MAYBE Problem: a__2nd(cons1(X,cons(Y,Z))) -> mark(Y) a__2nd(cons(X,X1)) -> a__2nd(cons1(mark(X),mark(X1))) a__from(X) -> cons(mark(X),from(s(X))) mark(2nd(X)) -> a__2nd(mark(X)) mark(from(X)) -> a__from(mark(X)) mark(cons(X1,X2)) -> cons(mark(X1),X2) mark(s(X)) -> s(mark(X)) mark(cons1(X1,X2)) -> cons1(mark(X1),mark(X2)) a__2nd(X) -> 2nd(X) a__from(X) -> from(X) Proof: DP Processor: DPs: a__2nd#(cons1(X,cons(Y,Z))) -> mark#(Y) a__2nd#(cons(X,X1)) -> mark#(X1) a__2nd#(cons(X,X1)) -> mark#(X) a__2nd#(cons(X,X1)) -> a__2nd#(cons1(mark(X),mark(X1))) a__from#(X) -> mark#(X) mark#(2nd(X)) -> mark#(X) mark#(2nd(X)) -> a__2nd#(mark(X)) mark#(from(X)) -> mark#(X) mark#(from(X)) -> a__from#(mark(X)) mark#(cons(X1,X2)) -> mark#(X1) mark#(s(X)) -> mark#(X) mark#(cons1(X1,X2)) -> mark#(X2) mark#(cons1(X1,X2)) -> mark#(X1) TRS: a__2nd(cons1(X,cons(Y,Z))) -> mark(Y) a__2nd(cons(X,X1)) -> a__2nd(cons1(mark(X),mark(X1))) a__from(X) -> cons(mark(X),from(s(X))) mark(2nd(X)) -> a__2nd(mark(X)) mark(from(X)) -> a__from(mark(X)) mark(cons(X1,X2)) -> cons(mark(X1),X2) mark(s(X)) -> s(mark(X)) mark(cons1(X1,X2)) -> cons1(mark(X1),mark(X2)) a__2nd(X) -> 2nd(X) a__from(X) -> from(X) CDG Processor: DPs: a__2nd#(cons1(X,cons(Y,Z))) -> mark#(Y) a__2nd#(cons(X,X1)) -> mark#(X1) a__2nd#(cons(X,X1)) -> mark#(X) a__2nd#(cons(X,X1)) -> a__2nd#(cons1(mark(X),mark(X1))) a__from#(X) -> mark#(X) mark#(2nd(X)) -> mark#(X) mark#(2nd(X)) -> a__2nd#(mark(X)) mark#(from(X)) -> mark#(X) mark#(from(X)) -> a__from#(mark(X)) mark#(cons(X1,X2)) -> mark#(X1) mark#(s(X)) -> mark#(X) mark#(cons1(X1,X2)) -> mark#(X2) mark#(cons1(X1,X2)) -> mark#(X1) TRS: a__2nd(cons1(X,cons(Y,Z))) -> mark(Y) a__2nd(cons(X,X1)) -> a__2nd(cons1(mark(X),mark(X1))) a__from(X) -> cons(mark(X),from(s(X))) mark(2nd(X)) -> a__2nd(mark(X)) mark(from(X)) -> a__from(mark(X)) mark(cons(X1,X2)) -> cons(mark(X1),X2) mark(s(X)) -> s(mark(X)) mark(cons1(X1,X2)) -> cons1(mark(X1),mark(X2)) a__2nd(X) -> 2nd(X) a__from(X) -> from(X) graph: a__from#(X) -> mark#(X) -> mark#(2nd(X)) -> mark#(X) a__from#(X) -> mark#(X) -> mark#(2nd(X)) -> a__2nd#(mark(X)) a__from#(X) -> mark#(X) -> mark#(from(X)) -> mark#(X) a__from#(X) -> mark#(X) -> mark#(from(X)) -> a__from#(mark(X)) a__from#(X) -> mark#(X) -> mark#(cons(X1,X2)) -> mark#(X1) a__from#(X) -> mark#(X) -> mark#(s(X)) -> mark#(X) a__from#(X) -> mark#(X) -> mark#(cons1(X1,X2)) -> mark#(X2) a__from#(X) -> mark#(X) -> mark#(cons1(X1,X2)) -> mark#(X1) mark#(2nd(X)) -> mark#(X) -> mark#(2nd(X)) -> mark#(X) mark#(2nd(X)) -> mark#(X) -> mark#(2nd(X)) -> a__2nd#(mark(X)) mark#(2nd(X)) -> mark#(X) -> mark#(from(X)) -> mark#(X) mark#(2nd(X)) -> mark#(X) -> mark#(from(X)) -> a__from#(mark(X)) mark#(2nd(X)) -> mark#(X) -> mark#(cons(X1,X2)) -> mark#(X1) mark#(2nd(X)) -> mark#(X) -> mark#(s(X)) -> mark#(X) mark#(