YES Problem: s(s(0())) -> f(s(0())) g(x) -> h(x,x) s(x) -> h(x,0()) s(x) -> h(0(),x) f(g(x)) -> g(g(f(x))) g(s(x)) -> s(s(g(x))) h(f(x),g(x)) -> f(s(x)) s(s(0())) -> k(0()) k(0()) -> 0() s(s(s(s(0())))) -> k(s(0())) k(s(0())) -> s(s(0())) s(s(s(s(s(s(s(s(s(s(s(s(0())))))))))))) -> k(s(s(0()))) k(s(s(0()))) -> s(s(s(s(s(s(s(s(s(s(0())))))))))) h(k(x),g(x)) -> k(s(x)) Proof: DP Processor: DPs: s#(s(0())) -> f#(s(0())) g#(x) -> h#(x,x) s#(x) -> h#(x,0()) s#(x) -> h#(0(),x) f#(g(x)) -> f#(x) f#(g(x)) -> g#(f(x)) f#(g(x)) -> g#(g(f(x))) g#(s(x)) -> g#(x) g#(s(x)) -> s#(g(x)) g#(s(x)) -> s#(s(g(x))) h#(f(x),g(x)) -> s#(x) h#(f(x),g(x)) -> f#(s(x)) s#(s(0())) -> k#(0()) s#(s(s(s(0())))) -> k#(s(0())) k#(s(0())) -> s#(s(0())) s#(s(s(s(s(s(s(s(s(s(s(s(0())))))))))))) -> k#(s(s(0()))) k#(s(s(0()))) -> s#(s(s(0()))) k#(s(s(0()))) -> s#(s(s(s(0())))) k#(s(s(0()))) -> s#(s(s(s(s(0()))))) k#(s(s(0()))) -> s#(s(s(s(s(s(0())))))) k#(s(s(0()))) -> s#(s(s(s(s(s(s(0()))))))) k#(s(s(0()))) -> s#(s(s(s(s(s(s(s(0())))))))) k#(s(s(0()))) -> s#(s(s(s(s(s(s(s(s(0()))))))))) k#(s(s(0()))) -> s#(s(s(s(s(s(s(s(s(s(0())))))))))) h#(k(x),g(x)) -> s#(x) h#(k(x),g(x)) -> k#(s(x)) TRS: s(s(0())) -> f(s(0())) g(x) -> h(x,x) s(x) -> h(x,0()) s(x) -> h(0(),x) f(g(x)) -> g(g(f(x))) g(s(x)) -> s(s(g(x))) h(f(x),g(x)) -> f(s(x)) s(s(0())) -> k(0()) k(0()) -> 0() s(s(s(s(0())))) -> k(s(0())) k(s(0())) -> s(s(0())) s(s(s(s(s(s(s(s(s(s(s(s(0())))))))))))) -> k(s(s(0()))) k(s(s(0()))) -> s(s(s(s(s(s(s(s(s(s(0())))))))))) h(k(x),g(x)) -> k(s(x)) TDG Processor: DPs: s#(s(0())) -> f#(s(0())) g#(x) -> h#(x,x) s#(x) -> h#(x,0()) s#(x) -> h#(0(),x) f#(g(x)) -> f#(x) f#(g(x)) -> g#(f(x)) f#(g(x)) -> g#(g(f(x))) g#(s(x)) -> g#(x) g#(s(x)) -> s#(g(x)) g#(s(x)) -> s#(s(g(x))) h#(f(x),g(x)) -> s#(x) h#(f(x),g(x)) -> f#(s(x)) s#(s(0())) -> k#(0()) s#(s(s(s(0())))) -> k#(s(0())) k#(s(0())) -> s#(s(0())) s#(s(s(s(s(s(s(s(s(s(s(s(0())))))))))))) -> k#(s(s(0()))) k#(s(s(0()))) -> s#(s(s(0()))) k#(s(s(0()))) -> s#(s(s(s(0())))) k#(s(s(0()))) -> s#(s(s(s(s(0()))))) k#(s(s(0()))) -> s#(s(s(s(s(s(0())))))) k#(s(s(0()))) -> s#(s(s(s(s(s(s(0()))))))) k#(s(s(0()))) -> s#(s(s(s(s(s(s(s(0())))))))) k#(s(s(0()))) -> s#(s(s(s(s(s(s(s(s(0()))))))))) k#(s(s(0()))) -> s#(s(s(s(s(s(s(s(s(s(0())))))))))) h#(k(x),g(x)) -> s#(x) h#(k(x),g(x)) -> k#(s(x)) TRS: s(s(0())) -> f(s(0())) g(x) -> h(x,x) s(x) -> h(x,0()) s(x) -> h(0(),x) f(g(x)) -> g(g(f(x))) g(s(x)) -> s(s(g(x))) h(f(x),g(x)) -> f(s(x)) s(s(0())) -> k(0()) k(0()) -> 0() s(s(s(s(0())))) -> k(s(0())) k(s(0())) -> s(s(0())) s(s(s(s(s(s(s(s(s(s(s(s(0())))))))))))) -> k(s(s(0()))) k(s(s(0()))) -> s(s(s(s(s(s(s(s(s(s(0())))))))))) h(k(x),g(x)) -> k(s(x)) graph: k#(s(s(0()))) -> s#(s(s(s(s(s(s(s(s(s(0())))))))))) -> s#(s(s(s(s(s(s(s(s(s(s(s(0())))))))))))) -> k#(s(s(0()))) k#(s(s(0()))) -> s#(s(s(s(s(s(s(s(s(s(0())))))))))) -> s#(s(s(s(0())))) -> k#(s(0())) k#(s(s(0()))) -> s#(s(s(s(s(s(s(s(s(s(0())))))))))) -> s#(s(0())) -> k#(0()) k#(s(s(0()))) -> s#(s(s(s(s(s(s(s(s(s(0())))))))))) -> s#(x) -> h#(0(),x) k#(s(s(0()))) -> s#(s(s(s(s(s(s(s(s(s(0())))))))))) -> s#(x) -> h#(x,0()) k#(s(s(0()))) -> s#(s(s(s(s(s(s(s(s(s(0())))))))))) -> s#(s(0())) -> f#(s(0())) k#(s(s(0()))) -> s#(s(s(s(s(s(s(s(s(0()))))))))) -> s#(s(s(s(s(s(s(s(s(s(s(s(0())))))))))))) -> k#(s(s(0()))) k#(s(s(0()))) -> s#(s(s(s(s(s(s(s(s(0()))))))))) -> s#(s(s(s(0())))) -> k#(s(0())) k#(s(s(0()))) -> s#(s(s(s(s(s(s(s(s(0()))))))))) -> s#(s(0())) -> k#(0()) k#(s(s(0()))) -> s#(s(s(s(s(s(s(s(s(0()))))))))) -> s#(x) -> h#(0(),x) k#(s(s(0()))) -> s#(s(s(s(s(s(s(s(s(0()))))))))) -> s#(x) -> h#(x,0()) k#(s(s(0()))) -> s#(s(s(s(s(s(s(s(s(0()))))))))) -> s#(s(0())) -> f#(s(0())) k#(s(s(0()))) -> s#(s(s(s(s(s(s(s(0())))))))) -> s#(s(s(s(s(s(s(s(s(s(s(s(0())))))))))))) -> k#(s(s(0()))) k#(s(s(0()))) -> s#(s(s(s(s(s(s(s(0())))))))) -> s#(s(s(s(0())))) -> k#(s(0())) k#(s(s(0()))) -> s#(s(s(s(s(s(s(s(0())))))))) -> s#(s(0())) -> k#(0()) k#(s(s(0()))) -> s#(s(s(s(s(s(s(s(0())))))))) -> s#(x) -> h#(0(),x) k#(s(s(0()))) -> s#(s(s(s(s(s(s(s(0())))))))) -> s#(x) -> h#(x,0()) k#(s(s(0()))) -> s#(s(s(s(s(s(s(s(0())))))))) -> s#(s(0())) -> f#(s(0())) k#(s(s(0()))) -> s#(s(s(s(s(s(s(0()))))))) -> s#(s(s(s(s(s(s(s(s(s(s(s(0())))))))))))) -> k#(s(s(0()))) k#(s(s(0()))) -> s#(s(s(s(s(s(s(0()))))))) -> s#(s(s(s(0())))) -> k#(s(0())) k#(s(s(0()))) -> s#(s(s(s(s(s(s(0()))))))) -> s#(s(0())) -> k#(0()) k#(s(s(0()))) -> s#(s(s(s(s(s(s(0()))))))) -> s#(x) -> h#(0(),x) k#(s(s(0()))) -> s#(s(s(s(s(s(s(0()))))))) -> s#(x) -> h#(x,0()) k#(s(s(0()))) -> s#(s(s(s(s(s(s(0()))))))) -> s#(s(0())) -> f#(s(0())) k#(s(s(0()))) -> s#(s(s(s(s(s(0())))))) -> s#(s(s(s(s(s(s(s(s(s(s(s(0())))))))))))) -> k#(s(s(0()))) k#(s(s(0()))) -> s#(s(s(s(s(s(0())))))) -> s#(s(s(s(0())))) -> k#(s(0())) k#(s(s(0()))) -> s#(s(s(s(s(s(0())))))) -> s#(s(0())) -> k#(0()) k#(s(s(0()))) -> s#(s(s(s(s(s(0())))))) -> s#(x) -> h#(0(),x) k#(s(s(0()))) -> s#(s(s(s(s(s(0())))))) -> s#(x) -> h#(x,0()) k#(s(s(0()))) -> s#(s(s(s(s(s(0())))))) -> s#(s(0())) -> f#(s(0())) k#(s(s(0()))) -> s#(s(s(s(s(0()))))) -> s#(s(s(s(s(s(s(s(s(s(s(s(0())))))))))))) -> k#(s(s(0()))) k#(s(s(0()))) -> s#(s(s(s(s(0()))))) -> s#(s(s(s(0())))) -> k#(s(0())) k#(s(s(0()))) -> s#(s(s(s(s(0()))))) -> s#(s(0())) -> k#(0()) k#(s(s(0()))) -> s#(s(s(s(s(0()))))) -> s#(x) -> h#(0(),x) k#(s(s(0()))) -> s#(s(s(s(s(0()))))) -> s#(x) -> h#(x,0()) k#(s(s(0()))) -> s#(s(s(s(s(0()))))) -> s#(s(0())) -> f#(s(0())) k#(s(s(0()))) -> s#(s(s(s(0())))) -> s#(s(s(s(s(s(s(s(s(s(s(s(0())))))))))))) -> k#(s(s(0()))) k#(s(s(0()))) -> s#(s(s(s(0())))) -> s#(s(s(s(0())))) -> k#(s(0())) k#(s(s(0()))) -> s#(s(s(s(0())))) -> s#(s(0())) -> k#(0()) k#(s(s(0()))) -> s#(s(s(s(0())))) -> s#(x) -> h#(0(),x) k#(s(s(0()))) -> s#(s(s(s(0())))) -> s#(x) -> h#(x,0()) k#(s(s(0()))) -> s#(s(s(s(0())))) -> s#(s(0())) -> f#(s(0())) k#(s(s(0()))) -> s#(s(s(0()))) -> s#(s(s(s(s(s(s(s(s(s(s(s(0())))))))))))) -> k#(s(s(0()))) k#(s(s(0()))) -> s#(s(s(0()))) -> s#(s(s(s(0())))) -> k#(s(0())) k#(s(s(0()))) -> s#(s(s(0()))) -> s#(s(0())) -> k#(0()) k#(s(s(0()))) -> s#(s(s(0()))) -> s#(x) -> h#(0(),x) k#(s(s(0()))) -> s#(s(s(0()))) -> s#(x) -> h#(x,0()) k#(s(s(0()))) -> s#(s(s(0()))) -> s#(s(0())) -> f#(s(0())) k#(s(0())) -> s#(s(0())) -> s#(s(s(s(s(s(s(s(s(s(s(s(0())))))))))))) -> k#(s(s(0()))) k#(s(0())) -> s#(s(0())) -> s#(s(s(s(0())))) -> k#(s(0())) k#(s(0())) -> s