/export/starexec/sandbox2/solver/bin/starexec_run_ttt2 /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- YES Problem: s(s(0())) -> f(s(0())) g(x) -> h(x,x) s(x) -> h(x,0()) s(x) -> h(0(),x) f(g(x)) -> g(g(f(x))) g(s(x)) -> s(s(g(x))) h(f(x),g(x)) -> f(s(x)) s(s(s(0()))) -> k(0()) k(0()) -> s(0()) s(s(s(s(0())))) -> k(s(0())) k(s(0())) -> s(s(0())) s(s(s(s(s(s(s(s(s(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#(s(s(0()))) -> k#(0()) k#(0()) -> s#(0()) s#(s(s(s(0())))) -> k#(s(0())) k#(s(0())) -> s#(s(0())) s#(s(s(s(s(s(s(s(s(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(s(s(0()))) -> k(0()) k(0()) -> s(0()) s(s(s(s(0())))) -> k(s(0())) k(s(0())) -> s(s(0())) s(s(s(s(s(s(s(s(s(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#(s(s(0()))) -> k#(0()) k#(0()) -> s#(0()) s#(s(s(s(0())))) -> k#(s(0())) k#(s(0())) -> s#(s(0())) s#(s(s(s(s(s(s(s(s(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(s(s(0()))) -> k(0()) k(0()) -> s(0()) s(s(s(s(0())))) -> k(s(0())) k(s(0())) -> s(s(0())) s(s(s(s(s(s(s(s(s(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(s(s(0())))) -> k#(s(0())) k#(s(s(0()))) -> s#(s(s(s(s(s(s(0()))))))) -> s#(s(s(0()))) -> k#(0()) k#(s(s(0()))) -> s#(s(s(s(s(s(s(0()))))))) -> s#(x) -> h#(0(),x) k#(s(s(0()))) -> s#(s(s(s(s(s(s(0()))))))) -> s#(x) -> h#(x,0()) k#(s(s(0()))) -> s#(s(s(s(s(s(s(0()))))))) -> s#(s(0())) -> f#(s(0())) k#(s(s(0()))) -> s#(s(s(s(s(s(0())))))) -> s#(s(s(s(s(s(s(s(s(0()))))))))) -> k#(s(s(0()))) k#(s(s(0()))) -> s#(s(s(s(s(s(0())))))) -> s#(s(s(s(0())))) -> k#(s(0())) k#(s(s(0()))) -> s#(s(s(s(s(s(0())))))) -> s#(s(s(0()))) -> k#(0()) k#(s(s(0()))) -> s#(s(s(s(s(s(0())))))) -> s#(x) -> h#(0(),x) k#(s(s(0()))) -> s#(s(s(s(s(s(0())))))) -> s#(x) -> h#(x,0()) k#(s(s(0()))) -> s#(s(s(s(s(s(0())))))) -> s#(s(0())) -> f#(s(0())) k#(s(s(0()))) -> s#(s(s(s(s(0()))))) -> s#(s(s(s(s(s(s(s(s(0()))))))))) -> k#(s(s(0()))) k#(s(s(0()))) -> s#(s(s(s(s(0()))))) -> s#(s(s(s(0())))) -> k#(s(0())) k#(s(s(0()))) -> s#(s(s(s(s(0()))))) -> s#(s(s(0()))) -> k#(0()) k#(s(s(0()))) -> s#(s(s(s(s(0()))))) -> s#(x) -> h#(0(),x) k#(s(s(0()))) -> s#(s(s(s(s(0()))))) -> s#(x) -> h#(x,0()) k#(s(s(0()))) -> s#(s(s(s(s(0()))))) -> s#(s(0())) -> f#(s(0())) k#(s(s(0()))) -> s#(s(s(s(0())))) -> s#(s(s(s(s(s(s(s(s(0()))))))))) -> k#(s(s(0()))) k#(s(s(0()))) -> s#(s(s(s(0())))) -> s#(s(s(s(0())))) -> k#(s(0())) k#(s(s(0()))) -> s#(s(s(s(0())))) -> s#(s(s(0()))) -> k#(0()) k#(s(s(0()))) -> s#(s(s(s(0())))) -> s#(x) -> h#(0(),x) k#(s(s(0()))) -> s#(s(s(s(0())))) -> s#(x) -> h#(x,0()) k#(s(s(0()))) -> s#(s(s(s(0())))) -> s#(s(0())) -> f#(s(0())) k#(s(s(0()))) -> s#(s(s(0()))) -> s#(s(s(s(s(s(s(s(s(0()))))))))) -> k#(s(s(0()))) k#(s(s(0()))) -> s#(s(s(0()))) -> s#(s(s(s(0())))) -> k#(s(0())) k#(s(s(0()))) -> s#(s(s(0()))) -> s#(s(s(0()))) -> k#(0()) k#(s(s(0()))) -> s#(s(s(0()))) -> s#(x) -> h#(0(),x) k#(s(s(0()))) -> s#(s(s(0()))) -> s#(x) -> h#(x,0()) k#(s(s(0()))) -> s#(s(s(0()))) -> s#(s(0())) -> f#(s(0())) k#(s(0())) -> s#(s(0())) -> s#(s(s(s(s(s(s(s(s(0()))))))))) -> k#(s(s(0()))) k#(s(0())) -> s#(s(0())) -> s#(s(s(s(0())))) -> k#(s(0())) k#(s(0())) -> s#(s(0())) -> s#(s(s(0()))) -> k#(0()) k#(s(0())) -> s#(s(0())) -> s#(x) -> h#(0(),x) k#(s(0())) -> s#(s(0())) -> s#(x) -> h#(x,0()) k#(s(0())) -> s#(s(0())) -> s#(s(0())) -> f#(s(0())) k#(0()) -> s#(0()) -> s#(s(s(s(s(s(s(s(s(0()))))))))) -> k#(s(s(0()))) k#(0()) -> s#(0()) -> s#(s(s(s(0())))) -> k#(s(0())) k#(0()) -> s#(0()) -> s#(s(s(0()))) -> k#(0()) k#(0()) -> s#(0()) -> s#(x) -> h#(0(),x) k#(0()) -> s#(0()) -> s#(x) -> h#(x,0()) k#(0()) -> s#(0()) -> s#(s(0())) -> f#(s(0())) h#(k(x),g(x)) -> k#(s(x)) -> k#(s(s(0()))) -> s#(s(s(s(s(s(s(0()))))))) h#(k(x),g(x)) -> k#(s(x)) -> k#(s(s(0()))) -> s#(s(s(s(s(s(0())))))) h#(k(x),g(x)) -> k#(s(x)) -> k#(s(s(0()))) -> s#(s(s(s(s(0()))))) h#(k(x),g(x)) -> k#(s(x)) -> k#(s(s(0()))) -> s#(s(s(s(0())))) h#(k(x),g(x)) -> k#(s(x)) -> k#(s(s(0()))) -> s#(s(s(0()))) h#(k(x),g(x)) -> k#(s(x)) -> k#(s(0())) -> s#(s(0())) h#(k(x),g(x)) -> k#(s(x)) -> k#(0()) -> s#(0()) h#(k(x),g(x)) -> s#(x) -> s#(s(s(s(s(s(s(s(s(0()))))))))) -> k#(s(s(0()))) h#(k(x),g(x)) -> s#(x) -> s#(s(s(s(0())))) -> k#(s(0())) h#(k(x),g(x)) -> s#(x) -> s#(s(s(0()))) -> k#(0()) h#(k(x),g(x)) -> s#(x) -> s#(x) -> h#(0(),x) h#(k(x),g(x)) -> s#(x) -> s#(x) -> h#(x,0()) h#(k(x),g(x)) -> s#(x) -> s#(s(0())) -> f#(s(0())) h#(f(x),g(x)) -> f#(s(x)) -> f#(g(x)) -> g#(g(f(x))) h#(f(x),g(x)) -> f#(s(x)) -> f#(g(x)) -> g#(f(x)) h#(f(x),g(x)) -> f#(s(x)) -> f#(g(x)) -> f#(x) h#(f(x),g(x)) -> s#(x) -> s#(s(s(s(s(s(s(s(s(0()))))))))) -> k#(s(s(0()))) h#(f(x),g(x)) -> s#(x) -> s#(s(s(s(0())))) -> k#(s(0())) h#(f(x),g(x)) -> s#(x) -> s#(s(s(0()))) -> k#(0()) h#(f(x),g(x)) -> s#(x) -> s#(x) -> h#(0(),x) h#(f(x),g(x)) -> s#(x) -> s#(x) -> h#(x,0()) h#(f(x),g(x)) -> s#(x) -> s#(s(0())) -> f#(s(0())) g#(s(x)) -> g#(x) -> g#(s(x)) -> s#(s(g(x))) g#(s(x)) -> g#(x) -> g#(s(x)) -> s#(g(x)) g#(s(x)) -> g#(x) -> g#(s(x)) -> g#(x) g#(s(x)) -> g#(x) -> g#(x) -> h#(x,x) g#(s(x)) -> s#(g(x)) -> s#(s(s(s(s(s(s(s(s(0()))))))))) -> k#(s(s(0()))) g#(s(x)) -> s#(g(x)) -> s#(s(s(s(0())))) -> k#(s(0())) g#(s(x)) -> s#(g(x)) -> s#(s(s(0()))) -> k#(0()) g