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(0()))) -> k(s(0())) k(s(0())) -> s(0()) 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())))))))) 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(0()))) -> k#(s(0())) 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())))))))) 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(0()))) -> k(s(0())) k(s(0())) -> s(0()) 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())))))))) 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(0()))) -> k#(s(0())) 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())))))))) 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(0()))) -> k(s(0())) k(s(0())) -> s(0()) 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())))))))) h(k(x),g(x)) -> k(s(x)) graph: k#(s(s(0()))) -> s#(s(s(s(s(s(s(s(0())))))))) -> 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(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(0())))))))))) -> k#(s(s(0()))) k#(s(s(0()))) -> s#(s(s(s(s(s(s(0()))))))) -> 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(0())))))))))) -> k#(s(s(0()))) k#(s(s(0()))) -> s#(s(s(s(s(s(0())))))) -> 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(0())))))))))) -> k#(s(s(0()))) k#(s(s(0()))) -> s#(s(s(s(s(0()))))) -> 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(0())))))))))) -> k#(s(s(0()))) k#(s(s(0()))) -> s#(s(s(s(0())))) -> 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(0())))))))))) -> k#(s(s(0()))) k#(s(s(0()))) -> s#(s(s(0()))) -> 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())) 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)) -> s#(x) -> 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(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(0())))))))))) -> k#(s(s(0()))) h#(f(x),g(x)) -> s#(x) -> 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(0())))))))))) -> k#(s(s(0()))) g#(s(x)) -> s#(g(x)) -> 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(0())))))))))) -> k#(s(s(0()))) g#(s(x)) -> s#(s(g(x))) -> 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(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(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(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(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(0())))))))))) -> k#(s(s(0()))) -> k#(s(s(0()))) -> s#(s(s(s(0())))) 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(0()))) -> k#(s(0())) -> k#(s(s(0()))) -> s#(s(s(s(s(s(s(s(0())))))))) s#(s(s(0()))) -> k#(s(0())) -> k#(s(s(0()))) -> s#(s(s(s(s(s(s(0()))))))) s#(s(s(0()))) -> k#(s(0())) -> k#(s(s(0()))) -> s#(s(s(s(s(s(0())))))) s#(s(s(0()))) -> k#(s(0())) -> k#(s(s(0()))) -> s#(s(s(s(s(0()))))) s#(s(s(0()))) -> k#(s(0())) -> k#(s(s(0()))) -> s#(s(s(s(0())))) 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(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())) -> 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(0()))) -> k#(s(0())) 