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(s(0()))) -> k(0()) k(0()) -> 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(0()))))))))))) -> k(s(s(0()))) k(s(s(0()))) -> 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(s(0()))) -> k#(0()) k#(0()) -> 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(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()))))))))) 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(s(0()))) -> k(0()) k(0()) -> 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(0()))))))))))) -> k(s(s(0()))) k(s(s(0()))) -> 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(s(0()))) -> k#(0()) k#(0()) -> 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(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()))))))))) 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(s(0()))) -> k(0()) k(0()) -> 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(0()))))))))))) -> k(s(s(0()))) k(s(s(0()))) -> 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(0()))))))))) -> 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(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(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(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(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(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(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(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(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(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(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(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(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(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(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(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())) k#(0()) -> s#(0()) -> s#(s(s(s(s(s(s(s(s(s(s(0()))))))))))) -> k#(s(s(0()))) k#(0()) -> s#(0()) -> s#(s(s(s(0())))) -> k#(s(0())) k#(0()) -> s#(0()) -> s#(s(s(0()))) -> k#(0()) k#(0()) -> s#(0()) -> s#(x) -> h#(0(),x) k#(0()) -> s#(0()) -> s#(x) -> h#(x,0()) k#(0()) -> 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(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)) -> k#(s(x)) -> k#(0()) -> s#(0()) h#(k(x),g(x)) -> s#(x) -> 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(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(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(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(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(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(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(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(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(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(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(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(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(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(0()))))))))))) -> k#(s(s(0()))) -> k#(s(s(0()))) -> s#(s(s(0()))) 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(0()))))))))))) -> k#(s(s(0()))) -> k#(0()) -> 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(s(s(0())))) -> k#(s(0())) -> k#(0()) -> s#(0()) s#(s(s(0()))) -> k#(0()) -> k#(s(s(0()))) -> s#(s(s(s(s(s(s(s(s(0()))))))))) s#(s(s(0()))) -> k#(0()) -> k#(s(s(0()))) -> s#(s(s(s(s(s(s(s(0())))))))) s#(s(s(0()))) -> k#(0()) -> k#(s(s(0()))) -> s#(s(s(s(s(s(s(0()))))))) s#(s(s(0()))) -> k#(0()) -> k#(s(s(0()))) -> s#(s(s(s(s(s(0())))))) s#(s(s(0()))) -> k#(0()) -> k#(s(s(0()))) -> s#(s(s(s(s(0()))))) s#(s(s(0()))) -> k#(0()) -> k#(s(s(0()))) -> s#(s(s(s(0())))) s#(s(s(0()))) -> k#(0()) -> k#(s(s(0()))) -> s#(s(s(0()))) s#(s(s(0()))) -> k#(0()) -> k#(s(0())) -> s#(s(0())) s#(s(s(0()))) -> k#(0()) -> k#(0()) -> 