#(s(x)) -> s#(g(x)) -> s#(x) -> h#(0(),x) g#(s(x)) -> s#(g(x)) -> s#(x) -> h#(x,0()) g#(s(x)) -> s#(g(x)) -> s#(s(0())) -> f#(s(0())) g#(s(x)) -> s#(s(g(x))) -> s#(s(s(s(s(s(s(s(s(0()))))))))) -> k#(s(s(0()))) g#(s(x)) -> s#(s(g(x))) -> s#(s(s(s(0())))) -> k#(s(0())) g#(s(x)) -> s#(s(g(x))) -> s#(s(s(0()))) -> k#(0()) g#(s(x)) -> s#(s(g(x))) -> s#(x) -> h#(0(),x) g#(s(x)) -> s#(s(g(x))) -> s#(x) -> h#(x,0()) g#(s(x)) -> s#(s(g(x))) -> s#(s(0())) -> f#(s(0())) g#(x) -> h#(x,x) -> h#(k(x),g(x)) -> k#(s(x)) g#(x) -> h#(x,x) -> h#(k(x),g(x)) -> s#(x) g#(x) -> h#(x,x) -> h#(f(x),g(x)) -> f#(s(x)) g#(x) -> h#(x,x) -> h#(f(x),g(x)) -> s#(x) f#(g(x)) -> g#(g(f(x))) -> g#(s(x)) -> s#(s(g(x))) f#(g(x)) -> g#(g(f(x))) -> g#(s(x)) -> s#(g(x)) f#(g(x)) -> g#(g(f(x))) -> g#(s(x)) -> g#(x) f#(g(x)) -> g#(g(f(x))) -> g#(x) -> h#(x,x) f#(g(x)) -> g#(f(x)) -> g#(s(x)) -> s#(s(g(x))) f#(g(x)) -> g#(f(x)) -> g#(s(x)) -> s#(g(x)) f#(g(x)) -> g#(f(x)) -> g#(s(x)) -> g#(x) f#(g(x)) -> g#(f(x)) -> g#(x) -> h#(x,x) f#(g(x)) -> f#(x) -> f#(g(x)) -> g#(g(f(x))) f#(g(x)) -> f#(x) -> f#(g(x)) -> g#(f(x)) f#(g(x)) -> f#(x) -> f#(g(x)) -> f#(x) s#(s(s(s(s(s(s(s(s(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(s(s(s(s(s(s(s(0()))))))))) -> k#(s(s(0()))) -> k#(s(0())) -> s#(s(0())) s#(s(s(s(s(s(s(s(s(0()))))))))) -> k#(s(s(0()))) -> k#(0()) -> s#(0()) s#(s(s(s(0())))) -> k#(s(0())) -> k#(s(s(0()))) -> s#(s(s(s(s(s(s(0()))))))) s#(s(s(s(0())))) -> k#(s(0())) -> k#(s(s(0()))) -> s#(s(s(s(s(s(0())))))) s#(s(s(s(0())))) -> k#(s(0())) -> k#(s(s(0()))) -> s#(s(s(s(s(0()))))) s#(s(s(s(0())))) -> k#(s(0())) -> k#(s(s(0()))) -> s#(s(s(s(0())))) s#(s(s(s(0())))) -> k#(s(0())) -> k#(s(s(0()))) -> s#(s(s(0()))) s#(s(s(s(0())))) -> k#(s(0())) -> k#(s(0())) -> s#(s(0())) s#(s(s(s(0())))) -> k#(s(0())) -> k#(0()) -> s#(0()) s#(s(s(0()))) -> k#(0()) -> k#(s(s(0()))) -> s#(s(s(s(s(s(s(0()))))))) s#(s(s(0()))) -> k#(0()) -> k#(s(s(0()))) -> s#(s(s(s(s(s(0())))))) s#(s(s(0()))) -> k#(0()) -> k#(s(s(0()))) -> s#(s(s(s(s(0()))))) s#(s(s(0()))) -> k#(0()) -> k#(s(s(0()))) -> s#(s(s(s(0())))) s#(s(s(0()))) -> k#(0()) -> k#(s(s(0()))) -> s#(s(s(0()))) s#(s(s(0()))) -> k#(0()) -> k#(s(0())) -> s#(s(0())) s#(s(s(0()))) -> k#(0()) -> k#(0()) -> s#(0()) s#(s(0())) -> f#(s(0())) -> f#(g(x)) -> g#(g(f(x))) s#(s(0())) -> f#(s(0())) -> f#(g(x)) -> g#(f(x)) s#(s(0())) -> f#(s(0())) -> f#(g(x)) -> f#(x) s#(x) -> h#(0(),x) -> h#(k(x),g(x)) -> k#(s(x)) s#(x) -> h#(0(),x) -> h#(k(x),g(x)) -> s#(x) s#(x) -> h#(0(),x) -> h#(f(x),g(x)) -> f#(s(x)) s#(x) -> h#(0(),x) -> h#(f(x),g(x)) -> s#(x) s#(x) -> h#(x,0()) -> h#(k(x),g(x)) -> k#(s(x)) s#(x) -> h#(x,0()) -> h#(k(x),g(x)) -> s#(x) s#(x) -> h#(x,0()) -> h#(f(x),g(x)) -> f#(s(x)) s#(x) -> h#(x,0()) -> h#(f(x),g(x)) -> s#(x) EDG