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(s(0()))) -> k(s(0())) k(s(0())) -> 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#(0()) -> k#(0()) s#(s(s(0()))) -> k#(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(0()) -> k(0()) s(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(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#(0()) -> k#(0()) s#(s(s(0()))) -> k#(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(0()) -> k(0()) s(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(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(0()))) -> k#(s(0())) k#(s(s(0()))) -> s#(s(s(s(s(s(s(s(s(0()))))))))) -> 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(0()))) -> k#(s(0())) k#(s(s(0()))) -> s#(s(s(s(s(s(s(s(0())))))))) -> 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(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(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#(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(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(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#(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(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(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)) -> 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(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(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#(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(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(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#(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(0()))) -> k#(s(0())) -> k#(s(s(0()))) -> s#(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(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())) -> 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(s(s(0()))))))))) s#(0()) -> k#(0()) -> k#(s(s(0()))) -> s#(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#(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(s(0()))) -> k#(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(0()) -> k(0()) s(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(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#(0()) -> k#(0()) k#(s(s(0()))) -> s#(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(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#(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(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#(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(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(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#(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(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(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#(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(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)) -> 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#(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(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(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#(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(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(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(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(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(s(0()))) -> k#(s(0())) -> k#(s(s(0()))) -> s#(s(s(s(s(s(s(s(s(0()))))))))) s#(s(0())) -> f#(s(0())) -> f#(g(x)) -> f#(x) s#(s(0())) -> f#(s(0())) -> f#(g(x)) -> g#(f(x)) s#(s(0())) -> f#(s(0())) -> f#(g(x)) -> g#(g(f(x))) SCC Processor: #sccs: 1 #rules: 21 #arcs: 112/576 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(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()))) 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(s(0()))) -> k(s(0())) k(s(0())) -> 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(0()) -> k(0()) s(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(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) = 1, [s](x0) = 0, [g](x0) = x0 + 1, [k](x0) = x0, [k#](x0) = x0 + 0, [0] = 0, [f#](x0) = x0 + 0, [h#](x0, x1) = 1, [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(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 >= 1 = g#(g(f(x))) g#(s(x)) = 1 >= 0 = s#(s(g(x))) g#(s(x)) = 1 >= 0 = s#(g(x)) g#(s(x)) = 1 >= 1 = g#(x) g#(x) = 1 >= 1 = h#(x,x) h#(k(x),g(x)) = 1 >= 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()))) h#(k(x),g(x)) = 1 >= 0 = s#(x) h#(f(x),g(x)) = 1 >= 0 = f#(s(x)) f#(g(x)) = x + 1 >= 1 = g#(f(x)) f#(g(x)) = x + 1 >= x + 0 = f#(x) h#(f(x),g(x)) = 1 >= 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)) = x + 1 >= x + 1 = 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(s(0()))) = 0 >= 0 = k(s(0())) k(s(0())) = 0 >= 0 = 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(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)) -> 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()))) 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(0()) -> k(0()) s(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(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(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)) -> 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()))) 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(0()) -> k(0()) s(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(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: 3 #rules: 11 #arcs: 79/225 