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())))))))) 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(0()))) -> k(s(0())) k(s(0())) -> s(0()) 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())))))))) h(k(x),g(x)) -> k(s(x)) graph: 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(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(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(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(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(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(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(0()))) -> k#(s(0())) k#(s(s(0()))) -> s#(s(s(s(s(0()))))) -> 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(0()))) -> k#(s(0())) k#(s(s(0()))) -> s#(s(s(s(0())))) -> 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(0()))) -> k#(s(0())) k#(s(s(0()))) -> s#(s(s(0()))) -> 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(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)) -> 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(0()))) -> k#(s(0())) h#(k(x),g(x)) -> s#(x) -> 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(0()))) -> k#(s(0())) h#(f(x),g(x)) -> s#(x) -> 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(0()))) -> k#(s(0())) g#(s(x)) -> s#(g(x)) -> 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(0()))) -> k#(s(0())) g#(s(x)) -> s#(s(g(x))) -> 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(0())))))))))) -> k#(s(s(0()))) -> k#(s(s(0()))) -> s#(s(s(0()))) 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(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(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(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(0())))))))))) -> k#(s(s(0()))) -> k#(s(s(0()))) -> s#(s(s(s(s(s(s(s(0())))))))) s#(s(s(0()))) -> k#(s(0())) -> k#(s(s(0()))) -> s#(s(s(0()))) s#(s(s(0()))) -> k#(s(0())) -> k#(s(s(0()))) -> s#(s(s(s(0())))) s#(s(s(0()))) -> k#(s(0())) -> k#(s(s(0()))) -> s#(s(s(s(s(0()))))) s#(s(s(0()))) -> k#(s(0())) -> k#(s(s(0()))) -> s#(s(s(s(s(s(0())))))) s#(s(s(0()))) -> k#(s(0())) -> k#(s(s(0()))) -> s#(s(s(s(s(s(s(0()))))))) 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)) -> 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: 20 #arcs: 103/529 DPs: k#(s(s(0()))) -> s#(s(s(s(s(s(s(s(0())))))))) 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(0()))) -> k#(s(0())) k#(s(s(0()))) -> 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(0()))))) k#(s(s(0()))) -> s#(s(s(s(0())))) k#(s(s(0()))) -> s#(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(0()))) -> k(s(0())) k(s(0())) -> s(0()) 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())))))))) 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(0())) -> k(0()) k(0()) -> 0() s(s(s(0()))) -> k(s(0())) k(s(0())) -> s(0()) 