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(0()) -> k(0()) s(k(0())) -> 0() s(s(0())) -> k(s(0())) k(s(0())) -> 0() 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()))))))) 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#(0()) -> k#(0()) s#(s(0())) -> k#(s(0())) 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()))))))) 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(0()) -> k(0()) s(k(0())) -> 0() s(s(0())) -> k(s(0())) k(s(0())) -> 0() 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()))))))) 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#(0()) -> k#(0()) s#(s(0())) -> k#(s(0())) 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()))))))) 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(0()) -> k(0()) s(k(0())) -> 0() s(s(0())) -> k(s(0())) k(s(0())) -> 0() 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()))))))) h(k(x),g(x)) -> k(s(x)) graph: k#(s(s(0()))) -> s#(s(s(s(s(s(s(0()))))))) -> 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())) -> k#(s(0())) k#(s(s(0()))) -> s#(s(s(s(s(s(s(0()))))))) -> 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(0()))))))))) -> k#(s(s(0()))) k#(s(s(0()))) -> s#(s(s(s(s(s(0())))))) -> s#(s(0())) -> k#(s(0())) k#(s(s(0()))) -> s#(s(s(s(s(s(0())))))) -> 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(0()))))))))) -> k#(s(s(0()))) k#(s(s(0()))) -> s#(s(s(s(s(0()))))) -> s#(s(0())) -> k#(s(0())) k#(s(s(0()))) -> s#(s(s(s(s(0()))))) -> 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(0()))))))))) -> k#(s(s(0()))) k#(s(s(0()))) -> s#(s(s(s(0())))) -> s#(s(0())) -> k#(s(0())) k#(s(s(0()))) -> s#(s(s(s(0())))) -> 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(0()))))))))) -> k#(s(s(0()))) k#(s(s(0()))) -> s#(s(s(0()))) -> s#(s(0())) -> k#(s(0())) k#(s(s(0()))) -> s#(s(s(0()))) -> 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(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(0()))))))))) -> k#(s(s(0()))) h#(k(x),g(x)) -> s#(x) -> s#(s(0())) -> k#(s(0())) h#(k(x),g(x)) -> s#(x) -> 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(0()))))))))) -> k#(s(s(0()))) h#(f(x),g(x)) -> s#(x) -> s#(s(0())) -> k#(s(0())) h#(f(x),g(x)) -> s#(x) -> 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(0()))))))))) -> k#(s(s(0()))) g#(s(x)) -> s#(g(x)) -> s#(s(0())) -> k#(s(0())) g#(s(x)) -> s#(g(x)) -> 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(0()))))))))) -> k#(s(s(0()))) g#(s(x)) -> s#(s(g(x))) -> s#(s(0())) -> k#(s(0())) g#(s(x)) -> s#(s(g(x))) -> 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(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(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(0()))))))))) -> k#(s(s(0()))) -> k#(s(s(0()))) -> s#(s(s(s(s(0()))))) 