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(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(0()) -> k(0()) s(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(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* k0(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(0()) -> k(0()) s(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(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* s{#,0}(68) -> 58* 00() -> 68*,61,59 s0(68) -> 60* s0(60) -> 61* s0(59) -> 60* h0(60,59) -> 61* h0(59,60) -> 61* h0(68,59) -> 60* h0(59,68) -> 60* h0(59,59) -> 60* h0(68,68) -> 60* h0(60,68) -> 61* h0(68,60) -> 61* k0(68) -> 60* k0(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(0()) -> k(0()) s(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(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}(64) -> 52* 00() -> 63*,55,53 s0(55) -> 56* s0(64) -> 55* s0(54) -> 55* s0(53) -> 54* s0(63) -> 64*,56,54 h0(53,54) -> 55* h0(63,63) -> 64*,54,56 h0(63,55) -> 56* h0(53,53) -> 54* h0(55,63) -> 56* h0(55,53) -> 56* h0(53,64) -> 55* h0(54,53) -> 55* h0(64,53) -> 55* h0(53,63) -> 64*,54,56 h0(63,64) -> 55* h0(53,55) -> 56* h0(64,63) -> 55* h0(54,63) -> 55* h0(63,54) -> 55* h0(63,53) -> 64*,54,56 k0(63) -> 64*,54 k0(64) -> 56* k0(53) -> 64*,54 k0(54) -> 56* f0(64) -> 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(0()) -> k(0()) s(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(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}(59) -> 45* s{#,0}(50) -> 45* s{#,0}(64) -> 45* 00() -> 57,59,64*,48,46 s0(64) -> 58*,49,47 s0(57) -> 58*,49,47 s0(48) -> 49* s0(49) -> 50* s0(59) -> 49* s0(46) -> 47* s0(58) -> 59*,50,48 s0(47) -> 48* h0(58,46) -> 59*,50,48 h0(46,59) -> 49* h0(59,64) -> 49* h0(49,46) -> 50* h0(48,46) -> 49* h0(58,57) -> 59*,50,48 h0(49,57) -> 50* h0(46,57) -> 58*,49,47 h0(46,49) -> 50* h0(46,47) -> 48* h0(48,64) -> 49* h0(46,58) -> 59*,50,48 h0(58,64) -> 59*,50,48 h0(57,47) -> 48* h0(59,57) -> 49* h0(57,48) -> 49* h0(46,64) -> 58*,49,47 h0(64,47) -> 48* h0(57,64) -> 49,47,58* h0(64,57) -> 47,49,58* h0(64,46) -> 47,49,58* h0(47,46) -> 48* h0(64,64) -> 47,49,58* h0(47,64) -> 48* h0(64,49) -> 50* h0(57,59) -> 49* h0(64,58) -> 48,59*,50 h0(57,58) -> 59*,48,50 h0(57,49) -> 50* h0(64,59) -> 49* h0(47,57) -> 48* h0(46,48) -> 49* h0(48,57) -> 49* h0(46,46) -> 47* h0(64,48) -> 49* h0(57,57) -> 58*,49,47 h0(59,46) -> 49* h0(57,46) -> 58*,49,47 h0(49,64) -> 50* k0(46) -> 58*,47 k0(64) -> 58* k0(57) -> 58*,47 k0(58) -> 49* k0(47) -> 49* f0(47) -> 59*,48 f0(58) -> 59*,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(0()) -> k(0()) s(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(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}(43) -> 37* s{#,0}(60) -> 37* s{#,0}(53) -> 37* 00() -> 50,52,59*,40,38 s0(38) -> 39* s0(51) -> 52*,42,40 s0(40) -> 41* s0(52) -> 53*,41,43 s0(41) -> 42* s0(39) -> 40* s0(60) -> 52*,40,42 s0(59) -> 60*,39,41,43 s0(53) -> 42* s0(50) -> 