(u(t)(t(b)(b(b)(x1)))) u(t)(t(b)(b(s)(s(t)(x1)))) = x1 >= x1 = u(u)(u(t)(t(b)(b(t)(x1)))) u(t)(t(b)(b(s)(s(u)(x1)))) = x1 >= x1 = u(u)(u(t)(t(b)(b(u)(x1)))) u(t)(t(u)(u(f7)(x1))) = x1 + 1 >= x1 + 1 = u(u)(u(t)(t(f7)(x1))) u(t)(t(u)(u(s)(x1))) = x1 + 1 >= x1 = u(u)(u(t)(t(s)(x1))) u(t)(t(u)(u(b)(x1))) = x1 >= x1 = u(u)(u(t)(t(b)(x1))) u(t)(t(u)(u(t)(x1))) = x1 >= x1 = u(u)(u(t)(t(t)(x1))) u(t)(t(u)(u(u)(x1))) = x1 >= x1 = u(u)(u(t)(t(u)(x1))) problem: DPs: t{#,(f7)}(f7(b)(b(s)(s(f7)(x1)))) -> t{#,(f7)}(f7(b)(b(f7)(x1))) t{#,(f7)}(f7(b)(b(s)(s(s)(x1)))) -> t{#,(f7)}(f7(b)(b(s)(x1))) t{#,(f7)}(f7(b)(b(s)(s(b)(x1)))) -> t{#,(f7)}(f7(b)(b(b)(x1))) t{#,(f7)}(f7(b)(b(s)(s(t)(x1)))) -> t{#,(f7)}(f7(b)(b(t)(x1))) t{#,(f7)}(f7(b)(b(s)(s(u)(x1)))) -> t{#,(f7)}(f7(b)(b(u)(x1))) TRS: b(s)(s(b)(b(f7)(x1))) -> b(b)(b(s)(s(s)(s(s)(s(f7)(x1))))) b(s)(s(b)(b(s)(x1))) -> b(b)(b(s)(s(s)(s(s)(s(s)(x1))))) b(s)(s(b)(b(b)(x1))) -> b(b)(b(s)(s(s)(s(s)(s(b)(x1))))) b(s)(s(b)(b(t)(x1))) -> b(b)(b(s)(s(s)(s(s)(s(t)(x1))))) b(s)(s(b)(b(u)(x1))) -> b(b)(b(s)(s(s)(s(s)(s(u)(x1))))) b(s)(s(b)(b(s)(s(f7)(x1)))) -> b(b)(b(t)(t(f7)(x1))) b(s)(s(b)(b(s)(s(s)(x1)))) -> b(b)(b(t)(t(s)(x1))) b(s)(s(b)(b(s)(s(b)(x1)))) -> b(b)(b(t)(t(b)(x1))) b(s)(s(b)(b(s)(s(t)(x1)))) -> b(b)(b(t)(t(t)(x1))) b(s)(s(b)(b(s)(s(u)(x1)))) -> b(b)(b(t)(t(u)(x1))) s(s)(s(b)(b(f7)(x1))) -> s(b)(b(s)(s(s)(s(s)(s(f7)(x1))))) s(s)(s(b)(b(s)(x1))) -> s(b)(b(s)(s(s)(s(s)(s(s)(x1))))) s(s)(s(b)(b(b)(x1))) -> s(b)(b(s)(s(s)(s(s)(s(b)(x1))))) s(s)(s(b)(b(t)(x1))) -> s(b)(b(s)(s(s)(s(s)(s(t)(x1))))) s(s)(s(b)(b(u)(x1))) -> s(b)(b(s)(s(s)(s(s)(s(u)(x1))))) s(s)(s(b)(b(s)(s(f7)(x1)))) -> s(b)(b(t)(t(f7)(x1))) s(s)(s(b)(b(s)(s(s)(x1)))) -> s(b)(b(t)(t(s)(x1))) s(s)(s(b)(b(s)(s(b)(x1)))) -> s(b)(b(t)(t(b)(x1))) s(s)(s(b)(b(s)(s(t)(x1)))) -> s(b)(b(t)(t(t)(x1))) s(s)(s(b)(b(s)(s(u)(x1)))) -> s(b)(b(t)(t(u)(x1))) s(t)(t(b)(b(f7)(x1))) -> s(b)(b(s)(s(f7)(x1))) s(t)(t(b)(b(s)(x1))) -> s(b)(b(s)(s(s)(x1))) s(t)(t(b)(b(b)(x1))) -> s(b)(b(s)(s(b)(x1))) s(t)(t(b)(b(t)(x1))) -> s(b)(b(s)(s(t)(x1))) s(t)(t(b)(b(u)(x1))) -> s(b)(b(s)(s(u)(x1))) s(t)(t(b)(b(s)(s(f7)(x1)))) -> s(u)(u(t)(t(b)(b(f7)(x1)))) s(t)(t(b)(b(s)(s(s)(x1)))) -> s(u)(u(t)(t(b)(b(s)(x1)))) s(t)(t(b)(b(s)(s(b)(x1)))) -> s(u)(u(t)(t(b)(b(b)(x1)))) s(t)(t(b)(b(s)(s(t)(x1)))) -> s(u)(u(t)(t(b)(b(t)(x1)))) s(t)(t(b)(b(s)(s(u)(x1)))) -> s(u)(u(t)(t(b)(b(u)(x1)))) s(t)(t(u)(u(f7)(x1))) -> s(u)(u(t)(t(f7)(x1))) s(t)(t(u)(u(b)(x1))) -> s(u)(u(t)(t(b)(x1))) s(t)(t(u)(u(t)(x1))) -> s(u)(u(t)(t(t)(x1))) s(t)(t(u)(u(u)(x1))) -> s(u)(u(t)(t(u)(x1))) s(u)(u(f7)(x1)) -> s(s)(s(f7)(x1)) s(u)(u(b)(x1)) -> s(s)(s(b)(x1)) s(u)(u(t)(x1)) -> s(s)(s(t)(x1)) s(u)(u(u)(x1)) -> s(s)(s(u)(x1)) t(s)(s(b)(b(f7)(x1))) -> t(b)(b(s)(s(s)(s(s)(s(f7)(x1))))) t(s)(s(b)(b(s)(x1))) -> t(b)(b(s)(s(s)(s(s)(s(s)(x1))))) t(s)(s(b)(b(b)(x1))) -> t(b)(b(s)(s(s)(s(s)(s(b)(x1))))) t(s)(s(b)(b(t)(x1))) -> t(b)(b(s)(s(s)(s(s)(s(t)(x1))))) t(s)(s(b)(b(u)(x1))) -> t(b)(b(s)(s(s)(s(s)(s(u)(x1))))) t(s)(s(b)(b(s)(s(f7)(x1)))) -> t(b)(b(t)(t(f7)(x1))) t(s)(s(b)(b(s)(s(s)(x1)))) -> t(b)(b(t)(t(s)(x1))) t(s)(s(b)(b(s)(s(b)(x1)))) -> t(b)(b(t)(t(b)(x1))) t(s)(s(b)(b(s)(s(t)(x1)))) -> t(b)(b(t)(t(t)(x1))) t(s)(s(b)(b(s)(s(u)(x1)))) -> t(b)(b(t)(t(u)(x1))) t(s)(s(f7)(x1)) -> t(t)(t(f7)(x1)) t(s)(s(s)(x1)) -> t(t)(t(s)(x1)) t(s)(s(b)(x1)) -> t(t)(t(b)(x1)) t(s)(s(t)(x1)) -> t(t)(t(t)(x1)) t(s)(s(u)(x1)) -> t(t)(t(u)(x1)) b(t)(t(b)(b(f7)(x1))) -> b(b)(b(s)(s(f7)(x1))) b(t)(t(b)(b(s)(x1))) -> b(b)(b(s)(s(s)(x1))) b(t)(t(b)(b(b)(x1))) -> b(b)(b(s)(s(b)(x1))) b(t)(t(b)(b(t)(x1))) -> b(b)(b(s)(s(t)(x1))) b(t)(t(b)(b(u)(x1))) -> b(b)(b(s)(s(u)(x1))) b(t)(t(b)(b(s)(s(f7)(x1)))) -> b(u)(u(t)(t(b)(b(f7)(x1)))) b(t)(t(b)(b(s)(s(s)(x1)))) -> b(u)(u(t)(t(b)(b(s)(x1)))) b(t)(t(b)(b(s)(s(b)(x1)))) -> b(u)(u(t)(t(b)(b(b)(x1)))) b(t)(t(b)(b(s)(s(t)(x1)))) -> b(u)(u(t)(t(b)(b(t)(x1)))) b(t)(t(b)(b(s)(s(u)(x1)))) -> b(u)(u(t)(t(b)(b(u)(x1)))) t(t)(t(b)(b(f7)(x1))) -> t(b)(b(s)(s(f7)(x1))) t(t)(t(b)(b(s)(x1))) -> t(b)(b(s)(s(s)(x1))) t(t)(t(b)(b(b)(x1))) -> t(b)(b(s)(s(b)(x1))) t(t)(t(b)(b(t)(x1))) -> t(b)(b(s)(s(t)(x1))) t(t)(t(b)(b(u)(x1))) -> t(b)(b(s)(s(u)(x1))) t(t)(t(b)(b(s)(s(f7)(x1)))) -> t(u)(u(t)(t(b)(b(f7)(x1)))) t(t)(t(b)(b(s)(s(s)(x1)))) -> t(u)(u(t)(t(b)(b(s)(x1)))) t(t)(t(b)(b(s)(s(b)(x1)))) -> t(u)(u(t)(t(b)(b(b)(x1)))) t(t)(t(b)(b(s)(s(t)(x1)))) -> t(u)(u(t)(t(b)(b(t)(x1)))) t(t)(t(b)(b(s)(s(u)(x1)))) -> t(u)(u(t)(t(b)(b(u)(x1)))) t(t)(t(u)(u(f7)(x1))) -> t(u)(u(t)(t(f7)(x1))) t(t)(t(u)(u(b)(x1))) -> t(u)(u(t)(t(b)(x1))) t(t)(t(u)(u(t)(x1))) -> t(u)(u(t)(t(t)(x1))) t(t)(t(u)(u(u)(x1))) -> t(u)(u(t)(t(u)(x1))) b(t)(t(u)(u(f7)(x1))) -> b(u)(u(t)(t(f7)(x1))) b(t)(t(u)(u(b)(x1))) -> b(u)(u(t)(t(b)(x1))) b(t)(t(u)(u(t)(x1))) -> b(u)(u(t)(t(t)(x1))) b(t)(t(u)(u(u)(x1))) -> b(u)(u(t)(t(u)(x1))) b(u)(u(t)(x1)) -> b(s)(s(t)(x1)) b(u)(u(f7)(x1)) -> b(s)(s(f7)(x1)) b(u)(u(b)(x1)) -> b(s)(s(b)(x1)) b(u)(u(u)(x1)) -> b(s)(s(u)(x1)) u(t)(t(b)(b(f7)(x1))) -> u(b)(b(s)(s(f7)(x1))) u(t)(t(b)(b(s)(x1))) -> u(b)(b(s)(s(s)(x1))) u(t)(t(b)(b(b)(x1))) -> u(b)(b(s)(s(b)(x1))) u(t)(t(b)(b(t)(x1))) -> u(b)(b(s)(s(t)(x1))) u(t)(t(b)(b(u)(x1))) -> u(b)(b(s)(s(u)(x1))) u(t)(t(b)(b(s)(s(f7)(x1)))) -> u(u)(u(t)(t(b)(b(f7)(x1)))) u(t)(t(b)(b(s)(s(s)(x1)))) -> u(u)(u(t)(t(b)(b(s)(x1)))) u(t)(t(b)(b(s)(s(b)(x1)))) -> u(u)(u(t)(t(b)(b(b)(x1)))) u(t)(t(b)(b(s)(s(t)(x1)))) -> u(u)(u(t)(t(b)(b(t)(x1)))) u(t)(t(b)(b(s)(s(u)(x1)))) -> u(u)(u(t)(t(b)(b(u)(x1)))) u(t)(t(u)(u(f7)(x1))) -> u(u)(u(t)(t(f7)(x1))) u(t)(t(u)(u(b)(x1))) -> u(u)(u(t)(t(b)(x1))) u(t)(t(u)(u(t)(x1))) -> u(u)(u(t)(t(t)(x1))) u(t)(t(u)(u(u)(x1))) -> u(u)(u(t)(t(u)(x1))) Polynomial Interpretation Processor: dimension: 1 interpretation: [u(f7)](x0) = x0 + 1, [u(u)](x0) = x0, [u(t)](x0) = x0, [t(u)](x0) = x0, [t(t)](x0) = x0, [t(f7)](x0) = x0, [u(b)](x0) = x0, [t(b)](x0) = x0, [t(s)](x0) = x0, [b(u)](x0) = x0, [s(u)](x0) = x0, [b(t)](x0) = x0, [s(t)](x0) = x0, [b(b)](x0) = x0, [s(b)](x0) = x0, [s(s)](x0) = x0, [b(f7)](x0) = x0 + 1, [s(f7)](x0) = x0 + 1, [b(s)](x0) = x0, [f7(b)](x0) = x0 + 1, [t{#,(f7)}](x0) = x0 orientation: t{#,(f7)}(f7(b)(b(s)(s(f7)(x1)))) = x1 + 2 >= x1 + 2 = t{#,(f7)}(f7(b)(b(f7)(x1))) t{#,(f7)}(f7(b)(b(s)(s(s)(x1)))) = x1 + 1 >= x1 + 1 = t{#,(f7)}(f7(b)(b(s)(x1))) t{#,(f7)}(f7(b)(b(s)(s(b)(x1)))) = x1 + 1 >= x1 + 1 = t{#,(f7)}(f7(b)(b(b)(x1))) t{#,(f7)}(f7(b)(b(s)(s(t)(x1)))) = x1 + 1 >= x1 + 1 = t{#,(f7)}(f7(b)(b(t)(x1))) t{#,(f7)}(f7(b)(b(s)(s(u)(x1)))) = x1 + 1 >= x1 + 1 = t{#,(f7)}(f7(b)(b(u)(x1))) b(s)(s(b)(b(f7)(x1))) = x1 + 1 >= x1 + 1 = b(b)(b(s)(s(s)(s(s)(s(f7)(x1))))) b(s)(s(b)(b(s)(x1))) = x1 >= x1 = b(b)(b(s)(s(s)(s(s)(s(s)(x1))))) b(s)(s(b)(b(b)(x1))) = x1 >= x1 = b(b)(b(s)(s(s)(s(s)(s(b)(x1))))) b(s)(s(b)(b(t)(x1))) = x1 >= x1 = b(b)(b(s)(s(s)(s(s)(s(t)(x1))))) b(s)(s(b)(b(u)(x1))) = x1 >= x1 = b(b)(b(s)(s(s)(s(s)(s(u)(x1))))) b(s)(s(b)(b(s)(s(f7)(x1)))) = x1 + 1 >= x1 = b(b)(b(t)(t(f7)(x1))) b(s)(s(b)(b(s)(s(s)(x1)))) = x1 >= x1 = b(b)(b(t)(t(s)(x1))) b(s)(s(b)(b(s)(s(b)(x1)))) = x1 >= x1 = b(b)(b(t)(t(b)(x1))) b(s)(s(b)(b(s)(s(t)(x1)))) = x1 >= x1 = b(b)(b(t)(t(t)(x1))) b(s)(s(b)(b(s)(s(u)(x1)))) = x1 >= x1 = b(b)(b(t)(t(u)(x1))) s(s)(s(b)(b(f7)(x1))) = x1 + 1 >= x1 + 1 = s(b)(b(s)(s(s)(s(s)(s(f7)(x1))))) s(s)(s(b)(b(s)(x1))) = x1 >= x1 = s(b)(b(s)(s(s)(s(s)(s(s)(x1))))) s(s)(s(b)(b(b)(x1))) = x1 >= x1 = s(b)(b(s)(s(s)(s(s)(s(b)(x1))))) s(s)(s(b)(b(t)(x1))) = x1 >= x1 = s(b)(b(s)(s(s)(s(s)(s(t)(x1))))) s(s)(s(b)(b(u)(x1))) = x1 >= x1 = s(b)(b(s)(s(s)(s(s)(s(u)(x1))))) s(s)(s(b)(b(s)(s(f7)(x1)))) = x1 + 1 >= x1 = s(b)(b(t)(t(f7)(x1))) s(s)(s(b)(b(s)(s(s)(x1)))) = x1 >= x1 = s(b)(b(t)(t(s)(x1))) s(s)(s(b)(b(s)(s(b)(x1)))) = x1 >= x1 = s(b)(b(t)(t(b)(x1))) s(s)(s(b)(b(s)(s(t)(x1)))) = x1 >= x1 = s(b)(b(t)(t(t)(x1))) s(s)(s(b)(b(s)(s(u)(x1)))) = x1 >= x1 = s(b)(b(t)(t(u)(x1))) s(t)(t(b)(b(f7)(x1))) = x1 + 1 >= x1 + 1 = s(b)(b(s)(s(f7)(x1))) s(t)(t(b)(b(s)(x1))) = x1 >= x1 = s(b)(b(s)(s(s)(x1))) s(t)(t(b)(b(b)(x1))) = x1 >= x1 = s(b)(b(s)(s(b)(x1))) s(t)(t(b)(b(t)(x1))) = x1 >= x1 = s(b)(b(s)(s(t)(x1))) s(t)(t(b)(b(u)(x1))) = x1 >= x1 = s(b)(b(s)(s(u)(x1))) s(t)(t(b)(b(s)(s(f7)(x1)))) = x1 + 1 >= x1 + 1 = s(u)(u(t)(t(b)(b(f7)(x1)))) s(t)(t(b)(b(s)(s(s)(x1)))) = x1 >= x1 = s(u)(u(t)(t(b)(b(s)(x1)))) s(t)(t(b)(b(s)(s(b)(x1)))) = x1 >= x1 = s(u)(u(t)(t(b)(b(b)(x1)))) s(t)(t(b)(b(s)(s(t)(x1)))) = x1 >= x1 = s(u)(u(t)(t(b)(b(t)(x1)))) s(t)(t(b)(b(s)(s(u)(x1)))) = x1 >= x1 = s(u)(u(t)(t(b)(b(u)(x1)))) s(t)(t(u)(u(f7)(x1))) = x1 + 1 >= x1 = s(u)(u(t)(t(f7)(x1))) s(t)(t(u)(u(b)(x1))) = x1 >= x1 = s(u)(u(t)(t(b)(x1))) s(t)(t(u)(u(t)(x1))) = x1 >= x1 = s(u)(u(t)(t(t)(x1))) s(t)(t(u)(u(u)(x1))) = x1 >= x1 = s(u)(u(t)(t(u)(x1))) s(u)(u(f7)(x1)) = x1 + 1 >= x1 + 1 = s(s)(s(f7)(x1)) s(u)(u(b)(x1)) = x1 >= x1 = s(s)(s(b)(x1)) s(u)(u(t)(x1)) = x1 >= x1 = s(s)(s(t)(x1)) s(u)(u(u)(x1)) = x1 >= x1 = s(s)(s(u)(x1)) t(s)(s(b)(b(f7)(x1))) = x1 + 1 >= x1 + 1 = t(b)(b(s)(s(s)(s(s)(s(f7)(x1))))) t(s)(s(b)(b(s)(x1))) = x1 >= x1 = t(b)(b(s)(s(s)(s(s)(s(s)(x1))))) t(s)(s(b)(b(b)(x1))) = x1 >= x1 = t(b)(b(s)(s(s)(s(s)(s(b)(x1))))) t(s)(s(b)(b(t)(x1))) = x1 >= x1 = t(b)(b(s)(s(s)(s(s)(s(t)(x1))))) t(s)(s(b)(b(u)(x1))) = x1 >= x1 = t(b)(b(s)(s(s)(s(s)(s(u)(x1))))) t(s)(s(b)(b(s)(s(f7)(x1)))) = x1 + 1 >= x1 = t(b)(b(t)(t(f7)(x1))) t(s)(s(b)(b(s)(s(s)(x1)))) = x1 >= x1 = t(b)(b(t)(t(s)(x1))) t(s)(s(b)(b(s)(s(b)(x1)))) = x1 >= x1 = t(b)(b(t)(t(b)(x1))) t(s)(s(b)(b(s)(s(t)(x1)))) = x1 >= x1 = t(b)(b(t)(t(t)(x1))) t(s)(s(b)(b(s)(s(u)(x1)))) = x1 >= x1 = t(b)(b(t)(t(u)(x1))) t(s)(s(f7)(x1)) = x1 + 1 >= x1 = t(t)(t(f7)(x1)) t(s)(s(s)(x1)) = x1 >= x1 = t(t)(t(s)(x1)) t(s)(s(b)(x1)) = x1 >= x1 = t(t)(t(b)(x1)) t(s)(s(t)(x1)) = x1 >= x1 = t(t)(t(t)(x1)) t(s)(s(u)(x1)) = x1 >= x1 = t(t)(t(u)(x1)) b(t)(t(b)(b(f7)(x1))) = x1 + 1 >= x1 + 1 = b(b)(b(s)(s(f7)(x1))) b(t)(t(b)(b(s)(x1))) = x1 >= x1 = b(b)(b(s)(s(s)(x1))) b(t)(t(b)(b(b)(x1))) = x1 >= x1 = b(b)(b(s)(s(b)(x1))) b(t)(t(b)(b(t)(x1))) = x1 >= x1 = b(b)(b(s)(s(t)(x1))) b(t)(t(b)(b(u)(x1))) = x1 >= x1 = b(b)(b(s)(s(u)(x1))) b(t)(t(b)(b(s)(s(f7)(x1)))) = x1 + 1 >= x1 + 1 = b(u)(u(t)(t(b)(b(f7)(x1)))) b(t)(t(b)(b(s)(s(s)(x1)))) = x1 >= x1 = b(u)(u(t)(t(b)(b(s)(x1)))) b(t)(t(b)(b(s)(s(b)(x1)))) = x1 >= x1 = b(u)(u(t)(t(b)(b(b)(x1)))) b(t)(t(b)(b(s)(s(t)(x1)))) = x1 >= x1 = b(u)(u(t)(t(b)(b(t)(x1)))) b(t)(t(b)(b(s)(s(u)(x1)))) = x1 >= x1 = b(u)(u(t)(t(b)(b(u)(x1)))) t(t)(t(b)(b(f7)(x1))) = x1 + 1 >= x1 + 1 = t(b)(b(s)(s(f7)(x1))) t(t)(t(b)(b(s)(x1))) = x1 >= x1 = t(b)(b(s)(s(s)(x1))) t(t)(t(b)(b(b)(x1))) = x1 >= x1 = t(b)(b(s)(s(b)(x1))) t(t)(t(b)(b(t)(x1))) = x1 >= x1 = t(b)(b(s)(s(t)(x1))) t(t)(t(b)(b(u)(x1))) = x1 >= x1 = t(b)(b(s)(s(u)(x1))) t(t)(t(b)(b(s)(s(f7)(x1)))) = x1 + 1 >= x1 + 1 = t(u)(u(t)(t(b)(b(f7)(x1)))) t(t)(t(b)(b(s)(s(s)(x1)))) = x1 >= x1 = t(u)(u(t)(t(b)(b(s)(x1)))) t(t)(t(b)(b(s)(s(b)(x1)))) = x1 >= x1 = t(u)(u(t)(t(b)(b(b)(x1)))) t(t)(t(b)(b(s)(s(t)(x1)))) = x1 >= x1 = t(u)(u(t)(t(b)(b(t)(x1)))) t(t)(t(b)(b(s)(s(u)(x1)))) = x1 >= x1 = t(u)(u(t)(t(b)(b(u)(x1)))) t(t)(t(u)(u(f7)(x1))) = x1 + 1 >= x1 = t(u)(u(t)(t(f7)(x1))) t(t)(t(u)(u(b)(x1))) = x1 >= x1 = t(u)(u(t)(t(b)(x1))) t(t)(t(u)(u(t)(x1))) = x1 >= x1 = t(u)(u(t)(t(t)(x1))) t(t)(t(u)(u(u)(x1))) = x1 >= x1 = t(u)(u(t)(t(u)(x1))) b(t)(t(u)(u(f7)(x1))) = x1 + 1 >= x1 = b(u)(u(t)(t(f7)(x1))) b(t)(t(u)(u(b)(x1))) = x1 >= x1 = b(u)(u(t)(t(b)(x1))) b(t)(t(u)(u(t)(x1))) = x1 >= x1 = b(u)(u(t)(t(t)(x1))) b(t)(t(u)(u(u)(x1))) = x1 >= x1 = b(u)(u(t)(t(u)(x1))) b(u)(u(t)(x1)) = x1 >= x1 = b(s)(s(t)(x1)) b(u)(u(f7)(x1)) = x1 + 1 >= x1 + 1 = b(s)(s(f7)(x1)) b(u)(u(b)(x1)) = x1 >= x1 = b(s)(s(b)(x1)) b(u)(u(u)(x1)) = x1 >= x1 = b(s)(s(u)(x1)) u(t)(t(b)(b(f7)(x1))) = x1 + 1 >= x1 + 1 = u(b)(b(s)(s(f7)(x1))) u(t)(t(b)(b(s)(x1))) = x1 >= x1 = u(b)(b(s)(s(s)(x1))) u(t)(t(b)(b(b)(x1))) = x1 >= x1 = u(b)(b(s)(s(b)(x1))) u(t)(t(b)(b(t)(x1))) = x1 >= x1 = u(b)(b(s)(s(t)(x1))) u(t)(t(b)(b(u)(x1))) = x1 >= x1 = u(b)(b(s)(s(u)(x1))) u(t)(t(b)(b(s)(s(f7)(x1)))) = x1 + 1 >= x1 + 1 = u(u)(u(t)(t(b)(b(f7)(x1)))) u(t)(t(b)(b(s)(s(s)(x1)))) = x1 >= x1 = u(u)(u(t)(t(b)(b(s)(x1)))) u(t)(t(b)(b(s)(s(b)(x1)))) = x1 >= x1 = u(u)(u(t)(t(b)(b(b)(x1)))) u(t)(t(b)(b(s)(s(t)(x1)))) = x1 >= x1 = u(u)(u(t)(t(b)(b(t)(x1)))) u(t)(t(b)(b(s)(s(u)(x1)))) = x1 >= x1 = u(u)(u(t)(t(b)(b(u)(x1)))) u(t)(t(u)(u(f7)(x1))) = x1 + 1 >= x1 = u(u)(u(t)(t(f7)(x1))) u(t)(t(u)(u(b)(x1))) = x1 >= x1 = u(u)(u(t)(t(b)(x1))) u(t)(t(u)(u(t)(x1))) = x1 >= x1 = u(u)(u(t)(t(t)(x1))) u(t)(t(u)(u(u)(x1))) = x1 >= x1 = u(u)(u(t)(t(u)(x1))) problem: DPs: t{#,(f7)}(f7(b)(b(s)(s(f7)(x1)))) -> t{#,(f7)}(f7(b)(b(f7)(x1))) t{#,(f7)}(f7(b)(b(s)(s(s)(x1)))) -> t{#,(f7)}(f7(b)(b(s)(x1))) t{#,(f7)}(f7(b)(b(s)(s(b)(x1)))) -> t{#,(f7)}(f7(b)(b(b)(x1))) t{#,(f7)}(f7(b)(b(s)(s(t)(x1)))) -> t{#,(f7)}(f7(b)(b(t)(x1))) t{#,(f7)}(f7(b)(b(s)(s(u)(x1)))) -> t{#,(f7)}(f7(b)(b(u)(x1))) TRS: b(s)(s(b)(b(f7)(x1))) -> b(b)(b(s)(s(s)(s(s)(s(f7)(x1))))) b(s)(s(b)(b(s)(x1))) -> b(b)(b(s)(s(s)(s(s)(s(s)(x1))))) b(s)(s(b)(b(b)(x1))) -> b(b)(b(s)(s(s)(s(s)(s(b)(x1))))) b(s)(s(b)(b(t)(x1))) -> b(b)(b(s)(s(s)(s(s)(s(t)(x1))))) b(s)(s(b)(b(u)(x1))) -> b(b)(b(s)(s(s)(s(s)(s(u)(x1))))) b(s)(s(b)(b(s)(s(s)(x1)))) -> b(b)(b(t)(t(s)(x1))) b(s)(s(b)(b(s)(s(b)(x1)))) -> b(b)(b(t)(t(b)(x1))) b(s)(s(b)(b(s)(s(t)(x1)))) -> b(b)(b(t)(t(t)(x1))) b(s)(s(b)(b(s)(s(u)(x1)))) -> b(b)(b(t)(t(u)(x1))) s(s)(s(b)(b(f7)(x1))) -> s(b)(b(s)(s(s)(s(s)(s(f7)(x1))))) s(s)(s(b)(b(s)(x1))) -> s(b)(b(s)(s(s)(s(s)(s(s)(x1))))) s(s)(s(b)(b(b)(x1))) -> s(b)(b(s)(s(s)(s(s)(s(b)(x1))))) s(s)(s(b)(b(t)(x1))) -> s(b)(b(s)(s(s)(s(s)(s(t)(x1))))) s(s)(s(b)(b(u)(x1))) -> s(b)(b(s)(s(s)(s(s)(s(u)(x1))))) s(s)(s(b)(b(s)(s(s)(x1)))) -> s(b)(b(t)(t(s)(x1))) s(s)(s(b)(b(s)(s(b)(x1)))) -> s(b)(b(t)(t(b)(x1))) s(s)(s(b)(b(s)(s(t)(x1)))) -> s(b)(b(t)(t(t)(x1))) s(s)(s(b)(b(s)(s(u)(x1)))) -> s(b)(b(t)(t(u)(x1))) s(t)(t(b)(b(f7)(x1))) -> s(b)(b(s)(s(f7)(x1))) s(t)(t(b)(b(s)(x1))) -> s(b)(b(s)(s(s)(x1))) s(t)(t(b)(b(b)(x1))) -> s(b)(b(s)(s(b)(x1))) s(t)(t(b)(b(t)(x1))) -> s(b)(b(s)(s(t)(x1))) s(t)(t(b)(b(u)(x1))) -> s(b)(b(s)(s(u)(x1))) s(t)(t(b)(b(s)(s(f7)(x1)))) -> s(u)(u(t)(t(b)(b(f7)(x1)))) s(t)(t(b)(b(s)(s(s)(x1)))) -> s(u)(u(t)(t(b)(b(s)(x1)))) s(t)(t(b)(b(s)(s(b)(x1)))) -> s(u)(u(t)(t(b)(b(b)(x1)))) s(t)(t(b)(b(s)(s(t)(x1)))) -> s(u)(u(t)(t(b)(b(t)(x1)))) s(t)(t(b)(b(s)(s(u)(x1)))) -> s(u)(u(t)(t(b)(b(u)(x1)))) s(t)(t(u)(u(b)(x1))) -> s(u)(u(t)(t(b)(x1))) s(t)(t(u)(u(t)(x1))) -> s(u)(u(t)(t(t)(x1))) s(t)(t(u)(u(u)(x1))) -> s(u)(u(t)(t(u)(x1))) s(u)(u(f7)(x1)) -> s(s)(s(f7)(x1)) s(u)(u(b)(x1)) -> s(s)(s(b)(x1)) s(u)(u(t)(x1)) -> s(s)(s(t)(x1)) s(u)(u(u)(x1)) -> s(s)(s(u)(x1)) t(s)(s(b)(b(f7)(x1))) -> t(b)(b(s)(s(s)(s(s)(s(f7)(x1))))) t(s)(s(b)(b(s)(x1))) -> t(b)(b(s)(s(s)(s(s)(s(s)(x1))))) t(s)(s(b)(b(b)(x1))) -> t(b)(b(s)(s(s)(s(s)(s(b)(x1))))) t(s)(s(b)(b(t)(x1))) -> t(b)(b(s)(s(s)(s(s)(s(t)(x1))))) t(s)(s(b)(b(u)(x1))) -> t(b)(b(s)(s(s)(s(s)(s(u)(x1))))) t(s)(s(b)(b(s)(s(s)(x1)))) -> t(b)(b(t)(t(s)(x1))) t(s)(s(b)(b(s)(s(b)(x1)))) -> t(b)(b(t)(t(b)(x1))) t(s)(s(b)(b(s)(s(t)(x1)))) -> t(b)(b(t)(t(t)(x1))) t(s)(s(b)(b(s)(s(u)(x1)))) -> t(b)(b(t)(t(u)(x1))) t(s)(s(s)(x1)) -> t(t)(t(s)(x1)) t(s)(s(b)(x1)) -> t(t)(t(b)(x1)) t(s)(s(t)(x1)) -> t(t)(t(t)(x1)) t(s)(s(u)(x1)) -> t(t)(t(u)(x1)) b(t)(t(b)(b(f7)(x1))) -> b(b)(b(s)(s(f7)(x1))) b(t)(t(b)(b(s)(x1))) -> b(b)(b(s)(s(s)(x1))) b(t)(t(b)(b(b)(x1))) -> b(b)(b(s)(s(b)(x1))) b(t)(t(b)(b(t)(x1))) -> b(b)(b(s)(s(t)(x1))) b(t)(t(b)(b(u)(x1))) -> b(b)(b(s)(s(u)(x1))) b(t)(t(b)(b(s)(s(f7)(x1)))) -> b(u)(u(t)(t(b)(b(f7)(x1)))) b(t)(t(b)(b(s)(s(s)(x1)))) -> b(u)(u(t)(t(b)(b(s)(x1)))) b(t)(t(b)(b(s)(s(b)(x1)))) -> b(u)(u(t)(t(b)(b(b)(x1)))) b(t)(t(b)(b(s)(s(t)(x1)))) -> b(u)(u(t)(t(b)(b(t)(x1)))) b(t)(t(b)(b(s)(s(u)(x1)))) -> b(u)(u(t)(t(b)(b(u)(x1)))) t(t)(t(b)(b(f7)(x1))) -> t(b)(b(s)(s(f7)(x1))) t(t)(t(b)(b(s)(x1))) -> t(b)(b(s)(s(s)(x1))) t(t)(t(b)(b(b)(x1))) -> t(b)(b(s)(s(b)(x1))) t(t)(t(b)(b(t)(x1))) -> t(b)(b(s)(s(t)(x1))) t(t)(t(b)(b(u)(x1))) -> t(b)(b(s)(s(u)(x1))) t(t)(t(b)(b(s)(s(f7)(x1)))) -> t(u)(u(t)(t(b)(b(f7)(x1)))) t(t)(t(b)(b(s)(s(s)(x1)))) -> t(u)(u(t)(t(b)(b(s)(x1)))) t(t)(t(b)(b(s)(s(b)(x1)))) -> t(u)(u(t)(t(b)(b(b)(x1)))) t(t)(t(b)(b(s)(s(t)(x1)))) -> t(u)(u(t)(t(b)(b(t)(x1)))) t(t)(t(b)(b(s)(s(u)(x1)))) -> t(u)(u(t)(t(b)(b(u)(x1)))) t(t)(t(u)(u(b)(x1))) -> t(u)(u(t)(t(b)(x1))) t(t)(t(u)(u(t)(x1))) -> t(u)(u(t)(t(t)(x1))) t(t)(t(u)(u(u)(x1))) -> t(u)(u(t)(t(u)(x1))) b(t)(t(u)(u(b)(x1))) -> b(u)(u(t)(t(b)(x1))) b(t)(t(u)(u(t)(x1))) -> b(u)(u(t)(t(t)(x1))) b(t)(t(u)(u(u)(x1))) -> b(u)(u(t)(t(u)(x1))) b(u)(u(t)(x1)) -> b(s)(s(t)(x1)) b(u)(u(f7)(x1)) -> b(s)(s(f7)(x1)) b(u)(u(b)(x1)) -> b(s)(s(b)(x1)) b(u)(u(u)(x1)) -> b(s)(s(u)(x1)) u(t)(t(b)(b(f7)(x1))) -> u(b)(b(s)(s(f7)(x1))) u(t)(t(b)(b(s)(x1))) -> u(b)(b(s)(s(s)(x1))) u(t)(t(b)(b(b)(x1))) -> u(b)(b(s)(s(b)(x1))) u(t)(t(b)(b(t)(x1))) -> u(b)(b(s)(s(t)(x1))) u(t)(t(b)(b(u)(x1))) -> u(b)(b(s)(s(u)(x1))) u(t)(t(b)(b(s)(s(f7)(x1)))) -> u(u)(u(t)(t(b)(b(f7)(x1)))) u(t)(t(b)(b(s)(s(s)(x1)))) -> u(u)(u(t)(t(b)(b(s)(x1)))) u(t)(t(b)(b(s)(s(b)(x1)))) -> u(u)(u(t)(t(b)(b(b)(x1)))) u(t)(t(b)(b(s)(s(t)(x1)))) -> u(u)(u(t)(t(b)(b(t)(x1)))) u(t)(t(b)(b(s)(s(u)(x1)))) -> u(u)(u(t)(t(b)(b(u)(x1)))) u(t)(t(u)(u(b)(x1))) -> u(u)(u(t)(t(b)(x1))) u(t)(t(u)(u(t)(x1))) -> u(u)(u(t)(t(t)(x1))) u(t)(t(u)(u(u)(x1))) -> u(u)(u(t)(t(u)(x1))) Polynomial