/export/starexec/sandbox/solver/bin/starexec_run_ttt2 /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/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(s(0()))))) -> k(s(0())) k(s(0())) -> s(s(s(0()))) s(s(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(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(s(0()))))) -> k#(s(0())) k#(s(0())) -> s#(s(0())) k#(s(0())) -> s#(s(s(0()))) s#(s(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()))))))))) k#(s(s(0()))) -> s#(s(s(s(s(s(s(s(s(s(0())))))))))) k#(s(s(0()))) -> s#(s(s(s(s(s(s(s(s(s(s(0()))))))))))) h#(k(x),g(x)) -> s#(x) h#(k(x),g(x)) -> k#(s(x)) TRS: s(s(0())) -> f(s(0())) g(x) -> h(x,x) s(x) -> h(x,0()) s(x) -> h(0(),x) f(g(x)) -> g(g(f(x))) g(s(x)) -> s(s(g(x))) h(f(x),g(x)) -> f(s(x)) s(s(s(0()))) -> k(0()) k(0()) -> s(0()) s(s(s(s(s(0()))))) -> k(s(0())) k(s(0())) -> s(s(s(0()))) s(s(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(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(s(0()))))) -> k#(s(0())) k#(s(0())) -> s#(s(0())) k#(s(0())) -> s#(s(s(0()))) s#(s(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()))))))))) k#(s(s(0()))) -> s#(s(s(s(s(s(s(s(s(s(0())))))))))) k#(s(s(0()))) -> s#(s(s(s(s(s(s(s(s(s(s(0()))))))))))) h#(k(x),g(x)) -> s#(x) h#(k(x),g(x)) -> k#(s(x)) TRS: s(s(0())) -> f(s(0())) g(x) -> h(x,x) s(x) -> h(x,0()) s(x) -> h(0(),x) f(g(x)) -> g(g(f(x))) g(s(x)) -> s(s(g(x))) h(f(x),g(x)) -> f(s(x)) s(s(s(0()))) -> k(0()) k(0()) -> s(0()) s(s(s(s(s(0()))))) -> k(s(0())) k(s(0())) -> s(s(s(0()))) s(s(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(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(s(s(0()))))))))))) -> s#(s(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(s(s(0()))))))))))) -> s#(s(s(s(s(0()))))) -> k#(s(0())) k#(s(s(0()))) -> s#(s(s(s(s(s(s(s(s(s(s(0()))))))))))) -> s#(s(s(0()))) -> k#(0()) k#(s(s(0()))) -> s#(s(s(s(s(s(s(s(s(s(s(0()))))))))))) -> s#(x) -> h#(0(),x) k#(s(s(0()))) -> s#(s(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(s(s(0()))))))))))) -> s#(s(0())) -> f#(s(0())) k#(s(s(0()))) -> s#(s(s(s(s(s(s(s(s(s(0())))))))))) -> s#(s(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(s(0())))))))))) -> s#(s(s(s(s(0()))))) -> k#(s(0())) k#(s(s(0()))) -> s#(s(s(s(s(s(s(s(s(s(0())))))))))) -> s#(s(s(0()))) -> k#(0()) k#(s(s(0()))) -> s#(s(s(s(s(s(s(s(s(s(0())))))))))) -> s#(x) -> h#(0(),x) k#(s(s(0()))) -> s#(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(s(0())))))))))) -> s#(s(0())) -> f#(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(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(0()))))) -> k#(s(0())) k#(s(s(0()))) -> s#(s(s(s(s(s(s(s(s(0()))))))))) -> s#(s(s(0()))) -> k#(0()) k#(s(s(0()))) -> s#(s(s(s(s(s(s(s(s(0()))))))))) -> s#(x) -> h#(0(),x) k#(s(s(0()))) -> s#(s(s(s(s(s(s(s(s(0()))))))))) -> s#(x) -> h#(x,0()) k#(s(s(0()))) -> s#(s(s(s(s(s(s(s(s(0()))))))))) -> s#(s(0())) -> f#(s(0())) k#(s(s(0()))) -> s#(s(s(s(s(s(s(s(0())))))))) -> s#(s(s(s(s(s(s(s(s(s(s(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(0()))))) -> k#(s(0())) k#(s(s(0()))) -> s#(s(s(s(s(s(s(s(0())))))))) -> s#(s(s(0()))) -> k#(0()) k#(s(s(0()))) -> s#(s(s(s(s(s(s(s(0())))))))) -> s#(x) -> h#(0(),x) k#(s(s(0()))) -> s#(s(s(s(s(s(s(s(0())))))))) -> s#(x) -> h#(x,0()) k#(s(s(0()))) -> s#(s(s(s(s(s(s(s(0())))))))) -> s#(s(0())) -> f#(s(0())) k#(s(s(0()))) -> s#(s(s(s(s(s(s(0()))))))) -> s#(s(s(s(s(s(s(s(s(s(s(s(s(0()))))))))))))) -> k#(s(s(0()))) k#(s(s(0()))) -> s#(s(s(s(s(s(s(0()))))))) -> s#(s(s(s(s(0()))))) -> k#(s(0())) k#(s(s(0()))) -> s#(s(s(s(s(s(s(0()))))))) -> s#(s(s(0()))) -> k#(0()) k#(s(s(0()))) -> s#(s(s(s(s(s(s(0()))))))) -> s#(x) -> h#(0(),x) k#(s(s(0()))) -> s#(s(s(s(s(s(s(0()))))))) -> s#(x) -> h#(x,0()) k#(s(s(0()))) -> s#(s(s(s(s(s(s(0()))))))) -> s#(s(0())) -> f#(s(0())) k#(s(s(0()))) -> s#(s(s(s(s(s(0())))))) -> s#(s(s(s(s(s(s(s(s(s(s(s(s(0()))))))))))))) -> k#(s(s(0()))) k#(s(s(0()))) -> s#(s(s(s(s(s(0())))))) -> s#(s(s(s(s(0()))))) -> k#(s(0())) k#(s(s(0()))) -> s#(s(s(s(s(s(0())))))) -> s#(s(s(0()))) -> k#(0()) k#(s(s(0()))) -> s#(s(s(s(s(s(0())))))) -> s#(x) -> h#(0(),x) k#(s(s(0()))) -> s#(s(s(s(s(s(0())))))) -> s#(x) -> h#(x,0()) k#(s(s(0()))) -> s#(s(s(s(s(s(0())))))) -> s#(s(0())) -> f#(s(0())) k#(s(s(0()))) -> s#(s(s(s(s(0()))))) -> s#(s(s(s(s(s(s(s(s(s(s(s(s(0()))))))))))))) -> k#(s(s(0()))) k#(s(s(0()))) -> s#(s(s(s(s(0()))))) -> s#(s(s(s(s(0()))))) -> k#(s(0())) k#(s(s(0()))) -> s#(s(s(s(s(0()))))) -> s#(s(s(0()))) -> k#(0()) k#(s(s(0()))) -> s#(s(s(s(s(0()))))) -> s#(x) -> h#(0(),x) k#(s(s(0()))) -> s#(s(s(s(s(0()))))) -> s#(x) -> h#(x,0()) k#(s(s(0()))) -> s#(s(s(s(s(0()))))) -> s#(s(0())) -> f#(s(0())) k#(s(s(0()))) -> s#(s(s(s(0())))) -> s#(s(s(s(s(s(s(s(s(s(s(s(s(0()))))))))))))) -> k#(s(s(0()))) k#(s(s(0()))) -> s#(s(s(s(0())))) -> s#(s(s(s(s(0()))))) -> k#(s(0())) k#(s(s(0()))) -> s#(s(s(s(0())))) -> s#(s(s(0()))) -> k#(0()) k#(s(s(0()))) -> s#(s(s(s(0())))) -> s#(x) -> h#(0(),x) k#(s(s(0()))) -> s#(s(s(s(0())))) -> s#(x) -> h#(x,0()) k#(s(s(0()))) -> s#(s(s(s(0())))) -> s#(s(0())) -> f#(s(0())) k#(s(s(0()))) -> s#(s(s(0()))) -> s#(s(s(s(s(s(s(s(s(s(s(s(s(0()))))))))))))) -> k#(s(s(0()))) k#(s(s(0()))) -> s#(s(s(0()))) -> s#(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(s(0()))) -> s#(s(s(s(s(s(s(s(s(s(s(s(s(0()))))))))))))) -> k#(s(s(0()))) k#(s(0())) -> s#(s(s(0()))) -> s#(s(s(s(s(0()))))) -> k#(s(0())) k#(s(0())) -> s#(s(s(0()))) -> s#(s(s(0()))) -> k#(0()) k#(s(0())) -> s#(s(s(0()))) -> s#(x) -> h#(0(),x) k#(s(0())) -> s#(s(s(0()))) -> s#(x) -> h#(x,0()) k#(s(0())) -> s#(s(s(0()))) -> s#(s(0())) -> f#(s(0())) k#(s(0())) -> s#(s(0())) -> s#(s(s(s(s(s(s(s(s(s(s(s(s(0()))))))))))))) -> k#(s(s(0()))) k#(s(0())) -> s#(s(0())) -> s#(s(s(s(s(0()))))) -> k#(s(0())) k#(s(0())) -> s#(s(0())) -> s#(s(s(0()))) -> k#(0()) k#(s(0())) -> s#(s(0())) -> s#(x) -> h#(0(),x) k#(s(0())) -> s#(s(0())) -> s#(x) -> h#(x,0()) k#(s(0())) -> s#(s(0())) -> s#(s(0())) -> f#(s(0())) k#(0()) -> s#(0()) -> s#(s(s(s(s(s(s(s(s(s(s(s(s(0()))))))))))))) -> k#(s(s(0()))) k#(0()) -> s#(0()) -> s#(s(s(s(s(0()))))) -> k#(s(0())) k#(0()) -> s#(0()) -> s#(s(s(0()))) -> k#(0()) k#(0()) -> s#(0()) -> s#(x) -> h#(0(),x) k#(0()) -> s#(0()) -> s#(x) -> h#(x,0()) k#(0()) -> s#(0()) -> s#(s(0())) -> f#(s(0())) h#(k(x),g(x)) -> k#(s(x)) -> k#(s(s(0()))) -> s#(s(s(s(s(s(s(s(s(s(s(0()))))))))))) h#(k(x),g(x)) -> k#(s(x)) -> k#(s(s(0()))) -> s#(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(s(0()))))))))) h#(k(x),g(x)) -> k#(s(x)) -> k#(s(s(0()))) -> s#(s(s(s(s(s(s(s(0())))))))) h#(k(x),g(x)) -> k#(s(x)) -> k#(s(s(0()))) -> s#(s(s(s(s(s(s(0()))))))) h#(k(x),g(x)) -> k#(s(x)) -> k#(s(s(0()))) -> s#(s(s(s(s(s(0())))))) h#(k(x),g(x)) -> k#(s(x)) -> k#(s(s(0()))) -> s#(s(s(s(s(0()))))) h#(k(x),g(x)) -> k#(s(x)) -> k#(s(s(0()))) -> s#(s(s(s(0())))) h#(k(x),g(x)) -> k#(s(x)) -> k#(s(s(0()))) -> s#(s(s(0()))) h#(k(x),g(x)) -> k#(s(x)) -> k#(s(0())) -> s#(s(s(0()))) h#(k(x),g(x)) -> k#(s(x)) -> k#(s(0())) -> s#(s(0())) h#(k(x),g(x)) -> k#(s(x)) -> k#(0()) -> s#(0()) h#(k(x),g(x)) -> s#(x) -> s#(s(s(s(s(s(s(s(s(s(s(s(s(0()))))))))))))) -> k#(s(s(0()))) h#(k(x),g(x)) -> s#(x) -> s#(s(s(s(s(0()))))) -> k#(s(0())) h#(k(x),g(x)) -> s#(x) -> s#(s(s(0()))) -> k#(0()) h#(k(x),g(x)) -> s#(x) -> s#(x) -> h#(0(),x) h#(k(x),g(x)) -> s#(x) -> s#(x) -> h#(x,0()) h#(k(x),g(x)) -> s#(x) -> s#(s(0())) -> f#(s(0())) h#(f(x),g(x)) -> f#(s(x)) -> f#(g(x)) -> g#(g(f(x))) h#(f(x),g(x)) -> f#(s(x)) -> f#(g(x)) -> g#(f(x)) h#(f(x),g(x)) -> f#(s(x)) -> f#(g(x)) -> f#(x) h#(f(x),g(x)) -> s#(x) -> s#(s(s(s(s(s(s(s(s(s(s(s(s(0()))))))))))))) -> k#(s(s(0()))) h#(f(x),g(x)) -> s#(x) -> s#(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)) -> 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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(s(s(0()))))))))))))) -> k#(s(s(0()))) -> k#(s(s(0()))) -> s#(s(s(s(s(s(s(s(s(s(s(0()))))))))))) s#(s(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(s(0())))))))))) s#(s(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(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(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(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(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(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(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(s(s(0()))))))))))))) -> k#(s(s(0()))) -> k#(s(0())) -> s#(s(s(0()))) s#(s(s(s(s(s(s(s(s(s(s(s(s(0()))))))))))))) -> k#(s(s(0()))) -> k#(s(0())) -> s#(s(0())) s#(s(s(s(s(s(s(s(s(s(s(s(s(0()))))))))))))) -> k#(s(s(0()))) -> k#(0()) -> s#(0()) s#(s(s(s(s(0()))))) -> k#(s(0())) -> k#(s(s(0()))) -> s#(s(s(s(s(s(s(s(s(s(s(0()))))))))))) s#(s(s(s(s(0()))))) -> k#(s(0())) -> k#(s(s(0()))) -> s#(s(s(s(s(s(s(s(s(s(0())))))))))) s#(s(s(s(s(0()))))) -> k#(s(0())) -> k#(s(s(0()))) -> s#(s(s(s(s(s(s(s(s(0()))))))))) s#(s(s(s(s(0()))))) -> k#(s(0())) -> k#(s(s(0()))) -> s#(s(s(s(s(s(s(s(0())))))))) s#(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(0()))))) -> k#(s(0())) -> k#(s(s(0()))) -> s#(s(s(s(s(s(0())))))) s#(s(s(s(s(0()))))) -> k#(s(0())) -> k#(s(s(0()))) -> s#(s(s(s(s(0()))))) s#(s(s(s(s(0()))))) -> k#(s(0())) -> k#(s(s(0()))) -> s#(s(s(s(0())))) s#(s(s(s(s(0()))))) -> k#(s(0())) -> k#(s(s(0()))) -> s#(s(s(0()))) s#(s(s(s(s(0()))))) -> k#(s(0())) -> k#(s(0())) -> s#(s(s(0()))) s#(s(s(s(s(0()))))) -> k#(s(0())) -> k#(s(0())) -> s#(s(0())) s#(s(s(s(s(0()))))) -> k#(s(0())) -> k#(0()) -> s#(0()) s#(s(s(0()))) -> k#(0()) -> k#(s(s(0()))) -> s#(s(s(s(s(s(s(s(s(s(s(0()))))))))))) s#(s(s(0()))) -> k#(0()) -> k#(s(s(0()))) -> s#(s(s(s(s(s(s(s(s(s(0())))))))))) s#(s(s(0()))) -> k#(0()) -> k#(s(s(0()))) -> s#(s(s(s(s(s(s(s(s(0()))))))))) s#(s(s(0()))) -> k#(0()) -> k#(s(s(0()))) -> s#(s(s(s(s(s(s(s(0())))))))) s#(s(s(0()))) -> k#(0()) -> k#(s(s(0()))) -> s#(s(s(s(s(s(s(0()))))))) s#(s(s(0()))) -> k#(0()) -> k#(s(s(0()))) -> s#(s(s(s(s(s(0())))))) s#(s(s(0()))) -> k#(0()) -> k#(s(s(0()))) -> s#(s(s(s(s(0()))))) s#(s(s(0()))) -> k#(0()) -> k#(s(s(0()))) -> s#(s(s(s(0())))) s#(s(s(0()))) -> k#(0()) -> k#(s(s(0()))) -> s#(s(s(0()))) s#(s(s(0()))) -> k#(0()) -> k#(s(0())) -> s#(s(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(s(0()))))) -> k#(s(0())) k#(s(0())) -> s#(s(0())) k#(s(0())) -> s#(s(s(0()))) s#(s(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()))))))))) k#(s(s(0()))) -> s#(s(s(s(s(s(s(s(s(s(0())))))))))) k#(s(s(0()))) -> s#(s(s(s(s(s(s(s(s(s(s(0()))))))))))) h#(k(x),g(x)) -> s#(x) h#(k(x),g(x)) -> k#(s(x)) TRS: s(s(0())) -> f(s(0())) g(x) -> h(x,x) s(x) -> h(x,0()) s(x) -> h(0(),x) f(g(x)) -> g(g(f(x))) g(s(x)) -> s(s(g(x))) h(f(x),g(x)) -> f(s(x)) s(s(s(0()))) -> k(0()) k(0()) -> s(0()) s(s(s(s(s(0()))))) -> k(s(0())) k(s(0())) -> s(s(s(0()))) s(s(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(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(s(s(0()))))))))))) -> s#(s(0())) -> f#(s(0())) k#(s(s(0()))) -> s#(s(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(s(s(0()))))))))))) -> s#(x) -> h#(0(),x) k#(s(s(0()))) -> s#(s(s(s(s(s(s(s(s(s(s(0()))))))))))) -> s#(s(s(0()))) -> k#(0()) k#(s(s(0()))) -> s#(s(s(s(s(s(s(s(s(s(s(0()))))))))))) -> s#(s(s(s(s(0()))))) -> k#(s(0())) k#(s(s(0()))) -> s#(s(s(s(s(s(s(s(s(s(s(0()))))))))))) -> s#(s(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(s(0())))))))))) -> s#(s(0())) -> f#(s(0())) k#(s(s(0()))) -> s#(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(s(0())))))))))) -> s#(x) -> h#(0(),x) k#(s(s(0()))) -> s#(s(s(s(s(s(s(s(s(s(0())))))))))) -> s#(s(s(0()))) -> k#(0()) k#(s(s(0()))) -> s#(s(s(s(s(s(s(s(s(s(0())))))))))) -> s#(s(s(s(s(0()))))) -> k#(s(0())) k#(s(s(0()))) -> s#(s(s(s(s(s(s(s(s(s(0())))))))))) -> s#(s(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(0())) -> f#(s(0())) k#(s(s(0()))) -> s#(s(s(s(s(s(s(s(s(0()))))))))) -> s#(x) -> h#(x,0()) k#(s(s(0()))) -> s#(s(s(s(s(s(s(s(s(0()))))))))) -> s#(x) -> h#(0(),x) k#(s(s(0()))) -> s#(s(s(s(s(s(s(s(s(0()))))))))) -> s#(s(s(0()))) -> k#(0()) k#(s(s(0()))) -> s#(s(s(s(s(s(s(s(s(0()))))))))) -> s#(s(s(s(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(s(s(0()))))))))))))) -> k#(s(s(0()))) k#(s(s(0()))) -> s#(s(s(s(s(s(s(s(0())))))))) -> s#(s(0())) -> f#(s(0())) k#(s(s(0()))) -> s#(s(s(s(s(s(s(s(0())))))))) -> s#(x) -> h#(x,0()) k#(s(s(0()))) -> s#(s(s(s(s(s(s(s(0())))))))) -> s#(x) -> h#(0(),x) k#(s(s(0()))) -> s#(s(s(s(s(s(s(s(0())))))))) -> s#(s(s(0()))) -> k#(0()) k#(s(s(0()))) -> s#(s(s(s(s(s(s(s(0())))))))) -> s#(s(s(s(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(s(s(0()))))))))))))) -> k#(s(s(0()))) k#(s(s(0()))) -> s#(s(s(s(s(s(s(0()))))))) -> s#(s(0())) -> f#(s(0())) k#(s(s(0()))) -> s#(s(s(s(s(s(s(0()))))))) -> s#(x) -> h#(x,0()) k#(s(s(0()))) -> s#(s(s(s(s(s(s(0()))))))) -> s#(x) -> h#(0(),x) k#(s(s(0()))) -> s#(s(s(s(s(s(s(0()))))))) -> s#(s(s(0()))) -> k#(0()) k#(s(s(0()))) -> s#(s(s(s(s(s(s(0()))))))) -> s#(s(s(s(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(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(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(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(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(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(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(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(s(0()))))) -> k#(s(0())) k#(s(s(0()))) -> s#(s(s(0()))) -> s#(s(s(s(s(s(s(s(s(s(s(s(s(0()))))))))))))) -> k#(s(s(0()))) k#(s(0())) -> s#(s(s(0()))) -> s#(s(0())) -> f#(s(0())) k#(s(0())) -> s#(s(s(0()))) -> s#(x) -> h#(x,0()) k#(s(0())) -> s#(s(s(0()))) -> s#(x) -> h#(0(),x) k#(s(0())) -> s#(s(s(0()))) -> s#(s(s(0()))) -> k#(0()) k#(s(0())) -> s#(s(s(0()))) -> s#(s(s(s(s(0()))))) -> k#(s(0())) k#(s(0())) -> s#(s(s(0()))) -> s#(s(s(s(s(s(s(s(s(s(s(s(s(0()))))))))))))) -> k#(s(s(0()))) k#(s(0())) -> s#(s(0())) -> s#(s(0())) -> f#(s(0())) k#(s(0())) -> s#(s(0())) -> s#(x) -> h#(x,0()) k#(s(0())) -> s#(s(0())) -> s#(x) -> h#(0(),x) k#(s(0())) -> s#(s(0())) -> s#(s(s(0()))) -> k#(0()) k#(s(0())) -> s#(s(0())) -> s#(s(s(s(s(0()))))) -> k#(s(0())) k#(s(0())) -> s#(s(0())) -> s#(s(s(s(s(s(s(s(s(s(s(s(s(0()))))))))))))) -> k#(s(s(0()))) k#(0()) -> s#(0()) -> s#(x) -> h#(x,0()) k#(0()) -> s#(0()) -> s#(x) -> h#(0(),x) h#(k(x),g(x)) -> k#(s(x)) -> k#(s(0())) -> s#(s(0())) h#(k(x),g(x)) -> k#(s(x)) -> k#(s(0())) -> 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(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)) -> k#(s(x)) -> k#(s(s(0()))) -> s#(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(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(s(0()))))) -> k#(s(0())) h#(k(x),g(x)) -> s#(x) -> s#(s(s(s(s(s(s(s(s(s(s(s(s(0()))))))))))))) -> k#(s(s(0()))) h#(f(x),g(x)) -> f#(s(x)) -> f#(g(x)) -> f#(x) h#(f(x),g(x)) -> f#(s(x)) -> f#(g(x)) -> g#(f(x)) h#(f(x),g(x)) -> f#(s(x)) -> f#(g(x)) -> g#(g(f(x))) h#(f(x),g(x)) -> s#(x) -> s#(s(0())) -> f#(s(0())) h#(f(x),g(x)) -> s#(x) -> s#(x) -> h#(x,0()) h#(f(x),g(x)) -> s#(x) -> s#(x) -> h#(0(),x) h#(f(x),g(x)) -> s#(x) -> s#(s(s(0()))) -> k#(0()) h#(f(x),g(x)) -> s#(x) -> s#(s(s(s(s(0()))))) -> k#(s(0())) h#(f(x),g(x)) -> s#(x) -> s#(s(s(s(s(s(s(s(s(s(s(s(s(0()))))))))))))) -> k#(s(s(0()))) g#(s(x)) -> g#(x) -> g#(x) -> h#(x,x) g#(s(x)) -> g#(x) -> g#(s(x)) -> g#(x) g#(s(x)) -> g#(x) -> g#(s(x)) -> s#(g(x)) g#(s(x)) -> g#(x) -> g#(s(x)) -> s#(s(g(x))) g#(s(x)) -> s#(g(x)) -> s#(s(0())) -> f#(s(0())) g#(s(x)) -> s#(g(x)) -> s#(x) -> h#(x,0()) g#(s(x)) -> s#(g(x)) -> s#(x) -> h#(0(),x) g#(s(x)) -> s#(g(x)) -> s#(s(s(0()))) -> k#(0()) g#(s(x)) -> s#(g(x)) -> s#(s(s(s(s(0()))))) -> k#(s(0())) g#(s(x)) -> s#(g(x)) -> s#(s(s(s(s(s(s(s(s(s(s(s(s(0()))))))))))))) -> k#(s(s(0()))) g#(s(x)) -> s#(s(g(x))) -> s#(s(0())) -> f#(s(0())) g#(s(x)) -> s#(s(g(x))) -> s#(x) -> h#(x,0()) g#(s(x)) -> s#(