51*,39,41 s0(42) -> 43* h0(38,53) -> 42* h0(38,59) -> 60*,39,41,43 h0(39,38) -> 40* h0(53,50) -> 42* h0(50,39) -> 40* h0(60,59) -> 40,52*,42 h0(41,59) -> 42* h0(50,40) -> 41* h0(41,38) -> 42* h0(38,51) -> 52*,42,40 h0(50,52) -> 53*,41,43 h0(42,59) -> 43* h0(50,38) -> 51*,39,41 h0(50,42) -> 43* h0(42,50) -> 43* h0(39,50) -> 40* h0(41,50) -> 42* h0(59,60) -> 52*,40,42 h0(50,60) -> 40,52*,42 h0(39,59) -> 40* h0(38,41) -> 42* h0(53,38) -> 42* h0(60,50) -> 40,42,52* h0(50,53) -> 42* h0(51,50) -> 52*,40,42 h0(59,59) -> 60*,39,41,43 h0(38,39) -> 40* h0(38,52) -> 53*,41,43 h0(60,38) -> 40,42,52* h0(59,52) -> 53*,41,43 h0(50,59) -> 60*,39,41,43 h0(50,51) -> 52*,40,42 h0(59,50) -> 60*,39,41,43 h0(38,38) -> 39* h0(38,40) -> 41* h0(50,41) -> 42* h0(38,60) -> 52*,42,40 h0(59,51) -> 40,52*,42 h0(59,53) -> 42* h0(38,50) -> 51*,39,41 h0(40,38) -> 41* h0(40,50) -> 41* h0(51,38) -> 52*,40,42 h0(42,38) -> 43* h0(51,59) -> 40,42,52* h0(59,40) -> 41* h0(52,50) -> 53*,43,41 h0(59,39) -> 40* h0(38,42) -> 43* h0(59,41) -> 42* h0(53,59) -> 42* h0(40,59) -> 41* h0(59,42) -> 43* h0(52,59) -> 41,43,53* h0(50,50) -> 51*,39,41 h0(52,38) -> 53*,41,43 h0(59,38) -> 60*,39,41,43 k0(39) -> 53*,41 k0(59) -> 51,60* k0(38) -> 51,60*,39 k0(60) -> 53* k0(50) -> 51,60*,39 k0(51) -> 53*,41 f0(39) -> 52*,40 f0(60) -> 52* f0(51) -> 52*,40 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(0()) -> k(0()) s(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(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}(35) -> 28* s{#,0}(46) -> 28* s{#,0}(55) -> 28* s{#,0}(74) -> 28* 00() -> 53,44,42,55,74*,31,29 s0(55) -> 32,45*,34 s0(33) -> 34* s0(45) -> 46*,33,35 s0(32) -> 33* s0(34) -> 35* s0(30) -> 31* s0(31) -> 32* s0(74) -> 34,32,54*,30 s0(43) -> 44*,33,31 s0(54) -> 55*,33,35,31 s0(44) -> 45*,34,32 s0(53) -> 54*,34,32,30 s0(46) -> 34* s0(42) -> 43*,32,30 s0(29) -> 30* h0(46,53) -> 34* h0(74,54) -> 55*,33,31,35 h0(74,34) -> 35* h0(45,53) -> 33,35,46* h0(53,54) -> 55*,31,35,33 h0(29,45) -> 46*,33,35 h0(55,74) -> 32,34,45* h0(42,29) -> 43*,32,30 h0(54,42) -> 55*,31,33,35 h0(43,29) -> 44*,33,31 h0(53,30) -> 31* h0(45,29) -> 46*,33,35 h0(42,33) -> 34* h0(29,46) -> 34* h0(74,53) -> 30,34,32,54* h0(43,74) -> 33,31,44* h0(33,42) -> 34* h0(31,74) -> 32* h0(32,29) -> 33* h0(29,33) -> 34* h0(74,46) -> 34* h0(29,32) -> 33* h0(31,29) -> 32* h0(74,55) -> 34,32,45* h0(29,44) -> 45*,34,32 h0(44,74) -> 32,34,45* h0(74,30) -> 31* h0(53,74) -> 30,34,32,54* h0(53,45) -> 46*,33,35 h0(29,53) -> 54*,34,30,32 h0(53,53) -> 54*,30,34,32 h0(29,29) -> 30* h0(74,32) -> 33* h0(53,31) -> 32* h0(29,54) -> 55*,33,31,35 h0(53,34) -> 35* h0(33,74) -> 34* h0(53,46) -> 34* h0(42,46) -> 34* h0(74,31) -> 32* h0(32,53) -> 33* h0(53,32) -> 33* h0(44,29) -> 45*,32,34 h0(31,53) -> 32* h0(33,29) -> 34* h0(44,42) -> 45*,34,32 h0(30,53) -> 