/export/starexec/sandbox2/solver/bin/starexec_run_ttt2-1.17+nonreach /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- YES Problem: filter(cons(X,Y),0(),M) -> cons(0(),n__filter(activate(Y),M,M)) filter(cons(X,Y),s(N),M) -> cons(X,n__filter(activate(Y),N,M)) sieve(cons(0(),Y)) -> cons(0(),n__sieve(activate(Y))) sieve(cons(s(N),Y)) -> cons(s(N),n__sieve(filter(activate(Y),N,N))) nats(N) -> cons(N,n__nats(s(N))) zprimes() -> sieve(nats(s(s(0())))) filter(X1,X2,X3) -> n__filter(X1,X2,X3) sieve(X) -> n__sieve(X) nats(X) -> n__nats(X) activate(n__filter(X1,X2,X3)) -> filter(X1,X2,X3) activate(n__sieve(X)) -> sieve(X) activate(n__nats(X)) -> nats(X) activate(X) -> X Proof: DP Processor: DPs: filter#(cons(X,Y),0(),M) -> activate#(Y) filter#(cons(X,Y),s(N),M) -> activate#(Y) sieve#(cons(0(),Y)) -> activate#(Y) sieve#(cons(s(N),Y)) -> activate#(Y) sieve#(cons(s(N),Y)) -> filter#(activate(Y),N,N) zprimes#() -> nats#(s(s(0()))) zprimes#() -> sieve#(nats(s(s(0())))) activate#(n__filter(X1,X2,X3)) -> filter#(X1,X2,X3) activate#(n__sieve(X)) -> sieve#(X) activate#(n__nats(X)) -> nats#(X) TRS: filter(cons(X,Y),0(),M) -> cons(0(),n__filter(activate(Y),M,M)) filter(cons(X,Y),s(N),M) -> cons(X,n__filter(activate(Y),N,M)) sieve(cons(0(),Y)) -> cons(0(),n__sieve(activate(Y))) sieve(cons(s(N),Y)) -> cons(s(N),n__sieve(filter(activate(Y),N,N))) nats(N) -> cons(N,n__nats(s(N))) zprimes() -> sieve(nats(s(s(0())))) filter(X1,X2,X3) -> n__filter(X1,X2,X3) sieve(X) -> n__sieve(X) nats(X) -> n__nats(X) activate(n__filter(X1,X2,X3)) -> filter(X1,X2,X3) activate(n__sieve(X)) -> sieve(X) activate(n__nats(X)) -> nats(X) activate(X) -> X TDG Processor: DPs: filter#(cons(X,Y),0(),M) -> activate#(Y) filter#(cons(X,Y),s(N),M) -> activate#(Y) sieve#(cons(0(),Y)) -> activate#(Y) sieve#(cons(s(N),Y)) -> activate#(Y) sieve#(cons(s(N),Y)) -> filter#(activate(Y),N,N) zprimes#() -> nats#(s(s(0()))) zprimes#() -> sieve#(nats(s(s(0())))) activate#(n__filter(X1,X2,X3)) -> filter#(X1,X2,X3) activate#(n__sieve(X)) -> sieve#(X) activate#(n__nats(X)) -> nats#(X) TRS: filter(cons(X,Y),0(),M) -> cons(0(),n__filter(activate(Y),M,M)) filter(cons(X,Y),s(N),M) -> cons(X,n__filter(activate(Y),N,M)) sieve(cons(0(),Y)) -> cons(0(),n__sieve(activate(Y))) sieve(cons(s(N),Y)) -> cons(s(N),n__sieve(filter(activate(Y),N,N))) nats(N) -> cons(N,n__nats(s(N))) zprimes() -> sieve(nats(s(s(0())))) filter(X1,X2,X3) -> n__filter(X1,X2,X3) sieve(X) -> n__sieve(X) nats(X) -> n__nats(X) activate(n__filter(X1,X2,X3)) -> filter(X1,X2,X3) activate(n__sieve(X)) -> sieve(X) activate(n__nats(X)) -> nats(X) activate(X) -> X graph: zprimes#() -> sieve#(nats(s(s(0())))) -> sieve#(cons(s(N),Y)) -> filter#(activate(Y),N,N) zprimes#() -> sieve#(nats(s(s(0())))) -> sieve#(cons(s(N),Y)) -> activate#(Y) zprimes#() -> sieve#(nats(s(s(0())))) -> sieve#(cons(0(),Y)) -> activate#(Y) sieve#(cons(s(N),Y)) -> activate#(Y) -> activate#(n__nats(X)) -> nats#(X) sieve#(cons(s(N),Y)) -> activate#(Y) -> activate#(n__sieve(X)) -> sieve#(X) sieve#(cons(s(N),Y)) -> activate#(Y) -> activate#(n__filter(X1,X2,X3)) -> filter#(X1,X2,X3) sieve#(cons(s(N),Y)) -> filter#(activate(Y),N,N) -> filter#(cons(X,Y),s(N),M) -> activate#(Y) sieve#(cons(s(N),Y)) -> filter#(activate(Y),N,N) -> filter#(cons(X,Y),0(),M) -> activate#(Y) sieve#(cons(0(),Y)) -> activate#(Y) -> activate#(n__nats(X)) -> nats#(X) sieve#(cons(0(),Y)) -> activate#(Y) -> activate#(n__sieve(X)) -> sieve#(X) sieve#(cons(0(),Y)) -> activate#(Y) -> activate#(n__filter(X1,X2,X3)) -> filter#(X1,X2,X3) activate#(n__sieve(X)) -> sieve#(X) -> sieve#(cons(s(N),Y)) -> filter#(activate(Y),N,N) activate#(n__sieve(X)) -> sieve#(X) -> sieve#(cons(s(N),Y)) -> activate#(Y) activate#(n__sieve(X)) -> sieve#(X) -> sieve#(cons(0(),Y)) -> activate#(Y) activate#(n__filter(X1,X2,X3)) -> filter#(X1,X2,X3) -> filter#(cons(X,Y),s(N),M) -> activate#(Y) activate#(n__filter(X1,X2,X3)) -> filter#(X1,X2,X3) -> filter#(cons(X,Y),0(),M) -> activate#(Y) filter#(cons(X,Y),s(N),M) -> activate#(Y) -> activate#(n__nats(X)) -> nats#(X) filter#(cons(X,Y),s(N),M) -> activate#(Y) -> activate#(n__sieve(X)) -> sieve#(X) filter#(cons(X,Y),s(N),M) -> activate#(Y) -> activate#(n__filter(X1,X2,X3)) -> filter#(X1,X2,X3) filter#(cons(X,Y),0(),M) -> activate#(Y) -> activate#(n__nats(X)) -> nats#(X) filter#(cons(X,Y),0(),M) -> activate#(Y) -> activate#(n__sieve(X)) -> sieve#(X) filter#(cons(X,Y),0(),M) -> activate#(Y) -> activate#(n__filter(X1,X2,X3)) -> filter#(X1,X2,X3) SCC Processor: #sccs: 1 #rules: 7 #arcs: 22/100 DPs: sieve#(cons(0(),Y)) -> activate#(Y) activate#(n__filter(X1,X2,X3)) -> filter#(X1,X2,X3) filter#(cons(X,Y),0(),M) -> activate#(Y) activate#(n__sieve(X)) -> sieve#(X) sieve#(cons(s(N),Y)) -> activate#(Y) sieve#(cons(s(N),Y)) -> filter#(activate(Y),N,N) filter#(cons(X,Y),s(N),M) -> activate#(Y) TRS: filter(cons(X,Y),0(),M) -> cons(0(),n__filter(activate(Y),M,M)) filter(cons(X,Y),s(N),M) -> cons(X,n__filter(activate(Y),N,M)) sieve(cons(0(),Y)) -> cons(0(),n__sieve(activate(Y))) sieve(cons(s(N),Y)) -> cons(s(N),n__sieve(filter(activate(Y),N,N))) nats(N) -> cons(N,n__nats(s(N))) zprimes() -> sieve(nats(s(s(0())))) filter(X1,X2,X3) -> n__filter(X1,X2,X3) sieve(X) -> n__sieve(X) nats(X) -> n__nats(X) activate(n__filter(X1,X2,X3)) -> filter(X1,X2,X3) activate(n__sieve(X)) -> sieve(X) activate(n__nats(X)) -> nats(X) activate(X) -> X Subterm Criterion Processor: simple projection: pi(cons) = 1 pi(filter) = 0 pi(activate) = 0 pi(n__filter) = 0 pi(s) = 0 pi(sieve) = [0,0] pi(n__sieve) = [0,0] pi(nats) = 0 pi(n__nats) = 0 pi(filter#) = [0,0] pi(activate#) = [0,0] pi(sieve#) = [0,0,0] problem: DPs: activate#(n__filter(X1,X2,X3)) -> filter#(X1,X2,X3) filter#(cons(X,Y),0(),M) -> activate#(Y) filter#(cons(X,Y),s(N),M) -> activate#(Y) TRS: filter(cons(X,Y),0(),M) -> cons(0(),n__filter(activate(Y),M,M)) filter(cons(X,Y),s(N),M) -> cons(X,n__filter(activate(Y),N,M)) sieve(cons(0(),Y)) -> cons(0(),n__sieve(activate(Y))) sieve(cons(s(N),Y)) -> cons(s(N),n__sieve(filter(activate(Y),N,N))) nats(N) -> cons(N,n__nats(s(N))) zprimes() -> sieve(nats(s(s(0())))) filter(X1,X2,X3) -> n__filter(X1,X2,X3) sieve(X) -> n__sieve(X) nats(X) -> n__nats(X) activate(n__filter(X1,X2,X3)) -> filter(X1,X2,X3) activate(n__sieve(X)) -> sieve(X) activate(n__nats(X)) -> nats(X) activate(X) -> X Size-Change Termination Processor: DPs: TRS: filter(cons(X,Y),0(),M) -> cons(0(),n__filter(activate(Y),M,M)) filter(cons(X,Y),s(N),M) -> cons(X,n__filter(activate(Y),N,M)) sieve(cons(0(),Y)) -> cons(0(),n__sieve(activate(Y))) sieve(cons(s(N),Y)) -> cons(s(N),n__sieve(filter(activate(Y),N,N))) nats(N) -> cons(N,n__nats(s(N))) zprimes() -> sieve(nats(s(s(0())))) filter(X1,X2,X3) -> n__filter(X1,X2,X3) sieve(X) -> n__sieve(X) nats(X) -> n__nats(X) activate(n__filter(X1,X2,X3)) -> filter(X1,X2,X3) activate(n__sieve(X)) -> sieve(X) activate(n__nats(X)) -> nats(X) activate(X) -> X The DP: activate#(n__filter(X1,X2,X3)) -> filter#(X1,X2,X3) has the edges: 0 > 2 0 > 1 0 > 0 The DP: filter#(cons(X,Y),0(),M) -> activate#(Y) has the edges: 0 > 0 The DP: filter#(cons(X,Y),s(N),M) -> activate#(Y) has the edges: 0 > 0 Qed