/export/starexec/sandbox/solver/bin/starexec_run_ttt2-1.17+nonreach /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files -------------------------------------------------------------------------------- YES Problem: f_0(x) -> a() f_1(x) -> g_1(x,x) g_1(s(x),y) -> b(f_0(y),g_1(x,y)) f_2(x) -> g_2(x,x) g_2(s(x),y) -> b(f_1(y),g_2(x,y)) f_3(x) -> g_3(x,x) g_3(s(x),y) -> b(f_2(y),g_3(x,y)) f_4(x) -> g_4(x,x) g_4(s(x),y) -> b(f_3(y),g_4(x,y)) f_5(x) -> g_5(x,x) g_5(s(x),y) -> b(f_4(y),g_5(x,y)) f_6(x) -> g_6(x,x) g_6(s(x),y) -> b(f_5(y),g_6(x,y)) f_7(x) -> g_7(x,x) g_7(s(x),y) -> b(f_6(y),g_7(x,y)) f_8(x) -> g_8(x,x) g_8(s(x),y) -> b(f_7(y),g_8(x,y)) f_9(x) -> g_9(x,x) g_9(s(x),y) -> b(f_8(y),g_9(x,y)) f_10(x) -> g_10(x,x) g_10(s(x),y) -> b(f_9(y),g_10(x,y)) Proof: DP Processor: DPs: f_1#(x) -> g_1#(x,x) g_1#(s(x),y) -> g_1#(x,y) g_1#(s(x),y) -> f_0#(y) f_2#(x) -> g_2#(x,x) g_2#(s(x),y) -> g_2#(x,y) g_2#(s(x),y) -> f_1#(y) f_3#(x) -> g_3#(x,x) g_3#(s(x),y) -> g_3#(x,y) g_3#(s(x),y) -> f_2#(y) f_4#(x) -> g_4#(x,x) g_4#(s(x),y) -> g_4#(x,y) g_4#(s(x),y) -> f_3#(y) f_5#(x) -> g_5#(x,x) g_5#(s(x),y) -> g_5#(x,y) g_5#(s(x),y) -> f_4#(y) f_6#(x) -> g_6#(x,x) g_6#(s(x),y) -> g_6#(x,y) g_6#(s(x),y) -> f_5#(y) f_7#(x) -> g_7#(x,x) g_7#(s(x),y) -> g_7#(x,y) g_7#(s(x),y) -> f_6#(y) f_8#(x) -> g_8#(x,x) g_8#(s(x),y) -> g_8#(x,y) g_8#(s(x),y) -> f_7#(y) f_9#(x) -> g_9#(x,x) g_9#(s(x),y) -> g_9#(x,y) g_9#(s(x),y) -> f_8#(y) f_10#(x) -> g_10#(x,x) g_10#(s(x),y) -> g_10#(x,y) g_10#(s(x),y) -> f_9#(y) TRS: f_0(x) -> a() f_1(x) -> g_1(x,x) g_1(s(x),y) -> b(f_0(y),g_1(x,y)) f_2(x) -> g_2(x,x) g_2(s(x),y) -> b(f_1(y),g_2(x,y)) f_3(x) -> g_3(x,x) g_3(s(x),y) -> b(f_2(y),g_3(x,y)) f_4(x) -> g_4(x,x) g_4(s(x),y) -> b(f_3(y),g_4(x,y)) f_5(x) -> g_5(x,x) g_5(s(x),y) -> b(f_4(y),g_5(x,y)) f_6(x) -> g_6(x,x) g_6(s(x),y) -> b(f_5(y),g_6(x,y)) f_7(x) -> g_7(x,x) g_7(s(x),y) -> b(f_6(y),g_7(x,y)) f_8(x) -> g_8(x,x) g_8(s(x),y) -> b(f_7(y),g_8(x,y)) f_9(x) -> g_9(x,x) g_9(s(x),y) -> b(f_8(y),g_9(x,y)) f_10(x) -> g_10(x,x) g_10(s(x),y) -> b(f_9(y),g_10(x,y)) TDG Processor: DPs: f_1#(x) -> g_1#(x,x) g_1#(s(x),y) -> g_1#(x,y) g_1#(s(x),y) -> f_0#(y) f_2#(x) -> g_2#(x,x) g_2#(s(x),y) -> g_2#(x,y) g_2#(s(x),y) -> f_1#(y) f_3#(x) -> g_3#(x,x) g_3#(s(x),y) -> g_3#(x,y) g_3#(s(x),y) -> f_2#(y) f_4#(x) -> g_4#(x,x) g_4#(s(x),y) -> g_4#(x,y) g_4#(s(x),y) -> f_3#(y) f_5#(x) -> g_5#(x,x) g_5#(s(x),y) -> g_5#(x,y) g_5#(s(x),y) -> f_4#(y) f_6#(x) -> g_6#(x,x) g_6#(s(x),y) -> g_6#(x,y) g_6#(s(x),y) -> f_5#(y) f_7#(x) -> g_7#(x,x) g_7#(s(x),y) -> g_7#(x,y) g_7#(s(x),y) -> f_6#(y) f_8#(x) -> g_8#(x,x) g_8#(s(x),y) -> g_8#(x,y) g_8#(s(x),y) -> f_7#(y) f_9#(x) -> g_9#(x,x) g_9#(s(x),y) -> g_9#(x,y) g_9#(s(x),y) -> f_8#(y) f_10#(x) -> g_10#(x,x) g_10#(s(x),y) -> g_10#(x,y) g_10#(s(x),y) -> f_9#(y) TRS: f_0(x) -> a() f_1(x) -> g_1(x,x) g_1(s(x),y) -> b(f_0(y),g_1(x,y)) f_2(x) -> g_2(x,x) g_2(s(x),y) -> b(f_1(y),g_2(x,y)) f_3(x) -> g_3(x,x) g_3(s(x),y) -> b(f_2(y),g_3(x,y)) f_4(x) -> g_4(x,x) g_4(s(x),y) -> b(f_3(y),g_4(x,y)) f_5(x) -> g_5(x,x) g_5(s(x),y) -> b(f_4(y),g_5(x,y)) f_6(x) -> g_6(x,x) g_6(s(x),y) -> b(f_5(y),g_6(x,y)) f_7(x) -> g_7(x,x) g_7(s(x),y) -> b(f_6(y),g_7(x,y)) f_8(x) -> g_8(x,x) g_8(s(x),y) -> b(f_7(y),g_8(x,y)) f_9(x) -> g_9(x,x) g_9(s(x),y) -> b(f_8(y),g_9(x,y)) f_10(x) -> g_10(x,x) g_10(s(x),y) -> b(f_9(y),g_10(x,y)) graph: g_10#(s(x),y) -> g_10#(x,y) -> g_10#(s(x),y) -> f_9#(y) g_10#(s(x),y) -> g_10#(x,y) -> g_10#(s(x),y) -> g_10#(x,y) g_10#(s(x),y) -> f_9#(y) -> f_9#(x) -> g_9#(x,x) f_10#(x) -> g_10#(x,x) -> g_10#(s(x),y) -> f_9#(y) f_10#(x) -> g_10#(x,x) -> g_10#(s(x),y) -> g_10#(x,y) g_9#(s(x),y) -> g_9#(x,y) -> g_9#(s(x),y) -> f_8#(y) g_9#(s(x),y) -> g_9#(x,y) -> g_9#(s(x),y) -> g_9#(x,y) g_9#(s(x),y) -> f_8#(y) -> f_8#(x) -> g_8#(x,x) f_9#(x) -> g_9#(x,x) -> g_9#(s(x),y) -> f_8#(y) f_9#(x) -> g_9#(x,x) -> g_9#(s(x),y) -> g_9#(x,y) g_8#(s(x),y) -> g_8#(x,y) -> g_8#(s(x),y) -> f_7#(y) g_8#(s(x),y) -> g_8#(x,y) -> g_8#(s(x),y) -> g_8#(x,y) g_8#(s(x),y) -> f_7#(y) -> f_7#(x) -> g_7#(x,x) f_8#(x) -> g_8#(x,x) -> g_8#(s(x),y) -> f_7#(y) f_8#(x) -> g_8#(x,x) -> g_8#(s(x),y) -> g_8#(x,y) g_7#(s(x),y) -> g_7#(x,y) -> g_7#(s(x),y) -> f_6#(y) g_7#(s(x),y) -> g_7#(x,y) -> g_7#(s(x),y) -> g_7#(x,y) g_7#(s(x),y) -> f_6#(y) -> f_6#(x) -> g_6#(x,x) f_7#(x) -> g_7#(x,x) -> g_7#(s(x),y) -> f_6#(y) f_7#(x) -> g_7#(x,x) -> g_7#(s(x),y) -> g_7#(x,y) g_6#(s(x),y) -> g_6#(x,y) -> g_6#(s(x),y) -> f_5#(y) g_6#(s(x),y) -> g_6#(x,y) -> g_6#(s(x),y) -> g_6#(x,y) g_6#(s(x),y) -> f_5#(y