/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: from(X) -> cons(X,n__from(n__s(X))) sel(0(),cons(X,XS)) -> X sel(s(N),cons(X,XS)) -> sel(N,activate(XS)) minus(X,0()) -> 0() minus(s(X),s(Y)) -> minus(X,Y) quot(0(),s(Y)) -> 0() quot(s(X),s(Y)) -> s(quot(minus(X,Y),s(Y))) zWquot(XS,nil()) -> nil() zWquot(nil(),XS) -> nil() zWquot(cons(X,XS),cons(Y,YS)) -> cons(quot(X,Y),n__zWquot(activate(XS),activate(YS))) from(X) -> n__from(X) s(X) -> n__s(X) zWquot(X1,X2) -> n__zWquot(X1,X2) activate(n__from(X)) -> from(activate(X)) activate(n__s(X)) -> s(activate(X)) activate(n__zWquot(X1,X2)) -> zWquot(activate(X1),activate(X2)) activate(X) -> X Proof: DP Processor: DPs: sel#(s(N),cons(X,XS)) -> activate#(XS) sel#(s(N),cons(X,XS)) -> sel#(N,activate(XS)) minus#(s(X),s(Y)) -> minus#(X,Y) quot#(s(X),s(Y)) -> minus#(X,Y) quot#(s(X),s(Y)) -> quot#(minus(X,Y),s(Y)) quot#(s(X),s(Y)) -> s#(quot(minus(X,Y),s(Y))) zWquot#(cons(X,XS),cons(Y,YS)) -> activate#(YS) zWquot#(cons(X,XS),cons(Y,YS)) -> activate#(XS) zWquot#(cons(X,XS),cons(Y,YS)) -> quot#(X,Y) activate#(n__from(X)) -> activate#(X) activate#(n__from(X)) -> from#(activate(X)) activate#(n__s(X)) -> activate#(X) activate#(n__s(X)) -> s#(activate(X)) activate#(n__zWquot(X1,X2)) -> activate#(X2) activate#(n__zWquot(X1,X2)) -> activate#(X1) activate#(n__zWquot(X1,X2)) -> zWquot#(activate(X1),activate(X2)) TRS: from(X) -> cons(X,n__from(n__s(X))) sel(0(),cons(X,XS)) -> X sel(s(N),cons(X,XS)) -> sel(N,activate(XS)) minus(X,0()) -> 0() minus(s(X),s(Y)) -> minus(X,Y) quot(0(),s(Y)) -> 0() quot(s(X),s(Y)) -> s(quot(minus(X,Y),s(Y))) zWquot(XS,nil()) -> nil() zWquot(nil(),XS) -> nil() zWquot(cons(X,XS),cons(Y,YS)) -> cons(quot(X,Y),n__zWquot(activate(XS),activate(YS))) from(X) -> n__from(X) s(X) -> n__s(X) zWquot(X1,X2) -> n__zWquot(X1,X2) activate(n__from(X)) -> from(activate(X)) activate(n__s(X)) -> s(activate(X)) activate(n__zWquot(X1,X2)) -> zWquot(activate(X1),activate(X2)) activate(X) -> X TDG Processor: DPs: sel#(s(N),cons(X,XS)) -> activate#(XS) sel#(s(N),cons(X,XS)) -> sel#(N,activate(XS)) minus#(s(X),s(Y)) -> minus#(X,Y) quot#(s(X),s(Y)) -> minus#(X,Y) quot#(s(X),s(Y)) -> quot#(minus(X,Y),s(Y)) quot#(s(X),s(Y)) -> s#(quot(minus(X,Y),s(Y))) zWquot#(cons(X,XS),cons(Y,YS)) -> activate#(YS) zWquot#(cons(X,XS),cons(Y,YS)) -> activate#(XS) zWquot#(cons(X,XS),cons(Y,YS)) -> quot#(X,Y) activate#(n__from(X)) -> activate#(X) activate#(n__from(X)) -> from#(activate(X)) activate#(n__s(X)) -> activate#(X) activate#(n__s(X)) -> s#(activate(X)) activate#(n__zWquot(X1,X2)) -> activate#(X2) activate#(n__zWquot(X1,X2)) -> activate#(X1) activate#(n__zWquot(X1,X2)) -> zWquot#(activate(X1),activate(X2)) TRS: from(X) -> cons(X,n__from(n__s(X))) sel(0(),cons(X,XS)) -> X