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(s(0()))) -> k#(0()) k#(0()) -> 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(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()))))))))) 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(s(0()))) -> k(0()) k(0()) -> 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(0()))))))))))) -> k(s(s(0()))) k(s(s(0()))) -> 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(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(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(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(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(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(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(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(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(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(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(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(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(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(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(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(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(0()))))))))))) -> k#(s(s(0()))) k#(0()) -> s#(0()) -> s#(x) -> h#(x,0()) k#(0()) -> s#(0()) -> s#(x) -> h#(0(),x) 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)) -> 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(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(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(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(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(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(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(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(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(0()))))))))))) -> k#(s(s(0()))) -> k#(s(0())) -> s#(s(0())) 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(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(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(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(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(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(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(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(0()))) -> k#(0()) -> k#(0()) -> 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: 22 #arcs: 124/676 DPs: 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(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(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(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(s(0()))) -> k(0()) k(0()) -> 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(0()))))))))))) -> k(s(s(0()))) k(s(s(0()))) -> s(s(s(s(s(s(s(s(s(0()))))))))) h(k(x),g(x)) -> k(s(x)) Arctic Interpretation Processor: dimension: 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(s(0()))) -> k(0()) k(0()) -> 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(0()))))))))))) -> k(s(s(0()))) k(s(s(0()))) -> s(s(s(s(s(s(s(s(s(0()))))))))) h(k(x),g(x)) -> k(s(x)) interpretation: [h](x0, x1) = x0 + x1, [g#](x0) = x0 + 2, [s](x0) = x0 + 0, [g](x0) = x0 + 2, [k](x0) = x0 + 