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())))))))) h(k(x),g(x)) -> k(s(x)) interpretation: [h](x0, x1) = x0 + x1 + 0, [g#](x0) = x0 + 4, [s](x0) = x0 + 0, [g](x0) = x0 + 4, [k](x0) = 0, [k#](x0) = x0 + 1, [0] = 0, [f#](x0) = x0 + 0, [h#](x0, x1) = x1 + 0, [s#](x0) = x0 + 1, [f](x0) = x0 + 0 orientation: k#(s(s(0()))) = 1 >= 1 = s#(s(s(s(s(s(s(s(0())))))))) s#(s(s(s(s(s(s(s(s(s(0())))))))))) = 1 >= 1 = k#(s(s(0()))) k#(s(s(0()))) = 1 >= 1 = s#(s(s(s(s(s(s(0()))))))) s#(s(s(0()))) = 1 >= 1 = k#(s(0())) k#(s(s(0()))) = 1 >= 1 = s#(s(s(s(s(s(0())))))) s#(s(0())) = 1 >= 0 = f#(s(0())) f#(g(x)) = x + 4 >= x + 4 = g#(g(f(x))) g#(s(x)) = x + 4 >= x + 4 = s#(s(g(x))) g#(s(x)) = x + 4 >= x + 4 = s#(g(x)) g#(s(x)) = x + 4 >= x + 4 = g#(x) g#(x) = x + 4 >= x + 0 = h#(x,x) h#(k(x),g(x)) = x + 4 >= x + 1 = k#(s(x)) k#(s(s(0()))) = 1 >= 1 = s#(s(s(s(s(0()))))) k#(s(s(0()))) = 1 >= 1 = s#(s(s(s(0())))) k#(s(s(0()))) = 1 >= 1 = s#(s(s(0()))) h#(k(x),g(x)) = x + 4 >= x + 1 = s#(x) h#(f(x),g(x)) = x + 4 >= x + 0 = f#(s(x)) f#(g(x)) = x + 4 >= x + 4 = g#(f(x)) f#(g(x)) = x + 4 >= x + 0 = f#(x) h#(f(x),g(x)) = x + 4 >= x + 1 = s#(x) s(s(0())) = 0 >= 0 = f(s(0())) g(x) = x + 4 >= 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 + 4 >= x + 4 = g(g(f(x))) g(s(x)) = x + 4 >= x + 4 = s(s(g(x))) h(f(x),g(x)) = x + 4 >= x + 0 = f(s(x)) s(s(0())) = 0 >= 0 = k(0()) k(0()) = 0 >= 0 = 0() s(s(s(0()))) = 0 >= 0 = k(s(0())) k(s(0())) = 0 >= 0 = s(0()) 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())))))))) h(k(x),g(x)) = x + 4 >= 0 = k(s(x)) problem: DPs: k#(s(s(0()))) -> s#(s(s(s(s(s(s(s(0())))))))) 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(0()))) -> k#(s(0())) k#(s(s(0()))) -> s#(s(s(s(s(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(0()))))) k#(s(s(0()))) -> s#(s(s(s(0())))) k#(s(s(0()))) -> s#(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(0()))) -> k(s(0())) k(s(0())) -> s(0()) 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())))))))) h(k(x),g(x)) -> k(s(x)) Restore Modifier: DPs: k#(s(s(0()))) -> s#(s(s(s(s(s(s(s(0())))))))) 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(0()))) -> k#(s(0())) k#(s(s(0()))) -> s#(s(s(s(s(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(0()))))) k#(s(s(0()))) -> s#(s(s(s(0())))) k#(s(s(0()))) -> s#(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(0()))) -> k(s(0())) k(s(0())) -> s(0()) 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())))))))) h(k(x),g(x)) -> k(s(x)) SCC Processor: #sccs: 2 #rules: 14 #arcs: 73/361 DPs: h#(f(x),g(x)) -> f#(s(x)) f#(g(x)) -> g#(g(f(x))) g#(s(x)) -> g#(x) g#(x) -> h#(x,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(0())) -> k(0()) k(0()) -> 0() s(s(s(0()))) -> k(s(0())) k(s(0())) -> s(0()) 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())))))))) 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(0())) -> k(0()) k(0()) -> 0() s(s(s(0()))) -> k(s(0())) k(s(0())) -> s(0()) 