sel(s(N),cons(X,XS)) -> sel(N,activate(XS)) minus(X,0()) -> 0() minus(s(X),s(Y)) -> minus(X,Y) quot(0(),s(Y)) -> 0() quot(s(X),s(Y)) -> s(quot(minus(X,Y),s(Y))) zWquot(XS,nil()) -> nil() zWquot(nil(),XS) -> nil() zWquot(cons(X,XS),cons(Y,YS)) -> cons(quot(X,Y),n__zWquot(activate(XS),activate(YS))) from(X) -> n__from(X) s(X) -> n__s(X) zWquot(X1,X2) -> n__zWquot(X1,X2) activate(n__from(X)) -> from(activate(X)) activate(n__s(X)) -> s(activate(X)) activate(n__zWquot(X1,X2)) -> zWquot(activate(X1),activate(X2)) activate(X) -> X graph: zWquot#(cons(X,XS),cons(Y,YS)) -> quot#(X,Y) -> quot#(s(X),s(Y)) -> s#(quot(minus(X,Y),s(Y))) zWquot#(cons(X,XS),cons(Y,YS)) -> quot#(X,Y) -> quot#(s(X),s(Y)) -> quot#(minus(X,Y),s(Y)) zWquot#(cons(X,XS),cons(Y,YS)) -> quot#(X,Y) -> quot#(s(X),s(Y)) -> minus#(X,Y) zWquot#(cons(X,XS),cons(Y,YS)) -> activate#(YS) -> activate#(n__zWquot(X1,X2)) -> zWquot#(activate(X1),activate(X2)) zWquot#(cons(X,XS),cons(Y,YS)) -> activate#(YS) -> activate#(n__zWquot(X1,X2)) -> activate#(X1) zWquot#(cons(X,XS),cons(Y,YS)) -> activate#(YS) -> activate#(n__zWquot(X1,X2)) -> activate#(X2) zWquot#(cons(X,XS),cons(Y,YS)) -> activate#(YS) -> activate#(n__s(X)) -> s#(activate(X)) zWquot#(cons(X,XS),cons(Y,YS)) -> activate#(YS) -> activate#(n__s(X)) -> activate#(X) zWquot#(cons(X,XS),cons(Y,YS)) -> activate#(YS) -> activate#(n__from(X)) -> from#(activate(X)) zWquot#(cons(X,XS),cons(Y,YS)) -> activate#(YS) -> activate#(n__from(X)) -> activate#(X) zWquot#(cons(X,XS),cons(Y,YS)) -> activate#(XS) -> activate#(n__zWquot(X1,X2)) -> zWquot#(activate(X1),activate(X2)) zWquot#(cons(X,XS),cons(Y,YS)) -> activate#(XS) -> activate#(n__zWquot(X1,X2)) -> activate#(X1) zWquot#(cons(X,XS),cons(Y,YS)) -> activate#(XS) -> activate#(n__zWquot(X1,X2)) -> activate#(X2) zWquot#(cons(X,XS),cons(Y,YS)) -> activate#(XS) -> activate#(n__s(X)) -> s#(activate(X)) zWquot#(cons(X,XS),cons(Y,YS)) -> activate#(XS) -> activate#(n__s(X)) -> activate#(X) zWquot#(cons(X,XS),cons(Y,YS)) -> activate#(XS) -> activate#(n__from(X)) -> from#(activate(X)) zWquot#(cons(X,XS),cons(Y,YS)) -> activate#(XS) -> activate#(n__from(X)) -> activate#(X) quot#(s(X),s(Y)) -> quot#(minus(X,Y),s(Y)) -> quot#(s(X),s(Y)) -> s#(quot(minus(X,Y),s(Y))) quot#(s(X),s(Y)) -> quot#(minus(X,Y),s(Y)) -> quot#(s(X),s(Y)) -> quot#(minus(X,Y),s(Y)) quot#(s(X),s(Y)) -> quot#(minus(X,Y),s(Y)) -> quot#(s(X),s(Y)) -> minus#(X,Y) quot#(s(X),s(Y)) -> minus#(X,Y) -> minus#(s(X),s(Y)) -> minus#(X,Y) minus#(s(X),s(Y)) -> minus#(X,Y) -> minus#(s(X),s(Y)) -> minus#(X,Y) activate#(n__zWquot(X1,X2)) -> zWquot#(activate(X1),activate(X2)) -> zWquot#(cons(X,XS),cons(Y,YS)) -> quot#(X,Y) activate#(n__zWquot(X1,X2)) -> zWquot#(activate(X1),activate(X2)) -> zWquot#(cons(X,XS),cons(Y,YS)) -> activate#(XS) activate#(n__zWquot(X1,X2)) -> zWquot#(activate(X1),activate(X2)) -> zWquot#(cons(X,XS),cons(Y,YS)) -> activate#(YS) activate#(n__zWquot(X1,X2)) -> activate#(X2) -> activate#(n__zWquot(X1,X2)) -> zWquot#(activate(X1),activate(X2)) activate#(n__zWquot(X1,X2)) -> activate#(X2) -> activate#(n__zWquot(X1,X2)) -> activate#(X1) activate#(n__zWquot(X1,X2)) -> activate#(X2) -> activate#(n__zWquot(X1,X2)) -> activate#(X2) activate#(n__zWquot(X1,X2)) -> activate#(X2) -> activate#(n__s(X)) -> s#(activate(X)) activate#(n__zWquot(X1,X2)) -> activate#(X2) -> activate#(n__s(X)) -> activate#(X) activate#(n__zWquot(X1,X2)) -> activate#(X2) -> activate#(n__from(X)) -> from#(activate(X)) activate#(n__zWquot(X1,X2)) -> activate#(X2) -> activate#(n__from(X)) -> activate#(X) activate#(n__zWquot(X1,X2)) -> activate#(X1) -> activate#(n__zWquot(X1,X2)) -> zWquot#(activate(X1),activate(X2)) activate#(n__zWquot(X1,X2)) -> activate#(X1) -> activate#(n__zWquot(X1,X2)) -> activate#(X1) activate#(n__zWquot(X1,X2)) -> activate#(X1) -> activate#(n__zWquot(X1,X2)) -> activate#(X2) activate#(n__zWquot(X1,X2)) -> activate#(X1) -> activate#(n__s(X)) -> s#(activate(X)) activate#(n__zWquot(X1,X2)) -> activate#(X1) -> activate#(n__s(X)) -> activate#(X) activate#(n__zWquot(X1,X2)) -> activate#(X1) -> activate#(n__from(X)) -> from#(activate(X)) activate#(n__zWquot(X1,X2)) -> activate#(X1) -> activate#(n__from(X)) -> activate#(X) activate#(n__from(X)) -> activate#(X) -> activate#(n__zWquot(X1,X2)) -> zWquot#(activate(X1),activate(X2)) activate#(n__from(X)) -> activate#(X) -> activate#(n__zWquot(X1,X2)) -> activate#(X1) activate#(n__from(X)) -> activate#(X) -> activate#(n__zWquot(X1,X2)) -> activate#(X2) activate#(n__from(X)) -> activate#(X) -> activate#(n__s(X)) -> s#(activate(X)) activate#(n__from(X)) -> activate#(X) -> activate#(n__s(X)) -> activate#(X) activate#(n__from(X)) -> activate#(X) -> activate#(n__from(X)) -> from#(activate(X)) activate#(n__from(X)) -> activate#(X) -> activate#(n__from(X)) -> activate#(X) activate#(n__s(X)) -> activate#(X) -> activate#(n__zWquot(X1,X2)) -> zWquot#(activate(X1),activate(X2)) activate#(n__s(X)) -> activate#(X) -> activate#(n__zWquot(X1,X2)) -> activate#(X1) activate#(n__s(X)) -> activate#(X) -> activate#(n__zWquot(X1,X2)) -> activate#(X2) activate#(n__s(X)) -> activate#(X) -> activate#(n__s(X)) -> s#(activate(X)) activate#(n__s(X)) -> activate#(X) -> activate#(n__s(X)) -> activate#(X) activate#(n__s(X)) -> activate#(X) -> activate#(n__from(X)) -> from#(activate(X)) activate#(n__s(X)) -> activate#(X) -> activate#(n__from(X)) -> activate#(X) sel#(s(N),cons(X,XS)) -> activate#(XS) -> activate#(n__zWquot(X1,X2)