Processor: DPs: s#(s(0())) -> f#(s(0())) g#(x) -> h#(x,x) s#(x) -> h#(x,0()) s#(x) -> h#(0(),x) f#(g(x)) -> f#(x) f#(g(x)) -> g#(f(x)) f#(g(x)) -> g#(g(f(x))) g#(s(x)) -> g#(x) g#(s(x)) -> s#(g(x)) g#(s(x)) -> s#(s(g(x))) h#(f(x),g(x)) -> s#(x) h#(f(x),g(x)) -> f#(s(x)) s#(s(s(0()))) -> k#(0()) k#(0()) -> s#(0()) s#(s(s(s(0())))) -> k#(s(0())) k#(s(0())) -> s#(s(0())) s#(s(s(s(s(s(s(s(s(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(s(s(0()))) -> k(0()) k(0()) -> s(0()) s(s(s(s(0())))) -> k(s(0())) k(s(0())) -> s(s(0())) s(s(s(s(s(s(s(s(s(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#(s(s(0()))) -> k#(0()) k#(s(s(0()))) -> s#(s(s(s(s(s(s(0()))))))) -> s#(s(s(s(0())))) -> k#(s(0())) k#(s(s(0()))) -> s#(s(s(s(s(s(s(0()))))))) -> s#(s(s(s(s(s(s(s(s(0()))))))))) -> k#(s(s(0()))) k#(s(s(0()))) -> s#(s(s(s(s(s(0())))))) -> s#(s(0())) -> f#(s(0())) k#(s(s(0()))) -> s#(s(s(s(s(s(0())))))) -> s#(x) -> h#(x,0()) k#(s(s(0()))) -> s#(s(s(s(s(s(0())))))) -> s#(x) -> h#(0(),x) k#(s(s(0()))) -> s#(s(s(s(s(s(0())))))) -> s#(s(s(0()))) -> k#(0()) k#(s(s(0()))) -> s#(s(s(s(s(s(0())))))) -> s#(s(s(s(0())))) -> k#(s(0())) k#(s(s(0()))) -> s#(s(s(s(s(s(0())))))) -> s#(s(s(s(s(s(s(s(s(0()))))))))) -> k#(s(s(0()))) k#(s(s(0()))) -> s#(s(s(s(s(0()))))) -> s#(s(0())) -> f#(s(0())) k#(s(s(0()))) -> s#(s(s(s(s(0()))))) -> s#(x) -> h#(x,0()) k#(s(s(0()))) -> s#(s(s(s(s(0()))))) -> s#(x) -> h#(0(),x) k#(s(s(0()))) -> s#(s(s(s(s(0()))))) -> s#(s(s(0()))) -> k#(0()) k#(s(s(0()))) -> s#(s(s(s(s(0()))))) -> s#(s(s(s(0())))) -> k#(s(0())) k#(s(s(0()))) -> s#(s(s(s(s(0()))))) -> s#(s(s(s(s(s(s(s(s(0()))))))))) -> k#(s(s(0()))) k#(s(s(0()))) -> s#(s(s(s(0())))) -> s#(s(0())) -> f#(s(0())) k#(s(s(0()))) -> s#(s(s(s(0())))) -> s#(x) -> h#(x,0()) k#(s(s(0()))) -> s#(s(s(s(0())))) -> s#(x) -> h#(0(),x) k#(s(s(0()))) -> s#(s(s(s(0())))) -> s#(s(s(0()))) -> k#(0()) k#(s(s(0()))) -> s#(s(s(s(0())))) -> s#(s(s(s(0())))) -> k#(s(0())) k#(s(s(0()))) -> s#(s(s(s(0())))) -> s#(s(s(s(s(s(s(s(s(0()))))))))) -> k#(s(s(0()))) k#(s(s(0()))) -> s#(s(s(0()))) -> s#(s(0())) -> f#(s(0())) k#(s(s(0()))) -> s#(s(s(0()))) -> s#(x) -> h#(x,0()) k#(s(s(0()))) -> s#(s(s(0()))) -> s#(x) -> h#(0(),x) k#(s(s(0()))) -> s#(s(s(0()))) -> s#(s(s(0()))) -> k#(0()) k#(s(s(0()))) -> s#(s(s(0()))) -> s#(s(s(s(0())))) -> k#(s(0())) k#(s(s(0()))) -> s#(s(s(0()))) -> s#(s(s(s(s(s(s(s(s(0()))))))))) -> k#(s(s(0()))) k#(s(0())) -> s#(s(0())) -> s#(s(0())