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())))))))) h(k(x),g(x)) -> k(s(x)) interpretation: [h](x0, x1) = 2, [g#](x0) = 5, [s](x0) = 2, [g](x0) = x0 + 4, [k](x0) = x0 + 0, [0] = 0, [f#](x0) = 1x0 + 4, [h#](x0, x1) = 4, [f](x0) = x0 + 0 orientation: h#(f(x),g(x)) = 4 >= 4 = f#(s(x)) f#(g(x)) = 1x + 5 >= 5 = g#(g(f(x))) g#(s(x)) = 5 >= 5 = g#(x) g#(x) = 5 >= 4 = h#(x,x) f#(g(x)) = 1x + 5 >= 5 = g#(f(x)) f#(g(x)) = 1x + 5 >= 1x + 4 = f#(x) s(s(0())) = 2 >= 2 = f(s(0())) g(x) = x + 4 >= 2 = h(x,x) s(x) = 2 >= 2 = h(x,0()) s(x) = 2 >= 2 = h(0(),x) f(g(x)) = x + 4 >= x + 4 = g(g(f(x))) g(s(x)) = 4 >= 2 = s(s(g(x))) h(f(x),g(x)) = 2 >= 2 = f(s(x)) s(s(0())) = 2 >= 0 = k(0()) k(0()) = 0 >= 0 = 0() s(s(s(0()))) = 2 >= 2 = k(s(0())) k(s(0())) = 2 >= 2 = s(0()) s(s(s(s(s(s(s(s(s(s(0())))))))))) = 2 >= 2 = k(s(s(0()))) k(s(s(0()))) = 2 >= 2 = s(s(s(s(s(s(s(s(0())))))))) h(k(x),g(x)) = 2 >= 2 = k(s(x)) problem: DPs: h#(f(x),g(x)) -> f#(s(x)) f#(g(x)) -> g#(g(f(x))) g#(s(x)) -> g#(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(0())) -> k(0()) k(0()) -> 0() s(s(s(0()))) -> k(s(0())) k(s(0())) -> s(0()) 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())))))))) h(k(x),g(x)) -> k(s(x)) Restore Modifier: DPs: h#(f(x),g(x)) -> f#(s(x)) f#(g(x)) -> g#(g(f(x))) g#(s(x)) -> g#(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(0())) -> k(0()) k(0()) -> 0() s(s(s(0()))) -> k(s(0())) k(s(0())) -> s(0()) 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())))))))) h(k(x),g(x)) -> k(s(x)) SCC Processor: #sccs: 2 #rules: 2 #arcs: 13/25 DPs: 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(0())) -> k(0()) k(0()) -> 0() s(s(s(0()))) -> k(s(0())) k(s(0())) -> s(0()) 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())))))))) 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(0()))) -> k(s(0())) k(s(0())) -> s(0()) 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())))))))) h(k(x),g(x)) -> k(s(x)) The DP: f#(g(x)) -> f#(x) has the edges: 0 > 0 Qed 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(0()))) -> k(s(0())) k(s(0())) -> s(0()) 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())))))))) 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(0()))) -> k(s(0())) k(s(0())) -> s(0()) 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())))))))) 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(0())))))))) 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(0()))) -> k#(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(0()))) -> k(s(0())) k(s(0())) -> s(0()) 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())))))))) h(k(x),g(x)) -> k(s(x)) Bounds Processor: bound: 0 enrichment: top-dp automaton: final states: {26} transitions: 00() -> 27* s0(27) -> 28* k{#,0}(28) -> 26* h0(27,27) -> 28* problem: DPs: k#(s(s(0()))) -> s#(s(s(s(s(s(s(s(0())))))))) 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()))))))) 