2nd(X)) -> mark#(X) -> mark#(cons1(X1,X2)) -> mark#(X2) mark#(2nd(X)) -> mark#(X) -> mark#(cons1(X1,X2)) -> mark#(X1) mark#(2nd(X)) -> a__2nd#(mark(X)) -> a__2nd#(cons1(X,cons(Y,Z))) -> mark#(Y) mark#(2nd(X)) -> a__2nd#(mark(X)) -> a__2nd#(cons(X,X1)) -> mark#(X1) mark#(2nd(X)) -> a__2nd#(mark(X)) -> a__2nd#(cons(X,X1)) -> mark#(X) mark#(2nd(X)) -> a__2nd#(mark(X)) -> a__2nd#(cons(X,X1)) -> a__2nd#(cons1(mark(X),mark(X1))) mark#(from(X)) -> a__from#(mark(X)) -> a__from#(X) -> mark#(X) mark#(from(X)) -> mark#(X) -> mark#(2nd(X)) -> mark#(X) mark#(from(X)) -> mark#(X) -> mark#(2nd(X)) -> a__2nd#(mark(X)) mark#(from(X)) -> mark#(X) -> mark#(from(X)) -> mark#(X) mark#(from(X)) -> mark#(X) -> mark#(from(X)) -> a__from#(mark(X)) mark#(from(X)) -> mark#(X) -> mark#(cons(X1,X2)) -> mark#(X1) mark#(from(X)) -> mark#(X) -> mark#(s(X)) -> mark#(X) mark#(from(X)) -> mark#(X) -> mark#(cons1(X1,X2)) -> mark#(X2) mark#(from(X)) -> mark#(X) -> mark#(cons1(X1,X2)) -> mark#(X1) mark#(s(X)) -> mark#(X) -> mark#(2nd(X)) -> mark#(X) mark#(s(X)) -> mark#(X) -> mark#(2nd(X)) -> a__2nd#(mark(X)) mark#(s(X)) -> mark#(X) -> mark#(from(X)) -> mark#(X) mark#(s(X)) -> mark#(X) -> mark#(from(X)) -> a__from#(mark(X)) mark#(s(X)) -> mark#(X) -> mark#(cons(X1,X2)) -> mark#(X1) mark#(s(X)) -> mark#(X) -> mark#(s(X)) -> mark#(X) mark#(s(X)) -> mark#(X) -> mark#(cons1(X1,X2)) -> mark#(X2) mark#(s(X)) -> mark#(X) -> mark#(cons1(X1,X2)) -> mark#(X1) mark#(cons1(X1,X2)) -> mark#(X2) -> mark#(2nd(X)) -> mark#(X) mark#(cons1(X1,X2)) -> mark#(X2) -> mark#(2nd(X)) -> a__2nd#(mark(X)) mark#(cons1(X1,X2)) -> mark#(X2) -> mark#(from(X)) -> mark#(X) mark#(cons1(X1,X2)) -> mark#(X2) -> mark#(from(X)) -> a__from#(mark(X)) mark#(cons1(X1,X2)) -> mark#(X2) -> mark#(cons(X1,X2)) -> mark#(X1) mark#(cons1(X1,X2)) -> mark#(X2) -> mark#(s(X)) -> mark#(X) mark#(cons1(X1,X2)) -> mark#(X2) -> mark#(cons1(X1,X2)) -> mark#(X2) mark#(cons1(X1,X2)) -> mark#(X2) -> mark#(cons1(X1,X2)) -> mark#(X1) mark#(cons1(X1,X2)) -> mark#(X1) -> mark#(2nd(X)) -> mark#(X) mark#(cons1(X1,X2)) -> mark#(X1) -> mark#(2nd(X)) -> a__2nd#(mark(X)) mark#(cons1(X1,X2)) -> mark#(X1) -> mark#(from(X)) -> mark#(X) mark#(cons1(X1,X2)) -> mark#(X1) -> mark#(from(X)) -> a__from#(mark(X)) mark#(cons1(X1,X2)) -> mark#(X1) -> mark#(cons(X1,X2)) -> mark#(X1) mark#(cons1(X1,X2)) -> mark#(X1) -> mark#(s(X)) -> mark#(X) mark#(cons1(X1,X2)) -> mark#(X1) -> mark#(cons1(X1,X2)) -> mark#(X2) mark#(cons1(X1,X2)) -> mark#(X1) -> mark#(cons1(X1,X2)) -> mark#(X1) mark#(cons(X1,X2)) -> mark#(X1) -> mark#(2nd(X)) -> mark#(X) mark#(cons(X1,X2)) -> mark#(X1) -> mark#(2nd(X)) -> a__2nd#(mark(X)) mark#(cons(X1,X2)) -> mark#(X1) -> mark#(from(X)) -> mark#(X) mark#(cons(X1,X2)) -> mark#(X1) -> mark#(from(X)) -> a__from#(mark(X)) mark#(cons(X1,X2)) -> mark#(X1) -> mark#(cons