) -> f#(s(0())) k#(s(0())) -> s#(s(0())) -> s#(x) -> h#(x,0()) k#(s(0())) -> s#(s(0())) -> s#(x) -> h#(0(),x) k#(s(0())) -> s#(s(0())) -> s#(s(s(0()))) -> k#(0()) k#(s(0())) -> s#(s(0())) -> s#(s(s(s(0())))) -> k#(s(0())) k#(s(0())) -> s#(s(0())) -> s#(s(s(s(s(s(s(s(s(0()))))))))) -> k#(s(s(0()))) k#(0()) -> s#(0()) -> s#(x) -> h#(x,0()) k#(0()) -> s#(0()) -> s#(x) -> h#(0(),x) h#(k(x),g(x)) -> k#(s(x)) -> k#(s(0())) -> s#(s(0())) h#(k(x),g(x)) -> k#(s(x)) -> k#(s(s(0()))) -> s#(s(s(0()))) h#(k(x),g(x)) -> k#(s(x)) -> k#(s(s(0()))) -> s#(s(s(s(0())))) h#(k(x),g(x)) -> k#(s(x)) -> k#(s(s(0()))) -> s#(s(s(s(s(0()))))) h#(k(x),g(x)) -> k#(s(x)) -> k#(s(s(0()))) -> s#(s(s(s(s(s(0())))))) h#(k(x),g(x)) -> k#(s(x)) -> k#(s(s(0()))) -> s#(s(s(s(s(s(s(0()))))))) h#(k(x),g(x)) -> s#(x) -> s#(s(0())) -> f#(s(0())) h#(k(x),g(x)) -> s#(x) -> s#(x) -> h#(x,0()) h#(k(x),g(x)) -> s#(x) -> s#(x) -> h#(0(),x) h#(k(x),g(x)) -> s#(x) -> s#(s(s(0()))) -> k#(0()) h#(k(x),g(x)) -> s#(x) -> s#(s(s(s(0())))) -> k#(s(0())) h#(k(x),g(x)) -> s#(x) -> s#(s(s(s(s(s(s(s(s(0()))))))))) -> k#(s(s(0()))) h#(f(x),g(x)) -> f#(s(x)) -> f#(g(x)) -> f#(x) h#(f(x),g(x)) -> f#(s(x)) -> f#(g(x)) -> g#(f(x)) h#(f(x),g(x)) -> f#(s(x)) -> f#(g(x)) -> g#(g(f(x))) h#(f(x),g(x)) -> s#(x) -> s#(s(0())) -> f#(s(0())) h#(f(x),g(x)) -> s#(x) -> s#(x) -> h#(x,0()) h#(f(x),g(x)) -> s#(x) -> s#(x) -> h#(0(),x) h#(f(x),g(x)) -> s#(x) -> s#(s(s(0()))) -> k#(0()) h#(f(x),g(x)) -> s#(x) -> s#(s(s(s(0())))) -> k#(s(0())) h#(f(x),g(x)) -> s#(x) -> s#(s(s(s(s(s(s(s(s(0()))))))))) -> k#(s(s(0()))) g#(s(x)) -> g#(x) -> g#(x) -> h#(x,x) g#(s(x)) -> g#(x) -> g#(s(x)) -> g#(x) g#(s(x)) -> g#(x) -> g#(s(x)) -> s#(g(x)) g#(s(x)) -> g#(x) -> g#(s(x)) -> s#(s(g(x))) g#(s(x)) -> s#(g(x)) -> s#(s(0())) -> f#(s(0())) g#(s(x)) -> s#(g(x)) -> s#(x) -> h#(x,0()) g#(s(x)) -> s#(g(x)) -> s#(x) -> h#(0(),x) g#(s(x)) -> s#(g(x)) -> s#(s(s(0()))) -> k#(0()) g#(s(x)) -> s#(g(x)) -> s#(s(s(s(0())))) -> k#(s(0())) g#(s(x)) -> s#(g(x)) -> s#(s(s(s(s(s(s(s(s(0()))))))))) -> k#(s(s(0()))) g#(s(x)) -> s#(s(g(x))) -> s#(s(0())) -> f#(s(0())) g#(s(x)) -> s#(s(g(x))) -> s#(x) -> h#(x,0()) g#(s(x)) -> s#(s(g(x))) -> s#(x) -> h#(0(),x) g#(s(x)) -> s#(s(g(x))) -> s#(s(s(0()))) -> k#(0()) g#(s(x)) -> s#(s(g(x))) -> s#(s(s(s(0())))) -> k#(s(0())) g#(s(x)) -> s#(s(g(x))) -> s#(s(s(s(s(s(s(s(s(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(0())) -> 