Interpretation Processor: dimension: 1 interpretation: [u(f7)](x0) = x0 + 1, [u(u)](x0) = x0, [u(t)](x0) = x0, [t(u)](x0) = x0, [t(t)](x0) = x0, [u(b)](x0) = x0 + 1, [t(b)](x0) = x0 + 1, [t(s)](x0) = x0, [b(u)](x0) = x0, [s(u)](x0) = x0, [b(t)](x0) = x0, [s(t)](x0) = x0, [b(b)](x0) = x0 + 1, [s(b)](x0) = x0 + 1, [s(s)](x0) = x0, [b(f7)](x0) = x0, [s(f7)](x0) = x0, [b(s)](x0) = x0, [f7(b)](x0) = x0, [t{#,(f7)}](x0) = x0 + 1 orientation: t{#,(f7)}(f7(b)(b(s)(s(f7)(x1)))) = x1 + 1 >= x1 + 1 = t{#,(f7)}(f7(b)(b(f7)(x1))) t{#,(f7)}(f7(b)(b(s)(s(s)(x1)))) = x1 + 1 >= x1 + 1 = t{#,(f7)}(f7(b)(b(s)(x1))) t{#,(f7)}(f7(b)(b(s)(s(b)(x1)))) = x1 + 2 >= x1 + 2 = t{#,(f7)}(f7(b)(b(b)(x1))) t{#,(f7)}(f7(b)(b(s)(s(t)(x1)))) = x1 + 1 >= x1 + 1 = t{#,(f7)}(f7(b)(b(t)(x1))) t{#,(f7)}(f7(b)(b(s)(s(u)(x1)))) = x1 + 1 >= x1 + 1 = t{#,(f7)}(f7(b)(b(u)(x1))) b(s)(s(b)(b(f7)(x1))) = x1 + 1 >= x1 + 1 = b(b)(b(s)(s(s)(s(s)(s(f7)(x1))))) b(s)(s(b)(b(s)(x1))) = x1 + 1 >= x1 + 1 = b(b)(b(s)(s(s)(s(s)(s(s)(x1))))) b(s)(s(b)(b(b)(x1))) = x1 + 2 >= x1 + 2 = b(b)(b(s)(s(s)(s(s)(s(b)(x1))))) b(s)(s(b)(b(t)(x1))) = x1 + 1 >= x1 + 1 = b(b)(b(s)(s(s)(s(s)(s(t)(x1))))) b(s)(s(b)(b(u)(x1))) = x1 + 1 >= x1 + 1 = b(b)(b(s)(s(s)(s(s)(s(u)(x1))))) b(s)(s(b)(b(s)(s(s)(x1)))) = x1 + 1 >= x1 + 1 = b(b)(b(t)(t(s)(x1))) b(s)(s(b)(b(s)(s(b)(x1)))) = x1 + 2 >= x1 + 2 = b(b)(b(t)(t(b)(x1))) b(s)(s(b)(b(s)(s(t)(x1)))) = x1 + 1 >= x1 + 1 = b(b)(b(t)(t(t)(x1))) b(s)(s(b)(b(s)(s(u)(x1)))) = x1 + 1 >= x1 + 1 = b(b)(b(t)(t(u)(x1))) s(s)(s(b)(b(f7)(x1))) = x1 + 1 >= x1 + 1 = s(b)(b(s)(s(s)(s(s)(s(f7)(x1))))) s(s)(s(b)(b(s)(x1))) = x1 + 1 >= x1 + 1 = s(b)(b(s)(s(s)(s(s)(s(s)(x1))))) s(s)(s(b)(b(b)(x1))) = x1 + 2 >= x1 + 2 = s(b)(b(s)(s(s)(s(s)(s(b)(x1))))) s(s)(s(b)(b(t)(x1))) = x1 + 1 >= x1 + 1 = s(b)(b(s)(s(s)(s(s)(s(t)(x1))))) s(s)(s(b)(b(u)(x1))) = x1 + 1 >= x1 + 1 = s(b)(b(s)(s(s)(s(s)(s(u)(x1))))) s(s)(s(b)(b(s)(s(s)(x1)))) = x1 + 1 >= x1 + 1 = s(b)(b(t)(t(s)(x1))) s(s)(s(b)(b(s)(s(b)(x1)))) = x1 + 2 >= x1 + 2 = s(b)(b(t)(t(b)(x1))) s(s)(s(b)(b(s)(s(t)(x1)))) = x1 + 1 >= x1 + 1 = s(b)(b(t)(t(t)(x1))) s(s)(s(b)(b(s)(s(u)(x1)))) = x1 + 1 >= x1 + 1 = s(b)(b(t)(t(u)(x1))) s(t)(t(b)(b(f7)(x1))) = x1 + 1 >= x1 + 1 = s(b)(b(s)(s(f7)(x1))) s(t)(t(b)(b(s)(x1))) = x1 + 1 >= x1 + 1 = s(b)(b(s)(s(s)(x1))) s(t)(t(b)(b(b)(x1))) = x1 + 2 >= x1 + 2 = s(b)(b(s)(s(b)(x1))) s(t)(t(b)(b(t)(x1))) = x1 + 1 >= x1 + 1 = s(b)(b(s)(s(t)(x1))) s(t)(t(b)(b(u)(x1))) = x1 + 1 >= x1 + 1 = s(b)(b(s)(s(u)(x1))) s(t)(t(b)(b(s)(s(f7)(x1)))) = x1 + 1 >= x1 + 1 = s(u)(u(t)(t(b)(b(f7)(x1)))) s(t)(t(b)(b(s)(s(s)(x1)))) = x1 + 1 >= x1 + 1 = s(u)(u(t)(t(b)(b(s)(x1)))) s(t)(t(b)(b(s)(s(b)(x1)))) = x1 + 2 >= x1 + 2 = s(u)(u(t)(t(b)(b(b)(x1)))) s(t)(t(b)(b(s)(s(t)(x1)))) = x1 + 1 >= x1 + 1 = s(u)(u(t)(t(b)(b(t)(x1)))) s(t)(t(b)(b(s)(s(u)(x1)))) = x1 + 1 >= x1 + 1 = s(u)(u(t)(t(b)(b(u)(x1)))) s(t)(t(u)(u(b)(x1))) = x1 + 1 >= x1 + 1 = s(u)(u(t)(t(b)(x1))) s(t)(t(u)(u(t)(x1))) = x1 >= x1 = s(u)(u(t)(t(t)(x1))) s(t)(t(u)(u(u)(x1))) = x1 >= x1 = s(u)(u(t)(t(u)(x1))) s(u)(u(f7)(x1)) = x1 + 1 >= x1 = s(s)(s(f7)(x1)) s(u)(u(b)(x1)) = x1 + 1 >= x1 + 1 = s(s)(s(b)(x1)) s(u)(u(t)(x1)) = x1 >= x1 = s(s)(s(t)(x1)) s(u)(u(u)(x1)) = x1 >= x1 = s(s)(s(u)(x1)) t(s)(s(b)(b(f7)(x1))) = x1 + 1 >= x1 + 1 = t(b)(b(s)(s(s)(s(s)(s(f7)(x1))))) t(s)(s(b)(b(s)(x1))) = x1 + 1 >= x1 + 1 = t(b)(b(s)(s(s)(s(s)(s(s)(x1))))) t(s)(s(b)(b(b)(x1))) = x1 + 2 >= x1 + 2 = t(b)(b(s)(s(s)(s(s)(s(b)(x1))))) t(s)(s(b)(b(t)(x1))) = x1 + 1 >= x1 + 1 = t(b)(b(s)(s(s)(s(s)(s(t)(x1))))) t(s)(s(b)(b(u)(x1))) = x1 + 1 >= x1 + 1 = t(b)(b(s)(s(s)(s(s)(s(u)(x1))))) t(s)(s(b)(b(s)(s(s)(x1)))) = x1 + 1 >= x1 + 1 = t(b)(b(t)(t(s)(x1))) t(s)(s(b)(b(s)(s(b)(x1)))) = x1 + 2 >= x1 + 2 = t(b)(b(t)(t(b)(x1))) t(s)(s(b)(b(s)(s(t)(x1)))) = x1 + 1 >= x1 + 1 = t(b)(b(t)(t(t)(x1))) t(s)(s(b)(b(s)(s(u)(x1)))) = x1 + 1 >= x1 + 1 = t(b)(b(t)(t(u)(x1))) t(s)(s(s)(x1)) = x1 >= x1 = t(t)(t(s)(x1)) t(s)(s(b)(x1)) = x1 + 1 >= x1 + 1 = t(t)(t(b)(x1)) t(s)(s(t)(x1)) = x1 >= x1 = t(t)(t(t)(x1)) t(s)(s(u)(x1)) = x1 >= x1 = t(t)(t(u)(x1)) b(t)(t(b)(b(f7)(x1))) = x1 + 1 >= x1 + 1 = b(b)(b(s)(s(f7)(x1))) b(t)(t(b)(b(s)(x1))) = x1 + 1 >= x1 + 1 = b(b)(b(s)(s(s)(x1))) b(t)(t(b)(b(b)(x1))) = x1 + 2 >= x1 + 2 = b(b)(b(s)(s(b)(x1))) b(t)(t(b)(b(t)(x1))) = x1 + 1 >= x1 + 1 = b(b)(b(s)(s(t)(x1))) b(t)(t(b)(b(u)(x1))) = x1 + 1 >= x1 + 1 = b(b)(b(s)(s(u)(x1))) b(t)(t(b)(b(s)(s(f7)(x1)))) = x1 + 1 >= x1 + 1 = b(u)(u(t)(t(b)(b(f7)(x1)))) b(t)(t(b)(b(s)(s(s)(x1)))) = x1 + 1 >= x1 + 1 = b(u)(u(t)(t(b)(b(s)(x1)))) b(t)(t(b)(b(s)(s(b)(x1)))) = x1 + 2 >= x1 + 2 = b(u)(u(t)(t(b)(b(b)(x1)))) b(t)(t(b)(b(s)(s(t)(x1)))) = x1 + 1 >= x1 + 1 = b(u)(u(t)(t(b)(b(t)(x1)))) b(t)(t(b)(b(s)(s(u)(x1)))) = x1 + 1 >= x1 + 1 = b(u)(u(t)(t(b)(b(u)(x1)))) t(t)(t(b)(b(f7)(x1))) = x1 + 1 >= x1 + 1 = t(b)(b(s)(s(f7)(x1))) t(t)(t(b)(b(s)(x1))) = x1 + 1 >= x1 + 1 = t(b)(b(s)(s(s)(x1))) t(t)(t(b)(b(b)(x1))) = x1 + 2 >= x1 + 2 = t(b)(b(s)(s(b)(x1))) t(t)(t(b)(b(t)(x1))) = x1 + 1 >= x1 + 1 = t(b)(b(s)(s(t)(x1))) t(t)(t(b)(b(u)(x1))) = x1 + 1 >= x1 + 1 = t(b)(b(s)(s(u)(x1))) t(t)(t(b)(b(s)(s(f7)(x1)))) = x1 + 1 >= x1 + 1 = t(u)(u(t)(t(b)(b(f7)(x1)))) t(t)(t(b)(b(s)(s(s)(x1)))) = x1 + 1 >= x1 + 1 = t(u)(u(t)(t(b)(b(s)(x1)))) t(t)(t(b)(b(s)(s(b)(x1)))) = x1 + 2 >= x1 + 2 = t(u)(u(t)(t(b)(b(b)(x1)))) t(t)(t(b)(b(s)(s(t)(x1)))) = x1 + 1 >= x1 + 1 = t(u)(u(t)(t(b)(b(t)(x1)))) t(t)(t(b)(b(s)(s(u)(x1)))) = x1 + 1 >= x1 + 1 = t(u)(u(t)(t(b)(b(u)(x1)))) t(t)(t(u)(u(b)(x1))) = x1 + 1 >= x1 + 1 = t(u)(u(t)(t(b)(x1))) t(t)(t(u)(u(t)(x1))) = x1 >= x1 = t(u)(u(t)(t(t)(x1))) t(t)(t(u)(u(u)(x1))) = x1 >= x1 = t(u)(u(t)(t(u)(x1))) b(t)(t(u)(u(b)(x1))) = x1 + 1 >= x1 + 1 = b(u)(u(t)(t(b)(x1))) b(t)(t(u)(u(t)(x1))) = x1 >= x1 = b(u)(u(t)(t(t)(x1))) b(t)(t(u)(u(u)(x1))) = x1 >= x1 = b(u)(u(t)(t(u)(x1))) b(u)(u(t)(x1)) = x1 >= x1 = b(s)(s(t)(x1)) b(u)(u(f7)(x1)) = x1 + 1 >= x1 = b(s)(s(f7)(x1)) b(u)(u(b)(x1)) = x1 + 1 >= x1 + 1 = b(s)(s(b)(x1)) b(u)(u(u)(x1)) = x1 >= x1 = b(s)(s(u)(x1)) u(t)(t(b)(b(f7)(x1))) = x1 + 1 >= x1 + 1 = u(b)(b(s)(s(f7)(x1))) u(t)(t(b)(b(s)(x1))) = x1 + 1 >= x1 + 1 = u(b)(b(s)(s(s)(x1))) u(t)(t(b)(b(b)(x1))) = x1 + 2 >= x1 + 2 = u(b)(b(s)(s(b)(x1))) u(t)(t(b)(b(t)(x1))) = x1 + 1 >= x1 + 1 = u(b)(b(s)(s(t)(x1))) u(t)(t(b)(b(u)(x1))) = x1 + 1 >= x1 + 1 = u(b)(b(s)(s(u)(x1))) u(t)(t(b)(b(s)(s(f7)(x1)))) = x1 + 1 >= x1 + 1 = u(u)(u(t)(t(b)(b(f7)(x1)))) u(t)(t(b)(b(s)(s(s)(x1)))) = x1 + 1 >= x1 + 1 = u(u)(u(t)(t(b)(b(s)(x1)))) u(t)(t(b)(b(s)(s(b)(x1)))) = x1 + 2 >= x1 + 2 = u(u)(u(t)(t(b)(b(b)(x1)))) u(t)(t(b)(b(s)(s(t)(x1)))) = x1 + 1 >= x1 + 1 = u(u)(u(t)(t(b)(b(t)(x1)))) u(t)(t(b)(b(s)(s(u)(x1)))) = x1 + 1 >= x1 + 1 = u(u)(u(t)(t(b)(b(u)(x1)))) u(t)(t(u)(u(b)(x1))) = x1 + 1 >= x1 + 1 = u(u)(u(t)(t(b)(x1))) u(t)(t(u)(u(t)(x1))) = x1 >= x1 = u(u)(u(t)(t(t)(x1))) u(t)(t(u)(u(u)(x1))) = x1 >= x1 = u(u)(u(t)(t(u)(x1))) problem: DPs: t{#,(f7)}(f7(b)(b(s)(s(f7)(x1)))) -> t{#,(f7)}(f7(b)(b(f7)(x1))) t{#,(f7)}(f7(b)(b(s)(s(s)(x1)))) -> t{#,(f7)}(f7(b)(b(s)(x1))) t{#,(f7)}(f7(b)(b(s)(s(b)(x1)))) -> t{#,(f7)}(f7(b)(b(b)(x1))) t{#,(f7)}(f7(b)(b(s)(s(t)(x1)))) -> t{#,(f7)}(f7(b)(b(t)(x1))) t{#,(f7)}(f7(b)(b(s)(s(u)(x1)))) -> t{#,(f7)}(f7(b)(b(u)(x1))) TRS: b(s)(s(b)(b(f7)(x1))) -> b(b)(b(s)(s(s)(s(s)(s(f7)(x1))))) b(s)(s(b)(b(s)(x1))) -> b(b)(b(s)(s(s)(s(s)(s(s)(x1))))) b(s)(s(b)(b(b)(x1))) -> b(b)(b(s)(s(s)(s(s)(s(b)(x1))))) b(s)(s(b)(b(t)(x1))) -> b(b)(b(s)(s(s)(s(s)(s(t)(x1))))) b(s)(s(b)(b(u)(x1))) -> b(b)(b(s)(s(s)(s(s)(s(u)(x1))))) b(s)(s(b)(b(s)(s(s)(x1)))) -> b(b)(b(t)(t(s)(x1))) b(s)(s(b)(b(s)(s(b)(x1)))) -> b(b)(b(t)(t(b)(x1))) b(s)(s(b)(b(s)(s(t)(x1)))) -> b(b)(b(t)(t(t)(x1))) b(s)(s(b)(b(s)(s(u)(x1)))) -> b(b)(b(t)(t(u)(x1))) s(s)(s(b)(b(f7)(x1))) -> s(b)(b(s)(s(s)(s(s)(s(f7)(x1))))) s(s)(s(b)(b(s)(x1))) -> s(b)(b(s)(s(s)(s(s)(s(s)(x1))))) s(s)(s(b)(b(b)(x1))) -> s(b)(b(s)(s(s)(s(s)(s(b)(x1))))) s(s)(s(b)(b(t)(x1))) -> s(b)(b(s)(s(s)(s(s)(s(t)(x1))))) s(s)(s(b)(b(u)(x1))) -> s(b)(b(s)(s(s)(s(s)(s(u)(x1))))) s(s)(s(b)(b(s)(s(s)(x1)))) -> s(b)(b(t)(t(s)(x1))) s(s)(s(b)(b(s)(s(b)(x1)))) -> s(b)(b(t)(t(b)(x1))) s(s)(s(b)(b(s)(s(t)(x1)))) -> s(b)(b(t)(t(t)(x1))) s(s)(s(b)(b(s)(s(u)(x1)))) -> s(b)(b(t)(t(u)(x1))) s(t)(t(b)(b(f7)(x1))) -> s(b)(b(s)(s(f7)(x1))) s(t)(t(b)(b(s)(x1))) -> s(b)(b(s)(s(s)(x1))) s(t)(t(b)(b(b)(x1))) -> s(b)(b(s)(s(b)(x1))) s(t)(t(b)(b(t)(x1))) -> s(b)(b(s)(s(t)(x1))) s(t)(t(b)(b(u)(x1))) -> s(b)(b(s)(s(u)(x1))) s(t)(t(b)(b(s)(s(f7)(x1)))) -> s(u)(u(t)(t(b)(b(f7)(x1)))) s(t)(t(b)(b(s)(s(s)(x1)))) -> s(u)(u(t)(t(b)(b(s)(x1)))) s(t)(t(b)(b(s)(s(b)(x1)))) -> s(u)(u(t)(t(b)(b(b)(x1)))) s(