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(0()))))))))) -> k#(s(s(0()))) -> k#(s(s(0()))) -> s#(s(s(0()))) s#(s(0())) -> k#(s(0())) -> k#(s(s(0()))) -> s#(s(s(s(s(s(s(0()))))))) s#(s(0())) -> k#(s(0())) -> k#(s(s(0()))) -> s#(s(s(s(s(s(0())))))) s#(s(0())) -> k#(s(0())) -> k#(s(s(0()))) -> s#(s(s(s(s(0()))))) s#(s(0())) -> k#(s(0())) -> k#(s(s(0()))) -> s#(s(s(s(0())))) s#(s(0())) -> k#(s(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#(0()) -> k#(0()) -> k#(s(s(0()))) -> s#(s(s(s(s(s(s(0()))))))) s#(0()) -> k#(0()) -> k#(s(s(0()))) -> s#(s(s(s(s(s(0())))))) s#(0()) -> k#(0()) -> k#(s(s(0()))) -> s#(s(s(s(s(0()))))) s#(0()) -> k#(0()) -> k#(s(s(0()))) -> s#(s(s(s(0())))) s#(0()) -> k#(0()) -> k#(s(s(0()))) -> s#(s(s(0()))) 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#(0()) -> k#(0()) s#(s(0())) -> k#(s(0())) 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()))))))) 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(0()) -> k(0()) s(k(0())) -> 0() s(s(0())) -> k(s(0())) k(s(0())) -> 0() 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()))))))) h(k(x),g(x)) -> k(s(x)) graph: 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#(0()) -> k#(0()) k#(s(s(0()))) -> s#(s(s(s(s(s(s(0()))))))) -> 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(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#(0()) -> k#(0()) k#(s(s(0()))) -> s#(s(s(s(s(s(0())))))) -> 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(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#(0()) -> k#(0()) k#(s(s(0()))) -> s#(s(s(s(s(0()))))) -> 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(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#(0()) -> k#(0()) k#(s(s(0()))) -> s#(s(s(s(0())))) -> s#(s(0())) -> k#(s(0())) k#(s(s(0()))) -> s#(s(s(s(0())))) -> 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#(0()) -> k#(0()) k#(s(s(0()))) -> s#(s(s(0()))) -> s#(s(0())) -> k#(s(0())) k#(s(s(0()))) -> s#(s(s(0()))) -> 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)) -> 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#(0()) -> k#(0()) h#(k(x),g(x)) -> s#(x) -> s#(s(0())) -> k#(s(0())) h#(k(x),g(x)) -> s#(x) -> 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#(0()) -> k#(0()) h#(f(x),g(x)) -> s#(x) -> s#(s(0())) -> k#(s(0())) h#(f(x),g(x)) -> s#(x) -> 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#(0()) -> k#(0()) g#(s(x)) -> s#(g(x)) -> s#(s(0())) -> k#(s(0())) g#(s(x)) -> s#(g(x)) -> 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#(0()) -> k#(0()) g#(s(x)) -> s#(s(g(x))) -> s#(s(0())) -> k#(s(0())) g#(s(x)) -> s#(s(g(x))) -> 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(0()))))))))) -> k#(s(s(0()))) -> k#(s(s(0()))) -> s#(s(s(0()))) 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(0()))))))))) -> k#(s(s(0()))) -> k#(s(s(0()))) -> s#(s(s(s(s(0()))))) 