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(0()))) -> k(s(0())) k(s(0())) -> s(0()) 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())))))))) h(k(x),g(x)) -> k(s(x)) Bounds Processor: bound: 0 enrichment: top-dp automaton: final states: {47} transitions: s{#,0}(56) -> 47* s{#,0}(50) -> 47* 00() -> 56*,50,48 s0(48) -> 49* s0(49) -> 50* s0(56) -> 49* h0(48,56) -> 49* h0(48,49) -> 50* h0(56,48) -> 49* h0(49,56) -> 50* h0(48,48) -> 49* h0(56,49) -> 50* h0(56,56) -> 49* h0(49,48) -> 50* k0(48) -> 50* k0(56) -> 50* f0(49) -> 50* problem: DPs: k#(s(s(0()))) -> s#(s(s(s(s(s(s(s(0())))))))) 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()))))))) 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(0()))) -> k(s(0())) k(s(0())) -> s(0()) 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())))))))) h(k(x),g(x)) -> k(s(x)) Bounds Processor: bound: 0 enrichment: top-dp automaton: final states: {41} transitions: s{#,0}(52) -> 41* s{#,0}(45) -> 41* 00() -> 51*,44,42 s0(51) -> 52*,45,43 s0(52) -> 44* s0(43) -> 44* s0(44) -> 45* s0(42) -> 43* h0(52,42) -> 44* h0(51,44) -> 45* h0(51,42) -> 52*,45,43 h0(42,51) -> 52*,43,45 h0(44,42) -> 45* h0(42,42) -> 43* h0(42,44) -> 45* h0(51,52) -> 44* h0(51,43) -> 44* h0(42,43) -> 44* h0(51,51) -> 52*,43,45 h0(52,51) -> 44* h0(43,51) -> 44* h0(42,52) -> 44* h0(43,42) -> 44* h0(44,51) -> 45* k0(42) -> 44* k0(43) -> 45* k0(52) -> 45* k0(51) -> 44* f0(43) -> 44* f0(52) -> 44* problem: DPs: k#(s(s(0()))) -> s#(s(s(s(s(s(s(s(0())))))))) 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()))))))) 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(0()))) -> k(s(0())) k(s(0())) -> s(0()) 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())))))))) h(k(x),g(x)) -> k(s(x)) Bounds Processor: bound: 0 enrichment: top-dp automaton: final states: {34} transitions: s{#,0}(52) -> 34* s{#,0}(47) -> 34* s{#,0}(39) -> 34* 00() -> 45,47,52*,37,35 s0(37) -> 38* s0(38) -> 39* s0(45) -> 46*,38,36 s0(35) -> 36* s0(52) -> 46*,36,38 s0(36) -> 37* s0(46) -> 47*,39,37 s0(47) -> 38* h0(45,37) -> 38* h0(47,52) -> 38* h0(45,46) -> 47*,39,37 h0(45,38) -> 39* h0(45,47) -> 38* h0(36,35) -> 37* h0(45,36) -> 37* h0(37,52) -> 38* h0(35,35) -> 36* h0(52,46) -> 37,39,47* h0(38,35) -> 39* h0(45,52) -> 36,46*,38 h0(35,45) -> 46*,36,38 h0(45,35) -> 46*,36,38 h0(52,35) -> 36,46*,38 h0(38,52) -> 39* h0(35,36) -> 37* h0(36,52) -> 37* h0(46,35) -> 47*,37,39 h0(35,47) -> 38* h0(47,35) -> 38* h0(52,45) -> 36,46*,38 h0(35,38) -> 39* h0(52,37) -> 38* h0(46,45) -> 47*,37,39 h0(46,52) -> 47*,37,39 h0(52,52) -> 36,46*,38 h0(45,45) -> 46*,36,38 h0(37,35) -> 38* h0(52,36) -> 37* h0(52,47) -> 38* h0(35,37) -> 38* h0(35,52) -> 36,46*,38 h0(47,45) -> 38* h0(36,45) -> 37* h0(37,45) -> 38* h0(35,46) -> 47*,37,39 h0(38,45) -> 39* h0(52,38) -> 39* k0(46) -> 38* k0(35) -> 47*,37 k0(36) -> 38* k0(52) -> 47* k0(45) -> 47*,37 f0(46) -> 47*,37 f0(36) -> 47*,37 problem: DPs: k#(s(s(0()))) -> s#(s(s(s(s(s(s(s(0())))))))) 