(X1,X2)) -> mark#(X1) mark#(cons(X1,X2)) -> mark#(X1) -> mark#(s(X)) -> mark#(X) mark#(cons(X1,X2)) -> mark#(X1) -> mark#(cons1(X1,X2)) -> mark#(X2) mark#(cons(X1,X2)) -> mark#(X1) -> mark#(cons1(X1,X2)) -> mark#(X1) a__2nd#(cons1(X,cons(Y,Z))) -> mark#(Y) -> mark#(2nd(X)) -> mark#(X) a__2nd#(cons1(X,cons(Y,Z))) -> mark#(Y) -> mark#(2nd(X)) -> a__2nd#(mark(X)) a__2nd#(cons1(X,cons(Y,Z))) -> mark#(Y) -> mark#(from(X)) -> mark#(X) a__2nd#(cons1(X,cons(Y,Z))) -> mark#(Y) -> mark#(from(X)) -> a__from#(mark(X)) a__2nd#(cons1(X,cons(Y,Z))) -> mark#(Y) -> mark#(cons(X1,X2)) -> mark#(X1) a__2nd#(cons1(X,cons(Y,Z))) -> mark#(Y) -> mark#(s(X)) -> mark#(X) a__2nd#(cons1(X,cons(Y,Z))) -> mark#(Y) -> mark#(cons1(X1,X2)) -> mark#(X2) a__2nd#(cons1(X,cons(Y,Z))) -> mark#(Y) -> mark#(cons1(X1,X2)) -> mark#(X1) a__2nd#(cons(X,X1)) -> mark#(X1) -> mark#(2nd(X)) -> mark#(X) a__2nd#(cons(X,X1)) -> mark#(X1) -> mark#(2nd(X)) -> a__2nd#(mark(X)) a__2nd#(cons(X,X1)) -> mark#(X1) -> mark#(from(X)) -> mark#(X) a__2nd#(cons(X,X1)) -> mark#(X1) -> mark#(from(X)) -> a__from#(mark(X)) a__2nd#(cons(X,X1)) -> mark#(X1) -> mark#(cons(X1,X2)) -> mark#(X1) a__2nd#(cons(X,X1)) -> mark#(X1) -> mark#(s(X)) -> mark#(X) a__2nd#(cons(X,X1)) -> mark#(X1) -> mark#(cons1(X1,X2)) -> mark#(X2) a__2nd#(cons(X,X1)) -> mark#(X1) -> mark#(cons1(X1,X2)) -> mark#(X1) a__2nd#(cons(X,X1)) -> mark#(X) -> mark#(2nd(X)) -> mark#(X) a__2nd#(cons(X,X1)) -> mark#(X) -> mark#(2nd(X)) -> a__2nd#(mark(X)) a__2nd#(cons(X,X1)) -> mark#(X) -> mark#(from(X)) -> mark#(X) a__2nd#(cons(X,X1)) -> mark#(X) -> mark#(from(X)) -> a__from#(mark(X)) a__2nd#(cons(X,X1)) -> mark#(X) -> mark#(cons(X1,X2)) -> mark#(X1) a__2nd#(cons(X,X1)) -> mark#(X) -> mark#(s(X)) -> mark#(X) a__2nd#(cons(X,X1)) -> mark#(X) -> mark#(cons1(X1,X2)) -> mark#(X2) a__2nd#(cons(X,X1)) -> mark#(X) -> mark#(cons1(X1,X2)) -> mark#(X1) a__2nd#(cons(X,X1)) -> a__2nd#(cons1(mark(X),mark(X1))) -> a__2nd#(cons1(X,cons(Y,Z))) -> mark#(Y) SCC Processor: #sccs: 1 #rules: 13 #arcs: 86/169 DPs: a__from#(X) -> mark#(X) mark#(cons1(X1,X2)) -> mark#(X1) mark#(cons1(X1,X2)) -> mark#(X2) mark#(s(X)) -> mark#(X) mark#(cons(X1,X2)) -> mark#(X1) mark#(from(X)) -> a__from#(mark(X)) mark#(from(X)) -> mark#(X) mark#(2nd(X)) -> a__2nd#(mark(X)) a__2nd#(cons(X,X1)) -> a__2nd#(cons1(mark(X),mark(X1))) a__2nd#(cons1(X,cons(Y,Z))) -> mark#(Y) mark#(2nd(X)) -> mark#(X) a__2nd#(cons(X,X1)) -> mark#(X) a__2nd#(cons(X,X1)) -> mark#(X1) TRS: a__2nd(cons1(X,cons(Y,Z))) -> mark(Y) a__2nd(cons(X,X1)) -> a__2nd(cons1(mark(X),mark(X1))) a__from(X) -> cons(mark(X),from(s(X))) mark(2nd(X)) -> a__2nd(mark(X)) mark(from(X)) -> a__from(mark(X)) mark(cons(X1,X2)) -> cons(mark(X1),X2) mark(s(X)) -> s(mark(X)) mark(cons1(X1,X2)) -> cons1(mark(X1),mark(X2)) a__2nd(X) -> 2nd(X) a__from(X) -> from(X) Open