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(0()))))))))) -> k#(s(s(0()))) -> k#(s(s(0()))) -> s#(s(s(s(s(s(s(0()))))))) s#(s(0())) -> k#(s(0())) -> k#(s(s(0()))) -> s#(s(s(0()))) s#(s(0())) -> k#(s(0())) -> k#(s(s(0()))) -> s#(s(s(s(0())))) s#(s(0())) -> k#(s(0())) -> k#(s(s(0()))) -> s#(s(s(s(s(0()))))) s#(s(0())) -> k#(s(0())) -> k#(s(s(0()))) -> s#(s(s(s(s(s(0())))))) 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)) -> 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: 19 #arcs: 94/484 DPs: k#(s(s(0()))) -> s#(s(s(s(s(s(s(0()))))))) 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())) -> k#(s(0())) k#(s(s(0()))) -> 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(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(0()) -> k(0()) s(k(0())) -> 0() s(s(0())) -> k(s(0())) k(s(0())) -> 0() 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()))))))) 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(0()) -> k(0()) s(k(0())) -> 0() s(s(0())) -> k(s(0())) k(s(0())) -> 0() 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()))))))) 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(0()))))))) 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(0())))))) s#(s(0())) = 0 >= 0 = k#(s(0())) k#(s(s(0()))) = 0 >= 0 = 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(0())))) k#(s(s(0()))) = 0 >= 0 = s#(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(0()) = 0 >= 0 = k(0()) s(k(0())) = 0 >= 0 = 0() s(s(0())) = 0 >= 0 = k(s(0())) k(s(0())) = 0 >= 0 = 0() 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(0()))))))) h(k(x),g(x)) = 0 >= 0 = k(s(x)) problem: DPs: k#(s(s(0()))) -> s#(s(s(s(s(s(s(0()))))))) 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())) -> k#(s(0())) k#(s(s(0()))) -> 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(0())))) k#(s(s(0()))) -> s#(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(0()) -> k(0()) s(k(0())) -> 0() s(s(0())) -> k(s(0())) k(s(0())) -> 0() 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()))))))) h(k(x),g(x)) -> k(s(x)) Restore Modifier: DPs: k#(s(s(0()))) -> s#(s(s(s(s(s(s(0()))))))) 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())) -> k#(s(0())) k#(s(s(0()))) -> 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(0())))) k#(s(s(0()))) -> s#(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(0()) -> k(0()) s(k(0())) -> 0() s(s(0())) -> k(s(0())) k(s(0())) -> 0() 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()))))))) h(k(x),g(x)) -> k(s(x)) SCC Processor: #sccs: 2 #rules: 8 #arcs: 67/256 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(0()) -> k(0()) s(k(0())) -> 0() s(s(0())) -> k(s(0())) k(s(0())) -> 0() 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()))))))) 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(0()) -> k(0()) s(k(0())) -> 0() s(s(0())) -> k(s(0())) k(s(0())) -> 0() 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()))))))) 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(0()))))))) 