s(g(x))) -> s#(x) -> h#(0(),x) g#(s(x)) -> s#(s(g(x))) -> s#(s(s(0()))) -> k#(0()) g#(s(x)) -> s#(s(g(x))) -> s#(s(s(s(s(0()))))) -> k#(s(0())) g#(s(x)) -> s#(s(g(x))) -> s#(s(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(s(s(0()))))))))))))) -> k#(s(s(0()))) -> k#(s(0())) -> s#(s(0())) s#(s(s(s(s(s(s(s(s(s(s(s(s(0()))))))))))))) -> k#(s(s(0()))) -> k#(s(0())) -> s#(s(s(0()))) s#(s(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(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(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(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(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(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(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(s(s(0()))))))))))))) -> k#(s(s(0()))) -> k#(s(s(0()))) -> s#(s(s(s(s(s(s(s(s(s(0())))))))))) s#(s(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(s(s(0()))))))))))) s#(s(s(s(s(0()))))) -> k#(s(0())) -> k#(s(0())) -> s#(s(0())) s#(s(s(s(s(0()))))) -> k#(s(0())) -> k#(s(0())) -> s#(s(s(0()))) s#(s(s(s(s(0()))))) -> k#(s(0())) -> k#(s(s(0()))) -> s#(s(s(0()))) s#(s(s(s(s(0()))))) -> k#(s(0())) -> k#(s(s(0()))) -> s#(s(s(s(0())))) s#(s(s(s(s(0()))))) -> k#(s(0())) -> k#(s(s(0()))) -> s#(s(s(s(s(0()))))) s#(s(s(s(s(0()))))) -> k#(s(0())) -> k#(s(s(0()))) -> s#(s(s(s(s(s(0())))))) s#(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(0()))))) -> k#(s(0())) -> k#(s(s(0()))) -> s#(s(s(s(s(s(s(s(0())))))))) s#(s(s(s(s(0()))))) -> k#(s(0())) -> k#(s(s(0()))) -> s#(s(s(s(s(s(s(s(s(0()))))))))) s#(s(s(s(s(0()))))) -> k#(s(0())) -> k#(s(s(0()))) -> s#(s(s(s(s(s(s(s(s(s(0())))))))))) s#(s(s(s(s(0()))))) -> k#(s(0())) -> k#(s(s(0()))) -> s#(s(s(s(s(s(s(s(s(s(s(0()))))))))))) s#(s(s(0()))) -> k#(0()) -> k#(0()) -> s#(0()) s#(s(0())) -> f#(s(0())) -> f#(g(x)) -> f#(x) s#(s(0())) -> f#(s(0())) -> f#(g(x)) -> g#(f(x)) s#(s(0())) -> f#(s(0())) -> f#(g(x)) -> g#(g(f(x))) SCC Processor: #sccs: 1 #rules: 25 #arcs: 151/841 DPs: k#(s(s(0()))) -> s#(s(s(s(s(s(s(s(s(s(s(0()))))))))))) s#(s(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(s(0())))))))))) s#(s(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)) -> 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(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()))) k#(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(s(0()))))) -> k(s(0())) k(s(0())) -> s(s(s(0()))) s(s(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(s(s(0()))))))))))) h(k(x),g(x)) -> k(s(x)) Arctic Interpretation Processor: dimension: 1 usable rules: s(s(0())) -> f(s(0())) g(x) -> h(x,x) s(x) -> h(x,0()) s(x) -> h(0(),x) f(g(x)) -> g(g(f(x))) g(s(x)) -> s(s(g(x))) h(f(x),g(x)) -> f(s(x)) s(s(s(0()))) -> k(0()) k(0()) -> s(0()) s(s(s(s(s(0()))))) -> k(s(0())) k(s(0())) -> s(s(s(0()))) s(s(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(s(s(0()))))))))))) h(k(x),g(x)) -> k(s(x)) interpretation: [h](x0, x1) = x0 + x1, [g#](x0) = x0 + 0, [s](x0) = x0 + 5, [g](x0) = x0 + 0, [k](x0) = x0 + 5, [k#](x0) = 0, [0] = 2, [f#](x0) = 0, [h#](x0, x1) = x0 + x1 + 0, [s#](x0) = 0, [f](x0) = 0 orientation: k#(s(s(0()))) = 0 >= 0 = s#(s(s(s(s(s(s(s(s(s(s(0()))))))))))) s#(s(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(s(0())))))))))) s#(s(s(s(s(0()))))) = 0 >= 0 = k#(s(0())) k#(s(s(0()))) = 0 >= 0 = s#(s(s(s(s(s(s(s(s(0()))))))))) s#(s(0())) = 0 >= 0 = f#(s(0())) f#(g(x)) = 0 >= 0 = g#(g(f(x))) g#(s(x)) = x + 5 >= 0 = s#(s(g(x))) g#(s(x)) = x + 5 >= 0 = s#(g(x)) g#(s(x)) = x + 5 >= x + 0 = g#(x) g#(x) = x + 0 >= x + 0 = h#(x,x) h#(k(x),g(x)) = x + 5 >= 0 = k#(s(x)) k#(s(s(0()))) = 0 >= 0 = s#(s(s(s(s(s(s(s(0())))))))) k#(s(s(0()))) = 0 >= 0 = s#(s(s(s(s(s(s(0()))))))) k#(s(s(0()))) = 0 >= 0 = s#(s(s(s(s(s(0())))))) k#(s(s(0()))) = 0 >= 0 = s#(s(s(s(s(0()))))) k#(s(s(0()))) = 0 >= 0 = s#(s(s(s(0())))) k#(s(s(0()))) = 0 >= 0 = s#(s(s(0()))) k#(s(0())) = 0 >= 0 = s#(s(s(0()))) k#(s(0())) = 0 >= 0 = s#(s(0())) h#(k(x),g(x)) = x + 5 >= 0 = s#(x) h#(f(x),g(x)) = x + 0 >= 0 = f#(s(x)) f#(g(x)) = 0 >= 0 = g#(f(x)) f#(g(x)) = 0 >= 0 = f#(x) h#(f(x),g(x)) = x + 0 >= 0 = s#(x) s(s(0())) = 5 >= 0 = f(s(0())) g(x) = x + 0 >= x = h(x,x) s(x) = x + 5 >= x + 2 = h(x,0()) s(x) = x + 5 >= x + 2 = h(0(),x) f(g(x)) = 0 >= 0 = g(g(f(x))) g(s(x)) = x + 5 >= x + 5 = s(s(g(x))) h(f(x),g(x)) = x + 0 >= 0 = f(s(x)) s(s(s(0()))) = 5 >= 5 = k(0()) k(0()) = 5 >= 5 = s(0()) s(s(s(s(s(0()))))) = 5 >= 5 = k(s(0())) k(s(0())) = 5 >= 5 = s(s(s(0()))) s(s(s(s(s(s(s(s(s(s(s(s(s(0()))))))))))))) = 5 >= 5 = k(s(s(0()))) k(s(s(0()))) = 5 >= 5 = s(s(s(s(s(s(s(s(s(s(s(0()))))))))))) h(k(x),g(x)) = x + 5 >= x + 5 = k(s(x)) problem: DPs: k#(s(s(0()))) -> s#(s(s(s(s(s(s(s(s(s(s(0()))))))))))) s#(s(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(s(0())))))))))) s#(s(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)) -> g#(g(f(x))) g#(s(x)) -> g#(x) g#(x) -> h#(x,x) 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()))) k#(s(0())) -> s#(s(s(0()))) k#(s(0())) -> s#(s(0())) h#(f(x),g(x)) -> f#(s(x)) f#(g(x)) -> g#(f(x)) f#(g(x)) -> f#(x) 