) -> zWquot#(activate(X1),activate(X2)) sel#(s(N),cons(X,XS)) -> activate#(XS) -> activate#(n__zWquot(X1,X2)) -> activate#(X1) sel#(s(N),cons(X,XS)) -> activate#(XS) -> activate#(n__zWquot(X1,X2)) -> activate#(X2) sel#(s(N),cons(X,XS)) -> activate#(XS) -> activate#(n__s(X)) -> s#(activate(X)) sel#(s(N),cons(X,XS)) -> activate#(XS) -> activate#(n__s(X)) -> activate#(X) sel#(s(N),cons(X,XS)) -> activate#(XS) -> activate#(n__from(X)) -> from#(activate(X)) sel#(s(N),cons(X,XS)) -> activate#(XS) -> activate#(n__from(X)) -> activate#(X) sel#(s(N),cons(X,XS)) -> sel#(N,activate(XS)) -> sel#(s(N),cons(X,XS)) -> sel#(N,activate(XS)) sel#(s(N),cons(X,XS)) -> sel#(N,activate(XS)) -> sel#(s(N),cons(X,XS)) -> activate#(XS) SCC Processor: #sccs: 4 #rules: 10 #arcs: 62/256 DPs: sel#(s(N),cons(X,XS)) -> sel#(N,activate(XS)) TRS: from(X) -> cons(X,n__from(n__s(X))) sel(0(),cons(X,XS)) -> X sel(s(N),cons(X,XS)) -> sel(N,activate(XS)) minus(X,0()) -> 0() minus(s(X),s(Y)) -> minus(X,Y) quot(0(),s(Y)) -> 0() quot(s(X),s(Y)) -> s(quot(minus(X,Y),s(Y))) zWquot(XS,nil()) -> nil() zWquot(nil(),XS) -> nil() zWquot(cons(X,XS),cons(Y,YS)) -> cons(quot(X,Y),n__zWquot(activate(XS),activate(YS))) from(X) -> n__from(X) s(X) -> n__s(X) zWquot(X1,X2) -> n__zWquot(X1,X2) activate(n__from(X)) -> from(activate(X)) activate(n__s(X)) -> s(activate(X)) activate(n__zWquot(X1,X2)) -> zWquot(activate(X1),activate(X2)) activate(X) -> X Subterm Criterion Processor: simple projection: pi(sel#) = 0 problem: DPs: TRS: from(X) -> cons(X,n__from(n__s(X))) sel(0(),cons(X,XS)) -> X sel(s(N),cons(X,XS)) -> sel(N,activate(XS)) minus(X,0()) -> 0() minus(s(X),s(Y)) -> minus(X,Y) quot(0(),s(Y)) -> 0() quot(s(X),s(Y)) -> s(quot(minus(X,Y),s(Y))) zWquot(XS,nil()) -> nil() zWquot(nil(),XS) -> nil() zWquot(cons(X,XS),cons(Y,YS)) -> cons(quot(X,Y),n__zWquot(activate(XS),activate(YS))) from(X) -> n__from(X) s(X) -> n__s(X) zWquot(X1,X2) -> n__zWquot(X1,X2) activate(n__from(X)) -> from(activate(X)) activate(n__s(X)) -> s(activate(X)) activate(n__zWquot(X1,X2)) -> zWquot(activate(X1),activate(X2)) activate(X) -> X Qed DPs: zWquot#(cons(X,XS),cons(Y,YS)) -> activate#(YS) activate#(n__from(X)) -> activate#(X) activate#(n__s(X)) -> activate#(X) activate#(n__zWquot(X1,X2)) -> activate#(X2) activate#(n__zWquot(X1,X2)) -> activate#(X1) activate#(n__zWquot(X1,X2)) -> zWquot#(activate(X1),activate(X2)) zWquot#(cons(X,XS),cons(Y,YS)) -> activate#(XS) TRS: from(X) -> cons(X,n__from(n__s(X))) sel(0(),cons(X,XS)) -> X sel(s(N),cons(X,XS)) -> sel(N,activate(XS)) minus(X,0()) -> 0() minus(s(X),s(Y)) -> minus(X,Y) quot(0(),s(Y)) -> 