#(s(0())) -> s#(s(0())) -> k#(0()) k#(s(0())) -> s#(s(0())) -> s#(x) -> h#(0(),x) k#(s(0())) -> s#(s(0())) -> s#(x) -> h#(x,0()) k#(s(0())) -> s#(s(0())) -> s#(s(0())) -> f#(s(0())) h#(k(x),g(x)) -> k#(s(x)) -> k#(s(s(0()))) -> s#(s(s(s(s(s(s(s(s(s(0())))))))))) h#(k(x),g(x)) -> k#(s(x)) -> k#(s(s(0()))) -> s#(s(s(s(s(s(s(s(s(0()))))))))) h#(k(x),g(x)) -> k#(s(x)) -> k#(s(s(0()))) -> s#(s(s(s(s(s(s(s(0())))))))) h#(k(x),g(x)) -> k#(s(x)) -> k#(s(s(0()))) -> s#(s(s(s(s(s(s(0()))))))) h#(k(x),g(x)) -> k#(s(x)) -> k#(s(s(0()))) -> s#(s(s(s(s(s(0())))))) h#(k(x),g(x)) -> k#(s(x)) -> k#(s(s(0()))) -> s#(s(s(s(s(0()))))) h#(k(x),g(x)) -> k#(s(x)) -> k#(s(s(0()))) -> s#(s(s(s(0())))) h#(k(x),g(x)) -> k#(s(x)) -> k#(s(s(0()))) -> s#(s(s(0()))) h#(k(x),g(x)) -> k#(s(x)) -> k#(s(0())) -> s#(s(0())) h#(k(x),g(x)) -> s#(x) -> s#(s(s(s(s(s(s(s(s(s(s(s(0())))))))))))) -> k#(s(s(0()))) h#(k(x),g(x)) -> s#(x) -> s#(s(s(s(0())))) -> k#(s(0())) h#(k(x),g(x)) -> s#(x) -> s#(s(0())) -> k#(0()) h#(k(x),g(x)) -> s#(x) -> s#(x) -> h#(0(),x) h#(k(x),g(x)) -> s#(x) -> s#(x) -> h#(x,0()) h#(k(x),g(x)) -> s#(x) -> s#(s(0())) -> f#(s(0())) h#(f(x),g(x)) -> f#(s(x)) -> f#(g(x)) -> g#(g(f(x))) h#(f(x),g(x)) -> f#(s(x)) -> f#(g(x)) -> g#(f(x)) h#(f(x),g(x)) -> f#(s(x)) -> f#(g(x)) -> f#(x) h#(f(x),g(x)) -> s#(x) -> s#(s(s(s(s(s(s(s(s(s(s(s(0())))))))))))) -> k#(s(s(0()))) h#(f(x),g(x)) -> s#(x) -> s#(s(s(s(0())))) -> k#(s(0())) h#(f(x),g(x)) -> s#(x) -> s#(s(0())) -> k#(0()) h#(f(x),g(x)) -> s#(x) -> s#(x) -> h#(0(),x) h#(f(x),g(x)) -> s#(x) -> s#(x) -> h#(x,0()) h#(f(x),g(x)) -> s#(x) -> s#(s(0())) -> f#(s(0())) g#(s(x)) -> g#(x) -> g#(s(x)) -> s#(s(g(x))) g#(s(x)) -> g#(x) -> g#(s(x)) -> s#(g(x)) g#(s(x)) -> g#(x) -> g#(s(x)) -> g#(x) g#(s(x)) -> g#(x) -> g#(x) -> h#(x,x) g#(s(x)) -> s#(g(x)) -> s#(s(s(s(s(s(s(s(s(s(s(s(0())))))))))))) -> k#(s(s(0()))) g#(s(x)) -> s#(g(x)) -> s#(s(s(s(0())))) -> k#(s(0())) g#(s(x)) -> s#(g(x)) -> s#(s(0())) -> k#(0()) g#(s(x)) -> s#(g(x)) -> s#(x) -> h#(0(),x) g#(s(x)) -> s#(g(x)) -> s#(x) -> h#(x,0()) g#(s(x)) -> s#(g(x)) -> s#(s(0())) -> f#(s(0())) g#(s(x)) -> s#(s(g(x))) -> s#(s(s(s(s(s(s(s(s(s(s(s(0())))))))))))) -> k#(s(s(0()))) g#(s(x)) -> s#(s(g(x))) -> s#(s(s(s(0())))) -> k#(s(0())) g#(s(x)) -> s#(s(g(x))) -> s#(s(0())) -> k#(0()) g#(s(x)) -> s#(s(g(x))) -> s#(x) -> h#(0(),x) g#(s(x)) -> s#(s(g(x))) -> s#(x) -> h#(x,0()) g#(s(x)) -> s#(s(g(x))) -> s#(s(0())) -> f#(s(0())) g#(x) -> h#(x,x) -> h#(k(x),g(x)) -> k#(s(x)) g#(x) -> h#(x,x) -> h#(k(x),g(x)) -> s#(x) g#(x) -> h#(x,x) -> h#(f(x),g(x)) -> f#(s(x)) g#(x) -> h#(x,x) -> h#(f(x),g(x)) -> s#(x) f#(g(x)) -> g#(g(f(x))) -> g#(s(x)) -> s#(s(g(x))) f#(g(x)) -> g#(g(f(x))) -> g#(s(x)) -> s#(g(x)) f#(g(x)) -> g#(g(f(x))) -> g#(s(x)) -> g#(x) f#(g(x)) -> g#(g(f(x))) -> g#(x) -> h#(x,x) f#(g(x)) -> g#(f(x)) -> g#(s(x)) -> s#(s(g(x))) f#(g(x)) -> g#(f(x)) -> g#(s(x)) -> s#(g(x)) f#(g(x)) -> g#(f(x)) -> g#(s(x)) -> g#(x) f#(g(x)) -> g#(f(x)) -> g#(x) -> h#(x,x) f#(g(x)) -> f#(x) -> f#(g(x)) -> g#(g(f(x))) f#(g(x)) -> f#(x) -> f#(g(x)) -> g#(f(x)) f#(g(x)) -> f#(x) -> f#(g(x)) -> f#(x) s#(s(s(s(s(s(s(s(s(s(s(s(0())))))))))))) -> k#(s(s(0()))) -> k#(s(s(0()))) -> s#(s(s(s(s(s(s(s(s(s(0())))))))))) s#(s(s(s(s(s(s(s(s(s(s(s(0())))))))))))) -> k#(s(s(0()))) -> k#(s(s(0()))) -> s#(s(s(s(s(s(s(s(s(0()))))))))) s#(s(s(s(s(s(s(s(s(s(s(s(0())))))))))))) -> k#(s(s(0()))) -> k#(s(s(0()))) -> s#(s(s(s(s(s(s(s(0())))))))) s#(s(s(s(s(s(s(s(s(s(s(s(0())))))))))))) -> k#(s(s(0()))) -> k#(s(s(0()))) -> s#(s(s(s(s(s(s(0()))))))) s#(s(s(s(s(s(s(s(s(s(s(s(0())))))))))))) -> k#(s(s(0()))) -> k#(s(s(0()))) -> s#(s(s(s(s(s(0())))))) s#(s(s(s(s(s(s(s(s(s(s(s(0())))))))))))) -> k#(s(s(0()))) -> k#(s(s(0()))) -> s#(s(s(s(s(0()))))) s#(s(s(s(s(s(s(s(s(s(s(s(0())))))))))))) -> k#(s(s(0()))) -> k#(s(s(0()))) -> s#(s(s(s(0())))) s#(s(s(s(s(s(s(s(s(s(s(s(0())))))))))))) -> k#(s(s(0()))) -> k#(s(s(0()))) -> s#(s(s(0()))) s#(s(s(s(s(s(s(s(s(s(s(s(0())))))))))))) -> k#(s(s(0()))) -> k#(s(0())) -> s#(s(0())) s#(s(s(s(0())))) -> k#(s(0())) -> k#(s(s(0()))) -> s#(s(s(s(s(s(s(s(s(s(0())))))))))) s#(s(s(s(0())))) -> k#(s(0())) -> k#(s(s(0()))) -> s#(s(s(s(s(s(s(s(s(0()))))))))) s#(s(s(s(0())))) -> k#(s(0())) -> k#(s(s(0()))) -> s#(s(s(s(s(s(s(s(0())))))))) s#(s(s(s(0())))) -> k#(s(0())) -> k#(s(s(0()))) -> s#(s(s(s(s(s(s(0()))))))) s#(s(s(s(0())))) -> k#(s(0())) -> k#(s(s(0()))) -> s#(s(s(s(s(s(0())))))) s#(s(s(s(0())))) -> k#(s(0())) -> k#(s(s(0()))) -> s#(s(s(s(s(0()))))) s#(s(s(s(0())))) -> k#(s(0())) -> k#(s(s(0()))) -> s#(s(s(s(0())))) s#(s(s(s(0())))) -> k#(s(0())) -> k#(s(s(0()))) -> s#(s(s(0()))) s#(s(s(s(0())))) -> k#(s(0())) -> k#(s(0())) -> s#(s(0())) s#(s(0())) -> k#(0()) -> k#(s(s(0()))) -> s#(s(s(s(s(s(s(s(s(s(0())))))))))) s#(s(0())) -> k#(0()) -> k#(s(s(0()))) -> s#(s(s(s(s(s(s(s(s(0()))))))))) s#(s(0())) -> k#(0()) -> k#(s(s(0()))) -> s#(s(s(s(s(s(s(s(0())))))))) s#(s(0())) -> k#(0()) -> k#(s(s(0()))) -> s#(s(s(s(s(s(s(0()))))))) s#(s(0())) -> k#(0()) -> k#(s(s(0()))) -> s#(s(s(s(s(s(0())))))) s#(s(0())) -> k#(0()) -> k#(s(s(0()))) -> s#(s(s(s(s(0()))))) s#(s(0())) -> k#(0()) -> k#(s(s(0()))) -> s#(s(s(s(0())))) s#(s(0())) -> k#(0()) -> k#(s(s(0()))) -> s#(s(s(0()))) s#(s(0())) -> k#(0()) -> k#(s(0())) -> s#(s(0())) s#(s(0())) -> f#(s(0())) -> f#(g(x)) -> g#(g(f(x))) s#(s(0())) -> f#(s(0())) -> f#(g(x)) -> g#(f(x)) s#(s(0())) -> f#(s(0())) -> f#(g(x)) -> f#(x) s#(x) -> h#(0(),x) -> h#(k(x),g(x)) -> k#(s(x)) s#(x) -> h#(0(),x) -> h#(k(x),g(x)) -> s#(x) s#(x) -> h#(0(),x) -> h#(f(x),g(x)) -> f#(s(x)) s#(x) -> h#(0(),x) -> h#(f(x),g(x)) -> s#(x) s#(x) -> h#(x,0()) -> h#(k(x),g(x)) -> k#(s(x)) s#(x) -> h#(x,0()) -> h#(k(x),g(x)) -> s#(x) s#(x) -> h#(x,0()) -> h#(f(x),g(x)) -> f#(s(x)) s#(x) -> h#(x,0()) -> h#(f(x),g(x)) -> s#(x) EDG Processor: DPs: s#(s(0())) -> f#(s(0())) g#(x) -> h#(x,x) s#(x) -> h#(x,0()) s#(x) -> h#(0(),x) f#(g(x)) -> f#(x) f#(g(x)) -> g#(f(x)) f#(g(x)) -> g#(g(f(x))) g#(s(x)) -> g#(x) g#(s(x)) -> s#(g(x)) g#(s(x)) -> s#(s(g(x))) h#(f(x),g(x)) -> s#(x) h#(f(x),g(x)) -> f#(s(x)) s#(s(0())) -> k#(0()) s#(s(s(s(0())))) -> k#(s(0())) k#(s(0())) -> s#(s(0())) s#(s(s(s(s(s(s(s(s(s(s(s(0())))))))))))) -> k#(s(s(0()))) k#(s(s(0()))) -> s#(s(s(0()))) k#(s(s(0()))) -> s#(s(s(s(0())))) k#(s(s(0()))) -> s#(s(s(s(s(0()))))) k#(s(s(0()))) -> s#(s(s(s(s(s(0())))))) k#(s(s(0()))) -> s#(s(s(s(s(s(s(0()))))))) k#(s(s(0()))) -> s#(s(s(s(s(s(s(s(0())))))))) k#(s(s(0()))) -> s#(s(s(s(s(s(s(s(s(0()))))))))) k#(s(s(0()))) -> s#(s(s(s(s(s(s(s(s(s(0())))))))))) h#(k(x),g(x)) -> s#(x) h#(k(x),g(x)) -> k#(s(x)) TRS: s(s(0())) -> f(s(0())) g(x) -> h(x,x) s(x) -> h(x,0()) s(x) -> h(0(),x) f(g(x)) -> g(g(f(x))) g(s(x)) -> s(s(g(x))) h(f(x),g(x)) -> f(s(x)) s(s(0())) -> k(0()) k(0()) -> 0() s(s(s(s(0())))) -> k(s(0())) k(s(0())) -> s(s(0())) s(s(s(s(s(s(s(s(s(s(s(s(0())))))))))))) -> k(s(s(0()))) k(s(s(0()))) -> s(s(s(s(s(s(s(s(s(s(0())))))))))) h(k(x),g(x)) -> k(s(x)) graph: k#(s(s(0()))) -> s#(s(s(s(s(s(s(s(s(s(0())))))))))) -> s#(s(0())) -> f#(s(0())) k#(s(s(0()))) -> s#(s(s(s(s(s(s(s(s(s(0())))))))))) -> s#(x) -> h#(x,0()) k#(s(s(0()))) -> s#(s(s(s(s(s(s(s(s(s(0())))))))))) -> s#(x) -> h#(0(),x) k#(s(s(0()))) -> s#(s(s(s(s(s(s(s(s(s(0())))))))))) -> s#(s(0())) -> k#(0()) k#(s(s(0()))) -> s#(s(s(s(s(s(s(s(s(s(0())))))))))) -> s#(s(s(s(0())))) -> k#(s(0())) k#(s(s(0()))) -> s#(s(s(s(s(s(s(s(s(s(0())))))))))) -> s#(s(s(s(s(s(s(s(s(s(s(s(0())))))))))))) -> k#(s(s(0()))) k#(s(s(0()))) -> s#(s(s(s(s(s(s(s(s(0()))))))))) -> s#(s(0())) -> f#(s(0())) k#(s(s(0()))) -> s#(s(s(s(s(s(s(s(s(0()))))))))) -> s#(x) -> h#(x,0()) k#(s(s(0()))) -> s#(s(s(s(s(s(s(s(s(0()))))))))) -> s#(x) -> h#(0(),x) k#(s(s(0()))) -> s#(s(s(s(s(s(s(s(s(0()))))))))) -> s#(s(0())) -> k#(0()) k#(s(s(0()))) -> s#(s(s(s(s(s(s(s(s(0()))))))))) -> s#(s(s(s(0())))) -> k#(s(0())) k#(s(s(0()))) -> s#(s(s(s(s(s(s(s(s(0()))))))))) -> s#(s(s(s(s(s(s(s(s(s(s(s(0())))))))))))) -> k#(s(s(0()))) k#(s(s(0()))) -> s#(s(s(s(s(s(s(s(0())))))))) -> s#(s(0())) -> f#(s(0())) k#(s(s(0()))) -> s#(s(s(s(s(s(s(s(0())))))))) -> s#(x) -> h#(x,0()) k#(s(s(0()))) -> s#(s(s(s(s(s(s(s(0())))))))) -> s#(x) -> h#(0(),x) k#(s(s(0()))) -> s#(s(s(s(s(s(s(s(0())))))))) -> s#(s(0())) -> k#(0()) k#(s(s(0()))) -> s#(s(s(s(s(s(s(s(0())))))))) -> s#(s(s(s(0())))) -> k#(s(0())) k#(s(s(0()))) -> s#(s(s(s(s(s(s(s(0())))))))) -> s#(s(s(s(s(s(s(s(s(s(s(s(0())))))))))))) -> k#(s(s(0()))) k#(s(s(0()))) -> s#(s(s(s(s(s(s(0()))))))) -> s#(s(0())) -> f#(s(0())) k#(s(s(0()))) -> s#(s(s(s(s(s(s(0()))))))) -> s#(x) -> h#(x,0()) k#(s(s(0()))) -> s#(s(s(s(s(s(s(0()))))))) -> s#(x) -> h#(0(),x) k#(s(s(0()))) -> s#(s(s(s(s(s(s(0()))))))) -> s#(s(0())) -> k#(0()) k#(s(s(0()))) -> s#(s(s(s(s(s(s(0()))))))) -> s#(s(s(s(0())))) -> k#(s(0())) k#(s(s(0()))) -> s#(s(s(s(s(s(s(0()))))))) -> s#(s(s(s(s(s(s(s(s(s(s(s(0())))))))))))) -> k#(s(s(0()))) k#(s(s(0()))) -> s#(s(s(s(s(s(0())))))) -> s#(s(0())) -> f#(s(0())) k#(s(s(0()))) -> s#(s(s(s(s(s(0())))))) -> s#(x) -> h#(x,0()) k#(s(s(0()))) -> s#(s(s(s(s(s(0())))))) -> s#(x) -> h#(0(),x) k#(s(s(0()))) -> s#(s(s(s(s(s(0())))))) -> s#(s(0())) -> k#(0()) k#(s(s(0()))) -> s#(s(s(s(s(s(0())))))) -> s#(s(s(s(0())))) -> k#(s(0())) k#(s(s(0()))) -> s#(s(s(s(s(s(0())))))) -> s#(s(s(s(s(s(s(s(s(s(s(s(0())))))))))))) -> k#(s(s(0()))) k#(s(s(0()))) -> s#(s(s(s(s(0()))))) -> s#(s(0())) -> f#(s(0())) k#(s(s(0()))) -> s#(s(s(s(s(0()))))) -> s#(x) -> h#(x,0()) k#(s(s(0()))) -> s#(s(s(s(s(0()))))) -> s#(x) -> h#(0(),x) k#(s(s(0()))) -> s#(s(s(s(s(0()))))) -> s#(s(0())) -> k#(0()) k#(s(s(0()))) -> s#(s(s(s(s(0()))))) -> s#(s(s(s(0())))) -> k#(s(0())) k#(s(s(0()))) -> s#(s(s(s(s(0()))))) -> s#(s(s(s(s(s(s(s(s(s(s(s(0())))))))))))) -> k#(s(s(0()))) k#(s(s(0()))) -> s#(s(s(s(0())))) -> s#(s(0())) -> f#(s(0())) k#(s(s(0()))) -> s#(s(s(s(0())))) -> s#(x) -> h#(x,0()) k#(s(s(0()))) -> s#(s(s(s(0())))) -> s#(x) -> h#(0(),x) k#(s(s(0()))) -> s#(s(s(s(0())))) -> s#(s(0())) -> k#(0()) k#(s(s(0()))) -> s#(s(s(s(0())))) -> s#(s(s(s(0())))) -> k#(s(0())) k#(s(s(0()))) -> s#(s(s(s(0())))) -> s#(s(s(s(s(s(s(s(s(s(s(s(0())))))))))))) -> k#(s(s(0()))) k#(s(s(0()))) -> s#(s(s(0()))) -> s#(s(0())) -> f#(s(0())) k#(s(s(0()))) -> s#(s(s(0()))) -> s#(x) -> h#(x,0()) k#(s(s(0()))) -> s#(s(s(0()))) -> s#(x) -> h#(0(),x) k#(s(s(0()))) -> s#(s(s(0()))) -> s#(s(0())) -> k#(0()) k#(s(s(0()))) -> s#(s(s(0()))) -> s#(s(s(s(0())))) -> k#(s(0())) k#(s(s(0()))) -> s#(s(s(0()))) -> s#(s(s(s(s(s(s(s(s(s(s(s(0())))))))))))) -> k#(s(s(0()))) k#(s(0())) -> s#(s(0())) -> s#(s(0())) -> f#(s(0())) k#(s(0())) -> s#(s(0())) -> s#(x) -> h#(x,0()) k#(s(0())) -> s#(s(0())) -> s#(x) -> h#(0(),x) k#(s(0())) -> s#(s(0())) -> s#(s(0())) -> k#(0()) k#(s(0())) -> s#(s(0())) -> s#(s(s(s(0())))) -> k#(s(0())) k#(s(0())) -> s#(s(0())) -> s#(s(s(s(s(s(s(s(s(s(s(s(0())))))))))))) -> k#(s(s(0()))) h#(k(x),g(x)) -> k#(s(x)) -> k#(s(0())) -> s#(s(0())) h#(k(x),g(x)) -> k#(s(x)) -> k#(s(s(0()))) -> s#(s(s(0()))) h#(k(x),g(x)) -> k#(s(x)) -> k#(s(s(0()))) -> s#(s(s(s(0())))) h#(k(x),g(x)) -> k#(s(x)) -> k#(s(s(0()))) -> s#(s(s(s(s(0()))))) h#(k(x),g(x)) -> k#(s(x)) -> k#(s(s(0()))) -> s#(s(s(s(s(s(0())))))) h#(k(x),g(x)) -> k#(s(x)) -> k#(s(s(0()))) -> s#(s(s(s(s(s(s(0()))))))) h#(k(x),g(x)) -> k#(s(x)) -> k#(s(s(0()))) -> s#(s(s(s(s(s(s(s(0())))))))) h#(k(x),g(x)) -> k#(s(x)) -> k#(s(s(0()))) -> s#(s(s(s(s(s(s(s(s(0()))))))))) h#(k(x),g(x)) -> k#(s(x)) -> k#(s(s(0()))) -> s#(s(s(s(s(s(s(s(s(s(0())))))))))) h#(k(x),g(x)) -> s#(x) -> s#(s(0())) -> f#(s(0())) h#(k(x),g(x)) -> s#(x) -> s#(x) -> h#(x,0()) h#(k(x),g(x)) -> s#(x) -> s#(x) -> h#(0(),x) h#(k(x),g(x)) -> s#(x) -> s#(s(0())) -> k#(0()) h#(k(x),g(x)) -> s#(x) -> s#(s(s(s(0())))) -> k#(s(0())) h#(k(x),g(x)) -> s#(x) -> s#(s(s(s(s(s(s(s(s(s(s(s(0())))))))))))) -> k#(s(s(0()))) h#(f(x),g(x)) -> f#(s(x)) -> f#(g(x)) -> f#(x) h#(f(x),g(x)) -> f#(s(x)) -> f#(g(x)) -> g#(f(x)) h#(f(x),g(x)) -> f#(s(x)) -> f#(g(x)) -> g#(g(f(x))) h#(f(x),g(x)) -> s#(x) -> s#(s(0())) -> f#(s(0())) h#(f(x),g(x)) -> s#(x) -> s#(x) -> h#(x,0()) h#(f(x),g(x)) -> s#(x) -> s#(x) -> h#(0(),x) h#(f(x),g(x)) -> s#(x) -> s#(s(0())) -> k#(0()) h#(f(x),g(x)) -> s#(x) -> s#(s(s(s(0())))) -> k#(s(0())) h#(f(x),g(x)) -> s#(x) -> s#(s(s(s(s(s(s(s(s(s(s(s(0())))))))))))) -> k#(s(s(0()))) g#(s(x)) -> g#(x) -> g#(x) -> h#(x,x) g#(s(x)) -> g#(x) -> g#(s(x)) -> g#(x) g#(s(x)) -> g#(x) -> g#(s(x)) -> s#(g(x)) g#(s(x)) -> g#(x) -> g#(s(x)) -> s#(s(g(x))) g#(s(x)) -> s#(g(x)) -> s#(s(0())) -> f#(s(0())) g#(s(x)) -> s#(g(x)) -> s#(x) -> h#(x,0()) g#(s(x)) -> s#(g(x)) -> s#(x) -> h#(0(),x) g#(s(x)) -> s#(g(x)) -> s#(s(0())) -> k#(0()) g#(s(x)) -> s#(g(x)) -> s#(s(s(s(0())))) -> k#(s(0())) g#(s(x)) -> s#(g(x)) -> s#(s(s(s(s(s(s(s(s(s(s(s(0())))))))))))) -> k#(s(s(0()))) g#(s(x)) -> s#(s(g(x))) -> s#(s(0())) -> f#(s