31* h0(42,45) -> 46*,33,35 h0(55,29) -> 32,45*,34 h0(42,42) -> 43*,30,32 h0(55,42) -> 45*,32,34 h0(53,44) -> 34,45*,32 h0(32,74) -> 33* h0(42,44) -> 45*,34,32 h0(29,30) -> 31* h0(33,53) -> 34* h0(46,29) -> 34* h0(42,43) -> 44*,31,33 h0(29,42) -> 43*,30,32 h0(54,29) -> 55*,33,31,35 h0(74,42) -> 30,34,32,54* h0(29,43) -> 44*,33,31 h0(30,42) -> 31* h0(55,53) -> 32,34,45* h0(42,30) -> 31* h0(30,29) -> 31* h0(42,55) -> 34,45*,32 h0(54,74) -> 33,31,55*,35 h0(31,42) -> 32* h0(42,54) -> 55*,31,33,35 h0(34,29) -> 35* h0(74,45) -> 46*,33,35 h0(54,53) -> 55*,33,31,35 h0(74,43) -> 33,31,44* h0(43,53) -> 31,33,44* h0(53,33) -> 34* h0(29,74) -> 34,54*,30,32 h0(42,32) -> 33* h0(53,55) -> 32,45*,34 h0(45,74) -> 46*,33,35 h0(74,29) -> 32,30,34,54* h0(34,53) -> 35* h0(53,42) -> 54*,30,34,32 h0(74,44) -> 45*,34,32 h0(29,31) -> 32* h0(44,53) -> 34,45*,32 h0(32,42) -> 33* h0(74,33) -> 34* h0(46,42) -> 34* h0(43,42) -> 44*,31,33 h0(42,34) -> 35* h0(29,34) -> 35* h0(53,43) -> 44*,31,33 h0(42,74) -> 34,30,32,54* h0(74,74) -> 30,34,32,54* h0(34,42) -> 35* h0(42,31) -> 32* h0(30,74) -> 31* h0(53,29) -> 54*,32,30,34 h0(46,74) -> 34* h0(29,55) -> 34,45*,32 h0(45,42) -> 46*,33,35 h0(42,53) -> 54*,34,30,32 h0(34,74) -> 35* k0(42) -> 43,54*,30 k0(53) -> 43,54* k0(43) -> 45*,32 k0(54) -> 45* k0(29) -> 43,54*,30 k0(30) -> 45*,32 k0(74) -> 54* f0(43) -> 44,55*,31 f0(30) -> 44,55*,31 f0(54) -> 44,55* 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())))))))) 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(s(0()))) -> k(s(0())) k(s(0())) -> 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}(38) -> 18* s{#,0}(56) -> 18* s{#,0}(63) -> 18* s{#,0}(26) -> 18* 00() -> 53,35,33,55,62*,21,19 s0(55) -> 56*,24,22,26 s0(23) -> 24* s0(37) -> 38*,24,26 s0(33) -> 34*,22,20 s0(38) -> 25* s0(24) -> 25* s0(34) -> 35*,21,23 s0(62) -> 63*,24,22,26,20 s0(35) -> 36*,24,22 s0(20) -> 21* s0(22) -> 23* s0(56) -> 25,23,37* s0(54) -> 55*,25,21,23 s0(36) -> 37*,25,23 s0(53) -> 54*,24,22,20 s0(63) -> 25,21,23,55* s0(21) -> 22* s0(25) -> 26* s0(19) -> 20* h0(38,53) -> 25* h0(19,56) -> 37*,23,25 h0(53,35) -> 36*,22,24 h0(33,35) -> 36*,22,24 h0(53,54) -> 55*,23,21,25 h0(19,21) -> 22* h0(62,20) -> 21* h0(33,36) -> 37*,25,23 h0(53,23) -> 24* h0(25,33) -> 26* h0(63,33) -> 23,25,21,55* h0(53,22) -> 23* h0(19,35) -> 36*,22,24 h0(19,36) -> 37*,23,25 h0(33,54) -> 55*,25,21,23 h0(62,19) -> 63*,26,20,24,22 h0(53,19) -> 54*,20,24,22 h0(53,20) -> 21* h0(56,33) -> 23,25,37* h0(19,33) -> 34*,22,20 h0(56,53) -> 37*,23,25 h0(19,54) -> 55*,23,21,25 h0(62,22) -> 23* h0(20,53) -> 21* h0(19,37) -> 38*,26,24 h0(63,62) -> 23,25,21,55* h0(34,19) -> 35*,21,23 h0(53,56) -> 23,25,37* h0(22,33) -> 23* h0(62,63) -> 21,23,55*,25 h0(54,19) -> 55*,25,21,23 h0(22,62) -> 23* h0(36,53) -> 25,23,37* h0(24,62) -> 25* h0(19,25) -> 26* h0(56,62) -> 