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()))))))) 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(0()))) -> k(s(0())) k(s(0())) -> s(0()) 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())))))))) h(k(x),g(x)) -> k(s(x)) Bounds Processor: bound: 0 enrichment: top-dp automaton: final states: {26} transitions: s{#,0}(32) -> 26* s{#,0}(48) -> 26* s{#,0}(41) -> 26* 00() -> 38,40,47*,29,27 s0(38) -> 39*,28,30 s0(30) -> 31* s0(31) -> 32* s0(48) -> 31,40*,29 s0(40) -> 41*,32,30 s0(41) -> 31* s0(39) -> 40*,31,29 s0(28) -> 29* s0(27) -> 28* s0(47) -> 48*,32,28,30 s0(29) -> 30* h0(47,31) -> 32* h0(27,47) -> 48*,32,30,28 h0(27,41) -> 31* h0(38,47) -> 48*,28,30,32 h0(39,38) -> 40*,31,29 h0(47,39) -> 40*,31,29 h0(41,38) -> 31* h0(30,38) -> 31* h0(38,27) -> 39*,28,30 h0(48,27) -> 40*,29,31 h0(27,39) -> 40*,31,29 h0(40,47) -> 32,41*,30 h0(31,27) -> 32* h0(29,38) -> 30* h0(48,47) -> 40*,29,31 h0(47,27) -> 48*,32,28,30 h0(47,28) -> 29* h0(39,27) -> 40*,29,31 h0(47,48) -> 40*,29,31 h0(47,41) -> 31* h0(47,30) -> 31* h0(27,40) -> 41*,32,30 h0(31,38) -> 32* h0(31,47) -> 32* h0(30,47) -> 31* h0(38,41) -> 31* h0(39,47) -> 40*,29,31 h0(28,47) -> 29* h0(41,47) -> 31* h0(38,39) -> 40*,31,29 h0(27,31) -> 32* h0(27,30) -> 31* h0(27,29) -> 30* h0(27,28) -> 29* h0(40,27) -> 41*,32,30 h0(28,27) -> 29* h0(27,38) -> 39*,30,28 h0(47,29) -> 30* h0(38,38) -> 39*,28,30 h0(38,30) -> 31* h0(38,40) -> 41*,30,32 h0(38,29) -> 30* h0(38,28) -> 29* h0(27,48) -> 40*,31,29 h0(27,27) -> 28* h0(40,38) -> 41*,30,32 h0(29,27) -> 30* h0(38,48) -> 40*,31,29 h0(28,38) -> 29* h0(47,38) -> 48*,32,28,30 h0(38,31) -> 32* h0(47,47) -> 48*,28,30,32 h0(29,47) -> 30* h0(41,27) -> 31* h0(48,38) -> 40*,31,29 h0(47,40) -> 41*,30,32 h0(30,27) -> 31* k0(27) -> 40*,29 k0(48) -> 41* k0(28) -> 41*,30 k0(39) -> 41*,30 k0(38) -> 40*,29 k0(47) -> 40* f0(48) -> 40* f0(28) -> 40*,29 f0(39) -> 40*,29 problem: DPs: k#(s(s(0()))) -> s#(s(s(s(s(s(s(s(0())))))))) 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()))))))) 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(0()))) -> k(s(0())) k(s(0())) -> s(0()) 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())))))))) h(k(x),g(x)) -> k(s(x)) Bounds Processor: bound: 0 enrichment: top-dp automaton: final states: {17} transitions: s{#,0}(54) -> 17* s{#,0}(49) -> 17* s{#,0}(34) -> 17* s{#,0}(24) -> 17* 00() -> 47,32,30,49,54*,20,18 s0(23) -> 24* s0(33) -> 34*,24,22 s0(18) -> 19* s0(32) -> 33*,21,23 s0(34) -> 23* s0(30) -> 31*,19,21 s0(31) -> 32*,22,20 s0(48) -> 49*,24,22,20 s0(49) -> 33*,21,23 s0(20) -> 21* s0(22) -> 23* s0(54) -> 19,21,23,48* s0(47) -> 48*,19,21,23 s0(21) -> 22* s0(19) -> 20* h0(47,31) -> 22,20,32* h0(30,49) -> 21,23,33* h0(18,19) -> 20* h0(47,22) -> 23* h0(18,34) -> 23* h0(21,54) -> 22* h0(47,33) -> 22,24,34* h0(47,19) -> 20* h0(54,32) -> 23,21,33* h0(30,30) -> 31*,19,21 h0(20,47) -> 21* h0(34,18) -> 23* h0(30,21) -> 22* h0(19,30) -> 