YES Problem: +(x,0()) -> x +(x,s(y)) -> s(+(x,y)) +(0(),s(y)) -> s(y) s(+(0(),y)) -> s(y) Proof: DP Processor: DPs: +#(x,s(y)) -> +#(x,y) +#(x,s(y)) -> s#(+(x,y)) s#(+(0(),y)) -> s#(y) TRS: +(x,0()) -> x +(x,s(y)) -> s(+(x,y)) +(0(),s(y)) -> s(y) s(+(0(),y)) -> s(y) TDG Processor: DPs: +#(x,s(y)) -> +#(x,y) +#(x,s(y)) -> s#(+(x,y)) s#(+(0(),y)) -> s#(y) TRS: +(x,0()) -> x +(x,s(y)) -> s(+(x,y)) +(0(),s(y)) -> s(y) s(+(0(),y)) -> s(y) graph: s#(+(0(),y)) -> s#(y) -> s#(+(0(),y)) -> s#(y) +#(x,s(y)) -> s#(+(x,y)) -> s#(+(0(),y)) -> s#(y) +#(x,s(y)) -> +#(x,y) -> +#(x,s(y)) -> s#(+(x,y)) +#(x,s(y)) -> +#(x,y) -> +#(x,s(y)) -> +#(x,y) SCC Processor: #sccs: 2 #rules: 2 #arcs: 4/9 DPs: +#(x,s(y)) -> +#(x,y) TRS: +(x,0()) -> x +(x,s(y)) -> s(+(x,y)) +(0(),s(y)) -> s(y) s(+(0(),y)) -> s(y) Subterm Criterion Processor: simple projection: pi(+#) = 1 problem: DPs: TRS: +(x,0()) -> x +(x,s(y)) -> s(+(x,y)) +(0(),s(y)) -> s(y) s(+(0(),y)) -> s(y) Qed DPs: s#(+(0(),y)) -> s#(y) TRS: +(x,0()) -> x +(x,s(y)) -> s(+(x,y)) +(0(),s(y)) -> s(y) s(+(0(),y)) -> s(y) Subterm Criterion Processor: simple projection: pi(s#) = 0 problem: DPs: TRS: +(x,0()) -> x +(x,s(y)) -> s(+(x,y)) +(0(),s(y)) -> s(y) s(+(0(),y)) -> s(y) Qed