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(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(s(s(0())))) -> k#(s(0())) -> k#(s(0())) -> s#(s(0())) s#(s(s(s(0())))) -> k#(s(0())) -> k#(s(s(0()))) -> s#(s(s(0()))) s#(s(s(s(0())))) -> k#(s(0())) -> k#(s(s(0()))) -> s#(s(s(s(0())))) s#(s(s(s(0())))) -> k#(s(0())) -> k#(s(s(0()))) -> s#(s(s(s(s(0()))))) s#(s(s(s(0())))) -> k#(s(0())) -> k#(s(s(0()))) -> s#(s(s(s(s(s(0())))))) s#(s(s(s(0())))) -> k#(s(0())) -> k#(s(s(0()))) -> s#(s(s(s(s(s(s(0()))))))) s#(s(s(0()))) -> k#(0()) -> k#(0()) -> s#(0()) s#(s(0())) -> f#(s(0())) -> f#(g(x)) -> f#(x) s#(s(0())) -> f#(s(0())) -> f#(g(x)) -> g#(f(x)) s#(s(0())) -> f#(s(0())) -> f#(g(x)) -> g#(g(f(x))) SCC Processor: #sccs: 1 #rules: 20 #arcs: 106/576 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(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()))) k#(s(0())) -> s#(s(0())) h#(k(x),g(x)) -> s#(x) h#(f(x),g(x)) -> f#(s(x)) f#(g(x)) -> g#(f(x)) f#(g(x)) -> f#(x) h#(f(x),g(x)) -> s#(x) TRS: s(s(0())) -> f(s(0())) g(x) -> h(x,x) s(x) -> h(x,0()) s(x) -> h(0(),x) f(g(x)) -> g(g(f(x))) g(s(x)) -> s(s(g(x))) h(f(x),g(x)) -> f(s(x)) s(s(s(0()))) -> k(0()) k(0()) -> s(0()) s(s(s(s(0())))) -> k(s(0())) k(s(0())) -> s(s(0())) s(s(s(s(s(s(s(s(s(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(s(s(0()))) -> k(0()) k(0()) -> s(0()) s(s(s(s(0())))) -> k(s(0())) k(s(0())) -> s(s(0())) s(s(s(s(s(s(s(s(s(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 + 4, [k](x0) = 0, [k#](x0) = 0, [0] = 0, [f#](x0) = 4x0, [h#](x0, x1) = 0, [s#](x0) = 0, [f](x0) = 4x0 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(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)) = 4x + 16 >= 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()))) k#(s(0())) = 0 >= 0 = s#(s(0())) h#(k(x),g(x)) = 0 >= 0 = s#(x) h#(f(x),g(x)) = 0 >= 0 = f#(s(x)) f#(g(x)) = 4x + 16 >= 0 = g#(f(x)) f#(g(x)) = 4x + 16 >= 4x = f#(x) h#(f(x),g(x)) = 0 >= 0 = s#(x) s(s(0())) = 0 >= 0 = f(s(0())) g(x) = x + 4 >= 0 = h(x,x) s(x) = 0 >= 0 = h(x,0()) s(x) = 0 >= 0 = h(0(),x) f(g(x)) = 4x + 16 >= 4x + 8 = g(g(f(x))) g(s(x)) = 4 >= 0 = s(s(g(x))) h(f(x),g(x)) = 0 >= 0 = f(s(x)) s(s(s(0()))) = 0 >= 0 = k(0()) k(0()) = 0 >= 0 = s(0()) s(s(s(s(0())))) = 0 >= 0 = k(s(0())) k(s(0())) = 0 >= 0 = s(s(0())) s(s(s(s(s(s(s(s(s(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(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()))) k#(s(0())) -> s#(s(0())) h#(k(x),g(x)) -> s#(x) h#(f(x),g(x)) -> f#(s(x)) h#(f(x),g(x)) -> s#(x) TRS: s(s(0())) -> f(s(0())) g(x) -> h(x,x) s(x) -> h(x,0()) s(x) -> h(0(),x) f(g(x)) -> g(g(f(x))) g(s(x)) -> s(s(g(x))) h(f(x),g(x)) -> f(s(x)) s(s(s(0()))) -> k(0()) k(0()) -> s(0()) s(s(s(s(0())))) -> k(s(0())) k(s(0())) -> s(s(0())) s(s(s(s(s(s(s(s(s(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(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()))) k#(s(0())) -> s#(s(0())) h#(k(x),g(x)) -> s#(x) h#(f(x),g(x)) -> f#(s(x)) h#(f(x),g(x)) -> s#(x) TRS: s(s(0())) -> f(s(0())) g(x) -> h(x,x) s(x) -> h(x,0()) s(x) -> h(0(),x) f(g(x)) -> g(g(f(x))) g(s(x)) -> s(s(g(x))) h(f(x),g(x)) -> f(s(x)) s(s(s(0()))) -> k(0()) k(0()) -> s(0()) s(s(s(s(0())))) -> k(s(0())) k(s(0())) -> s(s(0())) s(s(s(s(s(s(s(s(s(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: 9 #arcs: 73/289 DPs: g#(s(x)) -> g#(x) TRS: s(s(0())) -> f(s(0())) g(x) -> h(x,x) s(x) -> h(x,0()) s(x) -> h(0(),x) f(g(x)) -> g(g(f(x))) g(s(x)) -> s(s(g(x))) h(f(x),g(x)) -> f(s(x)) s(s(s(0()))) -> k(0()) k(0()) -> s(0()) s(s(s(s(0())))) -> k(s(0())) k(s(0())) -> s(s(0())) s(s(s(s(s(s(s(s(s(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(s(s(0()))) -> k(0()) k(0()) -> s(0()) s(s(s(s(0())))) -> k(s(0())) k(s(0())) -> s(s(0())) s(s(s(s(s(s(s(s(s(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(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()))) k#(s(0())) -> s#(s(0())) TRS: s(s(0())) -> f(s(0())) g(x) -> h(x,x) s(x) -> h(x,0()) s(x) -> h(0(),x) f(g(x)) -> g(g(f(x))) g(s(x)) -> s(s(g(x))) h(f(x),g(x)) -> f(s(x)) s(s(s(0()))) -> k(0()) k(0()) -> s(0()) s(s(s(s(0())))) -> k(s(0())) k(s(0())) -> s(s(0())) s(s(s(s(s(s(s(s(s(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: {46} transitions: s{#,0}(48) -> 46* 00() -> 47* s0(47) -> 48* h0(47,47) -> 48* 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(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(s(s(0()))) -> k(0()) k(0()) -> s(0()) s(s(s(s(0())))) -> k(s(0())) k(s(0())) -> s(s(0())) s(s(s(s(s(s(s(s(s(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* 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(s(s(0()))) -> k(0()) k(0()) -> s(0()) s(s(s(s(0())))) -> k(s(0())) k(s(0())) -> s(s(0())) s(s(s(s(s(s(s(s(s(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}(40) -> 37* 00() -> 38* s0(38) -> 39* s0(39) -> 40* h0(39,38) -> 40* h0(38,39) -> 40* h0(38,38) -> 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(s(s(0()))) -> k(0()) k(0()) -> s(0()) s(s(s(s(0())))) -> k(s(0())) k(s(0())) -> s(s(0())) s(s(s(s(s(s(s(s(s(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}(40) -> 31* 00() -> 32* s0(33) -> 34* s0(32) -> 40*,35,33 s0(34) -> 35* s0(40) -> 34* h0(32,33) -> 34* h0(32,32) -> 40*,33 h0(34,32) -> 35* h0(40,32) -> 34* h0(33,32) -> 34* h0(32,34) -> 35* h0(32,40) -> 34* k0(32) -> 35* f0(40) -> 