20* h0(33,54) -> 34*,24,22 h0(30,34) -> 23* h0(47,23) -> 24* h0(47,21) -> 22* h0(49,30) -> 33*,23,21 h0(19,54) -> 20* h0(47,34) -> 23* h0(34,54) -> 23* h0(22,47) -> 23* h0(48,47) -> 49*,24,20,22 h0(54,19) -> 20* h0(18,21) -> 22* h0(18,22) -> 23* h0(47,48) -> 49*,20,24,22 h0(22,18) -> 23* h0(23,47) -> 24* h0(32,47) -> 23,33*,21 h0(48,54) -> 49*,20,24,22 h0(47,30) -> 48*,19,23,21 h0(21,18) -> 22* h0(34,30) -> 23* h0(48,18) -> 49*,22,20,24 h0(18,20) -> 21* h0(31,47) -> 20,32*,22 h0(18,18) -> 19* h0(20,54) -> 21* h0(54,48) -> 20,22,49*,24 h0(30,47) -> 48*,19,23,21 h0(32,30) -> 33*,23,21 h0(47,54) -> 23,19,21,48* h0(31,30) -> 32*,20,22 h0(18,48) -> 49*,20,22,24 h0(30,48) -> 49*,22,20,24 h0(22,30) -> 23* h0(33,30) -> 34*,22,24 h0(33,18) -> 34*,22,24 h0(54,34) -> 23* h0(30,33) -> 34*,22,24 h0(49,18) -> 23,33*,21 h0(30,20) -> 21* h0(18,30) -> 31*,21,19 h0(31,54) -> 20,32*,22 h0(32,18) -> 33*,23,21 h0(18,31) -> 32*,20,22 h0(54,47) -> 23,19,21,48* h0(23,54) -> 24* h0(19,18) -> 20* h0(47,32) -> 21,23,33* h0(18,23) -> 24* h0(54,49) -> 23,21,33* h0(19,47) -> 20* h0(33,47) -> 34*,22,24 h0(23,18) -> 24* h0(48,30) -> 49*,20,22,24 h0(30,18) -> 31*,19,21 h0(30,22) -> 23* h0(47,18) -> 48*,23,19,21 h0(47,49) -> 23,33*,21 h0(30,32) -> 33*,21,23 h0(30,54) -> 19,23,21,48* h0(54,18) -> 23,19,48*,21 h0(47,20) -> 21* h0(54,31) -> 20,22,32* h0(18,49) -> 23,21,33* h0(34,47) -> 23* h0(54,22) -> 23* h0(49,47) -> 21,33*,23 h0(32,54) -> 23,33*,21 h0(20,18) -> 21* h0(54,54) -> 23,19,21,48* h0(31,18) -> 32*,22,20 h0(18,54) -> 23,21,19,48* h0(30,19) -> 20* h0(54,21) -> 22* h0(20,30) -> 21* h0(49,54) -> 23,33*,21 h0(54,20) -> 21* h0(22,54) -> 23* h0(21,30) -> 22* h0(18,32) -> 33*,23,21 h0(30,23) -> 24* h0(18,33) -> 34*,22,24 h0(30,31) -> 32*,22,20 h0(21,47) -> 22* h0(54,30) -> 19,23,48*,21 h0(54,23) -> 24* h0(18,47) -> 48*,23,21,19 h0(47,47) -> 48*,19,23,21 h0(54,33) -> 22,24,34* h0(23,30) -> 24* k0(48) -> 33* k0(19) -> 33*,21 k0(31) -> 33*,21 k0(18) -> 32,49*,20 k0(54) -> 49* k0(30) -> 32,49*,20 k0(47) -> 32,49* f0(48) -> 32,49* f0(19) -> 32,49*,20 f0(31) -> 32,49*,20 problem: DPs: k#(s(s(0()))) -> s#(s(s(s(s(s(s(s(0())))))))) 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(0()))) -> k(s(0())) k(s(0())) -> s(0()) 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())))))))) h(k(x),g(x)) -> k(s(x)) Bounds Processor: bound: 0 enrichment: top-dp automaton: final states: {2} transitions: s{#,0}(32) -> 2* s{#,0}(10) -> 2* s{#,0}(42) -> 2* s{#,0}(36) -> 2* 00() -> 33,29,27,35,41*,5,3 s0(33) -> 34*,4,8,6 s0(32) -> 9* s0(34) -> 35*,7,5,9 s0(30) -> 31*,7,9 s0(31) -> 32*,10,8 s0(3) -> 4* s0(35) -> 36*,10,8,6 s0(9) -> 10* s0(41) -> 42*,4,10,8,6 s0(6) -> 7* s0(7) -> 8* s0(28) -> 29*,7,5 s0(4) -> 5* s0(36) -> 31*,7,9 s0(27) -> 28*,4,6 s0(5) -> 6* s0(8) -> 9* s0(42) -> 35*,7,5,9 s0(29) -> 30*,8,6 h0(6,27) -> 7* h0(41,8) -> 9* h0(27,41) -> 42*,4,8,6,10 h0(33,28) -> 5,7,29* h0(33,35) -> 36*,10,8,6 h0(41,41) -> 42*,4,10,8,6 