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(s(0()))))) -> k(s(0())) k(s(0())) -> s(s(s(0()))) s(s(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(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(s(s(0()))))))))))) s#(s(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(s(0())))))))))) s#(s(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)) -> g#(g(f(x))) g#(s(x)) -> g#(x) g#(x) -> h#(x,x) 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()))) k#(s(0())) -> s#(s(s(0()))) k#(s(0())) -> s#(s(0())) h#(f(x),g(x)) -> f#(s(x)) f#(g(x)) -> g#(f(x)) f#(g(x)) -> f#(x) 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(s(0()))))) -> k(s(0())) k(s(0())) -> s(s(s(0()))) s(s(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(s(s(0()))))))))))) h(k(x),g(x)) -> k(s(x)) Arctic Interpretation Processor: dimension: 1 usable rules: s(s(0())) -> f(s(0())) g(x) -> h(x,x) s(x) -> h(x,0()) s(x) -> h(0(),x) f(g(x)) -> g(g(f(x))) g(s(x)) -> s(s(g(x))) h(f(x),g(x)) -> f(s(x)) s(s(s(0()))) -> k(0()) k(0()) -> s(0()) s(s(s(s(s(0()))))) -> k(s(0())) k(s(0())) -> s(s(s(0()))) s(s(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(s(s(0()))))))))))) h(k(x),g(x)) -> k(s(x)) interpretation: [h](x0, x1) = 0, [g#](x0) = 2, [s](x0) = 0, [g](x0) = x0 + 2, [k](x0) = 0, [k#](x0) = x0 + 0, [0] = 7, [f#](x0) = x0 + 0, [h#](x0, x1) = 0, [s#](x0) = 0, [f](x0) = x0 orientation: k#(s(s(0()))) = 0 >= 0 = s#(s(s(s(s(s(s(s(s(s(s(0()))))))))))) s#(s(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(s(0())))))))))) s#(s(s(s(s(0()))))) = 0 >= 0 = k#(s(0())) k#(s(s(0()))) = 0 >= 0 = s#(s(s(s(s(s(s(s(s(0()))))))))) s#(s(0())) = 0 >= 0 = f#(s(0())) f#(g(x)) = x + 2 >= 2 = g#(g(f(x))) g#(s(x)) = 2 >= 2 = g#(x) g#(x) = 2 >= 0 = h#(x,x) k#(s(s(0()))) = 0 >= 0 = s#(s(s(s(s(s(s(s(0())))))))) k#(s(s(0()))) = 0 >= 0 = s#(s(s(s(s(s(s(0()))))))) k#(s(s(0()))) = 0 >= 0 = s#(s(s(s(s(s(0())))))) k#(s(s(0()))) = 0 >= 0 = s#(s(s(s(s(0()))))) k#(s(s(0()))) = 0 >= 0 = s#(s(s(s(0())))) k#(s(s(0()))) = 0 >= 0 = s#(s(s(0()))) k#(s(0())) = 0 >= 0 = s#(s(s(0()))) k#(s(0())) = 0 >= 0 = s#(s(0())) h#(f(x),g(x)) = 0 >= 0 = f#(s(x)) f#(g(x)) = x + 2 >= 2 = g#(f(x)) f#(g(x)) = x + 2 >= x + 0 = f#(x) h#(f(x),g(x)) = 0 >= 0 = s#(x) s(s(0())) = 0 >= 0 = f(s(0())) g(x) = x + 2 >= 0 = h(x,x) s(x) = 0 >= 0 = h(x,0()) s(x) = 0 >= 0 = h(0(),x) f(g(x)) = x + 2 >= x + 2 = g(g(f(x))) g(s(x)) = 2 >= 0 = s(s(g(x))) h(f(x),g(x)) = 0 >= 0 = f(s(x)) s(s(s(0()))) = 0 >= 0 = k(0()) k(0()) = 0 >= 0 = s(0()) s(s(s(s(s(0()))))) = 0 >= 0 = k(s(0())) k(s(0())) = 0 >= 0 = s(s(s(0()))) s(s(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(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(s(s(0()))))))))))) s#(s(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(s(0())))))))))) s#(s(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)) -> g#(g(f(x))) g#(s(x)) -> g#(x) 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()))) k#(s(0())) -> s#(s(s(0()))) k#(s(0())) -> s#(s(0())) h#(f(x),g(x)) -> f#(s(x)) f#(g(x)) -> g#(f(x)) f#(g(x)) -> f#(x) 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(s(0()))))) -> k(s(0())) k(s(0())) -> s(s(s(0()))) s(s(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(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(s(s(0()))))))))))) s#(s(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(s(0())))))))))) s#(s(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)) -> g#(g(f(x))) g#(s(x)) -> g#(x) 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()))) k#(s(0())) -> s#(s(s(0()))) k#(s(0())) -> s#(s(0())) h#(f(x),g(x)) -> f#(s(x)) f#(g(x)) -> g#(f(x)) f#(g(x)) -> f#(x) 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(s(0()))))) -> k(s(0())) k(s(0())) -> s(s(s(0()))) s(s(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(s(s(0()))))))))))) h(k(x),g(x)) -> k(s(x)) SCC Processor: #sccs: 3 #rules: 15 #arcs: 103/400 DPs: k#(s(s(0()))) -> s#(s(s(s(s(s(s(s(s(s(s(0()))))))))))) s#(s(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(s(0())))))))))) s#(s(s(s(s(0()))))) -> k#(s(0())) k#(s(s(0()))) -> s#(s(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(0()))))))) k#(s(s(0()))) -> s#(s(s(s(s(s(0())))))) k#(s(s(0()))) -> s#(s(s(s(s(0()))))) k#(s(s(0()))) -> s#(s(s(s(0())))) k#(s(s(0()))) -> s#(s(s(0()))) k#(s(0())) -> s#(s(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(s(0()))))) -> k(s(0())) k(s(0())) -> s(s(s(0()))) s(s(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(s(s(0()))))))))))) h(k(x),g(x)) -> k(s(x)) Bounds Processor: bound: 0 enrichment: top-dp automaton: final states: {97} transitions: s{#,0}(99) -> 97* 00() -> 98* s0(98) -> 99* h0(98,98) -> 99* problem: DPs: k#(s(s(0()))) -> s#(s(s(s(s(s(s(s(s(s(s(0()))))))))))) s#(s(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(s(0())))))))))) s#(s(s(s(s(0()))))) -> k#(s(0())) k#(s(s(0()))) -> s#(s(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(0()))))))) k#(s(s(0()))) -> s#(s(s(s(s(s(0())))))) k#(s(s(0()))) -> s#(s(s(s(s(0()))))) k#(s(s(0()))) -> s#(s(s(s(0())))) k#(s(s(0()))) -> s#(s(s(0()))) k#(s(0())) -> s#(s(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(s(0()))))) -> k(s(0())) k(s(0())) -> s(s(s(0()))) s(s(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(s(s(0()))))))))))) h(k(x),g(x)) -> k(s(x)) Bounds Processor: bound: 0 enrichment: top-dp automaton: final states: {92} transitions: s{#,0}(95) -> 92* 00() -> 93* s0(93) -> 94* s0(94) -> 95* h0(93,94) -> 95* h0(93,93) -> 94* h0(94,93) -> 