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(s(s(0()))) -> k(0()) k(0()) -> s(0()) s(s(s(s(0())))) -> k(s(0())) k(s(0())) -> s(s(0())) s(s(s(s(s(s(s(s(s(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}(35) -> 24* s{#,0}(29) -> 24* 00() -> 25* s0(34) -> 35*,29,27 s0(35) -> 28* s0(28) -> 29* s0(27) -> 28* s0(26) -> 27* s0(25) -> 34*,28,26 h0(27,25) -> 28* h0(25,34) -> 35*,27,29 h0(34,25) -> 35*,27,29 h0(35,25) -> 28* h0(25,27) -> 28* h0(25,25) -> 34*,26 h0(25,26) -> 27* h0(25,35) -> 28* h0(25,28) -> 29* h0(26,25) -> 27* h0(28,25) -> 29* k0(25) -> 28* k0(26) -> 29* k0(34) -> 29* f0(26) -> 35*,27 f0(34) -> 35*,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(s(s(0()))) -> k(0()) k(0()) -> s(0()) s(s(s(s(0())))) -> k(s(0())) k(s(0())) -> s(s(0())) s(s(s(s(s(s(s(s(s(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}(34) -> 16* s{#,0}(22) -> 16* s{#,0}(29) -> 16* 00() -> 17* s0(18) -> 19* s0(34) -> 19,28*,21 s0(20) -> 21* s0(28) -> 29*,22,20 s0(27) -> 28*,19,21 s0(21) -> 22* s0(17) -> 27,29,34*,20,18 s0(29) -> 21* s0(19) -> 20* h0(20,17) -> 21* h0(17,18) -> 19* h0(17,28) -> 29*,22,20 h0(17,21) -> 22* h0(17,19) -> 20* h0(19,17) -> 20* h0(17,20) -> 21* h0(17,27) -> 28*,19,21 h0(17,34) -> 19,28*,21 h0(27,17) -> 28*,21,19 h0(34,17) -> 28*,19,21 h0(17,17) -> 27,34*,18 h0(18,17) -> 19* h0(28,17) -> 29*,20,22 h0(17,29) -> 21* h0(29,17) -> 21* h0(21,17) -> 22* k0(27) -> 21* k0(18) -> 21* k0(17) -> 29*,20 k0(34) -> 21* f0(18) -> 28*,19 f0(34) -> 28* f0(27) -> 28*,19 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(s(s(0()))) -> k(0()) k(0()) -> s(0()) s(s(s(s(0())))) -> k(s(0())) k(s(0())) -> s(s(0())) s(s(s(s(s(s(s(s(s(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}(28) -> 2* s{#,0}(22) -> 2* 00() -> 3* s0(3) -> 19,21,27*,6,4 s0(20) -> 21*,8,6 s0(22) -> 8* s0(6) -> 7* s0(7) -> 8* s0(28) -> 21*,8,6 s0(4) -> 5* s0(27) -> 28*,7,5,9 s0(5) -> 6* s0(8) -> 9* s0(21) -> 22*,7,9 s0(19) -> 20*,7,5 h0(19,3) -> 20*,7,5 h0(27,3) -> 28*,7,9,5 h0(3,3) -> 19,27*,4 h0(3,22) -> 8* h0(3,5) -> 6* h0(3,7) -> 8* h0(22,3) -> 8* h0(6,3) -> 7* h0(3,4) -> 5* h0(3,21) -> 22*,7,9 h0(7,3) -> 8* h0(8,3) -> 9* h0(3,19) -> 20*,5,7 h0(21,3) -> 22*,7,9 h0(28,3) -> 8,6,21* h0(5,3) -> 6* h0(3,20) -> 21*,6,8 h0(4,3) -> 5* h0(20,3) -> 21*,8,6 h0(3,6) -> 7* h0(3,27) -> 28*,5,7,9 h0(3,8) -> 9* h0(3,28) -> 6,8,21* k0(27) -> 22* k0(19) -> 22*,7 k0(3) -> 21*,6 k0(4) -> 22*,7 f0(19) -> 20,28*,5 f0(4) -> 20,28*,5 f0(27) -> 20,28* 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(s(s(0()))) -> k(0()) k(0()) -> s(0()) s(s(s(s(0())))) -> k(s(0())) k(s(0())) -> s(s(0())) s(s(s(s(s(s(s(s(s(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: 24/1