37*,23,25 h0(53,37) -> 38*,24,26 h0(53,53) -> 54*,20,24,22 h0(63,19) -> 55*,25,21,23 h0(35,33) -> 36*,24,22 h0(37,62) -> 26,38*,24 h0(55,62) -> 26,24,56*,22 h0(25,53) -> 26* h0(33,33) -> 34*,20,22 h0(25,19) -> 26* h0(62,34) -> 23,35*,21 h0(53,25) -> 26* h0(53,24) -> 25* h0(53,34) -> 35*,21,23 h0(53,38) -> 25* h0(37,53) -> 26,24,38* h0(33,21) -> 22* h0(19,22) -> 23* h0(62,56) -> 37*,23,25 h0(33,24) -> 25* h0(62,23) -> 24* h0(23,62) -> 24* h0(38,33) -> 25* h0(62,21) -> 22* h0(33,37) -> 38*,24,26 h0(62,36) -> 23,37*,25 h0(33,63) -> 55*,25,21,23 h0(62,53) -> 63*,26,20,24,22 h0(33,19) -> 34*,20,22 h0(62,54) -> 55*,23,21,25 h0(19,19) -> 20* h0(33,53) -> 54*,20,24,22 h0(23,33) -> 24* h0(62,62) -> 63*,26,20,24,22 h0(23,53) -> 24* h0(21,62) -> 22* h0(53,21) -> 22* h0(20,62) -> 21* h0(55,53) -> 56*,26,24,22 h0(19,23) -> 24* h0(33,55) -> 56*,22,24,26 h0(37,19) -> 38*,26,24 h0(24,19) -> 25* h0(20,19) -> 21* h0(62,38) -> 25* h0(25,62) -> 26* h0(33,62) -> 63*,20,24,26,22 h0(33,56) -> 37*,25,23 h0(24,33) -> 25* h0(56,19) -> 23,37*,25 h0(54,53) -> 55*,21,23,25 h0(62,35) -> 36*,22,24 h0(33,20) -> 21* h0(35,19) -> 36*,24,22 h0(53,63) -> 55*,23,21,25 h0(53,33) -> 54*,20,24,22 h0(53,36) -> 37*,25,23 h0(35,53) -> 36*,24,22 h0(33,38) -> 25* h0(53,55) -> 56*,24,26,22 h0(23,19) -> 24* h0(33,23) -> 24* h0(19,34) -> 35*,23,21 h0(62,25) -> 26* h0(22,19) -> 23* h0(34,53) -> 23,35*,21 h0(33,25) -> 26* h0(62,24) -> 25* h0(34,33) -> 35*,23,21 h0(21,19) -> 22* h0(53,62) -> 63*,26,20,24,22 h0(20,33) -> 21* h0(55,33) -> 56*,26,24,22 h0(38,62) -> 25* h0(19,62) -> 63*,22,26,20,24 h0(22,53) -> 23* h0(36,19) -> 37*,25,23 h0(33,34) -> 35*,21,23 h0(34,62) -> 21,35*,23 h0(19,20) -> 21* h0(55,19) -> 56*,26,24,22 h0(62,55) -> 26,22,24,56* h0(63,53) -> 21,55*,23,25 h0(37,33) -> 38*,26,24 h0(38,19) -> 25* h0(19,38) -> 25* h0(62,33) -> 63*,26,20,24,22 h0(36,33) -> 37*,23,25 h0(54,62) -> 21,55*,23,25 h0(21,33) -> 22* h0(19,24) -> 25* h0(24,53) -> 25* h0(33,22) -> 23* h0(36,62) -> 23,37*,25 h0(21,53) -> 22* h0(62,37) -> 38*,26,24 h0(54,33) -> 55*,23,25,21 h0(19,55) -> 56*,22,26,24 h0(35,62) -> 36*,24,22 h0(19,63) -> 55*,23,21,25 h0(19,53) -> 54*,22,20,24 k0(20) -> 36,56*,22 k0(62) -> 54,63* k0(19) -> 54,34,63*,20 k0(63) -> 56* k0(53) -> 54,34,63* k0(54) -> 36,56* k0(33) -> 54,34,63*,20 k0(34) -> 36,56*,22 f0(20) -> 35,55*,21 f0(63) -> 55* f0(34) -> 35,55*,21 f0(54) -> 35,55* 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()))) 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(s(0()))) -> k(s(0())) k(s(0())) -> 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}(49) -> 2* s{#,0}(41) -> 2* s{#,0}(11) -> 2* s{#,0}(53) -> 2* s{#,0}(36) -> 2* 00() -> 47,39,30,32,37,49,53*,5,3 s0(37) -> 38*,4,8,6 s0(33) -> 34*,7,9 s0(38) -> 39*,7,5,9 s0(32) -> 33*,8,6 s0(34) -> 35*,10,8 s0(30) -> 31*,4,6 s0(31) -> 32*,7,5 