95* f0(94) -> 95* problem: DPs: k#(s(s(0()))) -> s#(s(s(s(s(s(s(s(s(s(s(0()))))))))))) s#(s(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(s(0())))))))))) s#(s(s(s(s(0()))))) -> k#(s(0())) k#(s(s(0()))) -> s#(s(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(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(s(0()))))) -> k(s(0())) k(s(0())) -> s(s(s(0()))) s(s(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(s(s(0()))))))))))) h(k(x),g(x)) -> k(s(x)) Bounds Processor: bound: 0 enrichment: top-dp automaton: final states: {32} transitions: 00() -> 33* s0(33) -> 34* k{#,0}(34) -> 32* h0(33,33) -> 34* problem: DPs: k#(s(s(0()))) -> s#(s(s(s(s(s(s(s(s(s(s(0()))))))))))) s#(s(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(s(0())))))))))) k#(s(s(0()))) -> s#(s(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(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(s(0()))))) -> k(s(0())) k(s(0())) -> s(s(s(0()))) s(s(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(s(s(0()))))))))))) h(k(x),g(x)) -> k(s(x)) Bounds Processor: bound: 0 enrichment: top-dp automaton: final states: {83} transitions: s{#,0}(86) -> 83* 00() -> 84* s0(85) -> 86* s0(84) -> 85* h0(85,84) -> 86* h0(84,85) -> 86* h0(84,84) -> 85* f0(85) -> 86* problem: DPs: k#(s(s(0()))) -> s#(s(s(s(s(s(s(s(s(s(s(0()))))))))))) s#(s(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(s(0())))))))))) k#(s(s(0()))) -> s#(s(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(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(s(0()))))) -> k(s(0())) k(s(0())) -> s(s(s(0()))) s(s(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(s(s(0()))))))))))) h(k(x),g(x)) -> k(s(x)) Bounds Processor: bound: 0 enrichment: top-dp automaton: final states: {77} transitions: s{#,0}(81) -> 77* s{#,0}(90) -> 77* 00() -> 78* s0(79) -> 80* s0(80) -> 81* s0(90) -> 80* s0(78) -> 90*,81,79 h0(90,78) -> 80* h0(78,78) -> 90*,79 h0(78,79) -> 80* h0(80,78) -> 81* h0(78,90) -> 80* h0(78,80) -> 81* h0(79,78) -> 80* k0(78) -> 81* f0(90) -> 80* f0(79) -> 80* problem: DPs: k#(s(s(0()))) -> s#(s(s(s(s(s(s(s(s(s(s(0()))))))))))) s#(s(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(s(0())))))))))) k#(s(s(0()))) -> s#(s(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(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(s(0()))))) -> k(s(0())) k(s(0())) -> s(s(s(0()))) s(s(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(s(s(0()))))))))))) h(k(x),g(x)) -> k(s(x)) Bounds Processor: bound: 0 enrichment: top-dp automaton: final states: {70} transitions: s{#,0}(75) -> 70* s{#,0}(85) -> 70* 00() -> 71* s0(73) -> 74* s0(71) -> 84*,74,72 s0(85) -> 74* s0(74) -> 75* s0(72) -> 73* s0(84) -> 85*,75,73 h0(72,71) -> 73* h0(85,71) -> 74* h0(71,72) -> 73* h0(71,73) -> 74* h0(73,71) -> 74* h0(71,84) -> 85*,73,75 h0(71,74) -> 75* h0(71,71) -> 84*,72 h0(71,85) -> 74* h0(84,71) -> 85*,73,75 h0(74,71) -> 75* k0(71) -> 74* f0(72) -> 85*,73 f0(84) -> 85*,73 problem: DPs: k#(s(s(0()))) -> s#(s(s(s(s(s(s(s(s(s(s(0()))))))))))) s#(s(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(s(0())))))))))) k#(s(s(0()))) -> s#(s(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(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(s(0()))))) -> k(s(0())) k(s(0())) -> s(s(s(0()))) s(s(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(s(s(0()))))))))))) h(k(x),g(x)) -> k(s(x)) Bounds Processor: bound: 0 enrichment: top-dp automaton: final states: {62} transitions: s{#,0}(79) -> 62* s{#,0}(68) -> 62* s{#,0}(84) -> 62* 00() -> 63* s0(64) -> 65* s0(77) -> 78*,65,67 s0(79) -> 67* s0(65) -> 66* s0(67) -> 68* s0(84) -> 65,78*,67 s0(66) -> 67* s0(63) -> 77,79,84*,66,64 s0(78) -> 79*,66,68 h0(63,63) -> 77,84*,64 h0(63,79) -> 67* h0(66,63) -> 67* h0(63,67) -> 68* h0(84,63) -> 78*,67,65 h0(65,63) -> 66* h0(67,63) -> 68* h0(63,84) -> 67,65,78* h0(78,63) -> 79*,66,68 h0(63,78) -> 79*,68,66 h0(63,66) -> 67* h0(77,63) -> 78*,67,65 h0(63,64) -> 65* h0(79,63) -> 67* h0(64,63) -> 65* h0(63,65) -> 66* h0(63,77) -> 78*,67,65 k0(63) -> 79*,66 k0(77) -> 68* k0(64) -> 68* k0(84) -> 68* f0(77) -> 78*,65 f0(84) -> 78* f0(64) -> 78*,65 problem: DPs: k#(s(s(0()))) -> s#(s(s(s(s(s(s(s(s(s(s(0()))))))))))) s#(s(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(s(0())))))))))) k#(s(s(0()))) -> s#(s(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(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(s(0()))))) -> k(s(0())) k(s(0())) -> s(s(s(0()))) s(s(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(s(s(0()))))))))))) h(k(x),g(x)) -> k(s(x)) Bounds Processor: bound: 0 enrichment: top-dp automaton: final states: {53} transitions: s{#,0}(79) -> 53* s{#,0}(60) -> 53* s{#,0}(72) -> 53* 00() -> 54* s0(71) -> 72*,58,60 s0(55) -> 56* s0(79) -> 71*,57,59 s0(57) -> 58* s0(70) -> 71*,57,59 s0(72) -> 59* s0(56) -> 57* s0(54) -> 69,71,78*,57,55 s0(59) -> 60* s0(69) -> 70*,56,58 s0(58) -> 59* s0(78) -> 79*,56,58,60 h0(54,78) -> 79*,60,56,58 h0(58,54) -> 59* h0(78,54) -> 79*,56,58,60 h0(54,59) -> 60* h0(69,54) -> 70*,56,58 h0(54,70) -> 71*,59,57 h0(54,69) -> 70*,56,58 h0(56,54) -> 57* h0(54,72) -> 59* h0(55,54) -> 56* h0(54,58) -> 59* h0(79,54) -> 57,71*,59 h0(70,54) -> 71*,59,57 h0(54,55) -> 56* h0(57,54) -> 58* h0(59,54) -> 60* h0(54,56) -> 57* h0(54,54) -> 