t)(t(b)(b(s)(s(t)(x1)))) -> s(u)(u(t)(t(b)(b(t)(x1)))) s(t)(t(b)(b(s)(s(u)(x1)))) -> s(u)(u(t)(t(b)(b(u)(x1)))) s(t)(t(u)(u(b)(x1))) -> s(u)(u(t)(t(b)(x1))) s(t)(t(u)(u(t)(x1))) -> s(u)(u(t)(t(t)(x1))) s(t)(t(u)(u(u)(x1))) -> s(u)(u(t)(t(u)(x1))) s(u)(u(b)(x1)) -> s(s)(s(b)(x1)) s(u)(u(t)(x1)) -> s(s)(s(t)(x1)) s(u)(u(u)(x1)) -> s(s)(s(u)(x1)) t(s)(s(b)(b(f7)(x1))) -> t(b)(b(s)(s(s)(s(s)(s(f7)(x1))))) t(s)(s(b)(b(s)(x1))) -> t(b)(b(s)(s(s)(s(s)(s(s)(x1))))) t(s)(s(b)(b(b)(x1))) -> t(b)(b(s)(s(s)(s(s)(s(b)(x1))))) t(s)(s(b)(b(t)(x1))) -> t(b)(b(s)(s(s)(s(s)(s(t)(x1))))) t(s)(s(b)(b(u)(x1))) -> t(b)(b(s)(s(s)(s(s)(s(u)(x1))))) t(s)(s(b)(b(s)(s(s)(x1)))) -> t(b)(b(t)(t(s)(x1))) t(s)(s(b)(b(s)(s(b)(x1)))) -> t(b)(b(t)(t(b)(x1))) t(s)(s(b)(b(s)(s(t)(x1)))) -> t(b)(b(t)(t(t)(x1))) t(s)(s(b)(b(s)(s(u)(x1)))) -> t(b)(b(t)(t(u)(x1))) t(s)(s(s)(x1)) -> t(t)(t(s)(x1)) t(s)(s(b)(x1)) -> t(t)(t(b)(x1)) t(s)(s(t)(x1)) -> t(t)(t(t)(x1)) t(s)(s(u)(x1)) -> t(t)(t(u)(x1)) b(t)(t(b)(b(f7)(x1))) -> b(b)(b(s)(s(f7)(x1))) b(t)(t(b)(b(s)(x1))) -> b(b)(b(s)(s(s)(x1))) b(t)(t(b)(b(b)(x1))) -> b(b)(b(s)(s(b)(x1))) b(t)(t(b)(b(t)(x1))) -> b(b)(b(s)(s(t)(x1))) b(t)(t(b)(b(u)(x1))) -> b(b)(b(s)(s(u)(x1))) b(t)(t(b)(b(s)(s(f7)(x1)))) -> b(u)(u(t)(t(b)(b(f7)(x1)))) b(t)(t(b)(b(s)(s(s)(x1)))) -> b(u)(u(t)(t(b)(b(s)(x1)))) b(t)(t(b)(b(s)(s(b)(x1)))) -> b(u)(u(t)(t(b)(b(b)(x1)))) b(t)(t(b)(b(s)(s(t)(x1)))) -> b(u)(u(t)(t(b)(b(t)(x1)))) b(t)(t(b)(b(s)(s(u)(x1)))) -> b(u)(u(t)(t(b)(b(u)(x1)))) t(t)(t(b)(b(f7)(x1))) -> t(b)(b(s)(s(f7)(x1))) t(t)(t(b)(b(s)(x1))) -> t(b)(b(s)(s(s)(x1))) t(t)(t(b)(b(b)(x1))) -> t(b)(b(s)(s(b)(x1))) t(t)(t(b)(b(t)(x1))) -> t(b)(b(s)(s(t)(x1))) t(t)(t(b)(b(u)(x1))) -> t(b)(b(s)(s(u)(x1))) t(t)(t(b)(b(s)(s(f7)(x1)))) -> t(u)(u(t)(t(b)(b(f7)(x1)))) t(t)(t(b)(b(s)(s(s)(x1)))) -> t(u)(u(t)(t(b)(b(s)(x1)))) t(t)(t(b)(b(s)(s(b)(x1)))) -> t(u)(u(t)(t(b)(b(b)(x1)))) t(t)(t(b)(b(s)(s(t)(x1)))) -> t(u)(u(t)(t(b)(b(t)(x1)))) t(t)(t(b)(b(s)(s(u)(x1)))) -> t(u)(u(t)(t(b)(b(u)(x1)))) t(t)(t(u)(u(b)(x1))) -> t(u)(u(t)(t(b)(x1))) t(t)(t(u)(u(t)(x1))) -> t(u)(u(t)(t(t)(x1))) t(t)(t(u)(u(u)(x1))) -> t(u)(u(t)(t(u)(x1))) b(t)(t(u)(u(b)(x1))) -> b(u)(u(t)(t(b)(x1))) b(t)(t(u)(u(t)(x1))) -> b(u)(u(t)(t(t)(x1))) b(t)(t(u)(u(u)(x1))) -> b(u)(u(t)(t(u)(x1))) b(u)(u(t)(x1)) -> b(s)(s(t)(x1)) b(u)(u(b)(x1)) -> b(s)(s(b)(x1)) b(u)(u(u)(x1)) -> b(s)(s(u)(x1)) u(t)(t(b)(b(f7)(x1))) -> u(b)(b(s)(s(f7)(x1))) u(t)(t(b)(b(s)(x1))) -> u(b)(b(s)(s(s)(x1))) u(t)(t(b)(b(b)(x1))) -> u(b)(b(s)(s(b)(x1))) u(t)(t(b)(b(t)(x1))) -> u(b)(b(s)(s(t)(x1))) u(t)(t(b)(b(u)(x1))) -> u(b)(b(s)(s(u)(x1))) u(t)(t(b)(b(s)(s(f7)(x1)))) -> u(u)(u(t)(t(b)(b(f7)(x1)))) u(t)(t(b)(b(s)(s(s)(x1)))) -> u(u)(u(t)(t(b)(b(s)(x1)))) u(t)(t(b)(b(s)(s(b)(x1)))) -> u(u)(u(t)(t(b)(b(b)(x1)))) u(t)(t(b)(b(s)(s(t)(x1)))) -> u(u)(u(t)(t(b)(b(t)(x1)))) u(t)(t(b)(b(s)(s(u)(x1)))) -> u(u)(u(t)(t(b)(b(u)(x1)))) u(t)(t(u)(u(b)(x1))) -> u(u)(u(t)(t(b)(x1))) u(t)(t(u)(u(t)(x1))) -> u(u)(u(t)(t(t)(x1))) u(t)(t(u)(u(u)(x1))) -> u(u)(u(t)(t(u)(x1))) Polynomial Interpretation Processor: dimension: 1 usable rules: b(s)(s(b)(b(f7)(x1))) -> b(b)(b(s)(s(s)(s(s)(s(f7)(x1))))) b(s)(s(b)(b(s)(x1))) -> b(b)(b(s)(s(s)(s(s)(s(s)(x1))))) b(s)(s(b)(b(b)(x1))) -> b(b)(b(s)(s(s)(s(s)(s(b)(x1))))) b(s)(s(b)(b(t)(x1))) -> b(b)(b(s)(s(s)(s(s)(s(t)(x1))))) b(s)(s(b)(b(u)(x1))) -> b(b)(b(s)(s(s)(s(s)(s(u)(x1))))) b(s)(s(b)(b(s)(s(s)(x1)))) -> b(b)(b(t)(t(s)(x1))) b(s)(s(b)(b(s)(s(b)(x1)))) -> b(b)(b(t)(t(b)(x1))) b(s)(s(b)(b(s)(s(t)(x1)))) -> b(b)(b(t)(t(t)(x1))) b(s)(s(b)(b(s)(s(u)(x1)))) -> b(b)(b(t)(t(u)(x1))) b(t)(t(b)(b(f7)(x1))) -> b(b)(b(s)(s(f7)(x1))) b(t)(t(b)(b(s)(x1))) -> b(b)(b(s)(s(s)(x1))) b(t)(t(b)(b(b)(x1))) -> b(b)(b(s)(s(b)(x1))) b(t)(t(b)(b(t)(x1))) -> b(b)(b(s)(s(t)(x1))) b(t)(t(b)(b(u)(x1))) -> b(b)(b(s)(s(u)(x1))) b(t)(t(b)(b(s)(s(f7)(x1)))) -> b(u)(u(t)(t(b)(b(f7)(x1)))) b(t)(t(b)(b(s)(s(s)(x1)))) -> b(u)(u(t)(t(b)(b(s)(x1)))) b(t)(t(b)(b(s)(s(b)(x1)))) -> b(u)(u(t)(t(b)(b(b)(x1)))) b(t)(t(b)(b(s)(s(t)(x1)))) -> b(u)(u(t)(t(b)(b(t)(x1)))) b(t)(t(b)(b(s)(s(u)(x1)))) -> b(u)(u(t)(t(b)(b(u)(x1)))) b(t)(t(u)(u(b)(x1))) -> b(u)(u(t)(t(b)(x1))) b(t)(t(u)(u(t)(x1))) -> b(u)(u(t)(t(t)(x1))) b(t)(t(u)(u(u)(x1))) -> b(u)(u(t)(t(u)(x1))) b(u)(u(t)(x1)) -> b(s)(s(t)(x1)) b(u)(u(b)(x1)) -> b(s)(s(b)(x1)) b(u)(u(u)(x1)) -> b(s)(s(u)(x1)) interpretation: [u(u)](x0) = 0, [u(t)](x0) = 1, [t(u)](x0) = 0, [t(t)](x0) = 0, [u(b)](x0) = 0, [t(b)](x0) = 0, [t(s)](x0) = 0, [b(u)](x0) = 1, [s(u)](x0) = 0, [b(t)](x0) = 1, [s(t)](x0) = 0, [b(b)](x0) = 0, [s(b)](x0) = 1, [s(s)](x0) = x0 + 1, [b(f7)](x0) = 1, [s(f7)](x0) = 1, [b(s)](x0) = 1, [f7(b)](x0) = x0, [t{#,(f7)}](x0) = x0 orientation: t{#,(f7)}(f7(b)(b(s)(s(f7)(x1)))) = 1 >= 1 = t{#,(f7)}(f7(b)(b(f7)(x1))) t{#,(f7)}(f7(b)(b(s)(s(s)(x1)))) = 1 >= 1 = t{#,(f7)}(f7(b)(b(s)(x1))) t{#,(f7)}(f7(b)(b(s)(s(b)(x1)))) = 1 >= 0 = t{#,(f7)}(f7(b)(b(b)(x1))) t{#,(f7)}(f7(b)(b(s)(s(t)(x1)))) = 1 >= 1 = t{#,(f7)}(f7(b)(b(t)(x1))) t{#,(f7)}(f7(b)(b(s)(s(u)(x1)))) = 1 >= 1 = t{#,(f7)}(f7(b)(b(u)(x1))) b(s)(s(b)(b(f7)(x1))) = 1 >= 0 = b(b)(b(s)(s(s)(s(s)(s(f7)(x1))))) b(s)(s(b)(b(s)(x1))) = 1 >= 0 = b(b)(b(s)(s(s)(s(s)(s(s)(x1))))) b(s)(s(b)(b(b)(x1))) = 1 >= 0 = b(b)(b(s)(s(s)(s(s)(s(b)(x1))))) b(s)(s(b)(b(t)(x1))) = 1 >= 0 = b(b)(b(s)(s(s)(s(s)(s(t)(x1))))) b(s)(s(b)(b(u)(x1))) = 1 >= 0 = b(b)(b(s)(s(s)(s(s)(s(u)(x1))))) b(s)(s(b)(b(s)(s(s)(x1)))) = 1 >= 0 = b(b)(b(t)(t(s)(x1))) b(s)(s(b)(b(s)(s(b)(x1)))) = 1 >= 0 = b(b)(b(t)(t(b)(x1))) b(s)(s(b)(b(s)(s(t)(x1)))) = 1 >= 0 = b(b)(b(t)(t(t)(x1))) b(s)(s(b)(b(s)(s(u)(x1)))) = 1 >= 0 = b(b)(b(t)(t(u)(x1))) s(s)(s(b)(b(f7)(x1))) = 2 >= 1 = s(b)(b(s)(s(s)(s(s)(s(f7)(x1))))) s(s)(s(b)(b(s)(x1))) = 2 >= 1 = s(b)(b(s)(s(s)(s(s)(s(s)(x1))))) s(s)(s(b)(b(b)(x1))) = 2 >= 1 = s(b)(b(s)(s(s)(s(s)(s(b)(x1))))) s(s)(s(b)(b(t)(x1))) = 2 >= 1 = s(b)(b(s)(s(s)(s(s)(s(t)(x1))))) s(s)(s(b)(b(u)(x1))) = 2 >= 1 = s(b)(b(s)(s(s)(s(s)(s(u)(x1))))) s(s)(s(b)(b(s)(s(s)(x1)))) = 2 >= 1 = s(b)(b(t)(t(s)(x1))) s(s)(s(b)(b(s)(s(b)(x1)))) = 2 >= 1 = s(b)(b(t)(t(b)(x1))) s(s)(s(b)(b(s)(s(t)(x1)))) = 2 >= 1 = s(b)(b(t)(t(t)(x1))) s(s)(s(b)(b(s)(s(u)(x1)))) = 2 >= 1 = s(b)(b(t)(t(u)(x1))) s(t)(t(b)(b(f7)(x1))) = 0 >= 1 = s(b)(b(s)(s(f7)(x1))) s(t)(t(b)(b(s)(x1))) = 0 >= 1 = s(b)(b(s)(s(s)(x1))) s(t)(t(b)(b(b)(x1))) = 0 >= 1 = s(b)(b(s)(s(b)(x1))) s(t)(t(b)(b(t)(x1))) = 0 >= 1 = s(b)(b(s)(s(t)(x1))) s(t)(t(b)(b(u)(x1))) = 0 >= 1 = s(b)(b(s)(s(u)(x1))) s(t)(t(b)(b(s)(s(f7)(x1)))) = 0 >= 0 = s(u)(u(t)(t(b)(b(f7)(x1)))) s(t)(t(b)(b(s)(s(s)(x1)))) = 0 >= 0 = s(u)(u(t)(t(b)(b(s)(x1)))) s(t)(t(b)(b(s)(s(b)(x1)))) = 0 >= 0 = s(u)(u(t)(t(b)(b(b)(x1)))) s(t)(t(b)(b(s)(s(t)(x1)))) = 0 >= 0 = s(u)(u(t)(t(b)(b(t)(x1)))) s(t)(t(b)(b(s)(s(u)(x1)))) = 0 >= 0 = s(u)(u(t)(t(b)(b(u)(x1)))) s(t)(t(u)(u(b)(x1))) = 0 >= 0 = s(u)(u(t)(t(b)(x1))) s(t)(t(u)(u(t)(x1))) = 0 >= 0 = s(u)(u(t)(t(t)(x1))) s(t)(t(u)(u(u)(x1))) = 0 >= 0 = s(u)(u(t)(t(u)(x1))) s(u)(u(b)(x1)) = 0 >= 2 = s(s)(s(b)(x1)) s(u)(u(t)(x1)) = 0 >= 1 = s(s)(s(t)(x1)) s(u)(u(u)(x1)) = 0 >= 1 = s(s)(s(u)(x1)) t(s)(s(b)(b(f7)(x1))) = 0 >= 0 = t(b)(b(s)(s(s)(s(s)(s(f7)(x1))))) t(s)(s(b)(b(s)(x1))) = 0 >= 0 = t(b)(b(s)(s(s)(s(s)(s(s)(x1))))) t(s)(s(b)(b(b)(x1))) = 0 >= 0 = t(b)(b(s)(s(s)(s(s)(s(b)(x1))))) t(s)(s(b)(b(t)(x1))) = 0 >= 0 = t(b)(b(s)(s(s)(s(s)(s(t)(x1))))) t(s)(s(b)(b(u)(x1))) = 0 >= 0 = t(b)(b(s)(s(s)(s(s)(s(u)(x1))))) t(s)(s(b)(b(s)(s(s)(x1)))) = 0 >= 0 = t(b)(b(t)(t(s)(x1))) t(s)(s(b)(b(s)(s(b)(x1)))) = 0 >= 0 = t(b)(b(t)(t(b)(x1))) t(s)(s(b)(b(s)(s(t)(x1)))) = 0 >= 0 = t(b)(b(t)(t(t)(x1))) t(s)(s(b)(b(s)(s(u)(x1)))) = 0 >= 0 = t(b)(b(t)(t(u)(x1))) t(s)(s(s)(x1)) = 0 >= 0 = t(t)(t(s)(x1)) t(s)(s(b)(x1)) = 0 >= 0 = t(t)(t(b)(x1)) t(s)(s(t)(x1)) = 0 >= 0 = t(t)(t(t)(x1)) t(s)(s(u)(x1)) = 0 >= 0 = t(t)(t(u)(x1)) b(t)(t(b)(b(f7)(x1))) = 1 >= 0 = b(b)(b(s)(s(f7)(x1))) b(t)(t(b)(b(s)(x1))) = 1 >= 0 = b(b)(b(s)(s(s)(x1))) b(t)(t(b)(b(b)(x1))) = 1 >= 0 = b(b)(b(s)(s(b)(x1))) b(t)(t(b)(b(t)(x1))) = 1 >= 0 = b(b)(b(s)(s(t)(x1))) b(t)(t(b)(b(u)(x1))) = 1 >= 0 = b(b)(b(s)(s(u)(x1))) b(t)(t(b)(b(s)(s(f7)(x1)))) = 1 >= 1 = b(u)(u(t)(t(b)(b(f7)(x1)))) b(t)(t(b)(b(s)(s(s)(x1)))) = 1 >= 1 = b(u)(u(t)(t(b)(b(s)(x1)))) b(t)(t(b)(b(s)(s(b)(x1)))) = 1 >= 1 = b(u)(u(t)(t(b)(b(b)(x1)))) b(t)(t(b)(b(s)(s(t)(x1)))) = 1 >= 1 = b(u)(u(t)(t(b)(b(t)(x1)))) b(t)(t(b)(b(s)(s(u)(x1)))) = 1 >= 1 = b(u)(u(t)(t(b)(b(u)(x1)))) t(t)(t(b)(b(f7)(x1))) = 0 >= 0 = t(b)(b(s)(s(f7)(x1))) t(t)(t(b)(b(s)(x1))) = 0 >= 0 = t(b)(b(s)(s(s)(x1))) t(t)(t(b)(b(b)(x1))) = 0 >= 0 = t(b)(b(s)(s(b)(x1))) t(t)(t(b)(b(t)(x1))) = 0 >= 0 = t(b)(b(s)(s(t)(x1))) t(t)(t(b)(b(u)(x1))) = 0 >= 0 = t(b)(b(s)(s(u)(x1))) t(t)(t(b)(b(s)(s(f7)(x1)))) = 0 >= 0 = t(u)(u(t)(t(b)(b(f7)(x1)))) t(t)(t(b)(b(s)(s(s)(x1)))) = 0 >= 0 = t(u)(u(t)(t(b)(b(s)(x1)))) t(t)(t(b)(b(s)(s(b)(x1)))) = 0 >= 0 = t(u)(u(t)(t(b)(b(b)(x1)))) t(t)(t(b)(b(s)(s(t)(x1)))) = 0 >= 0 = t(u)(u(t)(t(b)(b(t)(x1)))) t(t)(t(b)(b(s)(s(u)(x1)))) = 0 >= 0 = t(u)(u(t)(t(b)(b(u)(x1)))) t(t)(t(u)(u(b)(x1))) = 0 >= 0 = t(u)(u(t)(t(b)(x1))) t(t)(t(u)(u(t)(x1))) = 0 >= 0 = t(u)(u(t)(t(t)(x1))) t(t)(t(u)(u(u)(x1))) = 0 >= 0 = t(u)(u(t)(t(u)(x1))) b(t)(t(u)(u(b)(x1))) = 1 >= 1 = b(u)(u(t)(t(b)(x1))) b(t)(t(u)(u(t)(x1))) = 1 >= 1 = b(u)(u(t)(t(t)(x1))) b(t)(t(u)(u(u)(x1))) = 1 >= 1 = b(u)(u(t)(t(u)(x1))) b(u)(u(t)(x1)) = 1 >= 1 = b(s)(s(t)(x1)) b(u)(u(b)(x1)) = 1 >= 1 = b(s)(s(b)(x1)) b(u)(u(u)(x1)) = 1 >= 1 = b(s)(s(u)(x1)) u(t)(t(b)(b(f7)(x1))) = 1 >= 0 = u(b)(b(s)(s(f7)(x1))) u(t)(t(b)(b(s)(x1))) = 1 >= 0 = u(b)(b(s)(s(s)(x1))) u(t)(t(b)(b(b)(x1))) = 1 >= 0 = u(b)(b(s)(s(b)(x1))) u(t)(t(b)(b(t)(x1))) = 1 >= 0 = u(b)(b(s)(s(t)(x1))) u(t)(t(b)(b(u)(x1))) = 1 >= 0 = u(b)(b(s)(s(u)(x1))) u(t)(t(b)(b(s)(s(f7)(x1)))) = 1 >= 0 = u(u)(u(t)(t(b)(b(f7)(x1)))) u(t)(t(b)(b(s)(s(s)(x1)))) = 1 >= 0 = u(u)(u(t)(t(b)(b(s)(x1)))) u(t)(t(b)(b(s)(s(b)(x1)))) = 1 >= 0 = u(u)(u(t)(t(b)(b(b)(x1)))) u(t)(t(b)(b(s)(s(t)(x1)))) = 1 >= 0 = u(u)(u(t)(t(b)(b(t)(x1)))) u(t)(t(b)(b(s)(s(u)(x1)))) = 1 >= 0 = u(u)(u(t)(t(b)(b(u)(x1)))) u(t)(t(u)(u(b)(x1))) = 1 >= 0 = u(u)(u(t)(t(b)(x1))) u(t)(t(u)(u(t)(x1))) = 1 >= 0 = u(u)(u(t)(t(t)(x1))) u(t)(t(u)(u(u)(x1))) = 1 >= 0 = u(u)(u(t)(t(u)(x1))) problem: DPs: t{#,(f7)}(f7(b)(b(s)(s(f7)(x1)))) -> t{#,(f7)}(f7(b)(b(f7)(x1))) t{#,(f7)}(f7(b)(b(s)(s(s)(x1)))) -> t{#,(f7)}(f7(b)(b(s)(x1))) t{#,(f7)}(f7(b)(b(s)(s(t)(x1)))) -> t{#,(f7)}(f7(b)(b(t)(x1))) t{#,(f7)}(f7(b)(b(s)(s(u)(x1)))) -> t{#,(f7)}(f7(b)(b(u)(x1))) TRS: b(s)(s(b)(b(f7)(x1))) -> b(b)(b(s)(s(s)(s(s)(s(f7)(x1))))) b(s)(s(b)(b(s)(x1))) -> b(b)(b(s)(s(s)(s(s)(s(s)(x1))))) b(s)(s(b)(b(b)(x1))) -> b(b)(b(s)(s(s)(s(s)(s(b)(x1))))) b(s)(s(b)(b(t)(x1))) -> b(b)(b(s)(s(s)(s(s)(s(t)(x1))))) b(s)(s(b)(b(u)(x1))) -> b(b)(b(s)(s(s)(s(s)(s(u)(x1))))) b(s)(s(b)(b(s)(s(s)(x1)))) -> b(b)(b(t)(t(s)(x1))) b(s)(s(b)(b(s)(s(b)(x1)))) -> b(b)(b(t)(t(b)(x1))) b(s)(s(b)(b(s)(s(t)(x1)))) -> b(b)(b(t)(t(t)(x1))) b(s)(s(b)(b(s)(s(u)(x1)))) -> b(b)(b(t)(t(u)(x1))) s(s)(s(b)(b(f7)(x1))) -> s(b)(b(s)(s(s)(s(s)(s(f7)(x1))))) s(s)(s(b)(b(s)(x1))) -> s(b)(b(s)(s(s)(s(s)(s(s)(x1))))) s(s)(s(b)(b(b)(x1))) -> s(b)(b(s)(s(s)(s(s)(s(b)(x1))))) s(s)(s(b)(b(t)(x1))) -> s(b)(b(s)(s(s)(s(s)(s(t)(x1))))) s(s)(s(b)(b(u)(x1))) -> s(b)(b(s)(s(s)(s(s)(s(u)(x1))))) s(s)(s(b)(b(s)(s(s)(x1)))) -> s(b)(b(t)(t(s)(x1))) s(s)(s(b)(b(s)(s(b)(x1)))) -> s(b)(b(t)(t(b)(x1))) s(s)(s(b)(b(s)(s(t)(x1)))) -> s(b)(b(t)(t(t)(x1))) s(s)(s(b)(b(s)(s(u)(x1)))) -> s(b)(b(t)(t(u)(x1))) s(t)(t(b)(b(f7)(x1))) -> s(b)(b(s)(s(f7)(x1))) s(t)(t(b)(b(s)(x1))) -> s(b)(b(s)(s(s)(x1))) s(t)(t(b)(b(b)(x1))) -> s(b)(b(s)(s(b)(x1))) s(t)(t(b)(b(t)(x1))) -> s(b)(b(s)(s(t)(x1))) s(t)(t(b)(b(u)(x1))) -> s(b)(b(s)(s(u)(x1))) s(t)(t(b)(b(s)(s(f7)(x1)))) -> s(u)(u(t)(t(b)(b(f7)(x1)))) s(t)(t(b)(b(s)(s(s)(x1)))) -> s(u)(u(t)(t(b)(b(s)(x1)))) s(t)(t(b)(b(s)(s(b)(x1)))) -> s(u)(u(t)(t(b)(b(b)(x1)))) s(t)(t(b)(b(s)(s(t)(x1)))) -> s(u)(u(t)(t(b)(b(t)(x1)))) s(t)(t(b)(b(s)(s(u)(x1)))) -> s(u)(u(t)(t(b)(b(u)(x1)))) s(t)(t(u)(u(b)(x1))) -> s(u)(u(t)(t(b)(x1))) s(t)(t(u)(u(t)(x1))) -> s(u)(u(t)(t(t)(x1))) s(t)(t(u)(u(u)(x1))) -> s(u)(u(t)(t(u)(x1))) s(u)(u(b)(x1)) -> s(s)(s(b)(x1)) s(u)(u(t)(x1)) -> s(s)(s(t)(x1)) s(u)(u(u)(x1)) -> s(s)(s(u)(x1)) t(s)(s(b)(b(f7)(x1))) -> t(b)(b(s)(s(s)(s(s)(s(f7)(x1))))) t(s)(s(b)(b(s)(x1))) -> t(b)(b(s)(s(s)(s(s)(s(s)(x1))))) t(s)(s(b)(b(b)(x1))) -> t(b)(b(s)(s(s)(s(s)(s(b)(x1))))) t(s)(s(b)(b(t)(x1))) -> t(b)(b(s)(s(s)(s(s)(s(t)(x1))))) t(s)(s(b)(b(u)(x1))) -> t(b)(b(s)(s(s)(s(s)(s(u)(x1))))) t(s)(s(b)(b(s)(s(s)(x1)))) -> t(b)(b(t)(t(s)(x1))) t(s)(s(b)(b(s)(s(b)(x1)))) -> t(b)(b(t)(t(b)(x1))) t(s)(s(b)(b(s)(s(t)(x1)))) -> t(b)(b(t)(t(t)(x1))) t(s)(s(b)(b(s)(s(u)(x1)))) -> t(b)(b(t)(t(u)(x1))) t(s)(s(s)(x1)) -> t(t)(t(s)(x1)) t(s)(s(b)(x1)) -> t(t)(t(b)(x1)) t(s)(s(t)(x1)) -> t(t)(t(t)(x1)) t(s)(s(u)(x1)) -> t(t)(t(u)(x1)) b(t)(t(b)(b(f7)(x1))) -> b(b)(b(s)(s(f7)(x1))) b(t)(t(b)(b(s)(x1))) -> b(b)(b(s)(s(s)(x1))) b(t)(t(b)(b(b)(x1))) -> b(b)(b(s)(s(b)(x1))) b(t)(t(b)(b(t)(x1))) -> b(b)(b(s)(s(t)(x1))) b(t)(t(b)(b(u)(x1))) -> b(b)(b(s)(s(u)(x1))) b(t)(t(b)(b(s)(s(f7)(x1)))) -> b(u)(u(t)(t(b)(b(f7)(x1)))) b(t)(t(b)(b(s)(s(s)(x1)))) -> b(u)(u(t)(t(b)(b(s)(x1)))) b(t)(t(b)(b(s)(s(b)(x1)))) -> b(u)(u(t)(t(b)(b(b)(x1)))) b(t)(t(b)(b(s)(s(t)(x1)))) -> b(u)(u(t)(t(b)(b(t)(x1)))) b(t)(t(b)(b(s)(s(u)(x1)))) -> b(u)(u(t)(t(b)(b(u)(x1)))) t(t)(t(b)(b(f7)(x1))) -> t(b)(b(s)(s(f7)(x1))) t(t)(t(b)(b(s)(x1))) -> t(b)(b(s)(s(s)(x1))) t(t)(t(b)(b(b)(x1))) -> t(b)(b(s)(s(b)(x1))) t(t)(t(b)(b(t)(x1))) -> t(b)(b(s)(s(t)(x1))) t(t)(t(b)(b(u)(x1))) -> t(b)(b(s)(s(u)(x1))) t(t)(t(b)(b(s)(s(f7)(x1)))) -> t(u)(u(t)(t(b)(b(f7)(x1)))) t(t)(t(b)(b(s)(s(s)(x1)))) -> t(u)(u(t)(t(b)(b(s)(x1)))) t(t)(t(b)(b(s)(s(b)(x1)))) -> t(u)(u(t)(t(b)(b(b)(x1)))) t(t)(t(b)(b(s)(s(t)(x1)))) -> t(u)(u(t)(t(b)(b(t)(x1)))) t(t)(t(b)(b(s)(s(u)(x1)))) -> t(u)(u(t)(t(b)(b(u)(x1)))) t(t)(t(u)(u(b)(x1))) -> t(u)(u(t)(t(b)(x1))) t(t)(t(u)(u(t)(x1))) -> t(u)(u(t)(t(t)(x1))) t(t)(t(u)(u(u)(x1))) -> t(u)(u(t)(t(u)(x1))) b(t)(t(u)(u(b)(x1))) -> b(u)(u(t)(t(b)(x1))) b(t)(t(u)(u(t)(x1))) -> b(u)(u(t)(t(t)(x1))) b(t)(t(u)(u(u)(x1))) -> b(u)(u(t)(t(u)(x1))) b(u)(u(t)(x1)) -> b(s)(s(t)(x1)) b(u)(u(b)(x1)) -> b(s)(s(b)(x1)) b(u)(u(u)(x1)) -> b(s)(s(u)(x1)) u(t)(t(b)(b(f7)(x1))) -> u(b)(b(s)(s(f7)(x1))) u(t)(t(b)(b(s)(x1))) -> u(b)(b(s)(s(s)(x1))) u(t)(t(b)(b(b)(x1))) -> u(b)(b(s)(s(b)(x1))) u(t)(t(b)(b(t)(x1))) -> u(b)(b(s)(s(t)(x1))) u(t)(t(b)(b(u)(x1))) -> u(b)(b(s)(s(u)(x1))) u(t)(t(b)(b(s)(s(f7)(x1)))) -> u(u)(u(t)(t(b)(b(f7)(x1)))) u(t)(t(b)(b(s)(s(s)(x1)))) -> u(u)(u(t)(t(b)(b(s)(x1)))) u(t)(t(b)(b(s)(s(b)(x1)))) -> u(u)(u(t)(t(b)(b(b)(x1)))) u(t)(t(b)(b(s)(s(t)(x1)))) -> u(u)(u(t)(t(b)(b(t)(x1)))) u(t)(t(b)(b(s)(s(u)(x1)))) -> u(u)(u(t)(t(b)(b(u)(x1)))) u(t)(t(u)(u(b)(x1))) -> u(u)(u(t)(t(b)(x1))) u(t)(t(u)(u(t)(x1))) -> u(u)(u(t)(t(t)(x1))) u(t)(t(u)(u(u)(x1))) -> u(u)(u(t)(t(u)(x1))) Polynomial Interpretation Processor: dimension: 1 usable rules: b(s)(s(b)(b(f7)(x1))) -> b(b)(b(s)(s(s)(s(s)(s(f7)(x1))))) b(s)(s(b)(b(s)(x1))) -> b(b)(b(s)(s(s)(s(s)(s(s)(x1))))) b(s)(s(b)(b(b)(x1))) -> b(b)(b(s)(s(s)(s(s)(s(b)(x1))))) b(s)(s(b)(b(t)(x1))) -> b(b)(b(s)(s(s)(s(s)(s(t)(x1))))) b(s)(s(b)(b(u)(x1))) -> b(b)(b(s)(s(s)(s(s)(s(u)(x1))))) b(s)(s(b)(b(s)(s(s)(x1)))) -> b(b)(b(t)(t(s)(x1))) b(s)(s(b)(b(s)(s(b)(x1)))) -> b(b)(b(t)(t(b)(x1))) b(s)(s(b)(b(s)(s(t)(x1)))) -> b(b)(b(t)(t(t)(x1))) b(s)(s(b)(b(s)(s(u)(x1)))) -> b(b)(b(t)(t(u)(x1))) s(s)(s(b)(b(f7)(x1))) -> s(b)(b(s)(s(s)(s(s)(s(f7)(x1))))) s(s)(s(b)(b(s)(x1))) -> s(b)(b(s)(s(s)(s(s)(s(s)(x1))))) s(s)(s(b)(b(b)(x1))) -> s(b)(b(s)(s(s)(s(s)(s(b)(x1))))) s(s)(s(b)(b(t)(x1))) -> s(b)(b(s)(s(s)(s(s)(s(t)(x1))))) s(s)(s(b)(b(u)(x1))) -> s(b)(b(s)(s(s)(s(s)(s(u)(x1))))) s(s)(s(b)(b(s)(s(s)(x1)))) -> s(b)(b(t)(t(s)(x1))) s(s)(s(b)(b(s)(s(b)(x1)))) -> s(b)(b(t)(t(b)(x1))) s(s)(s(b)(b(s)(s(t)(x1)))) -> s(b)(b(t)(t(t)(x1))) s(s)(s(b)(b(s)(s(u)(x1)))) -> s(b)(b(t)(t(u)(x1))) s(t)(t(b)(b(f7)(x1))) -> s(b)(b(s)(s(f7)(x1))) s(t)(t(b)(b(s)(x1))) -> s(b)(b(s)(s(s)(x1))) s(t)(t(b)(b(b)(x1))) -> s(b)(b(s)(s(b)(x1))) s(t)(t(b)(b(t)(x1))) -> s(b)(b(s)(s(t)(x1))) s(t)(t(b)(b(u)(x1))) -> s(b)(b(s)(s(u)(x1))) s(t)(t(b)(b(s)(s(f7)(x1)))) -> s(u)(u(t)(t(b)(b(f7)(x1)))) s(t)(t(b)(b(s)(s(s)(x1)))) -> s(u)(u(t)(t(b)(b(s)(x1)))) s(t)(t(b)(b(s)(s(b)(x1)))) -> s(u)(u(t)(t(b)(b(b)(x1)))) s(t)(t(b)(b(s)(s(t)(x1)))) -> s(u)(u(t)(t(b)(b(t)(x1)))) s(t)(t(b)(b(s)(s(u)(x1)))) -> s(u)(u(t)(t(b)(b(u)(x1)))) s(t)(t(u)(u(b)(x1))) -> s(u)(u(t)(t(b)(x1))) s(t)(t(u)(u(t)(x1))) -> s(u)(u(t)(t(t)(x1))) s(t)(t(u)(u(u)(x1))) -> s(u)(u(t)(t(u)(x1))) s(u)(u(b)(x1)) -> s(s)(s(b)(x1)) s(u)(u(t)(x1)) -> s(s)(s(t)(x1)) s(u)(u(u)(x1)) -> s(s)(s(u)(x1)) b(t)(t(b)(b(f7)(x1))) -> b(b)(b(s)(s(f7)(x1))) b(t)(t(b)(b(s)(x1))) -> b(b)(b(s)(s(s)(x1))) b(t)(t(b)(b(b)(x1))) -> b(b)(b(s)(s(b)(x1))) b(t)(t(b)(b(t)(x1))) -> b(b)(b(s)(s(t)(x1))) b(t)(t(b)(b(u)(x1))) -> b(b)(b(s)(s(u)(x1))) b(t)(t(b)(b(s)(s(f7)(x1)))) -> b(u)(u(t)(t(b)(b(f7)(x1)))) b(t)(t(b)(b(s)(s(s)(x1)))) -> b(u)(u(t)(t(b)(b(s)(x1)))) b(t)(t(b)(b(s)(s(b)(x1)))) -> b(u)(u(t)(t(b)(b(b)(x1)))) b(t)(t(b)(b(s)(s(t)(x1)))) -> b(u)(u(t)(t(b)(b(t)(x1)))) b(t)(t(b)(b(s)(s(u)(x1)))) -> b(u)(u(t)(t(b)(b(u)(x1)))) b(t)(t(u)(u(b)(x1))) -> b(u)(u(t)(t(b)(x1))) b(t)(t(u)(u(t)(x1))) -> b(u)(u(t)(t(t)(x1))) b(t)(t(u)(u(u)(x1))) -> b(u)(u(t)(t(u)(x1))) b(u)(u(t)(x1)) -> b(s)(s(t)(x1)) b(u)(u(b)(x1)) -> b(s)(s(b)(x1)) b(u)(u(u)(x1)) -> b(s)(s(u)(x1)) interpretation: [u(u)](x0) = 0, [u(t)](x0) = 0, [t(u)](x0) = 0, [t(t)](x0) = 0, [u(b)](x0) = 0, [t(b)](x0) = 0, [t(s)](x0) = 1, [b(u)](x0) = 0, [s(u)](x0) = 0, [b(t)](x0) = 0, [s(t)](x0) = 0, [b(b)](x0) = 0, [s(b)](x0) = 0, [s(s)](x0) = x0, [b(f7)](x0) = 0, [s(f7)](x0) = 1, [b(s)](x0) = x0, [f7(b)](x0) = x0, [t{#,(f7)}](x0) = x0 orientation: t{#,(f7)}(f7(b)(b(s)(s(f7)(x1)))) = 1 >= 0 = t{#,(f7)}(f7(b)(b(f7)(x1))) t{#,(f7)}(f7(b)(b(s)(s(s)(x1)))) = x1 >= x1 = t{#,(f7)}(f7(b)(b(s)(x1))) t{#,(f7)}(f7(b)(b(s)(s(t)(x1)))) = 0 >= 0 = t{#,(f7)}(f7(b)(b(t)(x1))) t{#,(f7)}(f7(b)(b(s)(s(u)(x1)))) = 0 >= 0 = t{#,(f7)}(f7(b)(b(u)(x1))) b(s)(s(b)(b(f7)(x1))) = 0 >= 0 = b(b)(b(s)(s(s)(s(s)(s(f7)(x1))))) b(s)(s(b)(b(s)(x1))) = 0 >= 0 = b(b)(b(s)(s(s)(s(s)(s(s)(x1))))) b(s)(s(b)(b(b)(x1))) = 0 >= 0 = b(b)(b(s)(s(s)(s(s)(s(b)(x1))))) b(s)(s(b)(b(t)(x1))) = 0 >= 0 = b(b)(b(s)(s(s)(s(s)(s(t)(x1))))) b(s)(s(b)(b(u)(x1))) = 0 >= 0 = b(b)(b(s)(s(s)(s(s)(s(u)(x1))))) b(s)(s(b)(b(s)(s(s)(x1)))) = 0 >= 0 = b(b)(b(t)(t(s)(x1))) b(s)(s(b)(b(s)(s(b)(x1)))) = 0 >= 0 = b(b)(b(t)(t(b)(x1))) b(s)(s(b)(b(s)(s(t)(x1)))) = 0 >= 0 = b(b)(b(t)(t(t)(x1))) b(s)(s(b)(b(s)(s(u)(x1)))) = 0 >= 0 = b(b)(b(t)(t(u)(x1))) s(s)(s(b)(b(f7)(x1))) = 0 >= 0 = s(b)(b(s)(s(s)(s(s)(s(f7)(x1))))) s(s)(s(b)(b(s)(x1))) = 0 >= 0 = s(b)(b(s)(s(s)(s(s)(s(s)(x1))))) s(s)(s(b)(b(b)(x1))) = 0 >= 0 = s(b)(b(s)(s(s)(s(s)(s(b)(x1))))) s(s)(s(b)(b(t)(x1))) = 0 >= 0 = s(b)(b(s)(s(s)(s(s)(s(t)(x1))))) s(s)(s(b)(b(u)(x1))) = 0 >= 0 = s(b)(b(s)(s(s)(s(s)(s(u)(x1))))) s(s)(s(b)(b(s)(s(s)(x1)))) = 0 >= 0 = s(b)(b(t)(t(s)(x1))) s(s)(s(b)(b(s)(s(b)(x1)))) = 0 >= 0 = s(b)(b(t)(t(b)(x1))) s(s)(s(b)(b(s)(s(t)(x1)))) = 0 >= 0 = s(b)(b(t)(t(t)(x1))) s(s)(s(b)(b(s)(s(u)(x1)))) = 0 >= 0 = s(b)(b(t)(t(u)(x1))) s(t)(t(b)(b(f7)(x1))) = 0 >= 0 = s(b)(b(s)(s(f7)(x1))) s(t)(t(b)(b(s)(x1))) = 0 >= 0 = s(b)(b(s)(s(s)(x1))) s(t)(t(b)(b(b)(x1))) = 0 >= 0 = s(b)(b(s)(s(b)(x1))) s(t)(t(b)(b(t)(x1))) = 0 >= 0 = s(b)(b(s)(s(t)(x1))) s(t)(t(b)(b(u)(x1))) = 0 >= 0 = s(b)(b(s)(s(u)(x1))) s(t)(t(b)(b(s)(s(f7)(x1)))) = 0 >= 0 = s(u)(u(t)(t(b)(b(f7)(x1)))) s(t)(t(b)(b(s)(s(s)(x1)))) = 0 >= 0 = s(u)(u(t)(t(b)(b(s)(x1)))) s(t)(t(b)(b(s)(s(b)(x1)))) = 0 >= 0 = s(u)(u(t)(t(b)(b(b)(x1)))) s(t)(t(b)(b(s)(s(t)(x1)))) = 0 >= 0 = s(u)(u(t)(t(b)(b(t)(x1)))) s(t)(t(b)(b(s)(s(u)(x1)))) = 0 >= 0 = s(u)(u(t)(t(b)(b(u)(x1)))) s(t)(t(u)(u(b)(x1))) = 0 >= 0 = s(u)(u(t)(t(b)(x1))) s(t)(t(u)(u(t)(x1))) = 0 >= 0 = s(u)(u(t)(t(t)(x1))) s(t)(t(u)(u(u)(x1))) = 0 >= 0 = s(u)(u(t)(t(u)(x1))) s(u)(u(b)(x1)) = 0 >= 0 = s(s)(s(b)(x1)) s(u)(u(t)(x1)) = 0 >= 0 = s(s)(s(t)(x1)) s(u)(u(u)(x1)) = 0 >= 0 = s(s)(s(u)(x1)) t(s)(s(b)(b(f7)(x1))) = 1 >= 0 = t(b)(b(s)(s(s)(s(s)(s(f7)(x1))))) t(s)(s(b)(b(s)(x1))) = 1 >= 0 = t(b)(b(s)(s(s)(s(s)(s(s)(x1))))) t(s)(s(b)(b(b)(x1))) = 1 >= 0 = t(b)(b(s)(s(s)(s(s)(s(b)(x1))))) t(s)(s(b)(b(t)(x1))) = 1 >= 0 = t(b)(b(s)(s(s)(s(s)(s(t)(x1))))) t(s)(s(b)(b(u)(x1))) = 1 >= 0 = t(b)(b(s)(s(s)(s(s)(s(u)(x1))))) t(s)(s(b)(b(s)(s(s)(x1)))) = 1 >= 0 = t(b)(b(t)(t(s)(x1))) t(s)(s(b)(b(s)(s(b)(x1)))) = 1 >= 0 = t(b)(b(t)(t(b)(x1))) t(s)(s(b)(b(s)(s(t)(x1)))) = 1 >= 0 = t(b)(b(t)(t(t)(x1))) t(s)(s(b)(b(s)(s(u)(x1)))) = 1 >= 0 = t(b)(b(t)(t(u)(x1))) t(s)(s(s)(x1)) = 1 >= 0 = t(t)(t(s)(x1)) t(s)(s(b)(x1)) = 1 >= 0 = t(t)(t(b)(x1)) t(s)(s(t)(x1)) = 1 >= 0 = t(t)(t(t)(x1)) t(s)(s(u)(x1)) = 1 >= 0 = t(t)(t(u)(x1)) b(t)(t(b)(b(f7)(x1))) = 0 >= 0 = b(b)(b(s)(s(f7)(x1))) b(t)(t(b)(b(s)(x1))) = 0 >= 0 = b(b)(b(s)(s(s)(x1))) b(t)(t(b)(b(b)(x1))) = 0 >= 0 = b(b)(b(s)(s(b)(x1))) b(t)(t(b)(b(t)(x1))) = 0 >= 0 = b(b)(b(s)(s(t)(x1))) b(t)(t(b)(b(u)(x1))) = 0 >= 0 = b(b)(b(s)(s(u)(x1))) b(t)(t(b)(b(s)(s(f7)(x1)))) = 0 >= 0 = b(u)(u(t)(t(b)(b(f7)(x1)))) b(t)(t(b)(b(s)(s(s)(x1)))) = 0 >= 0 = b(u)(u(t)(t(b)(b(s)(x1)))) b(t)(t(b)(b(s)(s(b)(x1)))) = 0 >= 0 = b(u)(u(t)(t(b)(b(b)(x1)))) b(t)(t(b)(b(s)(s(t)(x1)))) = 0 >= 0 = b(u)(u(t)(t(b)(b(t)(x1)))) b(t)(t(b)(b(s)(s(u)(x1)))) = 0 >= 0 = b(u)(u(t)(t(b)(b(u)(x1)))) t(t)(t(b)(b(f7)(x1))) = 0 >= 0 = t(b)(b(s)(s(f7)(x1))) t(t)(t(b)(b(s)(x1))) = 0 >= 0 = t(b)(b(s)(s(s)(x1))) t(t)(t(b)(b(b)(x1))) = 0 >= 0 = t(b)(b(s)(s(b)(x1))) t(t)(t(b)(b(t)(x1))) = 0 >= 0 = t(b)(b(s)(s(t)(x1))) t(t)(t(b)(b(u)(x1))) = 0 >= 0 = t(b)(b(s)(s(u)(x1))) t(t)(t(b)(b(s)(s(f7)(x1)))) = 0 >= 0 = t(u)(u(t)(t(b)(b(f7)(x1)))) t(t)(t(b)(b(s)(s(s)(x1)))) = 0 >= 0 = t(u)(u(t)(t(b)(b(s)(x1)))) t(t)(t(b)(b(s)(s(b)(x1)))) = 0 >= 0 = t(u)(u(t)(t(b)(b(b)(x1)))) t(t)(t(b)(b(s)(s(t)(x1)))) = 0 >= 0 = t(u)(u(t)(t(b)(b(t)(x1)))) t(t)(t(b)(b(s)(s(u)(x1)))) = 0 >= 0 = t(u)(u(t)(t(b)(b(u)(x1)))) t(t)(t(u)(u(b)(x1))) = 0 >= 0 = t(u)(u(t)(t(b)(x1))) t(t)(t(u)(u(t)(x1))) = 0 >= 0 = t(u)(u(t)(t(t)(x1))) t(t)(t(u)(u(u)(x1))) = 0 >= 0 = t(u)(u(t)(t(u)(x1))) b(t)(t(u)(u(b)(x1))) = 0 >= 0 = b(u)(u(t)(t(b)(x1))) b(t)(t(u)(u(t)(x1))) = 0 >= 0 = b(u)(u(t)(t(t)(x1))) b(t)(t(u)(u(u)(x1))) = 0 >= 0 = b(u)(u(t)(t(u)(x1))) b(u)(u(t)(x1)) = 0 >= 0 = b(s)(s(t)(x1)) b(u)(u(b)(x1)) = 0 >= 0 = b(s)(s(b)(x1)) b(u)(u(u)(x1)) = 0 >= 0 = b(s)(s(u)(x1)) u(t)(t(b)(b(f7)(x1))) = 0 >= 0 = u(b)(b(s)(s(f7)(x1))) u(t)(t(b)(b(s)(x1))) = 0 >= 0 = u(b)(b(s)(s(s)(x1))) u(t)(t(b)(b(b)(x1))) = 0 >= 0 = u(b)(b(s)(s(b)(x1))) u(t)(t(b)(b(t)(x1))) = 0 >= 0 = u(b)(b(s)(s(t)(x1))) u(t)(t(b)(b(u)(x1))) = 0 >= 0 = u(b)(b(s)(s(u)(x1))) u(t)(t(b)(b(s)(s(f7)(x1)))) = 0 >= 0 = u(u)(u(t)(t(b)(b(f7)(x1)))) u(t)(t(b)(b(s)(s(s)(x1)))) = 0 >= 0 = u(u)(u(t)(t(b)(b(s)(x1)))) u(t)(t(b)(b(s)(s(b)(x1)))) = 0 >= 0 = u(u)(u(t)(t(b)(b(b)(x1)))) u(t)(t(b)(b(s)(s(t)(x1)))) = 0 >= 0 = u(u)(u(t)(t(b)(b(t)(x1)))) u(t)(t(b)(b(s)(s(u)(x1)))) = 0 >= 0 = u(u)(u(t)(t(b)(b(u)(x1)))) u(t)(t(u)(u(b)(x1))) = 0 >= 0 = u(u)(u(t)(t(b)(x1))) u(t)(t(u)(u(t)(x1))) = 0 >= 0 = u(u)(u(t)(t(t)(x1))) u(t)(t(u)(u(u)(x1))) = 0 >= 0 = u(u)(u(t)(t(u)(x1))) problem: DPs: t{#,(f7)}(f7(b)(b(s)(s(s)(x1)))) -> t{#,(f7)}(f7(b)(b(s)(x1))) t{#,(f7)}(f7(b)(b(s)(s(t)(x1)))) -> t{#,(f7)}(f7(b)(b(t)(x1))) t{#,(f7)}(f7(b)(b(s)(s(u)(x1)))) -> t{#,(f7)}(f7(b)(b(u)(x1))) TRS: b(s)(s(b)(b(f7)(x1))) -> b(b)(b(s)(s(s)(s(s)(s(f7)(x1))))) b(s)(s(b)(b(s)(x1))) -> b(b)(b(s)(s(s)(s(s)(s(s)(x1))))) b(s)(s(b)(b(b)(x1))) -> b(b)(b(s)(s(s)(s(s)(s(b)(x1))))) b(s)(s(b)(b(t)(x1))) -> b(b)(b(s)(s(s)(s(s)(s(t)(x1))))) b(s)(s(b)(b(u)(x1))) -> b(b)(b(s)(s(s)(s(s)(s(u)(x1))))) b(s)(s(b)(b(s)(s(s)(x1)))) -> b(b)(b(t)(t(s)(x1))) b(s)(s(b)(b(s)(s(b)(x1)))) -> b(b)(b(t)(t(b)(x1))) b(s)(s(b)(b(s)(s(t)(x1)))) -> b(b)(b(t)(t(t)(x1))) b(s)(s(b)(b(s)(s(u)(x1)))) -> b(b)(b(t)(t(u)(x1))) s(s)(s(b)(b(f7)(x1))) -> s(b)(b(s)(s(s)(s(s)(s(f7)(x1))))) s(s)(s(b)(b(s)(x1))) -> s(b)(b(s)(s(s)(s(s)(s(s)(x1))))) s(s)(s(b)(b(b)(x1))) -> s(b)(b(s)(s(s)(s(s)(s(b)(x1))))) s(s)(s(b)(b(t)(x1))) -> s(b)(b(s)(s(s)(s(s)(s(t)(x1))))) s(s)(s(b)(b(u)(x1))) -> s(b)(b(s)(s(s)(s(s)(s(u)(x1))))) s(s)(s(b)(b(s)(s(s)(x1)))) -> s(b)(b(t)(t(s)(x1))) s(s)(s(b)(b(s)(s(b)(x1)))) -> s(b)(b(t)(t(b)(x1))) s(s)(s(b)(b(s)(s(t)(x1)))) -> s(b)(b(t)(t(t)(x1))) s(s)(s(b)(b(s)(s(u)(x1)))) -> s(b)(b(t)(t(u)(x1))) s(t)(t(b)(b(f7)(x1))) -> s(b)(b(s)(s(f7)(x1))) s(t)(t(b)(b(s)(x1))) -> s(b)(b(s)(s(s)(x1))) s(t)(t(b)(b(b)(x1))) -> s(b)(b(s)(s(b)(x1))) s(t)(t(b)(b(t)(x1))) -> s(b)(b(s)(s(t)(x1))) s(t)(t(b)(b(u)(x1))) -> s(b)(b(s)(s(u)(x1))) s(t)(t(b)(b(s)(s(f7)(x1)))) -> s(u)(u(t)(t(b)(b(f7)(x1)))) s(t)(t(b)(b(s)(s(s)(x1)))) -> s(u)(u(t)(t(b)(b(s)(x1)))) s(t)(t(b)(b(s)(s(b)(x1)))) -> s(u)(u(t)(t(b)(b(b)(x1)))) s(t)(t(b)(b(s)(s(t)(x1)))) -> s(u)(u(t)(t(b)(b(t)(x1)))) s(t)(t(b)(b(s)(s(u)(x1)))) -> s(u)(u(t)(t(b)(b(u)(x1)))) s(t)(t(u)(u(b)(x1))) -> s(u)(u(t)(t(b)(x1))) s(t)(t(u)(u(t)(x1))) -> s(u)(u(t)(t(t)(x1))) s(t)(t(u)(u(u)(x1))) -> s(u)(u(t)(t(u)(x1))) s(u)(u(b)(x1)) -> s(s)(s(b)(x1)) s(u)(u(t)(x1)) -> s(s)(s(t)(x1)) s(u)(u(u)(x1)) -> s(s)(s(u)(x1)) t(s)(s(b)(b(f7)(x1))) -> t(b)(b(s)(s(s)(s(s)(s(f7)(x1))))) t(s)(s(b)(b(s)(x1))) -> t(b)(b(s)(s(s)(s(s)(s(s)(x1))))) t(s)(s(b)(b(b)(x1))) -> t(b)(b(s)(s(s)(s(s)(s(b)(x1))))) t(s)(s(b)(b(t)(x1))) -> t(b)(b(s)(s(s)(s(s)(s(t)(x1))))) t(s)(s(b)(b(u)(x1))) -> t(b)(b(s)(s(s)(s(s)(s(u)(x1))))) t(s)(s(b)(b(s)(s(s)(x1)))) -> t(b)(b(t)(t(s)(x1))) t(s)(s(b)(b(s)(s(b)(x1)))) -> t(b)(b(t)(t(b)(x1))) t(s)(s(b)(b(s)(s(t)(x1)))) -> t(b)(b(t)(t(t)(x1))) t(s)(s(b)(b(s)(s(u)(x1)))) -> t(b)(b(t)(t(u)(x1))) t(s)(s(s)(x1)) -> t(t)(t(s)(x1)) t(s)(s(b)(x1)) -> t(t)(t(b)(x1)) t(s)(s(t)(x1)) -> t(t)(t(t)(x1)) t(s)(s(u)(x1)) -> t(t)(t(u)(x1)) b(t)(t(b)(b(f7)(x1))) -> b(b)(b(s)(s(f7)(x1))) b(t)(t(b)(b(s)(x1))) -> b(b)(b(s)(s(s)(x1))) b(t)(t(b)(b(b)(x1))) -> b(b)(b(s)(s(b)(x1))) b(t)(t(b)(b(t)(x1))) -> b(b)(b(s)(s(t)(x1))) b(t)(t(