0, [k#](x0) = 0, [0] = 0, [f#](x0) = x0 + 0, [h#](x0, x1) = x0 + x1, [s#](x0) = x0 + 0, [f](x0) = x0 + 0 orientation: k#(s(s(0()))) = 0 >= 0 = s#(s(s(s(s(s(s(s(s(0()))))))))) 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(0())))))))) s#(s(s(s(0())))) = 0 >= 0 = k#(s(0())) k#(s(s(0()))) = 0 >= 0 = s#(s(s(s(s(s(s(0()))))))) s#(s(0())) = 0 >= 0 = f#(s(0())) f#(g(x)) = x + 2 >= x + 2 = g#(g(f(x))) g#(s(x)) = x + 2 >= x + 2 = s#(s(g(x))) g#(s(x)) = x + 2 >= x + 2 = s#(g(x)) g#(s(x)) = x + 2 >= x + 2 = g#(x) g#(x) = x + 2 >= x = h#(x,x) h#(k(x),g(x)) = x + 2 >= 0 = k#(s(x)) 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)) = x + 2 >= x + 0 = s#(x) h#(f(x),g(x)) = x + 2 >= x + 0 = f#(s(x)) f#(g(x)) = x + 2 >= x + 2 = g#(f(x)) f#(g(x)) = x + 2 >= x + 0 = f#(x) h#(f(x),g(x)) = x + 2 >= x + 0 = s#(x) s(s(0())) = 0 >= 0 = f(s(0())) g(x) = x + 2 >= x = h(x,x) s(x) = x + 0 >= x + 0 = h(x,0()) s(x) = x + 0 >= x + 0 = h(0(),x) f(g(x)) = x + 2 >= x + 2 = g(g(f(x))) g(s(x)) = x + 2 >= x + 2 = s(s(g(x))) h(f(x),g(x)) = x + 2 >= x + 0 = f(s(x)) s(s(s(0()))) = 0 >= 0 = k(0()) k(0()) = 0 >= 0 = s(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(0()))))))))))) = 0 >= 0 = k(s(s(0()))) k(s(s(0()))) = 0 >= 0 = s(s(s(s(s(s(s(s(s(0()))))))))) h(k(x),g(x)) = x + 2 >= x + 0 = k(s(x)) problem: DPs: 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(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(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) 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(s(0()))) -> k(0()) k(0()) -> 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(0()))))))))))) -> k(s(s(0()))) k(s(s(0()))) -> 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(0()))))))))) 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(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) 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(s(0()))) -> k(0()) k(0()) -> 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(0()))))))))))) -> k(s(s(0()))) k(s(s(0()))) -> s(s(s(s(s(s(s(s(s(0()))))))))) h(k(x),g(x)) -> k(s(x)) Arctic Interpretation Processor: dimension: 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(s(0()))) -> k(0()) k(0()) -> 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(0()))))))))))) -> k(s(s(0()))) k(s(s(0()))) -> s(s(s(s(s(s(s(s(s(0()))))))))) h(k(x),g(x)) -> k(s(x)) interpretation: [h](x0, x1) = x0 + x1 + 0, [g#](x0) = x0 + 0, [s](x0) = x0 + 0, [g](x0) = x0 + 1, [k](x0) = x0 + 0, [k#](x0) = 0, [0] = 0, [f#](x0) = x0 + 0, [h#](x0, x1) = x0 + x1 + 0, [s#](x0) = 0, [f](x0) = x0 + 0 orientation: k#(s(s(0()))) = 0 >= 0 = s#(s(s(s(s(s(s(s(s(0()))))))))) 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(0())))))))) s#(s(s(s(0())))) = 0 >= 0 = k#(s(0())) k#(s(s(0()))) = 0 >= 0 = s#(s(s(s(s(s(s(0()))))))) s#(s(0())) = 0 >= 0 = f#(s(0())) f#(g(x)) = x + 1 >= x + 1 = g#(g(f(x))) g#(s(x)) = x + 0 >= 0 = s#(s(g(x))) g#(s(x)) = x + 0 >= 0 = s#(g(x)) g#(s(x)) = x + 0 >= x + 0 = g#(x) g#(x) = x + 0 >= x + 0 = h#(x,x) 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)) = x + 1 >= 0 = s#(x) h#(f(x),g(x)) = x + 1 >= x + 0 = f#(s(x)) f#(g(x)) = x + 1 >= x + 0 = g#(f(x)) f#(g(x)) = x + 1 >= x + 0 = f#(x) h#(f(x),g(x)) = x + 1 >= 0 = s#(x) s(s(0())) = 0 >= 0 = f(s(0())) g(x) = x + 1 >= x + 0 = h(x,x) s(x) = x + 0 >= x + 0 = h(x,0()) s(x) = x + 0 >= x + 0 = h(0(),x) f(g(x)) = x + 1 >= x + 1 = g(g(f(x))) g(s(x)) = x + 1 >= x + 1 = s(s(g(x))) h(f(x),g(x)) = x + 1 >= x + 0 = f(s(x)) s(s(s(0()))) = 0 >= 0 = k(0()) k(0()) = 0 >= 0 = s(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(0()))))))))))) = 0 >= 0 = k(s(s(0()))) k(s(s(0()))) = 0 >= 0 = s(s(s(s(s(s(s(s(s(0()))))))))) h(k(x),g(x)) = x + 1 >= x + 0 = k(s(x)) problem: DPs: 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(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(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) 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#(f(x),g(x)) -> f#(s(x)) f#(g(x)) -> g#(f(x)) f#(g(x)) -> f#(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(s(0()))) -> k(0()) k(0()) -> 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(0()))))))))))) -> k(s(s(0()))) k(s(s(0()))) -> 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(0()))))))))) 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(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) 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#(f(x),g(x)) -> f#(s(x)) f#(g(x)) -> g#(f(x)) f#(g(x)) -> f#(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(s(0()))) -> k(0()) k(0()) -> 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(0()))))))))))) -> k(s(s(0()))) k(s(s(0()))) -> 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(s(0()))) -> k(0()) k(0()) -> 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(0()))))))))))) -> k(s(s(0()))) k(s(s(0()))) -> s(s(s(s(s(s(s(s(s(0()))))))))) h(k(x),g(x)) -> k(s(x)) interpretation: [h](x0, x1) = x0, [g#](x0) = 2x0 + 6, [s](x0) = x0, [g](x0) = x0 + 1, [k](x0) = 0, [k#](x0) = 4, [0] = 0, [f#](x0) = 4x0 + 4, [h#](x0, x1) = 2x0 + 6, [s#](x0) = 2x0 + 4, [f](x0) = 2x0 orientation: k#(s(s(0()))) = 4 >= 4 = s#(s(s(s(s(s(s(s(s(0()))))))))) s#(s(s(s(s(s(s(s(s(s(s(0()))))))))))) = 4 >= 4 = k#(s(s(0()))) k#(s(s(0()))) = 4 >= 4 = s#(s(s(s(s(s(s(s(0())))))))) s#(s(s(s(0())))) = 4 >= 4 = k#(s(0())) k#(s(s(0()))) = 4 >= 4 = s#(s(s(s(s(s(s(0()))))))) s#(s(0())) = 4 >= 4 = f#(s(0())) f#(g(x)) = 4x + 8 >= 4x + 8 = g#(g(f(x))) g#(s(x)) = 2x + 6 >= 2x + 6 = s#(s(g(x))) g#(s(x)) = 2x + 6 >= 2x + 6 = s#(g(x)) g#(s(x)) = 2x + 6 >= 2x + 6 = g#(x) g#(x) = 2x + 6 >= 2x + 6 = h#(x,x) k#(s(s(0()))) = 4 >= 4 = s#(s(s(s(s(s(0())))))) k#(s(s(0()))) = 4 >= 4 = s#(s(s(s(s(0()))))) k#(s(s(0()))) = 4 >= 4 = s#(s(s(s(0())))) k#(s(s(0()))) = 4 >= 4 = s#(s(s(0()))) k#(s(0())) = 4 >= 4 = s#(s(0())) h#(f(x),g(x)) = 4x + 6 >= 4x + 4 = f#(s(x)) f#(g(x)) = 4x + 8 >= 4x + 6 = g#(f(x)) f#(g(x)) = 4x + 8 >= 4x + 4 = f#(x) s(s(0())) = 0 >= 0 = f(s(0())) g(x) = x + 1 >= x = h(x,x) s(x) = x >= x = h(x,0()) s(x) = x >= 0 = h(0(),x) f(g(x)) = 2x + 2 >= 2x + 2 = g(g(f(x))) g(s(x)) = x + 1 >= x + 1 = s(s(g(x))) h(f(x),g(x)) = 2x >= 2x = f(s(x)) s(s(s(0()))) = 0 >= 0 = k(0()) k(0()) = 0 >= 0 = s(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(0()))))))))))) = 0 >= 0 = k(s(s(0()))) k(s(s(0()))) = 0 >= 0 = 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(0()))))))))) 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(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) 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(s(0()))) -> k(0()) k(0()) -> 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(0()))))))))))) -> k(s(s(0()))) k(s(s(0()))) -> 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(0()))))))))) 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(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) 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(s(0()))) -> k(0()) k(0()) -> 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(0()))))))))))) -> k(s(s(0()))) k(s(s(0()))) -> s(s(s(s(s(s(s(s(s(0()))))))))) h(k(x),g(x)) -> k(s(x)) SCC Processor: #sccs: 1 #rules: 15 #arcs: 85/256 DPs: 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(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(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) 