69,78*,55 h0(72,54) -> 59* h0(71,54) -> 72*,58,60 h0(54,71) -> 72*,60,58 h0(54,79) -> 71*,59,57 h0(54,57) -> 58* k0(55) -> 59* k0(78) -> 59* k0(54) -> 71*,57 k0(69) -> 59* f0(69) -> 70,79*,56 f0(78) -> 70,79* f0(55) -> 70,79*,56 problem: DPs: k#(s(s(0()))) -> s#(s(s(s(s(s(s(s(s(s(s(0()))))))))))) s#(s(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(s(0())))))))))) k#(s(s(0()))) -> s#(s(s(s(s(s(s(s(s(0()))))))))) k#(s(s(0()))) -> s#(s(s(s(s(s(s(s(0())))))))) TRS: s(s(0())) -> f(s(0())) g(x) -> h(x,x) s(x) -> h(x,0()) s(x) -> h(0(),x) f(g(x)) -> g(g(f(x))) g(s(x)) -> s(s(g(x))) h(f(x),g(x)) -> f(s(x)) s(s(s(0()))) -> k(0()) k(0()) -> s(0()) s(s(s(s(s(0()))))) -> k(s(0())) k(s(0())) -> s(s(s(0()))) s(s(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(s(s(0()))))))))))) h(k(x),g(x)) -> k(s(x)) Bounds Processor: bound: 0 enrichment: top-dp automaton: final states: {43} transitions: s{#,0}(51) -> 43* s{#,0}(80) -> 43* s{#,0}(98) -> 43* s{#,0}(64) -> 43* 00() -> 44* s0(64) -> 50* s0(45) -> 46* s0(79) -> 80*,49,51,47 s0(62) -> 63*,50,48 s0(80) -> 63*,50,48 s0(48) -> 49* s0(49) -> 50* s0(60) -> 61*,46,48 s0(44) -> 78,62,60,80,98*,47,45 s0(50) -> 51* s0(63) -> 64*,49,51 s0(98) -> 46,50,79*,48 s0(61) -> 62*,49,47 s0(46) -> 47* s0(78) -> 79*,46,50,48 s0(47) -> 48* h0(44,48) -> 49* h0(44,61) -> 62*,49,47 h0(46,44) -> 47* h0(47,44) -> 48* h0(44,60) -> 61*,48,46 h0(79,44) -> 80*,47,49,51 h0(44,98) -> 50,48,79*,46 h0(48,44) -> 49* h0(44,44) -> 78,60,98*,45 h0(44,49) -> 50* h0(44,80) -> 48,50,63* h0(50,44) -> 51* h0(44,47) -> 48* h0(62,44) -> 63*,48,50 h0(78,44) -> 79*,48,46,50 h0(44,46) -> 47* h0(60,44) -> 61*,48,46 h0(44,64) -> 50* h0(44,63) -> 64*,49,51 h0(98,44) -> 48,79*,46,50 h0(80,44) -> 48,63*,50 h0(44,62) -> 63*,50,48 h0(44,79) -> 80*,49,47,51 h0(64,44) -> 50* h0(45,44) -> 46* h0(44,78) -> 79*,50,48,46 h0(63,44) -> 64*,49,51 h0(61,44) -> 62*,47,49 h0(44,45) -> 46* h0(44,50) -> 51* h0(49,44) -> 50* k0(44) -> 62,80*,47 k0(98) -> 64* k0(78) -> 64* k0(60) -> 64*,49 k0(45) -> 64*,49 f0(98) -> 79* f0(78) -> 61,79* f0(60) -> 61,79*,46 f0(45) -> 61,79*,46 problem: DPs: k#(s(s(0()))) -> s#(s(s(s(s(s(s(s(s(s(s(0()))))))))))) s#(s(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(s(0())))))))))) k#(s(s(0()))) -> s#(s(s(s(s(s(s(s(s(0()))))))))) TRS: s(s(0())) -> f(s(0())) g(x) -> h(x,x) s(x) -> h(x,0()) s(x) -> h(0(),x) f(g(x)) -> g(g(f(x))) g(s(x)) -> s(s(g(x))) h(f(x),g(x)) -> f(s(x)) s(s(s(0()))) -> k(0()) k(0()) -> s(0()) s(s(s(s(s(0()))))) -> k(s(0())) k(s(0())) -> s(s(s(0()))) s(s(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(s(s(0()))))))))))) h(k(x),g(x)) -> k(s(x)) Bounds Processor: bound: 0 enrichment: top-dp automaton: final states: {32} transitions: s{#,0}(95) -> 32* s{#,0}(55) -> 32* s{#,0}(74) -> 32* s{#,0}(41) -> 32* 00() -> 33* s0(73) -> 74*,39,41,37 s0(71) -> 72*,39,35,37 s0(55) -> 40* s0(37) -> 38* s0(33) -> 71,52,50,73,94*,36,34 s0(38) -> 39* s0(51) -> 52*,38,36 s0(95) -> 38,36,73*,40 s0(34) -> 35* s0(74) -> 38,40,54* s0(35) -> 36* s0(40) -> 41* s0(52) -> 53*,39,37 s0(72) -> 73*,38,36,40 s0(39) -> 40* s0(54) -> 55*,39,41 s0(36) -> 37* s0(94) -> 95*,39,35,41,37 s0(53) -> 54*,38,40 s0(50) -> 51*,35,37 h0(39,33) -> 40* h0(33,35) -> 36* h0(33,36) -> 37* h0(52,33) -> 53*,39,37 h0(33,54) -> 55*,41,39 h0(33,50) -> 51*,37,35 h0(40,33) -> 41* h0(33,51) -> 52*,36,38 h0(33,39) -> 40* h0(35,33) -> 36* h0(33,73) -> 74*,37,41,39 h0(33,33) -> 71,50,94*,34 h0(51,33) -> 52*,36,38 h0(33,74) -> 38,54*,40 h0(33,71) -> 72*,37,39,35 h0(38,33) -> 39* h0(33,37) -> 38* h0(95,33) -> 40,36,38,73* h0(33,53) -> 54*,40,38 h0(33,55) -> 40* h0(33,52) -> 53*,37,39 h0(33,94) -> 95*,37,41,39,35 h0(71,33) -> 72*,39,35,37 h0(33,72) -> 73*,36,40,38 h0(33,40) -> 41* h0(53,33) -> 54*,40,38 h0(33,38) -> 39* h0(33,95) -> 36,40,38,73* h0(34,33) -> 35* h0(50,33) -> 51*,35,37 h0(55,33) -> 40* h0(33,34) -> 35* h0(74,33) -> 54*,40,38 h0(37,33) -> 38* h0(94,33) -> 95*,41,39,35,37 h0(36,33) -> 37* h0(72,33) -> 73*,40,36,38 h0(54,33) -> 55*,41,39 h0(73,33) -> 74*,41,39,37 k0(71) -> 54* k0(94) -> 54* k0(33) -> 52,73*,36 k0(50) -> 54*,38 k0(34) -> 54*,38 f0(50) -> 72,51,95*,35 f0(94) -> 72,95* f0(34) -> 72,51,95*,35 f0(71) -> 72,51,95* problem: DPs: k#(s(s(0()))) -> s#(s(s(s(s(s(s(s(s(s(s(0()))))))))))) s#(s(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(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(s(0()))))) -> k(s(0())) k(s(0())) -> s(s(s(0()))) s(s(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(s(s(0()))))))))))) h(k(x),g(x)) -> k(s(x)) Bounds Processor: bound: 0 enrichment: top-dp automaton: final states: {20} transitions: s{#,0}(81) -> 20* s{#,0}(30) -> 20* s{#,0}(86) -> 20* s{#,0}(45) -> 20* s{#,0}(66) -> 20* 00() -> 21* s0(23) -> 24* s0(64) -> 65*,25,29,27 s0(45) -> 29* s0(24) -> 25* s0(79) -> 80*,25,23,29,27 s0(81) -> 65*,25,29,27 s0(65) -> 66*,28,26,30 s0(62) -> 63*,25,23,27 s0(80) -> 81*,24,28,26,30 s0(40) -> 41*,24,26 s0(22) -> 23* s0(41) -> 42*,25,27 s0(39) -> 40*,25,23 s0(43) -> 44*,29,27 s0(28) -> 29* s0(66) -> 44*,29,27 s0(27) -> 28* s0(26) -> 27* s0(44) -> 45*,28,30 s0(63) -> 64*,24,28,26 s0(86) -> 25,80*,23,29,27 s0(21) -> 79,64,39,41,62,81,86*,24,22 s0(42) -> 43*,28,26 s0(25) -> 26* s0(29) -> 30* h0(21,39) -> 40*,23,25 h0(21,80) -> 81*,30,28,24,26 h0(42,21) -> 43*,28,26 