b)(b(u)(x1))) -> b(b)(b(s)(s(u)(x1))) b(t)(t(b)(b(s)(s(f7)(x1)))) -> b(u)(u(t)(t(b)(b(f7)(x1)))) b(t)(t(b)(b(s)(s(s)(x1)))) -> b(u)(u(t)(t(b)(b(s)(x1)))) b(t)(t(b)(b(s)(s(b)(x1)))) -> b(u)(u(t)(t(b)(b(b)(x1)))) b(t)(t(b)(b(s)(s(t)(x1)))) -> b(u)(u(t)(t(b)(b(t)(x1)))) b(t)(t(b)(b(s)(s(u)(x1)))) -> b(u)(u(t)(t(b)(b(u)(x1)))) t(t)(t(b)(b(f7)(x1))) -> t(b)(b(s)(s(f7)(x1))) t(t)(t(b)(b(s)(x1))) -> t(b)(b(s)(s(s)(x1))) t(t)(t(b)(b(b)(x1))) -> t(b)(b(s)(s(b)(x1))) t(t)(t(b)(b(t)(x1))) -> t(b)(b(s)(s(t)(x1))) t(t)(t(b)(b(u)(x1))) -> t(b)(b(s)(s(u)(x1))) t(t)(t(b)(b(s)(s(f7)(x1)))) -> t(u)(u(t)(t(b)(b(f7)(x1)))) t(t)(t(b)(b(s)(s(s)(x1)))) -> t(u)(u(t)(t(b)(b(s)(x1)))) t(t)(t(b)(b(s)(s(b)(x1)))) -> t(u)(u(t)(t(b)(b(b)(x1)))) t(t)(t(b)(b(s)(s(t)(x1)))) -> t(u)(u(t)(t(b)(b(t)(x1)))) t(t)(t(b)(b(s)(s(u)(x1)))) -> t(u)(u(t)(t(b)(b(u)(x1)))) t(t)(t(u)(u(b)(x1))) -> t(u)(u(t)(t(b)(x1))) t(t)(t(u)(u(t)(x1))) -> t(u)(u(t)(t(t)(x1))) t(t)(t(u)(u(u)(x1))) -> t(u)(u(t)(t(u)(x1))) b(t)(t(u)(u(b)(x1))) -> b(u)(u(t)(t(b)(x1))) b(t)(t(u)(u(t)(x1))) -> b(u)(u(t)(t(t)(x1))) b(t)(t(u)(u(u)(x1))) -> b(u)(u(t)(t(u)(x1))) b(u)(u(t)(x1)) -> b(s)(s(t)(x1)) b(u)(u(b)(x1)) -> b(s)(s(b)(x1)) b(u)(u(u)(x1)) -> b(s)(s(u)(x1)) u(t)(t(b)(b(f7)(x1))) -> u(b)(b(s)(s(f7)(x1))) u(t)(t(b)(b(s)(x1))) -> u(b)(b(s)(s(s)(x1))) u(t)(t(b)(b(b)(x1))) -> u(b)(b(s)(s(b)(x1))) u(t)(t(b)(b(t)(x1))) -> u(b)(b(s)(s(t)(x1))) u(t)(t(b)(b(u)(x1))) -> u(b)(b(s)(s(u)(x1))) u(t)(t(b)(b(s)(s(f7)(x1)))) -> u(u)(u(t)(t(b)(b(f7)(x1)))) u(t)(t(b)(b(s)(s(s)(x1)))) -> u(u)(u(t)(t(b)(b(s)(x1)))) u(t)(t(b)(b(s)(s(b)(x1)))) -> u(u)(u(t)(t(b)(b(b)(x1)))) u(t)(t(b)(b(s)(s(t)(x1)))) -> u(u)(u(t)(t(b)(b(t)(x1)))) u(t)(t(b)(b(s)(s(u)(x1)))) -> u(u)(u(t)(t(b)(b(u)(x1)))) u(t)(t(u)(u(b)(x1))) -> u(u)(u(t)(t(b)(x1))) u(t)(t(u)(u(t)(x1))) -> u(u)(u(t)(t(t)(x1))) u(t)(t(u)(u(u)(x1))) -> u(u)(u(t)(t(u)(x1))) Polynomial Interpretation Processor: dimension: 1 usable rules: b(s)(s(b)(b(f7)(x1))) -> b(b)(b(s)(s(s)(s(s)(s(f7)(x1))))) b(s)(s(b)(b(s)(x1))) -> b(b)(b(s)(s(s)(s(s)(s(s)(x1))))) b(s)(s(b)(b(b)(x1))) -> b(b)(b(s)(s(s)(s(s)(s(b)(x1))))) b(s)(s(b)(b(t)(x1))) -> b(b)(b(s)(s(s)(s(s)(s(t)(x1))))) b(s)(s(b)(b(u)(x1))) -> b(b)(b(s)(s(s)(s(s)(s(u)(x1))))) b(s)(s(b)(b(s)(s(s)(x1)))) -> b(b)(b(t)(t(s)(x1))) b(s)(s(b)(b(s)(s(b)(x1)))) -> b(b)(b(t)(t(b)(x1))) b(s)(s(b)(b(s)(s(t)(x1)))) -> b(b)(b(t)(t(t)(x1))) b(s)(s(b)(b(s)(s(u)(x1)))) -> b(b)(b(t)(t(u)(x1))) s(s)(s(b)(b(f7)(x1))) -> s(b)(b(s)(s(s)(s(s)(s(f7)(x1))))) s(s)(s(b)(b(s)(x1))) -> s(b)(b(s)(s(s)(s(s)(s(s)(x1))))) s(s)(s(b)(b(b)(x1))) -> s(b)(b(s)(s(s)(s(s)(s(b)(x1))))) s(s)(s(b)(b(t)(x1))) -> s(b)(b(s)(s(s)(s(s)(s(t)(x1))))) s(s)(s(b)(b(u)(x1))) -> s(b)(b(s)(s(s)(s(s)(s(u)(x1))))) s(s)(s(b)(b(s)(s(s)(x1)))) -> s(b)(b(t)(t(s)(x1))) s(s)(s(b)(b(s)(s(b)(x1)))) -> s(b)(b(t)(t(b)(x1))) s(s)(s(b)(b(s)(s(t)(x1)))) -> s(b)(b(t)(t(t)(x1))) s(s)(s(b)(b(s)(s(u)(x1)))) -> s(b)(b(t)(t(u)(x1))) s(t)(t(b)(b(f7)(x1))) -> s(b)(b(s)(s(f7)(x1))) s(t)(t(b)(b(s)(x1))) -> s(b)(b(s)(s(s)(x1))) s(t)(t(b)(b(b)(x1))) -> s(b)(b(s)(s(b)(x1))) s(t)(t(b)(b(t)(x1))) -> s(b)(b(s)(s(t)(x1))) s(t)(t(b)(b(u)(x1))) -> s(b)(b(s)(s(u)(x1))) s(t)(t(b)(b(s)(s(f7)(x1)))) -> s(u)(u(t)(t(b)(b(f7)(x1)))) s(t)(t(b)(b(s)(s(s)(x1)))) -> s(u)(u(t)(t(b)(b(s)(x1)))) s(t)(t(b)(b(s)(s(b)(x1)))) -> s(u)(u(t)(t(b)(b(b)(x1)))) s(t)(t(b)(b(s)(s(t)(x1)))) -> s(u)(u(t)(t(b)(b(t)(x1)))) s(t)(t(b)(b(s)(s(u)(x1)))) -> s(u)(u(t)(t(b)(b(u)(x1)))) s(t)(t(u)(u(b)(x1))) -> s(u)(u(t)(t(b)(x1))) s(t)(t(u)(u(t)(x1))) -> s(u)(u(t)(t(t)(x1))) s(t)(t(u)(u(u)(x1))) -> s(u)(u(t)(t(u)(x1))) s(u)(u(b)(x1)) -> s(s)(s(b)(x1)) s(u)(u(t)(x1)) -> s(s)(s(t)(x1)) s(u)(u(u)(x1)) -> s(s)(s(u)(x1)) b(t)(t(b)(b(f7)(x1))) -> b(b)(b(s)(s(f7)(x1))) b(t)(t(b)(b(s)(x1))) -> b(b)(b(s)(s(s)(x1))) b(t)(t(b)(b(b)(x1))) -> b(b)(b(s)(s(b)(x1))) b(t)(t(b)(b(t)(x1))) -> b(b)(b(s)(s(t)(x1))) b(t)(t(b)(b(u)(x1))) -> b(b)(b(s)(s(u)(x1))) b(t)(t(b)(b(s)(s(f7)(x1)))) -> b(u)(u(t)(t(b)(b(f7)(x1)))) b(t)(t(b)(b(s)(s(s)(x1)))) -> b(u)(u(t)(t(b)(b(s)(x1)))) b(t)(t(b)(b(s)(s(b)(x1)))) -> b(u)(u(t)(t(b)(b(b)(x1)))) b(t)(t(b)(b(s)(s(t)(x1)))) -> b(u)(u(t)(t(b)(b(t)(x1)))) b(t)(t(b)(b(s)(s(u)(x1)))) -> b(u)(u(t)(t(b)(b(u)(x1)))) t(t)(t(b)(b(f7)(x1))) -> t(b)(b(s)(s(f7)(x1))) t(t)(t(b)(b(s)(x1))) -> t(b)(b(s)(s(s)(x1))) t(t)(t(b)(b(b)(x1))) -> t(b)(b(s)(s(b)(x1))) t(t)(t(b)(b(t)(x1))) -> t(b)(b(s)(s(t)(x1))) t(t)(t(b)(b(u)(x1))) -> t(b)(b(s)(s(u)(x1))) t(t)(t(b)(b(s)(s(f7)(x1)))) -> t(u)(u(t)(t(b)(b(f7)(x1)))) t(t)(t(b)(b(s)(s(s)(x1)))) -> t(u)(u(t)(t(b)(b(s)(x1)))) t(t)(t(b)(b(s)(s(b)(x1)))) -> t(u)(u(t)(t(b)(b(b)(x1)))) t(t)(t(b)(b(s)(s(t)(x1)))) -> t(u)(u(t)(t(b)(b(t)(x1)))) t(t)(t(b)(b(s)(s(u)(x1)))) -> t(u)(u(t)(t(b)(b(u)(x1)))) t(t)(t(u)(u(b)(x1))) -> t(u)(u(t)(t(b)(x1))) t(t)(t(u)(u(t)(x1))) -> t(u)(u(t)(t(t)(x1))) t(t)(t(u)(u(u)(x1))) -> t(u)(u(t)(t(u)(x1))) b(t)(t(u)(u(b)(x1))) -> b(u)(u(t)(t(b)(x1))) b(t)(t(u)(u(t)(x1))) -> b(u)(u(t)(t(t)(x1))) b(t)(t(u)(u(u)(x1))) -> b(u)(u(t)(t(u)(x1))) b(u)(u(t)(x1)) -> b(s)(s(t)(x1)) b(u)(u(b)(x1)) -> b(s)(s(b)(x1)) b(u)(u(u)(x1)) -> b(s)(s(u)(x1)) u(t)(t(b)(b(f7)(x1))) -> u(b)(b(s)(s(f7)(x1))) u(t)(t(b)(b(s)(x1))) -> u(b)(b(s)(s(s)(x1))) u(t)(t(b)(b(b)(x1))) -> u(b)(b(s)(s(b)(x1))) u(t)(t(b)(b(t)(x1))) -> u(b)(b(s)(s(t)(x1))) u(t)(t(b)(b(u)(x1))) -> u(b)(b(s)(s(u)(x1))) u(t)(t(b)(b(s)(s(f7)(x1)))) -> u(u)(u(t)(t(b)(b(f7)(x1)))) u(t)(t(b)(b(s)(s(s)(x1)))) -> u(u)(u(t)(t(b)(b(s)(x1)))) u(t)(t(b)(b(s)(s(b)(x1)))) -> u(u)(u(t)(t(b)(b(b)(x1)))) u(t)(t(b)(b(s)(s(t)(x1)))) -> u(u)(u(t)(t(b)(b(t)(x1)))) u(t)(t(b)(b(s)(s(u)(x1)))) -> u(u)(u(t)(t(b)(b(u)(x1)))) u(t)(t(u)(u(b)(x1))) -> u(u)(u(t)(t(b)(x1))) u(t)(t(u)(u(t)(x1))) -> u(u)(u(t)(t(t)(x1))) u(t)(t(u)(u(u)(x1))) -> u(u)(u(t)(t(u)(x1))) interpretation: [u(u)](x0) = x0 + 1, [u(t)](x0) = x0 + 1, [t(u)](x0) = x0 + 1, [t(t)](x0) = x0 + 1, [u(b)](x0) = x0 + 1, [t(b)](x0) = x0 + 1, [t(s)](x0) = 0, [b(u)](x0) = x0, [s(u)](x0) = x0 + 1, [b(t)](x0) = x0, [s(t)](x0) = x0 + 1, [b(b)](x0) = 0, [s(b)](x0) = 1, [s(s)](x0) = x0 + 1, [b(f7)](x0) = 0, [s(f7)](x0) = 1, [b(s)](x0) = x0, [f7(b)](x0) = x0, [t{#,(f7)}](x0) = x0 orientation: t{#,(f7)}(f7(b)(b(s)(s(s)(x1)))) = x1 + 1 >= x1 = t{#,(f7)}(f7(b)(b(s)(x1))) t{#,(f7)}(f7(b)(b(s)(s(t)(x1)))) = x1 + 1 >= x1 = t{#,(f7)}(f7(b)(b(t)(x1))) t{#,(f7)}(f7(b)(b(s)(s(u)(x1)))) = x1 + 1 >= x1 = t{#,(f7)}(f7(b)(b(u)(x1))) b(s)(s(b)(b(f7)(x1))) = 1 >= 0 = b(b)(b(s)(s(s)(s(s)(s(f7)(x1))))) b(s)(s(b)(b(s)(x1))) = 1 >= 0 = b(b)(b(s)(s(s)(s(s)(s(s)(x1))))) b(s)(s(b)(b(b)(x1))) = 1 >= 0 = b(b)(b(s)(s(s)(s(s)(s(b)(x1))))) b(s)(s(b)(b(t)(x1))) = 1 >= 0 = b(b)(b(s)(s(s)(s(s)(s(t)(x1))))) b(s)(s(b)(b(u)(x1))) = 1 >= 0 = b(b)(b(s)(s(s)(s(s)(s(u)(x1))))) b(s)(s(b)(b(s)(s(s)(x1)))) = 1 >= 0 = b(b)(b(t)(t(s)(x1))) b(s)(s(b)(b(s)(s(b)(x1)))) = 1 >= 0 = b(b)(b(t)(t(b)(x1))) b(s)(s(b)(b(s)(s(t)(x1)))) = 1 >= 0 = b(b)(b(t)(t(t)(x1))) b(s)(s(b)(b(s)(s(u)(x1)))) = 1 >= 0 = b(b)(b(t)(t(u)(x1))) s(s)(s(b)(b(f7)(x1))) = 2 >= 1 = s(b)(b(s)(s(s)(s(s)(s(f7)(x1))))) s(s)(s(b)(b(s)(x1))) = 2 >= 1 = s(b)(b(s)(s(s)(s(s)(s(s)(x1))))) s(s)(s(b)(b(b)(x1))) = 2 >= 1 = s(b)(b(s)(s(s)(s(s)(s(b)(x1))))) s(s)(s(b)(b(t)(x1))) = 2 >= 1 = s(b)(b(s)(s(s)(s(s)(s(t)(x1))))) s(s)(s(b)(b(u)(x1))) = 2 >= 1 = s(b)(b(s)(s(s)(s(s)(s(u)(x1))))) s(s)(s(b)(b(s)(s(s)(x1)))) = 2 >= 1 = s(b)(b(t)(t(s)(x1))) s(s)(s(b)(b(s)(s(b)(x1)))) = 2 >= 1 = s(b)(b(t)(t(b)(x1))) s(s)(s(b)(b(s)(s(t)(x1)))) = 2 >= 1 = s(b)(b(t)(t(t)(x1))) s(s)(s(b)(b(s)(s(u)(x1)))) = 2 >= 1 = s(b)(b(t)(t(u)(x1))) s(t)(t(b)(b(f7)(x1))) = 2 >= 1 = s(b)(b(s)(s(f7)(x1))) s(t)(t(b)(b(s)(x1))) = x1 + 2 >= 1 = s(b)(b(s)(s(s)(x1))) s(t)(t(b)(b(b)(x1))) = 2 >= 1 = s(b)(b(s)(s(b)(x1))) s(t)(t(b)(b(t)(x1))) = x1 + 2 >= 1 = s(b)(b(s)(s(t)(x1))) s(t)(t(b)(b(u)(x1))) = x1 + 2 >= 1 = s(b)(b(s)(s(u)(x1))) s(t)(t(b)(b(s)(s(f7)(x1)))) = 3 >= 3 = s(u)(u(t)(t(b)(b(f7)(x1)))) s(t)(t(b)(b(s)(s(s)(x1)))) = x1 + 3 >= x1 + 3 = s(u)(u(t)(t(b)(b(s)(x1)))) s(t)(t(b)(b(s)(s(b)(x1)))) = 3 >= 3 = s(u)(u(t)(t(b)(b(b)(x1)))) s(t)(t(b)(b(s)(s(t)(x1)))) = x1 + 3 >= x1 + 3 = s(u)(u(t)(t(b)(b(t)(x1)))) s(t)(t(b)(b(s)(s(u)(x1)))) = x1 + 3 >= x1 + 3 = s(u)(u(t)(t(b)(b(u)(x1)))) s(t)(t(u)(u(b)(x1))) = x1 + 3 >= x1 + 3 = s(u)(u(t)(t(b)(x1))) s(t)(t(u)(u(t)(x1))) = x1 + 3 >= x1 + 3 = s(u)(u(t)(t(t)(x1))) s(t)(t(u)(u(u)(x1))) = x1 + 3 >= x1 + 3 = s(u)(u(t)(t(u)(x1))) s(u)(u(b)(x1)) = x1 + 2 >= 2 = s(s)(s(b)(x1)) s(u)(u(t)(x1)) = x1 + 2 >= x1 + 2 = s(s)(s(t)(x1)) s(u)(u(u)(x1)) = x1 + 2 >= x1 + 2 = s(s)(s(u)(x1)) t(s)(s(b)(b(f7)(x1))) = 0 >= 4 = t(b)(b(s)(s(s)(s(s)(s(f7)(x1))))) t(s)(s(b)(b(s)(x1))) = 0 >= x1 + 4 = t(b)(b(s)(s(s)(s(s)(s(s)(x1))))) t(s)(s(b)(b(b)(x1))) = 0 >= 4 = t(b)(b(s)(s(s)(s(s)(s(b)(x1))))) t(s)(s(b)(b(t)(x1))) = 0 >= x1 + 4 = t(b)(b(s)(s(s)(s(s)(s(t)(x1))))) t(s)(s(b)(b(u)(x1))) = 0 >= x1 + 4 = t(b)(b(s)(s(s)(s(s)(s(u)(x1))))) t(s)(s(b)(b(s)(s(s)(x1)))) = 0 >= 1 = t(b)(b(t)(t(s)(x1))) t(s)(s(b)(b(s)(s(b)(x1)))) = 0 >= x1 + 2 = t(b)(b(t)(t(b)(x1))) t(s)(s(b)(b(s)(s(t)(x1)))) = 0 >= x1 + 2 = t(b)(b(t)(t(t)(x1))) t(s)(s(b)(b(s)(s(u)(x1)))) = 0 >= x1 + 2 = t(b)(b(t)(t(u)(x1))) t(s)(s(s)(x1)) = 0 >= 1 = t(t)(t(s)(x1)) t(s)(s(b)(x1)) = 0 >= x1 + 2 = t(t)(t(b)(x1)) t(s)(s(t)(x1)) = 0 >= x1 + 2 = t(t)(t(t)(x1)) t(s)(s(u)(x1)) = 0 >= x1 + 2 = t(t)(t(u)(x1)) b(t)(t(b)(b(f7)(x1))) = 1 >= 0 = b(b)(b(s)(s(f7)(x1))) b(t)(t(b)(b(s)(x1))) = x1 + 1 >= 0 = b(b)(b(s)(s(s)(x1))) b(t)(t(b)(b(b)(x1))) = 1 >= 0 = b(b)(b(s)(s(b)(x1))) b(t)(t(b)(b(t)(x1))) = x1 + 1 >= 0 = b(b)(b(s)(s(t)(x1))) b(t)(t(b)(b(u)(x1))) = x1 + 1 >= 0 = b(b)(b(s)(s(u)(x1))) b(t)(t(b)(b(s)(s(f7)(x1)))) = 2 >= 2 = b(u)(u(t)(t(b)(b(f7)(x1)))) b(t)(t(b)(b(s)(s(s)(x1)))) = x1 + 2 >= x1 + 2 = b(u)(u(t)(t(b)(b(s)(x1)))) b(t)(t(b)(b(s)(s(b)(x1)))) = 2 >= 2 = b(u)(u(t)(t(b)(b(b)(x1)))) b(t)(t(b)(b(s)(s(t)(x1)))) = x1 + 2 >= x1 + 2 = b(u)(u(t)(t(b)(b(t)(x1)))) b(t)(t(b)(b(s)(s(u)(x1)))) = x1 + 2 >= x1 + 2 = b(u)(u(t)(t(b)(b(u)(x1)))) t(t)(t(b)(b(f7)(x1))) = 2 >= 2 = t(b)(b(s)(s(f7)(x1))) t(t)(t(b)(b(s)(x1))) = x1 + 2 >= x1 + 2 = t(b)(b(s)(s(s)(x1))) t(t)(t(b)(b(b)(x1))) = 2 >= 2 = t(b)(b(s)(s(b)(x1))) t(t)(t(b)(b(t)(x1))) = x1 + 2 >= x1 + 2 = t(b)(b(s)(s(t)(x1))) t(t)(t(b)(b(u)(x1))) = x1 + 2 >= x1 + 2 = t(b)(b(s)(s(u)(x1))) t(t)(t(b)(b(s)(s(f7)(x1)))) = 3 >= 3 = t(u)(u(t)(t(b)(b(f7)(x1)))) t(t)(t(b)(b(s)(s(s)(x1)))) = x1 + 3 >= x1 + 3 = t(u)(u(t)(t(b)(b(s)(x1)))) t(t)(t(b)(b(s)(s(b)(x1)))) = 3 >= 3 = t(u)(u(t)(t(b)(b(b)(x1)))) t(t)(t(b)(b(s)(s(t)(x1)))) = x1 + 3 >= x1 + 3 = t(u)(u(t)(t(b)(b(t)(x1)))) t(t)(t(b)(b(s)(s(u)(x1)))) = x1 + 3 >= x1 + 3 = t(u)(u(t)(t(b)(b(u)(x1)))) t(t)(t(u)(u(b)(x1))) = x1 + 3 >= x1 + 3 = t(u)(u(t)(t(b)(x1))) t(t)(t(u)(u(t)(x1))) = x1 + 3 >= x1 + 3 = t(u)(u(t)(t(t)(x1))) t(t)(t(u)(u(u)(x1))) = x1 + 3 >= x1 + 3 = t(u)(u(t)(t(u)(x1))) b(t)(t(u)(u(b)(x1))) = x1 + 2 >= x1 + 2 = b(u)(u(t)(t(b)(x1))) b(t)(t(u)(u(t)(x1))) = x1 + 2 >= x1 + 2 = b(u)(u(t)(t(t)(x1))) b(t)(t(u)(u(u)(x1))) = x1 + 2 >= x1 + 2 = b(u)(u(t)(t(u)(x1))) b(u)(u(t)(x1)) = x1 + 1 >= x1 + 1 = b(s)(s(t)(x1)) b(u)(u(b)(x1)) = x1 + 1 >= 1 = b(s)(s(b)(x1)) b(u)(u(u)(x1)) = x1 + 1 >= x1 + 1 = b(s)(s(u)(x1)) u(t)(t(b)(b(f7)(x1))) = 2 >= 2 = u(b)(b(s)(s(f7)(x1))) u(t)(t(b)(b(s)(x1))) = x1 + 2 >= x1 + 2 = u(b)(b(s)(s(s)(x1))) u(t)(t(b)(b(b)(x1))) = 2 >= 2 = u(b)(b(s)(s(b)(x1))) u(t)(t(b)(b(t)(x1))) = x1 + 2 >= x1 + 2 = u(b)(b(s)(s(t)(x1))) u(t)(t(b)(b(u)(x1))) = x1 + 2 >= x1 + 2 = u(b)(b(s)(s(u)(x1))) u(t)(t(b)(b(s)(s(f7)(x1)))) = 3 >= 3 = u(u)(u(t)(t(b)(b(f7)(x1)))) u(t)(t(b)(b(s)(s(s)(x1)))) = x1 + 3 >= x1 + 3 = u(u)(u(t)(t(b)(b(s)(x1)))) u(t)(t(b)(b(s)(s(b)(x1)))) = 3 >= 3 = u(u)(u(t)(t(b)(b(b)(x1)))) u(t)(t(b)(b(s)(s(t)(x1)))) = x1 + 3 >= x1 + 3 = u(u)(u(t)(t(b)(b(t)(x1)))) u(t)(t(b)(b(s)(s(u)(x1)))) = x1 + 3 >= x1 + 3 = u(u)(u(t)(t(b)(b(u)(x1)))) u(t)(t(u)(u(b)(x1))) = x1 + 3 >= x1 + 3 = u(u)(u(t)(t(b)(x1))) u(t)(t(u)(u(t)(x1))) = x1 + 3 >= x1 + 3 = u(u)(u(t)(t(t)(x1))) u(t)(t(u)(u(u)(x1))) = x1 + 3 >= x1 + 3 = u(u)(u(t)(t(u)(x1))) problem: DPs: TRS: b(s)(s(b)(b(f7)(x1))) -> b(b)(b(s)(s(s)(s(s)(s(f7)(x1))))) b(s)(s(b)(b(s)(x1))) -> b(b)(b(s)(s(s)(s(s)(s(s)(x1))))) b(s)(s(b)(b(b)(x1))) -> b(b)(b(s)(s(s)(s(s)(s(b)(x1))))) b(s)(s(b)(b(t)(x1))) -> b(b)(b(s)(s(s)(s(s)(s(t)(x1))))) b(s)(s(b)(b(u)(x1))) -> b(b)(b(s)(s(s)(s(s)(s(u)(x1))))) b(s)(s(b)(b(s)(s(s)(x1)))) -> b(b)(b(t)(t(s)(x1))) b(s)(s(b)(b(s)(s(b)(x1)))) -> b(b)(b(t)(t(b)(x1))) b(s)(s(b)(b(s)(s(t)(x1)))) -> b(b)(b(t)(t(t)(x1))) b(s)(s(b)(b(s)(s(u)(x1)))) -> b(b)(b(t)(t(u)(x1))) s(s)(s(b)(b(f7)(x1))) -> s(b)(b(s)(s(s)(s(s)(s(f7)(x1))))) s(s)(s(b)(b(s)(x1))) -> s(b)(b(s)(s(s)(s(s)(s(s)(x1))))) s(s)(s(b)(b(b)(x1))) -> s(b)(b(s)(s(s)(s(s)(s(b)(x1))))) s(s)(s(b)(b(t)(x1))) -> s(b)(b(s)(s(s)(s(s)(s(t)(x1))))) s(s)(s(b)(b(u)(x1))) -> s(b)(b(s)(s(s)(s(s)(s(u)(x1))))) s(s)(s(b)(b(s)(s(s)(x1)))) -> s(b)(b(t)(t(s)(x1))) s(s)(s(b)(b(s)(s(b)(x1)))) -> s(b)(b(t)(t(b)(x1))) s(s)(s(b)(b(s)(s(t)(x1)))) -> s(b)(b(t)(t(t)(x1))) s(s)(s(b)(b(s)(s(u)(x1)))) -> s(b)(b(t)(t(u)(x1))) s(t)(t(b)(b(f7)(x1))) -> s(b)(b(s)(s(f7)(x1))) s(t)(t(b)(b(s)(x1))) -> s(b)(b(s)(s(s)(x1))) s(t)(t(b)(b(b)(x1))) -> s(b)(b(s)(s(b)(x1))) s(t)(t(b)(b(t)(x1))) -> s(b)(b(s)(s(t)(x1))) s(t)(t(b)(b(u)(x1))) -> s(b)(b(s)(s(u)(x1))) s(t)(t(b)(b(s)(s(f7)(x1)))) -> s(u)(u(t)(t(b)(b(f7)(x1)))) s(t)(t(b)(b(s)(s(s)(x1)))) -> s(u)(u(t)(t(b)(b(s)(x1)))) s(t)(t(b)(b(s)(s(b)(x1)))) -> s(u)(u(t)(t(b)(b(b)(x1)))) s(t)(t(b)(b(s)(s(t)(x1)))) -> s(u)(u(t)(t(b)(b(t)(x1)))) s(t)(t(b)(b(s)(s(u)(x1)))) -> s(u)(u(t)(t(b)(b(u)(x1)))) s(t)(t(u)(u(b)(x1))) -> s(u)(u(t)(t(b)(x1))) s(t)(t(u)(u(t)(x1))) -> s(u)(u(t)(t(t)(x1))) s(t)(t(u)(u(u)(x1))) -> s(u)(u(t)(t(u)(x1))) s(u)(u(b)(x1)) -> s(s)(s(b)(x1)) s(u)(u(t)(x1)) -> s(s)(s(t)(x1)) s(u)(u(u)(x1)) -> s(s)(s(u)(x1)) t(s)(s(b)(b(f7)(x1))) -> t(b)(b(s)(s(s)(s(s)(s(f7)(x1))))) t(s)(s(b)(b(s)(x1))) -> t(b)(b(s)(s(s)(s(s)(s(s)(x1))))) t(s)(s(b)(b(b)(x1))) -> t(b)(b(s)(s(s)(s(s)(s(b)(x1))))) t(s)(s(b)(b(t)(x1))) -> t(b)(b(s)(s(s)(s(s)(s(t)(x1))))) t(s)(s(b)(b(u)(x1))) -> t(b)(b(s)(s(s)(s(s)(s(u)(x1))))) t(s)(s(b)(b(s)(s(s)(x1)))) -> t(b)(b(t)(t(s)(x1))) t(s)(s(b)(b(s)(s(b)(x1)))) -> t(b)(b(t)(t(b)(x1))) t(s)(s(b)(b(s)(s(t)(x1)))) -> t(b)(b(t)(t(t)(x1))) t(s)(s(b)(b(s)(s(u)(x1)))) -> t(b)(b(t)(t(u)(x1))) t(s)(s(s)(x1)) -> t(t)(t(s)(x1)) t(s)(s(b)(x1)) -> t(t)(t(b)(x1)) t(s)(s(t)(x1)) -> t(t)(t(t)(x1)) t(s)(s(u)(x1)) -> t(t)(t(u)(x1)) b(t)(t(b)(b(f7)(x1))) -> b(b)(b(s)(s(f7)(x1))) b(t)(t(b)(b(s)(x1))) -> b(b)(b(s)(s(s)(x1))) b(t)(t(b)(b(b)(x1))) -> b(b)(b(s)(s(b)(x1))) b(t)(t(b)(b(t)(x1))) -> b(b)(b(s)(s(t)(x1))) b(t)(t(b)(b(u)(x1))) -> b(b)(b(s)(s(u)(x1))) b(t)(t(b)(b(s)(s(f7)(x1)))) -> b(u)(u(t)(t(b)(b(f7)(x1)))) b(t)(t(b)(b(s)(s(s)(x1)))) -> b(u)(u(t)(t(b)(b(s)(x1)))) b(t)(t(b)(b(s)(s(b)(x1)))) -> b(u)(u(t)(t(b)(b(b)(x1)))) b(t)(t(b)(b(s)(s(t)(x1)))) -> b(u)(u(t)(t(b)(b(t)(x1)))) b(t)(t(b)(b(s)(s(u)(x1)))) -> b(u)(u(t)(t(b)(b(u)(x1)))) t(t)(t(b)(b(f7)(x1))) -> t(b)(b(s)(s(f7)(x1))) t(t)(t(b)(b(s)(x1))) -> t(b)(b(s)(s(s)(x1))) t(t)(t(b)(b(b)(x1))) -> t(b)(b(s)(s(b)(x1))) t(t)(t(b)(b(t)(x1))) -> t(b)(b(s)(s(t)(x1))) t(t)(t(b)(b(u)(x1))) -> t(b)(b(s)(s(u)(x1))) t(t)(t(b)(b(s)(s(f7)(x1)))) -> t(u)(u(t)(t(b)(b(f7)(x1)))) t(t)(t(b)(b(s)(s(s)(x1)))) -> t(u)(u(t)(t(b)(b(s)(x1)))) t(t)(t(b)(b(s)(s(b)(x1)))) -> t(u)(u(t)(t(b)(b(b)(x1)))) t(t)(t(b)(b(s)(s(t)(x1)))) -> t(u)(u(t)(t(b)(b(t)(x1)))) t(t)(t(b)(b(s)(s(u)(x1)))) -> t(u)(u(t)(t(b)(b(u)(x1)))) t(t)(t(u)(u(b)(x1))) -> t(u)(u(t)(t(b)(x1))) t(t)(t(u)(u(t)(x1))) -> t(u)(u(t)(t(t)(x1))) t(t)(t(u)(u(u)(x1))) -> t(u)(u(t)(t(u)(x1))) b(t)(t(u)(u(b)(x1))) -> b(u)(u(t)(t(b)(x1))) b(t)(t(u)(u(t)(x1))) -> b(u)(u(t)(t(t)(x1))) b(t)(t(u)(u(u)(x1))) -> b(u)(u(t)(t(u)(x1))) b(u)(u(t)(x1)) -> b(s)(s(t)(x1)) b(u)(u(b)(x1)) -> b(s)(s(b)(x1)) b(u)(u(u)(x1)) -> b(s)(s(u)(x1)) u(t)(t(b)(b(f7)(x1))) -> u(b)(b(s)(s(f7)(x1))) u(t)(t(b)(b(s)(x1))) -> u(b)(b(s)(s(s)(x1))) u(t)(t(b)(b(b)(x1))) -> u(b)(b(s)(s(b)(x1))) u(t)(t(b)(b(t)(x1))) -> u(b)(b(s)(s(t)(x1))) u(t)(t(b)(b(u)(x1))) -> u(b)(b(s)(s(u)(x1))) u(t)(t(b)(b(s)(s(f7)(x1)))) -> u(u)(u(t)(t(b)(b(f7)(x1)))) u(t)(t(b)(b(s)(s(s)(x1)))) -> u(u)(u(t)(t(b)(b(s)(x1)))) u(t)(t(b)(b(s)(s(b)(x1)))) -> u(u)(u(t)(t(b)(b(b)(x1)))) u(t)(t(b)(b(s)(s(t)(x1)))) -> u(u)(u(t)(t(b)(b(t)(x1)))) u(t)(t(b)(b(s)(s(u)(x1)))) -> u(u)(u(t)(t(b)(b(u)(x1)))) u(t)(t(u)(u(b)(x1))) -> u(u)(u(t)(t(b)(x1))) u(t)(t(u)(u(t)(x1))) -> u(u)(u(t)(t(t)(x1))) u(t)(t(u)(u(u)(x1))) -> u(u)(u(t)(t(u)(x1))) Qed DPs: b#(u(x1)) -> b#(s(x1)) TRS: s(b(x1)) -> b(s(s(s(x1)))) s(b(s(x1))) -> b(t(x1)) t(b(x1)) -> b(s(x1)) t(b(s(x1))) -> u(t(b(x1))) b(u(x1)) -> b(s(x1)) t(s(x1)) -> t(t(x1)) t(u(x1)) -> u(t(x1)) s(u(x1)) -> s(s(x1)) Polynomial Interpretation Processor: dimension: 1 usable rules: s(b(x1)) -> b(s(s(s(x1)))) s(b(s(x1))) -> b(t(x1)) b(u(x1)) -> b(s(x1)) s(u(x1)) -> s(s(x1)) interpretation: [b#](x0) = x0, [u](x0) = 1, [t](x0) = 0, [s](x0) = 0, [b](x0) = 0 orientation: b#(u(x1)) = 1 >= 0 = b#(s(x1)) s(b(x1)) = 0 >= 0 = b(s(s(s(x1)))) s(b(s(x1))) = 0 >= 0 = b(t(x1)) t(b(x1)) = 0 >= 0 = b(s(x1)) t(b(s(x1))) = 0 >= 1 = u(t(b(x1))) b(u(x1)) = 0 >= 0 = b(s(x1)) t(s(x1)) = 0 >= 0 = t(t(x1)) t(u(x1)) = 0 >= 1 = u(t(x1)) s(u(x1)) = 0 >= 0 = s(s(x1)) problem: DPs: TRS: s(b(x1)) -> b(s(s(s(x1)))) s(b(s(x1))) -> b(t(x1)) t(b(x1)) -> b(s(x1)) t(b(s(x1))) -> u(t(b(x1))) b(u(x1)) -> b(s(x1)) t(s(x1)) -> t(t(x1)) t(u(x1)) -> u(t(x1)) s(u(x1)) -> s(s(x1)) Qed