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(s(0()))) -> k(0()) k(0()) -> 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(0()))))))))))) -> k(s(s(0()))) k(s(s(0()))) -> s(s(s(s(s(s(s(s(s(0()))))))))) h(k(x),g(x)) -> k(s(x)) Arctic Interpretation Processor: dimension: 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(s(0()))) -> k(0()) k(0()) -> 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(0()))))))))))) -> k(s(s(0()))) k(s(s(0()))) -> 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 + 2, [k](x0) = x0 + 0, [k#](x0) = x0 + 0, [0] = 0, [f#](x0) = x0 + 0, [s#](x0) = 0, [f](x0) = x0 + 0 orientation: k#(s(s(0()))) = 0 >= 0 = s#(s(s(s(s(s(s(s(s(0()))))))))) 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(0())))))))) s#(s(s(s(0())))) = 0 >= 0 = k#(s(0())) k#(s(s(0()))) = 0 >= 0 = s#(s(s(s(s(s(s(0()))))))) s#(s(0())) = 0 >= 0 = f#(s(0())) f#(g(x)) = x + 2 >= 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) 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())) s(s(0())) = 0 >= 0 = f(s(0())) g(x) = x + 2 >= 0 = h(x,x) s(x) = 0 >= 0 = h(x,0()) s(x) = 0 >= 0 = h(0(),x) f(g(x)) = x + 2 >= x + 2 = g(g(f(x))) g(s(x)) = 2 >= 0 = s(s(g(x))) h(f(x),g(x)) = 0 >= 0 = f(s(x)) s(s(s(0()))) = 0 >= 0 = k(0()) k(0()) = 0 >= 0 = s(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(0()))))))))))) = 0 >= 0 = k(s(s(0()))) k(s(s(0()))) = 0 >= 0 = 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(0()))))))))) 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(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) 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(s(0()))) -> k(0()) k(0()) -> 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(0()))))))))))) -> k(s(s(0()))) k(s(s(0()))) -> 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(0()))))))))) 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(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) 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(s(0()))) -> k(0()) k(0()) -> 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(0()))))))))))) -> k(s(s(0()))) k(s(s(0()))) -> s(s(s(s(s(s(s(s(s(0()))))))))) h(k(x),g(x)) -> k(s(x)) SCC Processor: #sccs: 2 #rules: 11 #arcs: 53/196 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(s(0()))) -> k(0()) k(0()) -> 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(0()))))))))))) -> k(s(s(0()))) k(s(s(0()))) -> 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(s(0()))) -> k(0()) k(0()) -> 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(0()))))))))))) -> k(s(s(0()))) k(s(s(0()))) -> 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(0()))))))))) 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(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(s(0()))) -> k(0()) k(0()) -> 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(0()))))))))))) -> k(s(s(0()))) k(s(s(0()))) -> 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: {67} transitions: s{#,0}(69) -> 67* 00() -> 68* s0(68) -> 69* h0(68,68) -> 69* problem: DPs: 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(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(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(s(0()))) -> k(0()) k(0()) -> 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(0()))))))))))) -> k(s(s(0()))) k(s(s(0()))) -> 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: {28} transitions: 00() -> 29* s0(29) -> 30* k{#,0}(30) -> 28* h0(29,29) -> 30* problem: DPs: 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(0()))))))))))) -> k#(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(s(0()))) -> k(0()) k(0()) -> 