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())) -> k#(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(0()) -> k(0()) s(k(0())) -> 0() s(s(0())) -> k(s(0())) k(s(0())) -> 0() 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()))))))) h(k(x),g(x)) -> k(s(x)) Bounds Processor: bound: 0 enrichment: top-dp automaton: final states: {24} transitions: 00() -> 25* s0(25) -> 26* k{#,0}(26) -> 24* h0(25,25) -> 26* k0(25) -> 26* problem: DPs: k#(s(s(0()))) -> s#(s(s(s(s(s(s(0()))))))) 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())))))) 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(0()) -> k(0()) s(k(0())) -> 0() s(s(0())) -> k(s(0())) k(s(0())) -> 0() 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()))))))) h(k(x),g(x)) -> k(s(x)) Bounds Processor: bound: 0 enrichment: top-dp automaton: final states: {37} transitions: s{#,0}(45) -> 37* s{#,0}(40) -> 37* 00() -> 45*,40,38 s0(38) -> 39* s0(45) -> 39* s0(39) -> 40* h0(39,38) -> 40* h0(45,38) -> 39* h0(45,39) -> 40* h0(38,39) -> 40* h0(38,38) -> 39* h0(39,45) -> 40* h0(45,45) -> 39* h0(38,45) -> 39* k0(39) -> 40* k0(38) -> 39* k0(45) -> 39* f0(39) -> 40* problem: DPs: k#(s(s(0()))) -> s#(s(s(s(s(s(s(0()))))))) 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())))))) 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(0()) -> k(0()) s(k(0())) -> 0() s(s(0())) -> k(s(0())) k(s(0())) -> 0() 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()))))))) h(k(x),g(x)) -> k(s(x)) Bounds Processor: bound: 0 enrichment: top-dp automaton: final states: {31} transitions: s{#,0}(35) -> 31* s{#,0}(41) -> 31* 00() -> 40*,34,32 s0(33) -> 34* s0(32) -> 33* s0(34) -> 35* s0(40) -> 41*,33,35 s0(41) -> 34* h0(41,32) -> 34* h0(40,34) -> 35* h0(40,33) -> 34* h0(32,33) -> 34* h0(32,32) -> 33* h0(34,32) -> 35* h0(34,40) -> 35* h0(40,32) -> 41*,33,35 h0(33,32) -> 34* h0(41,40) -> 34* h0(33,40) -> 34* h0(40,41) -> 34* h0(40,40) -> 41*,33,35 h0(32,34) -> 35* h0(32,41) -> 34* h0(32,40) -> 41*,33,35 k0(41) -> 34* k0(33) -> 34* k0(40) -> 41*,33 k0(32) -> 41*,33 f0(41) -> 34* f0(33) -> 34* problem: DPs: k#(s(s(0()))) -> s#(s(s(s(s(s(s(0()))))))) 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())))))) 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(0()) -> k(0()) s(k(0())) -> 0() s(s(0())) -> k(s(0())) k(s(0())) -> 0() 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()))))))) h(k(x),g(x)) -> k(s(x)) Bounds Processor: bound: 0 enrichment: top-dp automaton: final states: {24} transitions: s{#,0}(29) -> 24* s{#,0}(41) -> 24* s{#,0}(36) -> 24* 00() -> 34,36,41*,27,25 s0(34) -> 35*,28,26 s0(35) -> 36*,29,27 s0(41) -> 35*,28,26 s0(28) -> 29* s0(36) -> 28* s0(27) -> 28* s0(26) -> 27* s0(25) -> 26* h0(36,25) -> 28* h0(27,41) -> 28* h0(41,41) -> 35*,26,28 h0(27,25) -> 28* h0(25,34) -> 35*,28,26 h0(27,34) -> 28* h0(28,34) -> 29* h0(41,36) -> 