) -> f_5#(x) -> g_5#(x,x) f_6#(x) -> g_6#(x,x) -> g_6#(s(x),y) -> f_5#(y) f_6#(x) -> g_6#(x,x) -> g_6#(s(x),y) -> g_6#(x,y) g_5#(s(x),y) -> g_5#(x,y) -> g_5#(s(x),y) -> f_4#(y) g_5#(s(x),y) -> g_5#(x,y) -> g_5#(s(x),y) -> g_5#(x,y) g_5#(s(x),y) -> f_4#(y) -> f_4#(x) -> g_4#(x,x) f_5#(x) -> g_5#(x,x) -> g_5#(s(x),y) -> f_4#(y) f_5#(x) -> g_5#(x,x) -> g_5#(s(x),y) -> g_5#(x,y) g_4#(s(x),y) -> g_4#(x,y) -> g_4#(s(x),y) -> f_3#(y) g_4#(s(x),y) -> g_4#(x,y) -> g_4#(s(x),y) -> g_4#(x,y) g_4#(s(x),y) -> f_3#(y) -> f_3#(x) -> g_3#(x,x) f_4#(x) -> g_4#(x,x) -> g_4#(s(x),y) -> f_3#(y) f_4#(x) -> g_4#(x,x) -> g_4#(s(x),y) -> g_4#(x,y) g_3#(s(x),y) -> g_3#(x,y) -> g_3#(s(x),y) -> f_2#(y) g_3#(s(x),y) -> g_3#(x,y) -> g_3#(s(x),y) -> g_3#(x,y) g_3#(s(x),y) -> f_2#(y) -> f_2#(x) -> g_2#(x,x) f_3#(x) -> g_3#(x,x) -> g_3#(s(x),y) -> f_2#(y) f_3#(x) -> g_3#(x,x) -> g_3#(s(x),y) -> g_3#(x,y) g_2#(s(x),y) -> g_2#(x,y) -> g_2#(s(x),y) -> f_1#(y) g_2#(s(x),y) -> g_2#(x,y) -> g_2#(s(x),y) -> g_2#(x,y) g_2#(s(x),y) -> f_1#(y) -> f_1#(x) -> g_1#(x,x) f_2#(x) -> g_2#(x,x) -> g_2#(s(x),y) -> f_1#(y) f_2#(x) -> g_2#(x,x) -> g_2#(s(x),y) -> g_2#(x,y) g_1#(s(x),y) -> g_1#(x,y) -> g_1#(s(x),y) -> f_0#(y) g_1#(s(x),y) -> g_1#(x,y) -> g_1#(s(x),y) -> g_1#(x,y) f_1#(x) -> g_1#(x,x) -> g_1#(s(x),y) -> f_0#(y) f_1#(x) -> g_1#(x,x) -> g_1#(s(x),y) -> g_1#(x,y) SCC Processor: #sccs: 10 #rules: 10 #arcs: 49/900 DPs: g_10#(s(x),y) -> g_10#(x,y) TRS: f_0(x) -> a() f_1(x) -> g_1(x,x) g_1(s(x),y) -> b(f_0(y),g_1(x,y)) f_2(x) -> g_2(x,x) g_2(s(x),y) -> b(f_1(y),g_2(x,y)) f_3(x) -> g_3(x,x) g_3(s(x),y) -> b(f_2(y),g_3(x,y)) f_4(x) -> g_4(x,x) g_4(s(x),y) -> b(f_3(y),g_4(x,y)) f_5(x) -> g_5(x,x) g_5(s(x),y) -> b(f_4(y),g_5(x,y)) f_6(x) -> g_6(x,x) g_6(s(x),y) -> b(f_5(y),g_6(x,y)) f_7(x) -> g_7(x,x) g_7(s(x),y) -> b(f_6(y),g_7(x,y)) f_8(x) -> g_8(x,x) g_8(s(x),y) -> b(f_7(y),g_8(x,y)) f_9(x) -> g_9(x,x) g_9(s(x),y) -> b(f_8(y),g_9(x,y)) f_10(x) -> g_10(x,x) g_10(s(x),y) -> b(f_9(y),g_10(x,y)) Subterm Criterion Processor: simple projection: pi(g_10#) = 0 problem: DPs: TRS: f_0(x) -> a() f_1(x) -> g_1(x,x) g_1(s(x),y) -> b(f_0(y),g_1(x,y)) f_2(x) -> g_2(x,x) g_2(s(x),y) -> b(f_1(y),g_2(x,y)) f_3(x) -> g_3(x,x) g_3(s(x),y) -> b(f_2(y),g_3(x,y)) f_4(x) -> g_4(x,x) g_4(s(x),y) -> b(f_3(y),g_4(x,y)) f_5(x) -> g_5(x,x) g_5(s(x),y) -> b(f_4(y),g_5(x,y)) f_6(x) -> g_6(x,x) g_6(s(x),y) -> b(f_5(y),g_6(x,y)) f_7(x) -> g_7(x,x) g_7(s(x),y) -> b(f_6(y),g_7(x,y)) f_8(x) -> g_8(x,x) g_8(s(x),y) -> b(f_7(y),g_8(x,y)) f_9(x) -> g_9(x,x) g_9(s(x),y) -> b(f_8(y),g_9(x,y)) f_10(x) -> g_10(x,x) g_10(s(x),y) -> b(f_9(y),g_10(x,y)) Qed DPs: g_9#(s(x),y) -> g_9#(x,y) TRS: f_0(x) -> a() f_1(x) -> g_1(x,x) g_1(s(x),y) -> b(f_0(y),g_1(x,y)) f_2(x) -> g_2(x,x) g_2(s(x),y) -> b(f_1(y),g_2(x,y)) f_3(x) -> g_3(x,x) g_3(s(x),y) -> b(f_2(y),g_3(x,y)) f_4(x) -> g_4(x,x) g_4(s(x),y) -> b(f_3(y),g_4(x,y)) f_5(x) -> g_5(x,x) g_5(s(x),y) -> b(f_4(y),g_5(x,y)) f_6(x) -> g_6(x,x) g_6(s(x),y) -> b(f_5(y),g_6(x,y)) f_7(x) -> g_7(x,x) g_7(s(x),y) -> b(f_6(y),g_7(x,y)) f_8(x) -> g_8(x,x) g_8(s(x),y) -> b(f_7(y),g_8(x,y)) f_9(x) -> g_9(x,x) g_9(s(x),y) -> b(f_8(y),g_9(x,y)) f_10(x) -> g_10(x,x) g_10(s(x),y) -> b(f_9(y),g_10(x,y)) Subterm Criterion Processor: simple projection: pi(g_9#) = 0 problem: DPs: TRS: f_0(x) -> a() f_1(x) -> g_1(x,x) g_1(s(x),y) -> b(f_0(y),g_1(x,y)) f_2(x) -> g_2(x,x) g_2(s(x),y) -> b(f_1(y),g_2(x,y)) f_3(x) -> g_3(x,x) g_3(s(x),y) -> b(f_2(y),g_3(x,y)) f_4(x) -> g_4(x,x) g_4(s(x),y) -> b(f_3(y),g_4(x,y)) f_5(x) -> g_5(x,x) g_5(s(x),y) -> b(f_4(y),g_5(x,y)) f_6(x) -> g_6(x,x) g_6(s(x),y) -> b(f_5(y),g_6(x,y)) f_7(x) -> g_7(x,x) g_7(s(x),y) -> b(f_6(y),g_7(x,y)) f_8(x) -> g_8(x,x) g_8(s(x),y) -> b(f_7(y),g_8(x,y)) f_9(x) -> g_9(x,x) g_9(s(x),y) -> b(f_8(y),g_9(x,y)) f_10(x) -> g_10(x,x) g_10(s(x),y) -> b(f_9(y),g_10(x,y)) Qed DPs: g_8#(s(x),y) -> g_8#(x,y) TRS: f_0(x) -> a() f_1(x) -> g_1(x,x) g_1(s(x),y) -> b(f_0(y),g_1(x,y)) f_2(x) -> g_2(x,x) g_2(s(x),y) -> b(f_1(y),g_2(x,y)) f_3(x) -> g_3(x,x) g_3(s(x),y) -> b(f_2(y),g_3(x,y)) f_4(x) -> g_4(x,x) g_4(s(x),y) -> b(f_3(y),g_4(x,y)) f_5(x) -> g_5(x,x) g_5(s(x),y) -> b(f_4(y),g_5(x,y)) f_6(x) -> g_6(x,x) g_6(s(x),y) -> b(f_5(y),g_6(x,y)) f_7(x) -> g_7(x,x) g_7(s(x),y) -> b(f_6(y),g_7(x,y)) f_8(x) -> g_8(x,x) g_8(s(x),y) -> b(f_7(y),g_8(x,y)) f_9(x) -> g_9(x,x) g_9(s(x),y) -> b(f_8(y),g_9(x,y)) f_10(x) -> g_10(x,x) g_10(s(x),y) -> b(f_9(y),g_10(x,y)) Subterm Criterion Processor: simple projection: pi(g_8#) = 0 problem: DPs: TRS: f_0(x) -> a() f_1(x) -> g_1(x,x) g_1(s(x),y) -> b(f_0(y),g_1(x,y)) f_2(x) -> g_2(x,x) g_2(s(x),y) -> b(f_1(y),g_2(x,y)) f_3(x) -> g_3(x,x) g_3(s(x),y) -> b(f_2(y),g_3(x,y)) f_4(x) -> g_4(x,x) g_4(s(x),y) -> b(f_3(y),g_4(x,y)) f_5(x) -> g_5(x,x) g_5(s(x),y) -> b(f_4(y),g_5(x,y)) f_6(x) -> g_6(x,x) g_6(s(x),y) -> b(f_5(y),g_6(x,y)) f_7(x) -> g_7(x,x) g_7(s(x),y) -> b(f_6(y),g_7(x,y)) f_8(x) -> g_8(x,x) g_8(s(x),y) -> b(f_7(y),g_8(x,y)) f_9(x) -> g_9(x,x) g_9(s(x),y) -> b(f_8(y),g_9(x,y)) f_10(x) -> g_10(x,x) g_10(s(x),y) -> b(f_9(y),g_10(x,y)) Qed DPs: g_7#(s(x),y) -> g_7#(x,y) TRS: f_0(x) -> a() f_1(x) -> g_1(x,x) g_1(s(x),y) -> b(f_0(y),g_1(x,y)) f_2(x) -> g_2(x,x) g_2(s(x),y) -> b(f_1(y),g_2(x,y)) f_3(x) -> g_3(x,x) g_3(s(x),y) -> b(f_2(y),g_3(x,y)) f_4(x) -> g_4(x,x) g_4(s(x),y) -> b(f_3(y),g_4(x,y)) f_5(x) -> g_5(x,x) g_5(s(x),y) -> b(f_4(y),g_5(x,y)) f_6(x) -> g_6(x,x) g_6(s(x),y) -> b(f_5(y),g_6(x,y)) f_7(x) -> g_7(x,x) g_7(s(x),y) -> b(f_6(y),g_7(x,y)) f_8(x) -> g_8(x,x) g_8(s(x),y) -> b(f_7(y),g_8(x,y)) f_9(x) -> g_9(x,x) g_9(s(x),y) -> b(f_8(y),g_9(x,y)) f_10(x) -> g_10(x,x) g_10(s(x),y) -> b(f_9(y),g_10(x,y)) Subterm Criterion Processor: simple projection: pi(g_7#) = 0 problem: DPs: TRS: f_0(x) -> a() f_1(x) -> g_1(x,x) g_1(s(x),y) -> b(f_0(y),g_1(x,y)) f_2(x) -> g_2(x,x) g_2(s(x),y) -> b(f_1(y),g_2(x,y)) f_3(x) -> g_3(x,x) g_3(s(x),y) -> b(f_2(y),g_3(x,y)) f_4(x) -> g_4(x,x) g_4(s(x),y) -> b(f_3(y),g_4(x,y)) f_5(x) -> g_5(x,x) g_5(s(x),y) -> b(f_4(y),g_5(x,y)) f_6(x) -> g_6(x,x) g_6(s(x),y) -> b(f_5(y),g_6(x,y)) f_7(x) -> g_7(x,x) g_7(s(x),y) -> b(f_6(y),g_7(x,y)) f_8(x) -> g_8(x,x) g_8(s(x),y) -> b(f_7(y),g_8(x,y)) f_9(x) -> g_9(x,x) g_9(s(x),y) -> b(f_8(y),g_9(x,y)) f_10(x) -> g_10(x,x) g_10(s(x),y) -> b(f_9(y),g_10(x,y)) Qed DPs: g_6#(s(x),y) -> g_6#(x,y) TRS: f_0(x) -> a() f_1(x) -> g_1(x,x) g_1(s(x),y) -> b(f_0(y),g_1(x,y)) f_2(x) -> g_2(x,x) g_2(s(x),y) -> b(f_1(y),g_2(x,y)) f_3(x) -> g_3(x,x) g_3(s(x),y) -> b(f_2(y),g_3(x,y)) f_4(x) -> g_4(x,x) g_4(s(x),y) -> b(f_3(y),g_4(x,y)) f_5(x) -> g_5(x,x) g_5(s(x),y) -> b(f_4(y),g_5(x,y)) f_6(x) -> g_6(x,x) g_6(s(x),y) -> b(f_5(y),g_6(x,y)) f_7(x) -> g_7(x,x) g_7(s(x),y) -> b(f_6(y),g_7(x,y)) f_8(x) -> g_8(x,x) g_8(s(x),y) -> b(f_7(y),g_8(x,y)) f_9(x) -> g_9(x,x) g_9(s(x),y) -> b(f_8(y),g_9(x,y)) f_10(x) -> g_10(x,x) g_10(s(x),y) -> b(f_9(y),g_10(x,y)) Subterm