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(0()))))))))))) -> k(s(s(0()))) k(s(s(0()))) -> 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: {58} transitions: s{#,0}(61) -> 58* 00() -> 59* s0(60) -> 61* s0(59) -> 60* h0(60,59) -> 61* h0(59,60) -> 61* h0(59,59) -> 60* f0(60) -> 61* problem: DPs: 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(0()))))))))))) -> k#(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(s(0()))) -> k(0()) k(0()) -> 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(0()))))))))))) -> k(s(s(0()))) k(s(s(0()))) -> 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: {52} transitions: s{#,0}(56) -> 52* s{#,0}(63) -> 52* 00() -> 53* s0(55) -> 56* s0(54) -> 55* s0(53) -> 63*,56,54 s0(63) -> 55* h0(53,54) -> 55* h0(53,53) -> 63*,54 h0(55,53) -> 56* h0(54,53) -> 55* h0(53,63) -> 55* h0(53,55) -> 56* h0(63,53) -> 55* k0(53) -> 56* f0(63) -> 55* f0(54) -> 55* problem: DPs: 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(0()))))))))))) -> k#(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(s(0()))) -> k(0()) k(0()) -> 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(0()))))))))))) -> k(s(s(0()))) k(s(s(0()))) -> 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: {45} transitions: s{#,0}(58) -> 45* s{#,0}(50) -> 45* 00() -> 46* s0(57) -> 58*,50,48 s0(48) -> 49* s0(49) -> 50* s0(46) -> 57*,49,47 s0(58) -> 49* s0(47) -> 48* h0(58,46) -> 49* h0(49,46) -> 50* h0(48,46) -> 49* h0(46,57) -> 58*,50,48 h0(46,49) -> 50* h0(46,47) -> 48* h0(46,58) -> 49* h0(47,46) -> 48* h0(46,48) -> 49* h0(46,46) -> 57*,47 h0(57,46) -> 58*,50,48 k0(46) -> 49* k0(57) -> 50* k0(47) -> 50* f0(47) -> 58*,48 f0(57) -> 58*,48 problem: DPs: 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(0()))))))))))) -> k#(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(s(0()))) -> k(0()) k(0()) -> 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(0()))))))))))) -> k(s(s(0()))) k(s(s(0()))) -> 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: {37} transitions: s{#,0}(52) -> 37* s{#,0}(43) -> 37* s{#,0}(57) -> 37* 00() -> 38* s0(38) -> 50,52,57*,41,39 s0(51) -> 52*,41,43 s0(57) -> 42,40,51* s0(40) -> 41* s0(52) -> 42* s0(41) -> 42* s0(39) -> 40* s0(50) -> 51*,42,40 s0(42) -> 43* h0(39,38) -> 40* h0(41,38) -> 42* h0(38,51) -> 52*,41,43 h0(50,38) -> 51*,40,42 h0(38,41) -> 42* h0(38,39) -> 40* h0(38,52) -> 42* h0(57,38) -> 40,51*,42 h0(38,38) -> 50,57*,39 h0(38,40) -> 41* h0(38,57) -> 40,42,51* h0(38,50) -> 51*,42,40 h0(40,38) -> 41* h0(51,38) -> 52*,41,43 h0(42,38) -> 43* h0(38,42) -> 43* h0(52,38) -> 42* k0(39) -> 42* k0(38) -> 52*,41 k0(57) -> 42* k0(50) -> 42* f0(39) -> 51*,40 f0(50) -> 51*,40 f0(57) -> 51* problem: DPs: 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(0()))))))))))) -> k#(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(s(0()))) -> k(0()) k(0()) -> 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(0()))))))))))) -> k(s(s(0()))) k(s(s(0()))) -> 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: {28} transitions: s{#,0}(58) -> 28* s{#,0}(35) -> 28* s{#,0}(45) -> 28* 00() -> 29* s0(33) -> 34* s0(45) -> 34* s0(32) -> 33* s0(57) -> 58*,33,35,31 s0(34) -> 35* s0(30) -> 31* s0(31) -> 32* s0(43) -> 44*,34,32 s0(44) -> 45*,33,35 s0(58) -> 34,32,44* s0(42) -> 43*,33,31 s0(29) -> 42,44,57*,32,30 h0(29,45) -> 34* h0(42,29) -> 43*,33,31 h0(43,29) -> 44*,32,34 h0(45,29) -> 34* h0(32,29) -> 33* h0(29,33) -> 34* h0(29,32) -> 33* h0(31,29) -> 32* h0(29,44) -> 45*,33,35 h0(29,57) -> 58*,33,31,35 h0(29,29) -> 42,57*,30 h0(44,29) -> 45*,33,35 h0(33,29) -> 34* h0(29,30) -> 31* h0(29,42) -> 43*,33,31 h0(29,43) -> 44*,34,32 h0(30,29) -> 