28* h0(34,34) -> 35*,28,26 h0(34,25) -> 35*,28,26 h0(35,25) -> 36*,27,29 h0(28,41) -> 29* h0(25,36) -> 28* h0(25,27) -> 28* h0(35,41) -> 36*,27,29 h0(34,27) -> 28* h0(34,41) -> 35*,26,28 h0(41,34) -> 35*,26,28 h0(41,35) -> 29,27,36* h0(25,25) -> 26* h0(41,25) -> 28,35*,26 h0(25,26) -> 27* h0(34,28) -> 29* h0(36,41) -> 28* h0(25,35) -> 36*,27,29 h0(26,34) -> 27* h0(41,26) -> 27* h0(41,28) -> 29* h0(36,34) -> 28* h0(25,41) -> 35*,28,26 h0(35,34) -> 36*,29,27 h0(34,36) -> 28* h0(25,28) -> 29* h0(26,25) -> 27* h0(34,26) -> 27* h0(34,35) -> 36*,29,27 h0(41,27) -> 28* h0(28,25) -> 29* h0(26,41) -> 27* k0(25) -> 35*,26 k0(26) -> 36*,27 k0(41) -> 35* k0(35) -> 36*,27 k0(34) -> 35*,26 f0(26) -> 36*,27 f0(35) -> 36*,27 problem: DPs: k#(s(s(0()))) -> s#(s(s(s(s(s(s(0()))))))) 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())))))) 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(0()) -> k(0()) s(k(0())) -> 0() s(s(0())) -> k(s(0())) k(s(0())) -> 0() 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()))))))) h(k(x),g(x)) -> k(s(x)) Bounds Processor: bound: 0 enrichment: top-dp automaton: final states: {16} transitions: s{#,0}(30) -> 16* s{#,0}(22) -> 16* s{#,0}(37) -> 16* 00() -> 27,29,36*,19,17 s0(37) -> 19,21,29* s0(18) -> 19* s0(30) -> 21* s0(20) -> 21* s0(28) -> 29*,19,21 s0(36) -> 37*,22,18,20 s0(27) -> 28*,18,20 s0(21) -> 22* s0(17) -> 18* s0(29) -> 30*,22,20 s0(19) -> 20* h0(20,27) -> 21* h0(36,29) -> 22,20,30* h0(20,17) -> 21* h0(36,37) -> 19,29*,21 h0(27,21) -> 22* h0(19,36) -> 20* h0(17,18) -> 19* h0(30,36) -> 21* h0(27,18) -> 19* h0(30,17) -> 21* h0(21,27) -> 22* h0(36,36) -> 37*,18,20,22 h0(17,28) -> 29*,19,21 h0(17,30) -> 21* h0(17,37) -> 19,29*,21 h0(17,21) -> 22* h0(17,19) -> 20* h0(28,36) -> 21,19,29* h0(36,18) -> 19* h0(36,30) -> 21* h0(37,27) -> 29*,19,21 h0(36,28) -> 19,29*,21 h0(27,37) -> 19,29*,21 h0(19,17) -> 20* h0(17,20) -> 21* h0(20,36) -> 21* h0(36,20) -> 21* h0(27,30) -> 21* h0(27,29) -> 30*,22,20 h0(27,19) -> 20* h0(17,27) -> 28*,20,18 h0(27,28) -> 29*,19,21 h0(28,27) -> 29*,21,19 h0(37,17) -> 21,19,29* h0(29,36) -> 30*,20,22 h0(27,17) -> 28*,20,18 h0(17,17) -> 18* h0(18,36) -> 19* h0(18,17) -> 19* h0(27,27) -> 28*,20,18 h0(18,27) -> 19* h0(28,17) -> 29*,21,19 h0(17,36) -> 37*,22,20,18 h0(36,21) -> 22* h0(36,17) -> 37*,20,18,22 h0(29,27) -> 30*,22,20 h0(36,19) -> 20* h0(21,36) -> 22* h0(17,29) -> 30*,22,20 h0(29,17) -> 30*,20,22 h0(27,36) -> 37*,22,18,20 h0(27,20) -> 21* h0(37,36) -> 29*,21,19 h0(19,27) -> 20* h0(21,17) -> 22* h0(36,27) -> 37*,18,20,22 h0(30,27) -> 21* k0(27) -> 28,37*,18 k0(18) -> 29*,19 k0(28) -> 29*,19 k0(17) -> 28,37*,18 k0(36) -> 28,37* k0(37) -> 29* f0(18) -> 29*,19 f0(28) -> 29*,19 f0(37) -> 29* problem: DPs: k#(s(s(0()))) -> s#(s(s(s(s(s(s(0()))))))) 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(0()) -> k(0()) s(k(0())) -> 0() s(s(0())) -> k(s(0())) k(s(0())) -> 