(0())) g#(s(x)) -> s#(s(g(x))) -> s#(x) -> h#(x,0()) g#(s(x)) -> s#(s(g(x))) -> s#(x) -> h#(0(),x) g#(s(x)) -> s#(s(g(x))) -> s#(s(0())) -> k#(0()) g#(s(x)) -> s#(s(g(x))) -> s#(s(s(s(0())))) -> k#(s(0())) g#(s(x)) -> s#(s(g(x))) -> s#(s(s(s(s(s(s(s(s(s(s(s(0())))))))))))) -> k#(s(s(0()))) g#(x) -> h#(x,x) -> h#(f(x),g(x)) -> s#(x) g#(x) -> h#(x,x) -> h#(f(x),g(x)) -> f#(s(x)) g#(x) -> h#(x,x) -> h#(k(x),g(x)) -> s#(x) g#(x) -> h#(x,x) -> h#(k(x),g(x)) -> k#(s(x)) f#(g(x)) -> g#(g(f(x))) -> g#(x) -> h#(x,x) f#(g(x)) -> g#(g(f(x))) -> g#(s(x)) -> g#(x) f#(g(x)) -> g#(g(f(x))) -> g#(s(x)) -> s#(g(x)) f#(g(x)) -> g#(g(f(x))) -> g#(s(x)) -> s#(s(g(x))) f#(g(x)) -> g#(f(x)) -> g#(x) -> h#(x,x) f#(g(x)) -> g#(f(x)) -> g#(s(x)) -> g#(x) f#(g(x)) -> g#(f(x)) -> g#(s(x)) -> s#(g(x)) f#(g(x)) -> g#(f(x)) -> g#(s(x)) -> s#(s(g(x))) f#(g(x)) -> f#(x) -> f#(g(x)) -> f#(x) f#(g(x)) -> f#(x) -> f#(g(x)) -> g#(f(x)) f#(g(x)) -> f#(x) -> f#(g(x)) -> g#(g(f(x))) s#(s(s(s(s(s(s(s(s(s(s(s(0())))))))))))) -> k#(s(s(0()))) -> k#(s(0())) -> s#(s(0())) s#(s(s(s(s(s(s(s(s(s(s(s(0())))))))))))) -> k#(s(s(0()))) -> k#(s(s(0()))) -> s#(s(s(0()))) s#(s(s(s(s(s(s(s(s(s(s(s(0())))))))))))) -> k#(s(s(0()))) -> k#(s(s(0()))) -> s#(s(s(s(0())))) s#(s(s(s(s(s(s(s(s(s(s(s(0())))))))))))) -> k#(s(s(0()))) -> k#(s(s(0()))) -> s#(s(s(s(s(0()))))) s#(s(s(s(s(s(s(s(s(s(s(s(0())))))))))))) -> k#(s(s(0()))) -> k#(s(s(0()))) -> s#(s(s(s(s(s(0())))))) s#(s(s(s(s(s(s(s(s(s(s(s(0())))))))))))) -> k#(s(s(0()))) -> k#(s(s(0()))) -> s#(s(s(s(s(s(s(0()))))))) s#(s(s(s(s(s(s(s(s(s(s(s(0())))))))))))) -> k#(s(s(0()))) -> k#(s(s(0()))) -> s#(s(s(s(s(s(s(s(0())))))))) s#(s(s(s(s(s(s(s(s(s(s(s(0())))))))))))) -> k#(s(s(0()))) -> k#(s(s(0()))) -> s#(s(s(s(s(s(s(s(s(0()))))))))) s#(s(s(s(s(s(s(s(s(s(s(s(0())))))))))))) -> k#(s(s(0()))) -> k#(s(s(0()))) -> s#(s(s(s(s(s(s(s(s(s(0())))))))))) s#(s(s(s(0())))) -> k#(s(0())) -> k#(s(0())) -> s#(s(0())) s#(s(s(s(0())))) -> k#(s(0())) -> k#(s(s(0()))) -> s#(s(s(0()))) s#(s(s(s(0())))) -> k#(s(0())) -> k#(s(s(0()))) -> s#(s(s(s(0())))) s#(s(s(s(0())))) -> k#(s(0())) -> k#(s(s(0()))) -> s#(s(s(s(s(0()))))) s#(s(s(s(0())))) -> k#(s(0())) -> k#(s(s(0()))) -> s#(s(s(s(s(s(0())))))) s#(s(s(s(0())))) -> k#(s(0())) -> k#(s(s(0()))) -> s#(s(s(s(s(s(s(0()))))))) s#(s(s(s(0())))) -> k#(s(0())) -> k#(s(s(0()))) -> s#(s(s(s(s(s(s(s(0())))))))) s#(s(s(s(0())))) -> k#(s(0())) -> k#(s(s(0()))) -> s#(s(s(s(s(s(s(s(s(0()))))))))) s#(s(s(s(0())))) -> k#(s(0())) -> k#(s(s(0()))) -> s#(s(s(s(s(s(s(s(s(s(0())))))))))) s#(s(0())) -> f#(s(0())) -> f#(g(x)) -> f#(x) s#(s(0())) -> f#(s(0())) -> f#(g(x)) -> g#(f(x)) s#(s(0())) -> f#(s(0())) -> f#(g(x)) -> g#(g(f(x))) SCC Processor: #sccs: 1 #rules: 23 #arcs: 130/676 DPs: k#(s(s(0()))) -> s#(s(s(s(s(s(s(s(s(s(0())))))))))) s#(s(s(s(s(s(s(s(s(s(s(s(0())))))))))))) -> k#(s(s(0()))) k#(s(s(0()))) -> s#(s(s(s(s(s(s(s(s(0()))))))))) s#(s(s(s(0())))) -> k#(s(0())) k#(s(s(0()))) -> s#(s(s(s(s(s(s(s(0())))))))) s#(s(0())) -> f#(s(0())) f#(g(x)) -> g#(g(f(x))) g#(s(x)) -> s#(s(g(x))) g#(s(x)) -> s#(g(x)) g#(s(x)) -> g#(x) g#(x) -> h#(x,x) h#(k(x),g(x)) -> k#(s(x)) k#(s(s(0()))) -> s#(s(s(s(s(s(s(0()))))))) k#(s(s(0()))) -> s#(s(s(s(s(s(0())))))) k#(s(s(0()))) -> s#(s(s(s(s(0()))))) k#(s(s(0()))) -> s#(s(s(s(0())))) k#(s(s(0()))) -> s#(s(s(0()))) k#(s(0())) -> s#(s(0())) h#(k(x),g(x)) -> s#(x) h#(f(x),g(x)) -> f#(s(x)) f#(g(x)) -> g#(f(x)) f#(g(x)) -> f#(x) h#(f(x),g(x)) -> s#(x) TRS: s(s(0())) -> f(s(0())) g(x) -> h(x,x) s(x) -> h(x,0()) s(x) -> h(0(),x) f(g(x)) -> g(g(f(x))) g(s(x)) -> s(s(g(x))) h(f(x),g(x)) -> f(s(x)) s(s(0())) -> k(0()) k(0()) -> 0() s(s(s(s(0())))) -> k(s(0())) k(s(0())) -> s(s(0())) s(s(s(s(s(s(s(s(s(s(s(s(0())))))))))))) -> k(s(s(0()))) k(s(s(0()))) -> s(s(s(s(s(s(s(s(s(s(0())))))))))) h(k(x),g(x)) -> k(s(x)) Matrix Interpretation Processor: dim=1 usable rules: s(s(0())) -> f(s(0())) g(x) -> h(x,x) s(x) -> h(x,0()) s(x) -> h(0(),x) f(g(x)) -> g(g(f(x))) g(s(x)) -> s(s(g(x))) h(f(x),g(x)) -> f(s(x)) s(s(0())) -> k(0()) k(0()) -> 0() s(s(s(s(0())))) -> k(s(0())) k(s(0())) -> s(s(0())) s(s(s(s(s(s(s(s(s(s(s(s(0())))))))))))) -> k(s(s(0()))) k(s(s(0()))) -> s(s(s(s(s(s(s(s(s(s(0())))))))))) h(k(x),g(x)) -> k(s(x)) interpretation: [h](x0, x1) = 0, [g#](x0) = 0, [s](x0) = 0, [g](x0) = x0 + 1, [k](x0) = 0, [k#](x0) = 0, [0] = 0, [f#](x0) = x0, [h#](x0, x1) = 0, [s#](x0) = 0, [f](x0) = 3x0 orientation: k#(s(s(0()))) = 0 >= 0 = s#(s(s(s(s(s(s(s(s(s(0())))))))))) s#(s(s(s(s(s(s(s(s(s(s(s(0())))))))))))) = 0 >= 0 = k#(s(s(0()))) k#(s(s(0()))) = 0 >= 0 = s#(s(s(s(s(s(s(s(s(0()))))))))) s#(s(s(s(0())))) = 0 >= 0 = k#(s(0())) k#(s(s(0()))) = 0 >= 0 = s#(s(s(s(s(s(s(s(0())))))))) s#(s(0())) = 0 >= 0 = f#(s(0())) f#(g(x)) = x + 1 >= 0 = g#(g(f(x))) g#(s(x)) = 0 >= 0 = s#(s(g(x))) g#(s(x)) = 0 >= 0 = s#(g(x)) g#(s(x)) = 0 >= 0 = g#(x) g#(x) = 0 >= 0 = h#(x,x) h#(k(x),g(x)) = 0 >= 0 = k#(s(x)) k#(s(s(0()))) = 0 >= 0 = s#(s(s(s(s(s(s(0()))))))) k#(s(s(0()))) = 0 >= 0 = s#(s(s(s(s(s(0())))))) k#(s(s(0()))) = 0 >= 0 = s#(s(s(s(s(0()))))) k#(s(s(0()))) = 0 >= 0 = s#(s(s(s(0())))) k#(s(s(0()))) = 0 >= 0 = s#(s(s(0()))) k#(s(0())) = 0 >= 0 = s#(s(0())) h#(k(x),g(x)) = 0 >= 0 = s#(x) h#(f(x),g(x)) = 0 >= 0 = f#(s(x)) f#(g(x)) = x + 1 >= 0 = g#(f(x)) f#(g(x)) = x + 1 >= x = f#(x) h#(f(x),g(x)) = 0 >= 0 = s#(x) s(s(0())) = 0 >= 0 = f(s(0())) g(x) = x + 1 >= 0 = h(x,x) s(x) = 0 >= 0 = h(x,0()) s(x) = 0 >= 0 = h(0(),x) f(g(x)) = 3x + 3 >= 3x + 2 = g(g(f(x))) g(s(x)) = 1 >= 0 = s(s(g(x))) h(f(x),g(x)) = 0 >= 0 = f(s(x)) s(s(0())) = 0 >= 0 = k(0()) k(0()) = 0 >= 0 = 0() s(s(s(s(0())))) = 0 >= 0 = k(s(0())) k(s(0())) = 0 >= 0 = s(s(0())) s(s(s(s(s(s(s(s(s(s(s(s(0())))))))))))) = 0 >= 0 = k(s(s(0()))) k(s(s(0()))) = 0 >= 0 = s(s(s(s(s(s(s(s(s(s(0())))))))))) h(k(x),g(x)) = 0 >= 0 = k(s(x)) problem: DPs: k#(s(s(0()))) -> s#(s(s(s(s(s(s(s(s(s(0())))))))))) s#(s(s(s(s(s(s(s(s(s(s(s(0())))))))))))) -> k#(s(s(0()))) k#(s(s(0()))) -> s#(s(s(s(s(s(s(s(s(0()))))))))) s#(s(s(s(0())))) -> k#(s(0())) k#(s(s(0()))) -> s#(s(s(s(s(s(s(s(0())))))))) s#(s(0())) -> f#(s(0())) g#(s(x)) -> s#(s(g(x))) g#(s(x)) -> s#(g(x)) g#(s(x)) -> g#(x) g#(x) -> h#(x,x) h#(k(x),g(x)) -> k#(s(x)) k#(s(s(0()))) -> s#(s(s(s(s(s(s(0()))))))) k#(s(s(0()))) -> s#(s(s(s(s(s(0())))))) k#(s(s(0()))) -> s#(s(s(s(s(0()))))) k#(s(s(0()))) -> s#(s(s(s(0())))) k#(s(s(0()))) -> s#(s(s(0()))) k#(s(0())) -> s#(s(0())) h#(k(x),g(x)) -> s#(x) h#(f(x),g(x)) -> f#(s(x)) h#(f(x),g(x)) -> s#(x) TRS: s(s(0())) -> f(s(0())) g(x) -> h(x,x) s(x) -> h(x,0()) s(x) -> h(0(),x) f(g(x)) -> g(g(f(x))) g(s(x)) -> s(s(g(x))) h(f(x),g(x)) -> f(s(x)) s(s(0())) -> k(0()) k(0()) -> 0() s(s(s(s(0())))) -> k(s(0())) k(s(0())) -> s(s(0())) s(s(s(s(s(s(s(s(s(s(s(s(0())))))))))))) -> k(s(s(0()))) k(s(s(0()))) -> s(s(s(s(s(s(s(s(s(s(0())))))))))) h(k(x),g(x)) -> k(s(x)) Restore Modifier: DPs: k#(s(s(0()))) -> s#(s(s(s(s(s(s(s(s(s(0())))))))))) s#(s(s(s(s(s(s(s(s(s(s(s(0())))))))))))) -> k#(s(s(0()))) k#(s(s(0()))) -> s#(s(s(s(s(s(s(s(s(0()))))))))) s#(s(s(s(0())))) -> k#(s(0())) k#(s(s(0()))) -> s#(s(s(s(s(s(s(s(0())))))))) s#(s(0())) -> f#(s(0())) g#(s(x)) -> s#(s(g(x))) g#(s(x)) -> s#(g(x)) g#(s(x)) -> g#(x) g#(x) -> h#(x,x) h#(k(x),g(x)) -> k#(s(x)) k#(s(s(0()))) -> s#(s(s(s(s(s(s(0()))))))) k#(s(s(0()))) -> s#(s(s(s(s(s(0())))))) k#(s(s(0()))) -> s#(s(s(s(s(0()))))) k#(s(s(0()))) -> s#(s(s(s(0())))) k#(s(s(0()))) -> s#(s(s(0()))) k#(s(0())) -> s#(s(0())) h#(k(x),g(x)) -> s#(x) h#(f(x),g(x)) -> f#(s(x)) h#(f(x),g(x)) -> s#(x) TRS: s(s(0())) -> f(s(0())) g(x) -> h(x,x) s(x) -> h(x,0()) s(x) -> h(0(),x) f(g(x)) -> g(g(f(x))) g(s(x)) -> s(s(g(x))) h(f(x),g(x)) -> f(s(x)) s(s(0())) -> k(0()) k(0()) -> 0() s(s(s(s(0())))) -> k(s(0())) k(s(0())) -> s(s(0())) s(s(s(s(s(s(s(s(s(s(s(s(0())))))))))))) -> k(s(s(0()))) k(s(s(0()))) -> s(s(s(s(s(s(s(s(s(s(0())))))))))) h(k(x),g(x)) -> k(s(x)) SCC Processor: #sccs: 2 #rules: 12 #arcs: 91/400 DPs: g#(s(x)) -> g#(x) TRS: s(s(0())) -> f(s(0())) g(x) -> h(x,x) s(x) -> h(x,0()) s(x) -> h(0(),x) f(g(x)) -> g(g(f(x))) g(s(x)) -> s(s(g(x))) h(f(x),g(x)) -> f(s(x)) s(s(0())) -> k(0()) k(0()) -> 0() s(s(s(s(0())))) -> k(s(0())) k(s(0())) -> s(s(0())) s(s(s(s(s(s(s(s(s(s(s(s(0())))))))))))) -> k(s(s(0()))) k(s(s(0()))) -> s(s(s(s(s(s(s(s(s(s(0())))))))))) h(k(x),g(x)) -> k(s(x)) Size-Change Termination Processor: DPs: TRS: s(s(0())) -> f(s(0())) g(x) -> h(x,x) s(x) -> h(x,0()) s(x) -> h(0(),x) f(g(x)) -> g(g(f(x))) g(s(x)) -> s(s(g(x))) h(f(x),g(x)) -> f(s(x)) s(s(0())) -> k(0()) k(0()) -> 0() s(s(s(s(0())))) -> k(s(0())) k(s(0())) -> s(s(0())) s(s(s(s(s(s(s(s(s(s(s(s(0())))))))))))) -> k(s(s(0()))) k(s(s(0()))) -> s(s(s(s(s(s(s(s(s(s(0())))))))))) h(k(x),g(x)) -> k(s(x)) The DP: g#(s(x)) -> g#(x) has the edges: 0 > 0 Qed DPs: k#(s(s(0()))) -> s#(s(s(s(s(s(s(s(s(s(0())))))))))) s#(s(s(s(s(s(s(s(s(s(s(s(0())))))))))))) -> k#(s(s(0()))) k#(s(s(0()))) -> s#(s(s(s(s(s(s(s(s(0()))))))))) s#(s(s(s(0())))) -> k#(s(0())) k#(s(s(0()))) -> s#(s(s(s(s(s(s(s(0())))))))) k#(s(s(0()))) -> s#(s(s(s(s(s(s(0()))))))) k#(s(s(0()))) -> s#(s(s(s(s(s(0())))))) k#(s(s(0()))) -> s#(s(s(s(s(0()))))) k#(s(s(0()))) -> s#(s(s(s(0())))) k#(s(s(0()))) -> s#(s(s(0()))) k#(s(0())) -> s#(s(0())) TRS: s(s(0())) -> f(s(0())) g(x) -> h(x,x) s(x) -> h(x,0()) s(x) -> h(0(),x) f(g(x)) -> g(g(f(x))) g(s(x)) -> s(s(g(x))) h(f(x),g(x)) -> f(s(x)) s(s(0())) -> k(0()) k(0()) -> 0() s(s(s(s(0())))) -> k(s(0())) k(s(0())) -> s(s(0())) s(s(s(s(s(s(s(s(s(s(s(s(0())))))))))))) -> k(s(s(0()))) k(s(s(0()))) -> s(s(s(s(s(s(s(s(s(s(0())))))))))) h(k(x),g(x)) -> k(s(x)) Bounds Processor: bound: 0 enrichment: top-dp automaton: final states: {79} transitions: s{#,0}(81) -> 79* 00() -> 80* s0(80) -> 81* h0(80,80) -> 81* problem: DPs: k#(s(s(0()))) -> s#(s(s(s(s(s(s(s(s(s(0())))))))))) s#(s(s(s(s(s(s(s(s(s(s(s(0())))))))))))) -> k#(s(s(0()))) k#(s(s(0()))) -> s#(s(s(s(s(s(s(s(s(0()))))))))) s#(s(s(s(0())))) -> k#(s(0())) k#(s(s(0()))) -> s#(s(s(s(s(s(s(s(0())))))))) k#(s(s(0()))) -> s#(s(s(s(s(s(s(0()))))))) k#(s(s(0()))) -> s#(s(s(s(s(s(0())))))) k#(s(s(0()))) -> s#(s(s(s(s(0()))))) k#(s(s(0()))) -> s#(s(s(s(0())))) k#(s(s(0()))) -> s#(s(s(0()))) TRS: s(s(0())) -> f(s(0())) g(x) -> h(x,x) s(x) -> h(x,0()) s(x) -> h(0(),x) f(g(x)) -> g(g(f(x))) g(s(x)) -> s(s(g(x))) h(f(x),g(x)) -> f(s(x)) s(s(0())) -> k(0()) k(0()) -> 0() s(s(s(s(0())))) -> k(s(0())) k(s(0())) -> s(s(0())) s(s(s(s(s(s(s(s(s(s(s(s(0())))))))))))) -> k(s(s(0()))) k(s(s(0()))) -> s(s(s(s(s(s(s(s(s(s(0())))))))))) h(k(x),g(x)) -> k(s(x)) Bounds Processor: bound: 0 enrichment: top-dp automaton: final states: {30} transitions: 00() -> 31* s0(31) -> 32* k{#,0}(32) -> 30* h0(31,31) -> 32* problem: DPs: k#(s(s(0()))) -> s#(s(s(s(s(s(s(s(s(s(0())))))))))) s#(s(s(s(s(s(s(s(s(s(s(s(0())))))))))))) -> k#(s(s(0()))) k#(s(s(0()))) -> s#(s(s(s(s(s(s(s(s(0()))))))))) k#(s(s(0()))) -> s#(s(s(s(s(s(s(s(0())))))))) k#(s(s(0()))) -> s#(s(s(s(s(s(s(0()))))))) k#(s(s(0()))) -> s#(s(s(s(s(s(0())))))) k#(s(s(0()))) -> s#(s(s(s(s(0()))))) k#(s(s(0()))) -> s#(s(s(s(0())))) k#(s(s(0()))) -> s#(s(s(0()))) TRS: s(s(0())) -> f(s(0())) g(x) -> h(x,x) s(x) -> h(x,0()) s(x) -> h(0(),x) f(g(x)) -> g(g(f(x))) g(s(x)) -> s(s(g(x))) h(f(x),g(x)) -> f(s(x)) s(s(0())) -> k(0()) k(0()) -> 0() s(s(s(s(0())))) -> k(s(0())) k(s(0())) -> s(s(0())) s(s(s(s(s(s(s(s(s(s(s(s(0())))))))))))) -> k(s(s(0()))) k(s(s(0()))) -> s(s(s(s(s(s(s(s(s(s(0())))))))))) h(k(x),g(x)) -> k(s(x)) Bounds Processor: bound: 0 enrichment: top-dp automaton: final states: {70} transitions: s{#,0}(81) -> 70* s{#,0}(73) -> 70* 00() -> 81*,73,71 s0(71) -> 72* s0(81) -> 72* s0(72) -> 73* h0(81,71) -> 72* h0(72,71) -> 73* h0(71,72) -> 73* h0(81,72) -> 73* h0(72,81) -> 73* h0(81,81) -> 72* h0(71,71) -> 72* h0(71,81) -> 72* k0(71) -> 73* k0(81) -> 73* f0(72) -> 73* problem: DPs: k#(s(s(0()))) -> s#(s(s(s(s(s(s(s(s(s(0())))))))))) s#(s(s(s(s(s(s(s(s(s(s(s(0())))))))))))) -> k#(s(s(0()))) k#(s(s(0()))) -> s#(s(s(s(s(s(s(s(s(0()))))))))) k#(s(s(0()))) -> s#(s(s(s(s(s(s(s(0())))))))) k#(s(s(0()))) -> s#(s(s(s(s(s(s(0()))))))) k#(s(s(0()))) -> s#(s(s(s(s(s(0())))))) k#(s(s(0()))) -> s#(s(s(s(s(0()))))) k#(s(s(0()))) -> s#(s(s(s(0())))) TRS: s(s(0())) -> f(s(0())) g(x) -> h(x,x) s(x) -> h(x,0()) s(x) -> h(0(),x) f(g(x)) -> g(g(f(x))) g(s(x)) -> s(s(g(x))) h(f(x),g(x)) -> f(s(x)) s(s(0())) -> k(0()) k(0()) -> 0() s(s(s(s(0())))) -> k(s(0())) k(s(0())) -> s(s(0())) s(s(s(s(s(s(s(s(s(s(s(s(0())))))))))))) -> k(s(s(0()))) k(s(s(0()))) -> s(s(s(s(s(s(s(s(s(s(0())))))))))) h(k(x),g(x)) -> k(s(x)) Bounds Processor: bound: 0 enrichment: top-dp automaton: final states: {64} transitions: s{#,0}(77) -> 64* s{#,0}(68) -> 64* 00() -> 76*,67,65 s0(76) -> 77*,66,68 s0(77) -> 67* s0(65) -> 66* s0(67) -> 68* s0(66) -> 67* h0(77,65) -> 67* h0(65,66) -> 