h0(33,36) -> 31*,9,7 h0(27,33) -> 34*,4,8,6 h0(8,27) -> 9* h0(29,3) -> 30*,8,6 h0(41,32) -> 9* h0(42,33) -> 9,5,7,35* h0(30,3) -> 31*,7,9 h0(28,33) -> 7,29*,5 h0(33,42) -> 9,7,5,35* h0(29,33) -> 6,8,30* h0(27,34) -> 35*,9,5,7 h0(41,29) -> 8,30*,6 h0(3,30) -> 31*,7,9 h0(27,3) -> 28*,4,6 h0(3,3) -> 4* h0(31,27) -> 32*,10,8 h0(27,32) -> 9* h0(32,3) -> 9* h0(4,27) -> 5* h0(41,36) -> 31*,7,9 h0(3,5) -> 6* h0(27,5) -> 6* h0(35,33) -> 36*,10,8,6 h0(3,7) -> 8* h0(41,9) -> 10* h0(6,3) -> 7* h0(41,33) -> 42*,4,10,8,6 h0(8,33) -> 9* h0(31,41) -> 10,32*,8 h0(3,4) -> 5* h0(3,9) -> 10* h0(3,36) -> 31*,7,9 h0(33,33) -> 34*,4,6,8 h0(4,33) -> 5* h0(33,9) -> 10* h0(32,33) -> 9* h0(7,3) -> 8* h0(28,41) -> 7,29*,5 h0(33,8) -> 9* h0(32,27) -> 9* h0(35,41) -> 10,8,6,36* h0(5,27) -> 6* h0(8,3) -> 9* h0(3,34) -> 35*,5,7,9 h0(33,29) -> 6,8,30* h0(42,41) -> 35*,5,7,9 h0(33,30) -> 31*,7,9 h0(27,31) -> 32*,8,10 h0(3,41) -> 42*,4,6,8,10 h0(34,27) -> 35*,7,9,5 h0(30,33) -> 7,9,31* h0(3,33) -> 34*,4,6,8 h0(9,3) -> 10* h0(27,30) -> 31*,9,7 h0(6,33) -> 7* h0(41,4) -> 5* h0(27,29) -> 30*,6,8 h0(3,31) -> 32*,8,10 h0(34,41) -> 9,7,5,35* h0(33,41) -> 42*,4,10,8,6 h0(33,32) -> 9* h0(4,41) -> 5* h0(41,34) -> 5,7,9,35* h0(31,3) -> 32*,8,10 h0(9,33) -> 10* h0(41,30) -> 31*,7,9 h0(27,28) -> 29*,5,7 h0(27,8) -> 9* h0(31,33) -> 32*,10,8 h0(28,3) -> 29*,7,5 h0(28,27) -> 29*,7,5 h0(41,35) -> 10,8,36*,6 h0(27,7) -> 8* h0(33,27) -> 34*,4,6,8 h0(33,6) -> 7* h0(5,3) -> 6* h0(9,27) -> 10* h0(7,33) -> 8* h0(33,31) -> 32*,8,10 h0(4,3) -> 5* h0(36,3) -> 31*,7,9 h0(33,7) -> 8* h0(34,3) -> 35*,7,9,5 h0(42,3) -> 7,9,5,35* h0(3,35) -> 36*,6,8,10 h0(5,33) -> 6* h0(41,31) -> 10,32*,8 h0(3,29) -> 30*,6,8 h0(7,41) -> 8* h0(36,41) -> 9,7,31* h0(35,27) -> 36*,6,10,8 h0(7,27) -> 8* h0(27,27) -> 28*,4,6 h0(30,41) -> 9,31*,7 h0(41,28) -> 5,7,29* h0(33,4) -> 5* h0(3,42) -> 5,35*,7,9 h0(3,6) -> 7* h0(41,6) -> 7* h0(27,4) -> 5* h0(34,33) -> 35*,9,5,7 h0(3,27) -> 28*,4,6 h0(5,41) -> 6* h0(27,6) -> 7* h0(29,27) -> 30*,6,8 h0(3,8) -> 9* h0(33,34) -> 35*,9,7,5 h0(27,9) -> 10* h0(35,3) -> 36*,8,10,6 h0(41,5) -> 6* h0(27,42) -> 35*,9,5,7 h0(36,33) -> 9,31*,7 h0(41,7) -> 8* h0(29,41) -> 30*,8,6 h0(42,27) -> 7,9,5,35* h0(41,3) -> 42*,4,8,10,6 h0(33,3) -> 34*,4,8,6 h0(33,5) -> 6* h0(32,41) -> 9* h0(3,28) -> 29*,5,7 h0(41,42) -> 9,5,35*,7 h0(27,36) -> 31*,9,7 h0(9,41) -> 10* h0(6,41) -> 7* h0(41,27) -> 42*,4,10,8,6 h0(8,41) -> 9* h0(27,35) -> 36*,6,8,10 h0(36,27) -> 7,9,31* h0(30,27) -> 31*,7,9 h0(3,32) -> 9* k0(27) -> 29,35*,5 k0(41) -> 35* k0(28) -> 30,36*,6 k0(42) -> 36* k0(33) -> 29,35* k0(34) -> 30,36* k0(3) -> 29,35*,5 k0(4) -> 30,36*,6 f0(28) -> 29,35*,5 f0(4) -> 29,35*,5 f0(42) -> 35* f0(34) -> 29,35* problem: DPs: 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(0()))) -> k(s(0())) k(s(0())) -> s(0()) 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())))))))) h(k(x),g(x)) -> k(s(x)) SCC Processor: #sccs: 0 #rules: 0 #arcs: 24/1