0() 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()))))))) h(k(x),g(x)) -> k(s(x)) Bounds Processor: bound: 0 enrichment: top-dp automaton: final states: {2} transitions: s{#,0}(9) -> 2* s{#,0}(35) -> 2* s{#,0}(23) -> 2* s{#,0}(31) -> 2* 00() -> 29,21,19,31,35*,5,3 s0(23) -> 8* s0(30) -> 31*,7,5,9 s0(31) -> 8,6,22* s0(3) -> 4* s0(35) -> 4,8,6,30* s0(20) -> 21*,7,5 s0(22) -> 23*,7,9 s0(6) -> 7* s0(7) -> 8* s0(4) -> 5* s0(5) -> 6* s0(8) -> 9* s0(21) -> 22*,8,6 s0(29) -> 30*,4,8,6 s0(19) -> 20*,4,6 h0(19,31) -> 22*,6,8 h0(5,29) -> 6* h0(19,21) -> 22*,6,8 h0(29,23) -> 8* h0(6,35) -> 7* h0(29,21) -> 22*,6,8 h0(4,35) -> 5* h0(19,35) -> 4,6,30*,8 h0(29,3) -> 30*,4,8,6 h0(19,30) -> 31*,7,9,5 h0(35,6) -> 7* h0(30,3) -> 31*,7,9,5 h0(29,6) -> 7* h0(19,3) -> 20*,4,6 h0(5,19) -> 6* h0(22,29) -> 7,9,23* h0(21,29) -> 6,8,22* h0(29,5) -> 6* h0(3,30) -> 31*,5,7,9 h0(31,29) -> 6,22*,8 h0(35,8) -> 9* h0(6,19) -> 7* h0(20,29) -> 7,5,21* h0(3,3) -> 4* h0(31,35) -> 8,22*,6 h0(3,22) -> 23*,7,9 h0(29,19) -> 30*,4,6,8 h0(3,5) -> 6* h0(35,35) -> 4,8,6,30* h0(29,29) -> 30*,4,6,8 h0(3,7) -> 8* h0(22,3) -> 23*,7,9 h0(6,3) -> 7* h0(3,4) -> 5* h0(3,21) -> 22*,6,8 h0(7,3) -> 8* h0(19,29) -> 30*,4,6,8 h0(19,22) -> 23*,7,9 h0(23,29) -> 8* h0(35,4) -> 5* h0(35,21) -> 6,22*,8 h0(8,3) -> 9* h0(19,5) -> 6* h0(31,19) -> 6,8,22* h0(3,19) -> 20*,4,6 h0(19,6) -> 7* h0(5,35) -> 6* h0(7,29) -> 8* h0(21,3) -> 22*,8,6 h0(29,30) -> 31*,7,9,5 h0(19,19) -> 20*,4,6 h0(8,19) -> 9* h0(35,5) -> 6* h0(19,8) -> 9* h0(3,31) -> 6,22*,8 h0(3,23) -> 8* h0(4,19) -> 5* h0(35,7) -> 8* h0(31,3) -> 22*,6,8 h0(6,29) -> 7* h0(20,35) -> 7,5,21* h0(30,29) -> 31*,7,9,5 h0(19,23) -> 8* h0(29,7) -> 8* h0(29,20) -> 5,7,21* h0(29,35) -> 4,8,6,30* h0(5,3) -> 6* h0(20,19) -> 21*,7,5 h0(8,29) -> 9* h0(8,35) -> 9* h0(4,29) -> 5* h0(19,4) -> 5* h0(22,35) -> 23*,7,9 h0(3,20) -> 21*,5,7 h0(4,3) -> 5* h0(3,35) -> 4,6,8,30* h0(29,22) -> 23*,7,9 h0(7,35) -> 8* h0(3,29) -> 30*,4,6,8 h0(29,8) -> 9* h0(20,3) -> 21*,7,5 h0(35,19) -> 4,30*,6,8 h0(7,19) -> 8* h0(35,22) -> 23*,7,9 h0(3,6) -> 7* h0(23,19) -> 8* h0(22,19) -> 23*,7,9 h0(21,19) -> 22*,6,8 h0(29,31) -> 22*,6,8 h0(30,19) -> 31*,7,9,5 h0(29,4) -> 5* h0(35,30) -> 31*,7,5,9 h0(3,8) -> 9* h0(19,20) -> 21*,7,5 h0(23,35) -> 8* h0(35,3) -> 30*,4,8,6 h0(19,7) -> 8* h0(35,29) -> 4,8,6,30* h0(35,23) -> 8* h0(21,35) -> 8,22*,6 h0(23,3) -> 8* h0(30,35) -> 7,31*,9,5 h0(35,20) -> 21*,7,5 h0(35,31) -> 6,8,22* k0(20) -> 21,31*,5 k0(19) -> 20,30*,4 k0(35) -> 30* k0(29) -> 20,30* k0(30) -> 21,31* k0(3) -> 20,30*,4 k0(4) -> 21,31*,5 f0(20) -> 21,31*,5 f0(4) -> 21,31*,5 f0(30) -> 21,31* problem: DPs: 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(0()) -> k(0()) s(k(0())) -> 0() s(s(0())) -> k(s(0())) k(s(0())) -> 0() 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()))))))) h(k(x),g(x)) -> k(s(x)) SCC Processor: #sccs: 0 #rules: 0 #arcs: 20/1