67* h0(65,77) -> 67* h0(67,76) -> 68* h0(66,65) -> 67* h0(76,65) -> 77*,66,68 h0(77,76) -> 67* h0(76,77) -> 67* h0(76,67) -> 68* h0(65,65) -> 66* h0(67,65) -> 68* h0(65,67) -> 68* h0(65,76) -> 77*,66,68 h0(76,76) -> 77*,66,68 h0(66,76) -> 67* h0(76,66) -> 67* k0(76) -> 67* k0(65) -> 67* f0(77) -> 67* f0(66) -> 67* problem: DPs: k#(s(s(0()))) -> s#(s(s(s(s(s(s(s(s(s(0())))))))))) s#(s(s(s(s(s(s(s(s(s(s(s(0())))))))))))) -> k#(s(s(0()))) k#(s(s(0()))) -> s#(s(s(s(s(s(s(s(s(0()))))))))) k#(s(s(0()))) -> s#(s(s(s(s(s(s(s(0())))))))) k#(s(s(0()))) -> s#(s(s(s(s(s(s(0()))))))) k#(s(s(0()))) -> s#(s(s(s(s(s(0())))))) k#(s(s(0()))) -> s#(s(s(s(s(0()))))) TRS: s(s(0())) -> f(s(0())) g(x) -> h(x,x) s(x) -> h(x,0()) s(x) -> h(0(),x) f(g(x)) -> g(g(f(x))) g(s(x)) -> s(s(g(x))) h(f(x),g(x)) -> f(s(x)) s(s(0())) -> k(0()) k(0()) -> 0() s(s(s(s(0())))) -> k(s(0())) k(s(0())) -> s(s(0())) s(s(s(s(s(s(s(s(s(s(s(s(0())))))))))))) -> k(s(s(0()))) k(s(s(0()))) -> s(s(s(s(s(s(s(s(s(s(0())))))))))) h(k(x),g(x)) -> k(s(x)) Bounds Processor: bound: 0 enrichment: top-dp automaton: final states: {57} transitions: s{#,0}(62) -> 57* s{#,0}(77) -> 57* s{#,0}(72) -> 57* 00() -> 70,72,77*,60,58 s0(71) -> 72*,60,62 s0(77) -> 71*,61,59 s0(70) -> 71*,61,59 s0(72) -> 61* s0(60) -> 61* s0(59) -> 60* s0(61) -> 62* s0(58) -> 59* h0(70,58) -> 71*,59,61 h0(61,70) -> 62* h0(58,58) -> 59* h0(77,77) -> 59,71*,61 h0(58,61) -> 62* h0(60,58) -> 61* h0(70,72) -> 61* h0(58,60) -> 61* h0(70,61) -> 62* h0(70,70) -> 71*,59,61 h0(59,58) -> 60* h0(58,77) -> 59,71*,61 h0(70,60) -> 61* h0(71,77) -> 62,60,72* h0(77,59) -> 60* h0(70,59) -> 60* h0(77,72) -> 61* h0(58,70) -> 71*,59,61 h0(61,58) -> 62* h0(58,71) -> 72*,62,60 h0(60,77) -> 61* h0(72,58) -> 61* h0(77,71) -> 62,72*,60 h0(77,70) -> 59,71*,61 h0(59,70) -> 60* h0(60,70) -> 61* h0(77,58) -> 71*,59,61 h0(71,70) -> 72*,62,60 h0(71,58) -> 72*,60,62 h0(77,61) -> 62* h0(70,71) -> 72*,62,60 h0(72,70) -> 61* h0(70,77) -> 59,71*,61 h0(72,77) -> 61* h0(77,60) -> 61* h0(61,77) -> 62* h0(59,77) -> 60* h0(58,72) -> 61* h0(58,59) -> 60* k0(70) -> 72*,60 k0(71) -> 62* k0(77) -> 72* k0(59) -> 62* k0(58) -> 72*,60 f0(59) -> 72*,60 f0(71) -> 72*,60 problem: DPs: k#(s(s(0()))) -> s#(s(s(s(s(s(s(s(s(s(0())))))))))) s#(s(s(s(s(s(s(s(s(s(s(s(0())))))))))))) -> k#(s(s(0()))) k#(s(s(0()))) -> s#(s(s(s(s(s(s(s(s(0()))))))))) k#(s(s(0()))) -> s#(s(s(s(s(s(s(s(0())))))))) k#(s(s(0()))) -> s#(s(s(s(s(s(s(0()))))))) k#(s(s(0()))) -> s#(s(s(s(s(s(0())))))) TRS: s(s(0())) -> f(s(0())) g(x) -> h(x,x) s(x) -> h(x,0()) s(x) -> h(0(),x) f(g(x)) -> g(g(f(x))) g(s(x)) -> s(s(g(x))) h(f(x),g(x)) -> f(s(x)) s(s(0())) -> k(0()) k(0()) -> 0() s(s(s(s(0())))) -> k(s(0())) k(s(0())) -> s(s(0())) s(s(s(s(s(s(s(s(s(s(s(s(0())))))))))))) -> k(s(s(0()))) k(s(s(0()))) -> s(s(s(s(s(s(s(s(s(s(0())))))))))) h(k(x),g(x)) -> k(s(x)) Bounds Processor: bound: 0 enrichment: top-dp automaton: final states: {49} transitions: s{#,0}(73) -> 49* s{#,0}(66) -> 49* s{#,0}(55) -> 49* 00() -> 63,65,72*,52,50 s0(73) -> 65*,52,54 s0(64) -> 65*,52,54 s0(51) -> 52* s0(65) -> 66*,53,55 s0(52) -> 53* s0(72) -> 73*,53,55,51 s0(54) -> 55* s0(66) -> 54* s0(53) -> 54* s0(50) -> 51* s0(63) -> 64*,53,51 h0(72,50) -> 73*,55,53,51 h0(52,63) -> 53* h0(54,50) -> 55* h0(63,63) -> 64*,53,51 h0(53,50) -> 54* h0(65,72) -> 55,53,66* h0(50,52) -> 53* h0(66,63) -> 54* h0(50,63) -> 64*,53,51 h0(53,72) -> 54* h0(72,72) -> 73*,53,55,51 h0(66,50) -> 54* h0(65,63) -> 66*,53,55 h0(50,66) -> 54* h0(72,64) -> 52,65*,54 h0(51,63) -> 52* h0(72,51) -> 52* h0(50,73) -> 54,52,65* h0(54,72) -> 55* h0(50,53) -> 54* h0(51,50) -> 52* h0(64,50) -> 65*,54,52 h0(52,72) -> 53* h0(50,65) -> 66*,53,55 h0(72,53) -> 54* h0(72,73) -> 65*,52,54 h0(63,50) -> 64*,53,51 h0(73,63) -> 52,54,65* h0(50,72) -> 73*,53,55,51 h0(73,50) -> 54,65*,52 h0(72,52) -> 53* h0(63,51) -> 52* h0(72,65) -> 53,55,66* h0(50,51) -> 52* h0(50,64) -> 65*,54,52 h0(66,72) -> 54* h0(63,66) -> 54* h0(64,72) -> 52,54,65* h0(50,54) -> 55* h0(73,72) -> 54,65*,52 h0(63,52) -> 53* h0(63,73) -> 52,65*,54 h0(53,63) -> 54* h0(63,64) -> 65*,52,54 h0(64,63) -> 65*,52,54 h0(54,63) -> 55* h0(72,54) -> 55* h0(52,50) -> 53* h0(63,54) -> 55* h0(65,50) -> 66*,55,53 h0(63,53) -> 54* h0(51,72) -> 52* h0(63,65) -> 66*,53,55 h0(63,72) -> 73*,53,55,51 h0(72,66) -> 54* h0(72,63) -> 73*,55,53,51 h0(50,50) -> 51* k0(63) -> 65*,52 k0(64) -> 54* k0(72) -> 65* k0(50) -> 65*,52 k0(51) -> 54* k0(73) -> 54* f0(64) -> 65*,52 f0(73) -> 65* f0(51) -> 65*,52 problem: DPs: k#(s(s(0()))) -> s#(s(s(s(s(s(s(s(s(s(0())))))))))) s#(s(s(s(s(s(s(s(s(s(s(s(0())))))))))))) -> k#(s(s(0()))) k#(s(s(0()))) -> s#(s(s(s(s(s(s(s(s(0()))))))))) k#(s(s(0()))) -> s#(s(s(s(s(s(s(s(0())))))))) k#(s(s(0()))) -> s#(s(s(s(s(s(s(0()))))))) TRS: s(s(0())) -> f(s(0())) g(x) -> h(x,x) s(x) -> h(x,0()) s(x) -> h(0(),x) f(g(x)) -> g(g(f(x))) g(s(x)) -> s(s(g(x))) h(f(x),g(x)) -> f(s(x)) s(s(0())) -> k(0()) k(0()) -> 0() s(s(s(s(0())))) -> k(s(0())) k(s(0())) -> s(s(0())) s(s(s(s(s(s(s(s(s(s(s(s(0())))))))))))) -> k(s(s(0()))) k(s(s(0()))) -> s(s(s(s(s(s(s(s(s(s(0())))))))))) h(k(x),g(x)) -> k(s(x)) Matrix Interpretation Processor: dim=3 usable rules: s(s(0())) -> f(s(0())) g(x) -> h(x,x) s(x) -> h(x,0()) s(x) -> h(0(),x) f(g(x)) -> g(g(f(x))) g(s(x)) -> s(s(g(x))) h(f(x),g(x)) -> f(s(x)) s(s(0())) -> k(0()) k(0()) -> 0() s(s(s(s(0())))) -> k(s(0())) k(s(0())) -> s(s(0())) s(s(s(s(s(s(s(s(s(s(s(s(0())))))))))))) -> k(s(s(0()))) k(s(s(0()))) -> s(s(s(s(s(s(s(s(s(s(0())))))))))) h(k(x),g(x)) -> k(s(x)) interpretation: [0 0 0] [h](x0, x1) = [0 0 0]x1 [0 1 0] , [0 0 0] [s](x0) = [0 0 1]x0 [0 1 0] , [0 1 0] [g](x0) = [0 1 1]x0 [0 1 1] , [0 0 0] [k](x0) = [0 0 0]x0 [0 1 1] , [k#](x0) = [1], [0] [0] = [0] [1], [s#](x0) = [0 1 0]x0, [0] [f](x0) = [0] [0] orientation: k#(s(s(0()))) = 1 >= 1 = s#(s(s(s(s(s(s(s(s(s(0())))))))))) s#(s(s(s(s(s(s(s(s(s(s(s(0())))))))))))) = 1 >= 1 = k#(s(s(0()))) k#(s(s(0()))) = 1 >= 0 = s#(s(s(s(s(s(s(s(s(0()))))))))) k#(s(s(0()))) = 1 >= 1 = s#(s(s(s(s(s(s(s(0())))))))) k#(s(s(0()))) = 1 >= 0 = s#(s(s(s(s(s(s(0()))))))) [0] [0] s(s(0())) = [0] >= [0] = f(s(0())) [1] [0] [0 1 0] [0 0 0] g(x) = [0 1 1]x >= [0 0 0]x = h(x,x) [0 1 1] [0 1 0] [0 0 0] [0] s(x) = [0 0 1]x >= [0] = h(x,0()) [0 1 0] [0] [0 0 0] [0 0 0] s(x) = [0 0 1]x >= [0 0 0]x = h(0(),x) [0 1 0] [0 1 0] [0] [0] f(g(x)) = [0] >= [0] = g(g(f(x))) [0] [0] [0 0 1] [0 0 0] g(s(x)) = [0 