Criterion Processor: simple projection: pi(g_6#) = 0 problem: DPs: TRS: f_0(x) -> a() f_1(x) -> g_1(x,x) g_1(s(x),y) -> b(f_0(y),g_1(x,y)) f_2(x) -> g_2(x,x) g_2(s(x),y) -> b(f_1(y),g_2(x,y)) f_3(x) -> g_3(x,x) g_3(s(x),y) -> b(f_2(y),g_3(x,y)) f_4(x) -> g_4(x,x) g_4(s(x),y) -> b(f_3(y),g_4(x,y)) f_5(x) -> g_5(x,x) g_5(s(x),y) -> b(f_4(y),g_5(x,y)) f_6(x) -> g_6(x,x) g_6(s(x),y) -> b(f_5(y),g_6(x,y)) f_7(x) -> g_7(x,x) g_7(s(x),y) -> b(f_6(y),g_7(x,y)) f_8(x) -> g_8(x,x) g_8(s(x),y) -> b(f_7(y),g_8(x,y)) f_9(x) -> g_9(x,x) g_9(s(x),y) -> b(f_8(y),g_9(x,y)) f_10(x) -> g_10(x,x) g_10(s(x),y) -> b(f_9(y),g_10(x,y)) Qed DPs: g_5#(s(x),y) -> g_5#(x,y) TRS: f_0(x) -> a() f_1(x) -> g_1(x,x) g_1(s(x),y) -> b(f_0(y),g_1(x,y)) f_2(x) -> g_2(x,x) g_2(s(x),y) -> b(f_1(y),g_2(x,y)) f_3(x) -> g_3(x,x) g_3(s(x),y) -> b(f_2(y),g_3(x,y)) f_4(x) -> g_4(x,x) g_4(s(x),y) -> b(f_3(y),g_4(x,y)) f_5(x) -> g_5(x,x) g_5(s(x),y) -> b(f_4(y),g_5(x,y)) f_6(x) -> g_6(x,x) g_6(s(x),y) -> b(f_5(y),g_6(x,y)) f_7(x) -> g_7(x,x) g_7(s(x),y) -> b(f_6(y),g_7(x,y)) f_8(x) -> g_8(x,x) g_8(s(x),y) -> b(f_7(y),g_8(x,y)) f_9(x) -> g_9(x,x) g_9(s(x),y) -> b(f_8(y),g_9(x,y)) f_10(x) -> g_10(x,x) g_10(s(x),y) -> b(f_9(y),g_10(x,y)) Subterm Criterion Processor: simple projection: pi(g_5#) = 0 problem: DPs: TRS: f_0(x) -> a() f_1(x) -> g_1(x,x) g_1(s(x),y) -> b(f_0(y),g_1(x,y)) f_2(x) -> g_2(x,x) g_2(s(x),y) -> b(f_1(y),g_2(x,y)) f_3(x) -> g_3(x,x) g_3(s(x),y) -> b(f_2(y),g_3(x,y)) f_4(x) -> g_4(x,x) g_4(s(x),y) -> b(f_3(y),g_4(x,y)) f_5(x) -> g_5(x,x) g_5(s(x),y) -> b(f_4(y),g_5(x,y)) f_6(x) -> g_6(x,x) g_6(s(x),y) -> b(f_5(y),g_6(x,y)) f_7(x) -> g_7(x,x) g_7(s(x),y) -> b(f_6(y),g_7(x,y)) f_8(x) -> g_8(x,x) g_8(s(x),y) -> b(f_7(y),g_8(x,y)) f_9(x) -> g_9(x,x) g_9(s(x),y) -> b(f_8(y),g_9(x,y)) f_10(x) -> g_10(x,x) g_10(s(x),y) -> b(f_9(y),g_10(x,y)) Qed DPs: g_4#(s(x),y) -> g_4#(x,y) TRS: f_0(x) -> a() f_1(x) -> g_1(x,x) g_1(s(x),y) -> b(f_0(y),g_1(x,y)) f_2(x) -> g_2(x,x) g_2(s(x),y) -> b(f_1(y),g_2(x,y)) f_3(x) -> g_3(x,x) g_3(s(x),y) -> b(f_2(y),g_3(x,y)) f_4(x) -> g_4(x,x) g_4(s(x),y) -> b(f_3(y),g_4(x,y)) f_5(x) -> g_5(x,x) g_5(s(x),y) -> b(f_4(y),g_5(x,y)) f_6(x) -> g_6(x,x) g_6(s(x),y) -> b(f_5(y),g_6(x,y)) f_7(x) -> g_7(x,x) g_7(s(x),y) -> b(f_6(y),g_7(x,y)) f_8(x) -> g_8(x,x) g_8(s(x),y) -> b(f_7(y),g_8(x,y)) f_9(x) -> g_9(x,x) g_9(s(x),y) -> b(f_8(y),g_9(x,y)) f_10(x) -> g_10(x,x) g_10(s(x),y) -> b(f_9(y),g_10(x,y)) Subterm