h0(29,21) -> 30* h0(27,21) -> 28* h0(39,21) -> 40*,23,25 h0(23,21) -> 24* h0(45,21) -> 29* h0(63,21) -> 64*,28,24,26 h0(21,29) -> 30* h0(21,64) -> 65*,29,25,27 h0(21,27) -> 28* h0(21,28) -> 29* h0(81,21) -> 27,29,65*,25 h0(21,66) -> 27,29,44* h0(65,21) -> 66*,30,28,26 h0(21,23) -> 24* h0(21,22) -> 23* h0(21,86) -> 29,23,25,27,80* h0(21,63) -> 64*,28,24,26 h0(66,21) -> 27,29,44* h0(21,24) -> 25* h0(62,21) -> 63*,27,23,25 h0(26,21) -> 27* h0(28,21) -> 29* h0(43,21) -> 44*,27,29 h0(21,26) -> 27* h0(21,62) -> 63*,23,25,27 h0(21,65) -> 66*,30,28,26 h0(80,21) -> 81*,30,28,24,26 h0(79,21) -> 80*,27,29,23,25 h0(21,45) -> 29* h0(22,21) -> 23* h0(21,41) -> 42*,25,27 h0(21,40) -> 41*,24,26 h0(25,21) -> 26* h0(44,21) -> 45*,30,28 h0(21,25) -> 26* h0(40,21) -> 41*,24,26 h0(21,44) -> 45*,30,28 h0(21,81) -> 65*,29,25,27 h0(41,21) -> 42*,27,25 h0(86,21) -> 27,29,80*,23,25 h0(21,79) -> 80*,29,23,25,27 h0(64,21) -> 65*,27,29,25 h0(21,42) -> 43*,28,26 h0(21,43) -> 44*,29,27 h0(24,21) -> 25* h0(21,21) -> 79,39,62,86*,22 k0(21) -> 64,41,81*,24 k0(62) -> 43,66* k0(79) -> 66* k0(39) -> 43,66*,26 k0(22) -> 43,66*,26 k0(86) -> 66* f0(39) -> 63,40,80*,23 f0(86) -> 80* f0(79) -> 63,80* f0(62) -> 63,40,80* f0(22) -> 63,40,80*,23 problem: DPs: k#(s(s(0()))) -> s#(s(s(s(s(s(s(s(s(s(s(0()))))))))))) s#(s(s(s(s(s(s(s(s(s(s(s(s(0()))))))))))))) -> k#(s(s(0()))) TRS: s(s(0())) -> f(s(0())) g(x) -> h(x,x) s(x) -> h(x,0()) s(x) -> h(0(),x) f(g(x)) -> g(g(f(x))) g(s(x)) -> s(s(g(x))) h(f(x),g(x)) -> f(s(x)) s(s(s(0()))) -> k(0()) k(0()) -> s(0()) s(s(s(s(s(0()))))) -> k(s(0())) k(s(0())) -> s(s(s(0()))) s(s(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(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}(58) -> 2* s{#,0}(34) -> 2* s{#,0}(13) -> 2* s{#,0}(48) -> 2* s{#,0}(64) -> 2* 00() -> 3* s0(55) -> 56*,11,7,5,9 s0(12) -> 13* s0(33) -> 34*,13,11 s0(64) -> 10,57*,8,12,6 s0(45) -> 46*,11,7,9 s0(32) -> 33*,10,12 s0(57) -> 58*,13,11,7,9 s0(34) -> 12* s0(30) -> 31*,10,8 s0(31) -> 32*,11,9 s0(3) -> 55,45,27,29,43,57,63*,6,4 s0(48) -> 33*,10,12 s0(9) -> 10* s0(10) -> 11* s0(6) -> 7* s0(43) -> 44*,7,5,9 s0(56) -> 57*,10,8,12,6 s0(7) -> 8* s0(28) -> 29*,8,6 s0(4) -> 5* s0(27) -> 28*,7,5 s0(11) -> 12* s0(44) -> 45*,10,8,6 s0(63) -> 64*,13,11,7,5,9 s0(5) -> 6* s0(46) -> 47*,10,8,12 s0(58) -> 10,8,12,47* s0(47) -> 48*,13,11,9 s0(8) -> 9* s0(29) -> 30*,7,9 h0(3,58) -> 47*,8,10,12 h0(3,43) -> 44*,5,7,9 h0(29,3) -> 30*,7,9 h0(30,3) -> 31*,8,10 h0(43,3) -> 44*,7,9,5 h0(3,30) -> 31*,8,10 h0(27,3) -> 28*,7,5 h0(3,3) -> 55,27,43,63*,4 h0(32,3) -> 33*,12,10 h0(11,3) -> 12* h0(3,5) -> 6* h0(3,46) -> 47*,8,10,12 h0(3,7) -> 8* h0(6,3) -> 7* h0(47,3) -> 48*,9,11,13 h0(3,4) -> 5* h0(3,9) -> 10* h0(7,3) -> 8* h0(57,3) -> 58*,7,9,11,13 h0(3,12) -> 13* h0(63,3) -> 64*,7,9,5,11,13 h0(45,3) -> 46*,7,9,11 h0(3,34) -> 12* h0(8,3) -> 9* h0(3,64) -> 6,8,10,12,57* h0(64,3) -> 12,8,10,6,57* h0(44,3) -> 45*,8,10,6 h0(3,33) -> 34*,13,11 h0(9,3) -> 10* h0(3,31) -> 32*,11,9 h0(3,48) -> 10,12,33* h0(3,10) -> 11* h0(31,3) -> 32*,9,11 h0(28,3) -> 29*,8,6 h0(3,45) -> 46*,11,7,9 h0(5,3) -> 6* h0(4,3) -> 5* h0(34,3) -> 12* h0(3,47) -> 48*,13,11,9 h0(3,29) -> 30*,7,9 h0(3,57) -> 58*,13,11,7,9 h0(3,55) -> 56*,5,11,7,9 h0(3,6) -> 7* h0(10,3) -> 11* h0(3,63) -> 64*,5,13,11,7,9 h0(3,27) -> 28*,5,7 h0(3,8) -> 9* h0(3,11) -> 12* h0(3,56) -> 57*,6,8,10,12 h0(3,44) -> 45*,6,8,10 h0(33,3) -> 34*,11,13 h0(3,28) -> 29*,6,8 h0(48,3) -> 33*,10,12 h0(56,3) -> 57*,12,8,10,6 h0(55,3) -> 56*,7,9,5,11 h0(46,3) -> 47*,12,8,10 h0(58,3) -> 12,8,10,47* h0(12,3) -> 13* h0(3,32) -> 33*,10,12 k0(55) -> 47* k0(27) -> 31,47*,8 k0(63) -> 47* k0(43) -> 31,47* k0(3) -> 45,29,57*,6 k0(4) -> 31,47*,8 f0(43) -> 56,28,44,64* f0(63) -> 56,64* f0(4) -> 56,28,44,64*,5 f0(55) -> 56,44,64* f0(27) -> 56,28,44,64*,5 problem: DPs: s#(s(s(s(s(s(s(s(s(s(s(s(s(0()))))))))))))) -> k#(s(s(0()))) TRS: s(s(0())) -> f(s(0())) g(x) -> h(x,x) s(x) -> h(x,0()) s(x) -> h(0(),x) f(g(x)) -> g(g(f(x))) g(s(x)) -> s(s(g(x))) h(f(x),g(x)) -> f(s(x)) s(s(s(0()))) -> k(0()) k(0()) -> s(0()) s(s(s(s(s(0()))))) -> k(s(0())) k(s(0())) -> s(s(s(0()))) s(s(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(s(s(0()))))))))))) h(k(x),g(x)) -> k(s(x)) SCC Processor: #sccs: 0 #rules: 0 #arcs: 44/1 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(s(s(0()))) -> k(0()) k(0()) -> s(0()) s(s(s(s(s(0()))))) -> k(s(0())) k(s(0())) -> s(s(s(0()))) s(s(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(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(s(0()))))) -> k(s(0())) k(s(0())) -> s(s(s(0()))) s(s(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(s(s(0()))))))))))) h(k(x),g(x)) -> k(s(x)) The DP: f#(g(x)) -> f#(x) has the edges: 0 > 0 Qed DPs: g#(s(x)) -> g#(x) TRS: s(s(0())) -> f(s(0())) g(x) -> h(x,x) s(x) -> h(x,0()) s(x) -> h(0(),x) f(g(x)) -> g(g(f(x))) g(s(x)) -> s(s(g(x))) h(f(x),g(x)) -> f(s(x)) s(s(s(0()))) -> k(0()) k(0()) -> s(0()) s(s(s(s(s(0()))))) -> k(s(0())) k(s(0())) -> s(s(s(0()))) s(s(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(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(s(0()))))) -> k(s(0())) k(s(0())) -> s(s(s(0()))) s(s(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(s(s(0()))))))))))) h(k(x),g(x)) -> k(s(x)) The DP: g#(s(x)) -> g#(x) has the edges: 0 > 0 Qed