1 1]x >= [0 1 1]x = s(s(g(x))) [0 1 1] [0 1 1] [0 0 0] [0] h(f(x),g(x)) = [0 0 0]x >= [0] = f(s(x)) [0 1 1] [0] [0] [0] s(s(0())) = [0] >= [0] = k(0()) [1] [1] [0] [0] k(0()) = [0] >= [0] = 0() [1] [1] [0] [0] s(s(s(s(0())))) = [0] >= [0] = k(s(0())) [1] [1] [0] [0] k(s(0())) = [0] >= [0] = s(s(0())) [1] [1] [0] [0] s(s(s(s(s(s(s(s(s(s(s(s(0())))))))))))) = [0] >= [0] = k(s(s(0()))) [1] [1] [0] [0] k(s(s(0()))) = [0] >= [0] = s(s(s(s(s(s(s(s(s(s(0())))))))))) [1] [1] [0 0 0] [0 0 0] h(k(x),g(x)) = [0 0 0]x >= [0 0 0]x = k(s(x)) [0 1 1] [0 1 1] problem: DPs: k#(s(s(0()))) -> s#(s(s(s(s(s(s(s(s(s(0())))))))))) s#(s(s(s(s(s(s(s(s(s(s(s(0())))))))))))) -> k#(s(s(0()))) k#(s(s(0()))) -> s#(s(s(s(s(s(s(s(0())))))))) TRS: s(s(0())) -> f(s(0())) g(x) -> h(x,x) s(x) -> h(x,0()) s(x) -> h(0(),x) f(g(x)) -> g(g(f(x))) g(s(x)) -> s(s(g(x))) h(f(x),g(x)) -> f(s(x)) s(s(0())) -> k(0()) k(0()) -> 0() s(s(s(s(0())))) -> k(s(0())) k(s(0())) -> s(s(0())) s(s(s(s(s(s(s(s(s(s(s(s(0())))))))))))) -> k(s(s(0()))) k(s(s(0()))) -> s(s(s(s(s(s(s(s(s(s(0())))))))))) h(k(x),g(x)) -> k(s(x)) Restore Modifier: DPs: k#(s(s(0()))) -> s#(s(s(s(s(s(s(s(s(s(0())))))))))) s#(s(s(s(s(s(s(s(s(s(s(s(0())))))))))))) -> k#(s(s(0()))) k#(s(s(0()))) -> s#(s(s(s(s(s(s(s(0())))))))) TRS: s(s(0())) -> f(s(0())) g(x) -> h(x,x) s(x) -> h(x,0()) s(x) -> h(0(),x) f(g(x)) -> g(g(f(x))) g(s(x)) -> s(s(g(x))) h(f(x),g(x)) -> f(s(x)) s(s(0())) -> k(0()) k(0()) -> 0() s(s(s(s(0())))) -> k(s(0())) k(s(0())) -> s(s(0())) s(s(s(s(s(s(s(s(s(s(s(s(0())))))))))))) -> k(s(s(0()))) k(s(s(0()))) -> s(s(s(s(s(s(s(s(s(s(0())))))))))) h(k(x),g(x)) -> k(s(x)) Bounds Processor: bound: 0 enrichment: top-dp automaton: final states: {19} transitions: s{#,0}(62) -> 19* s{#,0}(40) -> 19* s{#,0}(44) -> 19* s{#,0}(27) -> 19* 00() -> 41,37,35,43,61*,22,20 s0(23) -> 24* s0(37) -> 38*,25,23 s0(38) -> 39*,24,26 s0(24) -> 25* s0(62) -> 24,22,43*,26 s0(35) -> 36*,21,23 s0(40) -> 26* s0(20) -> 21* s0(22) -> 23* s0(41) -> 42*,25,21,23 s0(39) -> 40*,25,27 s0(43) -> 44*,25,23,27 s0(36) -> 37*,24,22 s0(26) -> 27* s0(44) -> 24,39*,26 s0(61) -> 62*,25,21,23,27 s0(21) -> 22* s0(42) -> 43*,24,22,26 s0(25) -> 26* h0(24,41) -> 25* h0(43,61) -> 44*,25,23,27 h0(61,25) -> 26* h0(21,20) -> 22* h0(20,24) -> 25* h0(41,41) -> 42*,21,23,25 h0(26,20) -> 27* h0(61,20) -> 62*,27,21,25,23 h0(24,61) -> 25* h0(62,20) -> 22,43*,24,26 h0(44,61) -> 39*,26,24 h0(39,20) -> 40*,27,25 h0(61,40) -> 26* h0(20,40) -> 26* h0(41,38) -> 26,24,39* h0(26,35) -> 27* h0(61,42) -> 26,22,43*,24 h0(39,41) -> 27,40*,25 h0(41,39) -> 25,40*,27 h0(20,61) -> 62*,25,27,21,23 h0(40,35) -> 26* h0(43,41) -> 44*,25,23,27 h0(36,35) -> 37*,24,22 h0(61,61) -> 62*,21,25,23,27 h0(61,41) -> 62*,21,25,23,27 h0(41,24) -> 25* h0(43,35) -> 44*,27,23,25 h0(37,61) -> 25,38*,23 h0(43,20) -> 44*,27,25,23 h0(40,20) -> 26* h0(41,36) -> 37*,24,22 h0(20,44) -> 26,24,39* h0(35,35) -> 36*,21,23 h0(44,20) -> 39*,24,26 h0(41,20) -> 42*,21,25,23 h0(26,61) -> 27* h0(38,35) -> 39*,26,24 h0(41,43) -> 44*,25,27,23 h0(35,42) -> 43*,26,22,24 h0(35,25) -> 26* h0(41,62) -> 26,22,43*,24 h0(38,41) -> 39*,26,24 h0(61,24) -> 25* h0(35,61) -> 62*,21,25,23,27 h0(20,26) -> 27* h0(61,37) -> 25,38*,23 h0(20,43) -> 44*,25,27,23 h0(20,25) -> 26* h0(35,41) -> 42*,21,25,23 h0(36,61) -> 22,37*,24 h0(35,21) -> 22* h0(39,35) -> 40*,27,25 h0(42,20) -> 43*,22,24,26 h0(42,41) -> 43*,22,26,24 h0(44,35) -> 39*,26,24 h0(39,61) -> 40*,25,27 h0(20,36) -> 37*,24,22 h0(36,20) -> 37*,22,24 h0(42,35) -> 43*,26,24,22 h0(61,43) -> 25,44*,27,23 h0(20,42) -> 43*,26,24,22 h0(21,61) -> 22* h0(20,20) -> 21* h0(35,24) -> 25* h0(40,61) -> 26* h0(20,62) -> 26,43*,24,22 h0(35,36) -> 37*,22,24 h0(37,20) -> 38*,25,23 h0(62,41) -> 43*,22,26,24 h0(22,61) -> 23* h0(20,35) -> 36*,21,23 h0(41,37) -> 25,38*,23 h0(61,23) -> 24* h0(41,35) -> 42*,21,23,25 h0(61,36) -> 37*,22,24 h0(20,41) -> 42*,25,21,23 h0(41,40) -> 26* h0(24,20) -> 25* h0(41,61) -> 62*,21,25,27,23 h0(22,35) -> 23* h0(38,61) -> 39*,26,24 h0(38,20) -> 39*,24,26 h0(35,43) -> 44*,25,23,27 h0(21,41) -> 22* h0(44,41) -> 39*,26,24 h0(41,25) -> 26* h0(22,20) -> 23* h0(62,35) -> 43*,26,24,22 h0(36,41) -> 37*,24,22 h0(23,20) -> 24* h0(40,41) -> 26* h0(37,41) -> 23,38*,25 h0(20,37) -> 38*,25,23 h0(25,35) -> 26* h0(20,39) -> 40*,25,27 h0(61,26) -> 27* h0(41,26) -> 27* h0(35,22) -> 23* h0(61,62) -> 26,43*,24,22 h0(35,38) -> 39*,26,24 h0(20,23) -> 24* h0(25,20) -> 26* h0(25,41) -> 26* h0(37,35) -> 38*,23,25 h0(61,22) -> 23* h0(35,40) -> 26* h0(41,21) -> 22* h0(35,44) -> 39*,26,24 h0(61,38) -> 26,39*,24 h0(23,41) -> 24* h0(23,35) -> 24* h0(41,44) -> 39*,26,24 h0(35,37) -> 38*,25,23 h0(61,39) -> 25,40*,27 h0(35,23) -> 24* h0(35,39) -> 40*,25,27 h0(23,61) -> 24* h0(61,35) -> 62*,27,21,23,25 h0(20,22) -> 23* h0(42,61) -> 43*,22,26,24 h0(20,21) -> 22* h0(21,35) -> 22* h0(41,22) -> 23* h0(25,61) -> 26* h0(20,38) -> 39*,26,24 h0(22,41) -> 23* h0(35,26) -> 27* h0(62,61) -> 22,24,43*,26 h0(41,42) -> 43*,26,22,24 h0(24,35) -> 25* h0(35,20) -> 36*,21,23 h0(41,23) -> 24* h0(61,21) -> 22* h0(35,62) -> 43*,26,22,24 h0(61,44) -> 26,39*,24 h0(26,41) -> 27* k0(21) -> 39*,24 k0(20) -> 37,43*,22 k0(62) -> 39* k0(61) -> 43* k0(41) -> 37,43* k0(42) -> 39* k0(35) -> 37,43*,22 k0(36) -> 39*,24 f0(21) -> 37,43*,22 f0(62) -> 43* f0(42) -> 37,43* f0(36) -> 37,43*,22 problem: DPs: k#(s(s(0()))) -> s#(s(s(s(s(s(s(s(s(s(0())))))))))) s#(s(s(s(s(s(s(s(s(s(s(s(0())))))))))))) -> k#(s(s(0()))) TRS: s(s(0())) -> f(s(0())) g(x) -> h(x,x) s(x) -> h(x,0()) s(x) -> h(0(),x) f(g(x)) -> g(g(f(x))) g(s(x)) -> s(s(g(x))) h(f(x),g(x)) -> f(s(x)) s(s(0())) -> k(0()) k(0()) -> 0() s(s(s(s(0())))) -> k(s(0())) k(s(0())) -> s(s(0())) s(s(s(s(s(s(s(s(s(s(s(s(0())))))))))))) -> k(s(s(0()))) k(s(s(0()))) -> s(s(s(s(s(s(s(s(s(s(0())))))))))) h(k(x),g(x)) -> k(s(x)) Bounds Processor: bound: 0 enrichment: top-dp automaton: final states: {2} transitions: s{#,0}(62) -> 2* s{#,0}(46) -> 2* s{#,0}(56) -> 2* s{#,0}(12) -> 2* s{#,0}(40) -> 2* 00() -> 53,43,33,35,41,55,61*,5,3 s0(55) -> 56*,10,8,12,6 s0(37) -> 38*,10,8 s0(33) -> 34*,4,6 s0(38) -> 39*,11,9 s0(45) -> 46*,10,8,12 s0(34) -> 35*,7,5 s0(62) -> 11,7,5,55*,9 s0(3) -> 4* s0(35) -> 36*,8,6 s0(40) -> 11* s0(9) -> 10* s0(41) -> 42*,4,8,6 s0(10) -> 11* s0(39) -> 40*,10,12 s0(6) -> 7* s0(43) -> 44*,10,8,6 s0(56) -> 11,7,45*,9 s0(7) -> 8* s0(4) -> 5* s0(54) -> 55*,11,7,5,9 s0(36) -> 37*,7,9 s0(11) -> 12* s0(44) -> 