0() quot(s(X),s(Y)) -> s(quot(minus(X,Y),s(Y))) zWquot(XS,nil()) -> nil() zWquot(nil(),XS) -> nil() zWquot(cons(X,XS),cons(Y,YS)) -> cons(quot(X,Y),n__zWquot(activate(XS),activate(YS))) from(X) -> n__from(X) s(X) -> n__s(X) zWquot(X1,X2) -> n__zWquot(X1,X2) activate(n__from(X)) -> from(activate(X)) activate(n__s(X)) -> s(activate(X)) activate(n__zWquot(X1,X2)) -> zWquot(activate(X1),activate(X2)) activate(X) -> X Subterm Criterion Processor: simple projection: pi(from) = 0 pi(n__s) = 0 pi(n__from) = 0 pi(cons) = 1 pi(s) = 0 pi(activate) = 0 pi(minus) = [1,1] pi(zWquot) = [0,1] pi(n__zWquot) = [0,1] pi(activate#) = [0,0] pi(zWquot#) = [0,0,1,1] problem: DPs: activate#(n__from(X)) -> activate#(X) activate#(n__s(X)) -> activate#(X) activate#(n__zWquot(X1,X2)) -> zWquot#(activate(X1),activate(X2)) TRS: from(X) -> cons(X,n__from(n__s(X))) sel(0(),cons(X,XS)) -> X sel(s(N),cons(X,XS)) -> sel(N,activate(XS)) minus(X,0()) -> 0() minus(s(X),s(Y)) -> minus(X,Y) quot(0(),s(Y)) -> 0() quot(s(X),s(Y)) -> s(quot(minus(X,Y),s(Y))) zWquot(XS,nil()) -> nil() zWquot(nil(),XS) -> nil() zWquot(cons(X,XS),cons(Y,YS)) -> cons(quot(X,Y),n__zWquot(activate(XS),activate(YS))) from(X) -> n__from(X) s(X) -> n__s(X) zWquot(X1,X2) -> n__zWquot(X1,X2) activate(n__from(X)) -> from(activate(X)) activate(n__s(X)) -> s(activate(X)) activate(n__zWquot(X1,X2)) -> zWquot(activate(X1),activate(X2)) activate(X) -> X SCC Processor: #sccs: 1 #rules: 2 #arcs: 32/9 DPs: activate#(n__from(X)) -> activate#(X) activate#(n__s(X)) -> activate#(X) TRS: from(X) -> cons(X,n__from(n__s(X))) sel(0(),cons(X,XS)) -> X sel(s(N),cons(X,XS)) -> sel(N,activate(XS)) minus(X,0()) -> 0() minus(s(X),s(Y)) -> minus(X,Y) quot(0(),s(Y)) -> 0() quot(s(X),s(Y)) -> s(quot(minus(X,Y),s(Y))) zWquot(XS,nil()) -> nil() zWquot(nil(),XS) -> nil() zWquot(cons(X,XS),cons(Y,YS)) -> cons(quot(X,Y),n__zWquot(activate(XS),activate(YS))) from(X) -> n__from(X) s(X) -> n__s(X) zWquot(X1,X2) -> n__zWquot(X1,X2) activate(n__from(X)) -> from(activate(X)) activate(n__s(X)) -> s(activate(X)) activate(n__zWquot(X1,X2)) -> zWquot(activate(X1),activate(X2)) activate(X) -> X Size-Change Termination Processor: DPs: TRS: from(X) -> cons(X,n__from(n__s(X))) sel(0(),cons(X,XS)) -> X sel(s(N),cons(X,XS)) -> sel(N,activate(XS)) minus(X,0()) -> 0() minus(s(X),s(Y)) -> minus(X,Y) quot(0(),s(Y)) -> 0() quot(s(X),s(Y)) -> s(quot(minus(X,Y),s(Y))) zWquot(XS,nil()) -> nil() zWquot(nil(),XS) -> nil() zWquot(cons(X,XS),cons(Y,YS)) -> cons(quot(X,Y),n__zWquot(activate(XS),activate(YS))) from(X) -> n__from(X) s(X) -> n__s(X) zWquot(X1,X2) -> n__zWquot(X1,X2) activate(n__from(X)) -> from(activate(X)) activate(n__s(X)) -> s(activate(X)) activate(n__zWquot(X1,X2)) -> zWquot(activate(X1),activate(X2)) activate(X) -> X The DP: activate#(n__from(X)) -> activate#(X) has the edges: 0 > 0 The DP: activate#(n__s(X)) -> activate#(X) has the edges: 0 > 0 Qed DPs: quot#(s(X),s(Y)) -> quot#(minus(X,Y),s(Y)) TRS: from(X) -> cons(X,n__from(n__s(X))) sel(0(),cons(X,XS)) -> X sel(s(N),cons(X,XS)) -> sel(N,activate(XS)) minus(X,0()) -> 0() minus(s(X),s(Y)) -> minus(X,Y) quot(0(),s(Y)) -> 0() quot(s(X),s(Y)) -> s(quot(minus(X,Y),s(Y))) zWquot(XS,nil()) -> nil() zWquot(nil(),XS) -> nil() zWquot(cons(X,XS),cons(Y,YS)) -> cons(quot(X,Y),n__zWquot(activate(XS),activate(YS))) from(X) -> n__from(X) s(X) -> n__s(X) zWquot(X1,X2) -> n__zWquot(X1,X2) activate(n__from(X)) -> from(activate(X)) activate(n__s(X)) -> s(activate(X)) activate(n__zWquot(X1,X2)) -> zWquot(activate(X1),activate(X2)) activate(X) -> X EDG Processor: DPs: quot#(s(X),s(Y)) -> quot#(minus(X,Y),s(Y)) TRS: from(X) -> cons(X,n__from(n__s(X))) sel(0(),cons(X,XS)) -> X sel(s(N),cons(X,XS)) -> sel(N,activate(XS)) minus(X,0()) -> 0() minus(s(X),s(Y)) -> minus(X,Y) quot(0(),s(Y)) -> 0() quot(s(X),s(Y)) -> s(quot(minus(X,Y),s(Y))) zWquot(XS,nil()) -> nil() zWquot(nil(),XS) -> nil() zWquot(cons(X,XS),cons(Y,YS)) -> cons(quot(X,Y),n__zWquot(activate(XS),activate(YS))) from(X) -> n__from(X) s(X) -> n__s(X) zWquot(X1,X2) -> n__zWquot(X1,X2) activate(n__from(X)) -> from(activate(X)) activate(n__s(X)) -> s(activate(X)) activate(n__zWquot(X1,X2)) -> zWquot(activate(X1),activate(X2)) activate(X) -> X graph: SCC Processor: #sccs: 0 #rules: 0 #arcs: 0/1 DPs: minus#(s(X),s(Y)) -> minus#(X,Y) TRS: from(X) -> cons(X,n__from(n__s(X))) sel(0(),cons(X,XS)) -> X sel(s(N),cons(X,XS)) -> sel(N,activate(XS)) minus(X,0()) -> 0() minus(s(X),s(Y)) -> minus(X,Y) quot(0(),s(Y)) -> 0() quot(s(X),s(Y)) -> s(quot(minus(X,Y),s(Y))) zWquot(XS,nil()) -> nil() zWquot(nil(),XS) -> nil() zWquot(cons(X,XS),cons(Y,YS)) -> cons(quot(X,Y),n__zWquot(activate(XS),activate(YS))) from(X) -> n__from(X) s(X) -> n__s(X) zWquot(X1,X2) -> n__zWquot(X1,X2) activate(n__from(X)) -> from(activate(X)) activate(n__s(X)) -> s(activate(X)) activate(n__zWquot(X1,X2)) -> zWquot(activate(X1),activate(X2)) activate(X) -> X Subterm Criterion Processor: simple projection: pi(minus#) = 0 problem: DPs: TRS: from(X) -> cons(X,n__from(n__s(X))) sel(0(),cons(X,XS)) -> X sel(s(N),cons(X,XS)) -> sel(N,activate(XS)) minus(X,0()) -> 0() minus(s(X),s(Y)) -> minus(X,Y) quot(0(),s(Y)) -> 0() quot(s(X),s(Y)) -> s(quot(minus(X,Y),s(Y))) zWquot(XS,nil()) -> nil() zWquot(nil(),XS) -> nil() zWquot(cons(X,XS),cons(Y,YS)) -> cons(quot(X,Y),n__zWquot(activate(XS),activate(YS))) from(X) -> n__from(X) s(X) -> n__s(X) zWquot(X1,X2) -> n__zWquot(X1,X2) activate(n__from(X)) -> from(activate(X)) activate(n__s(X)) -> s(activate(X)) activate(n__zWquot(X1,X2)) -> zWquot(activate(X1),activate(X2)) activate(X) -> X Qed