s0(3) -> 4* s0(35) -> 36*,11,9 s0(48) -> 49*,11,7,5,9 s0(40) -> 41*,11,7,9 s0(49) -> 10,40*,8,6 s0(9) -> 10* s0(41) -> 35*,8,10 s0(10) -> 11* s0(39) -> 40*,10,8,6 s0(6) -> 7* s0(7) -> 8* s0(4) -> 5* s0(36) -> 10* s0(53) -> 4,10,8,6,48* s0(5) -> 6* s0(47) -> 48*,4,10,8,6 s0(8) -> 9* h0(38,53) -> 7,5,39*,9 h0(47,31) -> 5,32*,7 h0(37,4) -> 5* h0(10,30) -> 11* h0(38,47) -> 7,9,5,39* h0(30,49) -> 8,10,6,40* h0(3,53) -> 4,6,8,10,48* h0(6,53) -> 7* h0(53,35) -> 36*,9,11 h0(47,33) -> 9,34*,7 h0(47,39) -> 8,6,10,40* h0(9,30) -> 10* h0(30,4) -> 5* h0(36,37) -> 10* h0(37,32) -> 6,8,33* h0(6,37) -> 7* h0(30,7) -> 8* h0(30,30) -> 31*,4,6 h0(53,30) -> 4,48*,10,8,6 h0(53,49) -> 8,6,40*,10 h0(30,38) -> 39*,5,7,9 h0(30,3) -> 31*,4,6 h0(30,9) -> 10* h0(6,47) -> 7* h0(3,40) -> 41*,11,7,9 h0(5,47) -> 6* h0(30,34) -> 35*,8,10 h0(41,53) -> 8,35*,10 h0(39,37) -> 40*,6,8,10 h0(49,30) -> 10,8,40*,6 h0(30,36) -> 10* h0(3,49) -> 40*,6,8,10 h0(53,48) -> 49*,5,7,9,11 h0(47,36) -> 10* h0(40,47) -> 7,9,41*,11 h0(30,5) -> 6* h0(3,30) -> 31*,4,6 h0(47,34) -> 8,35*,10 h0(53,3) -> 4,48*,8,10,6 h0(5,53) -> 6* h0(37,47) -> 48*,4,8,6,10 h0(3,3) -> 4* h0(39,3) -> 40*,8,10,6 h0(48,47) -> 49*,7,5,11,9 h0(8,37) -> 9* h0(53,6) -> 7* h0(32,3) -> 33*,8,6 h0(4,53) -> 5* h0(40,37) -> 41*,7,9,11 h0(47,8) -> 9* h0(47,48) -> 49*,9,7,5,11 h0(37,37) -> 38*,4,8,6 h0(3,39) -> 40*,6,8,10 h0(36,53) -> 10* h0(7,53) -> 8* h0(3,5) -> 6* h0(32,47) -> 8,33*,6 h0(53,37) -> 4,48*,8,10,6 h0(47,7) -> 8* h0(47,41) -> 8,10,35* h0(53,53) -> 4,6,8,48*,10 h0(3,7) -> 8* h0(30,10) -> 11* h0(47,37) -> 48*,4,8,10,6 h0(6,3) -> 7* h0(47,30) -> 48*,4,10,8,6 h0(5,37) -> 6* h0(4,47) -> 5* h0(47,3) -> 48*,4,8,10,6 h0(53,8) -> 9* h0(3,4) -> 5* h0(3,9) -> 10* h0(53,31) -> 32*,5,7 h0(3,36) -> 10* h0(34,30) -> 35*,10,8 h0(49,53) -> 6,40*,8,10 h0(53,4) -> 5* h0(10,47) -> 11* h0(31,47) -> 7,32*,5 h0(30,47) -> 48*,4,8,10,6 h0(53,34) -> 8,35*,10 h0(53,9) -> 10* h0(53,38) -> 5,7,9,39* h0(7,3) -> 8* h0(37,53) -> 4,6,48*,10,8 h0(47,5) -> 6* h0(32,30) -> 33*,8,6 h0(37,48) -> 49*,5,9,11,7 h0(36,30) -> 10* h0(31,30) -> 32*,5,7 h0(32,53) -> 33*,6,8 h0(39,47) -> 40*,8,10,6 h0(47,6) -> 7* h0(53,32) -> 8,6,33* h0(49,37) -> 40*,6,8,10 h0(31,53) -> 7,32*,5 h0(33,37) -> 7,9,34* h0(30,48) -> 49*,5,11,7,9 h0(8,3) -> 9* h0(3,34) -> 35*,8,10 h0(30,53) -> 4,8,10,6,48* h0(37,7) -> 8* h0(4,30) -> 5* h0(41,47) -> 8,10,35* h0(33,30) -> 34*,7,9 h0(3,37) -> 38*,4,6,8 h0(3,41) -> 8,10,35* h0(37,31) -> 5,7,32* h0(7,37) -> 8* h0(32,37) -> 33*,8,6 h0(30,33) -> 34*,7,9 h0(3,33) -> 34*,7,9 h0(33,53) -> 7,9,34* h0(48,53) -> 7,5,11,9,49* h0(53,41) -> 8,35*,10 h0(10,53) -> 11* h0(9,3) -> 10* h0(6,30) -> 7* h0(9,37) -> 10* h0(3,31) -> 32*,5,7 h0(3,48) -> 49*,5,11,7,9 h0(31,37) -> 7,32*,5 h0(3,10) -> 11* h0(31,3) -> 32*,7,5 h0(41,30) -> 35*,10,8 h0(9,53) -> 10* h0(7,30) -> 8* h0(41,37) -> 