45*,11,7,9 s0(53) -> 54*,4,10,8,6 s0(61) -> 62*,4,10,8,12,6 s0(5) -> 6* s0(46) -> 39*,11,9 s0(8) -> 9* s0(42) -> 43*,7,5,9 h0(46,53) -> 11,9,39* h0(38,53) -> 39*,11,9 h0(4,61) -> 5* h0(41,8) -> 9* h0(43,61) -> 8,10,6,44* h0(39,33) -> 40*,10,12 h0(3,53) -> 54*,4,6,8,10 h0(6,53) -> 7* h0(53,35) -> 36*,6,8 h0(45,41) -> 46*,12,8,10 h0(33,35) -> 36*,8,6 h0(45,53) -> 12,46*,8,10 h0(61,5) -> 6* h0(53,54) -> 55*,7,9,5,11 h0(41,41) -> 42*,4,8,6 h0(46,61) -> 9,11,39* h0(61,54) -> 55*,5,7,11,9 h0(33,36) -> 37*,9,7 h0(46,41) -> 39*,11,9 h0(61,46) -> 39*,11,9 h0(44,61) -> 7,9,11,45* h0(61,40) -> 11* h0(3,43) -> 44*,6,8,10 h0(41,38) -> 39*,9,11 h0(61,42) -> 5,7,43*,9 h0(42,33) -> 43*,9,5,7 h0(3,61) -> 62*,4,6,8,10,12 h0(39,41) -> 40*,10,12 h0(41,54) -> 55*,9,11,5,7 h0(33,54) -> 55*,9,7,5,11 h0(56,61) -> 7,9,11,45* h0(3,40) -> 11* h0(41,39) -> 40*,10,12 h0(43,33) -> 44*,10,8,6 h0(33,42) -> 43*,9,7,5 h0(41,53) -> 54*,4,10,6,8 h0(56,33) -> 9,45*,11,7 h0(3,54) -> 55*,5,11,7,9 h0(56,53) -> 7,11,9,45* h0(41,10) -> 11* h0(43,3) -> 44*,8,10,6 h0(43,41) -> 44*,8,6,10 h0(3,62) -> 55*,5,11,7,9 h0(61,33) -> 62*,4,10,12,8,6 h0(54,61) -> 7,5,55*,9,11 h0(41,45) -> 46*,10,12,8 h0(61,61) -> 62*,4,10,8,6,12 h0(53,3) -> 54*,4,8,10,6 h0(53,56) -> 7,9,45*,11 h0(5,53) -> 6* h0(61,41) -> 62*,4,12,8,6,10 h0(61,6) -> 7* h0(34,61) -> 7,5,35* h0(3,3) -> 4* h0(39,3) -> 40*,12,10 h0(40,33) -> 11* h0(53,6) -> 7* h0(37,61) -> 8,10,38* h0(4,53) -> 5* h0(7,61) -> 8* h0(11,53) -> 12* h0(11,3) -> 12* h0(33,39) -> 40*,10,12 h0(33,43) -> 44*,10,8,6 h0(3,39) -> 40*,10,12 h0(41,36) -> 37*,7,9 h0(36,53) -> 37*,7,9 h0(7,53) -> 8* h0(3,5) -> 6* h0(11,41) -> 12* h0(3,46) -> 11,39*,9 h0(53,45) -> 10,46*,8,12 h0(53,37) -> 10,38*,8 h0(61,45) -> 10,46*,8,12 h0(53,53) -> 54*,4,6,8,10 h0(35,33) -> 36*,8,6 h0(61,11) -> 12* h0(3,7) -> 8* h0(55,61) -> 12,8,10,6,56* h0(41,9) -> 10* h0(6,3) -> 7* h0(41,33) -> 42*,4,8,6 h0(8,33) -> 9* h0(53,8) -> 9* h0(3,4) -> 5* h0(3,9) -> 10* h0(41,43) -> 44*,10,6,8 h0(3,36) -> 37*,7,9 h0(53,4) -> 5* h0(4,33) -> 5* h0(33,33) -> 34*,4,6 h0(33,9) -> 10* h0(41,62) -> 9,55*,11,5,7 h0(61,4) -> 5* h0(6,61) -> 7* h0(61,7) -> 8* h0(38,41) -> 9,39*,11 h0(53,34) -> 5,35*,7 h0(11,61) -> 12* h0(53,9) -> 10* h0(53,38) -> 11,39*,9 h0(33,11) -> 12* h0(53,46) -> 11,39*,9 h0(7,3) -> 8* h0(10,61) -> 11* h0(37,53) -> 8,38*,10 h0(61,34) -> 5,35*,7 h0(5,61) -> 6* h0(35,61) -> 8,6,36* h0(61,37) -> 10,38*,8 h0(33,8) -> 9* h0(8,61) -> 9* h0(45,3) -> 46*,12,8,10 h0(61,56) -> 7,11,9,45* h0(44,33) -> 45*,9,11,7 h0(35,41) -> 8,6,36* h0(36,61) -> 7,37*,9 h0(10,33) -> 11* h0(38,33) -> 39*,9,11 h0(33,37) -> 38*,10,8 h0(8,3) -> 9* h0(3,34) -> 35*,5,7 h0(56,41) -> 45*,11,7,9 h0(42,41) -> 43*,5,7,9 h0(61,53) -> 62*,4,12,10,8,6 h0(44,3) -> 45*,7,9,11 h0(53,44) -> 11,7,9,45* h0(3,37) -> 38*,8,10 h0(3,41) -> 42*,4,6,8 h0(62,53) -> 7,5,11,55*,9 h0(54,3) -> 55*,7,9,5,11 h0(39,61) -> 12,10,40* h0(3,33) -> 34*,4,6 h0(33,53) -> 54*,4,10,8,6 h0(53,41) -> 54*,4,6,8,10 h0(10,53) -> 11* h0(9,3) -> 10* h0(6,33) -> 7* h0(41,4) -> 5* h0(61,43) -> 10,8,6,44* h0(34,41) -> 7,5,35* h0(33,41) -> 42*,4,8,6 h0(3,10) -> 11* h0(4,41) -> 5* h0(53,11) -> 12* h0(41,34) -> 5,7,35* h0(9,33) -> 10* h0(11,33) -> 12* h0(40,61) -> 11* h0(55,53) -> 56*,6,12,8,10 h0(62,41) -> 5,11,7,9,55* h0(61,8) -> 9* h0(9,53) -> 10* h0(61,10) -> 11* h0(41,37) -> 10,38*,8 h0(33,55) -> 56*,10,12,8,6 h0(41,35) -> 8,36*,6 h0(61,36) -> 37*,7,9 h0(3,45) -> 46*,8,10,12 h0(40,3) -> 11* h0(53,40) -> 11* h0(33,6) -> 7* h0(5,3) -> 6* h0(41,40) -> 11* h0(7,33) -> 8* h0(3,38) -> 39*,11,9 h0(41,61) -> 62*,4,10,6,8,12 h0(33,44) -> 45*,9,7,11 h0(39,53) -> 40*,12,10 h0(61,3) -> 62*,4,12,8,10,6 h0(38,61) -> 39*,9,11 h0(41,46) -> 9,39*,11 h0(4,3) -> 5* h0(36,3) -> 37*,7,9 h0(33,7) -> 8* h0(44,41) -> 45*,11,7,9 h0(33,62) -> 55*,9,7,5,11 h0(34,3) -> 35*,7,5 h0(53,7) -> 8* h0(42,3) -> 43*,7,9,5 h0(62,3) -> 7,9,55*,5,11 h0(3,35) -> 36*,6,8 h0(38,3) -> 39*,9,11 h0(33,56) -> 9,7,45*,11 h0(5,33) -> 6* h0(45,33) -> 46*,10,12,8 h0(54,53) -> 55*,7,5,11,9 h0(41,11) -> 12* h0(7,41) -> 8* h0(45,61) -> 12,8,46*,10 h0(33,40) -> 11* h0(36,41) -> 9,7,37* h0(43,53) -> 44*,8,6,10 h0(40,41) -> 11* h0(37,41) -> 10,8,38* h0(53,33) -> 54*,4,10,8,6 h0(3,55) -> 56*,6,8,10,12 h0(46,33) -> 9,11,39* h0(61,62) -> 55*,7,5,9,11 h0(53,36) -> 37*,7,9 h0(35,53) -> 8,6,36* h0(33,4) -> 5* h0(3,42) -> 43*,5,7,9 h0(33,38) -> 39*,9,11 h0(3,6) -> 7* h0(53,55) -> 56*,10,12,8,6 h0(41,55) -> 56*,10,12,6,8 h0(8,53) -> 9* h0(10,3) -> 11* h0(34,53) -> 5,35*,7 h0(41,6) -> 7* h0(53,42) -> 5,7,9,43* h0(34,33) -> 35*,5,7 h0(53,62) -> 55*,7,9,5,11 h0(44,53) -> 45*,11,7,9 h0(5,41) -> 6* h0(55,33) -> 56*,10,12,8,6 h0(61,9) -> 10* h0(3,8) -> 9* h0(53,10) -> 11* h0(41,56) -> 9,11,7,45* h0(33,34) -> 35*,7,5 h0(61,38) -> 39*,11,9 h0(53,5) -> 6* h0(53,39) -> 40*,10,12 h0(35,3) -> 36*,8,6 h0(41,5) -> 6* h0(41,44) -> 45*,9,11,7 h0(37,33) -> 38*,10,8 h0(61,39) -> 10,40*,12 h0(62,33) -> 9,5,11,7,55* h0(36,33) -> 37*,9,7 h0(10,41) -> 11* h0(9,61) -> 10* h0(33,10) -> 11* h0(33,45) -> 46*,10,12,8 h0(55,41) -> 56*,12,8,6,10 h0(41,7) -> 8* h0(61,35) -> 8,36*,6 h0(33,46) -> 9,39*,11 h0(3,11) -> 12* h0(42,61) -> 7,5,9,43* h0(41,3) -> 42*,4,8,6 h0(33,61) -> 62*,4,10,8,12,6 h0(3,56) -> 11,7,9,45* h0(3,44) -> 45*,11,7,9 h0(33,3) -> 34*,4,6 h0(33,5) -> 6* h0(53,43) -> 10,44*,6,8 h0(62,61) -> 5,55*,7,11,9 h0(37,3) -> 38*,8,10 h0(41,42) -> 43*,9,5,7 h0(9,41) -> 10* h0(6,41) -> 7* h0(8,41) -> 9* h0(56,3) -> 7,9,45*,11 h0(40,53) -> 11* h0(54,41) -> 55*,5,11,7,9 h0(54,33) -> 55*,9,5,11,7 h0(55,3) -> 56*,12,8,10,6 h0(46,3) -> 9,39*,11 h0(61,44) -> 7,11,9,45* h0(61,55) -> 10,8,56*,6,12 h0(42,53) -> 5,43*,7,9 h0(53,61) -> 62*,4,10,8,6,12 k0(62) -> 45* k0(61) -> 55* k0(41) -> 43,35,55* k0(42) -> 37,45* k0(53) -> 43,55* k0(54) -> 45* k0(33) -> 43,35,55*,5 k0(34) -> 37,45*,7 k0(3) -> 43,35,55*,5 k0(4) -> 37,45*,7 f0(4) -> 43,35,55*,5 f0(62) -> 55* f0(42) -> 43,35,55* f0(34) -> 43,35,55*,5 f0(54) -> 43,55* problem: DPs: s#(s(s(s(s(s(s(s(s(s(s(s(0())))))))))))) -> k#(s(s(0()))) TRS: s(s(0())) -> f(s(0())) g(x) -> h(x,x) s(x) -> h(x,0()) s(x) -> h(0(),x) f(g(x)) -> g(g(f(x))) g(s(x)) -> s(s(g(x))) h(f(x),g(x)) -> f(s(x)) s(s(0())) -> k(0()) k(0()) -> 0() s(s(s(s(0())))) -> k(s(0())) k(s(0())) -> s(s(0())) s(s(s(s(s(s(s(s(s(s(s(s(0())))))))))))) -> k(s(s(0()))) k(s(s(0()))) -> s(s(s(s(s(s(s(s(s(s(0())))))))))) h(k(x),g(x)) -> k(s(x)) SCC Processor: #sccs: 0 #rules: 0 #arcs: 36/1