31* h0(58,29) -> 44*,32,34 h0(34,29) -> 35* h0(29,58) -> 34,44*,32 h0(57,29) -> 58*,33,31,35 h0(29,31) -> 32* h0(29,34) -> 35* k0(42) -> 45*,33 k0(29) -> 44*,32 k0(57) -> 45* k0(30) -> 45*,33 f0(42) -> 43,58*,31 f0(30) -> 43,58*,31 f0(57) -> 43,58* problem: DPs: 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(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(s(0()))) -> k(0()) k(0()) -> 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(0()))))))))))) -> k(s(s(0()))) k(s(s(0()))) -> 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: {18} transitions: s{#,0}(52) -> 18* s{#,0}(61) -> 18* s{#,0}(37) -> 18* s{#,0}(26) -> 18* 00() -> 19* s0(23) -> 24* s0(37) -> 25* s0(33) -> 34*,21,23 s0(51) -> 52*,24,22,26 s0(24) -> 25* s0(34) -> 35*,24,22 s0(35) -> 36*,25,23 s0(52) -> 25,36*,23 s0(20) -> 21* s0(22) -> 23* s0(36) -> 37*,24,26 s0(50) -> 51*,25,21,23 s0(61) -> 25,21,23,51* s0(21) -> 22* s0(25) -> 26* s0(19) -> 50,35,33,52,61*,22,20 h0(50,19) -> 51*,25,21,23 h0(19,21) -> 22* h0(19,50) -> 51*,23,21,25 h0(19,35) -> 36*,23,25 h0(19,36) -> 37*,26,24 h0(19,51) -> 52*,22,26,24 h0(19,33) -> 34*,23,21 h0(61,19) -> 51*,25,21,23 h0(19,37) -> 25* h0(34,19) -> 35*,24,22 h0(19,25) -> 26* h0(19,61) -> 51*,23,21,25 h0(25,19) -> 26* h0(19,22) -> 23* h0(19,52) -> 36*,23,25 h0(33,19) -> 34*,21,23 h0(19,19) -> 50,33,61*,20 h0(19,23) -> 24* h0(37,19) -> 25* h0(24,19) -> 25* h0(20,19) -> 21* h0(35,19) -> 36*,25,23 h0(51,19) -> 52*,26,24,22 h0(23,19) -> 24* h0(19,34) -> 35*,22,24 h0(22,19) -> 23* h0(21,19) -> 22* h0(36,19) -> 37*,26,24 h0(19,20) -> 21* h0(19,24) -> 25* h0(52,19) -> 25,36*,23 k0(20) -> 36*,23 k0(19) -> 35,52*,22 k0(61) -> 36* k0(33) -> 36*,23 k0(50) -> 36* f0(20) -> 34,51*,21 f0(33) -> 34,51*,21 f0(50) -> 34,51* f0(61) -> 51* problem: DPs: 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(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(s(0()))) -> k(0()) k(0()) -> 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(0()))))))))))) -> k(s(s(0()))) k(s(s(0()))) -> 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}(38) -> 2* s{#,0}(28) -> 2* s{#,0}(44) -> 2* s{#,0}(11) -> 2* 00() -> 3* s0(23) -> 24*,7,5 s0(37) -> 38*,11,7,9 s0(38) -> 8,10,27* s0(24) -> 25*,8,6 s0(3) -> 35,25,23,37,43*,6,4 s0(35) -> 36*,7,5,9 s0(9) -> 10* s0(10) -> 11* s0(6) -> 7* s0(43) -> 44*,11,7,5,9 s0(7) -> 8* s0(28) -> 10* s0(4) -> 5* s0(36) -> 37*,10,8,6 s0(27) -> 28*,11,9 s0(26) -> 27*,10,8 s0(44) -> 10,8,37*,6 s0(5) -> 6* s0(8) -> 9* s0(25) -> 26*,7,9 h0(3,43) -> 44*,5,11,7,9 h0(26,3) -> 27*,8,10 h0(43,3) -> 44*,7,9,5,11 h0(27,3) -> 28*,9,11 h0(3,3) -> 35,23,43*,4 h0(3,5) -> 6* h0(3,7) -> 8* h0(6,3) -> 7* h0(3,4) -> 5* h0(3,9) -> 10* h0(3,36) -> 37*,6,8,10 h0(7,3) -> 8* h0(8,3) -> 9* h0(3,26) -> 27*,8,10 h0(44,3) -> 8,10,6,37* h0(3,37) -> 38*,11,7,9 h0(9,3) -> 10* h0(3,23) -> 24*,5,7 h0(3,10) -> 11* h0(3,24) -> 25*,6,8 h0(3,25) -> 26*,7,9 h0(28,3) -> 10* h0(24,3) -> 25*,8,6 h0(5,3) -> 6* h0(3,38) -> 8,27*,10 h0(36,3) -> 37*,8,10,6 h0(4,3) -> 5* h0(38,3) -> 27*,8,10 h0(3,35) -> 36*,5,7,9 h0(25,3) -> 26*,7,9 h0(3,6) -> 7* h0(10,3) -> 11* h0(3,27) -> 28*,11,9 h0(3,8) -> 9* h0(35,3) -> 36*,7,9,5 h0(3,44) -> 6,8,10,37* h0(23,3) -> 24*,7,5 h0(37,3) -> 38*,7,9,11 h0(3,28) -> 10* k0(43) -> 38* k0(35) -> 26,38* k0(3) -> 25,37*,6 k0(4) -> 26,38*,7 k0(23) -> 26,38*,7 f0(43) -> 36,44* f0(35) -> 36,24,44* f0(23) -> 36,24,44*,5 f0(4) -> 36,24,44*,5 problem: DPs: 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(s(0()))) -> k(0()) k(0()) -> 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(0()))))))))))) -> k(s(s(0()))) k(s(s(0()))) -> 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: 32/1