8,10,35* h0(37,30) -> 38*,4,8,6 h0(10,37) -> 11* h0(40,3) -> 41*,7,9,11 h0(30,6) -> 7* h0(53,47) -> 4,6,8,48*,10 h0(53,40) -> 7,9,11,41* h0(5,3) -> 6* h0(47,32) -> 8,6,33* h0(3,38) -> 39*,5,7,9 h0(37,34) -> 8,10,35* h0(35,47) -> 9,11,36* h0(39,53) -> 40*,6,8,10 h0(4,3) -> 5* h0(36,3) -> 10* h0(37,5) -> 6* h0(47,35) -> 11,36*,9 h0(34,3) -> 35*,8,10 h0(53,7) -> 8* h0(3,47) -> 48*,4,6,8,10 h0(3,35) -> 36*,11,9 h0(38,3) -> 39*,7,9,5 h0(38,30) -> 39*,5,7,9 h0(47,4) -> 5* h0(33,47) -> 7,9,34* h0(30,40) -> 41*,11,7,9 h0(48,30) -> 49*,11,5,7,9 h0(8,30) -> 9* h0(37,9) -> 10* h0(47,49) -> 40*,8,6,10 h0(30,32) -> 33*,8,6 h0(37,41) -> 8,35*,10 h0(40,30) -> 41*,11,7,9 h0(53,33) -> 34*,7,9 h0(30,41) -> 8,35*,10 h0(53,36) -> 10* h0(35,53) -> 11,9,36* h0(34,47) -> 8,10,35* h0(3,6) -> 7* h0(8,53) -> 9* h0(10,3) -> 11* h0(34,53) -> 35*,8,10 h0(37,8) -> 9* h0(49,47) -> 6,40*,8,10 h0(37,35) -> 11,36*,9 h0(37,10) -> 11* h0(49,3) -> 40*,8,10,6 h0(37,39) -> 40*,8,6,10 h0(8,47) -> 9* h0(35,30) -> 36*,11,9 h0(3,8) -> 9* h0(53,10) -> 11* h0(7,47) -> 8* h0(48,37) -> 49*,7,9,11,5 h0(30,37) -> 38*,4,8,6 h0(53,5) -> 6* h0(53,39) -> 40*,8,6,10 h0(35,3) -> 36*,9,11 h0(37,40) -> 41*,9,11,7 h0(4,37) -> 5* h0(30,39) -> 40*,8,10,6 h0(37,33) -> 34*,7,9 h0(35,37) -> 9,11,36* h0(36,47) -> 10* h0(30,31) -> 32*,5,7 h0(37,6) -> 7* h0(38,37) -> 39*,7,9,5 h0(39,30) -> 40*,10,8,6 h0(41,3) -> 8,10,35* h0(47,53) -> 4,6,8,48*,10 h0(37,49) -> 8,6,10,40* h0(47,38) -> 5,9,7,39* h0(33,3) -> 34*,7,9 h0(37,3) -> 38*,4,8,6 h0(47,47) -> 48*,4,8,6,10 h0(30,35) -> 36*,11,9 h0(34,37) -> 10,8,35* h0(48,3) -> 49*,7,9,5,11 h0(37,36) -> 10* h0(37,38) -> 39*,5,9,7 h0(40,53) -> 7,41*,11,9 h0(47,10) -> 11* h0(5,30) -> 6* h0(47,40) -> 11,9,41*,7 h0(9,47) -> 10* h0(30,8) -> 9* h0(47,9) -> 10* h0(3,32) -> 33*,6,8 k0(48) -> 40* k0(31) -> 33,40*,6 k0(53) -> 48* k0(38) -> 33,40* k0(37) -> 38,31,48* k0(30) -> 38,31,48*,4 k0(3) -> 38,31,48*,4 k0(4) -> 33,40*,6 k0(47) -> 38,48* f0(48) -> 39,49* f0(38) -> 39,32,49* f0(31) -> 39,32,49*,5 f0(4) -> 39,32,49*,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(0()) -> k(0()) s(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(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: 28/1 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(0()) -> k(0()) s(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(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(0()) -> k(0()) s(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(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: 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(0()) -> k(0()) s(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(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(0()) -> k(0()) s(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(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