Criterion Processor: simple projection: pi(g_4#) = 0 problem: DPs: TRS: f_0(x) -> a() f_1(x) -> g_1(x,x) g_1(s(x),y) -> b(f_0(y),g_1(x,y)) f_2(x) -> g_2(x,x) g_2(s(x),y) -> b(f_1(y),g_2(x,y)) f_3(x) -> g_3(x,x) g_3(s(x),y) -> b(f_2(y),g_3(x,y)) f_4(x) -> g_4(x,x) g_4(s(x),y) -> b(f_3(y),g_4(x,y)) f_5(x) -> g_5(x,x) g_5(s(x),y) -> b(f_4(y),g_5(x,y)) f_6(x) -> g_6(x,x) g_6(s(x),y) -> b(f_5(y),g_6(x,y)) f_7(x) -> g_7(x,x) g_7(s(x),y) -> b(f_6(y),g_7(x,y)) f_8(x) -> g_8(x,x) g_8(s(x),y) -> b(f_7(y),g_8(x,y)) f_9(x) -> g_9(x,x) g_9(s(x),y) -> b(f_8(y),g_9(x,y)) f_10(x) -> g_10(x,x) g_10(s(x),y) -> b(f_9(y),g_10(x,y)) Qed DPs: g_3#(s(x),y) -> g_3#(x,y) TRS: f_0(x) -> a() f_1(x) -> g_1(x,x) g_1(s(x),y) -> b(f_0(y),g_1(x,y)) f_2(x) -> g_2(x,x) g_2(s(x),y) -> b(f_1(y),g_2(x,y)) f_3(x) -> g_3(x,x) g_3(s(x),y) -> b(f_2(y),g_3(x,y)) f_4(x) -> g_4(x,x) g_4(s(x),y) -> b(f_3(y),g_4(x,y)) f_5(x) -> g_5(x,x) g_5(s(x),y) -> b(f_4(y),g_5(x,y)) f_6(x) -> g_6(x,x) g_6(s(x),y) -> b(f_5(y),g_6(x,y)) f_7(x) -> g_7(x,x) g_7(s(x),y) -> b(f_6(y),g_7(x,y)) f_8(x) -> g_8(x,x) g_8(s(x),y) -> b(f_7(y),g_8(x,y)) f_9(x) -> g_9(x,x) g_9(s(x),y) -> b(f_8(y),g_9(x,y)) f_10(x) -> g_10(x,x) g_10(s(x),y) -> b(f_9(y),g_10(x,y)) Subterm Criterion Processor: simple projection: pi(g_3#) = 0 problem: DPs: TRS: f_0(x) -> a() f_1(x) -> g_1(x,x) g_1(s(x),y) -> b(f_0(y),g_1(x,y)) f_2(x) -> g_2(x,x) g_2(s(x),y) -> b(f_1(y),g_2(x,y)) f_3(x) -> g_3(x,x) g_3(s(x),y) -> b(f_2(y),g_3(x,y)) f_4(x) -> g_4(x,x) g_4(s(x),y) -> b(f_3(y),g_4(x,y)) f_5(x) -> g_5(x,x) g_5(s(x),y) -> b(f_4(y),g_5(x,y)) f_6(x) -> g_6(x,x) g_6(s(x),y) -> b(f_5(y),g_6(x,y)) f_7(x) -> g_7(x,x) g_7(s(x),y) -> b(f_6(y),g_7(x,y)) f_8(x) -> g_8(x,x) g_8(s(x),y) -> b(f_7(y),g_8(x,y)) f_9(x) -> g_9(x,x) g_9(s(x),y) -> b(f_8(y),g_9(x,y)) f_10(x) -> g_10(x,x) g_10(s(x),y) -> b(f_9(y),g_10(x,y)) Qed DPs: g_2#(s(x),y) -> g_2#(x,y) TRS: f_0(x) -> a() f_1(x) -> g_1(x,x) g_1(s(x),y) -> b(f_0(y),g_1(x,y)) f_2(x) -> g_2(x,x) g_2(s(x),y) -> b(f_1(y),g_2(x,y)) f_3(x) -> g_3(x,x) g_3(s(x),y) -> b(f_2(y),g_3(x,y)) f_4(x) -> g_4(x,x) g_4(s(x),y) -> b(f_3(y),g_4(x,y)) f_5(x) -> g_5(x,x) g_5(s(x),y) -> b(f_4(y),g_5(x,y)) f_6(x) -> g_6(x,x) g_6(s(x),y) -> b(f_5(y),g_6(x,y)) f_7(x) -> g_7(x,x) g_7(s(x),y) -> b(f_6(y),g_7(x,y)) f_8(x) -> g_8(x,x) g_8(s(x),y) -> b(f_7(y),g_8(x,y)) f_9(x) -> g_9(x,x) g_9(s(x),y) -> b(f_8(y),g_9(x,y)) f_10(x) -> g_10(x,x) g_10(s(x),y) -> b(f_9(y),g_10(x,y)) Subterm Criterion Processor: simple projection: pi(g_2#) = 0 problem: DPs: TRS: f_0(x) -> a() f_1(x) -> g_1(x,x) g_1(s(x),y) -> b(f_0(y),g_1(x,y)) f_2(x) -> g_2(x,x) g_2(s(x),y) -> b(f_1(y),g_2(x,y)) f_3(x) -> g_3(x,x) g_3(s(x),y) -> b(f_2(y),g_3(x,y)) f_4(x) -> g_4(x,x) g_4(s(x),y) -> b(f_3(y),g_4(x,y)) f_5(x) -> g_5(x,x) g_5(s(x),y) -> b(f_4(y),g_5(x,y)) f_6(x) -> g_6(x,x) g_6(s(x),y) -> b(f_5(y),g_6(x,y)) f_7(x) -> g_7(x,x) g_7(s(x),y) -> b(f_6(y),g_7(x,y)) f_8(x) -> g_8(x,x) g_8(s(x),y) -> b(f_7(y),g_8(x,y)) f_9(x) -> g_9(x,x) g_9(s(x),y) -> b(f_8(y),g_9(x,y)) f_10(x) -> g_10(x,x) g_10(s(x),y) -> b(f_9(y),g_10(x,y)) Qed DPs: g_1#(s(x),y) -> g_1#(x,y) TRS: f_0(x) -> a() f_1(x) -> g_1(x,x) g_1(s(x),y) -> b(f_0(y),g_1(x,y)) f_2(x) -> g_2(x,x) g_2(s(x),y) -> b(f_1(y),g_2(x,y)) f_3(x) -> g_3(x,x) g_3(s(x),y) -> b(f_2(y),g_3(x,y)) f_4(x) -> g_4(x,x) g_4(s(x),y) -> b(f_3(y),g_4(x,y)) f_5(x) -> g_5(x,x) g_5(s(x),y) -> b(f_4(y),g_5(x,y)) f_6(x) -> g_6(x,x) g_6(s(x),y) -> b(f_5(y),g_6(x,y)) f_7(x) -> g_7(x,x) g_7(s(x),y) -> b(f_6(y),g_7(x,y)) f_8(x) -> g_8(x,x) g_8(s(x),y) -> b(f_7(y),g_8(x,y)) f_9(x) -> g_9(x,x) g_9(s(x),y) -> b(f_8(y),g_9(x,y)) f_10(x) -> g_10(x,x) g_10(s(x),y) -> b(f_9(y),g_10(x,y)) Subterm Criterion Processor: simple projection: pi(g_1#) = 0 problem: DPs: TRS: f_0(x) -> a() f_1(x) -> g_1(x,x) g_1(s(x),y) -> b(f_0(y),g_1(x,y)) f_2(x) -> g_2(x,x) g_2(s(x),y) -> b(f_1(y),g_2(x,y)) f_3(x) -> g_3(x,x) g_3(s(x),y) -> b(f_2(y),g_3(x,y)) f_4(x) -> g_4(x,x) g_4(s(x),y) -> b(f_3(y),g_4(x,y)) f_5(x) -> g_5(x,x) g_5(s(x),y) -> b(f_4(y),g_5(x,y)) f_6(x) -> g_6(x,x) g_6(s(x),y) -> b(f_5(y),g_6(x,y)) f_7(x) -> g_7(x,x) g_7(s(x),y) -> b(f_6(y),g_7(x,y)) f_8(x) -> g_8(x,x) g_8(s(x),y) -> b(f_7(y),g_8(x,y)) f_9(x) -> g_9(x,x) g_9(s(x),y) -> b(f_8(y),g_9(x,y)) f_10(x) -> g_10(x,x) g_10(s(x),y) -> b(f_9(y),g_10(x,y)) Qed